Federal Reserve Bank of Minneapolis Research Department Staff Report 350

Revised May 2005

Productivity and the Post-1990 U.S. Economy^{†}

Ellen R. McGrattan Federal Reserve Bank of Minneapolis and University of Minnesota

Edward C. Prescott Arizona State University and Federal Reserve Bank of Minneapolis

ABSTRACT

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.

† 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.

1. 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 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 investments 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, these unaccounted investments will be called intangible investments.^{1} 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 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, 1929–2004.) A low profit share is not typical in booms. The reason the corporate profit share fell in the boom is simple accounting: Accounting 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 than is evident in the BEA data because adjusted corporate profit and corporate investment shares were both high.

1 We use this term because the bulk of the investments are not tangible.

2. 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} ∈ S.

Preferences of the stand-in household are ordered by

E ∑_{t=0}^{∞} β^{t} U(C_{t}/N_{t}, L_{t}/N_{t}),  (2.1)

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

Y_{1,t} = f^{c}(K_{1m,t}, K_{1u,t}, L_{1,t}, s_{t})
K_{1m,t+1} = (1 − δ_{1m})K_{1m,t} + X_{1m,t}
K_{1u,t+1} = (1 − δ_{1u})K_{1u,t} + X_{1u,t}

K̂_{1m,t+1} = [(1 − δ̂_{1m})K̂_{1m,t} + (1 − δ̂_{1x})X_{1m,t}]/(1 + π_{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, K̂_{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 π_{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 θ.

Stocks K_{1m,t} and K̂_{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 δ_{1m} and δ_{1u}, respectively. For tax purposes, capital consumption allowances are equal to δ̂_{1m}K̂_{1m,t} + δ̂_{1x}X_{1m,t} and can exceed δ_{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

Y_{2,t} = f^{nc}(K_{2m,t}, L_{2,t}, s_{t})
K_{2m,t+1} = (1 − δ_{2m})K_{2m,t} + X_{2m,t}
K̂_{2m,t+1} = [(1 − δ̂_{1m})K̂_{2m,t} + (1 − δ̂_{1x})X_{2m,t}]/(1 + π_{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, K̂_{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 α.

The rate of economic depreciation of noncorporate capital is δ_{2m}. For tax purposes, total depreciation is δ̂_{2m}K_{2m,t} + δ̂_{2x}X_{2m,t}. We assume that intangible capital investment in the noncorporate sector is negligible and therefore do not include it.^{2}

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}, K̂_{1m,t}, K_{2m,t}, K̂_{2m,t}, s_{t}). For convenience, let K_{t} = (K_{1m,t}, K_{1u,t}, K̂_{1m,t}, K_{2m,t}, K̂_{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}, … s_{t}), a fact that we use later.

The problem of the household is to maximize (2.1) subject to the period t budget constraints:

(1 + τ_{c,t})C_{t} + A_{t+1} = (1 − τ_{d,t})D_{1,t} + D_{2,t} + (1 − τ_{n,t})W_{t}L_{t} + (1 + i_{t})A_{t} + T_{t}, (2.2)

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 − τ_{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,

∑_{t} ∑_{s^{t}}(1 − τ_{d,t}(s^{t}))p_{t}(s^{t})D_{1,t}(s^{t}).

Corporate distributions are

D_{1,t} = p_{1,t}Y_{1,t} − W_{t}L_{1,t} − X_{1m,t} − q_{t}X_{1u,t}

2 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.

− τ_{1,t}[p_{1,t}Y_{1,t} − W_{t}L_{1,t} − δ̂_{1m}K̂_{1m,t} − δ̂_{1x}X_{1m,t} − τ_{1k,t}K_{1m,t} − q_{t}X_{1u,t}]
− τ_{1k,t}K_{1m,t} + τ_{x,t}X_{1m,t}.

Noncorporate firms maximize the present value of distributions, namely,

∑_{t} ∑_{s^{t}} p_{t}(s^{t})D_{2,t}(s^{t}).

Thus, noncorporate distributions are

D_{2,t} = p_{2,t}Y_{2,t} − W_{t}L_{2,t} − X_{2m,t}
− τ_{2,t}[p_{2,t}Y_{2,t} − W_{t}L_{2,t} − δ̂_{2m}K̂_{2m,t} − δ̂_{2x}X_{2m,t} − τ_{2k,t}K_{2m,t}]
− τ_{2k,t}K_{2m,t} + τ_{x,t}X_{2m,t}.

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_{1}Y_{1} − p_{2}Y_{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+γ)^{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 + γ)^{t}] is detrended consumption and ℓ_{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.

