Identifying the Returns to Lying When the Truth is Unobserved
description- – Consider an observed binary regressor D and an unobserved binary variable B, both of which affect some other variable Y. This paper considers nonparametric identification and estimation of the effect of D on Y, conditioning on B=0. For example, suppose Y is a person's wage, the unobserved B indicates if the person has been to college, and the observed D indicates whether the individual claims to have been to college. This paper then identifies and estimates the difference in average wages between those who falsely claim college experience versus those who tell the truth about not having college. We estimate this average returns to lying to be about 7% to 20%. Nonparametric identification without observing B is obtained either by observing a variable V that is roughly analogous to an instrument for ordinary measurement error, or by imposing restrictions on model error moments.
- – WP678
- – 2007-11-01
- – application/pdf
Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables
description- – This paper provides estimators of discrete choice models, including binary, ordered, and multinomial response (choice) models. The estimators closely resemble ordinary and two stage least squares. The distribution of the model's latent variable error is unknown and may be related to the regressors, e.g., the model could have errors that are heteroscedastic or correlated with regressors. The estimator does not require numerical searches, even for multinomial choice. For ordered and binary choice models the estimator is root N consistent and asymptotically normal. A consistent estimator of the conditional error distribution is also provided.
- – WP454
- – 1999-08-01
- – application/pdf
Asymptotic Trimming for Bounded Density Plug-in Estimators
description- – This paper proposes a form of asymptotic trimming to obtain root n convergence of functions of kernel estimated objects. The trimming is designed to deal with the boundary effects that arise in applications where densities are bounded away from zero.
- – WP479
- – 2000-10-30
- – application/pdf
Identification of the Binary Choice Model with Misclassification
description- – Misclassification in binary choice (binomial response) models occurs when the dependent variable is measured with error, that is, when an actual"one"response is sometimes recorded as a zero, and vice versa. This paper shows that binary choice models with misclassification are semiparametrically identified, even when the probabilities of misclassification depend in unknown ways on model covariates, and the distribution of the errors is unknown.
- – WP457
- – 2000-12-19
- – application/pdf
Nonparametric Censored and Truncated Regression
description- – The nonparametric censored regression model, with a fixed, known censoring point (normalized to zero), is y = max[0,m(x)+e], where both the regression function m(x) and the distribution of the error e are unknown. This paper provides consistent estimators of m(x) and its derivatives. The convergence rate is the same as for an uncensored nonparametric regression and its derivatives. We also provide root n estimates of weighted average derivatives of m(x), which equal the coefficients in linear or partly linear specifications for m(x). An extension permits estimation in the presence of a general form of heteroskedasticity. We also extend the estimator to the nonparametric truncated regression model, in which only uncensored data points are observed.
- – WP439
- – 2000-12-19
- – application/pdf
Nonparametric identification of the classical errors-in-variables model without side information
description- – This note establishes that the fully nonparametric classical errors-in-variables model is identifiable from data on the regressor and the dependent variable alone, unless the specification is a member of a very specific parametric family. This family includes the linear specification with normally distributed variables as a special case. This result relies on standard primitive regularity conditions taking the form of smoothness and monotonicity of the regression function and nonvanishing characteristic functions of the disturbances.
- – WP674
- – 2007-07-16
- – application/pdf
Nonparametric Identification of Regression Models Containing a Misclassified Dichotomous Regressor Without Instruments
description- – This note considers nonparametric identification of a general nonlinear regression model with a dichotomous regressor subject to misclassification error. The available sample information consists of a dependent variable and a set of regressors, one of which is binary and error-ridden with misclassification error that has unknown distribution. Our identification strategy does not parameterize any regression or distribution functions, and does not require additional sample information such as instrumental variables, repeated measurements, or an auxiliary sample. Our main identifying assumption is that the regression model error has zero conditional third moment. The results include a closed-form solution for the unknown distributions and the regression function.
- – WP675
- – 2007-07-01
- – application/pdf
Nonparametric Identification and Estimation of Nonclassical Errors-in-Variables Models Without Additional Information
description- – This paper considers identification and estimation of a nonparametric regression model with an unobserved discrete covariate. The sample consists of a dependent variable and a set of covariates, one of which is discrete and arbitrarily correlates with the unobserved covariate. The observed discrete covariate has the same support as the unobserved covariate, and can be interpreted as a proxy or mismeasure of the unobserved one, but with a nonclassical measurement error that has an unknown distribution. We obtain nonparametric identification of the model given monotonicity of the regression function and a rank condition that is directly testable given the data. Our identification strategy does not require additional sample information, such as instrumental variables or a secondary sample. We then estimate the model via the method of sieve maximum likelihood, and provide root-n asymptotic normality and semiparametric efficiency of smooth functionals of interest. Two small simulations are presented to illustrate the identification and the estimation results.
