Robert A. Moffitt

A COMPUTATIONALLY EFFICIENT QUADRATURE PROCEDURE FOR THE ONE-FACTOR MULTINOMIAL PROBIT MODEL

A PROBLEM OF ESTIMATION that has long confronted many economists is the difficulty of estimating the parameters of equations with limited dependent variables on cross-section time-series (i.e., panel) data. While there are widely available packaged computer programs for estimating either (a) cross-section probit and Tobit models or (b) simple permanent-transitory, random-effects panel models with continuous dependent variables, there are no available computationally feasible methods of combining these two models. This is because the likelihood function that arises in such a combined model contains multivariate normal integrals whose evaluation is quite difficult, if not impossible, with conventional approximation methods. There is a widespread feeling among those working in the area that one possible method of evaluation, the use of quadrature techniques, is in principle possible but is in practice computationally too burdensome to consider (e.g., Albright et al. [2, p. 13]; Hausman and Wise [6, p. 12]). In this note we point out that this is true only of standard quadrature techniques such as trapezoidal integration or its improved variants; Gaussian quadrature, on the other hand, is extremely efficient and is well within the bounds of computational feasibility on modern computers. In what follows, we state the nature of the integrals that need to be evaluated, provide a brief exposition of Gaussian quadrature, and provide a numerical illustration of its use in

The Growth of Earnings Instability in the U.S. Labor Market

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A Structural Model of Multiple Welfare Program Participation and Labor Supply

Work on estimating the labor supply effects of high marginal tax rates in welfare programs has been hindered by the difficulty of estimating the effects of participation in multiple welfare programs simultaneously. The authors solve this problem by applying methods of simulation estimation to a model of labor supply and multiple program participation. The results show asymmetric wage and tax rate effects, with fairly large wage elasticities of labor supply but very inelastic responses to moderate changes in cumulative marginal tax rates, implying that high welfare tax rates do not necessarily induce major reductions in work effort. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Unemployment insurance and the distribution of unemployment spells

Abstract In this paper administrative data from the unemployment-insurance (UI) system are used to examine the distribution of unemployment spells. Hazard plots of the data reveal a strong clustering around the benefit exhaustion point. In addition, estimation of the effects of the exhaustion point and of the UI benefit level on spell lengths obtained with a non-parametric proportional-hazards model - estimated by direct maximization of the general likelihood function - shows significant effects of both. However, the effect of the exhaustion point on the hazard is not proportional, making detection of its effect somewhat difficult.

Identification and estimation of dynamic models with a time series of repeated cross-sections☆

Abstract Repeated cross-sectional data contain information on independent cross-sections of individual units at two or more points in time. Estimation of dynamic models with such data is made difficult by the general lack of information on lagged dependent and independent variables and the consequent unobservability of the intertemporal covariances needed to identify and estimate dynamic models. It is demonstrated here that the parameters of such models, both linear and nonlinear, both with and without fixed individual effects, are identified and can be consistently estimated with the imposition of certain restrictions. The paper includes an examination of the identification and estimation with repeated cross-sectional data of dynamic discrete dependent variable models, which can be parameterized in terms of transition rates between the different cross-sections.

TRENDS IN THE TRANSITORY VARIANCE OF EARNINGS IN THE UNITED STATES

We decompose the rise in cross-sectional variance of male annual earnings in the United States from 1969 to 1996 into permanent and transitory components. We find that the variance of permanent earnings began rising in the the late 1970s and has continued to rise in the 1980s. The variance of transitory earnings also rose in the 1980s but declined in the 1990s. There are lags in the earnings process which require a structural model to pinpoint the exact calendar times at which the changes in trends occurred.

The Econometrics of Piecewise-Linear Budget Constraints A Survey and Exposition of the Maximum Likelihood Method

In this article maximum likelihood techniques for estimating consumer demand functions when budget constraints are piecewise linear are exposited and surveyed. Consumer demand functions are formally derived under such constraints, and it is shown that the functions are themselves nonlinear as a result. The econometric problems in estimating such functions are exposited, and the importance of the stochastic specification is stressed, in particular the specification of both unobserved heterogeneity of preferences and measurement error. Econometric issues in estimation and testing are discussed, and the results of the studies that have been conducted to date are surveyed.

Program Evaluation with Nonexperimental Data.

Statistical methods for program evaluation with nonexperimental data have been studied by economists and econometricians over the last 20 years. These methods are concerned with laying out the precise circumstances under which valid nonexperimental estimates of the effects of an intervention can be obtained, and then with methods for determining when and if those circumstances hold. This article provides a simple exposition of the methods of identification that have been developed and draws the lessons of those methods for future evaluation designs, data collection, and analysis.

The effect of food stamps on labor supply: A bivariate selection model

Abstract Although there is a large literature on the effects of U.S. transfer programs on labor supply, this is the first such study of the Food Stamp Program. We model the nonlinearity and nonconvexity of the budget constraint and use maximum-likelihood methods to estimate hours- of-work functions for female heads of household, the largest recipient group in the program. We also model the joint response to AFDC and Food Stamps and we account for the existence of a significant number of eligible households who do not participate in the programs. A three- equation, bivariate selection model is estimated on a sample of eligible households with maximum likelihood.

The Joint Choice of Retirement Age and Postretirement Hours of Work

In this paper we develop and estimate the first complete and internally consistent model of the effect of Social Security on the labor supply of the aged. We develop a simple life-cycle model that captures the effect of Social Security on the joint choice of the date of retirement and hours of work immediately after retirement. We show that in the presence of Social Security the budget constraint relating these choices is highly complex and nonlinear, and we develop a maximum likelihood procedure for the model that yields consistent parameter estimates. Our procedure avoids the selectivity biases present in prior studies that have ignored the nonlinearity of the constraint or have examined only self-selected subsamples that exclude nonretirees. Our results show that Social Security has a significant, though relatively small, effect on the age of retirement and postretirement hours of work, and that the effect of Social Security grows with advancing age.