âIntangible Capital and the Investment-q Relationâ
Transcription
âIntangible Capital and the Investment-q Relationâ
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. 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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