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



Hence, provided that E[(∆sξ.t)0(∆sξ.t)] and E[(ξ.t ξ)0(ξ.t ξ)] have rank K,
consistent estimators of β can be obtained by applying OLS on (12) or on (13),
which give, respectively,

(16) βbs =


(17) βbBP =


T

X (δsXt) 0 (δsXt)


t=s+1


T

Σ(xt- x) 0(xt- x)

t=1


T

X (δsXt) 0 (δsy-t)

t=s+1


-1 T


Σ(x t

t=1


- x) 0(yt - y)


s=1,...,T1,


The latter is the ‘between period’ (BP) estimator. The consistency of these esti-
mators simply relies on the fact that averages of a large number of repeated mea-
surements of an error-ridden variable give, under weak conditions, an error-free
measure of the true average at the limit,
provided that this average shows variation
along the remaining dimension, i.e., across periods
. Basic to these conclusions is
the assumption that
the measurement error has no period specific component. If
such a component is present, it will not vanish when taking plims of period means,
i.e., plim(υ.t) will no longer be zero, (14) and (15) will no longer hold, and so βδs
and βb BP will be inconsistent.

Table 24.1 reports between period estimates of β based on levels (column 2)
and on differences (column 5) - the latter removing the effect of technical changes
represented by a log-linear trend - as well as seven-period difference estimates
(column 7) for the four sectors and the two inputs.
5 Since K = 1 in this application,
the estimators read

βBP


b

βBPDC


∑t(xt - x)(yt - y)
P t ( X t x)2

∑t (∆ x t x)(∆ yt y)
P t (∆ X .t X)2

β∆7 =


y8 y 1


χ8 χ 1


Rows 1 and 3 can be interpreted as estimates of 1 and rows 2 and 4 as estimates
of
μ. This way of running original and reverse regressions in an EIV context can be
related to Frisch’s
confluence analysis [Frisch (1934, sections 5, 10, 11, and 14)], in
which he proposed taking regressions in different directions,
e.g., in the directions



More intriguing information

1. The name is absent
2. Activation of s28-dependent transcription in Escherichia coli by the cyclic AMP receptor protein requires an unusual promoter organization
3. Financial Development and Sectoral Output Growth in 19th Century Germany
4. Auctions in an outcome-based payment scheme to reward ecological services in agriculture – Conception, implementation and results
5. REVITALIZING FAMILY FARM AGRICULTURE
6. Der Einfluß der Direktdemokratie auf die Sozialpolitik
7. Exchange Rate Uncertainty and Trade Growth - A Comparison of Linear and Nonlinear (Forecasting) Models
8. Innovation Policy and the Economy, Volume 11
9. The name is absent
10. The name is absent
11. Quelles politiques de développement durable au Mali et à Madagascar ?
12. TECHNOLOGY AND REGIONAL DEVELOPMENT: THE CASE OF PATENTS AND FIRM LOCATION IN THE SPANISH MEDICAL INSTRUMENTS INDUSTRY.
13. Evolving robust and specialized car racing skills
14. The name is absent
15. Chebyshev polynomial approximation to approximate partial differential equations
16. Stakeholder Activism, Managerial Entrenchment, and the Congruence of Interests between Shareholders and Stakeholders
17. Structural Breakpoints in Volatility in International Markets
18. The name is absent
19. Elicited bid functions in (a)symmetric first-price auctions
20. The name is absent