Advertising, Innovation, and Economic Growth Laurent Cavenaile Pau - - PowerPoint PPT Presentation

Advertising, Innovation, and Economic Growth

Laurent Cavenaile Pau Roldan-Blanco

University of Toronto 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

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

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

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: U0 = +∞ e−ρt ln

• Ct
• dt,

s.t. ˙ At = rtAt + wt − Ct where limt→+∞ e− t

0 rsdsAt ≥ 0 and A0 ≥ 0 given. 5 / 26

Environment

Final good: Y = 1 1 − β 1

• qβ

j y 1−β j

dj where      yj ≡ Quantity of good j

• qj ≡ Perceived quality of good j

Perceived Quality:

Micro-foundations

• qjt =

q

• qjt
• +

, djt

• +
• where

     qjt ≡ Intrinsic quality level djt ≡ Extrinsic quality ‘shifter’

qj: function of R&D expenditures → ↑ qj → Sole engine of long-run growth. dj: function of ADV expenditures → ↑ dj → Taste shifter.

6 / 26

Environment

Final good: Y = 1 1 − β 1

• qβ

j y 1−β j

dj where      yj ≡ Quantity of good j

• qj ≡ Perceived quality of good j

Perceived Quality:

Micro-foundations

• qjt =

q

• qjt
• +

, djt

• +
• where

     qjt ≡ Intrinsic quality level djt ≡ Extrinsic quality ‘shifter’

qj: function of R&D expenditures → ↑ qj → Sole engine of long-run growth. dj: function of ADV expenditures → ↑ dj → 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 ≡ {qj}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: ⇒ p(yj) = q(qj, dj) · y

− 1

β

j

Production function: yj = ¯ Qℓj where ¯ Q ≡

1

qjdj

7 / 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 ≡ {qj}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: ⇒ p(yj) = q(qj, dj) · y

− 1

β

j

Production function: yj = ¯ Qℓj where ¯ Q ≡

1

qjdj

7 / 26

Intrinsic Improvements: R&D

• q(q, d)

Incumbents (n ≥ 1):

1 Internal R&D (on each owned j):

Technology: Poisson rate zj ⇒ Cost Rz(zj) Outcome: → qj,t+∆t = (1 + λI)qjt.

2 External R&D (for some random j):

Technology: Poisson rate X ⇒ Cost Rx(X, n) Outcome: → qj,t+∆t = (1 + λE)qjt. Successful innovation displaces old producer (creative destruction).

Entrants (n = 0, free entry):

Technology: Poisson rate xe ⇒ Cost Re(xe) Enter with n = 1 good (through external innovation).

8 / 26

Intrinsic Improvements: R&D

• q(q, d)

Incumbents (n ≥ 1):

1 Internal R&D (on each owned j):

Technology: Poisson rate zj ⇒ Cost Rz(zj) Outcome: → qj,t+∆t = (1 + λI)qjt.

2 External R&D (for some random j):

Technology: Poisson rate X ⇒ Cost Rx(X, n) Outcome: → qj,t+∆t = (1 + λE)qjt. Successful innovation displaces old producer (creative destruction).

Entrants (n = 0, free entry):

Technology: Poisson rate xe ⇒ Cost Re(xe) Enter with n = 1 good (through external innovation).

8 / 26

Intrinsic Improvements: R&D

• q(q, d)

Incumbents (n ≥ 1):

1 Internal R&D (on each owned j):

Technology: Poisson rate zj ⇒ Cost Rz(zj) Outcome: → qj,t+∆t = (1 + λI)qjt.

2 External R&D (for some random j):

Technology: Poisson rate X ⇒ Cost Rx(X, n) Outcome: → qj,t+∆t = (1 + λE)qjt. Successful innovation displaces old producer (creative destruction).

Entrants (n = 0, free entry):

Technology: Poisson rate xe ⇒ Cost Re(xe) 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) ≡ Rx(X, n) +

• j

Rz(zj) ⇒ R(n) n ց with n in the data [Fact #2] To obtain [Fact #2], it must be that: Rx(nX, n) > nRx(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: Rz(z) ∝ qz

ψ; and Rx(X, n) ∝ QX ψnσ

⇒ DRTS if ψ + σ > 1.

9 / 26

Extrinsic Improvements: ADV

• q(q, d)

ADV production function is Cobb-Douglas: Return to ADV: dj = θjmζ

j nη

Components:

1 θj

→ Advertising efficiency.

