How many consumers are rational?

Rationality places strong restrictions on individual consumer behavior. This paper is concerned with assessing the validity of the integrability constraints imposed by standard utility maximization, arising in classical consumer demand analysis. More specifically, we characterize the testable implications of negative semidefiniteness and symmetry of the Slutsky matrix across a heterogeneous population without assuming anything on the functional form of individual preferences. In the same spirit, homogeneity of degree zero is being considered. Our approach employs nonseparable models and is centered around a conditional independence assumption, which is sufficiently general to allow for endogenous regressors. It is the only substantial assumption a researcher has to specify in this model, and has to be evaluated with particular care. Finally, we apply all concepts to British household data: We show that rationality is an acceptable description for large parts of the population, regardless of whether we test on single or composite households.

Endogenous semiparametric binary choice models with heteroscedasticity

In this paper we consider endogenous regressors in the binary choice model under a weak median exclusion restriction, but without further specification of the distribution of the unobserved random components. Our reduced form specification with heteroscedastic residuals covers various heterogeneous structural binary choice models. As a particularly relevant example of a structural model where no semiparametric estimator has of yet been analyzed, we consider the binary random utility model with endogenous regressors and heterogeneous parameters. We employ a control function IV assumption to establish identification of a slope parameter 'â' by the mean ratio of derivatives of two functions of the instruments. We propose an estimator based on direct sample counterparts, and discuss the large sample behavior of this estimator. In particular, we show '√'n consistency and derive the asymptotic distribution. In the same framework, we propose tests for heteroscedasticity, overidentification and endogeneity. We analyze the small sample performance through a simulation study. An application of the model to discrete choice demand data concludes this paper.

Structural Measurement Errors in Nonseparable Models

This paper considers measurement error from a new perspective. In surveys, response errors are often caused by the fact that respondents recall past events and quantities imperfectly. We explore the consequences of recall errors for such key econometric is- sues as the identification of marginal effects or economic restrictions in structural models. Our identification approach is entirely nonparametric, using Matzkin-type nonseparable models that nest a large class of potential structural models. We establish that measurement errors due to poor recall are generally likely to exhibit nonstandard behavior, in particular be nonclassical and differential, and we provide means to deal with this situation. Moreover, our findings suggest that conventional wisdom about measurement errors may be misleading in many economic applications. For instance, under certain conditions left-hand side recall errors will be problematic even in the linear model, and quantiles will be less robust than means. Finally, we apply the main concepts put forward in this paper to real world data, and find evidence that underscores the importance of focusing on individual response behavior

Structural Measurement Errors in Nonseparable Models

This paper considers measurement error from a new perspective. In surveys, response errors are often caused by the fact that respondents recall past events and quantities imperfectly. We explore the consequences of recall errors for such key econometric is- sues as the identification of marginal effects or economic restrictions in structural models. Our identification approach is entirely nonparametric, using Matzkin-type nonseparable models that nest a large class of potential structural models. We establish that measurement errors due to poor recall are generally likely to exhibit nonstandard behavior, in particular be nonclassical and differential, and we provide means to deal with this situation. Moreover, our findings suggest that conventional wisdom about measurement errors may be misleading in many economic applications. For instance, under certain conditions left-hand side recall errors will be problematic even in the linear model, and quantiles will be less robust than means. Finally, we apply the main concepts put forward in this paper to real world data, and find evidence that underscores the importance of focusing on individual response behavior.Measurement Error; Nonparametric; Survey Design; Nonseparable Model; Identification; Zero Homogeneity; Demand

Welfare analysis using nonseparable models

This paper proposes a framework to model empirically welfare effects that are associated with a price change in a population of heterogeneous consumers. Individual demands are characterized by a nonseparable model which is nonparametric in the regressors, as well as monotonic in unobserved heterogeneity. In this setup, we first provide and discuss conditions under which the heterogeneous welfare effects are identified, and establish constructive identification. We then propose a sample counterpart estimator, and analyze its large sample properties. For both identification and estimation, we distinguish between the cases when regressors are exogenous and when they are endogenous. Finally, we apply all concepts to measuring the heterogeneous effect of a chance of gasoline price using US consumer data and find very substantial differences in individual effects.

Nonparametric identification in nonseparable panel data models with generalized fixed effects

This paper is concerned with extending the familiar notion of fixed effects to nonlinear setups with infinite dimensional unobservables like preferences. The main result is that a generalized version of differencing identifies local average structural derivatives (LASDs) in very general nonseparable models, while allowing for arbitrary dependence between the persistent unobservables and the regressors of interest even if there are only two time periods. These quantities specialize to well known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects. We extend the basic framework to include dynamics in the regressors and time trends, and show how distributional effects as well as average effects are identified. In addition, we show how to handle endogeneity in the transitory component. Finally, we adapt our results to the semiparametric binary choice model with correlated coefficients, and establish that average structural marginal probabilities are identified. We conclude this paper by applying the last result to a real world data example. Using the PSID, we analyze the way in which the lending restrictions for mortgages eased between 2000 and 2004.

Testing multivariate economic restrictions using quantiles: the example of Slutsky negative semidefiniteness

This paper is concerned with testing rationality restrictions using quantile regression methods. Specifically, we consider negative semidefiniteness of the Slutsky matrix, arguably the core restriction implied by utility maximization. We consider a heterogeneous population characterized by a system of nonseparable structural equations with infinite dimensional unobservable. To analyze the economic restriction, we employ quantile regression methods because they allow us to utilize the entire distribution of the data. Difficulties arise because the restriction involves several equations, while the quantile is a univariate concept. We establish that we may test the economic restriction by considering quantiles of linear combinations of the dependent variable. For this hypothesis we develop a new empirical process based test that applies kernel quantile estimators, and derive its large sample behavior. We investigate the performance of the test in a simulation study. Finally, we apply all concepts to Canadian individual data, and show that rationality is an acceptable description of actual individual behavior.

Identification and estimation in a correlated random coefficients binary response model

We study a linear index binary response model with random coefficients BB allowed to be correlated with regressors X. We identify the mean of the distribution of B and show how the mean can be interpreted as a vector of expected relative effects. We use instruments and a control vector V to make X independent of B given V. This leads to a localize-then-average approach to both identification and estimation. We develop a √n-consistent and asymptotically normal estimator of a trimmed mean of the distribution of BB, explore its small sample performance through simulations, and present an application

Specification Testing in Random Coefficient Models

In this paper, we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model, in particular linearity in coefficients, generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a random coefficient, i.e., whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We provide formal power analysis against global as well as against local alternatives. Moreover, we perform a Monte Carlo simulation study, and apply the tests to analyze the degree of nonlinearity in a heterogeneous random coefficients demand model. While we find some evidence against the popular QUAIDS specification with random coefficients, it is not strong enough to reject the specification at the conventional significance level