setting process within the sector can be summarized by an Ni — 1-tuple
of integers {Tij j ʌ'*2 which specifies when in the wage-setting cycle cohort j
moves . It is assumed that cohort 1 moves first (period 1): this defines the
beginning of the cycle, so that 1 ≤ Tij ≤ Ni. If Tij = 3, it means that
cohort j sets its wage in period 3 periods after the first. By convention, we
assume that the js are ordered so that Tij is strictly increasing. Clearly, we
have the restriction of Ni ≤ Ti: there cannot be more cohorts than contract
periods. If Ni = Ti, then one cohort moves in each period: if in addition the
the cohorts are of equal size Λij∙ = Ni 1, we define a uniform wage setting
process in sector i. If Ni < Ti, then there will be some periods when no
cohort moves. For example, we can consider a sector with 8 period contracts
in which there are two cohorts in which the second cohort moves 4 periods
after the first, Ti2 = 4. Alternatively, there might be three cohorts, with
timing {2, 6} so that the second cohort moves in period 2 and third in period
6.
In order to fully characterize the economy with non-uniform wage setting,
we also need to specify the calender date ti when the wage-setting process
starts3 for each contract length Ti. In the case of an economy with uniform
wage setting processes in all sectors, the start dates are irrelevant, since each
period is exactly the same in all sectors (i.e. the same proportion of wages
are reset).
We can therefore characterize the wage setting process in a GTE by
(T, a) ∈ Zf+ × Δn 1 , which gives the contract lengths and sizes of the N
sectors, (Ni,λi, ti) ∈ Z++ × Δn 1 × Z++ which describes the number and
relative size of the cohorts in each sector i, and the timing∕synchronization
of cohorts in that sector.
GTE := {(T, a) , {Ni,λi,ti'J
In the case where each sector has a uniform wage setting process, we have a
uniform GTE which is more simply parameterized by (T, α)since (Niιλi) =
(Ti, Ti 1 ) and ti is irrelevant (each period looks the same). A homogenous or
simple Taylor economy is one where there is just one sector with a uniform
wage-setting process.
The general price index P can be defined in terms of sectors, or subinter-
3Of course, this is not unique: all that is required for each sector is the start date of
one cycle, since then the start date of all cycles is given.