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{

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\no Federal Reserve Bank of Minneapolis\par
\no Research Department Staff Report 350
\medskip
\smallskip
\no Revised May 2005\par
\vskip 1.0truein

\no{\twelvepoint\bf Productivity and the Post-1990 U.S.~Economy${}^\dagger$}

\bigskip
\smallskip
\no{\smcaps Ellen R.~McGrattan}\nobreak\par
\no{Federal Reserve Bank of Minneapolis}\nobreak\par
\no{and University of Minnesota}

\bigskip
\smallskip
\no{\smcaps Edward C.~Prescott}\nobreak\par
\no{Arizona State University}\nobreak\par
\no{and Federal Reserve Bank of Minneapolis}

\vskip 1.5truein

{
\baselineskip=13pt

\noindent {ABSTRACT\ \hrulefill}
\vskip 5pt

\noindent
In this paper, we show that ignoring corporate intangible 
investments gives a distorted picture of the post-1990 U.S.~economy.
In particular, ignoring intangible investments in the late 1990s
leads one to conclude that productivity growth
was modest, corporate profits were low,
and corporate investment was at moderate levels.
In fact, the late 1990s was a boom period
for productivity growth, corporate profits, and 
corporate investment.
\vskip 5pt
\hrule
\bigskip

\no ${}^\dagger$
\colorit{Red}{Ellen R.~McGrattan is a monetary advisor
at the Federal Reserve Bank of Minneapolis and an adjunct
professor of economics at the University of Minnesota.
Edward C.~Prescott is the W.~P.~Carey Professor of Economics
at Arizona State University and a senior monetary advisor
at the Federal Reserve Bank of Minneapolis. Data are 
available at our website www.minneapolisfed.org. \ }
The authors thank Ricardo Caballero for helpful comments
on an earlier draft.  They also thank 
the National Science Foundation for financial support.
The views expressed herein are those of the authors and not necessarily
those of the Federal Reserve Bank of Minneapolis or the Federal Reserve
System.

}
}

\newpage
\footline={\hss\tenrm\folio\hss}
\pageno=1

\bigskip

\section{Introduction}

The standard measure of productivity is
gross domestic product
(GDP) per hour worked.  The thesis of this
paper is that this measure of productivity
is not a good measure of 
actual output produced per hour worked, which
we call {\it economic productivity}.  
The reason is that output is
understated by GDP because 
many investments are not accounted
for in the U.S.~Department of Commerce's
Bureau of Economic
Analysis (BEA) measure of product.
If the importance of these
unaccounted investments relative to GDP
remained constant over time, growth
in GDP per hour would be equal to
growth in economic productivity.
But in the post-1990 U.S.~economy,
the relative importance of these
investment\colorit{Red}{s\ } varied a lot.  We find that
excluding them in the measure
of U.S.~output leads to a large
underestimate of productivity growth
in the late 1990s.

In this paper, \colorit{Red}{these unaccounted investments\ }
will be called {\it intangible 
investment}\colorit{Red}{s}.\note{We use this term because
the bulk of the investments are not tangible.}
They are expenditures that increase future
profits but, by national accounting rules,
are treated as an operating expense rather
than as a capital expenditure.  
Examples 
include advertising, research and development, 
and, most important of all,
investments in building organizations.
Most intangible investments are not directly
observable, but they can be inferred using
standard growth theory and data from
the U.S.~national income and product accounts
(NIPA). We do this and show that movements 
in accounting and economic measures
of productivity are very different
during the 1990s.  In particular, we find that 
productivity growth prior to 1997 was
even weaker than suggested by GDP per hour
worked, that there was a productivity boom
in the late 1990s, and that productivity
growth returned to its low level 
\colorit{Red}{subsequent to the boom.}

Our accounting  has other implications,
in particular, for corporate profits and
corporate investment.
In the late 1990s output boom, the corporate
profit share reported by the BEA was low.
(See U.S.~Department of Commerce (1929--2002).)
A low profit share is not typical in booms.
The reason the corporate profit share fell
in the \colorit{Red}{boom\ } 
is simple accounting: \colorit{Red}{A}ccounting
profits understated economic profits because
corporations were making large intangible
investments in the late 1990s that they expensed.
Adding intangible investments to accounting profits
and to accounting investment implies a very different
picture of the U.S.~economy \colorit{Red}{than is evident
in the BEA data because adjusted corporate
profit and corporate investment shares were both high.}

\section{The Model Economy}

In this section, 
we present a version of the 
model economy that we used to analyze secular movements in 
corporate equity values. (See McGrattan and Prescott 2004.)
Here, we use the model to compare accounting
and economic measures of key aggregate
statistics.

The economy is populated by a large
number of identical, infinitely lived
households.  They make decisions
about consumption, labor supply, and saving.
These decisions are event contingent, where the 
events are generated by a finite state
Markov chain with stationary transition
probabilities.  The period $t$ state is $s_t\in S$.

Preferences of the stand-in household are ordered
by
$$
E \sum_{t=0}^\infty \beta^t\,  U(C_t/N_t,L_t/N_t) 
\EQN utility
$$
where $C_t$ is total consumption, $L_t$ is total labor
supply, and $N_t$ is the working-age population.

There are two stand-in firms, one for the corporate
sector and one for the noncorporate sector.
The constant-returns technology for the corporate sector, sector 1, 
is given by
$$\EQNalign{
  Y_{1,t}     &= f^c(K_{1m,t},K_{1u,t},L_{1,t},s_t)\cr
  K_{1m,t+1}  &= (1-\delta_{1m}) K_{1m,t}+ X_{1m,t}\cr
  K_{1u,t+1}  &= (1-\delta_{1u}) K_{1u,t}+ X_{1u,t}\cr
 \hat K_{1m,t+1} & = [(1-\hat \delta_{1m})\hat K_{1m,t}
                         +(1-\hat\delta_{1x})X_{1m,t}]/(1+\pi_{t,t+1})
}
$$
where $Y_{1,t}$ is the output of the sector,
$K_{1m,t}$ is the beginning-of-period stock of 
measured capital,
$K_{1u,t}$ is the beginning-of-period stock of 
unmeasured capital, 
$\hat K_{1m,t}$ is the beginning-of-period book value
of the stock of measured capital,
$L_{1,t}$ is the labor input,
$X_{1m,t}$ is new investment in measured capital,
$X_{1u,t}$ is new investment in unmeasured capital,
and $\pi_{t,t+1}$ is the inflation rate between $t$ and
$t+1$.  
Later, we use the fact that $f^c$ has a unit elasticity
between capital and labor, with the capital share equal to 
$\theta$.

