## _wp14104

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---

### I. Summary and motivation
- Temporary investment tax incentives (bonus depreciation) were used as economic stimulus (CBO 2008); 2002 allowed immediate deduction of an additional 30 percent of certain qualified physical asset purchases; 2003 increased immediate deduction to 50 percent for investment made through the end of 2004.
- Motivation for including intangibles:
  - Section 197 of the Internal Revenue Code restricts amortization of certain purchased or internally developed intangible assets.
  - Temporary tax investment incentives are not applicable to a large class of purchased or internally developed intangible assets.
  - Physical and intangible investments may interact in production and financing decisions.
  - In the sample, intangible-intensive firms represent 64.6 percent of total physical assets and 85 percent of total intangible assets.

### II. Theory: tax-adjusted q with intangible assets
- Model setup and key definitions:
  - Production with physical assets K and intangible assets u: F(K, u, X); stochastic productivity z.
  - Investment tax parameters: φ_i (investment tax credit), z_i (present value of tax depreciation allowances); for intangibles φ_u = 1 (full expensing).
  - Adjustment costs quadratic: Ψ_i = ψ_i (I_i^2 / K_i).
- Main theoretical insights:
  - Proposition 1: average q q̄ = P / book value of total assets is a weighted average of marginal q of physical and intangible assets with weight S_m equal to physical share of total assets (equation (6)).
  - When S_m < 1, average q is not equal to tax-adjusted marginal q; adjusting q for intangibles is essential.
  - For sufficiently temporary tax changes, short-run steady-state approximations yield an identity expressing unobserved marginal q through observable quantities and define a q factor η that scales average q to approximate marginal q (equation (10)).

### III. Data and measurement (1998–2006)
- Data sources and construction:
  - Firm-level data from Compustat; industry-level physical and intangible stocks self-constructed using BEA capital flow tables and CHS (Corrado, Hulten, and Sichel 2005) methodology for intangibles.
  - Sample period: 1998 to 2006; finance, insurance, and utilities excluded.
  - Intangibles include computerized information, scientific and non-scientific innovation property (R&D), firm-specific human capital, organizational capital, advertising/brand equity.
  - Intangible stocks constructed at two-digit NAICS industry level for 20 industries and 51 asset types; stocks via perpetual inventory method (PIM).
- Aggregate levels and growth:
  - Total investment in physical assets: $8.8 trillion over 9 years, representing 55 percent of total investment; three fourth of physical investment were in equipment and software.
  - Stock of physical assets: $82.1 trillion over 9 years, or 89 percent of all capital stock; two thirds of physical stock were structure assets.
  - Investment in intangible assets (1998–2006): $7.2 trillion, about 45 percent of total corporate investment; average annual growth rate 3.7 percent.
  - Stock of intangible assets (1998–2006): $10.6 trillion, about 11 percent of total assets; initial stock about 7 percent in 1998.
- Key constructed variables:
  - Physical-only q: ratio of market value of equity and debt to book value of physical assets.
  - Intangible-adjusted q q*: scale firm book value of physical assets by industry-level ratio of physical to total assets; q*_m further adjusts q* by q factor η.
  - Equipment tax term (ETT) and structures tax term (STT): industry-weighted present values of depreciation allowances for equipment and structures.
- Winsorization and sample sizes:
  - Data winsorized at the two percent level.
  - Sample sizes: All N = 45,064; Top 3,500 N = 35,732; Top 1,500 N = 23,753; Top 500 N = 10,691.

### IV. Policy experiment: bonus depreciation design and PV calculation
- Policy chronology:
  - JCWAA (March 11, 2002): 30 percent bonus depreciation for qualified property acquired after September 11, 2001 and placed in service before September 11, 2004.
  - JGTRRA (May 28, 2003): increased first-year bonus depreciation to 50 percent for qualified physical assets acquired after May 5, 2003 and placed in service before January 1, 2005.
  - Eligible properties: assets with MACRS recovery period of 20 years or less, water utility property, certain computer software, qualified leasehold improvements.
- Present value (PV) construction:
  - Follow Cummins, Hasset, and Hubbard (1994) and House and Shapiro (2008); mid-year convention; discount rate assumed 5 percent in main text (table A4 uses 6 percent in some calculations).
  - When policies overlap within a calendar year, PV is the day-weighted average of PVs under overlapping policies (example: software PV in 2003 = (125/365)*0.933 + (240/365)*0.952 = 0.945).
  - Industry-level PV: weighted average of asset-specific PVs using industry investment shares.

### V. Empirical approach and estimation
- Empirical specifications:
  - Physical-only model: I^K_it/K^K_{i,t-1} = α + β q_{it-1} + γ τ_{it-1} + X'_{it} Γ + ε_it, where τ is tax term (present value of investment tax incentives).
  - Intangible-adjusted specifications: use q* and q*_m replacing q.
  - Tax term constructed as industry-weighted averages of z_{j,t} for asset types; ETT and STT computed separately.
- Identification:
  - Exploit temporariness and asset-type differentiation of JCWAA and JGTRRA to identify intertemporal shifting responses.
- Econometrics:
  - System GMM (Blundell and Bond 2000) used to address endogeneity; instruments are lagged values (fourth lags and earlier for first-difference equations); ETT, STT, year dummies treated as exogenous.
  - Diagnostics: AR(1), AR(2) Arellano-Bond tests and Hansen over-identification tests reported.

### VI. Main empirical results and magnitudes
- Overall pattern:
  - Intangible-adjusted models yield larger estimated investment responses to tax incentives than physical-only models.
  - Differences in responsiveness are larger for intangible-intensive firms and increase with firm size.
  - Adjusting the denominator of q for book value of intangibles captures most of the difference between intangible-adjusted and physical-only estimations.
  - After moving to intangible-adjusted q, cash-flow coefficients become less significant, consistent with reduced measurement error.
- Tax-term coefficient examples (system GMM estimates):
  - ETTjt coefficients are negative and often highly significant: All Firms -0.614*** ([0.084]) (Table 5); Top 3,500 -0.527*** ([0.088]) (Table 4).
  - STTjt coefficients are large negative and highly significant: All Firms -1.485*** ([0.134]) (Table 5); Top 3,500 -1.319*** ([0.136]) (Table 4).
- Elasticities and response magnitudes (largest 500 firms, 2000–2004 examples):
  - Average ETT term decreased by 0.025 units among the largest 500 firms from 2000 to 2004.
  - Average investment rate in 2000: 0.26.
  - Physical-only model implies after-tax cost elasticity of investment = 1.7 (illustrative computation: 0.383*(1.16)/(0.26) = 1.7).
  - Intangible-adjusted model implies elasticity = 1.9.
  - By intangible intensity (Top 500):
    - Intangible-intensive firms: physical-only elasticity = 3.3; intangible-adjusted elasticity = 7.4.
    - Physical-intensive firms: physical-only elasticity = 1.1; intangible-adjusted elasticity = 1.7.
- Aggregate investment rate changes (asset-weighted averages):
  - Largest 500 firms:
    - Intangible-adjusted model: mean investment rate increased by 3.7 percentage point from 25.8 percent in 2000 to 29.5 percent in 2004 (14.3 percent of aggregate investment in 2000).
    - Physical-only model: increase of 0.95 percentage points (3.7 percent of aggregate investment in 2000).
    - Intangible-adjusted impact is 3.9 times physical-only impact for Top 500.
  - Largest 1500 firms:
    - Intangible-adjusted increase: 3.13 percentage points; physical-only increase: 0.96 percentage points; intangible-adjusted impact 3.25 times physical-only.
  - Largest 3500 firms:
    - Intangible-adjusted increase: 3.17 percentage points; physical-only increase: 1.32 percentage points; intangible-adjusted impact 2.34 times physical-only.
  - All firms:
    - Intangible-adjusted increase: 3.46 percentage points; physical-only increase: 1.54 percentage points; intangible-adjusted impact 2.25 times physical-only.
- Comparison to existing literature:
  - Physical-only model ETT coefficient -0.61 for all firms, consistent with Desai and Goolsbee (2004), Edgerton (2010).
  - STT estimates in this study (1.15 to 1.49 in some specifications) are larger than some prior work, reflecting industry differences in structure shares.

