Scottish Journal of Political Economy, Vol. 58, No. 3, July 2011 r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society. Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA, 02148, USA
RICH STATES, POOR STATES: CONVERGENCE AND POLARISATION IN INDIA Sanghamitra Bandyopadhyayn
Abstract
The distribution dynamics of incomes across Indian states are examined using the entire income distribution. Unlike standard regression approaches this approach allows us to identify specific distributional characteristics such as polarisation and stratification. The period between 1965 and 1997 exhibits the formation of two convergence clubs: one at 50% and another at 125% of the national average income. Income disparities across the states declined over the 1960s and then increased from the 1970s to the nineties. Conditioning exercises reveal that the observed polarisation is associated with the disparate distribution of infrastructure. In particular, education, the extent of irrigation and literacy are found to be associated with the formation of the lower convergence club.
I
Introduction
This paper documents the dynamics of income across Indian states over three decades (1965–1997), and provides some explanations of the observed income dynamics. Over the last decades, India’s population has exploded by almost threefold, and its GDP has increased almost 30–fold.1 This has been accompanied by a highly unequal process of growth and development across Indian states. While the richest states in India (e.g., Gujarat and Maharashtra) parallel middle-income countries such as Brazil and Poland in their levels of development, the states of Bihar and Orissa perform well below many SubSaharan African countries in economic growth and human development statistics. Understanding India’s disturbingly lopsided development process therefore remains crucial to both academics and policy makers. In the recent empirical growth literature on the convergence of GDPs across regions and countries, it has been popular to use the ‘growth regression’ approach (Barro and Sala-i-Martin, 1992). In this paper, however, I observe the distributional dynamics rather than just beta or sigma convergence. This method University of Birmingham 1 World Development Indicators, World Bank, estimates of GDP at current prices in US dollars. India’s GDP in 2010 is over 1.12 trillion US dollars, and is ranked the 11th richest country in the world.
n
414
R I C H S T AT E S , PO O R S T A T E S
415
involves examining the evolution of the state-level income distribution over time. Such an approach is necessary in understanding the empirics of catch-up more accurately but also in identifying the nature of the underlying distributional dynamics, namely whether there are long-run cohesive tendencies, polarisation, stratification or the emergence of convergence clubs. I then provide some explanations of the observed dynamics: several infrastructural indicators are found to be significantly associated with the evolution of the income distribution and the formation of convergence clubs. Some simple statistics reveal the wide disparities in growth across Indian states, for instance, Punjab’s income has been at least twice that of Bihar’s, Orissa’s and Rajasthan’s since 1965. Some states have doubled their incomes (real GDP per capita) between the mid-1960s and the 1990s, while the poorest states have remained well below the national average income. The analysis in the paper reveals the existence of two convergence clubs: while in the late 1960s there were some tendencies of cohesion, from the 1970s to the 1990s incomes have persistently become polarised. Finally, I identify some auxiliary factors which explain the observed dynamics. The paper focuses in particular on the role of a set of economic and social infrastructural indicators in explaining the observed polarisation. The results suggest that some infrastructural indicators, namely that of literacy (and education in general) and the extent of irrigated land robustly explain the formation of the lower convergence club. Of course, a large literature already studies unequal growth across Indian states. Studies which use the popular cross-section regression approach, namely Bajpai and Sachs (1996), Cashin and Sahay (1996), Nagaraj and Venganzones (1997), Aiyar (2001) and Trivedi (2003), emphasise diverging distributional characteristics but are unable to describe intra-distributional mobility. Convergence as an empirical concept, as defined by Solow (1956), is understood as a single economy approaching its theoretically derived steady state growth path. Standard empirical analyses only study the behaviour of the single (representative) economy. While such an empirical methodology can accurately uncover tendencies of divergence, it does not uncover the distributional patterns (of polarisation or stratification) that I wish to expose. Similarly, time series approaches as used by Carlino and Mills (1993) that estimate the univariate dynamics of income also remain incomplete in describing the dynamics of the entire cross-section. While a large literature in both Macroeconomics and Political Economy has discussed what drives such income disparities (see Durlauf and Quah 1999 for an overview), only recently have studies come to recognise the non-linear impact of the many drivers of economic growth. Kalaitzidakis and Mamuneas (2001), for instance, highlights the non-linear impact of education on economic growth. Standard empirical tools of panel or cross-section regression are not fashioned to explain the formation of convergence clubs at different parts of the income distribution.2 Theoretical contributions of (De Long, 1988; Galor and Zeira, 2 Standard methods of cross section and panel regression analyses have also been criticised for the conflicting and therefore misleading results the regression approach can result in. Quah
Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
416
S . B AN D Y O P AD H Y A Y
1993; Ben-David, 1994; Estaban and Ray, 1994; Durlauf and Johnson, 1995; Bernaud and Durlauf, 1996) allow for explicit patterns of cross-economy interaction, whereby economies cluster together into groups to emerge endogenously. They recognise that economies do not evolve in isolation, but in clubs and groups, and such distributional characteristics remain unexposed under standard empirical techniques for studying convergence. The analysis in this paper adopts this approach empirically. Bianchi (1995), Jones (1997), Desdoigts (1994), Fiaschi and Lavezzi (2003) and Grazia-Pittau, Zelli and Johnson (2010) study the evolution of the entire distribution over time using various non-parametric methods. In this paper, I use the distribution dynamics approach as presented in Quah (1997). It encompasses both time series and cross-section properties of the data simultaneously and presents itself as an ideal approach for large data sets. The intra-distribution dynamics information is encoded in a transition probability matrix, and the ergodic distribution associated with this matrix describes the long-term behaviour of the income distribution. I find evidence of two convergence clubs, namely a low income (poor) club of states and a high income club of states. There is also little evidence of mobility of states between the two clubs. This method can also be extended to identify factors governing the formation of these convergence clubs. Identification of some explanatory factors comprises a major part of the paper where I focus on the non-linear effects of infrastructural factors on the distribution dynamics. The findings reveal several infrastructural factors, such as the percentage of land irrigated and levels of education, among many others, that explain the formation of the poor convergence club. The rest of the paper is organised as follows. Section II discusses some simple dynamics and introduces the distribution dynamics approach. Section III describes the observed distribution dynamics and polarisation, and section IV presents a number of explanatory factors which are associated with the observed distribution dynamics. Section V presents a brief discussion of the results and section VI concludes.
