# Economic Growth and Regional Inequality in India

Gaurav Nayyar

Given the disparate levels of income and development among the states in India, do they exhibit any tendency in the data to converge to common steady-state paths? In a panel data study for 16 Indian states for the period from 1978-79 to 2002-03, it is found that (a) the states are not converging to identical levels of per capita income in the steady-state; (b) once factors that affect steady-state levels of income are controlled for, the poor states grow faster on average than the rich ones; and

#### (c) there is an increase in the dispersion of per capita incomes across states over time. This is indicative of Indian states converging to increasingly divergent steady-states, which may be attributed to increasing inter-state disparities in levels of private and public investment and an insignificant equalising impact of centre-state government transfers.

The author would like to thank Tim Besley, Maitreesh Ghatak, K L Krishna and Deepak Nayyar for valuable comments and suggestions.

Gaurav Nayyar (gaurav.nayyar@economics.ox.ac.uk) is a research scholar at the department of economics of the University of Oxford.

he objective of this paper is to analyse whether or not states in India, at disparate levels of income and development, exhibit any tendency in the data to converge to common steady-state paths. In doing so, it does not attempt to explicitly test a particular theoretical growth model. Instead, it seeks to identify empirical regularities indicative of convergence in the data. In providing a comprehensive empirical analysis of convergence across Indian states over time, the paper also explores the possible economic explanations for the ﬁndings that emerge from the data.The scope of the study is limited to an analysis of 16 major Indian states during the period from 1978-79 to 2002-03. The choice of time period is determined by three factors. First, the early 1980s were a turning point for the rate of economic growth in India. Between 1950 and 1980, growth in real GDP per capita was approximately 1 per cent per annum. In contrast, during the period from 1980 to 2000, growth in GDP per capita was approximately 4 per cent per annum. Second, the time period under consideration represents a period of economic reform in India, with initial liberalisation policies starting in the early 1980s, followed by wide-ranging reforms initiated in the early 1990s. Third, the choice of time period reduces the task to manageable proportions by ensuring the availability of comparable and complete data for the set of relevant variables.

The structure of the paper is as follows. Section 1 provides a brief review of the literature on the subject, in terms of both theory and evidence. Section 2 develops an analytical framework, which provides the foundations for the econometric analysis to follow. Section 3 sets out the econometric model. Section 4 reports the results. Section 5 provides economic explanations for the results of the econometric analysis. Section 6 discusses some policy implications. Section 7 draws together the conclusions.

The contribution of the paper to the literature on the subject is threefold. First, it extends the empirical analysis of the convergence phenomenon across Indian states up to 2002-03. This is crucial in light of the potential implications that economic liberalisation may have for regional inequality.1 Second, it addresses methodological concerns about using ﬁxed-effects estimation in the context of dynamic panel data models by employing generalised method of moments estimation. Third, it attempts to provide intuitive economic explanations for the trends observed in the data, thereby highlighting important policy issues.

##### 1 Review of Literature

##### 1.1 Growth Theory and Convergence

A major focus of recent work on growth empirics has been the issue of convergence. There is extensive literature on whether or

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not there are natural forces that lead to convergence in the levels of per capita income over time. Yet, there is some ambiguity about its precise deﬁnition.

Barro and Sala-i-Martin (1995) identify two notions of convergence. First, there is the concept of β-convergence, which captures the idea that a poor economy tends to grow faster than a rich one, thereby enabling the former to catch up with the latter. Solow (1956), in a seminal article, provides the basic framework for explaining this negative correlation between initial levels of income and subsequent growth rates. The key assumption driving such a convergence result in the Solow model is a standard neoclassical production function with diminishing returns to physical capital, i e, the poorer economy has lower levels of physical capital, and hence, higher marginal productivity of capital. Thus, for any given rate of investment, it will achieve a higher rate of growth in transition to the steady-state. The steady-state growth rate for each economy, however, is determined by an exogenously given rate of technological progress. Moreover, assuming the technology is freely available to everyone, the model predicts that all countries will eventually attain the same steady-state growth rate.

β-convergence as predicted by neoclassical theory, however, is dependent on the assumptions about the parameters of the model, in particular, the assumptions regarding rates of saving, depreciation, population growth and technological progress. The stronger notion of convergence, deﬁned as “unconditional or absolute convergence”, assumes that all these parameters are equal across countries, thereby implying that all countries converge to the same steady-state level of per capita income. But there is no evidence to suggest or reason to believe that these parameters should be common to different countries. Hence, what the Solow model really predicts is “conditional convergence”, where each country converges to a steady-state, which is determined by parameters speciﬁc to that country. Importantly, given different sets of parameters, the steady-state income level of one country may be entirely different from that of another.2

The second concept of convergence, known as σ-convergence, relates to the behaviour of cross sectional dispersion of incomes over time. For example, σ-convergence is said to occur if the dispersion of incomes across regions declines over time. Importantly, conditional β-convergence is consistent with σ-divergence. For instance, a change in relevant parameters that drives steady-state income levels apart in rich and poor regions will lead to σ-divergence, although each region may still be conditionally converging to a divergent steady-state. In fact, even unconditional β-convergence implies convergence in levels of income only in the absence of region-speciﬁc random disturbances that may push states away from each other.

