periods.
In Figure 4 we plot the output responses for 4 different GTEs. The
responses are normalized in the sense that the impact is set at 1. We have
the Taylor US economy as in Figure 3, we have the simple 2-period Taylor
case, the GTE with 90% 2-period and 10% 8-period contracts ,and finally the
GTE with 50% 3 period and 50% 4 period contracts (which gives the average
3.5 periods which is almost the same as Taylor’s US economy. If we compare
Taylor’s US economy with the simpler economy with mean contract length
3.5, we can see that Taylor’s US economy is more persistent: this is because
it includes longer contracts despite having the same mean. We can also
read off from Figure 4 the half lives of the impulse-response functions, which
gives us a quantitative measure of the degree of persistence. For example,
when there is simple Taylor economy with only 2-period contracts alongside
the GTE with 10% share of 8-period contracts, the half-life increases from
0.74 periods to 1.25 periods. This is also the case when we compare Taylor’s
US economy with the corresponding Simple Taylor Economy. In particular,
half-life increases from 3.5 periods to 4.4 periods.
5 Comparison with Calvo Economy
It has long been noted that Calvo contracts appear to be far more persistent
than Taylor contracts. In this section, we will show that if we focus on
the structure of contracts (as opposed to the wage-setting rule), the Calvo
economy is a special case of the GTE. Kiley (2002) considers a setup very
similar to ours (the main difference being that he focuses on price-setting) to
compare a simple Taylor economy with a Calvo economy. His findings are
that these two models imply very different dynamics both qualitatively and
quantitatively. In particular, he compares a simple Taylor economy with
2 period contracts and a Calvo economy with a reset probability ω = 0.5.
He concludes that: "...Staggering imparts much less persistence than does
partial adjustment for nearly all paramtererizations..." Kiley (2002).
What we show is that Kiley is making the wrong comparison. We can
directly describe the Calvo contract structure in terms of a GTE. When we
do this, the dynamics of the Calvo economy and the corresponding GTE
are very similar (they differ only because of different wage-setting behavior).
Indeed, the main reason for Kiley’s conclusion is that he is not comparing
like with like. The Taylor economy is described in terms of the distribution of
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