A New Approach to the Valuation of Intangible Capital

A New Approach to the Valuation of Intangible Capital ∗ Jason G. Cummins Division of Research and Statistics Board of Governors of the Federal Reserve System jason.g.cummins@frb.gov March 15, 2004 Abstract Intangible capital is not a distinct factor of production as is physical capital or labor. Rather it is the “glue” that creates value from other factor inputs. This perspectivenaturallysuggestsanempiricalmodelinwhichintangiblecapitalis defined in terms of adjustment costs. My estimates of these adjustment costs fromfirm-levelpaneldatasuggestthatnoappreciableintangiblesareassociated with R&D and advertising, whereas information technology creates intangibles with a 72% annual rate of return – a sizable figure that is nevertheless much smaller than that reported in previous studies. To build a bridge to previous research,Ishowthatmuchlargerestimatescanbeobtainedwithordinaryleast squares, amethodthatignoresthepossibilitythatthevalueofthe firmandits investment policy are simultaneously determined. JEL Classification: D24, E22. Keywords: Organizational capital, intellectual property, adjustment costs. BaruchLevhasbeeninstrumentalinshapingmythinkingaboutintangibleassets. Ithankhim ∗ forhisguidanceandforprovidingmewiththedatasetoninformationtechnologyinvestmentthathe and Suresh Radhakrishnan put together. I am also indebted to Stephen Bond whose collaboration laid the foundation for this research. Daniel Cooper provided research assistance. Ned Nadiri, the editors, CRIW conference participants, and Darrel Cohen all provided helpful comments and suggestions. I/B/E/S International Inc. provided the data on earnings expectations. The views presented are solely mine and do not necessarily represent those of the Board of Governors of the Federal Reserve System or its staff members.

1 Introduction In most circumstances, there are no direct measures of the return on intangible capital. As a result, researchers have relied primarily on the equity market to infer the value of intangibles. This valuation method is straightforward: If the equity market reveals the intrinsic value of the firm, then subtracting the value of the firm’s tangible assets from its market value reveals the value of the firm’s intangible assets. Using this method, Hall (2001) argued that U.S. companies accumulated an enormous stock of intangible capital in the 1990s.1 Despite the appealing simplicity of the equity market approach to measuring intangibles, it should be used with considerable caution. According to this method, Yahoo!’s intangibles were worth more than $100 billion in 2000. However, they were worth less than one-third of that amount in 2003. To be sure, this drop does not necessarily pose a problem for the equity market approach. Yahoo!’s market capitalization may reflect changes in expected profits or expected returns or both. But this example illustrates a potential pitfall of relying on the equity market to reveal the value of intangible capital. This value will be mismeasured to the extent that asset prices depart from their intrinsic values. The main drawback of the equity market approach is that it presents a catch-22: Investors must have information about intangibles to value them; but investors do not have the information they need because intangibles, by their very nature, are extraordinarily difficult to value. This circularity calls into question the underlying assumption of the equity market approach – that markets are strongly efficient. Howcanthevalue of the firmasrevealedby equitymarketsbe equal totheintrinsic value of the firm – defined as the present value of expected cash flows – when market participants know so little about the value of intangibles? 1The idea that the stock market reveals the quantity of capital in the absence of rents and adjustment costs was stated clearly by Baily (1981), who interpreted the stock market data from the 1970s as showing that energy price shocks effectively destroyed a great deal of capital. 1

To create an alternative proxy for the intrinsic value of the firm, I construct the discounted value of expected profits from analysts’ forecasts. I/B/E/S has collected data on profit forecasts for a large sample of companies since 1982. The analysts forecast profits for one and two years ahead as well as the growth rate of profits out to a five-year horizon. In making their forecasts, analysts assess whether a new supply-chain management system, say, is expected to add to intangible capital and, as a result, generate additional profits. Thus, if analysts expect intangibles to contribute materially to a company’s bottom line over a five-year period, then their forecasts should reflect the value of these intangibles. Ofcourse,analysts’forecastsarenotfoolproof. Afterall,themajorityofanalysts appear to have overestimated the growth rates of intangible-intensive companies in the late 1990s. And analysts offer little guidance about how to discount these forecasts. In fact, the discounted value of expected profits may be just as poor a proxy for a firm’s intrinsic value as the stock market is. However, these two proxies deviate from a firm’s intrinsic value for different reasons. The stock-market-based measure reflects any market inefficiency, whereas the analyst-based measure reflects the biases of analysts and any mistakes in the way the forecasts are discounted. The econometric setup explicitly recognizes that the two proxies measure the firm’s intrinsic value with different kinds of error. Ultimately, identification of the model’sparametersdependsonwhetherthereareinformativeinstrumentalvariables that are uncorrelated with the measurement errors in the two proxies. Theory offers little guidance about the nature of the measurement errors, and consequently, identification is an empirical issue that must be investigated with diagnostic tests, such as the test of the model’s overidentifying restrictions. For my empirical work, I complied a dataset that distinguishes firms’ expenditures on tangible capital, information technology (IT), and intellectual property (IP). Relying on these data, I use the stock-market- and analyst-based measures of the firm’s intrinsic value to estimate the return on each type of capital. Perhaps the 2

most interesting finding is that organizational capital created by IT generates a return of 72% at an annual rate. Despite its magnitude, this estimate is considerably smaller than comparable estimates in previous studies. To build a bridge to the previous research, I show that much larger estimates can be obtained with ordinary least squares (OLS), a method that ignores the possibility that the value of the firm and its investment policy are simultaneously determined. 2 The Valuation of Intangible Capital 2.1 Intangible Capital: An Instrumental Definition I distinguish between two types of intangibles: intellectual property and organizational capital. Broadly defined, IP includes patents, trademarks, copyrights, brand names, secret formulas, and so on. For my purposes, I define organizational capital asbusinessmodels,designs,androutinesthatcreatevaluefrominformationtechnology. Without a doubt, organizational capital is a broader concept than this narrow definition suggests. For example, innovative compensation policies and effective training programs are surely part of organizational capital. Indeed, the systematic focus on creating organizational capital can be traced to industrial pioneer Fredrick Winslow Taylor and his intellectual forbears. I adopt a definition based on IT not because IT is qualitatively different from any other method or technology that aids organizational efficiency but because sizable, measurable outlays are devoted to it. This two-part taxonomy suits my empirical model and the data. The data warrant brief explanation. Companies report expenditures on R&D and advertising, which create what I have defined as intellectual property. These expenditures can be capitalized to create the IP capital stock. Such a stock may seem essentially arbitrary – companies offer little guidance, for example, about how R&D and advertisingdepreciate–butthestockof property, plant, andequipmentisasimilarly unpalatable concept, even though researchers have become sufficiently inured to it.2 2Indeed, the accounting for physical assets in financial statements may be as deficient as the accountingforIP.Physicalassetsarecapitalizedathistoricalcostsandaredepreciatedinwaysthat 3