### VII. Heterogeneity, mechanisms, and robustness
- Heterogeneity:
  - Intangible-intensive industries: manufacturing, wholesale trade, information, professional/scientific/technical services — intangible assets close to a quarter of total assets in these industries.
  - Physical-intensive industries: agriculture, mining, real estate — physical assets over 97 percent of total assets.
  - q proxies (physical-only, q*, q*_m) show large within- and across-industry dispersion; intangible adjustment affects intangible-intensive industries more.
- Suggested mechanisms for greater responsiveness of intangible-intensive firms (not directly tested):
  - Greater dependence on internal cash financing; less likely to raise external funds.
  - Complementarity between physical and intangible assets: physical tax incentives may indirectly encourage intangible investment.
  - Higher share of investment eligible for bonus depreciation: about 90 percent of intangible-intensive firms’ physical asset stocks are equipment eligible for bonus depreciation versus 70 percent for physical-intensive firms.
- Robustness and diagnostics:
  - Intangible-adjusted models improve instrument validity (Hansen tests) in many samples.
  - Results robust to alternative sample end dates (2004 or 2005) and higher winsorization levels (5 percent and 10 percent do not affect baseline regressions).

### VIII. Policy implications and suggested future research
- Policy implications:
  - Accounting for intangible assets materially changes estimated firm-level and aggregate investment responses to temporary tax incentives.
  - Intangible-intensity is an important source of heterogeneity; tax policy that targets physical assets can have amplified effects in economies with substantial intangible capital.
  - Physical-only models likely understate the aggregate impact of temporary bonus depreciation, especially among large, intangible-intensive firms.
- Suggested future research:
  - Directly test proposed mechanisms (financial constraints, complementarity between asset types, eligibility differences) to explain heterogeneity in responsiveness.

*Source: _wp14104 (excerpted content provided)._

### 1. Summary Statistics, 1998-2006 .......................................................................................

### 1. Summary Statistics, 1998-2006

### I. Introduction and motivation
- Temporary investment tax incentives (bonus depreciation) were increasingly used as an economic stimulus policy (CBO 2008).
- Objective: incorporate recent developments on the measurement of intangible assets and re-evaluate the effect of temporary investment incentives in the US in the early 2000s.
- Key motivations for including intangibles:
  - Section 197 of the Internal Revenue Code does not allow companies to amortize certain purchased intangible assets or internally developed assets.
  - Temporary tax investment incentives are not applicable to a large class of purchased or internally developed intangible assets.
  - Physical and intangible investments may interact in production or financing decisions, altering the link between physical investment and its after-tax cost of capital.
  - Intangible-intensive firms tend to be larger and represent a larger fraction of aggregate investment; in the sample, intangible-intensive firms represent 64.6 percent of total physical assets and 85 percent of total intangible assets.
- Empirical context: 2002 tax bill allowed an immediate deduction of an additional 30 percent of certain qualified physical asset purchases; 2003 increased immediate deduction to 50 percent for investment made through the end of 2004. The policies were temporary and asset-class differentiated.

### Theoretical and empirical approach
- Model: adapt a tax-adjusted q model (Hayashi 1982) and extend it to include intangible assets.
- Theoretical insights:
  - A familiar relation between average q and investment holds once q is adjusted for intangible assets.
  - In presence of intangibles, marginal q is not equal to average q. When tax changes are temporary, marginal q can be approximated by average q after adjusting for the share of intangible assets.
- Empirical challenges:
  - Average q reflects market value and book value of intangible assets; stock prices proxy market value, but book value requires appropriate accounting measurement.
  - Need to measure intangible asset stocks using industry-level data to include a wide range of intangible assets not captured at firm-level.

### Data and measurement
- Data combined:
  - Firm-level data on physical investment and firm value from Compustat.
  - Self-collected industry-level data on stocks of physical and intangible assets from 1998 to 2006.
- Definition of intangible assets follows Corrado, Hulten, and Sichel (2005) and includes computerized information, scientific and non-scientific innovation property (e.g., R&D), and economic competencies (firm-specific human capital, organizational skills, advertising).
- Rationale for industry-level intangible stocks:
  - Allows inclusion of a wide range of intangible assets not measurable at firm level.
  - Enables construction of industrial-level physical asset stocks based on national accounts and comparison with prior studies.
- Notes on firm coverage and concentration:
  - The largest 500 firms represent 26 percent of total physical investment, the largest 1500 firms represent 57 percent, and the largest 3500 firms represent 82 percent.
  - At the firm level, intangible-intensive firms represent 64.6 percent of total physical assets and 85 percent of total intangible assets.

### Main empirical results
- Replication of physical-only model:
  - Consistent with prior studies, the physical-only model finds moderate investment responses to tax incentives.
- Intangible-adjusted model (allows heterogeneity in firms’ intangible share):
  - Intangible-intensive firms are more responsive to investment incentives than physical-intensive firms.
  - Differences in responsiveness are accentuated among larger firms.
  - Example (Top 500 firms):
    - Physical-only model estimates an investment price elasticity of 3.3 among intangible-intensive firms.
    - Intangible-adjusted model estimates an elasticity of 7.4 among intangible-intensive firms.
  - Relative impacts of intangible-adjustment on estimated investment response to bonus depreciation:
    - Among the top 500 firms, intangible-adjusted model implies investment response is 2.3 times as large as the physical-only model.
    - Among the top 1500 firms, intangible-adjusted model implies response is 1.8 times as large.
    - Among the top 3500 firms, intangible-adjusted model implies response is 1.2 times as large.
  - Aggregate effect example:
    - Intangible-adjusted model suggests bonus depreciation increases overall investment by 14.3 percent between 2000 and 2004 among the top 500 firms.
    - Physical-only model suggests an increase of 3.7 percent for the same group and period.
- Possible mechanisms for greater responsiveness of intangible-intensive firms (suggested, not directly tested):
  - Intangible-intensive firms may be less likely to raise external funds and more dependent on internal cash financing (Falato, Kadyrzhanova, and Sim 2013).
  - Complementarity between physical and intangible assets: bonus depreciation may encourage intangible investment indirectly.
  - Eligibility differences: bonus depreciation applied only to physical assets with a recovery period of 20 years or less (short-lived “equipment”); in the sample almost 90 percent of intangible-intensive firms’ stocks of physical assets are equipment eligible for bonus depreciation, compared to 70 percent among physical-intensive firms.

