Advertising, Innovation, and Economic Growth

Advertising, Innovation, and Economic Growth Laurent Cavenaile University of Toronto Pau Roldan-Blanco Banco de España Universitat de Barcelona February 26, 2019

Motivation Recent literature suggests role of intangibles for firm growth. Gourio and Rudanko ( 14), Foster, Haltiwanger and Syverson ( 08), McGrattan and Prescott ( 10, 14), Arkolakis ( 15), Fitzgerald and Priolo ( 18)... In the growth literature: Firm-level R&D as a key source of economic growth through innovation. Question: What determines R&D investment decision within the firm? Firm s perspective: Common view: Product quality improvement Sales & profits This paper: Broader choice among intangibles that relate to product quality. 1 / 26

Motivation Questions: 1 How does ADV affect R&D investment at the firm level? 2 What are the implications for: Innovation and long-run economic growth? Firm growth and firm dynamics? Design of industrial policy? Why is ADV relevant? 1 ADV and R&D serve similar purposes perceived quality of goods. 2 Both are large shares of U.S. GDP (R&D: 2.51%; ADV: 2.21%, 1981-2006). 3 Marketing literature identifies ADV returns across firm size (umbrella branding). 2 / 26

What We Do Model: Endogenous Growth Model of multi-product firms with ADV and R&D choices. Key Idea: ADV has spillover effect across products (Marketing literature). Dynamic trade-off: Per-product gains from ADV shapes R&D decision. Estimation: Calibration targeting facts across firm size: Figures [Fact #1] Deviations from proportional growth (Gibrat s law). [Fact #2] Decreasing R&D intensity. [Fact #3] Decreasing ADV intensity. [Fact #4] Decreasing R&D-to-ADV ratio. 3 / 26

Preview of Results / Roadmap 1 Theoretical: ADV-R&D interaction provides microfoundation for [Fact #1] & [#2]. 2 Quantitative: R&D-ADV substitution More efficient ADV decreases economic growth. Policy: R&D subsidies more effective in an economy with ADV than without. 3 Empirical: We find evidence in the U.S. for R&D-ADV substitution at firm-level. 4 / 26

Model 4 / 26

Environment Klette-Kortum ( 04) model of multi-product firms (cf. Akcigit and Kerr ( 18)). Continuous time, infinite horizon. Continuum of producers in monopolistic competition. Each producer has many goods, does ADV and R&D. Mass of potential entrants (free entry). Preferences: U 0 = + 0 e ρt ln ( C t ) dt, s.t. Ȧt = r t A t + w t C t where lim t + e t 0 rs ds A t 0 and A 0 0 given. 5 / 26

Environment Final good: Y = 1 1 β 1 0 q β j y y 1 β j Quantity of good j j dj where q j Perceived quality of good j Perceived Quality: ( q jt = q q jt }{{} +, d jt }{{} + ) Micro-foundations q jt Intrinsic quality level where d jt Extrinsic quality shifter q j: function of R&D expenditures q j d j: function of ADV expenditures d j Sole engine of long-run growth. Taste shifter. 6 / 26

Environment Production sector: Endogenous set F (measure F ) of incumbent firms. Firm indexed by (n, q), where n #{products} (firm s size) and q {q j} n j=1. Market structure: Firm owns good j if it has technological leadership. Firms improve goods via internal R&D (q ) and ADV (d ). Acquire/lose goods through external R&D. Demand from consumers: Production function: p(y j) = q(q j, d j) y 1 β j y j = Ql j 1 where Q q jdj 0 7 / 26

Intrinsic Improvements: R&D q(q, d) Incumbents (n 1): 1 Internal R&D (on each owned j): Technology: Poisson rate z j Cost R z(z j) Outcome: q j,t+ t = (1 + λ I )q jt. 2 External R&D (for some random j): Technology: Poisson rate X Cost R x(x, n) Outcome: q j,t+ t = (1 + λ E )q jt. Successful innovation displaces old producer (creative destruction). Entrants (n = 0, free entry): Technology: Poisson rate x e Cost R e(x e) Enter with n = 1 good (through external innovation). 8 / 26