As a practical matter, one must also distinguish between intellectual property and organizational capital because outlays on R&D, advertising, and IT have behaved differently over time. In particular, R&D and advertising appear to be declining in relative importance. Outlays on IT have soared while advertising as a proportion of nonfinancial corporate gross domestic profit has grown modestly, from 3.9% in 1980-89 to 4.1% in 1990-97. The comparable figures for R&D are 2.3% and 2.9% (Nakamura 1999). Hence, if intangibles create extraordinary gains in firm value, then arguably the most plausible driver is organizational capital, not intellectual property. So what exactly is organizational capital? As a purely mechanical matter, I define organizational capital as an adjustment cost from IT investment, defined as thedifferencebetweenthevalueofinstalledITandthatofuninstalledIT.3 Supposea companypurchasesdatabasesoftware. Byitself,databasesoftwaredoesnotgenerate any value. At a minimum, the software must be combined with a database and, perhaps, a sales force. Organizational capital defines how the database is used and, consequently, how software investment creates value. Another example helps illustrate the definition. Dell’s value depends on a unique organizational design that sells build-to-order computers directly to customers. Dell’s tangible capital stock differs little from that of Hewlett-Packard (HP), one of its main competitors, because both companies assemble computers. The reason that any given piece of tangible capital is more valuable at Dell than at HP relates to Dell’s unique business model and routines, organizational capital that combines the usual factors of production in a special way. HP cannot simply replicate Dell’s tangible capital stock and become as profitable as Dell. Hence, it does not make sense to think about organizational capital, or intangibles more generally, may be poor approximations of their service flow. Perpetual inventory capital stocks constructed from such data may also be only loose approximations of the service flow of capital. 3This rather narrow definition based on IT adjustment costs builds on a broader interpretation of organizational capital in terms of adjustment costs, as in, for example, Prescott and Visscher (1980). 4

as separate factors of production that can be purchased in a market. In most cases, intangibles are so closely connected with traditional factor inputs like a computer or a college graduate that their valuation as standalones is nearly impossible (see, for example, Lev 2001). This definition of organizational capital contrasts sharply with the tendency in the literature to think about intangible capital as being much like any other quasifixed factor of production. In that mold, firms buy intangibles as they would buy machinery. But intangibles, by and large, are different from other factors because companies cannot order or hire intangibles. Rather, intangible capital typically results from the distinctive way companies combine the usual factors of production. Treating intangibles as inputs misses this point altogether. Themodel in the next section formalizes thisobservation by defining intangibles aswhatever makesinstalled inputs more valuable than uninstalledinputs –thatis, whatevermakesaDelloutofthesamecomputersandcollegegraduatesthatHPcan buy. Realistically, this definition is not exhaustive because some intangibles are not associated with specific expenditures. For example, a good idea – in Dell’s case, selling computers over the Internet – can be thought of as a type of intangible capital. Nevertheless, most intangibles are closely associated with some sort of outlay; after all, at least some investment is usually needed to make a good idea profitable. My definition of organizational capital may seem similar to the more familiar concept of multifactor productivity (MFP) or IT-biased technical change. Indeed, organizational capital is like IT-biased technical change in that it boosts the marginal product of IT capital. However, the concepts differ in a critical respect: Organizational capital is costly to create; in contrast, IT-biased technical change and MFP require no specific outlays, and for that reason they are called “manna from heaven.” Organizational capital should also be distinguished from embodied technical change. Whereas embodied technical change characterizes the capabilities 5

of a particular asset – disk drives are more efficient and reliable than they used to be – organizational capital depends on how the firm uses an asset. In the example discussed above, both Dell and HP can buy the same technology embodied in a new disk drive, but the drive is more valuable at Dell because of Dell’s superior organizational capital. 2.2 Theoretical Model The model is a straightforward variant of the one developed by Hayashi and Inoue (1991),whoderivedanexpressionforthevalueofafirmwithmultiplecapitalgoods; it follows the derivation in Bond and Cummins (2000). Using a method similar to mine, Hall (1993a) relied on Hayashi and Inoue’s model to estimate the rate of return on R&D. The novel twist in my application is the idea that intangibles are like adjustment costs and therefore can be estimated econometrically. In each period, the firm chooses to invest in each type of capital good: I = t (I ,...,I ), where j indexes the N different types of capital goods and t indexes 1t Nt time.4 This decision is equivalent to choosing a sequence of capital stocks K = t (K ,...,K ), given K , to maximize V , the cum-dividend value of the firm, 1t Nt t 1 t − defined as ∞ V =E βtΠ(K ,I ,(cid:18) ) , (1) t t s s s s ( ) s=t X where E is the expectations operator conditional on the set of information available t atthebeginningofperiodt; βt discountsnetrevenueinperiodsbacktotimet; and s Π is the revenue function net of factor payments, which includes the productivity shock (cid:18) as an argument. Π is linear homogeneous in (K ,I ), and the capital goods s s s aretheonlyquasi-fixedfactorsor,equivalently,variablefactorshavebeenmaximized out of Π. For convenience in presenting the model, I assume that the firm pays no 4The firm index i is suppressed to economize on notation except when it clarifies the variables that vary by firm. 6

taxes, issues no debt, and has no current assets, although these considerations are incorporated into the empirical work. The firm maximizes equation (1) subject to the series of constraints: K =(1 δ )K +I s 0, (2) j,t+s j j,t+s 1 j,t+s − − ≥ where δ is the rate of physical depreciation for capital good j. In this formulation, j investmentissubjecttoadjustmentcostsbutbecomesproductiveimmediately. Furthermore, I assume that current profits are known so that the firm, when choosing I , knows both the prices and the productivity shock in period t. Other formulajt tions such as one including a production lag, a decision lag, or both are possible, but this specification is more parsimonious. Let the multipliers associated with the constraints in equation (2) be λ . j,t+s Then the first-order conditions for maximizing equation (1) subject to equation (2) are ∂Π t =λ j =1,...,N (3) jt − ∂I ∀ jt µ ¶ and ∂Π λ = t +(1 δ )βt E [λ ] j =1,...,N (4) jt ∂K − j t+1 t j,t+1 ∀ jt µ ¶ = E ∞ βt(1 δ )s ∂Π t+s . t s − j ∂K " j,t+s # s=0 µ ¶ X Combiningequations(3)and(4)andusingthelinearhomogeneityofΠ(K ,I ,(cid:18) ), t t t I get the following result: N N λ (1 δ )K +(cid:18) = Π +βt E λ (1 δ )K jt j j,t 1 t t t+1 t j,t+1 j jt − −  −  j=1 j=1 X X ∞   = E βt Π t t+s t+s " # s=0 X = V t. Hence, the value of the firm can be expressed as the sum of the installed values of the beginning-of-period capital stocks, which, according to equation (2) are equal 7