II
Some Simple Dynamics
Let us take a cursory look at some basic statistics on growth in India. GDP per capita and price data used for this paper has been obtained from O¨zler et al. (1996). GDP per capita data for 1989 to 1998 has also been obtained from the World Bank, compiled as a separate dataset, and from Government of India sources. Figure 1 highlights the states as ‘rich’ or ‘poor’ in 1965 and 1995. It is clear that there has been a lot of persistence for both the rich and poor states. Some rich states have remained rich, and some initially poor have remained poor. In the 1995 figure, we can see that there are now two new rich states, while one of the earlier rich states (West Bengal) is no longer rich. Clearly some upward (1993) shows that it is clearly possible to obtain beta convergence using the regression approach with a diverging income distribution over time – i.e. without sigma convergence. Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
417
R I C H S T AT E S , PO O R S T A T E S
1965
1995
Indian States: Rich ( ), Poor ( ) Figure 1. Legend for states: AP, Andhra Pradesh; AS, Assam; BR, Bihar; GJ, Gujarat; HP, Himachal Pradesh; J&K, Jammu and Kashmir; KR, Karnataka; MH, Maharashtra; MP, Madhya Pradesh; OR, Orissa; PB, Punjab; RJ, Rajasthan; TN, Tamil Nadu; UP, Uttar Pradesh; WB, West Bengal.
mobility has taken place. Let us take a look at some simple statistics of these states. The richest state, Punjab, already had a per capita income of 270 (in 1990 dollars for international comparability) in 1965 and 370 in 1988, reflecting an increase of 34% over the period, followed by another 21% rise by 1997. Gujarat’s and Maharashtra’s per capita income increased from 183 and 196 (in 1990 dollars) to 233 and 303, respectively (or a rise of 20% and 27%), and by another staggering 40% and 51% by 1997, respectively. By comparison, the Indian average per capita GDP (in 1990 dollars) was 153 in 1965 and 195 in 1988 (an increase of 27%), and increased by another 33% by 1997. Thus, Punjab was already almost twice as rich as the Indian average in 1965 and remained so at the end of the period. Maharashtra, Gujarat and Haryana’s income per capita also maintained a per capita income of almost twice the Indian average all throughout the period. On average, Punjab, Haryana, Gujarat and Maharashtra were at 123% of the national average in 1965 and over 152% in 1988, and grew another 36% as a group from 1988 to 1997. The poorest regions are also evident: Bihar, Orissa in the east, Rajasthan in the west, and Uttar Pradesh in the north have consistently had some of the lowest per capita GDPs. Bihar, Orissa and Uttar Pradesh and Rajasthan had GDPs per capita at 85% in 1965 and 80% in 1988 of the Indian average, respectively, and by 1997 grew only another 19% as a group. Bihar and Orissa had GDPs per capita of 122 and 121 in 1965 and 122 and 145 in 1988 (in 1990 dollars). Thus, over the entire period of study, the income of the richer states has been almost three times that of the poor states. Interestingly, while the growth Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
418
S . B AN D Y O P AD H Y A Y
rates of Madhya Pradesh, Assam, Andhra Pradesh, Uttar Pradesh, Orissa, and Bihar, the six poorest states, were all significantly below the national growth rate, they account for more than half of the Indian population. However, not all states that were rich or poor remained so. West Bengal, notably, with a GDP per capita of 196 in 1965 and 205 (in 1990 dollars) in 1988, fell steeply in its ranking from second to eighth by 1988. West Bengal was a high growth state along with Punjab, Haryana and Maharashtra in the 1960s but experienced dismal growth over the following years. Again, while the surge of growth in the 1980s benefited the four richest states, it also pushed up Karnataka and Tamil Nadu, whose 1988 per capita income increased by 21% and 36% between 1980 and 1988, respectively, and by a further 45% for each state by 1997. Analysing the same details reveals that between 1965 and 1997 the standard deviation (SD) of per capita income increased by 192%, while the inter-quartile range (IQR) increased by 137%. A significant increase in spread manifests itself clearly, in that the SD is about double that of the IQR. The changes, however, have an interesting implication. With the IQR accounting for the middle 50% of the distribution, the fact that the SD exceeds it by such a large amount can only be attributed to some high performers outperforming the rest of the intermediate and poor states. To summarise these back-of-the-envelope calculations of the dynamic spatial patterns of Indian regional growth: It reveals both persistence and mobility. While some rich states have remained rich, and the poor have remained poor, there have been some instances of high performers who have declined in their performance over the period, such as West Bengal, while others have picked up over the period, for example Karnataka and Tamil Nadu. Thus, apart from those consistent performers, there is plenty of evidence of relative success and failure all across India. III
The Distribution Dynamics
So far I have only taken a look at several snap-shots of how different Indian states have grown or fallen behind over time. For a more informative picture, I will now track the evolution of the entire income distribution over time; this will reveal the intra-distributional dynamics of GDP growth of the Indian states over the given period of time. Markov chains are used to approximate and estimate the laws of motion of the evolving distribution.3 The intra-distribution dynamics information is then encoded in a transition probability matrix. 3 The distribution dynamics approach (Quah, 1997) is based on treating a single income distribution as a random element in a field of income distributions, called the random field. The density function of the income distribution is estimated at each point in time and is then observed how it evolves over time. The primary tool used to track the evolution of the income distribution is the transition probability matrix, which will record the probabilities of persistence and mobility across the income distribution. Both stochastic kernels and transition
Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
R I C H S T AT E S , PO O R S T A T E S
419
To set up the transition probability matrix, the income distribution is divided into a number of ‘income states’; each spatial unit (i.e., Indian state) is then located within this income space. For example, in the lowest income state the poorest Indian states are included; in the highest income state the richest of the Indian states are included. The transition probability matrix then describes the probabilities with which the Indian states would transit from one income state to another. If the probability of transition from one income state to another is non-zero, then one deduces mobility. If these probabilities are small, or almost zero, one deduces persistence. There are, however, some drawbacks to the discretised approach. The most significant drawback is that the selection of income states is arbitrary. Such arbitrary sets of discretisations may lead to different results. The stochastic kernel improves on the transition probability matrix by allowing the space of income values to be a continuum of states.4 Using the stochastic kernel removes the arbitrariness in the discretisation of the states. One now has an infinite number of rows and columns replacing the transition probability matrix and observes a probability mass (the sloping surface) recording the probabilities of persistence and mobility.5 One can interpret the stochastic kernels as follows. Figure 2 presents two benchmark stochastic kernel contours. The vertical axis measures the time t income distribution, and the horizontal axis measures the time t1k income distribution. If the probability mass runs along the diagonal, as in the first panel in Figure 2 it indicates persistence in the Indian states’ relative positions and therefore exhibits low tendencies of mobility. Convergence is indicated when the probability mass runs parallel to the t axis in the second panel of Figure 2. If the probability mass were to run along the negative slope, it would imply overtaking of the economies in their rankings (not in figure). If the probability mass runs parallel to the t1k axis, it indicates that the probability of being in any income state at period t1k is independent of their position in period t; this, then, is evidence of low persistence (not in figure).
