An Empirical Examination of Endogenous Growth Theory by J. Ghneim

'^.02(f in> ,

An Empirical Examination of Endogenous Growth Models

A Thesis Presented to the Economics Department Brigham Young University

In Partial Fulfillment of the requirements for the degree Master of Science

ÂŠ Jabra Ghneim 1993 by Jabra F Ghneim December 1993

This thesis by Jabra F Ghneim is accepted in its present form by the Department of Economics of Brigham Young University as satisfying the requirement for the degree of Master of Science.

David E. Sp^encer, Committee Chair

Val E. Lambson, Committee member

Date

Val E. Lambson, Graduate Coordinator

CONTENTS

Introduction CHAPTER ONE:

Literature Review.

CHAPTER TWO: Formulation and Estimation of Econometric Models for Panel Data. Chapter Three:

Empirical Research

Summary and Conclusions. Appendices.

Introduction

Growth theory is a field that has been the subject of extensive research.during the past four decades. The dominating model in the field during most of that period was the neo-classical growth model. Continuous research on the model led to several extensions by Arrow (1962), Uzawa (1965), and Romer (1983).

Out of these extensions were born

a new class of models that are usually referred to in the literature as "The Endogenous Growth Models". The main object of this paper is to empirically investigate the basic assumptions and conclusions of these models.

Most of the empirical analysis that are related to

these models do not investigate the effects of specific government expenditure on economic growth.

They usually

address the effects general government expenditure or government expenditure less some specific expenditure.

This

paper is a modest attempt to compensate for that lacking and to address a topic that has been the corner stone of political debate during the past year. The main-obstacles for researchers in the field have been the lack of sufficient data that would give satisfactory and reliable statistical results. Most of the data available covers only a small time period starting in^l972.

The

unavailability of quarterly data compounds the problem and poses a serious obstacle.

In spite of all that, my 2

anxiousness to investigate the topic led me to find ways in the econometric literature, that deal with these problems. To overcome data shortage I used cross-section time series analysis.

This method generates a relatively big data set

that can be used to generate (according to theory) relatively reliable statistical results. This research paper is divided into three chapters.

the first chaptdr I presented the theory of-endogenous growth and the main models that are dedicated to it.

In the

second chapter I provided the reader with an exposition to cross-section time-series analysis.

At last, in the third

chapter I presented my empirical findings. Though this paper has answered some of my old questions it added a host of other questions that I am sure will inspire further research on my sid^^ I am grateful to a host of people who gave me the continual support that I really needed through the hours of despair and frustration I went through.

Val E. Lambson

comes on the top of that list. His continual support and encouragement during the past two years were always a source of inspiration.

It is he who led me to start investigating

growth theory in Fall semester of 1992 and this project is the first fruits of that inquiry.

Our "hall talks" on

political economics helped a great deal to shape my thinking about the role of government in the economy and converted me 3

to Libertarianism and for this I am really thankful.

I am

really thankful also to Dr. David Spencer and Dr. Kerk Phelps for their advice and the many helpful insights that they provided me with throughout the project. I am really thankful to my family and my "parallel" family Larry and Glenda Bolick without whom this project would not have been as easy to finish and it is to them that I dedicate this work.

I am also really grateful for the untiring support of

the department's computer support man, Shawn T. Jordan whose friendship, steadfastness and strength were a source of inspiration and strength.

I also give my thanks to my

friend Dominique Andriamanantoa whose cheerfulness and spirit kept me always going.

At last I give my thanks to

all my professors at the economics department who have been outstanding examples of scholarship and hard work.

Jabra F Ghneim Provo, Utah Fall 1993

Chapter I Literature Review Introduction

In this paper I will examine the effects of several govern足 ment policies on economic growth.

The literature on this

topic is vast and discussing all of it is beyond the capacity of this project.

In this part of the paper I will briefly

discuss the neo-classical growth models since all of the research that I will review is an alteration to the assump足 tions that that model presents.

Then I will review modern

growth theories and their implications concerning public policy, emphasizing a class of models that are called "The Endogenous Growth Models". At last I will present some of the results that empirical work in the field has yielded during the past few years. Neoclassical growth theory: Review

The model presented in this section represents the basis upon which consecutive growth models have built upon.

This

model was invented by both Solow and Denison who were attempt足 ing to explain the main features of United States growth experience.

The Neoclassical growth models are based on the

notion of market-clearing, perfect foresight by economic agents, perfect competition and diminishing marginal return. A simple version of these models was provided by Lucas (1988). 5

He considers "...a closed economy with competitive markets, with identical, rational agents and constant returns technolo gy.

At date t there are N(t) persons or, equivalently, man

hours devoted to production. The growth rate in population is exogenously given and per-capita consumption is given be a stream of units of a single good. Preferences over per-capita consumption streams are given by fe-"'-:— lc{t)

mt)dt

1-0

(1)

Production per-capita of the one good is divided into consump tion c(t) and capital accumulation.

If K(t) is the total

stock of capital and JC(t)is its rate of change then total production is given by N(t)c(t)+ k(t).

If we assiame that

production is dependent on capital, labor and on the level A(t) of technology and a Cobb-Douglas production function then we have the following constraint N{t)c{t)+k{t)=A{t)K{t)^N{t)^-^ 0<P <1,AM>0

(2)

Allocations that maximize (1) subject to (2) are found using the current-value Hamiltonian (H) which is defined by the following equation H{K,Q,c, t)

l-o

[c^-^-l] +0[AK-Pi\^i-P-J\rc]

(3)

which is just'the sum of the current period utility and the rate of increase in capital which is valued at price 6

0(t). Maximizing (H) with respect to c yields the result that goods must be allocated at each date to be equally valuable, on the margin, used either as consumption or as investment". Working through the above equations gives us the following very simple results that are characteristic of the Neoclassi足 cal growth models. a) Along a balan.ced path (in other words an equilibritam path), the rate pf growth of per-capita magnitudes (consumption and investment) is proportional to the rate of technical change. b) Low time preference

and low risk aversion induce high

savings rate which induces higher output levels and growth. A thrifty society will be in the long run wealthier than an impatient one but it would not grow faster. The above model and minor variations of it were used by growth theorists to explain what Kaldor (1961) calls "stylized facts" and "prominent features" of the data on economic growth from several developed and underdeveloped countries.

The

stylized facts presented below, according to Romer (1989), are phenomenon that any growth theory must explain 1) Output per worker shows continuing growth with no tendency for a falling rate of growth of productivity. 2) Capital per worker shows continuing growth. 3) Rate of return on capital is steady. 4) Capital-output ratio is steady. 5) Labor and capital receive constant shares of total income. 7

6) Wide differences in the rate.of growth of productivity across countries.

Empirical economic research in the field of economic growth yielded the following five results 1) In cross-section, mean growth shows no variation with level of per-capita income. 2) Growth in the voliame of trade is correlated with growth in output. 3)

Population growth is negatively correlated with income

growth. 4) Growth in inputs is not large enough to explain growth in output. 5) Both skilled and unskilled workers tend to migrate to high income countries While the Neoclassical .Growth Model provided a simple setting that is consistent with Kaldor*s stylized facts [Dixit 1976], it could not explain the data features that empirical research uncovered [Romer 1989].

