Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators

Abstract

This paper considers the nonparametric estimation of the densities of the latent variable and the error term in the standard measurement error model when two or more measurements are available. Using an identification result due to Kotlarski we propose a two-step nonparametric procedure for estimating both densities based on their empirical characteristic functions. We distinguish four cases according to whether the underlying characteristic functions are ordinary smooth or supersmooth. Using the loglog Law and von Mises differentials we show that our nonparametric density estimators are uniformly convergent. We also characterize the rate of uniform convergence in each of the four cases.1998 Academic Press

Microeconomic models with latent variables: applications of measurement error models in empirical industrial organization and labor economics

“…This result has been used in many empirical and theoretical studies, such as Li and Vuong (1998), Li, Perrigne, and Vuong (2000), Krasnokutskaya (2011), Schennach (2004a), and Evdokimov (2010.…”

Structural Econometric Methods in Auctions: A Guide to the Literature

“…Using this assumption, along with a regularity condition from work in nonparametric deconvolution methods by Li and Vuong (1998), they showed that the CIPV model is nonparametrically identified from a sample of bids. Moreover, CIPV can rationalize a sample of bids if and only if the inverse-bid function is monotonic.…”

“…The authors' estimation procedure combined methods developed by GPV with those of Li and Vuong (1998). Specifically, in the first stage of estimation they constructed a pseudo-sample of private signals using the inverse-bidding function and nonparametric estimates of the bid distributions.…”

“…If these two components are independent of each other and, when multiplied, comprise the bidders' valuations, identification obtains as long as two bids are observed at each auction. By assuming multiplicatively-separable components, she was able to relate her work to and leverage results from Li and Vuong (1998) as well as Li et al (2002).…”

Regressions with Berkson errors in covariates - a nonparametric approach

“…(In classical measurement error problems, the distribution of the error can be identified from repeated measurements via a Kotlarski-type equality [Schennach (2004), Li and Vuong (1998)]. However, such results do not yet exist for Berkson-type measurement error.)…”