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

or non-stationarity of the latent regressor is favourable from the point of view of
identification and estimability of the coefficient vector. Briefly, there should not be
‘too much structure’ on the second order moments of the latent exogenous regres-
sors across the panel, and not ‘too little structure’ on the second order moments
of the errors and disturbances; see Bi0rn (2000, section 2.b).

The focus of this paper is on the estimation of linear, static regression equations
from balanced panel data with additive, random measurement errors in the regres-
sors by means of methods utilizing instrumental variables (IV’s). We consider a
data set with N (≥ 2) individuals observed in T (≥ 2) periods and a relationship
between y (observable scalar) and a (1 × K) vector ξ (latent),

(1)           y_it = c+ξ_itβ+α_i+u_it,i=1,...,N; t =1,...,T,

where (y_it, ξ_it) is the value of (y, ξ) for individual i in period t, c is a scalar constant,
β isa(K × 1) vector and α_i is a zero (marginal) mean individual effect, which
we consider as random and potentially correlated with ξ_it , and u_it is a zero mean
disturbance, which may also contain a measurement error in y_it . We observe

(2)                   x_it = ξ_it + v_it,      i=1,...,N; t =1,...,T,

where v_it is a zero mean vector of measurement errors. Hence,

(3)                     y_it = c+x_itβ+_it,_it = α_i+u_it -v_itβ,

or in vector form,

⁽⁴⁾ yi∙ = ^eT^{c +} Xi∙ ^{β + e}i∙, ^ei∙ = ^eT^αi ⁺ ui∙ ^- Vi∙ ^{β, i} = 1 ,---,N,

where y_i∙ = (y_i 1,... ,y_iT) 0, X_i. = (xi₁,..., xT) 0, etc., and e_τ is the (T × 1) vec-
tor of ones. We denote _it as a composite error/disturbance. We assume that
(ξ_it ,u_it , v_it ,α_i) are independent across individuals [which excludes random period
specific components in (ξ_it, u_it, v_it)], and make the following basic basic orthog-
onality assumptions, corresponding to those in the EIV literature for standard

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