A common approach to dealing with missing data in econometrics is to estimate the model on the common subset of data, by necessity throwing away potentially useful data. In this paper we consider a particular pattern of missing data on explanatory variables that often occurs in practice and develop a new efficient estimator for models where the dependent variable is binary. We derive exact formulae for the estimator and its asymptotic variance. Simulation results show that our estimator performs well when compared to popular alternatives, such as complete case analysis and multiple imputation. We then use our estimator to examine the portfolio allocation decision of Italian households using the Survey of Household Income and Wealth carried out by the Bank of Italy.