The conventional test for the system GMM is 1) testing for instrument validity and 2) test for second order serial autocorrelation.
Are there pre-estimation tests that may be relevant i.e normality,heteroskedasticity, panel unit root tests, panel cointegration test
I do ask since almost 90% of academic papers reviewed seem to ignore these tests and stress mostly on the two .
The relevant tests are the Sagan Over-Identification test, Durbin-Wu-Hausman test and AB tests for AR(1) and AR(2).
Thank you Madichie. However, do we need to test for panel unit root and cointegration ?
It depends on whether N>T or T>N. If T>N and T is large, you may run a panel unit root.
I don't know the context of system GMM, but pre-estimation tests are to be avoided as much as possible, as a general rule. Even if normality is required in a given statistical test, it is not to be tested. If non-normality is severe, it will first act on the size, and of course the power, on the test. For the size, that can be addressed using e.g. the bootstrap. So the main issue is efficiency.
The GMM dynamic panel estimators are appropriate for large N and small T and generally pre-tests are not conducted. A large panel sample size is often used so that the Central Limit Theorem can be invoked for the asymptotic normality of coefficients even if the residuals are non-normal. Robust standard errors can be employed to deal with autocorrelation and heteroscedasticity. For a broader discussion and how to apply GMM methods in Stata see:
Roodman, D. (2009). How to do xtabond2: An introduction to "Difference" and "System" GMM in Stata. The Stata Journal, 9(1), 86-136. With very small T unit root testing would not typically be applied. If T is large GMM estimators can become unreliable because the number of instruments becomes large and the instrumented variables can be overfitted and so may not remove the endogenous components of the lagged dependent variable(s) as intended. When N is not large and T is moderate you may wish to use a bias corrected LSDV estimator to deal with dynamic panel bias, although these assume that all variables other than the lagged dependent variable are strictly exogenous. To apply a bias-corrected LSDV estimator to a potentially unbalanced dynamic panel in Stata see:
Bruno, G. (2005). Estimation and inference in dynamic unbalanced panel-data models with a small number of individuals. The Sata Journal, 5(4), 473-500. With moderate T you may wish to apply panel unit root tests. Second generation tests that deal with cross-sectional dependence are recommended. An example paper that uses Bruno's estimator and panel unit root tests is given in:
(1) Goda, T., Stewart, C. and Torres García, A. (2019) ‘Absolute Income Inequality and Rising House Prices’, forthcoming in Socio-Economic Review. An example application of GMM dynamic panel estimators without unit root testing is: Matousek, R., and Nguyen, T. N., and Stewart, C. (2017) ‘Note on a non-structural model using the disequilibrium approach: Evidence from Vietnamese banks’, Research in International Business and Finance, 41, pp. 125 – 135.
Chris Stewart
Guy Mélard Chekwube Madichie
Thank you all for your timely contribution . Your feedback is really helpful
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