Estimation of treatment effects with high-dimensional controls
We propose methods for inference on the average effect of a treatment on a scalar outcome in the presence of very many controls. Our setting is a partially linear regression model containing the treatment/policy variable and a large number p of controls or series terms, with p that is possibly much larger than the sample size n, but where only s << n unknown controls or series terms are needed to approximate the regression function accurately. The latter sparsity condition makes it possible to estimate the entire regression function as well as the average treatment effect by selecting an approximately the right set of controls using Lasso and related methods. We develop estimation and inference methods for the average treatment effect in this setting, proposing a novel "post double selection" method that provides attractive inferential and estimation properties. In our analysis, in order to cover realistic applications, we expressly allow for imperfect selection of the controls and account for the impact of selection errors on estimation and inference. In order to cover typical applications in economics, we employ the selection methods designed to deal with non-Gaussian and heteroscedastic disturbances. We illustrate the use of new methods with numerical simulations and an application to the effect of abortion on crime rates.
|Date of creation:||Dec 2011|
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- A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012.
"Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain,"
Econometric Society, vol. 80(6), pages 2369-2429, November.
- A. Belloni & D. Chen & Victor Chernozhukov & Christian Hansen, 2010. "Sparse models and methods for optimal instruments with an application to eminent domain," CeMMAP working papers CWP31/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
- Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
- Kane, John, 1997. "Myth and measurement: The new economics of the minimum wage : David Card and Alan B. Krueger, New Jersey: Princeton University Press, 1995, x + 422," International Review of Economics & Finance, Elsevier, vol. 6(2), pages 219-222.
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