Intangible Capital and the Investment-q Relation

TL;DR: In this article, the Tobin's q is used to explain both physical and intangible investment, and the authors show that it is a better proxy for both physical investment and intangible capital.

Abstract: The neoclassical theory of investment has mainly been tested with physical investment, but we show it also helps explain intangible investment At the firm level, Tobin's q explains physical and intangible investment roughly equally well, and it explains total investment even better Compared to physical capital, intangible capital adjusts more slowly to changes in investment opportunities The classic q theory performs better in firms and years with more intangible capital: Total and even physical investment are better explained by Tobin's q and are less sensitive to cash flow At the macro level, Tobin's q explains intangible investment many times better than physical investment We propose a simple, new Tobin's q proxy that accounts for intangible capital, and we show that it is a superior proxy for both physical and intangible investment opportunities

Summary

1 Introduction

• The neoclassical theory of investment was developed more than 30 years ago, when firms mainly owned physical assets like property, plant, and equipment (PP&E).
• The authors theory predicts that a firm’s physical and intangible investment rates should both be explained well by a version of Tobin’s q the authors call “total q,” which equals the firm’s market value divided by the sum of its physical and intangible capital stocks.
• While their intangible-capital measure has limitations, the authors believe, and the data confirm, that an imperfect proxy is better than setting intangible capital to zero.
• These results even hold using the literature’s standard measures that exclude intangibles.
• Again, the neoclassical theory of investment applies just as well, if not better, to intangible capital.

1.1 Related literature

• The empirical investment-q literature is extensive and dates back at least to Ciccolo (1975) and Abel (1980).
• Closer to their specifications, Baker, Stein, and Wurgler (2002) measure investment as the sum of CAPX, R&D, and SG&A, and they regress them on q. Gourio and Rudanko (2014) examine the relation between q and investment in customer capital, a type of intangible capital.
• Like us, they find that intangible capital has larger adjustment-cost parameters than physical capital, and including intangibles decreases physical capital’s estimated adjustment costs.
• Section 4 presents full-sample results, and Section 5 compares results across different types of firms, industries, and years.

2 Intangible capital and the neoclassical theory of investment

• And the authors argue that intangible capital fits well into the theory.
• The authors simplify and modify Abel and Eberly’s (1994) theory of investment under uncertainty to include two capital goods that they interpret as physical and intangible capital.
• The authors present a stylized model, since their goal is to provide theoretical motivation for their empirical work, not to make a theoretical contribution.
• Wildasin (1984), Hayashi and Inoue (1991), and others already provide theories of investment in multiple capital goods.
• First the authors present the model’s assumptions and predictions, then they discuss them.

2.1 Model assumptions and empirical implications

• The model features an infinitely lived, perfectly competitive firm i that holds Kphyit units of physical capital and Kintit units of intangible capital at time t.
• The second term equals the cost of adjusting the stock of capital type m.
• This prediction provides a rationale for measuring Tobin’s q as qtot, firm value divided by Ktot, the sum of physical and intangible capital.
• The next predictions follows immediately from Prediction 2 and forms the basis of their empirical work.
• Its q-slope is downward biased, meaning it produces upward-biased estimates of the adjustment-cost parameter γphy, because q∗it depends on the ratio Ktotit /K phy it , making the regressor negatively related to the disturbance.

2.2 Discussion

• To summarize, their simple theory predicts that total q helps explains physical, intangible, and total investment when the authors scale them by the firm’s total capital.
• While employee training and brand building may entail relatively low risk, investments like R&D projects are highly risky and sometimes fail completely.
• Of course, in reality physical and intangible capital may be complements, not substitutes.
• The theory highlights an important limitation of investment regressions.

3 Firm-level data

• The authors 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+).
• The authors use data from 1975 to 2011, although they use earlier data to estimate firms’ intangible capital.
• The authors sample starts in 1975, because this is the first year that FASB requires firms to report R&D.

