Limited Dependent Variable Models Research Articles

Parametric and semi‐parametric modelling of vacation expenditures

We analyse several limited dependent variable models explaining the budget share that Dutch families spend on vacations. To take account of the substantial number of zero shares, two types of models are used. The first is the single-equation censored regression model. We estimate and test several parametric and semiparametric extensions of the Tobit model. Second, we consider two-equation models, in which the participation decision and the decision on the amount to spend are treated separately. The first decision is modelled as a binary choice model; the second as a conditional regression. We estimate and test parametric and semiparametric specifications. Copyright 1996 by John Wiley & Sons, Ltd. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of t (This abstract was borrowed from another version of this item.)

Alternative transformations in a class of limited dependent variable models: alcohol consumption by US women

This study investigates alcohol consumption by women in the United States,using alternative specifications of the double-hurdle models which accommodate non-normal errors. The IHS double-hurdle model performs marginally better than the Box-Cox double-hurdle model but both models suggest very similar elasticities. The profile of a drinker includes white, black, smoker, homeowner, and residing in urban areas. Women who are older, pregnant or lactating, on special diet, and those with higher weight-height ratio are less likely to consume alcohol than others. Seasonal and regional variations are apparent. Smokers are more likely to consume alcohol and also consume more, while older women are less likely to drink and also drink less than others.

Circumventing the Curse of Dimensionality in Applied Work Using Computer Intensive Methods

Following recent advances in the development of simulation-based inference, we outline a suite of programs designed to circumvent the `curse of dimensionality' common to the class of so-called qualitative and limited dependent variable models. We discuss the nature of the dimensionality problem, briefly introduce the form of a simple simulation technique, outline the structure and capabilities of the programs, and provide a numerical experiment.

Comments on goodness-of-fitmeasures in binary choice models by frank windmeijer

Why study Pseudo-R2,s for limited dependent variable models? After all, even in the much clearer ordinary least squares case, R2 is a poor guide to model selection, at least when used by itself, because it never decreases and typically increases whenever an independent variable is added. There are even cases where R2 will tend to one when there is no relationship among the (nonstationary) variables whatsoever (Granger and Newbold, 1974). Surely applied researchers would not want to bother with such a statistic in the limited dependent variable case, particularly when the intuitive explainedvariation- to- total- variation interpretation is no longer available.

Rational expectations in limited dependent variable models

The appropriate characterizations of rational expectations solutions in one-limit and two-limit models are derived. We prove the existence and uniqueness of the rational expectations solution for each model. Our analysis is general without imposing serial independence and the parametric distributional assumption.

Life Duration of New Firms

The authors follow firms created in Portuguese manufacturing in 1983 and study the determinants of their lifetime. One fifth of them died during the first year of their lives and only 50 percent survived for four years. Duration and limited-dependent variable models are employed to ascertain the relative importance of industry- and firm-specific variables to in explaining the period between firm birth and its disappearance from economic activity. New firm failure varies negatively with firm start-up size, the number of plants operated by the firm, and the industry growth rate, and positively with the extent of entry in the industry. Copyright 1994 by Blackwell Publishing Ltd.

Coherency and estimation in simultaneous models with censored or qualitative dependent variables

This paper concerns estimation and inference in simultaneous limited dependent variable or simultaneous qualitative dependent variable models. We discuss the implications of the coherency condition which is required to ensure a unique implicit reduced form in such nonlinear models. A number of model specifications are examined, including the Simultaneous Prohit, Simultaneous Tohit, and Simultaneous Generalised Selectivity models, and we consider the usefulness of a conditional maximum likelihood (CML) methodology. We obtain a simple consistent estimator which is a natural counterpart to the CML estimator for standard simultaneous models. An application to a structural model of household labour supply is presented.

Evaluating Pseudo-R2's for binary probit models

Many applied researchers of limited dependent variable models found it disadvantageous that a widely accepted Pseudo-R2 does not exist for this type of estimation. The paper provides guidance for researchers in choosing a Pseudo-R2 in the binary probit case. The starting point is that R2 is best understood in the ordinary least squares (OLS) case with continuous data, which is chosen as the reference situation. It is considered which Pseudo-R2 is best able to mimic the OLS-R2. The results are surprisingly clear: a measure suggested by McKelvey-Zavoina performs the best under our criterion. However, in the more likely case of low Pseudo-R2's, a normalization of a measure proposed by Aldrich-Nelson which we suggest is almost as good as the McKelvey-Zavoina, and is in general easier to calculate. We also show that if the underlying R2 is predicted using cubic regressions given the Pseudo-R2, all measures perform much better.

A Computationally Practical Simulation Estimator for Panel Data

In this paper I develop a practical extension of McFadden's method of simulated moments estimator for limited dependent variable models to the panel data case. The method is based on a factorization of the MSM first order condition into transition probabilities, along with the development of a new highly accurate method for similating these transition probabilities. A series of Monte-Carlo tests show that this MSM estimator performs quite well relative to quadrature-based ML estimators, even when large numbers of quadrature points are employed. The estimator also performs well relative to simulated ML, even when a highly accurate method is used to simulate the choice probabilities. In terms of computational speed, complex panel data models involving random effects and ARMA errors may be estimated via MSM in times similar to those necessary for estimation of simple random effects models via ML-quadrature.

Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models

We apply a new simulation method that solves the multidimensional probability integrals that arise in maximum likelihood estimation of a broad class of limited dependent variable models. The simulation method has four key features: the simulated choice probabilities are unbiased; they are a continuous and differentiable function of the parameters of the model; they are bounded between 0 and 1; and their computation takes an effort that is nearly linear in the dimension of the probability integral, independent of the magnitudes of the true probabilities. We also show that the new simulation method produces probability estimates with substantially smaller variance than those generated by acceptance-rejection methods or by Stern's (1992) method. The simulated probabilities can therefore be used to revive the Lerman and Manski (1981) procedure of approximating the likelihood function using simulated choice probabilities by overcoming its computational disadvantages.

On the computation of semiparametric estimates in limited dependent variable models

Many semiparametric estimation methods for Limited Dependent Variable models exist. Not all these estimates have a closed form solution and it is therefore necessary to consider numerical optimisation algorithms in those cases. In this paper we discuss and compare several such algorithms for semiparametric estimates without a closed form solution.

Economic Motivations for Limited Dependent and Qualitative Variable Models*

The greater availability of survey data, a succession of papers dealing with the statistical issues arising from the analysis of such data and the appearance of software packages, such as UMDEP, have led to a remarkable increase in the application of limited dependent and qualitative variable models in economics. Economic analysis of the behaviour of individual decision makers often leads to models which are of a limited dependent or qualitative variable nature. This paper attempts to show how the use of these models naturally arises from the more general framework of modifications to traditional economic optimization problems.

On testing the logistic assumption in binary dependent variable models

This paper shows that the LM test for the validity of the logistic distribution commonly assumed in Binary Dependent Variable Models (i.e., the logit model) developed by Poirier (1980) can be obtained from a simple artificial regression. Monte Carlo simulations examine the small sample behaviour of the test statistic in comparison to the Information Matrix test for the logit model developed by Orme (1988) and Davidson and MacKinnon (1989), and two versions of the Reset test for limited dependent variable models suggested by Pagan and Vella (1989). Our results suggest that the LM test compares favourably under the null. The tests also appear to have varying power properties against different alternatives which suggests that they should all be used in investigating the validity of the logit model.

A pseudo-R2 measure for limited and qualitative dependent variable models

Abstract A pseudo- R 2 measure for limited and qualitative dependent variable models is proposed. A consistent estimator of the variance of the disturbance term is also suggested. The pseudo- R 2 measure is shown to have the same asymptotic limit as the conventional R 2 . The measure is adapted to the logit model in an empirical example of female car-ownership modeling. The pseudo- R 2 is applicable to a wide set of limited and qualitative dependent variable models and offers a valuable tool for model evaluation.

Bayesian inference in limited dependent variable models. An application to measuring strike duration

AbstractThis paper presents a straightforward set of Bayesian techniques for analyzing models involving limited dependent variables; the techniques are demonstrated in an analysis of Kennan's (1985) data on contract strikes in US manufacturing. The data are analyzed by deriving posterior distributions—including probability distributions—of hazard functions for strike duration using numerical Monte Carlo methods. The distributions are employed to derive coverage intervals for hazard functions, to assess the relative plausibility of nonnested hypotheses concerning the shape of the functions, and to assess the impact of industrial production on duration.

Simultaneous equations for hazards: Marriage duration and fertility timing

The concept of simultaneous equations has been a fundamental contribution of econometrics. While the concepts have been extended quite fruitfully to limited and qualitative dependent variable models, they have been rarely applied to hazard or duration (failure time) models. This paper develops an approach to simultaneity among hazard equations which is similar in spirit to simultaneous Tobit models. It introduces a class of continuous time models which incorporates two forms of simultaneity across related processes - when the hazard rate of one process depends (1) on the hazard rate of another process or (2) on the actual current state of or prior outcomes of a related multi-episode process. This paper also develops an approach to modeling the notion of ‘multiple clocks’ in which one process may depend on the duration of a related process, in addition to its own. Maximum likelihood estimation is proposed based on specific parametric assumptions. The model is developed in the context of and empirically applied to the joint determination of marital duration and timing of marital conceptions.

Asymptotic properties of a quast-maximum likelihood estimator in truncated regression model with serial correlation

Robinson (1982a) presented a general approach to serial correlation in limited dependent variable models and proved the strong consistency and asymptotic normality of the quasi-maximum likelihood e...

Residuals for limited dependent variable models

General residual expressions based on likelihood equations are given for regression models with censoring or truncation on the endogenous variable. Using nonparametric density estimation such general expressions may be used to obtain residuals for models estimated by, e.g., semiparametric estimators. The suggested approach is illustrated by numerical examples.

A note on the estimation of limited dependent variable models under rational expectations

In this paper we derive the expressions for the expected price in a disequilibrium model with upper and lower limits on prices under rational expectation, relaxing the assumption of perfect foresight made in earlier studies. We prove the uniqueness of the solution to the rational expectations model and outline the estimation method and iterative procedure.

On Limited Dependent Variable Models: Maximum Likelihood Estimation and Test of One-sided Hypothesis

The limited dependent variable models with errors having log-concave density functions are studied here. For such models with normal errors, the asymptotic normality of the maximum likelihood estimator was established by Amemiya [1]. We show, when the density of the error distribution is log-concave, that the maximum likelihood estimator exists with arbitrarily large probability for large sample sizes, and is asymptotically normal. The general theory presented here includes the important special cases of normal, logistic, and extreme value error distributions. The main results are established under rather weak conditions. It is also shown that, under the null hypothesis, the asymptotic distribution of the likelihood ratio statistic for testing a one-sided alternative hypothesis is a weighted sum of chi-squares.