In order to illustrate how FDH works, the Manufacturing Industry
Productivity Database from the National Bureau of Economic
Research (NBER), USA is considered. This database is downloadable
from the website of NBER [http://www.nber.org]. It contains annual
industry-level data on output, employment, payroll, and other
input costs, investment, capital stocks, and various
industry-specific price indices from 1958 on hundreds of
manufacturing industries (indexed by 4 digits numbers) in the
United States. We selected data from the year 1996 (458 industries)
with the following 4 input variables, , and 1 output variable,
(summary statistics are given in Table 12.5):
Table 12.6 summarizes the result of the analysis of US
manufacturing industries in 1996. The industry indexed by 2015 was
efficient in both input and output orientation. This means that it
is one of the vertices of the free disposal hull generated by the
458 observations. On the other hand, the industry 2298 performed
fairly well in terms of input efficiency (0.96) but somewhat badly
(0.47) in terms of output efficiency. We can obtain the efficient
level of inputs (or outputs) by multiplying (or dividing) the
efficiency score to each corresponding observation. For example,
consider the industry 2013, which used inputs
,
,
, and
to yield the output
. Since its FDH input efficiency score was 0.64,
this industry should have used the inputs
,
,
, and
to produce the observed
output
. On the other hand, taking into account that the FDH output
efficiency score was 0.70, this industry should have increased its
output upto
with the observed level of inputs.