3.2 Intangible capital

• The authors briefly review the U.S. accounting rules for intangible capital before defining their measure.
• Intangible assets created within a firm are expensed on the income statement and almost never appear as assets on the balance sheet.
• The authors define the stock of internal intangible capital as the sum of knowledge capital and organization capital, which they define next.
• Compustat, however, almost always adds them together in a variable misleadingly labeled “Selling, General and Administrative Expense” (item xsga).

3.3 Investment

• (12) We measure physical investment Iphy as capital expenditures (Compustat item capx), and the authors measure intangible investment, Iint, as R&D + 0.3×SG&A.the authors.
• This definition assumes 30% of SG&A represents an investment, as the authors assume when estimating capital stocks.
• For comparison, the authors also examine the literature’s standard physical investment measure, denoted ι∗ in their theory: ι∗it = Iphyit Kphyi,t−1 .

3.4 Cash flow

• Erickson and Whited (2012), Almeida and Campello (2007), and others measure free cash flow as c∗it = IBit +DPit Kphyi,t−1 , (14) where IB is income before extraordinary items and DP is depreciation expense.
• Specifically, the authors add intangible investments back into the free cash flow so that they measure the profits available for total, not just physical, investment: ctotit = IBit +DPit + (15) Lev and Sougiannis (1996) similarly adjust earnings for intangible investments, as do practitioners (Damodaran, 2001, n.d.).
• When available, the authors use simulated marginal tax rates from Graham (1996).
• The correlation between ctot and c∗ is 0.77.

3.5 Summary statistics

• The mean intangible intensity is 43% (45%), so almost half of capital is intangible in their typical firm/year.
• Researchers sometimes discard q 17 observations exceeding 10, arguing they are unrealistically large.
• The standard deviation of qtot is 74% lower than for q∗.
• The average physical and intangible investment rates are roughly equal, but physical investment is more volatile and right-skewed.
• Somewhat surprisingly, even manufacturing firms’ capital is 30–34% intangible on average.

4 Full-sample results

• In this section the authors test the theory’s predictions in their full sample.
• The next section compares results across subsamples.
• The authors begin with the classic OLS panel regressions of Fazarri, Hubbard, and Petersen (1988).
• The authors then correct for measurement-error bias in Section 4.2.

4.1 OLS results and comovement in investment

• Table 2 contains results from OLS regressions of investment on lagged q and firm and year fixed effects.
• This bias is especially severe for cash-flow coefficients (Erickson and Whited, 2000; Abel, 2014), so the authors exclude cash flow until the next subsection.
• The R2 here is indeed low (23.3%) relative to all the R2 values in Panel A, with one exception: Standard q explains standard investment slightly better than total q explains their new physical-investment measure, ιphy.
• 19 ιtot on both q proxies produces a positive and highly significant slope on qtot but a negative and less-significant slope on q∗.
• As their theory predicts, physical and intangible investment comove strongly within firms, because they share the same q.

4.2 Bias-corrected results

• For one, the authors measure intangible capital with error.
• The authors find that the cumulant estimator produces significantly different results depending on whether they use total or standard q. 11To see this, suppose the previous footnote’s assumptions hold, except they instead estimate the errors-in-variables model ιtotit = qitβ + uit, Table A3.
• Indeed, the authors find that SG&A investment has a cash-flow slope of 0.115, which is more than double intangible investment’s 0.050 slope .
• The authors simply conclude that physical investment is even more sensitive to cash flow than previously believed, R&D investment is insensitive to cash flow, and SG&A investment’s cash-flow sensitivity remains unclear.

5 Comparing subsamples

• Next, the authors compare results across firms, industries, and years.
• Doing so allows us to test their theory and compare adjustment costs across subsamples.
• The authors re-estimate the previous models in subsamples formed using three variables.
• First, the authors sort firms each year into quartiles based on their lagged intangible intensity (Table 4).

