Fulltext

Consumption, Fiscal Policy and Endogenous Growth: The Case of India

by Ila Patnaik

A thesis submitted to the University of Surrey for the Degree of Doctor in Philosophy Department Economics the of of

November 1995

Abstract

A Structural Adjustment Programme is typically accompanied by fiscal policy budget deficits India government changes aimed at reducing spending and as in in is impact The this thesis to the recent years. objective of of these changes on analyse the economy. Since the eventual disengagement of indebted countries from international lending agencies like the RV1Fand the World Bank has been seento come is SAP, the the one of objectives of and as small with econon-uc growth which differences in the long-run growth rate have a significant impact on standards of living, long-run focus the the steady state our is on effect of government spending policies on fiscal in impact We the of growth rate. which present an endogenous growth model is demand through the side and externalities arising policy non-Ricardian effects on from public capital on the supply side.

Preliminary results suggest that the Indian economy is non-Ricardian. An finite horizons, function that population growth, incorporates aggregate consumption liquidity constraints and tax distortions is estimated investigate non-Ricardian effects is imposed, demand.

With the that model on supply side parameters are observed or impact debt/GDP to the the calibrated examine of changes in ratio, the tax rate and the development in Simulations total share of expenditure goverrunent spending. suggest a impact investment long-run At the the very strong positive of public on growth rate. demand time that side effects though present, same our analysis shows non-Ricardian have only a marginal effect on our empirical analysis. The major policy implication that in from is decline the proportion of that the trend of a emerges our results present development spending is counter-productive to the objective of growth. A clear definition of the role of public investment and an analysis of the impact of the is for SAP. expenditure a successful essential components of public

DECLARATION

OF ORIGINALITY

1, Ila Patnaik, hereby declare that the material contained in this dissertation is, to the best of my knowledge, original.

Signed Dated

fNTER-LIBRARY

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DECLARATION

1, Ila Patnaik, hereby declare that the material contained in this dissertation may be inter-library loan. for for photocopying and made available

J',

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Acknowledgments

I would like to express my deepest gratitude to my supervisor Prof Paul Levine

from whom I receivedinvaluableinsights, ideas, guidanceand encouragementthroughout the duration of my research. I would also like to thank Prof Wojceich Charemza of the

University of Leicester for his suggestionsfor my empirical work. I am grateful for the financial support I received from the British Council and from the Department of Econon-ýcs, University of Surrey. I would also like to acknowledge the help I received from staff of the National Council for Applied Economic Research and the National Institute of Public Finance and Policy, New Delhi.

I am grateful for comments and criticisms offered by friends and colleagues husband finally, Fotis Mouzakis And I Thomas Krichel. to especially my am indebted and Ajay, without whose support this work would not have been possible.

Contents

Acknowledgment Table of notations

i-iii

Introduction

1-7

Chapter 1

8-29

Public Spending and Debt in India 1.1. Development Strategy

9

1.2. Financing Development

13

1.3. Growth of Public Expenditure

14

1.4. Tax Revenue

16

1.5. Growth of Public Debt

18

1.6. The External Crisis

20

1.7. Stabilisation and Structural Adjustment

21

1.8. Cut in Development Expenditure

24

Chapter 2

29-46

Debt Neutrality:

Theory and Evidence

2.1. A Representative Agent model

30

2.2. The Ricardian Equivalence Hypothesis

34

2.3. Empirical Studies

37

2.4. Excess Sensitivity

42

2.5. Evidence for India

44

Chapter 3

47-57

The Aggregate Consumption Function: Finite Horizons, Liquidity Constraints and Population Growth with Income Redistribution 3.1. Liquidity Constraints

47

3.2. Finite Horizons

48

3.3. Population Growth and Income Redistribution

49

3.4. Utifity Function

51

3.5. Aggregate Behaviour

54

Chapter 4

58-82

Estimation and Results 4.1. Eliminating Human and Non-human Wealth

58

4.2. Non-Lineanty

60

4.3. Properties of the Disturbance Term

61

4.4. GeneralisedMethod of Moments

64

4.5. Approachesto Estimation

68

4.6. Data

69

4.7. Restrictions

71

4.8. Estimation and Results

72

4.9. Supporting Evidence

75

Chapter 5

83-126

Policy Evaluation in an Endogenous Growth Model 5.1. Traditional Models of Growth

84

5.2. Endogenous Growth

85

5.3. The Model

87

5.3.1. Households

88

5.3.2. Private Sector Output and Investment.

90

5.3.3. The Government

92

5.3.4. Output Equilibrium.

93

5.3.5. The Steady-State

93

5.4. Fiscal Policy and Long-Run Growth

96

5.5. Calibration and Estimation for India

101

5.5.1. The Development Expenditure Multiplier

104

5.5.2. The Tax Multiplier

105

5.5.3. The Debt Multiplier

106

5.6. Non-Ricardian Effects

109

5.6.1. Finite Horizons

109

5.6.2. Liquidity Constraints

III

5.6.3. Distortionary Taxes

112

5.7. Reducing Debt

117

5.8. Effects of Demand and Supply Side Externalities

119

5.9. Conclusions

125

Conclusion

127-33

Appendix A: The Yaari-Blanchard

Linear Technology and

134

Curves Appendix B: The Data Set

Bibliography

and References

136

139-49

List of Tables

Table 1.1: Gross Fixed Capital Formation in the Public and Private Sectors Table 1.2: Direct and Indirect Tax revenues of the Centre and States combined Table 1.3: Total Outstanding Liabilities of the Government of India Table 1.4. Measures of Deficit of the Central Government Table 1.5: Development expenditure of Centre and States Table 2.1: Excess Sensitivity of Consumption Table 4.1: An Estimate of the Rate of Growth of Population of Unconstrained Consumers Table 4.2: Share of Agriculture in National Income Table 4.3: Per Capita NDP in agriculture Table 4.4: Change in Income Distribution in Rural India, 1970-80 Table 4.5: Changes in Poverty in Rural India, 1970-80 Table 5.1: Summary of Calibration Table 5.2-.The Multipliers for Selected Values of yl.

Table 5.3: The Multipliers for the Ricardian and Non-Ricardian Cases Table 5.4- The Debt Multipliers Table 5.5 - The Tax Multiplier Table 5.6- The Development Expenditure Multiplier

List of Figures

Fig 1.1: Gross Fixed Capital Formation in the Public and Private Sector Fig 5.1: The Yaari Blanchard and Linear Technology Curves Fig 5.2: yl. and the Development Expenditure Multiplier Fig 5.3: yI and the Tax Multiplier Fig 5A yl and the Debt Multiplier Fig 5.5: Finite Horizons and the Debt Multiplier Fig 5.6-.Finite Horizons and the Tax Multiplier Fig 5.7: Liquidity Constraints and the Tax Multiplier Fig 5.8. Growth, Tax Rate and Development Expenditure Fig 5.9- Growth, Tax Rate and yI Fig 5.10: Growth, Tax Rate and the Debt/GDP Ratio Fig 5.11 -.Liquidity Constraints and the Growth Rate Fig 5.12-.The Debt/GDP ratio and the Tax Multiplier Fig 5.13: The Debt/GDP ratio and the Development Expenditure Multiplier

Table of Notations (subscript t denotes the variable in period t) Ct

consumption

C

bliss level of consumption

Ct

effective consumption

CCt

consumption of constrained consumers

cut

consumption of unconstrained consumers

rt

interest pure real rate of

Yt

Gross Domestic Product

Yi,t

firm i output of

Tt

taxes

N,

labour income

it

investment private

G,

government expenditure

GCt

government consumption expenditure

Git

investment expenditure government

D,

domestic public debt

Ut

utility

W

total wealth

t

WU t

total wealth of unconstrained consumers

vt

non-human wealth

H,

human wealth

Ot

labour post-tax income

ii

QUt

a

post-tax labour incomeof unconstrainedconsumers

FD,

budget deficit

Kt

private physical capital

KGt

public physical capital

P

birth rate

p

death probability of

9

rate of growth of population of unconstrained consumers

9

rate of growth of total population

5

rate of time preference

Jf,t

labour input in efficiency units

gf,t

labour the efficiency of raw input measure of

7r

depreciation rate of

n

rate of growth of output

T

rate of taxation in development expenditure total government proportion of

spending CY

intertemporal elasticity of substitution

0

between private spending and measure of substitutability government consumption life-tme to wealth consume out of propensity by income labour tax received unconstrained proportion of post consumers

Y1

capital externality

iii

LIt'S

size of the cohort born during [s,s+I] who are still alive at the end of period expectations operator

L

Lag operator

Introduction

In advancedindustriahsedcountries the role of fiscal poficy has traditionafly been be to seen one of demand management. Govemment tax and spending decisions are consideredto be instrumentsfor correcting short-term macroeconomicimbalances.Though public expenditure has been an important tool to promote economic growth in developing countries, its role as such did not find a place in models of economic growth. Recent developmentsin macroeconomicsprovide us with a framework for analysingthe impact of fiscal policy on long-run growth. In this study we analysethe effect on econon& growth of fiscal changesthat typically accompanya structural adjustmentprogramme.

A large external debt and persistent current account deficits create circumstances borrows from lending under which a country international agencieslike the International Monetary Fund and the World Bank. The RVT views the causesof externalimbalanceto he in the divergence between aggregate demand and supply. This divergence is traced to demand too rapidly relative to the growth of that expand aggregate inappropriate policies To the economy. rectify this situation, the country concerned capacity in productive (SAP).

The Structural Adjustment Programme programme consistsof policy undertakesa

disbursement borrowing by be the the to of eachsuccessive country and adopted measures loan the is conditional upon the governmentadopting thesemeasures. stageof

The broad objectivesof a SAP are the attainmentof a viablebalanceof payments, from low inflation. long Apart term monetary and growth performance and satisfactory fiscal SAP both SAP The typical to measures. aim of a Is includes exchangerate policies, a in fiscal increase SAP demand, Under the to especially short run, and a supply. reduce

1)

measuresare treated as instrumentsof demandmanagement.This treatmentis typical of the approach that fiscal policy affects aggregate demand and levels of consumption, saving, investment and output, but leaves their long-run growth rates unaffected. The long-run

determined growth rate is exogenously.It may,for instance,dependon the rateof technical is progress which assumedto be determined,,not by actiVity within the economy, but, say, function is There for fiscal in long-run detem-dnation time. as a the the of no role policy of

growth rate in suchmodels.

Recently the belief that the crucial issue is growth rather than busMiesscycles and the counter cyclical fiscal and monetary policies of the government,has shifted the focus of macroeconomicsto growth. A boom in research tin the area has found explanationsof in factors growth various such that growth is endogenous.The engine of growth may be learning by doing or researchand developmentthat leadsto the creation and accumulation knowledge, of externalitiesassociatedwith private or public capital or human capital that from In training. endogenousgrowth theory governmentpolicy which educationand anses influences these factors has an important role to play in determining the long-run growth has basic The to this that the motivated study is similar premiseof which economy. rate of deterrmnants long-run 1980s that the the the of mid researchon econornic growth since in differences because growth rates, when even small econornic growth rate, are crucial for have much greater consequences standardsof cumulated over a generation or more, living than the kinds of short-term businessfluctuations that have typlcaUyoccupied most (1995)).

Sala-i-Martin (Barro the and attention of macroecononusts of

from the 1W comesWith It has also beenseenthat the eventualdisengagement (1993)).

(Bird focus We therefore on the objective of growth rather than sustainedgrowth have balance.

An that the understanding of effect of government poficles macroeconornic

even smafl effects on the long-run growth rate may prove to be eventuaflymore significant

than policiesthat aun to correct short-termmacro economicimbalances.We hereattempt to study the effects on growth of changesin government policy. In the present context,

for analysingthe effecton longendogenousgrowth modelsprovideus with the fi7amework run growth of the conditionalitiesintendedfor demandmanagement.

Our methodology is to study a country currently undergoing a typical Structural Adjustment Programme

India.

In 1980s, India the the growth of public expenditure in -

higher than the growth of revenue. A large part of the increase was in current was government expenditure. While the 1970s typically witnessedbalancedrevenue accounts, the 1980s saw chronic budget deficits. The eighties also saw a rise in the current account

deficit and a large external debt which assumedcrisis proportions by mid-1991. India turned to the ME and World Bank for loans. The government corarnitted itself to a Structural Adjustment Progran-ime.This commitment is detailed in the Government of India's letters of intent to the Rv1Fand World Bank. Apart from many measuresrelating to investment, foreign capital and other policies, the government industrial, export-import, included fiscal loan These the to measures. a reduction in accepted conditionality relating fiscal deficits, government spendingand tax rates.

Under the SAP the role of fiscal policy was clearly perceivedto be one of demand in have fact India This that the policy makers considered was regardlessof management. fiscal pol-icy crucial in promoting econonuc growth. Left to the private sector, it was

believed,there would be little investmentin infrastructure,educationetc., and economic by be The the slow. role of public sector, as envisaged the planners, was growth would invested in The the to private sector. govenu-nent industries and sectors complementary but for to the sector was private unwilling invest which were crucial econornic where

4 growth. Even today nearly half of government spending consists of such 'development' expenditure.However, over the last few years, especiallyunder the SAP, the proportion of development expenditure in total government spending has been falling. Since it is politically much more difficult to cut current consumption expenditure,the governmentcan its meet commitment of cutting the deficit and spendingby cutting pubtic investment.

If public investmentaffects the long-run growth rate of output then ignoring its role lead to results contrary to the objectives of the SAP. We, therefore, study the effects may not only of changesin the tax rate or the debt/GDP ratio that are intended to meet loan conditionalities, but also changesin the proportion of public investmentin total government spending,a fal-l-outof the government'scommitment to the IW and the World Bank. The fi7ameworkof an endogenousgrowth model allows us to analysethe impact of thesefiscal variableson the long-run growth rate.

Another development in macroeconomics that helps us analyse the case of a developing country more accurately is the modelling of non-Ricardian effects on consumption. The simple crowding-out hypothesis was negated by the Ricardian Equivalence theorem which defined conditions under which there would be no crowdingdebt It that the public would always crowd out private spending. out at all. contested view The hypothesis was shown to hold only under certain assumptionsthat included infinite horizons or the operation of an inter-generational bequest rnechanisn-ýan absence of liquidity constraints, lump sum taxes, no population growth and forward looking rational budget intertemporal Since the the constraint. government's consumers who understand Ricardian theorem was true under only very strict assumptions,the foHowmgdebateon the

focused how debt led deviation the to on violation of eachof its assumptions a effect of from the equivalence between taxes and debt. Though the conclusion was that of the

5 traditional view, the analysis was rigorous, the techniques Improved and the causes of

crowding out clearlydefined.

In a developing country, Ricardian assumptionsof infinite horizons, peffect credit markets, no population growth and non-distortionary taxes are unlikely to be satisfied.

Fol.lowing Hayashi (1982), Blanchard (1985) and Weil (1989) we introduce liquidity constraints, finite horizons and population growth into the modelling of consumer behaviour in the economy. To take account of structural changes that accompany the process of development, we allow for income redistribution. A discrete time model following Frenkel and Razin (1992) provides an estimable form of the consumption function.

We use the GenerafizedMethod of Moments to examinenon-Ricardianeffects on by (1982), Proposed Hansen this method has recently been employed for consumption. estimating aggregate consumption (Darby and Ireland (1994) and by the ESRC Macromodelling Bureau to re-estiMatethe Weale (1990) model). The method can provide

function the consistentand efficientestimateswhen is non-linear,regressorsare correlated disturbances heteroskedastic. the ten-n areautocorrelatedand/or error andwhen with Following Levine (1994) a steady state equilibrium model is constructed for a Using mostly closed economy vAth consumption, production and government sectors.

for estimatedor observedparameters,we computean order-of-magnitude-feel the effects debt/GDP development long-run the tax the the rate and proportion of ratio, growth of on expenditure in total government spending.

Chapter I proVidesan outline of the issuesconcerning fiscal policy and econorruc discuss We development, financing India. the the strategy of of plans and the growth in led debt in India.

This taxation that to the and spending public growth of of public pattern is

6

fol-lowedby a brief discussionon recent changesin the economyunder the Structural Adjustment Programme including changesin fiscal policy like tax rates and the proportion

development of expenditurem total governmentspending.

Chapters 2-4 relate to the consumption side of the model. We derive the

consumptionfunction first under Ricardianassumptionsand later model deviationsfrom these assumptions.Chapter 2 describesthe behaviour of a representativeagent who maximizes utility subject to his fife-time wealth. Horizons are assumedto be inýinite and taxes are lump sum. The government's budget constraint and solvency condition are defined. The household and government sector's intertemporal budget constraints are combined to provide a simpleexposition of the RicardianEquivalencetheorem.Methods of testing this proposition are discussedand the model is estimatedfor India.

The consumption function of the representativeagent in chapter 2 is derived under the assumptions of an absenceof liquidity constraints, population growti-i, distortionary define dropped.

We finite horizons.

In 3, these taxes and assumptions are chapter The individuals behaviour the then population. and aggregate over of consumption liquidity defined to constrained and unconstrained groups of of consist population is from This to to the group another. permits one us of migration possibifity with consumers include individuals with different consumptionbehaviour in one population. In chapter4 we in by function define terms the aggregate consumption of observable variables nrst 17--

defined Aggregate human terrns consumption now in is wealth. and non-human excluding discuss Next income lagged the consumption. we and of values and of current Method Moments.

The Generalized describe the of model methodology of estimation and is estimatedfor India and results are analysed.We then proVide supporting eVidencefor our

distribution. to resultsrelating income

7 Chapter 5 first presentsthe production function that underl-inesour growth model.

Output exhibitsconstantreturns to a broad conceptof capital that includesboth private infi7astructure. household Combining the this capital and public and government with

described in denve sectors earlier,we a model of endogenousgrowth a closedeconomy.

Conditionsfor steadystategrowth are definedand the model is calibratedfor India. We derive tax, debt and development expenditure multipliers to examine the impact of fiscal discuss implications long-run We then the of our results and the policy variableson growth. impact of non-Ricardianassumptionson the multipliers. This is followed by our conclusions

future discussion direction the research. of anda on

8

Chapter I Public Spending and Debt in India

In ntid- 1991 a severe balance of payment crisis forced India to borrow from the IMF. The loan for a Structural Adjustment Programme came with the conditionality that the fiscal deficit be reduced. The underlying theoretical basis of this policy is the increase in that view an public borrowing increasesaggregate demand. Tf-ýshas a spill-

over effect and so to reduce a balanceof trade deficit, fiscal deficit must be reduced.

The attempt to reduce the fiscal deficit in India has resulted in a reduction primarily in for investment. government spending earmarked public In this chapter we present a brief discussion of the econorruc changes in India beginning We the the since of planning process. also examine the most recent changes We the the the the reduced role of public sector. opening up of economy and including focus upon the reasons for the growth of public debt and measurestaken to reduce it briefly discuss We Structural Adjustment Programme the causes the under way. under for the growth of government expenditure and public debt, and for the balance of finally from borrow IMF forced India the to tackle the issue to that and payment crisis loan deficit fiscal high the the conditionality. as part of of The arrangementswith the RVIFand World Bank came with the conditionalities tccorrection of macro-economic imbalances, an internationally competitive economy, a ( SIngh the public sector" rapid increase in our exports, and improved efficiency of (1992)). The government committed itself to reduce the Union Government deficit to

9 6.5 per cent in 1991-92 and 5 percent in 1992-3. Half of the adjustment was to be achieved by higher taxes and the other half by lowering public expenditure. I

The attempt to reduce fiscal deficit led to a cut in public investment and development outlays, while current expenditure continued to rise. To examine the reasons for the growth of public debt we shall look at the pattern of public expenditure and taxation, budget deficits and the consequent growth of public debt. The discussion shall begin with a brief outline of India's development strategy which provided the for rationale public investment and expenditure.

I. I. Development Strategy

The major objectives of economic development in India were growth, self reliance and social justice. As there was little to redistribute but poverty, growth gained overriding importance. Industry was to be the engine of growth and development of the Indian economy. The major obstacle in the path of industrial be lack to the expansion was seen of adequate productive capacity. The strategy of industrialisation chosen emphasisedan increase in capital stock through a high rate of balance foreign Following 1957-58 of payment crisis a severe in investment. exchange be The to economy was a mixed economy and was also viewed as a major constraint. the path of development a planned one. The Indian planning model was inspired by the USSR. the planning model of

As the onus of promoting growth lay on the public

development bUFden financial large the of economic rested on the part of sector, a shoulders of the govertunent.

I The IMF by finance SlngJiĂ˝ August 27,199 Dr. Manmohan 1, and ciirculated in to the the as sent on minister, memorandum Parliament on December 16,1991.

10

Indian planners were pessimistic about the growth

of Indian exports and they

tried to overcome the foreign exchange constraint by reducing imports. This implied import substitution in as many products as possible. It also meant expanding the capacity to produce a large number of consumer goods. As the economy was viewed

as virtually closed, capital goods had to be produced domestically and the rate of growth of productive capacity was to be maximised by producing 'machine making machines'. Production of 'machine making machines' meant investment in large scale intensive industry involving large initial capital outlays, long gestation lags and capital

high risks. As private investorswere unlikely to undertakesuch investment,it fell upon the public sector to promote the capital and basic goods industry sector. Table 1.1 shows the Gross Fixed Capital Formation in the private and public sectors as a proportion of GDP. The relative size of the public sector remains quite high from the second plan period right upto 1990. This can be clearly seen in Figure. 1.1.

Industrial output saw a significant deceleration in growth in the period 1966-67 to 1981-82. There is considerable debate about the cause of this slowdown in growth in decade during from Some 6.9 5.0 the to this preceding period. per cent rate investment it the to that took place significant reduction in public economists attribute formation in (1984)).

(Bardhan Fixed 1970-71 the this time public capital sector at at 1950-51 1965-66, 11.3 the to per cent in period and prices grew at an annual rate of declined to a rate of less than half, that is 5.5 per cent, in the period 1966-67 to 198182. Since public investment accounts for nearly half the total gross fixed capital formation in the economy and about five times the amount in the private corporate back had this cut a considerable effect on growth. sector,

Table 1-1: Gross Fixed Capital Formation in the Public and Private Sectors as a per cent of GDP Year

Public Sector

Private Sector

1950-55

2.84

6.1

1955-60

5.26

7.54

1960-65

6.96

7.32

1965-70

6.34

8.72

1970-75

6.2

7.92

1975-80

8.02

9.88

1980-85

9.62

9.98

1985-90

10.4

11.6

1990-91

9.4

13.8

1991-92

9.5

12.7

1992-93

8.5

13.0

1993-94

8.4

12.5

Source- Economic Survey 1994-95 (1995), Government of India, New Delhi.

