Productivity changes due to changes in scale change are incorporated using Orea’s
(2002) generalisation of the Malmquist index as the contribution to output of the change
in the input mix from one year to the next (equation (6)).
SCIit = exp
K
0.5∑ (εk SFi ) ln(xikt Xxikt 1 )
ik i ikt ikt -1
k=1
(6)
K ∂ ln y
where SFi=(εi-1)/εi , εi =∑ εik and εik =------. The Malmquist index is
k=1 ∂lnxit
computed as the product of each of these components.
The remainder of our analysis focuses specifically on relative efficiency measures. We
hypothesize that a firm’s position relative to other firms in their sub-sector will
influence their decision to either remain as incumbent in the sub-sector, switch or exit.
Firms are likely to remain if they perform well and exit/switch either if they under-
perform relative to the average or find that potential profits elsewhere are attractive. The
sub-sector they switch to may be determined by the average performance of firms in
other sectors. Thus, the following three components of efficiency will influence a firm’s
reallocation decision: (i) the average efficiency level of the sub-sector they are in, (ii)
how well they are doing relative to other firms in that sub-sector, and (iii) the average
efficiency level of the sub-sector they intend (or are considering) moving to.13
3.2 Modelling the reallocation decision
We estimate random effects probit models of the sector switching and exit decisions. A
random effects approach is chosen given that controlling for unobserved heterogeneity
using fixed effects is complicated by the incidental parameters problem (Lancaster,
2000).14 In order to overcome problems associated with measuring productivity in
13 We recognize that the “closeness” of sectors from where a firm switches out of and into is also likely to
impact. There is no simple way given our data to account for this dimension, which is left for future
research. The same goes for trying to measure the cost of switching more generally, which is conceptually
comparable to the transactions costs, which are well known from for example the economic analysis of
agricultural supply response (Heltberg and Tarp, 2002).
14 The binary nature of the dependent variable leads to the incidental parameters problem which prevents
the unobserved heterogeneity from being treated as a fixed effect (Neyman and Scott, 1948). As an
11