Stocks $K_{1m,t}$ and $\hat K_{1m,t}$ can be different
if tax rules allow for differences between depreciation
for taxes and actual economic depreciation.  They can
also be different if there is inflation.
The stocks of measured and unmeasured capital
depreciate at rates $\delta_{1m}$ and $\delta_{1u}$,
respectively.  For tax purposes,
capital consumption allowances are equal to 
$\hat \delta_{1m}\hat K_{1m,t}$ $+$ $\hat\delta_{1x}X_{1m,t}$
and can exceed $\delta_{1m}K_{1m,t}$ because of
accelerated depreciation allowances or allowances 
by the IRS for expensing tangible investments.

The constant-returns
technology for the noncorporate sector, sector 2, is 
$$\EQNalign{
  Y_{2,t}     &= f^{nc}(K_{2m,t},L_{2,t},s_t)\cr
  K_{2m,t+1}  &= (1-\delta_{2m}) K_{2m,t}+ X_{2m,t}\cr
 \hat K_{2m,t+1} & = [(1-\hat \delta_{1m})\hat K_{2m,t}
                         +(1-\hat\delta_{1x})X_{2m,t}]/(1+\pi_{t,t+1})
}
$$
where $Y_{2,t}$ is the output of the sector,
$K_{2m,t}$ is the beginning-of-period stock of
measured capital, 
$\hat K_{2m,t}$ is the beginning-of-period book value
of the stock of measured capital,
$L_{2,t}$ is the labor input, and
$X_{2m,t}$ is new investment in measured capital.
Later, we use the fact that $f^{nc}$ has a unit elasticity
between capital and labor, with the capital
share equal to $\alpha$.

The rate of economic depreciation 
of noncorporate capital is $\delta_{2m}$.  
For tax purposes,
total depreciation is $\hat \delta_{2m}K_{2m,t}$
$+$ $\hat\delta_{2x}X_{2m,t}$.
We assume that intangible capital 
investment in the noncorporate
sector is negligible and therefore do not include 
it.\note{Most of the investment in
the noncorporate sector is in the household
and government sectors, with little or no
expenditures on items such as research and 
development, advertising, and investments in 
organizational capital. }

Policy in this economy is a set of tax rates 
and transfer functions
that depend on the state $s_t$.
Both the households and the firms pay taxes.

We consider recursive competitive equilibria
with equilibrium elements that are stationary 
functions of the economy's state vector.
Because of our assumption that $s_t$ is
a Markov process with time-invariant transition
probabilities,
the aggregate state in period $t$ is
$(K_{1m,t},$ $K_{1u,t},$ $\hat K_{1m,t}$, $K_{2m,t},$ 
$\hat K_{2m,t}$, $s_t)$.  For convenience, let
$K_t=(K_{1m,t}$, $K_{1u,t}$, $\hat K_{1m,t}$, $K_{2m,t}$, 
$\hat K_{2m,t})$.
For a stationary recursive equilibrium,
the state in period $t$ is a function of the period
$t$ event history
$s^t=(s_0,\ldots, s_t)$, a fact that we use later.

The problem of the household is to maximize
\Ep{utility} subject to 
the period $t$ budget constraints:
$$
   (1+\tau_{c,t}) C_t + A_{t+1} = (1-\tau_{d,t}) D_{1,t}
                           + D_{2,t} + (1-\tau_{n,t}) W_t L_t +
                           (1+i_t)A_t + T_t
\EQN budget
$$
where $A_t$ is asset holdings at the beginning of
period $t$. The household, during period $t$,
receives income from corporate and 
noncorporate distributions, $D_{1,t}$ and $D_{2,t}$, 
respectively, wages at after-tax 
rate $(1-\tau_{n,t}) W_t$, assets at after-tax rate $i_t$,
and net transfers from the government $T_t$.
Distributions $D_{1,t}$ and $D_{2,t}$ are both net
of taxes paid by corporate and noncorporate firms.

Corporate firms maximize the present value of
after-tax distributions to the household, namely,
$$
   \sum_t \sum_{s^t} (1-\tau_{d,t}(s^t)) p_t(s^t) D_{1,t}(s^t).
$$
Corporate distributions are 
$$\EQNalign{
  D_{1,t} & = p_{1,t} Y_{1,t}  -W_t L_{1,t} - X_{1m,t} - q_t X_{1u,t} \cr
   &\qquad -\tau_{1,t}\bigl[ p_{1,t}Y_{1,t}-W_t L_{1,t}
    -\hat \delta_{1m}\hat K_{1m,t} 
    -\hat \delta_{1x} X_{1m,t} 
    -\tau_{1k,t} K_{1m,t} -q_t X_{1u,t}\bigr]  \cr
  &\qquad -\tau_{1k,t} K_{1m,t}+\tau_{x,t} X_{1m,t}.
\cr
}
$$

Noncorporate firms maximize the present value of 
distributions, namely,
$$
   \sum_t \sum_{s^t} p_t(s^t) D_{2,t}(s^t).
$$
Thus, noncorporate distributions are
$$\EQNalign{
   D_{2,t} &= p_{2,t}Y_{2,t} -W_t L_{2,t} - X_{2m,t} \cr
       & \qquad -\tau_{2,t}[p_{2,t}Y_{2,t} -W_t L_{2,t} 
                  -\hat\delta_{2m} \hat K_{2m,t} 
                  -\hat\delta_{2x} X_{2m,t} 
                   -\tau_{2k,t}K_{2m,t}] \cr
       &\qquad -\tau_{2k,t} K_{2m,t}+\tau_{x,t}X_{2m,t}.\cr
}
$$
Note that income taxes are paid once on noncorporate
income (net of proprietors' implicit labor income).

There is a final goods producer that combines corporate
and noncorporate goods to solve
$$
    \max_{y_1,y_2}\ \  F(Y_1,Y_2)- p_1Y_1 -p_2Y_2.
$$
The composite output $Y=F(Y_1,Y_2)$ 
good is used for consumptions and investments:
$$ 
   Y_t = C_t + X_{1m,t} + q_t X_{1u,t} + X_{2m,t}+G_t
$$
where $G_t$ is government consumption.
The function $F$ displays constant returns to scale.
An implication is that equilibrium distributions
are zero, and therefore we do not consider these 
distributions.

There is growth in the economy due to population
growth and productivity.  We detrend
income and product variables by dividing
first by population and second by $(1+\gamma)^t$,
the trend in productivity.
To construct hours per capita, we divide
total labor input by population.
We adopt the notation of lowercase letters
for variables that are stationary.
For example, $c_t = C_t/[N_t (1+\gamma)^t]$
is detrended consumption and $\ell_t = L_t/N_t$
is detrended labor supply. 