5.1 Testing the theory in subsamples

• On three dimensions, the authors find that the classic q theory, including the theory in this paper, fits the data better in settings with more intangible capital.
• First, R2 values increase dramatically when the authors move from the lowest to highest intangible quartile (Table 4, Panel B).
• The authors find that violating the assumption about quadratic adjustment costs is unlikely to generate the empirical patterns in Table 4.
• If firms using more intangible capital are closer to the perfect-competition, constant-returns benchmark, this mechanism could explain why they exhibit lower cash-flow slopes and higher R2 and ρ2 values.
• The authors find mixed results when they use the Herfindahl index to 26 proxy for industry-level competition; different industry classifications deliver increasing, decreasing, or flat patterns across intangible-intensity subsamples.

5.2 Comparing adjustment costs across subsamples

• Table 4 shows interesting patterns in q-slopes across subsamples.
• As a result, firms using more intangible capital should have a higher intangible-investment q-slope relative to the sum of slopes for physical and intangible investment.
• This exercise provides a useful consistency check on their theory.
• To link q-slopes to firms’ optimal mix of capitals, their theory needs strong additional assumptions.
• Outside their simple theory, there may be alternate explanations for the pattern the authors find in q-slopes across firms.

6 Macro results

• The neoclassical theory of investment, including the theory in this paper, can easily be interpreted as a theory of the macroeconomy rather than a single firm.
• Bond q data are from Philippon’s web site.
• In stark contrast, intangible and total investment both have highly significant q-slopes, and they deliver R2 values of 57% and 61%, respectively.
• 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.
• To summarize, at the macro level, including intangibles makes q explain the level of investment much better, meaning the classic q theory fits the data much better than previously believed.

7.1 Robustness of main results across subsamples

• Tables 4-6 show that their main results are quite robust across subsamples.
• The authors see the reverse in four of ten subsamples, so they conclude that total q explains physical and intangible investment roughly equally well.
• Consider the increase in R2 when the authors move from the regression that ignores intangibles (specification 4 in the tables) to the regression that uses ιtot and qtot (specification 3).
• This pattern is mainly driven by τ2, which increases by 0.284 (65%) in the top quartile, but actually decreases by a statistically insignificant 0.018 (3%) in the lowest quartile.
• These same patterns are also present, but less dramatic, across industry and year subsamples.

7.2 What fraction of SG&A is an investment?

• Arguably the strongest assumption in their intangible-capital measure is that λ=30% of SG&A represents an investment, and λ is constant across firms and time.
• Table 8 shows that their main conclusions go though, at least qualitatively, when the authors use different values of λ ranging from zero to 100%.
• When λ is zero, firms’ intangible capital comes exclusively from R&D.
• The structural parameter λ affects both the investment and q measures.
• 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.

7.3 Alternate measures of intangible capital

• In addition to varying the SG&A multiplier λ, the authors try eight other variations on their intangiblecapital measure.
• Specifically, the authors vary δSG&A, the depreciation rate for organization capital; they exclude goodwill from firms’ intangible capital; they exclude all balance-sheet intangibles, which brings us closer to existing measures from the literature; they set firms’ starting intangible capital stock to zero; and they estimate firms’ starting intangible capital stock using a perpetuity formula, like Falato, Kadyrzhanov, and Sim (2013).
• The authors also drop the first five years of data for each firm, which makes the choice of starting intangible capital stock less important.
• The authors also try dropping the 47% of firm/years with missing R&D from their regressions.
• Table 9 provides details about these variations and their results.

7.4 Alternate estimators

• In addition to using the cumulant estimator to obtain unbiased q-slopes, the authors also use Biorn’s (2000) and Arellano and Bond’s (1991) instrumental variable (IV) estimators.
• Both estimators take first differences of the linear investment-q model, then use lagged regressors as instruments for the q proxy.
• Erickson and Whited (2012) show that these IV estimators are biased if measurement error is serially correlated, which is likely in their setting.
• This bias is probably most severe in the standard regressions that omit intangible capital, since omitting intangible capital is an important source of measurement error, and a firm’s intangible capital stock is highly serially correlated.
• Specifically, they produce lower q-slopes for ιint than ιphy, and lower q-slopes for ι∗ than ιphy .

