1. finance
2. investing
3. venture capital

F INANCE R ESEARCH S EMINAR
S UPPORTED BY U NIGESTION
“Intangible Capital and the Investment-q
Relation”
Prof. Luke TAYLOR
University of Pennsylvania, The Wharton School
Abstract
Including intangible capital significantly changes how we evaluate theories of
investment. We show that including intangible capital in measures of investment and
Tobin’s q produces a stronger investment-q relation, especially in macroeconomic
data and in firms that use more intangibles. These results lend support to the classic
q theory of investment, and they call for the inclusion of intangible capital in proxies
for firms’ investment opportunities. However, including intangible capital also
makes the investment-cash flow relation almost an order of magnitude stronger,
which supports newer investment theories. The classic q theory performs better in
settings with more intangible capital.
Friday, April 24, 2015, 10:30-12:00
Room 126, Extranef building at the University of Lausanne
Intangible Capital and the Investment-q Relation
Ryan H. Peters and Lucian A. Taylor*
April 6, 2015
Abstract:
Including intangible capital significantly changes how we evaluate theories of investment. We show
that including intangible capital in measures of investment and Tobin’s q produces a stronger
investment-q relation, especially in macroeconomic data and in firms that use more intangibles.
These results lend support to the classic q theory of investment, and they call for the inclusion
of intangible capital in proxies for firms’ investment opportunities. However, including intangible
capital also makes the investment-cash flow relation almost an order of magnitude stronger, which
supports newer investment theories. The classic q theory performs better in settings with more
intangible capital.
JEL codes: E22, G31, O33
Keywords: Intangible Capital, Investment, Tobin’s q, Measurement Error
* The Wharton School, University of Pennsylvania. Emails: [email protected],
[email protected]. We are grateful for comments from Andy Abel, Christopher Armstrong,
Andrea Eisfeldt, Vito Gala, Itay Goldstein, Jo˜
ao Gomes, Fran¸cois Gourio, Kai Li, Juhani Linnainmaa, Vojislav Maksimovic, Justin Murfin (discussant), Thomas Philippon, Michael Roberts, Shen
Rui, Matthieu Taschereau-Dumouchel, David Wessels, Toni Whited, Mindy Zhang, and the audiences at the 2014 NYU Five-Star Conference, Binghamton University, Penn State University
(Smeal), Rutgers University, University of Chicago (Booth), University of Maryland (Smith), University of Minnesota (Carlson), and University of Pennsylvania (Wharton). We thank Venkata
Amarthaluru and Tanvi Rai for excellent research assistance, and we thank Carol Corrado and
Charles Hulten for providing data. We gratefully acknowledge support from the Rodney L. White
Center for Financial Research and the Jacobs Levy Equity Management Center for Quantitative
Financial Research.
Tobin’s q is a central construct in finance and economics more broadly. Early manifestations of
the q theory of investment, including by Hayashi (1982), predict that Tobin’s q perfectly reflects a
firm’s investment opportunities. As a result, Tobin’s q has become the most widely used proxy for
investment opportunities, making it “arguably the most common regressor in corporate finance”
(Erickson and Whited, 2012).
Despite the popularity and intuitive appeal of q theory, its empirical performance has been disappointing.1 Regressions of investment rates on proxies for Tobin’s q leave large unexplained residuals.
Extra variables like free cash flow help explain investment, contrary to the theory’s predictions.
One potential explanation is that q theory, at least in its earliest forms, is too simple. A second
possible explanation is that we measure q, investment, and cash flow poorly.
This paper’s goal is to revisit the empirical implications of q theory after correcting an important
source of measurement error: the exclusion of intangible capital. Existing papers on the investmentq relation mainly focus on firms’ physical assets like property, plant, and equipment (PP&E). They
largely exclude intangible assets like brands, innovative products, customer relationships, patents,
software, databases, distribution systems, corporate culture, and human capital, probably because
these are difficult to measure. For example, U.S. accounting rules treat research and development
(R&D) spending as an expense rather than an investment, so the knowledge created by a firm’s
own R&D almost never appears as an asset on the balance sheet. That knowledge is nevertheless
part of the firm’s economic capital: It was costly to obtain and produces future expected benefits.
In general, “Assets” on the balance sheet excludes almost all intangible capital created within
U.S. firms. Corrado and Hulten (2010) estimate that intangible capital makes up 34% of firms’
total capital in recent years, so the measurement error from excluding intangibles is severe. In
this paper, we develop measures of q and investment that explicitly recognize the importance of
intangible capital, and we show that these measures produce a stronger investment-q relation. Our
results have important implications for how researchers measure investment opportunities, and for
how we assess investment theories.
Tobin’s q is defined as the ratio of capital’s market value to its replacement cost. Our measure of
1
See Hassett and Hubbard (1997) and Caballero (1999) for reviews of the investment literature. Philippon (2009)
gives a more recent discussion.
1
q, which we call “total q,” defines the firm’s total capital as the sum of its physical and intangible
capital. Similarly, our measure of total investment is the sum of physical and intangible investments
divided by the firm’s total capital. A firm’s intangible capital is the sum of its knowledge capital
and organization capital. We interpret R&D spending as an investment in knowledge capital, and
we apply the perpetual-inventory method to a firm’s past R&D to measure the replacement cost of
its knowledge capital. We similarly interpret a fraction of past selling, general, and administrative
(SG&A) spending as an investment in organization capital. Our measure of intangible capital builds
on the measures of Lev and Radhakrishnan (2005); Corrado, Hulten, and Sichel (2009); Corrado
and Hulten (2010, 2014); Eisfeldt and Papanikolaou (2013, 2014); Falato, Kadyrzhanova, and Sim
(2013); and Zhang (2014). One innovation is that our measure includes firms’ externally purchased
intangible assets, which do appear on the balance sheet. While our q measure has limitations, we
believe, and the data confirm, that an imperfect proxy is better than setting intangible capital to
zero. A virtue of the measure is that it is easily computed for the full Compustat sample. Code
for producing the measure will eventually be on the authors’ websites. Also, we show that our
conclusions are robust to several variations on the measure.
Our analysis begins with OLS panel regressions of investment rates on proxies for q and free cash
flow, similar to the classic regressions of Fazzari, Hubbard, and Petersen (1988). We compare a
specification that includes intangible capital in investment and q to the more typical specification
that regresses physical investment (CAPEX divided by PP&E) on “physical q,” the ratio of firm
value to PP&E. The specifications with intangible capital deliver an R2 that is 37–53% higher,
meaning we obtain better proxies for investment opportunities after including intangibles.
The OLS regressions suffer from two well known problems. The first is that the slopes on q
are biased due to measurement error in q. Second, the OLS R2 depends not just on how well q
explains investment, but also on how well our q proxies explain the true, unobservable q. To address
these problems, we re-estimate the investment models using Erickson, Jiang, and Whited’s (2014)
cumulant estimator. This estimator produces a statistic τ 2 that measures how close our q proxy
is to the true, unobservable q. Specifically, τ 2 is the R2 from a hypothetical regression of our q
proxy on the true q. We find that τ 2 is 10–20% higher when one includes intangible capital in the
2
investment-q regression, implying that total q is a better proxy for true q than physical q is.
Including intangible capital increases the estimated slope coefficients on q by 118–167%. Several
papers interpret the q-slopes as the inverse of a capital adjustment cost parameter. According
to this interpretation, we find that including intangible capital produces lower estimated capital
adjustment costs. Whited (1994) shows, however, that this interpretation is flawed, and that
q-slopes are difficult to interpret even after correcting for measurement-error bias.
Of more interest are the estimated slopes on cash flow. The classic q theory predicts a zero
slope on cash flow after controlling for q. Fazzari, Hubbard, and Petersen (1988) and others find
positive slopes on cash flow, which they interpret as evidence of financial constraints. Erickson
and Whited (2000) show that these slopes become insignificant after correcting for measurement
error in q. These papers measure cash flow as profits net of R&D and SG&A. Since R&D and at
least part of SG&A are investments rather than operating expenses, one should add them back
to obtain a more economically meaningful measure of cash flow available for investment. After
making this adjustment, we find cash-flow slopes that are highly significant and almost an order
of magnitude larger. This result is inconsistent with the q theory of investment under the classic
Hayashi (1982) conditions, which we describe in Section 5. The result lends support, however, to
more recent theories that predict positive cash-flow slopes even when firms invest optimally and
face no financial constraints.2 In these newer theories, cash flow and Tobin’s q (also called average
q) both contain information about marginal q, which is what really matters for investment. For
example, decreasing returns to scale can make cash flow informative about marginal q.
We show that our main results are consistent across firms with high and low amounts of intangible
capital, across the early and late subperiods, and across almost all industries. As expected, though,
some results are stronger where intangible capital is more important. For example, the increase in
R2 from including intangible capital is almost four times larger in the quartile of firms with the
highest proportion of intangible capital, compared to the lowest quartile. The increase in R2 is
larger in the high-tech and health industries than in the manufacturing industry.
Several important studies on investment and q use data only from manufacturing firms, possibly
2
Examples include Abel and Eberly (2004), Hennessy and Whited (2007), Gala and Gomes (2013), and Gourio
and Rudanko (2014).
3
because their capital is easier to measure.3 Indeed, our τ 2 statistics confirm that physical q, but
not total q, contains less measurement error in manufacturing firms and, more generally, in firms
with less intangible capital. Our results show that including intangible capital is important even in
the manufacturing industry, but is especially important if one looks beyond manufacturing to the
industries that increasingly dominate our economy.
We also find that the classic q theory fits the data better in firms, industries, and years with more
intangible capital. Specifically, R2 values are higher and cash-flow slopes are lower in subsamples
with more intangibles. These results even hold using the usual physical investment and q measures.
Ironically, q theory works better outside the manufacturing industry, where it is most often tested.
Our main results are even stronger in macroeconomic time-series data. Our macro measure of
intangible capital is from Corrado and Hulten (2014) and is conceptually similar to our firm-level
measure. Including intangible capital in investment and q produces an R2 value that is 17 times
larger and a slope on q that is nine times larger. Almost all the improvement comes from adjusting
the investment measure, not q. Our increase in R2 is even larger than the one Philippon (2009)
obtains from replacing physical q with a q proxy estimated structurally from bond data. Philippon’s
bond q is still a superior proxy for physical investment opportunities and performs better when we
estimate the model in first differences.
To help explain these results, we provide a simple theory of optimal investment in physical and
intangible capital. The theory predicts that total q is the best proxy for total investment opportunities, whereas physical q is a noisy proxy for total and even physical investment opportunities.
These predictions help explain why our regressions produce higher R2 and τ 2 values when we use
total rather than physical capital. The theory also predicts that omitting intangible capital from
investment regressions produces smaller q-slopes, which is consistent with our empirical results.
Two main messages emerge from our analysis. The first is methodological: Researchers should
include intangible capital in their proxies for Tobin’s q, investment, and cash flow. We provide
a simple way to do so. There is also an economic message: Including intangible capital changes
our assessment of investment theories. Including intangibles makes the classic q theory fit the
3
Examples include Fazzari, Hubbard, and Petersen (1988); Almeida and Campello (2007); Almeida, Campello,
and Galvao (2010); and Erickson and Whited (2012).
4
data better in terms of R2 but worse in terms of cash-flow slopes. Newer theories that predict an
investment-cash flow relation receive much more support than previously believed.
This study is part of the growing finance literature on intangible capital.4 Several authors examine
the effect of intangible investment on valuations,5 whereas we ask how well valuations explain
investment. Closer to this study, a few papers examine the relation between intangible investment,
q, and cash flow.6 These papers use a q proxy that is close to what we call physical q. Besides having
a different focus, our study is the first to fully include intangible capital not just in investment,
but also in q and cash flow. We show that including intangibles in all three measures is crucial for
delivering our main results.
The paper proceeds as follows. Section 1 describes the data and our measure of intangible capital.
Section 2 presents full-sample results, and Section 3 compares results across different types of firms
and years. Section 4 contains results for the overall macroeconomy. Section 5 presents our theory
of investment in physical and intangible capital. Section 6 explores the robustness of our empirical
results, and section 7 concludes.
1
Data
This section describes the data in our main firm-level analysis. Section 4 describes the data in our
macro time-series analysis.
The sample includes all Compustat firms except regulated utilities (SIC Codes 4900–4999), financial firms (6000–6999), and firms categorized as public service, international affairs, or non-operating
establishments (9000+). We also exclude firms with missing or non-positive book value of assets
or sales, and also firms with less that $5 million in physical capital, as is standard in the literature.
