Testing Subsets of Structural Parameters in the Instrumental Variables
开发了拉格朗日乘子和似然比统计量，用于检验工具变量回归模型中结构参数的子集假设，其渐近分布对工具质量稳健，并在Card（1995）教育回报数据中给出与2SLS Wald统计量不同的95%置信集。
We develop Lagrange multiplier and likelihood ratio statistics to test hypotheses on subsets of the structural parameters in an instrumental variables regression model. The asymptotic distributions of these statistics are robust to instrument quality. A key assumption is, however, that the instruments are valid for the remaining endogenous variables. We show that the statistics lead to 95% confidence sets for the return on education in data from Card (1995) that are considerably different from the confidence sets that result from the 2SLS Wald statistic, which is the common statistic used in the literature.