This called for

an extension and modification in the structure of the model and this is what I will discuss in the next section. Endogenous Growth Models:,

The rise of the role of public

policy

The growth model presented in the above section predicts that if all countries possessed the same preferences then they would converge to the same growth rate in the long-run. 8

Kaldor's sixth stylized fact and empirical research, shows that this is not the case. Uzawa (1965), Lucas (1988) and Romer (1983) investigated the assumption of constant returns to scale and provided theoretical evidence which suggested that the assumption of constant returns to scale might not be a realistic assump足 tion to adopt when explaining the divergence in growth rates among countries.

Investment in human capital, the develop足

ment of media, mass communication, externalities and the easy flow of information would allow for non-convexities in the production function and thus a breach in the constant returns to scale assumption.

For example, Lucas (1990)

using a calibrated example shows that including differences in human capital and the external benefits of human capital eliminates the difference in marginal productivity among countries.

The introduction of non-convexities and externa足

lities into growth models gave rise to a new breed of growth models which are now called Endogenous Growth Models.

These

models explore the idea that countries can grow without exogenous influences, just depending on externalities that occur because of the production and education processes.

the next section I will discuss these models and show how the introduction of non-convexities and externalities gave rise to the idea that public policy might contribute to economic growth and how these models go about explaining the 9

difference in growth rates among countries. Genesis of Endogenous Growth Models:

The Arrow Model

Arrow (1962) shows that investment in physical capital usually results in new technology and knowledge.

The idea

that existing knowledge can be used repeatedly at zero marginal co3t is the main force behind growth in this model. To understand this consider a production function F(K^L^A), where K is physical capital, L is labor, and A is the knowl足 edge component.

If the knowledge effect is acknowledged

then increasing returns follows directly.

Output can be

doubled if all tangible inputs are doubled and replicating all productive activities with no change in knowledge.

Once

the knowledge component is allowed to vary then there must be increasing returns. This argiament shows that it is impossible in a model with increasing returns to pay all factors of production their marginal product because this will exhaust all total output [Romer 1989]. To get around the problem of increasing returns Arrow limited his study to the case where the aggregate elasticity of output with respect to capital and knowledge is less than one. This formulation assures a "fragile steady-state" [Romer 1989], a decreasing growth rate and so economic growth keeps going by adding population growth.

In this model savings rate and

taxes can not influence economic growth. Romer (1989) criticizes the Arrow model on two grounds. 10

The first concerns the convergence of the integral defined over [O/OO) in the objective function [equation (1)].

Romer

argues that if growth takes place too fast then that func足 tion would diverge. The second criticism is that the model considers only the steady-state growth paths and do not examine the issue of increasing returns.

Romer (1983,1986)

expanded the model by going beyond the argument given above, that the aggregate elasticity of output with respect to capital and knowledge is less than one, and accommodated the model to the case where the elasticity is greater than one. It was found out that this formulation leads to a monotonically increasing growth rate rather than decreasing as might be the case.where the aggregate elasticity is less than one. Though public policy does hot.play any role in this model, since growth is motivated by the repeated use of existing knowledge, this model represents the genesis of other class足 es of endogenous growth models, that.implicate that public policy might affect growth positively.

Next I will consider

the first of such models, the Uzawa model. The Uzawa Model (1965)

While the externalities in the Arrow model depends on the link between investment in physical capital and technology which can be copied and used by all, the externality in the Uzawa model depends on - interaction effects of human capital. Uzawa uses a two capital goods model, human capital H and 11

physical capital. The model allows for physical labor and assumes that H and physical labor are good substitutes. Human capital input in this model resembles the physical capital input more than the physical labor input since it can be increased by investment. Accumulation of H is linear in H. The model also distinguishes between two types of human capital.

which is human capital used to produce

new consumption goods and ffg which is used to form new human capital.

So the rate of growth in human capital G can be

expressed by the equation 6 = 6H2.

This formulation allows

for no limitations on the accumulation of human capital. This assiunption is very crucial to the model since it- leads to unbounded growth in output. Other inputs can be acciamulated and there is no essential fixed factors. As seen from the assumptions this model does not depend increasing returns to generate growth but rather depends on the assumption that human capital can be accumulated without bounds.' In the Uzawa model rates of return on human and physical capital grow at the same rate because there is no deepening of physical capital relative to human capital, which means that physical'capital is not affected by the accumulation of human capital and knowledge like the Arrow model. Lucas (1988) uses the same model but he adds the assump足 tion of increasing returns and assumes that interaction of 12

human capital affects physical capital and causes the "deep足 ening" mentioned above.

In Lucas's model the amount of

human capital available is the average of human capital in the economy and physical capital increases relative to human capital and thus causes payments per workers and qualityadjusted wages to increase over time." Lucas concludes that if rates of return are to be equalized across countries then wages to human capital in high income countries are higher than lower income countries. Lucas suggests that if this model applies in reality then public policy can play a role in stimulating growth in the economy by subsidizing education.

Barro (1990) also argues

that government expenditure on education is viewed favorably by people and that it positively stimulates growth.

I will

come back to this argument when I discuss the Barro models later in this paper. Learning by doing in Endogenous Growth Models

' Krugman (1988) and Lucas (1988) developed a model with many possible goods that can be produced each with its own level of technology.

Like the Arrow model, benefits of

increases in technology are enjoyed by all.

The model

assumes that there is no capital used in production.

This

can be represented by the following two equations [Krugman 1988]

Yi — Aj:

— -6^ Yl

From the equations above it is assumed that the growth rate in technology and human capital depends on output level (6 is the rate of learning). Lucas uses an equivalent model in terms of labor L and human capital E,

Output of good i depends on the amount of

human capital per worker (H^/Li) in the industry i and is multiplied by the amount of labor devoted to the production of the good.

So from this formulation human capital grows

with output but its effects are totally external.

The above

two formulations represent learning by doing models. What the learning by doing model implies in terms of public policy is that, under an appropriate definition of preferences, it will be better for a country to be in an industry with rapid learning and rapidly increasing output. In this case if opening trade would lead to specialization in an industry with slow rate of learning will retard growth [Romer 1989].

In this case this model suggests that barri

ers to trade might be beneficial and enhance economic growth.

Empirical evidence does not support that idea.

Kruger (1983) and Harberger (1984) surveyed growth experi ences in poor countries and found out that inefficient trade barriers retarded growth and that their removal was accompa14

nied with several growth episodes. Adding Public Policy to Growth Models

From the discussion of the models above we can see that long-term growth can be generated without changes in tech足 nology or population alone but mainly on increasing returns due to human capital accumulation or the public good charac足 teristics of innovation and invention. .In those models private and social returns to investment diverge and that causes decentralized choices to cause suboptimal rates of growth. Barro (1990) includes government expenditure g as a sepa足 rate argument in the production function.

The general idea

behind that modification is that private inputs, represented by capital k, are not a close substitute for public inputs. This stems from the idea that private inputs can not replace public inputs if user costs are hard to implement.

