errors, clearly illustrate the attenuation effect. They have, however, different degree
of robustness. While βOLS is neither robust to firm specific heterogeneity nor to
trend effects, βWF and βOLSD are robust to firm specific heterogeneity (which is
potentially correlated with the regressand or the regressor), but not robust to trend
effects, and βOLSDC and βWFDC are robust to both firm specific heterogeneity and
a linear trend. For materials, unlike capital, βOLSD , βOLSDC , and βWFDC give
fairly equal estimates in all sectors.
Although these examples show that it is possible to construct consistent esti-
mators, which give estimates of reasonable size (at least for materials), from period
means, their efficiency may be low, since they do not exploit any inter-individual
variation in the data, and the latter often tends to dominate. Therefore there is
a potential to improve the estimation by considering methods which utilizes this
inter-individual variation. One such method is the GMM.
4 The principle of GMM estimation
Before elaborating the GMM procedures for our panel data situation, we de-
scribe some generalities of this procedure, referring to, e.g, Davidson and MacKin-
non (1993, Chapter 17) and Harris and Matyas (1999) for more detailed expositions.
Assume, in general, that we want to estimate the (K × 1) coefficient vector β in
the equation
(18) y=xβ+,
where y and are scalars and x isa(1× K) regressor vector. There exists an instru-
ment vector z, of dimension (1 × G), for x (G ≥ K), satisfying the orthogonality
conditions
(19) E(z0)=E[z0(y-xβ)]=0G,1.
These conditions are assumed to be derived from the economic theory and the
statistical auxiliary hypotheses (e.g., about disturbance/error autocorrelation) un-
derlying our model. We have n observations on (y, x, z), denoted as (yj , xj , zj),j =
10