Re-examination of convergence hypothesis among Indian states in panel stationarity testing framework with structural breaks

ABSTRACT

This article examines the conditional income convergence hypothesis for 17 major states in India for the period of 1960–2012. Univariate stationarity tests without structural breaks provide evidence against the convergence hypothesis. However, when two or more structural breaks are applied in per capita income series, the incomes of around 11–13 states are found to stochastically converge to the national average. This finding supports the convergence hypothesis for the panel as a whole after accounting for two data features, cross-sectional dependence and structural breaks in incomes, using a unified panel stationarity testing framework.

KEYWORDS:

• India
• panel unit root
• structural break
• convergence

JEL CLASSIFICATION:

• O40
• C12

Acknowledgements

We thank Prof. Russell Smyth (Monash university), participants of 10th Annual Conference on Economic Growth and Development (Indian Statistical Institute) and the two anonymous referees for helpful comments on earlier versions of this article. We thank Prof. Josep Lluís Carrion-i-Silvestre (University of Barcelona) for providing the GAUSS codes for estimating the unit root tests proposed in Carrion-i-Silvestre and Sansó (2007) and Bai and Carrion-i-Silvestre (2009). We, alone, are responsible for the views expressed therein and any remaining errors.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The three competing hypotheses on convergence as defined by Galor (1996) are: (1) the absolute convergence hypothesis, where per capita income of countries (or regions) converge to one another in the long term, irrespective of their initial conditions; (2) the conditional convergence hypothesis, where per capita income of countries that are identical in their structural characteristics converge to one another in the long term, irrespective of their initial conditions; and (3) the club convergence hypothesis, where per capita income of countries that are identical in their structural characteristics converge to one another in the long term, provided that their initial conditions are similar.

² Club convergence entails identifying subsets of states that share the same steady state (or clustering the income data into convergence clubs) and checking whether convergence holds up within these groups (Ghosh, Ghoshray, and Malki 2013). In club convergence models, one state is a leading state, known as the leader. All countries with an initial income gap less than a particular amount (refer to Chatterjee (1992) for details) will eventually catch up with the leader. In the steady state, all these countries will grow at the same rate and constitute an exclusive convergence club.

³ For details of this approach, refer to Barro and Sala-i-Martin (1992), Barro and Martin (1995)), Sala-i-Martin (1996) and Mankiw, Romer, and Weil (1992).

⁴ The notion of stochastic convergence implies that shocks to the income of a country (or a region within a country) relative to the average income of a group of countries (or regions) will be temporary. This entails testing the null hypothesis of a unit root in the log of the ratio of per capita income relative to the average. Failure to reject the null of the unit root suggests incomes are diverging and provides evidence against income convergence. Alternatively, rejection of the null hypothesis of the unit root supports income convergence. Since the test includes a constant term, stochastic convergence implies that incomes converge to a country- or region-specific compensating differential. Hence, stochastic convergence is consistent with conditional convergence (Strazicich, Lee, and Day 2004).

⁵ All the regression models employed in this article have both a constant term and linear time trend. With the inclusion of time trend in regression models, the notion of convergence can be interpreted as ‘catching up’ (definition 1, p. 165 Bernard and Durlauf’s (1996)). As Bernard and Durlauf’s (1996) pointed out that time-series tests for economies in a transition state (as is the case here) may erroneously accept the null of ‘no convergence’ when one economy’ per capita output (state in our case) is converging to the per capita output of an economy sitting at a unique steady state from far below. Alternatively stated, time series test may give spurious results if data for the economies in question are driven by transitional dynamics. The inclusion of intercept (or constant term) in time series testing will account for initial conditions ignoring the transitional part. Therefore, inclusion of both intercept and time trend in the testing procedure will take care of initial conditions as well as transitional dynamics respectively improving the power of the time series tests.

⁶ For details, refer to Smyth, Nielsen, and Mishra (2009).

⁷ For other versions and more technical details of the test, refer to Smyth, Nielsen, and Mishra (2009).

⁸ While the results as reported in this article use the Bartlett kernel, they were also estimated using the quadratic kernel. The results were not sensitive to the choice of kernel.

⁹ The latest base period used for compiling the net state domestic products.

¹⁰ The Republic of India, as of writing this article, is made up of 29 states and 6 union territories. However, one state (Telangana) was carved out of Andhra Pradesh in 2014. As the period of analysis for this study concludes in 2012, Telangana is not treated independently but is viewed as part of Andhra Pradesh.

¹¹ The average annual exchange rate between the Indian rupee and the US dollar during 2004‒05 was 1 US$ = 44 INR.

¹² The associated descriptive statistics table is given in the working paper version of this manuscript.

¹³ The study by Ghosh (2013) uses Phillips–Perron (PP) unit root test and Bandyopadhyay & Lusksic (2015) apply ADF, DF-GLS and KPSS tests without structural breaks.

¹⁴ The central government, led by Indira Gandhi, ordered the arrest of more than 1000 key political opponents in 1975 and declared a state of emergency that curbed the power of the press, reduced civil liberties to minimum and suspended elections. The emergency lasted for a 21-month period from June 1975 to March 1977 during which most of Gandhi’s political opponents were in prison. This period also witnessed other atrocities, most prominent of which was a forced mass-sterilization campaign spearheaded by Sanjay Gandhi, the Prime Minister’s son. The Emergency is one of the most controversial periods of independent India’s history.

¹⁵ For further details, refer to the report on the insurgency and peace efforts in Assam by the Centre for Development and Peace Studies (available at http://cdpsindia.org/assam_insurgency.asp).