An important factor was also that the cut backs from the mid-sixties onwards for in like the private that growth were crucial railways and electricity were on sectors industry in basic deceleration The the and capital goods where was seen mainly sector. industries basic included heavy halved.

These than as such mainly growth rates more transport machinery, non-electrical and and electrical products, metal metals, decline investment in The the only meant a not in public reduction equipment. infrastructure facilities like power, fuel and transport, much of which is in the public industries in for demand but that the the public capital goods of products also sector, investment generates.

12

Gross Fixed Capital Formation in the Public and Private Sectors 14 c

lg

12 10 8 6 4

(D

Public Private ---------------

2

LO

lqT LO

rLO

C) (.0

CY) (D

(D (D (3)

G) (D CF)

(N r-

00 rCY) T-

Too (Y) T-

14t 00 CF) T-

rl00 CY) Ir-

C) 0) (3) Ir-

cle) CY) 0) T-

Year

Fig. 1.1 Agriculture was the dominant sector in the Indian economy. It accounted for more than 50 per cent of the share of output and 70 per cent of the labour force employed. Growth in agriculture was initially expected to take place through an increase in irrigation and an improvement in land distribution. Food output, however, barely kept up with the rate of growth of population. Availability of food fluctuated drought The greatly with rainfall. in 1965 created shortages and forced India to import large quantities of wheat from the US under PL 480. The desire to reduce external

dependencefor food was crucial in bringing about the Green Revolution. Changesin the technology of wheat production were ushered in into certain pockets of the institutional the structure was conducive country which were well irrigated and where to the adoption of new technology. The technology was promoted by providing a number of subsidies on power, imported inputs, credit and machinery.

Ii

Due

to

the externalities and indivisibilities

involved

in investment in

infrastructure facilities in agriculture, public investment was crucial. Growth prospects Indian of agriculture are vitally dependent on public investment in irrigation, drainage

flood and control, in land shapingand land consolidation,in prevention of soil erosion and salinity, in the development of a widespread research and extension network, and

in rural electrification and provision of productive credit. The expansionof irrigation and state and community projects for tapping groundwater through public tube-wells, for flood control and for soil improvements can have dramatic results. Since the average size of land holdings even among the better-off farmers is small in many parts of the country, the capacity of the farmer to invest is limited. There is thus a need for investment supplementary public .

1.2. Financing Development Public expenditure in India consists of plan expenditure and non-plan is Plan expenditure. expenditure the outlay on Five Year Plans. These include outlays health, The energy, education, social services, etc. main on industry, agriculture, borrowing. from financing The the investments returns source of plan expenditure was debt. be Non-plan the to to expenditure was pay off adequate made were expected financed by be The to revenue. main sources of mainly current expenditure and was budgetary revenue were expected to be direct and indirect taxes and profits of public However, most public sector enterprises, except oil companies, enterprises. sector losses had be heavily to subsidised. and were running

14

1.3. Growth of Public Expenditure Plan expenditure covered government spending on infrastructure, power, capital

basic like iron health, and goods industries and steel plants, education, etc. Thesewere for long the term economic and industrial development of the country but essential largely investments. due long low Returns time. were unprofitable after a were and Non-plan or current expenditure consisted mainly of government spending on

inherited had defence India the colonial public administration, and subsidies. low The its high public sector efficiency. costs and administrative structure with in force labour half the the than organised sector. employed employed more Government consumption expenditure has two

components- compensation to

More employeesimply more employees and purchase of consumer goods and services.

Given the employment, other complementary transport, etc. office equipment, Compensation to becomes of consists employees committed. partially expenditure benefits to other and the pensions that and main component, are wages and salaries employees.

Public spending on education consists of spending in primary, secondary, including and higher engineering medical, universities, education vocational and is highly Education development, subsidised etc. and research management schools, level. higher the especially at

Government expenditure on health and education

92 About the on expenditure of cent per consists mainly on employment of persons.

health on salaries is 72 the on by expenditure of cent per education the governmentand (1992) 119).

(Bhattacharya p. and wages faster than in rate a at Total employment the public sector was rapidly growing to made 1984, was effort after which some the rate of growth of the population till

15 it slow down. Real wages in the public sector grew faster than per capita real national

in income the 'eighties. Average emolumentsin public enterprisesin 1988-89were 9.5 times per capita real national income against 8.7 times in 1980-8 1. (Bhattacharya (1992) p. 121-125).

Defence spending was high and rising becauseof external political uncertainties.

The defence budget accounts for about 4 per cent of GDP and 16 per cent of total government expenditure. Taking related expenditure into account it is probably higher 5 at per cent of GDP and 20 per cent of total government expenditure though it is still

low relatively in internationalcomparison(Bhattacharya(1992)).

Subsidies on food, fertilisers and exports were rising. The share of government expenditure on agriculture rose after the green revolution as the state provided incentives to farmers in the form of subsidies on seeds, fertilisers, credit, etc. Real

investment, both public and private in agriculture slowed down in the 'eighties. The in both implicit, sharp rise subsidies , open and eroded the surplus available for public investment in agriculture to a considerable extent. (RBI (I 994), p. 109) It is estimated that in the early seventies aggregate government expenditure was

declining in real terms. In the late seventiesnominal expendituregrowth rose to over 13 per cent per annum and real expenditure started growing quite rapidly. After 1979 but due higher inflation 18.6 the to to rate per cent norn-inalexpenditure growth rose Real growth rose sharply in the period real growth in expenditure remained stable.

(1992), 230-3 1). ( Rao Mundle 1983 p. and after Another trend in the pattern of public expenditure is the declining share of capital in The total public expenditure. economic classification of expenditure expenditure from from 1971-72 1987-88 to that the share of capital expenditure shrunk reveals

16

over 56 per cent of total central government expenditure to only 30 per cent. This was

mainly becauseof the dramatic increasesin the share of interest payments,subsidies and compensation to government employees (Mundle and Rao (1992) Table 3, p.233)

1.4. Tax Revenue The was a considerable growth in tax revenues over this period even though it did not increase at the samerate as public expenditure. The tax to GDP ratio rose from 6 per cent in 1950-51 to about II per cent by 1970-71 and further to about 17 percent in the eighties.

The increase in tax revenue was accompanied by a significant increase in the

indirect taxes. This was due to a fall in the contribution of direct taxes.They shareof fell from about 30 per cent of tax revenue in the early sixties to 14 per cent in 1989-90 (Mundle and Rao (1992) p.236). In the 1980's there has been a slight increase in the in direct Table 1.2. taxes seen of as share Table 1.2: Direct and Indirect Tax revenues of the Centre and States combined (as a per cent of GDP) Year

Direct

Indirect

Total

1980-81

2.6

11.9

14.5

1985-86

2.7

13.7

16.4

1990-91

2.7

13.8

16.5

1991-92

3.1

13.6

16.7

1992-93

3.2

13.0

16.2

1993-94(RE)

3.2

12.0

15ý2

111.9 Table (1994), Bombay, 1993-94, Report Bank India Annual Reserve Sourceof , p. 196.

17

The tax basefor both direct and indirect taxes is narrow. In the caseof indirect taxes most services are completely excluded from the tax base and many goods,

especiallythose produced in the informal sector escapetaxation. The basefor personal income tax has been rendered extremely narrow by excluding agricultural income, administrative difficulties of taxing the unorganised non-agricultural sector and the for provision exemptions and deductions for various purposes. The base for corporate taxes has been eroded by making generous deductions for depreciation and

reinvestment and contributions for a wide variety of social purposes. Though agriculture constitutes the largest sector in terms of output and employment, yet, problems of estimation and costs of collection prevent agricultural incomes from being taxed. This has created horizontal inequity in the system. It has prevented the taxation of large land owners and rich farmers. It has also provided a means of tax evasion for those who have income from both agricultural and non-agncultural sources. For the (up tax payers this led to marginal income tax rates that were very high to 97 per cent).

I This encouraged tax evasion. At the same time legal and tax administration machinery loose While income the tax actual magnitude of and evaders were not penalised. was

tax evasionis difficult to estimateand different studiessuggestdifferent figures, it can large be that enough to considerably affect tax revenues. it was easily said Apart from the inadequate growth in tax revenues, the income from non-tax behind. in lagging Implicit has to the revenues growth also contributed revenues by way of unrecovered costs are provided on a whole range of social and subsidies

by econormcservicesprovided the government.

18

1.5. Composition of Public Debt The 1980s saw a rapid rise in public expenditure in India. The current expenditure of the government as a ratio of GDP rose from 11.5 per cent in 1970-71 to almost 23.1 per cent in 1989-90. As mentioned above, wHe expenditure was rising, receipts were not rising at the same rate since taxes, especially direct taxes, were not buoyant. Over the 1980s, the gap between expenditure and receipts was increasing.

While there was a budgetary surplus in the 1970s, the 1980s saw a rise in budget

deficits. During the eightiesthe deficit on the budget was slowly rising and by 1989-90 the fiscal deficit rose to 12.8 per cent of the GDP. About 72 per cent of the gap was financed by domestic borrowing, 7 per cent from external assistanceand 21 per cent from deficit financing (Economic Survey, 1990-9 1).

Till the rrud-1980's, the government bond market was more or less a captive bought by financial institutions like banks and market as government securities were insurance companies to fulfil their Statutory Liquidity Ratio (SLR) requirements, bonds had 38.5 though to rates of interest on government per cent, even risen which debt larger in If low than the terms. public real was and even negative were very be had hold, institutions financial then the to the surplus would monetised as amount the Reserve Bank of India was obliged to lend to the government. In the 1980s special Patras like Indira V1kas issued bonds the and were under various schemes government Kisan Vikas Patras at non-iinalrates of interest of up to 9 to 10 percent. In addition, tax

high bonds.

The these to those interestratesof who purchased concessionswere given borrowing from households conu-nercial as well as the tax concessions government burden be to on the exchequer. a proved

19 This led to a substantial increase in interest debt.

The made payments on public interest rising payments since the 1980's are a consequence of three factors -the

increase in total debt, the increase in the interest rate and the

increase in the

proportion of high interest bearing liabilities in the government'sdebt. The internal liabilities of the Government of India have been classified into two categories, the "internal debt " and the "other liabilities". The internal debt consists of (i)market loans, (ii) Treasury Bills, (111)Special Securities issued to the RBI, (iv) Special Bearer Bonds,

(v) Balances and of expired loans, Prize Bonds, Premium Prize Bonds, etc.. "Other liabilities" comprise (i) small savings, (ii) state provident funds, (111)Public provident fund etc. These so-called "other liabilities" carry a higher rate of interest than internal debt and there has been a rise in the proportion of "other liabilities" in the government's total liabilities. The consequence of higher interest payments is a significant rise in the in debt/GDP debt.

Table 1.3 the the ratio shows sharp increase magnitude of public 1980-81. since

Table 1.3: Total Outstanding

Liabilities

(as Government India the a per of of

GDP) cent of Year

Total Liabilities

1980-81

43.9

1984-85

49.0

1985-86

52.4

1990-91

59.1

1991-92

57.8

1992-93

57.0

1993-94(RE)

58.7

Source- Reserve Bank of India, Annual Report 1993-94, (1994), Bombay, Table 111.4, 191.

110

This led to widespreadconcern at the rising public debt and a numberof studies like Seshan (1987), Rangarajan el aL (1989), Buiter and Patel (1990) and Chelliah (1992) concluded that the path was unsustainable. However, no serious attempt was made to curtail government borrowing. This was despite an official declaration of intent to arrest further deterioration of budget deficits made in the Long Term Fiscal Policy (LTFP) statement of 1985 which suggested certain specific measuresto reverse

the decline in public savings-a reduction in subsidiesand unproductiveadnunistrative expenditure and increasing the contribution of public enterprises through proper pricing and other policies. The Centre's borrowing remained at 7 per cent of GDP by did beyond 4 LTFP the target the against of per cent set and public saving not go 2.4 per cent despite the target of 4 per cent. The seventh five year plan finalised in 1985 provided for a rate of growth of non-plan expenditure no higher than the rate of in borrowing.

But GDP the growth of non-plan to of contain public an attempt growth (1992)).

(Jalan high during the times three seventh plan period as expenditure was

1.6. The External Crisis At the same time during the 1980s, a balance of payment crisis was developing. , 1979 saw the second oil price shock and a rise in US interest rates and LIBOR raising industrial debt.

Due burden to the recession in the of servicing the existing external the slow. growth was the rate, export exchange of uncompetitiveness and countries Some attempts at liberalisation saw growth in new industries like automobiles

As imports heavily both dependent technology and components. of on and electronics, 5.5 higher the over cent per of the economy grew at relatively much rates of growth

21 decade, imports grew rapidly. The widening current account deficit was Increasingly financed by non-concessional loans. According to World Bank debt data, India's total outstanding foreign debt increased from $18.7 billion in 1980 to $56.3 billion in 1989 debt to private creditors increased from about $2 to $21.4 billion during this and period ( Jalan(1992)). The Gulf crisis resulted in a higher import bill and a loss in foreign remittances. The collapse of the USSR Eastern led decline Europe to and a in

Indian exports.

The above trends led to a balance of payment crisis in June 1991. India was left with only two weeks imports worth of foreign exchange. Her credit rating fell sharply foreign and private lending was cut off For the first time there was a serious possibility default.

Faced with this crisis the government was forced to act. of

1.7. Stabilisation and Structural Adjustment Emergency stabilisation measuresaimed at reducing inflation, which had risen to 12 per cent, and the current account deficit, that stood at 3 per cent of GDP and 40 later Emergency that taken. import controls, eased, were per cent of exports, were

borrowing backed The imposed.

Gold rupee was external was undertaken. were devalued by 22 per cent. A scheme of tradable import entitlements for exporters was introduced. A tight monetary policy implied reducing money supply and raising rates of interest. The July 1991 budget set a target for reducing the central government's fiscal

deficit from 9 per cent to 6.5 per cent of GDP. The immediateaims of the measureswere to bring the current accountdeficit to 2.7 per cent of the GDP and inflation down to 9 per cent. Loans were negotiated with

The for World Bank IMF the reforms, the and stabilisation and structural adjustment.

1)1)

in as outlined the letters of intent from the finance minister to the IW and the World Bank, were

designed to remove impediments to domestic and foreign private

investment and to deregulate industry. The import regime drastically was simplified ,

tariffs were reduced, export subsidiessimplified and the rupee made convertible thus letting market forces determine the exchange rate. This trade and exchange rate

liberalisation was also accomparnedby tax reform, reform of public sector enterprises financial had direct the and sector which implications for the fiscal deficit. The tax reform consists of a cut in import duties, a streamlining of personal taxes- a cut in tax in rates and a reduction exemptions, restructuring of capital gains and wealth taxes.

New measures include an increase in the corporate tax rate, a reduction in generous

depreciation allowances that had tended to encouragecapital-intensive methods of in duties, interest banks, the tax and on gross receipt of increases excise production, a import duties.

2 the rates of a reduction in The reform of the financial sector consists primarily of a reduction in the Statutory Liquidity Ratio and a rationalisation of subsidised credit to priority sectors, firms' interest to capital markets, and access on restrictions and controls relaxation of banks.

The the to case of public sector in major reform sector public more autonomy from external and enterprises consisted of eliminating privileges such as protection

domestic competition and preferential accessto budget and bank resources.Though for 'exit closure or restructuring of money policy' the condition relating to an effective fulfilled, been has the reforms made in firms loosing the private and public sector not have largely been in line with the programme's objectives.

2- Memorandum Economic Policies for 1991-92 and 1992-93', in U. Kapila, (ed), 'Recent Developments in the Indian Economy' of Part-1,p. 322

23

The most important change appears to be in the opening up of the economy to foreign capital and the removal of exchange imports.

Consequently, in restrictions on 1994 India attained Article VIII status and joined the ranks of the 96 other such member countries of the M.

International monetary arrangements after the Bretton

Woods Conference required members of the EMF to restore current account convertibility. The obligation as defined in Article VIII

Sections 2,3 and 4 stipulates ,

that member countries should have no restrictions on current payments and avoid discriminatory currency practices. The first major step towards current account

convertibility was taken with the unification of the exchangerate and the removal of exchange restrictions on imports through the abolition of foreign exchange budgeting at the beginning of 1993-94. Relaxation in payment restriction in the case of a number final followed budget for August In 1994, 1994-95. transactions the the of invisible further liberalisation by taken towards of step current account convertibility was invisibles payments and acceptance of the obligations VIII of the RVIU,under which India is conunitted to forsake the use of exchange restrictions in current international balance the transactions as an instrument in managing of payments.

In 1993-94 imports stood at 10.5 percent of GDP. External debt had been

further 36 1992-93 40 to 1991-92 from 41 to per and per cent in percent in reduced $150 from 1991-92 investment foreign to in Direct 1993-94. million in quadrupled cent $620 million in 1993-94. In the first half of 1994-95, it was 50 per cent higher than in deficit The 9).

1994-95, (Economic Survey half 1993-94 first current account p. the of While in GDP 1994-95. down the 0.1 brought appear to reforms of nearly per cent was

far in the be their as the as the success to context of external sector, successful limited. be deficit to is concerned appears government expenditure and

24

1.8. Cut in Development Expenditure The rates targeted for the reduction fiscal deficit have not been achieved. For in example, though the gross fiscal deficit (GFD) was brought down from 8.39 per cent of GDP in 1990-91 to below 6 per cent in the next two years, there was a deterioration in the following years. The GFD to GDP ratio increased to 7.3 per cent in 1993-94 (Revised Estimates) as against budget estimates 4.7 data from As the RBI of per cent.

Annual Report 1993-94 indicates there was an increase in the revenue account gap from the budget estimates of 2.3 per cent of GDP to 4.2 per cent of GDP. This may be explained by both the shortfall in revenue proceeds and the overruns in expenditure.

The shortfall in revenue receipts in 1993-94 accounted for 37.2 per cent of the total in GFD during due 1993-94.

This decline in to the increase was customs and excise duties due to sluggish industrial activity and the reduction in custom duty rates. Total lower budget.

9.6 In the than the revenue collection was per cent estimated in following years, including in the 1995-96 budget, there has been a further reduction in

from Expenditures duties this revenue collection source. custom which would reduce budget by 48.0 9.6 the estimates; subsidies were per cent also grew per cent over higher while defence was 12.1 per cent higher. Both food and fertillser subsidies increased. Since 1992 the government has taken some steps in an attempt to cut the include These a reduction of posts at various growth of consumption expenditure. levels, overall cut in consumption of petrol, diesel, reduction in expenditure on The strength of the staff telephones and restriction on purchases of additional vehicles.

from fifty Government decline Central thousand of about showed an estimated of the March

1992 to March

1994 (Economic

Survey

1994-95, p. 16). However,

25

consumption expenditure still grew from 3.8 per cent of GDP to 4.1 per GDP cent of from 1992-93 to 1993-94 and led to a rise in revenue deficit.

Another major area of concern is the growing interest burden that accounted for 43.8 per cent of total non-plan expenditure and 53.4 per cent of revenue receipts in the 1994-95 budget. As discussed earlier this is the consequenceof the high fiscal deficits in the eighties that have resulted in the accumulation of a large public debt and of the application of market related interest rates in the sale of government securities that has led to an increase in the service cost on internal debt.

Table 1.4: Measures of Dericit of the Central Government (as a per cent of GDP at current market prices) Year

Gross Fiscal

Net Primary

Revenue

Deficit

Deficit

Deficit

1980-85

6.26

2.99

1.11

1985-90

8.21

3.80

2.58

1990-91

8.39

3.32

3.49

1991-92

5.90

1.46

2.64

1992-93

5.69

1.66

2.63

1993-94

4.71

0.44

2.25

7.29

2.72

4.24

(Budget Estimate) 1993-94 (Revised Estimate)

Source: Reserve Bank of India, Annual Report 1993-94, (1994), Bombay, Table 3.1 , 3 5.

In recent years there has been an increase in net primary deficit (defined as GFD less net lending less net interest payments). As Table 1.4 shows it has increased from 1.7 per cent of GDP in 1992-93 to 2.7 per cent of GDP in 1993-94 despite the target

'-)

of 0.44 per cent. This is likely to lead to a further rise in the debt to GDP ratio and interest burden in the future. Total debt servicing consisting of interest payments and repayment of debt was 112.8 per cent of total revenue receipts in 1993-94 (Economic Survey 1994-95). Table 1.4 also shows that instead of falling from 5.7 per cent to 4.7 per cent from 1992-93 to 1993-94 as was the budget estimate, the Gross Fiscal Deficit rose to 7.3 per cent.

The sharp deterioration in the revenue deficit has changed the composition of the G.FD such that it explained 58 per cent of GFD in 1993-94 as against 46 per cent in 1992-93 and 17.0 per cent in the first half of the eighties. In other words, 58 per cent borrowing in 1993-94 was to cover current expenditure. There was a of government squeeze in capital outlay from 2.3 percent of GDP in 1990-91 to 1.6 per cent In 199394 ( RBI (1994), p.36-37) The State Government budgets also show a similar trend "large budgetary gaps particularly on revenue account, rising non-developmental expenditure, reduction in the

availability

of

resources

fo r

investment

and

a

sluggish

revenue

from deficit doubled (I "(RBI, 1993-94 42) The 994) to overall nearly p. performance.

1994-95 while revenue deficit went up by one-third. The GFD is thus expected to be 28 per cent higher. As compared with an average surplus of 16.8 per cent of GFD in GFDConsequently, deficit 28 the of as compared per cent was revenue early eighties, finance being borrowing to 7.7 current expenditure to only utilised per cent of overall in the latter half of the 'eighties, 28.1 per cent of the overall borrowing was siphoned for funds finance The to capital outlay and net current expenditure. availability of off lending that reflects the states' investment operations gets correspondingly reduced.

While the central government had greater flexibility in its budget as it could borrow

I

from the public, the accessof state governmentsto borrowing public was much more limited. Consequently, state government's showed substantial shortfalls in actual outlays in relation to plan projections. Since the primary responsibility for investment

in social sectors, agriculture and irrigation is that of the states, there was a dechne in these areas (Jalan, 1992).

The composition of expenditure shows that non (i.