We use data from 1975 to 2011, although we use earlier data to estimate firms’ intangible capital.
Our sample starts in 1975, the first year that FASB requires firms to report R&D. We winsorize
4
In addition to the papers we cite elsewhere, this literature includes McGrattan and Prescott (2000); Hall (2001);
Hansen, Heaton and Li (2005); Brown, Fazzari, and Petersen (2009); Li and Liu (2012); Ai, Croce and Li (2013); and
Li, Qiu, and Shen (2014).
5
See Megna and Klock (1993); Klock and Megna (2001); Chambers, Jennings, and Thompson (2002); Villalonga
(2004); and Nakamura (2003).
6
See Baker, Stein, and Wurgler (2002); Almeida and Campello (2007); Chen, Goldstein, and Jiang (2007); Eisfelt
and Papanikolaou (2013); Belo, Lin, and Vitorino (2014); and Gourio and Rudanko (2014).
5
all regression variables at the 1% level to remove extreme outliers.
1.1
Tobin’s q
Our measure of physical q follows that of Fazzari, Hubbard and Petersen (1988), Erickson and
Whited (2012), and others. We define
phy
qit
=
Vit
Kitphy
.
(1)
We measure the firm’s market value V as the market value of outstanding equity (Compustat items
prcc f times csho), plus the book value of debt (Compustat items dltt + dlc), minus the firm’s
current assets (Compustat item act), which include cash, inventory, and marketable securities.
We measure the replacement cost of physical capital, K phy , as the book value of property, plant
and equipment (Compustat item ppegt). Erickson and Whited (2006) compare several alternate
measures of physical q, including the market-to-book-assets ratio, and find that the measure above
best explains investment. Section 6 explores other popular ways of measuring physical q.
Our measure of total q includes both physical and intangible capital in the denominator:
tot
=
qit
Vit
Kitphy
+ Kitint
,
(2)
where K int is the replacement cost of the firm’s intangible capital, defined in the next sub-section.
Section 5 provides a theoretical rationale for adding together physical and intangible capital in q tot .
A simpler but less satisfying rationale is that existing studies measure capital by summing up many
different types of physical capital into PP&E; our measure simply adds more types of capital to
that sum. The correlation between q phy and q tot is 0.82.
6
1.2
Intangible Capital and Investment
We briefly review the U.S. accounting rules for intangible capital before defining our measure.7 The
accounting rules depend on whether the firm creates the intangible asset internally or purchases it
externally.
Intangible assets created within a firm are expensed on the income statement and almost never
appear as assets on the balance sheet. For example, a firm’s spending to develop knowledge,
patents, or software is expensed as R&D. Advertising to build brand capital is a selling expense
within SG&A. Employee training to build human capital is a general or administrative expense
within SG&A. There are a few exceptions where internally created intangibles are capitalized on
the balance sheet, but these are small in magnitude.8
When a firm purchases an intangible asset externally, for example, by acquiring another firm,
the firm typically capitalizes the asset on the balance sheet as part of Intangible Assets, which
equals the sum of Goodwill and Other Intangible Assets. An exception is made for acquired R&D
on products not yet being sold, which is expensed as “in-process R&D” and does not appear on
the balance sheet. If the acquired asset is “separately identifiable,” such as a patent, software, or
client list, then the asset is booked at its fair market value in Other Intangible Assets. Acquired
assets that are not separately identifiable, such as human capital, are in Goodwill on the acquirer’s
balance sheet. Firms are required to impair balance-sheet intangibles over time as needed.
We define the firm’s replacement cost of intangible capital, denoted K int , to be the sum of its
internally created and externally purchased intangible capital. We define each in turn.
We measure externally purchased intangible capital as Intangible Assets from the balance sheet
(Compustat item intan). We set this value to zero if missing. We keep Goodwill in Intangible
Assets in our main analysis, because Goodwill does include the fair cost of acquiring intangible
assets that are not separately identifiable. Since Goodwill may be contaminated by non-intangibles,
7
Chapter 12 in Kieso, Weygandt, and Warfield (2010) provides a useful summary of the accounting rules for
intangible assets. They also provide references to relevant FASB codifications.
8
As explained below, our measure will capture these exceptions via balance-sheet Intangibles. Firms capitalize the
legal costs, consulting fees, and registration fees incurred when developing a patent or trademark. A firm may start
capitalizing software spending only after the product reaches “technological feasibility” (for externally sold software)
or reaches the coding phase (for internally used software). The resulting software asset is part of Other Intangibles
(intano) in Compustat.
7
such as a market premium for physical assets, in Section 7 we also try excluding Goodwill from
external intangibles and show that our results are almost unchanged. Balance-sheet Intangibles will
also include those few exceptions, described above, where an internally created intangible asset is
capitalized. Our mean (median) firm purchases only 19% (3%) of its intangible capital externally,
meaning the vast majority of firms’ intangible assets are missing from their balance sheets. There
are important outliers, however. For example, 41% of Google’s intangible capital in 2013 had been
purchased externally.
Measuring the replacement cost of internally created intangible assets is difficult, since they
appear nowhere on the balance sheet. Fortunately, we can construct a proxy by accumulating past
intangible investments, as reported on firms’ income statements. We define the stock of internal
intangible capital as the sum of knowledge capital and organization capital, which we define next.
A firm develops knowledge capital by spending on R&D. We estimate a firm’s knowledge capital
by accumulating past R&D spending using the perpetual inventory method:
Git = (1 − δR&D )Gi,t−1 + R&Dit ,
(3)
where Git is the end-of-period stock of knowledge capital, δR&D is its depreciation rate, and R&Dit
is real expenditures on R&D during the year. The Bureau of Economic Analysis (BEA) uses a
similar method to capitalize R&D, as do practitioners when valuing companies (Damodaran, 2001,
n.d.). For δR&D , we use the BEA’s industry-specific R&D depreciation rates, which range from
10% in the pharmaceutical industry to 40% for computers and peripheral equipment.9 We measure
annual R&D using the Compustat variable xrd. We use Compustat data back to 1950 to compute
(3), but our regressions only include observations starting in 1975. Starting in 1977, we set R&D
to zero when missing, following Lev and Radhakrishnan (2005) and others.10
9
The BEA’s R&D depreciation rates are from the analysis of Li (2012). Following the BEA’s guidance, we use a
depreciation rate of 15% for industries not in Li’s Table 4. Our results are virtually unchanged if we apply a 15%
depreciation rate to all industries.
10
We start in 1977 to give firms two years to comply with FASB’s 1975 R&D reporting requirement. If we see
a firm with R&D equal to zero or missing in 1977, we assume the firm was typically not an R&D spender before
1977, so we set any missing R&D values before 1977 to zero. Otherwise, before 1977 we either interpolate between
the most recent non-missing R&D values (if such observations exist) or we use the method in Appendix A (if those
observations do not exist). Starting in 1977, we make exceptions in cases where the firm’s assets are also missing.
8
One challenge in applying the perpetual inventory method in (3) is choosing a value for Gi0 , the
capital stock in the firm’s first non-missing Compustat record, which usually coincides with the
IPO. We estimate Gi0 using data on the firm’s founding year, R&D spending in its first Compustat
record, and average pre-IPO R&D growth rates. With these data, we estimate the firm’s R&D
spending in each year between its founding and appearance in Compustat. We apply a similar
approach to SG&A below. Appendix A provides additional details. Section 6 shows that a simpler
measure assuming Gi0 = 0 produces an even stronger investment-q relation than our main measure.
We consider that simpler measure a reasonable alternate proxy for investment opportunities.
Next, we measure the stock of organization capital by accumulating a fraction of past SG&A
spending using the perpetual inventory method, as in equation (3). The logic is that at least
part of SG&A represents an investment in organization capital through advertising, spending on
distribution systems, employee training, and payments to strategy consultants. We follow Hulten
and Hao (2008), Eisfeldt and Papanikoloau (2014), and Zhang (2014) in counting only 30% of SG&A
spending as an investment in intangible capital. We interpret the remaining 70% as operating costs
that support the current period’s profits. Section 6 shows that our conclusions are robust to using
values other than 30%, including zero, 100%, and a value estimated from the data. We follow
Falato, Kadyrzhanova, and Sim (2013) in using a depreciation rate of δSG&A = 20%, and in Section
6 we show that our conclusions are robust to alternate depreciation rates.
Measuring SG&A from Compustat data is not trivial. Although Compustat labels its xsga
variable “Selling, General and Administrative Expense,” Compustat usually adds R&D to SG&A
to produce xsga. We must therefore subtract xrd from xsga to isolate SG&A. Appendix A provides
additional details.
Our measure of internally created organization capital is almost identical to Eisfeldt and Papanikolaou’s (2012, 2013, 2014). They validate the measure in several ways. They document a
positive correlation between firms’ use of organization capital and Bloom and Van Reenen’s (2007)
managerial quality score. This score is associated with higher firm profitability, production efficiency, and productivity of information technology (IT) (Bloom, Sadun, and Van Reenen, 2010).
These are likely years when the firm was privately owned. In such cases, we interpolate R&D values using the nearest
non-missing values.
9
Eisfeldt and Papanikoloau (2013) show that firms using more organization capital are more productive after accounting for physical capital and labor, they spend more on IT, and they employ
higher-skilled workers. They show that firms with more organization capital list the loss of key
personnel as a risk factor more often in their 10-K filings. Practitioners also use our approach:
A popular textbook on value investing recommends capitalizing SG&A to measure assets missing
from the balance sheet (Greenwald et al., 2004).
Following Erickson and Whited (2012) and many others, we define the physical investment rate
as
ιphy
it =
Iitphy
phy
Ki,t−1
,
(4)
and we measure I phy as CAPEX. Our measure of total investment includes investments in both
physical and intangible capital. Specifically, we define the total investment rate as
ιtot
it =
Iitphy + Iitint
phy
int
Ki,t−1
+ Ki,t−1
,
(5)
and we measure intangible investment, I int , as R&D + 0.3×SG&A. This definition assumes 30%
of SG&A represents an investment, as we assume when estimating capital stocks. The correlation
between ιtot and ιphy is 0.88.
Our measure of intangible capital has the virtue of being easily computed for the full Compustat
sample. The measure has limitations, however, two of which we discuss next.
First, human capital is complicated by the fact that employees can bargain over their surplus and
quit.11 Our measure assumes that employee training creates human capital in the sense that it
raises firm profits for some period of time, which seems reasonable. To the extent that 0.3×SG&A
includes a firm’s spending on employee training, our measure includes this capital’s replacement
cost.
Second, we assume a constant depreciation rate for intangible capital, whereas the true rate is
likely random and not observed by the econometrician. For example, it might be appropriate to
11
Eisfeldt and Papankiloau (2013, 2014) analyze these features of human capital and their implications for intangible
investment, risk, and valuations.
10
write off a large portion of knowledge capital when a firm narrowly loses a patent race.12 The usual
physical-capital measures face a similar but less severe limitation. For example, a product-market
change could make a machine obsolete in ways that accounting book value does not accurately
reflect. This limitation generates measurement error in the replacement cost of intangible and
physical capital, and thereby in our investment and q measures. We treat measurement error
carefully in Section 2.2.
In Section 6 we show that our conclusions are robust to several alternate ways of measuring capital
and q. Overall, we believe, and the data confirm, that an imperfect proxy for intangible capital is
better than setting it to zero.
1.3
Cash Flow
Erickson and Whited (2012) and others measure free cash flow as
cphy
it =
IBit + DPit
phy
Ki,t−1
,
(6)
where IB is income before extraordinary items and DP is depreciation expense. This is the predepreciation free cash flow available for physical investment or distribution to shareholders. One
shortcoming of cphy is that it treats R&D and SG&A as operating expenses, not investments. For
that reason, we call cphy the physical cash flow. In addition to cphy , we use an alternate cash flow
measure that recognizes R&D and part of SG&A as investments. Specifically, we add intangible
investments back into the free cash flow so that we measure the profits available for investment in
either physical or intangible capital:
ctot
it =
IBit + DPit + Iitint (1 − κ)
phy
int
Ki,t−1
+ Ki,t−1
.
(7)
12
Suppose two firms make identical R&D investments in a race to patent a drug, and one firm wins the race by an
instant. The firms’ true q and future investment opportunities may be equal once we write off the loser’s knowledge
capital. Since our measure writes off only a fraction δR&D of the loser’s capital, however, our measure would likely
assign the loser a lower q. There is alternative interpretation, though, which is more in line with our measure: The
loser still possesses the knowledge capital, but it has received a negative productivity shock and therefore truly has
a lower q. In line with this interpretation, the winner will likely make larger future investments as it takes the drug
to market.
