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Equity Prices, Productivity Growth,
and the ‘New Economy’

Jakob B. Madsen and E. Philip Davis

2004-05


















ISSN 0908-7745

The activities of EPRU are financed by a grant from
The National Research Foundation

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EQUITY PRICES, PRODUCTIVITY GROWTH, AND ‘THE NEW
ECONOMY’1





Jakob B Madsen
Institute of Economics and EPRU
University of Copenhagen

and

E Philip Davis*
Department of Economics and Finance
Brunel University


6th February 2004





Abstract. The sharp increase in equity prices over the 1990s was widely attributed to permanently
higher productivity growth derived from the New Economy. This paper establishes a rational
expectations model of technology innovations and equity prices, which shows that under plausible
assumptions, productivity advances can only have temporary effects on the fundamentals of equity
prices. Using historical data on productivity of R&D capital, patent capital and fixed capital for 11
OECD countries, empirical evidence give strong support for the model by suggesting that
technological innovations indeed have only temporary effects on equity returns.

JEL Classification: G120, G3, O4

Key words: New economy, productivity, economic growth, equity prices.







* Corresponding author, address Department of Economics and Finance, Brunel University, Uxbridge, Middlesex, UB8
3PH, email e_philip_davis@msn.com
1 The authors are grateful for helpful comments and suggestions by participants in seminars at Brunel University, the
European University Institute, Oxford University, University of Copenhagen, University of Queensland, SUERF meeting
in Brussels, November 2001, Christian Groth, Søren Johansen and particularly three anonymous referees. The data for
software, IT equipment and communication equipment capital service over the period from 1980 to 2000 for nine OECD
countries from the paper Colecchia and Schreyer (2002) were kindly provided by Paul Schreyer at the OECD.

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2
Introduction

The worldwide increase in equity prices in the 1990s has been widely linked to permanent
productivity-growth effects and the significant generation of intangible assets during the information
and communication technology (ICT) revolution.2 It has been extensively argued that the
acceleration in productivity in the 1990s increased firms’ current and expected real cash flows and
therefore contributed to an increase in the value of firms.3 Hall (2000, 2001a) argued that the share
market run-up in the 1990s was justified by the increasing value of intangible assets consisting of “e-
capital” that has increased the expected cash flow of firms. Greenwood and Jovanovic (1999) and
Hobijn and Jovanovic (2001) argue that the rise in the stock market from the 1980s onwards was
linked to the rise of Information Technology (IT) based firms. However, the questions whether the
increase in equity prices in the 1990s can be attributed to increasing growth in intangible and
tangible capital productivity, and whether a sustainable higher capital productivity growth rate can be
expected in the future, have gone almost unexplored.4

This paper introduces and tests a Tobin’s q model of the interaction between capital productivity
shocks and equity prices to gauge the short and long term effects of the ICT revolution on equity
prices. Section 2 introduces some of the measurement issues and Section 3 develops a general
equilibrium model to show that innovations have only temporary effects on capital productivity and
hence on equity prices. In fact, changes in equity prices will precede the impact of the shock to
productivity if equity markets react in a forward-looking way to news of innovations. Furthermore,
productivity shocks lead to higher tangible and intangible capital stock in the long run, but equity
prices revert back to a long-run equilibrium. It is suggested that the analysis is of considerable
relevance given the growing prevalence of intangible as opposed to tangible capital in the New
Economy. Using historical data for real equity returns, tangible and intangible capital stock for 11
OECD countries, we test the predictions of the model in Section 4, with considerable support being
offered to its predictions.


2 Other factors that have been suggested as important factors behind the increase in stock prices in the 1990s include a
decrease in the risk premium, higher international liquidity, baby boomers, the disinflation, and irrational exuberance
(IMF, 2000, Shiller, 2000).
3 See Business Week, 2003, Campbell and Shiller, 2001, Economist, 2001, Greenwood and Jovanovic, 1999, Hobijn and
Jovanovic, 2001, IMF, 2000, Jovanovic and Rousseau, 2003, Keon, 1998, Laitner and Stolyarov, 2003.
4 An exception is the model of Datta and Dixon (2002) where it is shown that innovations increase profits of incumbents
and share prices, but that entry of new firms drive profits back to zero. As discussed below the model of Datta and Dixon
(2002) is quite different from the model presented in this paper.

