Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-22T04:24:45.613Z Has data issue: false hasContentIssue false
  • English
  • Français

A MULTIPLEX INTERDEPENDENT DURATIONS MODEL

Published online by Cambridge University Press:  09 November 2020

Zhongjian Lin  and
Ruixuan Liu
Zhongjian Lin*
Affiliation:
Emory University
Ruixuan Liu
Affiliation:
Emory University
*
Address correspondence to Zhongjian Lin, Department of Economics, Emory University, 1602 Fishburne Drive, GA30307, USA; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose a multiplex interdependent durations model and study its empirical content. The model considers an empirical stopping game of multiple agents making optimal timing decisions with incomplete information. We characterize the unique Bayesian Nash equilibrium of the stopping game in a system of simultaneous equations involving the conditional distribution of each duration with a moderate strategic interaction condition. The system of nonlinear simultaneous equations allows us to obtain constructive identification results of the interaction effects and other nonparametric model primitives. We propose two consistent semiparametric estimation methods based on different parameterizations of modeling components with right-censored duration data.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 6 , December 2021 , pp. 1238 - 1266
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This paper benefited greatly from insightful comments and suggestions provided by co-editor, Sokbae Lee, and two reviewers. We are grateful to Jaap Abbring, Jeffrey Campbell, Yingyao Hu, Qi Li, Xiaodong Liu, Essie Maasoumi, Áureo de Paula, Yuya Sasaki, Tiemen Woutersen, and Haiqing Xu for many thoughtful discussions. We also thank the audience at Tilburg University, Johns Hopkins University, University of Colorado, Boulder, and the ES 2017 European Meeting. All errors remaining are our own.