11
Lev and Sougiannis (1996) similarly adjust earnings for intangible investments, as do practitioners
(Damodaran, 2001, n.d.). Since accounting rules allow firms to expense intangible investments,
the effective cost of a dollar of intangible capital is only (1 − κ), where κ is the marginal tax rate.
When available, we use simulated marginal tax rates from Graham (1996). Otherwise, we assume
a marginal tax rate of 30%, which is close to the mean tax rate in the sample. The correlation
between ctot and cphy is 0.77.
1.4
Summary Statistics
Table 1 contains summary statistics. We define intangible intensity as a firm’s ratio of intangible
to total capital, at replacement cost. The mean (median) intangible intensity is 43% (45%), so
almost half of capital is intangible in our typical firm/year. Knowledge capital makes up only 24%
of intangible capital on average, so organization capital makes up 76%. The median firm has almost
no knowledge capital, since almost half of firms report no R&D. The average q tot is mechanically
smaller than q phy , since the denominator is larger. The gap is dramatic in some cases. For example,
Google’s physical q is 10.1 in 2013, but its total q is only 3.2. The standard deviation of q tot is
74% lower than for q phy . The standard deviation is lower even if we scale the standard deviations
by their respective means. Both q proxies exhibit significant skewness, which is a requirement of
the cumulant estimator we apply in Section 2.2. Total investment exceeds physical investment on
average, implying that investment is typically under-estimated when one ignores intangible capital.
This result is not mechanical, since ιtot adds intangibles to both the numerator and denominator.
Figure 1 shows that the average intangible intensity has increased over time, especially in the
1990s. The figure also shows that high-tech and health firms are heavy users of intangible capital, while manufacturing firms use less. Somewhat surprisingly, even manufacturing firms have
considerable amounts of intangible capital; their average intangible intensity ranges from 30–34%.
12
2
Full-sample Results
We begin with the classic panel regressions of Fazarri, Hubbard, and Petersen (1988). We then
correct for measurement-error bias in Section 2.2 and perform a placebo analysis in Section 2.3.
2.1
OLS Results
Table 2 contains results from OLS regressions of investment on lagged q, contemporaneous cash flow,
and firm and year fixed effects. The dependent variables in Panels A and B are, respectively, the
total and physical investment rates, ιtot and ιphy . The estimated slopes suffer from measurementerror bias, but the R2 values help gauge how well our q variables proxy for investment opportunities.
Most papers in the literature regress ιphy on q phy , as in column 2 of Panel B. That specification
delivers a within-firm R2 of 0.233, whereas a regression of ιtot on q tot (Panel A column 1) produces
an R2 of 0.320, higher by 0.087 or 37%. The 0.087 increase in R2 is highly statistically significant,
with a t-statistic of 22.13 This result implies that total q explains total investment better than
physical q explains physical investment.
Including intangibles produces a higher R2 for two reasons. First, comparing columns 1 and 2,
we see that q tot is better than q phy at explaining both total investment (Panel A) and physical
investment (Panel B). Second, R2 values are uniformly larger in Panel A than Panel B, indicating
that total investment rates are better explained by both q variables. One reason is that total investment is smoother over time than physical investment, largely because CAPX is lumpy compared
to SG&A and R&D: The within-firm volatility of physical (total) investment is 20.2% (15.4%).
It is tempting to run a horse by including q phy and q tot in the same regression. Since both
variables proxy for q with error, their resulting slopes would be biased in an unknown direction,
making the results difficult to interpret (Klepper and Leamer, 1984). For this reason, we do not
tabulate results from such a horse race. We simply note that regressing total investment on both q
proxies produces a positive and highly significant slope on q tot and a negative and less-significant
slope on q phy . Replacing total investment with physical investment in the horse race, both q proxies
13
Throughout, we conduct inference on R2 values using influence functions (Newey and McFadden, 1994). In a
regression y = βx + ǫ, this approach takes into account the estimation error in β, var(y), and var(x). We cluster by
firm, which accounts for autocorrelation both within and across regressions. Additional details available on request.
13
enter positively and significantly.
Columns 3 and 4 repeat the same specifications while controlling for cash flow. The patterns in
R2 are similar. For example, the specification with physical capital (column 5 of panel B) produces
an R2 of 0.238, whereas the specification with total capital (column 3 of panel A) delivers an R2
of 0.364, 53% higher.
To summarize, we find that including intangible capital in investment and Tobin’s q makes q a
better proxy for investment opportunities. One potential explanation is that total q is a better
proxy for the true, unobservable Tobin’s q. Another potential explanation is that the relation
between investment and this true q is stronger when one includes intangible capital. The next
section provide evidence supporting both explanations.
2.2
Bias-Corrected Results
A priori, we believe that total q is better than physical q at approximating the true, unobservable
q. We recognize, however, that total q is still a noisy proxy. For one, we measure intangible capital
with error. Also, Tobin’s q measures “average q,” but investment depends on “marginal q” in
theory.14 Average q equals marginal q in the classic q theory of investment, and also in our theory
in Section 5. To the extent that reality departs from these theories, average q measures marginal
q with error.
Since we only have a proxy for q, all the OLS slopes from the previous section suffer from
measurement-error bias. We now estimate the previous models while correcting this bias. We do
so using Erickson, Jiang, and Whited’s (2014) higher-order cumulant estimator, which supercedes
Erickson and Whited’s (2002) higher-order moment estimator.15 The cumulant estimator provides
14
Gala (2014) offers a framework for estimating marginal q and explores the differences between marginal and
average q.
15
Cumulants are polynomials of moments. The estimator is a GMM estimator with moments equal to higher-order
cumulants of investment and q. Compared to Erickson and Whited’s (2002) estimator, the cumulant estimator has
better finite-sample properties and a closed-form solution, which makes numerical implementation easier and more
reliable. We use the third-order cumulant estimator, which dominates the fourth-order estimator in the estimation
of τ 2 (Erickson and Whited, 2012; Erickson, Jiang, and Whited, 2014). Our conclusions are robust to using the
fourth-order cumulant estimator; results available upon request.
14
unbiased estimates of β in the following errors-in-variables model:
ιit = ai + qit β + zit α + uit
(8)
pit = γ + qit + εit ,
(9)
where p is a noisy proxy for the true, unobservable q, and z is a vector of perfectly measured control
variables. The cumulant estimator’s main identifying assumptions are that p has non-zero skewness,
and that u and ε are independent of q, z, and each other. In addition to delivering unbiased slopes,
the estimator also produces two useful test statistics. The first, ρ2 , is the hypothetical R2 from
(8). Loosely speaking, ρ2 tells us how well true, unobservable q explains investment, with ρ2 = 1
implying a perfect relation. The second statistic, τ 2 , is the hypothetical R2 from (9). It tells us
how well our q proxy explains true q, with τ 2 = 1 implying a perfect proxy.
For comparison, we also use the two instrumental-variable (IV) estimators advocated by Almeida,
Campello, and Galvao (2010). Both estimators take first differences of the linear investment-q
model, then use lagged regressors as instruments for the q proxy. The two IV estimators produce
similar results, so we only tabulate results using Biorn’s (2000) IV estimator.16 Erickson and
Whited (2012) show that the IV estimators are biased if measurement error is serially correlated,
which is likely in our setting. This bias is probably most severe in the usual regressions that omit
intangible capital: Omitted intangible capital is an important source of measurement error, and
a firm’s intangible capital stock is highly serially correlated. Since the cumulant estimators are
robust to serially correlated measurement error, we prefer them over the IV estimators.
Estimation results are in Table 3. Columns labelled “Physical” use the physical-capital measures
ιphy , q phy , and cphy . Columns labelled “Total” use the total-capital measures ιtot , q tot , and ctot .
Cumulants results are in Panel A. IV results are in Panel B.
The τ 2 estimates are higher with total rather than physical capital, indicating that total q is a
better proxy for the true, unobservable q than physical q is. For example, comparing columns 1
and 2 of Panel A, τ 2 increases from 0.492 to 0.591, a 20% increase. We are not aware of a formal
16
The second IV estimator is Arellano and Bond’s (1991) GMM estimator. Its results are available on request.
15
test for comparing τ 2 values, but this 0.099 increase in τ 2 values is considerably larger than their
individual bootstrapped standard errors, 0.010 and 0.007. Despite the improvement in τ 2 , total q
is still a noisy proxy for true q: The 0.591 value of τ 2 implies that total q explains only 59.1% of
the variation in true q. The improvement in τ 2 is smaller (10%) when we control for cash flow.
The ρ2 estimates are also higher with total rather than physical capital, indicating that the
unobservable, true q explains more of the variation in investment when we include intangibles.
The increase in ρ2 from including intangible capital is 0.054 (15%) without cash flow, and .106
(29%) with cash flow. Both increases are large relative to the standard errors for ρ2 . The ρ2
estimates using total capital, 0.426 and 0.477, indicate that q explains 43–48% of the variation
in investment. These result helps us assess how the simplest linear investment-q theory fits the
data. The theory explains almost half of the variation in investment, so there is still considerable
variation left unexplained. Judging by the higher ρ2 values with total capital, the theory fits the
data considerably better when one includes intangible capital in investment and q.
As expected, Panel B’s regressions in first differences produce lower R2 values than the regressions
in levels do. Even in first differences, though, R2 values roughly double when we include intangibles,
consistent with our results in levels.
Next, we discuss the bias-corrected slopes on q. Both estimators produce significantly larger
slopes on q when we include intangibles. The increase in coefficient moving from physical to total
capital ranges from 118–163%. The increase in q-slope is expected. In the usual physical-capital
regression, intangible investment is excluded from left-hand side, so it appears in the error term with
a negative sign. The error term is negatively related to physical q, because intangible investment is
positively related to physical q. The negative relation between the error term and regressor makes
the estimated q-slope smaller in the physical-capital regression.
Interpreting the q-slopes is difficult. The simplest q theories, like Hayashi’s (1982) or the one we
present in Section 5, predict that the inverse of the q-slope measures the marginal capital adjustment
cost. Whited (1994) and Erickson and Whited (2000) explain, though, that is impossible to obtain
meaningful adjustment-cost estimates from the q-slopes, even in the simplest q theories. The main
problem is that our regression corresponds to a large class of investment cost functions, so there
16
is no hope of identifying average adjustment costs without strong, arbitrary assumptions on the
cost function. If one moves beyond the simple q theory we describe in Section 5, it becomes even
harder to interpret our slopes on q (Gala and Gomes, 2013). We simply interpret our q-slopes as
determinants of the elasticity of investment with respect to q, and we show that including intangible
capital makes the slopes much larger.
Larger q-slopes do not necessarily imply larger economic significance, because the physical- and
total-capital measures have different standard deviations. Holding constant a one-unit increase in q,
the total-capital specification produces a 0.49 standard-deviation increase in ιtot , but the physicalcapital specification produces only a 0.15 standard-deviation increase in ιphy . On this dimension,
the total-capital specification delivers higher economic significance. The opposite obtains if we
compare one standard deviation changes in q. That difference, though, mainly reflects that q tot has
a standard deviation that is 74% lower than that of q phy (Table 1).
Finally, we discuss the estimated slope coefficients on cash flow. The simplest q theories predict a
zero slope, since q should perfectly explain investment. The data strongly reject this prediction: We
find significantly positive slopes on cash flow in all columns and panels. The cash-flow slopes become
nine (Panel A) or six (Panel B) times larger in magnitude when we move from the physical- to the
total-capital specification.17 This result is expected. Recall that we add back intangible investment
to move from cphy to ctot . As a result, when intangible investment is high, ctot also tends to be
high relative to cphy , creating a stronger investment-cash flow relation. This difference is the result
of having a more economically sensible measure of investment and hence free cash flow. In other
words, previous studies that only include physical capital have found slopes on cash flow that are
too small, because they fail to classify the resources that go toward intangible investments as free
cash flow available for investment.
One concern here is that measurement error in intangible investment may bias our cash-flow slopes
upward, since that same error is in both ιtot and ctot . Most of this measurement error likely comes
from the SG&A part of our ιtot measure. Even if we exclude SG&A so that intangible investment
17
Economic significance is also larger in the total-capital specification. For example, a one standard deviation
increase in ctot (0.19) is associated with a 0.026, or 0.138 standard-deviation, increase in ιtot . A one standard
deviation increase in cphy (0.62) is associated with a 0.009, or 0.039 standard-deviation, increase in ιphy .
