Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T01:41:40.821Z Has data issue: false hasContentIssue false
  • English
  • Français

INTERCEPT ESTIMATION IN NONLINEAR SELECTION MODELS

Published online by Cambridge University Press:  24 April 2023

Wiji Arulampalam Open the ORCID record for Wiji Arulampalam [Opens in a new window] ,
Valentina Corradi  and
Daniel Gutknecht
Wiji Arulampalam
Affiliation:
University of Warwick
Valentina Corradi*
Affiliation:
University of Surrey
Daniel Gutknecht
Affiliation:
Goethe University Frankfurt
*
Address correspondence to Valentina Corradi, Department of Economics, School of Economics, University of Surrey, Guildford GU2 7XH, UK; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data-driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then consider the case in which the monotonic index restriction does not hold and/or the set of observations with a propensity score close to one is thin so that convergence occurs at a rate that is arbitrarily close to the cubic rate. We explore the finite sample behavior in a Monte Carlo study and illustrate the use of our estimator using a model for count data with multiplicative unobserved heterogeneity.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 6 , December 2024 , pp. 1311 - 1363
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Footnotes

We are grateful to the Editor (Peter Phillips), the Co-Editor (Simon Lee), and three anonymous referees for their very useful and constructive comments. We also thank Christoph Breunig, Sarawata Chaudhuri, Xavier D’Haultfoeuille, Prosper Dovonon, Jean-Marie Dufour, Bernd Fitzenberger, Mathieu Marcoux, Jeff Racine, Joao Santos Silva, Victoria Zinde-Walsh, and seminar participants at the ESEM 2018, Kent, Frankfurt, ISNPS 2018, Surrey, Concordia University-Cireq, Humboldt University Berlin, the Econometrics Study Group Meeting in Bristol 2017, and ESEM 2017 for useful comments and suggestions.

