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

E( vi,t^uiθ ) = 0 K1,

E( ^ξit^uiθ ) = 0 K1,

^< E(^ξiθ ® vit) = 0KK,

E(^αivit) = 01K^,

E( ^αiuit ) = 0^,

where 0_mn denotes the (m×n) zero matrix and ® is the Kronecker product operator.

We can eliminate α_i from (3) by taking arbitrary backward differences ∆y_itθ =
yit — yiθ = dtθyi∙, ∆Xitθ = Xit - Xiθ = dtθXi∙, etc., where d_tfi is the (1 × T) vector
with element t equal to 1, element θ equal to -1 and zero otherwise. Premultiplying
(4) by d_tθ , we get³

(5)             ∆ Vi,_β = ∆ Xi,_β β + ∆ ⅛,.   t = 2 .....T ; θ =1 ,...,t-1.

In the next section, we present an interpretation of this model framework based
on production theory and a panel of manufacturing firms. In the following sec-
tions, we describe the estimation methods and introduce the additional assumptions
needed. Two kinds of estimation methods will be in focus: (i) Methods operating
on period means, illustrating applications of the repeated measurement property of
panel data (Section 3), and (ii) Generalized Method of Moments (GMM) procedures
(Sections 4-6). The GMM procedures involve a mixture of level and difference
variables and are of two kinds: (a) The equation is transformed to differences, as
in (5), and is estimated by GMM, and as instruments we use level values of the
regressors and/or regressands for other periods. (b) The equation is kept in level
form, as in (3), and is estimated by GMM, and as instruments we use differenced
values of the regressors and/or regressands for other periods. Our (a) procedures
extend and modify procedures proposed in Griliches and Hausman (1986), Wans-
beek and Koning (1991), Arellano and Bover (1995), Bi0rn (1992, 1996), Bi0rn and
Klette (1998, 1999), and Wansbeek (2001).

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