Rosa L. Matzkin

Nonparametric Estimation of Nonadditive Random Functions

We present estimators for nonparametric functions that are nonadditive in unobservable random terms. The distributions of the unobservable random terms are assumed to be unknown. We show that when a nonadditive, nonparametric function is strictly monotone in an unobservable random term, and it satisfies some other properties that may be implied by economic theory, such as homogeneity of degree one or separability, the function and the distribution of the unobservable random term are identified. We also present convenient normalizations, to use when the properties of the function, other than strict monotonicity in the unobservable random term, are unknown. The estimators for the nonparametric function and for the distribution of the unobservable random term are shown to be consistent and asymptotically normal. We extend the results to functions that depend on a multivariate random term. The results of a limited simulation study are presented. Copyright The Econometric Society 2003.

Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models

The author shows that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term. This identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term. The estimator is shown to be strongly consistent and a two step procedure for its calculation is developed. The paper also includes examples of economic models that satisfy the conditions necessary to apply the results. Copyright 1992 by The Econometric Society.

Restrictions of economic theory in nonparametric methods

This chapter describes several nonparametric estimation and testing methods for econometric models. Instead of using parametric assumptions on the functions and distributions in an economic model, the methods use the restrictions that can be derived from the model. Examples of such restrictions are the concavity and monotonicity of functions, equality conditions, and exclusion restrictions.The chapter shows, first, how economic restrictions can guarantee the identification of nonparametric functions in several structural models. It then describes how shape restrictions can be used to estimate nonparametric functions using popular methods for nonparametric estimation. Finally, the chapter describes how to test nonparametrically the hypothesis that an economic model is correct and the hypothesis that a nonparametric function satisfies some specified shape properties.

Testable Restrictions on the Equilibrium Manifold

The authors present a finite system of polynomial inequalities in unobservable variables and market data that observations on market prices, individual incomes and, aggregate endowments must satisfy to be consistent with the equilibrium behavior of some pure trade economy. Quantifier elimination is used to derive testable restrictions on finite data sets for the pure trade model. A characterization of observations on aggregate endowments and market prices that are consistent with a Robinson Crusoes economy is also provided. Copyright 1996 by The Econometric Society.

Nonparametric identification and estimation of polychotomous choice models

Abstract In this paper we provide conditions guaranteeing the identification of nonparametric polychotomous choice models. In these models, neither the subutility function of observable attributes nor the distribution of the unobservable random terms is specified parametrically. Sets of nonparametric functions that possess properties that are often implied by economic theory and satisfy the restrictions required to identify the models are described. We use the identification results to develop nonparametric strongly-consistent estimators for the subutility function of observable attributes. The results concern models in which the distribution of the unobservable random terms both depend and do not depend on the observable characteristics.

Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models

This paper introduces a semiparametric estimation method for Polychotomous Choice models. The method does not require a parametric structure for the systematic subutility of observable exogenous variables. The distribution of the random terms is assumed to be known up to a finite-dimensional parameter vector. In contrast, previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified. The systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory. The estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent. A computational technique to calculate the estimators is developed. Copyright 1991 by The Econometric Society.

Nonparametric Identification and Estimation of Nonadditive Hedonic Models

This paper studies the identification and estimation of preferences and technologies in equilibrium hedonic models. In it, we identify nonparametric structural relationships with nonadditive heterogeneity. We determine what features of hedonic models can be identified from equilibrium observations in a single market under weak assumptions about the available information. We then consider use of additional information about structural functions and heterogeneity distributions. Separability conditions facilitate identification of consumer marginal utility and firm marginal product functions. We also consider how identification is facilitated using multimarket data.

Medicare prescription drug coverage: consumer information and preferences.

We investigate prescription drug use, and information and enrollment intentions for the new Medicare Part D drug insurance program, using a sample of Medicare-eligible subjects surveyed before open enrollment began for this program. We find that, despite the complexity of competing plans offered by private insurers under Part D, a majority of the Medicare population had information on this program and a substantial majority planned to enroll. We find that virtually all elderly, even those with no current prescription drug use, can expect to benefit from enrollment in a Part D Standard plan at the low premiums available in the current market. However, there is a significant risk that many eligible seniors, particularly low-income elderly with poor health or cognitive impairment, will make poor enrollment and plan choices.

Identification in Nonparametric Simultaneous Equations Models

This paper provides conditions for identification of functionals in nonparametric simultaneous equations models with nonadditive unobservable random terms. The conditions are derived from a characterization of observational equivalence between models. We show that, in the models considered, observational equivalence can be characterized by a restriction on the rank of a matrix. The use of the new results is exemplified by deriving previously known results about identification in parametric and nonparametric models as well as new results. A stylized method for analyzing identification, which is useful in some situations, is also presented. Copyright 2008 The Econometric Society.

Semiparametric Estimation of Brand Choice Behavior

In the marketing literature there does not seem to be a widely accepted answer to the question of whether, when purchasing brands in a given product category, consumers react differently to a reduction in price and an increase in the deal discount. Previous studies that have attempted to address this issue have assumed that prices and deals have a linear effect on a brands indirect utility. In this article, we estimate the utility of price and discount nonparametrically. Instead of imposing a linear structure on this function, we require only that it be decreasing in price and increasing in deal amount. This specification allows for a general pattern of interaction effects between prices and deals to influence the systematic component of utility. Consistent with the recent literature on estimating brand choice models, we account for heterogeneity in brand preferences across consumers. We use both a semiparametric approach, in which the distribution of the stochastic components of brand utilities is specified parametrically, and a fully nonparametric approach, in which this distribution is left unspecified. We carry out our empirical analyses on household scanner panel datasets for four different product categories. Our empirical results reveal deviations from linearity in deal effects. In particular, deal effects appear to be concave for some products.