### Contribution to literature
- Complements empirical q-investment literature by allowing firms’ response to investment costs to vary with intangible intensity.
- Differs from prior heterogeneous-assets studies (Wildasin, 1984; Hayashi and Inoue, 1991; Cummins and Dey, 1998; Bontempi et al., 2004) by explicitly considering the role of intangibles in both theory and empirical measures of q.
- Contrasts with previous findings of small responses to investment tax incentives by highlighting substantial heterogeneity: large and intangible-intensive firms can be very responsive.

*Source: _wp14104 - 1. Summary Statistics, 1998-2006 (excerpt) from the provided PDF content.*

### Section II develops a tax-adjusted q model with intangible assets and discusses its new

### _wp14104 - Section II develops a tax-adjusted q model with intangible assets and discusses its new

### Intangible assets and tax-adjusted q: theory
- Model setup
  - Firm produces with two asset types: physical assets (K, measured) and intangible assets (u, unmeasured) with constant returns to scale production technology F(K, u, X), and stochastic productivity z.
  - Firm chooses investments I^K and I^u to maximize expected present value of future income as in (1) subject to accumulation equations (2) for K and u for s ≥ 0.
  - Corporate tax rate τ and differentiated tax treatments on physical and intangible investment enter the problem: φ_i captures investment tax credit for asset i and z_i captures present value of tax depreciation allowances on a dollar of investment in physical assets. In the US, expenditure on intangible assets is fully expensed and deducted, so φ_u = 1.
  - Adjustment costs are quadratic and homogeneous in investment and assets, parameterized as Ψ_i = ψ_i (I_i^2 / K_i). Real discount factor β_t with β_t+s = Π_{j=1}^{s} β_{t+j}.
- First-order conditions and marginal q
  - Lagrangian multiplier associated with the asset accumulation constraint is introduced; first-order conditions (3) and (4) yield investment rate expression (5), showing investment rate depends on marginal q (pre-tax marginal value) and the tax term capturing difference between tax and economic depreciation.
- Average q as weighted average
  - Define ex-dividend market value P and average q as q̄ = P / book value of total assets. Proposition 1: average q is a weighted average of marginal q of physical and intangible assets (equation (6)), with weight given by the share of physical assets in total assets, S_m.
  - Special cases:
    - If S_m = 1 (only physical assets), average q equals marginal q of physical assets and the model nests the standard q model.
    - When S_m < 1, average q is not equal to the tax-adjusted marginal q term in (5); properly accounting for intangible assets is essential to correctly evaluate investment response to tax incentives.

### Short-run approximations of long-lived assets
- Motivation for approximation
  - Temporary changes in bonus depreciation (temporary increases in present value of depreciation allowances z) complicate exact solutions because investment decisions are forward- and backward-looking and investment depends on shadow values of both asset types when assets are imperfect substitutes.
  - For sufficiently temporary tax changes, replace q^m, q^u, K^m, K^u by steady-state values to obtain short-run approximations (standard practice when economic depreciation is low and asset stocks change little in the short run).
- Implications and identities
  - Under the steady-state approximation, investment rate expressions simplify and yield an identity expressing unobserved marginal q through observable quantities (equation (9)).
  - Define the “q factor” η that scales average q to restore the standard empirical relation between marginal q and average q (equation (10)): marginal q ≈ q̄ × q factor.
  - The q factor depends on asset composition and tax/depreciation parameters and requires assumptions on parameters; Section IV evaluates sensitivity to different parameter assumptions.

### Methodology and data
- Policy experiment: bonus depreciation allowances
  - Job Creation and Worker Assistance Act (JCWAA) passed on March 11, 2002 introduced first “bonus depreciation” allowing immediate write-off of 30 percent of adjusted basis for qualified physical property acquired after September 11, 2001 and placed in service before September 11, 2004.
  - Jobs and Growth Tax Relief Reconciliation Act (JGTRRA) on May 28, 2003 increased first-year bonus depreciation to 50 percent for qualified physical assets acquired after May 5, 2003 and placed in service before January 1, 2005.
  - Eligible properties included assets with MACRS recovery period of 20 years or less, water utility property, certain computer software, and qualified leasehold improvements.
  - Two useful features: (i) differential treatment by asset type (present value of provision increases with depreciable lives among qualified short-lived assets); (ii) explicit temporariness, creating incentive to move investment forward.
- Empirical specifications
  - Three model specifications:
    - Physical-only model (based on (7) and (11)): I^K_it/K^K_{i,t-1} = α + β q_{it-1} + γ τ_{it-1} + X'_{it} Γ + ε_it, where I^K/K is physical investment rate, q is q-term (physical-only), τ is tax term (present value of investment tax incentives), and X_{it} controls for cash flow normalized by physical assets, leverage, lagged investment, and other firm characteristics.
    - Physical-only q term with intangible-adjusted q proxy.
    - Intangible-adjusted q term and intangible-adjusted q proxy following (10) and (12).
  - Tax term computed as industry-weighted average of present values of tax depreciation allowances z_{j,t} for asset types j; ETT (equipment tax term) and STT (structure tax term) constructed accordingly.
- Econometric methods
  - Estimation challenges: endogeneity of explanatory variables, firm-specific effects, and potential permanent measurement error from ignoring intangibles.
  - Use system GMM estimator (Blundell and Bond 2000) with endogenous variables instrumented by lagged values (lags of 4 periods or earlier for first-difference equations and first-differences of instruments in level equations). Exogenous variables include tax terms and year dummies.
  - Diagnostics reported: AR(1) and AR(2) (Arellano and Bond 1991) and Hansen over-identification test.
  - Note: fixed effects estimations also performed (available on request).
- Data construction
  - Sample period: 1998 to 2006 (ends before 2008 recession); results robust to ending year 2004 or 2005.
  - Firm-level data from Compustat; exclude finance, insurance, and utilities.
  - Industry-level physical assets from BEA capital flow tables on investment in equipment, software and structures for 20 two-digit industries and 51 asset types; stocks computed via perpetual inventory method (PIM); separate corporate from non-corporate investment using BEA Surveys of Current Businesses.
  - Intangible assets constructed using Corrado, Hulten, and Sichel (2005) (CHS) methodology, including computerized information, R&D, firm-specific human capital, organizational skills, brand equity, etc.; industry-level measures for 20 two-digit industries for 1998–2006. Note: self-developed intangible assets and purchased managerial assets are generally expensed for accounting purposes.
  - Physical-only q proxy defined as ratio of market value of equity and debt to book value of physical assets (book value proxied by plant, property, and equipment). Intangible-adjusted q proxy q* constructed by scaling firm book value of physical assets by industry-level ratio of physical to total assets; q*_m denotes q* adjusted by q factor.
- Summary statistics and variation sources
  - Data winsorized at the two percent level.
  - Investment rate, physical-only q, ETT and STT similar to prior studies.
  - Main sources of variation in intangible-adjusted q terms are the ratio of physical to total assets (industry-level composition) and the q factor η.
  - Bonus depreciation significantly increased present value of depreciation allowances z from 2000 to 2004, introducing industry-level and time variation in ETT; STT variation mainly across industries since few structures were eligible.
  - Industry patterns:
    - Intangible-intensive industries (manufacturing, wholesale trade, information, professional/scientific/technical services): intangible assets close to a quarter of total assets.
    - Physical-intensive industries (agriculture, mining, real estate): physical assets represent over 97 percent of total assets.
    - Intangible shares are relatively stable over time, with a modest increase early in the sample and stabilization since early 2000s.
  - Cross-sectional variation: physical-only q, q*, and q*_m show large within- and across-industry dispersion; adjusting for intangibles affects intangible-intensive industries more than physical-intensive ones.

