Computers, productivity, and input substitution.

Stiroh, Kevin J.

I. INTRODUCTION

The last two decades has been a puzzling time for many productivity analysts. While computer prices fell at extraordinary rates and firms invested hundreds of billions of dollars in new computer equipment, aggregate productivity growth remained sluggish. This "computer productivity paradox" has generated a large literature that examines the economic impact of the computer revolution.(1)

This paper offers a simple solution to the computer productivity paradox by making careful distinction between computers as an output from one sector and an input to other sectors. Data for 35 manufacturing and service sectors for 1947-1991 show that sectoral differences are crucial in understanding the impact of computers. Aggregate analysis is inappropriate since it obscures basic distinctions between a shifting production function in the computer-producing sector (multi-factor productivity growth) and movements along production functions in the computer-using sectors (substitution and capital accumulation). Once these differences are isolated, the growth impact of computers is readily observable.

The computer-producing sector experienced fundamental technological progress and now produces cheaper, better computers. The sectoral data show this as rapid Multi-Factor Productivity (MFP) growth for 1973-1991. Although aggregate MFP growth remains below historic averages, the computer-producing sector has clearly done its part - MFP growth in this sector is many times the economy average and has contributed over one-third of aggregate MFP growth for 19811991. The sectoral detail shows that the slowdown in aggregate productivity would have been much more severe were it not for such large MFP gains in the computer-producing sector.

For the other sectors of the economy, computers affect growth in a more traditional, although less glamorous, way. When the price of real computing power fell so dramatically in the 1970s and 1980s, firms responded by substituting away from relatively expensive labor and non-computer capital and investing heavily in cheap computers. For these sectors, the computer revolution affects output growth not by raising MFP, but by inducing firms to accumulate computers at extraordinary rates. Real computer services, for example, grew in excess of 20% per year in 14 out of 35 sectors for 1973-1991.

Although virtually all sectors are rapidly accumulating computer equipment, computers remain small in levels. In 1991, for example, computer investment was only 10% of private fixed investment so the growth contribution of computers remains small relative to sectoral aggregates of labor and non-computer capital. The rapid rates of accumulation, however, are clearly making computers a more important source of growth across sectors.

With this heavy investment also came the wide-spread expectation that computers would fundamentally alter the way firms operate and lead to higher MFP. The reality has been very different as the most computer-intensive sectors show steep declines in MFP growth after 1973. With three-quarters of all computers concentrated in three service sectors (Trade, FIRE, and Other Services), however, this finding must be interpreted with caution. As Griliches [1994] notes, output in these sectors is largely "unmeasurable" and thus MFP growth will be understated.

Nonetheless, it is quite reasonable that even computer-using sectors where output is easier to measure show no MFP gains. Computer investment creates a capital input that enters the production function like any other purchased input. Since constant-quality deflators embody productivity improvements in investment, the direct impact is seen through the rapid capital accumulation. Only if the adoption of computers leads to production externalities or spillovers would computer investment also increase MFP growth. The data, however, show no evidence of this.

II. COMPUTERS AND GROWTH

The national statistics most clearly show the computer revolution in the investment data. Over the last three decades, real computer investment increased from $0.1 billion in 1958 to $51 billion in 1991 and the price of computer investment fell 20% per year.(2) The literature on the computer productivity paradox questions why such a large increase in the quality and quantity of computers has not been manifest in the aggregate statistics, particularly productivity. Possible explanations for this puzzle include measurement errors, the small relative size of computers, realloaction of output, long learning lags, and market frictions.

It is not clear, however, that improved computers should dramatically improve aggregate MFP or even MFP in a typical sector. The fundamental technological change, e.g., more memory or Millions of Instructions Per Second (MIPS) per dollar of inputs, occurred in the computer-producing sector. Even if this sectoral MFP growth is measured correctly, the increase in aggregate MFP growth may be relatively small due to the small size of the sector. After all, gross output in the computer-producing sector was only 5% of aggregate value-added in 1991.

Computer-using sectors, on the other hand, take advantage of the technology-induced price declines and substitute towards the relatively cheap computer. In a strict sense, this input substitution induces firms to move along a given production isoquant but does not shift the production function or increase MFP.(3) The substitution towards computers increases the growth contribution of capital for both the computer-using sectors and in the aggregate. Since the constant-quality deflators embody the improvements in computers in new investment, growth is attributed to capital accumulation and not to MFP gains.

One could argue that computer investment would increase MFP growth in the computer-using sectors, but these explanations typically lie outside of the traditional neoclassical framework of Solow [1957] or Jorgenson [1990]. For example, a production spillover from computer investment in one sector could allow faster growth in another sector. Alternatively, if investment prices do not fully reflect quality improvements, then real investment and capital input will be under-measured. In both eases, computer investment increases measured MFP, but each example requires a specific departure from the neoclassical model. The importance of these non-traditional effects is an empirical question that is examined in Section III.