How to Obtain the R&D Facts (without ADV) Total firm-level R&D expenditure: R(n) R x (X, n) + j R z (z j ) R(n) n with n in the data [Fact #2] To obtain [Fact #2], it must be that: R x (nx, n) > nr x (X, 1) Decreasing Returns to Scale (DRTS) in R&D: A given growth rate is more costly to achieve for a firm of size n than for n firms of size one each. Parametrization: R z (z) qz ψ ; and R x (X, n) QX ψ n σ DRTS if ψ + σ > 1. 9 / 26

Extrinsic Improvements: ADV q(q, d) ADV production function is Cobb-Douglas: Return to ADV: d j = θ j m ζ j nη Components: 1 θ j Advertising efficiency. 2 m j Advertising expenditure (ζ < 1). 3 n Spillover effect (η > 0). Literature Simon ( 70), Simon and Arndt ( 80), Albion and Farris ( 81), Berndt ( 91), Sutton ( 91), Jones ( 95), Bagwell ( 07). 10 / 26

Extrinsic Improvements: ADV q(q, d) ADV production function is Cobb-Douglas: Return to ADV: d j = θ j m ζ j nη Components: 1 θ j Advertising efficiency. 2 m j Advertising expenditure (ζ < 1). 3 n Spillover effect (η > 0). Literature Tauber ( 81, 88), Sullivan ( 90), Smith and Park ( 92), Rangaswamy, Burke, and Oliver ( 93), Lane and Jacobson ( 95), Erdem ( 98), Morrin ( 99), Erdem and Sun ( 02), Balachander and Ghose ( 03), Büschken ( 07), Suppliet ( 15). 10 / 26

Obtaining ADV and R&D Facts Total firm-level ADV expenditure: M(n) j m j M(n) n with n in the data [Fact #3] In equilibrium: Details M(n) n n η+ζ 1 1 ζ Need η + ζ < 1 for [Fact #3] η < 1 Key Result: ADV-R&D interaction gives [Fact #1] & [#2]. Smaller firms are less efficient in ADV (η > 0) but obtain more per good (η < 1). Higher incentive to get additional good through R&D to advertise it later. Holds even if non-drts in R&D. 11 / 26

Value Functions 1 Incumbent firm (n, q), for n 1: { [ rv n(q) = max X,{z j,m j } j q j q π q(q j, d j) R z(z j) m j ( ) ) + z j V n (q\{q j} {q j(1 + λ I )} V n(q) ( ) ) + τ (V ] n 1 q\{q j} V n(q) + X ( ) ) } (E jv n+1 q {q j(1 + λ E )} V n(q) R x(x; n) + V n(q) 2 Entrant firm (n = 0): rv 0 V 0 = max x e >0 ( ) ] } {x e [E jv 1 {q j(1 + λ E )} V 0 R e(x e) V 0 = 0 (free entry) 12 / 26

Value Functions 1 Incumbent firm (n, q), for n 1: rv n(q) = max X,{z j,m j } j { [ π q(q j, d j) }{{} q j q Profit per good R z(z j) m j }{{} Internal R&D costs }{{} ADV costs + z j ( V n (q\{q j} {q j(1 + λ I )} + τ + X ( ) ) (V ] n 1 q\{q j} V n(q) ) ) V n(q) ( ) ) } (E jv n+1 q {q j(1 + λ E )} V n(q) R x(x; n) + V n(q) 2 Entrant firm (n = 0): rv 0 V 0 = max x e >0 ( ) ] } {x e [E jv 1 {q j(1 + λ E )} V 0 R e(x e) V 0 = 0 (free entry) 12 / 26

Value Functions 1 Incumbent firm (n, q), for n 1: rv n(q) = max X,{z j,m j } j { [ π q(q j, d j) R z(z j) m j q j q 2 Entrant firm (n = 0): ( ) ) + z j V n (q\{q j} {q j(1 + λ I )} V n(q) }{{} Internal innovation gain ( ) ) + τ (V ] n 1 q\{q j} V n(q) + X ( ) ) } (E jv n+1 q {q j(1 + λ E )} V n(q) R x(x; n) + V n(q) rv 0 V 0 = max x e >0 ( ) ] } {x e [E jv 1 {q j(1 + λ E )} V 0 R e(x e) V 0 = 0 (free entry) 12 / 26

