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This paper considers dynamic time series binary choice models. It proves near epoch dependence and strong mixing for the dynamic binary choice model with correlated errors. Using this result, it shows in a time series setting the validity of the dynamic probit likelihood procedure when lags of the dependent binary variable are used as regressors, and it establishes the asymptotic validity of Horowitz’s smoothed maximum score estimation of dynamic binary choice models with lags of the dependent variable as regressors. For the semiparametric model, the latent error is explicitly allowed to be correlated. It turns out that no long-run variance estimator is needed for the validity of the smoothed maximum score procedure in the dynamic time series framework.

In this paper, we consider the semiparametric identification and estimation of a heteroscedastic binary choice model with endogenous dummy regressors and no parametric restriction on the distribution of the error term. Our approach addresses various drawbacks associated with previous estimators proposed for this model. It allows for: general multiplicative heteroscedasticity in both selection and outcome equations; a nonparametric selection mechanism; and multiple discrete endogenous regressors. The resulting three-stage estimator is shown to be asymptotically normal, with a convergence rate that can be arbitrarily close to n-½ if certain smoothness assumptions are satisfied. Simulation results show that our estimator performs reasonably well in finite samples. Our approach is then used to study the intergenerational transmission of smoking habits in British households.

We develop a procedure for removing four major specification errors from the usual formulation of binary choice models. The model that results from this procedure is different from the conventional probit and logit models. This difference arises as a direct consequence of our relaxation of the usual assumption that omitted regressors constituting the error term of a latent linear regression model do not introduce omitted regressor biases into the coefficients of the included regressors.

We introduce an approach for semiparametric inference in dynamic binary choice models that does not impose distributional assumptions on the state variables unobserved by the econometrician. The proposed framework combines Bayesian inference with partial identification results. The method is applicable to models with finite space of observed states. We demonstrate the method on Rust's model of bus engine replacement. The estimation experiments show that the parametric assumptions about the distribution of the unobserved states can have a considerable effect on the estimates of per-period payoffs. At the same time, the effect of these assumptions on counterfactual conditional choice probabilities can be small for most of the observed states.

An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy interventions. Such predictions are more credible when made without arbitrary functional-form/distributional assumptions, and instead based solely on economic rationality, that is, that choice is consistent with utility maximization by a heterogeneous population. This paper investigates nonparametric economic rationality in the empirically important context of binary choice. We show that under general unobserved heterogeneity, economic rationality is equivalent to a pair of Slutsky-like shape restrictions on choice-probability functions. The forms of these restrictions differ from Slutsky inequalities for continuous goods. Unlike McFadden–Richter’s stochastic revealed preference, our shape restrictions (a) are global, that is, their forms do not depend on which and how many budget sets are observed, (b) are closed form, hence easy to impose on parametric/semi/nonparametric models in practical applications, and (c) provide computationally simple, theory-consistent bounds on demand and welfare predictions on counterfactual budge sets.

We consider fixed-effects binary choice models with a fixed number of periods T and regressors without a large support. If the time-varying unobserved terms are i.i.d. with known distribution F, Chamberlain (2010) shows that the common slope parameter is point identified if and only if F is logistic. However, he only considers in his proof T = 2. We show that the result does not generalize to T Ï 3: the common slope parameter can be identified when F belongs to a family including the logit distribution. Identification is based on a conditional moment restriction. Under restrictions on the covariates, these moment conditions lead to point identification of relative effects. If T = 3 and mild conditions hold, GMM estimators based on these conditional moment restrictions reach the semiparametric efficiency bound. Finally, we illustrate our method by revisiting Brender and Drazen (2008).

This paper considers random coefficients binary choice models. The main goal is to estimate the density of the random coefficients nonparametrically. This is an ill-posed inverse problem characterized by an integral transform. A new density estimator for the random coefficients is developed, utilizing Fourier—Laplace series on spheres. This approach offers a clear insight on the identification problem. More importantly, it leads to a closed form estimator formula that yields a simple plug-in procedure requiring no numerical optimization. The new estimator, therefore, is easy to implement in empirical applications, while being flexible about the treatment of unobserved heterogeneity. Extensions including treatments of nonrandom coefficients and models with endogeneity are discussed.

This paper uses discrete choice models, supported by GIS data, to analyse the National Land Use Database, a register of more than 21,000 English brownfields—previously used sites with or without contamination that are currently unused or underused. Using spatial discrete choice models, including the first application of a spatial probit latent class model with class-specific neighbourhood effects, we find evidence of large local differences in the determinants of brownfields redevelopment in England and that the reuse decisions of adjacent sites affect the reuse of a site. We also find that sites with a history of industrial activities, large sites, and sites that are located in the poorest and bleakest areas of cities and regions of England are more difficult to redevelop. In particular, we find that the probability of reusing a brownfield increases by up to 8.5 % for a site privately owned compared to a site publicly owned and between 15 and 30 % if a site is located in London compared to the North West of England. We suggest that local tailored policies are more suitable than regional or national policies to boost the reuse of brownfield sites.