Barro &

Martin (1992) discuss three kinds of such models in which the following is.assumed i) Production exhibits constant returns to .scale in private capital and government expenditure, together and diminishing returns in capital alone. ii) With a broad concept of private capital,. production involves decreasing returns to private inputs if the comple足 mentary government expenditure does not expand in a parallel manner. 15

iii) Government is doing no production and owns no capital. Government just buys a flow of output and makes it avail足 able. iv) The households are trying to maximize their utility using a utility function like equation (1) subject to a production function. In the first model, based* on piiblicly provided public goods, each producer has'property rights to*a specified quantity of public services. These services are rival but excludable; therefore an individual producer cannot trespass or congest the services provided to others.

This means that the pro足

duction function takes the following form y=Afc^"*5r*

(4)

where g is government purchases to each producer.

The

government runs a balanced budget and, in this version of the model,, levies a proportional tax at rate T=g/y on the quantity of output y. Because in this formulation each unit of g requires one unit of resources (measured by units of consumables), the natural efficiency condition is dy/dg=l which implies that g/y=a.

A government that seeks to maxi足

mize the utility of the repres-entative household would satisfy this condition even if it is using distortionary taxes. Barro shows that the model brings in a dependence of the 16

growth rate on the quantity of government's productive services.

If g/y and T are constant then the growth rate

always equals the steady-state growth rate. If the size of government was optimal, g/y-a, and the marginal tax rate, T, was zero then private and social returns are equal.

If t>0,

then social and private returns would diverge and the growth rate in a decentralized economy will be too low from a social perspective.

A Pareto optimal solution is achieved

by using lump-sum taxation or by subsidizing the purchase of capital goods-in the proportion r. The second version of the model treats public services as non-rival and non-excludable public goods.

In this case

aggregate quantity of government purchases, G, replaces the per-capita quantity g in each producer's production function which becomes of the following form y=Afci-ÂŤ(3ÂŤ

(5)

In this model also productive efficiency requires again that the marginal product of public services be equal to one. The comparison of private and social returns is the same as in the first model. If the size of government was optimal but government spending was financed with a proportional tax then the privately determined growth rate will again be below the socially optimal level and a Pareto optimal situaÂ tion would be achieved by shifting to lump-siam taxes. 17

The third version of the model allows for congestion. piiblic goods are rival but non-excludable.

The

The ratio of

total government expenditure to aggregate capital investment replaces per-capita government spending and total government spending in the first two models.

It can be seen that if

private producers increase their capital input, and thus output, then this will reduce the facilities available to other producers.

With no user fee-or lump sum taxation-this

distortion leads to excessive use of the public goods and causes private returns to capital to exceed social returns. Applying a user fee-or in other words a limp sum tax-insures equalizing social and private returns and assures a Pareto optimal outcome. According to .the formulation of the above models produc足 tive government expenditure accompanied with non-distortionary taxation sustains economic growth.

Productive govern足

ment expenditure includes resources devoted to property rights enforcement as well as activities that enter directly into the production function such as education and human knowledge.

Investors view such expenditure as a reduction

in r and thus increases savings and growth rates. Barro (1990) uses the first version of these models and argues that different sizes of government have two different effects on the growth rate in output. reduces consumption growth.

An increase in r

On the other hand an increase 18

in g/y raises dy/dk which raises consumption growth.

The

first effect dominates when government is small while the second dominates when government is big in which case gov ernment expenditure,constitutes a negative externality. Using a calibrated model Barro finds out that an increase in the ratio of non-productive.government consumption expendi ture to output reduces* growth and savings rate and has no effect on private sector productivity. King and Rebelo (1990) use a simple Neo-classical growth model with endogenous growth.

Human capital accumulation is

the driving force for growth and is responsible for repro ducing physical capital. The researchers calibrated the model and showed that an increase in taxation .will reduce human capital accumulation and thus will reduce growth in the taxed sector.

The substitution effect of taxation might

mitigate the direct effect of taxation.by causing an in crease in the marginal productivity of labor.

Calibration

was used to show the effects of taxation using parameters from the U.S economy.

An increase in the income tax rate

from 20% to 30% caused a reduction in capital stock by 18.2%, a 3.6% reduction in consumption, and a decline in growth rate from 2% annually to 0.37%.

The magnitude of the

effects of taxation on growth largely depend on production technology.and the structure of the tax system. A Neo classical growth model without endogenous growth was used 19

and was calibrated.

It was found out that public policy has

a much larger quantitative effect on welfare and growth in endogenous growth models than in the simple neo-classical model. In the following section I will review the empirical results from research on the relationship between public • policy and economic growth. Empirical Results on Goverxunent and Growth

* Landau (1983) studied 104 countries on a cross sectional basis using data on government consumption and other macro measures constructed in an earlier version of the SummersHeston data set.

That measure of government expenditure

excludes public investment and transfers but includes gov ernment spending on defence and education.

He found a

significant negative-relationship between the real growth rate in GDP per capita and government expenditures as a ratio to GDP.

Barro (1990) noted that these results are

hard to interpret because Landau held a measure of invest ment in education constant. Investment in human capital is part of the economy's broadly defined investment [Jorgenson & Pachon 1983]. Since one channel for a negative effect on growth would be through reduced investment, then the inter pretation of the results is different if investment in education is held constant. Kormendi and McGuire (1985) used the same measures for 20

government intervention as the ones used above but for 47 countries.

They averaged the data for each country over a

20 year period and then carried cross-section analysis. They found an insignificant negative relationship between average growth rates of real GDP and the share of government consumption spending in GDP. The problem with these results is that single period observations of variables contain many transitory elements and may relate poorly to expected future variables which drive growth responses. Grier and Tullock (1987) extended the Kormendi-McGuire form of analysis to 115 countries, using data on government consumption and other variables from the Summers-Heston data.

They used a pooled, cross-section, time-series analy足

sis using data averaged over 5-year intervals.

They found a

significantly negative relationship between the growth rate of real GDP and government consumption as a share of the GDP.

The same criticism for averaging applies here.

Barth and Bradley (1987) found a negative relationship between the growth rate of the real GDP and the share of government consumption spending for 16 OECD countries in the period 1971-1983.

They also found that the share of govern足

ment investment in GDP had a statistically insignificant effect on growth, although the point estimate was positive. However the last estimate applies when the ratio of private investment to GDP is held constant. 21

Barro (1989) studies 98 countries in the post World-War II era.

He modified the Summers-Heston data on government

consumption.

For the period 1970-1985/ he subtracted the

ratios to GDP of government spending on defence and educa足 tion from the ratios reported by Summers and Heston. This measure for government consumption represents the non-productive government consumption that I discussed earlier. Then he used the average value for each country from 1970 to 1985 and regressed it.on the growth rate of real GDP.

found a negative, significant relationship between the two variables.

This result indicates that resources devoted to

non-productive government services is associated with lower per capita growth.

Another result that he finds is that

there is a positive insignificant relationship between public investment as ratio of GDP and real per capita growth.

The point estimate is insignificantly different

from zero which supported his hypothesis .that countries come close to the quantity of public investment that maximizes the growth rate. Barro (1991) used the same data used above and the same measure for government consumption that he used in his 1990 paper.

He found that per capita growth and the ratio of

private investment to GDP are negatively related to the ratio of government consumption expenditure to GDP.

