Bartolucci, Francesco and Pigini, Claudia and Valentini, Francesco
(2021):
*MCMC Conditional Maximum Likelihood for the two-way fixed-effects logit.*

Preview |
PDF
MPRA_paper_110034.pdf Download (378kB) | Preview |

## Abstract

We propose a Markov chain Monte Carlo Conditional Maximum Likelihood (MCMC-CML) estimator for two-way fixed-effects logit models for dyadic data. The proposed MCMC approach, based on a Metropolis algorithm, allows us to overcome the computational issues of evaluating the probability of the outcome conditional on nodes in and out degrees, which are sufficient statistics for the incidental parameters. Under mild regularity conditions, the MCMC-CML estimator converges to the exact CML one and is asymptotically normal. Moreover, it is more efficient than the existing pairwise CML estimator. We study the finite sample properties of the proposed approach by means of a simulation study and three empirical applications, where we also show that the MCMC-CML estimator can be applied to binary logit models for panel data with both subject and time fixed effects. Results confirm the expected theoretical advantage of the proposed approach, especially with small and sparse networks or with rare events in panel data.

Item Type: | MPRA Paper |
---|---|

Original Title: | MCMC Conditional Maximum Likelihood for the two-way fixed-effects logit |

Language: | English |

Keywords: | Directed network, Fixed effects, Link formation, Metropolis algorithm, Panel data |

Subjects: | C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C23 - Panel Data Models ; Spatio-temporal Models C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling |

Item ID: | 110034 |

Depositing User: | Francesco Valentini |

Date Deposited: | 07 Oct 2021 04:48 |

Last Modified: | 07 Oct 2021 04:48 |

References: | Acemoglu, D., Ozdaglar, A., and Tahbaz-Salehi, A. (2015). Systemic risk and stability in financial networks. American Economic Review, 105(2):564–608. Andersen, E. B. (1970). Asymptotic properties of conditional maximum-likelihood estimators. Journal of the Royal Statistical Society: Series B (Methodological), 32(2):283–301. Ando, T., Bai, J., and Li, K. (2021). Bayesian and maximum likelihood analysis of large-scale panel choice models with unobserved heterogeneity. Journal of Econometrics. Attanasio, O., Barr, A., Cardenas, J. C., Genicot, G., and Meghir, C. (2012). Risk pooling, risk preferences, and social networks. American Economic Journal: Applied Economics, 4(2):134–67. Banerjee, A., Chandrasekhar, A. G., Duflo, E., and Jackson, M. O. (2013). The diffusion of microfinance. Science, 341(6144). Boneva, L. and Linton, O. (2017). A discrete-choice model for large heterogeneous panels with interactive fixed effects with an application to the determinants of corporate bond issuance. Journal of Applied Econometrics, 32(7):1226–1243. Caffo, B. S. and Booth, J. (2003). Monte carlo conditional inference for log-linear and logistic models: a survey of current methodology. Statistical Methods in Medical Research, 12(2):109–123. Caggiano, G., Calice, P., Leonida, L., and Kapetanios, G. (2016). Comparing logit-based early warning systems: Does the duration of systemic banking crises matter? Journal of Empirical finance, 37:104–116. Chamberlain, G. (1980). Analysis of covariance with qualitative data. The review of economic studies, 47(1):225–238. Charbonneau, K. B. (2017). Multiple fixed effects in binary response panel data models. The Econometrics Journal, 20(3):S1–S13. Chen, M., Fernández-Val, I., and Weidner, M. (2021). Nonlinear factor models for network and panel data. Journal of Econometrics, 220(2):296–324. Chen, Y., Diaconis, P., Holmes, S. P., and Liu, J. S. (2005). Sequential monte carlo methods for statistical analysis of tables. Journal of the American Statistical Association, 100(469):109–120. Cruz-Gonzalez, M., Fernández-Val, I., and Weidner, M. (2017). Bias corrections for probit and logit models with two-way fixed effects. The Stata Journal, 17(3):517–545. De Paula, Á. (2020). Econometric models of network formation. Annual Review of Economics, 12:775–799. Diaconis, P. and Gangolli, A. (1995). Rectangular arrays with fixed margins. In Discrete probability and algorithms, pages 15–41. Springer. Diaconis, P. and Sturmfels, B. (1998). Algebraic algorithms for sampling from conditional distributions. The Annals of statistics, 26(1):363–397. Dzemski, A. (2019). An empirical model of dyadic link formation in a network with unobserved heterogeneity. Review of Economics and Statistics, 101(5):763–776. Erdős, P. and Rényi, A. (1960). On the evolution of random graphs. Publ. Math. Inst. Hung.Acad. Sci, 5(1):17–60. Fafchamps, M. and Gubert, F. (2007). Risk sharing and network formation. American Economic Review, 97(2):75–79. Fernández-Val, I. and Weidner, M. (2016). Individual and time effects in nonlinear panel models with large N , T . Journal of Econometrics, 192(1):291–312. Geyer, C. J. (1991). Markov chain monte carlo maximum likelihood. Geyer, C. J. (1992). Practical markov chain monte carlo. Statistical science, pages 473–483. Geyer, C. J. (1994). On the convergence of monte carlo maximum likelihood calculations. Journal of the Royal Statistical Society: Series B (Methodological), 56(1):261–274. Geyer, C. J. and Thompson, E. A. (1992). Constrained monte carlo maximum likelihood for dependent data. Journal of the Royal Statistical Society: Series B (Methodological), 54(3):657–683. Graham, B. S. (2017). An econometric model of network formation with degree heterogeneity. Econometrica, 85(4):1033–1063. Hahn, J. and Newey, W. (2004). Jackknife and analytical bias reduction for nonlinear panel models. Econometrica, 72:1295–1319. Helpman, E., Melitz, M., and Rubinstein, Y. (2008). Estimating trade flows: Trading partners and trading volumes. The quarterly journal of economics, 123(2):441–487. Holland, P. W. and Leinhardt, S. (1981). An exponential family of probability distributions for directed graphs. Journal of the american Statistical association, 76(373):33–50. Huffer, F. W. and Wu, H. (1998). Markov chain monte carlo for autologistic regression models with application to the distribution of plant species. Biometrics, pages 509–524. Jochmans, K. (2018). Semiparametric analysis of network formation. Journal of Business & Economic Statistics, 36(4):705–713. Jochmans, K. and Otsu, T. (2019). Likelihood corrections for two-way models. Annals of Economics and Statistics, 2019(134):227–242. Laeven, L. and Valencia, F. (2018). Systemic banking crises revisited. IMF Working Paper 18/206, International Monetary Fund. Lancaster, T. (2000). The incidental parameter problem since 1948. Journal of econometrics, 95(2):391–413. Lazega, E. et al. (2001). The collegial phenomenon: The social mechanisms of cooperation among peers in a corporate law partnership. Oxford University Press on Demand. Newey, W. K. and McFadden, D. (1994). Large sample estimation and hypothesis testing. Handbook of econometrics, 4:2111–2245. Neyman, J. and Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica: Journal of the Econometric Society, pages 1–32. Pérez-Salvador, B. R., de-los Cobos-Silva, S., Gutiérrez-Andrade, M. A., and Torres-Chazaro, A. (2002). A reduced formula for the precise number of (0, 1)-matrices in a (r, s). Discrete mathematics, 256(1-2):361–372. Pigini, C. (2021). Penalized maximum likelihood estimation of logit-based early warning systems. International Journal of Forecasting, 37(3):1156–1172. Rasch, G. (1961). On general laws and the meaning of measurement in psychology. In Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, volume 4, pages 321–333. Varin, C. (2008). On composite marginal likelihoods. Asta advances in statistical analysis, 92(1):1–28. Varin, C., Reid, N., and Firth, D. (2011). An overview of composite likelihood methods. Statistica Sinica, pages 5–42. Wang, B.-Y. and Zhang, F. (1998). On the precise number of (0, 1)-matrices in a (r, s). Discrete mathematics, 187(1-3):211–220. Yan, T., Jiang, B., Fienberg, S. E., and Leng, C. (2019). Statistical inference in a directed network model with covariates. Journal of the American Statistical Association, 114(526):857–868. Zacchia, P. (2020). Knowledge spillovers through networks of scientists. The Review of Economic Studies, 87(4):1989–2018. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/110034 |