Estimation, Learning and Parameters of Interest in a Multiple Outcome Selection Model
研究两结果处理响应模型中四个跨体制相关系数的不可识别问题，利用协方差矩阵正定性实现学习，并推导常见处理参数的二元分布，通过模拟和儿童劳动对成绩影响的实证说明方法。
We describe estimation, learning, and prediction in a treatment-response model with two outcomes. The introduction of potential outcomes in this model introduces four cross-regime correlation parameters that are not contained in the likelihood for the observed data and thus are not identified. Despite this inescapable identification problem, we build upon the results of Koop and Poirier (1997 Koop , G. , Poirier , D. J. ( 1997 ). Learning about the across-regime correlation in switching regression models . Journal of Econometrics 78 : 217 – 227 . [CROSSREF] [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) to describe how learning takes place about the four nonidentified correlations through the imposed positive definiteness of the covariance matrix. We then derive bivariate distributions associated with commonly estimated “treatment parameters” (including the Average Treatment Effect and effect of Treatment on the Treated), and use the learning that takes place about the nonidentified correlations to calculate these densities. We illustrate our points in several generated data experiments and apply our methods to estimate the joint impact of child labor on achievement scores in language and mathematics.