17
comes only from R&D, we still find that including intangibles increases the estimated cash-flow
slope from 0.015 to 0.043, so our conclusion still holds directionally (results available on request).
To summarize, judging by the cash-flow slopes, the simplest q theories fit the data worse when we
include intangible capital. This result does not necessarily spell bad news for more recent theories
of q and investment, which have shown that non-zero slopes on cash flow may arise from many
sources. For example, the theories of Gomes (2001), Hennessy and Whited (2007), Abel and Eberly
(2011), and Gourio and Rudanko (2014) predict significant cash-flow slopes even in the absence
of financial constraints. For example, decreasing returns to scale can make cash flow informative
about marginal q, even after controlling for Tobin’s (average) q. Our contribution is to show that
the investment-cash flow relation is almost an order of magnitude larger than previously believed,
once we properly account for intangible capital.
2.3
Placebo Analysis
Are the results above mechanical? Specifically, would including intangibles produce a larger R2 , ρ2 ,
τ 2 , and q-slope even if our intangible measures were pure noise? Note that we can write our variables
as
phy
tot
qi,t−1
= qi,t−1
Ai,t−1
ιtot
= ιphy
Ai,t−1 Bi,t
i,t
i,t
Ai,t−1 ≡
Bi,t ≡
phy
Ki,t−1
phy
int
+ Ki,t−1
Ki,t−1
phy
int
Ii,t
+ Ii,t
.
phy
Ii,t
(10)
(11)
(12)
(13)
Equations (10) and (11) show that moving from the physical- to the total-capital specification
requires multiplying both sides of the regression by Ai,t−1 . In general, multiplying both sides of a
regression by an extra variable A can mechanically increase the regression’s R2 and slope coefficient,
even if A is pure noise.
Our results are not obvious or mechanical, however. While A may work to increase the slope and
18
R2 , there is a second force that may act in the opposite direction: We multiply the left- but not
the right-hand side of the regression by Bi,t , which is negatively related to Ai,t−1 .18 The negative
relation between B and A will work to reduce the regression’s slope and possibly its R2 as well. A
priori, the combined effects of A and B are not obvious.
We perform a placebo analysis to show that our results would not obtain if our intangible measures
were pure noise. We simulate intangible investment Ieint that has same mean, persistence, and
volatility as actual intangible investment, but is otherwise pure noise. Next, we compute simulated
e int by applying the perpetual-inventory method to Ieint , just as we do in
intangible capital stocks K
e int , along with actual values of I phy ,
the actual data. We use these simulated values of Ieint and K
K phy , q phy , and ιphy , to compute the placebo variables e
ιtot and qetot using formulas (10)-(13) above.
We use e
ιtot and qetot in OLS and cumulants regressions similar to those in Tables 2 and 3. Appendix
B contains additional details.
We find that a placebo OLS regression of e
ιtot on qetot produces an R2 of 0.247, slightly higher than
the 0.233 R2 from using physical capital alone, but well below the 0.320 R2 from using actual data
on total capital (Table 2). Even if we treated the placebo’s 0.247 R2 as the null-hypothesis value,
the observed 0.320 R2 would significantly exceed it with a t-statistic of 18. The placebo regression’s
ρ2 is 0.331, lower than the total-capital ρ2 (0.426) and even the physical-capital ρ2 (0.372, Table
3). The placebo regression’s τ 2 is 0.553, roughly halfway between the physical-capital τ 2 (0.492)
and the total-capital τ 2 (0.591, Table 3). The placebo regression produces a bias-corrected q-slope
of 0.046, higher than the physical-capital slope (0.036), but much lower than the total-capital slope
(0.093, Table 3). To summarize, our main results would not obtain even if our intangible-capital
measures were pure noise with similar statistical properties. Such noise could explain only half of
the observed increase in τ 2 . It could explain a much smaller fraction of the observed increases in
R2 and q-slopes. Noise could explain none of the observed increase in ρ2 .
18
Empirically, the within-firm correlation of Ai,t−1 and Bi,t is -0.14. A negative relation is expected, because
persistence in investment typically makes intangible investment high when the firm has more intangible capital. The
numerator of B is therefore large when the denominator of A is large, making A and B negatively related.
19
3
Comparing Subsamples
Next, we compare results across firms, industries, and years. Doing so allows us to check the
robustness of our main results, judge where and when including intangible capital matters most,
and test q theory in different settings.
We re-estimate the previous models in subsamples formed using three variables. First, we sort
firms each year into quartiles based on their lagged intangible intensity (Table 4). Second, we use
the Fama-French five-industry definition to compare the manufacturing, consumer, high-tech, and
health industries (Table 5). Third, we compare the early (1972–1995) and late (1996–2011) parts of
our sample (Table 6). For each subsample, we estimate a total-capital specification using ιtot , q tot ,
and ctot . The adjacent column presents a physical-capital specification using ιphy , q phy , and cphy .
We tabulate the difference in R2 , ρ2 , and τ 2 between the physical- and total-capital specifications.
We discuss results from Panel A, which includes just q. Results are qualitatively similar in Panel
B, which controls for cash flow.
Our main results are quite robust. Using total rather than physical capital produces higher R2
values in all ten subsamples. The increase in R2 ranges from 0.045–0.178, or from 25–60%. All
ten increases in R2 are statistically significant, with t-statistics ranging from 7 to 23. This result
means that including intangible capital produces a better proxy for investment opportunities even
in subsamples with less intangible capital. Including intangible capital produces higher values of
ρ2 and larger slopes on q and cash flow in nine out of ten subsamples. The only exceptions are in
the health industry, where including intangibles makes ρ2 and the cash-flow slope slightly lower.
As expected, including intangible capital is more important in firms and years with more intangible
capital. First we discuss R2 values. The increase in R2 is 0.178 (60%) in the highest intangible
quartile, compared to 0.045 (25%) in the lowest quartile. This 0.133 (=0.178-0.045) “difference in
difference” in R2 is highly statistically significant, with a t-statistic of 13.19 Including intangible
capital increases the R2 by 0.059 in the manufacturing industry, 0.092 in the consumer industry,
0.088 in the health industry, and 0.109 in the high-tech industry. These increases roughly line
up with the industries’ use of intangible capital. For example, 55% of the high-tech industry’s
19
Footnote 13 explains how we conduct inference on R2 values.
20
capital is intangible, on average, compared to 31% in the manufacturing industry. We see mixed
results for the year subsamples. In Panel A of Table 6, the increase in R2 is slightly higher in
the later subsample compared to the early subsample, which makes sense given that there is more
intangible capital in recent years (Figure 1). We see the opposite result in Panel B, which controls
for cash flow. The likely explanation for these mixed results is that our regressions include firm
fixed effects, which sweep out the effects of entry by intangible-intensive firms. Entry has largely
driven the increase in intangible usage over time.
Next we discuss τ 2 differences. Including intangible capital produces a higher τ 2 in subsamples
with more intangible capital. This result implies that total q is a better proxy for true q especially
in firms and years with the most intangible capital, which provides a useful consistency check. Some
of these improvements are dramatic. For example, τ 2 increases by 0.204 (46%) in the quartile with
the most intangible capital, by 0.130 (36%) in the health industry, by 0.130 (25%) in the tech
industry, and by 0.119 (25%) in the later subperiod. Including intangible capital produces a lower
τ 2 , however, in subsamples with less intangible capital, such as the manufacturing industry. Some
of these decreases appear to be statistically insignificant. To the extent that they are significant,
total q is a worse proxy for true q in contexts with less intangible capital. One potential explanation
is that setting intangible capital to zero may be more accurate than using our noisy measure when
intangible capital is already close to zero. Recall, though, that including intangibles produces a
higher R2 value in all ten subsamples. If the goal is to produce a good proxy for investment
opportunities, and not just a good proxy for the true q, then including intangible capital helps in
all subsamples.
In addition to comparing differences across subsamples, it is also interesting to compare levels.
On three dimensions, q theory fits the data better in subsamples with more intangible capital.
First, R2 values roughly double when we move from the lowest to highest intangible quartile. This
increase is economically and statistically significant whether one uses a physical-capital specification (t = 9) or a total-capital specification (t = 18). It is surprising that even the physical-capital
specification has a higher R2 in high-intangible firms, since physical q presumably has more measurement error in these firms. Indeed, we find that the physical-capital specification’s τ 2 is lower
21
(44% vs. 68%), meaning physical q has more measurement error, in firms with more intangibles.
The patterns are similar when we compare manufacturing to high-intangible industries, or compare
the early and late subsamples.
Second, ρ2 values also roughly double when we move from the lowest to highest intangible quartile.
This result means that the relation between investment and true q is much stronger in firms with
more intangible capital. The increase in ρ2 from the physical-capital specifications is so large that
it offsets the decrease τ 2 , leading to an increase in R2 . Again, the patterns are similar across
industries and years.
Third, cash-flow slopes are significantly lower in subsamples with more intangible capital. The
decrease in cash-flow slopes has a t-statistic above five when we compare the lowest vs. highest
intangible quartiles, manufacturing vs. high-tech, manufacturing vs. health, or recent vs. early
years, regardless of whether we look at the physical- or total-capital specifications. Chen and
Chen (2012) also find a weaker investment-cash flow sensitivity in recent years. We find that this
sensitivity is insignificantly negative in recent years when we use the physical-capital measures, but
it becomes significantly positive again when we use the total-capital measures.
Why does the classic q theory work better in firms and years with more intangibles? Financial
constraints cannot explain this result, because intangibles are associated with larger financial constraints (Almeida and Campello, 2007), which should make q theory perform worse. Presumably, q
theory’s other assumptions— perfect competition, constant returns to scale, quadratic adjustment
costs, etc.— are closer to reality in settings with more intangible capital. One additional clue is
that the investment-q relation is also stronger in younger firms (Table 10), which tend to have more
intangible capital. It is possible that younger firms face more competition and have not yet reached
the point of decreasing returns to scale, making classic q theory explain the data better.
4
Macro Results
Next, we investigate the investment-q relation in U.S. macro time-series data. Our sample includes
141 quarterly observations from 1972Q2–2007Q2, the longest period for which all variables are
22
available.
Data on aggregate physical q and investment come from Hall (2001), who uses the Flow of Funds
and aggregate stock and bond market data. Physical q, again denoted q phy , is the ratio of the value
of ownership claims on the firm less the book value of inventories to the reproduction cost of plant
and equipment. The physical investment rate, again denoted ιphy , equals private nonresidential
fixed investment scaled by its corresponding stock, both of which are from the Bureau of Economic
Analysis.
Data on the aggregate stock and flow of physical and intangible capital come from Carol Corrado
and are discussed in Corrado and Hulten (2014). Earlier versions of these data are used by Corrado,
Hulten, and Sichel (2009) and Corrado and Hulten (2010). Their measures of intangible capital
include aggregate spending on business investment in computerized information (from NIPA), R&D
(from the NSF and Census Bureau), and “economic competencies,” which include investments in
brand names, employer-provided worker training, and other items (various sources). As before, we
measure the total capital stock as the sum of the physical and intangible capital stocks. We compute
total q as the ratio of total ownership claims on firm value, less the book value of inventories, to the
total capital stock, and we compute the total investment rate as the sum of intangible and physical
investment to the total lagged capital stock. To mitigate problems from potentially differing data
coverage, we use Corrado and Hulten’s (2014) ratio of physical to total capital to adjust Hall’s
(2001) measures of physical q and investment. More precisely, we compute ιtot and q tot by applying
equations (10)-(13) to Hall’s (2001) data on q phy and ιphy and Corrado and Hulten’s (2014) data
on A and B.
The correlation between physical and total q is extremely high, 0.997. The reason is that total
q equals physical q times A, the ratio of physical to total capital, and A has changed slowly
and consistently over time (Figure 1). Of more importance is the change from physical to total
investment, which requires multiplying ιphy by A and B. The ratio of flows (B) is much more
volatile than the ratio so stocks (A), so the correlation between total and physical investment is
much smaller, 0.43.
For comparison, we also use Philippon’s (2009) aggregate bond q measure, which he obtains by
23
applying a structural model to data on bond maturities and yields. Bond q is available at the
macro level but not at the firm level. Philippon (2009) shows that bond q explains more of the
aggregate variation in what we call physical investment than physical q does. Bond q data are from
Philippon’s web site.
Figure 2 plots the time series of aggregate investment and q using physical capital (left panel)
and total capital (right panel). Except in a few subperiods, physical q explains physical investment
relatively poorly, as Philippon (2009) and others have shown. Total q explains total investment
much better, mainly because of a secular increase in intangible investment that is missing from the
physical-capital measures.