to the difference between the current capital stock and the current investment. Because three types of capital are included in the empirical work, the specific equation considered is V =λ (K I )+λ (KIT IT )+λ (KIP IP )+(cid:18) , (5) t K t t KIT t t KIP t t t − − − where investment in tangible capital (excluding IT), information technology, and intellectual property are I, IT, and IP, respectively; the capital stock (excluding IT)isdenotedbyK andtheITandIPcapitalstocksaredistinguishedbyappending IT and IP. According to equation (3), the multiplier on each capital stock is the gross marginal cost of an additional unit of capital, which is equal to the price of capital including adjustment costs. To be more concrete, I posit an adjustment cost function, C, that is additively separable from the net revenue function: ∂C λ =p + . (6) jt j ∂I j In this equation, the purchase price of capital is distinguishable from marginal adjustment costs, which are additional outlays needed to make investment productive. This separation is attractive because adjustment costs such as the costs of training workers to use new equipment and of integrating new and old equipment create intangible capital.5 Moreover, regarding empirical research, we have a well-developed literatureonestimatingadjustmentcosts econometrically, whereaswehavenopracticalwayofdirectlymeasuringthevalueofintangiblecapitalfromavailabledata. In fact, the estimated marginal adjustment costs are equal to the return on intangible capital in equilibrium. That is, note that firms will invest until the gross marginal cost of an additional unit of capital in equation (6) is equal to the marginal product of capital, defined by equation (4) also known as the Euler equation. Therefore, the equilibrium return on intangible capital can be equated with adjustment costs. 5For example, Hempell (2003) finds broad evidence that firms complement IT spending with training programs for their employees (see also Bresnahan, Brynjolfsson, and Hitt 2002). According to Hempell’s empirical results, firms that invest intensively in both training and IT perform significantly better than do competitors that forgo such investment. 8

Returning to the Dell-HP example, one might be tempted to characterize the difference between Dell and HP by saying that the level of MFP is higher at Dell than at HP. But this characterization is not sufficiently informative because it does not explain why Dell produces more with less. In contrast, the valuation equation (5) shows that it is possible to trace the sources of Dell’s superior valuation to its intangible capital, specifically the intangible capital associated with its previous investments in IT and IP. New software, say, is more valuable at Dell because of the way it is used. Although this approach is more informative than the one that attributes any difference to MFP, admittedly it still falls short. In particular, this approach fails to explain how software became more valuable at Dell; estimating (5) provides no blueprint for creating value. To gain further insight, we need considerably better data and more-detailed case studies. Interpreting the estimates of equation (5) is more complicated than it may seem at first glance. Although the multipliers are assumed to be constant, the value of intangible capital can vary over time and across firms; indeed, the comparison of Dell with HP suggests that this variance is a realistic possibility. Regrettably, the empirical framework is not rich enough to accommodate this consideration. In practice, the problem is not as bad as it may seem because I control for firm- and time-specificeffects. Nevertheless,totheextentthatthemultipliersarenotconstant after controlling for these effects, the empirical estimates of the multipliers will be averages across firms and time.6 Hence, econometricians must exercise extreme caution when interpreting the estimates as structural parameters, which they are not; rather, the estimates reveal the average return on intellectual property and organizational capital. Finally, this limitation is not unique to my formulation. On the contrary, my formulation is closely related to production- or cost-function 6Cross-sectional estimation does not sidestep this problem entirely because the estimates will still be averages across firms. Moreover, cross-sectional estimation is inadvisable because it does not controls for firm-specific effects. 9

estimation, in which the parameters are assumed to be constant across firms and time despite the debatable case for such an assumption. 3 Estimating the Empirical Valuation Equation Estimating the empirical valuation equation (5) would be straightforward if data on the intrinsic value of the firm were available and the error term were an innovation. As I will discuss in turn, neither of these conditions is likely to hold. As a result, estimates based on OLS will be biased. Identification is still possible in certain circumstances with generalized method of moments (GMM). However, the GMM approach does have some notable drawbacks, which I discuss in the final subsection. Two primary issues affect the estimation of equation (5): Theeconometriciancannotobservetheintrinsicvalueofthefirm. WhatIhave • called the equity market approach explicitly assumes that the stock market value of the firm, VE, equals the intrinsic value of the firm, V. Alternatively, one can argue that any market mismeasurement is orthogonal to the firm’s current capital stocks and investments. Because both of these conditions are atleastsuspect, Iproposeanalternativethatarguablyrestsonfirmerfooting. The econometrician also cannot observe the productivity shock, (cid:18), such as a • new product or process, but this shock affects both the value of the firm and its investment policy. As a result, OLS estimates will be biased. Instead of OLS, I use the system-GMM estimator proposed by Blundell and Bond (1998, 2000). They show that the system-GMM estimator performs well when there are fixed effects and the endogenous variables have near unit roots, as is true of all three types of capital. 3.1 Unobservable Value of the Firm The most widely used proxy for the intrinsic value of the firm is its stock market value. According to one view of the stock market, this approach makes good sense 10

because share prices reflect the discounted value of expected future distributions from the firm to shareholders. If they do, share price movements can be explained in one of two ways: as changes in expectations about future profits, changes that support future dividend payments; or as fluctuations in investors’ required rates of return. Hence, from the early 1990s to 2000, the rise in share prices of intangibleintensive companies may have been due to advance news of unprecedented profit growth. Alternatively, prices may have increased because investors decided that the stock market was much less risky than they had previously believed. As a result, they reduced their required rates of return. For example, Siegel (1998) argues that stocks, not bonds, have been the safest long-term investment vehicle. Accordingly, investors may have realized that they were irrationally fearful of stocks. When stocks are seen as posing little risk, rational investors will bid up stock prices. In other words, they will decide that the equity premium was too high in the past but that it is just right now.7 Anotherviewofthestockmarketcautionsthatsharepricesmaysometimeshave a life of their own, apart from the intrinsic level represented by the discounted value of future distributions. Observers have long recognized the theoretical possibility that share prices deviate from their intrinsic values because of a rational bubble.8 Outside this particular paradigm, numerous models show that noise traders, fads, or other psychological factors influence share prices. Although, I cannot explain the disconnect between asset prices and their intrinsic values, I can cite two well-known example of this phenomenon: tulip prices in 1634-37 and Japanese share prices in 1989. These anomalies in price behavior are difficult to dismiss on empirical 7McGrattan and Prescott (2000) use this argument to conclude that “it is troubling that economic theory failed so miserably to account for historical asset values and returns while, at the same time, it does so well in accounting for current observations.” The “current observations” in their study date from the beginning of 2000, so apparently economic theory needs some help in explaining the subsequent downturn (see also Kiley 2000). 8A rational bubble occurs when the expected discounted future price does not converge to zero in the limit. Both theoretical and empirical arguments can be used to rule out rational bubbles (see, for example, Campbell, Lo, and MacKinlay 1997, chapter 7). Hence, rational bubbles are unlikely to offer a persuasive explanation for behavior of financial markets. 11

