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8 Growth Theory and Convergence Across Indian States: A Panel Study

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Tim Callen, Christopher Towe, and Patricia Reynolds
Published Date:
February 2001
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Author(s)
Shekhar Aiyar

Introduction

India is a land of extraordinary diversity. Regions differ enormously in social, geographic, demographic, and linguistic terms. There are significant differences in levels of economic development, which have been an important preoccupation of policymakers since independence. The importance that has been placed on reducing these disparities has partly reflected the view that regional inequality is intrinsically unfair and could undermine the ability to achieve a consensus among the states on broader policy issues. Moreover, it has long been noted that poverty and other kinds of social deprivation are disproportionately the burden of low-income states. A more equitable income distribution among states, therefore, is consistent with the broader objective of poverty reduction.

There has been a surge of interest recently in analyzing trends in regional disparities from within the framework of neoclassical growth theory. Several papers have tried to ascertain whether the empirical record shows convergence or divergence among the Indian states, and they discuss the factors responsible. These papers have examined different samples of states over different time periods and arrived at sometimes conflicting conclusions. This study will argue, however, that they are all characterized by an inadequate appreciation of the way in which growth theory should treat India’s diversity. In particular, once the central distinction between absolute and conditional convergence has been appropriately drawn, it is possible to obtain a much clearer picture of the experience of the Indian states and the lessons that this experience holds for policymakers.

The subsequent section discusses some of the theory relevant to the empirical work that follows. In this context, some of the existing papers on regional economic development in India are reviewed and critiqued. The third section summarizes the facts about regional economic development in India. Correlations are explored between real income per capita and other variables that may play a role in the growth process. The fourth section presents the econometric study, along with a brief description of the methodology used and an interpretation of the results. This is followed by a conclusion.

Growth Theory

Steady States and Convergence

The traditional starting point for a study of growth is the Solow-Swan model,1 which makes restrictive assumptions about how the world works, and, in turn, yields well-defined and testable predictions. It assumes a constant returns-to-scale technology that is available to all countries in the world, as well as external technological change, savings rates, and population growth rates. On the basis of these assumptions it concludes that countries will converge toward a “steady state” in which output per capita grows at the rate of technological change and output per effective worker remains constant.2 In transition, the speed of per capita growth depends inversely on distance from the steady state, an effect due to diminishing returns to capital. Thus a poor country with a relatively low capital-labor ratio will enjoy high rates of return on capital, and consequently will grow faster than a rich country with a high capital-labor ratio and low rates of return on capital.

This last prediction—called convergence—has been examined empirically by many authors in recent years. The convergence predicted by theory is, however, contingent on the assumptions and parameters of the model; notably the assumptions of exogenous rates of technological change, saving, depreciation, and population growth. There is, however, no reason to believe that these parameters should be common to all countries, and the most cursory examination of the facts shows otherwise. Therefore, what the Solow model really predicts is “conditional convergence”—a country will converge to a steady state that is determined by parameters that are specific to that country, and this steady state may be entirely different from that of another country with a different set of parameters.

Thus, there is a crucial difference between conditional convergence and absolute convergence. Studies show that, for a heterogeneous group of countries, the former often holds in the absence of the latter.3 That is, if we control for possible differences in the steady states of countries, the evidence supports convergence; without controls, the data suggest divergence.

More recent research has led to the development of a range of neoclassical models in which a broader set of factors can affect the steady state of a country. These models incorporate optimizing behavior on the part of households and firms within an economy—typically embedded in the framework developed by Ramsey (1928)—and show that rates of time preference, the degree of openness to trade, the level of services provided by governments, and the degree of protection of property rights can influence the steady state of an economy.4 In addition, models that incorporate human as well as physical capital, e.g., Uzawa (1965) and Lucas (1988), illustrate that long-run growth can occur in the absence of technological change (as long as there is an accumulable factor not subject to diminishing returns), and that the speed of convergence depends on the stock of both human and physical capital.

Of course, in all these models, the rate of a country’s growth is affected by both the distance from the steady state (the more distant the steady state, the faster the growth) and shifts in the steady state itself. Indeed, there is some evidence that for many countries the most important part of the growth process is not the mechanics of convergence to a given steady state but factors leading to changes in the steady state itself (Islam, 1995). If policy activism can increase the steady state level of output per capita, then the growth rate of a country should jump up in response to the fact that the steady state is now further away.

Growth Theory and Regional Analysis

Growth theory has been used to analyze not just samples of several countries, but also samples of different regions within a country. The major theoretical difficulty with this approach is that, in the models discussed so far, economies are assumed to be closed to flows of both labor and capital. Obviously this is not usually the case across state boundaries within a particular country. On the other hand, if we assume unconstrained capital flows across regions, the Ramsey model yields the prediction of instantaneous convergence, which is never observed. Barro, Mankiw, and Sala-i-Martin (1995), however, have shown that if we assume that capital markets are not perfect—in the sense that a certain part of the capital stock (which includes human capital) cannot be used as collateral in interregional credit transactions—then the speed of convergence is not infinite, and lies within a plausible range for reasonable parameter values. The greater the mobility of capital, the quicker the convergence.

