Optimal Taxation and R&D Policies

Transcription

1 1 35 Optimal Taxation and R&D Policies Ufuk Akcigit Douglas Hanley Stefanie Stantcheva Chicago Pittsburgh Harvard June 23, 2015

2 2 35 Motivation: Widespread R&D and Industrial Policies Industrial policies are widespread, costly and not fully understood. EU: 9.6% of EU GDP on industrial policies in Lots of policies target innovation and R&D.

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5 35 Goal: Optimal Design of R&D and Corporate Taxation Little agreement on how effective these policies are and how to design them. In this paper: Optimal R&D and Corporate Taxation Policies. Consider heterogeneous firms Firm quality is private information. Firm faces uncertainty about its quality over time. R&D returns are stochastic. Spillovers between firms. Do not restrict policies ex ante: let optimal policy tools arise endogenously. First: optimal mechanism design, then consider simpler policies.

6 35 What we do: Model of R&D and endogenous growth with heterogeneous firms. Mechanism design setup: Firms are agents, government is the Principal. Derive analytically fully unrestricted optimal dynamic mechanism characterize allocations using wedges or implicit taxes and subsidies. Estimate important parameters of the model using patent data matched to Compustat (not yet today) Numerically illustrate life cycle path of optimal policies for firms (by age, quality..). How well do simpler policies perform (linear size-independent age-dependent, linear size and age-independent policies, etc..). Formulas in terms of sufficient statistics.

7 35 Related Literature R&D Policies and Growth: Acemoglu, Akcigit, Bloom and Kerr (2013), Atkeson and Burstein (2014), Lentz and Mortensen (2015). Empirics of R&D Policies: Bloom, Griffith, Van Reenen (2000), Criscuolo et al. (2013), Hall (1992), Goolsbee (1998), Romer (2001), Wilson (2009) Optimal Policy Design: Hopenhayn and Nicolini (1997), Golosov, Tsyvinski and Werning (2006), Shourideh (2012), Farhi and Werning (2013, 2014), Stantcheva (2014), Pavan, Segal and Toikka (2013).

8 Outline 1 Model 2 Optimal Unrestricted Mechanism 3 Simpler Policies and Sufficient Statistics 4 Conclusion

9 Outline 1 Model 2 Optimal Unrestricted Mechanism 3 Simpler Policies and Sufficient Statistics 4 Conclusion

10 10 35 Model: Summary Household Max consumption Government Policies spillovers q t Final Goods producer Intermediate Goods producers Y ( q t ) = Θ t k(θ t ) 1 β q(θ t ) β p(θ t ) dθ t Manager: effort l t R&D : q(θ t ) = q(θ t 1 ) + λ t (r(θ t 1 ), l(θ t ), θ t ) Produce k(θ t ) π(θ t, q t ) = max k {p(θt )k C(k, q t )}

11 11 35 Model: Intermediate Producers R&D Investments and Efforts Each producer can improve his quality q t through R&D: q t = (1 δ)q t 1 + λ t λ t : step size, δ: depreciation factor. The step size λ t (r t 1, l t, θ t ) depends on: R&D resources r t cost M t (r t ). Type θ t (managerial/firm quality). Managerial/firm effort: l t at cost φ t (l t ). λ θ > 0, λ r > 0, λ l > 0, 2 λ θ l > 0 (screening). Returns to R&D are stochastic, depend on stochastic type.

12 12 35 Model: Intermediate Producers Production Firm born with θ 1, evolves with Markov f t (θ t θ t 1 ). History: θ t = {θ 1,..., θ t } with probability P(θ t ) = f t (θ t θ t 1 )...f 1 (θ 1 ). Firm lifecycle is T periods (max time after which exogenous death). k(θ t ): quantity and q(θ t ): quality. Linear production cost: C (k, q t ) = k q t Aggregate quality (Spillovers): q t = Θ t q(θ t )P(θ t )dθ t Hence profits are: π(θ t, q t ) max k {p(θ t )k C (k, q t )} = q t (θ t )(1-β) 1 β β 1 β β q β t Final good: Y t = Θ t q(θ t ) β k(θ t ) 1 β P(θ t )d(θ t )

13 13 35 Government Policies Studied Fully unrestricted mechanism. Linear (size-independent) age-dependent corporate tax and R&D subsidies. Linear (size- and age-independent) corporate tax and R&D subsidies. Nonlinear (i.e., size dependent) corporate tax and R&D subsidies. What do these policies look like at optimum? What is the welfare gain from each?

