Qian, Hang (2011): Bayesian inference with monotone instrumental variables.
Download (287Kb) | Preview
Sampling variations complicate the classical inference on the analogue bounds under the monotone instrumental variables assumption, since point estimators are biased and confidence intervals are difficult to construct. From the Bayesian perspective, a solution is offered in this paper. Using a conjugate Dirichlet prior, we derive some analytic results on the posterior distribution of the two bounds of the conditional mean response. The bounds of the unconditional mean response and the average treatment effect can be obtained with Bayesian simulation techniques. Our Bayesian inference is applied to an empirical problem which quantifies the effects of taking extra classes on high school students' test scores. The two MIVs are chosen as the education levels of their fathers and mothers. The empirical results suggest that the MIV assumption in conjunction with the monotone treatment response assumption yield good identification power.
|Item Type:||MPRA Paper|
|Original Title:||Bayesian inference with monotone instrumental variables|
|Keywords:||Monotone instrumental variables; Bayesian; Dirichlet|
|Subjects:||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
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General
|Depositing User:||Hang Qian|
|Date Deposited:||08. Aug 2011 15:45|
|Last Modified:||16. Feb 2013 05:45|
Chen, M., Shao, Q., 1998. Monte Carlo estimation of bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics 8, 69-92.
Chernozhukov, V., Hong, H., Tamer, E., 2007. Estimation and confidence regions for parameter sets in econometric models. Econometrica 75 (5), 1243-1284.
Chernozhukov, V., Lee, S. S., Rosen, A., 2009. Intersection bounds: estimation and inference. CeMMAP working papers CWP19/09.
David, H. A., 1981. Order Statistics. Wiley. Gil-Pelaez, J., 1951. Note on the inversion theorem. Biometrika 38 (3-4), 481-482.
Imbens, G. W., Manski, C. F., 2004. Confidence intervals for partially identified parameters. Econometrica 72 (6), 1845-1857.
Imhof, J. P., 1961. Computing the distribution of quadratic forms in normal variables. Biometrika 48 (3-4), 419-426.
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., 1997. Monotone treatment response. Econometrica 65 (6), 1311-1334.
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, S200-S216.
Moschopoulos, P., 1985. The distribution of the sum of independent gamma random variables. Annals of the Institute of Statistical Mathematics 37, 541-544.
Provost, S. B., Cheong, Y.-H., 2000. On the distribution of linear combinations of the components of a dirichlet random vector. Canadian Journal of Statistics 28 (2), 417-425.
Qian, H., 2011. Sampling variation and monotone instrument variable under discrete distributions, MPRA paper.
Rosen, A. M., 2008. Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities. Journal of Econometrics, 146 (1), 107-117.
Ross, A., 2010. Computing bounds on the expected maximum of correlated normal variables. Methodology and Computing in Applied Probability 12, 111-138.