His

interpretation of the results is that government consumption 22

introduces distortions, such as higher taxes, but does not provide an offsetting stimulus to investment and growth.

also finds, like in his previous paper, that there is a little relation between growth and the quantity of public investment. Research on the relationship between government interven tion and economic growth usually uses three measures for the size of government ii) measures of the overall size of government, (ii) disaggregated.measures.of governinent expen diture or (iii) measures of the growth rate of government expenditure. Levine and Renelt (1992) argue that using the above mea sures presents some problems.

Governments may provide

growth-promoting public goods and design taxes to close the gap between private and social costs.

On the other hand it

may waste funds, funnel resources to endeavors that do not encourage growth, and impose taxes and regulations that distort private decisions.

Thus the above measures do not

capture the potentially important implications of how gov ernment expenditures are allocated.

The existence of non

linear relationship would complicate measurement even if government consumption promotes growth.

The authors con

ducted extreme bound analysis on regression analysis that examine the relation between economic growth and government expenditure.

They tested the relationship between the 23

ratios of government capital formation, government education expenditures, and government defence expenditures to GDP. They found that none of these measures is robustly correlat足 ed with growth rates.

Central-government surplus was posi足

tively and significantly related to growth in some formula足 tions. When other macro variables were added surplus's coefficient became insignificant.

The last result was that

none of the fiscal policy measures had a robust relationship with investment.

Each of the fiscal indicators they used

was insignificantly correlated with investment in the base regressions. Barro & Lee (1993) examined 116 countries from 1965-to 1985 and addressed the issue of the effects of several government actions on economic growth. Among the many conclusions they make, concerning the economic and social factors that affect economic growth in those countries, they found that the higher the level of government intervention, the lower the rate of economic growth.

A 10 percentage

point increase in the ratio of government consumption to the GDP, for example, lowers the growth rate by 1.6 percentage points per year.

They also found that political revolutions

and going to war reduces economic growth.

Barro and lee

argue that the higher the probability of a revolution, the less stable property rights are and, therefore, the lower the incentive to invest is. 24

CHAPTER II Formulation and Estimation of Econometric Models For Panel Data In an influential monograph, Haavelmo (1944) laid the foundation for the formulation of stochastic econometric models and panel data econometrics, a topic that dominates the discipline to this day.

He wrote

...we shall find two individualSr or the same individual in two different time periods^ maybe confronted with exactly the same set of specified influencing factors [and hence^ they have the same y*r •••7/ and still the two individuals may have different quantities y, neither of which may be equal to y*. We may try to explain such discrepancies by introducing more explaining factors, x.

But, usually, we shall soon exhaust

the number of factors which could be considered common to all individuals, and which, at the same time, were not merely of negligible influence upon y. The discrepancies y-y* for each individual may depend upon a great variety of factors, these factors maybe different from one individual to another, and they may vary with time for each individual. And further that ...the class of populations we are dealing with does not consist of infinity of different individuals, it consists of 25

an infinity of possible decisions which might be taken with respect to the value of y. The work presented by Haavelmo (1944), Marschak (1950, 1951), and Balestra and Nerlove (1966) is the laid the cornerstone for panel data econometrics (PDE). This field is concerned with analyzing data observed across countries or individuals in which the niomber of cross-sectional units is relatively small and the number of time periods is (poten足 tially) relatively large. There are two kinds of PDE models. The first is the fixed effects model and the second is the random effects model. The first is appropriate when it is desired to predict individual behavior. The second is more consistent with Haavelmo's view, quoted above, that the "population" we model in econometrics consists not of an infinity of individuals, in general, but of an infinity of decisions. A PDE model offers a certain number of advantages over pure cross-section or pure time series data sets. Hsiao (1985) specifies the following four as the most important First, the number of observations is typically much larger in panel data.

This situation is likely to produce more

reliable parameter estimates and enables a researcher to test more sophisticated models which incorporate less restrictive behavioral assumptions. Second, PDE alleviate the problem of multicollinearity. 26

When the explanatory variables vary in two dimensions they are less likely to be highly correlated. Third/ panel data sets makes it possible to estimate more dynamic structures. While time series data emphasize short term behavior, panel data sets reflect long-run behavior. Finally/ use of panel data may reduce estimation bias. The introduction of individual effects/ for example/ captu!res the effects of some variables not accounted for. In this research my emphasis will be on random effects models. In the next two section I will discuss the theoretical background for the specific formulation that I will later use in this paper.

.- â&#x20AC;˘ i .

Pooling of Cross-section and.Time Series Data Generalized Least Squares (GLS)

Before embarking on explaining PDE methods it is essential that I explain the GLS method. The classical linear regression model of the following form i'=pi+p2^i2+p3^i3+

(6)

is supposed to satisfy the following assumptions E{e/) =0^ E{zjZj)=0

for all i, for all i*j

If we do not make these two assumptions and retain all the 27

other assiamptions we get the GLS model. The description of the model becomes as follows (i) ^(Cj)=0

(ii)

(i=l,2,

,n)

(i,j=l,2,

,n)

(iii) Each of the explanatory variables is nonstochastic such that for each sample size "ll;

(7)

is a finite number different from zero for every k = 2 , 3 , . . . , K (iv) The number of observations exceeds the number of variÂ ables plus one. (v) No exact linear relationship exists between any of the explanatory variables. This model is called "generalized" because it includes other models as special cases. For the case of the classical linear model we define E{ze^)=a^lâ&#x20AC;&#x17E;

(8)

8'=[8i 82

where

and where I„ is an (nxn) identity matrix. In the case of GLS equation 12 becomes E[tz') = Q

(9)

where ®11 ®12 'In 0 = ®21 ®22 • • • • ^211

(10)

In this case the estimator for the regression equation becomes P=

-^(x'Q-^y)

(11)

and the variance-covariance matrix of this estimator is ^(P-P)(P-P)'=(X/Q-=^Z)-1

(12)

This estimator is called the generalized least squares or Aitken estimator.

This estimator is used to estimate PDE

models. In this paper two PDE models will be used and all are based on GLS estimatipn.

In the following section I will

discuss these models and how to analyze PDE models using them. Pooling of Cross-section and Time-Series Data

Kmenta (1986) introduced two types of PDE models. 29

These

models are (i) A Cross-sectionally Heteroskedastic and Timewise Autoregressive Model (ii) A Cross-sectionally Correlated and Timewise Autoregressive Model. (i) A Cross-sectionally Heteroskedastic and Timewise Autoregressive Model

When dealing with pure cross-sectional data it is usually assumed

that

disturbances

heteroskedastic.

are

mutually

independent

but

While in the case of pure time-series data

it is assumed that the disturbances are autoregressive but not necessarily heteroskedastic. In the case of pooled crosssectional and time-series data these two assumptions are combined in the following manner [Kmenta 1986] (i)

= a\

iii) {iii) Ejjj. = p8_j

(heteroskedasticity) {cross-sectional independence) {autozegression)

where

8,,-j\r(0,-^), 1-Pi

Vi,j.

