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The Tax-adjusted Q Model with Intangible Assets

Author(s):
Sophia Chen, and Estelle Dauchy
Published Date:
June 2014
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I. Introduction

Temporary investment tax incentives have increasingly been used as an economic stimulus policy because reductions in the after-tax cost of capital provide strong incentives for investment (CBO 2008). Whether these tax incentives are an effective tool to increase investment remains a topic of continued interest.2 The workhorse structural model in this literature is the q theory of investment developed by Hayashi (1982), who shows that marginal q is a sufficient statistic for investment when capital accumulation is subject to convex adjustment costs. Hayashi further shows that when production and adjustment costs are both linear and homogeneous in capital, the unobserved marginal q is equal to the observed average q.

The objective of this paper is to incorporate recent developments on the measurement of intangible assets and reevaluate the effect of temporary bonus depreciation in the US in the early 2000s using an extended tax-adjusted q model with intangible assets. Our definition of intangible assets follows Corrado, Hulten, and Sichel’s (2005) and includes computerized information, scientific and non-scientific innovation property, such as research and development (R&D), and economic competencies such as firm-specific human capital, organizational skills, and advertising.3

Introducing intangible assets complicates an otherwise standard q model in several ways. First, the shadow value of intangible assets is reflected in the market value of the firm, which in turn affects marginal q and average q. Second, tax treatments of physical assets are very different from that of intangible assets. Physical assets are capitalized for both tax and accounting purposes, while many intangible assets are fully depreciated for tax purposes.4 Temporary bonus depreciation tax incentives, such as partial expensing for physical assets, have been increasingly used in the US and elsewhere as a way to stimulate investment in the short-term.5 Third, the after-tax cost elasticity of physical investment may differ between firms with high and low intangible intensity likely as a result of financial constraints.6

We have reasons to believe that extending q models to incorporate intangible assets has empirical significance. Stock prices of US corporations reflect large amounts of accumulated intangible assets especially since 1990s (Hall, 2001; Nakamura, 2001).7 Recent studies suggest that investment in intangible assets, measured by their book value, represent half of investment in total assets in aggregate (Corrado et al. 2005) and in corporations (Dauchy 2013).8 Despite their increasing importance, intangible assets are not yet fully reflected in firms’ balance sheets. According to standard accounting practices, only a limited set of intangibles are recognized as assets. Investment in most intangibles is expensed.9 As a result, the presence of intangible assets affects the market value and the book value of assets disproportionately, contaminating usual measures of average q.

We address these issues both theoretically and empirically. We show that under constant returns to scale, physical investment is determined by the after-tax marginal value of physical assets, (hereafter tax-adjusted marginal q, or the q term) and the after-tax unit cost of physical investment (the tax term). The empirical implementation needs to address two challenges. First, average q reflects both the market value and the book value of intangible assets. Although stock prices can be use as a proxy for the former, the latter needs to be measured using appropriate accounting methods. Second, the tax-adjusted marginal q is not equal to average q. We show that, when tax changes are temporary, the tax-adjusted marginal q can be approximated by the observed market value per unit of assets (hereafter average q), the after-tax unit cost of physical investment, and the share of intangible assets.

Several episodes of temporary changes in tax depreciation allowances in the early 2000s—known as “bonus depreciation”—provide an opportunity to implement this empirical strategy. Under the 2002 tax bill, firms could immediately deduct an additional 30 percent of investment purchases of qualified physical assets and depreciate the remaining 70 percent under standard depreciation schedules.10 The immediate deduction was increased to 50 percent under the 2003 tax bill. These tax treatments were explicitly temporary: only investments made through the end of 2004 qualified. The temporary nature of these policies and differentiated treatments of assets based on asset class fits precisely into our analytical framework.

We estimate the model using a new and comprehensive database. We combine firm-level data on physical investment and firm value obtained from Compustat with industry-level data on the stocks of physical and intangible assets constructed in Dauchy (2013),11 and industry-level tax parts based on detailed information on the tax treatment of different types of assets, from 1998 to 2006.

We report three main empirical results. First, investment responses to tax incentives differ between intangible-intensive firms and physical-intensive firms. Second, the investment elasticity is generally larger in intangible-adjusted q models than in physical-only q models. Using our preferred specification with intangibles, the estimated investment elasticity to the after-tax cost of physical capital is 1.9, compare to 1.7 implied by a physical-only model. Third, the differences between physical-only and intangible-adjusted estimations are more pronounced for intangible-intensive firms and large firms. Among top 500 intangible-intensive firms, the result from a physical-only estimation implies an investment elasticity of 3.3 while our preferred estimation implies an elasticity of 7.4.12

Our paper contributes to the growing literature on intangible assets. Although the increasing importance of intangible assets is well recognized (Fullerton and Lyon, 1988; Nakamura, 2001; Corrado et al., 2009; Dauchy, 2013), to our knowledge this paper is the first to consider how intangible assets affect the evaluation of investment tax incentives.

Our paper is closely related to a large literature that empirically estimates the relationship between investment and q. It is well known that measurement error in q and misspecification problems, such as stock price bubbles and the presence of financial constraints (Hennessy et al., 2007) potentially weaken the direct link between q and investment. Although a rich empirical literature has addressed this issue, our paper complements it by considering a specific source of misspecification–intangible assets–and proposes an empirical strategy to address this problem. Our paper also naturally fits into the literature that considers heterogeneous assets in q models (Wildasin, 1984; Hayashi and Inoue, 1991; Cummins and Dey, 1998; Bontempi et al., 2004). Our paper is unique in this latter group because it considers the role of intangibles both in theory and in empirical measures of q. By contrast, most research extending q-models with heterogeneous assets focus on physical assets. Bond and Cummins (2000) consider a q model with physical and intangible assets to ask a very different question: whether the stock market correctly incorporates earning potentials of intangible assets. They show that when the stock of physical and intangible stocks are time invariant, the proxy for marginal q in the standard q model can be adjusted by the ratio of intangible investment to the stock of physical assets. Our approach differs from theirs by using different Euler equations for physical and intangible assets instead of a single equation and by adjusting q for taxes.

Previous studies on the impact of tax incentives on investment generally find little impact, suggesting implausibly high adjustment costs (Caballero and Engel, 1999), physical assets heterogeneity (Bontempi et al., 2004), exceptionally low cash flows or asymmetries in taxable status (Edgerton, 2010), or low take-up rates (Knittel, 2007).13 Our results suggest that previous estimates of the impact of the early 2000’s bonus depreciation episodes underestimate the effects of temporary tax incentives, particularly among large and intangible-intensive firms.

Section II of this paper develops a tax-adjusted q model with intangible assets and discusses its new implications for empirical estimation. Section III describes our empirical implementation of the model and the data. Section IV presents the results. Section V concludes.

II. Intangible Assets and Tax-Adjusted Q: Theory

Our model extends the q model of investment (Hayashi, 1982) to incorporate intangible assets as an essential input of production. Even though intangible assets are fully expensed for tax purposes, the market value of a firm fully reflects the after-tax value of intangible assets.

A. The model

Consider a firm that produces with two types of assets Km (physical assets, m for measured) and Ku (intangible assets, u for unmeasured) with a constant return to scale production technology F (Km, Ku, X), where X represents the stochastic productivity of the firm. The firm decides to invest in each type of assets Im and Iu to maximize the expected present value of its future income stream:

subject to

for i = {m,u}. Et is the expectations operator conditional on information available in period t. τ is the corporate tax rate. The firm faces differentiated tax treatments on physical and intangible investment. ki represents investment tax credit for assets i. zm captures the present value of tax depreciation allowances on a dollar of investment in physical assets. In the US as in many other countries, expenditure on intangible assets is fully expensed and deducted from the firm’s tax base. This is captured by zu = 1. As is standard in the literature, adjustment cost is a quadratic and linear homogeneous function of assets i, and is parameterized as Ψ(It+si,Kt+si)=ψ2Kti(ItiKti)2. We do not allow for interrelated adjustment costs. βts is the (possibly stochastic and time-varying) real discount factor applicable in period t to s-period-ahead payoffs with βt0 = 1 and βtj = βt1 · βt+1,1βt+j-1,1.

An important feature of the model is that we allow firms to accumulate intangible assets even though in standard accounting practices intangible investment is fully expensed. This distinction creates a discrepancy between the economic book value, Ktu, and the accounting book value,

zero, of intangible assets unless intangibles fully depreciate in each period.

Let qti be the Lagrangian multiplier associated with the law of motion (2) of assets i = {m,u}. The first order conditions with respect to Iti and Kt+1u are, respectively,

and

From (3), we obtain the following expression for investment rates of each type of assets:

This equation suggests that the investment rate in assets i,Iti/Kti, depends on its own (before tax) marginal value qti/[(1τt)ψ] (henceforth the marginal q) adjusted for differences between tax and economic depreciation of assets (1ktiτtzti)/[(1τt)ψ] (henceforth the tax term).

Let Pt denote the end-of-period (i.e. ex-dividend) market value of the firm and qt be the ratio of Pt to the book value of total assets: qtPt/(Kt+1m+Kt+1u). Since qt reflects the average market value of per unit of assets, we henceforth call it average q. In our model average q captures the average value the firm’s total assets including physical and intangible assets. We show in the next Proposition that, under constant return to scale in the production technology and adjustment costs, average q is a weighted average of the marginal q in physical and intangible assets.

Proposition 1The ratio of the ex-dividend market value to the book value of assets is a weighted average of the book value of physical and intangible assets.

whereqt=(VtDt)/(Kt+1m+Kt+1u)is the average q andSt+1mKt+1m/[Kt+1m+Kt+1u]is the share of physical assets in total assets.

Proof See Appendix E.

This result also has empirical implications. It suggests that the average q accounts for the both the market value (in the numerator) and the book value (in the denominator) of intangible assets.

It is easy to see that the extended model nests as a special case a standing q model with only physical assets: setting the share of physical assets Stm=1 in (6) gives qt=qtm, which suggests that average q is equal to the marginal value of physical assets. The investment rate in expression (5) is then equivalent to

which implies that the investment rate in physical assets can be expressed as a function of average q and the tax treatment of physical assets. Comparing this to the general case (5), it is clear that when Stm1, using average q is not equal to the tax-adjusted q term. We defer implications of this result to the empirical section of the paper. We conclude from this subsection that properly accounting for intangible assets is essential to correctly evaluate the investment response to tax incentives.

B. Short-run Approximations of Long-lived Assets

We are interested in establishing an empirical relation in the extended q model. Following equation (5),

Even though the marginal value of physical assets qtm is not observed, basic properties of temporary investment tax incentives yield an analytical relationship between qtm and observed variables.

Suppose the government credibly announces a temporary change in bonus depreciation allowances, which temporarily increases ztm. The exact solution to the impact of this change on physical investment is complicated for two reasons. First, the optimality conditions (3) and (4) imply that investment decisions are both forward-looking and backward-looking. Second, if physical and intangible assets are imperfect substitutes, investment depends on the shadow value of both types of assets. For sufficiently temporary tax changes, short-run approximations simplify the problem considerably. In particular, it is a good approximation to replace the backward-looking variables Ktm and Ktu and the forwarding-looking variables qtm and qtu with their associated steady-state values Km, Ku, qm and qu. Approximating long-lived assets with their steady-state values is standard in many settings.14 When the economic rate of depreciation is low, the stock of assets is much larger than the flow of investment. As a result, Ktm and Ktu change only slightly in the short-run. The rationale for approximating qtm and qtu with their steady-state levels is less common. The rationale for this comes from the optimality conditions. Expanding (4) gives

for i = {m, u}. Because the tax change is temporary, the system will eventually return to its steady-state, which means that future values of variables remain close to their steady-state level. The approximation error comes from the first few terms in the expansion. If both the economic depreciation rate and the discount rate are small, then future terms would dominate the expression of qti and the approximation error would be small. The interpretation is that the value of long-lived assets is forward-looking and mostly influenced by long-run considerations. Therefore, the effect of a temporary tax change only has mild effects. 15 The approximation of Stm and qt follow immediately: StmSm=Km/(Km+Ku) and qt≈q=qmSm+qu(1-Sm).

C. Investment Responses to a Temporary Tax Change

We now derive an analytical expression for the physical investment rate. Following (3), the steady-state value of investment rate Ii / Ki is related to the marginal value qi:

for i = {m, u}, which immediately implies

where η[1kuτzu+(1τ)ψ(IuKu)]/[1kmτzm+(1τ)ψ(ImKm)].

Combining these two equations gives an identity to express qm through q :

This expression is more than an accounting identity. It expresses the unobserved variable, qm, though q and Sm. q can be observed—although imperfectly—from companies’ financial statements. To construct Sm requires time-series of physical and intangible assets. Constructing η requires the time-series of tax rates and investment rates on physical and intangible assets. It also requires assumption about the unknown parameter ψ. As we shall discuss in more details in Section IV, we adopt an empirical strategy to study the sensitivity of our key findings with respect to different assumptions on this term.

Following (8) and (9), we have

This expression highlights how the standard empirical relation between marginal q and average q can be restored in the extended model by scaling the average q by 1/[Sm+η(1Sm)] (hereafter “q factor”). The new q term depends on the share of physical assets Sm and the relative intensity of physical and intangible investment (through η) in a non-linear way.

III. Methodology and Data

A. Bonus Depreciation Allowances

Our theory yields a new empirical relation between investment and temporary tax incentives. Several episodes of temporary bonus depreciation allowances during the early 2000s allow us to estimate the model. In an attempt to spur business investment, the Job Creation and Worker Assistance Act, passed on March 11, 2002 created a 30 percent first-year “bonus depreciation” allowance, enabling businesses to write off immediately 30 percent of the cost of eligible capital goods. The provision applied retroactively to certain business property acquired after September 11, 2001 and to assets purchased before September 11, 2004, and placed in service before January 1, 2005.16 On May 28, 2003 the Jobs and Growth Tax Relief Reconciliation Act increased the first-year bonus depreciation allowance for capital put in place after that date to 50 percent and extended it to December 31, 2004. Eligible property for this special treatment included property with a recovery period of 20 years or less, water utility property, certain computer software, and qualified leasehold improvements. 17

Two aspects of the bonus depreciation allowance make it a policy experiment suitable for our analytical framework. First, the provision provided differential treatments based on assets types. Among qualifying property, the present value of the provision was, putting aside the possibility of taxable losses (Edgerton, 2010), an increasing function of the depreciable lives of qualified, short-lived, capital assets, including most equipment and software assets but excluding a majority of structures assets, such as buildings and pipelines. Second, because the provision was explicitly temporary (although the deadline was later extended), it provided an incentive to move investment forward.

