In the Case of Heterogeneous Causal Effects, the Following Is $\left. E \left( u _ { i } \mid X _ { i } \right) = 0 \right)$

Short Answer

In the case of heterogeneous causal effects, the following is not true: a. in the circumstances in which OLS would normally be consistent (when $\left. E \left( u _ { i } \mid X _ { i } \right) = 0 \right)$ , the OLS estimator continues to be consistent.
b. OLS estimation using heteroskedasticity-robust standard errors is identical to TSLS.
c. the OLS estimator is properly interpreted as a consistent estimator of the average causal effect in the population being studied.
d. the TSLS estimator in general is not a consistent estimator of the average causal effect if an individual's decision to receive treatment depends on the effectiveness of the treatment for that individual.