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We propose instrumental variables (IV) estimators for averaged conditional treatment effects and the parameters upon which they depend in the context of a semiparametric outcome model with endogenous discrete treatment variables. For this model, the treatment impacts are unknown functions of a vector of indices that depend on a finite dimensional parameter vector. We develop the theory for an estimator of these impacts when they are averaged over regions of interest. We prove identification, consistency and N-asymptotic normality of the estimators. We also show that they are efficient under correct model specification. Further, we show that they are robust to misspecification of the propensity score model. In the Monte Carlo study, the estimators perform well over a wide variety of designs covering both correct and incorrect propensity score model specification.

This paper addresses the estimation of a semiparametric sample selection index model where both the selection rule and the outcome variable are binary. Since the marginal effects are often of primary interest and are difficult to recover in a semiparametric setting, we focus on developing an estimator for the marginal effects. This marginal effect estimator uses only observations where the selection probability is above a certain threshold. A key innovation is that this high probability set is adaptive to the data. We establish the large sample properties of the marginal effect estimator as well as those for an index estimator upon which it depends. Monte Carlo studies show that these estimators perform well in finite samples.

Semiparametric methods are widely employed in applied work where the ability to conduct inferences is important. To establish asymptotic normality for making inferences, bias control mechanisms are often used in implementing semiparametric estimators. The first contribution of this paper is to propose a mechanism that enables us to establish asymptotic normality with regular kernels. In so doing, we argue that the resulting estimator performs very well in finite samples.Semiparametric models are commonly estimated under a single index assumption. Because the consistency of the estimator critically depends on this assumption being correct, our second objective is to develop a test for it. To ensure that the test statistic has good size and power properties in finite samples, we employ a bias control mechanism similar to that underlying the estimator. Furthermore, we structure the test so that its form adapts to the model under the alternative hypothesis. Monte Carlo results confirm that the bias control and the adaptive feature significantly improve the performance of the test statistic in finite samples.

SUMMARY This paper formulates a likelihood-based estimator for a double-index, semiparametric binary response equation. A novel feature of this estimator is that it is based on density estimation under local smoothing. While the proofs differ from those based on alternative density estimators, the finite sample performance of the estimator is significantly improved. As binary responses often appear as endogenous regressors in continuous outcome equations, we also develop an optimal instrumental variables estimator in this context. For this purpose, we specialize the double-index model for binary response to one with heteroscedasticity that depends on an index different from that underlying the ‘mean response’. We show that such (multiplicative) heteroscedasticity, whose form is not parametrically specified, effectively induces exclusion restrictions on the outcomes equation. The estimator developed exploits such identifying information. We provide simulation evidence on the favorable performance of the estimators and illustrate their use through an empirical application on the determinants, and affect, of attendance at a government-financed school. Copyright  2009 John Wiley & Sons, Ltd.

We develop a √n-consistent and asymptotically normal estimator of the parameters (regression coefficients and threshold points) of a semiparametric ordered response model under the assumption of independence of errors and regressors. The independence assumption implies shift restrictions allowing identification of threshold points up to location and scale. The estimator is useful in various applications, particularly in new product demand forecasting from survey data subject to systematic misreporting. We apply the estimator to assess exaggeration bias in survey data on demand for a new telecommunications service.

In testing choice models, there are contexts in which it is important to focus on choice probabilities as opposed to the parameters of choice models. This paper examines the former by formulating a distance measure between parametric choice probabilities under the null hypothesis and either a nonparametric or a semiparametric alternative. To access where the parametric model is ‘unsatisfactory’, we apply the distance measure to ordered data subsets (‘index quantiles’). We establish the large-sample distribution of the test statistics, examine their asymptotic local power properties, and apply the tests to a model of labor force participation.

This paper provides a control function estimator to adjust for endogeneity in the triangular simultaneous equations model where there are no available exclusion restrictions to generate suitable instruments. Our approach is to exploit the dependence of the errors on exogenous variables (e.g. heteroscedasticity) to adjust the conventional control function estimator. The form of the error dependence on the exogenous variables is subject to restrictions, but is not parametrically specified. In addition to providing the estimator and deriving its large-sample properties, we present simulation evidence which indicates the estimator works well.

This paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function, where this function can be characterized by an index. The estimator is shown to be consistent, asymptotically normally distributed, and to achieve the semiparametric efficiency bound. Monte-Carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known, and that the small-sample behavior of the estimator in other cases is good.

This note argues that the recent emphasis on model size (e.g., dimensionality) for choosing among economic models is misleading. With a reasonable formulation of prior information, it is important to take into account the a priori theoretical economic rationale for an economic model.

In this paper, we propose a flexible class of discrete choice models. These models are flexible in that members of this class can approximate any discrete choice model obtained from utility maximization. All members of this class are intuitively easy to understand, consistent with utility maximization and do not suffer from the “independence of irrelevant alternatives” problem. In addition, there are members of this class for which maximum likelihood is a feasible estimation method even when the number of alternatives and/or attributes is large. Furthermore, appropriateness of specific functional forms can be explored graphically. We examine the properties of this class intuitively, theoretically, and in an empirical example.

Single-equation instrumental variable estimators (e.g., the k-class) are frequently employed to estimate econometric equations. This paper employs Kadane's (1971) small-σ method and a squared-error matrix loss function to characterize a single-equation class of optimal instruments, A. A is optimal (asymptotically for a small scalar multiple, σ, of the model's disturbance) in that all of its members are preferred to all non-members. From this characterization it is shown all k-class estimators and certain iterative estimators belong to A. However, non-iterative principal component estimators [e.g., Kloek and Mennes (1960)] are unlikely to belong to A. These latter instrumental variable estimators have been advocated [see Amemiya (1966) and Kloek and Mennes (1960)] for estimating ‘large’ econometric models.

Dalal and Klein (1985) obtained an approximation to discrete choice probabilities. This note justifies the use of this approximation in a forecasting context, where the forecast is made for a choice set of alternatives different from that used to initially estimate the model.

A NUMBER OF AUTHORS argue that a Bayesian posterior odds criterion is appropriate for model selection.2 This paper considers how to derive this criterion when there is minimal prior information. We propose minimizing measures of prior information relative to the models in question rather than relative to the parameters of the particular models. In so doing, we obtain an expression for the odds that is invariant to the parameterization of the particular models and overcomes certain well known finite sample limiting problems. We illustrate this procedure using two popular measures of information derived from the well known Shannon [26] measure. By minimizing these measures with the sample size held fixed, we obtain the same model selection criterion that Schwarz [25] derived asymptotically for large sample sizes. This expression has a number of desirable properties and is computationally no more

Choice under uncertainty may be viewed as choice between alternative probability distributions of returns. Under Von Neumann and Morgenstern's assumptions, an individual's optimal choice is a distribution that maximizes the expected utility of returns. In the theoretical analysis, the distribution functions are assumed to be known However, in most realistic cases, the distributions of returns are unknown and are estimated using available economic data. The traditional mode of analysis is to neglect the estimation risk and use the estimated distribution (in lieu of the true distribution) in determining the optimal choice under uncertainty. In this paper, we consider the portfolio choice problem and determine the effect of estimation risk on an individual's optimal choice under uncertainty.