Institutional Affiliation: Columbia University
|A Maximum Likelihood Method for the Incidental Parameter Problem|
This paper uses the invariance principle to solve the incidental parameter problem. We seek group actions that preserve the structural parameter and yield a maximal invariant in the parameter space with fixed dimension. M-estimation from the likelihood of the maximal invariant statistic yields the maximum invariant likelihood estimator (MILE). We apply our method to (i) a stationary autoregressive model with fixed effects; (ii) an agent-specific monotonic transformation model; (iii) an instrumental variable (IV) model; and (iv) a dynamic panel data model with fixed effects. In the first two examples, there exist group actions that completely discard the incidental parameters. In a stationary autoregressive model with fixed effects, MILE coincides with existing conditional and integrated li...
|Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak|
with Jack R. Porter, Gustavo A. Suarez: t0302
It is well-known that size-adjustments based on Edgeworth expansions for the t-statistic perform poorly when instruments are weakly correlated with the endogenous explanatory variable. This paper shows, however, that the lack of Edgeworth expansions and bootstrap validity are not tied to the weak instrument framework, but instead depends on which test statistic is examined. In particular, Edgeworth expansions are valid for the score and conditional likelihood ratio approaches, even when the instruments are uncorrelated with the endogenous explanatory variable. Furthermore, there is a belief that the bootstrap method fails when instruments are weak, since it replaces parameters with inconsistent estimators. Contrary to this notion, we provide a theoretical proof that guarantees the validity...
|Optimal Inference in Regression Models with Nearly Integrated Regressors|
with Michael Jansson: t0303
This paper considers the problem of conducting inference on the regression coefficient in a bivariate regression model with a highly persistent regressor. Gaussian power envelopes are obtained for a class of testing procedures satisfying a conditionality restriction. In addition, the paper proposes feasible testing procedures that attain these Gaussian power envelopes whether or not the innovations of the regression model are normally distributed.
|Optimal Invariant Similar Tests for Instrumental Variables Regression|
with Donald W.K. Andrews, James H. Stock: t0299
This paper considers tests of the parameter on endogenous variables in an instrumental variables regression model. The focus is on determining tests that have certain optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We consider tests that are similar and satisfy a natural rotational invariance condition. We determine tests that maximize weighted average power (WAP) for arbitrary weight functions among invariant similar tests. Such tests include point optimal (PO) invariant similar tests. The results yield the power envelope for invariant similar tests. This allows one to assess and compare the power properties of existing tests, such as the Anderson-Rubin, Lagrange multiplier (LM), and conditional likelihood ratio...
Published: Andrews, Donald W. K., Marcelo J. Moreira and James H. Stock. "Optimal Two-Sided Invariant Similar Tests For Instrumental Variables Regression," Econometrica, 2006, v74(3,May), 715-752.