have the fewer observations): Non-rejection of the OC’s when using the x’s as IV’s
(cf. χ2(βLx) in rows 1) and the y’s as IV’s (cf. χ2(βLy) in rows 2) - i.e., the output
variable in both cases - and rejection when using the y’s as IV’s in the materials-
output regression and the x’s as IV’s in the output-materials regression - i.e., the
material input variable in both cases. For capital, the orthogonality test statistics
once again come out with very low p values in all cases, which may again reflect
mis-specified dynamics or trend effects. There is, however, a striking difference
between Tables 24.3 and 24.4. In Table 24.3 - in which we make no adjustment
for non-stationarity in means and impose (D1) - we find uniform rejection of the
OC’s for capital in all sectors and for Wood Products and Paper Products for ma-
terials. In Table 24.4 - in which we make adjustment for non-stationarity in means
by deducting period means from the level variables and relax (D1) - we find non-
rejection when using output as instrument for all sectors for materials (p values
exceeding 5 %), and for capital in all sectors except Textiles and Wood Products (p
values exceeding 1 %). Note that the set of orthogonality conditions under test in
Tables 24.3 and 24.4 is larger than in Table 24.2, since it also includes Assumption
(D2), time invariance of the covariance between the firm specific effect αi and the
latent regressor ξit .
These estimates for the level equation, unlike those for the differenced equation
in Table 24.2, however, do not uniformly give marginal input elasticity estimates
of materials greater than one. Using level observations measured from year means
(Table 24.4) and relaxing mean stationarity of the latent regressor, we get esti-
mates exceeding one, while using untransformed observations and imposing mean
stationarity, we get estimates less than one. There are also substantial differences
for capital.
A tentative conclusion we can draw from the examples in Tables 24.2 - 24.4
is that overall GMM estimates of the input elasticity of materials with respect
to output tend to be larger than one if we use either the equation in differences
with IV’s in levels or the equation in levels, measuring the observations from their
25
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