Using Selective Sampling for Binary Choice Models to Reduce Survey Costs

Marketing problems sometimes concern the analysis of dichotomous variables, like for example ``buy'' and ``not buy'' and ``respond'' and ``not respond''. It can happen that one outcome strongly outnumbers the other, for example when many households do not respond (to a direct mailing, for example). Standard econometric methods would imply the collection of many data to obtain precise estimates and this can be rather costly. To cut back costs, we propose to implement a non-random sampling scheme and to correct for the subsequent sample selection bias in the econometric model. In this paper we put forward the relevant method, which does not lead to a loss in precision. Our illustration suggests an opportunity to collect 60\% less data points.