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Employment and Social Developments in Europe 2014
Annex 1: Price dynamics in the euro area
This Annex examines empirically the pass-through of changes in nominal compensation per employee (adjusted for labour pro-
ductivity) to output prices in the euro area. First, the transmission mechanisms will be specified, next the data will be discussed
followed by a brief presentation of the empirical results.
Specification
A composite good is produced of which the equilibrium price is determined by the marginal production cost, PMC. However, prices
adjust only slowly due to menu costs, administered prices, or backward-looking ’rule of thumb’ price setting behaviour. Moreover,
calculating the marginal cost and adjusting prices involves a cost that may exceed the potential gain. As a consequence, prices
are adjusted for only x percent of the composite good. In that case the price at moment t is set as
log(Pt) = (1-x)log( Pt-1) + x log(PRt) (A.1)
with
Pt: the price at t
PRt: the new price of the part that undergoes a price change
x: the share of the composite good that undergoes a price change.
with 0≤ x ≤ 1 and log(.) the natural logarithm operator.
However, not all information is available to calculate the marginal production cost. As a consequence, part of the prices that are
revised are set following a ‘rule of thumb’ rule while the other part is set based on marginal costs, i.e.
log(PRt) = y log(PMCt) + (1-y) log(PBt) (A.2)
with
PRt: the new price of the part that undergoes a price change
PMCt: the marginal cost
PBt: the ‘rule of thumb’ price
y: the share of the revised prices set along marginal cost calculation
with
0 ≤ y ≤ 1
The ‘rule of thumb’ for price changes is driven by an extrapolation of past inflation developments and adjustment to differences
between prices and marginal costs in the previous year (that are known at moment t), i.e.
log(PBt/PBt-1) = z1 log(Pt-1/Pt-2) + z2 log(PMCt-1 / Pt-1) (A.3)
Taking finite differences of equations (A.1) and (A.2) yields
log(Pt/Pt-1) = (1-x)log( Pt-1/Pt-2) + x log(PRt/PRt-1) (A.4)
log(PRt/PRt-1) = y log(PMCt/PMCt-1) + (1-y) log(PBt/PBt-1) (A.5)
Inserting (A.3) into (A.5) yields
log(PRt/PRt-1) = y log(PMCt/PMCt-1) + (1-y) [z1log(Pt-1/Pt-2)+ z2 log(PMCt-1 / Pt-1)] (A.6)
Inserting (A.6) into (A.4) yields
log(Pt/Pt-1)= (1-x+x z1 – x y z1) log( Pt-1/Pt-2) + x y log(PMCt/PMCt-1) + x (1-y) z2 log(PMCt-1/Pt-1) (A.7)
or on collecting terms
log(Pt/Pt-1)= (1-x+x z1 – x y z1) log( Pt-1/Pt-2) + x y log(PMCt/PMCt-1) + x (1-y) z2 log(PMCt-1/Pt-1) (A.7)
Finally, the production cost function (assuming a homothetic production function) read as
log(PMCt) = g1 log(Wt /PROD_Lt) + g2 log(PXt/PROD_Xt) (A.8)
with
W: nominal compensation per employee
PROD_L: labour productivity
PX: price of other production factors
PROD_X: productivity of other production factors.
234
Annex 1: Price dynamics in the euro area
This Annex examines empirically the pass-through of changes in nominal compensation per employee (adjusted for labour pro-
ductivity) to output prices in the euro area. First, the transmission mechanisms will be specified, next the data will be discussed
followed by a brief presentation of the empirical results.
Specification
A composite good is produced of which the equilibrium price is determined by the marginal production cost, PMC. However, prices
adjust only slowly due to menu costs, administered prices, or backward-looking ’rule of thumb’ price setting behaviour. Moreover,
calculating the marginal cost and adjusting prices involves a cost that may exceed the potential gain. As a consequence, prices
are adjusted for only x percent of the composite good. In that case the price at moment t is set as
log(Pt) = (1-x)log( Pt-1) + x log(PRt) (A.1)
with
Pt: the price at t
PRt: the new price of the part that undergoes a price change
x: the share of the composite good that undergoes a price change.
with 0≤ x ≤ 1 and log(.) the natural logarithm operator.
However, not all information is available to calculate the marginal production cost. As a consequence, part of the prices that are
revised are set following a ‘rule of thumb’ rule while the other part is set based on marginal costs, i.e.
log(PRt) = y log(PMCt) + (1-y) log(PBt) (A.2)
with
PRt: the new price of the part that undergoes a price change
PMCt: the marginal cost
PBt: the ‘rule of thumb’ price
y: the share of the revised prices set along marginal cost calculation
with
0 ≤ y ≤ 1
The ‘rule of thumb’ for price changes is driven by an extrapolation of past inflation developments and adjustment to differences
between prices and marginal costs in the previous year (that are known at moment t), i.e.
log(PBt/PBt-1) = z1 log(Pt-1/Pt-2) + z2 log(PMCt-1 / Pt-1) (A.3)
Taking finite differences of equations (A.1) and (A.2) yields
log(Pt/Pt-1) = (1-x)log( Pt-1/Pt-2) + x log(PRt/PRt-1) (A.4)
log(PRt/PRt-1) = y log(PMCt/PMCt-1) + (1-y) log(PBt/PBt-1) (A.5)
Inserting (A.3) into (A.5) yields
log(PRt/PRt-1) = y log(PMCt/PMCt-1) + (1-y) [z1log(Pt-1/Pt-2)+ z2 log(PMCt-1 / Pt-1)] (A.6)
Inserting (A.6) into (A.4) yields
log(Pt/Pt-1)= (1-x+x z1 – x y z1) log( Pt-1/Pt-2) + x y log(PMCt/PMCt-1) + x (1-y) z2 log(PMCt-1/Pt-1) (A.7)
or on collecting terms
log(Pt/Pt-1)= (1-x+x z1 – x y z1) log( Pt-1/Pt-2) + x y log(PMCt/PMCt-1) + x (1-y) z2 log(PMCt-1/Pt-1) (A.7)
Finally, the production cost function (assuming a homothetic production function) read as
log(PMCt) = g1 log(Wt /PROD_Lt) + g2 log(PXt/PROD_Xt) (A.8)
with
W: nominal compensation per employee
PROD_L: labour productivity
PX: price of other production factors
PROD_X: productivity of other production factors.
234
