Consistent Sets of Estimates for Regressions with Correlated or Uncorrelated Measurement Errors in Arbitrary Subsets of all Variables

Abstract

We consider the single equation errors-in-variables model and assume that a researcher is willing to specify an upper bound on the variance covariance matrix of ineasurement errors in the endogenous and exogenous variables. The measurement errora may show any pattern of correlations. It is shown tha[ as a result the set of ML estimates is bounded by an ellipsoid. When, in addition, the variance covariance matrix of the errors is constrained to be diagonal, the set of ML estimates is shown to be bounded by [he convex hull of 2R points (R being the number of error-ridden exogenous variables), lying on the surface of the ellipsoid. The results are applied to an empirical example and extensions to a simultaneous equa[ions system are briefly discussed.

Panel data analysis of U.S. coal productivity

“…For these reasons, we focus on labor productivity of individual mines, and develop methods that take into account heterogeneity in the data. 4 We model labor productivity separately for groups of mines de¯ned by regional location and overall type of technology. Mine-speci¯c¯xed e®ects are included to further capture the myriad of heterogeneous features (geology and di®erent types of capital con¯guration), and time e®ects are included to capture group-wide productivity variation.…”

“…Coal output is measured in clean short tons, and for aggregating 4 We discuss many of the salient aspects of our data below. See Ellerman, Stoker and Berndt (1999) for more details on the construction of our data.…”

Bounding parameters in a linear regression model with a mismeasured regressor using additional information

“…Bekker et al (1987) discuss the case of errors in regressors and the regression error being correlated. Iwata (1992) and Pratt (1986, 1987) show that bounds on these correlations may help find bounds on parameters of interest.…”

“…It has been shown that no informative bounds on the parameters of interest exist when measurement error is correlated with both the latent regressor and the error of the regression (Krasker and Pratt, 1986;Bekker et al, 1987;Erickson, 1989). Therefore, additional information is needed to find the bounds on the parameters of interest.…”

Chapter 24. Handling the Measurement Error Problem by Means of Panel Data: Moment Methods Applied on Firm Data

“…Even under non-identification, bounds on the parameters can be established from the distribution of the observable variables [see Fuller (1987, p. 11)]. These bounds may be wide or narrow, depending on the covariance structure of the variables; see, e.g., Klepper and Leamer (1984) and Bekker et al (1987). 2 The last two assumptions are stronger than strictly needed; time invariance of E(α i v it ) and E(α i u it ) is sufficient.…”