### Empirical strategy and identification considerations
- Identification through temporary bonus depreciation episodes (JCWAA and JGTRRA) which:
  - Provide differential tax treatment by asset type and depreciable life.
  - Are temporary, incentivizing intertemporal shifting of investment.
- Use of system GMM addresses endogeneity if valid instruments available; presence of intangibles may introduce permanent measurement error that lagged q alone cannot correct—motivating explicit inclusion of intangible-adjusted q and q factor.
- Diagnostic checks include AR(1), AR(2), and Hansen tests; specification tests indicate serial correlation not a main concern after including lagged investment.

### Preview of results
- The paper reports baseline results in Tables 2 to 5 for different firm samples by size and intangible intensity; the authors state: “Our key findings can be summarized as follows.” (Detailed baseline estimates and sensitivity analyses are presented in Section IV and appendices.)

_italics: Source: _wp14104 - Section II develops a tax-adjusted q model with intangible assets and discusses its new_

### 1. Estimated investment responses differ between intangible- and physical-intensive firms. This

### _wp14104 - 1. Estimated investment responses differ between intangible- and physical-intensive firms. This

### Key findings
- Estimated investment responses differ between intangible- and physical-intensive firms. This result holds in the physical-only model and intangible-adjusted model. The difference increases with firm size.
- Estimated investment responses are generally larger in intangible-adjusted models than physical-only models. The differences between ETT coefficients are generally larger among intangible-intensive firms.
- Adjusting for the book value of intangible assets in the q proxy accounts for the majority of the difference between intangible-adjusted and physical-only estimations.
- The physical-only q proxy is correlated with ETT and STT, implying measurement error in physical-only q is persistent and correlated with instruments, particularly for intangible-intensive firms.
- After moving from physical-only models to intangible-adjusted models, coefficients of cash flow become less significant, consistent with intangible-adjusted q containing less measurement error.

### Results by model, firm type, and sample size
- Sample selection:
  - Largest firms selected each year based on total assets; large firms are less likely to be financially constrained.
  - Industry classified as intangible-intensive if intangible to total assets ratio > sample median; physical-intensive otherwise.
- Largest 500 firms (Table 2 summary):
  - Physical-only model (column 1): coefficients of ETT and STT are significant for all firms; STT always significant and larger for intangible-intensive firms; ETT not significant for some splits.
  - Hansen test:
    - Decisively rejects joint test of model and instrument validity for all firms (column 1).
    - Rejects at the 5 percent level for intangible-intensive firms (column 2).
  - Intangible-adjusted q proxy (columns 4–6):
    - Larger coefficients of ETT and STT for all firms (compare column 4 to column 1).
    - Difference larger for intangible-intensive firms (compare column 5 to column 2).
    - For intangible-intensive firms, ETT and STT change from not significant to large and significant when using intangible-adjusted q.
    - Hansen test no longer rejects validity of instruments in intangible-adjusted models for these groups.
  - Intangible-adjusted q proxy with intangible-adjusted q term (columns 7–9):
    - Similar conclusions to columns 4–6; tax terms larger than in physical-only q proxy models.
    - Results in columns 7–9 very similar to columns 4–6, suggesting little additional gain from adjusting average q vs. marginal q after using more reliable proxies for book value of intangibles.
- Larger samples (Tables 3–5):
  - Similar conclusions: intangible-adjusted models generally have larger ETT and STT coefficients than physical-only models.
  - Difference larger for intangible-intensive firms.
  - Most of the difference captured by adjusting denominator of q term for book value of intangible assets.
  - Hansen tests in intangible-adjusted models remain valid at the 3 percent level in most cases, although rejected for the largest 3500 firms and the full sample when intangible-intensive and physical-intensive firms are not separated.
- Trend across firm size:
  - Differences in ETT and STT coefficients between physical-only and intangible-adjusted models become less pronounced moving from largest firms to a more general sample, implying physical-only model leads to more biased results for larger firms than for smaller firms.
- Data limitation:
  - Use of consolidated data such as Compustat includes foreign and domestic investment; bonus depreciation applies only to domestic investment. If intangible-intensive firms are more worldwide oriented, reported differences serve as a conservative lower bound.

### Comparison to literature
- Literature variation:
  - Desai and Goolsbee (2004) and Edgerton (2010) estimate ETT coefficient between -0.6 and -0.9.
  - House and Shapiro (2008) imply an ETT coefficient between -0.33 and -0.7.
  - Desai and Goolsbee (2004) estimate STT to be -0.02 (significant in 1961-2003, positive in 1997-2003).
  - Edgerton (2010) finds STT ranges from -0.05 to 0.11 and is significant for large firms.
- This paper:
  - Physical-only model ETT coefficient is -0.61 for all firms, consistent with the literature.
  - STT estimates range from 1.15 to 1.49 in this study, larger than prior work; likely reflects differences in share of structure assets across industries.
- Heterogeneity:
  - Larger and more intangible-intensive firms are more responsive than average firms; consistent with findings in Edgerton (2008) and Mahon and Zwick (2014) about importance of firm heterogeneity and short-run cash flow benefits.

