What Linear Estimators Miss: The Effects of Family Income on Child Outcomes
研究了当模型被错误假设为线性时，工具变量和固定效应估计的后果。以家庭收入与儿童结果之间的因果联系为例，发现非线性估计显示递增的凹关系，而线性估计因对低收入部分的大边际效应赋予小权重而遗漏了显著影响。
We assess the implications of nonlinearity for IV and FE estimation when the estimated model is inappropriately assumed to be linear. Our application is the causal link between family income and child outcomes. Our nonlinear IV and FE estimates show an increasing, concave relationship between family income and children's outcomes. We find that the linear estimators miss the significant effects of family income because they assign little weight to the large marginal effects in the lower part of the income distribution. We also show that the linear IV and FE estimates differ primarily because of different weighting of marginal effects.