##### 1.2 Cross-country and Regional Analysis

Most empirical work on the subject consists of running cross section regressions with subsequent growth rate of income as the dependent variable and initial income level as the primary independent variable. Other explanatory variables in such regressions are designed to control for differences in steady-states across countries [Mankiw, Romer and Weil 1992]. A serious limitation of

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february 9, 2008this econometric methodology is that only those differences in technology and preferences, which can be readily observed and measured, can be accounted for. However, differences in technology and preferences may have variables that are not readily measurable or even observable. In the framework of cross section regressions, it is not possible to control for such unobservable or immeasurable factors. Only a panel data approach can overcome this problem.3

In practice, growth empirics has not been conﬁned to cross country analysis. It has also been used to examine samples of different regions within countries. This is obviously important in large countries. Leading examples of the literature on regional growth empirics are Barro and Sala-i-Martin (1992) who analyse convergence across states of the US and Cashin (1995) who does the same for regions of Australia. Usually, such regional studies argue that absolute convergence approximates conditional convergence as they assume common steady-states across regions in view of homogeneity of technology, preferences and culture within a country. The application of this assumption to different states of India, however, is questionable. Stark differences between states, in initial conditions, make the assumption of convergence to identical steady-states unrealistic.4

##### 1.3 Growth Theory and Convergence: Literature on India

There exists literature, which attempts to analyse, empirically, convergence or divergence of income levels across Indian states. Cashin and Sahay (1996), Bajpai and Sachs (1996), Rao, Shand and Kalirajan (1999) and Singh and Srinivasan (2002) are four such papers, which analyse the relationship between per capita income, lagged per capita income, and the convergence coefﬁcient in a cross section regression framework. Let us analyse them in turn.

First, Cashin and Sahay (1996) examine four sub-periods between 1961 and 1991, for a sample of 20 Indian states. Although they ﬁnd evidence of unconditional and conditional convergence in all four sub-periods, their results are not statistically signiﬁcant.5 They conclude that for the period as a whole, there is evidence of weak convergence. Second, analysing a sample of 19 Indian states for the period 1961-1993 (divided into three subperiods), Bajpai and Sachs (1996) do not ﬁnd statistically signiﬁcant results of convergence for the period as a whole. It is only for the sub-period 1961-71 that they ﬁnd evidence of convergence. Third, Rao et al (1999) examine a sample of 14 major states over the period 1965-1994, divided into various sub-periods. Strikingly, they ﬁnd evidence of absolute and conditional divergence in every sub-period they consider. This is in sharp contrast to the results of the other two studies. Fourth, in the most recent study on the literature on the subject, for a sample of 14 major Indian states for the period from 1990-91 to 1998-99, Singh and Srinivasan (2002) ﬁnd weak evidence for both absolute and conditional convergence.

It is important to note a key feature of the regression models used in these studies. They assume a common intercept for different regions, thereby implying that all states of India are converging to or diverging from identical steady states (after controlling for time-varying observables). This is unrealistic.

Hence, not explicitly considering the possibility of different intercepts is a signiﬁcant drawback.

More recent work, however, does overcome this problem by employing a dynamic panel with ﬁxed effects framework. First, Nagaraj et al (2000) ﬁnd evidence of conditional convergence for 17 states over the period 1960-94. Second, for a sample of 19 states for the time period 1971-96, Aiyar (2001) ﬁnds strong evidence for absolute divergence but conditional convergence. Third, Trivedi (2002) reveals conclusions similar to those of Aiyar (2001) for 16 major states in India during the period from 1960 to 1992. Moreover, he also ﬁnds evidence of σ-divergence. Importantly, while the use of ﬁxed-effects estimation can bring about substantial gains in the robustness of empirical estimation, relative to a cross-sectional analysis, there is a growing scepticism in a section of the literature about the value and validity of such growth regressions that use high-frequency data. In particular, two limitations need to be noted. First, since the ﬁxed-effects estimator ignores between-region variation, the reduction in bias typically comes at the expense of higher standard errors [Pritchett 2000]. Second, ﬁxed-effects estimation tends to exacerbate the effect of any measurement error [Durlauf et al 2004].

In sum, two key points emerge from the existing literature analysing convergence across Indian states. First, there is robust evidence for unconditional divergence or the lack of unconditional convergence. Second, the evidence on conditional convergence is not entirely conclusive.6

##### 1.4 Present Exercise: Three Points of Departure

Unfortunately, empirical investigation of the convergence phenomenon across Indian states, in a panel data framework, has not extended beyond the mid-1990s.7 But there have been considerable changes in India’s economic policy since major economic reforms were initiated in the early 1990s. Liberalisation has reduced the degree of control exercised by the central government in many areas leaving much greater scope for state level initiatives. Hence, state level economic performance during the 1990s and beyond warrants closer attention. In view of the changed policy environment, it is imperative to empirically analyse the convergence phenomenon for the entire decade of the 1990s, and if possible further. Thus, in an attempt to provide a more comprehensive analysis of the issue in post-liberalisation India, we will analyse the presence of both unconditional and conditional β-convergence in income across Indian states8 for the period from 1978-79 to 2002-03, which has not been done so far.

Moreover, in order to account for differences in steady state variables, most empirical studies only control for levels of private investment. However, in order to capture more accurately the total savings rate of a state, we will instead control for levels of both private and public investment.

Finally, certain methodological concerns about the robustness of ﬁxed-effects estimation in the context of dynamic panel data models have been raised in the growth literature. Thus, unlike other recent studies on India, in addition to the ﬁxed-effects method of estimation, we will estimate our empirical speciﬁcation using the generalised method of moments (GMM) estimation

60 technique as well. It is worth noting that a small section of the literature even questions the suitability of GMM estimation for investigating long-term growth [Pritchett 2000]. In particular, we must be mindful of two caveats. First, it relies on a lack of serial correlation in the error terms of the growth equation, before ﬁrst differencing [Bond et al 2001]. Second, if explanatory variables are highly persistent, lagged levels can be weak instruments for ﬁrst differences, thereby rendering the GMM estimator to be biased in short samples [Easterly and Levine 2001].

##### 2 Analytical Framework

India is a country of extraordinary diversity, where some states are as large as many countries in Europe. Regions differ enormously in terms of geography, language, demography and social norms. Importantly, there are signiﬁcant differences in levels of economic development across Indian states. What is more, India is a rare example of a developing country with long-time series data for its constituent states. Although the data has its limitations, comparability across Indian states is likely to be better than the average cross-country study [Trivedi 2002]. Hence, there are good theoretical reasons to be interested in convergence within India.