References

REFERENCES

Abbring, J.H. (2012) Mixed hitting-time models. Econometrica 80(2), 783–819.Google Scholar
Abbring, J.H. & Ridder, G. (2015) Regular variation and the identification of generalized accelerated failure-time models. Econometric Theory 31(6), 1229–1248.CrossRefGoogle Scholar
Abbring, J.H. & van den Berg, G.J. (2003) The nonparametric identification of treatment effects in duration models. Econometrica 71(5), 1491–1517.CrossRefGoogle Scholar
Aguirregabiria, V. & Mira, P. (2007) Sequential estimation of dynamic discrete games. Econometrica 75(1), 1–53.CrossRefGoogle Scholar
Aguirregabiria, V. & Mira, P. (2019) Identification of games of incomplete information with multiple equilibria and common unobserved heterogeneity. Quantitative Economics 10(4), 1659–1701.CrossRefGoogle Scholar
Ahn, H. & Manski, C.F. (1993) Distribution theory for the analysis of binary choice under uncertainty with nonparametric estimation of expectations. Journal of Econometrics 56(3), 291–321.CrossRefGoogle Scholar
Andersen, P., Borgan, O., Gill, R., & Keiding, N. (1993) Statistical Models Based on Counting Processes. Springer.CrossRefGoogle Scholar
Aradillas-Lopez, A. (2010) Semiparametric estimation of a simultaneous game with incomplete information. Journal of Econometrics 157(2), 409–431.CrossRefGoogle Scholar
Bajari, P., Hahn, J., Hong, H., & Ridder, G. (2011) A note on semiparametric estimation of finite mixtures of discrete choice models with application to game theoretic models. International Economic Review 52(3), 807–824.CrossRefGoogle Scholar
Bajari, P., Hong, H., Krainer, J., & Nekipelov, D. (2010) Estimating static models of strategic interactions. Journal of Business & Economic Statistics 28(4), 469–482.CrossRefGoogle Scholar
Banerjee, A.V. (1992) A simple model of herd behavior. The Quarterly Journal of Economics 107(3), 797–817.CrossRefGoogle Scholar
Bernheim, D.B. (1994) A theory of conformity. Journal of Political Economy 102(5), 841–877.CrossRefGoogle Scholar
Bramoullé, Y., Djebbari, H., & Fortin, B. (2009) Identification of peer effects through social networks. Journal of Econometrics 150(1), 41–55.CrossRefGoogle Scholar
Brock, W.A. & Durlauf, S.N. (2001a) Discrete choice with social interactions. The Review of Economic Studies 68(2), 235–260.CrossRefGoogle Scholar
Brock, W.A. & Durlauf, S.N. (2001b) Interactions-based models. Handbook of Econometrics 5, 3297–3380.CrossRefGoogle Scholar
Chen, X. (2007) Large sample sieve estimation of semi-nonparametric models. Handbook of Econometrics 6, 5549–5632.CrossRefGoogle Scholar
Chernozhukov, V., Hong, H., & Tamer, E. (2007) Estimation and confidence regions for parameter sets in econometric models. Econometrica 75(5), 1243–1284.CrossRefGoogle Scholar
Chiappori, P.A., Komunjer, I., & Kristensen, D. (2015) Nonparametric identification and estimation of transformation models. Journal of Econometrics 188(1), 22–39.CrossRefGoogle Scholar
Coddington, E.A. (2012) An Introduction to Ordinary Differential Equations. Courier Corporation.Google Scholar
Cosslett, S.R. (1983) Distribution-free maximum likelihood estimator of the binary choice model. Econometrica 51, 765–782.CrossRefGoogle Scholar
de la Pena, V. & Gine, E. (1999) Decoupling: From Dependence to Independence. Springer.CrossRefGoogle Scholar
de Paula, Á. (2009) Inference in a synchronization game with social interactions. Journal of Econometrics 148(1), 56–71.CrossRefGoogle Scholar
Dechevsky, L. & Penev, S. (1998) On shape-preserving wavelet estimators of cumulative distribution functions and densities. Stochastic Analysis and Applications 16(3), 423–462.CrossRefGoogle Scholar
Drepper, B. & Effraimidis, G. (2015) Social Interaction Effects in Duration Models. Working Paper.Google Scholar
Durlauf, S.N. & Ioannides, Y.M. (2010) Social interactions. Annual Review of Economics 2(1), 451–478.CrossRefGoogle Scholar
Ekeland, I., Heckman, J., & Nesheim, L. (2004) Identification and estimation of hedonic models. Journal of Political Economy 112(1), 60–109.CrossRefGoogle Scholar
Elbers, C. & Ridder, G. (1982) True and spurious duration dependence: The identifiability of the proportional hazard model. The Review of Economic Studies 49(3), 403–409.CrossRefGoogle Scholar
Fan, Y. & Liu, R. (2018) Partial identification and inference in censored quantile regression. Journal of Econometrics 206, 1–38.CrossRefGoogle Scholar
Fermanian, J.D. (2001) Nonparametric estimation of competing risks models with covariates. Journal of Multivariate Analysis 85, 156–191.CrossRefGoogle Scholar
Glaeser, E. & Scheinkman, J.A. (2003) Nonmarket interactions. Advances in Economics and Econometrics 1, 339–370.CrossRefGoogle Scholar
Gowrisankaran, G. & Stavins, J. (2004) Network externalities and technology adoption: Lessons from electronic payments. RAND Journal of Economics 35(2), 260–276.CrossRefGoogle Scholar
Heckman, J.J. (1978) Dummy endogenous variables in a simultaneous equation system. Econometrica 46(4), 931–959.CrossRefGoogle Scholar
Heckman, J.J. & Singer, B. (1984a) The identifiability of the proportional hazard model. The Review of Economic Studies 51(2), 231–241.CrossRefGoogle Scholar
Heckman, J.J. & Singer, B. (1984b) A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52, 271–320.CrossRefGoogle Scholar
Honoré, B.E. & de Paula, Á. (2010) Interdependent durations. The Review of Economic Studies 77(3), 1138–1163.CrossRefGoogle Scholar