grounds. The recent stock market boom and at least partial bust may be another such anomaly. Indeed, Shiller (2000)arguesthatinvestorshavenotlearned that the stock market is less risky than they had previously thought. Rather, for a whole host of reasons, investors have been and continue to be “irrationally exuberant.” Highlighting the key distinction between these two views of the stock market is important. Whereas the first view treats market efficiency as a maintained hypothesis, the second treats market inefficiency as a maintained hypothesis. To illustrate the implications of this distinction, I pick a stream of expected profits. The first theory tells us what the (possibly time-varying) discount rate (that is, the return) must be to justify the observed stock price. The second theory tells us that the stock price differs from its intrinsic value for some reason outside the basic model – bubbles, noise traders, fads, or the like. It is very difficult to determine which of these explanations is preferable because they both rely on unobservable factors to explain the same data. If one is to have any confidence in either explanation, onemustexploitthetestableimplicationsof thedynamicstochasticstructureof the unobservable factors. Toward this end, I created a model based on joint research with Stephen Bond (2000, 2002). Suppose the stock market reveals the intrinsic value of the firm with some error, so that VE =V +µ , (7) t t t whereµ isthemeasurementerrorintheequityvaluationVE,regardedasameasure t t of the intrinsic value V . Substituting VE for V in equation (5) then gives the t t t empirical valuation equation with noisy share prices: VE =λ (K I )+λ (KIT IT )+λ (KIP IP )+(µ +(cid:18) ). (8) t K t t KIT t t KIP t t t t − − − Let us consider the effect of measurement error on the model’s dependent variable and ignore the difficulty presented by the unobservable productivity shock, which is considered in the following section. The conventional wisdom is that measurement 12

errorofthistypebiasesthestandarderrorsbutnotthecoefficientestimates(see,for example, Hausman 2001). However, this is wisdom is false when the measurement error is correlated with the explanatory variables. Toillustratetheargument,Iconsiderasimplifiedversionofequation(8)inwhich the firm has only IT capital. The coefficient estimate on IT capital – call it b KIT – will consist of the true return on IT, β , and the bias caused by measurement KIT error: plimb =β +β , KIT KIT µ,KIT where β is the coefficient estimate from a hypothetical regression of the mea- µ,KIT surement error on IT capital: β = COV(µ,KIT)/VAR(KIT). Clearly, no µ,KIT bias occurs if COV(µ,KIT) = 0; the measurement error is uncorrelated with the regressor and the conventional wisdom about measurement error in the dependent variable is correct. However, if the stock market overestimates the value of ITintensive companies, then β > 0, and therefore the return on IT investment µ,KIT willbeupwardlybiased. Becausemysampleisskewedtowardthosecompaniescommonly thought to have been overvalued compared with fundamentals – companies in the 1990s with big IT budgets – this bias could be substantial. If the stock market underestimates the value of IT-intensive companies, the bias will go in the other direction. Indeed, this type of downward bias implies that the true return on investment exceeded the estimated return during periods like the 1970s, when the stock market was arguably undervalued compared with fundamentals. In addition, one cannot sign the bias based on a priori reasoning in the multivariate case, but the estimated returns on IP and tangible capital are also likely to be biased. However, the IT and IP coefficients seem likely to be severely affected because the stock market appears to have overestimated the value of intangible-intensive companies in the 1990s. Rather than using the stock market to infer the value of intangibles, I rely on analysts’ profit forecasts. Intangible assets create value only to the extent that 13

they are expected to generate profits in the future. Professional analysts are paid to forecast the future profits of the firms they track and leading analysts are paid very well indeed for performing this role. Thus one can ask whether analysts are forecasting profit growth in line with the intangible asset growth that seems to be implied by stock market valuations. Though the popular press regularly lambastes analysts for being far too optimistic, the answer is no.9 After introducing the data in the next section, I show that analysts’ forecasts of future profits are informative. Combining these forecasts with a simple assumption about the discount rates βt , I construct an alternative estimate of the present value of current and future t+s net revenues as V =E Π +βt Π +...+βt Π . (9) t t t t+1 t+1 t+s t+s ¡ ¢ I then use this estimbate in place of the firm’s stock market valuation. Clearly the estimate V will also measure the firm’s intrinsic value V with some error ν. The t t potentialwaysofintroducingmeasurementerrorincludetruncatingtheseriesaftera b finitenumber of futureperiods, usingan incorrectdiscountrate, andusinganalysts’ forecasts,whichprojectnetprofitsratherthannetrevenues. Theresultingempirical valuation equation is V =λ (K I )+λ (KIT IT )+λ (KIP IP )+(ν +(cid:18) ). (10) t K t t KIT t t KIP t t t t − − − Asbdiscussed in the following section, identification will depend on whether the measurement error ν is uncorrelated with suitably lagged values of instruments such as capital stocks. This event seems plausible because the current measurement error obtained with analysts’ forecasts is unlikely to be correlated with lags of the capital stock. Ultimately, however, this question is an empirical one that can be investigated with tests of overidentifying restrictions. 9Armed with a time-varying, firm-specific discount rate, one can equate any stream of profit forecasts to observed stock prices at every observation; without additional restrictions an infinite number of paths of time-varying discount rates can equate the two. The key point is that extreme assumptions would be required to obtain the VE’s in the sample from the analysts’ forecasts of future profits. Share prices in my sample appear to be high in relation not only to current profits but also to the best available forecasts of likely future profits. 14

