time passes, the system could drive itself towards a critical state, on the edge
between stability and instability.
Once in this critical state, for each increase in monetary base we could see a
final increase in the monetary aggregate M of any size. At times, the process of
money creation would end soon, when money reaches an agent that is below its
threshold and therefore hoards the additional money he receives; but at times
the process could spread out and generate an avalanche, if many nodes involved
reach their own threshold and pass along money to others.
This interpretation could provide a good explanation of the variability ob-
served in the multiplier, and if the analogy with the sandpile model is correct,
the size of monetary cascades should be distributed according to a power-law.13
14
We now turn to data to see if a power law characterizes the size of the
multiplier. In this respect, there are a number of issues to keep in mind. First,
the central bank does not "drop" monetary base constantly and regularly in
fixed amounts in the economy; secondly, the temporal scale is such that different
avalanches may overlap, as there is no guarantee that the time between one
central bank intervention and the next is enough for the system to fully respond
and adjust to the first intervention; third, we have data available at regularly
intervals (bi-weekly or monthly), but an avalanche of money may take different
lengths of time to reach its full extent at different times; finally, we detrend the
multiplier, as its trend is likely to derive from long-run changes in behaviours
that we do not try to explain here and want to abstract from.15 Having all
these limitations in mind, we test for the presence of a power law in the size
distribution of the multiplier.16 Fig. 7 (in a log-log scale) shows the best fit of
the estimated Pareto distribution for the right tail (dashed-dotted line) with the
vertical dotted line showing the point from which the Pareto distribution has
been identified. Out of the 568 observations available (bi-weekly data for US,
February 1984-November 2005),17 only 157 were identified to be distributed
according to a power-law, and the estimated coefficient is 2.55.
According to this test, the evidence for a Pareto distribution in the data for
13A feature that is crucial in the sandpile model is the dispersion of the sand involved in
the avalanche. In the monetary system, of course, there is no dispersion of money, so that the
"pile" of money keeps growing in absolute size, but the relative size with respect to deposits,
that is what matters here, remains constant.
14While earlier studies of the sandpile model were done using a regular lattice to repre-
sent the interactions among sand grains, Goh et al (2003) study the avalanche dynamics of
the sandpile model on a scale-free network with heterogeneous thresholds and find that the
avalanche size distribution still follows a power law.
15The series is detrended using the Hodrick-Prescott filter.
16We apply a procedure that first tests for the presence of a Pareto distribution in the
data, identifies a region that with a 95% confidence interval follows such a distribution and
then applies bootstrapping techniques to find the Hill estimator for the coefficient of the
distribution.
17We also applied the same procedure to a constructed series for the multiplier, obtained as
the ratio between the monetary aggregate M1 and the monetary base, using US monthly data
for the period 01/1959-08/2006, with the resulting multiplier then detrended using the HP
filter. We obtained similar results in terms of the proportion of data appearing to be Pareto
distributed, though the estimate for the coefficient was lower, about 2.25.
10