Value Functions 1 Incumbent firm (n, q), for n 1: rv n(q) = max X,{z j,m j } j { [ π q(q j, d j) R z(z j) m j q j q ( ) ) + z j V n (q\{q j} {q j(1 + λ I )} V n(q) ( ) ) ] + τ (V n 1 q\{q j} V n(q) }{{} Creative destruction loss ( ) ) } + X (E jv n+1 q {q j(1 + λ E )} V n(q) R x(x; n) + V n(q) 2 Entrant firm (n = 0): rv 0 V 0 = max x e >0 ( ) ] } {x e [E jv 1 {q j(1 + λ E )} V 0 R e(x e) V 0 = 0 (free entry) 12 / 26

Value Functions 1 Incumbent firm (n, q), for n 1: { [ rv n(q) = max X,{z j,m j } j q j q π q(q j, d j) R z(z j) m j ( ) ) + z j V n (q\{q j} {q j(1 + λ I )} V n(q) ( ) ) + τ (V ] n 1 q\{q j} V n(q) 2 Entrant firm (n = 0): + X ( ) (E jv n+1 q {q j(1 + λ E )} V n(q) } {{ } External innovation gain ) R x(x; n) }{{} External R&D costs } + V n(q) rv 0 V 0 = max x e >0 ( ) ] } {x e [E jv 1 {q j(1 + λ E )} V 0 R e(x e) V 0 = 0 (free entry) 12 / 26

BGP Equilibrium Let F µ n #{Firms of size n 1}. All aggregates grow at rate g Q/ Q. ( g = x e + + n=1 F µ n X n ) λ E + zλ I Growth comes directly from: 1 External R&D by entrants. 2 External R&D by incumbents. 3 Internal R&D by incumbents. ADV impacts growth indirectly through its effect on R&D decision. 13 / 26

BGP Equilibrium Let F µ n #{Firms of size n 1}. All aggregates grow at rate g Q/ Q. g = ( x e + + n=1 F µ n X n ) } {{ } = τ (Creative destruction rate) λ E + zλ I Growth comes directly from: 1 External R&D by entrants. 2 External R&D by incumbents. 3 Internal R&D by incumbents. ADV impacts growth indirectly through its effect on R&D decision. 13 / 26

BGP Equilibrium Guess-and-verify: V n (q) = Γ q j q q j + Υ n Q Analytical Solutions Optimal R&D rates: Internal: External: z j = z X n n = n 1 (σ+ ψ) ) ψ 1 G (Υ n+1 Υ n ADV makes Υ n+1 Υ }{{} n in n Value of new product via R&D 1 Klette-Kortum ( 04): ψ + σ = 1 (CRTS in R&D); No ADV X n n constant in n Firm growth constant across size. 2 Akcigit-Kerr ( 18): ψ + σ > 1 (DRTS in R&D); No ADV X n n in n Facts #1 and #2. 3 Our specification: ψ + σ = 1; η + ζ < 1 (ADV spillover active) X n n in n Facts #1, #2, #3. 14 / 26

Invariant Firm-size Distribution Flow equations: # products Inflows Outflows n = 0 : F µ 1 τ = x e n = 1 : F µ 2 2τ + x e = F µ 1 (x 1 + τ) n 2 : F µ n+1 (n + 1)τ + F µ n 1 (n 1)x n 1 = F µ n (nx n + nτ) Analytical solution: µ n = x e F n 1 i=1 x i nτ n ; n 1 15 / 26

Quantitative Analysis 15 / 26

Baseline Calibration Parametrization: Assume CRTS in R&D cost function. R x = χ QX ψ n σ, with ψ + σ = 1. R z = χq jz ψ j. Entry cost function. R e = ν Qx e. Same cost-curvature in both R&D types. ψ = ψ > 1. Same step-size in both R&D types. λ E = λ I > 0. External identification: PARAM. VALUE TARGET SOURCE ρ 0.02 Discount rate Standard ψ 2 Elasticity of R&D Akcigit & Kerr (2018) β 0.1645 Profitability ratio Compustat ζ 0.1 Sales-ADV elasticity Tellis (2009) σ 1 ψ CRTS in R&D. Table: Externally calibrated parameters in baseline calibration. 16 / 26