3.2 Unobservable Productivity Shock Despite some important differences, empirical valuation equations (8) and (10) resemble production functions. This similarity is unfortunate because, as Griliches and Mairesse (1999) say, “In empirical practice, the application of panel methods to micro-data have produced rather unsatisfactory results.” Mairesse and Hall (1996) showthatattemptstocontrolforunobservedheterogeneityandsimultaneity–both likely sources of bias in the OLS results – have produced implausible estimates of productionfunctionparameters. Tobemorespecific, inmymodelIassumethatthe unobservable productivity shock consists of a firm-specific, a time-specific, and an idiosyncratic component. In this case, applying GMM estimators, which take first differencestoeliminateunobservablefirm-specificeffectsanduselaggedinstruments tocorrectfor simultaneityinthefirst-differenced equations, hasproduced especially unsatisfactory results. Blundell and Bond (1998, 2000) show that these problems are related to the weak correlation between the regressors and the lagged levels of the instruments. This insignificant correlation results in weak instruments in the context of the firstdifferenced GMM estimator. Bond and Blundell show that these biases can be dramatically reduced by incorporating more informative moment conditions that are valid under quite reasonable conditions. Essentially, their approach is to use lagged first differences as instruments for equations in levels, in addition to the usual lagged levels as instruments for equations in first differences. The result is the so-called system-GMM estimator, which I use as the preferred estimator. I then use DPD98 for GAUSS to perform the estimation (Arellano and Bond 1998).10 I conduct two types of diagnostic tests for the empirical models. First, I report the p-value of the test proposed by Arellano and Bond (1991) to detect first- and second-orderserialcorrelationintheresiduals. Thestatistics,whichhaveastandard 10In all specifications, I capture time effects by including year dummies in the estimated specifications. 15

normal distribution under the null, test for nonzero elements on the second offdiagonal of the estimated serial covariance matrix. Second, I report the p-value of the Sargan statistic (also know as Hansen’s J-statistic), which is a test of the model’s overidentifying restrictions; formally, it is a test of the joint null hypothesis that the model is correctly specified and that the instruments are valid. 3.3 Limits of the Empirical Approach If the GMM-based empirical approach is successfully implemented then that is the endofthestoryinmostapplications. However,intangibleassetsposeaspecialproblem. According to my model, intangibles are associated with specific investments, but clearly that is not the whole story; sometimes intangibles are not associated with any identifiable outlay. In that case, at least some of the intangibles end up in the error term as an omitted variable or as part of the unobservable productivity shock. Tofixideas,letussupposethefixedeffectintheunobservableproductivityshock representsintangiblecapital. Ifthefixedeffectembedsintangiblecapitalinthisway, the econometric solution may be worse than the problem. In particular, taking first differences will sweep out the effect of fixed intangible capital. As a result, the possibility that intangible capital determines the level of the firm’s intrinsic value will be completely missed. Let us take another interesting example, MFP is normally thought of as a black box but perhaps this box is full of what researchers mean by intangibles. Indeed, manyoftheexamplesusedtoillustratetherolethatintangiblesplayinorganizations have the flavor of MFP. That is, intangible capital comes from a good idea, like in Dell’s case, selling computers over the Internet or from a unique corporate culture createdbyaCEOlikeJackWelchorBillGates. Nevertheless,mostintangibleassets appear to be created by investment, as I argued in the introduction. After all, Dell 16

cannot sell computers over the Internet without its own computers, and Microsoft spends more than $5 billion annually on R&D and advertising. In summary, if one were to pursue an estimation strategy like GMM with instrumentsthatwerearguablyorthogonaltotheerrorterm, onemightrecoversomething closer to the direct impact of any asset on market value. However, one would by constructionmisstheroleofomittedintangiblesorintangiblesthatunderlietheproductivity shock. Thus, such instrumental variable strategies could be informative, but they could not provide the full set of answers about the role of intangibles. In fact, Brynjolfsson, Hitt, and Yang (2000, 2002) have taken this argument one step further: They say that the effect of intangible capital can be indirectly inferred fromOLSestimatesofthereturnonITcapital. Twopointsareworthmakingabout this argument: the first is methodological and the second empirical. First, OLS cannot be used to separate out all the direct and indirect effects of intangible capital. In particular, the return on, or the stock of, intangible capital cannot be inferred from the biased OLS coefficient on IT capital. When intangible capital is an omitted variable and IT capital is the only other type of capital, a straightforward analysis of omitted-variable bias reveals that the coefficient on IT capital is plimb =β +β β , KIT KIT KIC KIC,KIT where β is the return on intangible capital and β is the coefficient esti- KIC KIC,KIT mate from a hypothetical regression of the omitted intangible KIC on IT capital: β = COV(KIC,KIT)/VAR(KIT). For example, if one dollar of IT cap- KIC,KIT ital is associated with more than one dollar of omitted intangible capital, then β >1. KIC,KIT Using firm-level data, Brynjolfsson and others (2000,2002) estimate b with KIT OLS and find that each dollar of IT capital is associated with about ten dollars of market value. They interpret this finding as revealing the existence of a “large stock of intangible assets that are complementary with IT spending (emphasis added).” 17

However, that conclusion depends on assumptions about little understood relationships. Specifically, to say anything about the value of intangible capital, one must know the return on IT capital. And to say anything about the return on intangibles or the size of the stock of intangibles, one must break the value of intangible capital into its constituent components. Brynjolfsson and others solve these problems by assuming that adjustment costs are zero, in which case the returns to IT and intangible capital are equal to unity (β = β = 1) and the stock of intangible KIT KIC capital associated with IT capital can be backed out. According to this argument, the stock market does not literally value one dollar of IT capital at ten dollars. Rather, the estimate is a “marker” for the existence of a large stock of IT-related intangibles. The second concern is empirical: The results in Brynjolfsson and others (2000) contradict the authors’ interpretation of the estimate on IT capital. When the authors add a variable that measures organizational intangibles, ORG, to the regressions, β is almost totally unaffected.11 If the additional variable better KIT measures intangibles, as the authors argue persuasively, then b should fall sig- KIT nificantly because it is a marker for intangibles. Because the estimate is about unchanged, b must be biased for another reason, like the stock market mismea- KIT surement or simultaneity bias that I have highlighted. If it is biased for another reason, then one is wise to adopt an empirical technique that corrects for the bias. 4 Data 4.1 Sources and definitions The limiting factor in our empirical analysis is the availability of data on IT outlays. For IT expenditures I use a dataset compiled by Lev and Radhakrishnan (this 11In their subsequent paper, Brynjolfsson and others (2002) do not include thetelling regression from their first paper. Instead, they interact ORG with employment. Although the interpretation oftheeffectofORGiscomplicatedinthisinteraction,thetake-awaypointremainsthesame: The estimate on IT capital does not change significantly when ORG interacts with employment in the regression. 18