- – WP676
- – 2007-07-01
- – application/pdf
Weighted and Two Stage Least Squares Estimation of Semiparametric Truncated Regression Models
description- – This paper provides a root-n consistent, asymptotically normal weighted least squares estimator of the coefficients in the truncated regression model. The distribution of the errors is unknown and permits general forms of unknown heteroscedasticity. Also provided is an instrumental variables based two stage least squares estimator for this model, which can be used when the errors are correlated with some regressors. Estimation is based on a 'special' regressor as in Lewbel (2000). Our limiting distributions include a new result regarding asymptotic trimming for root-n convegence of density weighed extremum estimators.
- – WP525
- – 2002-02-14
- – application/pdf
A Rational Rank Four Demand System
description- – Past parametric tests of demand system rank employed polynomial Engel curve systems. However, by Gorman's (1981) theorem, the maximum possible rank of a utility derived polynomial demand system is three. The present paper proposes a class of demand systems that are utility derived, are close to polynomial, and have rank four. These systems nest rational polynomial demands, and so can be used to test ranks up to four. These systems are suitable for applications where high rank is likely, such as demand systems involving a large number of goods. A test of rank using this new class of systems is applied to UK consumer demand data.
- – WP463
- – 2003-03-01
- – application/pdf
Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power
description- – How much income would a woman living alone require to attain the same standard of living that she would have if she were married? What percentage of a married couple's expenditures are controlled by the husband? How much money does a couple save on consumption goods by living together versus living apart? We propose and estimate a collective model of household behavior that permits identification and estimation of concepts such as these. We model households in terms of the utility functions of its members, a bargaining or social welfare function, and a consumption technology function. We demonstrate generic nonparametric identification of the model, and hence of equivalence scales, consumption economies of scale, household members' bargaining power and other related concepts.
- – Barten scales
- – demand systems
- – household bargaining
- – bargaining power
- – consumer demand
- – adult equivalence scales
- – economies of scale
- – collective model
- – 2004-04-01
- – application/pdf
Identification of Endogenous Heteroskedastic Models
description- – This paper proposes a new method of obtaining identification in mismeasured regressor models, triangular systems, linear simultaneous equation systems, and structural vector autoregressions. Associated estimators take the form of ordinary two stage least squares or generalized method of moments. The method may be used in applications where other sources of identification such as instrumental variables or repeated measurements are not available. Identification comes from a heteroskedastic covariance restriction that is shown to be a feature of many endogeneity and measurement error models. Identification is also obtained in some semiparametric partly linear models. An empirical application and a Monte Carlo study are provided.
- – 2004-03-01
- – application/pdf
Demand Systems With Nonstationary Prices
description- – Relative prices are nonstationary and standard root-T inference is invalid for demand systems. But demand systems are nonlinear functions of relative prices, and standard methods for dealing with nonstationarity in linear models cannot be used. Demand system residuals are also frequently found to be highly persistent, further complicating estimation and inference. We propose a variant of the Translog demand system, the NTLOG, and an associated estimator that can be applied in the presence of nonstationary prices with possibly nonstationary errors. The errors in the NTLOG can be interpreted as random utility parameters. The estimates have classical root-T limiting distributions. We also propose an explanation for the observed nonstationarity of aggregate demand errors, based on aggregation of consumers with heterogeneous preferences in a slowly changing population. Estimates using US data are provided.
- – WP441
- – 2004-11-01
- – application/pdf
Simple Estimators For Hard Problems: Endogeneity in Discrete Choice Related Models
description- – This paper describes numerically simple estimators that can be used to estimate binary choice and other related models (such as selection and ordered choice models) when some regressors are endogenous or mismeasured. Simple estimators are provided that allow for discrete or otherwise limited endogenous regressors, lagged dependent variables and other dynamic effects, heteroskedastic and autocorrelated latent errors, and latent fixed effects.
