TWO-COUNTRY STOCK-FLOW-CONSISTENT MACROECONOMICS USING A CLOSED MODEL WITHIN A DOLLAR EXCHANGE REGIME. A complex, but still elementary model. The simplifying assumptions are enormous. There is no domestic or foreign investment in fixed or working capital
Yet the model contains nearly 90 equations!
The net worth of the US central bank has to be zero (all profits are distributed
to government, and the price of gold in dollars is assumed constant).
The net worth of the Japan central bank may become positive, because
The central bank can achieve a capital gain when the $ currency
Appreciates, that is when the number of yens per dollar xr$ goes up
B##d = V#e.(10 + 11.r# - 12.(r$ + dxr$e) - 13.YD#e/V#e)
B#$d = V#e.( 20 - 21.r# + 22.(r$ + dxr$e) - 23.YD#e/V#e)
H#d = V#e.( 30 - 31.r# - 32.(r$ + dxr$e) + 33.YD#e/V#e)
dxr$e is the expected rate of change
reserves = (Bcb#$d) + (or#.pg#)
= (xr$.Bcb#$s) + (or#.pg#)
= Bcb#$s.xr$ + xr$.Bcb#$s-1
+ or#.pg# + pg#.or#-1
The terms on the right are capital gains.
Similarities currency, which the Japanese central bank acquires, is:
There are no Rules of the game: the money stock does not change
A twin surplus arises in the steady state
There is a compensation mechanism at work: the rise in CB reserves is compensated by the fall in domestic credit
The current account surplus and the govt budget surplus are not constant anymore
They both grow at the rate of the interest rate
In the case of the deficit country, the US, there is no limit to this process: there is no fall in the Fed reserves, since the US dollar is the international currencyComparision with simplest model
the current account balance, which goes back towards zero