There are several other important reasons for analysing interregional differences in income levels in India. First, studies on the geographical distribution of poverty show that there is a considerable concentration of the poor in speciﬁc regions. A more equitable income distribution across states is then crucial for the broader objective of poverty reduction. Second, regional inequality may be perceived as unfair and hence may hinder the emergence of consensus among different states on important policy issues. Third, inter-regional income disparities may have political consequences and affect the stability of a federal system of government. Fourth, the process of economic liberalisation, initiated in the early 1990s, may have accentuated existing regional inequalities through a process of cumulative causation. It is, therefore, important to assess the actual outcome during this period of economic liberalisation, which has resulted in a greater role for state level policy initiatives.

Regional disparities among India’s major states are both large and persistent. In fact, the dispersion of per capita income and other social indicators is even greater than those commonly found in relatively homogeneous groups of countries such as the Organisation for Economic Cooperation and Development [Aiyar 2001].

Inter-state differences in levels of incomes are stark. The degree of dispersion in growth rates of per capita SDP across states increased signiﬁcantly in the 1990s, relative to the previous decade [Ahluwalia 2000].9 Importantly, while growth accelerated for the economy as a whole, it decelerated signiﬁcantly in the states of Bihar, Orissa and Uttar Pradesh, all of which had relatively low growth rates and levels of per capita income to begin with. Even so, it would not be correct to infer that all the richer states got richer relative to the poorer states. Interestingly, there was deceleration in Punjab and Haryana, both of which had relatively high rates of growth during the 1980s, and were also the richest states. Moreover, Rajasthan, which has been one of poorer states over the years, experienced a fairly high rate of growth of

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per capita SDP in the 1990s, relative to the previous decade. Large regional disparities in other indicators of development such as literacy rates and infant mortality rates are well documented in the literature as well [Ahluwalia 2000; Aiyar 2001].

Such evidence indicates the presence of large disparities in both levels and growth of income across Indian states. Thus, it may reveal certain patterns in the data, which are indicative of the presence or absence of convergence. Moreover, if there is convergence, the evidence may show whether it is conditional or absolute.

The general pattern seen in the data is that initially rich states have tended to remain rich while the poor states have tended to remain poor. The reason is simple. There is a positive correlation variables, i e, an equation for growth (the ﬁrst difference of log output) contains some dynamics in lagged output [Mankiw, Romer and Weil 1992; Barro 1991; Caselli et al 1996].

10

ln(yit) – ln(yit-τ) = βln(yit-τ) + ΨXit + ηi + μ+ εit

t

where y denotes real per capita income (real per capita net state domestic product – (NSDP)), i indexes the state, t indexes the time period, τ denotes the number of years between each successive observation, η is a state-speciﬁc ﬁxed effect, and μ is a yearspeciﬁc effect. X is a vector of explanatory variables, which here consists of loans extended by All-India Financial Institutions (AIFIs), government capital expenditure, the literacy rate and the

between initial income (per capita infant mortality rate. We use loans

Table 1: Correlations between Growth Rate and Initial Values of state domestic product) and subse-State and Control Variablesextended by AIFIs as a proxy for pri

quent growth (Table 1). This is indica- Per Capita Private Public Literacy Infant vate investment and government

SDP 1978 Investment Investment Rate Mortality

tive of absolute divergence since the 1978 1978 1978 Rate 1978 capital expenditure as a proxy for

1980s, if not earlier. Similarly, evi-Growth rate of public investment. Both are expressed per capita SDP

dence of conditional convergence may in per capita terms (see appendix for

(1978-79 – 2002-03) 0.615 0.451 0.361 0.508 -0.518

details).

be analysed by considering the corre-

Source: See appendix.

lation between the initial values of different steady state variables with subsequent growth in income. The data reveal that both investment and the literacy rate, in 1978, are positively correlated with growth during the period from 1978 to 2003 (Table 1).

Correlations by themselves establish little. However, they do provide some evidence of the fact that certain variables do inﬂuence subsequent growth and therefore, should be included in any econometric model analysing conditional convergence.

Nevertheless, since this paper does not attempt to test a speciﬁc theoretical growth model, there is uncertainty about the formulation of the vector of conditioning variables to be used in our empirical speciﬁcation. Hence, to ensure robustness of parameter estimates, we draw from the existing literature. For instance, in the baseline speciﬁcation used to test robustness of the several different variables used in the growth literature, Levine and Renelt (1992) identify the initial level of income, the rate of investment, the secondary school enrolment rate, and the rate of population growth. In another study, Sala-i-Martin (1997) chooses the initial level of income, life expectancy and primary school enrolment rate as they appear to be relatively “robust” in that they systematically seem to be signiﬁcant in most regressions analysed in the previous literature. Given this literature, we use the initial income level, the investment rate, educational human capital, and non-educational human capital (or suitable proxies for them) as conditioning variables in our analysis.

##### 3 Econometric Model

In a seminal study for the empirics of growth, Mankiw, Romer and Weil (1992) argue that an augmented Solow model, which expresses growth as an explicit function of the initial level of income and a set of other variables, included as determinants of the ultimate steady state, is a good way to analyse convergence. Most empirical growth models are based on the hypothesis of conditional convergence, where countries converge to parallel equilibrium growth paths, the levels of which are a function of certain

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february 9, 2008##### 3.1 Fixed-effects Model

We rewrite the above equation as a dynamic panel data model in which current output is regressed on lagged output and a set of control variables [Islam 1995]. In statistical terms, the two equations are equivalent; the only difference of interpretation being that the coefﬁcient of initial output (originally β) is now 1+β:

log(yit) = (1+β) log(yit-τ) + ΨXit + ηi + μ

t + εit

The ﬁxed effects formulation allows us to control for unobserved differences between the steady states of regions. This is imperative for if the ﬁxed effects are correlated with any explanatory variables in the model, their omission leads to an omitted variable bias. Moreover, it is important to include time-speciﬁc effects as the mean of the log output series will typically increase over time, given productivity growth at the all-India level.

Importantly, using annual data on per capita real income has the disadvantage of increasing serial correlation due to business cycle effects and shocks. In contrast, using long-period averages increases the probability of obscuring changes in the steady state that have occurred during the period.11 Hence, keeping in mind both these concerns, we use a panel of four-year spans (i e, τ = 4). Hence, for the period 1978-79 to 2002-03, we consider six panels.

