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数字资本和超星公司研究报告摘要本报告来自布鲁金斯学会的Hutchins Center Working Paper #73，作者为Prasanna Tambe和Lorin M. Hitt，来自宾夕法尼亚大学沃顿商学院。该报告探讨了数字资本和超星公司的关系，探索了数字资本对企业生产力和资产价值的影响。一、数字资本的定义和测算数字资本是指企业为实现信息技术整合而进行的投资，如信息系统、数据分析、人工智能等。这些投资创建了一种无形资产，即数字资本。为了测算数字资本的价值，作者使用了Hall的数量揭示定理，计算了数字资本的价格和数量。二、数字资本的演变趋势作者发现，数字资本的价格在2000年左右达到了峰值，然后开始下降。然而，数字资本的数量自1990年代以来一直在增加，到2016年，数字资本已经占据了企业资产的至少25%。此外，数字资本的集中度远远高于其他资产，主要集中在少数几家超星公司中。三、数字资本对企业生产力的影响研究表明，数字资本的累积是企业生产力增长的重要预测指标约三年后。换言之，企业的数字资本投资将在三年后对生产力产生积极影响。四、超星公司的兴起本研究还发现，数字资本的累积主要集中在少数几家超星公司中，这些公司拥有庞大的数字资本存量，远远超过其他公司。这可能是它们在市场上的竞争优势所在。五、结论本研究表明，数字资本对企业生产力和资产价值产生了重要影响。企业需要积极投资数字资本，以提高生产力和竞争力。同时，政府和监管机构也需要关注数字资本的发展趋势，以确保公平的市场竞争环境。六、实践意义本研究对企业和政府都有重要的实践意义。对于企业来说，投资数字资本是提高生产力和竞争力的重要策略。对于政府来说，需要关注数字资本的发展趋势，以确保公平的市场竞争环境。七、未来研究方向本研究还开辟了未来研究的方向。例如，进一步研究数字资本的影响机理，探索数字资本在不同行业中的应用等。

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M a r c h 2 0 2 1

_______________________________________________________________________

Hutchins Center Working Paper #7 3

T H I S P A P E R I S O N L I N E AT

https://www.brookings.edu/research/digital-capital-

and-superstar-firms

Digital Capital and Superstar Firms

Prasanna Tambe

University of Pennsylvania, Wharton

Lorin M. Hitt

University of Pennsylvania, Wharton

A B S T R A C T

General purpose technologies like information technology typically require complementary firm-specific

investments to create value. These complementary investments produce a form of capital, which is typically

intangible and which we call digital capital. We create an extended firm-level panel on IT labor investments (1990-

2016) using data from LinkedIn. We then apply Hall’s Quantity Revelation Theorem to compute both prices and

quantities of digital capital over recent decades. We find that 1) digital capital prices vary significantly over time,

peaking around the dot-com boom in 2000, 2) significant digital capital quantities have accumulated since the

1990s, with digital capital accounting for at least 25% of firms’ assets by the end of our panel, 3) that digital

capital has disproportionately accumulated in a small subset of “superstar” firms and its concentration is much

greater than the concentration of other assets, and 4) that digital capital accumulation predicts firm-level

productivity about three years in the future.

This paper is published as part of the Hutchins Center on Fiscal and Monetary Policy’s Productivity Measurement Initiative.

*Correspondence: erik.brynjolfsson@gmail.com. Digital Economy Laboratory, 366 Galvez St, Rm 328. Stanford, CA 94305,

USA. The authors are grateful for valuable feedback from Guy Berger, Di Mo, Diego Comin, Frank Nagle, Chad Syverson,

Jonathan Haskel, and Lynn Selhat and from seminar participants at MIT, the NBER Conference on Research on Income and

Wealth, the Workshop on Information Systems and Economics, the International Conference on Information Systems,

LinkedIn, the Brookings Institute Initiative on Productivity Measurement, the NBER Conference on Artificial Intelligence,

and the INFORMS Conference on Information Systems and Technology.

The authors did not receive financial support from any firm or person for this article or from any firm or person with a

financial or political interest in this article. They are currently not officers, directors, or board members of any organization

with an interest in this article. LinkedIn's Economic Graph Research and Insights team, as the data provider, had the chance

to review for possible release of confidential information and trade secrets prior to publication. They did not have editorial

control over other aspects of the paper.

