Growth Convergence and Spillovers among Indian States: What Matters? What Does Not?

Contributor Notes

Author’s E-Mail Address: skalra@imf.org, psodsriwiboon@imf.org

Convergence and spillovers across countries and within countries are old, but recurrent policy concerns, and India is no exception to this rule. This paper examines convergence and spillovers across Indian states using non-stationary panel data techniques. Results on convergence among Indian states are generally found to be similar, but more nuanced, than previous studies. Generally speaking, there is evidence of divergence over the entire sample period, convergence during sub-periods corresponding to structural breaks, and club convergence. There is strong evidence of club convergence among the high- and low-income states; the evidence for middle-income states is mixed. Dynamic spillover effects among states are small.

Abstract

Convergence and spillovers across countries and within countries are old, but recurrent policy concerns, and India is no exception to this rule. This paper examines convergence and spillovers across Indian states using non-stationary panel data techniques. Results on convergence among Indian states are generally found to be similar, but more nuanced, than previous studies. Generally speaking, there is evidence of divergence over the entire sample period, convergence during sub-periods corresponding to structural breaks, and club convergence. There is strong evidence of club convergence among the high- and low-income states; the evidence for middle-income states is mixed. Dynamic spillover effects among states are small.

I. Motivation

Convergence and spillovers across countries and within countries are old, but recurrent policy concerns. The concerns stems from a need to understand the drivers of growth, to look out for which policies work and which do not, and a search for spillovers across geographical domains. From a policy perspective, the genesis of the concerns is obvious. Regions that get left behind are, globally, more prone to disruptions and fissiparous tendencies, and represent lost opportunities and wasted human potential. And India is no exception to this rule. Not surprisingly, the need to understand what promotes growth, both in absolute and relative terms, is a perennial policy preoccupation.

This paper examines convergence and spillovers across Indian states. If much has been written on the issue, what more can be said? This paper aims to situate itself in an arguably dense literature, both from a technical standpoint and on the basis of some new results. From a methodological standpoint, it stands with a recent literature on non-stationary panel data econometrics, where techniques have been developed to examine convergence in other countries, including China (Pedroni and Yao, 2006). In particular, these techniques allow an analysis of spillovers across constituent units, which is not possible in standard cross-section or time series studies. These techniques also provide more reliable parameter estimates of convergence and spillovers.

Among the other innovations of this paper are a ranking procedure to group states on their performance, a restatement of convergence and divergence across states during 1960-2004, and explanation of per capita income disparities by indicators, such as sector shares, infrastructure, private investment, and spillovers, similar to past studies, but more nuanced. In addition, club convergence and dynamic spillover effects among states are studied. The analysis of dynamic spillovers has, to the best of our knowledge, not been undertaken in any other study of Indian states.

This paper is organized as follows. Section II provides an overview of studies on convergence across Indian states, aiming to contextualize this paper in the literature. Section III describes the data and establishes some preliminary stylized “facts”. Section IV provides a sketch of the non-stationary panel data techniques that characterize the econometrics of this paper. Section V gives the empirical results. Section VI concludes.

II. Literature Survey

A. Old Wine in Old Bottles?

Income convergence across Indian states has been explored previously in a number of studies using neoclassical growth regressions. These regressions estimate a relationship between (per capita) output growth rate and initial (per capita) level of output, providing a measure of β-convergence coefficient (Barro and Sala-i-Martin, 1992, 1995). Absolute convergence implies that initially poor states grow faster than the initially rich ones, regardless of heterogeneity across states. Conditional convergence defines a tendency to catch-up, controlling for heterogeneity across states. The studies include Cashin and Sahay (1996), Bajpai and Sachs (1996), Rao, Shand, and Kalirajan (1999), Nagaraj, et. al. (2000), Aiyar (2001), Sachs, Bajpai, and Ramiah (2002), Kochhar et. al. (2006), Purfield (2006) and Misra (2007). The studies differ across a number of dimensions, including the sample period, coverage of states, data sources, and estimation methodology (Table 1). The main points relate to:

Table 1.