Baseline Calibration Internal identification: 6 parameters left. Macro level: Target 4 aggregate moments. Micro level: Indirect inference Match 4 empirical slopes [Facts #1-#4]. Fact #1 Fact ( #2 Fact #3 Fact #4 ) ( ) ( ) Sales R&D ADV R&D log log log Sales Sales Sales ADV log(sales) 0.0325*** 0.1035*** 0.0317*** 0.0719*** (0.0029) (0.0089) (0.010) (0.012) Firm Controls Time & Ind. FE Obs. 24856 24856 24856 24856 R 2 0.09 0.50 0.28 0.45 Notes: Compustat data (1980-2015). Firms controls: age and financial constraint. Standard errors clustered by firm (in parentheses). Legend: * 10%; ** 5% ; *** 1%. Full Regressions 17 / 26

Model Fit MOMENT MODEL DATA SOURCE Aggregate moments Average growth rate g 0.02 0.02 Standard Entry rate x e/f 0.101 0.098 BDS Average R&D-Sales ratio Average R&D-ADV ratio Regression coefficients R(n) F µn n py n 0.153 0.102 Compustat R(n) F µn 24.15 26.40 Compustat n M(n) Firm growth coefficient β sales/sales -0.0326-0.0325 [Fact #1] R&D intensity coefficient β rd/sales -0.1030-0.1035 [Fact #2] ADV intensity coefficient β adv/sales -0.0353-0.0317 [Fact #3] R&D/ADV coefficient β rd/adv -0.0677-0.0719 [Fact #4] Table: Model with ADV, and CRTS in R&D: Targeted moments. Parameters Sensitivity 18 / 26

Effects of ADV on Growth Growth: g = λ E x e + λ I z + λ E (+) ( ) n X n F µ n ( ) ( ) 0.1 0.05 Entry rate 0 0 1 2 θ External intensity (x n ) 0.55 0.5 n=1 n=5 n=10 0.45 0 1 2 θ 0.5 Creative destruction 0.48 0 1 2 θ % of firms 20 10 Firm size distribution θ=1.1 (calib.) θ=0.3 0 1 2 3 4 5 6 7 8 910 Size (n) 1.5 1 0.02 0.01 Internal rate (z) 0 1 2 θ Growth Decomposition g INT EXT 0 0 1 2 θ g by 0.64 percentage points if ADV is banned (θ = 0). Welfare effects 19 / 26

Validation Exercises 19 / 26

Validation I: Standard Deviations by Size Correlations Stylized fact Variance of firm growth decreasing in firm size. (Hymer and Pashigian ( 62), Klette and Kortum ( 04), Amaral et al. ( 98), Sutton ( 02)) 1 0.8 0.6 St. Dev. growth (1st quintile = 1) Data Model 0.4 0.2 0 1 2 3 4 5 Size quintile St. Dev. R&D intensity (1st quintile = 1) 1 St. Dev. ADV intensity (1st quintile = 1) 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 1 2 3 4 5 Size quintile 0.2 1 2 3 4 5 Size quintile Figure: Standard deviations (% with respect to 1st quintile): Model vs Data. 20 / 26

Validation II: Verifying Substitution Empirically Calibrated model predicts ADV and R&D are substitutes at the firm level. Exercise: Verify substitutability in the data. U.S. R&D tax-credit episodes Exploit time- and state-variation. Data & Methodology Events: Starting in Minnesota (1982), U.S. states started implementing R&D tax credits. In 2009, 32 U.S. states offer tax credits with statutory rates ranging 2%-20%. Results: Today: Firm-level evidence. Paper: (i) State-level evidence; (ii) Other measures of intangibles (SG&A). 21 / 26

Validation II: Firm-level Evidence ( ) Adv Dependent variable: log Sales ; Regressors: Definitions Tax credit -0.0629* dummy (0.0380) State credit -1.748*** rate (0.453) Tax-adjusted -1.753*** state rate (0.468) Effective -1.901*** state rate (0.532) R&D 1.823*** user cost (0.567) Controls Time FE Industry FE State FE Observations 28743 27455 27455 25333 25333 R 2 0.42 0.42 0.42 0.43 0.43 Table: Effect of R&D subsidy on advertising intensity at the firm level. Notes: Data from Compustat from 1950 to 2009, Wilson (2009) and Falato and Sim (2014). Controls include sales, age, financial constraint, state tax and selling, general and administrative (SG&A) expenses. Standard errors are clustered at the firm level (in parentheses). Significance level: * 10%; ** 5%; *** 1%. 22 / 26

