ω = 0.25 (a common value used with quarterly data), there is a probability
of over 10% that a contract will survive for 8 periods (see for example Erceg
(1997), Wolman (1999)). We construct a GTE which has the same dis-
tribution of completed contract lengths as the Calvo distribution. We find
that this Calvo-GTE has almost exactly the same persistence as the Calvo
economy. This supports the idea that the persistence resulting from Calvo
contracts is explained by the presence of longer-term contracts. However,
it also shows that if we have the same distribution of contract lengths in a
GTE, the persistence is the same. This indicates that the two approaches
can be unified and are not so different. We also show that the view that
Calvo is more persitent than the equivalent Taylor economy is based on a
mis-calibration and inconsistent basis of comparison. The Taylor case is
specified in terms of completed contract lengths: the Calvo is usually looked
at in terms of contract age, which is very different from completed lifetime
of a contract. As we show in Dixon and Kara (2004), a reset probability of
ω = 0.25 leads to an average contract lifetime of 7 periods, not 4. Hence
simple Taylor economies of 4 quarters should be compared with Calvo reset
probabilities of ω = 0.4 for mean contract length to be equated.
The outline of the paper is as follows. In section 2 we outline the basic
structure of the Economy. The main innovation here is to allow for the
GTE contract structure. In section 3 we present the log-linearized general
equilibrium and discuss the calibration of the model in relation to recent
literature. In section 4 we explore the influence of longer term contracts on
persistence as compared to the simple Taylor economy, and in section 5 we
apply our methodology to evaluating persistence in the Calvo model.
2 The Model Economy
The approach of this paper is to model an economy in which there can
be many sectors with different wage setting processes, which we denote a
generalized Taylor economy.( GTE). As we will show later, an advantage of
the GTE approach is that it includes as special cases not only the standard
Taylor case of an economy where all wage contracts are of the same length,
but also the Calvo process.
The model in this section is an extension of Ascari (2000) and includes a
number of features essential to understanding the impact of monetary shock
on output in a dynamic equilibrium setting. The exposition aims to outline