A further methodological concern relates to the possible endogeneity of the explanatory variables in our empirical model. Simultaneity is likely given the nature of the regressors used. For example, it is not evident whether private investment affects economic growth by increasing physical capital in an economy or if economic growth affects private investment by inﬂuencing the level of savings available for investment. Instrumental variable estimation is the obvious solution to the endogeneity problem. In practice, however, it is extremely difﬁcult to ﬁnd good instruments.12

An alternative solution entails using lags of the explanatory variables, thereby ensuring that they are predetermined with respect to the dependent variable [Trivedi 2002]. What is more, statistically signiﬁcant 1.056, with an implied convergence rate, most of the variables employed as determinants of either growth λ, of –0.014.15 To test for convergence, however, we need to asceror the steady state income level, are likely to have an effect after a tain the sign of the estimate of β. Given our result, the estimated

lag anyway. Given the dimensions of Figure 1: Relationship between Growth of Per Capita NSDP β equals 0.056, which is positive. and Initial Level of Per Capita NSDP

the panel (τ = 4), an average of the This implies unconditional diver

.2

value of the variable over the past

gence at the rate of 1.4 per cent per four years is computed and used as a

annum over a four-year period.

.1

randomness in the value of a given | 0 | regression for the entire period be | |||||||
---|---|---|---|---|---|---|---|---|---|

variable in any one of the previous | tween 1978-79 and 2002-03. Regress | ||||||||

four years.13 At the same time, such a | -.1 | ing the level of per capita NSDP in | |||||||

four-year average retains valuable | 2002-03 on that in 1978-79, we ﬁnd | ||||||||

information | contained | in | the | -.2 | a | statistically | signiﬁcant, | positive | |

annual data. | 3.4 | 3.6 | 3.8 PCSD Pt-4 | 4 | 4.2 | β coefﬁcient, suggestingditional divergence. | uncon | ||

3.2 Generalised Method of Moments Model | In sum, both the panel data and cross section regression |

regressor. We use an average to avoid Moreover, we estimate a cross section

The most widely used alternative to ﬁxed-effects estimation14 is estimates provide no evidence of unconditional β-convergence GMM estimation. The method is to ﬁrst-difference the basic (Figure 1), i e, states are not converging to identical steady states. growth equation to eliminate the ﬁxed regional effects, and then Let us now turn to our analysis of conditional β-convergence. use instrumental variables estimation to address the correlation between the differenced lagged dependent variable and the in-4.1 Fixed-effects Model duced ﬁrst-order moving average [MA(1)] error term. The ﬁrst-The key result we ﬁnd is that the coefﬁcient on lagged per capita difference model is: SDP is 0.731 (Table 3, p 63). Given the way our equation is speci

ﬁed, this implies that the estimate of β equals –0.269. Hence, the Δlog(yit) = (1+β) Δlog(yit-4) + ΨΔ Xit + Δμcoefﬁcient on lagged income, in context of the regressand being

t + εit – εit-4 growth of SDP, is negative and statistically signiﬁcant at the 1 per Importantly, the log yit-4 of compo-Figure 2: Relationship between Growth of Per Capita NSDP Initial cent signiﬁcance level. This is evi-Level of NSDP

nent of Δlog(yit-4) will be correlated dence of conditional β-convergence,

.1

with the εit-4 component of the new

i e, once factors that affect steady composite error term, thereby implying

state levels of income are controlled

.05

that an ordinary least squares (OLS)

will yield inconsistent parameter esti

mates. Hence, this necessitates the use for, poor states in India grow faster

e (growth | x)

0

on average than rich ones (Figure 2).

What is more, the implied rate of

-.05

of instrumental variables estimation.

convergence is high at 0.067.Arellano and Bond (1991) developed -.1

Our results also reveal that boththe GMM approach to estimate dynamic

private and public investment have

-.15

panel data models. The approach is

a statistically signiﬁcant, positive

-.15 -.1 -.05 0 .05 .1

typically based on using lagged effect on the steady state level of in

e (pcsd pt4 | x)

levels of the series as instruments for co ef = -.4142079, se = .10012483, t = -4.14 come, and hence on transitional

Note: After controlling for other explanatory variables.

lagged ﬁrst differences. For instance, growth. Finally, the coefﬁcients on

Δlog(yit-4) can be instrumented using log(yit-8) and earlier lagged the other two conditioning variables in our model, the literacy levels where available. Due to constraints on data availability, we rate and the infant mortality rate, are positive and negative reuse log(yit-8), log(yit-12) and log(yit-16) as instruments for the spectively. The signs on the coefﬁcients conform to economic inendogenous regressor, Δlog(yit-4). tuition, which suggests a positive relationship between literacy and income levels, and a negative re-

Table 2: Unconditional Convergence or Divergence?

4 Results lationship between infant mortality

Dependent Variable → Log Per Capita NSDPt Log Per Capita NSDP 2002-03

At the outset, we test for unconditional and income levels. However, while

Explanatory Variables Ordinary Least Ordinary Least Squares

convergence. This analysis involves

Squares

the coefﬁcient on the infant mortality

(Pooled regression) (Cross section regression)

→

the imposition of certain restrictions rate is signiﬁcant at the 5 per cent lev-

Constant | -0.173 | -0.104 |
---|---|---|

(0.118) | (0.039) | |

[0.148] | [0.020] | |

Log per capita NSDPt-4 (column 1)/ | 1.056 | 1.088 |

per capita NSDP 1978-79 | (0.031) | (0.148) |

(column 2) | [0.000] | [0.000] |

R-Squared | 0.585 | 0.520 |

Implied λ (rate of convergence) | -0.014 | -0.0035 |

in the ﬁxed-effects speciﬁcation outlined above. In particular, a common intercept is assumed by eliminating the state-ﬁxed effects, and all control variables are omitted (Table 2). Strikingly, we ﬁnd that the coefﬁcient on the lagged income term, 1+β, is a

The values in the curly brackets refer to the standard errors and those in the square brackets refer to the p-values.

el of signiﬁcance, the coefﬁcient on the literacy rate is not statistically signiﬁcant even at the 10 per cent signiﬁcance level. This may be attributable to the high correlation between the literacy rate and the infant mortality rate (r = -0.85), thereby resulting in

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multicollinearity. The overall explanatory power of the model is Figure 3: Increasing Variance of Log Per Capita NSDP

good with an R-squared of 0.9402.16 σ - divergence σ - divergence .04

Keeping in mind the limitations of the ﬁxed effects panel

.035

framework, outlined earlier in the paper, we turn to the GMM

.03

model.

