Ex post versus ex ante
measures
of the user cost of capital
Nicholas Oulton
LSE and NIESR
June 2005
Roadmap
• Issues: ex post or ex ante?
• Theory: model of temporary equilibrium
leads to hybrid method
• How much difference does method make
in practice? Illustration using UK industry
data
Two measures required for each industry :
1. Growth of capital services : Kˆ t
2. Contributi on of capital : Capital share times Kˆ t
National accounting identity :
GOSt  i 1 qit K it
m
GOS : Gross operating surplus
qit : User cost (Rental price) of ith type of capital
K it :
Capital services from ith capital stock
Real user cost (rental price) of ith asset type :
qit  Tit rt   i (1   it )   it ( pi ,t 1 / pYt )
 it  ( pit  pi ,t 1 ) / pi ,t 1
Issues
• For growth accounting, we want to measure
actual (ex post) marginal products
• The ex post measure automatically satisfies the
national income identity
BUT …
• Firms make investment decisions based on the
required (not the ex post) rate of return and
anticipated (not actual) prices
• In practice, the ex post measure may produce
negative rental prices
True versus common ex post
measures
• The “true” ex post measure is the right one
for growth accounting
• The estimated (“common”) ex post
measure imposes the same rate of return
on all assets. This is right only if
expectations all turn out to be correct
MODEL
• Firms must look ahead one period.
• Investments must be expected to pay the
required rate of return.
• Future asset prices, output price and level
of demand not known with certainty.
• Asset stocks must be chosen in advance,
other inputs (eg labour) can be freely
varied later
MAIN RESULT
If production function is CES, then ratio of
expected marginal product to actual
marginal product is the same for all
assets.
NB: (expected) marginal product
= (expected) user cost
HYBRID METHOD
• Use ex ante user costs to construct index
of capital services
• To calculate contribution of capital, multiply
index of capital services by ex post share
of GOS in value of output
How much difference does method make?
Bank of England Industry Dataset:
31 industries in the market sector (exclude public sector)
7 assets:
Non-ICT
ICT
Buildings
Computers
Plant & machinery
Software
Vehicles
Communications
Intangibles
Depreciation: geometric (similar rates to BEA)
Computer and software prices: US, adjusted for
exchange rate changes
Methods
1. Ex post (common): solve for rate of return;
actual GOS
2. Ex ante (perfect foresight):
required rate of return is average actual rate in
market sector; actual prices; predicted GOS
3. Ex ante (AR):
required rate of return is average actual rate in
market sector; prices forecast by ARMA model;
predicted GOS
4. Hybrid: as ex ante (AR), but actual GOS
Capital services in the market sector, 1970 = 1.0
log scale
5
4
3
2
1
1970
1975
Ex post
1980
1985
Ex ante, p.f.
1990
Ex ante, AR
1995
2000
Hybrid
CONCLUSIONS
• Hybrid and ex post (common) methods produce
similar results
• Hybrid method eliminates negative rental prices
(1.7% of rental prices were negative for ex post)
• Hybrid method satisfies national income
accounting identity
• Hybrid methods uses exactly the same data as
is required for ex post (common) method