3. 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 Table A1 in the appendix, with formula specifying entries as a function of model variables. Table A2 reports the main categories of the U.S. national accounts, with average values relative to GDP in the 1990s. 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.^{3}

3.1. 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.

3 Numbered lines in Table A3 correspond to numbered lines in Table A1.

3.1.1. Adjustments for consumption tax

Our consumption taxes are all 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 falls 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 Table A3 (lines 4, 8, 10, and 14).

3.1.2. Adjustments for intermediate services

Corporate value added includes some services that are not included in our notion of final goods or services.^{4} 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 (Table A2, line 6). On the product side, we subtract these expenses from personal consumption expenditures (Table A2, line 16).

In our mapping from national accounts to model accounts in Table A3, these calculations are listed as “imputed personal business expense.” They appear under capital income (line 4) and private consumption (line 10).

3.1.3. 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.^{5} 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 Table A3, these calculations are summarized in imputed capital services under noncorporate capital income (line 8) and private consumption (line 10).

4 There have been major changes recently in the accounting of financial services. Most intermediate

services are now excluded from GDP.

5 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.

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 Table A3, these calculations are summarized in imputed capital services under noncorporate capital income (line 8) and public consumption (line 11).

3.1.4. 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.

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

NIPA profit = r_{1m}k_{1m} + r_{1u}k_{1u} − δ_{1m}k_{1m} − τ_{1k}k_{1m} − qx_{1u}
= (r_{1m} − δ_{1m} − τ_{1k})k_{1m} + q(r_{1u}/qk_{1u} − x_{1u}).  (3.1)

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:^{6}

i = r_{1u}/q − δ_{1u}  (3.2)
i = \frac{(1 − τ_{1})(r_{1m} − τ_{1k}) + τ_{1}δ_{1m}}{1 − τ_{x}} − δ_{1m}  (3.3)
x_{1u} = (γ + η + δ_{1u})k_{1u}  (3.4)
x_{1m} = (γ + η + δ_{1m})k_{1m}  (3.5)

on a balanced growth path, where i is the real interest rate and η is the population growth rate.

Equations (3.1)-(3.5) 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 τ_{1}, the corporate property tax rate τ_{1k}, the subsidy to investment τ_{x}, the tangible depreciation rate δ_{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 η is around 1 percent per year. Trend technology growth γ is around 2 percent per year.

The system of equations (3.1)-(3.5) is five equations in the five unknowns, r_{1u}/q −δ_{1u}, r_{1m}, qk_{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.^{7} This estimate is independent of our choice of δ_{1u}. Our estimate of net investment qx_{1u} − δ_{1u}k_{1u} is also independent of our choice of δ_{1u}. Net intangible investment averaged 2 percent of GDP.^{8}

The equilibrium path of intangible investment since 1990

6 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.

7 The inputs to this calculation are: τ_{1} = 0.37, τ_{1k} = 0.02, τ_{x} = 0, δ_{1m} = 0.06, x_{1m} = 0.099, i = 0.041,

γ = 0.02, and η = 0.01.

8 For convenience we will set δ_{1u} = 0 when we derive time series for q_{t}x_{1u,t}. We are in effect working

with net intangible investment.

We can infer the path for intangible investment using intratemporal 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 θ 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_{1}y_{1}), or equivalently one less the average corporate labor income share, 1 − wℓ_{1}/(p_{1}y_{1}). Using averages in the 1990s, we estimate an average corporate capital share of θ = 0.33. If intangible investments are chosen so that

\frac{w_{t}ℓ_{1,t}}{p_{1,t}y_{1,t}} = 1 − θ_{t}
= 1 − θ,

then q_{t}x_{1u,t} satisfies

w_{t}ℓ_{1,t} = (1 − θ)p_{1,t}y_{1,t}
= (1 − θ)[va_{1,t}^{accounting} + q_{t}x_{1u,t}]  (3.6)

where we have an estimate of θ and time series for corporate compensation (w_{t}ℓ_{1,t}) and accounting corporate value added (va_{1,t}^{accounting}). The unknown in equation (3.6) is the product q_{t}x_{1u,t}.

In Figure 1, we display the implied time series for intangible investment after 1990. What is striking about this figure is the sixfold 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^{9}

p_{1,t}y_{1,t} − w_{t}ℓ_{1,t} − δ_{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}/ℓ_{t}. The hours measure we use is described in Prescott and Ueberfeldt (2003) and based on the Current Population Survey. 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, 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.