B. Methodology

Empirical Specifications

Two empirical adjustments are necessary in the intangible-extended model. First, the average q of a firm—the ratio of market value to book value of assets should account for the book value of intangible assets (see discussions of Proposition 1). Second, the q term, which is a proxy for the marginal q, should be adjusted by a “q factor” capturing the firm’s intangible intensity (see equation (10)).

To evaluate the quantitative importance of these two adjustments, we first estimate a model with a physical-only q term and a physical-only q proxy. Then we estimate a model with a physical-only q term and an intangible-adjusted q proxy. Finally, we estimate a model with an intangible-adjusted q term and an intangible-adjusted q proxy.

Following equation (7), we specify a model with a physical-only q term as:

where Ii,tmKi,t1m is the investment rate in physical assets, qi,t1τt is the q term, 1Γj,tm1τt is the tax term with the present value of investment tax incentives Γj,tm=kj,tm+τtzj,tm, and Xk,i,t controls for firms’ idiosyncratic characteristics, including proxies for financial constraints CFi,tKi,t, cash flow normalized by physical assets, and Levi,t, the leverage ratio. We control for these firm-specific characteristics because previous literature has shown that financial constraints, such as measures of leverage and cash flows may lead to lower investment rates (Fazzari et al., 1988; Edgerton, 2010).18 Moreover, we following Christiano et al (2005) and Eberly et al. (2012) and include lagged investment rate as explanatory variable.19εi and εt are firm and time fixed effects, and εi,t is an idiosyncratic error. We defer discussions on our assumption on εi,t in the next subsection. In the period covered, no broad tax credits for physical investment have been available. 20 The tax term Γjm is computed as a weighted average of the present value of tax depreciation allowance: Γjm=Σa=1NmIajIjmza, where Ijm=Σa=1NmIaj is total investment in physical assets of industry j and za is the present value of tax depreciation allowances for a dollar of investment in asset a.

We specify a model with intangible-adjusted q term following equation (10).

where qi,tm=qi,tSjm+ηj(1Sjm),Sjm and ηj are the average value in industry j. Comparing equation (11) and (12) shows that the difference between a model with physical-only q term and a model with intangible-adjusted q term is captured by the difference between α and α=α*(S¯m+η¯(1S¯m))..

Discussion on Econometric Challenges

Estimating panel models such as (11) and (12) poses a number of econometric challenges. The basic issue is how to deal with the endogeneity of explanatory variables.

In (11), the error term εtit contain firm-specific effects εj and idiosyncratic shocks εit, similarly to ei and ei,t in (12). The choice of estimation method crucially depends on our assumption on the q term, the tax term, and components of the error term. For example, if the q term (similarly the tax term) is not strictly exogenous with respect to εi,t, then standard fixed effects or GLS models are inconsistent. In this case, it can be shown that the Generalized Method of Moments (GMM) estimator is consistent if a valid set of instruments is used (Arellano and Bond 1991, Blundell and Bond 2000). This result holds even when the lagged dependent variable and other endogenous explanatory variables are introduced into the model. If we assume that εi,t is not serially correlated, then properly lagged dependent variables can be used as instruments.

Previous empirical literature has extensively discussed sources of measurement errors in q models and suggested econometric remedies. Using average q as a proxy for marginal q is problematic in the presence of financial constraints (Fazzari et al., 1988), deviation from market price from fundamentals (Gilchrist et al., 1995; Bond and Cummins, 2000), or predetermined financial variables (Arellano and Bond, 1991). In our model, the presence of intangible assets introduces additional source of measurement error, because the market value captures the earning potentials of intangibles. If this error is permanent, using lagged values of average q alone cannot successfully correct for measurement errors.

Estimation methods

We estimate (11) and (12) using the system GMM estimator (Blundell and Bond 2000). Endogenous variables are contemporaneous values of firm-level financial variables, which include the q term, the cash flow rate, and the leverage ratio, and the lagged value of the investment rate. We use lagged values of instrumented variables from period t-4 or earlier values as instruments for the first-difference equations and lagged values of the first differences of instrumented variables from t-4 or earlier in the level equations. Exogenous variables include the tax terms and year dummies, and are also used as instruments.21

We report three diagnostic tests for each model we estimate. First, we report the AR(1) statistic proposed by Arellano and Bond (1991) and its p-value. These statistics test for first-order serial correlation in the full disturbance terms. Second, we report the AR(2) statistic and its p-value. These statistics test serial correlation in the innovation terms (εi,t and ei,t). Under the null hypothesis, both AR(1) and AR(2) have standard normal distributions. If AR(1) is rejected but not AR(2), variables dated t-3 or earlier are valid instruments of the first difference equations. Third, we report the Hansen statistic and its p-value to test whether our model is over-identified or if our instruments are jointly valid. This test is distributed as chi-square under the assumption that the set of instruments is uncorrelated with the error term. We note that a firm’s market value in excess of the value of its physical assets likely includes the value derived from intangible assets or overvaluation. Our empirical methodology does not allow us to distinguish these two; however, as long as we can appropriately capture for intangibles and if the remaining abnormal component in market value is not correlated with firms’ intangible intensity nor their tax treatment, our findings are still valid. This condition seems to hold in prior studies. For example, Bond and Cummins (2000) compare the stock market value to fundamental values. They show that the stock market does not seem to mismeasure the value of IT of intangible-intensive firms more than other firms.

C. Data

We use a comprehensive dataset on investment, assets, and relevant financial and tax information at the firm- and industry-level. The sample period is 1998 to 2006, which includes several episodes of temporary investment tax incentives, as described in Section IV.A. The main reason for starting in 1998 is the use of a comprehensive database on corporate intangible assets by industry developed during this period only (Dauchy, 2013).22 We end the sample period in 2006, before the start of the 2008 recession because economists recognize that this recession is different from previous business cycles in its causes and duration, and that the recovery has had unusual and unpredictable features (CBO, 2011).23 Our results are not sensitive to the use of an earlier ending year of 2004 or 2005.

Firm-specific variables are based on financial statements, obtained from Compustat.24 Like previous empirical studies using tax-adjusted q-models to estimate the impact of tax incentives on investment we exclude firms in industries that are subject to specific tax treatments, which are firms in North American Industry Classification System two-digit industry codes 52 (Finance and Insurance) and 22 (Utilities). Table 1 presents in details the definition of our variables of interest.

Table 1.Variables Definitions
Iijt/Kijt-1= capx128ijt / ppeveb187ijt = Investment rate;
qijt= MVAijt / BVAijt = Physical-only average q;
q*ijt= MVAijt / BVAijt * Smit = Average q adjusting for intangibles in BVA;
q*mijt= MVAijt / BVAijt * Smjt * q_factorjt = Intangible-adjusted marginal q;
(based on Chen & Dauchy model);
MVAijt= at6ijt + (csho25ijt *prcc199ijt) - ceq60ijt - txdb74ijt
= market value of assets;
BVAijt= ppeveb187ijt = book value of assets;
BVAaltijt= at6ijt = book value of assets;
(used in the alternative measure of physical-only q)
q_factorjt= 1 / {[Smjt + ηjt (1 - Smjt)](1 - τ)Ψ};
ηjt= [1 - kujt - τzujt + (1 - τ)Ψ(Iujt/Kujt)]/ [1 - kmjt - τzmjt + (1 - τ)Ψ(Imjt/Kmjt)];
CFijt/Kijt-1= (ib18ijt + dp14ijt)/ ppeveb187ijt
= Ratio of cash flow to capital stock;
Levijt= dltt9ijt / ceq607ijt = Leverage ratio
= Value of long-term debt to equity;
ETTjt and STTjt= (1 - τZmjt) / (1 - τ)
= Equipment and structures tax term.1
Sources: Compustat and authors’ calculations using various sources (see Appendix and Dauchy, 2013). Observations are at the firm level (subscript i) or industry level (subscript j). Compustat variables are listed as item and item #, where ppeveb (or item 187) = Property, plant and equipment (Ending balance, Schedule V); capx= Capital expenditures; at=Total assets; csho=Common shares outstanding; prcc=Annual price at closing; ceq=Total common and ordinary equity; txdb=Deferred taxes (Balance sheet); ib=Income before extraordinary items; dp=Depreciation and amortization; dltt9=Total long-term debt. All final variables constructed from Compustat are further winsorized at 2 percent at the top and bottom.

Equipment and structure tax terms are further defined in the Appendix.

Sources: Compustat and authors’ calculations using various sources (see Appendix and Dauchy, 2013). Observations are at the firm level (subscript i) or industry level (subscript j). Compustat variables are listed as item and item #, where ppeveb (or item 187) = Property, plant and equipment (Ending balance, Schedule V); capx= Capital expenditures; at=Total assets; csho=Common shares outstanding; prcc=Annual price at closing; ceq=Total common and ordinary equity; txdb=Deferred taxes (Balance sheet); ib=Income before extraordinary items; dp=Depreciation and amortization; dltt9=Total long-term debt. All final variables constructed from Compustat are further winsorized at 2 percent at the top and bottom.

Equipment and structure tax terms are further defined in the Appendix.

To construct industry-level physical assets, we use BEA’s capital flow table, which provides the distribution of investment in equipment, software and structures for 20 two-digit industries and 51 asset types. We isolate corporate from non-corporate investment using the annual BEA’s Surveys of Current Businesses. Stocks of physical assets are calculated based on the perpetual inventory method (PIM).25

Reliable measurement of intangible assets has not been available until recently because of data and methodology limitations. In this paper, we use a comprehensive methodology developed by Corrado, Hulten, and Sichel (2005, 2009) (hereafter CHS) for the United States, and increasingly used for other countries since then (Edquist, 2011; Marano and Haskel, 2006, 2009; Fukao et al., 2009; Jalava et al., 2007; Van Rooijen-Horsten, 2008). Following CHS, we obtain intangible investment by detailed intangible asset types and construct the stock of intangible assets based on the PIM.26 While CHS’s measures are at the aggregate level and end in 2000, we construct industry-level measures from 1998 to 2006 for 20 two-digit industries included in BEA’s physical asset tables (also excluding NAICS codes 52 and 22 for finance and insurance and utilities). Importantly, this method carefully identifies intangibles assets that are essential factors of production but have no physical appearance, for example, research and development (R&D), advertising, and investment in managerial skills.27 We obtain data for six broad types of intangible assets, including computerized information, scientific and non-scientific R&D, firm-specific human capital, organizational skills, and brand equity. None of these assets (except for software) is included in NIPA accounts. Instead self-developed intangible assets are expensed for accounting purposes (even if they provide long-term value to the firm), generally because they are difficult to measure. Likewise, purchased managerial skills are expensed for tax purposes. In sum, we carefully include intangible assets that are likely to be included in usual proxies for the numerator of q (the market value of assets), but are ignored in usual proxies of q. The data collection is, to our knowledge, the most comprehensive to this date for this time period. 28

It is worth noting that our methodology for calculating intangible assets and merging them with physical assets adjusts for potential discrepancies between tax and national accounts databases so that the distribution of investment across industries is consistent with our desire to correctly evaluate tax depreciation allowances at the industry level.29

Using our measure of physical and intangible assets, we calculate the share of physical assets in each industry. As shown in Table 1, we define the physical-only proxy for q as the ratio of the market value of equity and debt to the book value of physical assets. For the book value of physical assets we experimented with proxies generally used in the literature, but chose to present results based on the book value of plant, property, and equipment.30 To construct the book value of assets including intangible assets we scale a firm’s book value of physical assets by the industry-level ratio of physical assets to total assets (this ratio is defined as Sjm in our model). We denote by q* this intangible-adjusted q proxy. Finally, we adjust q* by the “q factor” and denote it by q*m (see Table 1 for details).

The variation of tax depreciation allowances by industry and over time is calculated based on the methodology explained and used in previous literature (House and Shapiro, 2008; Edgerton, 2010). We defer details on tax depreciation allowances and macroeconomic variables to Appendix B, C, and D.

D. Summary Statistics

As shown in Table 1, we define company-level data similarly to other papers using Compustat (Bond and Cummins 2000; Desai and Golsbee 2004; Edgerton 2010). It is important to note that compared to the data used in previous studies, the main additional, sources of variation among our explanatory variables is both at the industry-level and over time, depending on the q component or the tax component of tax-adjusted q. The main source of variation in the two intangible-adjusted terms (qijt*andqijt*m), in addition to the standard variation in the physical-only proxy for q, comes from the ratio Sjm of physical to total assets and the adjustment factor ηjt (or, equivalently, from the “q factor”). The variation in Sjm is essentially at the industry level because the composition of asset stocks does not change much over time. The variation of ηjt includes an additional element that makes it vary over time, in addition to across industries, because the present value of depreciation allowances Zjtm has been significantly increased from 2000 to 2004, due to temporary investment tax incentives (bonus depreciation) and reduced afterwards to levels under current law. The main source of variation in the ETT term is both at the industry-level and over time, again, due to temporary tax incentives.31 The variation in the STT term is mainly across industries, as few structures assets were eligible for bonus depreciation. It is important to note at this point that our model directly implies that the measurement error in physical-only q proxy is correlated with the tax term through Sjm and Zjtm, both of which are in the adjustment term ηjt. Therefore, we believe (and further discuss in the results) that our ability to empirically proxy for these factors reduces the measurement error in the q term.