Table 7 presents results from time-series regressions of investment on q. The top panel uses total
investment as the dependent variable, and the bottom panel uses physical investment. The first
two columns show dramatically higher R2 values and slope coefficients in the top panel compared
to the bottom. The result is similar for both total and physical q (columns 1 and 2), as expected.
This result implies a much stronger investment-q relation when we include intangible capital in our
investment measure. The 0.57 increase in R2 from including intangible capital (column 1 in Panel
A vs. column 2 in Panel B) is even larger than the 0.43 increase Philippon (2009) obtains by using
bond q in place of physical q (columns 2 vs. 3 in panel B).
Interestingly, bond q enters insignificantly in Panel A and explains very little variation in total
investment. We obtain the opposite result in Panel B: Bond q explains much more of the variation
in physical investment and is the only q variable that enters significantly. Why is bond q better at
explaining physical investment but worse at explaining total investment? Philippon (2009) offers
the following potential explanation: Growth options affect stocks more than bonds, and growth
options affect intangible investment more than physical investment. Put differently, physical and
intangible capital may have different values of marginal q; bond q may be a better proxy for
physical capital’s marginal q, whereas the traditional q measures, which use stock prices, may be
better proxies for intangible capital’s marginal q. A second possible explanation is about sample
selection: Firms with more intangible investment typically hold less debt, so they contribute less
to the aggregate bond-q measure.
24
As explained in Section 2, horse races between various q proxies produce results that are difficult
to interpret, so we do not tabulate them. We note, however, that horse races produce the same
inferences as the univariate regressions summarized above. For example, a regression of total
investment on both q tot and q bond produces a significantly positive slope on q tot and a positive but
insignificant slope on q bond .
We re-estimate the regressions in one-quarter and four-quarter differences. Results are available
upon request. Echoing our results above, regressions of investment on either total or physical q
generate larger slopes and R2 values when we use total rather than physical investment. The relation
between physical investment and either q variable is statistically insignificant in first differences,
whereas the relation between total investment and either q is always significant. In all these
specifications in differences, bond q enters with much higher statistical significance, drives out
both total and physical q in horse races, and generates higher R2 values. Bond q seems to better
capture high-frequency changes in investment opportunities, but total and physical q better capture
low-frequency changes, at least for total investment.
To summarize, in macro time-series data we find a much stronger investment-q relation when we
include intangible capital in our measure of investment. While total q is better than bond q at
explaining the level of total investment, bond q is better at explaining first differences, and bond q
is also better at explaining the level of physical investment.
5
A Theory of Intangible Capital, Investment, and q
In this section we present a theory of optimal investment in physical and intangible capital. Our
first goal is to provide a rationale for the empirical choices we have made so far. Specifically, we
provide a rationale for adding together physical and intangible capital in our measure of total q, and
we provide a rationale for regressing total investment on total q. More importantly, we illustrate
what can go wrong when one omits intangible capital and simply regresses physical investment
on physical q. The aim here is to help explain our empirical results, not to make a theoretical
contribution. Wildasin (1984), Hayashi and Inoue (1991), and others already provide theories
25
of investment in multiple capital goods. We provide a simple model in Section 6.1 to make the
economic mechanism as transparent as possible. Section 6.2 presents a slightly richer model and
shows that the main conclusions are robust. All proofs are in Appendix C.
5.1
Model with Perfect Substitutes and Analytical Predictions
We simplify and modify Abel and Eberly’s (1994) theory of investment under uncertainty to include
two capital goods. We interpret the two capital goods as physical and intangible capital, but they
are interchangeable within the model. The model features an infinitely lived, perfectly competitive
firm that holds K1t units of physical capital and K2t units of intangible capital at time t. (We
omit firm subscripts for notational ease. Parameters are constant across firms, but shocks and
endogenous variables can vary across firms unless otherwise noted.) Like Hall (2001), we assume
the two capital types are perfect substitutes, so what matters is total capital K ≡ K1 + K2 and
total investment I ≡ I1 + I2 . A similar assumption is implicit in almost all empirical work on the
investment-q relation: By using data on CAPEX and PP&E, both of which add together different
types of physical capital, researchers have treated these different types of physical capital as perfect
substitutes. The next subsection relaxes the perfect-substitutes assumption.
At each instant t the firm chooses the investment rates I1 and I2 that maximize firm value:
V (K, εt , p1t , p2t ) =
max
Z
∞
{I1,t+s , I2,t+s } 0
γ
Et [π (Kt+s , εt+s ) − Kt+s
2
It+s
Kt+s
2
(14)
− p1,t+s I1,t+s − p2,t+s I2,t+s ]e−rs ds
subject to
dKi = (Ii − δKi ) dt,
i = 1, 2
(15)
and I1t , I2t ≥ 0. The profit function π depends on a shock ε and is assumed linearly homogenous
in K. Equation (14) assumes the firm faces quadratic capital adjustment costs with parameter
γ. Capital prices p1t and p2t , along with profitability shock εt , fluctuate over time according to a
26
general stochastic diffusion process
dyt = µ (yt ) dt + Σ (yt ) dBt ,
(16)
where yt = [εt p1t p2t ]′ . All firms face the same capital prices p1t and p2t , but the shock εt can
vary across firms. We assume parameter values are such that I > 0 always. Equivalently, we
assume parameter values are such that q tot > min (p1 , p2 ) in all periods.
The two capital types are perfect substitutes in production, capital adjustment costs, and depreciation. The only potential differences between them are their prices p1 and p2 . We assume
non-negative investment, because otherwise the firm would optimally, yet unrealistically, take massive long-short positions. For example, if p1 > p2 , the firm could sell its entire K1 and buy an
equal amount of K2 , thereby booking a profit without incurring any adjustment costs, since total
investment I = 0. Since I1 , I2 ≥ 0, the firm will invest zero in the capital type with the higher
price. For example, if p1t > p2t , then I1t = 0 and It = I2t . Our main conclusions still hold if we
relax the non-negative investment constraint and instead assume separate capital adjustment costs
proportional to I12 and I22 .
Next we present our three main predictions. The first two are close to the model’s assumptions,
the third less so.
Prediction 1: Marginal q equals average q, the ratio of firm value to the total capital stock:
Vt
∂Vt
=
≡ q tot (εt , p1t , p2t ) .
∂K
K1t + K2t
(17)
This result provides a rationale for measuring q as firm value divided by the sum of physical
and intangible capital, which we call total q. The value of q tot depends on the shock ε and the
two capital prices, p1 and p2 . Marginal q equals ∂Vt /∂K and measures the benefit of adding an
incremental unit of capital (either physical or intangible) to the firm. Prediction 1 obtains because
we assume constant returns to scale, perfect competition, and perfect substitutes.
The firm chooses the optimal total investment rate by equating marginal q and the marginal cost
of investment. Applying this condition to (14) yields our next main prediction.
27
Prediction 2: The total investment rate ιtot is linear in q tot and the minimum capital price:
ιtot
t ≡
min (p1t , p2t )
1
I1t + I2t
.
= qttot −
K1t + K2t
γ
γ
(18)
If prices p1t and p2t are constant across firms i at each t, then the OLS panel regression
tot
ιtot
it = at + βqit + ηit
(19)
will produce an R2 of 100% and a slope coefficient β equal to 1/γ.
This result provides a rationale for regressing total investment on total q, as we do in our empirical
analysis. The result also tells us that the OLS slope β is an unbiased estimator of the inverse
adjustment cost parameter γ, assuming no measurement error. As discussed earlier, we avoid
making inferences about adjustment costs from our estimated q-slopes. The main reason, as Whited
(1994) explains, is that there is a large class of adjustment cost functions that correspond to
regression (19). We obtain the mapping above between β and γ thanks to strong simplifying
assumptions about the adjustment cost function.
We now use the theory to analyze the typical regression in the literature, which is a regression
of physical investment on physical q. As in our empirical analysis, we define ιphy = I1 /K1 and
q phy = V /K1 . Our next prediction shows how omitting intangible capital from these regressions
results in a lower R2 and biased slope coefficients.20
Prediction 3: The physical investment rate equals
ιphy
it


 0
=

 1
if p1t > p2t ,
phy
Kit
γ qit − min(p1t , p2t ) K1,i,t
.
(20)
if p1t ≤ p2t .
20
Similarly, Gourio and Rudanko (2014) show that simulated regressions of physical investment on physical q
produce lower q-slopes and R2 values when firms rely on both physical and “customer capital,” a type of intangible
capital. The mechanism in their theory is that product-market frictions require firms to spend resources to acquire
customers.
28
If prices p1t and p2t are constant across firms i at each t, then the OLS panel regression
e phy + ηeit
at + βq
ιphy
it
it = e
(21)
will produce an R2 less than 100% and a slope βe that is biased away from 1/γ.
Equation (20) follows from multiplying both sides of equation (18) by Kit /K1,i,t and recalling
that the firm only buys the cheaper capital type. There are two reasons why the R2 will be less
than 100% in regression (21). First, in periods when p1 > p2 , all firms’ physical investment will
equal zero, yet there will still be cross-sectional variation in q phy and hence non-zero regression
disturbances ηeit . Second, even in periods when p1 < p2 , the time fixed effects e
at will not perfectly
absorb the term min(p1t , p2t )Kit /K1,i,t in equation (20), because Kit /K1,i,t is not constant across
firms. As a result, we again have non-zero disturbances and hence an R2 less than 100%.
OLS estimates of βe are biased away from 1/γ for two reasons. First, regression (21) ignores that
ιphy is often zero, which biases the slope toward zero. Even in periods when ιphy is non-zero, the
variable min(p1t , p2t )Kit /K1,i,t from (20) is omitted from the regression and is likely correlated with
the regressor, q phy . The sign of this correlation and the resulting omitted-variable bias are unclear,
so we turn to simulations.
Details on the calibration and simulation are in Appendix D, and regression results with simulated
data are in Panel A of Table 8. As expected, a regression of the ιtot on q tot (equation 19) delivers a
100% R2 and an average slope equal to 1/γ. A regression of the ιphy on q phy (equation 21) delivers
an average R2 of only 49% and an average slope that is 51% lower than 1/γ, consistent with the
e Given the model’s simplicity, we do not push our simulations’ magnitudes.
predicted bias in β.
We simply note that the differences between the total- and physical-capital regressions could be
quantitatively large.
To summarize, our simple theory predicts that total q is the best proxy for total investment
opportunities. Less obviously, physical q is a relatively noisy proxy for physical investment opportunities. These predictions help explain why our empirical regressions produce higher R2 and τ 2
values when we use total rather than physical capital. The theory also predicts that a regression
29
of physical investment on physical q will produce downward-biased slopes on q and hence upwardbiased estimates of the adjustment-cost parameter. This result helps explain why we find smaller
estimated slopes on q when using physical capital alone in our actual regressions.
5.2
A Model with Imperfect Substitutes
The assumption that physical and intangible capital are perfect substitutes helps generate the
closed-form predictions above, but it is probably unrealistic.
We now relax this assumption
by replacing the linear capital aggregator K = K1 + K2 with the nonlinear capital aggregator
ψ (K1 , K2 ) = K1ρ K21−ρ in equation (14). Otherwise, the model is the same as before. We numerically solve and simulate this nonlinear model with ρ = 0.5. We then measure ιtot , ιphy , q tot , and
q phy as before. This exercise essentially assumes the world is nonlinear, then asks what happens
if the econometrician were to simply add together the two capital types as if they were perfect
substitutes, as we do in our empirical analysis.
Simulation results for the nonlinear model are in Panel B of Table 8. As in the simpler linear
model— and also in our empirical results— in the nonlinear model we find a higher R2 (97% versus
18%) using total rather than physical capital.21 The high R2 in the total-capital specification
implies that our simple linear empirical measures may be a good approximation even if the real
world is nonlinear. The low R2 in the physical-capital specification implies that setting intangible
capital to zero is inferior to including intangibles even in a simple, approximate manner. The
predicted regression slope using total capital is almost double the slope using physical capital,
consistent with the larger slopes we find in our empirical analysis when using total capital.
6
Robustness
This section shows that our main empirical conclusions are robust to several alternate ways of
measuring intangible capital and physical q.
21
The high R2 in the total-capital specification is expected, for two reasons. First, a regression of (I1 + I2 )/ψ on
V /ψ delivers nearly a 100% R2 . Second, K1 + K2 is almost perfectly correlated with ψ in simulated data. To see this
last point, note that the first-order Taylor approximation for ψ = K10.5 K20.5 around K1 = K2 = k is proportional to
K1 + K2 . This approximation holds well in simulated data, since firms strive to maximize ψ by setting K1 = K2 .