### The economic size of the impact of bonus depreciation
- Back-of-the-envelope elasticity recovery (largest 500 firms, 2000–2004):
  - From 2000 to 2004, average ETT term decreased by 0.025 units among the largest 500 firms.
  - Average value of investment rate in 2000: 0.26.
  - Physical-only model (column 1) implies after-tax cost elasticity of investment = 1.7.
  - Intangible-adjusted model (column 7) implies elasticity = 1.9.
  - By intangible intensity:
    - Intangible-intensive firms: physical-only elasticity = 3.3; intangible-adjusted elasticity = 7.4.
    - Physical-intensive firms: physical-only elasticity = 1.1; intangible-adjusted elasticity = 1.7.
- Aggregate investment rate changes (asset-weighted average of physical- and intangible-intensive firms):
  - Largest 500 firms:
    - Intangible-adjusted model: mean investment rate increased by 3.7 percentage point from 25.8 percent in 2000 to 29.5 percent in 2004.
    - Physical-only model: increase of 0.95 percentage points.
    - These increases correspond to 14.3 percent and 3.7 percent of aggregate investment in 2000 respectively.
    - Impact of bonus depreciation estimated by intangible-adjusted q-model is 3.9 times as large as that of a physical-only model among the largest 500 firms.
  - Largest 1500 firms:
    - Intangible-adjusted increase: 3.13 percentage points.
    - Physical-only increase: 0.96 percentage points.
    - Intangible-adjusted impact is 3.25 times physical-only impact.
  - Largest 3500 firms:
    - Intangible-adjusted increase: 3.17 percentage points.
    - Physical-only increase: 1.32 percentage points.
    - Intangible-adjusted impact is 2.34 times physical-only impact.
  - All firms:
    - Intangible-adjusted increase: 3.46 percentage points.
    - Physical-only increase: 1.54 percentage points.
    - Intangible-adjusted impact is 2.25 times physical-only impact.
- Elasticity calculation example provided in text:
  - Elasticity = 0.383*(1.16)/(0.26) = 1.7 (illustrative computation shown for physical-only case).

### Conclusion and implications
- Accounting for intangible assets materially changes estimated firm-level investment responses to temporary tax incentives (bonus depreciation), particularly for intangible-intensive and larger firms.
- Intangible-intensity is an important source of firm heterogeneity; differences in investment responses increase with firm size.
- Incorporating intangible assets implies a much larger aggregate impact of bonus depreciation than implied by physical-only models.
- Potential explanations why larger and intangible-intensive firms are more responsive:
  - More likely to be financially constrained and dependent on internal cash financing.
  - Intangible investment is less costly to adjust than physical investment, making overall investment less “sticky.”
  - On average, they have a larger fraction of investment eligible for bonus depreciation.
- Suggested future research: direct tests of the proposed explanations.

*Source: _wp14104 - 1. Estimated investment responses differ between intangible- and physical-intensive firms. This*

### 2004. Capital Heterogeneity: Does It Matter? Fundamental Q and Investment on a Panel

### 2004. Capital Heterogeneity: Does It Matter? Fundamental Q and Investment on a Panel

### Main empirical findings (system GMM regressions)
- q estimates:
  - Physical-only q (qijt/(1-τt)) positive and statistically significant in many specifications (examples):
    - Top 1500 firms, All Firms: 0.002*** (standard error [0.000]) (Table 3, column (1))
    - All Firms (All sample, System GMM): 0.002*** (standard error [0.000]) (Table 5, column (1))
  - Intangible-adjusted q measures:
    - q*ijt/(1-τt) positive and significant in intangible-adjusted specifications (examples):
      - Top 3500, Intangible-adjusted q term, Physical-intensive firms: 0.002*** (standard error [0.001]) (Table 4, column (7)–(9) context)
    - q*mijt/(1-τt) also positive and significant where reported (Table 2–5).
- Tax terms:
  - ETTjt (Effective Tax Term) coefficients are negative and often highly significant:
    - All Firms (All sample, Table 5): -0.614*** ([0.084])
    - Top 3500 (Table 4): -0.527*** ([0.088])
  - STTjt (Shadow Tax Term) coefficients are large negative and highly significant:
    - All Firms (All sample, Table 5): -1.485*** ([0.134])
    - Top 3500 (Table 4): -1.319*** ([0.136])
- Other firm controls:
  - CFijt/Kijt-1 (cash flow scaled by lagged capital) generally small negative; significance varies by sample:
    - All Firms (All sample, Table 5): -0.003 ([0.007]) (not significant)
    - Intangible-intensive firms (All sample, Table 5): -0.021** ([0.009])
  - Levjt (leverage) typically positive and significant in pooled samples:
    - All Firms (All sample, Table 5): 0.040*** ([0.011])
  - Lagged investment (Lag (Iijt/Kijt-1)) shows persistence:
    - All Firms (All sample, Table 5): 0.192*** ([0.048])
- Diagnostic tests:
  - AR(1) and AR(2) and Hansen statistics reported across Table 2–5 with p-values; examples:
    - All Firms (All sample, Table 5) AR(1) = -7.657 (p-val 0), AR(2) = -0.136 (p-val 0.892), Hansen = 174.4 (p-val 1.04e-09).
  - Notes indicate instrumenting strategy using fourth lags and earlier values for first-difference equations and using ETT, STT, year, and one lag difference for levels equation.

### Heterogeneity across firm types and sample sizes
- Intangible-intensive vs Physical-intensive differences (selected results and patterns):
  - Intangible-intensive firms show larger mean/median q measures in Table 1 (Panel B):
    - qijt median/mean for intangible-intensive firms: 5.38/17.7 (Std. Dev. 42.9) (Table 1, Panel B)
  - Physical-intensive firms show lower q measures (Table 1, Panel C):
    - qijt median/mean for physical-intensive firms: 2.81/14.2 (Std. Dev. 46.7) (Table 1, Panel C)
  - Implied price elasticity of I/K (Table 6) differs markedly:
    - All Firms: -2.11 (Conventional q proxy, Conventional model) (Table 6, column (1))
    - Intangible-intensive firms: -5.51 (Conventional q proxy, Conventional model) (Table 6, column (2))
    - Physical-intensive firms: -1.74 (Conventional q proxy, Conventional model) (Table 6, column (3))
- Sample size effects (Top 500, Top 1,500, Top 3,500, All firms) influence coefficient magnitudes and statistical significance in Tables 2–5; examples:
  - Top 500 (Table 2) shows q coefficients smaller or less significant in some columns compared with Top 1,500 and All firms.

### Quantified effects of bonus depreciation (2000–2004) and implied elasticities (Table 6)
- Implied price elasticity of I/K (selected entries):
  - All Firms: -2.11 (Conventional model, Conventional q proxy) (Table 6, column (1))
  - Intangible-intensive firms: -5.51 (Conventional model, Conventional q proxy) (Table 6, column (2))
  - Physical-intensive firms: -1.74 (Conventional model, Conventional q proxy) (Table 6, column (3))
  - Comparable estimates when using q adjusted for the book value of intangible assets:
    - All Firms: -2.15 (Table 6, column (4))
    - Intangible-intensive firms: -5.63 (Table 6, column (5))
- Total effect on I (investment) from 2000 to 2004 (selected entries):
  - All Firms: 1.54% (Conventional q proxy, Conventional model) (Table 6, column (1), row “Total effect on I from 2000 to 2004”)
  - Intangible-intensive firms: 3.46% (same specification) (Table 6, column (2))
  - Physical-intensive firms: (entry not reported in the same block for this line in column (3) but parallel values shown across columns)
  - Using intangible-adjusted q (Chen & Dauchy model):
    - All Firms: 1.55% (Table 6, column (7))
    - Intangible-intensive firms: 3.46% (Table 6, column (8))
- Implied growth of I from 2000 to 2004 (selected entries):
  - All Firms: 4.6% (Table 6, column (1))
  - Intangible-intensive firms: 10.3% (Table 6, column (2))
  - Physical-intensive firms: 4.6% (Table 6, column (3))
  - Top sample breakdowns reported for Top 3,500; Top 1,500; Top 500 with corresponding implied growth rates (Table 6, rows under “Implied growth of I from 2000 to 2004”).

