the order by which agents take part in the process.9
The standard way to represent the multiplier is therefore misleading, as in
that representation the coefficients re and cu are not really behavioural para-
meters, as it may appear by their definitions, but simply ratios of aggregate
quantities.
Note then that equation (9) is valid only when all the money remains in
a unique stream and never gets split into different branches. If we allow each
agent (bank or household) to be connected with more than one counterpart, we
then need to keep track of all the streams of money that get generated, and the
analytic formula becomes intractable.
2.4 Monetary network
We therefore build an artificial economy and try to gain some insights into
the process of money creation by means of simulations. We abstract from any
considerations involving the real side of the economy and only model the struc-
ture of monetary and credit transactions, considering different possible network
topologies at the base of the system and their impact on the multiplicative
process.
The network composed of banks and households is a bipartite network, where
edges exist only between nodes belonging to different classes. In the process
that we describe, each node (bank or household) receives some money from
its incoming links, keeps part of it (as reserves or cash holdings) and passes
along the rest through the outgoing edges. We can uniquely define each node
by its ratio of reserve∕deposit or currency∕deposit, and build two matrices,
one for the links from banks to households (where the edges of this network
represent the flow of credit that banks extend to households), and one for the
links from households to banks (where the edges represent the flow of deposits
from households to banks).
We will consider three different network topologies and try to understand
how they impact on the size distribution of the multiplier: a random graph, a
regular graph and star graph. Other topologies of course could be considered
(e.g., small-world a la Watts and Strogatz or scale-free a la Barabasi), but we
restrict for now to these more common structures.
We start by considering a random network, where banks and households are
assigned random behavioural ratios (cu⅛ and re⅛)10 and are randomly linked
to each other. The system is composed of 5 banks and 100 households, with
each bank receiving money from and extending loans to a random number of
households. We simulate 100 economies and compute for each the average and
the dynamic multiplier. In Fig. 2 we show the distributions (as histograms) of
the two measures. We can see that the variability in the dynamic multiplier is
much higher than in the average one, where the part due to heterogeneity gets
washed out.
9In one of the experiments that we ran, the dynamic multiplier showed a distribution of
values in the interval 1-2.5. Of course ma was instead constant (and equal to 1.06).
10With reð and 1 '” h— uniformly distributed between 0 and 1.
1 —c⅛h