Choice-based Sampling Research Articles

Efficiently Estimating Nested Logit Models with Choice-Based Samples Example Applications: Example Applications

Choice-based samples oversample infrequently chosen alternatives to obtain an effective representation of the behavior of people who select these alternatives. However, the use of choice-based samples requires recognition of the sampling process in formulating the estimation procedure. In general, this procedure can be accomplished by applying weights to the observed choices in the estimation process. Unfortunately, the use of such weighted estimation procedures for choice models does not yield efficient estimators. However, for the special case of the multinomial logit model with a full set of alternative-specific constants, the standard maximum likelihood estimator–-which is efficient–-can be used with adjustment of the alternative-specific constants. The same maximum likelihood estimator can also be used with adjustment to estimate nested logit models with choice-based samples. The proof of this property is qualitatively described, and examples demonstrate how to apply the adjustment procedure.

Efficiently Estimating Nested Logit Models with Choice-Based Samples

Choice-based samples oversample infrequently chosen alternatives to obtain an effective representation of the behavior of people who select these alternatives. However, the use of choice-based samples requires recognition of the sampling process in formulating the estimation procedure. In general, this procedure can be accomplished by applying weights to the observed choices in the estimation process. Unfortunately, the use of such weighted estimation procedures for choice models does not yield efficient estimators. However, for the special case of the multinomial logit model with a full set of alternative-specific constants, the standard maximum likelihood estimator–-which is efficient–-can be used with adjustment of the alternative-specific constants. The same maximum likelihood estimator can also be used with adjustment to estimate nested logit models with choice-based samples. The proof of this property is qualitatively described, and examples demonstrate how to apply the adjustment procedure.

Some Practical Guidance for the Implementation of Propensity Score Matching

Propensity Score Matching (PSM) has become a popular approach to estimate causal treatment effects. It is widely applied evaluating labour market policies, but empirical examples can be found in very diverse fields of study. Once the researcher has decided to use PSM, he is confronted with a lot of questions regarding its implementation. To begin with, a first decision has to be made concerning the estimation of the propensity score. Following that one has to decide which matching algorithm to choose and determine the region of common support. Subsequently, the matching quality has to be assessed and treatment effects and their standard errors have to be estimated. Furthermore, questions like what to do if there is choice-based sampling? or when to measure effects? can be important in empirical studies. Finally, one might also want to test the sensitivity of estimated treatment effects with respect to unobserved heterogeneity or failure of the common support condition. Each implementation step involves a lot of decisions and different approaches can be thought of. The aim of this paper is to discuss these implementation issues and give some guidance to researchers who want to use PSM for evaluation purposes.

Neighborhood income distributions

This paper studies purely empirically aspects of the distribution of income within small neighborhoods and contrasts it with the income distribution at higher level of aggregation, such as census tracts and metropolitan areas. It relies on a unique feature of the American Housing Survey, whose 1985, 1989 and 1993 waves provide data for small residential neighborhoods. These consist of a dwelling unit and up to ten of its nearest neighbors. The paper employs several parametric and non-parametric econometric tools to measure income sorting in US residential neighborhoods. It documents the patterns of dependence among neighbors' income and imperfect sorting, with moderate but very significant correlation among incomes of neighbors and of considerable income mixing in US neighborhoods. These results persist even if choice-based sampling and heterogeneity across the sample are accounted for. Neighborhoods associated with a randomly selected renter are more sorted than those associated with an owner even though such owners are more likely to define their neighborhoods.

Some Futures are Brighter than Others: the Net Benefits Received by Florida Bright Futures Scholarship Recipients

Using a choice-based sample of households in Florida, the authors provide new empirical evidence on the budgetary incidence of lottery-funded merit scholarships. Specifically, they estimate the benefits received from the Florida Bright Futures (FBF) scholarship and the lottery taxes paid for three typical households in Florida. They find that high socioeconomic (SES) households receive a net program benefit of almost $2,200, whereas low SES households incur a net programloss of almost $700. This result obtains because lower SES households tend to pay more in lottery taxes but are less likely to receive scholarships. Also, the lower SES households with members who do receive the FBF scholarship are more likely to receive the 75% partial scholarship (vs. the 100% full scholarship) than the higher SES households. The results indicate that lottery-funded merit scholarships redistribute income from lower income, non-White, and less educated households to higher income, White, well-educated households.

Predicting corporate financial distress: Reflections on choice-based sample bias

Financial distress precedes bankruptcy. Most financial distress models actually rely on bankruptcy data, which is easier to obtain. We obtained a dataset of financially distressed but not yet bankrupt companies supplying a major auto manufacturer. An early warning model successfully discriminated between these distressed companies and a second group of similar but healthy companies. Previous researchers argue the matched-sample design, on which some earlier models were built, causes bias. To test for bias, the dataset was partitioned into smaller samples that approach equal groupings. We statistically confirm the presence of a bias and describe its impact on estimated classification rates.