Policy 22 / 26

R&D Subsidy Efficiency Decreasing R&D intensity with size (Fact #2) can come from: 1 R&D-ADV interaction η + ζ < 1. 2 Decreasing RTS in R&D ψ + σ > 1. Determining source of RTS is relevant for effectiveness of R&D subsidy. Compare 2 economies: 1 Economy #1: Model with ADV and Constant RTS in R&D (baseline). 2 Economy #2: Model without ADV and Decreasing RTS in R&D (re-calibrated). 23 / 26

Comparing Calibrated Economies Comparison of Non-targeted Moments MOMENT MODEL MODEL DATA SOURCE with ADV w/o ADV Aggregate moments Average growth rate g 0.02 0.02 0.02 Standard Entry rate x e/f 0.101 0.097 0.098 BDS R(n) Average R&D/Sales F µn 0.153 0.097 0.102 Compustat n py n R(n) Average R&D/ADV F µn 24.15. 26.40 Compustat n M(n) Regression coefficients Firm growth coefficient β sales/sales -0.0326-0.0217-0.0325 [Fact #1] R&D intensity coefficient β rd/sales -0.1030-0.1041-0.1035 [Fact #2] ADV intensity coefficient β adv/sales -0.0353. -0.0317 [Fact #3] R&D/ADV coefficient β rd/adv -0.0677. -0.0719 [Fact #4] Table: Targeted moments. Model #1: ADV, CRTS in R&D; Model #2: No ADV, DRTS in R&D. Coefficients on Sales. Dependent variables: Sales growth rate, R&D/Sales, ADV/Sales, and R&D/ADV. 24 / 26

R&D Subsidies % change 800 600 400 200 Entry rate 0 0 0.25 0.5 Subsidy (s) % change Internal Innovation (z) 60 50 40 30 20 10 0 0 0.25 0.5 Subsidy (s) % change (s=0 to s=20%) External Innovation (x n ) 8 6 4 2 ADV; CRTS in R&D No ADV; DRTS in R&D 0 0 5 10 15 Size (n) g 0.035 0.03 0.025 Growth rate ADV; CRTS in R&D No ADV; DRTS in R&D Subsidy Calib. Calib. (s) w/adv w/o ADV 0% 2% 2% 25% 2.31% 2.25% 50% 2.79% 2.66% 75% 3.85% 3.56% 0.02 0 0.2 0.4 0.6 Subsidy (s) Table: Growth rates for different subsidy levels. 25 / 26

Conclusion We ask how ADV affects R&D, firm dynamics and economic growth. Theory: Model of firm dynamics and endogenous growth. Explicit ADV decisions inspired by Marketing literature. Quantitative Analysis: Interaction R&D-ADV can explain firm growth and R&D investment facts. ADV is detrimental to economic growth. We verify empirically that ADV crowds out R&D. Policy implications R&D subsidies. 26 / 26

Appendix 26 / 26

Appendix: Stylized Facts Back Calibration via indirect inference to match 4 facts: [Fact #1] Decreasing firm growth rate in firm size. [Fact #2] Decreasing R&D intensity in firm size. 0.4 0.3 Fact #1: Sales growth Q1 Q5: 83.0% decrease 0.2 0.15 Fact #2: R&D / Sales Q1 Q5: 72.6% decrease 0.2 0.1 0.1 0.05 0 0 1 2 3 4 5 1 2 3 4 5 Size Quintile Size Quintile Figure: Facts #1 #2: Compustat data (1980-2015). Size quintiles based on normalized sales. 26 / 26

Appendix: Stylized Facts Back Calibration via indirect inference to match 4 facts: [Fact #3] Decreasing ADV intensity in firm size. [Fact #4] Decreasing R&D-ADV ratio in firm size. 0.06 0.04 Fact #3: ADV / Sales Q1 Q5: 34.0% decrease 4 3 Fact #4: R&D / ADV Q1 Q5: 58.5% decrease 0.02 2 1 0 0 1 2 3 4 5 1 2 3 4 5 Size Quintile Size Quintile Figure: Facts #3 #4: Compustat data (1980-2015). Size quintiles based on normalized sales. 26 / 26

