arXiv 17 May 2018 · Econometrics · 4 citations (OpenAlex)
arXiv:1805.06855 · PDF · DOI · OpenAlex · Extracted main text
This paper proposes computationally efficient methods that can be used for instrumental variable quantile regressions (IVQR) and related methods with statistical guarantees. This is much needed when we investigate heterogenous treatment effects since interactions between the endogenous treatment and control variables lead to an increased number of endogenous covariates. We prove that the GMM formulation of IVQR is NP-hard and finding an approximate solution is also NP-hard. Hence, solving the problem from a purely computational perspective seems unlikely. Instead, we aim to obtain an estimate that has good statistical properties and is not necessarily the global solution of any optimization problem. The proposal consists of employing $k$-step correction on an initial estimate. The initial estimate exploits the latest advances in mixed integer linear programming and can be computed within seconds. One theoretical contribution is that such initial estimators and Jacobian of the moment condition used in the k-step correction need not be even consistent and merely $k=4\log n$ fast iterations are needed to obtain an efficient estimator. The overall proposal scales well to handle extremely large sample sizes because lack of consistency requirement allows one to use a very small subsample to obtain the initial estimate and the k-step iterations on the full sample can be implemented efficiently. Another contribution that is of independent interest is to propose a tuning-free estimation for the Jacobian matrix, whose definition nvolves conditional densities. This Jacobian estimator generalizes bootstrap quantile standard errors and can be efficiently computed via closed-end solutions. We evaluate the performance of the proposal in simulations and an empirical example on the heterogeneous treatment effect of Job Training Partnership Act.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chernozhukov, V. and Hansen, C (2008) Instrumental variable quantile regression: A robust inference approach | 1.000 | 6 | 3 | 100% |
| 2 | Chernozhukov, V. and Hansen, C (2006) Instrumental quantile regression inference for structural and treatment effect models | 0.874 | 6 | 2 | 100% |
| 3 | Johnson, D. S. and Garey, M. R (1979) Computers and intractability: A guide to the theory of NP-completeness | 0.843 | 4 | 3 | 75% |
| 4 | Chen, L.-Y. and Lee, S (2018) Exact computation of gmm estimators for instrumental variable quantile regression models | 0.737 | 3 | 2 | 100% |
| 5 | Chen, X., Ge, D., Wang, Z., and Ye, Y (2014) Complexity of unconstrained $ l_2-l_p $ minimization | 0.644 | 3 | 2 | 67% |
| 6 | Karp, R. M (1972) Reducibility among combinatorial problems | 0.644 | 3 | 2 | 67% |
| 7 | Abadie, A., Angrist, J., and Imbens, G (2002) Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings | 0.644 | 2 | 2 | 100% |
| 8 | Burer, S. and Saxena, A (2012) The milp road to miqcp | 0.644 | 2 | 2 | 100% |
| 9 | Candès, E. and Tao, T (2007) The dantzig selector: statistical estimation when p is much larger than n | 0.644 | 2 | 2 | 100% |
| 10 | Mazumder, R. and Radchenko, P (2017) The discrete dantzig selector: Estimating sparse linear models via mixed integer linear optimization | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 68 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Bias correction for quantile regression estimators | 0.737 | 3 | 3 |
| 2 | Averaging estimation for instrumental variables quantile regression | 0.405 | 1 | 1 |