A methodology for weighting observations from complex endogenous sampling

The methodology for weighting endogenous samples is extended in this study and applied to a multi-dimensional choice-based sample and an enriched sample. It is shown that a unified weight exists for a sample obtained from a complex endogenous sampling scheme. Problems with conventional weighting methods for samples from endogenous sampling, such as roadside surveys, are pointed out and an improved weighting scheme is proposed. Coefficient estimates of discrete choice models with and without weights are compared, and the importance of applying appropriate weights and a valid covariance estimator is pointed out.

Relative Importance Rankings for Pork Attributes by Asian-Origin Consumers in California: Applying an Ordered Probit Model to a Choice-Based Sample

AbstractThis paper reports on a study examining the ranking of selected attributes of fresh pork by Asian-origin consumers in San Francisco, California. Freshness is ranked as the most important attribute, followed by the attributes of the color of meat, lowness in fat, and the whiteness of fat. The attributes of price, freedom from chemicals, and being USDA labelled were also ranked to be of importance. Empirical results from an ordered probit model, postulated to explain respondents' importance rankings of attributes, suggested that particular demographic and socio-economic characteristics of Asian-origin consumers influenced the importance rankings of selected pork attributes. The findings suggest that Asian-origin consumers should not be treated as a single homogenous niche group in marketing, since there are identifiable sub-groups of these consumers with specific attitudes and preferences.

Regression models for choice-based samples with misclassification in the response variable

In this paper, we provide a general framework to deal with the presence of misclassification in the response variable in choice-based samples. The contaminated data sampling distribution is written as a function of the error-free conditional distribution of the dependent variable given the covariates and the conditional misclassification probabilities of the observable variable of interest given its latent values. We propose an extension of Imbens’ (Econometrica 60 (1992) 1187) efficient generalized method of moments to estimate this model and outline a specification test to detect the presence of this sort of measurement error. The performance of both the estimators and the test is investigated in a Monte Carlo simulation study, which shows very encouraging results.

James Heckman as a 'Law & Society' Scholar: An Appreciation

James Heckman was the 2000 Nobel Laureate in Economics. This short paper reviews the methodological and substantive contributions Heckman has made to the empirical study of law. Heckman's work is shown to be important because he has developed techniques to address fundamental problems such as how to separate law as cause and as effect. His work on selected or choice-based sampling has applications to almost every problem empirical researchers confront, since the sample we can actually observe is almost never randomly drawn from some larger population as classical statistical theory assumes. Substantively, his work on the effects of civil rights laws, job training programs, and other legal interventions in labor markets has profound implications for how we understand law's power to alter economic relationships. His critique of experimental approaches to studying social behavior has commonalities with interpretivist criticism of positivist social science.

Estimation in Discrete Choice Models with Choice-Based Samples

Estimation in Discrete Choice Models with Choice-Based Samples

Estimation in Discrete Choice Models with Choice-Based Samples

Students of applied statistics and econometrics need exposure to problems in the theory of estimation under ideal conditions. Such problems include heteroscedasticity, variable measurement error, and endogeneous covariates. One problem that is sometimes overlooked is whether the sample has been independently drawn. This article explores the importance of random sampling in behavioral models of choice. A popular method of data collection in those models is to sample individuals who have made the same choice, and then pool several such subsamples. For example, in a recreation demand model interviewers may intercept anglers at various lakes and streams. If the dependent variable is choice of fishing site, the resulting pooled data are called choice-based. This selection on the dependent variable presents problems in estimation. A weighted maximum likelihood estimator which overcomes the problem with the nonrandom nature of the sample is investigated with both a hypothetical and a real example.

Efficiency results of MLE and GMM estimation with sampling weights

This paper examines GMM and ML estimation of econometric models and the theory of Hausman tests with sampling weights. Weighted conditional GMM can be more efficient than weighted conditional MLE, an inefficient alternative to full information MLE under choice-based sampling, unless regressions have homoscedastic additive disturbances or sampling weights are independent of exogenous variables. GMM variances are necessarily smaller without sampling weights if GMM is the same as MLE or disturbances are homoscedastic, but not in general. Taking into account the dependence of sampling weights on parameters improves the efficiency of estimation.

The Baseball Draft

This article provides an analysis of the baseball draft. The objective is to determine whether the ability to recognize talent, that is, a player who will reach the major leagues, varies with the position of the player across different baseball clubs or with the level of schooling attoined by the player when he is drafted. The data set is a choice-based sample, and the author uses econometric techniques specifically developed for such samples. It is found that in the long term, there is no statistically significant difference between clubs in terms of their ability to find major league prospects. Also, the value of one attribute, namely college experience, was underestimated by the market for a substantial period of time. Eventually, however, the value of college experience was assimilated by the market.

