The name is absent

Let us just check that this will yield a contract structure equivalent to the
Calvo process. Since the wage setting process is uniform, we can consider the
representative period. In the sector with T_i period contracts, a proportion
a_i∕T_i contracts come to an end. Hence, using (25) and summing across all
sectors the total measure of all contracts in the economy coming to an end
in any period is —, since:

∞     ∞

∑ _T = Σ —² (1 - —   = —

i=l ^±г     i=l

As in the Calvo process, in the Calvo-GTE a proportion — of the population
comes to the end of a contract. If we look at this Calvo-GTE, the average
observed duration of contacts (completed and non-completed) will be — ^l.
To see why, let us derive the average age from the distribution of contract
lengths. The proportion of contracts age i is obtained by summing across
all cohorts who reset wages i periods ago. Clearly, this means we sum only
over sectors with completed contract lengths T > i

∞

_a∙ = ∑ —’ (1 - —)^t~^l

T >i

= — '' - —)ⁱ~^l ∑∑ (1 - —)^t~^l

T=l

= — (1 — —)^{i l}

Hence, as in Calvo, the average age of contracts in a Galvo-GTE is — ^l. So,
the average age of a contract in steady-state cross-section is — ^l, and the
average age of completed contracts is 2— ^l — 1. This is because in a uniform
wage process, on average each contract will be about half way through. In
continuous time they would be exactly half way through: but because of
the measurement of time in integers, it is not quite so: the average age is
more than half completed contract length: in fact it is 0.5 more¹². Thus for
example, if we measure the average age of two period contracts in a uniform
simple Taylor setting, the average age is 1.5 = Gp, not 1 as it would be in

1 X

T Σ * =
i=l

20

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