Indian States: Growth and Convergence Literature--A Survey of Results

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  • Sample period, estimation technique and controls for heterogeneity.

    • The initial- and end-point incomes vary across the studies. Some authors directly apply annual growth rates and use one-lagged initial income such as Bajpai and Sachs (1996), Nagaraj, et al. (2000), and Sachs, et al. (2002). Misra (2007) uses compound annual growth rates. Others attempt to take into account the business cycle by constructing the data on 5 years apart (Aiyar, 2001) or the data on 5 years average over non-overlapping periods (Purfield, 2006). Others apply their own justification for the time interval.

    • Earlier studies in the literature estimated cross-section growth/income regression equations, while later studies use panel regressions. Aiyar (2001) uses simple OLS and incorporates cross-section fixed effects. Nagaraj, et al. (2000) and Purfield (2006) use generalized method of moments (GMM) and take into account both cross-section and period fixed effects.

    • Control variables vary across the studies. Nagaraj, et al. (2000), Baddeley, et al. (2006), and Purfield (2006) find sector shares and infrastructure explain the bulk of the growth dispersion. The studies find strong positive correlation between states’ per capita output growth rate, and change in share of service sector, improvements in infrastructure (using number of telephone lines and transmission and distribution losses ratios as proxies).1 Aiyar (2001) and Purfield (2006) also record the positive effect of credit growth (to proxy for private investment), but Misra (2007) does not. Higher literacy rates also appear to support growth in some studies (Aiyar, 2001), but not in others (Purfield, 2006).

  • Absolute/conditional convergence.

    • Generally speaking, most studies conclude absolute and conditional convergence for the pre-1990s. Including the post-1990s period, a number of studies point to income divergence. This indicates the possibility of a structural change around 1990.

    • Cashin and Sahay (1996) finds absolute convergence, as well as conditional convergence with controls added for shares of economic sectors. Bajpai and Sachs (1996) find absolute convergence across 19 states only in the 1960s. Rao, Shand, and Kalirajan (1999) find income divergence across 14 states over 1965-1995. Nagaraj, et al. (2000), Aiyar (2001), Kochhar et. al. (2006) and Misra (2007) document absolute divergence, with conditional convergence using share of agricultural sector, price shocks, infrastructures, literacy rate, and state’s private investment as controls. Sachs, Bajpai, and Ramiah (2002) demonstrate overall income divergence across 14 Indian states during the period of 1980-1998, where the divergence within poorer states is more noticeable. Purfield (2006) confirms both absolute and conditional convergence during 1975-2003., with states’ growth determined mainly by their own policies in 1990s, private sector investment, size of government, and institutions.

Other studies also examine the distribution of states’ incomes. Cashin and Sahay (1996), Rao, Shand, and Kalirajan (1999), Bajpai and Sachs (1996), and Sachs, et. al. (2002) assess σ-convergence (which indicates convergence when the standard deviation of the logarithm of per capita states’ incomes falls). However, a reduction of dispersion measure over time does not provide information about income dynamics. Bandopadhyay (2003) estimates non-parametric stochastic kernels and transition probability matrices, and concludes that Indian states’ incomes are converging, but into two clubs.

B. Old Wine in New Bottles?

More recently, convergence has been addressed using newly developed non-stationary panel techniques. Quah (1993) and Evans (1998) argue that the strict conditions required for the derivation of growth regression are unlikely to be satisfied, potentially producing biased parameter estimates. Specifically, growth regressions provides valid inference if and only if the economies follow exact first-order autoregressive dynamics; the vector of control variables can account for all heterogeneity across economies; and the economies are not cross-sectionally dependent (Evans and Karras, 1996).

