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



5.a Additional assumptions

Our additional assumptions with respect to the errors and disturbances are the
non-autocorrelation assumptions:

Assumption (B1):


E(vi0tv)=0KK,t6= θ,


Assumption (C1):         E(uitu)=0,       t6= θ.

Sometimes, the following weaker assumptions, allowing for some autocorrelation,
will be sufficient:

Assumption (B2):

E(vi0tv)=0KK,

t — θ > τ.

Assumption (B3):

E(vi0tv) is invariant to t, θ,

t 6= θ,

Assumption (C2):

E(uitu) = 0,

t — θ

Assumption (C3):

E(uitu) is invariant to t, θ,

t 6= θ,

of which (B2) and (C2) allow for a (vector) moving average (MA) structure up to
order
τ ( 1), and (B3) and (C3) allow for time invariance of the autocorrelation.
The latter will, for example, be satisfied if the measurement errors and the distur-
bances have individual components, say
vit = v1i + v2it , uit = u1i + u2it , where v 1i ,
v2it, u1i, and u2it are independent IID processes.

Our additional assumptions with respect to the distribution of the latent regres-
sor vector
ξit are:

Assumption (D1):

Assumption (D2):

Assumption (E):


E(ξit)

E(αiξit)

rank(E[ξi0p(∆ξitθ)]) = K


is invariant to t,

is invariant to t,

for some p, t, θ different


Assumptions (D1) and (D2) hold when ξit is mean stationary for all i. Assump-
tion (E)
imposes non-IID and some form of autocorrelation or (covariance) non-
stationarity on
ξit . It excludes, for example, the case where ξit has an individual
component, so that
ξit = ξ1i + ξ2it, where ξ1i and ξ2it are independent (vector) IID

processes.

Assumptions (A) - (E) do not go very far in structuring the distributions of
the variables of the model. This has both its pros and cons. It may be possible

13



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