The Relationship Between Government Revenue, Government Expenditure and Economic Growth in India: An Empirical Investigation at the Sub-national Level

Abstract

This paper examines the relationship between government revenue, expenditure, and economic growth for Indian States in a panel framework while also identifying the drivers of States’ primary expenditure. On the one hand, the study confirms a long run relationship between revenue and expenditure thereby supporting ‘fiscal synchronization’ hypothesis whereas on the other, the existence of a long run association between expenditure and economic growth is detected providing support to the ‘Wagner's law’. Given the importance of primary expenditure in the overall expenditure, the study finds that the States’ primary expenditure has a persistent effect, with past decisions on primary expenditure influencing current-year decisions. States pursue countercyclical expenditure policy in case of positive and negative output gaps, with more pronounced countercyclicality during negative output gap periods. Regarding the States’ sensitivity to their debt levels, the study finds States responding to the level of debt countercyclically in case of positive output gap. The study recommends increasing capital expenditure and debt reduction during phases of positive output gaps to ensure long-term fiscal sustainability of Indian States.

Statistical Annex

Pedroni’s Co-integration Test

The Pedroni’s panel co-integration test which is based on the Engle Granger procedure is an improvement over the conventional co-integration tests since it allows for heterogeneity among individual members of the panel. This co-integration test evaluates the regression residual with I(1) variables in order to detect the presence of unit root. If the residuals of the regression turns out to be I(0), it implies that the variables under consideration are co-integrated. In its generalized form, Pedroni’s panel co-integration regression could be mathematically expressed as:

$${y}_{it }={\sigma }_{i }+{\delta }_{i}t+{\beta }_{i}{x}_{i,t}+{\epsilon }_{i,t}$$

(5.1)

where t = 1,….,T; and i = 1,….,N.

In Eq. (5.1), $y$ and $x$ are presumed to be I(1) and ${\sigma }_{i } \mathrm{and} {\delta }_{i}$ represents the individual and trend effects. In this test, the null hypothesis presupposes that the residual is I(1). Following this, the residual is tested for the presence of unit root, and if the null hypothesis is rejected, co-integration between the variables is assumed to exist. This co-integration test in fact provides eleven statistics which has varying degrees of properties (size and power for different N and T).

Kao’s Cointegration Test

For ensuring the robustness of existence of co-integration detected by the Pedroni’s test, Kao’s co-integration test is also undertaken. This test is also based on Engle Granger procedure and is also a two-stage procedure for detecting co-integration similar to Pedroni’s co-integration test (Kao’s regression equation has an algebraic expression that is comparable to Pedroni’s). However, this test differs from the Pedroni’s since it specifies cross-section specific intercepts and homogenous coefficients on the first stage regressors. Thus, in the first stage, Kao test assumes homogenous coefficient and different intercept of regression equation for every cross section, but in the second stage, it examines the stationary test of residual error series of regression equation at first stage. As the residual is tested for unit root and the null hypothesis is rejected, it implies that there exist co-integration amongst the variables.

Panel Fully Modified Ordinary Least Squares

Fully modified OLS (FMOLS) for elasticity estimation in panel co-integration analysis has been recommended by Pedroni (Pedroni, 1996). While estimating dynamic co-integrated panels, heterogeneity is a major issue encountered on account of the differences in means among the individuals as well as differences in individuals’ responses to short-run disturbances from co-integrating equilibrium. This is overcome by FMOLS estimator by incorporating the individual specific intercepts into the regression and by allowing serial correlation properties of the error processes to vary across individual members of the panel.

Following the Mitic et al. (2017) approach, the standard form of the OLS panel estimator is given in Eq. (5.2):

$${\beta }_{NT}= \left({\Sigma }_{i=1}^{N}{\Sigma }_{t=1}^{T} \left( ({{x}_{i,t}-{\overline{x} }_{i})}^{-1}\right) \right) {\Sigma }_{i=1}^{N} {\Sigma }_{t=1}^{T} \left({x}_{i,t}-{\overline{x} }_{i}\right) \left({y}_{i,t}- {\overline{y} }_{i}\right)$$

(5.2)

The covariance matrix represented by ${\Omega }_{i}$ of the vector error term is given by:

$$\left[\begin{array}{cc}{\Omega }_{11i}& {\Omega }_{12i}\\ {\Omega }_{21i}& {\Omega }_{22i}\end{array}\right]$$

where ${\Omega }_{11i}$ is the long-run variance of error term ${\varepsilon }_{i,t}$, ${\Omega }_{22i}$ is the long-run covariance matrix of ${\epsilon }_{i,t}$ and ${\Omega }_{21i}= {\Omega }_{12i}{\prime}$ shows the long- run covariance between independent variable and its residual vector.