30
6.1
What Fraction of SG&A Is An Investment?
Arguably the strongest assumption in our intangible-capital measure is that λ=30% of SG&A
represents an investment. Table 9 shows that our main conclusions are robust to using different
values of λ ranging from zero to 100%. When λ is zero, firms’ intangible capital comes exclusively
from R&D. No matter what λ value we assume, we find that including intangible capital produces
larger values of R2 , τ 2 , and ρ2 , as well as larger slopes on q.
Instead of assuming 30% of SG&A is investment, we can let the data tell us what the value of λ
is. The structural parameter λ affects both the investment and q measures. We estimate λ along
with the q-slope and firm fixed effects by maximum likelihood. Details are available on request.
The estimated λ values are 0.38 in the consumer industry, 0.51 in the high-tech industry, and 0.24
in the health-care industry. These estimates are in the neighborhood of our assumed 0.3 value,
which is comforting. However, we do not push these λ estimates strongly, for three reasons. First,
the investment-q relation is probably not the ideal setting for identifying λ. Second, the estimation
imposes two very strong identifying assumptions: the linear investment-q model is true, and we
measure all variables perfectly. Finally, the λ estimate in the manufacturing industry is constrained
at 1.0, which is implausibly large and likely a symptom of the previous two issues. The take-away
of this subsection, though, is that our main conclusions hold regardless of the λ value we use.
6.2
Alternate Measures of Intangible Capital
In addition to varying the SG&A multiplier λ, we try eight other variations on our intangible
capital measure. Specifically, we vary δSG&A , the depreciation rate for organization capital; we
exclude goodwill from firms’ intangible capital; we exclude all balance-sheet intangibles, which
brings us closer to existing measures from the literature; we set firms’ starting intangible capital
stock to zero; and we estimate firms’ starting intangible capital stock using a perpetuity formula,
like Falato, Kadyrzhanov, and Sim (2013). We also drop the first five years of data for each firm,
which makes the choice of starting intangible capital stock less important. We also try dropping
the 47% of firm/years with missing R&D from our regressions. Table 10 provides details about
these variations and their results. Our main results are robust in all these variations: Using total
31
rather than physical capital produces a stronger investment-q relation, as measured by R2 , ρ2 , τ 2 ,
and q-slope.
6.3
Alternate Measures of Physical Capital and Tobin’s q
There is no consensus in the literature on how to measure Tobin’s q. Our analysis so far uses the
physical q measure that is most popular in the investment-q literature, but the broader finance
literature uses a variety of measures. Next, we try some of these other definitions of physical q,
and we show that our measures that include intangible capital outperform them all.
We survey the most recent issues of the Journal of Finance, Journal of Financial Economics, and
Review of Financial Studies to find papers that measure Tobin’s q. We find at least nine different
definitions in the January 2013 through July 2014 issues. None of these papers, nor any other papers
we have seen, includes a firm’s internally created intangible capital in the denominator of q, as we
do in our total q measure. Some papers, though, do include externally purchased intangibles, since
they scale q by total book assets. Since external intangibles usually make up a very small fraction
of total intangibles (Section 1), these alternate definitions exclude almost all of firms’ intangible
capital. We therefore call these q measures from the literature alternate proxies for physical q.
We re-estimate our main physical-capital specifications using the five most popular alternate
definitions we find for Tobin’s q. For each one, we follow q theory’s prescription that investment
and q should have the same denominator (Hayashi and Inoue, 1991). Results and detailed definitions
are in Table 11. The most important result is that including intangible capital (row 1) generates a
larger R2 , τ 2 , and ρ2 value than in any of the physical-capital specifications (rows 2–7). Most of
the alternate physical q measures produce a slope on q that is even larger than the one from our
total q measure. Those alternate measures produce much worse model fit, however. Like Erickson
and Whited (2006), we find that the q proxies scaled by book assets— the “market-to-book-assets”
ratios— produce especially low R2 values, implying these are especially poor proxies for investment
opportunities.
32
7
Conclusion
We incorporate intangible capital into measures of investment and Tobin’s q, and we show that
the investment-q relation becomes stronger as a result. Specifically, measures that include intangible capital produce higher R2 values and larger slope coefficients on q, both in firm-level and
macroeconomic data. We also show that the investment-cash flow relation becomes much stronger
if one properly accounts for intangible investments. These results hold across several types of firms
and years. The increase in R2 , however, is especially large where intangible capital is most important, for example, in the high-tech and health industries. Estimation results also indicate that our
measure of total q is closer to the true, unobservable q than the standard physical q measure is.
Our results have two main implications. First, researchers using Tobin’s q as a proxy for firms’
investment opportunities should use a proxy that, like ours, includes intangible capital. One benefit
of our proxy is that it is easy to compute for a large panel of firms. Second, including intangible
capital changes our assessment of investment theories. Including intangibles makes the classic q
theory fit the data better in terms of R2 but worse in terms of the investment-cash flow sensitivity.
The latter result supports newer theories that predict an investment-cash flow relation. The classic
q theory fits the data better in settings where capital is more intangible.
Our results point toward several directions for future research. There is surely more work to
do on measuring intangible capital. It also would be interesting to know whether other existing
empirical results, in addition to the investment-q relation, change after including intangible capital.
We suspect several results would change, since Tobin’s q is pervasive and often enters regressions
with high significance. Finally, it would be interesting to use the investment-q framework to explore
the differences and interactions between physical and intangible capital.
33
Appendix A: Measuring Intangible Capital
A.1. Measuring SG&A
We measure SG&A as Compustat variable xsga minus xrd minus rdip. We add the following
screen: When xrd exceeds xsga but is less than cogs, or when xsga is missing, we measure SG&A
as xsga with no further adjustments, or zero if xsga is missing.
The logic behind this formula is as follows. According to the Compustat manual, xsga includes
R&D expense unless the company allocates R&D expense to cost of goods sold (COGS). For
example, xsga often equals the sum of “Selling, General and Administrative” and “Research and
Development” on the Statement of Operations from firms’ 10-K filings. To isolate (non-R&D)
SG&A, we must subtract R&D from xsga when Compustat adds R&D to xsga. There is a catch:
Compustat adds to xsga only the part of R&D not representing acquired in-process R&D, so our
formula subtracts rdip (In Process R&D Expense), which Compustat codes as negative. We find
that Compustat almost always adds R&D to xsga, which motivates our formula above. Standard &
Poor’s explained in private communication that “in most cases, when there is a separately reported
xrd, this is included in xsga.” As a further check, we compare the Compustat records and SEC
10-K filings by hand for a random sample of 100 firm-year observations with non-missing xrd. We
find that R&D is included in xsga in 90 out of 100 cases, is partially included in xsga in one case,
is included in COGS in seven cases, and two cases remain unclear even after asking the Compustat
support team. The screen above lets us identify obvious cases where xrd is part of COGS. This
screen catches six of the seven cases where xrd is part of COGS. Unfortunately, it is impossible to
identify the remaining cases without reading SEC filings. We thank the Compustat support team
from Standard & Poors for their help in this exercise.
We set xsga, xrd, and rdip to zero when missing. As for R&D, we make exceptions in years when
the firm’s assets are also missing. For these years we interpolate these three variables using their
nearest non-missing values.
A.2. Measuring Firms’ Initial Capital Stock
This appendix explains how we estimate the stock of knowledge and organization capital in firm
34
i’s first non-missing Compustat record. We describe the steps for estimating the initial knowledgecapital stock; the method for organization capital is similar. Broadly, we estimate firm i’s R&D
spending in each year of life between the firm’s founding and its first non-missing Compustat record,
denoted year one below. Our main assumption is that the firm’s pre-IPO R&D grows at the average
rate across pre-IPO Compustat records. We then apply the perpetual inventory method to these
estimated R&D values to obtain the initial stock of knowledge capital at the end of year zero. The
specific steps are as follows:
1. Define age since IPO as number of years elapsed since a firm’s IPO. Using the full Compustat
database, compute the average log change in R&D in each yearly age-since-IPO category.
Apply these age-specific growth rates to fill in missing R&D observations before 1977.
2. Using the full Compustat database, isolate records for firms’ IPO years and the previous two
years. (Not all firms have pre-IPO data in Compustat.) Compute the average log change
in R&D within this pre-IPO subsample, which equals 0.348. (The corresponding pre-IPO
average log change in SG&A equals 0.333).
3. If firm i’s IPO year is in Compustat, go to step 5. Otherwise go to the next step.
4. This step applies almost exclusively to firms with IPOs before 1950. Estimate firm i’s R&D
spending in each year between the firm’s IPO year and first Compustat year assuming the
firm’s R&D grows at the average age-specific rates estimated in step one above.
5. Obtain data on firm i’s founding year from Jay Ritter’s website. For firms with missing
founding year, estimate the founding year as the minimum of (a) the year of the firm’s first
Compustat record and (b) firm’s IPO year minus 8, which is the median age between founding
and IPO for IPOs from 1980-2012 (from Jay Ritter’s web site).
6. Estimate the firm i’s R&D spending in each year between the firm’s founding year and IPO
year assuming the firm’s R&D grows at the estimated pre-IPO average rate from step two
above.
35
7. Assume the firm is founded with no capital. Apply the perpetual inventory method in equation (3) to the estimated R&D spending from the previous steps to obtain Gi0 , the stock of
knowledge capital at the beginning of the firm’s first Compustat record.
We use estimated R&D and SG&A values only to compute firms’ initial stocks of intangible
capital. We never use estimated R&D in a regression’s dependent variable.
Appendix B: Placebo Analysis
The steps in the placebo analysis are as follows:
phy
1. Define xit = Iitint /Ki,t−1
. Using actual data, estimate the panel regression
xit = ai + at + θxi,t−1 + εit .
(22)
b and var (b
Collect the estimates b
ai , b
at , θ,
εit ).
2. For each firm i in our sample, randomly select some other firm j. Collect b
aj and the initial
values xj1 and Aj0 .
3. Create simulated values x
eit assuming x
ei1 = xj1 and
bxi,t−1 + εeit ,
x
eit = b
aj + b
at + θe
t > 1,
(23)
where εeit is drawn independently from N (0, var (b
εit )) . We set any negative values of x
eit to
zero, since xit is never negative in our data.
phy
int = x
.
4. Compute simulated values of intangible investment according to Iei,t
ei,t Ki,t−1
5. Compute the simulated intangible capital stock assuming firm i’s initial intensity is Aj,0 . Firm
e int = K phy /Aj,0 − K phy . Compute
i’s simulated starting intangible stock therefore equals K
i,0
i,0
i,0
e int applying the perpetual-inventory method to Ieint with a 20% depreciation
future periods’ K
i,t
rate, as in equation (3).
36
Appendix C: Proofs
Proof of Prediction 1. We can write the value function as
Vt = max
Z
∞
{It+s } 0
Et
("
γ
H (εt+s ) −
2
It+s
Kt+s
2
−
p∗t+s
)
#
It+s
Kt+s ,
Kt+s
(24)
where p∗t ≡ min (p1t , p2t ). p∗ also follows a general diffusion process with drift and volatility that
depend on xt . Since the objective function and constraints can be written as functions of total
capital K and not K1 and K2 individually, the firm’s value depends on K but not on K1 and
K2 individually. Following the same argument as in Abel and Eberly’s (1994) Appendix A, firm
value must be proportional to total capital K :
V (K, ε, p1 , p2 ) = Kq tot (ε, p1 , p2 ) .
(25)
Partially differentiating this equation with respect to K yields equation (17).
Proof of Prediction 2. Following a similar proof as in Abel and Eberly (1994), one can derive
the Bellman equation and take first-order conditions with respect to I to obtain
q tot
∂
=
∂I
" #
I
I
γ I 2
+ p∗
K = γ + p∗ ,
2 K
K
K
(26)
which generates equation (18). Details are available upon request.
Appendix D: Numerical solution of the investment model
We set π (K, ε) = Khεθ , and we assume the exogenous variables follow uncorrelated, positive,
mean-reverting processes:
(ε)
d ln εit = −φ ln εit dt + σε dBit
(p1 )
d ln p1t = −φ ln p1t dt + σp dBt
(p2 )
d ln p2t = −φ ln p2t dt + σp dBt
37
.
