This paper compares the size and power properties of the asymptotic tests based on the asymptotic standard errors with the bootstrap tests based on the bootstrap confidence interval in the Probit model. The asymptotic tests work surprisingly well even when the sample size is quite small (e.g., n = 30) for the test of exclusion hypothesis β = 0. The bootstrap tests work similarly well. It shares essentially the same size and power property of the asymptotic tests when the null hypothesis is β = 0. However, the small sample probit estimators can be seriously biased when β/σ is large. Consequently, when we are interested in the non-exclusion hypothesis such as β/σ = 1, the conventional asymptotic tests can suffer size distortion and low power. But, following our simulation results, the size of the bootstrap tests is quite robust to the presence of the bias and the power is much better. Therefore, the bootstrap approach has some limited usefulness in practice when we are interested in the non-exclusion tests such as β/σ = 1 in the probit model.
Master of Science (M.S.)
College of Business Administration
Length of Campus-only Access
Masters Thesis (Open Access)
Shen, Xiaobin, "Size And Power Property Of The Asymptotic Tests And The Bootstrap Tests In The Probit Model: Simulation Results" (2006). Electronic Theses and Dissertations. 6113.