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on Discrete Choice Models |
| By: | Hyungsik Roger Moon (Institute for Fiscal Studies and USC); Matthew Shum; Martin Weidner (Institute for Fiscal Studies and UCL) |
| Abstract: | We extend the Berry, Levinsohn and Pakes (BLP, 1995) random coefficients discrete choice demand model, which underlies much recent empirical work in IO. We add interactive fixed effects in the form of a factor structure on the unobserved product characteristics. The interactive fixed effects can be arbitrarily correlated with the observed product characteristics (including price), which accommodates endogeneity and, at the same time, captures strong persistence in market shares across products and markets. We propose a two step least squares-minimum distance (LS-MD) procedure to calculate the estimator. Our estimator is easy to compute, and Monte Carlo simulations show that it performs well. We consider an empirical application to US automobile demand. |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:20/14&r=dcm |
| By: | Cheng Hsiao; Qi Li; Jeffrey S. Racine |
| Abstract: | In this paper we propose a nonparametric kernel-based model specification test that can be used when the regression model contains both discrete and continuous regressors. We employ discrete variable kernel functions and we smooth both the discrete and continuous regressors using least squares cross-validation (CV) methods. The test statistic is shown to have an asymptotic normal null distribution. We also prove the validity of using the wild bootstrap method to approximate the null distribution of the test statistic, the bootstrap being our preferred method for obtaining the null distribution in practice. Simulations show that the proposed test has significant power advantages over conventional kernel tests which rely upon frequency-based nonparametric estimators that require sample splitting to handle the presence of discrete regressors. |
| Keywords: | Consistent test; Parametric functional form; Nonparametric estimation |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002074&r=dcm |
| By: | Karyne B. Charbonneau |
| Abstract: | This paper considers the adaptability of estimation methods for binary response panel data models to multiple fixed effects. It is motivated by the gravity equation used in international trade, where important papers such as Helpman, Melitz and Rubinstein (2008) use binary response models with fixed effects for both importing and exporting countries. Econometric theory has mostly focused on the estimation of single fixed effects models. This paper investigates whether existing methods can be modified to eliminate multiple fixed effects for two specific models in which the incidental parameter problem has already been solved in the presence of a single fixed effect. We find that it is possible to generalize the conditional maximum likelihood approach of Rasch (1960, 1961) to include two fixed effects for the logit. Surprisingly, despite many similarities with the logit, Manski’s (1987) maximum score estimator for binary response models cannot be adapted to the presence of two fixed effects. Monte Carlo simulations show that the conditional logit estimator presented in this paper is less biased than other logit estimators without sacrificing on precision. This superiority is emphasized in small samples. An application to trade data using the logit estimator further highlights the importance of properly accounting for two fixed effects. |
| Keywords: | Econometric and statistical methods |
| JEL: | C23 C25 F14 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:14-17&r=dcm |
| By: | Gery Geenens; Arthur Charpentier; Davy Paindaveine |
| Abstract: | Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametricallyestimating a copula density is addressed. Arguably the most popular nonparametric density estimator,the kernel estimator is not suitable for the unit-square-supported copula densities, mainly because it isheavily a↵ected by boundary bias issues. In addition, most common copulas admit unbounded densities,and kernel methods are not consistent in that case. In this paper, a kernel-type copula density estimatoris proposed. It is based on the idea of transforming the uniform marginals of the copula density intonormal distributions via the probit function, estimating the density in the transformed domain, whichcan be accomplished without boundary problems, and obtaining an estimate of the copula densitythrough back-transformation. Although natural, a raw application of this procedure was, however, seennot to perform very well in the earlier literature. Here, it is shown that, if combined with local likelihooddensity estimation methods, the idea yields very good and easy to implement estimators, fixing boundaryissues in a natural way and able to cope with unbounded copula densities. The asymptotic properties ofthe suggested estimators are derived, and a practical way of selecting the crucially important smoothingparameters is devised. Finally, extensive simulation studies and a real data analysis evidence theirexcellent performance compared to their main competitors. |
| Keywords: | copula density; transformation kernel density estimator; boundary bias; unbounded Density; local likelihood density estimation |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/159977&r=dcm |