Daniel Rock

University of Pennsylvania, Wharton

Erik Brynjolfsson

Stanford University and NBER

_________________________________________________________________________________________________________

Di g i t a l Capi t a l a n d S u p er st ar F i r m s 2

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1. Introduction

Superstar firms, unique in their capabilities to scale up innovations, have become increasingly important

in the US economy (Autor et al., 2020; Hall, 2018; Van Reenen, 2018; De Loecker et al., 2020).

Investments related to digital technologies are likely to play a particularly important role, reflecting,

among other things, economies of scale and network effects. For instance, as of February 2020, the five

most valuable firms in the S&P 500 were all firms from the tech industry – Microsoft, Google, Facebook,

Amazon, and Apple. Moreover, their share of stock market capitalization has been growing. Figure I

illustrates that as a fraction of the overall value of firms in the S&P 500 index, the value of the top five

most valuable firms has been increasing since about 2010, with an especially rapid rise in this fraction in

the last few years.

Much of the rise in the concentration of power in these firms has been attributed to intangible

investments (Crouzet and Eberly, 2018; Ayyagari et al., 2019; Covarrubias et al., 2019). For digitally-

focused firms, investments in the intangible assets needed to realize value from new technologies – like

cumulative investment in skills training, new decision-making structures within the firm, management

practices, and software customization – often account for significantly greater total costs than the

technologies themselves. These assets comprise digital intangible capital (hereafter, interchangeably

referred to in this paper as “digital capital”) (Hall, 2001; Brynjolfsson et al., 2002).

The importance of

these types of investments has been well documented and spans a number of academic literatures (e.g.,

see Bresnahan et al., 2002; Black and Lynch, 2001; Corrado et al., 2009; McGrattan and Prescott, 2010;

Eisfeldt and Papanikolaou, 2013; Sculley et al., 2014; Crouzet and Eberly, 2018; McGrattan, 2020; Wu et

al., 2020). As the economy becomes increasingly digitized, these assets can be expected to grow even

further in importance. For instance, there has been a wave of interest in the potential of data analytics and

artificial intelligence (AI) to become the next important general purpose technology that drives economic

growth and business value (Brynjolfsson et al., 2018).

The economics of these assets have both similarities to and differences from physical capital. Firms

invest in both physical capital, like factories or manufacturing equipment, and digital capital to increase

their capacity to produce in future years. While these assets take time to build, the market value of firms

should reflect the expected net present value of the cash flows they can generate in the future.

Furthermore, like physical capital, digital capital can depreciate over time and must be replenished

through additional investment. However, unlike physical capital, intangible capital is, by definition,

difficult, if not impossible, to see or touch. In addition, the value of intangible capital may be closely tied

to a particular firm and sensitive to external economic conditions, so it can fluctuate more than can the

value of physical assets such as buildings or property which are more fungible and typically have active

secondary markets.

Because of the differences in measurability between physical and intangible capital, generally

accepted accounting principles often fail to capture the value of new business processes or other types of

intangible capital on a firm’s balance sheet. Measurement of the stock of digital intangibles has proven

particularly elusive because gross investment in digital capital is largely invisible to researchers and

. . .

1. In a later section, we present a more comprehensive definition of digital intangible capital. We also compare it to the related

concept of “e-capital” as defined by Hall (2000).

_________________________________________________________________________________________________________

Di g i t a l Capi t a l a n d S u p er st ar F i r m s 3

HUT C HI N S CE N T ER ON FI S C A L & M ONE T AR Y P O L I CY A T B R O OK I N GS

depreciation rates are unknown, so the methods that are conventionally used to assess the accumulation

of capital stocks are not easily applied (e.g. see Hall, 1993). For other kinds of assets, one might use

market transactions (such as a lease or resale price) to derive prices, but there are no markets for

individual digital intangible capital assets through which prices can be directly and readily observed. Even

when the total value for bundles of these intangible assets can be estimated, fundamental distinctions,

such as their price and quantity, remain elusive. This price- quantity distinction is especially important

because it is the stock (quantity) of capital, not its value (price x quantity), that contributes to a firms’

productive capacity. When the price of digital capital rises, higher market values may reflect little or no

actual improvements in aggregate productive capacity, with most of the increase in market value

reflecting rents. On the other hand, if the price of digital capital is stable or falling, high values reflect

genuine improvements to productive capacity. As digital capital becomes a greater component of overall

capital stock, differences in the quantities of digital capital across firms (driven by the accumulated stock

as well as variations in the marginal cost of investment in digital capital), may increasingly explain

differences in performance between new digitally focused firms and older firms.

