5.0.5 Persistence in the Calvo and Calvo-GTE compared.
We now compare the Calvo- GTE and the standard Calvo economy. In the-
ory, the Calvo-GTE and the Calvo economy are exactly the same except for
the pricing decision. However, for computational purposes whilst the Calvo
economy effectively has an infinite lag structure (via the Koyck transform),
the Calvo-GTE has to be truncated. Hence we also introduce a Calvo-
Calvo-GTE : that is the GTE with the same contract structure and pricing
rule as the Calvo model, but truncated as in the Calvo-GTE. For the sim-
ulations, we truncated the distribution of contract lengths to 20 quarters
T = 1, ...20. with the 20 period contracts absorbing all of the weight from
the longer contracts. When we apply the standard Calvo pricing rule to
this truncated distribution, it yields a perceptible but negligible difference;
hence all of the visually apparent differences between the Calvo-GTE and
the standard Calvo model are due almost entirely to the difference in pricing
behaviour.
In Figure 5 we compare the impulse response for the Calvo-GTE which
has the same distribution of completed contract lengths as the Calvo dis-
tribution, with the standard Calvo economy for ω = 0.25. We find that
Calvo-GTE has almost exactly the same persistence as the Calvo economy.
The effect is as little larger for 5 quarters and a little less subsequently. We
also show the standard Taylor economy with the same mean contract length
rT = 7. Although the effect is a greater for the first 5 quarters, the effect dies
down and is significantly less thereafter. This reflects the fact that although
the mean contract lengths are the same, the longer contracts in the Calvo
and Calvo-GTE generate the extra persistence.
For comparison, Figure 6 shows the distributions of fractions of contracts
for three different specifications; Calvo-GTE, the Taylor 1993 calibration
of the US economy, and Calvo distribution of all durations (complete and
incomplete).
6 Conclusions
In this paper we have developed a general framework, the GTE which unifies
the previously disparate approaches of modelling dynamic price and wage
setting: Calvo and Taylor. The approach is a generalization of the simple
Taylor model to take into account the presence of a range of different contract
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