7.5 A mechanical result?

• A potential concern is that moving from the latter regression to the former requires multiplying both sides of the regression by Kphy/Ktot.
• Multiplying both sides of a regression by the same variable can potentially, but not necessarily, increase the R2 even if that variable is pure noise.
• The authors result is not mechanical or obvious, however.
• Moreover, if their measure of intangible investment were just noise, the authors would not find that it is well explained by q and comoves with physical investment.

8 Conclusion

• The neoclassical theory of investment has been applied almost exclusively to physical capital.
• In both their theory and firm-level data, physical and intangible investment comove strongly, and they are explained roughly equally well by Tobin’s q. Compared to physical capital, intangible capital’s convex adjustment costs are roughly twice as large, meaning intangible capital responds more slowly to changes in investment opportunities.
• A benefit of this new measure is that it can be easily computed for the full Compustat sample.
• This new Tobin’s q measure offers a simple way to improve corporate finance regressions without additional econometrics.
• Why the classic q-theory fits the data better in high-intangible settings is also an interesting open question.

Figures

Fig. 1. Capital intangibility over time. This figure plots the mean intangible capital intensity over time, both for our full sample and within industries. Intangible intensity equals Kint/(Kint+Kphy), the firm’s stock of intangible divided by its total stock of capital. We use the Fama-French fiveindustry definition and exclude industry “Other.”

Fig. 2. Investment-q relation in macro data. This figure plots Tobin’s q (solid lines) and the investment rates (dashed lines) over time for the aggregate U.S. economy. The top-left panel uses data from Hall (2001) and shows standard measures that exclude intangible capital. Standard q (q∗) is aggregate market value scaled by the physical-capital stock. Standard investment (ι∗) equals physical investment scaled by the physical-capital stock. The remaining panels also use data from Corrado and Hulten (2014). Total q is aggregate market value scaled by total capital, the sum of the physical- and intangible-capital stocks. The top-right panel shows ιphy, physical investment scaled by total capital. The bottom-left panel shows ιint, intangible investment scaled by total capital. The bottom right panel shows ιtot = ιphy + ιint. For each graph, the left axis is the value of q and the right axis is the investment rate.

Full text

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Intangible Capital and the Investment-q Relation
Ryan H. Peters and Lucian A. Taylor*
February 21, 2016
Abstract:
The neoclassical theory of investment has mainly been tested with physical investment, but we
show it also helps explain intangible investment. At the firm level, Tobin’s q explains physical and
intangible investment roughly equally well, and it explains total investment even better. Compared
to physical capital, intangible capital adjusts more slowly to changes in investment opportunities.
The classic q theory performs better in firms and years with more intangible capital: Total and even
physical investment are better explained by Tobin’s q and are less sensitive to cash flow. At the
macro level, Tobin’s q explains intangible investment many times better than physical investment.
We propose a simple, new Tobin’s q proxy that accounts for intangible capital, and we show that
it is a superior proxy for both physical and intangible investment opportunities.
JEL codes: E22, G31, O33
Keywords: Intangible Capital, Investment, Tobin’s q, R&D, Organization Capital
* The Wharton School, University of Pennsylvania. Emails: petersry@wharton.upenn.edu,
luket@wharton.upenn.edu. We thank Andy Abel for extensive guidance. We also thank Christo-
pher 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, Zexi Wang (discussant), David Wessels, Toni
Whited, Mindy Zhang, and the audiences at the 2015 European Financial Association Annual
Meeting, 2014 NYU Five-Star Conference, 2015 Trans-Atlantic Doctoral Conference, Bingham-
ton University, Federal Reserve Board of Governors, Northeastern University (D’Amore-McKim),
Penn State University (Smeal), Rutgers University, University of Chicago (Booth), University of
Lausanne and EPFL, University of Maryland (Smith), University of Minnesota (Carlson), and Uni-
versity 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 grate-
fully acknowledge support from the Rodney L. White Center for Financial Research and the Jacobs
Levy Equity Management Center for Quantitative Financial Research.

