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view/download model file: money_supply_and_banking_defaults.nlogo
The model represents a banking system in which customers interact among each other and with the bank, so that they can both deposit in account and borrow money making the money multiplier run. In the system default events could happen, first because of the failure of a specific bank and then of the other ones, conditioned to the first default. These events have effects on the aggregate money quantity.
The "world" of the simulation is divided in nine sectors, each one being related to a particular bank, which a group of customers is assigned to. Every customer has got an equal amount of money (determined by the quantity of money base) and he deposits it in his bank account. When the customers meet each other exchange a money amount, chosen by the user, and they can either take money from the account or borrow as much money as the part of deposit not in the compulsory reserve of his bank.
The amount of loans granted to customers determines, together with their insolvence rate and bank's equity, a default probability for each bank. Particularly, the failure of a specific bank (number 5) makes other banks' default be possible or not (in a conditional way). This process affects money amount in the system.
Start the simulation by clicking "setup". Then, after clicking "go", the turtles start moving and interacting in the way explained above; they keep on doing so until the "go" button remains pressed.
Button: setup
resets everything to the beginning values and releases in the simulated economy a number of turtles wwhich can be chosen using the "turtles_number" slider.
Button: go
if clicked, the model starts running.
Button: go once
if clicked, the model runs once.
Slider: turtles_number
this slider allows you to choose the number of turtles you would like to begin the simulation with.
Slider: money_base
this slider allows you to change the monetary base in the system.
Slider: reserve_ratio
with this slider you can change the reserve ratio fixed by the Central Bank.
Slider: rho
to change the correlation degree between each bank and the bank 5.
Slider: equity
this slider allows you to change the equity amount of each bank.
Slider: customers_default
it allows you to change the customers' default probability.
Slider: default_threshold
with it you can change the threshold over which the bank 5 is considered failed.
Switch: bank5_default?
this switch activates the possibility of bank 5's default.
Switch: conditional_default
it allows other banks' conditional default (only if the bank 5 is already failed).
Monitors: there are two monitors which show the total amount of money supply and the number of bank in default.
Plot: money supply
this plot shows the trend of this variable.
First of all, it is important to notice that the model begins running only if the amount of the exchange is smaller than the initial quantity of loan disponibility. Then, the behaviour of the money supply is not constant in the growth, but depends on the interaction between agents and on their borrowing possibility. Different combinations of loan possibility and amount of exchange make possible the restitution of loan borrowed by customers: if these amounts of money are not taken by other customers the total money supply decreases.
Notice the growth of default possibility as equity declines and rho and customers' insolvence grow up. Besides this, notice that the conditional default probability is always bigger than the non conditional one. This fact leads to many defaults if you consider the conditional aspect, even if the marginal default likelihood is not very significative.
After a first creation of money you can incentivate the recourse to banks' loans by varying the amount of the exchange : particularly, if this value is gradually diminished the model approssimates the result of the economic theory.
You may notice also the effect on the default number and the marginal probability given by the setting of the equity and customers' insolvence rate, and the effect on conditional likelihood given by the setting of rho.
The model could be extended by introducing the curreny and the cash ratio.
O. Blanchard, "Macroeconomics", 3rd edition.
E. Luciano, M. Marena, Course of Mathematical Finance (University of Turin), Lectures notes.