Nonparametric Analysis of Random Utility Models

This paper develops and implements a nonparametric test of Random Utility Models. The motivating application is to test the null hypothesis that a sample of cross-sectional demand distributions was generated by a population of rational consumers. We test a necessary and sufficient condition for this that does not rely on any restriction on unobserved heterogeneity or the number of goods. We also propose and implement a control function approach to account for endogenous expenditure. An econometric result of independent interest is a test for linear inequality constraints when these are represented as the vertices of a polyhedron rather than its faces. An empirical application to the U.K. Household Expenditure Survey illustrates computational feasibility of the method in demand problems with 5 goods.Comment: 54 pages, 2 figure

Nonparametric Estimation in Random Coefficients Binary Choice Models

This paper considers random coefficients binary choice models. The main goal is to estimate the density of the random coefficients nonparametrically. This is an ill-posed inverse problem characterized by an integral transform. A new density estimator for the random coefficients is developed, utilizing Fourier-Laplace series on spheres. This approach offers a clear insight on the identification problem. More importantly, it leads to a closed form estimator formula that yields a simple plug-in procedure requiring no numerical optimization. The new estimator, therefore, is easy to implement in empirical applications, while being flexible about the treatment of unobserved heterogeneity. Extensions including treatments of non-random coefficients and models with endogeneity are discussed.Inverse problems, Discrete choice models

Robustness, Infinitesimal Neighborhoods, and Moment Restrictions

This paper is concerned with robust estimation under moment restrictions. A moment restriction model is semiparametric and distribution-free, therefore it imposes mild assumptions. Yet it is reasonable to expect that the probability law of observations may have some deviations from the ideal distribution being modeled, due to various factors such as measurement errors. It is then sensible to seek an estimation procedure that are robust against slight perturbation in the probability measure that generates observations. This paper considers local deviations within shrinking topological neighborhoods to develop its large sample theory, so that both bias and variance matter asymptotically. The main result shows that there exists a computationally convenient estimator that achieves optimal minimax robust properties. It is semiparametrically efficient when the model assumption holds, and at the same time it enjoys desirable robust properties when it does not.Asymptotic minimax theorem, Hellinger distance, Semiparametric efficiency

"Empirical Likelihood-Based Inference in Conditional Moment Restriction Models"

This paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions. Our estimator generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994). Using a kernel smoothing method, we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood-based procedure. This yields a one-step estimator which avoids estimating optimal instruments. Our likelihood ratio-type statistic for parametric restrictions does not require the estimation of variance, and achieves asymptotic pivotalness implicitly. The estimation and testing procedures we propose are normalization invariant. Simulation results suggest that our new estimator works remarkably well in finite samples.

On testing conditional moment restrictions: The canonical case

Let (x, z) be a pair of random vectors. We construct a new smoothed empirical likelihood based test for the hypothesis that E(z|x) a.s. = 0, and show that the test statistic is asymptotically normal under the null. An expression for the asymptotic power of this test under a sequence of local alternatives is also obtained. The test is shown to possess an optimality property in large samples. Simulation evidence suggests that it also behaves well in small samples

Revealed Price Preference: Theory and Empirical Analysis

With the aim of determining the welfare implications of price change in consumption data, we introduce a revealed preference relation over prices. We show that an absence of cycles in this preference relation characterizes a model of demand where consumers trade-off the utility of consumption against the disutility of expenditure. This model is appropriate whenever a consumer's demand over a {\em strict} subset of all available goods is being analyzed. For the random utility extension of the model, we devise nonparametric statistical procedures for testing and welfare comparisons. The latter requires the development of novel tests of linear hypotheses for partially identified parameters. In doing so, we provide new algorithms for the calculation and statistical inference in nonparametric counterfactual analysis for a general partially identified model. Our applications on national household expenditure data provide support for the model and yield informative bounds concerning welfare rankings across different prices.Comment: 53 page

On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions

In this paper we make two contributions. First, we show by example that empirical likelihood and other commonly used tests for parametric moment restrictions, including the GMM-based J-test of Hansen (1982), are unable to control the rate at which the probability of a Type I error tends to zero. From this it follows that, for the optimality claim for empirical likelihood in Kitamura (2001) to hold, additional assumptions and qualifications need to be introduced. The example also reveals that empirical and parametric likelihood may have non-negligible differences for the types of properties we consider, even in models in which they are first-order asymptotically equivalent. Second, under stronger assumptions than those in Kitamura (2001), we establish the following optimality result: (i) empirical likelihood controls the rate at which the probability of a Type I error tends to zero and (ii) among all procedures for which the probability of a Type I error tends to zero at least as fast, empirical likelihood maximizes the rate at which probability of a Type II error tends to zero for "most" alternatives. This result further implies that empirical likelihood maximizes the rate at which probability of a Type II error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their Type I error probabilities.Empirical likelihood, Large deviations, Hoeffding optimality, Moment restrictions

Identifying Finite Mixtures in Econometric Models

Mixtures of distributions are present in many econometric models, such as models with unobserved heterogeneity. It is thus crucial to have a general approach to identify them nonparametrically. Yet the literature so far only contains isolated examples, applied to specific models. We derive the identifying implications of a conditional independence assumption in finite mixture models. It applies for instance to models with unobserved heterogeneity, regime switching models, and models with mismeasured discrete regressors. Under this assumption, we derive sharp bounds on the mixture weights and components. For models with two mixture components, we show that if in addition the components behave differently in the tails of their distributions, then components and weights are fully nonparametrically identified. We apply our findings to the nonparametric identification and estimation of outcome distributions with a misclassified binary regressor. This provides a simple estimator that does not require instrumental variables, auxiliary data, symmetric error distributions or other shape restrictions

The Influence of Hyperactivity of the Hypothalamic-pituitary-adrenal Axis and Hyperglycemia on the 5-HT2A Receptor-mediated Wet-dog Shake Responses in Rats

Hyperactivity of the hypothalamic-pituitary-adrenal (HPA) axis induces hyperglycemia and serotonin (5-HT)2A receptor supersensitivity. In the present study, to investigate the effect of hyperglycemia on the function of 5-HT2A receptors, we compared the 5-HT2A receptor-mediated wet-dog shake responses in rats treated with adrenocorticotropic hormone (ACTH), dexamethasone and streptozotocin. ACTH (100 &#956;g/rat per day, s.c.), dexamethasone (1 mg/kg per day, s.c.) and streptozotocin (60 mg/kg, i.p.) produced significant hyperglycemia at 14 days after the start of these treatments, and the hyperglycemia was most pronounced in the streptozotocin-treated rats. The wet-dog shake responses induced by (±)-1-(2,5-dimethoxy-4-iodophenyl)-2-aminopropane (DOI), a 5-HT2A receptor agonist, were significantly enhanced at 14 days after repeated treatment with ACTH and dexamethasone. However, streptozotocin-induced diabetes had no effect on the wet-dog shake responses. The results of the present study suggest that hyperglycemia is not strongly associated with the enhanced susceptibility of 5-HT2A receptors under the condition of hyperactivity of the HPA axis.</p