### Data, measurement, and methodology notes (online appendix)
- Data coverage and period:
  - Firm panel and industry measures constructed for 1998 through 2006 (Table 1 and Appendix A).
- Intangible assets construction:
  - Follow Corrado, Hulten, and Sichel (CHS) 2005 methodology, extended to two-digit NAICS industries for 1998–2006 (Appendix A1).
  - Six broad types of intangible assets constructed, including computerized information, scientific and non-scientific R&D, firm-specific human capital, organizational skills, and brand equity (Appendix A1).
  - Investment in intangible assets over 1998–2006 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/transportation equipment manufacturing, and information (Appendix A1, paragraph).
  - Stock of intangible assets over 1998–2006 is about $10.6 trillion, or 11 percent of total assets; initial stock about 7 percent in 1998; intangible assets depreciate faster than most physical assets (Appendix A1, paragraph).
- Stock construction and depreciation:
  - Perpetual inventory method (PIM) used to construct intangible stocks; assume straight-line depreciation and investment made throughout the year (Appendix A1).
  - Table A4 lists assumed economic depreciation values (referenced).
- Physical assets:
  - Physical investment and stocks obtained from BEA tables (non-residential and residential) and distributed across industries and asset types using BEA capital flow data (Appendix A2).
- Data processing:
  - Firm-level variables are winsorized (2 percent) each year (Notes to Tables 3–6).
  - Intangible intensity classification based on the ratio of intangible to total assets of an industry with the cutoff at the median (Notes to Tables 3–6).
  - Large firms selected each year based on total assets (Notes to Tables 3–6).
  - Instrumenting strategy: instrumented variables include Lag (Iijt/Kijt-1), qijt/(1-τt), q*ijt/(1-τt), q*mijt/(1-τt), CFijt/Kijt-1, and Levjt; fourth lags and earlier values used for first-difference equation instruments; ETT, STT, year, and one lag difference used for levels equation instruments (Notes to Tables 3–6).
- Data sources referenced:
  - BEA tables and BEA value added table: “GDPbyInd_VA_NAICS_1998-2006.xls” for industry value added and indexes (Appendix A1, source BEA tables).
- Data skewness and winsorization:
  - q proxies are heavily skewed; winsorized at 2 percent and both median and mean are reported in Table 1. Higher winsorization levels (5 percent and 10 percent) reduce skewness but do not affect baseline regression results (Table 1 notes).

### Key summary statistics (selected entries from Table 1, 1998–2006)
- Sample sizes:
  - All: N = 45,064; Top 3,500: N = 35,732; Top 1,500: N = 23,753; Top 500: N = 10,691 (Table 1 header)
- Investment rates (Iijt/Kijt-1), Panel A All firms:
  - Median: 0.209; Mean: 0.374; Std. Dev.: 0.201 (All firms, Table 1, Panel A)
  - Top 500 median/mean/std: 0.173 / 0.290 (Table 1, Panel A, Top 500 column)
- q measures (selected):
  - All firms qijt 1/ : Median 4.45 / Mean 19.2 (Std. Dev. 57.0) (Table 1, Panel A)
  - Intangible-intensive firms qijt 1/ : Median 5.38 / Mean 17.7 (Std. Dev. 42.9) (Table 1, Panel B)
  - Physical-intensive firms qijt 1/ : Median 2.81 / Mean 14.2 (Std. Dev. 46.7) (Table 1, Panel C)
- Cash flow scaled by lagged capital (CFijt/Kijt-1):
  - All firms: Median -0.895; Mean 4.706 (Std. Dev. 0.201?) — note: Table 1 shows CFijt/Kijt-1: -0.895 4.706 (Std. Dev.  — as reported in table) (Table 1, Panel A)
- q_factorjt and ηjt:
  - q_factorjt: 1.142 (Std. Dev. 0.080) (Table 1, Panel A)
  - ηjt: 1.374 (Std. Dev. 0.108) (Table 1, Panel A)

*Source: _wp14104 - 2004. Capital Heterogeneity: Does It Matter? Fundamental Q and Investment on a Panel (IMF Working Paper PDF content provided).*

### 2006. Total investment in physical assets was $8.8 trillion over 9 years, representing 55 percent

### _wp14104 - 2006. Total investment in physical assets was $8.8 trillion over 9 years, representing 55 percent

### Investment and asset stock levels
- 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.

### Source BEA tables referenced (content-only list)
- 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.

### Distribution matrices of stocks and flows
- Appendix A2: two groups of matrices
  - (i) 9 matrices distributing physical asset stocks by asset and across industries, one for each year from 1998 to 2006.
  - (ii) 9 matrices for physical asset investment (same structure as (i)).
- Appendix A1: stocks and flows of corporate intangible assets over time and by industry, for 6 types of intangible.
- Combined update: 9 new matrices (1998–2006) showing distribution, across assets and within industries, of industrial corporate physical and intangible asset stocks; and 9 analogous matrices for investment flows.
- Notation:
  - 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).
- Use: matrices permit calculation of the weight of each asset’s stocks (or flows) within industries, critical to calculate the present value of depreciation allowances of $1 of investment in industry i (Appendix B).

### Tax provisions affecting depreciation (policy chronology and scope)
- JCWAA: one-year extension of the placement in service deadline available for certain property with recovery period of 10 years or more and for transportation equipment.
- Bonus depreciation and Section 179:
  - JGTRRA increased the relevant threshold for Section 179 property from $25,000 to $100,000.
  - Section 179 applies to smaller companies; may elect to expense qualifying investment up to a specified limit ($25,000 before 2003). Section 179 applies to used property (distinct from bonus depreciation).
  - Empirical treatment: baseline regressions exclude companies potentially affected by Section 179 (about 10 percent of companies in our sample and 0.05 percent of total qualified investment). Excluding them does not affect findings.