It also convenient to introduce notation
for the marginal products of capital.  Let
$r_{1m,t}$, $r_{1u,t}$, and $r_{2m,t}$ 
be the marginal products of measured
corporate capital, unmeasured corporate capital,
and measured noncorporate capital, respectively.

We now are ready to lay out the national 
accounts for our model economy.

\section{National Accounts to Model Economy Accounts}

In this section, we specify the mapping from U.S.~national
accounts to the model economy accounts.  Our model accounts
are summarized in \colorit{Red}{Table A1\ } 
in the appendix, with formula specifying
entries as a function of model variables.  \colorit{Red}{Table A2\ }
reports the main categories of the U.S.~national
accounts, with average values relative to GDP in the 1990s.
\colorit{Red}{Table A3\ } specifies the model account numbers as 
a function of the statistics in the U.S.~national accounts
and the values of these statistics.\note{Numbered lines in 
\colorit{Red}{Table A3\ } correspond to numbered lines 
in \colorit{Red}{Table A1.}}

\subsection{Adjustments}

There are four important differences between
the accounts our model economy dictates and the 
U.S.~national accounts.
First, our model output does not 
include consumption taxes as part of consumption
and as part of value added, but NIPA GDP does.
A consequence of this 
is that, unlike NIPA, 
our accounts are consistent in using producer
prices for inputs and outputs.
Second, we treat some financial services
included in NIPA as
intermediate rather than as final. 
Third, our model treats expenditures on
all fixed assets as investment.
Thus, consumer
durables are treated as an investment in the model accounts
rather than as consumption expenditures.  
We introduce a consumer durable services sector
in much the same way as an owner-occupied housing 
sector is introduced into NIPA.
Households rent the consumer durables
to themselves.
A related adjustment is made for 
government capital. 
Finally, and most importantly for the purposes of 
this paper, 
our model output includes corporate intangible
investment.  Intangible
investments are
expensed and therefore not included in the national
accounts.


\subsubsection{Adjustments for consumption tax}

Our {\it consumption taxes} are all {\it non-property}
taxes on production and imports less subsidies
plus business current transfer payments.
The reason that we include business transfers
in consumption taxes is that they are mostly
liability payments, which de facto are a tax.
NIPA reports total consumption taxes, which we
must assign to the corporate and noncorporate sectors.
The sums of consumption and property taxes are reported
by sector.  We assign aggregate consumption taxes
to sectors in proportion to their sums of consumption
and property taxes.  We subtract the consumption
tax from the value added of each sector.

On the product side we assume that all components
of NIPA personal consumption expenditures, which 
include consumer
durable expenditures, are taxed at an equal rate.
In fact a small part of what we call consumption taxes
fall on other components of product, but we do
not have good estimates of how much.  Thus,
we make the simplifying assumption that all 
consumption taxes fall
on personal consumption expenditures.
Fortunately, the assignment does not affect
the results of this study.

The results of our adjustments for consumption taxes
are summarized in \colorit{Red}{Table A3\ } (lines 4, 8, 10, and 14). 

\subsubsection{Adjustments for intermediate services}

Corporate value added includes some 
services that are not included in our notion
of final goods or services.\note{There have
been major changes recently 
in the accounting of financial
services. Most intermediate services are
now excluded from GDP. }
In particular,
NIPA imputes to net interest and to consumption
an amount equal to the expenses of handling
life insurance and pensions, which are intermediate
goods in the production of a final good, namely,
a diversified
financial portfolio.  On the income
side, we subtract these expenses (which are about
1 percent of GDP) from corporate net interest
(\colorit{Red}{Table A2\ }, line 6).
On the product side, we subtract these
expenses from personal consumption expenditures 
(\colorit{Red}{Table A2\ }, line 16).

In our mapping from national accounts to model
accounts in \colorit{Red}{Table A3\ }, these calculations are 
listed as ``imputed personal business expense.'' 
They appear under capital income (line 4)
and private consumption (line 10).

\subsubsection{Adjustments for capital services}

We make adjustments in our model accounts
for consumer durables and government capital
so as to treat them like all other fixed
assets accounted for in NIPA.

The implicit rental price of consumer durables
that we use is consumer durable depreciation
divided by the value of the stock of durables
plus the after-tax return on capital.
Using estimates from McGrattan and Prescott
(2004), we assume that the return is
4.1 percent per year.\note{If $i$ is not
close to this value, then returns
to capital in the model are not consistent
with observed capital stocks and tax rates.}
The imputation to consumption is this rental
price times the stock of consumer durables.
There are two imputations to value added.
First, we add depreciation of consumer durables to
noncorporate depreciation.  Second, we add
the return on capital times the stock of consumer
durables to noncorporate profits.

In \colorit{Red}{Table A3}, these calculations
are summarized in imputed capital services
under noncorporate capital income (line 8)
and private consumption (line 10).

In NIPA, the services of government capital are equal
to its depreciation.  Thus, net income is zero.
We define net income of government capital as our average
after-tax return on capital (4.1 percent) 
times the value of this capital stock.   
We add this income to profits
of the noncorporate sector on the value added
side of the accounts and to public consumption
on the product side.

In \colorit{Red}{Table A3}, these calculations
are summarized in imputed capital services
under noncorporate capital income (line 8)
and public consumption (line 11).


\subsubsection{Adjustments for intangible investments}

The last adjustment we make to corporate income
is to add back investments that had been expensed.
We do not have direct measures of these expenses
but can infer them from our theory and NIPA data.
In this section, we use the theory to estimate
the average level of intangible investment
and the equilibrium path since 1990.

\medskip
\noindent{\sl The average level of intangible investment in the 1990s}

As in McGrattan and Prescott (2004), we can take
an indirect approach, using observations on
corporate profits and returns to tangible 
assets to estimate a return to intangible assets.
NIPA profit before corporate income tax is
$$\EQNalign{
 {\rm  NIPA\ profit\ } 
     &= r_{1m}k_{1m}+r_{1u} k_{1u} -\delta_{1m}k_{1m}
                       -\tau_{1k} k_{1m} - q x_{1u}\cr
     &= (r_{1m}-\delta_{1m}-\tau_{1k})k_{1m}+q(r_{1u}/q k_{1u}-x_{1u}).
\EQN profit\cr
}
$$
If economic and accounting depreciation are 
equal and returns are equated for all assets,
then the first-order conditions of the model in
Section 2 imply that the following hold:\note{We 
also did calculations allowing
for differences in the depreciation rates.  
Holding the corporate tax rate fixed, we find
a higher average level of intangible investment
if accounting depreciation exceeds economic depreciation.
Thus, to be conservative in our conclusions about 
the importance of intangible investment, we assume
economic and accounting depreciation are equal.}
$$
\EQNalign{
   i &= r_{1u}/q-\delta_{1u} \EQN i1\cr
\noalign{\smallskip}
   i &= {(1-\tau_1)(r_{1m}-\tau_{1k})+\tau_1\delta_{1m}\over 1-\tau_x} 
             -\delta_{1m} \EQN i2\cr
\noalign{\smallskip}
  x_{1u} &=  (\gamma+\eta +\delta_{1u}) k_{1u} \EQN x1u\cr
\noalign{\smallskip}
  x_{1m} &=  (\gamma+\eta +\delta_{1m}) k_{1m} \EQN x1m\cr
}
$$
on a balanced growth path, where $i$ is the real interest rate
and $\eta$ is the population growth rate.