Variance of log (per capita NSDP)

.025 .02 .015

.01

##### 4.2 Generalised Method of Moments Model

First, the GMM estimate reinforces our ﬁnding of conditional

β-convergence in the ﬁxed-effects model. Modiﬁed for the dif

ference in the way our equation is speciﬁed, the coefﬁcient on

.005

Time Time

the lagged SDP variable, β, is -0.526, thereby implying condi-

Table 3: Fixed-effects Estimation | tional | β-convergence. | Strik- |
---|---|---|---|

Dependent Variable → | Log Per Capita NSDPt | ingly, the implied rate of con- | |

Explanatory Variables ↓ Log per capita NSDPt-4 | Fixed-effects Model 0.731 (0.098) | vergence is 0.186, which is much higher than that predicted by the ﬁxed-effects method | |

[0.000] | (Table 4). | ||

Per capita loans given by all-India | 0.396 | As in the ﬁxed-effects mod | |

financial institutions Per capita government capital expenditure | (0.156) [0.023] 0.180(0.101) | el, coefﬁcients on private investment and public investment are positive and statisti | |

[0.098] | cally signiﬁcant at the 5 per | ||

Literacy rate | 0.188 (0.129) [0.166] | cent and 10 per cent signiﬁcance levels respectively. The | |

Infant mortality rate | -0.254 | coefﬁcient on the infant mor | |

(0.102) | tality rate is negative, as ex | ||

[0.029] R-squared 0.945 Implied λ (rate of convergence) 0.067 The values in the curly brackets refer to the standard | pected, and signiﬁcant at the 5 per cent level. Surprisingly, the coefﬁcient on the literacy | ||

errors and those in the square brackets refer to the p-values. State fixed-effects and year-specific effects are not reported. The number of observations used | rate is also negative. This counter-intuitive sign, howev | ||

is 96. | er, is not that important as the |

coefﬁcient on the literacy rate is not statistically signiﬁcant even at the 10 per cent level of signiﬁcance. Once again, the insigniﬁcant t-ratio on the literacy rate coefﬁcient along with its counterintuitive sign may be attributable to multicollinearity. The negative coefﬁcient on the literacy rate may also be a result of limited time series variation in the variable and lags in the effect of education on growth.

In sum, having used two alternate panel data estimation methods, we can conclude that there is strong and consistent evidence of conditional β-convergence.17

However, this robust ﬁnding of conditional β-convergence does not necessarily imply that states are actually converging in terms of levels of income. A good way of analysing whether or not poor states are catching up with richer states over time is to evaluate the changing distribution of state incomes over time. This is exactly the idea underlying the concept of σ-convergence. Hence, we examine the cross sectional dispersion in per capita real income levels across 16 states over time by estimating the variance of the log of per capita real SDP. In this analysis, a decline in the dispersion of per capita SDP levels over time is indicative of σ-convergence. However, such an analysis assumes that each person in a state has the same level of income, and that all 16 states have the same population. Thus, since we are concerned with living standards of people, a more suitable measure of the evolution of personal inequality is a population-weighted variance of the log of per capita real SDP. 18

Our results clearly document an increasing variance of the log of per capita NSDP (for

Table 4: Generalised Method of Moments both un-weighted and Estimation

population-weighted Dependent Variable → Change in Log Per Capita NSDP (NSDPt – NSDPt-4)

cases) between states

Explanatory Variables Generalised Method of Moments for the period under ↓ Estimation (Instrumental Variables estimation on a first-difference model)

consideration (Figure

Constant 0.057

3).19 Hence, there is evi

(0.032)dence of σ-divergence, [0.082]

which, in turn, is logi-Change in log per capita NSDP 0.474

t-4

(NSDP – NSDP) (0.231)

cally consistent with t-4t-8

[0.044]

our ﬁnding of absolute

Change in per capita loans given by 0.332 β-divergence, i e, states all-India financial institutions (0.162)are not converging in [0.044]

Change in per capita government 0.176

levels of income over

capital expenditure (0.101)

time. In sum, we can

[0.084]

conclude that inequality

Change in literacy rate -0.162in income levels be- (0.270)

[0.552]

tween Indian states is

Change in infant mortality rate -0.605

rising over time.20

(0.362)In view of such evi- [0.100]

dence, it is essential to Implied λ (rate of convergence) 0.186

analyse the causes for Instrumented: change in per capita Instruments: per capita NSDP (NSDP – NSDP) NSDP per capita

widening regional dis-t-4t-4t-8t-8,

NSDP per capita

t-12,

parities, for policymak

NSDP and other

t-16

ers would attempt to exogenous variables

The values in the curly brackets refer to the standard errors and

bring about a more

those in the square brackets refer to the p-values. The number of equal distribution of observations used is 96.

beneﬁts from growth.

##### 5 Intuitive Explanations for Divergent Steady-States

In our preceding econometric analysis, we found per capita private investment and per capita public investment to be crucial determinants of steady state income levels across states. Hence, in order to understand why Indian states are converging to very divergent steady states, it is necessary to analyse the determinants of both private and public investment, in the context of interstate dispersion. It is worth noting that this has not been explored in the literature on the subject so far.