We present summary statistics in Table 2. The investment rate, the q term as well as the equipment and structure terms are very similar to those found in previous papers (Bond and Cummins, 2000; Desai and Goolsbee, 2004; Edgerton, 2010). Measures of q based on financial statements greatly suffer from extreme values. To deal with outliers, we follow the literature by winsorizing the data at the two percent level.32 Recall that, although we experimented with multiple definitions for the physical-only q, we chose to present results where we proxy for the book value of physical assets with the value of property plant and equipment. This variable is generally much smaller than total assets (which is the other commonly used proxy for the denominator of q), implying a value of average q about 5 times larger than that of based on total assets.33 Moreover, the use of the book value of physical assets (qijt) is more relevant to our model than that of financial reports of total assets because we can use our industry-level share of physical assets to recover a value of the book value of assets including intangibles (i.e. qijt*). The resulting proxy for average q is skewed towards the upper end of the distribution, which is also typical in other literature.34

Table 2.Summary Statistics, 1998-2006
AllTop 3500Top 1500Top 500
N=45,064N=35,732N=23,753N=10,691
VariableMedian /MeanStd. Dev.Median /MeanStd. Dev.Median /MeanStd. Dev.Median /MeanStd. Dev.
Panel A: All firms
Iijt/Kijt-10.2090.3740.2010.3490.1860.3160.1730.290
qijt1/4.45/19.257.04.38/18.455.54.30/17.553.03.9/15.846.8
q*ijt1/3.66/15.746.33.62/15.045.03.52/13.341.03.28/12.138.0
q*mijt1/4.19/18.153.54.15/17.452.14.01/15.447.53.75/14.044.2
q_factorjt1.1420.0801.1410.0801.1410.0801.1420.079
ηjt1.3740.1081.3760.1091.3770.1091.3780.111
CFijt/Kijt-1−0.8954.706−0.6074.191−0.4083.638−0.3203.408
Levijt0.4051.3070.4501.3230.4851.3090.5151.286
Smjt0.8330.0790.8340.0790.8340.0790.8330.079
ETTjt1.1530.0751.1540.0751.1530.0751.1510.072
STTjt1.4850.0521.4850.0521.4860.0511.4860.050
Panel B: Intangible-intensive firms
Iijt/Kijt-10.1950.3590.1830.3240.1700.2900.1600.261
qijt1/5.38/17.742.95.35/16.941.55.34/16.340.24.94/15.639.3
q*ijt1/4.16/13.833.94.17/13.232.74.1/12.130.03.81/11.427.9
q*mijt1/5.01/16.640.45.02/15.939.04.92/14.535.84.59/13.733.4
q_factorjt1.2050.0341.2040.0341.2030.0351.2010.035
ηjt1.3290.1061.3330.1081.3340.1091.3390.113
CFijt/Kijt-1−0.8744.600−0.5053.846−0.3183.330−0.2703.171
Levijt0.3211.2000.3641.2290.3981.2550.4291.227
Smjt0.7730.0120.7730.0120.7740.0120.7740.012
ETTjt1.1190.0181.1190.0181.1190.0171.1200.017
STTjt1.5050.0131.5050.0131.5050.0131.5050.012
Panel C: Physical-intensive firms
Iijt/Kijt-10.2190.3570.2140.3370.2000.3130.1900.301
qijt1/2.81/14.246.72.82/13.744.32.74/13.12.61/11.912.036.4
q*ijt1/2.6/12.539.52.63/12.137.32.58/10.12.51/9.359.327.7
q*mijt1/2.71/13.644.32.75/13.141.82.68/10.92.61/10.110.131.6
q_factorjt1.0510.0461.0500.0461.0490.0461.0500.047
ηjt1.4360.0941.4370.0961.4380.0951.4380.098
CFijt/Kijt-1−0.5983.824−0.4163.507−0.2773.162−0.1812.677
Levijt0.5441.4480.5881.4430.6281.3740.6531.364
Smjt0.9250.0580.9260.0580.9280.0580.9270.059
ETTjt1.2150.0981.2150.0971.2140.0971.2090.097
STTjt1.4470.0711.4470.0701.4480.0701.4490.071
Notes:

Our different proxies of q are heavily skewed. The skewness of q has been shown in prior papers using similar dataset. Instead of top censoring the data, we winsorize it at 2 percent and show both median and mean in this table. The skewness is reduced with higher levels of winsorization (5 percent and 10 percent). However, higher levels of winsorization do not affect our baseline regression results.

Notes:

Our different proxies of q are heavily skewed. The skewness of q has been shown in prior papers using similar dataset. Instead of top censoring the data, we winsorize it at 2 percent and show both median and mean in this table. The skewness is reduced with higher levels of winsorization (5 percent and 10 percent). However, higher levels of winsorization do not affect our baseline regression results.

The investment rate has decreased over time to its lowest rate in 2003 and has continuously increased afterwards, although the rate in 2006 was still slightly smaller than that of the pre-2000 bubble. The sharpest reduction occurred during the 2001 recession, when firms’ investment rate was almost halved in one year.35 This is not surprising given the much smaller growth rate of GDP, and is in spite of a reduced long-term interest rate.36 Also, compared to the whole sample of corporations, top firms seem to have smaller investment rates, higher leverage, and more cash flows.

On average the intangible assets intensity of assets stocks and the tax cost-effectiveness of investment (reflected by smaller equipment tax terms) is not significantly different for large firms than for other firms.

Figures 1 and 2 show the variation of intangible intensity over time and by industry among intangible-intensive industries (Fig. 1) and physical-intensive industries (Fig. 2). These figures clearly show that most of the variation is between industries rather than over time. We see large and persistent differences in intangible intensity across industries. Among intangible-intensive industries, intangible assets represent close to a quarter of total assets in manufacturing, wholesale trade, information, and professional, scientific, and technical services. In contrast, physical assets represent over 97 percent of total assets in agriculture, mining, and real estate. In most industries, the intangible share is relatively stable overtime. In general, intangible share saw a modest increase at the beginning of the sample period but stabilized since the early 2000s.

Figures 3 to 5 show the interquartile range, the mean, and the median of the physical-only q proxy and the two intangible-adjusted q terms (q* and q*m) by industry, among firms in the sample. All three proxies feature large cross-sectional variation both within industry and across industries. Not surprisingly, adjusting for intangible assets affects the q proxy of intangible-intensive industries more than that of physical-intensive industries.

IV. Results

A. Baseline Results

We present our main results in Tables 3 to 6 for estimations using different samples of firms based on size and intangible intensity.37 Our results highlight how estimated investment responses to tax incentives differ before and after adjusting for intangible assets. As explained in the methodology section, we include the lagged value of the investment rate. All results are consistent with the lagged investment effect, providing evidence of a Christiano et al. (2005) type of investment adjustment costs.38

Table 3.System GMM Regressions, Top 500 Firms*
Physical-Only Q ProxyIntangible-Adjusted Q Proxy
Physical-Only Q TermPhysical-Only Q TermIntangible-Adjusted Q Term
IndependentAll FirmsIntangible-Intensive FirmsPhysical-Intensive FirmsAll FirmsIntangible-Intensive FirmsPhysical-Intensive FirmsAll FirmsIntangible-Intensive FirmsPhysical-Intensive Firms
Variables(1)(2)(3)(4)(5)(6)(7)(8)(9)
qijt/(1-τt)0.0010.002***0.003***
[0.001][0.000][0.001]
q*ijt/(1-τt)0.002***0.003***0.003***
[0.001][0.001][0.001]
q*mijt/(1-τt)0.002***0.003***0.003***
[0.000][0.001][0.001]
ETTjt−0.383***−0.894−0.172−0.435***−2.051***−0.288**−0.423***−2.016***−0.278**
[0.139][0.685][0.119][0.112][0.676][0.123][0.113][0.681][0.121]
STTjt−1.152***−1.604**−0.829***−1.061***−1.832***−1.017***−1.054***−1.811***−1.012***
[0.208][0.672][0.211][0.182][0.512][0.198][0.182][0.520][0.196]
CFijt/Kijt-1−0.025***−0.022**−0.017−0.0000.007−0.007−0.0000.006−0.006
[0.008][0.010][0.015][0.008][0.010][0.009][0.008][0.010][0.009]
Levjt−0.0060.044***0.0180.026**0.024**0.054**0.025**0.024**0.052**
[0.016][0.016][0.032][0.011][0.012][0.024][0.011][0.012][0.023]
Lag (Iijt/Kijt-1)0.039−0.0850.251*0.228***−0.0100.1620.228***−0.0190.166
[0.080][0.090][0.137][0.075][0.082][0.107][0.075][0.085][0.108]
Const.2.312***3.537**1.542***2.177***5.167***1.946***2.156***5.097***1.927***
[0.465][1.657][0.435][0.400][1.429][0.426][0.402][1.446][0.422]
Obs.10,7455,5383,67410,9625,7523,61710,9625,7523,617
N. of fixed effects1,8189997471,8451,0247501,8451,024750
AR(1)−2.775−0.391−3.432−5.125−1.716−3.356−5.096−1.593−3.355
p-val (AR(1))0.005520.6960.0006002.98e-070.08620.0007923.46e-070.1110.000794
AR(2)−2.633−2.690−1.3110.02840.829−0.1320.03310.818−0.0731
p-val (AR(2))0.008460.007150.1900.9770.4070.8950.9740.4130.942
Hansen123.995.5777.2681.0889.8088.4381.6591.3489.46
p-val0.0004340.06400.4380.3240.1330.1560.3080.1110.139

qijt/(1-τt) is the after-tax physical-only q; q*ijt/(1-τt) adjusted for the book value of intangible assets, q*mijt/1-τt) adjusted for the book value of intangible assets and the “q factor” that accounts for the difference between average q and marginal q.

Firm-level variables are winsorized each year at the 2 percent level on both sides.

Intangible intensity is defined based on the industry-level ratio of physical to total assets stocks (denoted Smjt in the model): if a company’s industry-level physical to total asset stock ratio is greater than the median in the sample, it belongs to a physical-intensive industry and to an intangible-intensive industry otherwise.

Top firms are selected each year based on total assets.

Standard errors (in brackets) are clustered at the firm level, *** for p<0.01, ** for p<0.05, * for p<0.1.

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1).

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1). The Hansen statistic is a test of overidentification restrictions, which is distributed as chi-square under the assumption that the set of instruments is uncorrelated with the error term.

Instrumented variables are Lag (Iijt/Kijt-1), qijt/(1-τt), q*ijt /(1-τt), q*mijt/(1-τt), CFijt/Kijt-1, and Levjt. Instruments for the first difference equation are lagged values of instrumented variable. We use the fourth lags and earlier values. Instruments for levels equation include a constant, ETT, STT, year fixed effects, and one lag difference of instrumented variables.

qijt/(1-τt) is the after-tax physical-only q; q*ijt/(1-τt) adjusted for the book value of intangible assets, q*mijt/1-τt) adjusted for the book value of intangible assets and the “q factor” that accounts for the difference between average q and marginal q.

Firm-level variables are winsorized each year at the 2 percent level on both sides.

Intangible intensity is defined based on the industry-level ratio of physical to total assets stocks (denoted Smjt in the model): if a company’s industry-level physical to total asset stock ratio is greater than the median in the sample, it belongs to a physical-intensive industry and to an intangible-intensive industry otherwise.

Top firms are selected each year based on total assets.

Standard errors (in brackets) are clustered at the firm level, *** for p<0.01, ** for p<0.05, * for p<0.1.

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1).

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1). The Hansen statistic is a test of overidentification restrictions, which is distributed as chi-square under the assumption that the set of instruments is uncorrelated with the error term.

Instrumented variables are Lag (Iijt/Kijt-1), qijt/(1-τt), q*ijt /(1-τt), q*mijt/(1-τt), CFijt/Kijt-1, and Levjt. Instruments for the first difference equation are lagged values of instrumented variable. We use the fourth lags and earlier values. Instruments for levels equation include a constant, ETT, STT, year fixed effects, and one lag difference of instrumented variables.

Table 4.System GMM Regressions, Top 1500 Firms*
Physical-Only Q ProxyIntangible-Adjusted Q Proxy
Physical-Only q TermPhysical-Only Q TermIntangible-Adjusted Q Term
Independent

Variables
All FirmsIntangible-Intensive FirmsPhysical-Intensive FirmsAll FirmsIntangible-Intensive FirmsPhysical-Intensive FirmsAll FirmsIntangible-Intensive FirmsPhysical-Intensive Firms
(1)(2)(3)(4)(5)(6)(7)(8)(9)
qijt/(1-τt)0.002***0.002***0.002**
[0.000][0.001][0.001]
q*ijt/(1-τt)0.002***0.002***0.002***
[0.000][0.001][0.001]
q*mijt/(1-τt)0.001***0.002***0.001***
[0.000][0.000][0.001]
ETTjt−0.368***−0.993*−0.219***−0.421***−1.799***−0.251***−0.412***−1.745***−0.252***
[0.095][0.546][0.078][0.078][0.477][0.076][0.079][0.483][0.076]
STTjt−1.202***−1.299***−0.856***−1.098***−1.556***−0.802***−1.098***−1.519***−0.804***
[0.147][0.427][0.141][0.129][0.407][0.136][0.129][0.413][0.136]
CFijt/Kijt-1−0.006−0.017−0.014−0.000−0.005−0.013−0.001−0.006−0.012
[0.008][0.011][0.013][0.007][0.010][0.010][0.007][0.010][0.009]
Levjt0.021*0.024*0.0090.026**0.0160.0160.026**0.0160.015
[0.013][0.014][0.021][0.011][0.013][0.019][0.011][0.013][0.019]
Lag (Iijt/Kijt-1)0.157**−0.0020.345***0.274***0.0700.428***0.271***0.0700.426***
[0.063][0.085][0.103][0.055][0.064][0.091][0.055][0.064][0.092]
Const.2.322***3.170***1.632***2.222***4.482***1.580***2.213***4.365***1.588***
[0.329][1.175][0.294][0.283][1.091][0.291][0.284][1.108][0.291]
Obs.23,91812,2268,47224,05012,1908,58724,05012,1908,587
N. of fixed effects4,1862,2451,7704,1992,2281,8014,1992,2281,801
AR(1)−5.472−1.767−4.012−6.807−2.944−4.592−6.787−2.924−4.571
p-val (AR(1))4.44e-080.07736.03e-0500.003244.38e-0600.003464.85e-06
AR(2)−1.634−1.724−0.9200.770−0.01300.0002320.7230.00470−0.0276
p-val (AR(2))0.1020.08470.3580.4410.9901.0000.4690.9960.978
Hansen105.097.9198.83100.494.3099.57101.095.71100.2
p-val0.01540.04610.04040.03200.07600.03620.02920.06290.0329

qijt/(1-τt) is the after-tax physical-only q; q*ijt/(1-τt) adjusted for the book value of intangible assets, q*mijt/1-τt) adjusted for the book value of intangible assets and the “q factor” that accounts for the difference between average q and marginal q.

Firm-level variables are winsorized each year at the 2 percent level on both sides.

Intangible intensity is defined based on the industry-level ratio of physical to total assets stocks (denoted Smjt in the model): if a company’s industry-level physical to total asset stock ratio is greater than the median in the sample, it belongs to a physical-intensive industry and to an intangible-intensive industry otherwise.

Top firms are selected each year based on total assets.

Standard errors (in brackets) are clustered at the firm level, *** for p<0.01, ** for p<0.05, * for p<0.1.

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1).

