Mt ( it )b = Ptyt, b>0, (2)
using logarithms and the real effective interest rate, r, with perfect prediction, it is
possible to write
lnMt = ln Pt + ln yt - b[ln rt + ln Pt+1 - ln Pt ]. (3)
For simplification sake, it is possible to assume that income, the money supply and the
real interest rate are constant, and then we have the following difference equation for
the price level
ln P 1 - ln(M / y) = ɪ+ [ln P - ln(M / y)] - ln r .
t+1 b l t
(4)
Hence, according to the initial price level, there is an infinite number of possible
trajectories for the previous equation. The usual solution is to assume/choose the initial
price level obtained from
ln P0 = ln(M / y) - In r, (5)
in order to ensure that the price equation does not lead to an explosive trajectory. One of
the critics put forward by Woodford (1994, 1995), is that this choice for the initial price
level has no support on economic theory and it is not derived, for instance, from some
money demand function optimisation.
The point made by LSW is that if consumers are non-Ricardian, and in the context of a
non-Ricardian fiscal regime, the wealth effects should show up through nominal
government debt, with the government budget constraint being then used to determine
a unique price level. Therefore, the proponents of the FTPL defend that the price level is
indeed determined by the government budget constraint,
6 A hypothesis used namely by Cochrane (1999) and Christiano and Fitzgerald (2000).