## Quantile Treatment Effects

The $42,000 question regarding any set of regression estimates is whether they have a causal interpretation. This is no less true for quantile regression than Ordinary Least Squares. Suppose we are interested in estimating the effect of a training program on earnings. OLS regression estimates measure the impact of the program on average earnings while quantile regression estimates can be used to measure the impact of the program on median earnings. In both cases, we must worry about whether the estimated program effects are contaminated by omitted variables bias.

Here too, omitted variables problems can be solved using instrumental variables, though IV methods for quantile models are a relatively new development, and are not yet as flexible as conventional 2SLS...

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