论文标题
线性计量经济学模型中偏置调整的治疗效果的界限
Bounds for Bias-Adjusted Treatment Effect in Linear Econometric Models
论文作者
论文摘要
在对未观察到的成比例选择的线性计量经济学模型中，估计的治疗效果中省略的可变偏差是立方方程的真正根，涉及估计的参数，而估计的参数是短和中间回归的。立方的根部是$δ$的函数，不可观察到的选择程度，以及$ r_ {max} $，这是假设的长期回归中的R平方，其中包括不可观察的混杂因素和所有可观察到的控件。在本文中，我提出并实施一种新型算法来计算$δ$ -R_ {max} $平面的相关区域的立方方程的根，并使用根来构建界限集以实现真实的治疗效果。该算法基于两个众所周知的数学结果：（a）立方方程的判别可用于划定来自三个真正根源区域的独特真正根部区域的划分区域，并且（b）多nommial方程的系数的微小变化会导致其根源的微小变化会导致其根部的微小变化，因为后者后来的函数是连续的。我通过将其应用于对儿童结果的孕产妇行为的分析来说明我的方法。
In linear econometric models with proportional selection on unobservables, omitted variable bias in estimated treatment effects are real roots of a cubic equation involving estimated parameters from a short and intermediate regression. The roots of the cubic are functions of $δ$, the degree of selection on unobservables, and $R_{max}$, the R-squared in a hypothetical long regression that includes the unobservable confounder and all observable controls. In this paper I propose and implement a novel algorithm to compute roots of the cubic equation over relevant regions of the $δ$-$R_{max}$ plane and use the roots to construct bounding sets for the true treatment effect. The algorithm is based on two well-known mathematical results: (a) the discriminant of the cubic equation can be used to demarcate regions of unique real roots from regions of three real roots, and (b) a small change in the coefficients of a polynomial equation will lead to small change in its roots because the latter are continuous functions of the former. I illustrate my method by applying it to the analysis of maternal behavior on child outcomes.