matrices provide an estimate of intra-distribution mobility taking place. In both cases, it is assumed that an economy (in our case, an Indian state) over a given time period (say, 1 year or 5 years) either remains in the same position, or changes its position in the income distribution. Such a change in position of an economy in the income distribution is called a transition. The transition probabilities are then encoded in the transition probability matrix for transitions over different sets of intervals in the income distribution. Low probabilities of transition indicate persistence, while higher probabilities indicate mobility. 4 Such refinement goes beyond the generalisation as well. It is well known that discretisation may remove the Markov property from an otherwise well-behaved Markov process, see Chung (1960). For further refinements proposed in discretising a continuous state-space Markov chain in the distribution dynamics context, see Bulli (2001). 5 There are further problems with the discretised approach. As these estimates are based on time stationary transition matrices, they are not reliable for long time periods for economic structural changes. I am also constrained by the small number of states with the Indian example, there by making it difficult to make inferential statements by bootstrapped P-values associated with the probabilities. For further methods highlighting how more information may be obtained from such transition matrices, see Fiaschi and Lavezzi (2003). Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
420
S . B AN D Y O P AD H Y A Y
Stoch. Kernel Contour(s)
2.0
2.0
1.5
1.5
India-Relative
India-Relative
Stoch. Kernel Contour(s)
1.0
0.5
1.0
0.5
0.5
1.0 1.5 Group-Relative
2.0
0.5
1.0 1.5 Group-Relative
2.0
Figure 2. Benchmark stochastic kernel contours: persistence and convergence.
Data on real per capita income has been obtained from O¨zler et al. (1996) and the World Bank. Figures 3–6 present the stochastic kernels for per capita income (relative to national average) of 1-year transitions for four sub-periods 1965–1970, 1971–1980, 1981–1988, and 1990–1997. In Figure 3, we observe the stochastic kernel for the period 1965–1970. There is evidence of two convergence clubs, namely, the two peaks observed. Interestingly, as is clearly revealed in the contour plot, the two clubs are aligned parallel to the original axis (vertical axis). This indicates some tendencies of convergence. The following years, however, provide increasing evidence of persistence and low probabilities of mobility. Over the periods 1965–1970, 1971– 1980, 1981–1988, 1990–1997 in Figures 3–6 one can see that the probability mass lengthens and shifts in line with the positive diagonal, and with the two peaks at the two ends of the probability mass. The cluster of states at the two peaks consist of low income economies at around 50% of the all India average and another at 125% of the average. Thus, the sub-sample periods, particularly during the later years, have shown cohesive forces substantially dissipating in influence. The result is that the rich states have forged ahead, while the poor have made little progress alongside a dispersing middle income group. For robustness, I estimate stochastic kernels over the different sub-periods and over 5 and 10 year periods. The results obtained (not presented for brevity and obtainable from the author) suggest the same results as those above: the pressing facts revealed are that of convergence over the late 1960s, with increasing divergence over the 1970s, 1980s and 1990s. To summarise: Two convergence clubs are observed – a poor income club and a rich income club. Over the period 1965–1970 some tendencies of convergence is obtained. Over the period of the 1970s to the 1990s, I obtain evidence of persistence, and increasing divergence, with evidence of intra-distributional mobility over the late 1960s. Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
421
6
1.5
4
6
2
4
0 1.5
2
Period t
Stochastic Kernel
R I C H S T AT E S , PO O R S T A T E S
1.0
0.5 0
d rio Pe
1.0
1.5
t
1.0 1 0.5 d t+ io r e P
0.5
1.0 1.5 Period t +1
8
1.5
6
8
4
6
2
4
0
2 1.5 Pe 1.0 rio d t
Period t
Stochastic Kernel
Figure 3. Relative income dynamics across Indian states, 1 year horizon, 1965–1970.
1.0
0.5
0 0.5
1.5 1.0 +1 t d o Peri
0.5
1.0 1.5 Period t +1
Figure 4. Relative income dynamics across Indian states, 1 year horizon, 1971–1980.
The stochastic kernels provide evidence of the formation of convergence clubs at two different points of the distribution – one at 50% of the national average, another at 125% of the national average. The evolution of these kernels over the three decades suggests that disparities have been widening. With the sample size very small, robustness statistics (such as bootstrapped standard errors for the probabilities) are statistically irrelevant here. Interestingly the composition of the two clubs (high and low income) does not drastically differ over the time periods. The Indian states which compose the lower income club (at 50% of the national average) are Assam, Bihar, Jammu and Kashmir, Orissa, Madhya Pradesh, Rajasthan, UP for all four periods. In the 1960s to 1980s Kerala was also part of the low income club. The high income club of states has varied slightly over the four decades: Delhi, Punjab, Haryana, Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
S . B AN D Y O P AD H Y A Y
6
1.5
4
6
2
4
0
2
1.5 Pe rio 1.0 d t
Period t
Stochastic Kernel
422
0.5
0 0.5
1.0
1.5 1.0 1 t d + Perio
0.5
1.0 Period t +1
1.5
15 10
15
5
10
0
5 0.6 Pe rio 0.4 d t
0 0.2
0.4 od Peri
0.6 Period t
Stochastic Kernel
Figure 5. Relative income dynamics across Indian states, 1 year horizon, 1981–1989.
0.4
0.2
0.6 t +1 0.2
0.4 0.6 Period t +1
Figure 6. Relative income dynamics across Indian states, 1 year horizon, 1990–1997.