2 mj

→ Advertising expenditure (ζ < 1).

3 n

→ Spillover effect (η > 0).

10 / 26

Extrinsic Improvements: ADV

• q(q, d)

ADV production function is Cobb-Douglas: Return to ADV: dj = θjmζ

j nη

Components:

1 θj

→ Advertising efficiency.

2 mj

→ Advertising expenditure (ζ < 1).

3 n

→ Spillover effect (η > 0).

10 / 26

Extrinsic Improvements: ADV

• q(q, d)

ADV production function is Cobb-Douglas: Return to ADV: dj = θjmζ

j nη

Components:

1 θj

→ Advertising efficiency.

2 mj

→ 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: dj = θjmζ

j nη

Components:

1 θj

→ Advertising efficiency.

2 mj

→ 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

mj ⇒ M(n) n ց 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

Obtaining ADV and R&D Facts

Total firm-level ADV expenditure: M(n) ≡

• j

mj ⇒ M(n) n ց 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:

rVn(q) = max

X,{zj ,mj }j qj ∈q

• π ·

q(qj, dj) − Rz(zj) − mj + zj

• Vn
• q\{qj} ∪ {qj(1 + λI)}
• − Vn(q)
• + τ
• Vn−1
• q\{qj}
• − Vn(q)
• + X
• EjVn+1
• q ∪ {qj(1 + λE)}
• − Vn(q)
• − Rx(X; n)
• + ˙

Vn(q)

2 Entrant firm (n = 0):

rV0− ˙ V0 = max

xe>0

• xe
• EjV1
• {qj(1 + λE)}
• − V0
• − Re(xe)
• ⇒ V0 = 0 (free entry)

12 / 26

Value Functions

1 Incumbent firm (n, q), for n ≥ 1:

rVn(q) = max

X,{zj ,mj }j qj ∈q

• π ·

q(qj, dj)

• Profit per good

− Rz(zj)

Internal R&D costs

− mj

• ADV

costs

+ zj

• Vn
• q\{qj} ∪ {qj(1 + λI)}
• − Vn(q)
• + τ
• Vn−1
• q\{qj}
• − Vn(q)
• + X
• EjVn+1
• q ∪ {qj(1 + λE)}
• − Vn(q)
• − Rx(X; n)
• + ˙

Vn(q)

2 Entrant firm (n = 0):

rV0− ˙ V0 = max

xe>0

• xe
• EjV1
• {qj(1 + λE)}
• − V0
• − Re(xe)
• ⇒ V0 = 0 (free entry)

12 / 26

Value Functions

1 Incumbent firm (n, q), for n ≥ 1:

rVn(q) = max

X,{zj ,mj }j qj ∈q

• π ·

q(qj, dj) − Rz(zj) − mj + zj

• Vn
• q\{qj} ∪ {qj(1 + λI)}
• − Vn(q)
• Internal innovation gain

+ τ

• Vn−1
• q\{qj}
• − Vn(q)
• + X
• EjVn+1
• q ∪ {qj(1 + λE)}
• − Vn(q)
• − Rx(X; n)
• + ˙

Vn(q)

2 Entrant firm (n = 0):

rV0− ˙ V0 = max

xe>0

• xe
• EjV1
• {qj(1 + λE)}
• − V0
• − Re(xe)
• ⇒ V0 = 0 (free entry)

12 / 26

Value Functions

1 Incumbent firm (n, q), for n ≥ 1:

rVn(q) = max

X,{zj ,mj }j qj ∈q

• π ·

q(qj, dj) − Rz(zj) − mj + zj

• Vn
• q\{qj} ∪ {qj(1 + λI)}
• − Vn(q)
• + τ
• Vn−1
• q\{qj}
• − Vn(q)
• Creative destruction loss
• + X
• EjVn+1
• q ∪ {qj(1 + λE)}
• − Vn(q)
• − Rx(X; n)
• + ˙

Vn(q)

2 Entrant firm (n = 0):

rV0− ˙ V0 = max

xe>0

• xe
• EjV1
• {qj(1 + λE)}
• − V0
• − Re(xe)
• ⇒ V0 = 0 (free entry)

12 / 26

Value Functions

1 Incumbent firm (n, q), for n ≥ 1:

rVn(q) = max

X,{zj ,mj }j qj ∈q

• π ·

q(qj, dj) − Rz(zj) − mj + zj

• Vn
• q\{qj} ∪ {qj(1 + λI)}
• − Vn(q)
• + τ
• Vn−1
• q\{qj}
• − Vn(q)
• + X
• EjVn+1
• q ∪ {qj(1 + λE)}
• − Vn(q)
• External innovation gain

