Limited Dependent Variable Models Research Articles

Equivalence Scales in an Intertemporal Setting with an Application to the Former West Germany

Equivalence scales provide answers to questions like how much a household with two children needs to spend compared to a couple to attain the same welfare level. These are important questions for child allowances, social benefits and to assess the cost of children over the life‐cycle for example. We discuss equivalence scales in an intertemporal setting with uncertainty. To estimate equivalence scales we use a panel from German households (GSOEP) containing subjective data on satisfaction with life and satisfaction with income to represent the welfare level. Because satisfaction is measured on a discrete scale we use limited dependent variable models for panel data in estimation. Using satisfaction with life data we find that larger households do not need any additional income to be as satisfied as a couple. Using satisfaction with income, however, yields equivalence scales that increase with household size.

Robust Estimation in Nonlinear Regression and Limited Dependent Variable Models

Classical parametric estimation methods applied to nonlinear regression and limited-dependent-variable models are very sensitive to misspecification and data errors. On the other hand, semiparametric and nonparametric methods, which are not restricted by parametric assumptions, require more data and are less efficient. A third possible estimation approach is based on the theory of robust statistics, which builds upon parametric specification, but provides a methodology for designing misspecification-proof estimators. However, this concept, developed in statistics, has so far been applied almost exclusively to linear regression models. Therefore, I adapt some robust methods, such as least trimmed squares, to nonlinear and limited-dependent variable models. This paper presents the adapted robust estimators, proofs of their consistency, suitable computational methods, as well as examples of regression models which the proposed estimators can be applied to.

The Interactions between R&D Investment Decisions and Compensation Policy

We use a system ofequations to investigate the endogenous relation between R&D investment and CEO compensation. Growth opportunity is positively related to the use ofstock options. Stock options positively affect R&D while restricted stock has a negative influence. These results suggest that CEO compensation should balance incentive alignment and efficient risk sharing with risk-averse managers. Stock options are also found to be negatively related to leverage, but positively related to convertible debt. Additionally, this analysis suggests that institutional ownership directly influences R&D investment by providing managerial oversight and indirectly by influencing the compensation policy. The study examines the interaction between R&D investment decisions and corporate compensation policy in 1,088 firms for fiscal year 1997. Two different two-stage limited dependent variable models in which equity-based awards and R&D investment are both endogenous are used. In the first model, we do not distinguish between the types of equity-based compensation (options or restricted stock). In the second model, we treat the type of stock compensation as an endogenous choice. Previous research recognizes the endogenous relation between investment opportunity and compensation policy, but models the determinants of these decisions separately. There are two benefits from estimating these relations as a system of equations. First, if the true relation is endogenous, single equation ordinary least squares will produce estimates that are inconsistent (Kmenta, 1986). Second, estimating these relations in a system allows us to draw inferences regarding causality in these relations. Specifically, it offers insight into the influence of compensation on R&D investment as well as the influence of investment opportunity on compensation policy. We note the following determinants of R&D investment. When we treat all stock-based incentives equally, R&D is positively related to equity-based compensation. When we separate the types of equity compensation into options or restricted stock, options exert a positive influence on R&D and restricted stock exerts a negative influence. These findings support the hypothesis that the linear payoff of restricted stock encourages managers to avoid risky investment and the nonlinear payoff of options motivates risk-taking behavior. The relation between age and R&D investment is concave, confirming the premise that both the very youngest CEOs, who seek short-term results to build their reputations and the very oldest CEOs, who have limited horizons due to their impending retirement have the incentives to invest less in uncertain long-term projects. We also observe a negative relation with poor financial solvency.

Analytic methods for examining race and ethnic disparity in the juvenile courts

Prior studies of juvenile court decision making and racial disparity are often criticized for their lack of methodological rigor. These studies are criticized for focusing their analyses on separate decision-making stages and not taking into account issues that are related to sample selection. This research attempted to address these issues through an analysis of juvenile court case records from the state of Hawaii. Different limited dependent variable models were used to estimate ethnic disparity in juvenile court outcomes. Comparisons of models according to the Bayesian Information Criteria (BICs) are used to assess the overall fit of these models. The findings indicate few substantive differences across models and a general leniency of the court in favor of White youth. The findings do reveal that there are differences in the accuracy with which these models predicted juvenile court outcomes. The usefulness of this method of model comparison for disparity research is discussed.

The degree of monopsony power in agricultural labour markets, and the impact of the agricultural minimum wage: an application to craft workers in England and Wales

This paper uses cross-section data to examine the determinants of wages for agricultural craft workers over the period 1991–1994. Using limited dependent variable models to take account of the censoring in the data resulting from the minimum wage, we have investigated the degree to which agricultural and broader labour markets are integrated, the impact of tied housing on wages, and the extent to which the minimum wage truncates the wage distribution.