Given the small size of the computer-producing sector and this input substitution story, there may not be a computer productivity paradox. The computer-producing sector experiences technological growth but is small and might not significantly impact aggregate MFP growth. The computer-using sectors substitute towards relatively cheap computers and the growth contribution of capital increases. The remainder of this section provides empirical estimates of these effects.

Data

The fundamental analysis of this paper is growth accounting at the sectoral level. To accomplish this, the widely circulated dataset of Jorgenson, Gollop and Fraumeni [1987] was updated through 1991. This dataset includes a complete set of input-output accounts and Gross Output production functions for 35 roughly 2-digit SIC sectors that comprise the private, domestic U.S. economy. See Jorgenson et al. [1987] for definitions and data sources.

Since the data come from many sources that are at different levels of aggregation, data constraints in large part determine the level of disaggregation. For example, the Bureau of Labor Statistics (BLS) estimates Gross Output for 183 detailed industries, the Bureau of Economic Analysis (BEA) estimates investment flows for 51 assets for 61 industries and BEA estimates Gross Product Originating (Value-Added) for 88 industries and aggregates. While a more detailed disaggregation would be desirable, particularly for the service sectors, data constraints make this impractical.

BEA includes computer investment in its asset class called "Office, Computing and Accounting Machinery (OCAM)." OCAM is composed primarily of computer equipment and serves as the measure of computer investment and capital throughout the paper. Each computer component of OCAM, e.g., personal computers, mainframes, displays, and printers, is separately deflated with a constant-quality price index to account for the large quality improvements.

To show the relative magnitude of each of the 35 sectors, Table I breaks down 1991 private, business Value-Added into the 35 component sectors.(4) The table also shows each sector's share of aggregate Value-Added, non-OCAM capital income, OCAM capital income and labor income.

Aggregate Results

The data is first aggregated across sectors and, under the assumptions of constant returns to scale and perfect competition, aggregate output growth can be decomposed as:

(1) [Delta]Q = [[Alpha].sub.1] *[Delta][K.sub.1] + [[Alpha].sub.2] * [Delta][K.sub.2]

+(1 - [[Alpha].sub.1] - [[Alpha].sub.2]) * [Delta]L + [v.sub.T]

where a [Delta] before a variable represents a rate of change, Q is aggregate real output, [K.sub.1] is the flow of non-OCAM capital services, [K.sub.2] is the flow of OCAM capital services, L is labor input, [[Alpha].sub.1] is the share of non-OCAM capital income in nominal output, [[Alpha].sub.2] is the share of OCAM capital in nominal output, and [v.sub.T] is the growth rate of multi-factor productivity (MFP) or the Solow residual. Time subscripts have been suppressed.(5)

Table II breaks down aggregate output growth into the contribution of capital (both non-OCAM and OCAM), the contribution of labor and the growth rate of MFP. The results are familiar - labor and capital make roughly equal contributions to growth, the contribution of labor has increased since 1973, and both output and MFP growth have slowed since 1973.

OCAM capital contributes 0.15 percentage points to aggregate growth for 1973-1991 due to the large average growth rate ([Delta][K.sub.2] = 20.44%) [TABULAR DATA FOR TABLE I OMITTED] but small weight ([[Alpha].sub.2] = 0.74%). Despite averaging only 2.4% of all capital services, this exceptional growth rate allowed OCAM capital to contribute 16% of capital's entire contribution to aggregate growth. Given their small relative size, computers are making an impressive contribution to aggregate economic growth.(6)

TABLE II

Sources of Aggregate Growth

 1947-1973 1973-1991 1947-1991

Value-Added 3.754 2.195 3.116
Contribution of Capital 1.133 0.959 1.061
Non-OCAM 1.107 0.807 0.984
OCAM 0.026 0.152 0.077
Contribution of Labor 1.050 1.138 1.086
Productivity 1.571 0.098 0.969

Contribution of an input is the average share-weighted growth rate.

Since all input series are quality-adjusted, the rapid accumulation of more productive computers increases the contribution of capital but does not directly impact MFP growth. MFP growth reflects only those factors, e.g., disembodied technical change, reduced inefficiency, returns to scale, or new production techniques, that are not embodied in the quality-adjusted capital and labor series. Thus, it is entirely consistent that the computer revolution is characterized by rapid capital accumulation but slow MFP growth at the aggregate level.

Sectoral Framework

The aggregate analyses done by Oliner and Sichel [1994] and above show that computers are a small source of growth in an absolute sense but a large source of growth relative to their size. More importantly, the growth contribution of computers is definitely increasing even at the aggregate level.

Aggregate growth accounting, however, misses important details in the relationship between computers and growth. Since computers have a different impact across sectors, one needs to analyze the sources of growth at a sectoral level. This type of sectoral approach has three distinct advantages over the aggregate analyses of Oliner and Sichel [1994] and above.