Note that in this model the value of the parameter p is allowed to vary from one cross-sectional unit to another. From these specifications we deduce {tis), {i*j)

=Pr®Oi

By making the appropriate substitution, we find that for this model where each of the O's is a (TxT) matrix

r. alv^

0 0

/ ^i=

(13)

pri

„r-i I

(14)

„T-i _r-2 _r-3

To find consistent estimates of the elements of (13) above we do the following steps: First, OLS is applied to all NxT observations and the resulting estimators are used to calculate the regression residuals eit •

And then these residuals are used to obtain

estimates of Pi where

or when T is small

p may exceed one in absolute value.

So, the following

estimation is used 0,=

—

(t=2,3,..., T)

(16)

The p is used to transform the observations in the following manner iit=Pl^A,l+P2-^it,2+.. • . t-l

(J)

fox t=l, fOZ t=2/3,....,T, t=l

^lt,k~^it,k~Pl^i,t-l,k t=2,3,...,T, /2 Kg i=l,2, ...,N, 1 • • t /

Next, we apply OLS to equation (I) above, for which we have NT observations. The resulting regression residuals flit can be used to estimate variances of u^t by the equation I"'

By substituting these results for Q in (13) we obtain the desired

estimates

regression 32

coefficients

and

their

variances.

Iteration of

this procedure continues

till

convergence is reached and this will lead to Maximum LikeliÂ hood estimates. The estimation procedure that will be used for this project uses the following estimation for

, 4^2^ ÂŽ i,t-1 i t

(i=l,2,..,JV; t=2,3,...,r)

This procedure assumes that the parameter value for all cross-sectional units.

(18)

has the same

Thus,- I will call this

procedure from now on the 'SAME' procedure, (ii) Cross-sectionally Correlated and Time Wise Autoregressive Model

In the above model it is assumed that the cross-sectional ufiits are mutually independent.

When this assumption is

dropped then we will have a more general model than the previous on and the specification of the behavior of the disturbances becomes as follows â&#x20AC;˘ff(8it)

{heteroskedasticity) =Ojj.

{mutual correlation)

{autoregression) 33

ffhexe

E(Ui^Uj^) =4)^^ E{Ui^Ujg)=Q {t*s) and where ®ii=_ <l>ii 1-Pi and i,j=l,2, The

and

initial value of

<l>iJ 1 - PiPj

t=l,2,

is assumed to have the following

properties

i-9i ^

1-PiPi

The matrix Q for this model is ...

®21^21 ®22^22 ••• ^2N^2N I ^N2^1t2

Where

is 34

°m^m

(19)

„r-i

Pi • • Pi

„r-2

_X-2

• Pi

„r-2 _r-3 pr Pi Pi •.

To obtain consistent elements of Q we apply lest squares to the pooled observations and calculate eit/ use the residuals to obtain

by applying equation (15) above.

Transform

variables as described in (I) and apply OLS to the transformed variables to get . fi/t The variances and covariances of Oij can then be estimated by

In this way we obtain consistent estimates of 'pi,

and

therefore, Q. The above procedure can be simplified by applying the Aitken estimation formulas (GLS) to the transformed variables. This would give the following P=

(22)

and

Asyn^totic var-cov (P)=

(23)

I will call this procedure MULSIGSQ. Strengths and Weaknesses of the Kmenta Technique

Baltagi [1992] points out that the main advantage of the method is that, like other pooled time-series & cross-section models, it gains from pooling a larger data set and more variation to explain the underlying economic relationship. The main disadvantage is that the true structure of the disturbances is unknown. Several methods have been developed to deal with this problem [Mizon 1984, Pagan 1984]. Theoret足 ically these methods generate the Kmenta method and the error components model as special caSes and thus suggests some inference tests. The problem with these methods is that they are not available in statistical computer software and that restricts their use to the theoretical level. Baltagi [1986] compared ,the Kmenta method with the error components method and found that for a large number of crosssectional units and a small time-series the error components method is more robust than the Kmenta method; while in the opposite case the Kmenta method is superior. The other problem that the Kmenta method has on the applied level is that little research on inference is done.

White

[1990] uses the usual inference techniques such as the t-test, F-test and a measure of

which is the Buse R^. 36

The avail-

ability of the Kmenta method on computer software and the availability of these inference tests with it makes it the most appealing to apply. The Buse

measures the variation in the dependent variable

for a given equation around the mean for that equation, this definition is given by R^=l-

where

(24)

&=y-X^ are the least squares residuals and Dj.=Ij,-jj'/T

, with j= (1,1,....,1)'. The matrix Dj transforms a given y^ from it's original observations into deviations around it's mean.

D j i s i d e m p o t e n t , a n d [( y ] ' ( y = y ' { y .

McElroy (1977) improved the aforementioned measure of R^ by using the GLS residuals

e=y-X^

in place of

can accommodate to multiequation systems. S'T

where

ยง

so that it

This is

(25)

S is the variance-covariance matrix.

The above measure is the one used in the software that was used for empirical research for this project.

CHAPTER III Enpirical Research Purpose

As shown in chapter one, modern theories on economic growth suggest that government policy in some areas such as defense, education, health,...,etc. might have an effect on the process of economic growth. It is the purpose of this research to see whether such a relationship exists and to check whether it is positive, as endogenous growth theory predicts, or negative. Data

I used data, covering the period 1972-1990, from 20 OECD countries, on government expenditure in the fields of defense, education, health and transportation. This data was extracted from the IMF's Government Finance Statistics and International Financial Statistics. According to endogenous growth theory these variables enter into the production function and affect output. Taxation and capital also have an effect on growth and thus data on taxation was included. The government expenditure variables represent expenditure by central government. The measure of capital that I used is gross fixed capital formation since that was the only measure available in the source that I used to extract the data. The 38

measure for taxation is the sum of taxes on Income, profits and capital gains since this the kind of taxes that directly affects production and output. A problem with cross-country data is that even after the data is transformed to a common currency, say the American dollar, we would not have a comparable measure that can give reliable results since such transformation would not take into consideration differences in the standard of living among countries; for this reason the data had to be transformed using a procedure that takes that into consideration.

This

procedure uses the theory of Purchasing Power Parity (PPP). Prices of hundreds of identically specified goods and services prevailing in each participating country are collected and processed. The price comparisons that emerge are estimates of the price parities for each country's currency at a niomber of aggregation levels, including an overall PPP.

The price

parities and PPPs are used to convert the countries' national currency expenditures to a common currency unit, thus making real quantity comparisons across countries possible. In order to convert a series reported in nominal foreign currency units to constant dollars the following steps are followed i) Deflate the series into constant foreign currency units. ii) Multiply the new series by the base year exchange rate. iii) Divide the resulting series by the base year PPP.

The

resulting series is the value of the series in American base 39

year dollars. This procedure would give comparable observations across countries.

The data used in this project was transformed

according to the same procedure. Enpirical Analysis

The main purpose of this part of the research is not to give definite policy conclusions but rather to preliminary test the nature of the relationship between some segments of government expenditure and economic growth. This field of study is vast and rich with theories as to what causes growth.

Thus the

variables included do not represent all that causes growth. The choice of the variables, analysis techniques and data sources was limited to what was available to the researcher, so the results claimed here are not definite and further research on the data set might yield different results. It is worth mentioning before reviewing the results that four of the twenty four OECD countries were omitted from the data set due to lack of information.

