5. New Keynesian Framework
4.3. National Labor Markets
Notice from equations (20) and (25) that the real wage differs between consumers and producers because
they use different price indexes. The ratio between real producer and real consumer wage is known as
one type of ”wedge” in Labor Market Economics (see, e.g., Landmann/Jerger 1999, pp. 136-138) and
equals PH /PHn PF1-n = (PH /PF)1-n = Tn-1 in the present set-up.
Nonetheless, by combining (20), (25), and (34) with the CPI (5) one obtains two equations in W/P =
(W/PH)T n-1 which can be solved for L:
Lt = TΓ-1ξ(-1 ( Y ) ~1 μ ^ɪi ) ~1 Y*. (37)
Equation (37) states that in an equilibrium on the perfectly competitive labor market, domestic employ-
ment positively depends on the aggregate productivity shock A and flexible-price real marginal production
cost (θ — 1) /θ, but negatively on the TOT T and domestic output Y.
Note that an analogous equation to (37) also holds abroad.
Combining equation (37) with the production function (21) and solving for Y, one finally obtains the
domestic flexible-price equilibrium output Yflex :
1
n (n-1)(p-1) ξ-1 / θ ∖ ξ-P 1
Ytf = Tt ξ-p At- θ-1-ɪJ Yξ-p.
(38)
The domestic flexible-price equilibrium output positively depends on the aggregate productivity shock
A, yet negatively on the TOT T and the flexible-price mark-up factor θ/(θ — 1).
Note that an analogous equation to (38) also holds abroad.
5. New Keynesian Framework
After having drawn the DSGE set-up and derived optimality conditions for both households and firms
(Section 3) as well as market clearing conditions under flexible prices (Section 4), let us now turn to the
New Keynesian framework. In order to establish such a framework, one has to introduce some form of
nominal rigidity in addition to the assumption of monopolistic competition. In the present case, we will
concentrate on sticky prices and forego sticky nominal wages as done, for instance, by Corsetti/Pesenti
(2001).
Log-linearizing the alternative market clearing and optimality conditions in the neighborhood of a non-
stochastic zero-inflation steady state will lead to a canonical representation of the equilibrium of the model
consisting of a dynamic IS curve, a New Keynesian Phillips curve (NKPC), and some form of monetary
policy rule, both at home and abroad, as well as an equation for the TOT. This makes it possible for
the fully micro-founded New Open Economy Macroeconomic literature to tie in with traditional Open
Economy Macroeconomic models of the Mundell-Fleming-Dornbusch type.
As there are two countries, altogether we will obtain a system of seven log-linear equations. This form
makes the model analytically tractable, especially for empirical applications: Leith/Malley (2007), e.g.,
estimate NKPCs for the G7 economies by using the generalized method of moments (GMM) estimator
based on log-linear equations. Rumler (2007) applies a similar approach for the Euro area countries.17
Finally, the monetary policy rules which will be introduced below shall be different across countries. This
is one of the crucial assumptions of this article.
17In contrast to Corsetti/Pesenti (2001) who present a closed-form solution of their (deterministic) model, the log-linear
approximation used here is considered to be advantageous since the link to empirical applications is immediate.
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