First, one can directly examine the fundamental technological change in the computer-producing sector. Since technology is the driving force behind the computer revolution, it is important to measure and quantify this. Second, one can isolate computer-using sectors and pinpoint where the accumulation of computers is concentrated and where computers are having the largest growth impact. Third, one can compare the accumulation of computer capital to MFP growth in each sector and search for production spillovers from computers. It is impossible to identify any of these effects with aggregate data.

The sectoral analog to equation (1) is based on a Gross Output production function that can be written as(7)

(2) [Delta][Y.sub.n] = [[Alpha].sub.K, 1, n] *[Delta][K.sub.1, n] + [[Alpha].sub.K, 2, n] *[Delta][K.sub.2, n]

+ [[Alpha].sub.L, n] *[L.sub.n] + [[Alpha].sub.E, n] *[Delta][E.sub.n] + [[Alpha].sub.M, n] *[Delta][M.sub.n] *[Delta][M.sub.n] + [v.sub.T, n],

[[Alpha].sub.K, 1, n] + [[Alpha].sub.K, 2, n] + [[Alpha].sub.L, n] + [[Alpha].sub.E, n] + [[Alpha].sub.M, n] = 1

n = 1...35

where [Y.sub.n] is Gross Output, [E.sub.n] is energy intermediate inputs, [M.sub.n] is material intermediate inputs, [Alpha] is the nominal share of the subscripted variable in Gross Output and [v.sub.T, n] is the MFP growth rate, all for sector n. Table III shows the 1991 nominal shares of each input in Gross Output and Value-Added for each of the 35 sectors. As a comparison, median and weighted average input shares are also reported.(8)

Equation (2) is used to measure the sources of growth for each of the 35 sectors and Table IV presents sectoral growth accounts for three time periods - 1947-1973, 1973-1991, and 1947-1991. The sectors of particular interest are the computer-producing sector (identified by *) and the computer-using sectors (identified by **).

Baily and Gordon [1988] also take a sectoral approach and present a detailed analysis of Average Labor Productivity (ALP) at the sectoral level from 1948 to 1987. Several important differences, however, distinguish this paper from Baily and Gordon.

The most important distinction is the focus on MFP rather than on ALP. The complete input-output analysis allows the growth contribution of computer capital services, [[Alpha].sub.K, 2, n] *[Delta][K.sub.2, n], to be isolated from the contribution of other inputs and MFP growth. Moreover, by explicitly estimating capital service prices from quality-adjusted deflators, the capital indices incorporate quality change and substitution between heterogeneous types of capital.

Baily and Gordon [1988] cite the lack of data on capital input by industry and estimate the following relationship

(3) [Delta]ALP = [Delta]Q - [Delta]L

where [Delta]ALP is the growth rate of average labor productivity, [Delta]Q is the growth rate in output, and [Delta]L is the growth rate of labor input.

Since ALP increases with the accumulation of all inputs as well as MFP growth, it is impossible to isolate and quantify the separate influences of the accumulation of computer capital, other purchased inputs, technology or spillovers from equation (3). Economic theory predicts that the rapid price decline in computing power will induce firms to substitute towards computers and away from other inputs, so this is an important limitation in the ALP framework.

A related difference is the use of a Gross Output production function that includes all productive inputs - capital, labor and intermediate goods - as opposed to the value-added approach in Baily and Gordon [1988]. Basu and Fernald [1995] show that value-added data can lead to misspecification and biased estimates of MFP since Gross Output is the fundamental model of production. Firms in fact use capital, labor, energy and material inputs to produce goods and services, while Value-Added simply measures each firm's contribution to GDP.(9)

A final difference is simply the later time period. Baily and Gordon [1988] present data by sector and estimate the share of the computer capital stock through 1987. Computer technology has changed dramatically since 1987 as constant-quality prices continued to fall, quality improved and personal computers became the dominant form of computer investment.

The Computer-Producing Sector

The production of computers takes place in the Census industry "computer and office equipment" (SIC #357) and is included in the broader "Non-Electrical Machinery" sector (SIC #35). After computers were introduced into the national accounts in 1958, the composition of this sector changed dramatically [TABULAR DATA FOR TABLE III OMITTED] [TABULAR DATA FOR TABLE IV OMITTED] with the share of computers rising from near zero in 1958 to 33% in 1991. Other forms of more traditional industrial equipment, e.g., "construction and related machinery" and "metalworking machinery," declined in share reflecting the changing structure of the U.S. economy away from manufacturing and towards services.

The growth accounts for the computer-producing sector (Non-Electrical Machinery), identified by * in Table IV on page 183, show rapid acceleration in MFP growth from 0.21% a year for 1947-1973 to 1.42% a year for 1973-1991. More than half of the 2.63% annual growth in gross output was due to increased MFP growth for 1973-1991.

