A class of binary response models for grouped duration data

This paper explores the relationship between conventional models for binary response such as the probit and logit, and the proportional hazard (PH) and related specifications for grouped duration data. I outline a general class of hazard models for grouped duration data based upon the choice of period-specific distribution functions, facilitating a thorough analysis of the implications of various specifications and consideration of various issues of model identification. This class of models nests, among others, the proportional hazard, probit, and logit specifications for interval survival. I consider the implications of various specifications for hazard behaviour, focusing on familiar specifications. While the specifications will generally yield results that are quite similar along a number of dimensions, there are significant differences. The probit model generates non-proportional effects of variables on the discrete hazard, while the logit and PH tend to show only slight non-proportionality. Furthermore, while the effects of variables on the derivatives are considerably larger for the probit specification, the time-pattern of the probit effects is relatively insensitive to changes in explanatory variables. I illustrate these issues by providing an example taken from Katz's (1986) unemployment data from the Panel Study of Income Dynamics.     

Efficient estimation of probit models with correlated errors

Maximum Likelihood (ML) estimation of probit models with correlated errors typically requires high-dimensional truncated integration. Prominent examples of such models are multinomial probit models and binomial panel probit models with serially correlated errors. In this paper we propose to use a generic procedure known as Efficient Importance Sampling (EIS) for the evaluation of likelihood functions for probit models with correlated errors. Our proposed EIS algorithm covers the standard GHK probability simulator as a special case. We perform a set of Monte Carlo experiments in order to illustrate the relative performance of both procedures for the estimation of a multinomial multiperiod probit model. Our results indicate substantial numerical efficiency gains for ML estimates based on the GHK–EIS procedure relative to those obtained by using the GHK procedure.     

The dynamic invariant multinomial probit model: Identification,pretesting and estimation

We present a new specification for the multinomial multiperiod probit model with autocorrelated errors. In sharp contrast with commonly used specifications, ours is invariant with respect to the choice of a baseline alternative for utility differencing. It also nests these standard models as special cases, allowing for data-based selection of the baseline alternatives for the latter. Likelihood evaluation is achieved under an Efficient Importance Sampling (EIS) version of the standard GHK algorithm. Several simulation experiments highlight identification, estimation and pretesting within the new class of multinomial multiperiod probit models.     

Econometric methods for fractional response variables with an application to 401(k) plan participation rates

We develop attractive functional forms and simple quasi-likelihood estimation methods for regression models with a fractional dependent variable. Compared with log-odds type procedures, there is no difficulty in recovering the regression function for the fractional variable, and there is no need to use ad hoc transformations to handle data at the extreme values of zero and one. We also offer some new, robust specification tests by nesting the logit or probit function in a more general functional form. We apply these methods to a data set of employee participation rates in 401(k) pension plans.     

Parametric and semi-parametric estimation of the binary response model of labour market participation

This paper compares the familiar probit model with three semiparametric estimators of binary response models in an application to labour market participation of married women. This exercise is performed using two different cross-section data sets from Switzerland and Germany. For the Swiss data the probit specification cannot be rejected and the models yield similar results. In the German case the probit model is rejected, but the coefficient estimates do not vary substantially across the models. The predicted choice probabilities, however, differ systematically for a subset of the sample. The results of this paper indicate that more work is necessary on specification tests of semiparametric models and on simulations using these models.     

Smoothly mixing regressions

This paper extends the conventional Bayesian mixture of normals model by permitting state probabilities to depend on observed covariates. The dependence is captured by a simple multinomial probit model. A conventional and rapidly mixing MCMC algorithm provides access to the posterior distribution at modest computational cost. This model is competitive with existing econometric models, as documented in the paper's illustrations. The first illustration studies quantiles of the distribution of earnings of men conditional on age and education, and shows that smoothly mixing regressions are an attractive alternative to nonBayesian quantile regression. The second illustration models serial dependence in the S&P 500 return, and shows that the model compares favorably with ARCH models using out of sample likelihood criteria.     

A zero-inflated ordered probit model,with an application to modelling tobacco consumption

Data for discrete ordered dependent variables are often characterised by “excessive” zero observations which may relate to two distinct data generating processes. Traditional ordered probit models have limited capacity in explaining this preponderance of zero observations. We propose a zero-inflated ordered probit model using a double-hurdle combination of a split probit model and an ordered probit model. Monte Carlo results show favourable performance in finite samples. The model is applied to a consumer choice problem of tobacco consumption indicating that policy recommendations could be misleading if the splitting process is ignored.     

