This study uses annual data for the period of 1950/51 to 2004/05 for its estimation purposes. The data for domestic savings and investment were taken from the National Accounts Statistics of India (2006). Data for foreign capital inflows are obtained from the Centre of Monitoring Indian Economy (2006), whilst GDP figures are available from the Reserve Bank of India (2006). All the variables, except for GDP (which was already in constant prices), are converted into constant prices with appropriate deflators.
The study uses the GDP at factor cost deflator for the household sector savings and investment; the GDP at market prices deflator for the public sector savings and investment; and the GDCG (unadjusted) deflator for the private corporate savings, private corporate investment and foreign capital inflows.
All data are in Rupees for the 1993/94 base year and all variables are converted to Naperian logs. To estimate savings and investment in India, the economy is divided into three broad sectors. These are the household sector, the public sector and the private corporate sector. The household, private and public sector savings are then added up to give gross domestic savings. Similarly, household, private and public sector investments are added to give the total as gross domestic investment. The transformed variables comprise the real, logged measures of household savings (LHHS) and investment (LHHI); private savings (LPRS) and investment (LPRI); public savings (LPUS) and investment (LPUI); gross domestic savings (LGDS) and investment (LGDI), foreign capital inflows (LFCI) and real GDP (LGDP).
A major drawback in measuring savings and investment in India is the difficulty involved in direct estimation of household consumption and investment expenditures.
The household sector is treated as a residual in the national accounts where household savings in physical assets is identical to household investment. Thus, for our estimation purposes, to avoid double counting, household savings in physical assets component is eliminated from gross domestic savings. In addition, in our estimations, household savings equals savings in financial assets only.
The author would also like to point out that initially all variables were divided by the labour force and then converted to Naperian logs to put the variables in per worker terms, consistent with the growth models. However, the data for the labour force, taken from the Indian Planning Commission are only available for the census years of 1951, 1961, 1971, 1981, 1991 and 2001. The values for other years were estimated using
simple interpolations. An earlier paper was presented at the Reserve Bank of India and this was criticized on the ground of unreliable labour force data.11
Further to this, the author decided not to use per capita data or per worker data for estimation purposes because of the large variation between the labour force and the population. This is due to (i) the huge demographic change in India which has led to a significant changing participation rate; and (ii) the cohort labour force which includes part-time labour, child labour and the existence of underemployment.
Lastly, it is important to note that the Indian savings and investment data is not without issues and it be said that the data does suffer from some errors.12 However, the Central Statistical Organisation who is responsible for the preparation of the savings/investment data has followed a uniform methodology in preparing the data throughout the period of this study, thus allowing econometric analysis of the data.
11 This being the earlier study by the Verma and Wilson (2005).
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CHAPTER FOUR
UNIT ROOT TESTS AND STRUCTURAL BREAKS*
4.1 Introduction
The previous chapter discusses the apparent important issues of trends and breaks in the measures of savings, investment, foreign capital inflows and GDP in India. Therefore, it becomes important to determine whether or not the variables contain a trend and whether that trend is deterministic or stochastic. This is known as the unit root test which is also a preliminary step in testing for cointegration and causality. Unit root tests are conducted to verify the stationarity properties (absence of trend and long-run mean reversion) of the time series data so as to avoid spurious regressions. A series is said to be (weakly or covariance) stationary if the mean and autocovariances of the series do not depend on time. If an economic time series is characterised by non-stationarities, then the classical t-test and F-test are inappropriate because the limiting distributions of the asymptotic variances of the parameter estimates are infinite (Fuller 1985). This often leads to spurious results in conventional regression analysis.1
Traditionally, the Augmented Dickey-Fuller (Dickey and Fuller (1979, 1981) and the Phillip-Perron (1988) tests have been widely used to test for stationary. However, Perron (1989) argues that most economic time series are characterised by stochastic rather than deterministic nonstationarity. Perron shows that many apparent non-stationary macroeconomic variables are indeed non-stationary if one allows for structural changes in the intercept or trends. Structural change can complicate the tests for trends;
a policy regime change can result in a structural break that makes an otherwise
1 According to Granger and Newbold (1974), a spurious regression has a highR and t-statistics that 2 appear to be significant, but the results are without any economic meaning.
A modified version of this chapter has been published by the author in the Journal of Quantitative
stationary series appear to be non-stationary (Enders 1995, p.211). Also, when there are structural breaks, the traditional Augmented Dickey-Fuller and the Phillip-Perron test statistics are biased toward the non-rejection of a unit root.
As mentioned in chapter three of this study, during the period from 1950 and 2005, the Indian economy has gone through a number of structural changes such as regime shifts, numerous wars, droughts, the green revolution and financial reforms leading to the deregulation in 1991. In other words, India has experienced a number of structural breaks in the macroeconomic variables over the past five decades. In the context of India, there are limited studies that have considered the issue of breaks in the data. For example Wallack (2003), Sinha and Tejani (2004) and Balakrishina and Paramsewaran (2007) determine a single break date in GDP. While Sahoo et al. (2001) determine break dates for gross domestic savings and GDP but again, they only consider one structural break. As the literature review in chapter two reveals, none of the India studies, or for that matter any studies examine the relationships of savings, investment, foreign capital inflows and growth within the cointegration and error correction framework that accommodate two structural breaks.
Applying traditional unit root tests alone is insufficient and problematic as significant structural breaks in the time series data are very likely. Therefore, the aim of this chapter is firstly to test for unit roots using traditional unit root tests; and secondly, to test for unit root in the presence of any potential structural breaks for the variables of gross domestic savings, gross domestic investment, foreign capital inflows and GDP for India. The structure for the rest of chapter is as follows: Section 4.2 discusses the traditional unit roots tests, which do not take into account structural breaks and presents empirical results of the Augmented Dickey-Fuller and Phillip-Perron tests. Section 4.3 explains the unit root tests that take into account one structural break. Empirical results
of Perron’s (1997) Innovational Outlier Model and the Additive Outlier Models are examined. Section 4.4 discusses and applies the new Lee and Strazicich (2003), Minimum Lagrange Multiplier Unit Root Test which endogenously determines two structural breaks. Finally, section 4.5 provides some concluding remarks.