For the more recent period of 1981-1991, the results are even more striking. While output growth remained constant at 2.63% per year, the average growth rate of MFP jumped to 2.69% and all inputs except capital actually shrunk.(10) During the 1980s, virtually all output growth in the computer-producing sector was due to technological progress. When the recession year of 1991 is excluded, the average rate of MFP growth rises to 3.05%.

It may be hard to cleanly interpret these results due to the broad definition of the sector. The computer-producing sector is an aggregate that includes the production of many types of machinery from several industries and the "computer and office equipment" industry accounted for at most one-third of production in the sector. While labor, energy and material may be shrinking for the entire sector, for example, it seems unlikely that inputs to the "computer and office equipment" industry are declining. Rather, the composition of the sector is changing from production of heavy equipment that is material and labor intensive to the production of computers that is OCAM-capital intensive and experiencing rapid technological progress.

To form a rough estimate for the growth of MFP in just the "computer and office equipment" industry (SIC #357), one can turn to the dual price problem. For 1973-1991, output in the "computer and office equipment" industry experienced an annual price decline of 6.4% and averaged a 20% nominal share of the sector. Interpreting the 6.4% price decline entirely as MFP growth, assuming no other technology advances and applying the one-fifth weight gives a back-of-the-envelope estimate of MFP at 1.26% a year for the sector. This is consistent with the estimated rate of MFP growth of 1.42% per year for the Non-Electrical Machinery sector.

For the period for 1981-1991, the average price decline is 12.0% and the share is about 25% which implies a rate of MFP growth of 3.0%. Again, this is close to the estimates from the growth accounts. This suggests that the annual growth of MFP in the "computer and office equipment" industry is a remarkable 6% to 12% for the past 20 years.

While the computer-producing sector experienced such strong MFP growth, the aggregate economy was in the midst of the much-publicized productivity slowdown. Aggregate MFP growth across the 35 sectors, for example, fell from 1.57% per year for 1947-1973 to 0.10% for 1973-1991. There was a modest MFP revival in the 1980s, especially in manufacturing, but the aggregate MFP growth of 0.43% per year for 1981-1991 remained far below the 2.69% in the computer-producing sector.

A sectoral decomposition shows that, when one accounts for the relative size, 0.16 percentage points of the aggregate MFP growth for 1981-1991 is due to MFP growth in the computer-producing sector.(11) Although MFP growth was extraordinary in this sector, the small size of the sector keeps this contribution small in an absolute sense. When compared to the other sectors, however, the computer-producing sector is clearly making a substantial contribution to aggregate MFP growth as more than one-third of aggregate MFP growth in the 1980s was from the computer-producing sector alone.(12)

The Computer-Using Sectors

To examine the impact of OCAM as a capital input, sectors are labeled "computer-using" if the nominal value of OCAM capital services exceeds 4.0% of total capital services in 1991.13 Eight sectors meet this classification - Printing and Publishing, Stone, Clay and Glass, Non-Electrical Machinery, Electrical Machinery, Instruments, Trade, FIRE and Other Services - and are identified by ** in Table IV.(14)

These computer-using sectors account for 88% of all OCAM capital services and just three sectors - Trade, FIRE and Other Services - account for nearly 77% of all OCAM services. While the computer revolution may appear to be everywhere, computers are actually highly concentrated in only a few sectors. These computer-using sectors account for 63% of total value-added in the private economy and are the sectors where one would expect to find computers, but it is interesting to note that computers play a very small role in the production of more than one-third of private GDP.

The first step is to compare the growth contribution of OCAM for 1947-1973 to 19731991. All eight computer-using sectors show large increases in the growth contribution of OCAM capital. While this reflects the selection criteria, all sectors show that OCAM capital became a much more important source of growth. The contribution is not always large in an absolute sense, but computers are clearly increasing as a source of growth.

Table IV also shows substantial substitution between inputs in these computer-using sectors. As the contribution of OCAM increased in the 1970s and 1980s, the growth rate of output fell for all eight sectors and the contribution of other inputs generally declined. Only Printing and Publishing and Instruments showed an increase in the contribution of more than one input besides OCAM capital. If computers are growing rapidly while the growth of output and other inputs is slowing, the sectors must be rapidly substituting towards computers.

The substitution towards OCAM capital was not limited to only the eight computer-using sectors. Out of 35 sectors, only two - Apparel and Coal Mining - showed decreases in the growth contribution of OCAM capital. The Petroleum and Gas, Paper, Primary Metals, Fabricated Metals, Motor Vehicles, Miscellaneous Manufacturing, Transportation, Communication and Gas Utilities sectors all showed large increases in the growth contribution of OCAM capital and declines from non-OCAM capital. This contribution is sometimes small, but these sectors clearly substituted towards the relatively cheap OCAM capital.