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3
2.
Innovations, capital productivities and share returns

The New Economy brought with it expectations of productivity-induced increases in the growth in
cash flow per share among share investors and several economists. Two closely related arguments
have been used to account for the ICT-induced rise in equity prices in the second half of the 1990s
which appears to have resumed in 2003. Some argue that the ICT revolution, or more generally the
New Economy, has brought productivity growth rates up to a sustainable higher level, thus resulting
in higher growth in expected earnings per share. Others have argued that the New Economy has
created sufficient intangible wealth to merit the higher share prices in the late 1990s (Hall, 2000,
2001a, McGrattan and Prescott, 2001). These two arguments are closely related, because the value of
the capital stock equals the discounted value of earnings in general equilibrium. This section
examines these arguments and discusses the data issues relating to the measurement of intangibles.

2.1
The New Economy and productivity

Considering the productivity growth effects on share prices of the New Economy, the main
international organisations and researchers have attributed a large part of the increase in equity prices
in the 1990s to accelerations in actual and expected labour productivity and potential output.5 The
problem with this line of reasoning is that labour productivity and potential output are severely
biased proxies for firms’ cash flow. The relevant productivity measure for firms’ cash flow is the
marginal productivity of capital, which has moved in a direction which was historically quite
different from the growth in labour productivity and potential output. To see the consequences of
using labour productivity and potential output as measures of earnings per unit of capital, consider
the Cobb-Douglas production function,
α
1
Y
BL K α
−
=
, where B represents total factor productivity
(TFP), Y is aggregate value-added output, K is capital services and L is labour services. The growth
in marginal productivities of labour and capital are given by:


∆ ln(Y / L) = (1−α)∆ ln(K / L) + ∆ ln B ,




(1)


∆ ln(Y / K) = α
− ∆ ln(K / L) + ∆ ln B .




(2)

5 For example, in the IMF’s World Economic Outlook (2000) and in Kennedy et al (1998) of the OECD, the growth in
potential output is used as a proxy for expected dividend growth in a version of Gordon’s growth model of equity
valuation. Elsewhere, IMF (2000) suggests that labour productivity growth is the relevant measure of dividend growth.
Similarly, a series of articles in the Economist and Business Week have argued that labour productivity is the relevant
productivity measure for share prices (see for instance, Business Week, 2003, and Economist, 2001). Finally, Campbell
and Shiller (2001) suggest that many analysts attribute the equity price boom in the 1990s partly to the accelerating
labour productivity in the same period.

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4

Comparing these equations, it is evident that TFP growth enhances growth in both capital and labour
productivities. Capital deepening, however, increases the marginal productivity of labour but lowers
the marginal productivity of capital and therefore explains why the real interest rate/return on equity
tends towards a constant mean in the long run, while real wages show a continuous rise in the long
run. Historically, capital deepening has counterbalanced total factor productivity growth to such an
extent that tangible capital productivity has tended to decline only slightly in the OECD countries.

The K/L ratio has increased geometrically by 3.5% annually in the OECD countries used in this
study over the period from 1960 to 2001 (see notes to Figure 1 below), whereas TFP has increased
by 1.5% only on average, when α is set to 0.7; thus suggesting a strong growth in labour productivity
but a slight decline in capital productivity. The bias from using the growth in potential output as a
proxy for the growth in capital productivity is even larger than using labour productivity. The bias is
given by ∆ lnY − ∆ ln(Y / K ) = ∆ ln(K ) . The bias was 34% over the period from 1980 to 1992 and
22% from 1993 to 2001 for the countries used in this study. From these numbers it is evident that
share valuation based on growth in labour productivity or in potential output, severely overestimates
the value of shares and is overly sensitive to fluctuations in labour productivity and potential output
growth rates.

