In this paper, we propose a fix to the size distortions of tests for structural parameters in the simultaneous equations model by computing critical value functions based on the conditional distribution of test statistics. The conditional tests can then be used to construct informative...

The two-stage least-squares (2SLS) instrumental variables estimator is commonly used to address endogeneity. However, the estimator suffers from bias that is exacerbated when the instruments are only weakly correlated with the en- dogenous variables and when many instruments are used. In this...

We consider inference in the linear regression model with one endoge- nous variable and potentially weak instruments. We construct confidence sets for the coefficient on the endogenous variable by inverting the Anderson-Rubin, Lagrange multiplier, and conditional likelihood-ratio tests. Our...

This paper considers tests of the parameter on endogenous variables in an instrumental variables regression model. The focus is on determining tests that have some optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We...

We provide an argument for the limitation of Edgeworth expansions to many commonly used statistics in the weak instrument framework. However, we show that Edgeworth expansions hold for approximately similar tests regardless of the identification conditions. Finally, we consider simulation...