The goal here is to solve for the function q tot (ε, p1 , p2 ) . Following the approach in Abel and Eberly
(1994), one can show that the solution satisfies
q tot (r + δ) = πK (K, ε) − cK (I, K, p1 , p2 ) + E dq tot /dt.
(27)
We numerically solve this equation by applying Ito’s lemma, substituting in the dynamics above,
and using the following parameter values:
θ = 2, h = 2.5, r = 0.2, δ = 0.1, γ = 100, φ = 2, σε = 0.1, σp = 0.2.
We choose a high discount rate r and adjustment costs γ so that q tot is finite.
phy tot
phy
We simulate a large panel of data on ιtot
it , ιit , qit , and qit , then we estimate the panel regressions
(19) and (21) by OLS. We repeat the simulation 50 times to obtain average simulated R2 and slope
estimates.
38
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42
.7
.3
Intangible Intensity
.4
.5
.6
1970
1980
1990
Year
All
Manufacturing
Healthcare
2000
2010
Consumer
High Tech
Figure 1. This figure plots the mean intangible capital intensity over time, both for our full sample
and within industries. Intangible intensity equals K int /(K int + K phy ), the firm’s stock of intangible
divided by its total stock of capital. We use the Fama-French five-industry definition and exclude
industry “Other.”
43
.2
2
1950 1960 1970 1980 1990 2000 2010
Year
0
.08
1
.14
.09
1
2
.1
q
3
.16
Investment
.11
.18
3
4
.12
5
4
Total
.13
Physical
1950 1960 1970 1980 1990 2000 2010
Year
q
Investment
Figure 2. This figure plots Tobin’s q and the investment rates for the aggregate U.S. economy.
The left panel uses data from Hall (2001) and includes only physical capital in q and investment.
The right panel also uses data from Corrado and Hulten (2014) and includes both physical and
intangible capital in q and investment. For each graph, the left axis is the value of q and the right
axis the investment rate.
44
Table 1
Summary Statistics
Statistics are based on the sample of Compustat firms from 1975 to 2011. The physical capital stock, K phy , is
measured as PP&E. We estimate the intangible capital stock, K int , by applying the perpetual inventory method to
firms’ intangible investments, defined as R&D+0.3×SG&A; we then add in firms’ balance-sheet intangibles. Intangible
intensity equals K int /(K int + K phy ). Knowledge capital is the part of intangible capital that comes from R&D. The
numerator for both q variables is the market value of equity plus the book value of debt minus current assets. The
denominator for all “phy” variables is K phy . The denominator for all “tot” variables is K int + K phy . The numerator
for ιphy is I phy =CAPEX, and the numerator for ιtot is I phy + I int = CAPEX+R&D+0.3×SG&A. The numerator
for physical cash flow is income before extraordinary items plus depreciation expenses; the numerator for total cash
flow is the same but adds back I int net a tax adjustment.
Variable
Intangible capital stock ($M)
Physical capital stock ($M)
Intangible intensity
Knowledge capital / Intangible capital
Mean
427
1237
0.43
0.24
Median
41.7
77.9
0.45
0.01
Std
1991
6691
0.27
0.37
Skewness
11.6
16.5
-0.01
1.65
Physical q (q phy )
Physical investment (ιphy )
Physical cash flow (cphy )
3.14
0.19
0.15
0.93
0.11
0.16
7.22
0.24
0.62
4.41
3.52
-1.63
Total q (q tot )
Total investment (ιtot )
Total cash flow (ctot )
1.11
0.22
0.16
0.57
0.16
0.15
1.91
0.19
0.19
3.76
2.80
0.52
45
Table 2
OLS Results
Results are from OLS regressions of investment on Tobin’s q, cash flow, and firm and year fixed effects.
The variable ι denotes investment, q denotes Tobin’s q at the end of the previous fiscal year, and c denotes
cash flow contemporaneous with investment. The numerator for both q variables is the market value of
equity plus the book value of debt minus current assets. The denominator for all “phy” variables is K phy .
The denominator for all “tot” variables is K int + K phy . The numerator for ιphy is I phy =CAPEX, and
the numerator for ιtot is I phy + I int = CAPEX+R&D+0.3×SG&A. The numerator for physical cash flow is
income before extraordinary items plus depreciation expenses; the numerator for total cash flow is the same
but adds back I int net a tax adjustment. Bootstrapped standard errors clustered by firm are in parentheses.
We report the within-firm R2 . All regressions include 141,800 firm-year observations from Compustat from
1975 to 2011.
(1)
(2)
(3)
(4)
Panel A: Total investment (ιtot )
q tot
0.052
(0.001)
q phy
0.044
(0.001)
0.012
(0.000)
ctot
R2
0.320
(0.005)
0.243
(0.005)
0.010
(0.000)
0.241
(0.007)
0.296
(0.007)
0.364
(0.005)
0.313
(0.005)
Panel B: Physical investment (ιphy )
q tot
0.062
(0.001)
q phy
0.061
(0.001)
0.017
(0.000)
cphy
R2
0.244
(0.005)
0.233
(0.005)
46
0.017
(0.000)
0.030
(0.003)
0.032
(0.003)
0.248
(0.005)
0.238
(0.005)
Table 3
Bias-Corrected Results
Results are from regressions of investment on lagged Tobin’s q and contemporaneous cash flow. Columns
marked “Physical” use the physical-capital variables ιphy , q phy , and cphy . Columns marked “Total” use
the total-capital variables ιtot , q tot , and ctot . Panel A shows results from the cumulant estimator with firm
fixed effects. ρ2 is the within-firm R2 from a hypothetical regression of investment on true q, and τ 2 is
the within-firm R2 from a hypothetical regression of our q proxy on true q. Panel B shows results from
instrumental-variable estimation of a first-differenced model that uses three lags of cash flow and Tobin’s q
used as instruments for the first difference of Tobin’s q. Bootstrapped standard errors clustered by firm are
in parentheses. Data are from Compustat from 1975 to 2011.
Physical
Total
Physical
Total
Panel A: Cumulants Estimator (N =141,800)
q
0.036
(0.001)
0.093
(0.001)
Cash flow (c)
0.035
(0.000)
0.092
(0.001)
0.015
(0.003)
0.138
(0.008)
ρ2
0.372
(0.007)
0.426
(0.008)
0.371
(0.007)
0.477
(0.007)
τ2
0.492
(0.010)
0.591
(0.007)
0.494
(0.009)
0.544
(0.007)
Panel B: Instrumental-Variable Estimator (N =88,700)
q
0.012
(0.002)
0.030
(0.004)
Cash flow (c)
R2
0.038
(0.006)
0.062
(0.004)
47
0.011
(0.002)
0.024
(0.005)
0.026
(0.002)
0.156
(0.008)
0.046
(0.005)
0.095
(0.005)
Table 4
Comparing Firms With Different Amounts of Intangible Capital
This table shows results from subsamples formed based on yearly quartiles of intangible intensity, which equals the
ratio of a firm’s intangible to total capital. The column labels show each quartile’s mean intangible intensity. Results
are from regressions of investment on lagged q, contemporaneous cash flow, and firm fixed effects. Slopes on q, cash
flow, as well as ρ2 and τ 2 values, are from the cumulant estimator. R2 is from the OLS estimator that adds year fixed
effects. Columns labeled “Physical” use the physical-capital measures ιphy , q phy and cphy , while columns labeled
“Total” use the total-capital measures ιtot , q tot and ctot , as defined in the notes for Table 1. ∆ denotes the difference
between the Total and Physical specifications. Bootstrapped standard errors clustered by firm are in parentheses.
Data are from Compustat from 1975-2011.
Quartile 1
(8% intangible)
Physical
Total
Quartile 2
(33% intangible)
Physical
Total
Quartile 3
(56% intangible)
Physical
Total
Quartile 4
(76% intangible)
Physical
Total
0.035
(0.002)
0.033
(0.001)
Panel A: Regressions Without Cash Flow
q
0.065
(0.006)
R2
0.182
0.227
(0.011)
(0.010)
0.045
0.195
0.262
(0.012)
(0.012)
0.067
0.248
0.352
(0.011)
(0.010)
0.104
0.299
0.477
(0.008)
(0.010)
0.178
0.197
0.307
(0.018)
(0.012)
0.110
0.282
0.386
(0.027)
(0.019)
0.104
0.379
0.470
(0.022)
(0.023)
0.091
0.561
0.582
(0.016)
(0.012)
0.021
∆τ 2
0.682
0.599
(0.064)
(0.027)
-0.083
0.514
0.507
(0.048)
(0.024)
-0.007
0.483
0.525
(0.027)
(0.021)
0.042
0.439
0.643
(0.014)
(0.011)
0.204
N
35438
35453
35453
35442
35442
35467
35467
∆R2
ρ2
∆ρ2
τ2
0.125
(0.005)
35438
0.052
(0.006)
0.100
(0.004)
0.083
(0.003)
0.085
(0.002)
Panel B: Regressions With Cash Flow
q
0.066
(0.008)
0.120
(0.006)
0.053
(0.006)
0.099
(0.005)
0.033
(0.002)
0.083
(0.003)
0.033
(0.001)
0.085
(0.002)
Cash flow (c)
0.182
(0.032)
0.222
(0.026)
0.072
(0.017)
0.148
(0.021)
0.011
(0.009)
0.103
(0.019)
-0.003
(0.004)
0.114
(0.012)
R2
0.208
0.267
(0.012)
(0.010)
0.059
0.214
0.315
(0.012)
(0.012)
0.101
0.255
0.403
(0.010)
(0.010)
0.148
0.301
0.515
(0.008)
(0.008)
0.214
0.238
0.345
(0.021)
(0.014)
0.107
0.309
0.438
(0.025)
(0.019)
0.129
0.370
0.521
(0.018)
(0.015)
0.151
0.552
0.641
(0.017)
(0.014)
0.089
∆τ 2
0.633
0.568
(0.078)
(0.031)
-0.065
0.484
0.466
(0.044)
(0.024)
-0.018
0.496
0.482
(0.027)
(0.017)
-0.014
0.446
0.596
(0.013)
(0.011)
0.150
N
35438
35453
35442
35467
∆R2
ρ2
∆ρ2
τ2
35438
35453
48
35442
35467
Table 5
Comparing Industries
This table shows results from industry subsamples. We use the Fama-French five-industry definition, excluding the
industry “Other.” Remaining details are the same as in Table 4.
Manufacturing
(31% intangible)
Physical
Total
Consumer
(48% intangible)
Physical
Total
High Tech
(55% intangible)
Physical
Total
Health
(62% intangible)
Physical
Total
0.033
(0.001)
0.038
(0.002)
Panel A: Regressions Without Cash Flow
q
0.041
(0.002)
R2
0.186
0.245
(0.010)
(0.009)
0.059
0.214
0.306
(0.011)
(0.012)
0.092
0.354
0.463
(0.008)
(0.011)
0.109
0.258
0.346
(0.013)
(0.014)
0.088
0.206
0.297
(0.011)
(0.011)
0.091
0.290
0.385
(0.014)
(0.018)
0.095
0.549
0.580
(0.013)
(0.012)
0.031
0.545
0.538
(0.024)
(0.020)
-0.007
∆τ 2
0.655
0.606
(0.044)
(0.028)
-0.049
0.539
0.540
(0.036)
(0.027)
0.001
0.511
0.641
(0.014)
(0.014)
0.130
0.365
0.495
(0.025)
(0.024)
0.130
N
40280
36884
36884
31680
31680
11207
11207
∆R2
ρ2
∆ρ2
τ2
0.108
(0.005)
40280
0.042
(0.002)
0.105
(0.004)
0.084
(0.001)
0.094
(0.003)
Panel B: Regressions With Cash Flow
q
0.040
(0.002)
0.104
(0.006)
0.041
(0.002)
0.106
(0.007)
0.032
(0.001)
0.085
(0.002)
0.038
(0.002)
0.094
(0.003)
Cash flow (c)
0.083
(0.014)
0.275
(0.021)
0.048
(0.010)
0.188
(0.031)
0.001
(0.004)
0.087
(0.012)
-0.003
(0.009)
-0.020
(0.032)
R2
0.202
0.313
(0.010)
(0.009)
0.111
0.236
0.388
(0.011)
(0.012)
0.152
0.355
0.490
(0.008)
(0.011)
0.135
0.258
0.361
(0.014)
(0.015)
0.103
0.227
0.379
(0.010)
(0.011)
0.152
0.309
0.488
(0.014)
(0.016)
0.179
0.541
0.621
(0.013)
(0.011)
0.080
0.547
0.532
(0.024)
(0.018)
-0.015
∆τ 2
0.635
0.535
(0.044)
(0.032)
-0.100
0.520
0.451
(0.033)
(0.021)
-0.069
0.518
0.606
(0.014)
(0.013)
0.088
0.364
0.500
(0.024)
(0.023)
0.136
N
40280
36884
31680
11207
∆R2
ρ2
∆ρ2
τ2
40280
36884
49
31680
11207
Table 6
Comparing Time Periods
This table shows results from the early (1975–1995) and late (1996–2011) subsamples. The 1995 breakpoint produces
subsamples of roughly equal size. Remaining details are the same as in Table 4.