− Rx(X; n)

External R&D costs

• + ˙

Vn(q)

2 Entrant firm (n = 0):

rV0− ˙ V0 = max

xe>0

• xe
• EjV1
• {qj(1 + λE)}
• − V0
• − Re(xe)
• ⇒ V0 = 0 (free entry)

12 / 26

Value Functions

1 Incumbent firm (n, q), for n ≥ 1:

rVn(q) = max

X,{zj ,mj }j qj ∈q

• π ·

q(qj, dj) − Rz(zj) − mj + zj

• Vn
• q\{qj} ∪ {qj(1 + λI)}
• − Vn(q)
• + τ
• Vn−1
• q\{qj}
• − Vn(q)
• + X
• EjVn+1
• q ∪ {qj(1 + λE)}
• − Vn(q)
• − Rx(X; n)
• + ˙

Vn(q)

2 Entrant firm (n = 0):

rV0− ˙ V0 = max

xe>0

• xe
• EjV1
• {qj(1 + λE)}
• − V0
• − Re(xe)
• ⇒ V0 = 0 (free entry)

12 / 26

BGP Equilibrium

Let Fµn ≡ #{Firms of size n ≥ 1}. All aggregates grow at rate g ≡ ˙ ¯ Q/¯ Q. g =

• xe +

+∞

• n=1

FµnXn

• λE + zλI

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 Fµn ≡ #{Firms of size n ≥ 1}. All aggregates grow at rate g ≡ ˙ ¯ Q/¯ Q. g =

• xe +

+∞

• n=1

FµnXn

• λE + zλI

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 Fµn ≡ #{Firms of size n ≥ 1}. All aggregates grow at rate g ≡ ˙ ¯ Q/¯ Q. g =

• xe +

+∞

• n=1

FµnXn

• λE + zλI

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 Fµn ≡ #{Firms of size n ≥ 1}. All aggregates grow at rate g ≡ ˙ ¯ Q/¯ Q. g =

• xe +

+∞

• n=1

FµnXn

• λE + zλI

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 Fµn ≡ #{Firms of size n ≥ 1}. All aggregates grow at rate g ≡ ˙ ¯ Q/¯ Q. g =

• xe +

+∞

• n=1

FµnXn

• = τ

(Creative destruction rate)

λE + zλI 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 Fµn ≡ #{Firms of size n ≥ 1}. All aggregates grow at rate g ≡ ˙ ¯ Q/¯ Q. g =

• xe +

+∞

• n=1

FµnXn

• = τ

(Creative destruction rate)

λE + zλI 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: Vn(q) = Γ

• qj∈q

qj + Υn ¯ Q

Analytical Solutions

Optimal R&D rates: Internal: zj = z External: Xn n = n

1−(σ+ ˜ ψ) ˜ ψ−1 G

• Υn+1 − Υn
• → ADV makes Υn+1 − Υn
• Value of new

product via R&D

↓ in n

1

Klette-Kortum (’04): ψ + σ = 1 (CRTS in R&D); No ADV

• Xn

n constant in n ⇒

Firm growth constant across size.

2

Akcigit-Kerr (’18): ψ + σ > 1 (DRTS in R&D); No ADV

• Xn

n ց in n

⇒ Facts #1 and #2.

3

Our specification: ψ + σ = 1; η + ζ < 1 (ADV spillover active)

• Xn

n ց in n

⇒ Facts #1, #2, #3.

14 / 26

BGP Equilibrium

Guess-and-verify: Vn(q) = Γ

• qj∈q

qj + Υn ¯ Q

Analytical Solutions

Optimal R&D rates: Internal: zj = z External: Xn n = n

1−(σ+ ˜ ψ) ˜ ψ−1 G

• Υn+1 − Υn
• → ADV makes Υn+1 − Υn
• Value of new

product via R&D

↓ in n

1

Klette-Kortum (’04): ψ + σ = 1 (CRTS in R&D); No ADV

• Xn

n constant in n ⇒

Firm growth constant across size.

2

Akcigit-Kerr (’18): ψ + σ > 1 (DRTS in R&D); No ADV

• Xn

n ց in n

⇒ Facts #1 and #2.