Equations \Ep{profit}-\Ep{x1m} can be solved for
the average level of intangible
investment and capital.
This is done as follows.
We use BEA data to get estimates of the 
corporate income tax rate $\tau_1$, 
the corporate property tax rate $\tau_{1k}$,
the subsidy to investment $\tau_x$,
the tangible depreciation rate $\delta_{1m}$, and
corporate tangible investment $x_{1m}$.  
We can use either the noncorporate returns or
estimates of preference parameters to get the
real interest rate $i$.
Population growth $\eta$ 
is around 1 percent per year.  Trend technology growth
$\gamma$ is around 2 percent per year. 

The system of equations \Ep{profit}-\Ep{x1m}
is five equations in the five unknowns, 
$r_{1u}/q-\delta_{1u}$, $r_{1m}$, $q k_{1u}$, $k_{1m}$,
and $qx_{1u}$.   Using data from the 
1990s, our estimate of the average value
of intangible capital $qk_{1u}$ is 0.65 times
GDP.\note{The inputs to this
calculation are: $\tau_1=0.37$, $\tau_{1k}=0.02$,
$\tau_x=0$, $\delta_{1m}=0.06$, $x_{1m}=0.099$,
$i=0.041$, $\gamma=0.02$, and $\eta=0.01$.}
This estimate is independent of our choice of
$\delta_{1u}$.  Our estimate of net investment
$q x_{1u}-\delta_{1u}k_{1u}$ is also independent
of our choice of $\delta_{1u}$.  Net 
intangible investment averaged 2 percent of 
GDP.\note{For convenience we will set $\delta_{1u}=0$
when we derive time series for $q_tx_{1u,t}$.
We are in effect working with net intangible investment.}

\medskip
\noindent{\sl The equilibrium path of intangible investment since 1990}

We can infer the path for intangible \colorit{Red}{investment\ }
using intratemperal first-order conditions of the model.
We use two approaches that lead to similar
quantitative implications for productivity in
the 1990s.  The two approaches rely on different
assumptions about cost shares over the business
cycle. 

Our first approach assumes that the capital 
income share does not vary over the cycle.
Let $\theta$ be the capital share in the
corporate sector, which we take to be
the average corporate capital income share,
$(r_{1m}k_{1m}
+r_{1u}k_{1u})/(p_1y_1)$, or equivalently one
less the average corporate labor income share,
$1-w\ell_1/(p_1y_1)$.
Using averages in the 1990s, we estimate
an average 
corporate capital share of $\theta=0.33$.
If intangible investments are chosen
so that 
$$\EQNalign{
  {w_t\ell_{1,t}\over p_{1,t}y_{1,t}}
                  &=1-\theta_t\cr
                  &=1-\theta,\cr
}
$$
then $q_t x_{1u,t}$ satisfies
$$\EQNalign{
   w_t\ell_{1,t}
      &= (1-\theta)p_{1,t}y_{1,t} \cr
      &= (1-\theta)[{\rm va}_{1,t}^{accounting}+q_t x_{1u,t}]\EQN way1\cr
}
$$
where we have an estimate of $\theta$ and
time series for corporate compensation
\colorit{Red}{($w_t\ell_{1,t}$)
and accounting corporate value added 
(${\rm va}_{1,t}^{accounting}$).\ }
The unknown in equation \Ep{way1}
is the product $q_tx_{1u,t}$.

In Figure 1, we display the implied time series for
intangible investment after 1990.
What is striking about this figure is the six-fold
increase in the level of intangible
investments between 1997 and 2000.
This represents a very large
change in investment.
This change in investment has consequences
for output, profits, and total investment.

Output is the sum of corporate and noncorporate income,
namely, $y_t$, after the relevant
adjustments to the national accounts are made.
Economic corporate profits are capital income,
which is corporate income less labor income and
depreciation.  If we assume an intangible
depreciation rate of zero, then economic
corporate profits are given by\note{In McGrattan
and Prescott \colorit{Red}{(2004)}, we do a sensitivity analysis
that includes varying $\delta_{1u}$.}
$$
p_{1,t} y_{1,t}-w_t \ell_{1,t}-\delta_{1m} k_{1m,t}.
$$
Economic corporate investment is the
sum of tangible plus intangible investments.
Economic profit shares and investment shares 
are defined relative to output $y_t$
rather than GDP.

In Figure 2, we compare the standard measure
of productivity, real GDP per hour worked,
with our economic measure $y_t/\ell_t$.
We normalize hours to be 1 in 1990
so that we can directly compare the 
magnitudes of GDP and $y$.
We also divide both measures by $1.02^t$,
the historical trend.

The figure shows
that economic productivity
fell faster than accounting productivity
in the early 1990s but grew much 
faster at the end of the 1990s.
Notice that economic 
productivity is higher than accounting
productivity in
1990 because output $y$ is 8 percent
higher than GDP.  A comparison with
Figure 1 illustrates how important
the movements in intangible  investment
are for output.

In Figure 3, we plot the accounting
measure of corporate profits relative
to GDP and our economic corporate
profits relative to output.
Our measure is significantly
higher because we do not subtract
intangible investment or property
tax. Our measure also includes the
small part of corporate
net interest that is not
intermediate services.  
Our profit share is about 12
percent \colorit{Red}{whereas\ } NIPA's profit share
is 7.5 percent.  

Of particular significance is the fact that
the patterns are very different.
In the late 1990s, economic profits
are high while NIPA profits are low.

In Figure 4, we plot the accounting
measure of the corporate investment share,
namely corporate tangible investment
relative to GDP and our economic
measure which is total corporate 
investment---tangible and intangible---divided 
by output $y$.
Notice that the standard 
accounting measure shows
only a modest investment boom
in the late 1990s,
while our measure shows a bigger investment boom.

