On Hypothesis Testing: A Selective Look at the Lagrange Multiplier, Likelihood Ratio and Wald Tests

Abstract

This paper discusses some issues related to the use of the Lagrange multiplier, likelihood ratio and Wald tests in econometrics. In particular, the paper focuses on three issues: (i) the Wald test with nonlinear constraints; (ii) conflict among criteria and size correction; and (iii) the derivation of an improved LM statistic. Some Monte Carlo simulation results illustrate the discussion.