Collapsing instruments in a system GMM model is useful in treating the problem of instrument proliferation. However, the instructions given to xtabond2 of Stata suggest that "In large samples, collapse reduces statistical efficiency. ". Should we collapse instruments in large samples?
To better understand this question, let's consider the case of a sample of 1300 firms where 300 instruments have been used by xtabond2. The panel is balanced and covers more than 10 years. By collapsing, the number of instruments decreases to 45. The estimates between the two approaches are different. What results should a researcher report?
Roodman (2006, 2009) advises that when using GMM dynamic panel methods the number of instruments should be reported and it should be remembered that including too many instruments can cause the endogenous variables to be overfitted and, therefore, fail to remove their endogenous components. Too many instruments also weakens the power of the Hansen test for instrument validity. A telltale sign of too many instruments is a perfect Hansen statistic of unity. As a rule-of-thumb there are too many instruments if the number of instruments exceeds the number of cross-sectional units, N. Indeed, this rule may be too liberal and the number of instruments should probably be even lower than this. It is advisable to test the robustness of the results to reducing the number of instruments. Instruments can be reduced by limiting the number of GMM-style instruments and/or “collapsing” GMM-style instruments into a single column. “Also because of the risks, beware of taking comfort in a Hansen test p value below 0.1. View higher values, such as 0.25, as potential signs of trouble.” (Roodman, 2006, p. 43). I would suggest that if by not collapsing the instruments the number of instruments exceed the number of cross sectional units you should collapse the instruments. Otherwise you can consider not collapsing the instruments. I would try both methods and compare the results. If the results are not sensitive to collapsing instruments your results are robust.
Roodman, D (2006). “How to Do xtabond2: An Introduction to ‘Difference’ and ‘System’ GMM in Stata”, Center for Global Development, Working Paper Number 103.
Hi. As to me, time dimension of your panel data requires of time dummies to employ in the model. I think you perform some robustness check analyses to answer your question. Relating to the number of instruments, i totally agree with Chris Stewart. One dimension of robustness check is to divide your sample into two by considering time, i.e. first and second five years. The other one could be inspired by the following: Insert your independent variables into the model sequentially after the lag of your dependent variable. In each stel, you can evaluate whether your estimation results stay robust. If they stay robust and pass all the diagnostic check, e.g. sargan and hansen j, ar tests etc, then you can find the appropriate specification. Finally, i strongly recommend you consider the validity of sub group of instruments as well. Best.
The collapse should create one instrument for each variable and lag distance, rather than one for each time period, variable, and lag distance. In large
samples, collapse reduces statistical efficiency. But in small samples it can avoid the bias that arises as the number of instruments climbs toward the number of observations. When instruments are many, they tend to overfit the instrumented variables and bias the results toward those of OLS/GLS. Collapse also greatly curtails computational demands by reducing the width of the
instrument matrix.
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