9 In McGrattan and Prescott (2004), we do a sensitivity analysis that includes varying δ_{1u}.

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 − θ_{t} be the corporate labor income share in period t and let 1 − α_{t} be the noncorporate labor income share in period t. Thus, our second approach assumes that

\frac{1 − θ_{t}}{1 − α_{t}} = \frac{1 − θ}{1 − α},  (3.7)

where θ and α are found by taking averages over our sample period. For the corporate sector, the average is θ = 0.33. For the noncorporate sector, the average is α = 0.496.^{10}

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 (3.7) 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 (3.7) yields

(\frac{w_{t}ℓ_{1,t}}{p_{1,t}y_{1,t}} ) (\frac{p_{2,t}y_{2,t}}{w_{t}ℓ_{2,t}} ) = \frac{1 − θ}{1 − α}.

10 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 1.

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_{t}x_{1u,t} = p_{1,t}y_{1,t} − va_{1,t}^{accounting}.

In Figure 5, we plot the equilibrium path for the implied investment in intangibles. As before, we find a sixfold 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}/ℓ_{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 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.

4. Supporting Evidence

As we noted earlier, we do not have direct measures of all intangible investments. 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 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.

5. 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.^{11} They, as do we, use hours worked estimates based on the Current Population Survey.^{12}

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 late 1990s with productivity growth well in excess of the 2 percent historical trend. Prior and subsequent to this boom, average productivity growth was about half of the level of trend growth.

11 See, for example Jorgenson et al. (2003, p. 45) and Groningen Growth and Development Centre and

The Conference Board (2004).

12 There are two other measures of U.S. hours worked. The BEA estimate, which uses state unem-

ployment 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.

Our accounting resolves the puzzle of why corporate accounting profits were so low in the 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.)

6. References

Board of Governors of the Federal Reserve (1945–2004), Flow of Funds Accounts of the United States (Washington, DC: Federal Reserve System).

Eldridge, Lucy P., Marilyn E. Manser, and Phyllis Flohr Otto (2004), “Alternative Measures of Supervisory Employee Hours and Productivity Growth,” Monthly Labor Review, 127(4): 9–28.

Groningen Growth and Development Centre and The Conference Board (2004), 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,” 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 (forthcoming), “Taxes, Regulations, and the Value of U.S. and U.K. Corporations,” Review of Economic Studies.

Prescott, Edward C. and Alexander Ueberfeldt (2003), “U.S. Hours and Productivity Behavior using CPS Hours Worked Data: 1959-I to 2003-II,” Mimeo, Federal Reserve Bank of Minneapolis.

U.S. Department of Commerce, Bureau of Economic Analysis (1929–2004), Survey of Current Business (Washington, DC: U.S. Government Printing Office).

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. Table A1 lists the account categories for our model along with formulas for variables in the model. 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. Table A3 provides a mapping between these accounts. In the main text, we provide justifications for the calculations summarized here.

Table A1. Model Economy Accounts

Model Expression

1 Corporate Domestic Value Added  p_{1}y_{1}
2  Depreciation  δ_{1m}k_{1m}
3  Labor income  wℓ_{1}
4  Capital income  r_{1m}k_{1m}+r_{1u}k_{1u}−δ_{1m}k_{1m}
5 Noncorporate Domestic Value Added  p_{2}y_{2}
6  Depreciation  δ_{2m}k_{2m}
7  Labor income  wℓ_{2}
8  Capital income  r_{2m}k_{2m}−δ_{2m}k_{2m}
9 Total Domestic Value Added  y

Domestic Product

10  Private consumption  c
11  Public consumption  g
12  Corporate measured investment  x_{1m}
13  Corporate unmeasured investment  qx_{1u}
14  Noncorporate investment  x_{2m}
15 Total Domestic Product  y

Table A2. National Accounts, Average in 1990s Relative to GDP

1 Corporate Domestic Value Added  0.589
2  Consumption of fixed capital  0.066
3  Compensation of employees  0.378
4  Corporate profits with IVA and CCadj  0.075
5  Taxes on production and imports^{a}  0.056
6  Net interest and miscellaneous payments  0.013
7 Noncorporate Domestic Value Added  0.400
8  Consumption of fixed capital  0.053
9  Compensation of employees  0.240
10  Rental income of persons with IVA  0.014
11  Proprietors’ income with IVA and CCadj  0.068
12  Taxes on production and imports^{a}  0.020
13  Net interest and miscellaneous payments  0.051
14 Statistical discrepancy  0.011
15 Total Domestic Value Added  1.000

