Benjamin Mills
Job Market Candidate

Stanford University
Department of Economics
579 Jane Stanford Way
Stanford, CA 94305
(646) 265-2584

Curriculum Vitae

Econometrics, Industrial Organization

Expected Graduation Date:
June, 2020

Dissertation Committee:

Han Hong (Primary):

Guido Imbens:

Joe Romano:

Frank Wolak:


Inference Under First-Stage Sign Information in the Instrumental Variables Model Job Market Paper (Draft coming soon)

This paper concerns inference on the coefficient of a single endogenous variable in the instrumental variables model when the some knowledge of the first stage sign is known to the researcher. To study the properties of tests in the IV model that have correct size under weak instruments, current literature often focus on tests that are invariant to orthogonal transformations of the instruments. In the homoskedastic case, the conditional likelihood ratio (CLR) test is considered "near optimal" because, in most cases, the power of the CLR test is shown to be close to that of the two-sided power envelope for this class of invariant tests. We present novel size-correct tests that presume knowledge of the sign of the first-stage coefficients, and are not invariant. We find that when the sign of the first-stage sign is known, one of these novel tests, CLR+, numerically dominates both CLR and the two-sided invariant power envelope in terms of asymptotic power. To demonstrate the ubiquity of first-stage sign knowledge in empirical work, we survey papers published in the American Economic Review 2014-2018 that use instrumental variables and find that over 80% presume knowledge of the first-stage sign. These findings suggest a larger class of tests that researchers may consider, both in studying the optimality of tests, and in empirical research.

Tests Based on t-Statistics for IV Regression with Weak Instruments (with Marcelo J. Moreira and Lucas Vilela). Journal of Econometrics, 182(2), 351-363. Supplement.

This paper considers tests of the parameter of an endogenous variable in an instrumental variables regression model. The focus is on one-sided conditional t-tests. Theoretical and numerical work shows that the conditional 2SLS and Fuller t-tests perform well even when instruments are weakly correlated with the endogenous variable. When the population F-statistic is as small as two, their power is reasonably close to the power envelopes for similar and non-similar tests which are invariant to rotation transformations of the instruments. This finding is surprising considering the bad performance of two-sided conditional t-tests found in Andrews, Moreira, and Stock (2007). We show these tests have bad power because the conditional null distributions of t-statistics are asymmetric when instruments are weak. Taking this asymmetry into account, we propose two-sided tests based on t-statistics. These novel tests are approximately unbiased and can perform as well as the conditional likelihood ratio (CLR) test.

Quasi-Maximum Likelihood Estimation Under First-Stage Sign Information in the Instrumental Variables Model