Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression

We propose a novel statistic for testing the structural parameters in Instrumental Variables Regression. The statistic is straightforward to compute and has a limiting distribution that is pivotal with a degrees of freedom parameter that is equal to the number of tested parameters. It therefore differs from the Anderson-Rubin statistic, whose limiting distribution is pivotal but has a degrees of freedom parameter that is equal to the number of instruments, and the Likelihood based, Wald, Likelihood Ratio and Lagrange Multiplier, statistics, whose limiting distributions are not pivotal. We analyze the relationship between the statistic and the concentrated likelihood of the structural parameters and show that its' limiting distribution is not affected by weak instruments. We discuss examples of the non-standard shapes of the asymptotically pivotal confidence sets that can be constructed using the statistic and investigate its power properties. To show its importance for practical purposes, we apply the statistic to the Angrist-Krueger (1991) data and find similar results as in Staiger and Stock (1997).