2.2
Some estimates of capital productivity and the New Economy

The estimates above are based on the tangible capital stock. However, several economists have
argued that tangible capital stock is too narrow a concept of capital and that the creation of
intangibles has been a vital part of the new economy (see for instance Brynjolfsson et al, 2002).
Patent applications and R&D expenditures are probably the most accepted measures of the
innovative activity, including the creation of intangibles during the ICT revolution.6 Hall (2001b)
argues that the increase in the market value of firms in the 1990s are related to intellectual property
and, to a much lesser extent, to advertising and R&D and writes that “much of the increase of firms
in the past decades appears to be related to the development of successful differentiated products,
protected to some extent from competition by intellectual property rights relating to technology and
brand names” (p 1189). That the New Economy is well indicated by patent data is well documented.
During the 1990s, for instance, ICT patent applications in the OECD countries grew at an annual rate

6 See for instance Griliches (1990) and Grupp (1998) for discussions of the merits in using patenting and R&D data as
indicators of the innovative activity.

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5
of 9% in the OECD countries, which is almost 50% higher than the growth rate of total patent
applications (OECD, 2003). Furthermore, about a third of all OECD patent applications were ICT-
related (OECD, 2003).

To get a picture of the historical paths of the marginal productivities of tangible and intangible
capital stock, Figure 1 displays the unweighted average of the three Y/K ratios for the 11 countries
that are used in this study. These 11 countries are listed in the notes to Figure 1 and are referred to
the G11 countries as shorthand. The three ratios are the productivities of the tangible capital stock,
R&D capital stock, and patent capital stock. We use the Cobb-Douglas productivity assumption
under which the marginal productivity of capital type i is given by (1-αi)Y/Ki, which varies
proportionally to Y/Ki, where (1-α)i is the share of income going to capital type Ki, ∑(1−α ) =1−α .
i
US data on R&D expenditure are used over the period from 1953 to 1965 since R&D data are not
available for other countries before 1965. The patent capital stock is measured as patents applied for
by residents and non-residents.7 The capital data are constructed using the perpetual-inventory
method as detailed in the data appendix.

Figure1: Output-Capital Ratios, G11
3
2.5
R&D
2
Patents
Tangibles
1.5
1
0.5
0
1870
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000

Notes. The figures are computed as an unweighted average for the following 11 countries: Australia, Canada, Denmark,
n
Fra ce, Germany, Italy, Japan, the Netherlands, Sweden, the UK and the US. The output-R&D capital stock ratio is
divided by five and is spliced to the US data before 1965. The output-patent capital stock ratio is measured in millions of
USD in 1995 prices at 1996 purchasing power parity. See the data appendix for data sources.


7 Patent applications are almost always used in economic analysis as opposed to patents granted, because applications
measure most precisely the timing of the innovation relevant for share price expectations and because the time lag
between the lodgement of the application and the time at which the patent is granted, vary substantially over time. See
Griliches (1994) for discussion of these issues.

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6
Figure 1 shows that capital productivity measured by the ratio of output to the tangible capital stock
has been declining over the past century. R&D capital productivity has been diminishing over the
past 50 years, but at a declining rate, which, as argued in Section 3 below, is a result of a slow
convergence towards the steady state. Patent capital stock productivity has also decreased over the
past 130 years, but it appears that it has stabilised at the equivalent of 1 million USD at 1995
constant prices per patent.8 Common for all three indicators is the property that capital productivities
have not been increasing in the long run.9 Coupled with the fact that labour productivities have been
growing at a steady rate of 2-3% in the G11 countries over the past 130 years, this result underlines
the point made in the previous sub-section, namely that growth in labour productivity is a directly
misleading proxy for growth in returns to capital. This is particularly true over the past two decades
where the returns to R&D effort and patenting have also been declining.

