Session 2: What Does OLS Estimate?

Linear projection; OLS as weighted contrasts and weighted causal effects; binary, ordered, and continuous treatments; choosing the estimand first.

When: TBA · Where: TBA

Materials

Overview

  • Starting point with no causal assumptions: OLS as a linear projection
  • Binary treatment: when OLS recovers the ATE, and the weights it puts on effects once covariates enter
  • Ordered discrete and continuous treatments: OLS as a weighted average of slopes
  • Where the clean results stop: unordered treatments and additive OLS reweighting effects
  • From “regression first” to “estimand first”: the average linear regression function and average derivative effects

Readings

  • Angrist and Pischke (2009), Chapter 3.
  • Słoczyński, T. (2022). “Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights.” Review of Economics and Statistics, 104(3), 501–509.
  • Yitzhaki, S. (1996). “On Using Linear Regressions in Welfare Economics.” Journal of Business & Economic Statistics, 14(4), 478–486.
  • Graham, B. S., and C. C. de Xavier Pinto (2022). “Semiparametrically Efficient Estimation of the Average Linear Regression Function.” Journal of Econometrics, 226(1), 115–138.