Table V decomposes the growth contribution of OCAM into the nominal share and the growth rate for 1947-1973 and 1973-1991. The results suggests that rapid accumulation of computers is perhaps the defining characteristic of the computer revolution. With 14 sectors showing growth rates of OCAM in excess 20% for 1973-1991, computers are definitely making an impact. Since the largest sectors accumulated OCAM capital most quickly, the aggregate growth rate of OCAM capital was a very rapid 20.44% per year for 1973-1991.

As a caveat, these growth accounting results may understate the impact of computers for several reasons. The computer-producing sector sells computer equipment to other sectors in two ways. Computers are an investment good, which is directly accounted for in the OCAM capital services, but computers are also an intermediate good that is included in [M.sub.n]. In 1991, 43% of gross output from the computer-producing sector was sold as investment goods and 47% was sold as intermediate goods, e.g., computers installed in airplanes or embedded in factory machines.(15) This channel is not explored here, but preliminary evidence suggests that intermediate purchases of computers are important.

[TABULAR DATA FOR TABLE V OMITTED]

A second reason is that OCAM only includes computers in the literal sense, e.g., mainframe processors, displays, printers, storage devices, and personal computers. Other high-tech goods such as communications, scientific or photocopy equipment embody much the same technology as traditional computers, but are not examined here. According to BEA [1993], investment in computer equipment is only 37.7% of 1991 real investment in "information processing and related equipment." This suggests that the analysis understates the impact of the advances in information technology.

III. SECTORAL MFP AND COMPUTERS

This section examines the relationship between OCAM investment and MFP growth. Casual inspection shows the perhaps surprising result of a negative relationship between OCAM and MFP growth. For most computer-using sectors, the average growth rate of MFP fell while OCAM capital grew. The large literature on the computer productivity paradox is motivated by previous findings of this type, e.g., Baily and Gordon [1988] and Berndt and Morrison [1995, 1991].

According to the input substitution story sketched and documented in Section II, however, the direct impact of the computer revolution for most sectors is faster accumulation, substitution, and an increased growth contribution from computers. New products that are only possible with cheap computer power, e.g., complex derivatives in the finance sector, are directly attributable to the services from computers. This increases the contribution of capital services but not MFP growth in the computer-using sector.

There is no a priori reason to expect faster MFP growth in the computer-using sectors if firms are simply substituting one input for another or getting new output from new capital. MFP growth increases only if more output can be produced from the same inputs, i.e., a shift in the production function. For example, a positive production spillover from computer investment would lead to faster MFP growth in the computer-using sectors. Previous evidence for this, however, is mixed.

Bresnahan [1986] finds evidence of positive down-stream spillovers for computer-users, Griliches and Siegel [1992] show a positive correlation between MFP growth and computer investment for 4-digit manufacturing industries, Lichtenberg [1993] finds excess returns to computer capital and labor using firm data, Brynjolfsson and Hitt [1994] find excess returns to computer investment, Bartelsman, Caballero and Lyons [1994] find a long-run relationship between industry productivity and suppliers that could represent "technological linkages," and Bresnahan and Trajtenberg [1995] provide a theoretical model where innovation leads to downstream spillovers. This evidence suggests that computers may have a non-traditional impact on growth.

It is not obvious, however, that these effects are really production spillovers. The Bresnahan [1986, 742] study, for example, deals with "improved products whose prices do not fully reflect their enhanced downstream value." This is not MFP in the conventional sense, i.e., more output from the same inputs. Rather, this is a problem of mismeasurement where downstream users receive a windfall gain due to incorrect pricing. As Griliches [1991, 13] states, these "are not real knowledge spillovers. They are just consequences of conventional measurement problems." The same criticism applies to Bartelsman et al. [1994, 1083] who hypothesize that the linkage could reflect "unpriced specialization/quality."

On the other hand, some evidence suggests that computers have no impact on productivity. Baily and Gordon [1988] show that computer-intensive industries have experienced weak ALP growth. In a series of papers by Berndt and Morrison [1995, 1991] and Berndt, Morrison and Rosenblum [1992], the authors find evidence of over-investment in high-tech equipment, i.e., marginal costs of high-tech equipment exceed marginal benefits, and a negative correlation between hightech capital intensity and both MFP and ALP for 2-digit manufacturing industries.

To examine the relationship between computers and MFP, the following cross-sectional regressions were estimated

(5) [Delta]MF[P.sub.n] = [Alpha] + [[Beta].sub.1][Delta][K.sub.2, n] + [[Epsilon].sub.n]

(6) [Delta]MF[P.sub.n] = [Alpha] + [[Beta].sub.1][Delta]([K.sub.2, n]/[K.sub.n]) + [[Epsilon].sub.n]

[TABULAR DATA FOR TABLE VI OMITTED] where [Delta] represent the average growth rate of each variable for either 1947-1991 or 1973 - 1991. MF[P.sub.n] is multi-factor productivity, [K.sub.2, n] is the flow of OCAM services and [K.sub.n] is flow of total capital services, all for sector n.(16)

The results in Table VI support the growth accounting results, Baily and Gordon [1988] and Berndt and Morrison [1995] as the data show little relationship between OCAM growth and MFP growth. This is true if OCAM growth is measured as the quantity of OCAM capital services, the share of OCAM capital in total capital services, if the recession year of 1991 is excluded, or if the service sectors are excluded.

