IV. Factors Behind Differential - 3

The problem with such simple diagrams
is that the mechanisms through
which the economy reaches one or the
other equilibrium are not fully spelled
out. There are now several theoretical
models in the literature which try to do
that rigorously, and also get away from
the naive informational presumptions
implicit in the diagram. We shall briefly
touch upon the main ideas in a few of
them. Olivier Cadot (1987) has a model
of corruption as a gamble, where every
time an official asks for a bribe in a bilateral
situation, there is a risk of being
reported to and sacked by a superior officer.
The optimal Nash strategy of a
corrupt official is derived under alternative
assumptions about the information
structure. The comparative-static results
show that a higher time discount
rate, a lower degree of risk-aversion,
and a lower wage rate will induce him,
under certain conditions, to be more
corrupt. Then Cadot goes on to introduce
corruption also at the level of the
superior officer who can be bribed (beyond
a certain threshold) to cover up
lower-level corruption. The interaction
of corruption at different hierarchical
levels of administration leads to multiple
equilibria (one with only petty corruption
and the other with more pervasive
corruption), as the probability of
being sacked diminishes with the general
level of corruption in the civil service,
and corruption at each level feeds
on the other. In the rent-seeking litera-

ture also it has been pointed out by
Arye L. Hillman and Eliakim Katz
(1987) that there are extra social costs
when there is a hierarchical structure
such that a lowly customs official is
obliged to pay a part of his take of
bribes to a superior. The usual presumption
of that literature—which is, as
we have seen, in any case questionable—
that bribes used in contesting a
rent do not entail a social cost because
they are only transfers, is seriously vitiated
when one takes into account multitiered
rent-seeking, with the official positions
to which the bribes accrue are
themselves contested with real resources.
Andvig and Karl O. Moene (1990) in
their model assume, as in Cadot (1987),
that the expected punishment for corruption
when detected declines as more
officials become corrupt, because it is
cheaper to be discovered by a corrupt
rather than a noncorrupt superior.
There is a bell-shaped frequency distribution
of officials with respect to their
costs of supplying corrupt services. On
the demand side the potential bribers’
demand for corrupt services decreases
as the bribe size increases and as the
fraction of officials who are corrupt decreases
(raising the search cost for a potential
bribee). This model generates
two stable stationary equilibria of the
Nash type and highlights how the profitability
of corruption is positively related
to its frequency and how temporary
shifts may lead to permanent
changes in corruption.