Integrated Time Series in Binary Choice Models

Though binary choice and multiple choice models have been a popular tool of microeconometrics for many years, there are macroeconomic time series that are connected with discrete decisions of authorities. Therefore it is very important to develop an appropriate tool for statistical inference for such macroeconomic time series. Macroeconomic continuous time series may be stationary as well as integrated of order one as well as nonstationary. In this paper asymptotic distributions of maximum likelihood estimator and sample proportionwhen regressors included in binary choice models are nonstationaryare derived. Most of the work done on the asymptotic properties of maximum likelihood estimators in the case of nonstationary regressors concerns time series integrated of order 1. The aim of this paper is to extend the existing theory, include regressors integrated of order 2 in a model with stationary and integrated of order 1 regressors as well as analyze asymptotic behavior of maximum likelihood estimator. The derivations and results of the experiment show that in the case of different orders of integration of regressors, the rate of convergence for some parameters equals 4 / 3 T whereas for some of them equals 4 / 1 T . When we only have regressors integrated of order 1 or integrated of order 2, the rate of convergence equals 4 / 1 T and finite sample properties of maximum likelihood estimators are poor.