Examples of the empirical literature on regional growth are Easterlin (1960a and 1960b) and Barro and Sala-i-Martin (1992a), who examine convergence across the states of the United States; Cashin (1995) for the regions of Australia; and Barro and Sala-i-Martin (1992b) and Shioji (1993), who look at convergence across Japanese prefectures. It is conventional in studies of this type to argue that conditional convergence may be approximated by absolute convergence, with the assumption of a common steady state across regions justified in view of the homogeneity in preferences, culture, and technology within a country, as well as the existence of a common central authority and similar institutional arrangements.

It is questionable, however, whether this assumption can be applied to the different regions of India, since their differences make it less likely that they would tend toward identical steady states. This diversity is reflected in a number of indicators including life expectancy, literacy rates, rates of investment, population density, the structure of economic activity, the degree of urbanization, and the prevalence of the rule of law. The section on regional disparities (below) documents some of this diversity, illustrating the proposition that differences between Indian states are stark enough to warrant the hypothesis of different steady states.

Earlier Work on India

There is already a sizable body of work that examines differences in regional economic development within India, including Chaudhry (1966), Nair (1985), Majumdar and Kapur (1980), Rao (1985), and Ghuman and Kaur (1993). However, these contributions are devoted to an analysis of income trends or movements in the rankings of states according to various criteria, and are not embedded within a framework that enables testing for the convergence predicted by theory. Three recent papers move in this direction: Cashin and Sahay (1996), Bajpai and Sachs (1996), and Rao, Shand, and Kalirajan (1999).

All three papers make use of an empirical growth equation derived by Barro and Sala-i-Martin (1992a), which gives the relationship between income per capita, lagged income per capita, and the convergence coefficient:5

where i indexes the economy, t is time, τ is the length of the observation period, y denotes per capita income, and ε is a random disturbance term. λ is the convergence coefficient, which gives a measure of how quickly an economy is closing the gap between its current position and its steady state.6 It is apparent that λ may be recovered from the coefficient on lagged income.

It is useful to note two key features of equation (1). The first is the constant term C, which is not indexed by economy and therefore incorporates the assumption that all economies have the same steady state. The second is that the length of the observation period, τ is crucial to the exercise undertaken. This is because equation (1) is valid only under the assumption that there are no factors at work to change the steady state during the observation period; this may be valid for small values of τ but certainly not for large values.

Cashin and Sahay take τ=10 and examine the four subperiods between 1961 and 1991, for a sample of 20 Indian states. Although they find evidence of convergence in all four subperiods, their results are not statistically significant. It is only when they introduce additional variables that control for the share of agriculture and manufacturing in total output (which can be viewed as structural variables that proxy for differing steady states) that some, but not all, of the estimated coefficients become significant. They conclude that there is evidence of (weak) convergence over the period taken as a whole.7

Bajpai and Sachs follow a very similar approach, examining a sample of 19 Indian states between 1961 and 1993, which is subdivided into three periods. They, too, have difficulty in obtaining statistically significant results. Only for the subperiod 1961–71 do they find evidence of convergence; for the period as a whole, the hypothesis of convergence is rejected. When the initial share of agriculture in output is included as a control variable, the results improve marginally but their qualitative conclusions are not altered.

Rao, Shand, and Kalirajan look at a sample of 14 states over the period 1965–94, divided into various subperiods. They find evidence of divergence in every subperiod they consider, both in the basic regression and the regression with the share of the primary sector as a control. The difference between their results and those of the other two papers mentioned is startling. So, it is worth emphasizing that they work with a smaller sample of states and that their data source for state product estimates is different.

Certain common points may be noted about all three papers. First, they assume a common intercept for different regions, implying that all the states of India have an identical steady state toward which they are converging or from which they are diverging. In doing this, they follow in the tradition of the interregional empirical work discussed earlier.

Second, all these studies introduce an explanatory variable—such as the share of agriculture, the share of manufacturing, or a weighted sectoral index—to control for production shocks that are correlated across regions. As would be expected if there were heterogeneous steady states, the introduction of these additional variables causes an increase in the estimate of λ. For example, Cashin and Sahay find that introducing the control not only leads to a significant estimate of λ for the period as a whole, but also drastically raises the estimate. Similarly, in Bajpai and Sachs, the one significant convergence coefficient found (for the period 1961–71) is raised with the introduction of the control. In Rao et al., the speed of divergence is reduced for every subperiod that they examine once the share of the primary sector is taken into account. While these earlier studies point in the direction of conditional convergence, however, the fact that they do not explicitly consider the possibility of different intercepts is an important drawback.