These countries are Portugal,

Ireland, Iceland and Greece. Two major groups of analysis were conducted.

The first

investigated the effects of specific government expenditure on economic growth in the whole OECD group, and the second investigated t];ie same relationships for the Group of Seven countries

(G7)-

United

Kingdom,

Germany, Italy, Canada and Japan. 40

United

States,

France,

The reason for this

segregation stems from the idea that the G7 countries are tied together in a stronger relationship than the whole OECD group in terms of monetary policy and trade. Since the econometric estimation techniques that I used are based on the assumptions of whether or not the cross-sectional units are interdepen足 dent, the differences or the similarities in the results obtained would be of great interest to the researcher. Within each group I conducted two types of regressions using differ足 ent transformations of the variables.

The first type dealt

with the effects of the specific government expenditures, as a percentage of GDP, on growth in GDP. The second type dealt with the effects of per capita government expenditure on growth in per capita GDP.

As pointed by K.remer (1993)

population growth plays a very crucial role in economic growth through it's effect on technological change.

Since no data

was available on technological change variables the inclusion of population, through per capita measures, might improve the explanatory power of the model. In some regressions I included the traditional variable of capital. The proxy for it was Gross Fixed Capital Formation. A measure of taxation, the sum of individual income, capital gains and profits taxes, For the purpose of this jstudy many regression equations were estimated mainly to see whether the results are consistent and robust or not.

These results will not be presented in the 41

following sections but have been included in the appendix to this paper and they will be referred to according to their numbers. The variables' definitions are included also in the appendix. OECD Grovth Regpressions

In this part I will study the OECD group. The results for this group are in tables 8â&#x20AC;&#x201D;24 in appendix B where I will refer the reader when necessary.

The definitions of the variables

are included in appendix A. Tables 8-16 are logarithmic transformations of the variables thus they can be interpreted as elasticities.

As seen, the

defense share has a negative effect on economic growth; . This result was robust in sign and significance (at levels between 10% and 0.005%).

This result contradicts Barro's

assumption that defense expenditure has a positive impact on economic growth. The negative relationship between educatione's share in GDP and GDP growth, and the statistical signifiÂ cance of these results (at the 5% and 10% levels of signifiÂ cance), was also robust throughout the spectriim of analysis. This runs also in contrast to the endogenous growth theories of economic growth which assume that such expenditure would enhance economic growth.

Expenditure on transportation and

communication showed a positive and statistically significant (at the 10% level of significance) relationship with economic growth.

The sign of this relationship was also robust 42

throughout while it's significance was mostly at the 10% level. This result is in accord with the Marshall-Young-Romer model [1961,1928,1987] model.

This model

assumes that

investment in infrastructure and communipations enhances the process of specialization in production and thus output and growth. As for health expenditure share the results were, not decisive. The sign of the relationship fluctuated and did not show any consistency.

The results were not significant

statistically throughout the spectrum. The results for capital formation and taxation did not show the same robustness as the other variables. positive significant (at the 5%

level of

For capital, a significance)

relationship with economic growth was obtained 95% of the time in all the regressions I conducted.

While the effects of

taxation fluctuated and did not show any robustness. The effect of taxation on economic growth was not decisive the sign fluctuated throughout the analysis and it had no statistical significance at all. When I studied the effect of specific government expenditure shares on GDP growth without transforming them logarithmically the results obtained were similar to those obtained from the first set of analysis.

These results are included in tables

18-24 in appendix B. Per Capita GDP Groirth Regressions 43

In the Endogenous Growth' Theory literature, researchers emphasize the relationship between growth in per capita GDP and government spending per capita rather than an aggregate measure of each.

Also as I explained earlier population

growth is thought to have a positive effect on economic growth and thus it's inclusion might improve the explanatory power of the model. Due to these assumptions I.analyzed the effects of per capita government expenditure on defense, education and transportation on growth in per capita GDP.

Again many

regressions were conducted using different formulations and different transformations of the - variables.

J chose to

display the one that yielded the minimum AIC.

The following

formulation was obtained using the MULSIGSQ procedure GRTH2 = Po+Pi PCD^F+Pj PCEDCT+pj PCTRANS where GRTh2=growth in per capita GDP defense expenditure PCEDU=per expenditure

capita

PCDEF=per capita education

government

PCTRANS=per capita government transportation

and communication expenditure. The results were as follows

t-stat

.0177

-.452E-5

-.125E-4

.26E-4

3.53

-.44

-1.3738

2.068

Buse R2=.2237

AIC=.804

SSE=299.17

F-stat=1.573

From the above table it is seen that there is also a negative relationship between growth in per capita GDP and per capita central government spending on defense and education. The coefficient for defense is not significant at any level but it is still higher than the ones obtained in other formulations. The negativity of the relationship held also in all those other formulations.

The relationship between per

capita government expenditure on education and growth in per capita GDP is significant at the 10% level of significance. A positive relationship exists also between growth in per capita GDP and transportation-communication expenditure. This result is significant at the' 1% level and was also robust in all the other formulations that were analyzed. These results are consistent with the results that were obtained in the previous section. Group of Seven (G7) Analysis

The Group of Seven (G7) constitutes the seven biggest industrial countries in the world. These seven countries are naturally members of OECD. I conducted the same analysis that I conducted in the previous section on the G7 data.

As will

be seen, the results obtained by regressing specific govern足 ment expenditure shares on growth in GDP were mostly consis足 tent with the results obtained for OECD except for taxation. On the other hand the results for per capita growth in GDP 45

were consistent with the results obtained for OECD. In the following two sections I will present these results. G7 GDP Groirth Regressions

The results of these regressions are shown in tables 1-8 in appendix B.

As can be seen from the tables defense expendi足

ture still maintains a significant negative relationship with growth in GDP in spite of the significant positive relation足 ship in table-4 the significant negative relationship persist足 ed throughout the spectrum of analysis at levels of statisti足 cal significance between .025% and 10%. As for the relation between education expenditure share and growth in GDP it can be seen from tables 3,4 and 5 the relationship is a negative and significant one (at levels of significance between 10% and 0.025%). The relationship between communication and transportation shares and growth in GDP was positive and significant (at the .005% level) throughout all the analysis. The effect of gross fixed capital formation on GDP growth showed equivalent robustness and was positive and significant at the .005% level. The results for health was similar to the results obtained for the OECD group.

The sign fluctuated considerably and it

was not significant at any level in all the analysis that I carried out.

The result in table-5 is a representative for

the results obtained from other formations. 46

The unconventional result came when analyzing the effect of taxation on growth in GDP.

As seen in tables 3 and 5 in

appendix A, taxation has a positive effect on growth in GDP and the relation is significant at the 10%.and 5% levels of significance.

This result is counter intuitive to what one

might expect.

In spite of that it suggests a strong income

effect. An increase in taxation of capital gains, individual income, and profits might be leading individuals to supply more labor and thus enhancing growth in output.

