298 J. Roy
Ta b le 1 .Characterisation of the two approaches selected for implementationAggregated Disaggregated
Aggregation of data High Low
Estimation technique Theoretical distributions Monte Carlo Simulation
Depth of historical data 25 years 7 years
Horizon for projection 1 year – static 15 years – dynamicwas obtained, then an analysis would have to be conducted to understand the sources
of differences and eventually decide on which approach seems more reliable. The
next two sections will describe the implementation and the results obtained under the
two approaches.
4 The aggregated approach
Under this approach, the aggregate demand for subsidies by the credit unions will be
estimated using 25 historical observations of the aggregate rate of subsidy defined as
the sum of the subsidies for the year divided by the total assets of the credit unions
at the beginning of the year. Three theoretical distributions were selected, namely
the Weibull, the Gamma and the Lognormal. Each of these distributions was fitted to
the historical cumulative distribution of the rate of subsidy. These three distributions
have some common features: they are characterised by two parameters and they
accommodate asymmetry.
Before providing the results of the estimation process, it is appropriate to mention
that this approach implies two strong hypotheses. First, one must assume that the de-
mand for subsidy has had and will continue to have a distribution that is stable in time.
This is indeed a strong assumption as both internal and external structural conditions
have evolved significantly. Internally, a strong consolidation of credit unions has taken
place which resulted in more than halving their total number giving rise to bigger and
hopefully stronger units. Externally, the monetary policy of the Bank of Canada has
changed over the years and the strong emphasis now put on the control of inflation
will avoid the high nominal interest rates that took place in the early 1980s and which
generated massive credit problems. Second, this approach also assumes implicitly
that there is no serial correlation, which is most likely contrary to reality as there
were clearly periods of good times and bad times that extended over several years.
Overall, the first assumption points to overestimating the current demand, whereas
the second may lead to underestimating demand in extended periods of difficulties.
One may hope that the net effect of the two biases is small. Finally, the depth of the
historical data allows the inclusion of two periods of difficulties, which may represent
other unknown difficulties that may arise in the future.
With these considerations in mind, we estimated the parameters of the three distri-
butions using non-biased OLS; the results are shown in Table 2 together with various
statistics. Overall, the statistics seem to show a reasonably good fit of the distributions