Appendix 1: Test Procedures for Panel Unit Roots
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Kochhar et. al. (2006) and others use the ratio of transmission and distribution (T&D) losses to generating capacity of state level electricity boards to indicate the quality infrastructure and institutions.
Existing studies examine structural breaks using aggregative data for India, such as the growth rate of real GDP, real per capita GNP, and international trade (Table 3). Wallack (2003), Rodrik and Subramaniam (2004), Hausmann et. al. (2005), Virmani (2005), and Kohli (2006) find evidence of a break around 1980. Wallack (2003) alone records another break in 1993, although the evidence is weak.
In addition, the possibility of structural breaks in state level data is tested, following Andrew (1993) and Bai (1994) structural break tests at unknown date, using the difference between the growth paths of high and low income groups. Two possible break dates are found, 1980 and 1992.
If (yit − yjt) ~ I (0) for all i, j pairs, then
The common parameter hypothesis of LLC test is restrictive. The IPS and MW tests are considered generalizations of the LLC test. The IPS test is at least as flexible as MW test, and both are more flexible than LLC test as they do not require any parameter commonality. Computationally, the IPS test is easier than the LLC and MW tests. The IPS test simply averages individual ADF tests and use adjustment values to render the asymptotic standard normal distribution. MW test, on the other hand, requires simulation of the p-value. The distributions for individual ADF based unit root tests are nonstandard and depend on Brownian motion functions, and the simulation is non-trivial. The MW test is more conservative in which it is invariant to cross-sectional dependencies than the other two tests.
The test might fail to capture the transition property toward stochastic convergence although the actual path is converging.
Detailed results are available on request.
Although the set-up of the convergence tests allows for time and cross-sectional fixed effect, the instruments are not enough to filter out structural changes.
Development expenditure includes spending on education, public health, family planning, water supply, and relief after natural calamities.
We estimate the generalized impulses as in Pesaran and Shin (1998) which constructs an orthogonal set of innovations that does not depend on the VAR ordering.