Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection

The topic of this paper is inference in models in which parameters are defined by moment inequalities and/or equalities. The parameters may or may not be identified. This paper introduces a new class of confidence sets and tests based on generalized moment selection (GMS). GMS procedures are shown to have correct asymptotic size in a uniform sense and are shown not to be asymptotically conservative. The power of GMS tests is compared to that of subsampling, m out of n bootstrap, and "plug-in asymptotic" (PA) tests. The latter three procedures are the only general procedures in the literature that have been shown to have correct asymptotic size in a uniform sense for the moment inequality/equality model. GMS tests are shown to have asymptotic power that dominates that of subsampling, m out of n bootstrap, and PA tests. Subsampling and m out of n bootstrap tests are shown to have asymptotic power that dominates that of PA tests.

[1]  Marc Henry,et al.  Inference in Incomplete Models , 2006, 2102.12257.

[2]  D. Andrews,et al.  Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure , 2008 .

[3]  V. Chernozhukov,et al.  Estimation and Confidence Regions for Parameter Sets in Econometric Models , 2007 .

[4]  J. Pratt.  Length of Confidence Intervals , 1961 .

[5]  Ilya Molchanov,et al.  Sharp identification regions in games , 2008 .

[6]  Patrik Guggenberger,et al.  VALIDITY OF SUBSAMPLING AND “PLUG-IN ASYMPTOTIC” INFERENCE FOR PARAMETERS DEFINED BY MOMENT INEQUALITIES , 2007, Econometric Theory.

[7]  Azeem M. Shaikh,et al.  Inference for identifiable parameters in partially identified econometric models , 2006 .

[8]  E. Tamer,et al.  Market Structure and Multiple Equilibria in Airline Markets , 2009 .

[9]  Steven Berry,et al.  Confidence Regions for Parameters in Discrete Games with Multiple Equilibria, with an Application to Discount Chain Store Location , 2004 .

[10]  Donald W. K. Andrews,et al.  Hybrid and Size-Corrected Subsampling Methods , 2007 .

[11]  A. Galichon,et al.  A Test of Non-Identifying Restrictions and Confidence Regions for Partially Identified Parameters , 2009, 2102.04151.

[12]  Frank Schorfheide,et al.  Boosting Your Instruments: Estimation with Overidentifying Inequality Moment Conditions , 2006 .

[13]  Azeem M. Shaikh,et al.  Inference for the identified set in partially identified econometric models , 2006 .

[14]  D. Andrews,et al.  Invalidity of the Bootstrap and The M Out Of N Bootstrap for Confidence Interval Endpoints Defined by Moment Inequalities , 2009 .

[15]  D. Andrews.  Inconsistency of the Bootstrap when a Parameter is on the Boundary of the Parameter Space , 2000 .

[16]  D. Andrews,et al.  ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP , 2009, Econometric Theory.

[17]  Donald W. K. Andrews,et al.  Consistent Moment Selection Procedures for Generalized Method of Moments Estimation , 1999 .

[18]  K. DonaldW..  Generalized Method of Moments Estimation When a Parameter Is on a Boundary , 1999 .

[19]  Anna Mikusheva.  Uniform Inference in Autoregressive Models , 2007 .

[20]  D. Andrews.  Estimation When a Parameter is on a Boundary , 1999 .

[21]  A. Kudô,et al.  A multivariate analogue of the one-sided test , 1963 .

[22]  Francesca Molinari,et al.  Asymptotic Properties for a Class of Partially Identified Models , 2006 .

[23]  Adam M. Rosen,et al.  Confidence Sets for Partially Identified Parameters that Satisfy a Finite Number of Moment Inequalities , 2006 .

[24]  J. Hahn,et al.  Specification testing under moment inequalities , 2008 .

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

[26]  D. Andrews,et al.  Applications of Subsampling, Hybrid, and Size-Correction Methods , 2006 .

[27]  Jörg Stoye,et al.  More on Confidence Intervals for Partially Identified Parameters , 2008 .

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

[29]  C. Manski,et al.  Inference on Regressions with Interval Data on a Regressor or Outcome , 2002 .

[30]  Charles F. Manski,et al.  Confidence Intervals for Partially Identified Parameters , 2003 .

[31]  Federico A. Bugni.  Bootstrap Inference in Partially Identi…ed Models , 2009 .