Gujarat and Maharashtra have dominated the top five ranks for all four decades examined. West Bengal, while a member of the high income club previously, dropped out of it in the mid-1970s. In the 1990s, Andhra Pradesh and Tamil Nadu joined the high income group. Clearly, the evidence obtained is in confirmation of the simple statistics discussed in section II. These results confirm the findings in Trivedi (2003) which also highlight the formation of clubs with kernel density estimates of the Indian state income distribution between 1960 and 1992. The stochastic kernels improve over these estimates by providing the intra-distribution dynamics of how these clubs evolve over time. IV
Explanations of Polarised Economic Growth Across Indian States ^ Infrastructural Di¡erences
Differential growth and development across regions is very often attributed to different levels of infrastructural development. While the choice of a particular Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
R I C H S T AT E S , PO O R S T A T E S
423
kind of infrastructure addressed in the paper can be considered ad hoc in choice, the role of infrastructure remains important, particularly for developing economies. The growth-equipment investment nexus is particularly strong in LDCs, and is attributed to the high returns to equipment investment in LDCs. Similar relationships have also been found between human and social infrastructure, literacy, health and various organisational practises. Theoretical studies by Stokey (1991) and Galor and Zeira (1993) demonstrate a positive relationship between human capital accumulation and economic growth. Empirical studies by Barro and Lee (2010) and Benhabib and Spiegel (1994) also evince that there exists a strong association between educational attainment and economic growth. King and Levine (1992) and Benhabib and Spiegel (2000) highlight the positive association between finance and economic growth, and for India in particular Burgess and Pande (2005) also find evidence of rural credit expansion in having increased Indian income per capita and reduced poverty between the 1960s and the 1990s. Rud (2008) discusses the role of electrification in advancing industrial development across Indian states. Recent studies have already sought to identify such non-linear relationships using non-parametric methods (e.g. Kalaitzidakis and Mamuneas, 2001; Fiaschi and Lavezzi, 2003). The distribution dynamics method is an appropriate method to explore non-linear relationships. The conditioning methodology in the distribution dynamics approach is similar to that of traditional panel or crosssection regression approaches. While with standard methods of panel regression one compares E(Y) and EðYjXÞ to deduce conditional convergence, the distribution dynamics approach compares the entire distributions of Y to YjX. When no change in the conditioned and unconditioned distributions is observed, one concludes that the conditioning variable does not explain the distribution dynamics. Quah (1997) shows that just as stochastic kernels can provide information about how distributions evolve over time, they can also describe how a set of conditioning factors alter the mapping between any two distributions. Hence, in order to understand if a hypothesised set of factors explains a given distribution one can estimate a stochastic kernel mapping the unconditioned distribution to the conditioned one. If one then obtains convergence, one deduces conditional convergence. In the next section the data used for the conditioning analysis is described and then the results of the conditioning exercise are presented. IV.1
Conditioning on various infrastructural indicators
IV.1.1 The data The following infrastructural indicators6 (panel data) are used for the analysis. The states covered for the analysis are stated in the appendix, and the period of study is 1977–1993. There are no missing observations. 6 The infrastructure indicators’ data set has been provided by the India team, Development Centre, OECD, Paris. The author gratefully acknowledges thanks to A. Varoudakis and M. Veganzones for kindly providing the data set.
Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
424
S . B AN D Y O P AD H Y A Y
Table 1 Results of Factor Analysis Components F1 F2 F3
Eigen value
Cumulative R2
12.41 1.22 1.00
0.83 0.91 0.97
Per capita electrical consumption (in kilowatt hours). Per capita industrial consumption of electricity (in kilowatt hours). Percentage of villages electrified. Percentage of gross cropped area irrigated. Road length (in km per 1000 sq. km). Number of motor vehicles per 1000 population. Rail track length (in km per 1000 sq. km). Literacy rates (in percentage of the age group). Primary school enrolment (age 6–11, in percentage of the age group). Secondary school enrolment (age 11–17, in percentage of the age group). Infant mortality (in percentage). Number of bank offices per 1000 population. Bank deposits (as a percentage of the SDP). Bank credit (as a percentage of the SDP).
To generalise my infrastructure results, I construct a single index accounting for the each state’s infrastructural base. I use factor analysis to obtain a general index of infrastructure. This technique is a method of data reduction and attempts to describe the indicators as linear combinations of a small number of latent variables. I accept the first factor (f1, called INFRA) to be the general index of infrastructure, which takes an eigenvalue of 12.41 (out of a total of 17 indicators); the results are in Table 1.7 The weights associated with each infrastructure variable are in Table 2. IV.2
The conditioning distribution dynamics
The distribution dynamics of the index INFRA in Figure 7 shed some interesting light on the changes in the spatial distribution of infrastructure. Although the upper half of the probability mass lies on the diagonal, the bottom half twists sharply anti-clockwise and runs parallel to the vertical line passing through 1. This implies that lower income group states have observed convergence in their levels of infrastructure. While this result does not shed any light on its role in explaining the observed polarisation of incomes across Indian states, it highlights how poorer states have had similar levels of infrastructure, an insight which will be useful later on.
7
See Bandyopadhyay (2004).
Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
425
R I C H S T AT E S , PO O R S T A T E S
Table 2 Factor Loadings
Total power consumption Power consumption in industrial sector Percentage of villages electrified Percentage of net area operated with irrigation Length of road network per 1000 sq. km Number of motor vehicles per 1000 inhabitants Length of rail network per 1000 sq. km Literacy rate of adult population Primary school enrolment rate Secondary school enrolment rate Infant mortality rate Bank offices per 1000 people Bank deposits as a percentage of SDP Bank credit as a percentage of SDP
F1
F2
F3
0.97 0.95 0.99 0.95 0.97 0.89 0.61 0.98 0.97 0.98 0.96 0.91 0.75 0.58
0.16 0.12 0.04 0.20 0.12 0.07 0.47 0.04 0.04 0.13 0.05 0.24 0.57 0.68
0.10 0.04 0.08 0.18 0.10 0.37 0.60 0.15 0.08 0.02 0.22 0.30 0.28 0.40
1
Period t
0
−1
−2
−3 −3
−2
−1 0 Period t +1
1
Figure 7. Infrastructure dynamics across Indian states: contour plot, 1978–1993.