Appendix: Micro-foundations Back Micro-foundations for ADV: 1 ADV in utility: [ADV alters preferences] U = + 0 s.t. Ȧ t = r ta t + w t 1 0 pjtyjtdj. e ρt ln(c t)dt, where C t = 1 1 β 2 Goodwill ADV: [Effects of ADV accumulate] 1 0 q β jt y 1 β jt dj q j = q(q j, d j), with ḋ j = m j δd j 3 Informative ADV: [ADV is informative, not persuasive] Go In all cases y demand j in d j. 26 / 26

Appendix: Informative ADV Back to Microfoundations Back to Baseline Model Informative ADV: U = 1 0 q j y j dj α 2 1 0 q 2 j y 2 j dj Consumers prior: q j N (µ j, σ 2 j ). ADV signal: s j = q j + ω j, ω j N (0, σ 2 ω). ADV expenditures decrease variance of signal (σ 2 ω). Posterior: ( µj /σj 2 + s j /σω 2 q j N + σω 2, σ 2 j } {{ } µ post Then, yj demand µ post p j = α(µ 2 post + σpost) 2. [ 1 + 1 σ 2 j σ 2 ω ] 1 } {{ } σpost 2 σ post σ 2 ω µ post σ 2 ω ) > 0 always > 0 if σ j high enough 26 / 26

Appendix: ADV Intensity Back Assume q(q, d) = q(1 + d). ADV problem: ] max [π (q j + q j d j ) m j {m j } where Q f = ( q j q q 1 α j ) α. j s.t. q j d j = θ q j Q f Q1 ζ m ζ j nη Total eq m firm-level ADV intensity: M(n) n = (ζθ π) 1 1 ζ q j q q 1 1 ζ j Q f 1 1 ζ Qn η+ζ 1 1 ζ 26 / 26

Appendix: Equilibrium R&D Choices in BGP Back Assuming x e > 0, the value of firm n 1 is V n(q f ) = Γ q j q f q j + Υ n Q, where: and Υ n, for n 1, is the solution to: Υ n+1 Υ n + Γ(1 + λ E ) = ϑ ( Γ = ν Υ1 1 + λ E ρυ nn ψ 1 σ (Υ n 1 Υ σ+ ψ 1 n)τn ψ 1 γn η 1 ζ + ) ψ 1 ψ 1 σ ψ ( where ϑ ψ ) χ 1 ψ ( ψ 1) ψ 1 The optimal R&D rates are: is a parameter, with boundary condition Υ 0 = 0. z j = ( λ I (ν Υ 1) ψ χ(1 + λ E ) ) 1 ψ 1 x n = n 1 σ ψ ψ 1 ( ν Υ1 + Υ n+1 Υ n ψ χ ) 1 ψ 1 26 / 26

Appendix: Stylized Facts Full Regressions Back Fact #1 Fact ( #2 Fact #3 Fact #4 ) ( ) ( ) Sales R&D ADV R&D log log log Sales Sales Sales ADV log(sales) 0.0325*** 0.1035*** 0.0317*** 0.0719*** (0.00288) (0.00892) (0.01000) (0.0120) Firm Age 0.00441*** 0.00296* 0.000688 0.00227 (0.000367) (0.00161) (0.00190) (0.00219) Fin. Const. 0.00270 0.00538* 0.00745* 0.00207 (0.00172) (0.00304) (0.00432) (0.00498) Time FE Industry FE Obs. 24856 24856 24856 24856 R 2 0.09 0.50 0.28 0.45 Notes: Compustat data (1980-2015). Age measured as time since the first observation in the data. Financial Constraints measured as the ratio of sales minus purchases of common and preferred stock, and firm size. Standard errors clustered by firm. * 10%; ** 5% ; *** 1%. 26 / 26