volume) from Information Week, which is in turn based on surveys by the Gartner Group. The total sample is an unbalanced panel of firms that appeared in the Information Week 500 list between 1991 and 1997 and for which Compustat and I/B/E/S data are available. The variables used in the empirical analysis are defined as follows: VE is the sum of the market value of common equity (defined as the number • of common shares outstanding multiplied by the end-of-fiscal-year common stock price) and the market value of preferred stock (defined as the firm’s preferred dividend payout divided by Standard & Poor’s preferred dividend yield obtained from Citibase). V is the present value of analysts’ profit forecasts. Let Π and Π denote it i,t+1 • firm i’s expected profits in periods t and t + 1, formed using beginning-ofb period information. Let g denote firm i’s expected growth rate of profits in it the following periods, formed using beginning-of-period information. Notice that the stock market valuation of the firm, VE, is dated at time t 1 so − that the market information set contains these forecasts. Then to calculate the implied level of profits for periods after t+1, I allow the average of Π it and Π to grow at the rate g . Let this average be Π¯ .12 i,t+1 it it The resulting discounted sequence of profits defines V in the following way: it V it = Π it +β t Π i,t+1 +β2 t (1+g it )Π¯ it +β3 t (b1+g it )2Π¯ it (1+g )3Π¯ b +β4(1+g )3Π¯ +β5 it it t it it t r¯ g¯ − 12In principle, theperiod for calculating V should beinfinity. However, analysts estimate g over a period of five years. Thus to match the period for which information exists, I set the forecast horizon to five years. A terminal value corbrection accounts for the firm’s value beyond year five. The correction assumes that the growth rate for profits beyond this five-year horizon is equal to thatfortheeconomy. Specifically,Icreateagrowthperpetuitybydividingthelastyearofexpected earnings by (r¯ g¯) where I assume that r¯is the mean nominal interest rate for the sample period − as a whole (about 15%, which includes a constant 8 % risk premium) and g¯ is the mean nominal growth rate of the economy for the sample period as a whole (about 6%). 19

The constant discount factor reflects a static expectation of the nominal interest rate over this five-year period; that is, I use the Treasury bill interest rate in year t (plus a fixed 8% risk premium as suggested by Brealey and Myers (2000) among others). D is the book value of debt, which is the sum of short- and long-term obligt • ations. C is net current assets, essentially cash on hand. t • I and K are capital expenditures and the current-cost net stock of property, • plant, and equipment (both excluding IT). In constructing the current-cost stock, I follow the perpetual inventory method and use an industry-level rate of economic depreciation derived from Hulten and Wykoff (1981). IT and KIT are IT expenditures and the current-cost net stock of IT. IT • outlays are from the Information Week survey. Again, in constructing the current-cost stock, I follow the perpetual inventory method, and I use a depreciation rate consistent with annual economic depreciation of 40%. IP and KIP are IP expenditures and the current-cost net stock of IP. IP • expendituresarethesumofR&Dandadvertising. Inconstructingthecurrentcost stock, I once more follow the perpetual inventory method, and I use a depreciation rate consistent with annual economic depreciation of 25%. The estimation sample includes all firms with at least four consecutive years of complete data. Four years of data are required to calculate first differences and to use lagged variables as instruments. I determine whether the firm satisfies the four-year requirement after I delete several observations that appear to be recording or reporting errors. Also, a few observations were deleted because V <0.13 13The data and programs for this study are available at www.insitesgroup.com/jason. b 20

We turn now to a description of the sample (table 1). The first two rows of the table define the different proxies for the intrinsic value of the firm. The total value of the firm consists of three components: the return to equity holders, VE or V; the return to debt holders, D; and an adjustment for net current assets, C. At both the b mean and the median values, the stock-market-based value is about three-quarters greater than the analyst-based value. Another notable feature of the sample is that spending on IT and IP is a large fraction of total investment spending at the mean and median values. 4.2 A Look at Analysts’ Forecasts To lay the foundation for using the analyst-based proxy for the intrinsic value of the firm, I compare the analysts’ forecasts of long-term growth, g , with realizations of it growth over a three-year period. My results show that analysts expected profits to grow at an annual rate of 11.3% for the mean firm in my sample. Over a three-year period, profits actually grew just a touch more slowly than estimated, at a rate of 11%. A visual comparison of actual and expected profit growth is revealing (figure 1). Threefeaturesofthedataareapparent. First,analystsdonotforecastnegativelongterm growth. That practice is sensible because such forecasts would be equivalent to saying that the company was essentially worthless. Second, analysts are loath to forecast exceedingly high long-term growth rates – another sensible practice. Few companies generate profit growth in excess of 30% and analysts cannot easily identify ex ante those that may realize such growth. Finally, actual profit growth is highly variable. Some companies grow at fast rates or suffer large retrenchments. TheOLS regression line describes the average relationship between the two variables. Actual and expected earnings growth are positively related – the slope of the regression line is 0.74 with a standard error of 0.15 – but realized earnings 21

growth often differs widely from analysts’ expectations.14 Moreover, the forecasts tend to be overly optimistic on average. In addition, analysts do not issue particularly accurate long-range forecasts; evidently, a lot can happen to a company over a three-year period, and most of what happens cannot be anticipated. However, the key requirement for my purposes is not forecast accuracy but the ability of analysts’ forecasts to capture the expected future returns on which the firm’s investment decisions are based. Judged according to this metric, analysts’ forecasts appear to be reasonable and informative assessments about companies’ future prospects. 5 Empirical Results Empirical results appear in two stages. I present OLS estimates of the empirical valuation equations in levels and within-groups (table 2). After establishing that these results are consistent with the sort of bias I have described, I present the results from two GMM estimators (table 3). First, I present a standard estimator thattakesfirstdifferencesintheempiricalequationsanduseslaggedcapitalstocksas instrumentalvariables. Forreasonsdescribedinsection3.2, thecoefficientestimates are likely to be downwardly biased in this case. Second, I present results from the system-GMM estimator. The diagnostic statistics indicate that system-GMM is well-behaved when the analyst-based measure of intrinsic value is used and that the results themselves are quite sensible. 5.1 OLS results In the specification in the first column of table 2, the coefficient on IT capital substantially and significantly exceeds unity, as does the coefficient on IP capital. Meanwhile, the estimate of the return on tangible capital is significantly less than 14I haveleft a few extreme observations out ofthe figure in orderto maintain a 1:1 aspect ratio. However, in fitting the regression, I have included these observations. 22