Regional Disparities: The Empirical Record

Facts

Tables 8.18.4 and Figures 8.18.3 (on the following pages) highlight some of the regional disparities among 19 of India’s states for which data have been gathered. It will be immediately apparent that these disparities are both enormous and persistent. The dispersion of per capita income, literacy rates, rates of urbanization, and other social and demographic indicators are all greater than those commonly found in relatively homogenous groups of countries (such as the OECD, or Europe).

Table 8.1.Per Capita Real Income, 1971–96
Income in 1971 (1990/91 prices)Rank in 1971Income in 1996 (1990/91 prices)Rank in 1996Annualized Growth Rate 1971–96 (percent)Rank
Andhra Pradesh2,992105,50472.45
Assam2,737133,872141.414
Bihar2,056182,170190.219
Gujarat4,24037,37542.28
Haryana4,48628,32432.54
Himachal Pradesh3,46865,38681.812
Jammu and Kashmir2,803123,806161.216
Karnataka3,27985,77862.37
Kerala3,03895,126102.19
Madhya Pradesh2,476164,014131.910
Maharashtra4,00549,51823.41
Manipur1,949194,257123.12
Orissa2,445173,813151.811
Punjab5,47319,87912.46
Rajasthan3,33074,285111.017
Tamil Nadu2,972116,29453.03
Tripura2,568143,130180.818
Uttar Pradesh2,486153,617171.513
West Bengal3,69355,17891.415
Source: Central Statistical Organization.
Source: Central Statistical Organization.
Table 8.2.Population and Urbanization, 1971–96
Population 1971 (millions of persons)Population 1996 (millions of persons)Annualized Population Growth Rate 1971–96 (percent)Land Area (square kilometers)Population Density 1971 (persons per square kilometer)Population Density 1996 (persons per square kilometer)Urban Population 1961 (percent of population)Urban Population 1991 (percent of population)
Andhra Pradesh43.572.02.0275,04515826217.426.8
Assam14.626.72.478,4381863407.211.1
Bihar56.495.42.1173,8773245498.413.2
Gujarat26.744.82.1196,02413622925.834.4
Haryana10.018.22.444,21222641217.324.8
Himachal Pradesh3.55.61.955,673631016.48.7
Jammu and Kashmir4.68.52.5101,236458416.623.8
Karnataka29.348.22.0191,79115325122.330.9
Kerala21.331.01.538,86354879815.126.5
Madhya Pradesh41.772.52.2443,4469416314.323.2
Maharashtra50.486.32.2307,71316428028.238.7
Manipur1.12.02.422,32749909.027.7
Orissa21.934.41.8155,7071412216.313.4
Punjab13.622.11.950,36227043923.129.7
Rajasthan25.848.42.5342,2397514116.322.9
Tamil Nadu41.258.41.4130,05831744926.734.2
Tripura1.63.02.510,4861532868.815.3
Uttar Pradesh88.3150.72.1294,41130051212.919.9
West Bengal44.373.62.088,75249982924.527.4
Source: Central Statistical Organization.
Source: Central Statistical Organization.
Table 8.3.Literacy, 1971–96
Literacy in 1971 (percent of population)Rank in 1971Literacy in 1991 (percent of population)Rank in 1991Literacy in 1996 (percent of population)Rank in 1996
Andhra Pradesh251444165116
Assam29115312733
Bihar201738194419
Gujarat3646256610
Haryana271256116211
Himachal Pradesh328943715
Jammu and Kashmir191948145812
Karnataka31956105714
Kerala601901911
Madhya Pradesh221544155215
Maharashtra393652724
Manipur337607686
Orissa261349135713
Punjab345588669
Rajasthan191838184818
Tamil Nadu392634668
Tripura3110606762
Uttar Pradesh221642175017
West Bengal336589667
Source: National Sample Survey Organization.
Source: National Sample Survey Organization.
Table 8.4.Social Indicators, 1976–96
Infant Mortality Rate 1976 (percent of live births)Rank in 1976Infant Mortality Rate 1996 (percent of live births)Rank in 1996Poverty Rate 1978 (percent of population below poverty line)Poverty Rate 1994 (percent of population below poverty line)Annualized Percent Change in Poverty Rate
Andhra Pradesh123963947.029.42.9
Assam144107612
Bihar731164.860.40.4
Gujarat1541362739.933.81.0
Haryana11476910
Himachal Pradesh1158616
Jammu and Kashmir682
Karnataka80362752.937.62.1
Kerala54115153.229.23.7
Madhya Pradesh15112991563.944.12.3
Maharashtra92455467.843.52.7
Manipur
Orissa149111031662.140.32.7
Punjab98554226.921.61.4
Rajasthan15514861351.643.51.1
Tamil Nadu112654254.934.92.8
Tripura
Uttar Pradesh19815861346.740.20.9
West Bengal58551.826.04.2
Source: The World Bank
Source: The World Bank

Figure 8.1.Per Capita Income in Selected States, 1971–96

Source: Central Statistical Organization.

