Estimating Dynamic Panel Data Discrete Choice Models with Fixed Effects

Abstract

In this paper, I consider the estimation of dynamic binary choice panel data models with fixed effects. I use a Modified Maximum Likelihood Estimator (MMLE) that reduces the order of the bias in the Maximum Likelihood Estimator from O(T-1) to O(T-2), without increasing the asymptotic variance. I evaluate its performance in finite samples where T is not large, using Monte Carlo simulations. In Probit and Logit models containing lags of the endogenous variable and exogenous variables, the estimator is found to have a small bias in a panel with eight periods. A distinctive advantage of the MMLE is its general applicability. Identification issues about policy parameters of interest that arise in this kind of models are also addressed. In contrast with linear models, parameters of interest typically depend on the distribution of the individual effects. I discuss the relevance of mean effects across individuals and show an instance in which the entire distribution is needed. Compared with simple MLE, simulation results show that MMLE improves significantly the estimation of the distribution of the effect of interest.

Currency crisis early warning systems: Why they should be dynamic

“…It is the first paper to use Kauppi and Saikkonen's (2008) exact ML methodology to estimate a dynamic discrete-choice EWS. Furthermore, it extends this methodology to panels by drawing on work by Carro (2007). The forecasting abilities of static and dynamic binary EWSs are then compared and discussed in a unified evaluation framework designed specifically for EWSs (Candelon et al, 2012).…”

“…4 Second, it can be used to construct EWSs for any type of crisis, not just currency crises, as in our application. Furthermore, we extend this time series framework to a dynamic fixed effects panel EWS by including the score correction proposed by Carro (2007). 5 As will be seen, the dynamic model with the lagged binary dependent variable which we propose outperforms (both in-sample and out-of-sample) the specifications considered in the previous EWSs, and the traditional static logit in particular.…”

“…In this section, we therefore propose a dynamic version of the fixed effects panel model by elaborating on the work of Carro (2007). Note that this framework can embody all three of the dynamic specifications proposed for time series.…”

Fixed effects estimation of structural parameters and marginal effects in panel probit models

“…This analysis is motivated by similar studies in labor economics in which panel binary choice processes have been widely used to model female labor force participation decisions (see, e.g., Hyslop (1999), Chay and Hyslop (2000) and Carro (2007)). I find that fixed effects estimators, while biased for index coefficients, give very similar estimates to their bias-corrected counterparts of marginal effects in static models.…”

“…and Arellano (2003), Hahn andKuersteiner (2004), HN04, andCarro (2007); see also Arellano and Hahn (2007) for a recent survey of this literature and additional references. These studies aim to provide what I refer to as large-T consistent estimates because they rely on an asymptotic approximation to the behavior of the estimator that lets both the number of individuals n and the time dimension T grow with the sample size.…”