Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractWhile the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary dataset containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors-in-variables models with continuously distributed variables. Our main identifying assumption is that, conditional on the value of the true regressors, some "measure of location" of the distribution of the measurement error (e.g. its mean, mode or median) is equal to zero. The proposed approach relies on the eigenvalue-eigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to "order" the eigenfunctions so that the decomposition is unique. We propose a convenient sievebased estimator, derive its asymptotic properties and investigate its finite-sample behavior through Monte Carlo simulations. An example of application to the relationship between earnings and divorce rates is also provided.

Could education promote the Israeli-Palestinian peace process?

“…In our case this assumption is not fulfilled because of the discreteness of R combined with finite amount of data. Therefore, the proof that Hu and Schennach (2006) propose is not be applicable in our case.…”

“…and Douglas (2001) shows that nonparametric item response models are only identifiable in an asymptotic sense, i.e., when the number of items tends to infinity, in which case the problem would be the one analyzed by Hu and Schennach (2006). For parametric models identification reduces to showing that the number of constraints of the form: p(r 1 , r 2 , ..., r M ) = p(r 1 , r 2 , ..., r M |a, τ m,r )f (a)da generated by the different combinations of responses limits the values of the parameters to a unique set.…”

“…Hu and Schennach (2006) consider a nonlinear measurement error model that is related to the model presented here. These authors relate the joint densities of the observable variables to the joint densities of the unobservable variables in the same way as equation 6 shows.…”

Tikhonov regularization for nonparametric instrumental variable estimators

“…Further, Chen and Ludvigson (2009) consider asset pricing models with functional speci…cations of habit preferences; Chernozhukov, Imbens and Newey (2007) estimate nonseparable models for quantile regression analysis; Loubes and Vanhems (2004) discuss the estimation of the solution of a di¤erential equation with endogenous variables for microeconomic applications. Other related works include Chernozhukov and Hansen (2005), Florens, Johannes and Van Bellegem (2005), Horowitz (2006), Hoderlein and Holzmann (2007), and Hu and Schennach (2008).…”

Nonparametric identification of the classical errors-in-variables model without side information

“…1 This negative result for what is perhaps the most natural regression model has long guided the search for solutions to the errors-in-variables problem towards approaches that rely on additional information (beyond x and y), such as instruments, repeated measurements, validation data, known measurement error distribution, etc (e.g., Hausman, Newey, Ichimura, and Powell (1991), Newey (2001), Schennach (2004a), Schennach (2004b), Schennach (2007), Hu and Schennach (2006), Hu and Ridder (2004), among many others). Nevertheless, since the seminal work of Geary (1942), a large number of authors (e.g.…”