Figure 8.2.The Evolution of Real Per Capita Income Across States

(In 1990/91 rupees)

Source: Central Statistical Organization.

Figure 8.3.The Evolution of Literacy Rates

(In percent)

Source: Central Statistical Organization.

Table 8.1 and Figures 8.1 and 8.2 summarize movements in per capita real income during the 1971–96 period. The states can be conveniently grouped into three categories according to their status in 1971: the six poorest—Maniput, Bihar, Orissa, Madhya Pradesh, Uttar Pradesh, and Tripura; seven middle-income states—Assam, Jammu and Kashmir, Tamil Nadu, Andhra Pradesh, Kerala, Rajasthan, and Himachal Pradesh; and the five richest states—Punjab, Haryana, Gujarat, Maharashtra, and West Bengal.

The income gaps have been profound. In 1971, Punjab, the richest state, was more than twice as rich as the poorest state, Manipur; by 1996 the difference was even more marked, with Punjab enjoying more than three times the income-level of the poorest state, Bihar. Differences in growth rates also have been large. For example, Maharashtrian incomes grew annually at a rapid pace of 3.4 percent over the period as a whole, while Bihari incomes remained almost stagnant, increasing at an annual rate of only 0.2 percent. There has also been considerable variation in performance within the three groups.

Regional disparities are seen in other indicators of development (Table 8.2). Annual population growth in the two southernmost states of India, Tamil Nadu and Kerala, was only about 1.4 percent and 1.5 percent, respectively, during the period, whereas population growth reached 2.5 percent in Rajasthan and 2.4 percent in Manipur. There are significant differences in urbanization across states—for example, Himachal Pradesh in 1991 was still overwhelmingly rural, while in Maharashtra the proportion of city dwellers was approaching 40 percent.

Table 8.3 and Figure 8.3 document literacy across states. In 1971, Kerala, with a literacy rate of 60 percent, was well ahead of any other state; all other states had a rate under 40 percent. In 1991, Kerala remained at the top of the list, and Bihar and Rajasthan remained the most illiterate states.8 During this 20-year period, literacy improved in every state without exception, but not at a rapid pace (apart from Haryana and Himachal Pradesh, which both doubled their literacy rates over 20 years).

The literacy charts for 1996 show a remarkable improvement for almost every state.9 Bihar and Rajasthan are now the only states in India with a literacy rate under 50 percent, and Kerala is approaching OECD standards of literacy. The dispersion of literacy rates, as shown in Figure 8.4), after increasing steadily up to the 1990s, also diminished over the last five years. Regional disparities remain profound, however, and female literacy continues to lag in every state. In Bihar and Rajasthan female literacy in 1996 was only 29 percent.

Figure 8.4.Standard Deviation of Log Real Income

Source: Central Statistical Organization.

Other social indicators also vary widely across the states (Table 8.4). For example, the gap between infant mortality and poverty rates in the best-off and worst-off states is enormous in both cases. In the case of infant mortality, Kerala’s record is again outstanding, and that of the “heartland” states is dismal. In accordance with the conventional wisdom that diverse social indicators tend to move together, the infant mortality rate is fairly closely correlated with the literacy rate across the Indian states—in 1996 the correlation was 0.74, with the expected negative sign.

Patterns

The evidence surveyed so far presents a picture of large disparities in both levels and growth rates of per capita income. Some interesting patterns may be gleaned from this record, which have a bearing on whether or not the convergence predicted by growth theory has been at work, and, if it has, whether it is conditional or absolute in nature.

It is generally the case that initially rich states have tended to remain rich and initially poor states have tended to remain poor. This implies a positive correlation between initial income and final income. But, more troublingly, there is also a positive correlation between initial income and growth. Table 8.5 shows the simple correlation coefficient between growth rates (broken up by decade) and the initial values of certain variables. The correlation between income at the beginning of the decade and the growth rate over the decade is negative only for the 1970s. It is small but positive for the 1980s, and large and positive for the five years of the 1990s. For the period as a whole, the correlation between initial income and growth is positive. All this is at least suggestive of absolute divergence since the 1980s (if not before) and, moreover, of accelerating divergence.

