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.

[1]  John Haslett,et al.  Application of ‘delete = replace’ to deletion diagnostics for variance component estimation in the linear mixed model , 2004 .

[2]  M. Arellano,et al.  Another look at the instrumental variable estimation of error-components models , 1995 .

[3]  R. J. Martin.  Leverage, influence and residuals in regression models when observations are correlated , 1992 .

[4]  Edward W. Frees,et al.  Influence Diagnostics for Linear Longitudinal Models , 1997 .

[5]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[6]  R. Cook,et al.  Assessing influence on predictions from generalized linear models , 1990 .

[7]  Stanley Lemeshow,et al.  Logistic regression diagnostics in ridge regression , 2018, Comput. Stat..

[8]  Sik-Yum Lee,et al.  Local influence for incomplete data models , 2001 .

[9]  Cheng Hsiao,et al.  Analysis of Panel Data , 1987 .

[10]  Yat Sun Poon,et al.  Conformal normal curvature and assessment of local influence , 1999 .

[11]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[12]  M. Arellano.  Panel Data Econometrics , 2002 .

[13]  Yutaka Tanaka,et al.  LOCAL INFLUENCE IN PRINCIPAL COMPONENT ANALYSIS OF A CORRELATION MATRIX , 2003 .

[14]  Lei Shi,et al.  Deletion, replacement and mean-shift for diagnostics in linear mixed models , 2012, Comput. Stat. Data Anal..

[15]  Christopher J. Nachtsheim,et al.  Diagnostics for mixed-model analysis of variance , 1987 .

[16]  David R. Cox,et al.  Some algebra and geometry for hierarchical models, applied to diagnostics , 1998 .

[17]  J. A. Díaz-García,et al.  SENSITIVITY ANALYSIS IN LINEAR REGRESSION , 2022 .

[18]  S. Chatterjee.  Sensitivity analysis in linear regression , 1988 .

[19]  Peter Schmidt,et al.  Efficient estimation of models for dynamic panel data , 1995 .

[20]  Lei Shi,et al.  Stepwise local influence analysis , 2011, Comput. Stat. Data Anal..

[21]  John Haslett,et al.  A Simple Derivation of Deletion Diagnostic Results for the General Linear Model with Correlated Errors , 1999 .

[22]  R. Cook.  Assessment of Local Influence , 1986 .

[23]  Hongtu Zhu,et al.  PERTURBATION AND SCALED COOK'S DISTANCE. , 2012, Annals of statistics.

[24]  Peter Schmidt,et al.  Efficient estimation of dynamic panel data models: Alternative assumptions and simplified estimation , 1997 .

[25]  E. Ronchetti,et al.  Robust inference with GMM estimators , 2001 .

[26]  Jeffrey M. Wooldridge,et al.  Solutions Manual and Supplementary Materials for Econometric Analysis of Cross Section and Panel Data , 2003 .

[27]  L. Hansen,et al.  Finite Sample Properties of Some Alternative Gmm Estimators , 2015 .

[28]  M. Arellano,et al.  Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations , 1991 .

[29]  Anthony C. Atkinson,et al.  Robust Diagnostic Regression Analysis , 2000 .

[30]  J. Brian Gray,et al.  Applied Regression Including Computing and Graphics , 1999, Technometrics.

[31]  Lei Shi,et al.  Case deletion diagnostics in multilevel models , 2008 .

[32]  Ronald Christensen,et al.  Case-deletion diagnostics for mixed models , 1992 .

[33]  J. Ibrahim,et al.  Perturbation selection and influence measures in local influence analysis , 2007, 0803.2986.

[34]  Gemai Chen,et al.  Influence Measures for General Linear Models With Correlated Errors , 2009 .

[35]  L. Hansen.  LARGE SAMPLE PROPERTIES OF GENERALIZED METHOD OF , 1982 .

[36]  Mario Miguel Ojeda,et al.  Local influence in multilevel regression for growth curves , 2004 .