Institutional Affiliation: Yale University
|Inference with Weak Instruments|
with James H. Stock: t0313
This paper reviews recent developments in methods for dealing with weak instruments (IVs) in IV regression models. The focus is more on tests and confidence intervals derived from tests than on estimators. The paper also presents new testing results under "many weak IV asymptotics," which are relevant when the number of IVs is large and the coefficients on the IVs are relatively small. Asymptotic power envelopes for invariant tests are established. Power comparisons of the conditional likelihood ratio (CLR), Anderson- Rubin, and Lagrange multiplier tests are made. Numerical results show that the CLR test is on the asymptotic power envelope. This holds no matter what the relative magnitude of the IV strength to the number of IVs.
|Optimal Invariant Similar Tests for Instrumental Variables Regression|
with Marcelo Moreira, 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.
|Estimation of Polynomial Distributed Lags and Leads with End Point Constraints|
with Ray C. Fair: t0079
This paper considers the use of the polynomial distributed lag (PDL) technique when the lag length is estimated rather than fixed. We focus on the case where the degree of the polynomial is fixed, the polynomial is constrained to be zero at a certain lag length q, and q is estimated along with the other parameters. We extend the traditional PDL setup by allowing q to be real-valued rather than integer-valued, and we derive the asymptotic covariance matrix of all the parameter estimates, including the estimate of q. The paper also considers the estimation of distributed leads rather than lags, a case that can arise if expectations are assumed to be rational.
Published: Journal of Econometrics, Vol.53, No. 1-3, pp. 123-139 July-Sept 1992