Case deletion diagnostics for GMM estimation

Generalized method of moment (GMM) is an important estimation method for econometric models. However, it is highly sensitive to the outliers and influential observations. This paper studies the detection of influential observations using GMM estimation and establishes some useful diagnostic tools, such as residual and leverage measures. The case deletion technique is employed to derive diagnostic measures. Under linear moment conditions, an exact deletion formula is derived, and under nonlinear moment condition an approximate formula is suggested. The results are applied to efficient instrumental variable estimation and dynamic panel data models. In addition, generalized residuals and leverage measure for GMM estimator are defined and discussed. Two real data sets are used for illustration and a simulation study is conducted to confirm the usefulness of the proposed methodology.