Edward Vytlacil

Independence, Monotonicity, and Latent Index Models: An Equivalence Result

The selection model and instrumental variable, local average treatment effect (LATE) framework are widely interpreted as alternative, competing frameworks. This note shows that the assumption of an unobserved index crossing a threshold that defines the selection model is equivalent to the independence and monotonicity assumptions at the center of the LATE approach. The underlying assumptions of the two approaches are equivalent.

Three observations on wages and measured cognitive ability

Abstract This paper summarizes our recent research on the relationship between wages and measured cognitive ability. In it, we make three main points. First, we find that wage payment by ability does vary across race and gender in the US, and that the fraction of wage variance explained by cognitive ability is modest. Second, measured cognitive ability and schooling are so highly correlated that one cannot separate their effects without imposing strong, arbitrary parametric structure in estimation which, when tested, is rejected by the data. Third, controlling for cognitive ability, personality traits (socialization skills) are correlated with earnings, although they primarily operate through schooling attainment.

Instrumental Variables Methods for the Correlated Random Coefficient Model: Estimating the Average Rate of Return to Schooling When the Return is Correlated with Schooling

This paper considers the use of instrumental variables to identify a correlated random coefficients model in which coefficients are correlated with (or stochastically dependent on) the regressors. A correlated random coefficients model is central to the human capital earnings model. Conditions are given under which instrumental variables identify the average rate of return. These conditions are applied to David Cards version of Gary Beckers Woytinsky lecture.

Local Instrumental Variables

This paper unites the treatment effect literature and the latent variable literature. The economic questions answered by the commonly used treatment effect parameters are considered. We demonstrate how the marginal treatment effect parameter can be used in a latent variable framework to generate the average treatment effect, the effect of treatment on the treated and the local average treatment effect, thereby establishing a new relationship among these parameters. The method of local instrumental variables directly estimates the marginal treatment effect parameters, and thus can be used to estimate all of the conventional treatment effect parameters when the index condition holds and the parameters are identified. When they are not, the method of local instrumental variables can be used to produce bounds on the parameters with the width of the bounds depending on the width of the support for the index generating the choice of the observed potential outcome.

Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs, and to Forecast their Effects in New Environments

This chapter uses the marginal treatment effect (MTE) to unify and organize the econometric literature on the evaluation of social programs. The marginal treatment effect is a choice-theoretic parameter that can be interpreted as a willingness to pay parameter for persons at a margin of indifference between participating in an activity or not. All of the conventional treatment parameters as well as the more economically motivated treatment effects can be generated from a baseline marginal treatment effect. All of the estimation methods used in the applied evaluation literature, such as matching, instrumental variables, regression discontinuity methods, selection and control function methods, make assumptions about the marginal treatment effect which we exposit. Models for multiple outcomes are developed. Empirical examples of the leading methods are presented. Methods are presented for bounding treatment effects in partially identified models, when the marginal treatment effect is known only over a limited support. We show how to use the marginal treatment in econometric cost benefit analysis, in defining limits of policy experiments, in constructing the average marginal treatment effect, and in forecasting the effects of programs in new environments.

Cognitive Ability, Wages, and Meritocracy

This paper presents new evidence from the NLSY on the importance of meritocracy in American society. In it, we find that general intelligence, or g -- a measure of cognitive ability--is dominant in explaining test score variance. The weights assigned to tests by g are similar for all major demographic groups. These results support Spearmans theory of g. We also find that g and other measures of ability are not rewarded equally across race and gender, evidence against the view that the labor market is organized on meritocratic principles. Additional factors beyond g are required to explain wages and occupational choice. However, both blue collar and white collar wages are poorly predicted by g or even multiple measures of ability. Observed cognitive ability is only a minor predictor of social performance. White collar wages are more g loaded than blue collar wages. Many noncognitive factors determine blue collar wages.

Simple Estimators for Treatment Parameters in a Latent-Variable Framework

This note derives simply computed closed-form expressions for the average treatment effect, the effect of treatment on the treated, the local average treatment effect, and the marginal treatment effect in a latent-variable framework for both normal and nonnormal models. Asymptotic standard errors for versions of these parameters that average over observed characteristics are also obtained. The performances of the derived estimators are also evaluated in Monte Carlo experiments under correct specification and misspecification.

Liar’s Loan? Effects of Origination Channel and Information Falsification on Mortgage Delinquency

This paper presents an analysis of mortgage delinquency between 2004 and 2008 using a loan-level data set from a major national mortgage bank. Our analysis highlights two problems underlying the mortgage crisis: a reliance on mortgage brokers who tend to originate lower-quality loans and a prevalence of low-documentation loans—known in the industry as “liars loans”—that result in borrower information falsification. While over three-quarters of the difference in delinquency rates between bank and broker channels can be attributed to observable loan and borrower characteristics, the delinquency difference between full- and low-documentation mortgages is due to unobservable heterogeneity, about half of it potentially due to income falsification.

The relationship between treatment parameters within a latent variable framework

Abstract If responses to a treatment vary among people, a variety of parameters can be defined [Heckman, J., Robb, R. 1985. Alternative methods for evaluating the impact of interventions. In: Heckman J., Singer B. (Eds.), Longitudinal Analysis of Labor Market Data. Cambridge University Press, New York, pp. 156–245; Heckman, J., 1997, first draft 1995, Instrumental variables: a study of implicit behavioral assumptions used in making program evaluations. Journal of Human Resources 32, 441–462]. We show a simple relationship between various treatment parameters when the treatment parameters are defined within a common, latent variable framework.

Partial Identification in Triangular Systems of Equations With Binary Dependent Variables

This paper studies the special case of the triangular system of equations in Vytlacil and Yildiz (2007), where both dependent variables are binary but without imposing the restrictive support condition required by Vytlacil and Yildiz (2007) for identification of the average structural function (ASF) and the average treatment effect (ATE). Under weak regularity conditions, we derive upper and lower bounds on the ASF and the ATE. We show further that the bounds on the ASF and ATE are sharp under some further regularity conditions and an additional restriction on the support of the covariates and the instrument.