Appendix: Baseline Calibration Back PARAM. VALUE DESCRIPTION λ 0.0143 Innovation step χ 0.0017 Scale in internal R&D χ 0.6256 Scale in external R&D ν 0.7206 Scale in entrant s R&D η 0.8527 Spillover effect θ 1.1022 ADV efficiency Table: Internally calibrated parameters. Model with CRTS in R&D and with ADV. 26 / 26

Appendix: Sensitivity Analysis Back MOMENT λ χ χ ν η θ Aggregate moments Average growth rate g 1.63 0.11-0.63 0.04-0.40-0.22 Entry rate x e/f -0.04 1.62 0.02-4.49-6.65 0.40 R(n) Average R&D-Sales ratio F µn -0.01-0.46 0.06 0.76 0.94-0.09 n py n R(n) Average R&D-ADV ratio F µn -0.01-0.52 0.04 0.89 0.30-0.74 n M(n) Regression coefficients Firm growth coefficient β sales/sales -13.14-15.55-2.09-12.79-14.48-1.24 R&D intensity coefficient β rd/sales -0.14-2.01-0.45 4.81-0.47-0.59 ADV intensity coefficient β adv/sales -0.43-0.31-0.18 0.25-16.42-0.38 R&D/ADV coefficient β rd/adv 0.02-2.92-0.59 7.24 8.04-0.70 Table: Moments elasticities relative to parameters. 26 / 26

Appendix: Effects of ADV on Welfare Back Ex-post welfare decomposition: U(C 0, g) = ln(c 0 )/ρ }{{} Level effect (+) + g/ρ 2 }{{} Growth effect ( ) 70 Welfare 70 65 Welfare Decomposition θ calib Growth Effect (left) Level Effect (right) 7 6 65 60 5 60 55 4 50 3 55 0.2 0.4 45 0.6 0.8 1 0.2 0.4 0.6 θ θ 0.8 1 Figure: Welfare decomposition. 2 26 / 26

Appendix: Validation Correlations Back DATA MODEL corr(r&d intensity, firm growth) 0.15 0.25 corr(adv intensity, firm growth) 0.10 0.22 autocorr(r&d intensity) 0.92 0.89 autocorr(adv intensity) 0.88 0.76 autocorr(r&d/adv ratio) 0.92 0.92 Table: Correlation and Autocorrelation Coefficients: Model vs Data. 26 / 26

Appendix: Data and Methodology Back Data Sources: Use our Compustat sample (1950-2009). Data on state- and federal-level R&D tax credit from Wilson (2009) and Falato and Sim (2014) until 2009. Methodology: Changes in R&D tax credit change the relative price of R&D. Test effect of variation in R&D cost on ADV expenditures. Look at effect on ADV intensity at both the state and firm level. 26 / 26

Appendix: R&D Tax Credit Measures Back We use 4 measures of tax credit rates: 1 Statutory credit rate Stated rate. 2 Credit rate adjusted for tax on credit: Tax credit subject to corporate taxation in some states. tax-adjusted rate it = statutory rate it (1 s it tax rate it) s it % R&D credit subject to taxation. 3 Credit rate adjusted for base definition: m }{{} it = statutory rate it(1 s it τit) e Effective rate in state i ( 1 1 n τ e it Adjusts for tax being deductible in some states. ) n (1 + r t+s) s 4 R&D user cost: Hall and Jorgenson ( 67) formula for R&D (Bloom et al. ( 02)) State and federal effective tax credits and tax rates. s=1 Formal definition 26 / 26

Appendix: R&D User Cost Back to Definitions Back to Evidence ( R&D user cost )it = 1 (m it + m ft ) z (τit e + τ ft e ) 1 (τit e + τ ft e ) [r t + δ] where: m it : Effective tax credit in state i. m ft τ e : Federal effective tax credit. : Effective tax rates accounting for tax deductibility. z : PDV of depreciation tax allowances. r : Real interest rate. δ : R&D depreciation rate. 26 / 26

Appendix: Standard Deviation by Firm Size Comparison St. Dev. growth (1st quintile = 1) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Data 0.2 Model: ADV CRTS Model: DRTS no ADV 0.1 1 2 3 4 5 Size quintile St. Dev. R&D intensity (1st quintile = 1) 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 1 2 3 4 5 Size quintile Figure: Standard deviations (% with respect to 1st quintile): Data vs Models. Back 26 / 26