Our second approach to measuring the path
of intangible investment assumes that 
the ratio of labor income shares across sectors
is constant.   Let $1-\theta_t$ be the corporate
labor income share in period $t$ and let $1-\alpha_t$
be the noncorporate labor income share in period
$t$.   Thus, our second approach assumes that
$$
   {1-\theta_t\over 1-\alpha_t} = {1-\theta\over 1-\alpha}
\EQN{way2}
$$
where $\theta$ and $\alpha$ are found by taking
averages over our sample period.   For the corporate sector,
the average is $\theta=0.33$.  For noncorporate sector,
the average is $\alpha=0.496$.\note{The
capital cost share for the noncorporate sector
is high because a significant
fraction of this sector's capital is housing and
consumer durables, which have a capital cost share
near one.}

Assuming that corporate income shares stay constant
puts a lower bound on the increase of intangible investment
during the late 1990s as capital income shares are
almost surely
procyclical.   The reason is simple.  If accounting
profits are low relative to trend, we are attributing
the difference to expensed investments.  However,
accounting profits may appear even lower if 
compared to boom-time levels.  When we assume that
income shares vary over the cycle, then we find
a larger gap between economic and accounting profits
in booms and, hence, a larger amount of intangible investment.

Equation \Ep{way2} and observables can be used
to find the value of intangible investment in units
of the consumption good as follows.
Substituting for the labor shares in \Ep{way2}
yields
$$
   \left( w_t\ell_{1,t}\over p_{1,t}y_{1,t}\right)
   \left( p_{2,t}y_{2,t}\over w_t\ell_{2,t}\right)
      = {1-\theta\over 1-\alpha}.
$$
This equation can be solved for corporate value
added, $p_{1,t}y_{1,t}$, as a function of observables.
Variable $p_{1,t}y_{1,t}$ can be used along
with accounting value added in the corporate sector
to find the value of unmeasured investment, that is,
$$
  q_tx_{1u,t}= p_{1,t}y_{1,t}-{\rm va}_{1,t}^{accounting}.
$$

In Figure 5, we plot the equilibrium path 
for the implied investment in intangible\colorit{Red}{s}.
As before we find a six-fold
increase in the level of intangible
investments between 1997 and 2000.
The main difference between the measures
in Figure 1 and Figure 5 are the magnitudes.
Assuming varying income shares implies a
higher absolute value of intangible investment
at the peak in 2000.

What are the consequences for productivity?
In Figure 6, we compare the standard measure
of productivity, real GDP per hour worked,
with the economic measure $y_t/\ell_t$
adjusted for the intangible investment in 
Figure 5.
Again, we normalize hours to be 1 in 1990
so that we can directly compare the 
magnitudes of GDP and $y$.
We also divide both measures by $1.02^t$,
the historical trend.

As in the case of fixed corporate shares, 
we find that economic productivity
fell faster than accounting productivity
in the early 1990s but grew much 
faster at the end of the 1990s.
The rise in productivity is somewhat higher
in the case \colorit{Red}{where\ } corporate income shares
vary.  Over the period 1997--2000, we
estimate that productivity rose 3.2 percent
per year in the case with fixed corporate income
shares and 4 percent per year  in the case
with varying corporate income shares.   
However, both cases show a much different
picture than GDP per hour.


\section{Supporting Evidence}

As we noted earlier, we do not have 
direct measures of all intangible investments.
\colorit{Red}{But there\ } are some direct measures of one
important component
of intangible investment, namely research
and development.
In Figure 7, we plot expenditures for
research and development performed
by industry.  Some of these expenditures
are capital expenditures and therefore
are not included in our notion of
intangible investments.  However, we find
a similar pattern of investment.
Investment in \colorit{Red}{research and development\ } fell rapidly 
in the first half of the 1990s and rose rapidly
in the second half.
This is what we find for total intangible 
investment.

\section{Summary}

U.S.~growth in GDP per hour worked, which we call
accounting productivity, was well below trend in the
1973--1995 period and then recovered to the
historical level of 2 percent per year growth
beginning in 1995. (See Figure 2.)
This picture is what most of the leading researchers
in productivity accounting find.\note{See, for example
Jorgenson et al.~(2003, p.~45) and 
Groningen Growth and Development Centre and The
Conference Board (2004).}
They, as do we, use hours worked estimates based
on the Current Population Survey.\note{There
are two other measures of U.S.~hours worked.
The BEA estimate, which uses state 
unemployment tax records to estimate the
number of paid workers, and the BLS estimate, which uses
an establishment survey to estimate the number 
of paid workers. The BEA hours estimate, which
is an annual series, paints the same picture
as CPS hours.  The BLS hours estimate, which is
a quarterly series, paints a different picture in the
post-2000 period.  With the BLS estimate
of aggregate hours, estimated productivity
growth is 1 percent higher in the 2000--2003 period.
See Kunze (2004) and Eldridge, Manser, and Otto
(2004) for details.}

We find
that economic productivity, which includes corporate
intangible investment in output, displays a very
different pattern.
As shown in Figure 2,
we find that there was a productivity growth boom
in the \colorit{Red}{late 1990s  with  productivity growth
well in excess of the
2 percent historical trend.} Prior and subsequent
to this boom, average productivity growth was 
\colorit{Red}{about half of the level of trend growth.}

Our accounting resolves the puzzle of why corporate
accounting profits were so low in the \colorit{Red}{late 1990s\ }  boom.
Corporations were making large intangible investments, which
lowered their accounting profits, but not their economic
profits.  The economic profits share of economic income was
high in the boom. (See Figure 3.) Our accounting
also resolves the puzzle of why investment share of 
output was not much higher in this boom than standard
accounting figures indicate.  With the accounting numbers
dictated by economic theory, the share increases, and 
increases a lot in the boom. (See Figure 4.)

\newpage
\section{References}
\smallskip
{
                                                                                
\baselineskip=15pt
\parskip = 8pt
\parindent= -.25truein
\leftskip = .25truein

Eldridge, Lucy P., Marilyn E.~Manser, and
Phyllis Flohr Otto (2004),
``Alternative measures of supervisory
employee hours and productivity growth,''
{\it Monthly Labor Review}, April, 9--28.

Federal Reserve Board of Governors (1945--2002),
{\it Flow of Funds Accounts of the United States}
(Washington, D.C.: Federal Reserve Board).

Groningen Growth and Development Centre and The
Conference Board (2004),
{\it Total Economy Database}, 
(www.ggdc.net).

Jorgenson, Dale W., Mun S.~Ho, and Kevin J.~Stiroh (2003),
``Lessons for Europe from the U.S.~Growth Resurgence,''
{\it CESifo Economic Studies}, 49(1): 27--47.