To address these problems, time-series methods for panel application have been proposed in the literature. In this approach, the definition of income convergence comes from the notion of unit roots and cointegration. This approach has several advantages. It is robust to problems of endogeneity, omitted variables, simultaneity, and measurement error. More importantly, it does not require arbitrary start and end point assumption. In particular, time series panels assume that states are close to limiting distributions, despite their initial conditions. It, therefore, allows for a better understanding of the actual path of the series involved, which is crucial to understanding potential convergence over time. The approach is especially suitable to Indian states, as the short data span is compensated for by variation in the cross-section dimension.

Non-stationary panel techniques have been applied to examine convergence for developed and some developing economies. Fleissig and Strauss (2001) test stochastic convergence for OECD countries and a European subsample. Choi (2004) implements multiple unit root tests in panel data for 48 US states. McCoskey (2002) applies the technique to a panel data set of Sub-Saharan African countries. Pedroni and Yao (2006) explore regional income divergence in China, comparing pre- and post-reform periods.

The structure of the panel time series models is similar to the neoclassical growth regression. Typically, the cross-sectional growth regression takes the form:

(1)(1/T) log(yi,T/yi,0)=αi+β logyi,0+γ Xi,0+εi,t i=1,2,,N

where y is per capita income, Xi is a vector of controls for cross-section heterogeneity in levels and growth rates of per capita income, α, β, γ and are parameters, and εi,t is an error term with a zero mean and finite variance. Nagaraj, et al. (2000) and Purfield (2006) apply Arellano-Bond multivariate dynamic model to this regression, with a first-order autoregressive-distributed lag model so that (1) can be rewritten as:

(2)yi,t=δi+λ.yi,t1+εi,torΔyi,t=δi+φ.yi,t1+εi,twhereδi=[(λ1)γ/β]Xi,λ(1+βT)1/T,φ(λ1).

Equation (2) is then comparable to an ADF regression of the form:

(3)Δyi,t=δi+ρiyi,t1+L=1piϕi,LΔyi,tL+ui,t

However, the conceptual frameworks are different. The dynamic panel regression (2) utilizes a vector of controls to remove the heterogeneity across states, pools all states, and interprets the convergence directly from the first-order lagged coefficient. As shown in Section IV, the non-stationary panel approach does not explicitly allow for controls, but instead uses deviations from mean in the estimating equation to control for heterogeneity, and uses lagged differences to capture serial correlation patterns. Moreover, the estimating equation for each state is done separately, and then the t-statistics or p-values are combined to conduct a panel unit root test. Convergence is then determined by the stationarity of differences across series (Appendix 1).

III. Data and Stylized “Facts

We use data for Indian states over the period 1960-2004.2 More recent data are perhaps available, but a part of the motivation is to keep the dataset comparable with other studies. An analysis with more recent data would be instructive as well, but is kept for further research. Moreover, the addition of a few more additional years would be preferable, but is unlikely to change the main results of the analysis given the relative weight of the observations in the sample. Annual per capita real net state domestic product is used to proxy for state-level income. The sample includes 15 major Indian states: Andhra Pradesh, Assam, Bihar, Gujarat, Haryana, Karnataka, Kerala, Madhya Pradesh, Maharashtra, Orissa, Punjab, Rajasthan, Tamil Nadu, Uttar Pradesh, and West Bengal. From this data, with the admitted caveat on sample length, the following stylized “facts” may be noted.

  • All states grew, but differentially so that income gaps widened. By 2003, average per capita income in India was twice as high as in 1970.

  • Over this period, ranked by per capita income (Table 2), states can be grouped into three categories: high-income states (Gujarat, Haryana, Maharashtra, Punjab, and Tamil Nadu); medium-income states (Andhra Pradesh, Karnataka, Kerala, West Bengal, and Rajasthan), and low-income states (Assam, Bihar, Orissa, Madhya Pradesh, and Uttar Pradesh).

    Table 2.