14 Outline 1 Model 2 Optimal Unrestricted Mechanism 3 Simpler Policies and Sufficient Statistics 4 Conclusion

15 15 35 Direct Revelation Mechanism with Spillovers In this section: θ t = pθ t 1 + ψ t, with ψ t distributed N(0, σ 2 ψ ). History θ t and effort l t are private info. Government sees: step size λ, realized quality q, R&D spending r, and production k. Direct revelation: Firm reports θ t(θ t ). History of reports: θ t = {θ 1 (θ 1),...θ t(θ t )}. Allocations as function of history of reports: {λ(θ t ), r(θ t ),T t (θ t )}. Maximize { household consumption (wlog, zero weight on manager): E T ( 1 ) } t 1 t=1 R {π(θ t, q t ) M t (r(θ t )) T t (θ t )} First: let s assume full depreciation δ = 1.

16 35 Incentive compatibility and a First-order Approach Lifetime expected utility from assigned allocations under truthful reporting: V 1 (θ 1 ) V 1 ({λ(θ s ), r(θ s ), T s (θ s )} T s=1, θ 1) = T t=1( 1 R )t 1 { Θ t { Tt (θ t ) φ t (λ(θ t ), r(θ t 1 ), θ t } P(θ t θ 1 )dθ t } Utility for a given sequence of realizations θ T : Ũ(θ T ) = T ( 1 ) t 1 { t=1 R Tt (θ t ) φ t (λ(θ t ), r(θ t 1 ), θ t ) } Envelope condition (Pavan, Segal and Toikka, 2014): V t (θ t ) θ t = E{ T Ũ(θ s=t I T ) t,s θ s } I t,s : impulse response of shock θ t on time s shock θ s. For AR(1) is p s t. Informational { rent: ( V 1 (θ 1 ) = )} 1 F E 1 (θ 1 ) f 1 (θ 1 ) T Ũ({λ(θ t=1 I s ),r(θ s ),T s (θ s )} T s=1,θt ) 1,t θ t + V 1 (θ 1 ).

17 17 35 Program: Maximize Virtual Surplus with Spillovers Notation: λ(θ t ) = λ(r(θ t 1 ), l(θ t ), θ t ). max T t=1 ( 1 R )t+1 { {π t (θ t, q t ) M t (r(θ t )) φ(l(θ t )) Θ t 1 F 1 (θ 1 ) f 1 p t [φ (l(θ t )) λ(θt )/ θ t (θ 1 ) λ(θ t ] V 1 (θ )/ l 1 )}P(θ t )dθ t } t s.t.: q t Θ t λ(θ t )P(θ t )dθ t = Solve using this first-order approach, then verify global (IC) ( sufficiency ) ex post (Farhi and Werning, 2013). Cohort-by-cohort problem (pooling across cohorts can be a second step).

18 18 35 Wedges: Measures of Implicit taxes and Subsidies Implicit corporate tax: (1 τ(θ t )) π t(θ t ) λ t λ(θ t ) l t = φ lt (λ(θ t ), r(θ t 1 ), θ t ) Implicit R&D subsidy: (1 s(θ t ))M t(r(θ t )) = 1 { R E πt+1 (θ t+1 } ) λ(θt+1 ) (1 τ(θ t+1 )) λ t+1 r t Net R&D subsidy: s(θ t ) = s(θ t ) { 1 1 M t(r(θ t )) R E πt+1 (θ t+1 } ) λ(θt+1 ) τ(θ t+1 ) λ t+1 r t

19 19 35 Sufficient Statistics: Elasticities and Coefficient of Complementarity Elasticity of x t w.r.t y t : ε xy,t x t y t y t x t Hicksian coefficient of complementarity between x and y in λ: For {x, y} {θ t, r t 1, l t } ρ xy = 2 λ x y λ λ λ x y λ t (r, l, θ) = rlθ ρ θl = ρ θr = ρ lr = 1. λ t (r, l, θ) = r + l + θ ρ θl = ρ θr = ρ lr = 0.