This paper uses an alternative approach to create measures of changes in the prices and quantities of

digital capital in US firms over the last three decades. Earlier work has shown that under certain

assumptions, the quantities of a firm’s capital stock–and specifically, its intangible capital stock–can be

inferred from the value of its securities (Solow et al., 1960; Baily, 1981), and that the values inferred using

this method reasonably describe the accumulation of intangible assets in US firms over the second half of

the twentieth century (Hall, 2001). However, to the best of our knowledge, no prior work has applied

these methods to firm-level data. This precludes the application of these intangible capital stock measures

to explaining the distribution of productivity among firms.

While Hall computed his estimates on aggregate (economy-level) data, it has previously not been

possible to perform these estimates at the firm level because the recursive nature of the approach requires

a relatively long time series. Existing data on firm-level digital investments such as the CI Technology

Database (or CITDB, also known as the Harte-Hanks database) is too short and lacks the necessary year-

to-year consistency needed for Hall’s approach.

Thus, an indispensable input to this analysis is a new

firm-level data series on a key input to many forms of digital capital

: IT-labor based on data from

LinkedIn, a popular online professional networking platform (http://www.linkedin.com).

To compute these measures, we use LinkedIn profiles to track the employment of information

technology workers by firms, and we make a variety of adjustments to account for sampling differences

across occupations, regions, and industries.

The data source that is generated extends and improves

upon prior approaches that computed IT labor inputs from employment data (e.g., Tambe and Hitt

(2012b)). With this longer and more precise series on IT labor, combined with other, more conventional,

firm-level financial data, we can recover estimates of digital capital quantities and prices from a time

series of changes in digital capital values.

The central contribution of this work then is in using new IT investment data along with Hall’s

approach to provide the first firm-level measures of prices and quantities of digital intangible capital.

. . .

2. This reflects, among other things, significant changes in data collection methods and sampling.

3. Such a measure potentially misses some forms of digital capital, such as open source software repositories. Later in the paper,

we are explicit about the mapping between a firm’s IT labor measure and its digital capital.

4. Details of this measure construction and benchmark tests of the data are provided later in the paper.

_________________________________________________________________________________________________________

Di g i t a l Capi t a l a n d S u p er st ar F i r m s 4

HUT C HI N S CE N T ER ON FI S C A L & M ONE T AR Y P O L I CY A T B R O OK I N GS

Prior work has reported correlations between IT investments, firms’ market value, and the risk-reward

profile of firms’ traded assets. This tells us something important about the value and pricing of these

assets (Bharadwaj et al., 1999; Brynjolfsson et al., 2002; Dewan et al., 2007). The value the market

assigns to these assets, however, cannot tell us about their productivity or contribution to economic

growth. By using Hall’s approach with firm-level data, this paper is able to directly tie the flow of services

that firms derive from their digital intangible capital to economic outcomes such as productivity. The

identification of these flows and their economic properties can then be used to explain productive

differences across firms. The ability to measure digital capital also creates further possibilities to measure

the implications of digital capital accumulation for important macroeconomic trends.

This work builds on prior research connecting IT investments to differences in the productivity of US

firms (Dewan and Min, 1997; Stiroh, 2002; Brynjolfsson and Hitt, 2003), and the important role in this

relationship played by complementary organizational investments (Bresnahan et al., 2002). In contrast to

these latter studies, we measure the quantity of intangible capital directly rather than making inferences

about its presence through observing correlations between business practices and IT investment,

productivity, or market value. While this approach cannot identify the specific business practices that

make up digital capital, it has the advantage of creating an aggregate measure of the overall stock of

digital capital without having to identify and measure all of its constituent investments. Once this stock is

identified, it becomes possible to study the properties of digital capital and the statistical distribution of

these digital capital assets across firms and over time. As noted earlier, the separation of price and

quantity of digital capital also enables a distinction between digital capital-related rents and increases in

productive capacity.

Our approach reveals four important facts about the role of digital capital in explaining features of the

modern economy. First, the market value of digital capital rose sharply during the late 1990’s but then fell

in the early 2000’s, reflecting changes in the price of digital capital during the dot-com boom and

subsequent bust.

