Section 2. In our view, it constitutes a better gauge of y than gross output or sales, since it
corresponds to the volume of the contractible output that remains once intermediate inputs
have been remunerated (i.e., the sum of pre-tax profits, wages and perks).20
To identify shocks to firm performance we proceed along the lines of Section 2. The first
step is to filter out the predictable component. To this end we consider equation (4):
A(L,p)yjt = z,jtθ + εjt
where yj∙t is the log of real value added for firm j at time t. In the presence of a random
walk permanent component and/or serially correlated transitory effects (for instance, an
MA(q) process), estimates in levels are inconsistent because of a short T problem. Taking
the first difference of the data eliminates this problem and yields:
A(L,p)∆yit = ∆z'tθ + ∆εjt
(22)
Also notice that the first difference eliminates firm-fixed effects (if any) that may in-
fluence the level of the firm’s output, such as size. Included in ∆zfjt is a full set of time
dummies, sector dummies, location dummies, year/sector and year/location interactions.21
The orthogonality condition that identifies the parameters of (22) in the general case is:
E (∆εjt∣Ωt-ρ-2) = 0
(23)
where Ωt-q-2 denotes the information set on which the agents condition. The residual from
(22) constitutes our measure of output on which the payment to the worker should be made
20When alternative measures of performance (such as gross output or sales) are used, the results are very
similar.
21Sector dummies are for agriculture and fishery; mining; food and tobacco products; textile and leather
products; paper, wood products and publishing; chemicals and petroleum; primary and fabricated metal
products; machinery and electric/electronics; energy, gas and water; constructions; retail and wholesale
trade and hotels; transport and telecommunications; credit, insurance and business services; and other
private services (agriculture and fishery is the excluded category). Location dummies are for North, Center
and South (Center is the excluded category). By including these dummies we explicitly remove shocks to
firm performance pertaining to a given location and a given industrial sector at a point in time. In terms of
the agency model these components should not enter the optimal contract, because they can be separated
from effort, given that they are common to all firms in a given location or sector at each point in time.
19