Table 8.5.Correlations Between Growth Rates and Initial Values of State and Control Variables
Annualized Growth Rate 1971–81Annualized Growth Rate 1981–91Annualized Growth Rate 1991–96Annualized Growth Rate 197l–96
Log Real Per Capita Income 1971–0.260.33
Log Real Per Capita Income 19810.04
Log Real Per Capita Income 19910.60
Literacy Rate 19710.110.48
Literacy Rate 19810.04
Literacy Rate 19910.53
Literacy Rate (excluding Kerala) 19710.180.66
Literacy Rate (excluding Kerala) 19810.16
Literacy Rate (excluding Kerala) 19910.56
PVK 19710.010.51
PVK 19810.34
PVK 19910.69

This conjecture is reinforced by Figure 8.5, which depicts the standard deviation of the log of real per capita income over time.10 Again, there is a clear upward trend for the period as a whole, which grows more pronounced from the mid-1980s onward. It is interesting that the rapid absolute divergence of the 1990s coincides with the period of India’s economic liberalization program. Although the precise relationship between liberalization and divergence must await a study that focuses specifically on this issue, liberalization appears to have disproportionately benefited those states with high current per capita incomes. One possible explanation is that these states had better social and economic infrastructures in place and were in a better position to take advantage of the reduction in impediments to private economic activity.

Figure 8.5.Standard Deviation of Literacy Rate

Source: Central Statistical Organization.

Conditional convergence is examined by considering two variables that might have a bearing on a region’s steady state, the literacy rate (LIT) and private capital investment (PVK), the latter of which is proxied by the amount of credit extended in a region by India’s Scheduled Commercial Banks (SCB).11 The correlation of private investment in the initial year with growth in the subsequent decade is positive for all three subperiods. Moreover, in each subperiod, this correlation is stronger than the correlation with initial income. As with initial income, the correlation is weakest in the 1970s and strongest in the 1990s.

As expected, initial literacy is also positively correlated with growth in every subperiod. For the period as a whole, this correlation is stronger than that with initial income. As noted earlier, Kerala is also an outlier with respect to the other states in our sample. Excluding Kerala leads to much higher correlations in every subperiod, and a very high positive correlation for the period as a whole. Correlations by themselves establish very little, but Table 8.5 does comprise circumstantial evidence that literacy and private investment are variables that influence subsequent growth, and that should therefore be controlled for in ascertaining conditional convergence.

Econometric Analysis

Methodology

The previous discussion strongly suggests that an econometric study of convergence across regions in India needs to control for differences in steady states. This can be achieved in a framework consisting of a dynamic panel with fixed effects, as described in Knight, Loayza, and Villanueva (1993), Islam (1995), and Lancaster and Aiyar (1999).

Our general specification is described by the following equation:

where i indexes the region, t the time period, y denotes real per capita income, τ denotes the number of years between each successive observation, η is a region-specific time invariant fixed effect, and ε is a random disturbance term. W is a vector of explanatory variables, which in our case comprises two variables, LIT and PVK. δ is the corresponding coefficient vector. The coefficient on the log of lagged income, γ, is equal to e-λτ, where λ is the convergence coefficient.

This fixed-effects formulation allows us to control for unobserved differences between the steady states of regions in addition to the observed differences captured by the W vector.12 Identification of the fixed effects is only possible in a panel framework—the previously cited studies of Indian regional development all used a cross-section approach and so could not identify fixed effects. To the extent that the fixed effects are correlated with the explanatory variables (including lagged income), their omission leads to an omitted-variable bias. Since the presumed correlation with lagged income is positive, the coefficient for this variable would be biased upward in a cross-section study, implying that the convergence coefficient λ will be underestimated.13 Thus, consideration of a fixed-effects framework would be expected to yield higher estimates of convergence relative to the cross-section studies that have gone before.

Estimation of a dynamic panel with fixed effects presents technical difficulties. Lancaster (1997) describes a method for obtaining consistent, likelihood-based estimates by seeking an orthogonal reparameterization of the fixed effects in the model. Unfortunately, this estimator is not applicable in the present case since it does not allow for the possibility of heteroskedasticity in the sample. Chamberlain’s Π-matrix approach has been widely used for panel studies of this nature. Its use is precluded here, however, since we have only 19 states in our sample, and the weighting matrix becomes nearly singular. We therefore employ the Least Squares with Dummy Variables (LSDV) estimator. This estimator is known to be inconsistent in the direction of N, but Amemiya (1967) has shown that it is consistent in the direction of T and asymptotically equivalent to maximum likelihood estimation. Moreover, it seems that in practice the estimates obtained by LSDV and the Π-matrix approach are very similar, at least in cross-country panel studies (Islam, 1995).

Using data for each consecutive year has the disadvantage of increasing the likelihood of serial correlation due to business cycle effects. Using long period averages, however, risks obscuring changes in the steady state that have occurred during the period. In order to balance these two concerns, the present study uses a panel of five-year spans (τ=5). For example, for the first observation, the dependant variable is the log of real per capita net state domestic product in 1976, and lagged income on the tight-hand side (RHS) is for the year 1971. To minimize the risk of simultaneity bias, the other control variables are also lagged five years. Standard errors are estimated using White’s variance-covariance matrix, which is robust to heteroskedasticity of an unknown form.