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1). The Hansen statistic is a test of overidentification restrictions, which is distributed as chi-square under the assumption that the set of instruments is uncorrelated with the error term.

Instrumented variables are Lag (Iijt/Kijt-1), qijt/(1-τt), q*ijt /(1-τt), q*mijt/(1-τt), CFijt/Kijt-1, and Levjt. Instruments for the first difference equation are lagged values of instrumented variable. We use the fourth lags and earlier values. Instruments for levels equation include a constant, ETT, STT, year fixed effects, and one lag difference of instrumented variables.

qijt/(1-τt) is the after-tax physical-only q; q*ijt/(1-τt) adjusted for the book value of intangible assets, q*mijt/1-τt) adjusted for the book value of intangible assets and the “q factor” that accounts for the difference between average q and marginal q.

Firm-level variables are winsorized each year at the 2 percent level on both sides.

Intangible intensity is defined based on the industry-level ratio of physical to total assets stocks (denoted Smjt in the model): if a company’s industry-level physical to total asset stock ratio is greater than the median in the sample, it belongs to a physical-intensive industry and to an intangible-intensive industry otherwise.

Top firms are selected each year based on total assets.

Standard errors (in brackets) are clustered at the firm level, *** for p<0.01, ** for p<0.05, * for p<0.1.

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1).

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1). The Hansen statistic is a test of overidentification restrictions, which is distributed as chi-square under the assumption that the set of instruments is uncorrelated with the error term.

Instrumented variables are Lag (Iijt/Kijt-1), qijt/(1-τt), q*ijt /(1-τt), q*mijt/(1-τt), CFijt/Kijt-1, and Levjt. Instruments for the first difference equation are lagged values of instrumented variable. We use the fourth lags and earlier values. Instruments for levels equation include a constant, ETT, STT, year fixed effects, and one lag difference of instrumented variables.

Table 5.System GMM Regressions, Top 3500 Firms*
Physical-Only Q ProxyIntangible-Adjusted Q Proxy
Physical-Only Q TermPhysical-Only Q TermIntangible-Adjusted Q Term
IndependentAll FirmsIntangible-Intensive FirmsPhysical-Intensive FirmsAll FirmsIntangible-Intensive FirmsPhysical-Intensive FirmsAll FirmsIntangible-Intensive FirmsPhysical-Intensive Firms
Variables(1)(2)(3)(4)(5)(6)(7)(8)(9)
qijt/(1-τt)0.001***0.001***0.001**
[0.000][0.000][0.001]
q*ijt/(1-τt)0.001***0.002***0.002**
[0.000][0.001][0.001]
q*mijt/(1-τt)0.001**0.001***0.002**
[0.000][0.000][0.001]
ETTjt−0.527***−1.475***−0.323***−0.547***−1.823***−0.277***−0.544***−1.785***−0.283***
[0.088][0.447][0.072][0.083][0.427][0.068][0.086][0.431][0.069]
STTjt−1.319***−1.669***−0.911***−1.348***−1.724***−0.904***−1.352***−1.697***−0.908***
[0.136][0.444][0.129][0.134][0.410][0.120][0.135][0.415][0.122]
CFijt/Kijt-1−0.011−0.019*−0.016−0.014*−0.021*−0.028***−0.015*−0.021*−0.029***
[0.008][0.011][0.010][0.008][0.013][0.010][0.008][0.013][0.010]
Levjt0.026**0.0190.0200.026**0.023*−0.0020.027**0.023*−0.002
[0.011][0.013][0.018][0.011][0.013][0.019][0.011][0.013][0.018]
Lag (Iijt/Kijt-1)0.210***0.0730.380***0.191***0.0700.321***0.189***0.0710.314***
[0.052][0.074][0.102][0.054][0.073][0.089][0.054][0.072][0.090]
Const.2.690***4.283***1.841***2.756***4.764***1.787***2.762***4.679***1.806***
[0.306][1.132][0.284][0.299][1.056][0.257][0.304][1.069][0.261]
Obs.35,69218,06312,78135,78917,98612,95235,78917,98612,952
N. of fixed effects6,6933,4982,8466,7033,4772,8746,7033,4772,874
AR(1)−7.030−2.961−4.774−6.628−3.065−4.769−6.580−3.087−4.692
p-val (AR(1))00.003071.80e-0600.002171.85e-0600.002022.70e-06
AR(2)−0.338−0.8690.407−0.538−1.0260.116−0.660−1.012−0.0271
p-val (AR(2))0.7350.3850.6840.5900.3050.9080.5100.3120.978
Hansen149.498.34104.4142.789.51101.3142.888.87102.7
p-val1.06e-060.04340.01715.75e-060.1380.02775.60e-060.1480.0225

qijt/(1-τt) is the after-tax physical-only q; q*ijt/(1-τt) adjusted for the book value of intangible assets, q*mijt/(1-τt) adjusted for the book value of intangible assets and the “q factor” that accounts for the difference between average q and marginal q.

Firm-level variables are winsorized each year at the 2 percent level on both sides.

Intangible intensity is defined based on the industry-level ratio of physical to total assets stocks (denoted Smjt in the model): if a company’s industry-level physical to total asset stock ratio is greater than the median in the sample, it belongs to a physical-intensive industry and to an intangible-intensive industry otherwise.

Top firms are selected each year based on total assets.

Standard errors (in brackets) are clustered at the firm level, *** for p<0.01, ** for p<0.05, * for p<0.1.

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1).

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1). The Hansen statistic is a test of overidentification restrictions, which is distributed as chi-square under the assumption that the set of instruments is uncorrelated with the error term.

Instrumented variables are Lag (Iijt/Kijt-1), qijt/(1-τt), q*ijt /(1-τt), q*mijt/(1-τt), CFijt/Kijt-1, and Levjt. Instruments for the first difference equation are lagged values of instrumented variable. We use the fourth lags and earlier values. Instruments for levels equation include a constant, ETT, STT, year fixed effects, and one lag difference of instrumented variables.

qijt/(1-τt) is the after-tax physical-only q; q*ijt/(1-τt) adjusted for the book value of intangible assets, q*mijt/(1-τt) adjusted for the book value of intangible assets and the “q factor” that accounts for the difference between average q and marginal q.

Firm-level variables are winsorized each year at the 2 percent level on both sides.

Intangible intensity is defined based on the industry-level ratio of physical to total assets stocks (denoted Smjt in the model): if a company’s industry-level physical to total asset stock ratio is greater than the median in the sample, it belongs to a physical-intensive industry and to an intangible-intensive industry otherwise.

Top firms are selected each year based on total assets.

Standard errors (in brackets) are clustered at the firm level, *** for p<0.01, ** for p<0.05, * for p<0.1.

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1).

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1). The Hansen statistic is a test of overidentification restrictions, which is distributed as chi-square under the assumption that the set of instruments is uncorrelated with the error term.

Instrumented variables are Lag (Iijt/Kijt-1), qijt/(1-τt), q*ijt /(1-τt), q*mijt/(1-τt), CFijt/Kijt-1, and Levjt. Instruments for the first difference equation are lagged values of instrumented variable. We use the fourth lags and earlier values. Instruments for levels equation include a constant, ETT, STT, year fixed effects, and one lag difference of instrumented variables.

Table 6.System GMM Regressions, All Firms*
Physical-Only Q ProxyIntangible-Adjusted Q Proxy
Physical-Only Q TermPhysical-Only Q TermIntangible-Adjusted Q Term
IndependentAll FirmsIntangible-Intensive FirmsPhysical-Intensive FirmsAll FirmsIntangible-Intensive FirmsPhysical-Intensive FirmsAll FirmsIntangible-Intensive FirmsPhysical-Intensive Firms
Variables(1)(2)(3)(4)(5)(6)(7)(8)(9)
qijt/(1-τt)0.002***0.002***0.002**
[0.000][0.000][0.001]
q*ijt/(1-τt)0.002***0.002***0.002***
[0.000][0.001][0.001]
q*mijt/(1-τt)0.002***0.002***0.002**
[0.000][0.000][0.001]
ETTjt−0.614***−1.992***−0.336***−0.623***−2.036***−0.335***−0.616***−1.990***−0.338***
[0.084][0.448][0.071][0.081][0.446][0.070][0.084][0.450][0.071]
STTjt−1.485***−1.938***−1.025***−1.471***−1.962***−1.014***−1.482***−1.934***−1.020***
[0.134][0.446][0.130][0.133][0.444][0.129][0.134][0.448][0.130]
CFijt/Kijt-1−0.003−0.021**−0.013−0.002−0.021**−0.013−0.003−0.021**−0.014
[0.007][0.009][0.009][0.007][0.009][0.009][0.007][0.009][0.009]
Levjt0.040***0.034**0.048**0.039***0.033**0.047**0.040***0.034**0.047**
[0.011][0.013][0.024][0.011][0.013][0.024][0.011][0.013][0.024]
Lag (Iijt/Kijt-1)0.192***0.0650.364***0.198***0.0660.367***0.191***0.0650.363***
[0.048][0.064][0.087][0.048][0.064][0.086][0.048][0.064][0.087]
Const.3.029***5.261***2.003***3.017***5.345***1.982***3.026***5.252***1.998***
[0.300][1.146][0.278][0.295][1.140][0.276][0.299][1.151][0.278]
Obs.45,06422,70216,00545,06422,70216,00545,06422,70216,005
N. of fixed effects9,5875,0003,9379,5875,0003,9379,5875,0003,937
AR(1)−7.657−3.241−5.362−7.763−3.256−5.419−7.633−3.226−5.361
p-val (AR(1))00.001198.22e-0800.001136.00e-0800.001088.29e-08
AR(2)−0.136−1.5281.1620.0591−1.5161.249−0.144−1.5441.102
p-val (AR(2))0.8920.1260.2450.9530.1290.2120.8850.1220.270
Hansen174.499.7997.35170.5100.297.56173.2100.197.98
p-val1.04e-090.03500.05003.26e-090.03320.04861.51e-090.03360.0457

qijt/(1-τt) is the after-tax physical-only q; q*ijt/(1-τt) adjusted for the book value of intangible assets, q*mijt/(1-τt) adjusted for the book value of intangible assets and the “q factor” that accounts for the difference between average q and marginal q.

Firm-level variables are winsorized each year at the 2 percent level on both sides.

Intangible intensity is defined based on the industry-level ratio of physical to total assets stocks (denoted Smjt in the model): if a company’s industry-level physical to total asset stock ratio is greater than the median in the sample, it belongs to a physical-intensive industry and to an intangible-intensive industry otherwise.

Top firms are selected each year based on total assets.

Standard errors (in brackets) are clustered at the firm level, *** for p<0.01, ** for p<0.05, * for p<0.1.

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1).

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1). The Hansen statistic is a test of overidentification restrictions, which is distributed as chi-square under the assumption that the set of instruments is uncorrelated with the error term.

Instrumented variables are Lag (Iijt/Kijt-1), qijt/(1-τt), q*ijt /(1-τt), q*mijt/(1-τt), CFijt/Kijt-1, and Levjt. Instruments for the first difference equation are lagged values of instrumented variable. We use the fourth lags and earlier values. Instruments for levels equation include a constant, ETT, STT, year fixed effects, and one lag difference of instrumented variables.

qijt/(1-τt) is the after-tax physical-only q; q*ijt/(1-τt) adjusted for the book value of intangible assets, q*mijt/(1-τt) adjusted for the book value of intangible assets and the “q factor” that accounts for the difference between average q and marginal q.

Firm-level variables are winsorized each year at the 2 percent level on both sides.

Intangible intensity is defined based on the industry-level ratio of physical to total assets stocks (denoted Smjt in the model): if a company’s industry-level physical to total asset stock ratio is greater than the median in the sample, it belongs to a physical-intensive industry and to an intangible-intensive industry otherwise.

Top firms are selected each year based on total assets.

Standard errors (in brackets) are clustered at the firm level, *** for p<0.01, ** for p<0.05, * for p<0.1.

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1).

AR(1) and AR(2) are tests of first order and second order serial correlation of residuals, which under the null of no serial correlation are distributed as N(0,1). The Hansen statistic is a test of overidentification restrictions, which is distributed as chi-square under the assumption that the set of instruments is uncorrelated with the error term.

Instrumented variables are Lag (Iijt/Kijt-1), qijt/(1-τt), q*ijt /(1-τt), q*mijt/(1-τt), CFijt/Kijt-1, and Levjt. Instruments for the first difference equation are lagged values of instrumented variable. We use the fourth lags and earlier values. Instruments for levels equation include a constant, ETT, STT, year fixed effects, and one lag difference of instrumented variables.

Our key findings can be summarized as follows.

1. Investment responses to equipment tax incentives (hereafter ETT term) and structural tax incentives (hereafter STT term) differ between intangible-intensive firms and physical-intensive firms. This result holds both in the model with physical-only q term and models with intangible-adjusted q terms.

2. Estimated investment responses to both ETT and STT terms are generally larger in models with an intangible-adjusted q term than models with a physical-only q term, suggesting that using physical-only q term is likely to under estimate the response of investment to tax incentives. The differences between coefficients on ETT obtained in these estimations are generally larger for intangible-intensive firms, implying that the adjusting for intangible assets is more important for intangible-intensive firms.

3. Accounting for intangible assets affects the estimated impacts of the ETT and STT terms more for larger firms than for smaller firms.

4. Adjusting for the book value of intangible assets in the q proxy accounts for the majority of the difference between intangible-adjusted estimations and physical-only estimations.

5. The physical-only q proxy is correlated with the ETT and STT terms; therefore measurement errors in q affect estimates of the coefficients on ETT and STT terms.

We now discuss these findings in more details. We start by presenting results for large firms, and then compare them to results based on the whole sample. As is well documented in previous literature (Fazzari et al., 1988; Almeida et al., 2004, 2007), large firms are less likely to be financially constrained. As a result, their investment behavior may be more responsive to changes in tax incentives. On the other hand, if tax incentives somehow relax financial constraints, temporary tax incentives may have an impact on constrained firms’ investment behavior beyond that described by the neoclassical q-model of investment.39 By running separate regressions on large firms, we leave the data sort out which of these two opposite effects is larger.