    Rank of India States Income, 1970-2003

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    Sources: Indian authorities; and IMF staff estimates.
    Table 3.

    Survey of Structural Breaks in Indian Economic Data

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  • States’ growth rates were positively correlated with average per capita income. Moreover, growth accelerated in the richer states; poorer states grew moderately. High-income states grew at average annual rates of 3-4 percent over 1970-2003, while low-income states grew at only at 1½ -2 percent.

  • Among the medium-income group states, Andhra Pradesh and Karnataka grew at much higher rates than the group average; Kerala, Rajasthan, and West Bengal at lower than average rates. As a result, income difference between high- and low- income states more than doubled. By the end of the period, the average per capita income of the five richest states in 2003 was 2½ times as much as that of the poorest states.

  • Reforms of the 1980s/1990s appear to have intensified divergence across states.3 The reforms of the early 1980s included liberalization of international trade and relaxation of business-related rules and regulations. The reforms of the early 1990s induced further trade liberalization, financial liberalization, and privatization of non-financial enterprises as well as banks. A casual examination of the data suggests two surges in income gap, corresponding to the launch of the two waves of policy reforms.4 Numerically, the gap between log real net SDP per capita of the five richest and five poorest states increased by around 20 basis points in 1980, as well as 13 basis points in 1992. The surges went down after a year, but the income gap continued to expand. Accordingly, we conclude two structural break dates in 1980 and 1992.

IV. The Econometrics of Non-stationary Panels

In time-series analysis concepts, two series are defined as convergent if the difference between them is “stable”. Specifically, stochastic income convergence implies that income disparities between the series follow a mean stationary stochastic process. This can be characterized as follows. Let yit be the logarithm of per capita income for state i at time t, i =1, 2, …, N and t =1,2, …, T. yit contains a unit root or is integrated of order 1. Generally, convergence implies that any pair of states i and j converge, pair wise, if the difference yityjt is stationary or limkE(yi,t+kyj,t+k | It)=μi. Then, yit and yjt are cointegrated. If the mean, µi, is zero, there is absolute convergence in per capita incomes; if µi is not zero, there is conditional convergence. Conditional convergence implies that income growth paths for the states are parallel by the distance, µi, in limit.

For panels, convergence can be similarly defined between the elements of the panel. It is equivalent to convergence of every pair of yit and yjt within the set. Testing pair wise convergence for all states, however, tends to have low power for short samples, thus increasing the probability of failing to reject the null hypothesis of no cointegration. Evans and Karras (1996) show that all members yit and yjt cointegrating pair wise implies that all members cointegrate individually with a common time effect, y¯t.5 Deviations of y1,t+k, y2,t+k ,…, yN,,t+k from their cross-economy average, y¯t, are expected to approach a constant value as k goes to infinity, conditional on current information, limkE(yi,t+ky¯t+k | It)=μi for all i. Taking into account the serially-correlated nature of the series, empirically, an augmented Dickey-Fuller (ADF) test can be conducted using:

(4)Δ(yi,ty¯t)=δi+ρi(yi,t1y¯t1)+L=1piϕi,LΔ(yi,tLy¯tL)+ui,t

The autoregressive coefficient, ρi, is crucial to test income convergence, while δi takes into account idiosyncratic differences across states. The lagged difference terms capture higher order serial correlation, and the number of lags, pi, is chosen to eliminate serial correlation in the error term.

In the convergence tests, we employ three panel tests for unit root (Appendix 1):

  • Levin, Lin, and Chu (2002, hereafter LLC) test uses pooled within-dimension estimators. It treats parameter of interest as common across members of the panel, while other parameters can vary across members.

  • Im, Pesaran, and Shin (2003, hereafter IPS) test allows all parameters to vary across members of panel. The test statistics are based on the group mean between-dimension of the individual test statistics.