unity.15 Accordingtothisfirstpassatthedata, onedollarofITcapitalisassociated with about two dollars of unmeasured intangibles and one dollar of IP capital is associated with about one dollar of unmeasured intangibles. Thus, my basic results parallel those reported by Brynjolfsson and others even though (1) I do not use the same firms or estimation period, (2) I use different techniques for constructing the capital stocks, and (3) I use different regressors.16 The pattern of estimates in column 1 is similar to that in column 2, where V replaces VE. In particular, whether one uses an analyst-based or a market-based b definition of intrinsic value does not make much difference when one estimates in levels with OLS. However, the estimates on IT capital are considerably smaller in columns 3 and 4, where net current assets are accounted for in valuing the firm. Apparently, large IT capital stocks are associated with relatively abundant net current assets. Microsoft, for example, has a large stock of IT and has amassed a huge cashcushiononitsbalancesheet. Whenoneignoresthisrelationship, thecoefficient on IT capital picks up both the effect of intangibles and the omitted effect of net current assets. Thus, to develop an accurate picture of the role of IT capital, one must define the value of the firm carefully. So far the results have not controlled for unobserved heterogeneity. As a result, the estimates are difficult to interpret because the firm-specific effect is surely correlated with contemporaneous capital investments. To sweep out the firm-specific effect, I include within-group estimates presented in columns 5 and 6, which express all of the variables as deviations from within-firm means. In this case, the coefficients on IT are significantly negative in both specifications, and the coefficients on the other types of capital appear downwardly biased in the final column. These findings are not surprising because the capital stocks are highly persistent. 15Recall from the theoretical model that the beginning-of-period capital stocks belong on the right-hand side of the empirical valuation equation. According to equation (2), the beginningof-period capital stocks are equal to the difference between the current capital stock and current investment. Hence, the relevant regressors are (K I ) and so on. t t 16Icouldnotinvestigatetheeffectsofthesediffere − ncesbecauseBrynjolfssonandhiscollaborators declined to share their data. 23

Although unit-root tests are useless for short panels, the (unreported) AR(1) coefficient estimates from regressions of the current capital stocks on their first lags are all greater than 0.92. In such situations, the received wisdom from the literature on production function estimation indicates that one should expect downward bias from within-group estimates.17 5.2 GMM results The GMM estimates are useful because the within-group results do nothing to controlforsimultaneitybias. Suchbiasmustbeimportantbecausethevalueofthefirm (no matter how it is measured) and its investment policy are jointly determined. To see the intuition behind this point, compare the empirical valuation equation with an empirical investment equation based on Tobin’s Q. In the current setup, the firm’s intrinsic value is a function of the capital stock and investment, whereas the reverse is true in an equation that relates the investment rate to Tobin’s Q. Put simply, increases in market value may cause investment in IT (and other types of capital) but the reverse may be true, too. To deal with simultaneity bias (and eliminate the firm-specific effect at the same time), I estimate the first-differenced empirical valuation equations with GMM, using lagged levels of the capital stocks as instruments (table 3). LookingfirstattheSargantest,weseethatthep-valuesincolumns1and2ofthe table do not indicate a decisive rejection of the model’s overidentifying restrictions. This result does not mean, however, that the instruments are informative. Indeed, in unreportedresults, Iconfirmthatonecannotrejectweakinstrumentswhenusing the partial R2 or first-stage F-statistic as criteria. If the instruments used in the first-differencedequationsareweak,thentheresultsshouldbebiasedinthedirection 17In fact, it is not unusual for production function estimates of the capital share to go from 0.3 in levels to negative values in within-groups. By comparison, the magnitude of the bias in table 2 may seem surprisingly large, but one should keep in mind that production functions are estimated in logs. 24

ofwithin-groups.18 Indeed,acomparisonofcolumns1and2oftable3withcolumns 5 and 6 of table 2 shows that the direction and magnitude of the bias are similar in the first-differenced and within-group estimates. To address concerns about weak instruments, I use the system-GMM estimator in columns 3 and 4 of table 3. The Sargan test indicates that the model using VE is decisively rejected while the one using V is not. This result suggests that the instruments are correlated with the market’s, but not with the analysts’, misb measurement of companies’ intrinsic values. Why might this correlation occur? As I have argued, intangibles are difficult to value. If, say, the lagged change in the stock of intangibles is correlated with the extent to which the market overstates the firm’s intrinsic value, then the system-GMM estimator will tend to be rejected. In contrast, for reasons I have discussed, we have little reason to worry that analysts’ forecast errors are correlated with the lagged change in the stock of intangibles, and the Sargan test supports this conjecture. Therefore, my preferred estimates use the analyst-based measure of the firm’s intrinsic value. In column 4, the coefficient estimates on tangible and IP capital are insignificantly different from unity (although they are significantly different from zero), and the coefficient on IT capital is significantly greater than unity. Taken at face value, the coefficient on IT capital implies that organizational capital earns a 72% annual rate of return, a figure that may seem excessive. However, two points are worth nothing. First, the evidence of excess returns is statistically weak because the 95% confidence interval encompasses returns as low as 7%. Second, in my model the return on IT capital includes the effect of adjustment costs; indeed, that is how organizational capital is defined in equation (6). This possibility is seldom noted 18The technical explanation for this statement depends on two things. First, weak instruments willbias2SLSinthedirectionofOLS.Second,thefirst-differencedGMMestimatorcoincideswitha 2SLS estimator when the fixed effects are removed with the orthogonal deviations transformation; and OLS transformed to orthogonal deviations coincides with within-groups. Therefore, weak instruments will bias this particular 2SLS estimator (which coincides with first-differenced GMM) in the direction of within-groups. 25

because researchers usually estimate the return on ITwith a static production function, which assumes that capital is in a steady-state equilibrium so that adjustment costs are zero by construction.19 The coefficient on IP capital is less than unity, a result consistent with earlier findings that R&D earns a somewhat less than normal rate of return (see, for example, Hall 1993b). Perhaps firms cannot reap the full benefit of their IP investments becauseofthenonexclusivenatureofsometypesofR&D(see,forexample,Griliches 1979; Jaffe 1986; Bernstein and Nadiri 1989). However, one must exercise caution in drawing such a conclusion because the 95% confidence interval encompasses returns as large as 20%, a result more in line with the recent findings in Hand (2002). Finally, the estimate on tangible capital (excluding IT) is slightly less than unity. This outcome is consistent with lower rates of return on these types of capital and with recent studies in which estimated adjustment costs are quite modest in size (see, for example, Bond and Cummins 2000a). 6 Conclusion The dramatic rise of the stock market in the 1990s led some observers to conclude thatintangible capital wasan increasingly importantcontributor to thebottomline at many companies. However, the abrupt and sustained decline in the stock market that began in 2000 seemed to suggest just the opposite. This reversal highlighted thedesirabilityofalternativemeasurementstrategiesthatwoulddistinguishbetween the gyrations of the stock market and the value created by intangibles. My empirical approach offers such an alternative strategy and provides a different perspective about what intangibles are and how researchers can estimate their 19To see the implications of my approach in the context of a production function, notice that the marginal product of capital in my model is equal to the traditional user cost plus adjustment costs. Forexample,abstractingfromtaxesandsettingthepriceofcapitalequaltounity,Icalculate equilibrium condition in my model as ∂Π =r+δ + ∂C . As long as adjustment costs are ∂KIT KIT ∂KIT positive, the estimated return on capital can exceed (r+δ ), the usual required rate of return KIT under the equilibrium condition in production function framework. 26