The Probability That a Smoker Does Not Purchase Tobacco: A Note

In this note we are concerned with the estimation of the probability that a smoker does not purchase tobacco during a survey. Usually, tobacco demand has been estimated using limited dependent variable models under the assumption that an important proportion of smokers declared a zero expenditure in tobacco. However, if the probability of non purchasing by a smoker is negligible, zeros could be ignored and the demand equation could be estimated on positive expenditure data using traditional estimation methods. Here we estimate this probability and find that it is extremely small. A novelty of this work is the use of data on the quantity and frequency of tobacco purchases during the week of the survey, instead of the more commonly used expenditure data.

Nonparametric Unfolding of Binary Choice Data

This paper shows a general nonparametric unfolding technique for maximizing the correct classification of binary choice or two-category data. The motivation for and the primary focus of the unfolding technique are parliamentary roll call voting data. However, the procedures that implement the unfolding also can be applied to the problem of unfolding rank order data as well as analyzing a data set that would normally be the subject of a probit, logit, or linear probability analysis. One aspect of the scaling method greatly improves Manski's “maximum score estimator” technique for estimating limited dependent variable models. To unfold binary choice data two subproblems must be solved. First, given a set of chooser or legislator points, a cutting plane must be found such that it divides the legislators/choosers into two sets that reproduce the actual choices as closely as possible. Second, given a set of cutting planes for the binary choices, a point for each chooser or legislator must be found which reproduces the actual choices as closely as possible. Solutions for these two problems are shown in this paper. Monte Carlo tests of the procedure show it to be highly accurate in the presence of voting error and missing data.

A Box–Cox Double‐hurdle Model

The double‐hurdle model with dependence is extended by incorporating the Box–Cox transformation. The model nests a range of popular limited dependent variable models, including the Gaussian double‐hurdle, the generalized Tobit, and two‐part models. Estimates of US beef consumption suggest that the Box–Cox specification outperforms all other restrictive models. Price elasticities are small and similar to findings in the literature. Household age composition and demographic variables also play significant roles in determining beef consumption. Income and cross‐price elasticities are insignificant.

SIMULATION-BASED ECONOMETRIC METHODS

The accessibility of high-performance computing power has always influenced theoretical and applied econometrics. Gouriéroux and Monfort begin their recent offering, Simulation-Based Econometric Methods, with a stylized three-stage classification of the history of statistical econometrics. In the first stage, lasting through the 1960's, models and estimation methods were designed to produce closed-form expressions for the estimators. This spurred thorough investigation of the standard linear model, linear simultaneous equations with the associated instrumental variable techniques, and maximum likelihood estimation within the exponential family. During the 1970's and 1980's the development of powerful numerical optimization routines led to the exploration of procedures without closed-form solutions for the estimators. During this period the general theory of nonlinear statistical inference was developed, and nonlinear micro models such as limited dependent variable models and nonlinear time series models, e.g., ARCH, were explored. The associated estimation principles included maximum likelihood (beyond the exponential family), pseudo-maximum likelihood, nonlinear least squares, and generalized method of moments. Finally, the third stage considers problems without a tractable analytic criterion function. Such problems almost invariably arise from the need to evaluate high-dimensional integrals. The idea is to circumvent the associated numerical problems by a simulation-based approach. The main requirement is therefore that the model may be simulated given the parameters and the exogenous variables. The approach delivers simulated counterparts to standard estimation procedures and has inspired the development of entirely new procedures based on the principle of indirect inference.

Bayesian Estimation of Limited Dependent Variable Spatial Autoregressive Models

A Gibbs sampling (Markov chain Monte Carlo) method for estimating spatial autoregressive limited dependent variable models is presented. The method can accommodate data sets containing spatial outliers and general forms of non‐constant variance. It is argued that there are several advantages to the method proposed here relative to that proposed and illustrated in McMillen (1992) for spatial probit models.

THE ET INTERVIEW: PROFESSOR JAMES TOBIN

Professor James Tobin is a figure of truly historic significance in the economics profession. He is one of the major developers of modern macroeconomic theory. He has contributed fundamental knowledge to the theory of investment, of consumption, of money and banking, and of economic growth. His theoretical work made possible the development of the capital asset pricing model that has been a central paradigm in modern finance. His work on limited-dependent variable models has started a field within econometrics.

Postestimation Uncertainty in Limited Dependent Variable Models

Many political science research articles that use limited dependent variable models report estimated quantities, in particular, fitted probabilities, predicted probabilities, and functions of such probabilities, without indicating that such estimates are subject to uncertainty. This practice, along with the reporting of “percentage correctly predicted,” can overstate the precision of reported results. In light of this, the present article describes a variety of measures of uncertainty that authors can include alongside estimates generated by limited dependent variable models. It also proposes an alternative to “percentage correctly predicted” and illustrates its calculations with congressional cosponsorship data from Krehbiel (1995).