##### 5.1 Determinants of Private Investment

Regressing the ﬂow of loans extended by AIFIs (proxy for private investment) on levels of per capita SDP and other control variables in the ﬁxed-effects framework we have employed so far,

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we ﬁnd a statistically signiﬁcant, positive relationship (Table 5). In other words, the distribution of private investment in India is disproportionately in favour of the more afﬂuent states, thereby highlighting one possible explanation for increasingly divergent steady states. This ﬁnding is intuitively robust for two reasons. First, private corporate investment is likely to ﬂow to states with good infrastructure, good governance and a literate workforce, which are attributes generally associated with richer states. What is more, economic liberalisation may have actually led to greater divergence in investment levels by increasing the mobility of private corporate investment.21 Second, private household investment is likely to be higher in states with higher savings rates which, in turn, are generally those with higher levels of per capita income.

The estimated regression, however, will suffer from reverse causality, as it is likely that higher ﬂows of ﬁnancial assistance are resulting in higher levels of per capita SDP. This will render OLS estimates to be inconsistent. Hence, we use the infant mortality rate to instrument for per capita SDP, the endogenous variable in our regression model. In particular, infant mortality rates may affect ﬂows of ﬁnancial assistance through per capita SDP in the following way. Lower infant mortality rates, indicative of a better health system in the state, result in higher levels of per capita income by improving labour pro

more favourable distribution of state government expenditure in the richer states is attributable mainly to their higher revenue-raising capacity, i e, with identical tax rates, states with higher levels of per capita income raise higher per capita tax revenue, thereby enabling them to ﬁnance higher levels of public investment. Once again, to address the problem of reverse causality,23 we employ instrumental variables estimation. For the same reasons as before, we use the infant mortality rate (IMR) as an instrument for per capita SDP, the endogenous variable in our model. Notably, instrumental variables estimation does not change our ﬁnding of a positive relationship between per capita capital expenditure and per capita SDP.24

##### 5.3 Intergovernmental (Centre-State) Transfers

As noted before, higher levels of per capita capital expenditure in richer states are mainly attributable to their higher revenueraising capacity. Therefore, ceteris paribus, states with lower per capita incomes will have to levy taxes at higher rates in order to provide an equivalent level of capital expenditure for infrastructure facilities. Alternately, poorer states will need greater transfers from the centre to provide them with that extra revenue. Such an argument for redistributive transfers is made on the grounds of “horizontal equity” [Boadway and Flatters 1982].

Previous empirical work on the subject

ductivity. Subsequently, higher levels of per capita income result in higher savings, which, in turn, increase the ﬂow of loans provided by AIFIs.

Intuitively, the instrument is exogenous, as there is no logical direct relationship between infant mortality rates and ﬂows of loans extended by AIFIs (independent of per capita income levels). At the same time, for the instrument to be relevant, infant mortality rates must be highly correlated with levels of per capita SDP. The relevance of the instrumental variable is reﬂected in the ﬁrst stage F-statistic, which equals 11.24.22 Importantly, results of our instrumental variable regression do not alter the conclusion that the volume of private investment is increasing in per capita real income levels.

##### 5.2 Determinants of Public Investment

Regressing per capita capital expenditure (proxy for public investment) on per capita SDP in a ﬁxed-effects framework employed hitherto in the study, we ﬁnd that richer states do actually have signiﬁcantly higher per capita capital expenditures (Table 6). Thus, this is another pos-

Table 5: Determinants of Private Investment

Dependent Per Capita Loans Given Per Capita Loans Given Variable → by All-India Financial by All-India Financial Institutions Institutions

Explanatory Fixed-effects Estimation Fixed-effects Estimation Variables (Ordinary Least (Instrumental Variables

↓ Squares) Estimation)

Per Capita NSDP 0.279 0.238

(0.079) (0.090)

[0.001] [0.011]

Literacy rate 0.298 0.534

(0.058) (0.207)

[0.000] [0.012]

Per capita government 0.151 0.207 capital expenditure (0.028) (0.076)

[0.000] [0.008]

R-Squared 0.881 0.854

Instrumented: per capita NSDP instrument: infant mortality rate First stage F-Statistic = 11.24

The values in the curly brackets refer to the standard errors and those in the square brackets refer to the p-values. State fixed-effects and time trend are not reported. The number of observations used is 96.

Table 6: Determinants of Public Investment

Dependent Variable → | Per Capita Government Capital Expenditure | Per Capita Government Capital Expenditure |

Explanatory Variables ↓ | Fixed-effects Estimation (Ordinary Least Squares) | Fixed-effects Estimation (Instrumental Variables Estimation) |

Per Capita NSDP | 0.252 (0.137) [0.072] | 0.327 (0.147)[0.032] |

R-Squared | 0.782 | 0.733 |

Instrumented: per capita NSDP instrument: log (infant mortality rate) First stage F-statistic = 10.55

reveals that inter-governmental transfers in India have had a signiﬁcant redistributive impact. In analysing the equalising effects of the different categories of transfers from the central to state governments, Rao and Singh (2001) reveal simple correlation coefﬁcients, which support the view that transfers have favoured states with lower levels of per capita SDP.25 Intuitively, such an equalising effect should bring down differences in per capita income levels across states.

However, regressing both Finance

Comission and Planning Commission transfers (in turn) on per capita SDP levels in a ﬁxed-effects framework, we do not ﬁnd a statistically signiﬁcant, inverse relationship (Table 7, p 65). While this is not entirely conclusive, it is certainly indicative of the fact that conditional on political and economic factors,26 which may affect the bargaining power of states, the equalising impact of centre-state transfers is ambiguous. This is particularly important in the post-liberalisation India as economic reform has changed the nature of central government control of the economy in a way that increases the potential for greater disparities across states, thereby putting a greater burden

sible explanation for states converging to The values in the curly brackets refer to the standard errors and those in the on an effective system of centre-state

square brackets refer to the p-values. State fixed-effects and time trend are increasingly divergent steady states. The not reported. The number of observations used is 96. transfers.

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Hence, in sum, we can attribute increasing divergences in attract greater private investment and improve human developsteady state income levels across states to growing interstate dis-ment indicators, attributable to their greater ability to devote parities in levels of private investment, levels of public investment, more resources on building quality physical and social and an ambiguous equalising impact of centre-state transfers. infrastructure.

