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

The estimators β^b_Dx and βe_Dx can be modified by extending x_i(t,t-1) to (x_i(t,t-1) :
y_i⁰_(t,t-1)) and xit to (x_it : y_it) in (41), also exploiting Assumption (C1) and the
OC’s in the y’s. This is indicated be replacing subscript Dx by Dy or Dxy on the
estimator symbols.

Table 24.2 contains, for the four manufacturing sectors and the two inputs, the
overall GMM estimates obtained from the complete set of differenced equations.
The standard deviation estimates are computed as described in the Appendix.⁷ The
estimated input-output elasticities (column 1, rows 1 and 3) are always lower than
the inverse output-input elasticities (column 2, rows 2 and 4). This ‘attenuation
effect’, also found for the OLS estimates (cf. Table 24.1), agrees with the fact
that β^b _Dx and β^b _Dy can be interpreted as obtained by running standard 2SLS on
the ‘original’ and on the ‘reverse regression’ version of (40), respectively. Under
both normalizations, the estimates utilizing the y instruments (column 2) tend to
exceed those based on the x instruments (column 1). Using the optimal weighting
(columns 4 and 5), we find that the estimates are more precise, according to the
standard deviation estimates, than those in columns 1 and 2, as they should be. The
standard deviation estimates for capital are substantially higher than for materials.

Sargan-Hansen orthogonality test statistics, which are asymptotically distributed
as χ² with a number of degrees of freedom equal to the number of OC’s imposed
less the number of coefficients estimated (one in this case) under the null hypothesis
of orthogonality [cf. Hansen (1982), Newey (1985), and Arellano and Bond (1991)],
corresponding to the asymptotically efficient estimates in columns 4 and 5, are re-
ported in columns 6 and 7. For materials, these statistics indicate non-rejection of
the full set of OC’s when using the x’s as IV’s for the original regression (rows 1)
and the y’s as IV’s for the reverse regression (rows 2) - i.e., the output variable
in both cases - with p values exceeding 5%. The OC’s when using the y’s as IV’s
for the original regression and the x’s as IV’s for the reverse regression - i.e., the
material input variable in both cases - is however rejected. For capital the tests
come out with very low p values in all cases, indicating rejection of the OC’s. This

22

<<   20   21   22   23   24   25   26   >>

More intriguing information