Info-metric Methods for the Estimation of Models with Group-Specific Moment Conditions

Motivated by empirical analyses in economics using repeated cross-section data, we propose info-metric methods (IM) for estimation of the parameters of statistical models based on the information in population moment conditions that hold at group level. The info-metric estimation can be viewed as the primary approach to a constrained optimization. The estimators can also be obtained via the dual approach to this optimization, known as Generalized Empirical Likelihood (GEL). In a companion paper, we provide a comprehensive framework for inference based on GEL with the grouped-specific moment conditions. In this chapter, we compare the computational requirements of the primary and dual approaches. We also describe the IM/GEL inference framework in the context of a linear regression model that is estimated using the information that the mean of the error is zero for each group. For the latter setting, we use analytical arguments and a small simulation study to compare the properties of IM/GEL-based inferences to those of inferences based on certain extant methods. The IM/GEL methods are illustrated through an application to estimation of the returns to education in which the groups are defined via information on family background.