Understanding Generalised Method of Moments

This video tries to simplify the understanding of generalised method of moments (GMM) technique in such a manner that beginners can comprehend. The video series will contain eight other tutorials: (1) How to Estimate One-step Difference GMM; (2) How to Estimate Two-step Difference GMM; (3) How to Estimate One-step System GMM; (4) How to Estimate Two-step System GMM; (5) How to Estimate Decide between Difference or System GMM; (6) How to Interpret GMM Output; (7) How to Generate Long-run GMM Coefficients; and (8) How to Plot Year Dummies in Difference and System GMM. So, what is GMM? A generic method for estimating parameters in statistical models; Uses moment conditions that are functions of the model parameters and the data, such that their expectation is zero at the parameters' true values; it is a dynamic panel estimator. And what is a panel data? It is also called longitudinal data; a multi-dimensional data involving measurements over time; contains observations of multiple phenomena obtained over multiple time periods for the same firms, individuals, countries etc. Watch my video on “Tips to Building Panel Data” for more information.
Why use GMM? It controls for: endogeneity of the lagged dependent variable in a dynamic panel model - when there is correlation between the explanatory variable and the error term in a model; omitted variables bias; unobserved panel heterogeneity; and measurement errors. How do you decide between performing the difference or system GMM? Rule-of-thumb given by Bond (2001): (1) The dynamic model should be initially estimated by pooled OLS and the LSDV approach (i.e., using the ‘within’ or fixed effects approach); (2) The pooled OLS estimate for ɸ should be considered an upper-bound estimate, while the corresponding fixed effects estimate should be considered a lower-bound estimate; (3) If the difference GMM estimate obtained is close to or below the fixed effects estimate, this suggests that the former estimate is downward biased because of weak instrumentation and a system GMM estimator should be preferred instead. It is also advisable to use system GMM if variable exhibits a random walk (persistent).

Two GMM diagnostic tests. The first is the test for instruments validity performed using Hansen (1982) J test and Sargan (1985) test of over-identifying restrictions: tests the null hypotheses of overall validity of the instruments used. Failure to reject these null hypotheses give support to the choice of the instruments. The second test is that for autocorrelation/serial correlation of the error term. It tests the null hypothesis that the differenced error term is first and second order serially correlated. Failure to reject the null hypothesis of no second-order serial correlation implies that the original error term is serially uncorrelated and the moment conditions are correctly specified. There are some challenges to estimating GMM. They are complicated and so can easily generate invalid estimates; GMM codes can be easily manipulated to yield different results; Does not account for cross-sectional dependence (CSD); Does not account for structural breaks; Not advisable for panel with very long time series (use PMG, MG and DFE estimators); Susceptible to variables listed in the IV set; Too many instruments weaken the Sargan/Hansen test and yield implausible p-values; Results are biased if instruments outnumber individual units in the panel; The problem of how many is “too many” instruments. Monte Carlo simulation evidence suggests that cutting the number of over-identifying instruments in half can reduce the bias by 40%. References used for this video tutorial are from: Arellano & Bond (1991): Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment. Review of Economic Studies Limited. 58(1) 277-297; Arellano & Bover (1995): Another Look at the Instrumental Variable Estimation of Error-Components Models. Journal of Econometrics 68 (1): 29 – 51; Blundell & Bond (1998): Initial Conditions and Moment Restrictions in Dynamic Panel Data Models. Journal of Econometrics 87: 115–144; Roodman D. (2009): How To Do xtabond2: An Introduction to “Difference” and “System” GMM in Stata; and Roodman D. (2014): Xtabond2: Stata Module to Extend xtabond Dynamic Panel Data Estimator. Statistical Software Components.

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