The Econometric Analysis of Constructed Binary Time Series

Macroeconometric and Financial researchers often use secondary or constructed binary random variables that differ in terms of their statistical properties from the primary random variables used in microeconometric studies. One important di¤erence between primary and secondary binary variables is that while the former are, in many instances, independently distributed (i.d.) the later are rarely i.d. We show how popular rules for constructing binary states determine the degree and nature of the dependence in those states. When using constructed binary variables as regressands a common mistake is to ignore the dependence by using a probit model. We present an alternative non-parametric method that allows for dependence and apply that method to the issue of using the yield spread to predict recessions.