A concern regarding results of this type is that computer investment is highly concentrated in the sectors where output is particularly hard to measure. Griliches [1994, 11] argues that the "computer paradox" may be due to the difficulty in measuring output in the computer-intensive service sectors. Since MFP growth is precisely the difference between measured output growth and measured input contributions, any unmeasured output directly biases MFP growth downward. With 77% of all OCAM services concentrated in three service sectors where output is notoriously hard to measure (Trade, FIRE, and Other Services), mismeasurement of service output probably contributes to the weak findings.(17) Berndt and Morrison [1995, 1991], however, find similar results for only manufacturing industries and these results are qualitatively similar when the service sectors are excluded.

Potential errors in measuring output do not, however, change the main conclusion of large substitution towards computers. As the relative price of computing power falls, firms are purchasing more computers and relatively less of other inputs. Since primary input growth is measured independently of output growth, input substitution and changes in the growth contribution of the inputs is not subject to the same downward biases as the measurement of MFP growth. Even if output and MFP are poorly measured, sectors are clearly substituting towards relatively cheap computer capital and rapidly accumulating computers.

IV. CONCLUSIONS

This paper explores the relationship between computers and economic growth at both the aggregate and sectoral level. The data show that the rapid technological advances in the production of computers have translated into higher multi-factor productivity for the computer-producing sector, substantially contributed to aggregate multi-factor productivity growth, and led to a large substitution towards computers as an input for computer-using sectors.

The analysis focuses on private, business investment in OCAM and the direct growth impact from investment and accumulation of computer capital. A more broadly defined measure of computer technology could include spending on inputs that are complements to computers such as software, computers as intermediate inputs, or the purchase of other high-tech equipment that embodies much the same technology as computers. By narrowing the focus to just computer investment and capital, the results highlight the substitution towards computers as an input but likely underestimate the true impact of the computer revolution on economic growth.

Nonetheless, these results show that computers have made a clear and increasing contribution to economic growth. The contribution of computer capital to aggregate output growth increased from 0.03 percentage points per year for 1947-1973 to 0.19 percentage points for 1981-1991. Similarly, the contribution of the computer-producing sector to aggregate multi-factor productivity growth increased from 0.01 percentage points to 0.16 percentage points for the same periods. Perhaps more importantly, many sectors are taking advantage of the lower price of computer services and substituting towards computers as a production input.

As a final point, the massive price declines and related computer investment have continued since 1991. According to BEA [1995], the price of new computer equipment fell 16% a year from 1991 to 1994 and real computer investment increased 30% a year. Businesses are still investing heavily in computer equipment and taking advantage of the relative price decline. As firms continue to substitute towards cheap computers, computers will become an increasingly important source of U.S. economic growth.

APPENDIX

A production function shows how a given technology transforms a flow of inputs into a flow of outputs. To estimate a production function, one needs an estimate of the flow of real productive services from capital and not a measure of the existing capital stock. This conceptual distinction goes back at least as far as Solow [1957] and has been empirically implemented in many growth accounting studies such as Jorgenson [1990], BEA [1992], and Oliner and Sichel [1994]. This section outlines the methodology used to estimate the flow of capital services.

The real capital stock, [A.sub.n, i, t] for each sector n for each asset i at time t is calculated with BEA constant dollar investment data via the "perpetual inventory method" as

(A 1) [A.sub.n, i, t] = (1 - [[Delta].sub.i])*[A.sub.n, i, t - 1] + [I.sub.n, i, t]

where [[Delta].sub.i] is depreciation and [I.sub.n, i, t] is investment, all in sector n = 1...35 for asset i = 1...51 at time t = 1948...1991. The BEA investment series actually begin in 1929, so the initial capital stock for each sector for each asset, [A.sub.n, i, 1947], is estimated using a perpetual inventory from 1929 to 1947 assuming the capital stock begins at zero in 1929. [[Delta].sub.i] is assumed constant across sectors and taken from Hulten and Wykoff [1981].

From the acquisition prices of new investment, [P.sub.A, n, i, t], one can calculate the user-cost of capital, [P.sub.K, n, i, t], according to a user-cost of capital formula

as

(A2) [P.sub.K, n, i, t] = [P.sub.A, n, i, t - 1] *[r.sub.t] + [P.sub.A, n, i, t]

*[[Delta].sub.i] - ([P.sub.A, n, i, t - 1] *[r.sub.t] + [P.sub.A, n, i, t]

where [r.sub.t] is the discount rate.