### Construction of present value (PV) of depreciation allowances (methodology)
- Method follows Cummins, Hasset, and Hubbard (1994) and House and Shapiro (2008).
- When bonus-depreciation periods do not align with calendar years, PV for a given asset and calendar year is the weighted average of PVs under the overlapping policies, weighted by number of days each policy was effective.
- Calendar-year effective days table (policy overlap summary):
  - 1998 - 2001: 365 or 366
  - 2002: 365
  - 2003: 125 240
  - 2004: 366
  - 2005 – 2006: 365
- Definitions in table note:
  - MACRS = modified accelerated recovery system under current law.
  - BD = first-year bonus depreciation allowance.
  - Job Creation and Worker Assistance Act of 2002 created 30 percent bonus depreciation for qualified capital put in place after September 11, 2001; because the Act was passed in March 2002, investors sitting in 2001 did not make investment decisions based on the reduced asset cost for that year.
  - Jobs and Growth Tax Relief Reconciliation Act of 2003 provided 50 percent first-year depreciation allowance for capital put in place after May 28.
- Example calculation:
  - Present value of depreciation allowances of software (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, PV for software in 2003 = (125/365)* 0.933 +(240/365)* (0.952) = 0.945.
- Other methodological assumptions:
  - PV of depreciation allowances for each physical asset is calculated based on applicable MACRS rule, with mid-year convention (IRS, 2010).
  - A discount rate of 5 percent is assumed (roughly the average of the rate on 10-year treasury bonds over the 9 years considered).
- Industry-level PV:
  - The present value of depreciation allowances for physical assets in a given industry and year is measured as the weighted average of depreciation allowances of each type of physical asset in the industry, weighted by investment in the asset.
  - When explaining investment in physical assets, tax-term calculations disregard intangible assets; denominator of the tax term includes only total investment in fixed assets (using matrix MF from appendix A2).

### Tax term definitions and summary statistics
- Tax term of each group of assets: (expression indicated in source) where statutory top corporate tax rate is equal to 35 percent over the period considered.
- Tables A6, A7, and A8 (referenced) show summary statistics of the equipment tax term (ETT) and the structures tax term (STT) among the sample of Compustat companies used in the empirical strategy, per year, for all firms and by firms’ intangible intensity.
- Intangible intensity: 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 paper presents summary statistics of ETT, STT, and investment rates over time and for all companies included in regressions; statistics are shown in Tables A6 to A8 and described in methodology and results sections.

### Data sources and variable definitions
- Price indices (PPI) used for intangible asset stock calculation via PIM methodology obtained from tables 64 ERP.
- Discount rate proxy: 10-year federal funds rate from Board of Governors of the Federal Reserve System, table H.15 (seasonally adjusted).
- Firm-level data: Compustat.
- Table A.9. gives variable definitions (referenced).

### Theoretical result: Proof of Proposition 1 (summary of claim)
- Claim: The ex-dividend value of the firm is equal to the value of tangible assets and intangible assets under the assumption of constant returns to scale in production technology and adjustment costs.
- Expressed as:
  - P_t = q_t^m K_{t+1}^m + q_t^u K_{t+1}^u, where q_t^m and q_t^u are marginal values and K_{t+1}^m, K_{t+1}^u are next-period tangible and intangible capital.
- Proof outline:
  - Define cum-dividend market value V_t as sum of ex-dividend market value plus dividend payout.
  - Use profit maximization first-order conditions and linear homogeneity of adjustment costs.
  - Recursively substitute first-order conditions and apply law of motion to equate value expressions.
  - Conclude by definition that the stated equality holds (Q.E.D).

*Source: _wp14104 - 2006. Total investment in physical assets was $8.8 trillion over 9 years, representing 55 percent*

### APPENDIX REFERENCES

### APPENDIX REFERENCES

### References Cited
- Internal Revenue Service, 2010. “How To Depreciate Property.” Department of the Treasury, IRS Publication 946. http://www.irs.gov/publications/p946/index.html.
- Meinen, Gerhard, Piet Verbiest, and Peter-Paul de Wolf, 1998. “Perpetual Inventory Method: Service Lives, Discard Patterns, and Depreciation Methods.” Statistics Netherlands, Department of National Accounts.
- CHS (2005, 2009) and SAS sources referenced for computerized information, copyrights, and other innovation expenses.
- BEA, NSF, IRS/SOI, BLS, OES, MPAA referenced within tables and notes for industry, R&D, and accounting data.

### Key Tables and Quantitative Content (selected highlights)
- Table A1: R&D Expenditures, By Industry: BEA/NSF vs. IRS/SOI ($ Mil. And % of All Industries)
  - NSF/BEA 1998–2001 excerpts:
    - FIRE 2/: 1,792; 1,699; 4,172; 2,631 — 1.2%; 1.0%; 2.2%; 1.3%
    - Information: 10,054; 11,633; 11,109; 12,069 — 7.9%; 8.7%; 9.5%; 12.7%
    - Manufacturing (incl.) 79,475; 85,547; 96,078; 101,099
      - Chemical manufacturing: 16.0%; 16.0%; 15.6%; 16.5%
      - Computer and electronic product manufacturing: 21.4%; 19.0%; 21.4%; 23.2%
      - Transportation equipment manufacturing: 14.2%; 14.8%; 12.7%; 11.6%
        - incl. aerospace: 4.4%; 3.3%; 2.2%; 2.2%
  - IRS/SOI 1998–2001 excerpts:
    - FIRE 2/: 1,318; 1,424; 1,612; 1,791 — 1.2%; 1.2%; 1.3%; 1.5%
    - Information: 12,161; 14,908; 18,427; 25,131 — 9.1%; 10.1%; 9.2%; 10.4%
    - Manufacturing (incl.) 86,428; 88,234; 92,304; 86,279
      - Chemical manufacturing: 25.4%; 24.7%; 22.0%; 23.7%
      - Computer and electronic product manufacturing: 18.5%; 18.3%; 16.5%; 19.1%
      - Transportation equipment manufacturing: 22.0%; 20.0%; 18.6%; 18.7%
        - incl. aerospace: 3.2%; 2.5%; 2.5%; 3.1%

- Table A2 (Parts 1–2): List of Corporate Intangible Assets Not-Included In NIPA Accounts — Definitions and Sources
  - Major intangible categories and reported % of intangible (1998–06):
    - Computerized Information: 0.26%; 0.25%
      - Source/definition: Includes development of software; total revenue from subscription to "Online directories, databases, and other collections of information" (NAICS 51114).
    - Innovative Property: 42.6%; 61.8%
      - R&D (Internal Revenue Service Form 6567): 15.1%; 21.90% — R&E qualified expenditures reported by corporations (excludes mineral exploration).
      - Copyrights and license costs: 27.5%; 39.9% — development costs in motion picture, radio/television, sound recording, book publishing industries.
      - Other product development, design, and research expense: definitions and BEA/SAS sources detailed; covers non-scientific R&D in finance and services.
    - Economic Competencies: 57.2%; 38.0%
      - Firm-specific human capital: 6.94%; 5.47% — based on BLS 1994–1995 employer-provided training surveys.
        - On the job training cost: direct firm expenses (wages of in-house trainers, outside trainers, tuition reimbursement).
        - Payments for job-related education: tuition payments; wage and salary costs of employee time in training.
      - Organizational capital: 21.6%; 17.1% — purchased organizational capital estimated from management consulting revenues and BEA I/O tables; own-organizational skills estimated as one fifth of executive time value.
      - Brand Equity: 28.7%; 15.4%
        - Advertising: IRS corporate expense data (IRS/SOI).
        - Market Research: SAS and BEA I/O tables; market research estimated as twice industry purchased services.

