year means, with IV’s in differences. If we use the non-adjusted equation in levels
with IV’s in differences, the GMM estimates tend to be less than one. For capital,
the picture is less clear. Overall, there is a considerable difference between the
elasticity estimates of materials and those of capital. An interpretation we may give
of this difference is that the underlying production technology is non-homothetic;
cf. Section 2.
7 Concluding remarks
In this paper, we have constructed and illustrated several estimators which may
handle jointly the heterogeneity problem and the measurement error problem in
panel data. These problems may be untractable when only pure (single or repeated)
cross section data or pure time series data are available. The estimators considered
are estimators operating on period specific means, inter alia, the between period
(BP) estimator, and Generalized Method of Moments (GMM) estimators. The
GMM estimators use either equations in differences with level values as instruments,
or equations in levels with differenced values as instruments. In both cases, the
differences may be taken over one period or more.
In GMM estimation, not only instruments constructed from the observed re-
gressors (x’s), but also instruments constructed from the observed regressands (y’s)
may be useful, even if both are, formally, endogenous variables. Our empirical ex-
amples - using materials and capital input data and output data for firms in a
single regressor case - indicate that for both normalizations of the equation, GMM
estimates using y instruments tend to exceed those using x instruments. Even if
the GMM estimates, unlike the OLS estimates, are consistent, they seem to some
extent to be affected by the ‘attenuation’ known for the OLS in errors-in-variables
situations. Using levels as instruments for differences or vice versa as a general es-
timation strategy within a GMM framework, however, may raise problems related
to ‘weak instruments’; cf. Nelson and Startz (1990) and Staiger and Stock (1997).
It is left for future research to explore these problems, e.g., by means of Monte
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