1 Introduction
The neoclassical theory of investment was developed more than 30 years ago, when firms mainly
owned physical assets like property, plant, and equipment (PP&E). As a result, empirical tests of the
theory have focused almost exclusively on physical capital. Since then, the U.S. economy has shifted
toward service- and technology-based industries, which has made intangible assets like human
capital, innovative products, brands, patents, software, customer relationships, databases, and
distribution systems increasingly important. Corrado and Hulten (2010) estimate that intangible
capital makes up 34% of firms’ total capital in recent years. Despite the importance of intangible
capital, researchers have almost always excluded it when testing investment theories.
Is there a role for intangible capital in the neoclassical theory of investment? If so, how must
we adapt our empirical tests? Is the theory still relevant in an economy increasingly dominated
by intangible capital? For example, Hayashi’s (1982) classic q-theory of investment predicts that
Tobin’s q, the ratio of capital’s market value to its replacement cost, perfectly summarizes a firm’s
investment opportunities. As a result, Tobin’s q has become “arguably the most common regressor
in corporate finance” (Erickson and Whited, 2012). How should researchers proxy for investment
opportunities in an increasingly intangible economy, and how well do those proxies work?
To answer these questions, we revisit the basic empirical facts about the relation between corporate
investment, Tobin’s q, and free cash flow. A very large investment literature, both in corporate
finance and macroeconomics, is built upon these fundamental facts, so it is important to understand
how the facts change when we account for intangible capital. We show that some facts do change
significantly, and we discuss the implications for our theories of investment. Most importantly, we
show that the classic q theory of investment, despite originally being designed to explain physical
investment, also helps explain intangible investment. In other words, the neoclassical theory of
investment is still quite relevant. An important component of our analysis is a new Tobin’s q
proxy that accounts for intangible capital. We show that this new proxy captures firms’ investment
opportunities better than other popular proxies, thus offering a simple way to improve corporate
finance regressions without additional econometrics.
To guide our empirical work, we begin with a theory of a firm that invests optimally in physical
1

and intangible capital over time. The theory is a standard neoclassical investment-q theory in the
spirit of Hayashi (1982) and Abel and Eberly (1994). Like physical capital, intangible capital is
costly to obtain and helps produce future profits, albeit with some risk. For this fundamental
reason, it makes sense to treat intangible capital as capital in the neoclassical framework. Our
theory predicts that a firm’s physical and intangible investment rates should both be explained
well by a version of Tobin’s q we call “total q,” which equals the firm’s market value divided by the
sum of its physical and intangible capital stocks.
We test this and other predictions using data on public U.S. firms from 1975 to 2011. We
measure a firm’s intangible capital as 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, which includes human capital, brand, customer relationships,
and distribution systems. 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).
We define a firm’s total capital as the sum of its physical and intangible capital, both measured at
replacement cost. Guided by our theory, we measure total q as the firm’s market value divided by
its total capital, and we scale the physical and intangible investment rates by total capital.
While our intangible-capital measure has limitations, we believe, and the data confirm, that an
imperfect proxy is better than setting intangible capital to zero. A benefit of the measure is that it
is easily computed for all public U.S. firms back to 1975, and it only requires Compustat data and
other easily downloaded data. Code for computing the measure will eventually be on the authors’
websites.
Our analysis begins with OLS panel regressions of investment on q. Consistent with our theory,
total q explains physical and intangible investment roughly equally well: Their within-firm R
2
values are 21% and 28%, respectively. Total q explains the sum of physical and intangible investment
(“total investment”) even better, delivering an R
2
of 33%. Judging by R
2
, the neoclassical theory of
2