  • Maddala and Wu (1999, hereafter MW) is similar to IPS test, but pools marginal significance values across members of panel.6

In addition to the above tests, we also use bootstrap techniques to get better sample specific IPS adjustment terms and MW p-values. While a distinct advantage of the IPS and MW tests is that they allow for heterogeneous dynamics which are useful for panel applications, the tests could suffer from a small-sample size distortion as they depend on asymptotic properties. Pedroni and Yao (2006) suggest that, in practice, the test performance can be improved by replacing the IPS large-sample adjustment terms and MW p-value by a bootstrap to condition the Monte Carlo simulation on both sample size and specific number of fitted lags. The bootstrap procedures are elaborated in Appendix 1.

Finally, we examine closely the transition across periods and cross-sectional dimensions. McCoskey (2002) and Choi (2004) argue that stochastic convergence could be problematic in the presence of structural breaks in the data, and the standard tests may be biased and size-distorted.7 Convergence across all states through the entire period is first tested. Then possible break dates are explored. The full sample is divided into subsamples and again tested for convergence according to each break. As regards the cross-section dimension, the possibility of club convergence is explored.

V. Convergence Revisited: A Non-stationary Panel Approach

This section presents the empirical results of application of the non-stationary panel approach to Indian states. First, diagnostic tests are conducted for the 15 states’ income per capita. All series are integrated of order one, i.e. are I(1).8 The remainder of the section presents: (i) income convergence tests, for the entire sample period, subsamples, and cross-sectional subsets; and (ii) macroeconomic determinants of income dynamics.

A. Convergence and Structural Change

Results on convergence among Indian states are generally found to be similar, but more nuanced, than previous studies. Generally speaking, there is evidence of divergence over the entire sample period, convergence during sub-periods corresponding to structural breaks, and club convergence. Over the entire sample period, non-convergence in states’ per capita income is not rejected. Table 4 shows the numerical results. Individually, only two states, Madhya Pradesh and Rajasthan, displayed income convergence to the common trend, y¯t. Once accumulated into the panel, the null hypothesis of non-convergence (where the differences, yi,ty¯tcontain unit roots) cannot be rejected. The results are confirmed by all three tests.

Table 4.

Panel Unit Root Test Results for All Indian States

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Sources: Indian authorities; and IMF staff estimates.

The results are from LLC, IPS, and MW panel unit test for the long run convergence.

Δ(yi,ty¯t)=δi+ρi(yi,t1y¯t1)+k1ρiϕi,kΔ(yi,tky¯tk)+ui,t

For details, see Appendix 1. State real net domestic product per capita is used as a proxy for the state income. Annual data ranges from 1960-2003.ADF test statistic, ρi, and related p-value for each individual together with panel test statistics. The p-values are estimated by Monte Carlo simulation as the ADF test statistics are nonstandard t distribution. Column 1-2 shows results for the whole sample 1960-2003. We then split the sample according to reform period. We report pre-1980 results in columns 3-4 and post-1980 result in columns

There was convergence during subsamples.

  • In the pre-1980s, Indian states’ per capita incomes were cointegrated. Of the 15 states in the sample, 7 states displayed strong tendency toward convergence (the null of non-convergence is rejected at less than 5 percent), and Assam’s ADF statistic rejects the null at around 8 percent. Combining these results into panel, all test statistics except the LLC ADF statistic now reject the null.

  • During 1980-1992, the rejection of the null of nonconvergence is individually weaker, but mutually stronger than in the pre-1980s. Only 3 out of 15 states show income convergence to the group, and only one rejects the null at less than 5 percent significance level. The combined results suggest conditional convergence in the panel. All test statistics firmly reject the unit root null at less than 1 percent significance level.

  • Post-1992, the results are similar to 1980-1992. The individual results shows 5 out of 15 states can reject the null hypothesis of unit root in the differences, yi,ty¯t. The panel results yet robustly reject the null where LLC, IPS, and MW tests reach the agreement. These results again indicate overall income convergence.