The modified OLS estimator provides FMOLS estimator as Eq. (5.3):

$${\widehat{\beta }}_{FMOLS}= {\left({\Sigma }_{i=1}^{N} {\widehat{L}}_{22i}^{-1} {\Sigma }_{t=1}^{T} {\left({x}_{i,t}-{\overline{x} }_{i}\right)}^{2}\right)}^{-1}{\Sigma }_{i=1}^{N}{\widehat{L}}_{11i}^{-1} {\widehat{L}}_{22i}^{-1} ({\Sigma }_{t=1}^{T}\left({x}_{i,t}-{\overline{x} }_{i}\right){y}_{i,t}^{*}-T{\widehat{\delta }}_{i})$$

(5.3)

where, ${L}_{11i}=\left({\Omega }_{11i}- {\Omega }_{21i}{\prime}{\Omega }_{21i}^{-1}{\Omega }_{21i}\right)$, ${L}_{12i}=0$, ${L}_{21i}= {\Omega }_{21i}{\Omega }_{21i}^{-1/2}$, ${L}_{22i}={\Omega }_{21i}^{1/2}$

$${y}_{i,t}^{*}=\left({y}_{i,t}-{\overline{y} }_{i}\right)-\left(\frac{\widehat{{L}_{21i}}}{\widehat{{L}_{22i }}}\right)\Delta {x}_{i,t}+ \left(\frac{{\widehat{L}}_{21i}-{\widehat{L}}_{22i}}{{\widehat{L}}_{22i}}\right)\beta \left({x}_{i,t}- {\overline{x} }_{i}\right)$$

and ${\widehat{\delta }}_{i}={\widehat{\Gamma }}_{21i}+ {\widehat{\Omega }}_{21i}^{0}- \left(\frac{\widehat{{L}_{21i}}}{{\widehat{L}}_{22i}}\right) ({\widehat{\Gamma }}_{22i}+ {\widehat{\Omega }}_{22i}^{0})$

Panel Dynamic Ordinary Least Squares

Panel dynamic ordinary least squares (DOLS) proposed by Kao and Chiang (2000) is an extension of the time series DOLS put forth by Stock and Watson (1993). DOLS offers certain built-in advantages over OLS and FMOLS estimation. Firstly, the issue of asymptotic bias prevalent in OLS estimation is well addressed in DOLS estimation by including lags and leads of the difference series of variables. Secondly, the adoption of DOLS is useful in coping with the problem of serial correlation irrespective of the order of integration and the existence or absence of co-integration. Thirdly, DOLS is more computationally convenient than OLS or FMOLS. Fourthly, the usage of DOLS is justified even when the dependent variable is endogenous since DOLS estimator are asymptotically unbiased and normally distributed. Fifthly, the DOLS estimator accounts for the heteroscedasticity between the groups by computing the mean group estimator. Finally, the ‘t’ statistic obtained by the DOLS tends to follow the standard normal distribution as compared to the ‘t’ statistic computed using OLS or FMOLS.

The Dynamic OLS estimator can be computed using the following regression Eq. (5.4):

$${y}_{i,t} = \beta_{i}^{\prime} {x}_{i,t}+ {\Sigma }_{j=-q}^{q} {\varsigma }_{ij}\Delta {x}_{i, t+j}+{\gamma }_{li}^{\prime}{D}_{li}+{\varepsilon }_{i,t}$$

(5.4)

where q denotes the number of lags or leads required.

Two-Way System Generalized Method of Moments (GMM)

The two-way system generalized method of moments (GMM) is an econometric technique used to estimate a system of equations where endogenous variables are jointly determined. This method involves the use of instrumental variables (IVs) to account for the endogeneity of explanatory variables. The GMM estimator uses a set of moment conditions based on the orthogonality conditions between the errors and IV. It is a preferred choice over other econometric techniques due to its ability to handle various data structures, address endogeneity issues, and provide consistent and efficient estimates. However, it can be computationally intensive, and the validity of the IV used in the GMM estimator must be carefully evaluated to ensure they meet the necessary assumptions. Moreover, the two-way system GMM requires the correct specification of moment conditions and weighting matrix, which can be challenging in certain cases.