This paper surveys the available methods for estimating models with sample selection bias. I initially examine the fully parameterized model proposed by Heckman (1979) before investigating departures in two directions. First, I consider the relaxation of distributional assumptions. In doing so I present the available semi-parametric procedures. Second, I investigate the ability to tackle different selection rules generating the selection bias. Finally, I discuss how the estimation procedures applied in the cross-sectional case can be extended to panel data.

Estimating Models with Sample Selection Bias: A Survey

The nonlinear fixed-effects model has two shortcomings, one practical and one methodological. The practical obstacle relates to the difficulty of computing the MLE of the coefficients of non-linear models with possibly thousands of dummy variable coefficients. In fact, in many models of interest to practitioners, computing the MLE of the parameters of fixed effects model is feasible even in panels with very large numbers of groups. The result, though not new, appears not to be well known. The more difficult, methodological issue is the incidental parameters problem that raises questions about the statistical properties of the ML estimator. There is relatively little empirical evidence on the behaviour of the MLE in the presence of fixed effects, and that which has been obtained has focused almost exclusively on binary choice models. In this paper, we use Monte Carlo methods to examine the small sample bias of the MLE in the tobit, truncated regression and Weibull survival models as well as the binary probit and logit and ordered probit discrete choice models. We find that the estimator in the continuous response models behaves quite differently from the familiar and oft cited results. Among our findings are: first, a widely accepted result that suggests that the probit estimator is actually relatively well behaved appears to be incorrect; second, the estimators of the slopes in the tobit model, unlike the probit and logit models that have been studied previously, appear to be largely unaffected by the incidental parameters problem, but a surprising result related to the disturbance variance estimator arises instead; third, lest one jumps to a conclusion that the finite sample bias is restricted to discrete choice models, we submit evidence on the truncated regression, which is yet unlike the tobit in that regardit appears to be biased towards zero; fourth, we find in the Weibull model that the biases in a vector of coefficients need not be in the same direction; fifth, as apparently unexamined previously, the estimated asymptotic standard errors for the ML estimators appear uniformly to be downward biased when the model contains fixed effects. In sum, the finite sample behaviour of the fixed effects estimator is much more varied than the received literature would suggest.

https://papers.ssrn.com/sol3/Delivery.cfm/ectj_123.pdf?abstractid=558834&mirid=1

The Behaviour of the Maximum Likelihood Estimator of Limited Dependent Variable Models in the Presence of Fixed Effects

This chapter surveys existing approaches to modeling labor supply and identifies important gaps in the literature that could be addressed in future research. The discussion begins with a look at recent policy reforms and labor market facts that motivate the study of labor supply. The analysis then presents a unifying framework that allows alternative empirical formulations of the labor supply model to be compared and their resulting elasticities to be interpreted. This is followed by critical reviews of alternative approaches to labor-supply modeling. The first review assesses the difference-in-differences approach and its relationship to natural experiments. The second analyzes estimation with non-linear budget constraints and welfare-program participation. The third appraises developments of family labor-supply models including both the standard unitary and collective labor-supply formulations. The fourth briefly explores dynamic extensions of the labor supply model, characterizing how participation decisions, learning-by-doing, human capital accumulation and habit formation affect the analysis of the lifecycle model. At the end of each of the four broad reviews, we summarize a selection of the recent empirical findings. The concluding section asks whether the developments reviewed in this chapter place us in a better position to answer the policy-reform questions and to interpret the trends in participation and hours with which we began this review. © 1999 Elsevier Science B.V. All rights reserved.

/pdf/labor-supply-a-review-of-alternative-approaches-wly9lwhuij.pdf

Labor Supply: A Review of Alternative Approaches

This study examines the effect of the timing of follow-ups, different incentives, length, and presentation of the questionnaire on the response rate and response quality in an online experimental setting. The results show that short questionnaires have a higher response rate, although long questionnaires still generate a surprisingly high response. Furthermore, vouchers seem to be the most effective incentive in long questionnaires, while lotteries are more efficient in short surveys. A follow-up study revealed that lotteries with small prizes, but a higher chance of winning are most effective in increasing the response rate. Enhancing questionnaires with visual elements, such as product images, lead to a higher response quality and generate interesting interaction effects with the length of the questionnaire and the incentives used. Finally, the timing of the follow-up has no significant influence on the response rate.

/pdf/response-rate-and-response-quality-of-internet-based-surveys-1f8y78dptz.pdf

Response Rate and Response Quality of Internet-Based Surveys, An Experimental study

Estimates of pain prevalence and severity in adults: United States, 2012.

We use panel data to analyze the determinants of speaking fluency and wages of immigrants. Our model takes account of two problems that may bias OLS estimates of the impact of speaking fluency on earnings. First, subjective variables on an ordinal discrete scale, such as self-reported language ability, can suffer from misclassification errors. The model decomposes misclassification errors into a time-persistent and a time-varying component. Second, the model accounts for correlated unobserved heterogeneity in language and earnings equation, The main finding is that these two generalizations of the standard model both lead to substantial changes in the estimated effect of speaking fluency on earnings.

/pdf/language-fluency-and-earnings-estimation-with-misclassified-5daz5uqyl9.pdf

Language Fluency and Earnings: Estimation with Misclassified Language Indicators

https://www.rand.org/content/dam/rand/pubs/working_papers/2006/RAND_WR331.pdf

Obesity and health in Europeans aged 50 years and older.

In this paper, two models of individual labor supply are discussed. The first one is the by now classical Hausman-type model with convex piecewise linear budget constraints, in which both random preferences and optimization errors are incorporated by means of normally distributed random variables. Estimated coefficients are plausible but the model has the shortcoming that unemployment for males is not captured and that the simulated hours distribution misses the spikes in the sample distribution of working hours. Therefore, an alternative model is introduced which explicitly takes into account demand side restrictions on working hours. The difference with the standard model is the replacement of the optimization error by the assumption that each individual can choose from a finite set of wage hours packages and either picks the job offer yielding highest utility or decides not to work. It turns out that this model captures the sample distribution of working hours very well, for males as well as females. Wage and income elasticities according to the two models are similar and in line with other recent findings in The Netherlands. Dead weight loss calculations for the second model which explicitly take the hours restrictions into account, imply that the dead weight loss is much smaller than as calculated with the standard model.

/pdf/labor-supply-income-taxes-and-hours-restrictions-in-the-2yvl2auhwn.pdf

Labor supply, income taxes, and hours restrictions in the Netherlands

This paper presents a discrete choice static neo-classical labor supply model for married or cohabiting couples in the Netherlands. The model simultaneously explains the participation decision and the desired number of hours worked. Due to its discrete nature, institutional details of the tax system can be fully incorporated. The model is estimated using Dutch cross-section data. The results are used to simulate the first order labor supply effects of several proposed reforms of the Dutch income tax system. In particular, it is shown that some of the proposed reforms would have a negative effect on the number of married females who prefer a small part-time job. This pitfall is avoided in the proposal that has gone to Parliament.

A.H.O. van Soest

Papers

Language Fluency and Earnings: Estimation with Misclassified Language Indicators

Obesity and health in Europeans aged 50 years and older.

Labor supply, income taxes, and hours restrictions in the Netherlands

Family labor supply and proposed tax reforms in the Netherlands

Coherency and regularity of demand systems with equality and inequality constraints