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.

[1]  Rosa L. Matzkin,et al.  Nonparametric estimation of nonadditive hedonic models , 2005 .

[2]  J. Powell,et al.  c ○ 2004 The Review of Economic Studies Limited Endogeneity in Semiparametric Binary Response Models , 2001 .

[3]  C. L. Benkard,et al.  Demand Estimation with Heterogeneous Consumers and Unobserved Product Characteristics: A Hedonic Approach , 2004 .

[4]  G. Imbens,et al.  Identification and Estimation of Triangular Simultaneous Equations Models without Additivity , 2002 .

[5]  Andrew Chesher,et al.  Local identification in nonseparable models , 2002 .

[6]  A. Chesher.  Quantile driven identification of structural derivatives , 2001 .

[7]  A. Lewbel,et al.  Demand Systems with and without Errors , 2001 .

[8]  Rosa L. Matzkin,et al.  Panel Data Estimators for Nonseparable Models with Endogenous Regressors , 2001 .

[9]  Edward Vytlacil,et al.  Local Instrumental Variables , 2000 .

[10]  Jason Abrevaya,et al.  Rank estimation of a generalized fixed-effects regression model , 2000 .

[11]  J. Horowitz,et al.  Semiparametric Estimation of a Censored Regression Model with an Unknown Transformation of the Dependent Variable , 1999 .

[12]  J J Heckman,et al.  Local instrumental variables and latent variable models for identifying and bounding treatment effects. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[13]  R. Sherman,et al.  Rank estimators for monotonic index models , 1998 .

[14]  Rosa L. Matzkin,et al.  Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand , 1998 .

[15]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[16]  O. Linton,et al.  A kernel method of estimating structured nonparametric regression based on marginal integration , 1995 .

[17]  Mary Beth Walker,et al.  Stochastic specification in random production models of cost minimizing firms , 1995 .

[18]  W. Newey,et al.  Kernel Estimation of Partial Means and a General Variance Estimator , 1994, Econometric Theory.

[19]  Rosa L. Matzkin.  Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models , 1992 .

[20]  A. Pakes,et al.  The Dynamics of Productivity in the Telecommunications Equipment Industry , 1992 .

[21]  Geert Ridder,et al.  The Non-Parametric Identification of Generalized Accelerated Failure-Time Models , 1990 .

[22]  Mary Beth Walker,et al.  The Random Utility Hypothesis and Inference in Demand Systems , 1989 .

[23]  C. Roehrig,et al.  Conditions for Identification in Nonparametric and Parametic Models , 1988 .

[24]  M. McElroy.  Additive General Error Models for Production, Cost, and Derived Demand or Share Systems , 1987, Journal of Political Economy.

[25]  Aaron K. Han.  A non-parametric analysis of transformations , 1987 .

[26]  Aaron K. Han.  Non-parametric analysis of a generalized regression model: the maximum rank correlation estimator , 1987 .

[27]  J. Heckman,et al.  The Identifiability of the Proportional Hazard Model , 1984 .

[28]  J. Heckman,et al.  A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data , 1984 .

[29]  Chris Elbers,et al.  True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model , 1982 .

[30]  A. Azzalini.  A note on the estimation of a distribution function and quantiles by a kernel method , 1981 .

[31]  Tony Lancaster,et al.  ECONOMETRIC METHODS FOR THE DURATION OF UNEMPLOYMENT , 1979 .

[32]  James J. Heckman,et al.  A Beta-logistic Model for the Analysis of Sequential Labor Force Participation by Married Women , 1975, Journal of Political Economy.

[33]  J. Heckman.  Effects of Child-Care Programs on Women's Work Effort , 1974, Journal of Political Economy.

[34]  Eugene F. Schuster,et al.  Joint Asymptotic Distribution of the Estimated Regression Function at a Finite Number of Distinct Points , 1972 .

[35]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[36]  V. Chernozhukov,et al.  An IV Model of Quantile Treatment Effects , 2002 .

[37]  Joel L. Horowitz,et al.  Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable , 1996 .

[38]  Rosa L. Matzkin.  Restrictions of economic theory in nonparametric methods , 1994 .

[39]  James J. Heckman,et al.  Identifying the Hand of the Past: Distinguishing State Dependence from Heterogeneity , 1991 .

[40]  W. Härdle.  Smoothing Techniques: With Implementation in S , 1991 .

[41]  Bryan W. Brown,et al.  THE IDENTIFICATION PROBLEM IN SYSTEMS NONLINEAR IN THE VARIABLES , 1983 .

[42]  D. McFadden.  Conditional logit analysis of qualitative choice behavior , 1972 .

[43]  E. Nadaraya.  On Estimating Regression , 1964 .

[44]  G. S. Watson,et al.  Smooth regression analysis , 1964 .

[45]  E. Nadaraya,et al.  Some New Estimates for Distribution Functions , 1964 .

[46]  M. Shum.  A semiparametric estimator for dynamic optimization models , with an application to a milk quota market , 2022 .

[47]  Richard Blundell,et al.  Endogeneity in Nonparametric and Semiparametric Regression Models , 2022 .