A study of

the tax structure in the G7 countries might also prove to be useful in finding the cause of this positive relationship. This result has also been suggested as a possibility in endogenous growth literature. King and Rebelo (1990) suggest that the income effect might dominate and mitigate the negative effect of taxation.

Similar implications can be

found in Chamley (1993) who argues that a sudden removal of capital income taxation might lower welfare.

Jones, Rodolfo

and Rossi (1993) also argue using calibrated models that at some phases of growth taxation might have a positive or no effect in consumption growth. Per Capita GDP Regressions The model that I will use here is of the form GRTH2 = po+pi PCDEF+^2 i'CEDU'+Pa PCTRANS+^^ PCCPTL The SAME procedure was used to obtain the above model and 47

the results were as follows P.

-.41E-1

.167E-4

-.786E-4

.197E-3

-1.5

.6958

-2.423

2.551

t-stat

SSE=97.573

.98E-5

AIC=.791

Buse R^=.1524

1.1747

F-stat=3.673

As seen in the above table, education and transportation expenditure still hold the same negative relationship with per capita GDP growth. level.

These results are significant, at the 1%

Per capita gross fixed capital formation has a

positive relationship with per capita GDP growth and the result is significant at the 25% level. The result that was- contrary 'to the results obtained previously was the relationship between per capita GDP growth and per capita defense expenditure for the G7.

As obvious

from the above table the relationship is positive and is significant at the 25% level.

This result-persisted in the

different formulations I conducted in almost every case. This result agrees with the assumption by Barro (1990).

Defense

expenditure per capita assures the investors of the safety and stability in a country and thus enhances investment.

Summary and Conclusions Barro (1990) assumes that government expenditure on educa足 tion and defense, in the presence of non-distortionary taxes, stimulates and encourages economic growth.

This assumption

encouraged further investigation of the topic by the author; that led him to the study of a class of economic growth models that are called in literature "Endogenous Growth Models". These are based on the possibility that increasing returns to scale in production might exist making it easy for production to expand in proportions that are greater than the proportions of inputs used. It is argued that this is possible due to the existence of externalities in production. These models along with their assumptions were discussed in detail in chapter one. These models are used by some scholars to justify certain public policies that economic growth.

would, according to them,

enhance

It is argued by the proponents of these

models that spending on programs that encourage human capital acciamulation, improve infrastructure and protect rights of individuals would encourage economic growth, again in the presence of non-distortionary taxes (namely lump-sum taxes). The above models provoked the author to investigate whether public policy of that kind would produce the results antici足 pated by theoreticians; and though somebody might argue that theory is always right, the author's belief, that governments can never fair in a manner that would bring about general 49

good, excited him to empirically investigate the effect of government spending and taxation on the process of economic growth. As shown in chapter one, most of the research done in this field is theoretical and rarely deals with the effects of specific government expenditures on economic growth, and where reference is made to specifics it is mentioned in the form of assumptions taken for granted.

In such models usually the

effects of general government spending-are the ones that are studied.

Empirical research in the field, though abundant,

also ignores the effects of specific government expenditures on economic growth.

This project is a modest try to compen足

sate for this lacking. In this paper I investigated the effects of central govern足 ment defense, education, health, and transportation expendi足 ture on economic growth represented by growth in the Gross Domestic Product (GDP).

In some of the formulations that I

studied I also added variables representing taxation and physical capital.

The sample consisted of 20 of the OECD

countries, the other four were omitted due to the lack of sufficient data. The period covered was 1972-1991. The data was transformed into real^ constant American dollars using the Purchasing Power Parity method which makes the resulting data comparable to that of the United States.

The size of the

data set for each individual country is small and thus if 50

individual country regressions were conducted it would not have produced reliable results. The data on specific govern足 ment expenditures is only available for the.years 1972-1991. For this reason cross-sectional .time-series techniques were used. By pooling the data from individual countries together a larger data set is generated and more reliable results could be obtained. Two sets of analysis were conducted.

The first set dealt

with all 20 countries of the sample together, and the other set dealt with the G7 countries. ' Within e.ach set, the variables were transformed in two different ways. The effect of per capita government expenditures on growth in per capita GDP was examined and then the effect of the share of govern足 ment expenditures in GDP was also examined. For the OECD group defense and education expenditures shares in GDP in all cases were negatively related to economic growth and in almost all cases was also statistically .significant. Transportation and communication expenditures shares in GDP showed a positive relationship with economic growth in all cases while it was significant also in almost all cases. Health expenditure share, and though it showed a consistently negative relationship with growth in GDP, was never statisti足 cally significant. The effect of taxation's share in GDP does not show consistency, in terms of it's sign, for the OECD countries. It fluctuates between negative and positive though 51

the negativity shows up more than the positivity.

At last

capital shows consistently a positive and statistically significant positive relationship.

This is consistent with

the traditional and the modern theories of growth. As for per capita regressions they did not differ significantly from those I have just discussed. The results acquired for the G7 countries were similar for government expenditures though the degrees of statistical significance were lower for the education, and health vari足 ables.

On the other hand the negative relationship between

defense and income growth strengthened. The surprise came in the taxation variable.

For this group taxation (individual

and corporate) showed a positive relationship with economic growth; and though negative relationships showed in some regressions the positive relation showed a more frequent and stronger presence suggesting a strong income effect. This paper is the first of .it's kind in terms of the variables studied and the econometric methodology. It is the belief of the author that much more work needs to be done to further this project by increasing the sample size, by using quarterly data, and by using more variables; this can be achieved by

examining the

effects of sub-categories of

specific government expenditure on growth in GDP.

The

econometric literature is full of econometric techniques that can be used also, the only hurdle is the lack of computer 52

software that apply those techniques. The researcher started with a set of questions to answer about the subject of economic growth.

During the course of

this research most of those questions were answered but at the same time he was presented with a whole set of questions that he must answer which will be the subject of many future projects.

APPENDIX A

Vari2d>les' Definition List

GRTHl: Growth in real GDP (1985 prices) GRTH2: Growth in per capita income. DEF: Defense expenditure PDEF= DEF/GDP

LPDEF=LOG(PDEF)

PCDEF: per capita defense expenditure EDU: Education Expenditure

PEDU:EDU/GDP

LPEDU=log(PEDU)

PCEDU= per capita education-expenditure TRANS: Transportation Expenditure

PTRANS: TRANS/GDP

LPTRANS=Log(PTRANS) PCTRANS=Per

capita

transportation

expenditure. HLTH: Health Expenditure PHLTH: HLTH/GDP

LPHLTH=Log(PHLTH)

PCHLTH=per capita health TAX=Tax on capital gains, profits and individual income. PTAX=TAX/GDP

LPTAX=Log (PTAX)

CPTL=Gross fixed capital formation. PCCPTL=per capita gross fixed capital formation. PCPTL=CPTL/GDP LPCPTL=Log (PCPTL).

