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

Acknowledgements: I thank Harald Goldstein and Bernt P. Stigum for helpful
comments, which led to improvement in the organization of the paper. The usual
disclaimer applies.

Notes

¹ Identification under non-normality of the true regressor is, however, possible by utilizing
moments of the distribution of the observable variables of order higher than the second [see
Reiers0l (1950)]. Even under non-identification, bounds on the parameters can be established
from the distribution of the observable variables [see Fuller (1987, p. 11)]. These bounds may
be wide or narrow, depending on the covariance structure of the variables; see, e.g., Klepper and
Leamer (1984) and Bekker et al. (1987).

²The last two assumptions are stronger than strictly needed; time invariance of E(α_iv_it) and
E(α_iu_it) is sufficient. A modification to this effect will be of minor practical importance, however.

³ Premultiplication of (4) by d_tθ is not the only way of eliminating αi .Any(1× T ) vector
c_tθ such that c_tθ e_T = 0, for example the rows of the within individual transformation matrix
I_T - e_T e_T⁰ /T , where I_T is the T dimensional identity matrix, has this property.

⁴ Here and in the following plim always denotes probability limits when N goes to infinity and
T is finite.

⁵We report no standard error estimates in Table 24.1, since some of the methods are inconsis-
tent.

⁶ The OC’s involving y’s can be treated similarly. Essential and redundant moment conditions
in the context of AR models for panel data are discussed in, inter alia, Ahn and Schmidt (1995),
Arellano and Bover (1995), and Blundell and Bond (2000). This problem resembles, in some
respects, the problem for static measurement error models discussed here.

⁷ All numerical calculations are performed by means of procedures constructed by the author
in the GAUSS software code.

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