Computation of maximum score type estimators by mixed integer programming

In this paper we show that optimization of a family of “maximum score type” estimators can be effectively reformulated as a Mixed Integer Programming (MIP) problem. The maximum score type family includes Manski’s classic maximum score estimator, but also more recently proposed estimators that optimize profit, utility and absolute deviation objective functions, all of which are similarly irregular in that they are discontinuous in model parameters. The MIP formulation of this family of estimators allows them to be computed exactly using standard commercial software packages such as GAMS. Applying the MIP algorithm to Horowitz’s (1993) transport choice model and data we find it compares very favorably to currently used alternatives. Furthermore, our exact estimates lead to a very different interpretation of this data showing that, at least in the context considered, economic interpretation is sensitive to choice of computation procedure. Finally, using simulated data to explore the domain of applicability of the MIP approach, we find it will be most effective in modeling data with 2-5 parameters and 250-1000 observations.