APPENDIX B Table-1

£?i?ri/l=Po+Pi

LPED^+pj LPTRANS

SAME •*

t-stat

BR2=.1649

.141

.598E-2

-.597E-2

.2968E-1

1.837

.62657

-1.128

3.0769

AIC=.835

F-stat=3.607

Table-2

GJ?THl=Po+Pi LPDEF+^2 LPEDU+^^ LPCPTL SAME

t-stat BR^=.18b6

.10495

-.643E-2

.525E-2

.613E-1

-1.25

.5701

3.34

1.61 • AIC=.b37

F-stat=4.2

Table-3

GRTffl=Po+Pi LPDEF+^2 i-P.EDCT'+Pa LPTAX

MULSI6SQ

t-stat

-.286E-1

-.167E-1

-.714E-2

.1768E-1

-.744

-2.164

-1.312

1.4735

6R^=.385

AIC=.793

F-stat=1.72

TeQ)le-4

PDEF+^2 PEDU+fi3 PCPTL SAME

t-stat

-.06

.413

-.54

.36

-2.2967

1.817

-1.33

3.565

AIC=.837

F-stat=4.264

Table-5

(?i?2Wl=P(,+pi PDEF+^2 PEDU+^^ PTRANS+^^ PHLTH+^^ PTAX+^^ PCPTL

SAME

t-stat

-.643

.1426

-.876

1.2257

-.5

.255

.248

-2.550

.35

-2.31

1.4768

-.25

1.6917

2.125

r)r)/_.

t!L A

Table-6

GKr/fI=Po+Pj^ PDEF+^2 PEDU+^^ PTRANS MULSI6SQ

t-stat

BR2=.34

.031

-.23

.122

-.72

1.6103

-.752

.294

-.94E-1

AIC=.84

F-stat=.98

Table-7

(?i?rHJL=Po+Pi PDEF+^2 P-EDU+Pa PTRANS SAME

BR2=.1424

2.603

-1.152

.767

-.625

t-stat

2.007

.27

•

-.125

AIC-.80-

F-stat=2.3

T2d>le-8

C?i?3!firi=Po+Pi LPDEF+Pz LPEDU+^2 LPTRANS+P^ LPHLTH+^z LPTAX+^^

SAME

/3i

t-stat BR"=.394

.012

-.9E-2

-.4E-2

.24E-2

.42E-3

.5E-2

.013

.95

-2.4

-1.775

.6038

-.2118

1.244

1.736

F-stat=l.932

AIC=.64

Table-9

MULSI6SQ Pi

t-stat

-.55

-.7E-2

-.4E-2

.584

-.5E-3

-.152

.904

.425

-2.244

-1.39

.165

-.287

-.467

1.368

AIC=.65

F-stat=2.361

Table-10

(SRrill=Pq + P^ LPDEF+^2 LPEDU+^^ lptrans+^^ LPHLTH MULSIGSQ Pi

t-stat

-.407

-.73E-2

-.42E-2

.43

-.lE-3

-.347

-2.62

-1.82

1.387

-.0736

BR2=.5434

AIC=.754

F-st£it=2.985

Table-11

SAME

t-stat

.154

-.76E-2

-.287E-2

.466E-2

.24E-3

.134

-2.3

-1.27

1.378

.12027

BR2=.4024

AIC=.742

F-stat=1.903

Table-12

GRra'I=po+Pi LPDEF+^^ LPEDU+Pg LPTA^+p^ LPCPTL

MULSIGSQ

-.55E-2

-.72E-2

-.31E-2

-.lE-2

.89E-2

-.45

-3.002

-1.558

-.3154

1.55

t-stat

BR'=.56

AIC=.752

F-stat=3.62

Table-13

C?i2IHl=Po+Pi LPDEF+^2 LPEDU+^j LPHLTH MULSIGSQ

t-stat

-.117

-.72E-2

-.21E-2

.103

-1.0601

-2.57

-1.24

.061

Table-14

(?i?rHl=Po+ Pi LPDEF+P2 LPEDU*^^ LPCPTL SAME

t-stat

.404E-2

-.696

-.22E-2

.0114

.3352

-2.44

-1.2

1.887

Table-15

MULSIGSQ

t-stat

BR2=.498

-.512E-2

-.74E-2

-.33E-2

.84E-2

-.451

-3.1

-1.783

1.5157

AIC=.806

F-Stat=4.4

Table-16

C?J?RIFI=PO+PI LPDEF+^2 LPEDU+^3 LPTRANS MULSIGSQ

t-stat

BR2=.55

-.46E-2

-.7-51E-2

-.42E-2

.423E-2

-.43

-3.136

-1.8217

1.43

AIC=.805

F-stat=4.066 63

Table-17

(?J?RIFI=PO+PI LPDEF+^2 LPJSDU+PJ LPTRANS SAME

t-stat

BR2=.404

.125E-2

-.745E-2

-.287E-2

.467E-E2

.10912 -

-2.5175

-1.2858

1.454

AIC=.79

F-stat=2.529

Table-18

(?i?rifl=Po+P^ PDEF+P^ PEDU+^^ PTRANS+^4^ PHLSTf+Pg PTAX+^^ PCPTL

SAME Pi

.013

-.2

-.112

1.4063

-1.261

-.901

BR"==.335

AIC=.632

.3E-1

-.2E-2

.32E-1

.058

.186

-.025

.6.58

F-stat=1.07

•

t-stat

CO OJ

Table-19

GKTfri=Po+Pi PDjEF+Pa PEDU+^^ PTRANS+[i^ PHLTH

MDLSIGSQ

t-stat

.346

-.322

-.255

.173 •

6.41

-2.526

-2.408

1.45

AIC=.755

BR"=.553

.74E-2 .09

F-stat=2.6y3

Table-20 SAME

t-stat

.03

-.26

-.1162

.1426

.05

4.644

-1.678

-1.082

1.0188

.535

11 iQPP

.388

AIC=.748

F-stat=.968

Table-21

GR7WI=Po+P^ PDEF+^2 PEDU+^j PTRANS MULSIGSQ P째

.0344

-.314

-.244

.168

6-5

-2.675

-2.335

1.42

Table-22 SAME

t-stat

.0272

-.23

-.11

^15

4.9

-1.589

-1.0338

1.0632

Aic=.Vy9

f-stat=1.184

Table-23

£3RrJfl=Po+Pi PDEF+^2 -P-EDZJ+Pa PCPTL. . MULSIGSQ

t-stat BR^=.378

.0287

-.28

-.1684

.03

3.235

-2.1131

-1.88

1.0279

F-stat=3.014

AIC=.8U4

Table-24

•

SAME

t-stat BR'=.33

.0273

-.182

-.064

.053

4.88

-1.26

-.72

1.935

F-stat=l.917

AIC=.7«3

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An Empirical Examination of Endogenous Growth Models Jabra F Ghneim Economics Department

M.S Degree, December 1993

ABSTRACT

Examining the data for 20 OECD countries, for the- period 1972-1991 it was found that central government expenditure on defense and education had a significant negative relationship with growth in GDP. Health expenditure had a negative insignificant relationship with GDP growth. The relationship between taxation and GDP growth fluctuated and did not show any statistical significance. Capital formation ^ and expenditure on transportation had a significant positive relationship with GDP growth. The results for the G7 countries were similar to that of the OECD countries except for taxation where a positive significant relationship showed up indicating a strong income effect.

COMMITTEE APPROVAL:

David E. ^Spencer, Committee Chair

Val E. Lambson, Committee member

Val E. Lambson, Graduate Coordinator