Table 3 presents system GMM estimates among top 500 firms. The sample of top firms is selected in each year based on the size of total assets. Columns 1 to 3 are base on the model (equation 11) with a physical-only q proxy and physical-only q term, for all firms (column 1), intangible-intensive firms (column 2) and, physical-intensive firms (column 3). Intangible intensity is defined based on the industry-level ratio of physical to total assets stocks (denoted Sjtm in the model): if a company’s industry-level physical to total asset stock ratio is greater than the median in the sample, it belongs to a physical-intensive industry and to an intangible-intensive industry otherwise.40 Columns 4 to 6 are based on the model with an intangible-adjusted q proxy and physical-only q term (i.e. with q*). Columns 6 to 9 are base on the model with intangible-adjusted q proxy and intangible-adjusted q term (i.e. with q*m).41

In Column 1, the coefficients on the ETT and STT terms are significant and in the range of estimated values implied by previous papers (Edgerton 2010; Desai and Goolsbee 2004).42 However, the results vary significantly between intangible-intensive firms (column 2) and physical-intensive firms (column 3). While the coefficients on the STT term are always significant and larger for intangible-intensive firms than physical-intensive firms, the coefficients for the ETT terms are not significant. Moreover, the Hansen test decisively rejects the joint test of model and instrument validity for all firms (column 1), and for intangible-intensive firms at the 6% level (column 2). These results are consistent with the presence of an important measurement error component in the physical-only q term that is both persistent over time and correlated with our instruments, particularly for intangible-intensive firms.

Using the intangible-adjusted q proxy (q*), we obtain larger coefficients for both the ETT and the STT terms in regressions with all firms (comparing column 4 to column 1).

The difference between regressions with an intangible-adjusted q proxy and with a physical-only q proxy is larger for intangible-intensive firms (comparing column 5 to column 2). For intangible-intensive firms, the coefficients on the ETT and STT terms change from not significant (column 2) to large and significant in the model with q* (column 5). The Hansen test no longer rejects the validity of instruments. For physical-intensive firms, the coefficients on the ETT and STT terms also become larger than those using a physical-only q proxy, but the differences are less pronounced (columns 6 and 3). The Hansen test does not reject the validity of instruments in all samples.

Estimations with an intangible-adjusted q proxy and an intangible-adjusted q term (columns 7 to 9) lead to similar conclusions: the tax terms are larger than in models with a physical-only q proxy and the difference between the two models is again larger for intangible-intensive firms. Quantitatively, these estimates are very close to columns 4 to 6. This comparison suggests that after using more reliable proxies for the book value of intangible assets in calculating q, the additional gain from adjusting for the discrepancy between average q and marginal q is small (i.e., the additional gain from q* to q*m). This is not surprising considering that we have essentially used the same additional information on intangible assets (i.e. the share of intangible assets in total assets) for both adjustments. Another interesting result is that as the regressions move from models with a physical-only q to models with intangible-adjusted q terms (q* and q*m), coefficients on the cash flow ratio become less significant. This is consistent with our interpretation that intangible-adjusted q proxies suffer much less from measurement error than the physical-only proxy: cash flow contains less information on the future valuation of the firm that is not already included in our adjusted q terms.

Another implication of our results is that the measurement error in physical-only q term is correlated with the tax terms, contrary to what is assumed in previous papers (Desai and Goolsbee 2004, Edgerton 2010). One interpretation of this correlation is that the tax incentives on different types of physical assets are different. Firms differ in the composition of physical assets and this composition effect is likely to be correlated with intangible intensity. Because more intangible-intensive firms likely suffer from more measurement error in physical-only proxies of q, the effectiveness of after-tax costs of physical assets (captured by the ETT and STT terms) is more contaminated by it. Our results also confirm that accounting for intangible assets is more important for intangible-intensive firms than for physical-intensive firms.

We reach similar conclusions in results obtained from larger samples. Table 4 shows results for top 1500 firms, Table 5 for top 3500 firms, and Table 6 for all firms. In these regressions, models with intangible-adjusted q terms (q* and q*m) have larger coefficients on the ETT and STT terms than models with the physical-only q term. Again, the difference is larger for intangible-intensive firms than for physical-intensive firms. Similar to the top 500 sample, most of the difference can be captured by models where the denominator of the q term is adjusted for the book value of intangible assets. Further adjusting for the discrepancy between average q and marginal q delivers quantitatively similar results. The Hansen test in models with the adjusted q terms remains valid at the 3% level in most cases, although it is rejected for the sample of top 3500 firms and the full sample when intangible-intensive and physical-intensive firms are not separated (column 4). Finally, as in results with top 500 firms, the cash flow term loses its significance in models based on intangible adjusted q terms, suggesting that intangible-adjusted q more accurately informs about future firm’s valuation than physical-only q.

Another interesting result is that as we move from the largest firms to a more general, larger sample, the differences in estimated coefficients on the ETT and STT terms between models with physical-only q and intangible-adjusted q become less pronounced. This implies that in order to correctly estimate the investment response to tax incentives, accounting for intangible assets is more important for large firms than small firms. In other words, the bias in the estimated impact of tax incentives that result from models with a physical-only q term larger for larger firms than for smaller firms. One interpretation is that larger firms are less likely to be financially constrained; as a result, their investment response more closely resembles predictions from models without financial frictions such as ours. Our model is not aimed to study financial constraints directly; our results nevertheless imply that the interaction between financial constraints and intangible assets may be an important source of heterogeneous responses to tax incentives. We leave this interesting topic to future research.

B. Interpretations: The Economic Size of the Impact of Temporary Tax Incentives

The purpose of temporary tax incentives from 2001 to 2004 was to increase investment in the short term, reflected by the coefficients on the ETT. To interpret the size of the estimated effect of tax incentives, we look at the change in the ETT term from 2000 (i.e., one year before the first bonus depreciation incentive) to 2004 (the last year when the tax incentive was in effect) and to the change in the ETT term from 2004 to 2006 (when the tax incentive was almost fully phased out). These changes can be obtained from appendix tables A6 to A8. In addition, using changes in the average investment rates over the same periods (obtained in the same tables) and the estimated coefficients on the ETT terms, a simple back-of-the-envelope calculation can recover the impact of exogenous changes in the cost of capital on investment rate.43 For instance, for the sample of top 500 firms, the average ETT decreased by 0.025 units from 2000 to 2004. With an average value of the investment rate of 0.26 in 2000, the model with a physical-only q term (column 1) estimates that the investment rate increased by 0.0024, implying an after-tax cost elasticity of investment of 1.7. In models using q* and q*m (our preferred estimation), the estimated elasticity increases to 2.0 and 1.9 respectively.44 The differences between these estimations are more pronounced when we separate firms by intangible intensity. Among intangible-intensive firms, the physical-only model implies an elasticity of 3.3 while our preferred estimation implies an elasticity of 7.4. Among physical-intensive firms, the implied elasticity is 1.1 for the physical-only estimation and 1.7 for our preferred estimation.

V. Conclusion

This paper sheds new lights on the effectiveness of investment tax incentive policies. We evaluate how accounting for intangible assets affects estimations of investment responses to tax incentives. We collect a comprehensive database of corporate intangible assets from 1998 to 2006 using multiple sources of investment data. We develop a theoretical model of investment with intangible assets and an empirical methodology to estimate investment response to temporary tax incentives in the US in the early 2000s.

Our results suggest that intangible assets are an important source of heterogeneity of investment responses to tax incentives. Investment responses to tax incentives differ between intangible-intensive firms and physical-intensive firms. When the q-proxy reflects a model that explicitly accounts for intangible assets, our estimated investment responses to tax incentives are generally larger than when the q-proxy reflects a model without intangible assets. The difference between intangible-adjusted estimations and physical-only estimations are larger for intangible-intensive firms than for physical-intensive firms. This difference is also larger for larger firms than for smaller firms.

Appendix
Appendix A: Methodology for Measuring the Stocks and Flows of Intangible and Physical Assets

A. Intangible Assets

In this paper we construct a proxy for the stock and flow of intangible assets of US firms. We start from the methodology developed by Corrado et al. (2005, 2009) (hereafter CHS) for the United States and replicated in other countries (Edquist, 2011; Marano and Haskel, 2006, 2009; Fukao et al., 2009; Jalava et al., 2007; Van Rooijen-Horsten, 2008). We extend this methodology by focusing on US incorporated firms. We measure intangible assets by types of assets and by two-digit NAICS industries from 1998 through 2006. To our knowledge, this data collection methodology provides the most comprehensive measure of corporate intangible assets (to this date) for this time period.

Although we do not have direct access to corporations’ tax returns (which are Internal Revenue Service’s confidential documents), we believe that our careful collection of intangible assets closely covers companies that file Internal Revenue Service (IRS) tax form 1120 for tax purposes, and therefore pay the corporate tax. The CHS methodology uses various sources for intangible assets, including the Bureau of Economic Analysis (BEA)’s Survey of Current Businesses for intangibles that are included in national NIPA accounts as physical assets (e.g., computer software). Other sources for non-NIPA intangible assets are presented in Table A2. NIPA aggregate investment and capital stocks are based on data collected from either “establishments” or “companies.” In the Industry section of A Guide to the NIPA’s, the BEA states that45

Establishments are classified into an SIC industry on the basis of their principal product or service, and companies are classified into an SIC industry on the basis of the principal SIC industry of all their establishments. Because large multi-establishment companies typically own establishments that are classified in different SIC industries, the industrial distribution of the same economic activity on an establishment basis can differ significantly from that on a company basis.

This is very important because multi-establishment corporations (such as Multinational corporations or MNCs) can operate in industries that are radically different from their establishments (or branches); however, corporate tax filings are prepared by the parent company and the corporate group’s industry classification is generally that of the parent. For purposes of calculating tax allowances and the welfare impact of corporate taxation, we need to focus on industry classifications from tax filings, which may radically differ from filings in NIPA.

Nevertheless, the distribution found in NIPA accounts has at least one advantage over that found in tax filings. Tax filings are based on consolidated returns, including not only domestic corporations and their domestic subsidiaries, but also their foreign subsidiaries. By contrast, NIPA accounts only cover domestic operations. In order to accurately calculate depreciation allowances and the welfare impact of taxation, we are only interested in domestic corporations.

Fortunately, the BEA’s Survey of Current Businesses also collects information on the corporate status of the companies surveyed. Corporations—including parents and their subsidiaries—file tax returns separately from their owners. By contrast, non-corporate businesses (such as partnerships) do not pay the corporate tax. Since our focus is on the corporate sector, we start by separating corporate from non-corporate investment. Then we distribute corporate investment across industries based on NIPA accounts by assuming that intangible assets have the same distribution across sectors than equipment and software assets. The latter are obtained from the Bureau of Economic Analysis (BEA)’s current cost net stocks and investments in physical assets (as explained below); however, when industry classification of corporate investment is also available from the IRS/SOI, we use industry-level data from the Internal Revenue Service (IRS/SOI). This is the case for two intangible assets: research and development or R&D spending and advertising.

We recognize that the distribution of investment across industries might still suffer from classification error but we believe that our careful approach greatly reduces the industry distribution. To provide evidence that the remaining classification error is not large, we present in appendix table A1 a simple comparison of measuring corporate intangible investment from the corporate part of BEA’s Survey of Current Businesses as compared to IRS/SOI Tax Filings for R&D intangibles, which are common to both sources. The table shows that, although the distribution of R&D expenditures across industries is not precisely the same between BEA/NSF accounts and IRS tax filings, the industry ranking and the relative importance (size) of R&D across industries are generally preserved. For example, both in the IRS and the BEA’s distributions, the share of R&D spending is the largest for the manufacturing industry, followed by information and finance.

Table A1R&D Expenditures, By Industry: BEA/NSF vs. IRS/SOI ($ Mil. And % of All Industries) 1/
NSF/BEA1998199920002001
FIRE 2/1,7921,6994,1722,631
1.2%1.0%2.2%1.3%
Information10,05411,63311,10912,069
7.9%8.7%9.5%12.7%
Manufacturing (incl.)79,47585,54796,078101,099
Chemical manufacturing16.0%16.0%15.6%16.5%
Computer and electronic product manufacturing21.4%19.0%21.4%23.2%
Transportation equipment manufacturing14.2%14.8%12.7%11.6%
⇢ incl. aerospace4.4%3.3%2.2%2.2%
IRS/SOI
FIRE 2/1,3181,4241,6121,791
1.2%1.2%1.3%1.5%
Information12,16114,90818,42725,131
9.1%10.1%9.2%10.4%
Manufacturing (incl.)86,42888,23492,30486,279
Chemical manufacturing25.4%24.7%22.0%23.7%
Computer and electronic product
manufacturing18.5%18.3%16.5%19.1%
Transportation equipment manufacturing22.0%20.0%18.6%18.7%
⇢ incl. aerospace3.2%2.5%2.5%3.1%
Notes:

Sources: IRS/SOI: R&E tax credit claims and U.S. corporate tax returns claiming the credit, by selected NAICS industry; and National Science Foundation (used by the BEA): Table 5.1: Investment in R&D.

Finance, insurance, and real estate.

Notes:

Sources: IRS/SOI: R&E tax credit claims and U.S. corporate tax returns claiming the credit, by selected NAICS industry; and National Science Foundation (used by the BEA): Table 5.1: Investment in R&D.

Finance, insurance, and real estate.

Investment in physical assets (also referred to as tangible, or fixed assets) is also obtained from BEA’s NIPA accounts.

In order to accurately estimate the stock and the depreciation rate of intangible assets, whenever possible, we collect investment in intangible assets over as many years as their economic lives. When investment data in intangible assets is not available for all years, we extend the available data over time based on each industry’s growth rate of gross domestic value added, obtained from the BEA (see details below).

We obtain data for six broad types of intangible assets, including computerized information, scientific and non-scientific R&D, firm-specific human capital, organizational skills, and brand equity. None of these assets (except for software) is included in NIPA accounts. Instead they are directly expensed for accounting purposes, generally because they are difficult to measure. Table A2 presents in detail our sources for measuring various types of intangible assets, as well as the methodology we use to calculate the part of these assets that generates long-term revenue (and therefore can be considered as investment). CHS (2005) provide more details on the reason why these data provide a comprehensive measure of detailed intangible assets available. The first column shows non-NIPA intangible assets. The second column shows our data sources. The third column defines each intangible asset. Some corporate intangible assets can be directly measured. For other intangible assets, the disaggregation between the corporate and the non-corporate sectors is based on NIPA shares of physical assets between the corporate and the non-corporate sectors, and specified in column 4. This method is also used to separate corporate and non-corporate physical assets within industries (see appendix A2 on physical assets). Table A3 shows the total value and the average annual growth rate of investment in intangible assets by industry from 1998 to 2006. Over this period, investment in intangible assets amounted to $7.2 trillion, represented about 45 percent of total corporate investment, and grew at an average annual rate of 3.7 percent. Almost 47 percent of this investment was concentrated in 3 industries: finance and insurance, metals, machinery, electronic, electrical, and transportation equipment manufacturing, and information.

