Handling the measurement error problem by means of panel data: Moment methods applied on firm data

Briefly, the reason why the existence of variables observed along two dimensions
makes the EIV identification problem more manageable, is partly (i) the repeated
measurement property of panel data - each individual and each period is ‘replicated’
- so that the effect of measurement errors can be reduced by taking averages, which,
in turn, may show sufficient variation to permit consistent estimation, and partly
(ii) the larger set of other linear data transformations available for estimation.
Such transformations may be needed to compensate for uni-dimensional ‘nuisance
variables’ like unobserved individual or period specific heterogeneity, which are
potentially correlated with the regressor.

From the panel data literature disregarding the EIV problem we know that
the effect of, say, additive (fixed or random) individual heterogeneity within a
linear model can be eliminated by deducting individual means, taking differences
over periods, etc. [see Hsiao (1986, Section 1.1) and Baltagi (2001, Chapter 2)].
Such transformations, however, may magnify the variation in the measurement er-
ror component of the observations relative to the variation in the true structural
component, i.e., they may increase the ‘noise/signal ratio’. Data transformations
intended to ‘solve’ the latent heterogeneity problem may then aggravate the EIV
problem. Several familiar estimators for panel data models, including the fixed
effects within-group and between-group estimators, and the random effects Gen-
eralized Least Squares (GLS) estimators will then be inconsistent, although to a
degree depending, inter alia, on the way in which the number of individuals and/or
periods tend to infinity and on the heterogeneity of the measurement error process.
See Griliches and Hausman (1986) and Bi0rn (1992, 1996) for examples for one
regressor models.

If the distribution of the latent regressor vector is not time invariant and the
second order moments of the measurement errors and disturbances are structured
to some extent, several consistent instrumental variables estimators of the coeffi-
cient of the latent regressor vector exist. Their consistency is robust to correlation
between the individual heterogeneity and the latent regressor. Serial correlation

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