Extended Models for Quantal Response Data

There is much current interest in trying to improve the fit of the classical logit and probit models for quantal response data. This is done through transforming the dose scale and/or embedding a classical model in a richer parametric family. This paper provides an historical review of the development of this work, and attempts to make practical recommendations. Much of the work extends directly to the case of logistic regression.     

On the existence of maximum likelihood estimates in random effects models for clustered multivariate binary data

We consider a class of random effects models for clustered multivariate binary data based on the threshold crossing technique of a latent random vector. Components of this latent vector are assumed to have a Laird–Ware structure. However, in place of their Gaussian assumptions, any specified class of multivariate distribution is allowed for the random effects, and the error vector is allowed to have any strictly positive pdf. A well known member of this class of models is the multivariate probit model with random effects. We investigate sufficient and necessary conditions for the existence of maximum likelihood estimates for the location and the association parameters. Implications of our results are illustrated through some hypothetical examples.     

Computing marginal likelihoods from a single MCMC output

In this article, we propose new Monte Carlo methods for computing a single marginal likelihood or several marginal likelihoods for the purpose of Bayesian model comparisons. The methods are motivated by Bayesian variable selection, in which the marginal likelihoods for all subset variable models are required to compute. The proposed estimates use only a single Markov chain Monte Carlo (MCMC) output from the joint posterior distribution and it does not require the specific structure or the form of the MCMC sampling algorithm that is used to generate the MCMC sample to be known. The theoretical properties of the proposed method are examined in detail. The applicability and usefulness of the proposed method are demonstrated via ordinal data probit regression models. A real dataset involving ordinal outcomes is used to further illustrate the proposed methodology.     

A modified GMDH approach for social science research: exploring patterns of relationships in the data

Group Method of Data Handling (GMDH) is a way with which a system of models self-organize themselves by forming higher-order polynomials and selecting the ones with best power of prediction by certain criterion. This method is helpful when we explore patterns of relationships in the data under investigation. In this paper the author presents a modified version of the GMDH algorithm emphasizing the parsimony of models and the behavior of individual parameter estimates as well as of the whole model, and utilizing the consistency and accuracy of bootstrap estimates. This approach is suitable for most research social scientists conduct. An example, the 1907 Romanian Peasant Rebellion, is used to illustrate how to employ the GMDH algorithm when the research topic has been theory-laden. The findings show that GMDH is an appropriate method that social scientists can utilize in their pursuit of a model that is most parsimonious and theoretically meaningful at the same time. Possible extensions of the modified approach, which in its present form works on linear regression type of models, to logit and probit models are also considered.     

Testing for Misspecification in Binary Response Models with Competing Distributions*

In empirical studies, the probit and logit models are often used without checks for their competing distributional specifications. It is also rare for econometric tests to be focused on this issue. Santos Silva [Journal of Applied Econometrics (2001 ), Vol. 16, pp. 577–597] is an important recent exception. By using the conditional moment test principle, we discuss a wide class of non‐nested tests that can easily be applied to detect the competing distributions for the binary response models. This class of tests includes the test of Santos Silva (2001 ) for the same task as a particular example and provides other useful alternatives. We also compare the performance of these tests by a Monte Carlo simulation.     

Simple solutions to the initial conditions problem in dynamic,nonlinear panel data models with unobserved heterogeneity

I study a simple, widely applicable approach to handling the initial conditions problem in dynamic, nonlinear unobserved effects models. Rather than attempting to obtain the joint distribution of all outcomes of the endogenous variables, I propose finding the distribution conditional on the initial value (and the observed history of strictly exogenous explanatory variables). The approach is flexible, and results in simple estimation strategies for at least three leading dynamic, nonlinear models: probit, Tobit and Poisson regression. I treat the general problem of estimating average partial effects, and show that simple estimators exist for important special cases. Copyright © 2005 John Wiley & Sons, Ltd.     