3

Our specification: ψ + σ = 1; η + ζ < 1 (ADV spillover active)

• Xn

n ց in n

⇒ Facts #1, #2, #3.

14 / 26

BGP Equilibrium

Guess-and-verify: Vn(q) = Γ

• qj∈q

qj + Υn ¯ Q

Analytical Solutions

Optimal R&D rates: Internal: zj = z External: Xn n = n

1−(σ+ ˜ ψ) ˜ ψ−1 G

• Υn+1 − Υn
• → ADV makes Υn+1 − Υn
• Value of new

product via R&D

↓ in n

1

Klette-Kortum (’04): ψ + σ = 1 (CRTS in R&D); No ADV

• Xn

n constant in n ⇒

Firm growth constant across size.

2

Akcigit-Kerr (’18): ψ + σ > 1 (DRTS in R&D); No ADV

• Xn

n ց in n

⇒ Facts #1 and #2.

3

Our specification: ψ + σ = 1; η + ζ < 1 (ADV spillover active)

• Xn

n ց in n

⇒ Facts #1, #2, #3.

14 / 26

BGP Equilibrium

Guess-and-verify: Vn(q) = Γ

• qj∈q

qj + Υn ¯ Q

Analytical Solutions

Optimal R&D rates: Internal: zj = z External: Xn n = n

1−(σ+ ˜ ψ) ˜ ψ−1 G

• Υn+1 − Υn
• → ADV makes Υn+1 − Υn
• Value of new

product via R&D

↓ in n

1

Klette-Kortum (’04): ψ + σ = 1 (CRTS in R&D); No ADV

• Xn

n constant in n ⇒

Firm growth constant across size.

2

Akcigit-Kerr (’18): ψ + σ > 1 (DRTS in R&D); No ADV

• Xn

n ց in n

⇒ Facts #1 and #2.

3

Our specification: ψ + σ = 1; η + ζ < 1 (ADV spillover active)

• Xn

n ց in n

⇒ Facts #1, #2, #3.

14 / 26

BGP Equilibrium

Guess-and-verify: Vn(q) = Γ

• qj∈q

qj + Υn ¯ Q

Analytical Solutions

Optimal R&D rates: Internal: zj = z External: Xn n = n

1−(σ+ ˜ ψ) ˜ ψ−1 G

• Υn+1 − Υn
• → ADV makes Υn+1 − Υn
• Value of new

product via R&D

↓ in n

1

Klette-Kortum (’04): ψ + σ = 1 (CRTS in R&D); No ADV

• Xn

n constant in n ⇒

Firm growth constant across size.

2

Akcigit-Kerr (’18): ψ + σ > 1 (DRTS in R&D); No ADV

• Xn

n ց in n

⇒ Facts #1 and #2.

3

Our specification: ψ + σ = 1; η + ζ < 1 (ADV spillover active)

• Xn

n ց in n

⇒ Facts #1, #2, #3.

14 / 26

Invariant Firm-size Distribution

Flow equations: # products Inflows Outflows n = 0 : Fµ1τ = xe n = 1 : Fµ22τ + xe = Fµ1(x1 + τ) n ≥ 2 : Fµn+1(n + 1)τ + Fµn−1(n − 1)xn−1 = Fµn(nxn + nτ) Analytical solution: µn = xe F n−1

i=1 xi

nτ n ; ∀n ≥ 1

15 / 26

Quantitative Analysis

15 / 26

Baseline Calibration

Parametrization:

Assume CRTS in R&D cost function. → Rx = χ¯ QX

ψnσ, with

ψ + σ = 1. → Rz = χqjz

ψ j .

Entry cost function. → Re = ν ¯ Qxe. Same cost-curvature in both R&D types. → ψ = ψ > 1. Same step-size in both R&D types. → λE = λI > 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

Parametrization:

Assume CRTS in R&D cost function. → Rx = χ¯ QX

ψnσ, with

ψ + σ = 1. → Rz = χqjz

ψ j .