-development expenditure e. interest payments, administrative services, pensions and miscellaneous general services) rose faster than the development component from an averageof 22.9 per cent in the late eighties to 3 1.1 per cent in 1994-95.

The increased reliance on borrowing both from the Centre and the market higher future further the implies repayments and interest payments in which would budgets development Centre State For the combined the rising and expenditure. curtail have interest for increased payments and administrative expenses committed outlays from 9.9 per cent of GDP in 1985-86 to 11.6 per cent in 1993-94. The combined GDP from 3.2 has declined 5.0 to of per cent per cent government sector capital outlay from has 32.4 The increased share of non-development expenditure over this period. to this 42.4 rise expected total and is period over to expenditure of cent per per cent

further.

The overall picture that emerges from the above account of government development fall and the outlays capital of proportion in a is spending and expenditure

1.5 Table the that of proportion in shows total government expenditure. expenditure 1980.

10 by declined has than since development expenditure per cent more

28 Table 1.5: Development expenditure of Centre and States (as a per cent of total expenditure) Year

Development Expenditure

1980-81

66.0

1984-85

64.6

1985-86

65.1

1990-91

58.8

1991-92

55.5

1992-93

55.7

1993-94 (R.E)

54.3

Source-. Reserve Bank of India Annual Report 1993-94, (1994), Bombay, Table 111.10 p. 197. , To analyse the effect of the ongoing changesin government expenditure and debt in India we shall first test the Ricardian equivalence hypothesis. We then present a This both Ricardian Ricardian the the models. nonand general model encompassing behavioural determine for is India that the to parameters underlying model estimated debt Finally, impact in determining the we present a model of on growth. of are crucial both from by driven private capital and capital externalities arising endogenous growth is deficit fiscal Since to the and the revenue equal infrastructure. and public capital

lending domestic grants and revenue receipts minus net and capital expenditures by is to capital cut in a reduce it possible the it gap, overall resource measuring Therefore, examine we expenditure. than consumption government expenditures rather the the borrowing, tax in change and rate change in the effect of not just government GDP. long-run the of rate growth total to on government investment ratio of public for the the than causes We limit the scope of this study to the effects, rather The development of in economy political expenditure. non-development versus growth

29

the forces that generate the pressures on current expenditures of the government at the investment in India is another study in itself (for example, Bardhan expense of public (1989)).

30

Chapter 2 Debt Neutrality Theory and Evidence

Standard econonk theory suggests that an expansionary fiscal policy raises aggregatedemand in an economy. It leadsto a reduction in private spending, especiallyin investment private associated with an increase in real interest rates caused by fiscal expansion.This phenomenonis referred to as 'crowding-out'. Barro, (1974) suggestedthat the underlying premisesof the crowding out hypothesisis that consumersperceivea cut in

taxesto be a rise in permanentincome.If consumerswere rationaland far sighted,they would expect a cut in current taxes to be followed by a rise in taxes at some time in the future. They would, therefore, not perceive the cut as a rise in permanentincome and would not change their consumption levels. This hypothesis has come to be known as Ricardian EquiValence.'

In this chapter we shall discuss the Ricardian Equivalence theorem of debtSection I sets out the representativeagent model. Section 2 introduces the neutrahty. discusses into hypothesis.

Section 3 examinessome of Barro's the model and govenunent the evidenceon Ricardian Equivalence.In section4 we exarninethe evidencefor India.

2.1

A Representative Agent Model

Consumptionis determinedby fife-tuneresourcesratherthanincomein the current be income Life-time thought of as a which can resources represent permanent period. horizon.

If flow be the that throughout current planning can sustained constant resource income exceeds permanent income, the individual saves. He can acquire physical or

' The hypothesis is associatedwith Ricardo( 1951) in whose vntings this idea finds its first articulation. Even though Ricardo had doubts about the equivalence hypothesis,the proposition continued to be linked with his name. '17heterin Ricardian Equivalence %vas first introduced to macroeconomistsby James Buchanan ( 1976).

31

financialassets.Both yield the samerate of return andareassumedto be

perfectsubstitutes

in his portfolio basket.If current incomef9s short of permanentincome,the individual borrows. Debt is treatedas a negative asset.There are no constraintsor imperfectionsin the market which prevent him fi7omborrowing

at the market rate of interest.

Preferencesare assumedto be intertemporafly additive. Lifetime utility is the sum

of the sub-utilitiesof consumptionin eachperioddiscountedat the subjectivediscountrate.

This reflectsthe impatiencebecauseof which consumers attacha lower weightto the utility future of consumption.The utility functionof the representative consumerat time t maybe written as ut

(-ýZ, ), 1 4c =

t+i

(2.1)

i=O

6 is the constant rate of time preferenceand u() is a time invanant, concaveutility where function. As in Barro, (1974) it is assumedthat agents take account of the welfare and resources of their prospective descendants.This inter-generationalinteraction is modelled by assurningthat an agent maximisesutility subject to a budget constraint over an infinite horizon. Thus, although an agent hasa finite fife, his planning horizon is infinite to take care family. infinite horizon his immortal The planning assumptionthus corresponds of extended to finite lived individuals connectedvia a pattern of operative inter-generationaltransfers.

These transfers are assumedto be bequeststhat are basedon altruism and assumedto be non-negative.

The consumer'sbudget identity in period t may be written as

(I+r) V, I+ f4 - C, where

(2.2)

12

Vt = non-humanwealthat the end

of pefiodt

r= rate of interestassumedconstant Q= consumptionin penodt f2t = post tax labour income in

pefiod t

Rearranging (2.2) and solving forward in time the budget identity become the solvency constraint 00

[ct+i

+ r)v, -,

-

Qt+i

(2.3)

providedthat the transversalitycondition lim i-400 -(I

+ r)

Vt+i :::::: 0

holds or that wealth

does not grow at a rate faster than the rate of interest.

The representative agent's intertemporal budget constraint implies that the total value of consumption over time is equal to the total human and non-human wealth by is by Non-human V, and includes the the possessed consumer. wealth represented financial and non-financial assetsowned by the consumer. Human wealth is the present income future disposable be by and may represented stream of value of a

i=o

+ r)

t+i

(2.4)

Maximising the representative individual's objective function (2.1) subject to the intertemporal budget constraint (2.3), we obtain the first order condition

33

(2.5)

++ r) (where ý is the Lagrangemultiplier) along with the intertemporalbudget constraint.

Thus,

constantfor all i The Euler equation is :

öu(c+11)

=1+

u'(cý)

(2.6)

1+ r)

The two instantaneous utility functions that we encounter frequently in the literature are the quadratic and the constant elasticity of substitution utility functions. if the utility function is quadratic Ct

Ct)

2

derive is bliss level C Euler Then the the can of effective consumption. we where equation,

Ct

-a+,

8Ct-, 9)

where, a

+ r)

(I

(2.7)

8 and, = (I +0

The other form of the utility function that we shall come across in the following function isoelastic or the constant elasticity of substitution chapters is the .

34

ct

U(c CY

ln(Ct)

if

YCY 0,

YCF >

(2.8)

if G=1

is where cy the intertemporal elasticity of substitution. It measureshow responsive is the ratio of consumption in the two periods to relative prices. Estimates of cy vary substantially but usually lie around or below unIty ( Blanchard and Fischer(1987) 44).

In p. case cy = 1, the utility function is logarithmic in form. In the case of the logarithmic utility function the Euler equation is linear and of the form

C=

t

alP'-t-i

P where,

(2.9)

r) (1+45)

2.2. The Ricardian Equivalence Hypothesis If it is assumedthat the utility function is logarithmic then by combining (2.9)VVqth the budget constraint (2.3) we can show that

Vt-l IWO

ct = ýt

+ Yý

(2.10)

lifetime to it of 6/1+6. out the consume propensity marginal represents and where ýt = (2.10) the human consumption represents wealth. and non-human of wealth which consists

labour discounted tax R value of post function of the representativeagent.Since is the income, it is not independentof taxes.

be that It that into introduce policies the shown the We now model. can government have a transitory effect on income are incapable of having an effect on consumption.

35 We can then demonstrate that if it is assumed in Barro(1974) that consumers as

understandthe implications of the governmentbudget constraint,they do not regard a tax cut given government spending as permanent. They are fully aware that a cut in , , contemporaneous taxes implies a future tax increase.Hence, under these circumstances leads tax to no change in consumption. It leads to only a transitory change in a cut income which has no effect on consumption.

It is assumedthat the government obtains no revenuefrom the creation of money.

The governmentsectorhasa budgetidentityof the forrn Dt = (I + r)Dt Gt - Tt -1+

debt D, where is public at the end of period t.

D-

forward identity (2.11) in budget becomes time, the the solvency solving and

Rearranging

constraint co

+r) D,

-

I-G

-

iýo -(I+

r)-

[Tt+i

(2.12)

t+i

provided that the transversality condition

lim

D=0 t+1 J, + r)

holds. According to

be debt to must eventually run primairy surpluses a government vAth a positive be though is This the even can solvent government as condition a weak solvency solvent.

its real debt and its debt/GDP ratio grows WIthouta bound. Our definition of solvency faster does the than interest real adjusted growth this that grow not ratio merely requires debt/GDP to does It long as a in referred is which ratio the stable require a not run. rate (1995)).

Levine Krichel (Buiter Patel(I 99 1), and and strong solvency condition is The Ricardian equivalence theorem assumesthat the representative individual He fiscal in looking" the "forward government. affairs of and rational regard to the

'36

understands the implications of the intertemporal government budget constraint specified in equation (2.12). He recognises the future tax obligations implicit in the

issueof current period and existing governmentdebt We and its servicing. can rewrite the individual's intertemporalbudget constraintas

00

co

ct+l + r)-

i=o -(I

Q, since = N,

+ r)vt-, + j=0

+ r)

[Nt+i - T+i

T, -

labour in N, where = earnings period t (assumedto be exogenous) and T, = Tax payments (net of transfers) in period t.

We can integrate the private and public sectors by substituting the government constraint into the representative agent's budget constraint. The budget constraint of

the representativeindividual is now

co

co c +

i=o

r)

t+l

(I + r)[V, ] D, = -, -,

1=0

I

(N,

+

+i

G, +I) (2.13)

Thus if the agent is rational and understands the government's budget constraint and incorporates it into his own, his intertemporal budget constraint is representedby (2.13).

Using (2.10) we can now show that 00

c

t

(I + r)lvt]+I] -D t-I

(I + r) i=o

(Nt+i

Gt+j) -

(2.14)

The consumption function of the rational representativeagent is now independent

leaves in Any debt taxes level t change taxes after. the or or of issued in period of

37 consumption unaffected. A fise in govemment spending has a negative net wealth effect and reduces consumption. This is becausethe government would have to raise taxes at some time to pay for higher spending,thus reducing the lifetime wealth of the consumer.

(2.14) therefore representsthe consumptionfunction correspondingto the Barro-Ricardian model. Keeping the level of government spending constant it demonstratesthat if the , consumer incorporates the government'sintertemporal budget constraint into his own, a

in change the level of taxes does not affect his life-time wealth i.e. it has no net wealth A effect. shift fi7omcurrent taxesto a deficit has no impact on aggregatedemand.

2.3.

Empirical Studies The most common approach to empiricaHy test the Ricardian theorem was to

include fiscal variables in a regressionof private consumption in order to test whether a debt financed tax cut led to an increase in private consumption expenditure (Feldstein(1982), Kon-nendi(1983)). Pfivate consumption was specified as a ffinction of income, taxes.,government expenditure and private wealth including public debt and the The the these. terms tested model was restrictions placed on of in proposition was led different in for US. Differences to the measurementand restrictions estimated usuatly This approach was criticised on the grounds of the arbitrarinesswith which conclusions. from from Tl-ýs included the the not specifying resulted model. or excluded variables were did The the test the of assumptions theoretical not explicitly approach model. underlying incorporated behaviour the into not was expectations equivalence proposition and based defive (1985) FoHowing Aschauer explicitly on a model we estimating model.

based function Ricardian assumptionsand a government expenditureexpectation on rationalexpectations.

38 We assumethat utility is a function of the total consumption by an individual of

both public and private goods.

C* =C +OG tt

(2.15)

C* denotes the level of "effective" consumption in period t. It Is a linear where t combination of private consumption Ct and government goods and servicesG,. In . terms of effective consumption, the budget constraint of the representative individual

is:

00

00

+ r)-

ct+1 ::--(1+ r)[V,

]+1 Dt-, -,

i=o -(I

+ r)-

(Nt, + (0 1)G, -

Thus the present discounted value of effective consumption is constrained by the economy wide wealth plus the present discounted value of labour earrungsplus (0- 1) times the value of government expenditure. Rearranging

(I + r)D,

Go

(I + r)V,

i=O

1+ r)

t+i -N t+i -(O-I)G,

+i]=0(2.16)

Maximising effective consumption (2.15) subject to the budget constraint (2.16) and if

the utility function is assumedto be quadraticthen ct

= cc+ (r

where, a

+ r)

(2.17) and

+ r)

39

is bliss level is C If E, the the expectationsoperator where of effective consumption. information in the to t then conditional on availableup expectedconsumption period be defined t period may as E C*=oc+ PC* +pt tt t-I

is where p, the error term.

Lagging equation (2.15) by one period and substituting into equation (2.18) gives ]+ OGt Ct OGt-l Ct P[Ct-I EtC*t = u. + + + + pt -

(2.19)

EC*=c* where ttt If G, = E, G, + X, -,

(2.20)

Xt is the error term. where We obtain

OEt-I Gt Ct+ POG, PC, +ýt + cc+ -_1 -, Or, Ct =a+ PCt_l + POGt-l - 0E, Gt + ýt _1 (2.21)

in includes revisions ýt errors, the measurement of effect where the error term expectationsand shocks. basis of the values past of on predicted The value of government spending is G, G, E, at the of is value It that expected deficits. assumed and spending govemment _1 by is I time tgiven

(L)FDtvt Et- Gt =y+ 6(L)Gt- I+ co I+ I

(2.22)

40

where L is the lag operator and FDt is the government deficit in period t. The error term vt is such that it satisfiesthe orthogonality condition E(vtj 1, )=0,1, -,

being the

information set available to the agent at time t so that vt is serially uncorrelated. If expectations depend only on last period's spending and deficits he obtains the following the two equation system

Gt =y+F,

Gt-I +w FDt-j + vt

(2.23)

and Ct = cc' + PCt-I + fl G,

+ ODt-I

+ 7r,

where cc' = cc- Oy Tj =

O(p

- F-

)

(2.24)

ýt -- (1) Ricardian Equivalence requires that the cross equation restrictions are not because imply they that the consumer takes the government's tax and violated

into decisions As be to expenditure account. expectationsare assumed rational the behaviour budget is the government's which satisfies intertemporal constraint correctly individual by consumers. predicted Aschauer(1985) found evidence in support of Ricardian Equivalence. He lagged highly the the that of consumption value is estimated coefficient on reports level fixed holding implying the that to of government unity significant and equal The follows point estimate a random walk. spending - private consumption expenditure for substitutability of public spending for private consumption is positive and is from different five level. the zero at percent significantly

41

Further, likelihood ratio statistics suggest that the data does not reject the hypothesis at conventional significance levels. First government spending and

consumption functions are estimatedsubject to the restrictions on consumption.Next the system is estimated without imposing the restrictions. To test the hypothesis of Ricardian equivalence he examines the validity of the restrictions. This is done by calculating the log-likelihood ratio test statistic. If Ll is the value of the likelihood function for the maximum of the unconstrained model and LO is the value when the constraints are imposed then the likelihood ratio test statistic is computed as LR 2(LI-LO).

This statistic has a X2 distribution with degrees of freedom equal to the

is less than the value of the x If LR the number of restrictions. estimated value of

2

distribution at a given level of significance then it indicates that there is no significant discrepancy between the constrained and the unconstrained values of the log-likelihood function and thus we the null hypothesis that the constrained model is-true cannot be

rejected.

Gupta (1992a) estimates the model for some developing countries. IFEsresults lagged IFEs the that consumption is coefficient of evidence suggests are mixed. from different is in all cases and not significantly statistically significant and positive 0 from different is it 0.65 the In India in unity. significantly and is most cases. unity be is found in India to is negative and coefficient of government expenditure statistically

different

from

unity.

However,

the

null

Equivalencecannot be rejectedby the likelihood ratio test.

hypothesis

of

Ricardian

42

2.4. Excess Sensitivity

The Ricardian Equivalence hypothesis assumes the existence of perfect credit markets. Evidence indicates a role for current income in explaining consumption over

and above that which is due to a revision in expectationof future incomeas signalled by current income (Flavin(1981), Hayashi(1982), Jappelli and Pagano(1989)). Flavin (198 1) analysedthe role of current income in providing new information about the fUture.

Shefound that the responseof consumptionto current income beyond that attributable was to the role of current income in signal-lingchangesin permanentincome. The permanent hypothesis income suggests that individual consumption depends on the resources available to the consumer over his entire lifetime. However, if a consumer is constrained by credit market imperfections and is unable to borrow and lend the he amount requires to undertake his optimal consumption plan then his desired be consumption will constrained by his current income.

To take account of the 'excess sensitivity' of consumption to current income, Hayashi (1982) explicitly included the presenceof some householdsin the economy who income. 'excess The their only current sensitivity' of consumption expenditure consume to contemporaneous disposable income may be attributed to liquidity constraints. If liquidity constrained consumers are significant in proportion then aggregateconsumption revealsexcesssensitivity to current income.

The economy is assumedto comprise of two groups of consumers- the liquidity

consumers. constrainedconsumersandthe unconstrained

43

Aggregate consumption is assumedto be the sum of the consumption of constrainedandunconstrainedconsumers.

Ct= Cý+ ctu

(2.25)

where Q= Aggregate consumption CtC= Consumption of constrainedconsumers

Cý = Consumptionof unconstrainedconsumers We assumethat unconstrainedconsumersreceive a proportion

k, of total post

tax labour income, f4. Constrained consumersthus receive a proportion (I ?, ) of total - ý labour income.

Sincethey consumetheir current income, tax post

ctc=(I -x )f4

(2.26)

If the value of ý. is estimated to be unity, then one can conclude that all consumersare forward looking. The aggregate consumption ffinction is thus a generalisation which income hypothesis the includes permanent as a specialcase.

The consumption of unconstrained consumers may be defined following (2.7) as

cu -oc+PCu t

+e, t- ,

(2.27)

distributed is be to to term the any and uncorrelated normally e, assumed error where information available to the consumer in period t- I including consumption in period in future Since t-1. income, the error term changes in current income signal changes

44

may include changes in consumption expenditure which occur due to the revision in expectation of future income.

Aggregate consumption may be defined (2.25) (2-27) using and as CĂ˝

Ct =a+ ocu +Cc +e ttt

(2.28)

Adding and subtractingOCt-I on the right handsidewe get ct

)+Ct o(CU cc cc + + -oct-I t-I t-,

+e t

(2.29)

Lagging (2.26) by one time period and substituting in (2.29) and using (2.25) we

obtain ct =a+

oct-

(I - k)(Qt - ont-, )+ et I+

(2.30)

X can be interpreted as the degree of excess sensitivity of consumption to current

income. If there exist no credit constraintsk shouldbe one.

2.5. Evidence for India To test the hypothesis for India we estimate (2.27), the constrained is data (2.30), The the model estimated using annual unconstrained model. model, and for India for the penod 1960 to 1989. The data source is International Financial Statistics published by the IMF (various issues). Variables are measured in real per disposable f2t, instrument for is Per GDP the terms. current capita used as an capita income. Since the error term may be correlated with f2t, we estimate the model by instrumental NLIV variables. using

lagged values of estimates using one period

income, investment private sector and government spending are consumption, 2.1.

Table We Wald the compute in statistic to test the restrIction. presented

45

Table 2.1 : Excess Senstivity of Consumption Parameter

Estimate [p values in parentheses]

a

15.09 [0.039]

p

0.30 [0.111]

I-k

0.547 [0.000]

Durbin Watson Statistic

1.93

LM test for first order Serial Correlation

0.12 [0.727]

LM test for functional form

1.64 [0.201]

LM test for Heteroscedasticity

2.39 [0.122]

LM test for Normality

2.80 [0.247]

Wald test of restriction (k = 1) = 142.35

Wald Statistic indicates that the restricted model is not the true model.

This indicates that there is evidence of excess sensitivity of consumption to income.

This suggests that the assumption of the Ricardian model that there are perfect credit biased however be for The India. estimate of excess sensitivity may markets is not true because we have not taken into account the effect of other possible violations of the Ricardian model into account. For instance, the presence of finite horizons, rather than

lead here, horizons permanent to of response as assumed greater a would infinite income unconstrained consumers to current income than suggestedby the model

46 I, n

(1-Ă˝, ) degree The the that the our mean estimate of of excess sensitivity, would above. is by higher than what it would of received proportion income constrained consumers,

be if we took into account finite horizons. In the next chapterwe extendthe model to include the assumptions of finite horizons and population growth.

47

Chapter 3

The Aggregate Consumption Function: Finite Horizons, Liquidity Constraints and Population Growth with Income Redistribution

The model presentedhere is confined to the analysisof a closed economy. NonRicardian effects are introduced in the aggregateconsumption function by the inclusion of liquidity constraints following Hayashi (1982), finite horizons following Blanchard (1985), population growth following Weil (1989) and aflowmg for a transfer of consumersfi7omthe group of constrained (unconstrained) to the group of unconstrained (constrained) consumers.Any one of thesefactors leadsto a deviation from Ricardian Equivalence.Time discrete following Frenkel and Razin (1992). is 3.1. Liquidity Constraints As describedin Section 2.5 the economy is assumedto comprise of two groups of liquidity the consumers constrained consumers and the unconstrainedconsumers.The intertemporal budget to the unconstrained consumersmaximise utility subject constraint.

Their consumption expenditure can be more than or less than their current income. They

haveaccessto the credit market.Hence,they saveor dissave.Assumingthat a personis born with zero net wealth, they become owners of all the nation's financial and physical be The the portfolio of an unconstrainedconsumer may component of wealth in wealth. positive or negative.

Aggregate consumption is the sum of the consumption of the constrained and

unconstrainedconsumers. ct = Qc + QU

48

where Ct = Aggregate consumption

CtC= Consumptionof constrainedconsumers CtU= Consumptionof unconstrained consumers We assumethat unconstrainedconsumersreceivea proportion k, of total post tax labour income, Qt. Constrained consumersthus receive a proportion (I Ă˝, ) of total post tax labour income. Sincethey consumetheir current income,

Ctc(I-k )92t

(3.2)

If the value of k is estimated to be unity, then one can conclude that all consumersare forward looking.