References

REFERENCES

Ahn, H. & Powell, J. (1993) Semiparametric estimation of censored selection models with a nonparametric selection mechanism. Journal of Econometrics 58, 3–29.CrossRefGoogle Scholar
Andrews, D. & Schafgans, M. (1998) Semiparametric estimation of the intercept of a sample selection model. Review of Economic Studies 65, 497–517.CrossRefGoogle Scholar
Armstrong, T. & Kolesar, M. (2018) A simple adjustment for bandwidth snooping. Review of Economic Studies 85, 732–765.CrossRefGoogle Scholar
Armstrong, T. & Kolesar, M. (2020) Simple and honest confidence intervals in nonparametric regression. Quantitative Economics 11(1), 1–39.CrossRefGoogle Scholar
Blair, J., Edwards, C., & Johnson, J. (1976) Rational “Chebyshev” approximations for the inverse of the error function. Mathematics of Computation 30(136), 827–830.CrossRefGoogle Scholar
Calonico, S., Cattaneo, M., & Titiunic, R. (2014) Robust nonparametric confidence interval for regression discontinuity design. Econometrica 82, 2295–2326.CrossRefGoogle Scholar
Chamberlain, G. (1986) Asymptotic efficiency in semi-parametric models with censoring. Journal of Econometrics 32, 189–218.CrossRefGoogle Scholar
D’Haultfoeuille, X. & Maurel, A. (2013) Another look at identification at infinity of sample selection models. Econometric Theory 29, 213–224.CrossRefGoogle Scholar
Das, M., Newey, W.K., & Vella, F. (2003) Nonparametric estimation of sample selection models. Review of Economic Studies 70(1), 33–58.CrossRefGoogle Scholar
Deb, P. & Trivedi, P. (2006) Specification and simulated likelihood estimation of a non-normal treatment-outcome model with selection: Application to health care utilization. The Econometrics Journal 9, 307–331.CrossRefGoogle Scholar
Fan, J. & Gijbels, I. (1992) Variable bandwidth and local linear regression smoothers. Annals of Statistics 20(4), 2008–2036.CrossRefGoogle Scholar
Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and Its Applications . Monographs on Statistics and Applied Probability, 66. Chapman and Hall/CRC.Google Scholar
Fan, Y. and Guerre, E. (2016) Multivariate local polynomial estimators: Uniform boundary properties and asymptotic linear representation. In Gozalez-Rivera, G., Hill, R., and Lee, T.-H. (eds.), Essays in Honor of Aman Ullah . Advances in Econometrics, 36, pp. 489–538. Emerald.Google Scholar
Feller, W. (1968) An Introduction to Probability Theory and Its Applications , vol. 1. Wiley.Google Scholar
Goh, C. (2018) Rate-optimal estimation of the intercept in a semiparametric sample-selection model. Unpublished manuscript, University of Wisconsin–Milwaukee.Google Scholar
Gourieroux, C., Monfort, A., & Trognon, A. (1984) Pseudo maximum likelihood methods: Applications to Poisson models. Econometrica 52(3), 701–720.CrossRefGoogle Scholar
Hall, P. & Racine, J. (2015) Infinite order cross-validated local polynomial regression. Journal of Econometrics 185, 510–525.CrossRefGoogle Scholar
Ham, J. & LaLonde, R. (1996) The effect of sample selection and initial conditions in duration models: Evidence from experimental data on training. Econometrica 64, 175–205.CrossRefGoogle Scholar
Hayfield, T. & Racine, J. (2008) Nonparametric econometrics: The np package. Journal of Statistical Software 27(5), 1–32.CrossRefGoogle Scholar
Heckman, J. (1979) Sample selection bias as a specification error. Econometrica 47, 153–161.CrossRefGoogle Scholar
Heckman, J. (1990) Variety of selection bias. American Economic Review 80(2), 679–694.Google Scholar
Honoré, B. & Hu, L. (2020) Selection without exclusion. Econometrica 88(3), 1007–1029.CrossRefGoogle Scholar
Jochmans, K. (2015) Multiplicative-error models with sample selection. Journal of Econometrics 184, 315–327.CrossRefGoogle Scholar
Khan, S. & Tamer, E. (2010) Irregular identification, support conditions, and inverse weight estimation. Econometrica 78(6), 2021–2042.Google Scholar
Klein, R. & Spady, R. (1993) An efficient semiparametric estimator for binary response models. Econometrica 61(2), 387–421.CrossRefGoogle Scholar
Lewbel, A. (2007) Endogenous selection or treatment model estimation. Econometric Theory 13, 32–51.CrossRefGoogle Scholar
Li, Q. & Racine, J. (2004) Nonparametric estimation of regression functions with both categorical and continuous data. Journal of Econometrics 119(1), 99–130.Google Scholar
Li, Q. & Racine, J. (2008) Nonparametric estimation of conditional CDF and quantile functions with mixed categorical and continuous data. Journal of Business and Economic Statistics 26(4), 423–434.CrossRefGoogle Scholar
Masry, E. (1996) Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis 17(6), 571–599.CrossRefGoogle Scholar
Olivetti, C. (2006) Changes in women’s hours of market work: The role of returns to experience. Review of Economic Dynamics 9, 557–587.CrossRefGoogle Scholar
Powell, J., Stock, J., & Stoker, T. (1989) Semiparametric estimation of index coefficients. Econometrica 57, 1403–1430.CrossRefGoogle Scholar
Racine, J. (1993) An efficient cross-validation algorithm for window width selection for nonparametric kernel regression. Communications in Statistics 22(4), 1107–1114.CrossRefGoogle Scholar
Ruppert, D. & Wand, M. (1994) Multivariate locally weighted least squares regression. Annals of Statistics 22(3), 1346–1370.CrossRefGoogle Scholar
Schafgans, M. (1998) Ethnic wage differences in Malaysia: Parametric and semiparametric estimation of the Chinese–Malay wage gap. Journal of Applied Econometrics 13, 481–504.3.0.CO;2-I>CrossRefGoogle Scholar
Schafgans, M. (2000) Gender wage difference in Malaysia: Parametric and semiparametric estimation. Journal of Development Economics 63, 351–368.CrossRefGoogle Scholar
Schafgans, M. & Zinde-Walsh, V. (2002) On intercept estimation in the sample selection model. Econometric Theory 18, 40–50.CrossRefGoogle Scholar
Sherman, B. (1993) The limiting distribution of the maximum rank correlation estimator. Econometrica 61(1), 123–137.CrossRefGoogle Scholar
Terza, J. (1998) Estimating count data models with endogenous switching: Sample selection and endogenous treatment effects. Journal of Econometrics 84, 129–154.CrossRefGoogle Scholar
Vytlacil, E. (2002) Independence, monotonicity, and latent index model: An equivalent result. Econometrica 70, 331–341.CrossRefGoogle Scholar
Windmeijer, F. & Santos Silva, J. (1998) Endogeneity in count data models: An application to demand for health care. Journal of Applied Econometrics 12(3), 281–294.3.0.CO;2-1>CrossRefGoogle Scholar
Supplementary material: PDF

Arulampalam et al. supplementary material

Arulampalam et al. supplementary material

Download Arulampalam et al. supplementary material(PDF)
PDF 295 KB