Unfortunately, good measures of the returns to scale, ?, are unavailable at the firm level.
Therefore, in our calculations, we lump together the output growth effect, (1/? -1) ? ln Q,
together with the productivity growth effect to yield a general index of efficiency change.9 It is best
to think of this scale/productivity term as reflecting all changes in unit costs not accounted for by
changes in input prices.10 Only under constant returns to scale, ? = 1, would this term
correspond to the standard productivity effect.
Using this decomposition, we can now explore how changing incentives have led to a
reallocation of resources and increases in productivity. For this purpose, we estimate
simultaneously a supply equation for real output growth and an equation of productivity growth.
The supply equation is specified as follows:
(5) Δ ln(Q) = α + βΔC + τ DUMEXt _1 + p (DUMEXt _1 ΔC) + γ (Δ lnA) + σ Ut_1 + ε i
where ΔC measures the changes in relative costs; DUMEX is a dummy variable that
takes a value 1 if the firms exported in 1993 (more than 10% of their sales for Gabon) and zero
otherwise; ΔlnA is the scale/productivity growth term computed above as a residual of the
decomposition of the sources of growth in unit costs; and Ut-1 is utilization of capacity in 1993.
Output may increase either because of favorable changes in relative prices (output and
input prices), or because of an increase in productivity. In general, we expect firms to increase
9 Also, it should be noted that we take the total rental cost of capital to be 10% of the replacement cost
of the capital stocks or the resale value of the capital stocks, depending on which is reported. (Firms
were given a choice in the interviews.) Past values of capital stock are constructed using investment
series. Obviously these are crude approximations of the conceptually appropriate measures, but since
they only affect the shares of intermediates in total costs, they should not qualitatively change the
results on these variables. Their effect on the productivity residual is less innocuous, however, precisely
because it is a residual.
10 Our assumption that firms frictionlessly adjust all of their factor stocks is unrealistic. Nonetheless,
equation 4 should yield a reasonably good approximation to the effects of relative price changes on unit
production costs. However the productivity effect should be viewed with more caution, since it is inferred
residually as the difference between a number of imperfectly measured variables.
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