Services sector and economic growth in India

Abstract

This study examines the long-run equilibrium and short-run dynamic relationship between services sector and Gross Domestic Product (GDP) and between services and nonservices sectors in India. The model is estimated using the optimal single-equation and the maximum-likelihood system estimators. All the estimators consistently suggest the cointegrating relationship between services sector and GDP as well as between services and nonservices sectors. The estimates of long-run elasticity parameters are statistically significant and dimensionally consistent across the estimators. The conventional Cumulative Sum (CUSUM) and the new CUSUM and Moving Sum (MOSUM) tests suggest the stability of the equilibrium residuals and reinforce the cointegrating relationship between the model series. The error correction model provides some support for unidirectional Granger-causality from services sector to GDP. The impulse response and variance decomposition analyses instead suggest the bidirectional causality between services sector and GDP and between services and nonservices sectors. The stable growth of services sector is essentially crucial to absorb the adverse effects of exogenous weather shocks in agriculture and industry and provide resilience to the economy.

Acknowledgements

I am grateful to an anonymous referee of the journal for very useful comments and suggestions. However, I am solely responsible for any error and omissions that may remain in this article.

Notes

¹ For a related discussion on the relationship between public infrastructure and private output, see Brox and Fader (2005).

² The ADF test uses an explicit AR(m) specification and includes the lagged dynamic regressors of the dependent variable to sap serial correlation and ensure white-noise residuals. While the choice of too small truncation lag m results in serial correlation and bias in ADF test statistic, the use of too large lag length reduces the power of ADF test. The test suggested by Phillips and Perron (1988) instead estimates the long-run variance of regression residuals using a variant of Newey and West (1987) estimator to remove serial correlation, and employs a nonparametric correction to SEs. The ADF and PP tests are equivalent asymptotically, but differ discernibly in finite samples, and such difference arises from the difference in the methods used to correct serial correlation in these tests.

³ The KPSS test tests the null of no unit root and stationarity against the alternative of a unit root and nonstationarity. The test statistic is sensitive to truncation lag used in the long-run covariance matrix of residuals, and tends to decline monotonically as the lag-length increases.

⁴ The PP test is performed using the spectral estimation lag windows of lw = 1 and lw = 4. Similarly, the KPSS test is performed using the lag windows of lw = 1 and lw = 4 for the residual variance of Newey and West estimator (1987). The results obtained under both the lag windows provided similar evidence for the null and are, therefore, reported only for one of the lag windows (lw = 4) for both PP and KPSS tests to conserve space. The results for the lag window of lw = 1 for both PP and KPSS tests are available from the author on request.

⁵ The conventional selection rules, such as Schwarz Information Criterion (SIC) and AIC, tend to select the values of k that are generally too small for the unit root to have good sizes (Ng and Perron, 2001). The penalty assigned to overfitting in information criteria under-estimates the cost of a low-order model when the unit root process has a negative moving-average root and, hence, it tends to select a lag length that is too small. Ng and Perron (2001) use MAIC on the GLS detrended data and show substantial power gains of DF-GLS test.

⁶ The results for the PP and KPSS unit root tests on the residual series for the lag window of lw = 1 are available from author on request.

⁷ The use of 5% critical values from Phillips and Ouliaris (1990) also provided similar evidence for the null for the ADF and PP tests for both models (5) and (6).

⁸ The CUSUM test ‘band tests’ the null of cointegration, rather than no cointegration, among the level variables.

⁹ The CUSUM and CUSUM of Squares (CUSUMSQ) tests have been commonly used to test the stability (constancy) of model parameters, and examine the structural break in a regression function. Ploberger and Krämer (1992) replace the recursive residuals by OLS residuals and provide a OLS residual-based rendition of the CUSUM test of Brown et al. (1975). They show that the CUSUM test for the constancy over time of the coefficients of a linear regression model, which is usually based on recursive residuals, can also be applied to OLS residuals. Hao and Inder (1996) derive asymptotic distribution of the OLS-based CUSUM test to test structural break in cointegrated regression models. The CUSUM test for the null of parameter constancy and that for the null of cointegration have the same behaviour under the null hypothesis, but are different under the alternative (Xiao and Phillips, 2002).