Honoré, B.E. & de Paula, Á. (2018) A new model for interdependent durations. Quantitative Economics 9(3), 1299–1333.CrossRefGoogle Scholar
Horowitz, J. (1999) Semiparametric estimation of a proportional hazard model with unobserved heterogeneity. Econometrica 67(5), 1001–1028.CrossRefGoogle Scholar
Horowitz, J. & Mammen, E. (2007) Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions. Annals of Statistics 35(6), 2589–2619.CrossRefGoogle Scholar
Horst, U. & Scheinkman, J.A. (2006) Equilibria in systems of social interactions. Journal of Economic Theory 130, 44–77.CrossRefGoogle Scholar
Hu, Y. & Lin, Z. (2020) Binary Choice with Misclassification and Social Interactions, with an Application to Peer Effects in Attitude. Working paper.Google Scholar
Jacho-Chavez, D., Lewbel, A., & Linton, O. (2010) Identification and nonparametric estimation of a transformed additively separable model. Journal of Econometrics 156(2), 392–407.CrossRefGoogle Scholar
Jackson, M., Lin, Z., & Yu, N. (2020) Adjusting for Peer-Influence in Propensity Scoring When Estimating Treatment Effects. Working paper.CrossRefGoogle Scholar
Khan, S. & Nekipelov, D. (2018) Information structure and statistical information in discrete response models. Quantitative Economics 9(2), 995–1017.CrossRefGoogle Scholar
Kortram, R.A., van Rooij, A.C.M., Lenstra, A.J., & Ridder, G. (1995) Constructive identification of the mixed proportional hazards model. Statistica Neerlandica 49(3), 269–281.CrossRefGoogle Scholar
Lancaster, T. (1979) Econometric methods for the duration of unemployment. Econometrica 47(4), 939–956.CrossRefGoogle Scholar
Lancaster, T. (1985) Simultaneous equations models in applied search theory. Journal of Econometrics 28(1), 113–126.CrossRefGoogle Scholar
Lee, L.F. (2007) Identification and estimation of econometric models with group interactions, contextual factors and fixed effects. Journal of Econometrics 140(2), 333–374.CrossRefGoogle Scholar
Lillard, L.A. (1993) Simultaneous equations for hazards: Marriage duration and fertility timing. Journal of Econometrics 56(1-2), 189–217.CrossRefGoogle ScholarPubMed
Lin, D. & Ying, Z. (1995) Semiparametric analysis of general additive-multiplicative hazard models for counting processes. Annals of Statistics 23(5), 1712–1734.CrossRefGoogle Scholar
Lin, Z. & Xu, H. (2017) Estimation of social-influence-dependent peer pressures in a large network game. The Econometrics Journal 20(3), 86–102.CrossRefGoogle Scholar
Liu, N., Vuong, Q., & Xu, H. (2017) Rationalization and identification of binary games with correlated types. Journal of Econometrics 201(2), 249–268.CrossRefGoogle Scholar
Liu, R. (2020) A competing risks model with time-varying heterogeneity and simultaneous failure. Quantitative Economics 11(2), 535–577.CrossRefGoogle Scholar
Manski, C.F. (1991) Nonparametric estimation of expectations in the analysis of discrete choice under uncertainty. Nonparametric and Semiparametric Methods in Econometrics and Statistics: Proceedings of the Fifth International Symposium in Economic Theory and Econometrics, vol. 5, pp. 259–275. Cambridge University Press.Google Scholar
Manski, C.F. (1993) Identification of endogenous social effects: The reflection problem. The Review of Economic Studies 60(3), 531–542.CrossRefGoogle Scholar
Martinussen, T. & Scheike, T.H. (2002) A flexible additive multiplicative hazard model. Biometrika 89(2), 283–298.CrossRefGoogle Scholar
Martinussen, T. & Scheike, T.H. (2007) Dynamic Regression Models for Survival Data. Springer Science & Business Media.Google Scholar
Matzkin, R.L. (1991) Semiparametric estimation of monotone and concave utility functions for polychotomous choice models. Econometrica 59, 1315–1327.CrossRefGoogle Scholar
Morris, S. & Shin, H.S. (2003) Global games: Theory and applications. Advances in Economics and Econometrics 56–114.CrossRefGoogle Scholar
Mueller, H. (1991) Smooth optimum kernel estimators near endpoints. Biometrika 78, 521–530.CrossRefGoogle Scholar
Park, A. & Smith, L. (2008) Caller number five and related timing games. Theoretical Economics 3, 231–256.Google Scholar
Ridder, G. (1990) The non-parametric identification of generalized accelerated failure-time models. The Review of Economic Studies 57(2), 167–181.CrossRefGoogle Scholar
Tamer, E. (2003) Incomplete simultaneous discrete response model with multiple equilibria. The Review of Economic Studies 70(1), 147–165.CrossRefGoogle Scholar
Tamer, E. (2010) Partial identification in econometrics. Annual Review of Economics 2(1), 167–195.CrossRefGoogle Scholar
Vives, X. (2005) Complementarities and games: New developments. Journal of Economic Literature 43(2), 437–479.CrossRefGoogle Scholar
Wan, Y. & Xu, H. (2014) Semiparametric identification of binary decision games of incomplete information with correlated private signals. Journal of Econometrics 182(2), 235–246.CrossRefGoogle Scholar
Xiao, R. (2018) Identification and estimation of incomplete information games with multiple equilibria. Journal of Econometrics 203(2), 328–343.CrossRefGoogle Scholar
Xu, H. (2014) Estimation of discrete games with correlated types. The Econometrics Journal 17(3), 241–270.CrossRefGoogle Scholar
Xu, H. (2018) Social interactions in large networks: A game theoretical approach. International Economic Review 59(1), 257–284.CrossRefGoogle Scholar