Large sample theory of maximum likelihood estimates in semiparametric biased sampling models

Vardi [Ann.Statist.13 178-203 (1985)] introduced an $s$-sample biased sampling model with known selection weight functions, gave a condition under which the common underlying probability distribution $G$ is uniquely estimable and developed simple procedure for computing the nonparametric maximum likelihood estimator (NPMLE) $\mathbb{G}_n$ of $G$. Gill, Vardi and Wellner thoroughly described the large sample properties of Vardi’s NPMLE, giving results on uniform consistency, convergence of $\sqrt{n}(\mathbb{G}-G)$ to a Gaussian process and asymptotic efficiency of $\mathbb{G}_n$. Gilbert, Lele and Vardi considered the class of semiparametric $s$-sample biased sampling models formed by allowing the weight functions to depend on an unknown finite-dimensional parameter $\theta$ .They extended Vardi’s estimation approach by developing a simple two-step estimation procedure in which $\hat{\theta}_n$ is obtained by maximizing a profile partial likelihood and $\mathbb{G}_n \equiv \mathbb{G}_n(\hat{\theta}_n)$ is obtained by evaluating Vardi’s NPMLE at $\hat{\theta}_n$. Here we examine the large sample behavior of the resulting joint MLE $(\hat{\theta}_n,\mathbb{G}_n)$, characterizing conditions on the selection weight functions and data in order that $(\hat{\theta}_n, \mathbb{G}_n)$ is uniformly consistent, asymptotically Gaussian and efficient. Examples illustrated here include clinical trials (especially HIV vaccine efficacy trials), choice-based sampling in econometrics and case-control studies in biostatistics.

A Microeconomic Analysis of Homelessness: An Empirical Investigation Using Choice-Based Sampling

This study estimates a structural model of the probability of homelessness by drawing data from two sources. The observations on the housed come from the American Housing Survey and the data on the homeless come from a separate study dealing exclusively with the homeless. Since the survey on the homeless targeted a larger fraction of that population, the sample is choice-based. The results suggest that older males with low incomes and high levels of depression are more likely to be homeless. Improvement in the number and quality of homeless shelters is expected to increase substantially the number of homeless. The policy simulations provide support for cash transfers to the very poor to reduce their likelihood of becoming homeless and for a weakening of housing codes to increase the availability of inexpensive, low-quality rental housing.

Trade-Area Models and Choice-Based Samples: Methods

The use of choice-based data to generate parameters of a trade-area gravity model is described in detail in this paper. The importance of being able to estimate parameters with data collected from individuals who have selected a particular alternative is explained. The main advantage of the new method is that it allows the efficient use of easily collected data. It also allows inferences to be made about the distance-decay rates and attraction parameters, even when only a small subset of stores is sampled from an area. This new version of the retail gravity model has been tested extensively with data for 6 major retail centers in Dallas. The detailed studies include a demonstration of the conventional approaches to trade-area mapping and an explanation of exactly what is different about the method proposed here. Interpretation of the model results indicates areas where a store either gains an unexpectedly high (or low) share of its sales. These methods have immediate application in screening potential locations because the variables used to run the model are generic and easily gathered for other cases. The results also encourage the rethinking of the Huff-based gravity model.

Modelling different types of automobile insurance fraud behaviour in the Spanish market

From a microeconomic point of view, the control of insurance fraud requires a detailed knowledge of the insureds’ behaviour. In this paper, we present discrete-choice models for fraud behaviour and we estimate the influence of the insured and claim characteristics on the probability of committing fraud. Data correspond to a Spanish sample. Correction for choice-based sampling is introduced in the estimation due to the oversampling of fraud claims. The structure of the Spanish automobile insurance market is also discussed. Our results differ according to the type of fraud behaviour that is under consideration.

The Importance of Accommodation on the Timing of Disability Insurance Applications: Results from the Survey of Disability and Work and the Health and Retirement Study

Using data from the 1978 Survey of Disability and Work and the 1992 Health and Retirement Study, we test the importance of accommodation and other policy variables on the timing of application for Social Security Disability Insurance benefits following the onset of a work-limiting condition. We correct for choice-based sampling in the Survey of Disability and Work by extending the Manski and Lerman (1977) correction to the likelihood function of our continuous time hazard model, we find that this correction significantly affects the results. Similar findings emerge from these two data sets. Accommodation significantly reduces the speed of application and more generous benefits increase the speed of applying for SSDI.

Sample Attrition in Panel Data: The Role of Selection on Observables

The traditional formulation of the attrition problem in econometrics treats it as a special case of the partial-population section bias model in which selection (attrition) is based on model unobservables. This paper considers instead the treatment of attrition as a special case of selection on observables. The analysis compares and contrasts the identifica- tion assumptions and estimation procedures for this case with those of the usual case of selection on unobservables. Selection on observables case has rarely been considered in the econometric literature on the problem and hence the framing of the problem in these terms, as presented here, is apparently new. The selection on observables problem is made nontri- vial by the assumption that selection occurs on endogenous observables; leading examples are lagged dependent variables from earlier periods in the panel. Among other things, it is shown in the paper that (i) weighted least squares using estimated attrition equations to construct the weights is one method of consistent estimation in this case; (ii) simply conditio- ning on the observables does not, by itself, generate consistent estimates; and (iii) that the model is closely related to the choice-based sampling model.