Results

Table 8.6 presents the results of two regressions. Regression 1 illustrates the statistical effect of assuming a common steady state. In this case, a common intercept is assumed for every region and the other control variables are omitted. The results are dramatic—the coefficient on lagged income is a statistically significant 1.07, with an implied convergence rate of minus 0.013. In other words, we find evidence of absolute divergence at the rate of 1.3 percent over a five-year period.

Table 8.6.Regressions with the Log of Real Per Capita Income as the Dependent Variable1
Regression 1Regression 2
Constant–0.469 (0.272)
Yi,t–τ1.069 (0.033)0.369 (0.129)
LIT0.762 (0.277)
PVK0.147 (0.035)
Lambda2–0.013 (0.006)0.199 (0.070)
R-squared0.9020.946
Adjusted R-squared0.9020.930

Standard errors reported in parentheses.

Coefficient of convergence.

Standard errors reported in parentheses.

Coefficient of convergence.

Regression 2 includes fixed-effects coefficients for each state, and the control variables, LIT and PVK. An F-test rejects, at the 5 percent level of significance, the null hypothesis that all the fixed effects are equal to one another. In other words, the hypothesis of a common steady state is implausible.

Both control variables have a positive and significant effect on growth. The coefficient on LIT is 0.76, which implies that a 1 percentage point increase in literacy corresponds to an increase in the five-year period growth rate of per capita income of almost 8/10 of a percentage point. The strength of this relationship probably reflects the fact that literacy proxies for other social indicators that tend to move in a similar direction, such as life expectancy and various measures of health. The coefficient on PVK is 0.15, which implies that a 1 percentage point increase in investment per person raises the growth rate by 0.15 percentage points.

The effect of the conditioning variables in Regression 2 is extremely strong, and so we would expect to find much stronger convergence than that found by previous studies. This is indeed the case; the coefficient on lagged income is 0.0379, which implies an extremely high convergence coefficient of 0.199 and a half-life of about 3½ years.14

Table 8.7 lists the fixed effects recovered from Regression 2. Since we did not, in our study, work from an explicit production function, it is not possible to attach a precise interpretation to these region-specific effects, other than to note that they act as proxies for each region’s steady state.15 However, in their role as steady state proxies, and given that we have already controlled for literacy and the amount of investment, we may regard them as a measure of the efficiency with which the different regions are converting inputs into outputs. Thus they are related to the conventional notion of total factor productivity (TFP) with the important difference that TFP is computed for individual economies on the basis of only their own time series data, whereas the fixed effects here are inherently based on an intertegional comparison.

Table 8.7.Fixed-Effects Estimates
Fixed EffectRank
Andhra Pradesh4.8915
Assam4,76914
Bihar4.63118
Gujarat4.9173
Haryana5.1301
Himachal Pradesh4.8876
Jammu and Kashmir4.8974
Karnataka4.80012
Kerala4.55019
Madhya Pradesh4.8578
Maharashtra4.8469
Manipur4.82810
Orissa4.76015
Punjab5.1302
Rajasthan4.8677
Tamil Nadu4.71616
Tripura4.69717
Uttar Pradesh4.80211
West Bengal4.77913

We find that the fixed effects are highly and positively correlated with initial income; the simple correlation coefficient is 0.65. Their correlation with growth rates over the period as a whole is also positive at 0.32. These results are in line with what we would expect from studies of samples of heterogeneous countries. An examination of the legions by rank of their fixed effects yields one rather striking result, namely, Kerala’s place at the bottom of the fable, comfortably under even Bihar. This would be an indication that Kerala has been inefficient in translating its enviable human capital resources into commensurate increases in output per capita, but may also reflect the fact that much of Kerala’s educated population has been able to migrate elsewhere. Punjab and Haryana top the table, and, in general, initial income is a good predictor of a state’s rank by this measure. Note that the large values obtained for the fixed effects and their considerable dispersion suggest that there are important factors determining the steady states of regions that are not accounted for by this study.

Policy Implications

These results strongly suggest that states in India are converging to different steady states, and that these steady states are determined, at least in part, by literacy rates and private investment. The question then naturally arises as to what governments can do to improve literacy and attract private investment, thus raising the steady state output of their region and generating rapid growth. There are undoubtedly numerous factors that determine LIT and PVK for a given region. Here we consider only two that are amenable to direct manipulation by policymakers—capital expenditures by state governments on social infrastructure (SOC) and capital expenditures by state governments on economic infrastructure (ECO). The first variable measures expenditures on categories such as education, water supply, sanitation, and medical and public health, while the second variable represents expenditures on transportation, power and electricity, telecommunications, and irrigation projects. Both variables are measured in thousands of Rs per person.