Entry cost function. → Re = ν ¯ Qxe. Same cost-curvature in both R&D types. → ψ = ψ > 1. Same step-size in both R&D types. → λE = λI > 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 Sales

log R&D

Sales

• log ADV

Sales

• log R&D

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 R2 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 xe/F 0.101 0.098 BDS Average R&D-Sales ratio

• n Fµn

R(n) pyn

0.153 0.102 Compustat Average R&D-ADV ratio

• n Fµn

R(n) M(n)

24.15 26.40 Compustat Regression coefficients Firm growth coefficient β∆sales/sales

• 0.0326
• 0.0325

[Fact #1] R&D intensity coefficient βrd/sales

• 0.1030
• 0.1035

[Fact #2] ADV intensity coefficient βadv/sales

• 0.0353
• 0.0317

[Fact #3] R&D/ADV coefficient βrd/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 = λE xe

(+)

+ λI z

(−) + λE n

Xn

(−)

F µn

(←)

1 2 0.05 0.1 θ Entry rate 1 2 0.48 0.5 θ Creative destruction 1 2 1 1.5 θ Internal rate (z) 1 2 0.45 0.5 0.55 θ External intensity (xn)

n=1 n=5 n=10

1 2 0.01 0.02 θ Growth Decomposition

g INT EXT

1 2 3 4 5 6 7 8 910 10 20 Size (n) % of firms Firm size distribution

θ=1.1 (calib.) θ=0.3

⇒ 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 2 3 4 5 0.2 0.4 0.6 0.8 1

Size quintile

• St. Dev. growth (1st quintile = 1)

Data Model

1 2 3 4 5 0.2 0.4 0.6 0.8 1

Size quintile

• St. Dev. R&D intensity (1st quintile = 1)

1 2 3 4 5 0.2 0.4 0.6 0.8 1

Size quintile

• St. Dev. ADV intensity (1st quintile = 1)

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: 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

Dependent variable: log Adv

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 R2 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

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 xe/F 0.101 0.097 0.098 BDS Average R&D/Sales

• n Fµn

R(n) pyn

0.153 0.097 0.102 Compustat Average R&D/ADV

• n Fµn

R(n) M(n)

24.15 . 26.40 Compustat Regression coefficients† Firm growth coefficient β∆sales/sales

• 0.0326
• 0.0217
• 0.0325

[Fact #1] R&D intensity coefficient βrd/sales

• 0.1030
• 0.1041
• 0.1035

[Fact #2] ADV intensity coefficient βadv/sales

• 0.0353

.

• 0.0317

[Fact #3] R&D/ADV coefficient βrd/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

0.25 0.5 200 400 600 800 Subsidy (s) % change Entry rate 0.25 0.5 10 20 30 40 50 60 Subsidy (s) % change Internal Innovation (z) 5 10 15 2 4 6 8 Size (n) % change (s=0 to s=20%) External Innovation (xn)

ADV; CRTS in R&D No ADV; DRTS in R&D

0.2 0.4 0.6 0.02 0.025 0.03 0.035 Subsidy (s) g 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%

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. 1 2 3 4 5 0.05 0.1 0.15 0.2 Size Quintile Fact #2: R&D / Sales 1 2 3 4 5 0.1 0.2 0.3 0.4 Size Quintile Fact #1: Sales growth

Q1 − Q5: 72.6% decrease Q1 − Q5: 83.0% decrease

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. 1 2 3 4 5 0.02 0.04 0.06 Size Quintile Fact #3: ADV / Sales 1 2 3 4 5 1 2 3 4 Size Quintile Fact #4: R&D / ADV

Q1 − Q5: 34.0% decrease Q1 − Q5: 58.5% decrease

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 =

+∞

e−ρt ln(Ct)dt, where Ct = 1 1 − β

1

• qβ

jt y 1−β jt

dj s.t. ˙ At = rtAt + wt − 1

0 pjtyjtdj.

2 Goodwill ADV: [Effects of ADV accumulate]

• qj =

q(qj, dj), with ˙ dj = mj − δdj

3 Informative ADV: [ADV is informative, not persuasive]

Go

In all cases ⇒ y demand

j

↑ in dj .

26 / 26

Appendix: Informative ADV

Back to Microfoundations Back to Baseline Model

Informative ADV: U = 1 qjyjdj − α 2 1 q2

j y 2 j dj

Consumers’ prior: qj ∼ N(µj, σ2

j ).

ADV signal: sj = qj + ωj, ωj ∼ N(0, σ2

ω).

ADV expenditures decrease variance of signal (σ2

ω). Posterior:

qj ∼ N

• µj/σ2

j + sj/σ2 ω

σ−2

j

+ σ−2

ω

• ≡µpost

,

• 1

σ2

j

+ 1 σ2

ω

−1

• ≡σ2

post

• Then, y demand

j

= µpost − pj α(µ2

post + σ2 post) .