3.2. Finite Horizons The group of unconstrainedconsumersconsist of overlapping generationswhich, from identical.

To capture the "fife-cycle" aspect and to deal vvith issuesin apart age, are K_

in behaviour the which change over fife are important, we would need to aflow for differences in propensity to consume across agents. However, t1iis makes aggregation impossible. To allow aggregation it is assumed,following Blanchard (1985), that agents face throughout their life, a constant instantaneousprobability of death, p. Their expected life I/p is constant throughout life. The aggregation problem is solved becausethough levels have have different horizon different they the of wealth, same ages and aggents are of index fies between horizon (1/p) the to the anywhere zero same propensity consume. and lin-king infinite horizon let If to then the case. caseas a p go zero we obtain and infinity. we As noted earlier, it is assumed that each agent is born vvith zero net wealth.

Consumers leave neither assets,nor debt to their cWdren. The model thus assumesthe

debt bequest Because life-time that motive. is and the assumption of uncertain absenceof a

49

loan inherited by borrower's that the not childrenwho would serviceit, it is assumed each is loan direct Perfect the associatedwith a prenuum. surchargeon is an insurance which loanable for funds the the competition and zero profit condition in would ensure market

that at the endof a penod,after taking nsk into account,eachlendereamsa returnequalto the risk free return (I + r). Since a proportion p of the population is expectedto die in A (I to the survive. expected is p) of population each period, only a proportion interest, free interest higher lender than r, the risk rate of charges a rate of competitive because p per cent of the population is not going to be alive to repay the loan and pay the interest on it. The competitive lender thus charges(I + r)/(l - p) so that the safe return is (I - p) [(I + r)/ (I - p)] =I+r.

Alternatively, it can be assumedthat the agent owns assetswhich he lends out. He life R* him borrower that Iýs The interest a includes a return pays assets. on receives dies.

Since individual he for in the only insuranceprenýum return which inheritsthe assetsif (I he is (I - p) proportion of the population going to survive, will end up paying only - p) R* and therefore if the securerate of return is I+r,

the zero profit condition ensuresthat

decision for individual borrowing (I - p) R* = (I + r)/(l - p). The effectivecost of relevant is making

He-cycle ignore (I To of aspects (I + r) / also we aggregation, ease - p).

labour income and assume that labour income is constant throughout the consumer's fifetime.

3.3. Population Growth and Income Redistribution income by It is assumedthat the economy is characterised population growth and the to rate at grow The assumed is consumers of population unconstrained redistribution. four divided be groupsinto The over may total any period population g.

50

A. Thosewho were constrainedat the beginningof the period

andconstrainedat the endof

the penod.

B. Thosewho were constrainedat the beginningof the periodand

unconstrained at the end

of the penod.

C. Thosewho were unconstrainedat the beginningof the period and

unconstrained at the

endof the penod.

D. Those who were unconstrainedat the beginningof the period and.constrainedat the end of the penod.

Since our definition of unconstrained consumersis one that includes those who borrow depending saveor on whether the component of wealth in their portfolio is positive or negative, a change in an individual's position ftom constrained to unconstrainedcan by in come about either a change the credit market such that more (or less) people have by to access credit or a redistribution of income. In a country where a credit market is developing or one where a developed credit market is liberalised, one would expect a become beginning the the to number of consumers who are constrained at of period if by during If the they to that the time. there period get access credit end of unconstrained

be the credit availabilitysucha changecould the resultof a redistribution was no changein have income fi7om the capacityto save,to the constrained. the rich, who of Group D consumers could either be the victims of tighter credit controls or a beginning better distribution.

Agents the off at of the who were worsening of mcome by doing it, become the the end of of so incapable save a part of could period and could

both fafl D B due If the their the to zero, was and in of groups a real size income. period constrained and the unconstrainedgroups are assumedto grow at the rate of growth of (g If D, larger B then than g*), in any period group total population, g*. group is -

51

is be whereg the growth in the sizeof the unconstrained group,wifl positive. If group D larger than group B, it suggestsa net transfer from the unconstrainedto the constrained is group and (g - g*) wifl be negative. In the absenceof transfers, the rate of population growth of the unconstrained group would be g*. In an economy undergoing structural

changewe would expectboth group B andD to be non-zero.

3.4. Utility Function The utility function is assumedto be of the constant elasticity of substitution type intertemporal is the A where elasticity of substitution unity. constant elasticity of substitution utility function may be written as I ct

) U(C,

I-Y,

ln(Ct)

if

0, >

if cy=I

The single period utility function of the consumer is thus logarithmic. a is the intertemporal elasticity of substitution. Considerthe unconstrainedconsumerbom in period ffinction The at time t Ă˝! s, in the absence consurner's intertemporal utility s. unconstrained death is by fi7om given of any uncertainty apart u-

t's

I

I-t

00

i=t

1+6

ly logC'i, logG"s + y, s Ii

(3.3)

U,,, denote CI, 5 denotes the the time consumptionof and and rate preference of where i+ (1, 1). goods respectively over period pubfic privateand Wealth of an individual consistsof two components:non-humanwealth that financial human the and presentvalue assets consists of and physical wealth which includes

52 of the expectedfuture streamof labour income. Real net financial and physicalwealth at the is by The Vj,.

At this taxation end of penod i given of non-labour income. stagewe ornit

budgetconstraintof an individualmaybe definedas [(I +r)/(l -p)] Vl-j,, +Q%, -C'ý,

(3.4)

income, " labour Q, is total tax post whereunconstrainedconsumersreceive which a part of f4, and r is the risk fi7eereal rate of interest.r is assumedto be constant.Rewriting (3.4) as, Vi-

(vi, +c-i" -

=

I's

I+r

Q'i")

Solvingforward in t4ne andsubstitutingwe have cui"

(c

+(ý-

.

u

I+ I's

i+ i's

+r

faster does than Combining with the transversalitycondition that wealth not grow at a rate i. interest the rate of e.

V""

0

JIM i -> oc) +

budget the consolidated we arrive at

lifetimeindividual's the constraintover t

t=o

I+r

t=o

I+rIp

n.

i+t, s

I+r

(3.5)

v I-I's

budget intertemporal (3.3) by subject to the The consumer maximises utifity defined fon-n(2.9) in is linear the Euler of (3.5).

The and as equation resulting constraint U

ýC u ýs= (I+r) / (I + 6) +,,

Combining (3.5) and (3.6) leadsto Uls

[(I +Hu +r)/(l = ýt -p)V,-,,s ts)]

(3.6)

53

where ýt = (p + 6)/(l + 8) and H'

human defined is wealth of unconstrained consumers ,,

by

uu i's

), t=O

i+t,s

(3.7)

In the infinite horizon case we found ýt = 6/(l + 6) [ (2.10)] which correspondsto p=O

here. ýt Is againinterpretedas the marginalpropensityto consume lifetime out of wealth.

The amountan individualconsumesout of an additionalunit of lifetimewealthat anypoint depends how he weighs presentconsumptionrelative to future consumptionand time of on his upon probability of being alive to consume it later. If the degree of impatience was infinitely high, the rate of time preference 5 would be very high and ýt would be nearly unity. In other words, he would consumeevery extra unit of wealth right away. The lower the degreeof impatience,the more the individual would be preparedto wait to consumehis lower be the the value of the marginal propensity to consume out of wealth and would lifetime wealth. If the rate of time preferencewas zero, the marginal propensityto consume Heinle be life the to the out of equal p, reciprocal of expectancyof the wealth would individual. In that caseit can be shown that if the individual expectedto five for n years he he his that consumption out such consumesan equal amount in each year. would smooth Since here the marginal propensity is equal to the average propensity he would consume I /n amount of his wealth in eachyear.

In terms of the probability of survival, the higher is the probability of survival, the lower is the marginal propensity to consume out of lifetime wealth becauseof the need to five longer high If to the individual expects and period. p is very spreadconsumption over a for a very short period he will consumea very high proportion of his wealth. If 5 and p are

both low then ýi WIllbe low aswell.

54 3.5. Aggregate Behaviour We now look at the aggregate behaviour of unconstrained consumers to

incorporatethe effect of populationgrowth and incomeredistribution.If L, is the size of the cohort bom duringthe period [s,s+ I] who are still aliveat the endof periodt then L. Ă˝, (1-p)"L, =

The unconstrainedgroup can increaseor decreasem size both due to natural .

birth and transferto and fi7omthe constrainedgroup. Let 0 be the 'birth rate' (assumed includes both birth and augration during a period such that 1-,,,= P(I-p)I-t-, that contant) is is bom in in LĂ˝, L, the the t. t where population period and still alive period and (assumed If the the constant),then population size at end of period. g= population growth 1, = (I +g)Lo. Hence we must havethat t Lo g)

Lt =(I+ tt

(3.8)

I I+ g)-1(1 - p)t-s+ L =)OLO t's S---Oo S---Oo

Performing the summationleads to 1/(I+D) = (1-p) / (p + g) which determinesthe 'birth 0= have P. For -p +g. smaHp, g we rate'

Aggregatevariablesaredefinedast cut

(3.9)

Lt, C't, S= -co t

H"t

(3.10)

L Hut, t's S=-OC

have (3.10) first differences Taking we of etc. t- I

H't - H't- i=L,

[Lt, 1] Hut,s -LHu Hutj + I's ts , S= -co

t- I.S

P[(I-p) / H' P(I-p)L, (3.11) hand The first tenn on the right is equal to side of ,= -, (I +g)]IH'

IH " L,= H' t since human wealth of all age groups is equal according But Ă˝,.

55

to our 'perpetualyouth' or constantprobabilityof deathassumption.Using (3.7) human wealth of cohort s accumulatesaccordingto u (H -p)] s-Q'i-,,s) 1-1,

(3.12)

Using (3.12) and the definition of aggregate human capital, the summation on the right u hand side of (3.11) can be shown to be (I+r)(H' t-I -0 t-1).

Hence aggregatehumanwealth of the unconstrainedgroup accumulatesaccordingto 11-P('-P)I(I+g)]IT, (I+r)(Hu, [(I-p)/(I+g)]Flu, = = -, -Quj)

+F-t

(3.13)

iid(O, s c) Et-

in human t. in that period the made are the wealth expectation of revisions F,t represents Under the assumption that expectations are rational, it is orthogonal to the set of Aggregate household I tthe to and is serially uncorrelated. at available infonnation human wealth of unconstrained consumers may be expressedas 00

H't =I(Ip t=o

(I + r)( IĂ˝

Ă˝))

Q't

+ Et

for in the aggregate expression The presence of the growth rate of population income labour to future those fact yet of is indicative the that the expected humanwealth of households. by is by birth transfer) not owned current join the unconstrainedgroup (by or by interest the by discounted income the augmented labour of rate ffiture real Aggregate is the population. of growth of rate and survival of probability financial defined wealth.

V,, total non-human wealth, is as the sum of physical and be total capital the to durables private assumed Ignoring consumer physical wealth is by held debt Dt, is the government Financial to Kt. of consist assumed wealth stock

the households private Since all own the and sector private households. constitute

56 capital stock, the sector as a whole does not have any other financial assetsor liabilities

in a closed economy apart from public debt. Individual householdfinancial assetsand liabilities in the private sector will balanceout. We thus assumethat the financial only wealth of the householdsector as a whole is governmentdebt. Thus Vt = Dt + Kt. If Vt is the sum of capital stock and financial assetsin period t, we assumethat the return earned on it is equal to r. If the net rate of return on capital stock was different from that on government debt then households would sell government debt buy and physical capital, assuming that no risks are involved in either. In equilibrium, therefore, the marginal rate of transformation which is the net return on capital is equal to the real risk free rate of interest.

Aggregating financial and physical wealth, the first ten-n in the summation L, Výt CP ý, becausethe newly born consumersborn in period [t, t+l] inherit no financial or physical fi-om Hence, I t+ corresponding to can only start accumulating onwards. wealth which (3.13) we have (3.14)

vt = (I+r)vt-l +f2ut- cut is Vt non-humanwealth at the end of period t. where

The aggregateconsumptionfunction of unconstrainedconsumersis now

cu, = ýt((I+r)V, + K) + ut; ut - ýd -,

(o, Cy2u)

has been to the to term the consumer'sutifity shocks capture added error random u, where function. (3.13), (3.14) and (3-15) present our model of aggregate consumptIon of

unconstrainedconsumers.

The aggregate consumption function may be summarised as follows:

57

ct

=

ctc

+

ct

u

ctc--.: (i -x Pt Cut = g((I+r)Vt-l + Hut) + ut; ut fid -

(O, o-2,,)

Vt = (1+r)Vt-l +nut Cut H't = f(l+O (1+9)/ (1-p) j(H',

-i

+ st; ct - iid (0,o;,:)

where C, =Aggregate consumption Ct'= Consumption of constrained consumers Ct" = Consumption of unconstrained consumers f4= post tax labour income income labour tax post of unconstrained consumers Vt = Non human wealth H", = Human wealth of unconstrained consumers X= proportion of total post tax labour income received by unconstrained consumers instantaneous p= constant probability of death interest free the of r= risk rate g= rate of growth of population of unconstrained consumers lifetime to consume out of wealth p= marginal propensity (= (p + 6)/(l + 6)

6= rate of time preference) where

58

Chapter 4 Estimation and Results

In this chapterwe estimatefor India the aggregateconsumptionfunctiondefinedIn the previouschapter.We discussthe difficultiesencounteredin estimationand presentour methodology and results.

4.1. Eliminating Human and Non-human Wealth Aggregate consumptionis expressedas a function of human and non-humanwealth difficulties for estimation.Human wealth R cannot be observed. There are this and creates two standardways of dealingwith this problem. The first method proposed by Hansenand Sargent (1980), seeksto obtain a closed forrn expressionfor H, in terms of observable labour is They that assume variables. mcome a part of an n-vanate autoregressiveprocess is linear lagged derive fonnula for in fL the and which current and an explicit valuesof the n

discount in the ten-n the and coefficients the autoregression. variablesand non-hear in Estimates of parametersare obtained by estimating the consumption function and the nby likelihood.

To maximum make the number of process jointly vanate autoregressive finite finite, it is that the to order of autoregressionis and necessary assume parameters known a pnori. The secondmethod which we adopt fbHowsHayashi (1982) who avoids an from function. human by human the treatment wealth wealth eliminating of expficit Non-human wealth is held by householdsin many forms apaft from financial assets.

These may be gold, housesetc. accuratemeasuresfor which are not easyas not only does

but households by fluctuate declared they as part of their their value are also not always To from by We this the equation. can avoid problem eliminating non-humanwealth wealth.

59

eHminatehumanand non-humanwealth fi7omthe consumptionfunction of unconstrained consumerslet us define oc=(I+r)(I+g)/(I-p); R=I+r. The lag operator is defined such that LY,t=Y, L -,;

2)(t=YM-2and

for so on any variable X.

Ignoring the superscript u for unconstrained consumersfor the time being, and rewriting the equationsusing the lag operator and rearranging, ýt[K +RLVt] + u,

[1-aL]R=

-aLf4

+Ft

RLVt = Qt-C, -V,

(4.2) (4.3)

We multiply (4.3) by [I fi7om (4.2).

Substituting the the and subtract resulting equation -aL] (Ct-u, )/ýt from (4.1) for FL+RLV, we expressthe consumptionfunction as expression [I-.aL] (Q-ut)/Vt=[I (Ct-Vt) -ccL] - "Qt-f-st

(4.4)

The above expressiondoes not contain the unobservableterm human wealth and can be simpHfiedand estimated along vAth (3.14) as a system of equationssirnýilarto the in (1982).

Hayashi However, the systemof equationscontainsthe variable non-human one does for (4.2) India.

Rearranging gives us not exist wealth, an accuratemeasureof which [92,-C, ]/[I -RL] Substituting in (4.4) we arrive at [I -(xL] (Ct-ut)/ýt = ([ I -aL]/[ I -RL]) [f2t -Ct]- f2t +[ I -aL] Ct -FFt

We have now eliminatedhuman and non-humanwealth fi7omthe consumption fi-inction of unconstrainedconsumers.Tlýs expressionis equivalentto

60 C't

+ r)

+g+ 1---p c Ut1+81

I+g

(I+r)2

cu

1+8

-p

t-2 -

P+6) P+9) ý) y6) _ D P+6

P+5 +

1+ 6)61 2

+8 +8)

1+

I+glý-2-0+0

1+

I-P

1

Ut- I+ 1ý

pg) p

(4.5)

The above definesthe consumptionfUnctionof unconstrainedconsumers.

From (3.1) and (3.2) we have C't

Ct (I f2t ? ) = - - ý,

(4.6)

Lagging (4.6) and substitutingfor fft, Cu, andCut-2in(4.5) we get -, r)

+g+I-

P]C, 1+8

-p

I+

+

-,

+ r)

[(I I+

gCt-2

r)2 1+6

1-1n) g+

+ g)

-p I+g +

f2t-2

r)2

1+61

+ r)

where p,

+ Pt

8)

p

6t-l +p8

+

+g + r)2

+ig "t-2

-p

&t

+ r)

+I i-

ut-I

+ ut

P)

(4.7)

The above defines the aggregate consumption function in terrns of lagged values of

income. labour lagged Both tax variablesare valuesof post consumptionand currentand is data be for But to this them, can obtained possible estimate equation. so it observableand before we do so, we look at some of its properties.

4.2. Non-Linearity A preliminary exan-dnationof the above equation suggeststhat it may be rewntten as

61 Ct :::: ý (XI C-t-I + CC2C-t-2 + OC3f4

+ (X4 ý4-1 + ()t5Qt-2 + Pt

where II-p '+g

I-P

oc, =(I+r)

+

1+61

I+g CC2

=+

r)2

(4.8)

OC3 =

[ ot 4+

g

r)

I-P

Oc5

+ r)

2

I+g

LIP 1+8

+

1+9 ý+ 8)

-

1+8

Therefore, OC5::": -U-2

GC3and

is p, the error term.

The model is then of the fon-n of an autoregressivedistributed lag model with two lags of income and consumption and a moving average error term. However, if the model is linear fail to take into account the non-linearrestriction that estimatedas a model we OC5 ":::::: -(X2 (Y-3.

If the five parameterscc,,

be written as five one-to-onefUnctionsof the a5 could ..-,

five 6, X, been have defined then the set of underlying parametersr, g, and p model could = intrinsically linear. here being due However, to the non-linear restrictionCC5 as

-a2

CC3

the

I one-to-one' or identification condition is not met. If we were to estimate (4.8) by NonLinear Least Squaresmethod and solve the resulting 4 independentequations for the 5 be 5 k, there no unique solution. would underlying parametersr, g, p, and 4.3. Properties of the disturbance term We have defined the disturbanceterrn as (

+ r)

1) -ili+-5

I+ + r)2

I-P

F-t_j

+(P+5) 1+8)

F,

t

g tý-2 -(I+

rI+-

ý

2) ýd(O, cyu independentof F,- iid(O,cy,: where ut -

62 is pt thus a sum of two moving averageprocesses,an MA(l) and an MA(2) process.Both

ut andFt areidenticaflyandindependentlydistributedwith meanzero andconstantvariance.

They areuncorrelatedwith eachother at all leadsandlags.

Sincethe aboveerror term is fairly non-standardwe analyseit in somedetail.We derive it's varianceand autocovarianceand definethe variance-covariance Let matrix. us it by simplify redefining p, as :": 'Ă˝+0A-,

Pt

+02'Ă˝-2+e,

+ke,

-,

(-Ili++ 5) whereet = & 5t i

0, = -(I + r)( I+ -+99) I-P I+g 02 =(I+r)2

I-p

+ r)

2 2),

Since F-,- iid(O,a,,

have e, we

fid(O,

2) Cye

C7e2=

where .

Var(e,)=

2

GE,

Since the u,'s and F,,'s are uncorrelated with each other at all leads and lags and are white be noise processesit can shown that E(uiuj) = E(eiej)=O, i; j: E(u,u,)

= CYU2

2

E(eiei)= (Y, , _,

E(uiei-j)=0 for afl

Using the aboveresultswe canderivethe meanandvarianceof p, as E(pt) =0 Var(pt)=

=Gu

2[(1+012

::--Gu

(1+()

+02

+02 12

2)

2)CVU2

+(1

+(I

+k2)Cye

2/cy 2] )(Te +X2 u

yo, say

The first autocovananceof p, is

2

63 (u, + 01 (Ut-1

+ 01 Ut-2

2+ Cyu 2[01( 1+02) ==Cyu

=-a.

02 + Ut-1 + 02

Ut-2+

et+Z et-, )x

Ut-3+

e, +ý -,

et-2

kcy, 2

2/cy 2] XCTe + u

-yi, say

The secondautocovariance is 2 E(PtPt-2)==Cyu [021=Cyu2Y2, say

AH other autocovariances arezero. k>2 E(p,p, -k)=O, Thus P,'s are uncorrelatedbeyond two penods.

The vanance-covanancematrix of the error term may be written as YO Yl YI

Y0

Y2 0

Y2

YI

0

y2

YI

YO YI

y2

YI

ý ) V(P, cy, u 0

0

0

0

0

0

0

0

Y0

0

0

0

0

0

0

Y2

YI

0

0

0

y2

0 0 0

0

y2

0

Y0 'Yl

Y2-

YI

Y0

YI

y2

YI

Y0

is T the numberof observations. where C7270 u 2

li

jj -

Uyl CY

2Y2

u 0

=

li

-jl =2 11 >2 -jl

Substituting for the expressionsfor O's and X we have

lTxT

64

Yo

1+ (I+r

)2

9p

1+

+(I+r

)4

(L+g

(Y p

+(I+(I+r)2)

CF

e 2 u

ý

1+ -+g

y,

(-ý,

1+(I+r

(I

)2

I-P

_+-gý)

ý12 +)

r

2 e

I+g Y2

-(I+r)2

I-p

The error ten-nis thus a moving averageprocessof order two.

4.4. Generalised Method of Moments In a single equation dynamic model vvith serially correlated disturbances,a lagged

endogenousvariableon the tight handsideacts as a sourceof inconsistencyfor OLS or NLS estimators.If laggedvaluesof consumptionare not independentof the error term they do not satisfy the conditions for pre-deterrninedness.From the definition of the human revision of expectationsof wealth we can seethat labour income wil-I be correlated included with e, which is in pt. The error ten-nis thus correlatedwith the regressors.