It seems reasonable that government spending in these areas contributes to human capital and promotes private investment.16 Therefore we regress LIT and PVK in turn on both SOC and ECO, in the same fixed-effects panel framework followed thus far. Table 8.8 documents the results, which suggest that both SOC and ECO are significant in accounting for the litetacy rate, with coefficients of 2.54 (0.50) and 0.69 (0.22), respectively. These policy variables appear to play an even more important role in influencing private investment; in the equation for PVK, the coefficients on SOC and ECO are 4.77 (1.77) and 3.64 (1.03), respectively. These regressions are therefore indicative of two channels through which governments can attempt to alter the steady states of their economies.

Table 8.8.“Production Function” Regressions with LIT and PVK as Outputs1
Dependent VariableLITPVK
SOC2.54 (0.50)4,77 (1.77)
ECO0.69 (0.22)3.64 (1.03)
R-squared0.640.78

Standard errors reported in parentheses.

Standard errors reported in parentheses.

To test the robustness of these results, we also fit a Cobb-Douglas “production function” with LIT and PVK taken one by one as the outputs; the inputs are SOC and ECO, along with a multiplicative region-specific efficiency parameter. The results of this regression, in which coefficients represent elasticities, are detailed in Table 8.9. The elasticities of the literacy rate with respect to SOC and ECO are, respectively, 0.24 (0.05) and 0.10 (0.08), although the latter estimate is no longer statistically significant. The elasticities of private investment with respect to SOC and ECO are, respectively, 0.65 (0.10) and 0.46 (0.15). These elasticity estimates, which are both large and highly significant, appear to confirm the efficacy of government investment in infrastructure in attracting private investment and improving the stock of human capital. It is noteworthy that the regressions indicate that social expenditures have an even greater impact than expenditure on physical infrastructure.17

Table 8.9.“Production Function” Regressions with In (LIT) and In (PVK) as Outputs1
Dependent VariableIn (LIT)In (PVK)
SOC0.24 (0.05)0.65 (0.10)
ECO0.10 (0.09)0.46 (0.15)
R-squared0.610.81

Standard errors reported in parentheses.

Standard errors reported in parentheses.

Conclusion

One of the main purposes of this study was to show that in a country as diverse as India, there is a meaningful difference between conditional and absolute convetgence. It has been shown that the neoclassical model’s prediction of convergence is of a conditional nature and that convergence among the Indian states is proceeding apace. By demonstrating a concomitant process of absolute divetgence, however, our work suggests that the really important and interesting feature of regional growth is not an economy’s distance from its steady state (that is being closed rapidly at any point in time), but the factors that determine that steady state. This conclusion is important, since it suggests that there is scope for policy to improve the growth rate of per capita incomes.

We have identified two factors that seem to be extremely important in determining a region’s steady state level of income: literacy and per capita private investment. In particular, even modest improvements in literacy and private investment appear to have a substantial positive effect on growth. Furthermore, the results suggest that both literacy and private investment can be influenced by policy, and hence individual state governments can play an important role in enhancing their own growth prospects.

In practice, however, the ability of state governments to increase expenditures on social and economic infrastructure is greatly dependent on their financial positions. This ability has been adversely affected by rising deficits in recent years, owing to stagnant revenue collections and increasing expenditures on civil service salaries and interest payments. Thus, fiscal reform—particularly at the state level and with respect to fiscal-federal relations—will be an important ingredient for improving steady state levels of incomes across India. Enhancing the flow of private investment spending on infrastructure will also be important. Recent efforts by some states to liberalize private sector participation in the power sector and to implement Build, Operate, and Transfer systems for roads and bridges are encouraging and would be bolstered by further liberalization and deregulation at the central government level.

In addition, significant differences in growth performance and steady states have been found that are not explained by literacy and private investment rates. If cross-country studies and anecdotal evidence are anything to go by, we would suspect the fixed effects to capture factors like the degree to which the rule of law is observed and enforced, the degree of bureaucratic control and inefficiency in the economy (which bears a strong relationship to the pervasiveness of corruption), the relations between organized labor and industry and the laws governing these relations, the laws pertaining to other spheres such as land reform, tax regimes, and urban regulation, and the extent to which foreign investment permits diffusion of new technologies and products and breeds competition. This study does not establish these relationships. By showing how important differences in steady states are, however, and by assessing the importance of two key variables in their determination, it does leave the door open for future research (which must await the availability of appropriate data) to investigate the role played by these other suggested factors.