can be argued that th
It
e productivity effects of the Second Industrial Revolution, which started
around 1870, are quite instructive for projecting the earnings effects of the ICT revolution.10 The
great inventions in the latter part of the 19th century such as the invention of electricity and the
internal combustion machine, led in fact to declining and not increasing tangible and patent capital
productivities as seen from Figure 1. A strong reduction in patent capital stock productivity can
particularly be identified over the period from 1885 to 1913, which suggests diminishing returns to
the patent capital stock. Thereafter patent capital stock and tangible capital stock productivities
stabilised at a constant mean up to 1960, which covers a period in which the great inventions
diffused (Gordon, 2000, Perez, 2002). The decrease in tangible capital stock productivities over the
period from 1885 to 1913 is associated with a strong increase in the tangible and patent capital stock
over the same period, and at least some of the tangible stock capital accumulation was associated
with the high inventive activity in that period. Tangible capital accumulation is often associated with
technological advances or embodied technological progress as shown by Hulten (1975) and
advocated by Gordon (2003). Accordingly, the capital accumulation process during the Second
Industrial Revolution was associated with declining tangible capital productivity and, therefore,
diminishing returns to capital.

8 One potential problem associated with the patenting capital stock productivities for long run analysis is that the real
value of patents may have changed over time. However, there is no clear evidence that the real value of patents has
fluctuated in this manner (see Griliches, 1994).
9 Earlier data suggest that the patent capital stock and tangible capital stock productivities for the UK and the US were
declining before 1870 and suggest that capital productivities have been declining over the past two centuries for these
two countries. Very little data are available for other countries before 1870.
10 The exact dating
h
of t e Second Industrial Revolution differs among economists. Greenwood and Jovanovic (1999), for
instance, date it to the period from 1890 to 1930, whereas Perez (2002) refers to the period after 1875 as the Third
Industrial Revolution.

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7

The lessons from the Second Industrial Revolution suggest that the declining capital productivities
which are identified in Figure 1 over the past two decades, may well continue into the near future but
at a declining rate as the diffusion process advances. The diffusion process is likely to be shorter than
the experience from the first two industrial revolutions. Gordon (2000), for instance, argues that the
reorganisation and the development of new systems as a consequence of the New Economy have
been substantially easier than the implementation of the innovations which occurred in the latter part
of the 19th century. Almost all workstations have computers today, whereas for example it took
several decades to switch factories from centralised steam-driven power to decentralised electro
motors in the last century. Hence, the delayed benefits of the New Economy may not be as large as
thought by many investors.

2.3
The New
share prices and intangibles
Economy,

m
A nu ber of economists have argued
rices in
that the rising share p
the 1990s in the OECD countries
flected increasing values of intangibles that have
re
been created as a by-product of investment in ICT
products, R&D, advertisement, and new brand names. Hall (2000, 2001a) and McGrattan and
Prescott (2001) estimated the value of intangibles indirectly, whereas Nakamura (2001) provided a
direct measure of the value of intangibles. A key question is whether these estimates can justify the
value of shares in 2000 and at the end of 2003, and hence the expectations of higher earnings growth
which has been induced by the ICT revolution.

nical
Hall (2000, 2001a) defines intangibles as tech
and organizational know-how that have been
reated by graduates using com
c
puters and software and names it e-capital. Since intangibles cannot
be measured using this definition, Hall (2000) estimated the value of intangibles by subtracting the
value of physical stock from the value of the stock market and found the value of e-capital to exceed
the value of tangible capital stock for US corporations in 1999.11 However, for Hall’s measure of
intangible to be correct, share prices should reflect earnings expectations in an efficient share market.
Basing the fundamental value of shares on analysts’ earnings forecasts, Bond and Cummins (2000)
found that share prices increased substantially more than their value based on analysts earning
forecasts during the 1990s. This suggests analysts’ estimates of intangibles to be well below market’s
estimates but in line with managers’ expectations since the estimates of Bond and Cummins (2000)

11 Hall’s method has been met with strong criticism (see for instance, Cummins, 2000, and Lamont, 2000).

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8
also show a strong relationship between investment and the value of shares based on analysts earning
forecasts. Coupled with the finding that Tobin’s q does not provide incremental information on the
investment function when analysts’ earnings expectations are allowed for in their regression analysis,
these results suggest that analysts and managers believed in a much lower increase in the value of
intangibles during the 1990s than the share market.

