Predicting birth-rates through German micro-census data: a comparison of probit and Boolean regression

Abstract

This paper investigates the complex interrelationships of qualitative socio-economic variables in the context of Boolean Regression. The data forming the basis for this investigation are from the German Micro-census waves of 1996 2002 and comprise about 400 000 observations. Boolean Regression is used to predict how birth events depend on the socio-economic characteristics of women and their male partners. Boolean Regression is compared to Probit. The data set is split into two halves in order to determine which method yields more accurate predictions. It turns out that Probit is superior, if a given socio-economic type is substantiated by less than about 30 observations, whereas Boolean Regression is superior to Probit, if a given socio-economic type is verified by more than about 30 observations. Therefore a "hybrid" estimation method, combining Probit and Boolean Regression, is proposed and used in the remainder of the paper. Different methods of interpreting the results of the estimations are introduced, relying mainly on simulation techniques. With respect to the reasons for the prevailing low German fertility rates, it is evident that these could be decisively higher if people had higher incomes and earned more with relative ease. From a methodological perspective, the paper demonstrates that Scientific Use Files of socio-economic data comprising hundred thousands or even millions of observations, and which have been made available recently, are the natural field of application for Boolean Regression. Possible consequences for future social and economic research are discussed. --