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Appendix 8.1: Data

An important starting point for constructing the database used was data provided by Cashin and Sahay, which is gratefully acknowledged. This data was extended and updated using data on Net Domestic Product for each state taken from the consolidated series prepared by the Central Statistical Organization (CSO). Population charts were from the census for those years in which the census was conducted; midyear estimates are available in different issues of CSO publications such as the Statistical Pocket Book of India and the Statistical Abstract of India. Literacy rates were obtained from census data when available and survey rounds conducted by the National Sample Survey Organization (NSSO) otherwise. Survey results are reported in the NSSO’s journal, Sankhya. For 1976 and 1986 literacy rates were constructed by linear interpolation. Infant mortality rates and poverty charts were based on World Bank estimates.

The charts for state capital expenditures on social and economic infrastructure were taken from various monthly issues of the Reserve Bank of India Bulletin and Supplements to the Bulletin. Data on credit extended by India’s Scheduled Commercial Banks are available at the state level in different issues of the Reserve Bank of India’s Statistical Tables Relating to Banking. Urbanization charts were taken from census data.

1

See, for example, Solow (1956).

2

Output per effective worker refers to output produced by labor as measured in efficiency units; with exogenous labor-augmenting technological change, each unit of labor becomes more productive in each successive period.

3

The cross-country growth literature is too vast to document here. Examples are Baumol (1982), Barro (1991), and Mankiw, Romer, and Weil (1992).

4

For a survey of such models, see Barro and Sala-i-Martin (1995).

5

Equation (1) is derived from the standard Ramsey model with a Cobb-Douglas product ton function. In this model one is able to obtain two differential equations: one describing the evolution of capital per effective worker and the other describing the evolution of consumption per effective worker. A log linearization of this system of differential equations enables us to express the growth rate of the economy near the steady state as a function of lagged income, to which we add an error term to obtain equation (1). For a complete derivation see Appendix 2A of Chapter 2 in Barro and Sala-i-Martin (1995).

6

It can be shown that the “half-life” of the convergence process is given by (In2)/λ. Thus, for example, a convergence coefficient of .05 corresponds to a half-life of 14 years—this is the period it takes for the economy to close half the distance between its current level of output per effective worker and its steady state level.

7

Cashin and Sahay also carry out an exercise that is not repeated in this paper: they examine the role of interstate migration in the convergence process. They find that the response of migration to interstate differences in income is “anemic,” and that controlling for migration makes very little difference to their estimate of convergence.

8

Kerala is exceptional among the Indian states for the sharp and persistent dichotomy between its social indicators, which are of an almost first-world standard, and its levels of per capita income and growth performance, which are relatively mediocre. For a discussion of this issue, see Ramachandran (1997).

9

Statistics like this inevitably lead to suspicions about the quality of data available. In fact the literacy charts for 1991 are from the population census while the charts for 1996 are from the 52nd round of the National Sample Survey. While the two sources often arrive at different estimates of the number of people in the economy, the number of literate persons, etc., their estimates of literacy rates are usually thought to be comparable.

10

A narrowing trend for this measure of dispersion is sometimes referred to as σ-convergence, which is quite different from the β-convergence discussed in this paper.

11

PVK is measured in thousands of rupees per person. There are reasons to be somewhat wary of this proxy. Although lending by the SCBs to the private sector dwarfs lending by other institutions, credit tends to be extended not just for new investments bur also as working capital. Nonetheless, we would expect there to be a strong correlation between credit extended for the two different purposes. This is certainly the case at the national level—the correlation between SCB credit extended and gross private capital formation was 0.93 over the period in question.

12

The reason for adopting a fixed-effects formulation instead of a random effects one is that, in the latter approach, one must assume that the effects are uncorrected with the exogenous variables included in the model. This is almost certainly not the case in the framework assumed above. The fixed effect may be thought of as representing “technology,” or the efficacy with which inputs are transformed into outputs; it seems inevitable that this is not independent of an explanatory vector of variables important to the growth process.

13

This is just another way of making the point that absolute convergence differs from conditional convergence: the former will always tend to be smaller than the latter because of the bias arising from the omission of appropriate conditioning variables.

14

Although this convergence coefficient is quite high, it is worth bearing in mind that this is the rate of convergence after controlling for steady states, and that inequalities of income and growth in India are seemingly driven by wide differences in steady states rather than by slow convergence. Other studies have also found very high rates of convergence with the introduction of suitable control variables—notably Caselli, Esquivel, and Lefort (1996), who estimated a convergence rate of 0.128 (implying a half-life of 5½ years) for a sample of 97 heterogeneous countries.

15

Knight, Loayza, and Villanueva (1993) and Islam (1995) start with an explicit neoclassical production function, and are thus able to derive the relationship μi = (1–e-λτ) In A(0)i, where μ is the fixed effect and A(0) represents “technology” broadly defined in the initial period of observation.

16

Studies indicating a complementarity between public infrastructure and private investment include Greene and Villanueva (1991) and Seitz and Licht (1992).

17

The positive impact of state government health and education expenditures on human capital formation has also been studied in Reserve Bank of India (1993).

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