Qian, Hang (2011): Sampling Variation, Monotone Instrumental Variables and the Bootstrap Bias Correction.
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This paper discusses the finite sample bias of analogue bounds under the monotone instrumental variables assumption. By analyzing the bias function, we first propose a conservative estimator which is biased downwards (upwards) when the analogue estimator is biased upwards (downwards). Using the bias function, we then show the mechanism of the parametric bootstrap correction procedure, which can reduce but not eliminate the bias, and there is also a possibility of overcorrection.This motivates us to propose a simultaneous multi-level bootstrap procedure so as to further correct the remaining bias. The procedure is justified under the assumption that the bias function can be well approximated by a polynomial. Our multi-level bootstrap algorithm is feasible and does not suffer from the curse of dimensionality. Monte Carlo evidence supports the usefulness of this approach and we apply it to the disability misreporting problem studied by Kreider and Pepper(2007).
|Item Type:||MPRA Paper|
|Original Title:||Sampling Variation, Monotone Instrumental Variables and the Bootstrap Bias Correction|
|English Title:||Sampling Variation, Monotone Instrumental Variables and the Bootstrap Bias Correction|
|Keywords:||Monotone instrumental variables; Bootstrap; Bias correction|
|Subjects:||C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63 - Computational Techniques; Simulation Modeling
C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models; Multiple Variables > C31 - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
|Depositing User:||Hang Qian|
|Date Deposited:||07. Aug 2011 23:13|
|Last Modified:||19. Feb 2013 10:00|
Cain, M., 1994. The moment-generating function of the minimum of bivariate normal random variables. The American Statistician 48, 124-125.
Chernozhukov, V., Lee, S. S., Rosen, A., 2009. Intersection bounds: estimation and inference. CeMMAP working papers CWP19/09.
Clark, C. E., 1961. The greatest of a finite set of random variables. Operations Research 9, 145-162.
David, H. A., 1981. Order Statistics. Wiley.
Davidson, R., MacKinnon, J., 2002. Fast double bootstrap tests of nonnested linear regression models. Econometric Reviews 21 (4), 419-429.
Davidson, R., MacKinnon, J. G., 2007. Improving the reliability of bootstrap tests with the fast double bootstrap. Computational Statistics & Data Analysis 51 (7), 3259-3281.
Kreider, B., Pepper, J. V., 2007. Disability and employment: Reevaluating the evidence in light of reporting errors. Journal of the American Statistical Association 102, 432-441.
Manski, C. F., Pepper, J. V., 2000. Monotone instrumental variables, with an application to the returns to schooling. Econometrica 68 (4), 997-1012.
Manski, C. F., Pepper, J. V., 2009. More on monotone instrumental variables. Econometrics Journal 12 (s1), 200-216.
Ross, A., 2010. Computing bounds on the expected maximum of correlated normal variables. Methodology and Computing in Applied Probability 12, 111-138.