A socioeconomic analysis of the determinants of fertility: the case of Vietnam.

This paper is an economics-based quantitative analysis of the determinants of individual fertility in Vietnam, measured as the number of children ever born. In addition to the conventional linear model, two limited dependent variable models, Poisson and ordered-logit, are estimated using data from the 1988 Vietnam Demographic and Health Survery. We find, among other things, that husbands‘ characteristics are almost as important as those of wives in determining fertility, perhaps a reflection of the still dominant role of husbands in Vietnamese families. Both paternal and maternal education have important impacts on fertility. Of special interest is the evidence that supports the attitudinal effect of education over the opportunity-cost effect.

Household Consumption of Cheese: An Inverse Hyperbolic Sine Double‐Hurdle Model with Dependent Errors

AbstractThe dependent double‐hurdle model is generalized by an inverse hyperbolic sine transformation of the dependent variable. The resulting specification features a flexible parameterization, accommodates heteroskedastic errors, and nests a range of common limited dependent variable models. Results for U.S. household cheese consumption suggest that the homoskedastic and normal double‐hurdle model is misspecified. Income elasticities are small and vary across household groups. Foodstamp recipients are more responsive to income changes than nonrecipients. Foodstamp recipients are also less likely to consume cheese but, conditional on consumption, spend more than nonrecipients.

Rent-seeking and political tenure: First estimates

This paper computes a measure of rent-seeking based on costs of tenure. Within a political tenure type model, a new incumbency variable is introduced and a variant to existing datasets is presented. Consistent ML rent-seeking estimates are computed for our sample of OECD democracies. The statistical advances in limited dependent variable models in particular, the decomposition of the Tobit estimates enabled us to compute rent-seeking estimates as costs of tenure the Tobit partial derivatives and to compute the impact of explanatory variables on the probability of being above the limit which we interpret as the probability of tenure.

Household travel consumption: Applications of limited dependent variable models : Pan, Ming-Chu, Ph.D. Clemson University, 1994. 110 pp.

Household travel consumption: Applications of limited dependent variable models : Pan, Ming-Chu, Ph.D. Clemson University, 1994. 110 pp.

PSEUDO‐R2 MEASURES FOR SOME COMMON LIMITED DEPENDENT VARIABLE MODELS

Abstract. A large number of different Pseudo‐R2 measures for some common limited dependent variable models are surveyed. Measures include those based solely on the maximized likelihoods with and without the restriction that slope coefficients are zero, those which require further calculations based on parameter estimates of the coefficients and variances and those that are based solely on whether the qualitative predictions of the model are correct or not. The theme of the survey is that while there is no obvious criterion for choosing which Pseudo‐R2 to use, if the estimation is in the context of an underlying latent dependent variable model, a case can be made for basing the choice on the strength of the numerical relationship to the OLS‐R2 in the latent dependent variable. As such an OLS‐R2 can be known in a Monte Carlo simulation, we summarize Monte Carlo results for some important latent dependent variable models (binary probit, ordinal probit and Tobit) and find that a Pseudo‐R2 measure due to McKelvey and Zavoina scores consistently well under our criterion. We also very briefly discuss Pseudo‐R2 measures for count data, for duration models and for prediction‐realization tables.

Individual cigarette consumption and addiction: a flexible limited dependent variable approach.

A variety of limited dependent variable models have been used in microeconometric studies of smoking. We present a general model of the simultaneous decisions of how much to smoke and whether to quit, which allows a more flexible parameterization and distributional assumptions. The model incorporates the fixed costs associated with quitting and allows for the separate influence of addiction on participation and consumption. The model is applied to data on smoking from the 1984-85 UK Health and Lifestyle Survey, and is shown to outperform a range of nested models that have been used extensively in the empirical literature.

ON THE INTERPRETATION OF COVARIATE ESTIMATES IN INDEPENDENT COMPETING‐RISKS MODELS*

ABSTRACTCompeting‐risks models are becoming increasingly pervasive in applied research to explain the factors determining both the time in a state (i.e. unemployment) and the exit route from the state (is. leaving unemployment for a job or non‐participation). However, as in many limited dependent variable models, the interpretation of the covariate estimates requires care. Despite assertions to the contrary in many published papers, it is shown that the estimated qualitative effect of a covariate on the hazard for risk j typically conveys no information on its qualitative effect on either the likelihood of, or expected time until, exit via j. This is because such magnitudes depend on the qualitative and quantitative effects of the covariate on other risks which cannot be ignored. The point is demonstrated by using UK data on the unemployment to re‐employment transitions of a sample of male job losers.

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 semi-parametric 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 semi-parametric specifications.