A Note on the Theme of Too Many Instruments

A Note on the Theme of Too Many Instruments

August 2007, revised May 2008 | David Roodman
The Difference and System GMM estimators are increasingly popular due to their ability to handle dynamic panels with fixed effects and endogeneity. However, these estimators often generate a large number of instruments, which can lead to overfitting and weaken the Hansen test of instrument validity. This paper reviews the effects of instrument proliferation and describes methods to control it. It illustrates the dangers by replicating two studies: Forbes (2000) on income inequality and Levine et al. (2000) on financial development. Results in both studies appear driven by previously undetected endogeneity. The paper discusses the risks of instrument proliferation, including overfitting endogenous variables, imprecise estimation of the optimal weighting matrix, and downward bias in standard errors. It also highlights the weakness of the Hansen test when instrument counts are high. The paper concludes that researchers should be cautious about the number of instruments used in GMM and test results for sensitivity to reductions in instrument count. The use of Difference-in-Hansen tests is recommended to assess the validity of instruments. The paper emphasizes the importance of careful instrument selection and testing to ensure the validity of GMM results.The Difference and System GMM estimators are increasingly popular due to their ability to handle dynamic panels with fixed effects and endogeneity. However, these estimators often generate a large number of instruments, which can lead to overfitting and weaken the Hansen test of instrument validity. This paper reviews the effects of instrument proliferation and describes methods to control it. It illustrates the dangers by replicating two studies: Forbes (2000) on income inequality and Levine et al. (2000) on financial development. Results in both studies appear driven by previously undetected endogeneity. The paper discusses the risks of instrument proliferation, including overfitting endogenous variables, imprecise estimation of the optimal weighting matrix, and downward bias in standard errors. It also highlights the weakness of the Hansen test when instrument counts are high. The paper concludes that researchers should be cautious about the number of instruments used in GMM and test results for sensitivity to reductions in instrument count. The use of Difference-in-Hansen tests is recommended to assess the validity of instruments. The paper emphasizes the importance of careful instrument selection and testing to ensure the validity of GMM results.
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