In the classicallinear regressionmodel tt X'D+u

for xj a (kxl) vector of explanatory variables.The value of P, Pois assumedto satisfy the

condition E(xtut) =0 The consumption function we want to estimate contains lagged values of be income. labour It lagged tax the can easily post values of consumption and current and ] Further, Cov[C, COV[Ct-2, 0.

0 term the that containsF, error # since p, and Pt] shown tL :; -I,

disturbance human to term the the the revision in expectationof wealth,we would expect be correlatedwith current incomeas well. If current labour incomechanges,households

65

may revise their expectations of fiiture labour income. Since the disturbance term first lag are correlatedvAth pt. contains F-,and F-, income and its -,, Thus xt, which in our caseis a (5x I) vector of the explanatoryvariablesthat include lagged values of consumption and income, is not orthogonal to the error term. Or, E(xp, ):Ă˝-,

0. Supposethere exist a set of r variablesthat are uncorrelatedvAth P,but correlatedwith is (rxl) If an x,. z,

E(Apt)=O then are the r vector of such explanatory variables

orthogonality conditions.

If we define 0 as an (axl) vector of parameterswe can define consumptionas the ffinction

h(yq,p).

In our casedefining 0 as a (5xl) vector of r,p, g, 6 and X we have II-p

h(x,, P) = (I + r)

I+g

L-P

!

-+g- +

1+81

+ r)

I+g +

+ r)'

r)2

+g1-I+ +p

I-P

1 +8 4-8

CI-2

1+5

(

1 ++ 89

f2 t-2

P) h(xt, that pt=Ctso If Dodenotesthe true value of 0 then the population orthogonality conditions are E (zt (C,-h(xt,po))=O T, in the If the number of observations sampleare the correspondingsampleaverageis

g(o) =I

(z, (C, T

h(xt, -

(r the that the > condition rank and a) identification requires an order condition independent be linearly D' where the T of plim of columns

66 D^I

Og(p) ap, P=ýT

(Hamilton (1995), p.422). A solution exists if there are as many orthogonality only conditions as there are co-ordinates in the parametervector to be estimated.The attempt is

to make the abovesampleversion of the populationorthogonalityconditionsas closeas possible to zero. This is done by choosing a weighing matrix which selectsthe particular linear combination of orthogonality conditions that are to be used in estimation.

It is required that the number of linear combinations of the sample orthogonality conditions are equal to the number of parameters to be estimated. A model is overidentified when the number of orthogonality conditions exceedsthe number of parameters to be estimated or r>a.

In this case more orthogonality conditions are used than are

(1982) Hansen to the parameters. needed estimate suggesteda test of whether al-lsample by be to g(P) are as close moments represented expected if the zero as would P)) If E(z4(Q-h(x,, truly moments were zero. the true population corresponding population If test the sample this the gives of over-identifying restrictions. us moments are zero

instruments, is linear the that significantly combinationof we obtain, using a moments different from zero,, then our sample average does not represent the true population

ffinction Q is Q, T T. the the cntenon as numberof observationsand is where moments. definedbelow, hasaX2distributionwith (r-a) degreesof freedom.If T.Q is not significantly different fi7omzero then we cannotreject the hypothesisthat the samplemomentsare as if be truly the moments were population to corresponding expected close zero as would be The the then to set of instruments. in said is over-identified model zero.

Hansen (1982) showed that the minimum asymptotic vanance of the estimator

P to chosen was nuninuse when obtained was

67

Q=

g(3)W1g(3)

where 12 Id

Cov[z ipi,

Tj 2:

zt

=1

zjpjl

is Z where an (rxT) matrix of the T observations of each of the r instruments.E is the variance-covariancematnX of the error terin. that is chosento minirnisethe criterion function [T 2

zliz

g(o)

is known as the Generalised Method of Moments estimator and is both consistentand asymptoticaflyefficient.

An estimateof TEZ can be obtainedby the Newey-West (1987) estimatoras STwhere Iq

s T

=S

0, T

+

1]

-[v/(q ,fI V=j

+

1)(ยง

+s

V,t

) V.

where T

s

(

11 zt ct h(x,, 0))(z h(x, ct-v t-V VA Tt= -, -,, v+1(

where

have lag length.

Since is Po. the shown we maximum q is a consistentestimator of

is 2.

MA(2) MA(2) to MA(l) set q process error we process, an that p, a sum of an and an Generallsed (1982) is Hansen's To summarize, the estimation procedure we adopt

Method of Moments. A set of instrumentswith at least as many instrumentsas the number

is An be the of matrix to variance of chosen. estimate estimated -covanance of parameters

68 the error tenn is obtained by the Newey-West (1987) procedure. The moving average process is specified to be of order two. If the system is overidentified in the set of instruments as shown by Hansen's (1982) test of overidentifying restrictions then the sample moments are expected to represent the true population moments. Esurnated

parameterscanbe shownto be both consistentandasymptoticallyefficient.

4.5. Approaches to Estimation It is pertinent at this stageto look at some of the existing studiesto examinehow they have approachedthe estimationof a similar consumptionfunction. As far as I know, g, the measureof population growth and income distribution has not been explicitly estimated in any empirical work. Some other studieshave estimatedthe consumptionfunction under the assumption that p, the probability of death and/or I-k, the proportion of liquidity

constrainedconsumersarezero.

Hayashi(l 982) estimatesthe model for the US assuminginfinite horizons. Nonhuman wealth is not deleted and the model is estimated as a two equation system begin To dynamics function the of non-humanwealth. and comprising of the consumption in disregards the he ten-n the the system and estimates error process average moving with,

by NLIV intending to use GMM if the residualsindicate the presenceof serial correlation.

He, however, finds no indication of significant autocorrelation and hencedoes not have to it. for correct X=l for for Ricardian (1988) that Razin the test Leiderman and p=O, restriction be is The to for taxes Israel. data governed assumed and income of gross evolution monthly least is by The by an autoregressiveprocess of order one. system estunated a non-finear is imposed. interest Though that The the some mention authors rate of procedure. squares different from be the is to problem accepted, commonly is what seem estimates parameter

69

dealt it indicative However, The estimates not is of potentiallyseveren-iisspecificatIon. with. beyond feasible Rmits do the are and not satisfy the inequality restrictions imposed by The be 209 per cent to common sense. proportion of unconstrainedconsumersis estunated is be While The the total time to the of population. rate of negative. preference estimated likelihood ratio statistic fails to reject the Ricardian hypothesisthese results are obtained in biased be Estimates as a consequenceof correlation a potentially rnisspecifiedmodel. could

betweenthe error term andthe regressorsor the presenceof serialcorrelation.

Haque (1988) estimates the model for 16 developing countries assurning the fi7om human liquidity Both the eliminated are wealth and non-human constraints. absenceof function. His estimate rejects the. hypothesis of finite horizons and thus supports the (1989) Monteil by Haque improved This Ricardian model. who and upon model was finite liquidity for both aowing developing for it constraintsand countries a set of estimate horizons. The model is first estimatedin linear form. It is reported that the signsof some of instance, For the that they sign report to the coefficients were contrary what was expected. for The frequently theory (x5. most with the at variance was coefficient estimated of NLIV the is parameters. to of underlying estimates then extract estimated using equation increments 0.0 1), (with 1.10 fi7om 1 1.0 imposed to choosing of Values of I +r are ranging basis On the the above of residuals. the of squared sum weighted the value that minimised for for 16 be 15 hypothesis countries Ricardian of is rejected it can the that tests concluded

liquidity due but and the to constraints been has of effect only estimated which the model households that they The evidence that horizons. no finite uncover report authors not horizons. time exhibit short (1993)(to Bureau Macrornodelling reESRC Darby and Ireland (1994) and the for Moments Method Generalized (1990) of the Weale employ the model) estimate

70

estimating a consumption function for the UK. The system of equations consists of regressorsthat are correlated with the error term and there is a moving averageprocessin

the error ten-n.However, non-humanwealth is includedas a regressor.In our case,we eliminatewealthfi7omthe consumptionfunction.

4.6. Data All variables were measuredin real terms. Gross Domestic Product was used as a for labour income as there are no accurate series available for labour's share of proxy income. The only accurate series on wages and salaries are for those employed in the organised sector who are about 8 per cent of the labour force. In other words, accurate seriesfor more than 90 per cent of the work force are not available.Since labour income is in following in both the the the correlated with revision expectations current and periods, is lag income its the term, a component of error which are correlated with and one period

the error term and cannot be used as instruments.We use the secondand third lag of income as instruments.Other instrumentsusedwere private and public investment,exports, imports, taxes, government consumption spending and fiscal deficit lagged by two time

periods.

A measureof aggregate consumption was used instead of aggregatenon-durable in because is This at any point time consumption might not strictly correct consumption. for example, a previously purchased arise without any act of consumer spending when,

is Also, durable consumerexpenditureat time t would good used. consumer

not

includes in the t the to time purchase of expenditure when consumption correspond fi7om flow durable Ideal-ly previously of services goods. one should add a consumer durables to current consumer expenditure and subtract current purchased consumer

In durable to goods obtaina correctmeasureof consumption. an empirical expenditureson

71

analysis of consumption, the measure of consumption should consist of consumer expenditureson non-durablesandservicesandan imputedflow from the stockof consumer durables.

Since data for durable consumption was not avaable no adjustment be could made. This might introduce some inaccuracy in our results, especially since the

consumptionof consumerdurablesin India hasbeenrising.While total consumptionshows increase, an current consumption does not increase as much if the increaseis due to an increasein the purchase of consumer durables. If a consumer spendshis current income

durable then he has not 'consumed'his entire incomeas the good partly on a consumer him flow gives a of servicesIn the future. If no adjustment is made in the data he may, for example, appear to be constrained when he would not be if consumption was measured accurately.

The source of this data was various issues of the annual Econornic Survey

by Government Statistics India Yearbook International Financial the the of and of pubfished fuH data for by Monetary Fund.

International The the set was avaýable the period pubfished 1951 to 1989. With two lags our sampleperiod became 1953 to 1989.

4.7. Restrictions The probability of death, p is assumedto be positive in the finite horizon case and is horizon We Thus in infinite the the expect probability non-negative. would p case. zero

Or, 0:!! lie between death <1. Ă˝ to p and one. zero of The real rate of return on physical and financial capital, r, is equal to the marginal long This the the transformation in economy in run. is again non-negative. rate of product I +g, can be assumedto be non-negativeas long as population grows at a rate higher than

72

labour If percent. all income was earnedby constrainedconsumers?ý,would be equal -100

to zero. And if there were no constrainedconsumersin the economyat all, k would be equalto one.We would thus expect0 :!ý ý, :!ý 1. We assumethat the rate of time preference is non-negative or, 6>0. There is either some impatience but it be that or none cannot consumingtomorrow is preferred to consumingtoday.

We choosea sampleperiod over which the underlying parameterswere expectedto

be relativelystablesincewe are assumingthat the valueof the parameters we areestimating does not change over time. This assumption implies, for instance, that even if income distribution is changing and g is different fi-orn the rate of growth of the population, X the income by the proportion of unconstrained consumersdoes not proportion of received change significantly over this period. Unless the parameterscould be estimated as timebe for the model would varying, valid only short time periods over which our assumptionof the constancyof parametersis approximatelytrue. We, therefore, needto choosea sample

believe better these thananyother. conditions periodwhich we would approximate The 1950's was the decade immediately after independenceand saw a rapid borrowing The 1980's Indian the transfon-nationof economy. vAtnessedsubstantialexternal beginning deficits.

In balance the ten-ns of the sixties of governmentpoficies of payment and

it did to the endof the seventieswas a relativelystableperiodas not seemajorchanges.

4.8. Estimation and Results

The model cannot be estimatedas defined by (4.7) becausethe rank condition for identification is clearly not satisfied. We therefore impose the value of p as a

horizons 50 Assuming the that the is years value of p is average planning restnction. below.

The 0.02. results obtained are presented imposed at

73

Estimate of (4.7) with the restriction p=0.02

Parameter Estimate I+r 1.14163

Standard Error 1.14768

I+g

933232 .

1045.47

1/1+5

969000 .

1083.99

696562 .

100177

x

R-squared = 822669 .

Durbin-Watson statistic = 2.55465

The rank condition still appears to be unsatisfied since the condition number (the ratio of the maximum to the minimum eigenvalue) of the correlation matnx of the parameter is high. identified.

The Restricting the therefore estimates very model may still not further by imposing income by for 0.7 the model received a value of proportion of

following the results. unconstrainedconsumers,we obtain Estimate of (4.7) with the restriction p=0.02;

k=0.7

Standard Error Parameter Estimate 1.11733 1.14163 I+r I+g

933232 .

1041.83

1/1+5

969000 .

1080.20

However, again the rank condition still appears to be unsatisfied by the same criterion.

We impose the values of r and 6 to achieveidentification. r, the real rate of return on be be financial to the marginal rate of product understood capital may and physical 15 Rates the per cent are of around of return return on capital. transformation since it is 6, Bank.

At 3.2 World by time the the the rate of subjective of cent value per reported the the consumer, non-negativity constraint imposed unconstrained satisfies of preference

74

by the assumptionof rationality.If we imposer at 14.16percentas aboveand the rate of time preference at 3.2 per cent we obtain the following resultsTable 4.1 : An estimate of the rate of growth of population of unconstrained consumers

Parameter Estimate I+g 884747 .

R-squared = 830332 .

Q=0.265764

Standard Error t-statistic 059429 14.8875 .

Durbin-Watson statistic = 2.56419 TQ= 5.57

(X2

=

19.0 at 5% significance level)

The data is trending and given the small sample size it is difficult to reject the hypothesis that it is trend stationary in which case the t-statistics can still be assumed to be valid. Andrews and McDermott (1995) provide a justification for the use of standard asymptotic approximations in models with

deterministically trending

distribution The variables. asymptotic of generalised method of moment estimators and corresponding test statistics of deterministically trending variables are shown to be normal and chi-square respectively, the same as with non-trending variables.

Our results may be surnmarisedas follows-.

Parameter

Value

r

0.14

p

0.02

9

-0.12 0.032 0.7

75 X. the proportion Of post tax labour income receivedby the group of unconstrained consumersis assumedto be 70 per cent. Though the 'constrained' group is not observable,

it would not be unreasonable to suggestthat the officially classified'poor' who five below the poverty line and constituted nearly 50 per cent of the population in 1977-78, might be included in this group. This group receives nearly 18 per cent of household income.

Further, nearly 70 per cent of the households who have an annual income below the national average receive about 35 per cent of total household income. We would consequentlyexpect that the constrainedgroup would constitute around 50 to 70 per cent of the total population and receivebetween 18 to 35 per cent of householdincome. A value X is X 0.7 I0.3 or the group of constrainedconsumersreceives30 that of of suggests income. labour income labour Since per cent of constitutes the major component of

householdincome,the figure seemsreasonable.

An interesting result which has emergedin this estimateis the value of g which is from be The to the transfer to unconstrained negative suggests a net value estimated -0.12. the constrainedgroup. Since this is likely to be more country specific that the values of the in Indian look the taking to towards economy place changes other parameters,we need if to that period see the evidencesupports our results. over

4.9. Supporting Evidence A developing economy undergoing structural change, as it witnessesgrowth, is likely to find some sectors growing and others, like agriculture, declining. Within each

in to to to the those maintain are able environment a position adapt changing well, as sector India become As living their witnessed standards, while others worse off or improve

76 economic growth led by a capital intensivemanufacturing sector, the shareof agriculture in GDP fell faster than the shareof the population dependenton it.

Table 4.2 Year

Share of Agriculture in National Income Shareof Agriculture and Allied Activity in National Income

1950-51

54.04

1960-61

56.05

1970-71

49.19

1975-76

46.76

1984-85

37.91

Source: National Accounts Statistics,CSO, New Deh. Table 4.3:Per Capita NDP in Agriculture Year

Per capita NDP in Agriculture 1970-71 prices (in Rs)

1954-58

421.95

1958-67

401.91

1968-77

398.83

1976-83

415.61

Source- V. M. Dandekar (1986) "Agriculture, Employment and Poverty" EPW, Review of Agriculture, September.Vol. XM NO 38/39, pp A90-AIOO.Table 5 on pA-93.

The share of agriculture in employment has remained about 70 percent. As Table 4.3 shows, per capita NDP in agriculture fell. The effect of this decline was not evenly both technical the rural was undergoing entire population itself as agriculture spread over independence At Indian institutional the time agriculture was charactensed change. of and

77

by subsistencefarn-dng,antiquatedmethodsof production land tenuresystems.Land and labour and productivity were nýserably low. Agricultural holdings were small and uneconornical.The pattern of land tenure, where the cultivator often did not own the land, had to pay high rents and had no security of tenancy, failed to for provide incentives improvement. Techniques of production were old and inefficient. Use of both farm yard manure and chemical fertilisers was little. Seedswere often of poor quality. Less than 20 percent of the cultivated land was irrigated. 70 per cent of the population dependedon agriculture and as the pressure on land grew, disguised unemployment increased.There little for because lack infrastructure like the was scope raising yields of of necessary modem

inputs,irrigation,financeandmarketing.

In the 1960s the government adopted a policy of promoting modem agricultural techniques.The Green Revolution was charactensedby the availability of high yield variety disease fertilisers, facilities, and resistant seeds, pesticides, credit, marketing, storage in first later then provided to other agricultural machineryetc., certain selectedareasat and I investment however, These techniques, and only a small required substantial areas. modem (Rudra (1969)). fanners to minority of were able undertake such expenditure The overwhehrdngmajority of cultivators with small holdings were unableto reap

inputs faster The full benefits thanthe priceof output and the rose of modernisation. cost of (1986)).

Gulati In income. ( Swamy decline in their there was a caseswhere small and net farmers also leasedin part of their holdings, rising rentals and the tendencyof landowners high due land for to the profitability of modem techniques,there to resume self cultivation

deterioration the the smafl-owner-cum-tenant of econonuc condition in absolute was an cu tivator.

78

As demographic pressureincreasedand techniquesof production changed,small LX. J. and mediumpeasantsexperienceda deteriorationin their economiccondition.While some were able to cope with this adverseenvironment,there is evidencethat a large proportion

of them becamevery poor. A significantproportion of those who could be describedas Iunconstrained' slipped below the poverty fine thus becoming qualified for what we might

'constrained'. cafi We assume that rural households belonging to the top four per capita income deciles who account for nearly 90 per cent of rural savings(NCAER (1980), p.27) can be called 'unconstrained'. In a longitudinal study where a very large sample of families identified in 1970-71 were fbHowed through into 1981-82, it was found that there was large significant evidenceof scaleimpoverishmentof small and medium farmers.

Table 4.4 indicates that there was a significant decline in the income of those rural householdswho were in the top four income decilesin 1970-71.

Table 4.4: Change in income distribution in Rural India 1970-80 Per capita income

Mean level of income per earner(Rs.

Percentagechange

decile (1970-71)

per annum 1980-81prices)

over 1970-80

1970-71

1980-81

(Follow through)

7

4360.16

3684.25

-15.50

8

4360.57

4151.30

-4.80

9

6464.98

5106.45

-21.01

10

12615.11

6903.52

-46.07

Source-Changein householdincome,interclassmobility and incomedistributionin rural India -A longitudinal study, New Delhi, NCAER, 1986, Table 3.9.

79

On examiningthe evidenceon householdsavingand incomedistributionwe could identify at least one set of consumers who may be cafled constrained. This was the population officially identified 'poor'. The poverty line definition calls those people poor who cannot afford to meet a certain day requirement of food and the associatedlevel of non-food items. The Planning Conunission estimated that in 1979-80 about 317 million persons (48.4 per cent of the total population) lived below the poverty fine which was defined as 'the mid-point of the monthly per capita expenditureclasshaving a day calone mtake of 2,400 per person in rural areasand 2,100 in urban areas.At 1979-80 prices these mid-points were Rs. 76 in rural areasand Rs. 88 in urban areas.50.7 per cent of the rural population and 40.3 per cent of the urban population was identified as poor (Planning Commission (198 1)). Since these consumersaccounted for hardly 5 per cent of household savings(NCAER (1980), p.27), they fit into our definition of constrained.

Though we would expect many of those eaming more than this low level of

identify do be to the entire group of constrained to constrained,we not attempt income, living below It the poverty that to that persons we assume consumers. would suffice say

fineform a subsetof the setof constrainedconsumers.

If a group of persons who fon-nally belonged to the set of unconstrained from he below that they the the migrated we could say poverty consumers, slipped for be This a significant proportion of could said unconstrainedto the constrained group. large 'poor'.

By become 1981-82, top the proportion of a small and medium peasantswho four 1970-71 decileswere officiafly 'poor'.

80 Table 4.5: Changes in Poverty in Rural India, 1970-80 Per capita income decile (1970-71)

Percentagebelow poverty Line 1970-71

1981-82

6

27.09

44.06

7

0.00

51.12

8

0.00

49.45

9

0.00

40.90

10

0.00

32.61

Source: Changesin poverty and consumption pattern in Rural India between 1970-71 and 1981-82 -A longitudinal analysis,NCAER, New Deh, 1986, Table 2.1.

Let us now look at another subset of the group of unconstrained consumers.

Organisedsectorworkers are the richestclassof workers whetherin tenns of per capita force.

In form 8 They the the of work per cent only poverty. consumption or incidence of kept has 1965-66 to pace with only and organised sector employment grew rapidly up in increases impressive During time, tl-ýs occurred per worker very population thereafter.

incomesin the organisedsector.Publicsectorworkersmorethan doubledtheir real income between 1960-61 and 1984-85. The real incomesof private orgatusedsector workers rose by more than 60 percent. In the unorganisedsector, where workers employed are amongst

income in increase those the lowest trend of either per there worker all at the was no paid, who

(1988)).

(Sen those or who worked in agriculture workers wage were

If we identify organisedsector workers as a subsetof the set of unconstrained faster that the this expanding not the of group was suggests size evidence above workers,

81 than population growth. Real incomes of those we may consider constrained who were employed in the unorganisedsector were not rising and the ratio of their averageincomes

to organisedsectorworkers feHfi7omabout a third in the sixtiesto a fifth in the eighties (Sen (1988)). There is no evidenceof a net transfer to the 'unconstrained' group.

The ratio of Gross Domestic Savingsto GDP increasedfi7om6.8 percent in 195354 to 23.7 percent in 1990-91. Even over the period of estimationthe savingsratio changed

It increasedfi7om11.9percentin 1959-60to 23.2 percentin 1978-79.This is substantiaRy. in conformity with the hypothesisof a worsening income distribution.

