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

1 Introduction and basic model

Panel data are a valuable source of information for theory-data confrontation in
contemporary econometrics. The panel data available are frequently from indi-
viduals, firms, or other kinds of micro units. A primary reason for the strongly
increasing utilization of panel data during the last three decades seems to be the
opportunity which such data offer for ‘controlling for’ unobserved individual and/or
time specific heterogeneity which may be correlated with the included explanatory
variables. As is well known, the effect of individual heterogeneity in a panel data
set relative to a linear equation can be removed by measuring all variables from
their individual means or by operating on suitably differenced data.

Micro data, including panel data, and inferences drawn from such data may,
however, have deficiencies following from measurement errors. Not only observa-
tion errors in the narrow sense, but also departures between theoretical variable
definitions and their observable counterparts in a wider sense may be present. A
familiar property of the Ordinary Least Squares (OLS) in the presence of random
measurement errors (errors-in-variables, EIV) in the regressors is that the slope
coefficient estimator is inconsistent. In the one regressor case (or the multiple
regressor case with uncorrelated regressors), under standard assumptions, the esti-
mator is biased towards zero, often denoted as attenuation. More seriously, unless
some ‘extraneous’ information is available, e.g., the existence of valid parameter
restrictions or valid instruments for the error-ridden regressors, slope coefficients
cannot in general be identified from standard data [see Fuller (1987, section 1.1.3)].¹
This lack of identification in EIV models, however, relates to uni-dimensional data,
i.e., pure (single or repeated) cross-sections or pure time-series. If the variables are
observed as panel data, exhibiting two-dimensional variation, it may be possible to
handle jointly the heterogeneity problem and the EIV identification problem and
estimate slope coefficients consistently and efficiently without extraneous informa-
tion, provided that the distribution of the latent regressors and the measurement
errors satisfy certain weak conditions.

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