To construct the conditioned distribution with the infrastructure variables, it is first important to ascertain the exogeneity/endogeneity of the variables. Granger causality tests confirm the endogeneity of the infrastructure index. To allow the conditioned distribution to be free from feedback effects (or bi-directional causality), it is estimated by regressing state GDPs on a two-sided distributed lag of the time varying conditioning variables. I then extract the fitted residuals for subsequent analysis. This will result in a conditioned distribution free from feedback effects irrespective of the exogeneity of the righthand side variables. The method derives from Sims (1972), implemented in Quah (1996), where endogeneity (or the lack of it) is determined by regressing the Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
426
S . B AN D Y O P AD H Y A Y
Table 3 Conditioning regressions (two sided projections) of growth rates on infrastructure Infrastructure Lead 4 3 2 1 0 Lag 1 2 3 4 Constant Sum of co-efficients R2
Co-efficients in two-sided projections
0.03 (0.04) 0.065 (0.01) 0.072 (0.016) 0.071 (0.014) 0.042 (0.010)
0.054 0.17
0.01 (0.01) 0.02 (0.03) 0.068(0.012) 0.074 (0.018) 0.067 (0.016) 0.04 (0.011) 0.014 (0.012)
0.011 0.15
0.005 (0.003) 0.012 (0.004) 0.03 (0.021) 0.07 (0.02) 0.079 (0.012) 0.069 0.033 0.008 0.005
(0.012) (0.011) (0.005) (0.004)
0.011 0.12
Note: Figures in parentheses are white heteroskedasticity consistent standard errors.
endogenous variable on the past, current and future values of the exogenous variables, and observing whether the future values of the exogenous variables have significant zero co-efficients. If they are zero, then one deduces that there exists no ‘feedback’ or bi-directional causality. The residuals constitute the variation of the dependent variable unexplained by the set of exogenous variables, irrespective of endogeneity. The results for these two-sided regressions are tabulated in Table 3. All projections in Table 3 suggest that infrastructure at lead 1 though lag 2 is significant for predicting GDP, but not consistently for other leads and lags. Fit does not improve with increasing lags (or leads). There is a fairly stable set of co-efficients of the two-sided projections. The residuals of the second lead-lag projections are used as the conditioned distribution of GDP on infrastructure, though the final results are unaltered by using residuals from other projections. In Figure 8, one observes conditional convergence for the lower income convergence club. This suggests that the inter-state distribution of infrastructure is associated with the formation of the lower convergence club. If one could perform a further set of tests to establish causality within the distribution dynamics framework, this could substantiate the low infrastructure-low growth hypothesis for the poor states in India. Given that the methodology to address endogeneity in a non-parametric framework does not exist, the finding here suggests that the states in the lower convergence club all have poor infrastructure. One can also undertake more general tests using the distribution dynamics framework. I have performed some further conditioning tests with the individual infrastructure variables. Figure 9 presents the stochastic kernel mapping each state’s income (relative to the national average) to the conditioned distribution with education. I construct a composite index of education by factor Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
R I C H S T AT E S , PO O R S T A T E S
427
2
3
1
2
0
1 0 2.5 2.0 P 1.5 -GD 1.0 ative l 0.5 e R dtione ondi
el
R
2.5 2.0 1.5 1.0
Relative-GDP
Stochastic Kernel
2 3 1
0
at
P
D
-G
ive
0 1 2 Conditioned-Relative-GDP
C
2.5 2.0 1.5 1.0 0.5 0.0 2.0 Re la 1.5 tiv e . 1.0 G DP
2 Relative.GDP
Stochastic Kernel
Figure 8. Relative per capita incomes across Indian states: infrastructure conditioning.
2.0 1.5 1.0 .GDP 0.5 lative e . R ned ditio Con
1
0 0
2 1 Conditioned.Relative.GDP
Figure 9. Relative per capita incomes across Indian states: education conditioning.
analysis,8 using three indicators of educational attainment: percentage of the population literate, primary school enrolment rates and secondary school enrolment rates. I run the two-sided lead-lag regressions to account for endogeneity, and extract the residuals to obtain the relevant conditioned distribution. The conditioning results reveal that for the lower income states the kernel twists anticlockwise, with the bulk of the probability mass running parallel to the ‘original’ axis. Most of the upper half of the kernel runs along the diagonal. This implies that for lower income groups, and at the very upper end of the income distribution, education is associated with the distribution of the states’ GDP. I also obtain tendencies of conditional convergence for conditioning with percentage of cropped land irrigated, as revealed in Figure 10. Here again we 8
The results are not presented here and are obtainable from the author.
Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
428
S . B AN D Y O P AD H Y A Y
1.5 1.0 0.5
2.0
. DP ive G
. Relat oned
nditi
Co
1.5
1.0
0.5
2.5 2.0 1.5 1.0 0.5 0.0
Relative.GDP
2.0
Stochastic Kernel
2.5 2.0 1.5 1.0 0.5 0.0 Re 2.0 la tiv 1.5 e . 1.0 G DP
0.5 1.0 2.0 1.5 Conditoned.Relative.GDP.on.Irrigated. areas-5years
Figure 10. Relative per capita incomes across Indian states: percentage of irrigated land conditioning.
observe conditional convergence in the lower tail of the kernel.9 When the conditioning is performed only with literacy (percentage of population literate), I obtain conditional convergence for the lower income club (presented in Figure 11). The lower half of the stochastic kernel twists anticlockwise and runs parallel to the original axis. Per capita consumption of industrial power also appears to be consistently significant across all specifications. Other indicators of power consumption, i.e., that of percentage of villages with electricity and per capita total consumption, do not consistently appear as significant explanatory indicators. I repeat the same analysis with state development expenditure. I generate residuals from the lead-lag regressions of GDP on state development 9 The states of Punjab and Haryana are examples of the radical benefits from the Green Revolution implemented in the mid sixties, which involved creating extensive irrigation facilities, alongside radical land reforms and provision of credit institutions. Recent media reports (Call for ‘green revolution’ in India, Financial Times, 10 February 2010), however, have cast doubt on the extent to which the positive effects of the Green Revolution (undertaken in the 1970s) via irrigation and high yielding varieties of rice and wheat may extend to the highly populous 21st century India. The Green Revolution as undertaken then is seen to have outgrown its remit and requires new agricultural policy to diversify the composition of the agricultural basket beyond that of wheat and rice. This has manifested itself in recent years in very high food prices (lentils, vegetables, meat, and milk products). It is not clear (nor yet empirically established) whether the current food price crisis has had or is likely to have a significant impact upon the levels of productivity of the Bread Basket zone (Punjab, Haryana in the west, and West Bengal in the east) in the economic literature. It is also the case that it is likely not to have had a negative impact on the growth rate of the Indian agricultural sector as a whole (given the high growth rate of agricultural GDP of these states, India remains a food exporting country). What is, however, clear is that the diversion of the cropping patterns away from food essentials towards commercial crops (many of which are due to the recent establishment of multi-national food corporations in India) has resulted in the steep rise in the prices of several essential food items. Without (central) state level policy intervention via a ‘second’ Green Revolution to encourage higher production of food crops, this will continue to affect levels of poverty and individual welfare due to the high food prices. This is unlikely to affect the growth rates of the states that have already benefitted from the 1970s Green Revolution and we will likely see them continue to contribute to both the domestic and world food market.
Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
429
2.0
1.5 1.0
1.5
0.5
1.0 0.5
0.0 2.0
1.5 1.0
0
0.5
diti
Con
1.
. DP ive G
. Relat oned
1.
0.
P D
5
0
5
1.0
2.
.G ive at el R
0.0
1.5
Relative.GDP
Stochastic Kernel
R I C H S T AT E S , PO O R S T A T E S
1.0 0.5 2.0 1.5 Conditioned.Relative.GDP.on. LiteratePopn
Figure 11. Relative per capita incomes across Indian states: percentage of population literate.
expenditure, which serve to be the conditioned distribution. The results (presented in the appendix) indicate persistence and immobility for most of the income distribution. A closer look, however, reveals that at higher income levels (those above the national average) and below 50% of the national average the kernel twists anticlockwise. This result implies that state domestic expenditure marginally affects the dynamics of the distribution at higher and lower ends. The relative insignificance of state development spending in our estimates does not necessarily mean that such spending is irrelevant for reducing growth disparities, since other significant variables in the model may themselves be affected strongly by development spending. The impact of roads, education and infant mortality may be reflecting in part the development spending on physical and social infrastructure. Further tests were conducted to test for conditional convergence with the other individual variables used in the analysis, but no evidence of conditional convergence was obtained.10 To summarise our results: I observe conditional convergence for the lower income club when conditioning with the infrastructure index. I also observe instances of conditional convergence for the lower convergence club, with conditioning on education (index), literacy and percentage of land irrigated. The results obtained depart from those found by earlier empirical studies by isolating conditional convergence at specific parts of the income distribution. These results would go uncovered by using standard methods of estimating 10 All these ‘explanatory factors’ were also tested using standard panel regression methods, i.e., standard ‘growth regressions’, where each one of these factors was found to be significantly associated with the state level growth rates and no conditional convergence. Clearly we would not have been able to identify the distribution-specific effects of these variables using the panel regression method, but these are highlighted using the distribution dynamics method. Results of these regressions are available on request from the author.
Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
430
S . B AN D Y O P AD H Y A Y
conditional convergence with regression analysis. I have uncovered specific factors (low levels of education, literacy, percentage of irrigated land) which are associated with low GDP outcomes.
V
Interpretation of the Results
The results obtained using the distribution dynamics approach highlight the need for infrastructural investment in the low income club of states. Indeed, this finding is supported by several developing countries’ experiences and a large literature supporting the role of infrastructural development at the early stages of economic development. To attribute the differences in growth and development across Indian states only to infrastructural differences is to ignore many other crucial elements which would explain their differences. In the least, one would expect underdeveloped financial markets, unstable macroeconomic structures, nature of institutional development to be fundamental issues that underpin regional differences in growth and productivity. The cross-country growth literature has attributed divergences in growth across regions to a large number of factors,11 including factors of international trade, finance, labour migration and the integrated nature of industrial development across the regions, among others. Of the several factors discussed here, there are a few obvious ones to consider for the Indian case, especially that of neighbouring state effects. A neighbouring state effect rests on the benefits of technological spill-overs via the spread of the industrial base. The four richest states (Punjab, Haryana, Gujarat and Maharashtra) are all concentrated in the west of India, with Punjab and Haryana, and Gujarat and Maharashtra bordering each other. In the conditioning exercise, I also therefore test for the effects of neighbouring states. However, I do not find any evidence of such an effect.12 This result is unlike Quah (1996)’s study of the US and the EU where he finds evidence for a neighbouring state effect in explaining the existence of convergence clubs. Indeed, it is interesting that we do not obtain such an effect for the Indian rich income club. A possible explanation is that the composition of GDP for the richer states is very different. While economic growth trajectories in Punjab and Haryana are primarily driven by growth in the agricultural sector (with both states considered part of the ‘Bread Basket of India’), Gujarat and Maharashtra’s high growth rates are attributable to their high growth rates in the industrial sector. With different engines of growth in the two sets of states it is therefore not surprising that a neighbouring state effect was not found.13 While many of the richer states are all clustered in Western India, there is no such clear spatial pattern for the poor states. However, the bulk of them are 11 Jonathan Temple’s ‘Economic Growth Resources’ is an excellent repository of the literature on economic growth and factors which explain the empirics of convergence and divergence. http://www.bris.ac.uk/Depts/Economics/Growth/datasets.htm 12 Figures not presented here, but are obtainable from the author. 13 If data were available it would have been interesting to observe whether inter-state road networks may have served as a possible determinant of the formation of the rich income clubs.
Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
431
R I C H S T AT E S , PO O R S T A T E S
Table 4 Rural and urban population percentages in Indian states Low income club states
High income club states
Urban
Rural
Assam Bihar J&K Orissa Rajasthan Uttar Pradesh Madhya Pradesh
12.72 10.47 24.88 14.97 23.38 20.78
87.28 89.53 75.12 85.03 76.62 79.22 26.67
Delhi Gujarat Haryana Karnataka Maharashtra Punjab 73.33
Average
19.12
80.88
Average (excluding Delhi) 35.34
Urban
Rural
93.01 37.35 29.00 33.98 42.40 33.95
6.99 62.65 71.00 66.02 57.60 66.05 64.66
located in North India.14 Structurally, the poor states bear some similarities: in all cases their industrial base is significantly underdeveloped, contributing o15% on average to the state GDP, and all of them have a poor service sector. No neighbouring state effect was obtained with these states either. Indeed, it is also no surprise that the rich states belonging to the high income club have a lower percentage of rural population than states in the lower income club. The differences across the rich club states and the poor club states are quite stark, as is clear from Table 4. For the lower income club, the average percentage of population living in urban and rural areas is 19.12% and 80.88%, respectively. However, the average percentage of population living in urban areas for the rich club is over 35%. Haryana records the lowest level of urban population (29% of the total population) of the rich states, which is still higher than the highest level of urban population in the poor club, namely Madhya Pradesh at 27%. In summary, the rich states club and the poor states club are composed of two distinctly different types of states. The rich states club is composed of states which are infrastructurally developed at the level of a middle income country, both in terms of agriculture and industry, and are relatively urbanised. The poor states club is composed of states which are neither agriculturally nor industrially developed, and which have low levels of urbanisation. Moreover, several states have had mixed fortunes. For instance, Tamil Nadu rose to become one of India’s richest states via speedy development of its heavy industrial sector since the late-1980s. On the other hand, West Bengal’s formerly robust industrial sector has languished since the mid-1970s due to the oil crises and subsequent disinvestment despite the rise of its agricultural sector in the 1980s. The policy implications which derive from these findings are the need for concerted investment in infrastructural development in the poor states, in particular for the six poorest states. The infrastructural variables that have been revealed in the paper to be associated with the lower convergence club are that of 14 Other poor states are in North East India but are not included in the study due to very low population densities.
Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
432
S . B AN D Y O P AD H Y A Y
education and the extent of irrigation, and it is these that the paper points towards as requiring the most intensive investments. VI Conclusion This paper has examined the convergence of growth and incomes across Indian states using an empirical model of dynamically evolving distributions. The main stylised facts are the existence of ‘twin-peaked’ dynamics over the period 1965– 1997, with the Indian inter-state distribution polarising into two income convergence clubs. One of these clubs is situated at 50% of the national average, with the other at 125% of the national average, thereby comprising a ‘poor states’ club and a ‘rich states’ club, respectively. Some cohesive tendencies are observed in the 1960s, only to dissipate over the following three decades. These findings contrast with those emphasised in works of Aiyar (2001), Bajpai and Sachs (1996), Nagaraj and Venganzones (1997) where divergent tendencies are highlighted but increasing polarisation and club convergence remains undocumented. Using the same empirical tools further reveals that such dynamics are associated with the spatial distribution of infrastructure. Infrastructure is found to explain the formation of only the lower convergence club and not the upper club, a result which would not have been revealed with standard tools of crosssection, panel regressions or time series analyses. I also found tendencies of conditional convergence with individual infrastructure variables such as the percentage of land irrigated and literacy at different parts of the distribution. Therefore, the results obtained with the distribution dynamics method go one step further than the standard methods. However, future research would benefit from a well-defined model defining the channels through which infrastructure promotes growth. The empirical results suggest that the association between infrastructural indicators and economic growth is significant. This relationship is especially prominent for the lower income states. The findings thus have strong policy implications for Indian infrastructural development, specifically for education, health, roads, railway networks, power and electricity supply. Inasmuch as the majority of the poorer states remain in the poor club, it is clear that these infrastructural indicators are areas for policy attention. Indeed, the Indian government (and the respective state governments) have undertaken investments in these areas, but the empirics in this paper suggest that their efforts have not yet been fully successful. Acknowledgements I would like to thank Chris Adam, Marcel Fafchamps, Henry Overman, Danny Quah, Tony Venables and Diana Weinhold, and participants at seminars at the London School of Economics, Royal Holloway College, University of Houston and University of Oxford, and an anonymous referee for useful comments. Funding from the Economic and Social Research Council, UK, is gratefully acknowledged. All errors are mine. Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
R I C H S T AT E S , PO O R S T A T E S
433
References AIYAR, S. (2001). Growth theory and convergence across Indian states: a panel study. In T. Callen, P. Reynolds and C. Towe (eds.), India at the Crossroads: Sustaining Growth and Reducing Poverty. IMF. BAJPAI, N. and SACHS, J. (1996). Trends in inter-state inequalities of income in India. Discussion Paper No. 528, Harvard Institute for International Development, Cambridge, MA, May. BANDYOPADHYAY, S. (2004). Twin peaks – distribution dynamics of economic growth across Indian states. In A. Shorrocks and R. van der Hoven (eds.), Growth, Inequality and Poverty: Prospects for Pro-Poor Growth. Oxford: Oxford University Press. BARRO, R. J. and LEE, J.-W. (2010). A New data set of Educational Attainment in the World 1950–2010, NBER Working Paper No. 1590. BARRO, R. J. and SALA-I-MARTIN, X. (1992). Convergence. Journal of Political Economy, 100, 2, pp. 223–51. BEN-DAVID, B. (1994). Converging clubs or diverging economies. Working Paper 922, CEPR, London. BENHABIB, J. and SPIEGEL, M. (1994). The role of human capital in economic development: evidence from aggregate cross-country data. Journal of Monetary Economics, 34, pp. 143– 73. BENHABIB, J. and SPIEGEL, M. M. (2000). The role of financial development in growth and investment. Journal of Economic Growth, 5, 4, pp. 341–60. BERNAUD, A. and DURLAUF, S. (1996). Interpreting tests of the convergence hypothesis. Journal of Econometrics, 71, 1/2, pp. 161–73. BIANCHI, M. (1995). Testing for convergence: a bootstrap test for multi-modality. Journal of Applied Econometrics, 21, pp. 393–409. BULLI, S. (2001). Distribution dynamics and cross-country convergence: a new approach. Scottish Journal of Political Economy, 48, 2, pp. 226–43. BURGESS, R. and PANDE, R. (2005). Do rural banks matter? Evidence from the Indian social banking experiment. American Economic Review, 95, 3, pp. 780–95. CARLINO, G. and MILLS, L. (1993). Are U.S. regional incomes converging? A time series analysis. Journal of Monetary Economics, 32, pp. 335–46. CASHIN, P. and SAHAY, R. (1996). Internal migration, centre-state grants, and economic growth in the states of India. IMF Staff Papers 43(1). CHUNG, K. (1960). Markov Chains with Stationary Transition Probabilities. New York: Springer-Verlag. DE LONG, J. B. (1988). Productivity growth, convergence, and welfare. American Economic Review: A Comment, 78, 5, pp. 11, 38–55. DESDOIGTS, A. (1994). Changes in the World Income Distribution: A Non-Parametric Approach to Challenge the Neo-Classical Convergence Argument. PhD thesis, European University Florence. DURLAUF, S. and JOHNSON, P. (1995). Multiple regimes and cross country growth behaviour. Journal of Applied Econometrics, 10, 4, pp. 365–84. DURLAUF, S. N. and QUAH, D. T. (1999). The new empirics of economic growth. In J. B. Taylor and M. Woodford (eds.), Handbook of Macroeconomics. (1st edn, Vol. 1, Chapter 4). Amsterdam: Elsevier, pp 235–308. ESTABAN, J. and RAY, D. (1994). On the measurement of polarisation. Econometrica, 62, 4, pp. 818–51. FIASCHI, D. and LAVEZZI, A. M. (2003). Distribution dynamics and nonlinear growth. Journal of Economic Growth, Springer, 8, 4, pp. 379–401. GALOR, O. and ZEIRA, J. (1993). Income distribution and macroeconomics. Review of Economic Studies, 60, 1, pp. 35–52. GRAZIA-PITTAU, M., ZELLI, R. and JOHNSON, P. A. (2010). Mixture models, convergence clubs and polarization. Review of Income and Wealth, 56, 1, pp. 102–22. JONES, C. I. (1997). On the evolution of the world income distribution. Journal of Economic Perspectives, 11, 3, pp. 19–36. KALAITZIDAKIS, P., MAMUNEAS, T. P., SAVVIDES, A. and STENGOS, T. (2001). Measures of human capital and nonlinearities in economic growth. Journal of Economic Growth, 6, 3, pp. 229–54. Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
