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

fixed effect max aj in each industry is used as a benchmark value that represents the highest
attainable efficiency level. Productive efficiency Ei of firm i is then estimated as:

ʌ       α^

Ei =---ⁱ- ∙ 100 [%]                              (2)

max αj

At least one firm in an industry will meet the benchmark value and the remaining firms will
have positive efficiency estimates between 0 and 100 percent.⁵

Several caveats of the fixed effects approach should be mentioned. First, recent develop-
ments in efficiency measurement provide models that allow the distinction between a firm’s
inefficiency and unobserved heterogeneity (see Greene, 2005). Accordingly, the fixed effects
do not only capture “pure” productive efficiency differences between firms but also other (un-
observed) differences, such as diverging management or marketing strategies. However, for our
sample of approximately 39,000 firms, Greene’s approach is computationally too demanding.⁶
Second, because prices of inputs and outputs are not available at the firm level, we do not mea-
sure a pure input-output quantity relationship with the production function, since all inputs as
well as the output are measured in monetary terms. Accordingly, the estimated fixed effects in-
dicate not only that at a given level of inputs some firms produce higher output than others, but
also that some firms can obtain higher market prices for their output, or benefit from lower input
prices. Our interpretation of this measurement issue is that the fixed effects also measure a type
of price efficiency of firms. However, we are confident that using inputs and outputs in monetary
terms is not a major drawback, which is supported by evidence from Mairesse and Jaumandreu
(2005), who find that using a nominal output measure in a production function estimation yields
a quite negligible difference in comparison to using a real output measure. Furthermore, mone-
tary values allow the aggregation of multiple outputs into a single output measure as well as the
aggregation of different inputs and make aggregation of inputs and outputs of different qualities
feasible, since prices will adjust for those differences.

3.2 Data

Our analysis is based on micro data from the German Cost Structure Census⁷ of Manufactur-
ing for the 1992 to 2005 period (see Fritsch, Gorzig, Hennchen and Stephan, 2004). The Cost
Structure Census is gathered and compiled by the German Federal Statistical Office (Statistis-

⁵Note that in the second step analysis the fixed effects are not expressed relatively to the maximum fixed effect
in the respective industry, since this would affect the scale of the estimated industry effects. All other results remain
unchanged when absolute instead of relative fixed effects are used in the regression analysis.

⁶One further shortcoming of the “true” fixed effects stochastic frontier model is that it leads to biased parameter
estimates and biased estimates of productive efficiencies for panels with relatively few observations, as in our case
(cf. Greene, 2005).

⁷Aggregate figures are published annually in Fachserie 4, Reihe 4.3 of the German Federal Statistical Office
(various years).

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