The following decade of the eighties VAtnesseda surprisingly large build up of food in unsold stocks the Indian economy. This happenedat a time when per capita NDP in agriculture remainedstagnantand per capita food production for the population as a whole increasedonly marginally. The food surplus has been attributed to underconsumptionof large sections of the rural population whose purchasing power was timited by declining income (Patnaik,1987).

To summarise,our estimate suggeststhat a transfer has been taking place fi7omthe group of 'unconstrained'consumersto the group of 'constrained' consumers.The

in development be located India's the this transfer process- the can nature of causesof intensive industrial The growth of a capital manufacturing and agrarian growth. pattern of has 70 India's per cent of population not created adequate employment and sector force depend Only 8 the to on agriculture. about per cent of work Is employed in continues has industry 1964-65.

Modenusation this proportion not risen sInce and of orgamsed impoverishment by large been has the scale of mass of small accompanied agriculture fives below 'poverty fine'.

40 As India the the cent of population still peasantsand about per develops from a predominantly agrarian to a modem industrial nation, the traditional

82 fast is be displaced first. likely to Unless to sufficiently grow peasant the most sectors other

large labour force by impoverishment the of the section the of a absorb released agriculture, likely to continue. population is

83

Chapter 5 Policy Evaluation in an Endogenous Growth Model

Recent developments in growth theory have shifted the focus of attention from the effects of fiscal policy on the levels of saving and consumption to those on growth. In

traditional growth models the long-run rate of growth was determinedby the rate of exogenous technical progress. Growth rates across economieswith accessto this technology were expected to converge. Failing to observe such convergence across the have been made to explain the differences in long-run growth rates in world, attempts terms of economic activity within each economy. In the new theory growth rates are determined by endogenous factors like the accumulation of knowledge and human (1986), ((Romer (1988)), (1990)), infrastructure (Romer Lucas R&D capital or public (Barro (1990)). Output displays increasing or constant returns to these factor inputs in

the aggregateproduction function becauseof the externalitiesinvolved.

As we have seen earlier, the representative agent Barro-Ricardian model with infinite horizons predicts debt neutrality. If government financing policy does not affect in investment, has no effect on growth either exogenous it aggregate consumption and its composition. or endogenous growth models given government spending and However, in an exogenous growth, overlapping generations model with YaariBlanchard-Weil consumers, financing policy affects the levels of consumption, saving by being determined The investment. the rate of technical progress growth rate, and that is exogenously given, is not affected.

In an endogenous growth overlapping generations model with Yaari-Blanchardlevel both distortionary financing the Weil consumers and taxes, of policy affects

84

consumption, saving and investment and the rate of growth. In this chapter ýý, -e shall adopt such a model of endogenous growth and analyse the effect of budgetary policy in India. The driving force behind economic growth is assumedto be a combination of R&D, learning by doing, human capital and public infrastructure.

5.1. Traditional

Models of Growth

In the traditional model of growth the assumption of diminishing returns to capital in the production of output leads to a decreasing rate of return on investment and rate of growth of output. In the absence of technological change per capita, output converges to a steady state value with no per capita growth. Sustained economic growth is possible when technological progress takes place. It is assumed that this technological progress is a function of time and is exogenous to the production

function. The production function which relates output to the stock of accumulated labour displays decreasing returns with respect to each of physical capital goods and these factors of production. Given the amount of labour employed, an increase in the less increase in Technical than stock of capital yields a proportionate output. change, however, can prevent this tendency towards a zero rate of profit. In its absence,capital and output would grow at the rate of growth of population such that the per capita labour but in is the presence of augmenting technical change, capital growth rate zero; labour the the the of rate of growth of population and sum and output can grow at long-run imposed The thus technical on the model growth rate is progress. augmenting it. by determined economic activity witl-iin and not

85

5.2. Endogenous Growth Extending the work of Arrow (1962) and Uzawa (1965), Romer (1986)

relcindled the debate on what determines long-run growth questioning models of exogenous growth and convergence. He proposed an alternative view for prospects of long term growth where per capita output can grow without bound and even at a monotonically increasing rate. With increases in the stock of capital, the rate of investment and the rate of return on capital may increase rather than decrease.This is due to the departure from the assumption of diminishing returns that is essentially made in traditional models (Ramsey (1928), Cass(1965)

,

Koopmans (1965)). The

model endogenises knowledge or technological progress that drives long-run growth.

Investment produces knowledge. It is not merely the firm creating the knowledge that benefits; other producers benefit from it as well. Knowledge as an input has positive external effects on the production possibilities of other firms. In the aggregate function for production consumption goods, the stock of knowledge as an input increasing it exhibits returns, so will not be optimal to stop acquiring knowledge at any stage. This is in contrast to a situation where it is optimal at some stage not to use an

because its diminishing.

The capital marginal product is production additional unit of diminishing doubling investment is be knowledge to to returns, subject assumed in of

knowledge. double The development the stock of assumptionof not will researchand diminishing returns in the production of knowledge is required to ensure that

does fast. too not grow consumption Romer's

(1986) model departs essentially ftom

in the earlier models

least knowledge be to that is assumed an input with increasing or at assumption be Production to the of consumption good is assumed constant marginal product.

86

globally convex, not concave as a function of the stock of knowledge when all other inputs are held constant. Without upsetting the basic argument the definition of this input can include the know-how acquired through learning by doing, R&D, the accumulation of human capital through education, public infrastructure and other

factors of production that have a public good characterand exhibit externalities.

Barro (1990) defines the production function to include the input of public services which raise the productivity of private capital. The government invests

in both the material infrastructure like public highways,railways, telecommunications immaterial infrastructure like the and education and training, and health. He incorporates a public sector into an endogenous growth model where he assumes diminishing broad than to concept of capital which constant rather returns a both human encompasses and non-human capital. The role of public services as an input to private production creates a potentially positive linkage between government broad In Barro that assumes even with a concept of private other words, and growth. human includes that physical capital, capital and aspects of privately owned capital knowledge, production displays decreasing returns to private inputs if complementary in Constant does returns apply to this a parallel manner. not expand infrastructure broad measure of reproducible capital as long as the public service input changesin the same proportion as private capital.

The effect of finite horizons is incorporated in an endogenous growth model by Alogoskoufis and van der Ploeg (1990) who show that fiscal policy is not neutral when Butter der (199 1) Ploeg death Alogoskoufis and and van is positive. the probability of (1991) include the effect of both finite horizons and population growth in a model of flat form distortions Tax the a of in reach similar conclusions. and growth endogenous

87

rate income tax is incorporated by Barro (1990) who does not include the above Blanchard-Weil non-Ricardian effects but assumesexternalities arising from the flow of public services. Externalities arising from the stock of public capital have been incorporated in Jappelli and Meana (1994). Our specification provides a generalisation of the above models and incorporates the various mechanismsby which fiscal policy can affect the long-run growth rate. In this model fiscal policy has both a supply side

demand and a side effect.

5.3. The Model We develop an endogenous growth model which draws upon early chapters capturing non-Ricardian Blanchard-Weil effects due to finite horizons and population growth and includes tax distortions and externalities due to public capital stock as in Krichel and Levine (1995) and Futagan-Ă˝,Morita and Shibata (1993). We also include

the effect of liquidity constraints on the demandfunction. The structure of property in born that equilibrium new generations are with endowments whose rights is such have This they to the some share growth. a claim rate of way endogenous nses at value

in it human born in their they the absorbed as is are capital stock existencewhen of by in is (1991)).

(Buiter This to the model allowing workers ensured capital In Barro by the externality. production an economy-wide returns created appropriate (1990) the externality arises from the flow of public services while we include the by health, infrastructure, etc. effect of past government spending on education, Behaviour from the of the that capital. of public externality arises stock assuming

determine the the output equilibrium and government producers consumers, conditions.

88

We present a closed economy model driven by capital externalities arising from public and private capital. The closed economy assumption may not be strictly

true for India today but considering the technical difficulties involved in an open economy endogenous growth model, we keep the analysis simple by assuming a closed economy. Further, since imports account for about 10 per cent of GDP and the current deficit account stands at 0.1 per cent of GDP, our results should not be significantly by this assumption. affected

5.3.1. Households The aggregate consumption function is as defined in Chapter 3. We include distortionary taxes at the rate -c.Capital is assumedto earn a rate of return rt in period depreciate Defining the the consumption of unconstrained consumers as and at rate 7c. beginning function W",, the the total of at of wealth of unconstrained consumers a have, ignoring the terms t error we period and

ýtwu

Wt"

(5.1)

(5.2)

t+ (I + rt(I - -c))V, 1

Human wealth in period t can be shown to be

ut+

+ g) [H't-i

rt 1-p

-

Qu

t-11

Labour income earnedby unconstrainedconsumersis

(5.3)

89 Qu

Ă˝-(Y, - (r, + t=

(5.4)

Tj

Since aggregate consumption of unconstrained consumers depends on the value of

lifetime wealth, the evolution of consumptiondependson the evolution of We wealth. therefore turn to the evolution of aggregatewealth which is a combination of human and non-humanwealth.

(3.14) may be redefined in the presence of distortionary taxes as (I +r(I -r))V, +KY,- C', -,

Using the above, (5.1) and (5.2) we obtain Wt" =p+9 fg ++ 1+g

rt

-C)]

P wtu +6

(5.5)

1

The value of wealth in period t is expressed in terms of its value in period t- I and in terms of human wealth in period t. The evolution of aggregate wealth thus depends between human It the reflects asymmetry and non-human upon its composition. death If the were zero and there was no population growth, we probability of wealth.

have would P+

wtu-1

rt(i -u +6

(5.6)

vvt-1

The asymmetry thus disappearswith the removal of uncertainty regarding the length of life and the evolution of wealth no longer depends on the magnitude of human wealth in the current period. It depends on its aggregate value rather than its composition.

From (5.1 and (5.5) it follows that C tu

++

rtQ- -r)]

IP 1 +5

Ct" t-I

(5.7)

90

I+ r Cu If g=O p=O -c=0, and for a constantrate of interest, Ctu = , , I+g I-

which

corresponds to the Euler equation in the representative agent model with infinite

horizons. In addition if there are no liquidity constraintsthen aggregate consumption Ct

+r Ct_l This shows that non-Ricardian behaviour of aggregate consumption .

from four sources: finite horizons, population growth, distortionary taxes and arises liquidity constraints. Effect on growth on each of these sources will be explored later.

Using (5.1) ), (5.2) and (5.5) we have

t

=[i+«I-T)]

I+g

l+8

u t-1

Vt)(1 g)[i+«, TA +,. -p

P+ö

+-g

(5.8)

in describes behaviour the the consumption which of unconstrainedconsumers terms be lagged lagged This may referred to as the of consumption and non-human wealth. discrete time Yaari-Blanchard consumption function. '

5.3.2. Private Sector Output and Investment.

The representative firm f produces homogeneous output with the following CobbDouglas constant returns to scale production function at time t Y

J,, =F(K,, f, f)=K"t, t1f

K, where Jt, i

I-cc fJ t'if

(5.9)

Or, input in labour J, efficiency units. is is private physical capital and f rf (5.10)

et,iLt'i

where F, ,f

The labour Lt. crucial input is a measure of the efficiency of raw

is in drives this that this measure efficiency that model endogenous growth assumption be Kt Let function private the aggregate ratio economy-wide capital-labour of is a .

C= For small r, g, p, X and 6 this correspondsto the

(r-8)C - (p+g)(p+5)V in continuous time.

91

capital. In addition to the externality from private capital, the government affects labour efficiency by providing physical capital in the form infrastructure of which may

be broadened to include education, health, etc., accumulated out of the economy's single output. This is captured by

(K) &

(K)

1-y,

Ai

t,f

(5.11)

L

KG, where is public capital and yj is the contribution of public capital to the economy-

labour.

This way workers inherit the benefits of past investment. wide efficiency of Assuming identical firms that are constant in number, and aggregating, we arrive at the function aggregate production

Yt =

ýKý)

1-Y2

y2G

(K

t)

(5.12)

(1-(x)yl depends firms in B the the economy. and on constantnumberof where Y2=1It is assumedthat the government does not produce. It buys output, including from infrastructure hospitals, This dams, the private sector. schools etc., canals, roads, has Private the to capital private sector without any user charges. a is made available a2yt

dirninishýing marginal product given by

'Y2(1 aK2

t

-

yj)%

tt

Kt

<0. However, if the

increase investment in remains constant, i. e. with every ratio of public to private in investment, is then the there public increase a corresponding private investment is is The to equal its average product. and marginal product of private capital constant be expressed as average product of capital may )

yt

Kt

1-Y2

(5.13)

=BG.

t

92

If the ratio

KG' Kt

is a constant then the production function displays constant returns to

the input private capital and technology is linear Also, if yj=O i. e. public expenditure .

has no role to play in raising the efficiency of labour then YT"ý1and the production function can be expressed as Y=BKt as in Romer (1986) where B>O is the constant net marginal product of private capital. Technology in this case is linear.

We assume that firm f ignores the externality in choosing capital stock. The marginal product of capital

is NVK=

DY/,DK = (xK'-' J'-' = (xY/K. The marginal cost of

(including depreciation at a rate 7r)=rt+7r. Equating the private marginal capital product of capital to the cost of capital gives Kt Yt

--=rt

(X

(5.14)

K(r)

+ 71

Net private investment is then given by the addition to capital stock less the depreciation in period t It = Kt - (I - Tr)Kt-,

(5.15)

5.3.3. The Government The government provides an amount Gc, of public consumption goods using the for GI, the technology privately produced good, and purchases an amount of as same the latter to

invest in infrastructure.

Total

government expenditure is then

Gt = Gct+Gl, which is financed by a combination of taxation (Tt) and borrowing (D, ) (We ignore bonds.

The D, or rule out seigniorage). are single period where

by borrowing identity is given goverrurnent

93

Dt = (I + rt)Dt

+ Gt - Tt -I

(5.16)

and public sector capital accumulatesaccordingto G1+

n)K t-

Gtl

(5.17)

assun-ungthe same depreciation rate as in the private sector. Since the defiru I

of

capital is broad, public sector investment GIt is assumedto include public expenditure on health, education, etc. Since only profits net of depreciation are taxed at the rate T total receipts are Tt=-c(Yt-7cK,).

5.3.4. Output Equilibrium.

We assumethat the market always clears. Equilibrium in the output market gives

Y =C +1 +G tttt

(5.19)

Thus, given the government choice of fiscal policy variables Gct, GI, and T, the supply

demand and sidesof the economyare now fully determined.

5.3.5. The Steady-State We seek a balanced growth steady-state in which all stocks and flows are growing at the same enclogenous rate n, the steady-state value of nt. The debt/GDP ratio is is be is It the to strong solvency constant which condition. assumed assumedthat rt is

flow If the express all macroeconon-iic rate r. we stock and variables as constant at balanced GDP We the then growth state ratios steady remain in unchanged. ratios of

denote the t to these subscript the without notation ratios to ease same retain burden. notational

94

Consumption of constrained consumers who receive only labour income and

consumetheir entire income is given by (r+ 7c)K,

XI

(5.20)

- -c

We can substitute for the expression for non-labour income from (5.14) where Kt(r+Tc) Post-tax labour income of unconstrained consumers can be now defined in terms of total income. Consumption of constrained consumers defined as a ratio of GDP in the steady state is

ýtc )(I-CCXI--c =c =(I-k yt

(5.21)

We can now obtain the consumption of unconstrainedconsumersin the steady state from (p+g)(p+5)[1-r(I-t)]/(I-p))(D+K) (5.22)

GDP be The capital output ratio may as expressedas a ratio of (5.23)

K(r) = oc/r+Tc

for is for that depreciation the private sameas Given that the rate of public capital GDP in of as ratio the a as state steady capital capital we obtain public (I + n)Gl (n + 7E)

(5.24)

in GDP. investment G1 is the share of public where GDP be function as expressedas a ratio of can The aggregate production

log

B+

logK+ *y 2

(1 - Y2)109-

G' (n +7r)

0

(5.25)

95

In the steady state public and private capital grow at the same depreciate rate n and at the same rate 7r. Thus the ratio of public to private capital is constant and so is linear in private capital. production In a steady state public debt grows at the rate n. Thus the government budget

be constraint may expressedas (I+n)Dt = (I+r)Dt-I + Gt -Tt

(5.26)

Rearranging, we express the solvency condition in the steady state as [(r-n)/(I+n)]D

=T -G =[1-7cK],c -G

(5.27)

The market equilibrium in the steady state may be defined as ratios of GDP as I=C'+C'+l

+G +n)]K(r)-G --c)-[(n+7c)/(l

(5.28)

To summarise the steady-state form of the model may be expressedas

[1-r(1-t)J/(1-p)} (D+K) [(r-n)/(l+n)]D=T-Cx--(1-7cK(r)),

u-G

(5.22)

(5.27)

K=a / r+7c=K(r)

(5.23)

logB+Y2 log(K(r))+(I-Y2)log(yGI(n+n))ýO

(5.25)

cu=l-[(n+7c)/(l+n)]K(r)-G-(I-X)

(1-a)(l-, c)

(5.28) (5.21)

(5.22) defines the aggregate consumption of the group of unconstrained consumers. is in It the strong the is the (5.27) steady state. government the solvency condition of (5.25) is (5.23) debt/GDP the that and ratio constant. implies which condition solvency

96

describe the supply side of the (5.23) defines the steady state capital output model. ratio. (5.25) defines the production function. (5.28) is the market equilibrium condition. Together these define consumption, the government budget constraint,

production and market equilibrium in the steadystate.

Futagan-ii, Morita and Shibata (1993) who assume externalites arising from the stock of public and private capital on the supply side and from distortionary taxes on

the demand side find that the steady state equilibrium path is unique and exhibits saddlepath stability. In a model of overlapping generations and enclogenousgrowth where externalities on the supply side arise from the stock of capital and on the demand side due to finite horizons, Alogoskoufis and van der Ploeg (1991) also find that the steady state equilibrium is saddlepath stable. The condition of solvency of the is public sector sufficient to ensure saddlepath stability. Corresponding to this boundary condition there is a single value of the forward looking variable initial for time consumption at some which the system converges to a steady state. For all other initial values of consumption we have explosive behaviour. Strictly speaking, the stability of the steady state equilibrium in our model can be examined by linearizing investigating dynamics.

However, the the transitional around steady state and since our be is is later it Ricardian,, to near model shown very close to Futagami, Morita and Shibata (1993) and so we can draw upon their results and assumethat the system will

exhibit saddlepathstability.

5.4. Fiscal Policy and Long-Run Growth This section studies the steady-state of the economy defined above. Given fiscal

instruments, -c, GC and GI we have five equations In five endogenousvanables

97

C,, r, D,,K and growth n. Since we wish to focus on the effects of government debt D. the distortionary tax rate -c, and the mix of government spending as between consumption and investment, we will characterise fiscal policy in terms of D and -i making total government spending endogenous. Let GI=yG making the third fiscal instrument the proportion y.

To compute an "order of magnitude feel" for their effects on long-run growth we derive multipliers for estimating the change in the rate of growth when there is a in fiscal change policy variables.

Substituting the value of consumption and eliminating G we arrive at the YaariBlanchard consumption relationship. f(n, r, D, -c)=((I+g)(r(l--c))+g-5-n(1+6))(l-[(n+7c)/(l+n)]K(r)

+ [(r-n)/(1+n)] D-t(1-itK(r)-( 1-?.)( 1-r)(1-a))) -I(p+g)(p+6)[l+r(l-,

u)]/(I-p))(D+K(r))=O

(5.29)

The production function may be derived as D)+Iog(l+n)[(r-n)/(I+n)] D919Y)ýY21ogK(r)+(I-Y2)(109Y+109('E(I g(n, r, -nK(r)log(n+-K)) +IogB=O

(5.30)

The two relationships determine r and n given D, -cand y.

interest locus describes f(n, D,, the The relationship and growth rates of r, r)=O behaviour, Yaari-Blanchard private equilibrium, output consumption with consistent locus YaariWe budget the this term investment the constraint. government and sector locus D,, The (YB) the consistent with Blanchard relationship g(n, r, r,y)=O is curve.

investment linear technology, and the balanced growth and our private sector

98

goverment

budget constraint. We call the relationship the linear technology (LT)

curve.

Consider incremental changes in the exogenous fiscal dD, dT, dy variables and the corresponding incremental changes dn and dr along the YB and LT curves.

Differentiating, these incremental changes satisfy

fndn+fr dr +fDdD +fcdz =O 9ndn +grdr+gDdD+grd-c+ gydy--O it where can be shown that under very lax conditions we expect f,,g,,g, >01 fn, fD, fc, gn, gr, gD

<0

(Details are presented in Appendix B). Keeping fiscal policy and

income distribution fixed, the slope of the YB curve is given by (c-'n/c9r)f-O=-ffn r/ Since fn <0 and fr >0 therefore - fr/ffi > 0. In other words, (cn/or)f-o >0 or the YIB is fiscal is its Turning LT to the curve upward sloping. curve when policy given, slope (an1&)g=O by = -gr/ gn where we expect gn `Ă˝ 0 and gr `Ă˝ 0 and so, the LT curve is given is downward-sloping.

In l the case when public investment irrelevant and Y2: is --": as in Romer(1986) we have K(r) =B and the LT curve is vertical. In an exogenous growth is by interest is LT the the the rate of and curve not affected rate of growth model

honzontal.

We now look at the effect of fiscal variables on the YB and LT curves. To look at dr--d-c=O. have debt let GDP We in then to the the effect of a change ratio of

f. d,,+fDdD=O.Given dn/dD=-fl)/f,, if f., fD<O, dn/dD <0. Thus growth decreasesas a down.

YB The debt curve shifts everything else remaining constant. result of the rise in

99

Similarly, keeping r, -c and y fixed, dr--d-c=dy=O, have we gndn+gDdD=o and so dn/dD=-gE'/gn -If

9D, gn<O

then dn/dD<Oand the LT curve shifts downwardswhen debt

increases.The combinedeffect of an increase debt is in a reduction

The Yaari-Blanchard

in long-run growth.

and Linear Technology Curves :

Effect of a rise in the Debt/GDP ratio

rate of growth

n

rate of interest

r

Figure 5.1

We can derive the debt/GDP ratio multiplier [aNADD]

fD-gDf g,

f<0. wherefrgn-grn

frgnr'

gfrn

From the expectedsigns of the partial derivativeswe can expect

to be negative. This implies that an increase in the steady state ratio of public debt to GDP reduces long-run growth given the ratio of government consumption to This the tax to and ratio. effect is not contrary our expectations spending government

100

in a non-Ricardianworld. Since debt is considerednet wealth in such a world, public an increase in debt would raise consumption spending and reduce private savings available for investment. It should thus have a growth reducing effect if long-run

depends growth on the level of investment.