Income convergence/divergence broadly corresponds to periods of structural change during the sample period, along the lines of the three growth episodes. Pre-1980, the states’ growth per capita rates were low (around ½ percent per annum) and volatile. Starting 1981, growth picked up strongly (3 percent in 1980-92), and the reforms seemed to benefit all states equally. After 1992, on average, the states continued to grow at nearly 4 percent, but differentially. Thereafter, the growth momentum was sustained in the high-income states, and some medium income states also speeded up. However, growth slowed down in most low-income states. There was thus a tendency for income divergence among the low-income states post-1992, but not enough to overpower convergence among other states, pointing to possible “club convergence”. We now turn to this phenomenon of club convergence which is examined using sub-group analyses through time and cross-sectional dimensions to further pinpoint the sources of income dispersion.9

F2

Indian States: Average Real State Net Domestic Product Per Capita

Citation: IMF Working Papers 2010, 096; 10.5089/9781451982732.001.A001

B. The determinants of per capita income differentials

To examine the determinants of per capita differentials across states, we follow the literature and test for the role of the share of service sector in total output, private sector credit per capita, the share of development expenditure in total government expenditure, infrastructure measures (T&D loss ratio and number of telephone lines), literacy rate, and the share of private sector employment (Figure 1).10

Figure 1.
Figure 1.

Indian States Growth: Explanatory Variables

Citation: IMF Working Papers 2010, 096; 10.5089/9781451982732.001.A001

In addition to these “conventional” measures, we construct a spatial distance index to capture possible spillover effect among states as a potential determinant of growth. We construct six indicator variables which take a value of 1 when the pair i, j is high-high, high-medium, high-low, medium-medium, medium-low, and low-low income states respectively and zero otherwise. Then, we weigh the indicator by the reciprocal of spatial distance between capital city of state i, j in hundreds of miles. The coefficient on spatial distance index captures the interaction between state i, j and is scaled down by the distance between two states.

The estimated regression takes the form:

(5)yij=α+xijβ+εi  ,i=1,2,..,N;j=1,2,..,N

where

yij is a N(N1)2x 1

vector of difference in log of per capita income between state i and j, i.e.,

yij=1Tt=1T(lnyitlnyjt) ij

and

xij is a N(N1)2x K

matrix of difference in factors between state i and j, i.e.,

xijk=1Tt=1T(xiktxjkt) ij;k=1,,K

and β is a K x 1 vector of coefficients.

Our main empirical results are as follows (Table 7). The main determinants of per capita income differentials among states are share of the service sector, private sector credit per capita, and development expenditure. The factor loadings for these variables are always positive and significant in all specifications. Specifically, a 1 percent difference in share of service sector contributes to about 0.02 percent difference in per capita income between states; a 1 percent difference in development expenditure results in approximately 0.07 percent difference in per capita income; private investment is the largest contributor to per capita income differentials (0.5 percent).

Other variables are not statistically significant: the number of telephone lines is the only variable that is significant, but the effect is almost negligible; T&D loss ratio has correct sign as expected, but is not significant; literacy rate and employment in private sector are statistically insignificant.

From a policy perspective, these results are intuitive and important. The results confirm the significant role for development policy and expenditures and of the availability of credit. They also affirm the role of the private sector in promoting growth. The statistical insignificance of some factors, in particular the literacy rate, should not be interpreted as these factors not being important. It is possible that spending on education and other key areas such as health, which are included in development spending, are already good proxies.

Interestingly, spillover effects among states are not strong. Most of the parameter estimates are not significantly different from zero, except for low-low income state pairs. The negative estimates show potential crowding out effect between high-high income states, while positive spillover effects are noticeable in all other combination.

C. Club Convergence and Dynamic Spillover Effects

There is strong evidence of club convergence among the high- and low-income states; the evidence for middle-income states is mixed (Table 5).

Table 5.

Club convergence

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Sources: Indian authorities; and IMF staff estimates.

