Yingyao Hu

Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information

Virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information (e.g., validation data, known error distributions, repeated measurements, or instruments). In contrast, we establish that the fully nonparametric classical errors-in-variables model is identifiable from data on the regressor and the dependent variable alone, unless the model takes a very specific parametric form. This parametric family includes (but is not limited to) the linear specification with normally distributed variables as a well-known special case. This result relies on standard primitive regularity conditions taking the form of smoothness constraints and nonvanishing characteristic functions’ assumptions. Our approach can handle both monotone and nonmonotone specifications, provided the latter oscillate a finite number of times. Given that the very specific unidentified parametric functional form is arguably the exception rather than the rule, this identification result should have a wide applicability. It leads to a new perspective on handling measurement error in nonlinear and nonparametric models, opening the way to a novel and practical approach to correct for measurement error in datasets where it was previously considered impossible (due to the lack of additional information regarding the measurement error). We suggest an estimator based on non/semiparametric maximum likelihood, derive its asymptotic properties, and illustrate the effectiveness of the method with a simulation study and an application to the relationship between firm investment behavior and market value, the latter being notoriously mismeasured. Supplementary materials for this article are available online.

Estimation of nonlinear models with mismeasured regressors using marginal information

We consider the estimation of nonlinear models with mismeasured explanatory variables, when information on the marginal distribution of the true values of these variables is available. We derive a semi-parametric MLE that is is shown to be pn consistent and asymptotically normally distributed. In a simulation experiment we find that the finite sample distribution of the estimator is close to the asymptotic approximation. The semi-parametric MLE is applied to a duration model for AFDC welfare spells with misreported welfare benefits. The marginal distribution of the correctly measured welfare benefits is obtained from an administrative source.

On Deconvolution as a First Stage Nonparametric Estimator

We reconsider Taupin’s (2001) Integrated Nonlinear Regression (INLR) estimator for a nonlinear regression with a mismeasured covariate. We find that if we restrict the distribution of the measurement error to the class of range-restricted distributions, then weak smoothness assumptions suffice to ensure sqrt(n) consistency of the estimator. The restriction to such distributions is innocuous, because it does not affect the fit to the data. Our results show that deconvolution can be used in a nonparametric first step without imposing restrictive smoothness assumptions on the parametric model.

Identifying Dynamic Games with Serially-Correlated Unobservables ∗

In this article, we consider the nonparametric identification of Markov dynamic games models in which each firm has its own unobserved state variable, which is persistent over time. This class of models includes most models in the Ericson and Pakes (1995) and Pakes and McGuire (1994) framework. We provide conditions under which the joint Markov equilibrium process of the firms’ observed and unobserved variables can be nonparametrically identified from data. For stationary continuous action games, we show that only three observations of the observed component are required to identify the equilibrium Markov process of the dynamic game. When agents’ choice variables are discrete, but the unobserved state variables are continuous, four observations are required.

A Simple Estimator for Dynamic Models with Serially Correlated Unobservables

We present a method for estimating Markov dynamic models with unobserved state variables which can be serially correlated over time. We focus on the case where all the model variables have discrete support. Our estimator is simple to compute because it is noniterative, and involves only elementary matrix manipulations. Our estimation method is nonparametric, in that no parametric assumptions on the distributions of the unobserved state variables or the laws of motions of the state variables are required. Monte Carlo simulations show that the estimator performs well in practice, and we illustrate its use with a dataset of doctors’ prescription of pharmaceutical drugs.

IDENTIFICATION OF PAIRED NONSEPARABLE MEASUREMENT ERROR MODELS

This paper studies the paired nonseparable measurement error models, where two measurements, X and Y , are produced by mutually independent unobservables, U , V , and W , through the system, X = g ( U,V ) and Y = h ( U,W ). We propose restrictions to identify the marginal distribution of the common component U and the conditional distributions of X and Y given U . Applying this method to twin panel data, we find the following robust reporting patterns for years of education: (1) self reports are accurate only when the true years of education are 16 or 18, typically corresponding to advanced university degrees in the US education system; (2) sibling reports are accurate whenever the true years of education are 12, 14, 16, and 18, which are typical diploma years.

Bounding the Effect of a Dichotomous Regressor With Arbitrary Measurement Errors

This note considers a nonlinear regression model containing a 0-1 dichotomous regressor when it is subject to arbitrary measurement errors in the sample. The key identification assumption requires that the third conditional moment of the regression error is zero. This note suggests that the effect of the latent dichotomous variable may be bounded away from zero using the observed moments.

Closed-Form Identication of Dynamic Discrete Choice Models with Proxies for Unobserved State Variables

For dynamic discrete choice models of forward-looking agents where a continuous state variable is unobserved but its proxy is available, we derive closed-form identication of the structure by explicitly solving integral equations. In therst step, we derive closed-form identication of Markov components. In the second step, we plug therst-step identifying formulas into linear restrictions to obtain closed-form identication of structural param- eters.

Nonparametric Identification of First-Price Auctions WithNon-Separable Unobserved Heterogeneity

We propose a novel methodology for nonparametric identification of first-price auction models with independent private values, which allows for one-dimensional auctionspecific unobserved heterogeneity, based on recent results from the econometric literature on nonclassical measurement error in Hu and Schennach (2008). Our approach can accommodate a wide variety of applications in which some location of the conditional distribution of bids (e.g. min or max of the support, mean, etc.) is increasing in the unobserved heterogeneity. This includes settings in which the econometrician fails to observe the reserve price, the cost of bidding, the number of bidders, or some factor (“quality”) with a non-linear effect on bidder values.