Table A2List of Corporate Intangible Assets Not-Included In NIPA Accounts, Definitions and Sources
Type of Intangible AssetInvestmentStock
1-Computerized InformationSource1/Definition(% of intangible, 1998-06)
This only includes development of software because software is included in NIPA since 1998SAS (see CHS 2005, 2009), and NIPA accounts I-O use tables for industry use. NIPA accounts for the corporate share. 1/Total revenue from subscription to “Online directories, databases, and other collections of information” from publishers of databases (NAICS 51114); does not include print directories, databases, other collections of information (other media directories, databases, and other).0.26%0.25%
2- Innovative Property42.6%61.8%
2-1- R&DInternal Revenue Service Form 6567. Corporate share obtained from source.R&E qualified expenditures reported by corporations. Does not include mineral exploration, because this is included in NIPA.15.1%21.90%
2-2- Copyrights and license costsCHS (2005, 2009) NIPA accounts for the corporate share. 2/These innovation expenses lead to new copyrights and licenses. Cost of developing original performances or products in the arts and entertainment industry. These costs lead to new copyrights ad licenses. Composed of (1) development costs in the motion picture industry, and (2) in the radio and television, sound recording, and book publishing industries. (No estimate for the arts is included.)
2-3- Other product development, design, and research expenseBureau of Economic Analysis (BEA) and accounts and SAS (see CHS 2005, 2009); NIPA accounts I-O use tables for industry use. NIPA accounts for the corporate share. 1/These costs do not necessarily lead to new a patent or a copyright. This item covers non-scientific R&D in finance and services industries. Includes (i) New product development costs in the financial services industries, crudely estimated as 20 percent of intermediate purchases (from BEA), 3/, (ii) Costs in new architectural and engineering designs, estimated as half of industry revenue for taxable employers in architecture and engineering services (NAICS 5413), including geophysical and mapping surveys, and (iii) R&D in social sciences and humanities, estimated as twice industry revenue for taxable employers in R&D in the social sciences and the humanities (NAICS 54172). 4/27.5%39.9%
3- Economic Competencies57.2%38.0%
3-1- Firm-specific human capitalBased on a broad survey of employer-provided training, conducted by the Bureau of Labor Statistics (BLS) in 1994 and 1995. NIPA accounts for the corporate share.Cost of developing labor force skills6.94%5.47%
3-1-1- On the job training costBLS and BEA (see CHS, 2005, 200)9. NIPA accounts for the corporate share. 5/Direct firm expenses (Wages and salaries of in-house trainers, payments to outside trainers, tuition reimbursement, and contributions to outside training funds)
3-1-2- Payments for job-related educationBLS and BEA (see CHS, 2005, 2009). NIPA accounts for the corporate share. 6/Tuition payments for job-related education. Wage and salary costs of employee time in formal and informal training.
3-2- Organizational capitalSAS, and Occupational Employment Statistics (OES) Surveys from the Bureau of Labor Statistics. (see CHS, 2005, 2009). NIPA accounts for the corporate share.(i) Purchased “organizational” or “structural” capital, estimated using SAS data on the revenues of the management consulting industry, and distributed across industries using BEA I/O use tables, and (ii) Own-organizational skills, estimated as one fifth of the value of executive time using BLS data on employment and wages in executive occupations (OES). 5/21.6%17.1%
3-3- Brand Equity
3-3-1- AdvertisingInternal Revenue Service. Corporate share from the source.Expenditures on advertising services, from IRS/SOI data on corporate expenses on advertising. 7/28.7%15.4%
3-3-2- Market ResearchSAS (see CHS 2005, 2009), and NIPA accounts I-O use tables for industry use. NIPA accounts for the corporate share. 1/Market research for the development of brands and trademarks, estimated as twice industry purchased services (revenues of the market and consumer research industry as reported in SAS), and distributed across industries based on BEA I/O use tables.
Notes:

Input-Output tables from NIPA over time are used to distribute professional services across industries based on their use.

CHS (2005, 2009) use data from the Motion Picture Association of America (MPAA).

Intermediate purchases for finance industries (NAICS 521,523,525) from BEA’s GDP-by-industry data.

SAS, Table 6.1 for professional, scientific, and technical services (NAICS 54).

Estimates for other years were derived from (1) the detail by industry on per employee costs reported in BLS surveys in 1994 (Table 9 for Selected expenditures by industry), and (2) trends in the use of education / educational costs by industry (from BEA I/O use table).

Estimates for other years were derived from (1) the detail by industry on per employee costs reported in BLS surveys in 1994 (Table 11), and (2) trends in aggregate FTE employment by industry (from BEA).

Internal Revenue Service, Returns of Active Corporations (Table 6).

Notes:

Input-Output tables from NIPA over time are used to distribute professional services across industries based on their use.

CHS (2005, 2009) use data from the Motion Picture Association of America (MPAA).

Intermediate purchases for finance industries (NAICS 521,523,525) from BEA’s GDP-by-industry data.

SAS, Table 6.1 for professional, scientific, and technical services (NAICS 54).

Estimates for other years were derived from (1) the detail by industry on per employee costs reported in BLS surveys in 1994 (Table 9 for Selected expenditures by industry), and (2) trends in the use of education / educational costs by industry (from BEA I/O use table).

Estimates for other years were derived from (1) the detail by industry on per employee costs reported in BLS surveys in 1994 (Table 11), and (2) trends in aggregate FTE employment by industry (from BEA).

Internal Revenue Service, Returns of Active Corporations (Table 6).

Table A3Investment (Total) and Average Annual Growth Rate Of Corporate Physical And Intangible Assets, 1998 To 2006 ($ Bil.)
InvestmentAAGR
Equipment,Equipment,
IndustryTotalSoftwareStructuresIntangiblesTotalSoftwareStructuresIntangibles
Agriculture, forestry, fishing, hunting$30886%12%2%0.61%0.02%5.14%1.44%
Mining54333.257.89.010.44.515.27.8
Utilities522.3651.643.25.25.82.09.95.7
Construction622.1167.71.430.8(0.4)(1.6)4.31.9
Food, beverage, tobacco, textile, apparel,
leather577.5927.53.169.40.50.65.70.4
Wood, paper, printing, petroleum, chemical 1/1,14443.44.452.32.10.95.83.0
Metal, machinery, computer, electronic 2/2,04038.04.257.91.40.95.71.4
Wholesale70833.25.161.82.60.11.44.1
Retail1,02025.821.652.61.1(0.2)1.42.0
Transportation, Couriers and Warehousing87577.711.111.21.40.16.70.0
Information1,96937.88.353.92.70.74.34.1
Finance and insurance1,67325.15.669.35.01.81.46.5
Real estate, rental & leasing518.4962.914.222.80.0(2.7)1.66.2
Professional & technical services80349.53.547.03.82.81.44.9
Management of companies & enterprises246.4921.93.274.93.72.21.44.3
Administrative & waste services325.2648.45.246.42.30.90.83.8
Educational services303.9825.027.947.14.53.44.55.3
Health care & social assistance90052.223.524.45.75.15.37.5
Arts, entertainment, & recreation142.2527.740.232.22.61.12.54.8
Accommodation and food services570.3226.540.732.92.90.42.56.3
Other services, excluding public administration292.734.934.430.81.6(0.9)0.85.6
US Totals16,10641.513.445.12.81.05.33.7
Notes:

Includes plastics, rubber, nonmetallic minerals manufacturing;

includes electrical equipment, transportation equipment, furniture, miscellaneous manufacturing.

Notes:

Includes plastics, rubber, nonmetallic minerals manufacturing;

includes electrical equipment, transportation equipment, furniture, miscellaneous manufacturing.

To obtain the stock of intangible assets, we use the data obtained for investment in intangible assets and assumes that these assets depreciate according to the perpetual inventory method (PIM). The PIM is also used by NIPA accounts to age the stock of physical assets, and is explained in Meinen et al. (1998). The net stock an asset in year t and in year t prices is defined as:

where d is the recovery period of the asset, It is the amount invested in the asset in current dollars, Pti,tI is the price index of year t with base year t-i, and CCt is the consumption of the capital asset in year t. Assuming straight-line depreciation of intangible assets, we have

where

Equation (A2) assumes that investment is made throughout the year, while the gross capital stock in year t and in year t prices (GSCt,t) is generally obtained in December. Table A4 shows our assumed values of economic depreciation of various assets. For intangible assets, we follow previous literature (CHS, 2005; Fraumeni, 1997). Table A5 shows the total stock of intangible assets over 1998-2006 and the compounded annual growth rate. The stock of intangible assets was about $10.6 trillion, or 11 percent of total assets, which is relative terms is the much smaller as a share of total assets than investment in intangible assets. The reason is essentially that in spite of its large rate of growth, the initial stock of intangible assets is a small share of total assets (about 7 percent in 1998) and intangible assets depreciate at a faster rate than most structures and equipment assets.

Table A4Rate Of Economic Depreciation And Present Value Of Tax Depreciation Allowances 1/
Physical assets 2/NPV of tax depreciation

allowances
Capital structures category in purchasers’ pricesTax

life
Tax method

(Declining

balance)
Economic

depreciation
Bonus

depreciation
MACRS30%50%
(4), (5), (9) Computers, peripheral, software, office, accounting equipment52000.3120.9040.9330.952
(6) Communication equipment52000.150.9040.9330.952
(7a), (7b) Nonmedical and medical instrument and related equipment72000.1350.840.9050.92
(8) Photocopy and related equipment52000.180.9040.9330.952
(11) Fabricated metal products72000.0920.840.9050.92
(12) Engines and turbines151500.0520.6940.7860.847
(13) Metalworking machinery72000.1230.840.9050.92
(14) Special industry machinery, n.e.c.72000.1030.840.9050.92
(15) General industrial, incl. materials, equipment72000.1070.840.9050.92
(16) Electrical transmission, distribution & industrial apparatus72000.050.840.9050.92
(18a), (18b) Light and other trucks, buses and trailers52000.1230.9040.9330.952
(19) Autos52000.1650.9040.9330.952
(20) Aircraft72000.110.840.9050.92
(21) Ships and boats102000.0610.7810.8680.89
(22) Railroad equipment72000.0590.840.9050.92
(24) Furniture and fixtures72000.1380.840.9050.92
(26*) Agricultural machinery, including tractors71500.1450.840.9050.92
(27*) Construction machinery, including tractors52000.1630.9040.9330.952
(28) Mining and oilfield machinery72000.150.840.9050.92
(29) Service industry machinery72000.1650.840.9050.92
(30) Electrical equipment, n.e.c.72000.1830.840.9050.92
(31) Other nonresidential equipment72000.1470.840.9050.92
(33) Residential (landlord durables)52000.1180.9040.9330.952
(6) Commercial buildings39SL0.0220.3950.3950.395
(11) Hospital and institutional buildings39SL0.0190.3950.3950.395
(12) Other nonresidential buildings, excluding farm39SL0.0250.3950.3950.395
(5) Industrial buildings39SL0.0310.3950.3950.395
(16) Electric light and power201500.0210.6220.8110.811
(15) and (17) Gas and Telecommunications151500.0240.6940.8470.847
(21a) Petroleum and natural gas–wells151500.0750.6940.8470.847
(22) Other mining construction52000.0450.9040.9520.952
(9), (10) Religious buildings and Educational buildings39SL0.0190.3950.3950.395
(14) Railroads201500.0280.6220.8110.811
(19) Farm nonresidential structures201500.0240.6220.8110.811
(23) Other nonresidential non-building structures39SL0.0230.3950.3950.395
(30a) - (32) Single & multi family structures, nonfarm, Manufactured homes27.5SL0.0140.5040.5040.504
(33) Improvements151500.0230.69411
(34) Other27.5n/a0.0230.5040.5040.504
Intangible assets 3/
Computerized Informationn/an/a0.33111
Scientific and non scientific R&Dn/an/a0.2111
Firm-Specific Human Capital, organizational capitaln/an/a0.4111
Brand Equityn/an/a0.6111
Notes: n.e.c. = not elsewhere classified;

The half-year convention is assumed. (i.e., investment is assumed to be installed in the middle of the first year, and therefore depreciates during half of the first year. The present value of tax depreciation allowances is calculated with a discount rate of 6% (approximately equal to the average nominal federal fund rate on 10-year Treasury bonds over the period). Under MACRS, assets with recovery periods above 20 years are depreciated based on straight-line. For assets with recovery periods of 20 years or less, the tax depreciation allowances each year is the maximum between straight line and declining balance.

The numbers in parenthesis preceding asset types are conform to the ones used in BEA physical assets tables.

The rates of economic depreciation of intangible assets are the same as in CHS (2005), except for computerized information, which is based on estimates by Fraumeni (1997).

Notes: n.e.c. = not elsewhere classified;

The half-year convention is assumed. (i.e., investment is assumed to be installed in the middle of the first year, and therefore depreciates during half of the first year. The present value of tax depreciation allowances is calculated with a discount rate of 6% (approximately equal to the average nominal federal fund rate on 10-year Treasury bonds over the period). Under MACRS, assets with recovery periods above 20 years are depreciated based on straight-line. For assets with recovery periods of 20 years or less, the tax depreciation allowances each year is the maximum between straight line and declining balance.

The numbers in parenthesis preceding asset types are conform to the ones used in BEA physical assets tables.

The rates of economic depreciation of intangible assets are the same as in CHS (2005), except for computerized information, which is based on estimates by Fraumeni (1997).

