The bivariate probit model, maximum likelihood estimation, pseudo true parameters and partial identification. (English) Zbl 1452.62942
Summary: This paper examines the notion of “identification by functional form” for two equation triangular systems for binary endogenous variables by providing a bridge between the literature on the recursive bivariate probit model and that on partial identification. We evaluate the impact of functional form on the performance of (quasi) maximum likelihood estimators, and investigate the practical importance of available instruments in both cases of correct and incorrect distributional specification. Finally, we calculate average treatment effect bounds and demonstrate how properties of the estimators are explicable via a link between the notion of pseudo-true parameters and the concepts of partial identification.
MSC:
| 62P20 | Applications of statistics to economics |
Keywords:
average treatment effect; binary outcome models; copula; identified set; instrumental variables; misspecificationSoftware:
SemiParBIVProbitReferences:
| [1] | Azzalini, A.; Capitanio, A., Statistical applications of the multivariate skew normal distribution, J. R. Stat. Soc. Ser. B Stat. Methodol., 61, 3, 579-602 (1999) · Zbl 0924.62050 |
| [2] | Azzalini, A.; Dalla Valle, A., The multivariate skew-normal distribution, Biometrika, 83, 4, 715-726 (1996) · Zbl 0885.62062 |
| [3] | Bryson, A.; Cappellari, L.; Lucifora, C., Does union membership really reduce job satisfaction?, British J. Ind. Relations, 42, 3, 439-459 (2004) |
| [4] | Carrasco, R., Binary choice with binary endogenous regressors in panel data: Estimating the effect of fertility on female labor participation, J. Bus. Econom. Statist., 19, 4, 385-394 (2001) |
| [5] | Chesher, A., Nonparametric identification under discrete variation, Econometrica, 73, 5, 1525-1550 (2005) · Zbl 1152.91707 |
| [6] | Chesher, A., Instrumental variable models for discrete outcomes, Econometrica, 78, 2, 575-601 (2010) · Zbl 1229.60015 |
| [7] | Chesher, A.; Rosen, A. M., What do instrumental variable models deliver with discrete dependent variables?, Amer. Econ. Rev., 103, 3, 557-562 (2013) |
| [8] | Chesher, A.; Rosen, A. M., Generalized instrumental variable models, Econometrica, 85, 3, 959-989 (2017) · Zbl 1410.62199 |
| [9] | Deadman, D.; MacDonald, Z., Offenders as victims of crime?: an investigation into the relationship between criminal behaviour and victimization, J. R. Stat. Soc. Ser. A, 167, 1, 53-67 (2003) |
| [10] | Dong, Y.; Lewbel, A., A simple estimator for binary choice models with endogenous regressors, Econometric Rev., 34, 1-2, 82-105 (2015) · Zbl 1491.62203 |
| [11] | Falk, A.; Lalive, R.; Zweimüller, J., The success of job applications: a new approach to program evaluation, Labour Econ., 12, 6, 739-748 (2005) |
| [12] | Freedman, D. A.; Sekhon, J. S., Endogeneity in probit response models, Political Anal., 18, 2, 138-150 (2010) |
| [13] | Greene, W. H., Econometric Analysis (2012), Prentice Hall: Prentice Hall Upper Saddle River, NJ |
| [14] | Han, S.; Vytlacil, E., Identification in a generalization of bivariate probit models with dummy endogenous regressors, J. Econometrics, 199, 63-73 (2017) · Zbl 1452.62916 |
| [15] | Heckman, J. J., Dummy endogenous variables in a simultaneous equation system, Econometrica, 46, 4, 931-959 (1978) · Zbl 0382.62095 |
| [16] | Heyde, C. C., Quasi-likelihood and its Application: A General Approach to Optimal Parameter Estimation (1997), Springer-Verlag: Springer-Verlag New York · Zbl 0879.62076 |
| [17] | Johnson, N. L.; Kotz, S.; Balakrishnan, N., (Continuous Univariate Distributions, vol. 2. Continuous Univariate Distributions, vol. 2, Wiley Series in Probability and Statistics (1995)) · Zbl 0821.62001 |
| [18] | Jones, A., Identification of treatment effects in Health Economics, Health Econ., 16, 11, 1127-1131 (2007) |
| [19] | Jones, A. M., Applied Econometrics for Health Economists: A Practical Guide (2007), Radcliffe publishing |
| [20] | Jones, A. M.; Koolman, X.; Van Doorslaer, E., The impact of supplementary private health insurance on the use of specialists in european countries, Ann. Econ. Stat., 83 (2007) |
| [21] | (Jones, A. M.; O’Donnell, O., Econometric Analysis of Health Data (2002), Wiley: Wiley Chichester) |
| [22] | Lewbel, A., Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables, J. Econometrics, 97, 1, 145-177 (2000) · Zbl 0970.62082 |
| [23] | Lewbel, A.; Dong, Y.; Yang, T. T., Comparing features of convenient estimators for binary choice models with endogenous regressors, Canad. J. Econ., 45, 3, 809-829 (2012) |
| [24] | Li, C.; Poskitt, D. S.; Zhao, X., Bounding the Effect of Private Health Insurance on Dental Care Utilisation (2016), Paper presented at the 3rd Annual Conference of the International Association for Applied Econometrics, Milan |
| [25] | Li, C.; Poskitt, D. S.; Zhao, X., Bounds for Average Treatment Effect: A Comparison of Non-parametric and Quasi Maximum Likelihood Estimators (2018), Department of Econometrics and Business Statistics Working Paper Series 25/18, Monash University |
| [26] | Maddala, G., Limited-dependent and Qualitative Variables in Econometrics (1983), Cambridge University Press · Zbl 0527.62098 |
| [27] | Manski, C. F.; Pepper, J. V., Monotone instrumental variables: with an application to the returns to schooling, Econometrica, 68, 4, 997-1010 (2000) · Zbl 1016.62133 |
| [28] | Marra, G.; Radice, R., Estimation of a semiparametric recursive bivariate probit model in the presence of endogeneity, Canad. J. Statist., 39, 2, 259-279 (2011) · Zbl 1219.62068 |
| [29] | Morris, S., The impact of obesity on employment, Labour Econ., 14, 3, 413-433 (2007) |
| [30] | Mourifié, I.; Méango, R., A note on the identification in two equations probit model with dummy endogenous regressor, Econom. Lett., 125, 3, 360-363 (2014) · Zbl 1311.62100 |
| [31] | Shaikh, A. M.; Vytlacil, E. J., Partial identification in triangular systems of equations with binary dependent variables, Econometrica, 79, 3, 949-955 (2011) · Zbl 1219.62184 |
| [32] | White, H., Maximum likelihood estimation of misspecified models, Econometrica, 50, 1-25 (1982) · Zbl 0478.62088 |
| [33] | Wilde, J., Identification of multiple equation probit models with endogenous dummy regressors, Econom. Lett., 69, 3, 309-312 (2000) · Zbl 0956.91062 |
| [34] | Zhang, X.; Zhao, X.; Harris, A., Chronic diseases and labour force participation in Australia, J. Health Econ., 28, 1, 91-108 (2009) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
