completed contract lengths: the average completed contract in Calvo economy
is ⅜ — 1, which is almost twice the length of the expected contract duration
(1∕ω). Hence, we find that Kiley compares a Calvo economy with ω = 0.5
which implies an average contract length of 3 periods with a 2-period Taylor
contract. If we compare Calvo ω = 0.5 with a Taylor economy with 3-period
contracts, the persistence properties of the Calvo and Taylor are similar9.
5.0.3 Calvo contracts as a special case of a GTE
Two main features of the Calvo setup stand out as different form the standard
Taylor setup. First its "stochastic" nature: at the firm level, the length of the
wage contract is random; second, that the model is described in terms of the
"age" of contracts (which includes uncompleted durations) and the hazard
rate (the reset probability ω). The second feature is easy to remedy: we can
look at either Taylor or Calvo contracts and describe them in terms of either
the distribution of completed contract durations (lifespans) or in terms of
the distribution of ages all durations (complete and incomplete): it is simply
two ways of describing the same process. On the first issue. the stochastic
nature of the Calvo model at the firm level does affect the wage setting
decision. However, apart form the wage setting decision we can describe the
Calvo process in deterministic terms at the aggregate level because the firm
level randomness washes out. At the aggregate level, the precise identity of
individual firms does not matter: what matters is population demographics
in terms of proportions of firms setting contracts of particular lengths at
particular times. Because there is a continuum of firms, the behavior of
contracts at the aggregate level can be seen as a purely deterministic process.
First, we set aside the precise level of wages and observe the duration of
wages. We focus on the "demographics" of the contract lengths in a Calvo
process10. If we take a snapshot of the economy in period t we will observe a
proportion ω of wages changing of the remaining (1 — ω) firm∕unions do not.
We observe the distribution of durations : a proportion ω(1 — ω)s 1 have been
been in place for s periods. These are non-completed durations for (1 — ω)
9See Dixon and Kara (2004)
10For a discussion of "life span" and "age", in the unemployment duration literature,
see Salant (1977), Carlson and Horrigan (1983). These studies present some examples and
show that E [T ∣ s] = 2v 1. However, in discrete time specification needs to be a small
adjustment in this formula, as pointed out by Carlson and Horrigan (1983) (cf. Luckett
(1979))
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