Second, the value of digital capital began to rise again from 2010 onward, with the timing coinciding

with a wave of innovations based on mobile technologies, cloud computing, big data, data science, and

most recently, artificial intelligence (AI). With the important exception of the period corresponding with

the dot-com boom and subsequent bust, the long run increases in value can largely be attributed to

changes in digital capital quantities, rather than prices. Quantities of digital capital rise fairly steadily and

substantially over the course of our nearly thirty-year panel. By the end of the panel, digital capital

quantities account for 20-25% of the levels of physical capital for firms in our sample.

Third, there is substantial heterogeneity among firms in terms of quantities of digital capital they

own. The majority of the increase in quantities concentrated in a subset of superstar firms, which we

define as those within the top decile of our sample in terms of market value. This concentration can be

observed not only in terms of aggregate digital capital accumulation, but also for the development of

digital capital on a per-employee basis, and it contrasts with patterns of accumulation of other assets such

as those classified as property, plant, and equipment. Furthermore, heterogeneity has been increasing

during the course of our panel, as the top firms have pulled increasingly further away from the rest.

Fourth, by creating firm-level measures of digital capital quantities, we can estimate how the

accumulation of this form of capital contributes to productivity and growth. In productivity regressions,

we estimate the contributions of our digital capital quantity measures alongside IT capital stock measures.

We find that the contribution of digital capital to growth during this period was approximately double that

of IT capital stock. Moreover, current year levels of digital capital are most predictive of productivity levels

_________________________________________________________________________________________________________

Di g i t a l Capi t a l a n d S u p er st ar F i r m s 5

HUT C HI N S CE N T ER ON FI S C A L & M ONE T AR Y P O L I CY A T B R O OK I N GS

about three years in the future, suggesting that while its value is reflected in firm’s stock prices

immediately, it takes several years to fully install into the firm and become productive. Consistent with

this finding, the contribution of digital capital to productivity in long-differences grows larger over longer

difference lengths. This is consistent with the finding in Brynjolfsson and Hitt (2003) that the

contributions of computer investments themselves are also greater over longer differences.

In sum, because we have access to technology and skill data at the firm level, we can estimate not only

how quantities of digital capital have been growing, but also how these quantities vary across firms, and

how this might be connected to the growing importance of superstar firms in the US economy.

2. Theoretical framework: Asset values and adjustment costs

2.1 Defining digital capital

In this paper, “digital capital” refers to factors of production that are 1) complementary to recorded

investments in IT assets (such as hardware and software), but 2) that are not otherwise recorded on a

firm’s balance sheets. Examples include employee training that is related to new information

technologies, firm-specific human capital related to technology systems, and the development and

implementation of business processes and other forms of organizational transformation required to

support or use new information technologies. There are many other forms of intangible capital that are

not digital intangible capital, such as brands and intellectual property, and some of these have been

studied in the literature. If these types of capital are not (conditionally) correlated with the firm’s IT

investment, they will not be measured by the empirical approach we use below and therefore are not

measured as digital capital. Some capital that complements IT investment, such as general human capital,

is not owned by the firm and it is not part of the firm’s digital capital.

Firms produce digital capital through investment. Like other types of capital, digital capital produces

a flow of services that is useful for business operations. Unlike most forms of tangible capital, however,

digital capital cannot easily be used for collateral and it cannot be exchanged on secondary markets. This

makes it hard to measure the unit price of digital capital, and therefore, to infer quantities from measures

of value.

2.2 Theoretical framework

Our goal is to reveal differences in firms’ quantities of digital capital. The notion that the value of a firm’s

securities reveals its capital stock has appeared in several forms in the literature (Solow et al., 1960; Baily,

1981).

In this paper, we rely principally on Hall’s formulation, which is applied to intangible assets. Hall

argues that under assumptions of 1) competitive markets, 2) constant returns to scale production, and 3)

full factor adjustment, prices and quantities of tangible and intangible capital can be recovered from the

value of a firm’s securities (Hall, 2001). The main difference in our approach is that we estimate key

parameters with firm-level data, using a time-series of investment into a correlate of the firm’s intangible

investment. In addition, rather than using the total value of a firm’s securities as our dependent variable,

we use the component of its market value correlated with IT investment. After separating digital capital

values into prices and quantities, we use the quantities to estimate the contribution of digital capital to

productivity.

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