Table A5Stock (Total) and Compounded Annual Growth Rate Of Corporate Physical And Intangible Assets, 1998 To 2006 ($ Bil.)
StockCAGR
IndustryTotalEquipment, SoftwareStructuresIntangiblesTotalEquipment, SoftwareStructuresIntangibles
Agriculture, forestry, and fishing3,16849%51%0.29%3.17%3.31%3.03%5.54%
Mining4,72121.577.11.50.70.91.6707
Utilities8,60223.675.90.50.10.60.117.4
Construction2,48979.29.910.90.10.30.131.7
Food, beverage, tobacco, textile, apparel, leather1,94552.127.320.50.30.43.11.5
Wood, paper, printing, petroleum, chemical 1/5,38356.027.716.30.50.81.66.6
Metal, machinery, computer, electronic 2/8,75749.729.021.30.20.30.61.2
Wholesale2,33644.633.721.70.10.20.50.6
Retail6,58318.473.68.10.40.91.11.3
Transportation, couriers and warehousing8,45355.243.31.50.10.80.14.6
Information8,47739.638.422.03.32.313.184.0
Finance and insurance5,30421.739.039.30.20.50.20.7
Real estate, rental & leasing3,38743.651.94.50.10.30.40.4
Professional & technical services2,33149.726.623.70.41.80.57.8
Management of businesses and enterprises557.8428.331.040.80.40.71.31.4
Administrative & waste services1,28151.833.514.61.35.44.44.3
Educational services1,92114.776.58.81.12.02.85.8
Health care & social assistance6,99927.968.14.00.33.70.47.6
Arts, entertainment & recreation1,37414.081.84.10.10.30.22.8
Accommodation and food services5,59314.681.73.70.64.00.720.2
Other services, excluding public administration2,96716.579.83.70.10.90.24.5
US Totals92,62836.252.311.40.32.10.48.8
Notes:

Includes plastics, rubber, nonmetallic minerals manufacturing;

includes electrical equipment, transportation equipment, furniture, miscellaneous manufacturing

Notes:

Includes plastics, rubber, nonmetallic minerals manufacturing;

includes electrical equipment, transportation equipment, furniture, miscellaneous manufacturing

BEA tables:

  • BEA value added table: “GDPbyInd_VA_NAICS_1998-2006.xls”- industry value added, gross output and intermediate inputs, and components of value added, in current dollars and corresponding quantity and price indexes (2005=100) for 1998-2006.

A2. Physical Assets

To isolate investments and stocks of physical and intangible assets by industry, assets, and over time, we use BEA’s physical asset tables (listed below). First, we use the stocks and flows of non-residential (tables 4.1 and 4.7) and residential (Tables 5.1. and 5.7) physical assets by legal form of organization to isolate corporate stock (or investment) in equipment and structures in each year. Second, for each year, we distribute the corporate amounts of investment and stocks in these broad asset types—obtained from step one–across detailed asset types, using BEA tables 2.1 and 2.7, which provide detailed stocks and flows of private physical assets for 75 detailed asset types. Third, for each year and each asset, we distribute the resulting corporate stocks and flows across industries, using the 1997 BEA’s capital flow data, based on the Survey of Current Businesses. This implies that the total distribution, across assets, of investments and stocks of corporate physical assets varies not only over time (step two), but also across industries (step 3).

We obtain one matrix for each year showing the distribution of corporate stocks (or flows) across detailed physical assets and two-digit industries: 9 matrices (one for each year from 1998 to 2006) showing the distribution, across assets and within industries, of industrial corporate physical asset stocks; and 9 matrices showing the distribution, across assets and within industries, of industrial corporate physical asset flows.

  • MS[ms_a,i,t] = matrix showing total stocks (or levels) ms in physical assets a (a=1-A1), by industry I (i=1 to N) at time t (t=1998-2006). A1 is the number of tangible assets and N is the number of industries.

  • MF[mf_a,i,t] = matrix showing total investment (or flow) mf in physical assets a (a=1-A1), by industry I (i=1 to N) at time t (t=1998-2006).

Tables A3 and A5 show the total amount of physical assets by type and industry from 1998 to 2006. Total investment in physical assets was $8.8 trillion over 9 years, representing 55 percent of total assets, three fourth of which were in equipment and software. The stock of physical assets was $82.1 trillion over 9 years, or 89 percent of all capital stock, two third of which were in structure assets, due to their longer recovery period.

BEA tables:

  • Table 2.1. Current-Cost Net Stock of Private Physical Assets, Equipment and Software, and Structures by Type

  • Table 2.7. Investment in Private Physical Assets, Equipment and Software, and Structures by Type

  • Table 4.1. Current-Cost Net Stock of Private Nonresidential Physical Assets by Industry Group and Legal Form of Organization

  • Table 4.7. Investment in Private Nonresidential Physical Assets by Industry Group and Legal Form of Organization

  • Table 5.1. Current-Cost Net Stock of Residential Physical Assets by Type of Owner, Legal Form of Organization, Industry, and Tenure Group

  • Table 5.7. Investment in Residential Physical Assets by Type of Owner, Legal Form of Organization, Industry, and Tenure Group

  • Capital Flows: table 4-“NIPAx123EqSoft”-Capital flow table, in purchasers’ prices, with NIPA equipment and software categories as rows, with 123 columns of using industries, and table 5-“NIPAx123Struc”-Capital flow table, in purchasers’ prices, with NIPA structures categories as rows, with 123 columns of using industries.

A3. The distribution of corporate investment and stock by asset, industry, and over time

Appendix A2 provides two groups of matrices: (i) 9 matrices distributing physical asset stocks by asset and across industries, one for each year from 1998 to 2006, and (ii) the same as (i) for physical asset investment. Appendix A1 provides the stocks and flows of corporate intangible assets over time and by industry, for 6 types of intangible. We update the annual matrices of physical assets from appendix A2 with intangible assets. This provides 9 new matrices (one for each year from 1998 to 2006) showing the distribution, across assets and within industries, of industrial corporate physical and intangible asset stocks, and 9 similar matrices for corporate physical and intangible asset investment flows.

  • NS[ns_a,i,t] = matrix showing total stocks (or levels) ns in physical assets a (a=1-A2), by industry I (i=1 to Ni) at time t (t=1998-2006), where A2 is the number of physical and intangible assets.

  • NF[nf_a,i,t] = matrix showing total investment (or flow) nf in physical assets a (a=1-A2), by industry I (i=1 to Ni) at time t (t=1998-2006).

These matrices permit to calculate the weight wi,a,t of each assets stocks (or flows) within industries, which are critical in order to calculate the present value of depreciation allowances of $1 of investment in industry i, as explained in appendix B.

Appendix B: Tax Parts

We follow Cummins, Hasset, and Hubbard (1994) and House and Shapiro (2008) to construct the tax parts. Many changes in the federal treatment of depreciable assets for tax purposed have been implemented during our period of interest, and especially from 2002 to 2004. These changes were temporary investment tax incentives based on asset types. Bonus depreciation allowances from 2002 to 2004 only applied to short-lived investment assets, defined as equipment and structure assets with a recovery period of 20 years or less.

The calculation of the present value of tax depreciation allowances takes account of the fact that the periods covering bonus depreciation were not always the same as the calendar year. In this case, the PV of depreciation allowance for a given asset and a given calendar year is calculated as the weighted average of the PV of depreciation allowances available for that year, weighted by the number of days when the policy was effective:

where DAa,1 and #days1 (respectively DAa,2 and #days2) are respectively the present values of depreciation allowances and the number of calendar days when they are available under policies 1 (respectively policy 2). Table A4 shows the PV of depreciation allowances for each asset and under alternative policies effective during 1998-2006. The table below shows the number of effective days of each policy.

Calendar yearMACRSBD 30%BD 50%
1998 - 2001365 or 366
2002365
2003125240
2004366
2005–2006365
Note: MACRS = modified accelerated recovery system under current law. BD = first-year bonus depreciation allowance. The Job Creation and Worker Assistance Act of 2002 created 30 percent bonus depreciation for qualified capital put in place after September 11, 2001. However, because the Act was passed in March 2002, investors sitting in 2001 did not make their investment decisions based on the reduced asset cost for that year. The Jobs and Growth Tax Relief Reconciliation Act of 2003 provided 50 percent first-year depreciation allowance was for capital put in place after May 28.
Note: MACRS = modified accelerated recovery system under current law. BD = first-year bonus depreciation allowance. The Job Creation and Worker Assistance Act of 2002 created 30 percent bonus depreciation for qualified capital put in place after September 11, 2001. However, because the Act was passed in March 2002, investors sitting in 2001 did not make their investment decisions based on the reduced asset cost for that year. The Jobs and Growth Tax Relief Reconciliation Act of 2003 provided 50 percent first-year depreciation allowance was for capital put in place after May 28.

For instance, as shown in table A4, the present value of depreciation allowances of software, which has a tax life of 5 years, is 0.933 under 30 percent bonus depreciation and 0.952 under 50 percent bonus depreciation. Because both policies overlap in year 2003, the PV of depreciation allowances of software in 2003 is given by (125/365)* 0.933 +(240/365)* (0.952), or 0.945. The present value of depreciation allowances for each physical asset is calculated based on the applicable MACRS rule, with mid-year convention (IRS, 2010). A discount rate of 5 percent is assumed, which is roughly the average of the rate on 10-year treasury bonds over the 9 years considered. Finally, the present value of depreciation allowances for physical assets in a given industry and a given year (DAi,t) is measured as the weighted average of depreciation allowances of each types of physical assets in the industry, weighted by investment in the asset:

where Wi,a,t=Ii,a,t/Ii,t is the proportion of investment in asset a and industry i in year t.

As this paper is interested in explaining investment in physical assets, calculations of the tax term of the cost of capital disregard intangible assets, implying that the denominator of wi,a,t only includes total investment in fixed assets. Using matrix MF from appendix A2, this gives Wi,a,t=mfi,a,t/Σk=1A1mfi,k,t

Tables A6, A7, and A8 show summary statistics of the equipment tax term and the structures tax terms among the sample of Compustat companies used in our empirical strategy, per year, for all firm and by firms’ intangible intensity. Intangible intensity is constructed as a simple dummy equal to 1 if a firm’s ratio of (industry-level) intangible stock is above the sample’s median in a given year, and zero otherwise. The tax term of each group of assets is TaxTermi,t=(1DAi,t*τ/1τ), where τ is the statutory top corporate tax rate, and equal to 35 percent over the period considered.

Appendix C: Selected summary statistics

We present summary statistics of the equipment and structures tax terms (ETT and STT) and of the investment rates, over time and for all companies that are included in our regressions. These statistics are shown in Tables A6 to A8, for all companies and for sub-samples based on intangible intensity, and on firm size. We further describe these statistics in the methodology section and the results section of the main paper.

Table A6Selected Statistics for Sample Firms, All Firms From 1999 To 2006
AllTop 3500Top 1500Top 500
N=45,064N=35,732N=23,753N=10,691
VariableMeanStd. Dev.MeanStd. Dev.MeanStd. Dev.MeanStd. Dev.
ETTjt
19991.1610.0721.1620.0711.1610.0701.1601.160
20001.1600.0721.1610.0711.1610.0711.1591.159
20011.1600.0711.1610.0711.1610.0711.1591.159
20021.1410.0751.1420.0751.1420.0751.1401.140
20031.1370.0771.1380.0761.1380.0761.1361.136
20041.1350.0781.1350.0781.1350.0771.1341.134
20051.1640.0741.1640.0741.1630.0731.1611.161
20061.1670.0771.1670.0761.1650.0751.1621.162
STTjt
19991.4890.0451.4880.0461.4890.0451.4901.490
20001.4890.0451.4880.0461.4880.0451.4901.490
20011.4890.0461.4880.0461.4880.0461.4891.489
20021.4840.0551.4840.0551.4840.0551.4841.484
20031.4820.0571.4830.0561.4830.0561.4831.483
20041.4810.0581.4820.0581.4820.0561.4831.483
20051.4850.0511.4850.0501.4860.0491.4881.488
20061.4830.0541.4830.0531.4850.0511.4861.486
Iijt/Kijt-1
19990.2580.4810.2570.4720.2410.4440.2170.217
20000.3370.5860.3200.5510.2860.5000.2580.258
20010.1840.2390.1880.2330.1810.2230.1700.170
20020.1330.1710.1340.1630.1320.1560.1290.129
20030.1300.1750.1280.1660.1230.1600.1150.115
20040.1840.3250.1720.2970.1600.2680.1510.151
20050.2040.3440.1930.3200.1780.2840.1620.162
20060.2300.3890.2210.3690.2040.3330.1990.199
Table A7Selected Statistics for Sample Firms, Intangible Intensive Firms, From 1999 To 2006
AllTop 3500Top 1500Top 500
N=45,064N=35,732N=23,753N=10,691
VariableMeanStd. Dev.MeanStd. Dev.MeanStd. Dev.MeanStd. Dev.
ETTjt
19991.1380.0001.1380.0001.1380.0001.1381.138
20001.1290.0131.1300.0121.1300.0111.1311.131
20011.1290.0131.1300.0121.1300.0121.1311.131
20021.1080.0121.1090.0111.1090.0111.1101.110
20031.1030.0121.1030.0121.1040.0111.1041.104
20041.1000.0121.1010.0121.1010.0111.1021.102
20051.1290.0131.1300.0121.1300.0121.1311.131
20061.1290.0131.1290.0131.1300.0121.1311.131
STTjt
1999
20001.5100.0001.5100.0001.5100.0001.5101.510
20011.5060.0121.5060.0111.5060.0111.5061.506
20021.5060.0121.5060.0111.5060.0111.5061.506
20031.5040.0151.5040.0151.5040.0141.5041.504
20041.5040.0151.5040.0151.5040.0151.5041.504
20051.5040.0151.5040.0151.5040.0151.5041.504
20061.5060.0111.5060.0111.5060.0111.5061.506
Iijt/Kijt-11.5060.0111.5060.0111.5060.0111.5061.506
1999
2000
20010.1650.2970.1580.3040.1410.1610.1370.137
20020.4080.6630.3840.6240.3470.5810.3060.306
20030.1870.2400.1910.2330.1860.2240.1790.179
20040.1190.1480.1200.1380.1190.1310.1200.120
20050.1090.1360.1080.1240.1040.1180.0980.098
20060.1570.2840.1470.2500.1380.2270.1340.134
Table A8Selected Statistics for Sample Firms, Physical Intensive Firms, From 1999 To 2006
AllTop 3500Top 1500Top 500
N=45,064N=35,732N=23,753N=10,691
VariableMeanStd. Dev.MeanStd. Dev.MeanStd. Dev.MeanStd. Dev.
ETTjt
19991.2040.0941.2030.0931.2020.0921.1981.198
20001.2060.0941.2040.0931.2030.0921.1971.197
20011.2050.0941.2040.0931.2030.0921.1981.198
20021.1860.0991.1860.0981.1860.0981.1811.181
20031.2260.0991.2240.0981.2240.0991.2201.220
20041.2250.1001.2220.1001.2210.1001.2191.219
20051.2470.0931.2450.0931.2430.0941.2381.238
20061.2500.0931.2480.0941.2450.0951.2401.240
STTjt
1999
20001.4650.0611.4650.0611.4650.0611.4671.467
20011.4630.0621.4640.0611.4650.0611.4671.467
20021.4630.0621.4640.0621.4640.0621.4661.466
20031.4560.0751.4570.0741.4570.0741.4581.458
20041.4230.0781.4250.0771.4250.0771.4251.425
20051.4200.0791.4220.0781.4240.0771.4231.423
20061.4300.0661.4320.0651.4350.0641.4361.436
Iijt/Kijt-11.4260.0671.4280.0661.4320.0661.4331.433
1999
2000
20010.2180.3980.2080.3510.1920.3310.1800.180
20020.2330.4290.2320.4140.2040.3480.1910.191
20030.1810.2380.1840.2320.1740.2220.1590.159
20040.1540.1960.1530.1880.1490.1820.1410.141
20050.1680.2160.1620.2040.1580.2020.1450.145
20060.2410.3890.2280.3670.2120.3350.1970.197
Appendix D: Macroeconomic Variables

Price indices (PPI and CPI), used to calculate the stock of intangible assets based on the PIM methodology (see above) are obtained from tables 64 and 68 or the ERP. The 10-year federal funds rate, used as a proxy for the discount rate (see Appendix B) is taken from Board of Governors of the Federal Reserve System, table H.15 (seasonally adjusted).