Kunze, Kurt (2004),
``U.S.~Hours Worked Data,'' 
memo, Bureau of Economic Analysis, August.
                                                                                
McGrattan, Ellen R.~and Edward C.~Prescott (2004),
``Taxes, Regulations, and the Value of
U.S.~and U.K.~Corporations''
(Staff Report 309, Federal Reserve Bank of Minneapolis).

U.S.~Department of Commerce,
Bureau of Economic Analysis (1929--2002),
{\it Survey of Current Business}
(Washington, D.C.: U.S.~Government Printing Office).


}

\newpage

\appendix{}{Appendix}

In this appendix, we display the national accounts 
that we work with, the NIPA categories
before we make our adjustments, and a mapping from 
the national accounts to the model accounts.  
\colorit{Red}{Table A1\ } lists the account categories for our model
along with formulas for variables in the model.
\colorit{Red}{Table A2\ } lists the NIPA categories along
with average values relative to GDP in the 1990s,
which give the reader a sense of the magnitudes of
the adjustments.
\colorit{Red}{Table A3\ } provides a mapping between these accounts.
In the main text, we provide justifications for the
calculations summarized here.

\bigskip
\bigskip

{

\baselineskip=14pt

\bigskip
\centerline{\bf\smcaps \colorit{Red}{Table A1}.\ \ Model Economy Accounts}
\medskip
\hrule
\vskip 1pt
\hrule
\vskip 2pt
$$\vbox{\settabs 
\+ ${\scriptstyle 2222}$ 
   & Corporate unmeasured investment plus lots of extra
   & $r_{1m}k_{1m}+r_{1u}k_{1u}-\hat\delta_{1m}\hat k_{1m} $ &\cr
\vskip -10pt
\+ &   
   & {\smcaps Model Expression}  &\cr
\+ ${\scriptstyle 1}$ & {\smcaps Corporate Domestic Value Added}  
   & $p_1y_1$ &\cr
\+ ${\scriptstyle 2}$ & \ \ \ Depreciation
   &  $\delta_{1m}k_{1m}$  &\cr
\+ ${\scriptstyle 3}$ & \ \ \ Labor income
   &  $w\ell_1$ &\cr
\+ ${\scriptstyle 4}$ & \ \ \ Capital income
   &  $r_{1m}k_{1m}\!+\!r_{1u}k_{1u}\!-\!\delta_{1m}k_{1m}$ &\cr
\medskip
\+ ${\scriptstyle 5}$ & {\smcaps Noncorporate Domestic Value Added} 
   & $p_2y_2$ &\cr
\+ ${\scriptstyle 6}$ & \ \ \ Depreciation
   &  $\delta_{2m}k_{2m}$ &\cr
\+ ${\scriptstyle 7}$ & \ \ \ Labor income 
   &  $w\ell_2$ &\cr
\+ ${\scriptstyle 8}$ & \ \ \ Capital income
   & $r_{2m}k_{2m}\!-\!\delta_{2m}k_{2m}$ &\cr
\medskip
\+ ${\scriptstyle 9}$ & {\smcaps Total Domestic Value Added}
  & $y$ &\cr
\bigskip
\+ & {\smcaps Domestic Product} &  &  & \cr
\+ ${\scriptstyle 10}$&
\ \ \ Private consumption
  & $c$ &\cr 
\+ ${\scriptstyle 11}$&
\ \ \ Public consumption 
  & $g$ & \cr 
\+ ${\scriptstyle 12}$&
\ \ \ Corporate measured investment
  & $x_{1m}$ &\cr
\+ ${\scriptstyle 13}$&
\ \ \ Corporate unmeasured investment
  & $qx_{1u}$ &\cr
\+ ${\scriptstyle 14}$&
\ \ \ Noncorporate investment
  & $x_{2m}$ &\cr
\medskip
\+ ${\scriptstyle 15}$& {\smcaps Total Domestic Product}
  & $y$ &\cr
}
$$
\vskip -7pt
\hrule
\vskip 1pt
\hrule

\newpage
\centerline{\ }
\vskip -.5truein
\centerline{\bf\smcaps \colorit{Red}{Table A2}.\ \ National Accounts, Average in 1990s
Relative to GDP}
\medskip
\hrule
\vskip 1pt
\hrule
\vskip 2pt
$$\vbox{\settabs 
\+ ${\scriptstyle 2222}$ 
   & Government consumption expenditures and gross investment plus extr
   & Averages 
   &\cr
\vskip -10pt
\+ ${\scriptstyle 1}$ & {\smcaps Corporate Domestic Value Added}  
   & \hfil 0.589&\cr
\+ ${\scriptstyle 2}$ & \ \ \ Consumption of fixed capital
   & \hfil 0.066&\cr
\+ ${\scriptstyle 3}$ & \ \ \ Compensation of employees 
   & \hfil 0.378&\cr
\+ ${\scriptstyle 4}$ & \ \ \ Corporate profits with IVA and CCadj
   & \hfil 0.075&\cr
\+ ${\scriptstyle 5}$ & \ \ \ Taxes on production and imports${}^a$ 
   & \hfil 0.056&\cr
\+ ${\scriptstyle 6}$ & \ \ \ Net interest and miscellaneous payments
   & \hfil 0.013&\cr
\smallskip
\+ ${\scriptstyle 7}$ & {\smcaps Noncorporate Domestic Value Added} 
   & \hfil 0.400&\cr
\+ ${\scriptstyle 8}$ & \ \ \ Consumption of fixed capital
   & \hfil 0.053&\cr
\+ ${\scriptstyle 9}$ & \ \ \ Compensation of employees
   & \hfil 0.240&\cr
\+ ${\scriptstyle 10}$ & \ \ \ Rental income of persons with IVA
   & \hfil 0.014&\cr
\+ ${\scriptstyle 11}$ & \ \ \ Proprietors' income with IVA and CCadj
   & \hfil 0.068&\cr
\+ ${\scriptstyle 12}$ & \ \ \ Taxes on production and imports${}^a$
   & \hfil 0.020&\cr
\+ ${\scriptstyle 13}$ & \ \ \ Net interest and miscellaneous payments
   & \hfil 0.051&\cr
\+ ${\scriptstyle 14}$ & Statistical discrepancy
   & \hfil 0.011&\cr
\smallskip
\+ ${\scriptstyle 15}$ & {\smcaps Total Domestic Value Added}
  & \hfil 1.000 &\cr
\smallskip
\+ & {\smcaps Domestic Product} &  &  & \cr
\+ ${\scriptstyle 16}$& \ \ \ Personal consumption expenditures
   & \hfil 0.670&\cr 
\+ ${\scriptstyle 17}$& \ \ \ \ \ \ Durable goods
   & \hfil 0.082&\cr 
\+ ${\scriptstyle 18}$& \ \ \ \ \ \ Nondurable goods and services
   & \hfil 0.588&\cr 
\+ ${\scriptstyle 19}$& \ \ \ Government consumption expenditures 
                              and gross investment 
   & \hfil 0.189& \cr 
\+ ${\scriptstyle 20}$& \ \ \ \ \ \ Consumption expenditures
   & \hfil 0.156& \cr 
\+ ${\scriptstyle 21}$& \ \ \ \ \ \ Gross investment
   & \hfil 0.033& \cr 
\+ ${\scriptstyle 22}$& \ \ \ Gross private domestic investment${}^b$
   &  &\cr
\+ ${\scriptstyle 23}$& \ \ \ \ \ \ Corporate 
   & \hfil 0.099& \cr 
\+ ${\scriptstyle 24}$& \ \ \ \ \ \ Noncorporate
   & \hfil 0.055& \cr 
\+ ${\scriptstyle 25}$& \ \ \ Net exports of goods and services
   & \hskip 2pt $-0.013$ &\cr
\smallskip
\+ ${\scriptstyle 26}$& {\smcaps Total Domestic Product}
  & \hfil 1.000&\cr
\smallskip
\+ & {\smcaps Addendum:}
  & &\cr
\+ ${\scriptstyle 27}$&
\ \ \ Consumption taxes 
  & \hfil 0.047&\cr
\+ ${\scriptstyle 28}$&
\ \ \ Consumption of fixed capital, durable goods
  & \hfil 0.062&\cr
\+ ${\scriptstyle 29}$&
\ \ \ Current-cost net stock of government fixed assets
  & \hfil 0.604&\cr
\+ ${\scriptstyle 30}$&
\ \ \ Current-cost net stock of consumer durable goods
  & \hfil 0.308&\cr
\vskip -3pt
}
$$
\hrule
\vskip 1pt
\hrule
}
\vskip -8pt
{ \baselineskip=9pt

