Roger W. Klein

An efficient semiparametric estimator for binary response models

This paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of th e 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. Copyright 1993 by The Econometric Society.

The effect of estimation risk on optimal portfolio choice

Abstract This paper determines the effect of estimation risk on optimal portfolio choice under uncertainty. In most realistic problems, the parameters of return distributions are unknown and are estimated using available economic data. Traditional analysis neglects estimation risk by treating the estimated parameters as if they were the true parameters to determine the optimal choice under uncertainty. We show that for normally distributed returns and ‘non-informative’ or ‘invariant’ priors, the admissible set of portfolios taking the estimation uncertainty into account is identical to that given by traditional analysis. However, as a result of estimation risk, the optimal portfolio choice differs from that obtained by traditional analysis. For other plausible priors, the admissible set, and consequently the optimal choice, is shown to differ from that in traditional analysis.

The effect of limited information and estimation risk on optimal portfolio diversification

Abstract This paper analyzes the optimal portfolio choice problem when security returns have a joint multivariate normal distribution with unknown parameters. For the case of limited, but sufficient (sample plus prior) information, we show that for a general family of conjugate priors, the optimal portfolio choice is obtained by the use of a mean-variance analysis that differs from traditional mean-variance analysis due to estimation risk. We also consider two illustrative cases of insufficient sample information and minimal prior information and show that in these cases it is asymptotically optimal for an investor to limit diversification to a subset of the securities. These theoretical results corroborate observed investor behavior in capital markets.

MODEL SELECTION WHEN THERE IS "MINIMAL" PRIOR INFORMATION

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

Estimating new product demand from biased survey data

Abstract Market researchers often conduct surveys asking respondents to estimate their future demand for new products. However, projected demand may exhibit systematic bias. For example, the more respondents like a product, the more they may exaggerate their demand. We found evidence of such exaggeration in a recent survey of demand for a potential new video product. In this paper, we develop a computationally tractable procedure that corrects for a general form of systematic bias in demand projections. This general form is characterized by a monotonictransformation of projected demand, and covers exaggeration bias as a special case.

Does Increasing Parents’ Schooling Raise the Schooling of the Next Generation? Evidence Based on Conditional Second Moments

This paper investigates the degree of intergenerational transmission of education for individuals from the National Longitudinal Survey of Youth 1979. Rather than identifying the causal effect of parental education via instrumental variables we exploit the feature of the transmission mechanism responsible for its endogeneity. More explicitly, we assume the intergenerational transfer of unobserved ability is invariant to the economic environment. This, combined with the heteroskedasticity resulting from the interaction of unobserved ability with socioeconomic factors, identifies this causal effect. We conclude the observed intergenerational educational correlation reflects both a causal parental educational effect and a transfer of unobserved ability.

Estimating the Return to Endogenous Schooling Decisions via Conditional Second Moments

This paper employs conditional second moments to identify the impact of education in wage regressions where education is treated as endogenous. This approach avoids the use of instrumental variables in a setting where instruments are frequently not available. We employ this methodology to estimate the returns to schooling for a sample of Australian workers. We find that accounting for the endogeneity of education in this manner increases the estimated return to education from 6 percent to 10 percent.

Specification tests for binary choice models based on index quantiles

Abstract 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.

Bias corrections in testing and estimating semiparametric, single index models

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.

Some results on an approximation to joint distributions of utility functions

Abstract 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.