Consistent Moment Selection Procedures for Generalized Method of Moments Estimation

This paper considers a generalized method of moments (GMM) estimation problem in which one has a vector of moment conditions, some of which are correct and some incorrect. The paper introduces several procedures for consistently selecting the correct moment conditions. The procedures also can consistently determine whether there is a sufficient number of correct moment conditions to identify the unknown parameters of interest. The paper specifies moment selection criteria that are GMM analogues of the widely used BIC and AIC model selection criteria. (The latter is not consistent.) The paper also considers downward and upward testing procedures. All of the moment selection procedures discussed in this paper are based on the minimized values of the GMM criterion function for different vectors of moment conditions. The procedures are applicable in time-series and cross-sectional contexts. Application of the results of the paper to instrumental variables estimation problems yields consistent procedures for selecting instrumental variables.

[1]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[2]  A. Gallant,et al.  Which Moments to Match? , 1995, Econometric Theory.

[3]  Hirotugu Akaike,et al.  On entropy maximization principle , 1977 .

[4]  H. Akaike.  Fitting autoregressive models for prediction , 1969 .

[5]  D. Andrews.  A Stopping Rule for the Computation of Generalized Method of Moments Estimators , 1997 .

[6]  A. Gallant,et al.  Estimation of Stochastic Volatility Models with Diagnostics , 1995 .

[7]  R. Nishii.  Maximum likelihood principle and model selection when the true model is unspecified , 1988 .

[8]  R. Shibata.  Selection of the order of an autoregressive model by Akaike's information criterion , 1976 .

[9]  K. Back,et al.  Implied Probabilities in GMM Estimators , 1993 .

[10]  Richard J. Smith.  Non-Nested Tests for Competing Models Estimated by Generalized Method of Moments , 1992 .

[11]  M. Hashem Pesaran,et al.  A Generalised R2 Criterion for Regression Models Estimated by the Instrumental Variable Method , 1994 .

[12]  H. White,et al.  Instrumental Variables Regression with Independent Observations , 1982 .

[13]  V. Solo.  The Statistical Theory of Linear Systems E. J. Hannan and Manfred Deistler John Wiley & Sons, 1988 , 1992, Econometric Theory.

[14]  Donald W. K. Andrews,et al.  Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models , 2001 .

[15]  D. Pollard,et al.  Simulation and the Asymptotics of Optimization Estimators , 1989 .

[16]  On the central limit theorem and iterated logarithm law for stationary processes , 1975, Bulletin of the Australian Mathematical Society.

[17]  E. Hannan,et al.  The statistical theory of linear systems , 1989 .

[18]  Benedikt M. Pötscher,et al.  Order Estimation in ARMA-Models by Lagrangian Multiplier Tests , 1983 .

[19]  Takeshi Amemiya,et al.  Selection of Regressors , 1980 .

[20]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[21]  M. Eichenbaum,et al.  A Time Series Analysis of Representative Agent Models of Consumption Andleisure Choice Under Uncertainty , 1986 .

[22]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[23]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[24]  D. Andrews.  Generic Uniform Convergence , 1992, Econometric Theory.

[25]  B. M. Potscher.  Model Selection Under Nonstationarity: Autoregressive Models and Stochastic Linear Regression Models , 1989 .

[26]  R. Kohn.  Consistent Estimation of Minimal Subset Dimension , 1983 .

[27]  E. J. Hannan.  Testing for Autocorrelation and Akaike's Criterion , 1982 .

[28]  E. Hannan.  The Estimation of the Order of an ARMA Process , 1980 .