\noindent \item{} {\eightpoint  
\colorit{Red}{NOTE: IVA, inventory valuation adjustment;
CCadj, capital consumption adjustment.}
\vskip -10pt
\noindent \item{${}^a$} {\eightpoint This category includes 
business transfers and excludes subsidies.}
\vskip -15pt
\noindent \item{${}^b$} {\eightpoint
The breakdown into corporate and noncorporate 
investments is based on data from the {\it Flow of Funds Accounts}
(\colorit{Red}{Board of Governors of the Federal Reserve System\ } 
(1945--2002)).  
For corporate investment, we sum 
investment of nonfinancial corporate business,
financial corporations, and 10\% of farm business. 
}

}

\newpage

{ \baselineskip=14pt

\centerline{\bf\smcaps \colorit{Red}{Table\ A3}.\ \ Mapping from National Accounts to Model
Accounts${}^a$}
\medskip
\hrule
\vskip 1pt
\hrule
\vskip 1pt
$$\vbox{\settabs 
\+ ${\scriptstyle 2222}$ 
   & Corporate unmeasured investment plus lots of extra spa
   & {\smcaps MMModel}& {\smcaps MMNIPA}& \cr
\vskip -10pt
\+ 
         &   & \hfil {\smcaps Model} & \hfill \ \ {\smcaps NIPA}&\cr
\vskip -6pt
\+ ${\scriptstyle 1}$ 
         & {\smcaps Corporate Domestic Value Added} ($p_1y_1$)& & &\cr
\+ ${\scriptstyle 2}$ 
         & \ \ \ Depreciation ($\delta_{1m}k_{1m}$)&\hfil 0.066& &\cr
\+       & \ \ \ \ \ \ Consumption of fixed capital& &\hfill 0.066&\cr
\+ ${\scriptstyle 3}$ 
         & \ \ \ Labor income ($w\ell_1$) &\hfil 0.378& &\cr
\+       & \ \ \ \ \ \ Compensation& &\hfill 0.378&\cr
\+ ${\scriptstyle 4}$ 
         & \ \ \ Capital income ($r_{1m}k_{1m}\!+\!r_{1u}k_{1u}
                            \!-\!\delta_{1m}k_{1m}$)&\hfil 0.120& &\cr
\+       & \ \ \ \ \ \ Corporate profits with IVA and CCadj& &\hfill 0.075&\cr
\+       & \ \ \ \ \ \ Net interest and miscellaneous payments& &\hfill 0.013&\cr
\+       & \ \ \ \ \ \ Less: Imputed personal business expense${}^b$& & \hfill $-0.010$&\cr
\+       & \ \ \ \ \ \ Taxes on production and imports& &\hfill 0.056&\cr
\+       & \ \ \ \ \ \ Less: Consumption taxes& &\hfill $-0.034$&\cr
\+       & \ \ \ \ \ \ Corporate unmeasured investment& &\hfill $\underline{0.020}$&\cr
\+       & & &\hfill 0.120&\cr
\vskip -6pt
\+ ${\scriptstyle 5}$ 
         & {\smcaps Noncorporate Domestic Value Added} ($p_2y_2$)& & &\cr
\+ ${\scriptstyle 6}$ 
         & \ \ \ Depreciation ($\delta_{2m}k_{2m}$)&\hfil 0.115& &\cr
\+       & \ \ \ \ \ \ Consumption of fixed capital& &\hfill 0.053&\cr
\+       & \ \ \ \ \ \ Consumption of fixed capital, durable goods& &\hfill $\underline{0.062}$&\cr
\+       & & &\hfill 0.115&\cr
\+ ${\scriptstyle 7}$ 
         & \ \ \ Labor income ($w\ell_2$)&\hfil 0.251&  &\cr
\+       & \ \ \ \ \ \ Compensation& &\hfill 0.192&\cr
\+       & \ \ \ \ \ \ 70\% Proprietors' income with IVA and CCadj& &\hfill 0.048&\cr
\+       & \ \ \ \ \ \ Statistical discrepancy& &\hfill $\underline{0.011}$&\cr
\+       & & &\hfill 0.251&\cr
\+ ${\scriptstyle 8}$ 
         & \ \ \ Capital income ($r_{2m}k_{2m}\!-\!\delta_{2m}k_{2m}$)&\hfil 0.132& &\cr
\+       & \ \ \ \ \ \ Rental income of persons with CCadj& &\hfill 0.014&\cr
\+       & \ \ \ \ \ \ 30\% Proprietors' income with IVA and CCadj& &\hfill 0.020&\cr
\+       & \ \ \ \ \ \ Net interest and miscellaneous payments& &\hfill 0.051&\cr
\+       & \ \ \ \ \ \ Current surplus of government enterprises& &\hfill 0.001&\cr
\+       & \ \ \ \ \ \ Taxes on production and imports& &\hfill 0.020&\cr
\+       & \ \ \ \ \ \ Imputed capital services${}^c$& &\hfill 0.038&\cr
\+       & \ \ \ \ \ \ Less: Consumption taxes& &\hfill $-\underline{0.012}$&\cr
\+       & & &\hfill 0.132&\cr
\smallskip
\+ ${\scriptstyle 9}$ & {\smcaps Total Domestic Value Added} ($y$)&\hfil 1.062&\hfill 1.062&\cr
}
$$
\hrule
\vskip 1pt
\hrule
\vskip -5pt
\noindent
{\eightpoint See footnotes at the end of the table.}

