This note shows that the local average treatment effect (LATE) assumptions of Angrist and Imbens are weaker than imposing an ordered, discrete-choice selection model if one imposes the standard assumption of constant thresholds in the latter. However, the note extends results of Vytlacil to show that the LATE assumptions are equivalent to an ordered, discrete-choice selection model if one allows for random thresholds in the latter. A nonparametric representation result for ordered, discrete-choice models is produced as a by-product of these results.

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.

This paper considers two problems that arise in determining the role of cognitive ability in explaining the level of and change in the rate of return to schooling. The first problem is that ability and schooling are so strongly dependent that it is not possible, over a wide range of variation in schooling and ability, to independently vary these two variables and estimate their separate impacts. The second problem is that the structure of panel data makes it difficult to identify main age and time effects or to isolate crucial education-ability-time interactions which are needed to assess the role of ability in explaining the rise in the return to education.

This paper uses the marginal treatment effect (MTE) to unify the nonparametric literature on treatment effects with the econometric literature on structural estimation using a nonparametric analog of a policy invariant parameter; to generate a variety of treatment effects from a common semiparametric functional form; to organize the literature on alternative estimators; and to explore what policy questions commonly used estimators in the treatment effect literature answer. A fundamental asymmetry intrinsic to the method of instrumental variables (IV) is noted. Recent advances in IV estimation allow for heterogeneity in responses but not in choices, and the method breaks down when both choice and response equations are heterogeneous in a general way.

Accounting for individual-level heterogeneity in the response to treatment is a major development in the econometric literature on program evaluation. A substantial body of empirical evidence demonstrates that econometric models fit on individual-level data manifest heterogeneity in treatment effects that is present even after conditioning on observables. An important distinction is the one between evaluation models where participation in the program being evaluated is based, at least in part, on unobserved idiosyncratic responses to treatment and models where participation is not based on unobserved idiosyncratic responses. This is the distinction between selection on unobservables and selection on observables. The validity of entire classes of evaluation estimators hinges on whether or not they allow agents to act on unobserved idiosyncratic responses. In a wide variety of applications, the available evidence suggests that not only are ex post (postenrollment) responses heterogeneous, but that ex ante decisions to participate in programs are based, in part, on these heterogeneous responses (Heckman and Vytlacil, 2000b, 2001).

This study examines the relation between securitization and loan performance using a comprehensive dataset from a major national mortgage lender. Loans remaining on the bank's balance sheet ex post incurred higher delinquency rates than sold loans, contrasting the negative relation between screening efforts and ex ante probability of loan sale explored by prior studies. Moreover, the performance gap between sold and retained loans was wider among the subsample of loans that were perceived as easier to resell. The investors'seeming advantage over the originating bank can mostly be explained by information revealed during the time between loan origination and sale.

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 “liar's 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.

This paper examines the properties of instrumental variables (IV) applied to models with essential heterogeneity, that is, models where responses to interventions are heterogeneous and agents adopt treatments (participate in programs) with at least partial knowledge of their idiosyncratic response. We analyze two-outcome and multiple-outcome models, including ordered and unordered choice models. We allow for transition-specific and general instruments. We generalize previous analyses by developing weights for treatment effects for general instruments. We develop a simple test for the presence of essential heterogeneity. We note the asymmetry of the model of essential heterogeneity: outcomes of choices are heterogeneous in a general way; choices are not. When both choices and outcomes are permitted to be symmetrically heterogeneous, the method of IV breaks down for estimating treatment parameters.

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.