⇒     

∂σpost ∂σ2

ω > 0

always

∂µpost ∂σ2

ω > 0

if σj high enough

26 / 26

Appendix: ADV Intensity

Back

Assume q(q, d) = q(1 + d). ADV problem: max

{mj}

• j
• π · (qj + qjdj) − mj
• s.t. qjdj = θ qj

Qf ¯ Q1−ζmζ

j nη

where Qf =

• qj∈q q

1 α

j

α . Total eq’m firm-level ADV intensity: M(n) n = (ζθ π)

1 1−ζ

• qj∈q q

1 1−ζ

j

Qf

1 1−ζ

¯ Qn

η+ζ−1 1−ζ 26 / 26

Appendix: Equilibrium R&D Choices in BGP

Back

Assuming xe > 0, the value of firm n ≥ 1 is Vn(qf ) = Γ

qj ∈qf qj + Υn ¯

Q, where: Γ = ν − Υ1 1 + λE and Υn, for n ≥ 1, is the solution to: Υn+1 − Υn + Γ(1 + λE) = ˜ ϑ

• ρΥnn

σ ˜ ψ−1 − (Υn−1 − Υn)τn σ+ ˜ ψ−1 ˜ ψ−1

− γn

η 1−ζ + σ ˜ ψ−1

˜

ψ−1 ˜ ψ

where ˜ ϑ ≡ ˜ ψ

• ˜

χ ( ˜ ψ−1) ˜

ψ−1

1

˜ ψ is a parameter, with boundary condition Υ0 = 0.

The optimal R&D rates are: zj =

• λI(ν − Υ1)
• ψ

χ(1 + λE)

• 1
• ψ−1

xn = n

1−σ− ˜ ψ ˜ ψ−1

• ν − Υ1 + Υn+1 − Υn

˜ ψ ˜ χ

• 1

˜ ψ−1 26 / 26

Appendix: Stylized Facts – Full Regressions

Back

Fact #1 Fact #2 Fact #3 Fact #4

∆Sales Sales

log R&D

Sales

• log ADV

Sales

• log R&D

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 R2 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 xe/F

• 0.04

1.62 0.02

• 4.49
• 6.65

0.40 Average R&D-Sales ratio

• n Fµn

R(n) pyn

• 0.01
• 0.46

0.06 0.76 0.94

• 0.09

Average R&D-ADV ratio

• n Fµn

R(n) M(n)

• 0.01
• 0.52

0.04 0.89 0.30

• 0.74

Regression coefficients Firm growth coefficient β∆sales/sales

• 13.14
• 15.55
• 2.09
• 12.79
• 14.48
• 1.24

R&D intensity coefficient βrd/sales

• 0.14
• 2.01
• 0.45

4.81

• 0.47
• 0.59

ADV intensity coefficient βadv/sales

• 0.43
• 0.31
• 0.18

0.25

• 16.42
• 0.38

R&D/ADV coefficient βrd/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(C0, g) = ln(C0)/ρ

• Level effect

(+)

+ g/ρ2

• Growth effect

(−)

0.2 0.4 0.6 0.8 1 55 60 65 70 θ Welfare 0.2 0.4 0.6 0.8 1 45 50 55 60 65 70 θ Welfare Decomposition 0.2 0.4 0.6 0.8 1 2 3 4 5 6 7

θcalib Growth Effect (left) Level Effect (right)

Figure: Welfare decomposition.

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 rateit = statutory rateit · (1 − sit · tax rateit) sit ≡ % R&D credit subject to taxation.

3 Credit rate adjusted for base definition:

mit

• Effective rate

in state i

= statutory rateit(1 − sit · τ e

it)

• 1 − 1

n

n

• s=1

(1 + rt+s)−s

• τ e

it ≡ Adjusts for tax being deductible in some states.

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.

Formal definition 26 / 26

Appendix: R&D User Cost

Back to Definitions Back to Evidence

• R&D user cost
• it = 1 − (mit + mft) − z (τ e

it + τ e ft)

1 − (τ e

it + τ e ft)

[rt + δ] where: mit : Effective tax credit in state i. mft : Federal effective tax credit. τ e : 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

1 2 3 4 5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Size quintile

• St. Dev. growth (1st quintile = 1)

Data Model: ADV − CRTS Model: DRTS − no ADV 1 2 3 4 5 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Size quintile

• St. Dev. R&D intensity (1st quintile = 1)

Figure: Standard deviations (% with respect to 1st quintile): Data vs Models.

Back 26 / 26