##### 6 Policy Relevance 7 Conclusion

The preceding analysis has established possible reasons for why It is possible to draw together some conclusions that emerge from Indian states are converging to increasingly divergent steady-our empirical analysis of convergence among 16 major Indian

states. In view of these intuitive explana- Table 7: Are Intergovernmental Transfers Redistributive? states for the period 1978-79 to 2002-03.

tions, it is equally important to ascertain Dependent Finance Commission Planning Commission First, there is no evidence of absolute Variable → Transfers Transfers

whether or not government policy can in- β-convergence. This result holds true for

Explanatory Fixed-effects Estimation Fixed-effects Estimation ﬂuence steady state income levels of dif-Variables (Ordinary Least Squares) (Ordinary Least Squares) both cross section and panel estimation,

ferent states. We analyse this proposition, ↓ thereby implying that there is no tend-

NSDP per capita -0.027 0.485

although in a limited sense, by exploring ency for states to converge to identical

(0.366) (0.413)the relationship between different deter- [0.941] [0.241] steady states. Second, in contrast, there

minants of per capita real income levels The values in the curly brackets refer to the standard errors and those in the is robust evidence of conditional square brackets refer to the p-values. The level of population, lagged fiscal and per capita capital expenditure, a vari-deficit per capita and a political affiliation dummy variable27 have been β-convergence. After controlling for phy

used as control variables. Their coefficients are not reported as they are not

able, which can be determined to a large sical capital formation, both public and

directly relevant for our hypothesis. State fixed-effects and time trend are also not reported. The number of observations used is 96.

extent by policymakers. private, and proxies for human capital, both ﬁxed-effects estimation and GMM estimation reveal that ini

6.1 Public Expenditure and Private Investment tially poorer states do converge faster to their divergent steady Regressing per capita loans extended by AIFIs on per capita gov-states. Third, there is no evidence of σ-convergence. In fact, inernment expenditures incurred by different states in a ﬁxed- creasing dispersion in per capita real incomes across states over effects framework, we ﬁnd a positive, signiﬁcant relationship time implies the existence of σ-divergence. In sum, given these (Table 8). Moreover, the elasticity of private investment with re-three crucial ﬁndings, we can conclude that states in India are spect to government capital expenditure is 0.277. This implies converging to very different steady states. Moreover, we ﬁnd that that public investment, which is higher in this may be attributable to increasing inter-

Table 8: Impact of Government Policy on richer states, “crowds in” private invest-Determinants of Per Capita Real Income Levels state disparities in levels of private and

ment. In fact, several studies reveal a com-Dependent Per Capita Loans Literacy Infant public investment and an insigniﬁcant

Variable → Given by All-India Rate Mortality

plementarity between public infrastructure Financial Institutions Rate equalising impact of centre-state govern

investment and private investment as bet-Explanatory Variables ment transfers. ter social and physical infrastructure is un-↓ Interestingly, these conclusions suggest

Per capita government 0.277 0.351 -0.328

doubtedly an important consideration in that a really important feature of regional

capital expenditure (0.014) (0.028) (0.025)

the location decisions for private invest- disparities in India is not a state’s distance

[0.000] [0.000] [0.000]

ment [Greene et al 1991]. Constant -0.435 0.876 0.265 away from its steady state but rather the

(0.032) (0.063) (0.056)factors, which determine that steady state.

[0.000] [0.000] [0.000]

###### 6.2 Public Expenditure and Human This has obvious policy implications for

R-Squared 0.868 0.887 0.753

Development correctives can be introduced with respect

The values in the curly brackets refer to the standard errors and those in

Intuitively, public capital expenditure on the square brackets refer to the p-values. Since the dependent variable to these factors.28 and all independent variables are expressed in natural logarithms,

social infrastructure, including education the coefficients on the latter can be interpreted as elasticities. Fixed-In our analysis, we identiﬁed per capita effects not reported. The number of observations used is 96.

and health, is likely to contribute to human capital formation. In fact, the positive impact of state government expenditures on human capital formation is well documented in the literature [Reserve Bank of India 1993].

Regressing the literacy rate on per capita public expenditure in a ﬁxed-effects panel framework, we ﬁnd a statistically signiﬁcant, positive relationship. Doing the same for the infant mortality rate, we ﬁnd a statistically signiﬁcant, negative relationship (Table 8). Thus, we can conclude that government capital expenditure has considerable inﬂuence on improving the stock of human capital. The elasticities of the literacy rate and infant mortality rate with respect to public capital expenditure are 0.351 and –0.328 respectively.

It is important to note, however, that these conclusions in themselves are also, in a sense, an explanation for differing steady states. This is because better-off states can

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february 9, 2008private investment, literacy rate, infant mortality rate, and per capita public investment as important determinants of a state’s steady state level of income. Importantly, we ﬁnd the ﬁrst three to be signiﬁcantly inﬂuenced by the fourth, which is a policy-driven variable, thereby implying that state governments can play an important role in enhancing their own growth prospects. What is more, per capita public investment, the policy-driven variable, itself can be used to improve steady state levels of income. Thus, public investment, as also public expenditure on education and health is of critical importance. In practice, of course, the impact of government policy depends upon the ability of states to increase levels of capital expenditure as well as to ensure efﬁciency in its use. The former, in turn, depends greatly on the ﬁscal situation of state governments together with centre-state government transfers.

notes 20 As a digression, the above analysis cannot be used Cashin, P (1995): ‘Economic Growth and

1 Moreover, at present, the world is captivated by the mega economies, China and India, with their high growth rates. Rapid growth in China over the past 25 years has led to a signiﬁcant increase in regional inequalities. This is widely accepted. It is, therefore, essential to explore and to assess how rapid economic growth in India over the past 25 years has shaped regional income inequalities.

2 In the Solow version of the neoclassical model, the country’s savings and population growth rates, and other technological parameters including the depreciation rate determine the steady state income level of country.

3 Islam (1995) employs the least-squares dummy variables method.

4 The enormous diversity is reﬂected in regional variation in variables such as rates of investment, population growth, literacy rates and infant mortality rates.