On the effect of obesity on employment in the presence of observed and unobserved confounding

The aim of this paper was to estimate the effect of obesity on the employment probability for Italian men and women accounting for both observed and unobserved confounding. We use microdata collected by the Italian National Statistical Office for the year 2009 during a multi‐scope survey of Italian households. The employment–obesity relationship is estimated after controlling for observed confounding by using probit regression and a propensity score weighting approach. To control for both observed and unobserved confounding (endogeneity), a semiparametric recursive bivariate probit model is employed instead. Our findings suggest that obesity has a significant negative effect on the employment probability and that endogeneity might not be an important issue.     

Sequential numerical integration in nonlinear state space models for microeconometric panel data

This paper discusses the estimation of a class of nonlinear state space models including nonlinear panel data models with autoregressive error components. A health economics example illustrates the usefulness of such models. For the approximation of the likelihood function, nonlinear filtering algorithms developed in the time‐series literature are considered. Because of the relatively simple structure of these models, a straightforward algorithm based on sequential Gaussian quadrature is suggested. It performs very well both in the empirical application and a Monte Carlo study for ordered logit and binary probit models with an AR(1) error component. Copyright © 2008 John Wiley & Sons, Ltd.     

New Men and New Women? A Comparison of Paid Work Propensities from a Panel Data Perspective

British Household Panel Survey data for waves 1–5 (1991–5) is used to compare paid work participation rates of men and women. Year-on-year persistence in paid work propensities is high, but greater for men than women. Non-work persistence is higher for women. Using panel data probit regression models, we also investigate why men's and women's participation rates differ, comparing the roles of differences in observable characteristics and differences in rates of return to these characteristics, while also controlling for unobserved heterogeneity. Most of the difference in participation rates is accounted for by the differences in returns associated with the presence of children, especially young ones.     

Corporate Sustainability and Economic Performance: an Empirical Analysis of a Voluntary Environmental Program in the USA

Voluntary environmental programs (VEPs) are designed based on a win–win approach to environmental protection that reconciles environmental protection and economic performance. Despite the claims about VEPs, there has been an ongoing debate over their efficacy with regard to whether environmental goals are balanced by economic interests on both theoretical and empirical grounds. To resolve this controversy, this paper empirically investigates a public VEP by the US Environmental Protection Agency: Green Lights (GL). For this, the paper constructs a treatment effects regression model to account for the effects of non‐random assignment for GL participants and non‐participants. The proposed model can simultaneously estimate probit models that predict corporate participation in the GL program and linear models that test the extent to which this participation contributes to economic performance. The results indicate significant positive effects of corporate participation in the GL program on economic performance, providing support for the win–win perspective. Copyright © 2013 John Wiley & Sons, Ltd and ERP Environment     

中国利率期限结构对经济周期波动的预测能力检验——基于动态Probit模型的研究途径

本文对我国利率期限结构对经济周期波动的预测能力进行实证研究.首先,利用时差相关分析方法选择我国经济周期波动的利差先行指标.然后,利用基于利差先行指标的动态Probit模型检验我国利率期限结构对经济周期波动状态的预测能力,并且对静态Probit模型和动态Probit模型、各种动态Probit模型之间的预测效果也进行了比较.研究结果表明,我国利率期限结构变动对未来3个月的经济周期波动状态具有比较稳定的指示作用,利用经济状态先验信息的动态Probit模型的预测效果优于静态Probit模型.     

The impact of obesity on employment

Using data from two rounds of the Health Survey for England I investigate the impact of obesity on employment. I use three approaches: a univariate probit model; propensity score matching; and IV regression using a recursive bivariate probit model. Conditional on a comprehensive set of covariates, the findings show that obesity has a statistically significant and negative effect on employment in both males and females. In males the endogeneity of obesity does not significantly affect the estimates, and the magnitude of effect is similar across the three methods. In females, failure to account for endogeneity leads to underestimation of the negative impact of obesity on employment.     

The Multinomial Probit Model Revisited: A Discussion of Parameter Estimability,Identification and Specification Testing

In this paper we examine the multinomial probit model in the light of recent developments in the field of simulation-based inference. We focus upon five broad areas: specification of multinomial choice models; parameter estimability and the use of simulation techniques, parameter identification; specification testing; and practical issues in simulation-based inference. Although the substitution of simulated probabilities for difficult to compute multidimensional integrals represents a significant step, by examining the more tenuous task of identification and in particular the identification of covariance parameters, we show how the specification and estimation of the multinomial probit still represents a formidable task.