The user-cost of capital is the rental price of capital. In equilibrium, the rental price equals the opportunity cost of investment plus economic depreciation less capital gains. This expression is adjusted for tax factors - the investment tax credit, capital gains and capital consumption allowances - using tax parameters as in Jorgenson and Yun [1989].

At the level of the individual asset, the flow of real capital services, [K.sub.n, i, t] is assumed proportional to the lagged stock of assets, [A.sub.n, i, t - 1]. The flow of total capital services, [K.sub.n, t], is a Divisia quantity index of the 51 heterogeneous assets as

(A3) ln([K.sub.n, t]) - ln([K.sub.n, t - 1])

[summation of (ln([K.sub.n, i, t])] where i = 1 to 51 - ln([K.sub.n, i, t - 1]))*[v.sub.n, i, t]

where [v.sub.n, i, t] is equal to the average share of nominal capital services from asset i in sector n and is calculated as

(A4) [Mathematical Expression Omitted]

The flow of real capital services in sector n, [K.sub.n, t] represents the flow of productive services from all capital goods into production in that sector. [K.sub.n, t] can be decomposed into two components for the growth accounting - [K.sub.l, n, t] represents capital services from all assets except OCAM and [K.sub.2, n, t] represents OCAM capital services.

I would like to thank Barbara Fraumeni, Zvi Griliches, Mun Ho, Lauren Johnston, Dale Jorgenson, Madhu Khanna, Greg Mankiw, Bob McGuckin, Thomas Saving, two anonymous referees, seminar participants at Bentley College, Harvard University, and the 1996 WEA International Conference. The conclusions represent the views of the author only.

1. For example, Baily and Gordon [1988], Gordon [1990], Berndt and Morrison [1991], Griliches and Siegel [1992], Brynjolfsson and Hitt [1994], Sichel [1994], Oliner and Sichel [1994], Berndt and Morrison [1995], Jorgenson and Stiroh [1995] and Lehr and Lichtenberg [1996]. See Brynjolfsson [1993] for a review of nearly 20 papers on the topic.

2. Computers first enter the National Income and Product Accounts (NIPA) in 1958 and hedonic quality adjustments were officially incorporated in 1986. The purpose of the hedonic approach is to account for the dramatic quality change and transform investment series into standardized "constant-quality" units that can be compared over time. See Sadee [1996] for a recent update of the BEA methodology and Gordon [1990] for a more general treatment.

3. See Baily and Gordon [1988] and Triplett [1994].

4. Private, business Value-Added is about 80% of GDP. Government and household sectors account for the rest.

5. See the Appendix for details on defining, estimating and aggregating capital services.

6. These estimates are consistent with Oliner and Sichel [1994] who estimate a growth contribution from computing equipment of 0.16 percentage points a year for 1970-1992. They focus on Computer and Peripheral Equipment, a subaggregate of OCAM, which explains the slightly different growth contribution.

7. Using an earlier version of this data, Basu and Fernald [1996, 1995] conclude that sectors on average have slightly diminishing returns to scale. Constant returns to scale, however, seems to be a reasonable approximation.

8. Data was not available for OCAM investment for Government Enterprises.

9. Real Gross Output, of course, still relies crucially on official price deflators for output and inputs that may be problematic in some sectors.

10. The 1981-1991 growth accounting results are not shown in any table and are as follows: the annual contribution of non-OCAM capital fell to 0.17%, the contribution of OCAM capital increased slightly to 0.15% and the contribution of labor, energy and materials were negative, 0.19%, -0.05% and -0.15%, respectively.

11. This applies a "Demur" weight to the sectoral productivity growth rate. See Jergenson et al. [1987] for details.

12. According to the official numbers in BLS [1996], MFP growth for the private business economy increased from 0.1% per year for 1973 - 1981 to 0.7% per year for 1982-1991. This increase was primarily due to faster MFP growth in the manufacturing sectors and is consistent with the 35-sector data.

13. This criteria was subjectively chosen to isolate sectors that are the most computer-intensive. There is a clear distinction in factor payments between the computer-using sectors and the other sectors.

14. Other Services includes computer-related services (SIC #737) such as software sales, programming services, data processing, rentals and repairs. Even in 1991, computer-related services are small, accounting for only about 5% of total gross output in the Other Services sector.

15. Consumption and government purchases are relatively small at 3% and 6%, respectively.

16. Agriculture, Non-Metallic Mining and Government Enterprises were excluded from the regression since computer capital was zero for early years. This left a cross-section of 32 sectors.

17. Griliches [1992] details the difficulties in measuring prices, output, and productivity growth in the service sectors. To avoid this problem, one needs to assess each sector individually and generate alternative output measures which is beyond the scope of this paper.

REFERENCES

Baily, Martin N., and Robert J. Gordon. "The Productivity Slowdown and Explosion of Computer Power." Brookings Papers on Economic Activity, 2, 1988, 145.

Bartelsman, Eric J., Ricardo J. Caballero, and Richard K. Lyons. "Customer- and Supplier-Driven Externalities." The American Economic Review, 84(4), September 1994, 1,075-84.

