Small Sample Performance of Instrumental Variables Probit Estimators: A Monte Carlo Investigation

In this paper I revisit the question of how several estimator of an endogenous probit regression model perform in small samples. Modern software usually contains two estimator that can be used to estimate such a model. A simple generalized least squares estimator suggested by Amemiya and explored by Newey is computationally simple, though not necessarily efficient. A maximum likelihood estimator is also used, though its properties are less apparent in small samples. The paper uses a simple experimental design employed by Rivers and Vuong (1988) to estimate the parameters of an endogenous probit model and conduct subsequent tests of parameter significance. Although Rivers and Vuong (1988) find that their two-stage conditional maximum likelihood (2SCML) performs well in terms of bias and mean square error, and similarly to other consistent alternatives, they did not examine how well the estimators perform in significance tests. In the probit model it is not altogether clear what the magnitude of the parameters actually mean; however, getting the correct signs and being able to test for parameter significance is important. So, this paper can be seen as an important extension of their work. I add to the list of estimators compared, increase the dimension of the experimental design, and explore the size of significance tests based on these estimators. Most importantly, the effect of instrument strength is explored. Other dimensions that affect the performance of the estimators are modeled, including sample size, proportion of observations equal to 1, correlation between instruments and endogenous variables, correlation between endogenous regressor and equation error, and overidentication. Finally, the estimators are used in an example to examine the effect of managerial incentives on the use of foreign-exchange derivatives.