Let us now look at the effect of a change in the tax rate. We assumethat dr--dD=O. Now, f,,dn+fd-c=O or dn/d-c=-f,/f,,. If f, f,, <0 as expected, dn/dT <0. In other words when the tax rate increases less is available for private sector saving and investment and when investment is lower, the growth rate is lower in an endogenous growth model. Hence the YB shifts down.

To look at what happens to the LT curve, let dr--dD=dy--O. We have g. dn+g,d-c=O. So, dn/d-c=-g,/g,,. If g,>O, g,,<O then dn/dc >0. The LT curve shifts upwards when the tax rate increases. This is because more can be invested by the government while budget in The total the satisfying its intertemporal constraint. effect of change tax rate in not clearly in any one direction. We can derive the tax rate multiplier as [G-N/O']D, y

fr-gTfr 7--g,

/ fr9n-

gfr n.

While the denominator is negative, the numerator can be either positive or negative.

An increase in taxes thus has an ambiguous effect on growth. The reason for this is that as the tax rate increases,given the debt/GDP ratio, a higher government spendingGDP ratio consistent with the government budget constraint can be reached. Part of this additional spending goes on infrastructure which enhancesgrowth. However, taxes in interest for tax distortionary the r, an rate reduces rate increase given a real and, are investment hence depresses GDP growth. and private which savings as a proportion of Let us now look at the effect of the third fiscal policy variable y. Since YB is not a function of y, it does not shift due to a shift in y. On the LT curve we assumethat the

101

tax rate and debt/GDP ratio remaining constant we have dn/dy---gýgnIf g,>O and will g. <O then dn/dy >0. The LT shifts upwards. An increase in the proportion of

government spendingon infrastructureraisesthe growth rate. We can show 113N119'YID, / frgn-grfn 'gyfr -c

>O

The result that an increase in the proportion of government spending investment on and development purposes raises growth

is again in accord with

the basic

characteristicsof the growth model presentedhere.

5.5. Calibration

and estimation for India

In this section we present the data used and the results obtained. We use the values

of parameterson the demand side as in the previous chapter to calibrate the above Other model. observed variables are those reported in the Economic Survey 1993-94, Government of India and Yearbook of the International Financial Statistics published by the International Monetary Fund.

We assume that r. the implicit risk free real interest rate relevant for consumption

decislons,is 14.16 per cent, the proportion of labour income receivedby unconstrained households is 70 per cent, the probability of death, p, is 0.019 and 6, the rate of time 0.032. preference, is The Economic Survey 1993-94 reports a rate of growth of population over 1981-91 to be 2.14 per cent. GDP grew at an average rate of approximately 4.5 per cent over is for GDP 1991-92 Domestic Private Investment Gross decade. as a percent of this be is 64 GDP Consumption be 14.0 to calculated as a percent of per cent. reported to figures by IW. ftom the the provided per cent

Government spending constitutes 22

Governments State Central The GDP. total the outlay of government and per cent of

II0-

and Union Territories is categorised as development and non-development expenditure. Non-development expenditure includes defence, tax collection charges, police, etc. To analyse the impact of government spending on productivity, we choose y to be development expenditure as a proportion of total government expenditure.

This includes public investment in infrastructure, education and health. Table 1.5 has development that total shows government expenditure spending as a proportion of declined by about 10 per cent in the last decade. and was 54.3 per cent in 1993-94.

Table 5.1: Summary of Calibration.

Value

Parameter Depreciation Rate =n0.05 Real Rate of Interest =r0.14 Rate of time preference =60.032 Consumption/GDP =C0.64 Gov. Exp. /GDP =G0.22 Gov. Debt/GDP =D0.60 death probability of

p

0.019

liquidity parameter

X

0.70

rate of growth of population =g

0.0214

GDP growth =n

0.045

Development Exp. /Gov. Exp. =y

0.543

Capital Extemality =yI Y2

1-(1-a)yi

Report, issues), Annual (Various India, Government of Sources Economic Survey, Reserve Bank of India, Bombay.

Depreciation be 5 is physical of depreciation, to cent. per chosen the rate of -x, be tear expected may and as wear as well technological obsolescence capital through human broader is as Our includes and 10 concept of capital per cent. to be roughly

103

well as physical capital. Since we expect a much lower depreciation rate for human

capital we choosethe averagedepreciationrate for our broad concept of capital to be 5 per cent. is the contribution of public capital to the production externality i. e., it is the yj contribution of public capital to the economy-wide efficiency of labour. As yi is neither

estimated nor observed, it is imposed. Since we do not know its value, we impose different values of yj and calibrate the model. To each level of yj corresponds I-Y2 Ă˝'Yl (1-cc), the elasticity of aggregate output to public capital stock. The value of cc, the income be to to share of accruing private capital, was revealed approximately 29 per cent. So the higher is yi the higher is the elasticity I-Y2.

The marginal products of private and public capital can be shown to be Y2(Y/K) and (I -Y2)(Y/ KG). Since the ratio of both public and private investment to GDP is each be II the approximately per cent, marginal product of private and public capital may by comparing the value compared

(1-Y2)to Of Y2

If Y2 ýI-Y2

i. e.

Y2":--0.5,

the two

be increased by reallocating resources marginal products are equal and output cannot

from the public to the private sector or vice versa. Our calibration showsthat (x=0.29 between Allocation public and private sectors is of capital when y1=0.7. and Y2=--I-Y2 by from be )< (1 0.5 If the then efficient. raised reallocating investment output can -72 is large.

5.2 The Table too the then public sector size of public to the private sector different the values of model is calibrated at shows the values of the multipliers when Yi.

104

Table 5.2: The Multipliers Yl

O)IVO'y

0.2

0.03232

0.5

0.07678

0.7

0.10404

0.9

0.12960

for selected values of yj

cýtVaD

an/&T

-0.00497

-0.0625

-0.01202

0.06384

-0.02174

0.14130

-0.02772

0.21393

5.5.1. The Development Expenditure Multiplier The development expenditure multiplier, (o-'nl&y),measuresthe change in long run steady state growth rate corresponding to a change in the proportion of development in debt /GDP total the tax the expenditure government spending when rate and ratio increase in the proportion of development For are unchanged. yl=0.2 a one per cent in in long-run by leads to the growth rate expenditure government spending an increase 0.03 per cent. Similarly if yj were 0.7 the rise in the long-run growth rate would be 0.1 in development A the ten proportion of expenditure then per cent reduction per cent. implies aI per cent decline in the long run growth rate.

105

yl and the development multiplier

expenditure

0.14 cu 1-

Z

0.12 0.1

Cu 0.

0.08

ýw Z;

75 0.06 orEE 0.

cleveloýment expenditure multiplier

0.04

0.02

*0

0 ci

C4 ci

Cf) C:)

'RT C=;

LO 6

(0 C;

r-

00 C=;

0') C;

71

Figure 5.2 Any increase in the proportion of public investment to total government spending long-term the raises growth rate whatever the efficiency of the public sector. However,

when yj

higher, in development the is a reduction ratio of expenditure to total

larger be in This to government expenditure reduces growth a extent. can seen Figure 5.2. The higher is yi, the contribution of the public sector to raising the economy-wide is long-term labour, in the the on greater effect growth of a reduction the efficiency of investment to total government spending. proportion of public 5.5.2. The Tax Multiplier While growth rates unambiguously increase as debt declines or as government in the things the change remaining same, spending on infrastructure increases, other is defined. in The by brought tax the tax rate not so well change about a growth (anlar), multiplier,

due in long-run to a the steady state growth change measures

budget Given D the tax the government and y are unchanged. rate, when change in T,

106

constraint a rise in the tax rate allows higher public spending and thus investment.

When yj is high, then a rise in the tax rate which reallocates resources to the public sector raises long-term growth rate. The tax multiplier is therefore positive. However, when yj is low, higher taxes imply an increase in public investment at the cost of private saving which leads to a reduction in private investment. An increase in tax rate reduces long-run growth rate when the contribution of the public sector to the growth potential of the economy is relatively lower.

yl and the tax multiplier 0.25 0.2 0.15 0.1 0.05

0 -0.05

-0.1 -0.15

I

CN

multiplier

-tax c4-)

Ă˝

le

LÂŁ)

(0

r-

00

0)

yl

Figure 5.3 Figure 5.3 shows how the value of the tax multiplier rises with an increase in yi. We

from to tax the the negative positive asyj rises. that changes multiplier rate of sign see

5.5.3. The Debt Multiplier long-run (65'n/aD), debt the The steady state growth change in measures multiplier, 5.2 Table debt/GDP D, the due to a change in ratio, when 'r and y are unchanged.

107

shows that if yi were 0.2, a one per cent increase the debt/GDP in ratio leads to a reduction in the long run growth rate by 0.005 per cent. Or, a hundred per cent increase in the debt/GDP ratio would reduce growth rate by 0.5 per cent. At yl=0.7 a hundred per cent increase in D

would reduce the growth rate by 2.17 per cent.

,yl and the debt multiplier 0 c114

CY)

le

LO

(0

r, -

OD

c;

c;

ci

채

c;

-0.005

-0.01 -0.015 -0.02 -0.025 debt multiplie -0.03 YI

Figure 5.4 We observe in Figure 5.4 that the absolute value of the multiplier rises when yj

Is

higher and a rise in the debt ratio reduces long-term growth to a larger extent. If taxes debt is by then a reduction in achieved remain unchanged, reducing government

development half Since constitutes nearly expenditure of total government spending. is be larger higher debt longthe the the yl, effect of a reduction in on will spending, term growth rate.

As discussed in detail earlier, the ratio of development expenditure in the face in is declining the to the total commitment of expenditure rapidly government's

108

reduce public borrowing under the SAP. Our calibration suggeststhat the effect of the decline in the ratio of development expenditureon the growth rate is quite significant.

17) Assuming a mean level of yi, reducing the development from proportion of spending the present y=54.3 per cent say by another 10 per cent to 44.3 per cent, keeping the tax rate and the debt/GDP ratio unchanged, will reduce growth by more than 0.7 per cent. The pattern of government spending therefore has a significant effect on the longrun growth rate of the economy. For, instance if half of defence expenditure, which is about 20 per cent of total government spending, was diverted to development purposes y would increase from 54.3 to 64.3 and the long-run growth rate would rise by about 0.76 per cent.

A 0.5 per cent increase in growth could be achieved either by a less than 10 per cent rise in the ratio of development expenditure in total expenditure or by a 50 per cent in debt/GDP from larger 0.6.

The the the reduction ratio present second is much in Since total government expenditure stands at about 22 per cent of GDP magrutude.

half development development than of it is expenditure, expenditure and slightly more higher GDP. be Thus 12 to the of growth same extent per cent could stands at about large increase development by than a reduction expenditure rather in a small achieved

in debt.

The effect of small changes in more than one fiscal variable can be analysed as Since

follows. dn

NNN OD

dD +-

we

have

n=n(D, y,,r),

the

total

effect

is

given

by

dy +- dT If the fiscal deficit Is reduced by rals'ng the tax rate, -c, .

Cn-1 C'Y

infrastructure to total remains spending government spending the of proportion while

109

unchanged, then the total effect on long term growth rate can be measured by

an cn dn = dD + d-,. aT c9D On the other hand,the tax rate could be kept

constantand the fiscal deficit could be

by reduced cutting public spending. Government expenditure can be reduced either by a reduction in both consumption spending and investment such that y remains unchanged, or by a reduction in one such that y changes. If, say, the reduction is

brought about by a cut in the expenditure on infrastructure, because of which y an

on dD + dy Here the first term changes, the total effect on growth would be dn = . aD Cly

is positive since debt hasbeenreducedand the secondterm is negativesincethere is a fall in y which reduces growth. The total effect on growth depends on which effect is larger.

5.6. Non-Ricardian

Effects

In this section we examine some of the implications that arise from the violation of Ricardian assumptions. We first look at the values the tax and debt multipliers would take on if the planning horizons of the unconstrained consumers were different. We liquidity look the constraints. effect of at next

5.6.1. Finite horizons If the probability of death is higher the effect of the shorter time horizon on the larger is non-Ricardian effects on consumption of unconstrained consumers revealed as debt 5.5 Figure the that the multiplier increases absolute value of shows growth rates.

This death our expectation accords unity. well with approaches of the probability as

110

that if consumers have shorter planning horizons then debt public is treated as net wealth and consumption rises crowding out private investment and reducing the rate of

growth in our model. When p=O the value of the multiplier is non-zero because of other non-Ricardian effects, namely distortionary taxes, population growth and liquidity constraints and the public capital externality.

Finite horizons and the debt multiplier

c -o.

-0

75 E -0.1

-0

-0.25 p=the probability

of death

Figure 5.5 Similarly the value of the tax multiplier would be higher if the probability of death by horizons higher higher.

Shorter time represented a value of p, other were in imply have the tax the small changes rate much would same, parameters remaining larger effects on growth. Again the multiplier is non-zero when p=O because of other 5.6.

Figure be This seen in can non-Ricardian effects.

ill

Finite horizons and the tax multiplier 0.6 0.5 0.4 CL

0.3 E x 2 0.2 0.1

---7

ax multiplier,,

0 C)

ci

04 C)

CO

Ict

LO

66C;

p=the probabilitY

(D C)

rC)

00

(3)

C;

of death

Figure 5.6

5.6.2. Liquidity

constraints

We now examine the effect of liquidity constraints on the tax multiplier.

As Figure 5.7 shows the value of the tax multiplier falls as we approach the Ricardian (k=l). case

This is because if a higher proportion of income is received by forward

looking consumers then the effect of a change in the tax rate on consumption will be lower and the magnitude of crowding out is smaller. Hence the effect of a change in the tax rate on the growth rate is smaller.

112

Liquidity constraints and the tax multiplier 0.08 0.07 0.06 U.05

75 0.04 E 0.03 x 0.02 ix

0.01

multipli

0 C)

CN 666C;

00

qt

LO C=;

(D CD

t-C)

00 Ci

CF) Ci

the proportion of income received by unconstrained consumers

Figure 5.7

5.6.3. Distortionary

Taxes

To examine the effect of distortionary taxes we assumethat p=g=O and k=l as in the Ricardian case. Now the deviation from Ricardian Equivalence is due only to distortionary taxes and the public capital externality. We re-estimate the multipliers how 'quasi-Ricardian' 0.5.

Table 5.3 these the shows us mean value of yj = at finite horizons, there the case exist non-Ricardian when multipliers compare with population

growth,

liquidity

distortionary constraints and

taxes. Since the

development expenditure multiplier is determined on the supply side of the model we look at the tax and debt multipliers which would be affected by non-Ricardian effects

demand. on

113

Table 5.3: The Multipliers

for the Quasi Ricardian and Non-Ricardian Cases

Multiplier

QuasiRicardian Non-Ricardian

cýlvaD

-0.0154

-0.0153

Cýn/c't

0.0599

0.0638

The tax and debt multipliers in the Quasi Ricardian case are only marginally lower than in the non-Ricardian case. Clearly the effect of finite horizons, population growth and liquidity constraints is not very large. We examine the relation between the tax rate and the long-run growth rate in Figure 5.8,5.9,5.10

look 5.11.

We and also

at the choice of the tax rate that maximises growth. This is considered to be the coptimal' tax rate.

We first examine the relationship between the tax rate and the growth rate in Figure 5.8. yj is assumedto be the mean level of 0.5. Figure 5.8 shows the optimal tax for different levels of y, the ratio of development to total government spending. rate Given the level of y at 0.54 growth rate can be raised by raising the tax rate to about 40 per cent. If y were higher by 10 or 20 percentage points, growth rates achieved higher be at any tax rate. relatively would

114

Growth, Tax Rate and Development Expenditure 0.09 0.08 I-Iolo,

0.07 0.06 0.05 0.04 0.03

y=0.54

0.02

y=0.64

0.01

Y=0.74

0

0.2

0.3

0.4

0.5

0.6

0.7

Tax rate

Figure 5.8

As discussed earlier the effect of distortionary taxes on the long-run growth rate depends on the contribution of public capital stock to the economy wide efficiency of labour. We see that the optimal tax rate is different at different values of yi. Figure 5.9 indicates that if yj =0.25 the maximum growth rate is achieved when the tax rate is is higher When higher The 25 tax the the rate. yj =0.75 optimal yi, is per cent. around the optimal tax rate is around 57 per cent.

115

Growth, Tax Rate and Yl 0.08

0.07 100.00 1

0.06 000,

IN

0.05 0.04 (9 0.03

0.02 -yl=0.25 ---

0.01

-------

0 40.2

0.3

0.4

0.5

yl=0.5 yl--0.75

0.6

0.7

Tax Rate

Figure 5.9

Figure 5.10 shows growth rates at different levels of the tax rate corresponding to the debt /GDP ratio. yj is assumedto be the mean level of 0.5. Again growth rate can be increased from its present level by raising the tax rate up to about 40 per cent. If the debt/GDP ratio is lower then growth rates are relatively higher for all -c.

116

Growth, Tax rate and the Debt/GDP ratio 0.08 0.07 0.06

/

0.05 0.04 0.03 0.02

D=0.4 D=0.5

0.01

D=0.6

0 0.2

0.3

0.4

0.5

0.6

0.7

Tax Rate

Figure 5.10

Finally Fig. 5.11 shows the optimal tax rate for different values of the liquidity k.

It also shows that the effect on growth of changing the proportion of parameter

income received by unconstrainedconsumers.It can be seenthat this effect is quite income by increase Increasing the the proportion of earned rich will not growth small. don't. labour income If the though they poor all post-tax save and substantially even ( ?, long by 1), be the = run growth rate unconstrained consumers received was to liquidity higher.

For be 0.2 the the present value of parameter of per cent about would 70 per cent, the optimal tax rate is about 40 per cent. This is not sigruficantly affected

by the value of X.

117

Liquidity Constraints

and Growth rate

0.08 0.07 .00, ".

0.06

100,

- -- --------

0000

.000,

0.05 0.04 0.03 0.02 X=0.7

0.01

/X=0.4

0 0.2

0.3

0.4

0.5

0.6

0.7

Tax rate

Figure 5.11

5.7. Reducing Debt The effect of a reduction in debt has been examined above by looking at the induced in by the growth rate change small changes in the debt/GDP ratio. The derived level debt/GDP the the multipliers were at current of ratio of 0.6. In Figure 5.12 and Figure 5.13 we observe that if the debt/GDP ratio was considerably reduced

then the developmentexpenditureand the tax multiplier acquire much higher values.A development in increase the proportion of expenditure in total government small

in long-run the tax the rate can raise steadystate growth rate spendingor an increaseII lower levels debt/GDp the of ratio. more effectively at

118

The debt/GDP ratio and the tax IlluiLlpilul 0. '.

0.1 0.09 0.08 0.07 U.uo 0.05 0.04 0.03 0.02

I

0.01

0!

multiplier

-tax

Ă˝

11111i111 C)

v-ci

CN C;

c1f) C;

44, 6

U) C)

(D C=i

rci

00 C;

0) C;

DebVGDP

Figure 5.12

The debt/GDP ratio and the development expenditure multiplier 0.084 0.082 0.08 CL x

0.078 U.Utb 0.074

EE CL

0.072 -

0.07 CD ,a0.068

development expenditure multiplier

0.066 0

clq

c;

le

(0

c; c; Debt/GDP

Figure 5.13

00

T-

119

5.8 Effects of Demand and Supply Side externalities

In this section we impose restrictions on the k, g, -c and yj to parameters p, evaluate the relative importance of the non-Ricardian effects for empirical analysis and

obtain a range of specificationsincluding the 'pure' Ricardian, and models similar to Alogoskoufis and van der Ploeg (1990) and Buiter (1991) among others. The endogenous growth character of the model is retained throughout by the assumption that there are externalities arising from private capital.

In the 'pure' Ricardian case we assume that there are no public capital externalities, no liquidity constraints, no population growth, horizons are infinite and taxes are non-distortionary. So p=g=

I- X= -i = yj = 0.

The aggregate consumption function can be shown to be I+r

Ct

1+(5

Ct-I

In function defined in (2.9) the the of a representative agent. consumption which as GDP steady state expressing consumption as a ratio of

ÂŤ1+n)(l+5)-(1+rÂťC =O Since taxes are lump-sum, the government budget constraint is G=T-(r-n)/(I+n)D The market equilibrium condition is +n) )K -

function 'Yaari-Blanchard' is consumption The 'Ricardian' equivalent of the f(n, r, D) = ((I+n)(1+6)-(I+r))(

I- ((n+7r)/(I+n)

)K - T+(r-n)/(I+n)D)

=

120

Assuming that yi =0 as in Romer (1986) i. e. public capital has no externalities then the

LT curve becomes logB + log K(r) =

The debt multiplier hasbeendefined as [aNlaD]

/ frgn-grfn ` grfD-gDfr -r,y'-

In this case9D=0 and if n=r- 5, fDapproacheszero and the debt multiplier approaches zero. The tax and development expenditure multipliers are also both zero. In other words, when consumers have infinite horizons, there are no liquidity constraints, no population growth, taxes are lump sum, public capital has no externalities and the growth rate is equal to the real interest rate minus the pure rate of time preference, fiscal policy is neutral.

In the Yaari-Blanchard case when only p#0,

and we assumethat there are no

liquidity constraints, population growth or externalities associated with public capital and n= r-5, non-Ricardian effects arise as the probability of death is positive. Due to finite horizons public debt is considered net wealth and this raises consumption and investment hence long in turn the net and reduces reduces run reduces saving which growth rate. The restrictions that g=0,

X=1, -c= 0, yj =0 and n=r-5,

reduce our

der (1990) be As Ploeg Alogoskoufis to the specification. can seen in and van model Table 5.4 if p=0.02

lump debt find the the taxes that sum, are value of when we

in debt/GDP leads decrease 100 Thus the to a ratio percent a multiplier is -0.0013. finite horizons, in Our in the that a presenceof 0.13 percent rise the growth rate. result

long-run their debt/GDP in the corresponds with growth rate, the ratio affects change in included both the horizons finite When are growth population and conclusions. debt (1991) (1991) Bulter der Ploeg the Alogoskoufis and and van in as model

121

multiplier becomes-0.00 18. In other words, in if addition to finite horizonswe include the population growth rate the absolute value of the debt multiplier rises by 0.0005.