The results are from LLC, IPS, and MW panel unit root test for long run convergence.

Δ(yi,ty¯t)=δi+ρi(yi,t1y¯t1)+k1ρiϕi,kΔ(yi,tky¯tk)+ui,t

For details, see Appendix 1. State real net domestic product per capita is used as a proxy for the state income. Annual data ranges from 1960-2003.States are divided into 3 subgroups based on growth performance, and first ranked using real net states domestic product per capita.Then Kendall’s coefficient of concordance is computed. There is no significant rank change over whole period or in sub-periods.The data is then split into high, medium, and low income groups and testsed for convergence.The ADF test statistic, each individual together with panei, and related p-value for each individual together with panel test statistics are provided. The p-values are estimated by Monte Carlo simulation as the ADF test statistics are nonstandard t distribution. Column 1-2 shows results for the whole sample 1950—2003. Then the sample is split according to reform period.
  • High- and low- income states display convergence for both entire period and each sub-period. For high-income group, over the full sample, the non-convergence hypothesis is firmly rejected by bootstrapped IPS and MW tests, while the IPS test using large sample adjustment is rejected at 10 percent significance level. The rejection of non-convergence is much stronger in all sub-periods (less than 1 percent significance level; all tests). For low-income group, over the full sample, non-convergence is rejected with the large sample adjusted IPS together with bootstrapped IPS tests (not rejected with LLC and MW tests). For the sub-samples, the rejection of non-convergence is uniform and stronger.

  • Medium-income states exhibit divergence over the full sample period; convergence for pre-1980 and 1980-1992, but not for post-1992. Individually, Kerala is the only state that can reject the null of non-convergence. These nonrejections are also accumulated into the panel. Medium-income states appear to be converged in pre-1992, but diverged in subsequent periods. All tests solidly reject the null in pre-1980 and 1980-1992. Nonetheless, in post-1992, states never reject the null for neither individual nor panel.

  • Divergence among the medium income group results from two states, Andhra Pradesh and Karnataka. The growth rate of Andhra Pradesh increased from 1¼ percent in pre-1980s to 3½ percent in 1980-1992, then to almost 5 percent post-1992. For Karnataka, the growth rate surged from 1¾ percent, to 2¾ percent, to 5¼ percent, respectively. Both states emerge as the leaders in the information technology, and positioned themselves as the top IT exporting states. Andhra Pradesh is also a mineral rich state, while Karnataka is a manufacturing hub for the largest public sector industries.

  • Excluding these two states, there is evidence of convergence among the medium-income states also. While previous results indicate divergence for the entire sample period as well as post-1992, there is now convergence in all periods, and the results are robust (Table 6). For the entire period, the null of individual unit roots for Kerala and West Bengal is rejected at less than 5 percent significance level. All tests reject the null of non-convergence. Post-1992 results are slightly weaker. Only Kerala can reject the unit root null. Panel-wise, non-convergence is rejected with both IPS and MW statistics (but not with LLC statistics).

Table: 6

Medium-Income States without Andhra Pradesh and Karnataka

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Sources: Indian authorities: and IMF staff estimates.

The results are from LLC, IPS, and MW panel unit root test for long run convergence.

Δ(yi,ty¯t)=δi+ρi(yi,t1y¯t1)+k1ρiϕi,kΔ(yi,tky¯tk)+ui,t

For details, see Appendix 1. State real net domestic product per capita is used as a. proxy for the state income. Annual data ranges from 1960–2003.The ADF test statistic, ρi, and related p-value fior each individual together with panel test statistics are provide. The p-values are estimated by Monte Carlo simulation as the ADF test statistics are nonstandard t distribution.
Table 7.

Income Divergence across Indian States: Regression Analysis

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Sources: Indian authorities; and IMF staff estimates.