Appendix E: Proof of Proposition 1

We shall first show that the ex-dividend value of the firm Pt is equal to the value of tangible assets and intangible assets under the assumption of constant return to scale in the production technology and adjustment costs:

where qtm and qtu are the marginal value of Kt+1m and Kt+1u respectively.

To show this, let Vt denote the cum-dividend market value. Vt is the sum of the firm’s exdividend market value plus dividend payout:

where dividend Dt is given by

Profit maximization in (1) implies

Linear homogeneity of adjustment costs imply Ψ(It+si,Kt+si)=ψIt+siKt+siIt+siψ2(It+siKt+si)2Kt+si. Using the first order condition (3) gives

Recursively substituting the first order condition (4) gives

Equating (A3) and (A4) and collecting terms gives

where the first equality follows from the first order condition (3) and the last equality follows from the law of motion (2). Finally, by definition of qt=PtKt+tm+Kt+1u, it follows that

Q.E.D.

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Appendix References

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Estelle P. Dauchy (corresponding author): New Economic School, Nakhimovsky Prospekt 47, Room 1721, Moscow, Russia. We thank participants at various seminars and conferences for helpful comments. We thank Zhou Yi (Joey) for research assistance.

See Appendix A for details. Tables A3 and A5 show the value of investments and stocks of corporate intangible assets by industry over 1998-2006. Tables A1 and A2 show that scientific R&D in the corporate sector, which is often associated with intangible property (because it is easy to measure) represents a relatively small share of intangible assets over 1998-2006 (15 percent of total investment in intangible assets, as opposed to 27 percent for non-scientific R&D, 22 percent for organizational capital, and 29 percent for brand equity).

Self-constructed intangible assets are generally fully expensed. Certain purchased intangibles such as R&D, patents, copyrights, software, trademarks, and computer lists are generally amortized over 3 to 15 years (although R&D and patents can be expensed if purchased separately). Economic competencies are not considered in the tax code (for more details, see Internal Revenue Code Sections 162 and 174 for R&D and Section 197 for purchased intangibles).

Although self-created R&D is fully expensed, most governments also provide tax credits for R&D. For example, the U.S. pioneered the use of R&D tax credit in 1981. In 2012, India allows for 200 percent super deduction for R&D expenditures. A number of OECD countries including Denmark, France, Italy, and Portugal significantly boosted their R&D tax incentives in the last decade.

Robinson and Sansing (2008) show that the marginal tax rate also matters because financing and tax considerations have opposite effects on firms’ incentives to invest in internally developed intangible assets. Using the difference between the book value and the market value of assets as proxy for intangible assets, they also find that firms with high levels of intangibles relative to tangible assets have smaller effective tax rates (ETR), and that the effect of debt-financing on the ETR is smaller for these firms, probably because of the trade-off between debt and intangible assets’ financing (both debt and internally developed intangibles are expensed for tax purposes). They conclude that any paper interested in intra-industry variation in tax-favored investment should consider for both sources of corporate finance. Our paper is interested in the variation in firms’ tax preferences across industries and we explicitly take into account intangible assets.

It is also recognized that firm-specific intangible assets is important in explaining large variations in average firm value, see Gleason and Klock (2006), Megna and Mueller (1991). Corrado et al (2005, 2006) evaluate that from the 1950’s decade to the 2000-03 periods, the ratio of intangible assets to NIPA tangible assets increased almost threefold from .54 to 1.36. Their measure of the annual average value of intangible assets (from which we base our own measure of intangible assets at the industry level) in 2000-03 is 1.23 trillion, which is very close to what Nakamura (2000) finds using stock market data.

Because intangible assets depreciate faster, the stock of intangible assets is smaller than that of physical assets.

According to US Generally Accepted Accounting Principles (GAAP) and International Financial Reporting Standards (IFRS), intangible assets are recognized only when probable future economic benefits and costs can be reliably measured. Goodwill is recognized only in recognized business combinations. Internally generated intangibles are not recognized as assets with limited exceptions of development costs of computer software.

See Appendix B for details. In practice, bonus depreciation is an additional tax depreciation allowance on top of current law (MACRS rules). Tables A6 to A8 show the impact of these tax policies over time on the “tax parts” of q for publicly traded corporations in our sample.

We use industry-level data on intangible assets instead of firm-level data because at the industry level, available information by different types of intangibles is more detailed and potentially more reliable.

The literature has not reached a consensus on the elasticity of investment with respect to the cost of capital. Early estimations using aggregate data generally imply small elasticity. More recent estimations with firm level data are generally larger. For example, Desai and Goolsbee (2004) estimate the coefficients of the equipment tax term to be between 0.6 and 0.9, which correspond to elasticity of 2.7 and 4. Edgerton (2010) shows similar results. House and Shapiro (2008) use data of U.S. bonus depreciation and find the supply elasticity of investment to be large. Their results would imply elasticity between 1.3 and 3.0. Our results for the full sample suggest relative large elasticity and moderate adjustment costs, in line with recent studies. Our results for intangible-intensive firms suggest larger elasticity than previous studies.

Most of the existing empirical research is based on the neoclassical model of investment developed by Jorgenson (1963), and extended by Hayashi (1982) and Summers (1981). Edgerton (2010) finds that the effectiveness of tax incentives depends on firms’ taxable status, but that most of this difference is actually explained by low cash flows. Bloom et al. (2009) find that the effectiveness of tax incentives may be dampened by time-varying uncertainty.

There is a long tradition in macroeconomic models to approximate capital stocks around their steady state values to analyze investment dynamics to temporary shocks (see, for example, Stokey, Lucas, and Prescott, 1989 for a discussion).

House and Shapiro (2008) estimate investment supply elasticity in a model with temporary investment incentives. Using a numerical model, they show that the steady-state value is good approximation for marginal q. For example, assuming an annual depreciation rate of 5 percent and a moderate adjustment cost (corresponding to ψ =20), the approximation error in marginal q for a one year duration of tax changes is 0.016.

Taxpayers who had already filed their 2001 tax returns before this new provision was passed could still take advantage of the bonus depreciation provision by filing an amended return.

More details about the policy are provided in Appendix B.

See Hennessy et al. (2007) for a q model with financial constraints in the absence of investment tax incentives.

Christiano et al. (2005) propose a model with an adjustment costs depending on lagged and current investment. Eberly et al. (2012) find that when lagged investment is included as a regressor, the explanatory power of the q and cash flow terms, though significant, are much smaller in magnitude, and the R-square almost doubles.

During 1998-2006, only conditional tax credits were available for specific expenditures (e.g., renewable energy), small corporations (under Internal Revenue Code Sections 179 and 168), or qualified employment. For a list of business tax credit, see: http://www.irs.gov/businesses/small/article/0,,id=99839,00.html

In the presence of serially correlated errors, the first and second lags are not valid instruments. We base our choice of higher lags on the Hansen test. By construction, the tax terms are exogenous, as they are determined by policy variables and historical information on the composition of asset stocks (see appendix B).

In addition, we believe that temporary bonus depreciation policy enacted in the early 2000s has different incentive effects than permanent-law tax depreciation allowances and permanent changes in the tax code, since their goal is to target short term investment.

According to “The Budget and Economic Outlook: An Update” (August 2011, Congressional Budget Office, U.S. Congress), business investment in equipment, software, and structures less depreciations decreased sharply during the recession, and was at its lowest in more than half a century, in part due to idle industrial capacity and vacant real estate, reducing the need for businesses to invest as they usually would (p. 61).

Following previous research, extreme values of many financial statements variables are winsorized at the 2nd and 98th percentiles (Desai and Goolsbee, 2004, Edgerton, 2010; Dauchy and Martinez, 2008; Moyen, 2004).

See data Appendix A for details on the construction of investment and stocks of physical assets at the industry level.

The 2013 comprehensive revision on US National Income and Product Accounts (NIPA) was the first attempt to capitalize R&D and other intangible investment, such as entertainment, literary, and artistic original, in national accounts. The revision used a methodology similar to CHS to construct intangible assets from investment data. See http://www.bea.gov/gdp-revisions/.

As explained in Table A1 (see also Dauchy, 2013), we follow CHS (2005, 2006) to only identify intangible assets that provide long-term value to the firm. For instance, for developed organizational and management skills we use data from the BLS’ Occupational Employment Statistics survey and approximate this part as one fifth of the value of executive time.

See Appendix A for more details on data sources and their measurement.

See Appendix A and B (in particular Table A1) and Dauchy (2013) for details. The distribution across industries is based on the BEA and the IRS, as described in appendix A1. As shown in the appendix, the methodology used in this paper to distribute investment and stocks of corporations (i.e. companies subject to corporate taxation) across industries closely reflect actual investment given available data, and even if BEA’s Survey of Current Businesses covers a different set of companies than IRS’s tax returns.

For example, Eberly et al. (2012) and Bond and Cummins (2000) use the book value of plant, property and equipment as the denominator of q. Desai and Goolsbee (2004) and Edgerton (2010) use the book value of total assets as the denominator of q. For the book value of assets, the literature generally uses total assets reported in firms’ financial statements (Compustat item #6). Although we experimented with total assets, we chose to use a measure that is more closely related to physical assets (for instance, total assets include many financial assets). Although we do not report results based on total assets, we note that they do not change our main conclusions and are available upon request. An alternative way to proxy for the book value of physical assets is to re-construct it using the perpetual inventory method and investment data from firms’ financial statements (as in Bond and Cummins, 2000). Although sound methodologically, this method also suffers from the choice of the depreciation rate (and the recovery period), the choice of the initial stock of investment, and the availability of enough historical data on firm-level investment.

See appendix B for a detailed description of depreciation allowances during our period, and our calculation of the two tax terms. Appendix table A4 shows the change in the NPV of depreciation allowances, by detailed asset types, from current law to 30% and 50% bonus depreciation. Tables A6, A7, and A8 show the variation over time of the ETT and the STT terms among firms in our regression samples.

To deal with outliers in measured q, it is standard in the literature to exclude negative values of q, and either winsorize or truncate the data. Desai and Goolsbee (2004) winsorize average q at the 1 percent level. Edgerton (2010) winsorizes the q ratio at the 2 percent level. Bond and Cummins (2000) truncate the data by eliminating from their sample all values of q that are greater than 50.

The choice between total assets and PPE does not alter our baseline regression results in any significant way. Results based on total assets are available upon request.

The resulting mean of average q (after winsorization) is 4 to 5 times larger than the median. (for instance, the median and the mean of q* respectively are 4.2 and 19 for the whole sample). Although not shown in this paper, when instead we use reported total assets (Compustat item 6), average q is also skewed upward, which is also the case in previous literature (Edgerton, 2010).

Although Table 2 shows summary statistics over all years, we show more summary statistics over time and by group for selected variables in appendix tables A6 to A8. All company-level variables are winsorized by 2 percent at the top and bottom of the distribution (this includes the investment rate, average q, the cash flow ratio and the leverage ratio).

The real rate of GDP growth dropped from 4.4 percent to 2.7 percent from 1998 to 2006 (Economic Report of the President, Council of Economic Advisors, 2012). The yield on 10-year Treasury bonds was also smaller in 2006 than in 1998 (4.97 percent compared to 5.35 percent). http://www.gpo.gov/fdsys/browse/collection.action?collectionCode=ERP

Our baseline results as reported in Tables 3 to 6 are based on q proxies using PPE as the book value, 2 percent of winsorization and parameter value ψ=1. We run regressions separately with q proxies using total assets as the book value. We also experimented with other levels of winsorization (including 1, 5, and 10 percent) and use alternative parameter value ψ=0.1 or 10. Our results are not affected in any significant way. Tables are available upon request.

Christiano et al. (2005) proposes a model with an adjustment costs depending on lagged and current investment (see also Eberly et al., 2012).

Many empirical studies have found that proxies for internal funds have explanatory power on investment. However empirical studies of financing constraints find that the neoclassical model is precisely rejected for the group of constrained firms, meaning that the standard neoclassical model with convex costs yields reasonable estimates (see Hasset and Hubbard, 2002 for a brief review of the literature).

See appendix A for a description of the construction of industry-level intangible-intensity.

Refer to the Data section and Table 1 for definitions of the q terms. Here we show results using the physical-only q term with total assets as the denominator. In the Appendix, we show results using the physical-only q term with physical assets as the denominator.

The literature has not reached a consensus on the elasticity of investment with respect to the cost of capital. Early estimations using aggregate data generally imply small elasticity. More recent estimations with firm level data are generally smaller but still imply substantial adjustment cost. For example, Desai and Goolbes (2004) estimate the coefficients of the ETT term to be between 0.6 and 0.9. Edgerton (2010) shows similar results. House and Shapiro (2008) show their finding that the supply elasticity of investment to the temporary bonus depreciation is much larger compared to previous literature using aggregate data. Their results imply a coefficient on the tax term to be between 0.33 and 0.7.

We also directly estimate marginal effects and find similar results than these back-of-the envelope calculations

Although we base our reported elasticity calculations on estimated marginal effects, it is possible to do a quick back-of-the-envelope calculation of reach similar values. For instance this simple calculation of the elasticity of the ETT in the model with a physical-only q proxy based on Table 2, column 1 can be calculated as e=β^*ETT2000¯/I/K2000¯=0.383*(1.16)/(0.26)=1.7.

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