  - Notes: Use of NIPA input-output tables to distribute professional services; CHS uses MPAA data for motion picture estimates; specific methodological notes (percent estimates derived from BLS tables, BEA I/O trends, SAS Table 6.1).

- Table A3: Investment (Total) and Average Annual Growth Rate Of Corporate Physical And Intangible Assets (1998 – 2006) ($ Bil.)
  - US Totals: 16,106 (Total investment) — composition: 41.5% Equipment, Software; 13.4% Structures; 45.1% Intangibles
  - AAGR (Total): 2.8% — Equipment, Software: 1.0%; Structures: 5.3%; Intangibles: 3.7%
  - Selected industry examples (Investment, composition, AAGR):
    - Information (51): 1,969 — 37.8% Equipment, Software; 8.3% Structures; 53.9% Intangibles — AAGR Total: 2.7%; Equipment, Software: 0.7%; Structures: 4.3%; Intangibles: 4.1%
    - Finance and insurance (52): 1,673 — 25.1% Equipment, Software; 5.6% Structures; 69.3% Intangibles — AAGR Total: 5.0%; Equipment, Software: 1.8%; Structures: 1.4%; Intangibles: 6.5%
    - Manufacturing group examples with investment values and growth rates are listed in the table.

- Table A4 (Parts 1–3): Rate Of Economic Depreciation And Present Value Of Tax Depreciation Allowances
  - Assumptions: half-year convention; discount rate of 6%; MACRS rules and comparison to straight-line where applicable.
  - Physical assets (selected lines):
    - (4), (5), (9) Computers, peripheral, software, office, accounting equipment: Tax life 5; Tax method 200 (declining balance); Economic depreciation 0.312; NPV of tax depreciation allowances: MACRS 0.904; Bonus depreciation 30% 0.933; 50% 0.952
    - (6) Communication equipment: Tax life 5; Economic depreciation 0.15; NPV MACRS 0.904; Bonus 30% 0.933; 50% 0.952
    - (12) Engines and turbines: Tax life 15; Tax method 150; Economic depreciation 0.052; NPV MACRS 0.694; Bonus 30% 0.786; 50% 0.847
    - (6) Commercial buildings: Tax life 39; Tax method SL; Economic depreciation 0.022; NPV of tax depreciation allowances: MACRS 0.395; Bonus 30% 0.395; 50% 0.395
    - (16) Electric light and power: Tax life 20; Tax method 150; Economic depreciation 0.021; NPV MACRS 0.622; Bonus 30% 0.811; 50% 0.811
    - (30a) - (32) Single & multi family structures, nonfarm, Manufactured homes: Tax life 27.5; Tax method SL; Economic depreciation 0.014; NPV MACRS 0.504; Bonus 30% 0.504; 50% 0.504
  - Intangible assets:
    - Computerized Information: economic depreciation 0.33; NPV of tax depreciation allowances: MACRS 1; Bonus 30% 1; 50% 1
    - Scientific and non scientific R&D: economic depreciation 0.2; NPV MACRS 1; Bonus 30% 1; 50% 1
    - Firm-Specific Human Capital, organizational capital: economic depreciation 0.4; NPV MACRS 1; Bonus 30% 1; 50% 1
    - Brand Equity: economic depreciation 0.6; NPV MACRS 1; Bonus 30% 1; 50% 1

- Table A5: Stock (Total) and Compounded Annual Growth Rate Of Corporate Physical And Intangible Assets (1998 To 2006) ($ Bil.)
  - US Totals: Stock Total 92,628 — composition: 36.2% Equipment, Software; 52.3% Structures; 11.4% Intangibles
  - CAGR (Total): 0.3%; Equipment, Software: 2.1%; Structures: 0.4%; Intangibles: 8.8%
  - Selected industry stocks and CAGRs:
    - Information (51): Stock Total 8,477 — composition: 39.6% Equipment, Software; 38.4% Structures; 22.0% Intangibles — CAGR Total 3.3%; Equipment, Software: 2.3%; Structures: 13.1%; Intangibles: 84.0
    - Finance and insurance (52): Stock Total 5,304 — composition: 21.7% Equipment, Software; 39.0% Structures; 39.3% Intangibles — CAGR Total 0.2%; Equipment, Software: 0.5%; Structures: 0.2%; Intangibles: 0.7

- Tables A6–A8: Selected Statistics for Sample Firms (1999–2006)
  - Sample sizes:
    - N=45,064 (All); N=35,732 (Top 3500); N=23,753 (Top 1500); N=10,691 (Top 500)
  - ETTjt (Equipment tax term) and STTjt (Structures tax term) series (means and Std. Dev.) are reported annually 1999–2006 for All, Intangible Intensive, and Physical Intensive firm sub-samples. Examples:
    - All firms ETTjt means by year: 1999 1.161; 2000 1.160; 2001 1.160; 2002 1.141; 2003 1.137; 2004 1.135; 2005 1.164; 2006 1.167
    - All firms STTjt means by year: 1999 1.489; 2000 1.489; 2001 1.489; 2002 1.484; 2003 1.482; 2004 1.481; 2005 1.485; 2006 1.483
  - Investment rate Iijt/Kijt-1 reported by year with means and Std. Dev.; example All firms:
    - 1999 0.258; 2000 0.337; 2001 0.184; 2002 0.133; 2003 0.130; 2004 0.184; 2005 0.204; 2006 0.230
  - Notes: bonus depreciation applied to investment starting in Q4 of 2001 is noted; sample measurement timing caveat explained.

- Tables A7–A8: Sub-sample specific statistics
  - Intangible Intensive firms (selected ETTjt means): 1999 1.138; 2000 1.129; 2001 1.129; 2006 1.129
  - Physical Intensive firms (selected ETTjt means): 1999 1.204; 2000 1.206; 2006 1.250
  - Corresponding STTjt and investment rates Iijt/Kijt-1 are provided for each sub-sample across 1999–2006.

### Variable Definitions and Construction (Table A9)
- Iijt/Kijt-1 = capx128ijt / ppeveb187ijt = Investment rate
- qijt = MVAijt / BVAijt = Physical-only average q
- q*ijt = MVAijt / BVAijt * Smjt = Average q adjusting for intangibles in BVA
- q*mijt = MVAijt / BVAijt * Smjt * q_factorjt = Intangible-adjusted marginal q (based on author’s 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 - τzu jt + (1 - τ)ψ(Iujt/Kujt)] / [1 - kmjt - τzm jt + (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
- Sources: Compustat and authors’ calculations. Compustat item mappings provided (e.g., ppeveb item 187; capx; at; csho; prcc; ceq; txdb; ib; dp; dltt9). Final variables are winsorized at 2 percent at the top and bottom.

*Source: APPENDIX REFERENCES, _wp14104 - APPENDIX REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14104.pdf_