The T.S. Kim Memorial Seminar, September 14, 2006
Unmeasured Investment and the
U.S. 1990s Hours Boom
Ellen R. McGrattan and Edward C. Prescott
Arizona State University and
Federal Reserve Bank of Minneapolis
1
The U.S. 1990s Boom
• It is puzzling from the perspective of the standard
growth model
• Because …
2
1990s Hours Boom
Hours boomed
but labor
productivity
did not.
3
Resolution of Puzzle: Unmeasured Investment
• Standard measurement and theory mask real economic story
• Economic output includes a lot of unmeasured investment
• Tech boom led to
–
–
–
–
Very large increase in unmeasured investment
Large increase in market hours
Large increase in economic output
Sizable increase in economic output per hour
4
Outline
• Show 1990s is puzzling for standard model
• Extend model to include intangible, which is not
measured, capital investment
• Permit nonneutral technological change with respect to
producing intangible capital and measured output
• Show there is no puzzle when the 1990s is viewed
through the lens of this extended model
5
Show 1990s a puzzle for standard theory
6
Theory without Unmeasured Investment
• Stand-in household maximizes

E   t [log ct  log(1  ht )]N t
t 0
s. t.
ct  xt  wt ht  rt kt  taxest  transferst
kt 1  [(1   )kt  xt ]/(1   )
taxest   ct ct   ht wt ht  taxes on capitalt
7
• Stand-in firm's technology
Yt 

1
At Kt H t
• Use BEA & CPS data to determine TFP path { At }
• Compute perfect foresight equilibrium path given TFPs,
tax rates, and populations
8
Predicted and Actual Per-Capita Hours
Large deviation
from theory!
TFP increase
small and taxes
rose.
9
Something Important Is Missing …
Our conjecture is unmeasured investment
Observations leading to this conjecture
10
Profits Fell in the Boom
Would predict
high profits
in the boom.
11
R&D and High Tech Sector Boomed
• Private business R&D increased much more than GDP in
the 1990s
• Many new high tech firms – e.g., in Silicon Valley
12
Growth Model with Unmeasured Investment
• Household/business owners solve

max E   t [log ct   log(1  ht )]N t
t 0
subject to
ct  xm,t  qt xu ,t  rm,t km ,t  ru ,t ku ,t  wt ht  taxest  transferst
km,t 1  [(1   m )km,t  xm,t ]/(1   )
ku ,t 1  [(1   u )ku ,t  xu ,t ]/(1   )
where subscript m/u denotes measured/unmeasured and q is a price
13
Technologies
• Technology 1 – producing goods and services

y  A1F km1 , ku , h1

• Technology 2 – producing intangible capital
xu  A G
2

2
2
k m , ku , h

• Total stock of intangible used by producers and researchers
14
Two Types of Intangible Investment
• Two types of intangible investment
– Expensed: capital owners finance  with reduced profits
– Sweat: worker owners finance 1   with uncompensated time
• Parameter  has tax implications
15
Before Using the Extended Model
Must Revise Data in Light of Theory
16
Starting Point: National Accounts
NIPA INCOME
NIPA PRODUCT
Capital consumption
Personal consumption
Taxes on production
Government consumption
Compensation less sweat
Government investment
Profits less expensed
Private tangible investment
Net interest
Net exports
17
Revised National Accounts
TOTAL INCOME
TOTAL PRODUCT
Capital consumption
Personal consumption
Taxes on production
Government consumption
Compensation less sweat
Government investment
Profits less expensed
Private tangible investment
Net interest
Net exports
Capital gains
Intangible investment
18
Revised National Accounts
TOTAL INCOME
TOTAL PRODUCT
Capital consumption
Personal consumption
Taxes on production
Government consumption
Compensation
Government investment
Profits
Private tangible investment
Net interest
Net exports
Intangible investment
19
Two Additional Steps
• Construct sub accounts and hours for:
– Business: corporate and noncorporate
– Nonbusiness: households, government, nonprofits
because business sector is relevant for our model
• Use BEA and CPS data to set parameters
20
Using the Model
• Find TFPs from observables
• Must use equilibrium conditions given unmeasured
investment not observed
• As for previous analysis, do not use intertemporal
marginal condition for tangible capital
• Compute perfect foresight equilibrium path given TFPs
21
Start with Sequences of TFPs
• With period t observations on NIPA products, total hours,
tax rates
– Intratemporal marginal condition → sector hours
– Sector rental rates equated → sector tangible capital stocks
– Sector wage rates equated → intangible investment output
• Current observation and equilibrium conditions imply all
inputs and outputs to the two production functions
• Except for intangible capital
22
Finding the path of intangible Capital Stock
• Begin with a steady state value for 1990
• Intertemporal condition →
ku ,t 1  gt (ku ,t , xu ,t )
• Boundary condition is
ku ,2006  balanced growth value
23
• Start out with 1990 tangible capital stock and 1990
implied intangible capital stock
• Given population, tax rates, and implied TFPs, computed
perfect foresight equilibrium path
• Intertemporal marginal conditions for tangible capital
investment never used as case in the standard model
analysis
• Path could go way off
24
Implied Sectoral TFPs
Which are
very different
from standard
TFP measure
estimated for
US.
25
Observations in Close Conformity with Theory
26
Predicted and Actual Hours
Predicts
large increase
in hours:
consistent
with US.
27
Predicted and Actual Business Labor Productivities
Predicts
below trend
and then
above at end
of 1990s:
consistent
with US.
28
Predicted and Actual Tangible Investment
Only a modest
deviation
in tangible
investment.
29
Comparing Theory and NIPA Wages
• Income account statistics not used in determining implicit
TFPs and intangible capital stocks
• Consequently this is a demanding test
30
Question
• Does model yield accurate predictions for NIPA
compensation?
• To answer,
– Put a BEA accountant in model economy
– Accountant estimates household’s compensation as:
wt ht  1    qt xu,t
31
Predicted and Actual Business Compensation
Theory and
data match up
surprisingly
well!
32
Implications for Capital Gains
• We put Flow of Funds accountant in model
• Accountant computes capital gains on businesses
• This is another demanding and independent test
33
Compare FOF Gains to Change in Business Value
• Business value in t:
Vt  1   d ,t 1   x ,t  K m,t 1
value of tangible


   1   d ,t  1   p ,t  1    1   h,t   qt Ku ,t 1
value of intangible
which depends on value of intangible stock
34
U.S. Non-Real Estate Capital Gains
Above-trend
gains in late
1990s as
implied by
theory.
35
The 1990s in Light of Theory with Unmeasured
Investment
36
Model: Total and Measured Output
Large
differences
between
accounting
and economic
measures due
to intangible
investment.
37
Net Intangible Investment Share of Total Output
Bottom line:
Intangible
Investment
was large in
the 1990s!
Too Big to
Ignore!
38
Model: Total and Measured Business Labor
Productivity
Large
differences
between
accounting
and economic
measures due
to intangible
investment.
39
Conclusions
• The growth model with unmeasured investment
accounts for a variety of macro observations
–
Growth
–
Business cycle phenomena
–
Depressions
–
Stock market
– And, the 1990s boom
40