Domestic Product

16  Personal consumption expenditures  0.670
17  Durable goods  0.082
18  Nondurable goods and services  0.588
19  Government consumption expenditures and gross investment  0.189
20  Consumption expenditures  0.156
21  Gross investment  0.033
22  Gross private domestic investment^{b}
23  Corporate  0.099
24  Noncorporate  0.055
25  Net exports of goods and services  −0.013
26 Total Domestic Product  1.000

Addendum:

27  Consumption taxes  0.047
28  Consumption of fixed capital, durable goods  0.062
29  Current-cost net stock of government fixed assets  0.604
30  Current-cost net stock of consumer durable goods  0.308

NOTE: IVA, inventory valuation adjustment; CCadj, capital consumption adjustment.

a This category includes business transfers and excludes subsidies. b The breakdown into corporate and noncorporate investments is based on data from the Flow of Funds

Accounts (Board of Governors of the Federal Reserve System, 1945–2004). For corporate investment, we sum investment of nonfinancial corporate business, financial corporations, and 10 percent of farm business.

Table A3. Mapping from National Accounts to Model Accounts^{a}

Model  NIPA
1 Corporate Domestic Value Added (p_{1}y_{1})
2 Depreciation (δ_{1m}k_{1m}) 0.066
Consumption of fixed capital  0.066
3 Labor income (wℓ_{1}) 0.378
Compensation  0.378
4 Capital income (r_{1m}k_{1m}+r_{1u}k_{1u}−δ_{1m}k_{1m}) 0.120
Corporate profits with IVA and CCadj  0.075
Net interest and miscellaneous payments  0.013
Less: Imputed personal business expense^{b}  −0.010
Taxes on production and imports  0.056
Less: Consumption taxes  −0.034
Corporate unmeasured investment  \underline{0.020}

0.120

5 Noncorporate Domestic Value Added (p_{2}y_{2})
6 Depreciation (δ_{2m}k_{2m}) 0.115
Consumption of fixed capital  0.053
Consumption of fixed capital, durable goods  \underline{0.062}

0.115

7 Labor income (wℓ_{2}) 0.251
Compensation  0.192
70% Proprietors’ income with IVA and CCadj  0.048
Statistical discrepancy  \underline{0.011}

0.251

8 Capital income (r_{2m}k_{2m}−δ_{2m}k_{2m}) 0.132
Rental income of persons with CCadj  0.014
30% Proprietors’ income with IVA and CCadj  0.020
Net interest and miscellaneous payments  0.051
Current surplus of government enterprises  0.001
Taxes on production and imports  0.020
Imputed capital services^{c}  0.038
Less: Consumption taxes  −\underline{0.012}

0.132

9 Total Domestic Value Added (y)  1.062  1.062

See footnotes at the end of the table.

Table A3. Mapping from National Accounts to Model Accounts (cont.)

Model  NIPA

Domestic Product

10 Private consumption (c) 0.611
Personal consumption expenditures  0.670
Less: Consumption taxes  −0.042
Imputed capital services^{c}  0.013
Consumption of fixed capital, durable goods  0.062
Less: Consumption expenditures, durable goods  −0.082
Less: Imputed personal business expense^{b}  −\underline{0.010}

0.611

11 Public consumption (g) 0.180
Government consumption expenditures  0.156
Imputed capital services^{c}  \underline{0.025}

0.180

12 Corporate measured investment (x_{1m}) 0.099
Gross domestic private investment, corporate  0.099
13 Corporate unmeasured investment (qx_{1u}) 0.020
Corporate unmeasured investment  0.020
14 Noncorporate investment (x_{2m}) 0.152
Gross domestic private investment, noncorporate  0.055
Personal consumption expenditures, durable goods  0.082
Less: Consumption taxes  −0.005
Government investment  0.033
Net exports  −\underline{0.013}

0.152

15 Total Product (y)  1.062  1.062

a Model and NIPA values based on averages over 1990s in Table A2. b Expense is for handling life insurance and pension plans. c Imputed capital services are equal to 4.1% times the current-cost net stock of government fixed assets

and consumer durables goods.

Figure 1. Intangible Investment (Corporate Income Shares Fixed)

Figure 2. Productivity Relative to a 2% Trend (Corporate Income Shares Fixed)

Figure 3. Corporate Profit Shares of Income (Corporate Income Shares Fixed)

Figure 4. Corporate Investment Shares of Income (Corporate Income Shares Fixed)

Figure 5. Intangible Investment (Corporate Income Shares Varying)

Figure 6. Productivity Relative to a 2% Trend (Corporate Income Shares Varying)

Figure 7. Industry Research and Development 25