The dynamic panel approach also allows an examination of spillover effects between groups of states over time. We characterize the dynamic relationship among high-, medium- and low-income states as a system of equations:

(6)yitH=j=1pαjHy i,tjH+j=1qαjMy i,tjM+j=1rαjLy i,tjL+fiyH+uityHyitM=j=1pαjHy i,tjH+j=1qαjMy i,tjM+j=1rαjLy i,tjL+fiyM+uityMyitL=j=1pαjHy i,tjH+j=1qαjMy i,tjM+j=1rαjLy i,tjL+fiyL+uityL

  • yitH = log of per capita income of high income states; i = 1,..,5 and t=1,…,30

  • fiyH = fixed effects of high income state i

  • yitM = log of per capita income of medium income states; i =1,..,5 and t=1,…,30

  • fiyM = fixed effects of medium income state i

  • yitL = log of per capita income of low income states; i =1,..,5 and t=1,…,30

  • fiyL = fixed effects of low income state i

  • The number of lags is chosen by minimizing the AIC and SBIC.

The dynamic estimated spillover effects are also small (Figures 2-5).11 Over entire sample period, there are spillover effects among states where a positive shock had positive and permanent effect within the group as well as on other groups. The within-group effect appears to have been relatively large, while the between-group effects were smaller. In general, the spillovers between high-medium income groups are stronger than high-low and medium-low income groups. Numerically, the spillover effects are quite small. A one standard deviation increase in income in one state transfers to only 0.01-0.07 standard deviation increase in income in other states. The bottom line seems to be that states that are ahead do not seem to pull the lagging states along.

Figure 2.
Figure 2.

Spillovers among Indian states (full sample)

Citation: IMF Working Papers 2010, 096; 10.5089/9781451982732.001.A001

Figure 3.
Figure 3.

Spillovers among Indian states (pre-1980)

Citation: IMF Working Papers 2010, 096; 10.5089/9781451982732.001.A001

Figure 4.
Figure 4.

Spillovers among Indian states (1980-92)

Citation: IMF Working Papers 2010, 096; 10.5089/9781451982732.001.A001

Figure 5.
Figure 5.

Spillovers among Indian states (post-1992)

Citation: IMF Working Papers 2010, 096; 10.5089/9781451982732.001.A001

In the sub-sample analysis, the results confirm divergence across states, particularly in the post-1992 period. The interaction between states is not quite evidenced in pre-1980 as well as post-1992 periods. The shock dies out very quickly after a few years. In pre-1980, shock from one state, however, results in more volatile growth to other states. Similarly, in post-1992, the spillover effects are very small and negligible. Most responses are flat around zero. On the other hand, during the period 1980-92, states were possibly more interconnected, with evidence of spillover effects, albeit weak ones.

VI. Concluding Remarks

Convergence and spillovers across countries and within countries are old, but recurrent policy concerns, and India is no exception to this rule. With this motivation, this paper has examined convergence and spillovers across Indian states, using non-stationary panel data techniques. Results on convergence among Indian states are generally found to be similar to but more nuanced than previous studies. Generally speaking, there is evidence of divergence over the entire sample period (1960-2003), convergence during sub-periods corresponding to structural breaks, and club convergence. There is strong evidence of club convergence among the high-and low-income states; the evidence for middle-income states is mixed. Dynamic spillover effects among states are small.

There is evidence of three growth episodes for India. In these episodes, high income states experienced high and stable growth on average, medium income states grew fast, some catching up with high states; some low income stated picked up, but gaps with the high and middle income stated were persistent; and some states continued to lag in the race. From a policy perspective, states that forged ahead were those that benefited from advances in the services sector, those with better infrastructure and credit availability, and those that engaged efficiently in development spending. The lack of dynamic spillovers may also be pointing to a need for better infrastructure and connectivity throughout the country to allow a dissemination of the benefits of growth across the country.

Growth Convergence and Spillovers among Indian States: What Matters? What Does Not?
Author: Piyaporn Sodsriwiboon and Sanjay Kalra