\newpage
\centerline{\bf\smcaps \colorit{Red}{Table\ A3}.\ \ Mapping from National Accounts to Model
Accounts (cont.)}
\medskip
\hrule
\vskip 1pt
\hrule
\vskip 1pt
$$\vbox{\settabs 
\+ ${\scriptstyle 2222}$ 
   & Corporate unmeasured investment plus lots of extra spa
   & {\smcaps MMModel}& {\smcaps MMNIPA}& \cr
\vskip -10pt
\+ 
         &   & \hfil {\smcaps Model} & \hfill {\smcaps NIPA}&\cr
\vskip -6pt
\+ 
         & {\smcaps Domestic Product}& & &\cr
\+ ${\scriptstyle 10}$ 
         & \ \ \ Private consumption ($c$)&\hfil 0.611& &\cr
\+       & \ \ \ \ \ \ Personal consumption expenditures& &\hfill 0.670&\cr
\+       & \ \ \ \ \ \ Less: Consumption taxes& &\hfill 
                         $-0.042$&\cr
\+       & \ \ \ \ \ \ Imputed capital services${}^c$& &\hfill 0.013&\cr
\+       & \ \ \ \ \ \ Consumption of fixed capital, durable goods& &\hfill $0.062$&\cr
\+       & \ \ \ \ \ \ Less: Consumption expenditures, durable goods& &\hfill $-0.082$&\cr
\+       & \ \ \ \ \ \ Less: Imputed personal business expense${}^b$
         & & \hfill $-\underline{0.010}$&\cr
\+       & & & \hfill 0.611&\cr
\+ ${\scriptstyle 11}$ 
         & \ \ \ Public consumption ($g$) &\hfil 0.180& &\cr
\+       & \ \ \ \ \ \ Government consumption expenditures& &\hfill 0.156&\cr
\+       & \ \ \ \ \ \ Imputed capital services${}^c$& &\hfill $\underline{0.025}$&\cr
\+       & & & \hfill 0.180&\cr
\+ ${\scriptstyle 12}$ 
         & \ \ \ Corporate measured investment ($x_{1m}$) &\hfil 0.099& &\cr
\+       & \ \ \ \ \ \ Gross domestic private investment, corporate& &\hfill 0.099&\cr
\+ ${\scriptstyle 13}$ 
         & \ \ \ Corporate unmeasured investment ($qx_{1u}$) &\hfil 0.020& &\cr
\+       & \ \ \ \ \ \ Corporate unmeasured investment& &\hfill 0.020&\cr
\+ ${\scriptstyle 14}$ 
         & \ \ \ Noncorporate investment ($x_{2m}$) &\hfil 0.152& &\cr
\+       & \ \ \ \ \ \ Gross domestic private investment, noncorporate& &\hfill 0.055&\cr
\+       & \ \ \ \ \ \ Personal consumption expenditures, durable goods & &\hfill 0.082&\cr
\+       & \ \ \ \ \ \ Less: Consumption taxes& &\hfill $-0.005$&\cr
\+       & \ \ \ \ \ \ Government investment& &\hfill 0.033&\cr
\+       & \ \ \ \ \ \ Net exports& &\hfill $-\underline{0.013}$&\cr
\+       & & &\hfill 0.152&\cr
\smallskip
\+ ${\scriptstyle 15}$ & {\smcaps Total Product} ($y$)&\hfil 1.062&\hfill 1.062&\cr
}
$$
\hrule
\vskip 1pt
\hrule
\noindent
}
\vskip -8pt
{ \baselineskip=9pt

\noindent \item{${}^a$} {\eightpoint Model and NIPA values based on 
averages over 1990s in \colorit{Red}{Table A2}.}
\vskip -15pt
\noindent \item{${}^b$} {\eightpoint Expense is 
for handling life insurance and pension plans.}
\vskip -15pt
\noindent \item{${}^c$} {\eightpoint Imputed capital services
are equal to 4.1\% times the current-cost net stock of government
fixed assets and consumer durables goods.}

}

{\baselineskip=15pt

\newpage
\def\epsfsize#1#2{.43#1}
\centerline{\epsffile{slfig1b.eps}}
\vskip -10pt
\centerline{Figure 1. Intangible Investment} 
\centerline{(Corporate Income Shares Fixed)}

\bigskip
\def\epsfsize#1#2{.43#1}
\centerline{\epsffile{slfig2b.eps}}
\vskip -10pt
\centerline{Figure 2. Productivity Relative to a 2\% Trend}
\centerline{(Corporate Income Shares Fixed)}

\newpage
\def\epsfsize#1#2{.43#1}
\centerline{\epsffile{slfig3b.eps}}
\vskip -10pt
\centerline{Figure 3. Corporate Profit Shares of Income}
\centerline{(Corporate Income Shares Fixed)}

\bigskip
\def\epsfsize#1#2{.43#1}
\centerline{\epsffile{slfig4b.eps}}
\vskip -10pt
\centerline{Figure 4. Corporate Investment Shares of Income}
\centerline{(Corporate Income Shares Fixed)}

\newpage
\def\epsfsize#1#2{.43#1}
\centerline{\epsffile{slfig1.eps}}
\vskip -10pt
\centerline{Figure 5. Intangible Investment}
\centerline{(Corporate Income Shares Varying)}

\bigskip
\def\epsfsize#1#2{.43#1}
\centerline{\epsffile{slfig2.eps}}
\vskip -10pt
\centerline{Figure 6. Productivity Relative to a 2\% Trend}
\centerline{(Corporate Income Shares Varying)}

\newpage
\def\epsfsize#1#2{.43#1}
\centerline{\epsffile{slfig5.eps}}
\vskip -10pt
\centerline{Figure 7. Industry Research and Development}


}

\bye