Early
(39% intangible)
Physical
Total
Late
(47% intangible)
Physical
Total
Panel A: Regressions Without Cash Flow
q
0.043
(0.002)
R2
0.209
0.265
(0.008) (0.009)
0.056
0.268
0.349
(0.007) (0.008)
0.081
0.262
0.334
(0.010) (0.011)
0.072
0.479
0.510
(0.011) (0.010)
0.031
∆τ 2
0.615
0.590
(0.026) (0.022)
-0.025
0.477
0.596
(0.011) (0.011)
0.119
N
69753
72047
72047
∆R2
ρ2
∆ρ2
τ2
0.105
(0.003)
0.033
(0.001)
69753
0.086
(0.001)
Panel B: Regressions With Cash Flow
q
0.044
(0.002)
0.103
(0.004)
0.033
(0.001)
0.086
(0.002)
Cash flow (c)
0.074
(0.009)
0.260
(0.017)
-0.008
(0.004)
0.032
(0.010)
R2
0.233
0.352
(0.007) (0.009)
0.119
0.268
0.365
(0.007) (0.008)
0.097
0.299
0.436
(0.010) (0.011)
0.137
0.474
0.518
(0.011) (0.010)
0.044
∆τ 2
0.564
0.495
(0.025) (0.021)
-0.069
0.482
0.588
(0.011) (0.011)
0.106
N
69753
72047
∆R2
ρ2
∆ρ2
τ2
69753
50
72047
Table 7
Time-Series Macro Regressions
Results are from 141 quarterly observations from aggregate U.S. data, 1972Q2:2007Q2. In the top panel, the dependent variable is total investment (physical + intangible), deflated by the total capital stock. In the bottom panel,
the dependent variable is physical investment deflated by the physical capital stock. Physical q equals the lagged
aggregate stock and bond market value divided by the physical capital stock; Hall (2001) computes these measures
from the Flow of Funds. Total q includes intangible capital by multiplying physical q by the ratio of physical to
total capital; the ratio is from Corrado and Hulten’s (2014) aggregate U.S. data. Bond q is constructed by applying
the structural model of Philippon (2009) to bond maturity and yield data; these data are from Philippon’s web site.
Newey-West standard errors with autocorrelation up to twelve quarters are in parentheses. Standard errors for the
OLS R2 values are computed via bootstrap.
(1)
(2)
(3)
Panel A: Total investment (ιtot )
Total q
0.017
(0.003)
Physical q
0.012
(0.002)
Bond q
OLS R2
0.055
(0.032)
0.610
(0.040)
0.646
(0.038)
0.139
(0.060)
Panel B: Physical investment (ιphy )
Total q
0.003
(0.003)
Physical q
0.002
(0.003)
Bond q
OLS R2
0.061
(0.009)
0.047
(0.038)
51
0.035
(0.034)
0.462
(0.059)
Table 8
Regressions Using Simulated Data
This table shows results of regressing investment on q in simulated panel data. Panel A uses data
simulated from a linear model that assumes physical and intangible capital are perfect substitutes.
Panel B uses data simulated from a model that relaxes this assumption and aggregates the two
capital types according to K10.5 K20.5 . We numerically solve the models, simulate large panels of
data, and regress investment on q and time fixed effects. Details on both models are in Section
5. Details on the simulations are in Appendix D. Model (1) regresses total investment on total
q, whereas model (2) regresses physical investment on physical q. Specifically, model (1) defines
investment as ιtot = (I1 + I2 )/(K1 + K2 ) and q as q tot = V /(K1 + K2 ), where I1 and I2 are the
investment rates in physical and intangible capital, respectively, K1 and K2 are the two capital
stocks, and V is firm value. Model (2) defines investment as ιphy = I1 /K1 and q as q phy = V /K1 .
We assume γ = 100, so the bias in 1/γ is the percent difference between the q-slope and 0.01.
There is no reason the estimated slopes should equal 1/γ in the nonlinear model, so in Panel B we
do not quantify the bias.
Regression
R2
Slope on q
1.000
0.489
0.0100
0.0049
0.972
0.181
0.0108
0.0058
Bias in 1/γ
Panel A: Linear Model
(1) Total investment on total q
(2) Physical investment on physical q
Panel B: Nonlinear Model
(1) Total investment on total q
(2) Physical investment on physical q
52
0
-51%
Table 9
Robustness: What Fraction of SG&A Is An Investment?
Results are from regressions of investment on q and firm fixed effects. Slopes on q, as well as ρ2 and τ 2 values, are from the cumulant
estimator. R2 is from the OLS estimator that also includes year fixed effects. The first column reproduces results from Tables 2 and 3
using our main physical-capital measures, q phy and ιphy . The remaining columns show results using variations of the total-capital measures,
q tot and ιtot . Each variation uses a different SG&A multiplier. The multiplier, shown in the table’s top row, is the fraction of SG&A that
represents an investment rather than an operating expense. Our main total-capital measures assume a 0.3 multiplier. Each regression uses
141,800 firm-year Compustat observations from 1975 to 2011.
53
Physical
Capital
0.0
0.1
0.2
Total Capital with Alternate SG&A Multipliers
0.3
0.4
0.5
0.6
0.7
q
0.036
(0.001)
0.069
(0.001)
0.078
(0.001)
0.086
(0.001)
0.093
(0.001)
0.099
(0.001)
0.105
(0.001)
0.112
(0.002)
R2
0.233
(0.005)
0.279
(0.005)
0.303
(0.005)
0.314
(0.005)
0.320
(0.005)
0.323
(0.005)
0.325
(0.005)
ρ2
0.372
(0.007)
0.407
(0.008)
0.418
(0.008)
0.424
(0.008)
0.426
(0.008)
0.426
(0.008)
τ2
0.492
(0.010)
0.548
(0.008)
0.576
(0.008)
0.585
(0.007)
0.591
(0.007)
0.595
(0.008)
0.8
0.9
1.0
0.117
(0.002)
0.123
(0.002)
0.128
(0.002)
0.134
(0.002)
0.325
(0.006)
0.324
(0.006)
0.323
(0.006)
0.322
(0.006)
0.320
(0.006)
0.428
(0.008)
0.429
(0.008)
0.427
(0.008)
0.427
(0.008)
0.426
(0.008)
0.425
(0.008)
0.594
(0.008)
0.592
(0.008)
0.592
(0.008)
0.588
(0.008)
0.586
(0.009)
0.584
(0.009)
Table 10
Robustness: Alternate Measures of Intangible Capital
Results are from regressions of investment on q and firm fixed effects. Slopes on q, as well as ρ2 and τ 2 values, are
from the cumulant estimator. We report the within-firm R2 from the OLS estimator that also includes year fixed
effects. The first two rows reproduce results from Tables 2 and 3 with our main physical-capital measures (ιphy and
q phy ) and total-capital measures (ιtot and q tot ). Rows 2–8 show results using variations of our total-capital measure.
Rows three and four use alternate values of δSG&A , the depreciation rate for organization capital. Row five excludes
goodwill from balance-sheet intangibles. Row six excludes all balance-sheet intangibles. Row seven assumes firms
have no intangible capital before entering Compustat, which corresponds to setting Gi0 = 0 in equation (3). Row
eight estimates firms’ starting intangible capital using a perpetuity formula that assumes the firm has been alive
forever before entering Compustat. The initial stock of knowledge capital (for example) is Gi0 = R&Di1 /δR&D ,
where R&Di1 is the R&D amount in firm i’s first Compustat record. Rows 9a and 9b use our main measures but
drop each firm’s first five years of data. Rows 10a and 10b use our main measures but drop firm/year observations
with missing R&D. Data are from Compustat from 1975 to 2011.
1. Physical capital (from Tables 2, 3)
2. Total capital (from Tables 2, 3)
3. δSG&A =10%
4. δSG&A =30%
5. Exclude goodwill
6. Exclude balance-sheet intangibles
7. Zero initial intangible capital
8. FKS initial multiplier
9. Drop first five years per firm
a. Physical capital
b. Total capital
10. Exclude observations with missing R&D
a. Physical capital
b. Total capital
R2
τ2
ρ2
Slope on q
Observations
0.233
(0.005)
0.320
(0.005)
0.330
(0.005)
0.315
(0.005)
0.322
(0.005)
0.299
(0.005)
0.335
(0.005)
0.289
(0.005)
0.492
(0.010)
0.591
(0.007)
0.602
(0.008)
0.586
(0.007)
0.593
(0.007)
0.570
(0.009)
0.600
(0.007)
0.563
(0.008)
0.372
(0.007)
0.426
(0.008)
0.434
(0.008)
0.420
(0.008)
0.427
(0.008)
0.420
(0.008)
0.445
(0.008)
0.396
(0.008)
0.036
(0.001)
0.093
(0.001)
0.094
(0.001)
0.092
(0.001)
0.093
(0.001)
0.085
(0.001)
0.096
(0.001)
0.091
(0.001)
141,800
0.125
(0.005)
0.201
(0.007)
0.327
(0.021)
0.416
(0.022)
0.227
(0.014)
0.289
(0.016)
0.032
(0.002)
0.084
(0.004)
82,174
0.293
(0.007)
0.411
(0.009)
0.479
(0.011)
0.621
(0.010)
0.486
(0.013)
0.515
(0.013)
0.035
(0.001)
0.087
(0.001)
75,426
54
141,800
141,800
141,800
141,800
141,800
141,800
141,800
82,174
75,426
Table 11
Robustness: Alternate Measures of Physical Capital
Results are from regressions of investment on q and firm fixed effects. Slopes on q, as well as ρ2 and τ 2 values,
are from the cumulant estimator. R2 is from the OLS estimator that also includes year fixed effects. The first two
rows reproduce results from Tables 2 and 3 with our main total-capital measures (ιtot and q tot ) and physical-capital
measures (ιphy and q phy ) . Rows 3–7 show results using variations of our physical-capital measure. Variation 1
computes q as the market value of equity (csho times prccf , from CRSP) plus assets (at) minus the book value of
equity (ceq + txbd from Compustat) all divided by assets (at). Variation 2 computes q as the market value of equity
(csho times prccf ) plus book value of debt (dltt) plus book value of preferred equity (pstkrv) minus inventories (invt)
and deferred taxes (txdb) divided by book value of capital (ppegt). Variation 3 computes q as the market value of
assets divided by the book value of assets (at), where the market value of assets equals the book value of debt (lt)
plus the market value of equity (csho times prccf ). Variation 4 is the same as Variation 1 but computes book equity
as total assets less total liabilities (lt) and preferred stock (pstkrv) plus deferred taxes (txdb) and convertible debt
(dcvt). Variation 5 computes q as the book value of assets (at) less the book value of equity (ceq) plus the market
value of equity (csho times prccf ) all over the book value of assets. In each variation, the dependent variable is
physical investment, measured as CAPEX divided by the same denominator as in the q measure. Data are from
Compustat from 1975 to 2011.
Specification
1. Total capital (from Tables 2, 3)
2. Physical capital (from Tables 2, 3)
3. Physical capital variation 1
4. Physical capital variation 2
5. Physical capital variation 3
6. Physical capital variation 4
7. Physical capital variation 5
R2
0.320
(0.005)
0.233
(0.005)
0.127
(0.003)
0.259
(0.006)
0.127
(0.003)
0.127
(0.004)
0.127
(0.003)
55
τ2
0.591
(0.007)
0.492
(0.010)
0.259
(0.010)
0.514
(0.012)
0.261
(0.008)
0.258
(0.009)
0.259
(0.008)
ρ2
0.426
(0.008)
0.372
(0.007)
0.290
(0.008)
0.407
(0.008)
0.290
(0.009)
0.294
(0.009)
0.290
(0.009)
Slope on q
0.093
(0.001)
0.036
(0.001)
0.101
(0.003)
0.033
(0.001)
0.100
(0.003)
0.102
(0.003)
0.101
(0.003)
N
141,800
141,800
137,060
137,209
141,800
137,209
141,618