What Drives the Productive Efficiency of a Firm?: The Importance of Industry, Location, R&D, and Size

homothetic production technology; that is, the marginal rate of technical substitution is homo-
geneous of degree zero with regard to inputs. Third, given homotheticity and because the test
ofH0 that ∑β=1 yields a p-value of 0.89, we conclude that the estimated technology is linearly
homogeneous.¹⁴

Output elasticities can be calculated from the translog estimates using the formula σyi =
^{d l}ny∕∂ ln x_i = ^βi + ^в2_i ^lnxi ⁺ ∑ βij lnxj. The output elasticities at different values of produc-
i= j

tion inputs (1, 5, 25, 50, 75, 95, and 99 quantiles) are shown in Table 2. Note that they all add
up to about unity and are not very different from median production shares of production inputs
as reported in Table A.1 in the data appendix, exactly what one would expect according to neo-
classical theory (Chambers, 1988). This is further support for the plausibility of our production
function estimates.¹⁵

Table 2: Output elasticities of input factors at different input levels

Input factor                                Output elasticity at input level

Notes: p1, p5, p95 and p99 are the 1^st , 5^th, 95^th, and 99^th percentiles, respectively; Q1 and Q3 are lower and
upper quantiles.

Comparing the output elasticities at different hypothetical scales of production tells us a few
more things about production technology. First of all, the sum of elasticities is never statistically
different from one. This is because the elasticities are obtained from parameter estimates that
are in accordance with a homothetic production function. Second, as the input scale increases,
the marginal products of labor and capital are decrease, whereas the marginal productivity of
the material (intermediates) is increases, thus making the substitution of labor and capital by
material more profitable. This implies that the larger the scale ofa firm in terms of its inputs, the
more profitable it is for the firm to rely on intermediate inputs. Note that the elasticity gradually
increases from 0.194 for the first percentile of the input value to 0.470 for the 99th percentile.
This finding is in line with evidence from previous studies that large manufacturing firms, in
particular, have increased their outsourcing intensity in recent years (Gorzig and Stephan, 2002).

¹⁴The sum of single input estimates is 0.9945 with a standard error of 0.01691.

¹⁵As an alternative to a single production function for all industries we also estimated industry-specific translog
function at the 3- and 4-digit level respectively, but obtained less satisfactory results, e.g. negative output elasticities
or returns to scale significantly outside the range [0.5, 1.5]. Given that the common production function estimation
over all industries yields plausible results, we are convinced that this approach is appropriate.

<<   <   9   10   11   12   13   14   15   >   >>