Macroeconomic Interdependence in a Two-Country DSGE Model under Diverging Interest-Rate Rules



3. New Open Economy Macroeconomic Model

Benigno/Benigno (2006) contribute to the literature as they manage to show that it is possible
to design ”specific targeting rules” for non-cooperating central banks, which have the property to
assign the incentive to independent central banks to replicate the cooperative allocation such that
possible welfare losses from non-cooperation can be avoided.

There are also numerous articles dealing with small open economy DSGE models such as, e.g., Clarida
et al. (2001) or Gail/Monaceiii (2005), where the model of the latter coincides with the one discussed
in Gall (2008, chapter 7). Nonetheless, some of their features are useful for two-country frameworks,
too, such that these articles shall also be briefly summarized.

Clarida et al. (2001) show that the log-linear representation of a small open economy is isomor-
phic to a closed economy since all structural equations of the small open economy are identical
to their closed-economy counterparts, except that they are related to the terms of trade. As a
result, the policy problem of the small open economy is isomorphic to the policy problem of the
closed economy. Moreover, also the optimal monetary policies under discretion as well as under
commitment are analogous to the closed-economy case, but they affect the terms of trade.

GAll/MonACeill (2005) explore the size of welfare losses of suboptimal monetary policies com-
pared to the benchmark case of optimal monetary policy, which is associated with the complete
stabilization of the output gap and producer prices. The suboptimal monetary policies under
scrutiny are a (stylized) producer price inflation-based Taylor rule, a (stylized) consumer price
inflation-based Taylor rule and a credible peg of the nominal exchange rate. The authors find that
the producer price inflation-based Taylor rule features the lowest welfare losses, followed by the
consumer price inflation-based Taylor rule and the peg of the nominal exchange rate.

In GAll (2008, chapter 8) one can find possible extensions to the basic, closed-economy New Keynesian
framework, which might also be intriguing to open economy researchers.

3. New Open Economy Macroeconomic Model

The subsequent model is based on the Obstfeld/Rogoff (2001) two-country DSGE framework, which
extends the basic Obstfeld/Rogoff (1995) model by introducing uncertainty.

3.1. Preferences, Consumption and Price Indexes

Suppose world population is constant over time and consists of a continuum of measure 1 of infinitely
lived atomistic households characterized by identical preferences. Assume further perfect information
and rational expectations on part of all agents. There are two countries, where domestic households live
on the segment [0
, n] of the unit interval while foreign households live on the remaining segment (n, 1].

The discounted stream of expected period utilities of the representative domestic household reads as
follows:
3

Ut = Et


X

s=t


βs-t


Cs1




μ 'Ms y -ε


Ls1-ξ     .


(1)


The above utility function is a constant elasticity of substitution (CES) composite separable in its ar-
guments real consumption
C, real money balances M/P (where P denotes the domestic consumer price
index (CPI)), and leisure
—L such that the partial derivatives of the utility function with respect to one
variable are independent of all other variables.
β denotes an intertemporal discount factor (0 < β < 1).

3 Note that a possible superscript i to distinguish individual variables is suppressed throughput the analysis for legibility
reasons.



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