434
S . B AN D Y O P AD H Y A Y
KING, R. G. and LEVINE, R. (1992). Financial indicators and growth in a cross section of countries. Technical report, World Bank Policy Research Working Paper No. 819, World Bank. NAGARAJ, R. A. V. and VENGANZONES, M. (1997). Long run growth trends and convergence across Indian states. Technical report. Technical paper no.131, OECD Development Centre, Paris. O¨ZLER, B. G. D. and RAVALLION, M. (1996). A database on poverty and growth in India. Technical report. Poverty and Human Resources Division, Policy Research Department, The World Bank. QUAH, D. (1993). Galton’s fallacy and tests of the convergence hypothesis. Scandinavian Journal of Economics, 95, 4, pp. 427–43. QUAH, D. (1996). Twin peaks: growth and convergence in models distribution dynamics. Economic Journal, 106, 437, pp. 1045–55. QUAH, D. (1997). Empirics for growth and distribution: stratification, polarisation and convergence clubs. Journal of Economic Growth, 2, 1, pp. 27–59. RUD, J. P. (2008). Electricity Provision and Industrial Development: Evidence from India. London School of Economics mimeo. SIMS, C. A. (1972). Money, income and causality. American Economic Review, 62, 4, pp. 540–52. SOLOW, R. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70, 1, pp. 65–94. STOKEY, N. L. (1991). Human capital, product quality and growth. Quarterly Journal of Economics, 106, pp. 587–616. TRIVEDI, K. (2003) Regional convergence and catch-up in India between 1960 and 1992. Technical report. Oxford University Economics Department Working Paper.
Date of receipt of final manuscript: 7 August 2010
Appendix A: Data Appendix States used in the study: Andhra Pradesh Assam Bihar Delhi Gujarat Haryana Jammu and Kashmir Karnataka Kerala Madhya Pradesh Maharashtra Orissa Punjab Rajasthan Tamil Nadu Uttar Pradesh West Bengal Other states were excluded from the study due to the incomplete data available over the given period. These states together constitute for over 80% of the national population. Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
R I C H S T AT E S , PO O R S T A T E S
435
Price data that has been used to deflate the nominal GDPs has also been obtained from the above mentioned data set, and is the adjusted CPIAL index. State development expenditure constitutes of expenditure on both economic and social services. The economic services include agriculture and allied activities, rural development, special area programmes, irrigation and flood control, energy, industry and minerals, transport and communications, science technology and environment; the social services include education, medical and public health, family welfare, water supply and sanitation, housing, urban development, labour and labour welfare, social security and welfare, nutrition, and relief on account of natural calamities. Appendix B: The Distribution Dynamics Approach Quah (1997) exploits a duality property from Markov process theory to provide a model of distribution dynamics. To model the distribution dynamics, one observes a scalar stochastic process, and then derives the implied unobservable sequence of distributions associated with this process. This hypothesised distribution sequence is then defined to be the dual to the observed scalar stochastic process. The property is reversed (the mathematics involved, however, remaining unaffected) to track the distribution dynamics as follows: while the sequence of distributions is observed, its dual, the scalar stochastic process, is implied, though unobserved. The dynamics of the scalar process is described in a transition probability matrix, while the dual to this, the stochastic kernel, describes the ‘law of motion’ of the sequence of distributions. These will serve as models which describe the distribution dynamics across the Indian states. The following clarifies the concepts discussed above. Let Ft be the measure corresponding to the cross-country income distribution at time t. The stochastic kernel which measure the evolution from Ft to Ft11 is a mapping Mt from the Cartesian product of income values and Borel measurable sets to [0,1], such that Z ðB1Þ HBorel-measurable A; Ftþ1 ðAÞ ¼ MðA; yÞ d Ft ðyÞ: It is Mt which encodes all the information about the evolution, or the law of motion of the sequence of distributions over time periods t and t11. It contains information of the intra-distributional dynamics, hence revealing specific external shapes of the distribution, unrevealed in standard empirical procedures. Mt is assumed to be time-invariant, (and in this case, leaving out an error term, inclusion of which would render the model analogous to a first order vector auto-regression in distributions rather than scalars or finite dimensional vectors), one can re-write the above expression as Ftþ1 ¼ M Ft :
ðB2Þ
For simplicity in calculations, iterating the above equation and leaving out the error term, one can write: FtþS ¼ MS Ft : Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.
ðB3Þ
436
S . B AN D Y O P AD H Y A Y
As s !1 it is possible to characterise the long run distribution – this is called the ergodic distribution and it predicts the long term behaviour of the underlying distribution. If Ft1s degenerates to a point mass one can conclude that there is a tendency to global convergence. If Ft1s tends towards a bi-modal distribution (the case with the Indian states) one can conclude that there is a tendency for polarisation, with the rich and the poor being pulled apart. Dierent variants of equation (B1) allow the researcher to derive the various spectral characteristics of Mt, such as intra-distributional mobility and the speed of convergence.
2.0 1.5
2.0
1.0
1.5
0.5
1.0
0.0
0.5
2.0 la 1.5 tiv 1.0 e. G DP
Re
Relative.GDP
Stochastic Kernel
Appendix C: Conditioning Dynamics with State Development Expenditure
2
1
0.0 2.0 P 1.5 e. GD 1.0 lativ e . 0.5 R ned ditio Con
0 1 2 0 Conditioned.Relative.GDP.on.Devex
Figure C1. Relative per capita incomes across Indian states: state development expenditure conditioning.
Scottish Journal of Political Economy r 2011 The Author. Scottish Journal of Political Economy r 2011 Scottish Economic Society.