¹⁰ The OLS estimators of a regression are ‘super-consistent’ when the model series are cointegrated. Instead of approaching their true values at a rate proportional to n ^−1/2, the OLS estimates will approach them at a rate proportional to n ⁻¹ (Davidson and MacKinnon, 1993). The ‘super-consistency’ properity allows to asymptotically ignore the problems of endogeniety bias and serial correlation. In small samples, however, the OLS estimates become biased, and such bias leads to inferential problems for the significance of the parameters of long-run model.

¹¹ The efficiency of IV estimator hinges highly on the quality and validity of instruments. The instruments that are weekly related to regressors and are nonorthogonal to residual term can still produce biased and inconsistent estimates. If several regressors in a model need to be instrumented, then the requirements for any surrogate to pass as a valid instrument for endogenous regressors also become more stringent (Staiger and Stock, 1997).

¹² The FMOLS estimator provides valid t-statistics for the long-run coefficients of static regression in levels and resolves the problem of statistical inference.

¹³ Sawa (1978) argues that the AIC tends to choose the model with a higher lag order than the true model, but the bias is small or negligible when k < [T/10].

¹⁴ For a discussion on the effect of other factors, such as exports, on the growth and productivity in India, see Singh (2003).

¹⁵ It does not seem appropriate to perform CUSUM test on the residuals of OLS regression in the presence of endogeneity (Westerlund, 2005).

¹⁶ Since cumulative sum in CS _n is replaced by moving sum in MS _n , the critical values for MS _n should intuitively be in the vicinity of the critical value for CS _n . By this analogy, the MS _n statistics do not seem to reject the null of cointegration between services sector and GDP and between services and nonservices sectors.

¹⁷ The estimates of all the models are corrected for AR(1) serial correlation using the Hildreth–Lu search procedure.

¹⁸ For a discussion on different approaches to estimating long-run relationships, see Inder (1993) and Harris and Sollis (2005).

¹⁹ The ML system estimator is useful to examine the number of cointegrating vectors and the equilibrium relationships among the model variables in a multivariate setting. The limitation of imposing, at the most, a single cointegrating vector applies only to a multivariate model, and is not relevant for the bi-variate model used in the study.

²⁰ The univariate test statistics are based on the estimated residuals of each of the VAR equation and include three central moments of estimated residuals (SD, skewness and kurtosis), Lagrange Multiplier (LM) test (Engle, 1982) for Autoregressive Conditional Heteroskedasticity (ARCH) and the modified version of Shenton–Bowman test for the normality of individual residual series (Shenton and Bowman, 1977; Doornik and Hansen, 1994). The multivariate test statistics are based on estimated auto- and cross-correlations of the residuals of overall VAR system and include LM test for first and fourth-order autocorrelation (Godfrey, 1988) and the χ² test for normality. The χ² test for normality is based on the multivariate version of the univariate Shenton–Bowman test. The results of these tests are not reported to conserve space.

²¹ The impulse response and variance decomposition analyses decompose the determinants of endogenous variable into the innovations identified with a specific variable. If the innovations are characterized by contemporaneous correlation, then the results can be sensitive to the Cholesky ordering scheme of the system variables. The plots of the impulse response functions and the quantitative analysis in terms of variance decomposition showed consistent results across alternative ordering schemes. The results are, therefore, reported only for one-ordering scheme given by for Model I and [DlnNS, D lnS] for Model II to conserve space.

²² In the impulse response analysis carried out for a time horizon of 20 years, the impulse responses of all the series converged to zero very fast. For a vivid depiction of graphs, the impulse response functions are plotted only for a time horizon of 10 years. The plots of the impulse response functions for a 20 year period are available from the author on request.

²³ The variance decomposition shows k-step ahead forecast error variance of each variable explained by its own innovations and the innovations of other variables in the system. The forecast error variance is the sum total of the variances and covariances of all innovation series.