5 It is only after controlling for variables capturing the share of agriculture and manufacturing in total output, that some of their estimated coefﬁcients are signiﬁcant.

6 Most studies reveal results indicative of conditional convergence, implying that the long-term growth rate and initial income levels share a negative relationship, once differences in steady states are controlled for.

7 Singh and Srinivasan (2002) extends up to 199899, but uses cross section regression analysis.

8 Names: Andhra Pradesh, Assam, Bihar, Gujarat, Haryana, Himachal Pradesh Karnataka, Kerala, Madhya Pradesh, Maharashtra, Orissa, Punjab, Rajasthan, Tamil Nadu, Uttar Pradesh and West Bengal.

9 For instance, variation in average annual growth rates during the 1980s ranged from a low of 2.1 per cent for Madhya Pradesh to a high of 4 per cent for Rajasthan. In contrast, during the 1990s, it ranged from a low of 1.1 per cent per annum in Bihar to a high of 7.6 per cent in Gujarat.

10 This equation is consistent with several neoclassical growth models, which accept as a solution a log-linearisation around the steady state of the form ln y (t) – ln y (0) = -(1- e-λτ) ln y (0) + (1- e-λτ) ln y* [Barro and Sala-i-Martin 1995]

11 Moreover, using longer time intervals will reduce the number of observations in time and thereby accentuate the “Nickell (1981) bias” in dynamic panel data models with ﬁxed effects.

12 Variables that are highly correlated with the endogenous explanatory variables but not correlated with the error term in the regression model.

13 For instance, say due to a exogenous shock.

14 “Within-groups” estimator.

15 The implied rate of convergence, λ, is computed by dividing the estimate of β by 4, which represents are panel of four-year spans.

16 It is important to note that the estimates are computed using heteroscadasticity corrected, Huber/ White/Sandwich estimates of standard errors. This variance estimator ensures robustness of our estimates as it produces consistent standard errors even if the residuals are not identically distributed.

17 It is important to note that the estimation of both models relies on panels of four-year spans. Despite the rationale provided earlier, this may be considered somewhat arbitrary. Importantly, however, altering the panel length to three or ﬁve years does not change the results in any signiﬁcant way.

18 In this estimation, the weights are simply the population shares of the states in the total population of the 16 states under consideration.

19 Data used to construct Figure 3 is not reported due to the lack of space.

to draw any conclusion about the inequality of income between people. This is because the population-weighted variance ﬁgure assumes that all individuals in a given state have the same level of income, thereby understating the true level of inter-personal inequality.

21 This is attributable to a wide-ranging reforms package, which includes the elimination of the central government’s ability to direct investment to particular areas [Ahluwalia 2000].

22 For the case of a single endogenous regressor, Staiger and Stock (1997) suggest declaring instruments as weak if the ﬁrst stage F-statistic is less than 10.

23 Higher per capita capital expenditure may be resulting in higher levels of per capita SDP.

24 It is important to note here while public investment is crucial for creating adequate economic and social infrastructure facilities, it is a poor substitute for private investment in many sectors of the economy where private entrepreneurs are likely to be more competitive and efﬁcient.

25 Finance Commission transfers are statutory through sharing of tax revenues, while Planning Commission transfers are based on certain norms with some discretion.

26 Following Khemani (2003), we control for population, lagged ﬁscal deﬁcit per capita and a political afﬁliation dummy variable as economic and political factors, which inﬂuence centre-state transfers

27 “Political Afﬁliation” dummy variable is equal to 1 for states where the party ruling a state is the same as that ruling at the centre and 0 otherwise.

28 So does the divergence of real incomes per capita across states over time, particularly in a political democracy with a federal system.

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##### Appendix

For the time period 1978-79 to 2002-03, we consider six panels, with each panel covering a four-year span: 1978-79 to 1982-83, 1982-83 to 1986-87, 1986-87 to 1990-91, 1990-91 to 199495, 1994-95 to 1998-99, and 1998-1999 to 20022003. Data on levels per capita NSDP, at 1993-94 constant prices, based on National Accounts Statistics, are taken from EPW Research Foundation (2003). Data for the more recent years are obtained from Ministry of Statistics and Programme Implementation (2004). Unfortunately, there are no comprehensive state-wise data on private investment or capital formation. Hence, following Rao et al (1999),

Economic Growth’, Quarterly Journal of Econo

mics, Vol 50, pp 65-94. Staiger, D and J H Stock (1997): ‘Instrumental

Variables Regression with Weak Instruments’,

Econometrica, Vol 65, pp 557-86. Temple, J (1999): ‘The New Growth Evidence’, Journal of

Economic Literature, Vol 37, No 1, pp 112-56.

we use loans extended by AIFIs as a proxy for private investment. The variable is expressed in per capita terms. While not perfect, the correlation between this variable and levels of private investment at the national level is strong at 0.85 for the period in question. Data for loans extended by AIFIs are obtained from the IDBI Report on Development Banking in India (various issues). Similarly, no state-wise data are available for levels of public investment or levels of gross capital formation in the public sector. Hence, we use data on state-wise capital expenditure as a proxy for public investment [Reserve Bank of India, Handbook of Statistics, various issues]. The correlation between the two at the national

– (2000): ‘Growth Regressions and What the Textbooks Don’t Tell You’, Bulletin of Economic Research, Vol 52, No 3, pp 181-205.

Trivedi, K (2002): ‘Regional Convergence and Catch-up in India between 1960 and 1992’, Working Paper, Nufﬁeld College, University of Oxford.

level is strong at 0.84. The variable is expressed in per capita terms. Data on the level of population are taken from EPW Research Foundation (2003). We use the infant mortality rate and the literacy rate as a proxy for non-educational and educational capital respectively. While data on the former are taken from Compendium of India’s Fertility and Mortality Indicators (1999) and Ministry of Health and Family Welfare (2004), data on the latter are from National Human Development Report (2001). Data on real ﬁscal deﬁcit are taken from Reserve Bank of India, Handbook of Statistics

on the Indian Economy, various issues.

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