5. New Keynesian Framework
5.1. Dynamic IS Curves
It is straightforward to derive the dynamic IS curves for both countries by log-linearizing the domestic
intertemporal Euler equation for real consumption (18) and its foreign analog around the non-stochastic
zero-inflation steady state as shown in Appendix A.4. Accordingly, one obtains:18
yt = Et[yt+1] + 1 {Et[∏t+1] -'it}- (1 - n)Et[∆tt+1], (39)
ρ
У* = Et[y*+1] + p{Et[∏t*+ι] — !*} + nEt[∆tt+1]• (40)
These two dynamic IS curves represent aggregate demand in both countries, where (39) can be interpreted
as follows: current domestic demand is higher than its zero-inflation steady-state value if the expected
domestic output deviation Et[yt +1] is positive (interpretable as an expected boom at home). There is also
a clear positive relation of current demand to expected CPI inflation Et[πt+1] (households consume more
today if prices are expected to augment in the future) and a negative relation to current deviations from
the zero-inflation steady-state nominal interest rate it (investing in nominal bonds is relatively attractive
compared to buying consumption goods).
Moreover, there are also spill-over effects from abroad, which affect current domestic demand through
expected movements in the TOT Et [∆tt+1]: current domestic demand negatively depends on an expected
increase in the TOT since TOT expected to augment mean that imported goods become more expensive
relative to domestic goods.19 1 - n denotes the degree of openness of the home country to the foreign
country (see Gall 2008, pp. 155-156). Since the degree of openness coincides with the size of the foreign
country due the definition of the domestic CPI (2), there is no home bias in consumption, different to
what is discussed in Pappa (2004, pp. 770-771).
Note that an analogous interpretation for (40) also holds abroad.
It may also be useful to introduce the domestic real interest rate r, which can be obtained via the Fisher
relation:
Et[Pt+1]
(1 + it ) = ---p--- (1+ rt ) ,
Pt
whose log-linear version reads
it = Et[πt+1] + rt. (41)
Note that an analogous equation to (41) also holds for the foreign real interest rate r*.
Note further that i = i* = r = r* = (1 — β)/β denotes the zero-inflation steady-state nominal and
real interest rates, both at home and abroad, which can easily be obtained by solving the zero-inflation
steady-state version of the domestic intertemporal Euler equation for real consumption (18) and its foreign
analog for i and i*, respectively (C-ρ = Et [Ct+ρ1] = C-ρ, Pt = Et [Pt+1] = P).
5.2. New Keynesian Phillips Curves
The NKPCs for both countries can be derived by log-linearizing the price-setting equations of domestic
and foreign firms around the non-stochastic zero-inflation steady-state as shown in Appendix A.5. In
order to obtain the short-run ”trade-off” between PPI inflation and the output gap represented by a
18Note that except for all types of interest rates, lower-case Latin letters denote natural logarithms of the corresponding
variables. The hats above these log variables signify, except for all types of interest rates, percentage deviations from
their zero-inflation steady-state values. In case of any interest rate these hats denote deviations measured in percentage
points. The zero-inflation steady-state values themselves are denoted by upper bars.
19The TOT are expected to increase over time if either the domestic currency is expected to depreciate or if expected
foreign PPI inflation will be higher than expected domestic PPI inflation, where these rates of inflation will be discussed
below in more detail.
13