The name is absent

Empirical CDF

0.9          ...................■........... ■.......................-

0.8     ....................:.. ʃ/.................:.......................-

0.7 -■ ■■..................j√^rj-......................^:.......................-

0.6 ---_:..............√^j. .........................:.......................-

0.5        ...............;........................■.......................-

0.4 --;.....7-∣-............■........................:.......................-

0.3-----7-................:........................:.......................-

0.2    _jf-.................i........................:.......................-

0.1  -■  .....................i........................:.......................-

01--------------------------------i----------------------------------i---------------------------------

1                           1.5                           2                          2.5

Value of the multiplier

Figure 1: Empirical cdf of average (dotted line) and dynamic (solid line) multi-
pliers.

system and interrupts the multiplicative process of money creation. This implies
that heterogeneity is important, and can not be simply averaged out. In fact,
the value of the multiplier computed with (9) is different from the one we would
obtain by using averages of all the reserve∕deposit and currency∕deposit ratios:

n

¹ + n ∑^cu^

ma = —----^h≡^-_k’               (1°)

n                  tv

n V^cm ⁺ ɪ ∑^reb
h=l         b=l

where к is the number of banks and n the number of households in the economy.
Here indexes represent individual banks and households. Under homogeneity
(Vb, re_b = re; Vh, cu_h = cu), (8) = (9) = (1°). But with heterogeneous agents,
this is not in general true, as it can be seen from a simple experiment. We create
1°° different economies, each characterized by 1°°° banks and 1°°° households
with randomly drawn individual ratios and derive the empirical cumulative dis-
tribution function (cdf) for the dynamic multiplier computed using (9) and for
the one computed using averages as in (1°). As can be seen in Fig. 1, the
average multiplier m_a varies over a restricted range of values, as much of the
variability is washed out by the averaging.

When the behavioural parameters are heterogeneous, the value of the dy-
namic multiplier depends, among other things, on the position where the process
starts (for an exogenous intervention, where the CB “drops” the monetary base).
The system is in fact path dependent and the order by which agents take part
in the process becomes relevant. This is confirmed by our simulations when we
compute the dynamic multiplier 1°°° times for the same economy, each time
changing the order by which agents are activated. Results show that the multi-
plier can vary over a wide range of values, for the same economy, depending on

<<   3   4   5   6   7   8   9   >>

More intriguing information