Basu, Susanto, and John G. Fernald. "Are Apparent Productive Spillover a Figment of Specification Error?" Journal of Monetary Economics, 36, 1995, 165-88.

-----. "Returns to Scale in U.S. Production: Estimates and Implications." Manuscript, 1996.

Berndt, Ernst R., and Catherine J. Morrison. "Assessing the Productivity of Information Technology Equipment in U.S. Manufacturing Industries." NBER Working Paper #3582, 1991.

-----. "High-Tech Capital Formation and Economic Performance in U.S. Manufacturing Industries." Journal of Econometrics, Vol. 65, 1995, 9-43.

Berndt, Ernst R., Catherine J. Morrison, and Larry S. Rosenblum. "High-Tech Capital Formation and Labor Composition in U.S. Manufacturing Industries: An Exploratory Analysis." NBER Working Paper #4010, 1992.

Bresnahan, Timothy F. "Measuring the Spillovers from Technical Advance: Mainframe Computers in Financial Services." The American Economic Review, 76(4), September 1986, 741-55.

Bresnahan, Timothy F., and M. Trajtenberg. "General Purpose Technologies: Engines of Growth?" Journal of Econometrics, Vol. 65, 1995, 83-108.

Brynjolfsson, Erik. "The Productivity Paradox of Information Technology: Review and Assessment." Communications of the ACM, 35(12), 1993, 66-77.

Brynjolfsson, Erik, and Lorin Hitt. "Computers and Economic Growth: Firm-Level Evidence." Manuscript, 1994.

Bureau of Economic Analysis. National Income and Product Accounts of the United States. Washington: Department of Commerce, 1992.

-----. "National Income and Product Accounts." Survey of Current Business, 73(7), July 1993, 7-25.

-----. "National Income and Product Accounts." Survey of Current Business, 75(7), July 1995, 1-23.

Bureau of Labor Statistics. "Multifactor Productivity Trends, 1994." USDL-95-518, January 17, 1996.

Gordon, Robert J. The Measurement of Durable Goods Prices. Chicago: University of Chicago Press, 1980.

Griliches, Zvi. "The Search for R&D Spillovers." NBER Working Paper #3768, 1991.

-----. "Productivity, R&D and the Data Constraint." The American Economic Review, 84(1), March 1994, 123.

-----. Output Measurement in the Service Sector. Chicago: University of Chicago Press, 1992.

Griliches, Zvi, and Donald Siegel. "Purchased Services, Outsourcing, Computers and Productivity in Manufacturing," in Output Measurement in the Service Sector, edited by Zvi Griliches. Chicago: University Of Chicago Press, 1992.

Hulten, Charles, and Frank C. Wykoff. "The Estimation of Economic Depreciation Using Vintage Asset Prices," in The Measurement of Capital, edited by Dan Usher. Chicago: The University of Chicago Press, 1981.

Jorgenson Dale W. "Productivity and Economic Growth," in Fifty Years of Economic Measurement, edited by Ernst R. Berndt and Jack E. Triplett. Chicago: The University of Chicago Press, 1990.

Jorgenson, Dale W., Frank M. Gollop, and Barbara M. Fraumeni. Productivity and U.S. Economic Growth. Cambridge: Harvard University Press, 1987

Jorgenson, Dale W., and Kevin Stiroh. "Computers and Growth." Economics of Innovation and New Technology, Vol. 3, 1995, 295-316.

Jorgenson, Dale W., and Kun-Young Yun. Tax Reform and the Cost of Capital. New York: Oxford University Press, 1989.

Lehr, William, and Frank R. Lichtenberg. "Computer Use and Productivity Growth in Federal Government Agencies, 1987 to 1992." NBER Working Paper #5616, 1996.

Lichtenberg, Frank R. "The Output Contributions of Computer Equipment and Personnel: A Firm-Level Analysis." NBER Working Paper #4540, 1993.

Oliner, Stephen D., and Daniel E. Sichel. "Computers and Output Growth Revisited: How Big is the Puzzle?" Brookings Papers on Economic Activity 2, 1994, 273-318.

Sadee, Nadia. "Computer Prices in the National Accounts: An Update from the Comprehensive Revision." National Income and Wealth Division, BEA, 1996.

Sichel, Daniel E. "The Computer Paradox and the Productivity Slowdown: Is Mismeasurement the Culprit." Brookings Working Paper, 1991.

Solow, Robert M. "Technical Change and the Aggregate Production Function." Review of Economics and Statistics, No. 39, 1957, 312-20.

Triplett, Jack E. "Comments on Oliner and Sichel [1994]." Brookings Papers on Economic Activity, 2, 1994, 318-24.

Stiroh: Economist, The Conference Board, New York Phone 1-212-339-0481, Fax 1-212-7014 Email stiroh@conference-board.org