McGrattan and Prescott (2001) estimate the value of intangibles in the US corporate sector to be 80%
of the value of their tangible capital stock over the period from 1987 to 2000, which is up from 40%
over the period from 1955 to 1962. Their method is based on the equilibrium conditions that equate
the after-tax returns for all assets, that is, the after-tax profits per unit of intangible and tangible
capital stock in the corporate sector equals profits per unit of tangible capital stock in the non-
corporate sector (including imputed services to consumer durables and government capital). Thus,
their method rests on the highly restrictive assumptions that the equity risk premium is the same in
the two sectors and that the value of intangibles is zero in the non-corporate sector. Both restrictions
bias the estimations of intangible capital upwards and McGrattan and Prescott (2001) also admit that
the estimates of intangible capital stock are on the high side. Similarly Hansen et al (2004) argue that
assumption of no intangible capital stock in the non-corporate sector is a “seemingly hard to defend
restriction” (p 8).

ictions of a standard growth m
Based on the pred
odel, Nakamura (2001) estimated the value of the
tang
in
ible capital stock of US corporations to be USD 6.25 trillion in 2000, which exceeds the figure
estimated by Hall (2000). Nakamura (2001) assumes that the steady state value of the intangible
capital stock equals investment in intangibles divided by their depreciation rates under the
assumption of no labour augmenting technological progress and no growth in employment. The
following items were included in his estimates of intangible investment; 1) expenditures to R&D
($181 bn in 2000); 2) software investment ($183 bn); 3) expenditures on advertising ($233 bn); 4)
artistic expenditures ($50 bn); 5) innovative expenditures by financial corporations ($50 bn); and 6)
items unaccounted for ($303 bn).12 Dividing this sum of $1 trillion by a depreciation rate of 16% he
finds the steady state stock of intangibles of $6.25 trillion.

The estimates of Nakamura rest on the assumptions
o Harrod-neutral technological progress,
of zer
ero growth in the labour force, a
z
depreciation rate of 16%, zero adjustment cost associated with

12 Two other estimates are presented by Nakamura (2001). They are not discussed here to preserve space.

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9
investment in intangibles, and the absence of externalities associated with the investment in
intangibles. The zero-externality assumption has been questioned by Smithers and Wright (2000) and
Gordon (2003), who argue that intangible investment that increases the value of an individual firm
need not add to the aggregate value of firms because some of intangible investments are undertaken
to gain market shares. Smithers and Wright (2000) argue that advertisement, for instance, is an
intangible investment in customers by the individual firm, but, at the same time, lowers the customer
capital of competing firms and is hence unlikely to significantly affect the aggregate value of the
intangible capital stock. Similarly, Gordon (2000) argues that a large fraction of the ICT investment
that has been generated by individual firms as a by-product of the New Economy has involved taking
profits and customers away from other companies in a zero-sum game. R&D expenditures, however,
have been found to add almost fully to the aggregate value of intangibles (Megna and Klock, 1993).

Since intangibles are by their very nature immeasurable but created from expenditures on factors of
roduction, the growth in expenditures on item
p
s from which they are assumed to have been
generated, will give an indication of the potential growth in their importance. Brynjolfsson et al
(2002), for instance, argue that investment in computers and communication equipment lead to
investment in unmeasured complementary intangibles such as organizational restructuring and
business process design. Thus, the ratio of the capital stock of the factors of production that are
assumed to generate the intangibles, and tangible capital stock will give an indication of the growth
of the potential importance of intangible relative to tangible capital during the ICT revolution.
Figure 2. Ratio of R&D and ICT capital stock to Tangible
%
Capital Stock, USA
35
30
25
20
15
10
5
0
1953
1958
1963
1968
1973
1978
1983
1988
1993
1998
Notes: ICT capital stock is the sum of the stock of computer, software, and communication capital stock and tangibles is measured as
total fixed capital stock excluding the land, consumer durable goods and inventories. See data appendix for data sources.

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