This suggests that the effect of Blanchard-Weil demographics are significant when taxes are lump sum and there arise no externalities due to public capital.

The model incorporates tax distortions in the form of a flat rate income tax

imposed on all labour and non-labour income as in Barro (1990) and Futagami,Morita Shibata (1993), Jappelli and Meana (1994) and Krichel and and Levine (1995). When

none of the other Ricardian assumptionsare violated the debt multiplier is found to be non-zero at -0.001. The non-zero effects of government borrowing on long-run growth are entirely due to distortionary taxes. We can again look at how the multipliers would be affected if there one or more of the other assumptions of the

Ricardian theorem were violated as well.

When finite horizons and population growth are incorporated in the model with tax distortions the absolute value of the debt multiplier becomes higher. At p=0.02, g debt is 0.0027 the the =0 value of multiplier and at p=0.02, -

g=0.02

it is -0.0030.

In comparison with the lump sum tax case these values are nearly double indicating the importance of tax distortions. These results suggest that models like Alogoskoufis and (1990,1991) der Ploeg van

(1991) into Buiter taking and while account effects of

finite horizons and population growth on the demand side, ignore more important demand side non-Ricardian effects due to distortionary taxes.

When the stock of public capital affects the economy-wide efficiency of labour, due long-run fiscal the not only to non-Ricardian growth rate is the effect of policy on

demand side effects but due to the direct effect of public spendingon infrastructure, development health creates and physical which expenditure and other education,

122

human capital. We see that the multipliers are much larger in magnitude when the

externality arising from public spending is taken into account. Our results are summarised in Tables 5.4,5.5 and 5.6. At yl=0.5 the tax multiplier is now positive which indicates that higher taxes that finance public investment serve to raise growth, outweighing negative demand side effects.

Table 5.4: The Debt Multiplier

Case Pure Ricardian Finite Horizons Finite Horizons and Population Growth Public Capital Externality Finite Horizons and Public Capital Externality Finite Horizons, Population Growth Capital Public and Externality Liquidity Constraints, Finite Horizons, Population Growth Capital Public and Externality

Distortion None

Lump sum axes 0

p=0.02 p=0.02 g=0.02 yj = 0.5

-0.0013 -0.0018

-0.001 -0.0027 -0.0030

-0.0065

-0.0061

yj = 0.5 0.02 p

-0.0074

-0.0074

0.5 0.02 0.02

-0.0078

-0.0079

yj p g yj k p g

0.5 0.7 0.02 0.02

Distortionary Taxes

3

-0.0088

2 We set r=0.077 so that n= r- 5. All other parametersretain their previous values. by two the deterimne ot taxes gotips the liquidity to paid of share lump need have taxes \ke constraints ' in the care when we and sum do this multiplier. for calculate value so not this and an arbitru-), imposing avoid we Since there is no evidence consumers.

123

Table 5.5: The Tax Multiplier Case Distortion Pure Ricardian None Finite Horizons p=0.02 Finite Horizons and p=0.02 Population Growth g=0.02 Public Capital yj = 0.5 Externality Finite Horizons and yj = 0.5 Public Capital p 0.02 Externality Finite Horizons,, 0.5 yj Population Growth p 0.02 Capital Public and g 0.02 Externality Liquidity yj 0.5 Constraints, Finite ?, 0.7 Horizons, 0.02 p Population Growth g 0.02 Capital Public and Externality

Distortionary Taxes -0.0478 -0.0481 -0.0764 0.1267 0.1305

0.1168

0.1196

124

Table 5.5: The Development Expenditure Multiplier Case Pure Ricardian Finite Horizons Finite Horizons and Population Growth Public Capital Externality Finite Horizons and Public Capital Externality Finite Horizons, Population Growth and Public Capital Externality Liquidity Constraints, Finite Horizons, Population Growth Capital Public and Externality

Distortion None

Lump sum Taxes 0 0 0

Distortionary Taxes 0 0 0

0.0850

0.0710

yj = 0.5 p 0.02

0.0858

0.0726

0.5 0.02 0.02

0.0874

0.0754

p=0.02 p=0.02 g=0.02 yj = 0.5

yj p g

yj 0.5 ?, 0.7 p 0.02 g 0.02

0.0765

When we include only the externality due to public capital then the value of the debt multiplier is -0.0065, while if we include all the non-Ricardian demand side effects due to finite horizons, population growth, tax distortions and liquidity constraints it is in This ten the that growth rate reduction would per cent of a effect means -0.0088. by in by in first 0.065 the long second per cent and case run growth rate the raise the have been demand ignoring though they By 0.088 per cent. side effects, non-Ricardian be long in the very found to exist, the anticipated change run growth rate would not it is 4.5088, level 4.5 to to when rise From anticipated different. the current per cent of Even the 4.5065 they case in are ignored. when demand side effects are included and

125

development of expenditure and the tax rate, there is only a marginal change in the

value of the multiplier when theseeffects are ignored.

The strongest effects arise from public capital externalities, and in their absence from tax distortions. Our results thus appear to suggest that in an enclogenousgrowth model which takes into account strong supply side effects caused by externalities ansing from public investment, ignoring non-Ricardian effects on the demand side would not significantly affect our results. Ignoring Blanchard-Weil demographics may on the one hand lead to loss of generality and perhaps reduce the accuracy of our results, but more may be gained by the analytical simplicity achieved by making Ricardian assumptions on the demand side.

5.9. Conclusion Our analysis reveals the significance of the violations of Ricardian assumptions. Our indicate that though non-Ricardian effects are potentially significant the effect results

horizons liquidity does finite constraints not change our and of population growth, drastically. results The major policy implications that arise from the above results are that the growth by be the tax Indian either raising effectively rate the most raised can economy rate of be The development tax by rate can raised expenditure. raising the Proportion of or

fold those that bringing tax by the the sectors at structure present of into effectively base be the tax Rationalising tax the could while widening system enjoy exemption. have As taxes. that paid as we is the of income proportion raising more effective in

the tax to restructure and rationalise strean-dine, there discussedearlier, is an attempt SAP. the structure under

126

On the other hand, there is no attempt to development On the raise expenditure. contrary, y has declined in this period. Cutting public investment is going to reduce the long term growth potential of the economy. Such a policy is counter-productive and though there seems to be a general awareness of the implications of reducing public investment, it is still being followed to meet the government's commitment under the SAP to cut deficit. Clearly, the emphasis needs to shift from simply cutting the deficit, to cutting it by reducing non-development expenditure and to diverting spending from government consumption to public investment. Unless the policy framework of the SAP clearly defines the role of public investment and takes into account the effect of long-run borrowing countries concerned might government Policies on growth, definition follow A to of the role of clear continue such counter-productive policies. labour its investment to the can economy wide efficiency of contfibution and public long-run be the the towards rate in to growth state steady raising step a prove economy.

127

Conclusion

In this thesis we examine the effects of fiscal policy on the long-run steady state

growth rate in the fi7ameworkof an enclogenous growth model of India. We first exarnine the Ricardian hypothesisthat predicts that fiscal policy has no effect on consumption and investment in an economy. Next we estimatenon-Ricardian effects on the demand private side and calibrate our model which has public capital externalities on the supply side to determine the impact of changes in tax rate, debt /GDP ratio and the proportion of government spending on development on the long-run steady state growth rate of the economy.

Since Ricardian Equivalence predicts that fiscal policy is neutral we first examine the Ricardian model for India. Underlying the Ricardian equivalence theorem is the hypothesis and the assumption that there are no credit market permanent income imperfections.Liquidity constraintsmagnify the responseof current consumptionto current income. Our results suggest an 'exces sensitivity' of consumption to disposableincome in India. This implies that the Ricardian assumptionof perfect credit markets Is Violated for

India.

The representative agent model prevents us fi7om analysing the effect on income looking forward between the permanent consumption of a transfer of population income the their "unconstrained" those current consume who and consumerswhom we cafl for function describe that We, allows consumption therefore, aggregate an CC constrained".

between be for transfer to there a both groups of consumersto exist in one populationand lie death that have can of probability The constant a consumers unconstrained the groups.

128

betweenzero and one.They own the all physicalandfinancialwealthm the economy,have access to credit and they smooth consumption over their lifetimes. If we define their probability of death p as zero then they would representBarro's inýte horizon consumers.

The liquidity parameter, X, representsthe fact that in an economy, especiallyin a poor developing country not aH consumerscan be describedas unconstrainedas they do

have not accessto credit. The transferof consumersfi7omone group to anothercancome for instance, by a liberalisation of the credit market or by a redistribution of income about, and wealth. The parameter of population growth of unconstrainedconsumers,g, captures the changein the consumption pattern of an economyundergoing structural transformation.

An interesting result that emerged from our results was the value of g that was be from The to to transfer the estimated negative suggests value a net unconstrained -0.12.

the constrainedgroup for the period under consideration.Our estimate indicates income in is 1960-80. the the that to of population penod some sections redistfibution unfavourable Figures for rural income distribution and poverty levels suggest that India's process of development,with its emphasison large-scalecapital-intensiveindustry and modernisation by been has in the accompanied paupensationof country, of agriculture selectedpockets of in by is hypothesis the This the of a rise evidence the supported also peasantry. a section of food build-up the stocks. of aggregatesavingsratio and from in the effect of public and private Production externalities our model anse broad defined Capital laboUr. to sense a in is of capital on the economy-vvideefficiency health, Public human 1mgation, include inffastructure and spendingon educattorĂ˝ capital. formation.

In on capital spending government of telecommunications, part etc., is transport, that have the process planning to role in a crucial India the public sector was envisaged by Fiscal planners and regarded was policy the growth. of economic to rate aimed speedup

129

Policy makers as an important tool in India's development strategy. Public investment

intended to proVideboth the physicalinfi7astructure and the human capital requiredfor economic growth. In recent years, however, the rising burden of government consumption expenditure and higher interest payments has squeezed the resources available for development expenditure.The government's

commitment to developmentexpenditurehas

been further unden-ninedunder the Structural Adjustment Programme. Since on the one hand, there is no clearly defined role for public investment, and on the other there is pressureto cut total spendingand reduce deficits, we observethat in recent years there has been a reduction in the proportion of development expenditure in total government spending.

We analysedthe effect of fiscal measures changesin the debt/GDP ratio, the tax development in the rate and proportion of expenditure total government spending on the objective of economic growth in a steady state model of endogenous growth. The is in the effects significanceof non-Ricardian observedearlier examined our analysisof the indicate finite fiscal Our the that though results potentially effect of changes. effect of horizons, liquidity constraints and population growth can be important, the effect of these from The strongest non-Ricardian effects arise non-Ricardian assumptions is marginal. distortionary taxes. When fiscal policy has a strong impact on growth, due the externalities demand investment, fi7om the side non-Ricardian effect only significant public arising distortions.

The fi7om to the insensitive presenceof tax relatively are multipliers originates in In liquidity the terms horizons, finite of model. constraints and population growth by them that simplicity ignoring analytical this achieVing while suggests modelling strategy detect Although the lose presence of we terms application. empirical of in much we will not implications for it has ve'Y n-unor firýite horizons at the estimated value of the parameter

130

growth. This suggeststhat in future research for we can assumethat Barro's assumptions householdbehaviourhold without a loss of generality.In other words, the contributionof this study in ten-nsof modellingstrategyfies in not just imposingthe demandside effects but estimatingthe consumptionfunction to detennine them, to assessthe impact of the non-Ricardianeffects for fiscal policy analysisand show which of them have important implicationsfor growth.

The multipfiers,derived suggestthat a in reduction the debt/GDP ratio leadsto an in increase the long-run growth rate. The effect of the tax rate is ambiguous.When the contribution of public capital to the economy-wide efficiency of labour is high an increasein the tax rate increasesthe long-run rate of economic growth. If, however, the contribution of the public sector is low comparedto that of private investmentthen an increasein the tax rate which reduces private investment, has a negative effect on the long-run growth rate.

Whenthe contributionof public capitalto the economy-, labour is Aideefficiencyof greater than that of private capital, then reducing the tax rate will decreasethe growth rate. The investment in governmentspending on the longthe effect of reducing proportion of public is run growth rate always found to be negative. In our cafibrationfor India we find that the development is the magnitude of expenditure multiplier nearly six times the value of the debt/GDP ratio multiplier. Whatever the contribution of public capital to the economy-vAde in labour, If the objective the change public Investment is positive. of a effect efficiency of

is to achievea higher rate of long-run economicgrowth in India, a reductionin pubfic investment is clearly contrary to this objective.

The explanation of why the proportion of public investment in total government be despite SAP faffing is the could growth, on effect negative Its sharply under spending As balance in SAP than growth. rather is on short-terrn macroeconomic that the emphasis a

131

distinct from the 1XV, the World Bank, whose horizon for an adjustmentprogramme is usually longer, emphasisessupply side measures.Recently, it has been also emphasisingthe role of human capital. To take account of this, government spending health on and

educationin India hasbeenincreasedin the lasttwo years.Also, it is proposedthat a Poficy Framework Paper be drafted jointly by the borrowing government,the INV and the World Bank. The objective is to achievea better balancebetween and short term goals of the ROF

andthe objectiveof long-rungrowth.

The major limitation of the framework adopted in this study is that it is a closed economy model.

While this may be acceptable for India at the present level of

development, such a model may not approximate reality for another country or for India in the future. A closed economy model prevents us fi7omanalysingthe effect of inflow and from to the country. Since capital is not homogenous,this is not a outflow of capital and triVial issue. For example, the inflow may be of foreign capital which comes with new technology and contributes significantly to the economy-vride efficiency of labour. The like highly be technical engineersand and scientific personnel of educated outflow may

doctors('brain drain') whosetraininghasinvolvedsignificantinvestment.

Research in endogenous growth theory is opening up many avenues. For instance, we could follow Barro and Sala-i-Martin (1995) in analysing the effect of investment. foreign Intellectual diffusion through property technology imitation and/or fights could be granted by a government to foreign investors if spill-over effects on irnItation diffusion higher through flow technology than of of the were profit growth of

been have issues settled not designs. Though many relating to open economy models (1995) Sala-l-Martin Barro them. to and solve there attempts are satisfactorily,

132

introduce credit constraints on international borrowing, variations in the time preference parameter and adjustment costs to deal with some issues.

We could also explore the possibility of extending the above model to examine the impact of military expenditure on growth rate. In a similar model Berthelemy et. al.(1995) analyse the interrelationships between military expenditure and growth in a

model where investment in education creates skilled labour which increasesthe endogenously determined rate of growth. Since both education and defence are nonin rival use,,they are public goods and have to be financed by taxation. Therefore there

is a trade-off between them. By raising security defencecontributesto social welfare.

But if it leads to lower civilian spending which is also assumed to contribute to welfare

then the total effect may be either way. There is thus a case for analysing both economic growth and welfare in

framework that incorporates defence and a

development expenditure. In our model development expenditure (which includes labour in to the the economy and therefore education) serves raise overall efficiency of

into from We take to growth. could also account spill-over effects contributes investment in military R&D

infrastructure defence in the aggregate related and

defence development function.

Both then expenditure and expenditure production from here Since private capital and externalities would arise contribute to growth. be defence the infrastructure spending model would as well as education and public in health, if it Also, that in broader its analysis. public investment education, is assumed be life then the population it could included in infrastructure, etc. raise the quality of of impact the We function. then of military expenditure on study could the social welfare but (1995) Berthelemy range of incorporating a wider al. et. in as growth and welfare phenomena.

133

In this study we have demonstrated the applicability of recent developmentsin macroeconomicsto issuesof growth and developmentin LDCs in just one aspect- that of fiscal policy. The scope of our study is however much larger for example, endogenous diffusion, has bearing issues theory technology to intellectual growth a on many relating few doubt, labour, No the years will next and so on. property rights, the migration of framework development in in the boom within research many of these aspectsof witness a

growth models. of enclogenous

134

Appendix A The Yaari-Blanchard

and Linear Technology Curves

Here we examine the slope of the The Yaan-Blanchard and Linear Technology curves. Consider incremental changes in the exogenous fiscal variables dD, ft, dy and the corresponding incremental changes dn and dr along the YB and LT curves.

Differentiating, these incremental changes satisfy

fndn+fr dr +fDdD +fzd-c=O 9ndn +grdr+gDdD+grd-c+ g7d7--O Hence keeping fiscal policy and income distribution fixed, the slope of the YB curve is by given

(O'War)f-ý-o'::::: fn '-fr/ fn=-(1+8)C-ý(K+D)<O From (5.29) ýC-TI(D+K)=O >0, +r(I K+D>O, C>O, so u))/(l and 71=(p+g)(p+6)(I since -, -p) have (5.29) from ý=O. Also if Note then ý=r(l-, u)-5-n(1+5)>O. that p+g=O we (D+K(r))-, I {(p+6)(p+g)(I +g)(I q fr=ý(D-[(n+Tc)/(l +n)](I --c))K'(r))+C(I r)--T)/(l-p) -, K'(r)>O (c-rdcr)f.

YB the >0 In fr/fn 0. > or other words, Since fn <0 and fr >0 therefore 0 is upward sloping. curve by is its is fiscal slope given policy given, Turning to the LT curve when gn

ý(1-Y2*1+r)D 9n":::

/(I I +n)] / (n+7r))+ G)-(l /(I+n)2

135

gr'Y2 {K'(r) I/ (K(r) I -(I -Y2)(D/ G+( -cTcK'(r)ý/ G)

Hence gn":ýOand gr":ýOif D<G/n+7c and -c-K<GK(r)y2/(I G=O. For 3 the n+7c<O and -Y2). .I first of these conditions is satisfied if D<3 (i. e., a debt/GDP ratio less than 300%). We G=0.3 (on basis).

If l >1/2, again, the second expect y2 -c<0.5 and Tc<O. an annual is From if K<6, these considerations we satisfied condition not a stringent condition. deduce that, under very lax conditions, the LT cuirve is downward-slo ping.

The remaining partial derivatives are fD=(r-n)/(

1+n)-i

f, =-r(I +g)C-ý(l -TcK+k(l -a))+{(p+g)(p+6)/(l

I r(D+K) -p)

/G {(I g,r= -y2)(I -TcK) 9D=-(I-y2)(r-n)G/(I+n) ( I gy:--"': -Y2)/ Y

From these results we can unambiguously sign

9D<O

We require and gy>0.

f--O Finally fr<O >O. along g., and gives which consumption to positive obtain -nK(r))>O C/V if fD<O extraordinarily < Hence requires which fD=, r-n have that qV/C(r-n)-TI. we f,, To gy g,, expect we debt/GDP to summarise violate. ratios large capitaUGDP and fn, fD, fc, gn, gir,gD

>0.

7

136

Appendix B The Data Set

Year 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989

CONS 8648 9327 9108 9735 8825 8838 10174 10528 11617 11970 12520 13180 14730 17530 18530 21770 26220 26240 28510 29800 32100 35130 42870 51910 52750 54110 62530 68670 74290 99080 113560 125460 145610 160320 174380 196600 201060 261600 289640

GDP 9966 9774 13638 10073 10258 12217 12598 14034 14793 16201 17177 18476 21237 24765 26145 29571 34611 36674 40387 43163 46247 51005 62007 73235 78761 84894 96067 104190 114356 136013 159760 178132 207589 231387 261920 291974 332616 394992 442769

GOVC 560 590 600 640 670 720 790 920 990 1090 1210 1460 1880 2010 2300 2500 2790 3050 3420 3800 4460 4750 5100 6140 7350 8210 8670 9620 11030 13080 15360 18270 21140 24350 29260 35070 41330 47200 53070

POP 360.18 366.3 372.75 379.57 386.62 394.22 402.23 410.69 419.61 429.02 439 451.01 462.03 472.13 482.71 493.39 504.34 515.6 527.18 539.08 551.23 563.53 575.89 588.3 600.76 613.27 625.82 646 660 675 690 705 720 736 750.86 766.14 781.37 796.6 811.82

CPI 26.2 25.9 26.8 25.5 24.3 26.5 28 29.3 30.3 31.2 31.8 32.7 33.6 33.8 41.7 46.4 52.6 54.2 55.1 57.9 59.8 62.9 74.1 94.7 100 92.2 100 102.5 109 121.6 137.3 148.1 165.6 179.5 189.4 205.9 224.1 245.4 261.1

EX 716 578 531 593 609 605 561 581 640 642 660 685 793 816 810 1157 1199 1358 1413 1535 1608 1971 2523 3329 4036 5142 5408 5726 6418 6711 7806 8803 9771 11744 10895 12452 15674 20232 27658

137

YEAR 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989

IIN4 890 702 610 700 774 841 1035 906 961 1122 1090 1131 1223 1349 1409 2078 2008 1909 1582 1634 1825 1867 2955 4519 5265 5074 6020 6811 9143 12549 13608 14293 15831 17134 19658 20096 22244 28235 35328

DEBT

3083 3514 4124 4629 5137 6121 6573 7230 7970 8490 9140 10580 10960 11580 12230 13380 14590 16820 18400 17400 20130 22160 28110 30580 36780 45340 52770 67360 74680 88780 108360 131540 153290 180170 208770

DEF 0 76 181 367 351 398 677 734 697 649 600 880 1090 1170 1240 1720 1460 1080 1020 1360 1600 2180 1700 2360 3200 3690 3790 5080 6300 8860 8730 10730 13330 17580 22250 27200 27880 33090 29230

PSI 775 859 603 572 652 917 1225 1107 922 1214 1441 1533 1606 1848 2121 2211 3181 3376 3373 4217 4571 5256 4983 6578 8918 8823 9192 11171 13335 14327 16686 23232 20684 22680 23873 33890 33210 40720 55218

GSI 259 303 256 292 436 499 666 833 815 900 1142 1147 1445 1681 1948 2216 2135 2331 2167 2259 2808 3290 3740 4751 5557 7583 8584 7846 9883 11818 11767 16781 20100 20381 24915 29056 34020 34666 39149

138

CONS Private household Consumption GDP Gross domestic Product GOVC Government Consumption Expenditure Population POP Consumer Price Index CPI Exports EX Imports IM Domestic Public Debt DEBT Fiscal Deficit DEF Private Sector Investment PSI Public Investment GSI At current prices

11)9

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