- – WP604
- – 2004-08-01
- – application/pdf
Endogenous Selection Or Treatment Model Estimation
description- – In a sample selection or treatment effects model, common unobservables may affect both the outcome and the probability of selection in unknown ways. This paper shows that the distribution function of potential outcomes, conditional on covariates, can be identified given an observed variable V that affects the treatment or selection probability in certain ways and is conditionally independent of the error terms in a model of potential outcomes. Selection model estimators based on this identification are provided, which take the form of either simple weighted averages or GMM or two stage least squares. These estimators permit endogenous and mismeasured regressors. Empirical applications are provided to estimation of a firm investment model and a returns to schooling wage model.
- – WP462
- – 2005-04-01
- – application/pdf
Modeling Heterogeneity
description- – My goal here is to provide some synthesis of recent results regarding unobserved heterogeneity in nonlinear and semiparametric models, using as a context Matzkin (2005a) and Browning and Carro (2005), which were the papers presented in the Modeling Heterogeneity session of the 2005 Econometric Society World Meetings in London. These papers themselves consist of enormously heterogeneous content, ranging from high theory to Danish milk, which I will attempt to homogenize. The overall theme of this literature is that, in models of individual economic agents, errors at least partly reflect unexplained heterogeneity in behavior, and hence in tastes, technologies, etc.,. Economic theory can imply restrictions on the structure of these errors, and in particular can generate nonadditive or nonseparable errors, which has profound implications for model specification, identification, estimation, and policy analysis.
- – WP650
- – 2005-10-01
- – application/pdf
Price Dimension Reduction in Demand Systems With Many Goods
description- – Estimation of demand systems with many goods is empirically difficult because demand functions depend, flexibly and usually nonlinearly, on the prices of all goods. The standard solution is to impose strong, empirically questionable behavioral restrictions on price elasticities via separability. This paper proposes an alternative based on applying statistical dimension reduction methods to the price vector, and deriving the resulting restrictions on demand functions that remain due to Slutsky symmetry and other implications of utility maximization. The results permit estimation of the effects of income and of prices of some goods on the demand functions for every good without imposing any separability. We illustrate the results by reporting estimates of the effects of gasoline prices on the demands for many goods.
- – WP668
- – 2006-11-01
- – application/pdf
Identification and Nonparametric Estimation of a Transformed Additively Separable Model
description- – Let r(x,z) be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses identification and consistent estimation of the unknown functions H, M, G and F, where r(x, z) = H[M (x, z)] and M(x,z) = G(x) + F(z). An estimation algorithm is proposed for each of the model's unknown components when r(x, z) represents a conditional mean function. The resulting estimators use marginal integration, and are shown to have a limiting Normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives. Their small sample performance is studied in a Monte Carlo experiment. We empirically apply our results to nonparametrically estimate and test generalized homothetic production functions in four industries within the Chinese economy.
- – WP652
- – 2006-08-21
- – application/pdf
Tricks With Hicks: The EASI Demand System
description- – We propose an Exact Affine Stone Index (EASI) demand system, which delivers the convenient properties of Hicksian demands in an empirically simple framework. Like the Almost Ideal Demand (AID) system, EASI budget shares are linear in parameters given real expenditures. However, unlike AID, EASI demands can have any rank and its Engel curves can be polynomials or splines of any order in real expenditures. EASI error terms equal random utility parameters to account for unobserved preference heterogeneity. EASI demand functions can be estimated using ordinary GMM, and, like AID, an approximate EASI model can be estimated by linear regression.
- – WP651
- – 2006-06-01
- – application/pdf
Shape Invariant Demand Functions
description- – Shape invariance is a property of demand functions that is convenient for semiparametric demand modelling. All known shape invariant demands are derived from utility functions that, up to monotonic transformation, are called IB/ESE (independent of base - equivalence scale exact) utility functions, because they yield IB/ESE equivalence scales, which are widely used in welfare calculations. This paper provides a counterexample, i.e., a shape invariant demand system that is not derived from a transform of IB/ESE utility. A general theorem is then provided that characterizes all shape invariant demand systems. The usual practice of equating shape invariance with the IB/ESE utility class is shown to be not quite right, but it can be made valid by testing for the small class of exceptions noted here. In particular, all the exceptions have rank two, so any rank three or higher shape invariant system must be derived from transforms of IB/ESE utility.
- – WP669
- – 2007-05-01
- – application/pdf
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