return. In my model, intangible capital is not a distinct factor of production as is physical capital or labor; indeed, I assume that intangibles, unlike a computer or a collegegraduate, cannotbepurchasedinamarket. Norareintangiblessomekindof relabeled MFP. Rather, intangible capital is the “glue” that creates value from the usualfactorinputs. Thisperspectivenaturallysuggestsanempiricalmodelinwhich intangible capital is defined in terms of adjustment costs. As such, intangibles are the difference between the value of installed inputs and that of uninstalled inputs. In my empirical approach, I use two proxies for the intrinsic value of the firm, one based on the firm’s stock market value and the other based on analysts’ profit forecasts. In addition, I use a GMM estimation technique to control for unobserved heterogeneity and simultaneity bias in specifications with nearly integrated regressors. Using the analyst-based proxy and the GMM technique, I find no evidence of economically important intangibles associated with investment in intellectual property or physical capital apart from IT. However, my estimates suggest that organizational capital created by information technology generates a 72% annual rate of return. These findings come with a caveat. Controlling for simultaneity bias and unobserved heterogeneity removes intangibles that may have been swept into the error term, either as omitted variables or as part of the unobservable productivity shock. Nevertheless, alternative empirical approaches are unpalatable to say the least. Indeed, my OLS estimates seem to imply a strong role for intangibles, but they are unreliable because the value of the firm and its investment policy are jointly determined. In the end, how best to characterize the heterogeneity across firms and what role intangibles play remain open questions. Are intangibles part of the unobservable productivity shock? Are intangibles some fixed (or quasi-fixed) factor that interacts in complex ways with other inputs? The answers to these questions remain unresolved. 27

Finally, I consider whether my approach suggests ways to incorporate intangible capital into national income accounting. At a basic level, the implications are not encouraging. Factor inputs in the national accounts have prices, but such prices are often difficult to measure accurately. In contrast, my approach starts with the assumption that intangibles are nearly impossible to value as standalones. In particular, intangibles have unobservable shadow prices that depend on expectations. This setup makes the return on intangibles impossible to measure directly and uncertain by construction. These two features render intangible capital particularly ill suited to national income accounting. Nevertheless, my approach does suggest a road map for improving the national accounts. A key ingredient for better understanding the scope of intangibles is detailed data on the types of outlays that are closely connected with intangibles. In this regard, the national accounts could be considerably improved. I focused on IT, R&D, and advertising but it would be desirabletohavedataonothertypesofoutlays, suchaseducation, on-the-jobtraining programs, and the like. 28

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Table 1: Descriptive statistics for variables used in empirical analysis, 1991—97 (Millions of current dollars) Standard First Third Variable Mean Deviation Quartile Median Quartile (VE +D C)1 12,315 23,225 2,321 5,086 12,402 − (V +D C)2 7,208 15,308 1,179 2,942 7,379 − K 5,822 10,107 734 2,051 6,453 b KIT 922 2,013 135 337 802 KIP 1,726 4,289 0 292 1,304 I 769 1,696 107 298 729 IT 223 461 35.0 81.1 200 IP 383 997 0 53.0 255 Note. In this and subsequent tables, as well as in the chart, the sample contains firms with at least four years of complete data; N=253, for a total of 1,503 observations. 1. Stock-market-based value. 2. Analyst-based value.

Table 2: OLS estimates of the valuation equations, 1992—97 Level Within-group Dependent variable Dependent variable (VE +D ) (V +D ) (VE +D C ) (V +D C ) (VE +D C ) (V +D C ) t t t t t t − t t t − t t t − t t t − t (1) (2) (3) (4) (5) (6) b b b (K I ) 0.753 0.482 0.821 0.550 0.892 0.182 t t − (0.075) (0.064) (0.064) (0.048) (0.216) (0.169) (KIT IT ) 3.19 3.14 1.97 1.91 -6.67 -8.63 t t − (0.491) (0.416) (0.415) (0.316) (0.836) (0.656) (KIP IP ) 2.07 1.54 1.84 1.31 2.67 0.383 t t − (0.211) (0.179) (0.179) (0.136) (0.685) (0.537) Diagnostic Tests (p-values) Serial correlation1 First-order 0.070 0.066 0.143 0.169 0.930 0.886 Second-order 0.086 0.086 0.171 0.214 0.245 0.317 R¯2 0.451 0.401 0.474 0.457 0.107 0.171 Note. Year dummies are included (but not reported) in all specifications. Robust standard errors on coefficients are in parentheses. For estimation N=253 but we drop the first year, leaving a total of 1,250 observations. 1. The test for serial correlation in the residuals is asymptotically distributed as N(0,1) under the null of no serial correlation.

Table 3: GMM estimates of the valuation equations, 1992—97 First-differences System Dependent variable Dependent variable (VE +D C ) (V +D C ) (VE +D C ) (V +D C ) t t − t t t − t t t − t t t − t (1) (2) (3) (4) b b (K I ) 0.399 0.007 1.75 0.846 t t − (0.478) (0.197) (0.144) (0.135) (KIT IT ) -12.9 -11.3 0.725 1.72 t t − (1.33) (1.30) (0.390) (0.327) (KIP IP ) 9.72 3.93 0.652 0.684 t t − (1.80) (1.01) (0.273) (0.257) Diagnostic tests (p-values) Serial correlation First-order 0.656 0.634 0.883 0.644 Second-order 0.345 0.488 0.326 0.463 Sargan test1 0.047 0.360 0.000 0.073 Note. In the first-differences estimator, the instrumental variables are the levels of the capital stocks in periods t 3 and t 4. In the system estimator, the valuation equation in − − first-differences is estimated jointly with the valuation equation in levels. The instrumental variables for the first-differenced equation are the levels of the capital stocks in period t 3 − and t 4. The instrumental variables for the levels equation are the first-differences of the − capital stocks in period t 2. See also notes to table 2. − 1. Thetestoftheoveridentifyingrestrictions,calledaSargantest,isasymptoticallydistributed as χ2 , where n is the number of instruments and p is the number of parameters. (n p) −