20 20 35 Optimal R&D Subsidy and Corporate Tax τ(θ t ) + Optimal Corporate Tax: πt (θ t, q t ) q t π t (θ t, q t ) λ t } {{ } Externality 1 1 τ(θ t ) = 1 ( ) F 1 (θ 1 ) f 1 p t 1 ε λθ,t 1 + ρθl,t ε λ(1 τ),t (θ 1 ) θ t ε }{{} λ(1 τ),t }{{} Type distribution Efficiency and persistence Cost Optimal R&D Subsidy: tension between externality and asymmetric info. s(θ t ) = + 1 F 1 (θ 1 ) f 1 p t (θ 1 ) }{{} Type distribution and persistence 1 1 M t R E( λ(θt+1 ) πt+1 (θ t+1, q t+1 ) r t q }{{ t+1 } Externality (1 τ(θ t+1 )) π t+1(θ t, q t+1 ) λ t+1 λ t+1 θ t+1 λ t+1 r t 1 λ t+1 (ρ lr ρ θr )) }{{} Complementarity coefficients

21 21 35 Special Cases for the Optimal R&D Subsidy when only Externality Matters Multiplicatively separable step size: λ t (r, l, θ) = h 1 (r)h 2 (θ)h 3 (l) has ρ lr = ρ θl = ρ θr = 1. s(θ t ) = ( 1 1 h 1 M t (r(θt )) R E (r(θ t )) h 2 (θ t+1 )h 3 (l(θ t+1 πt+1 (θ )) t+1 ), q t+1 ) r t q t+1 CES step size: λ(l, r, θ) = (α 1 l (1 ρ) + α 2 r (1 ρ) + α 3 θ (1 ρ) ) 1 ρ 1 ρ lr = ρ θl = ρ θr = ρ. ( ( s(θ t 1 1 λ(θ ) = t ) ρ M t (r(θt )) R E ) πt+1 (θ t+1 ), q α t+1 ) 2 r(θ t ) q t+1 has

22 A Simple Numerical Illustration Next step: Estimation from Patent data matched to Compustat. Functional forms: λ(r, l, θ) = w(θ, r) = (αr (1 ρ) + (1 α)θ (1 ρ) ) 1 1 ρ l. Two cases: ρ = 0.8 and ρ = 1.2 (keep average λ constant across two cases). α = 0.2. Constant elasticity disutility: φ(l) = l1+γ 1+γ. γ = 2 generates Frisch elasticity of 0.5. Constant elasticity R&D cost: M t (r) = r 1+κ 1+κ κ = 1 (typically quadratic R&D cost estimates). AR(1) process for type: θ t = pθ t 1 + ψ t p = 0.9, σ 2 ψ =

23 23 35 Policies for Old and New Firms, ρ = 0.8 Can incentivize less and less effort and R&D over time. Optimal to make young firms invest most. An almost constant net subsidy is optimal (but as T, s t 0.)

24 24 35 Wedges for Higher and Lower Quality Firms, ρ = 0.8 Gross subsidy tracks corporate tax (else too high disincentive on R&D). Higher quality firms are subsidized to produce more (big externality). Optimal subsidy highly nonlinear.

25 25 35 Policies for Higher and Lower Quality Firms, ρ = 0.8 Monotonic allocations: high quality firms have more inputs. Allocations get flatter over time: less able to screen.

26 26 35 Policies for Old and New Firms, ρ = 1.2 As ρ is higher, s is lower.

27 27 35 Wedges for Higher and Lower Quality Firms, ρ = 1.2 As ρ is higher, s is lower.

28 Policies for Higher and Lower Quality Firms, ρ =

29 29 35 Case with no Depreciation: Externality Persists Forever T πs (θ s, q s ) s=t q s 1 q s ) λ t λ t l t ) 1 τ(θ t ) = ) ( ) 1 + ρ θl,t ε λ(1 τ),t τ(θ t ) + E ( T s=t( R 1 )s t π s (θ s, 1 F 1 ( (θ 1 ) f 1 p t 1 ελθ,t (θ 1 ) θ t ε λ(1 τ),t s(θ t 1 1 ) = M t (r(θt )) R E( λ T t+1 πs (θ r t s, q s ) + s=t+1 q s 1 F 1 (θ 1 ) f 1 p t λ t+1 λ t+1 φ (l t+1 ) 1 (ρ (θ 1 ) r t θ t+1 λ λ t+1 t+1 lr ρ θr )) l t+1 Same special cases apply when subsidy only set based on (now persistent) externality.

30 Outline 1 Model 2 Optimal Unrestricted Mechanism 3 Simpler Policies and Sufficient Statistics 4 Conclusion

31 Optimal Linear (Size-independent) Age-Dependent Policies Linear age-dependent corporate tax τ t and R&D subsidy s t. Manager s optimization problem: T max {s ti,r ti } T t=1 t=1 ( ) 1 t 1 ((1 τ t )π ti (1 s t )M t (r ti) φ t (l ti)) R Hence π ti ((1 τ t ), s t 1, q t ((1 τ t ), s t 1 ))) and r t 1i ((1 τ t ), s t 1, q t ((1 τ t ), s t 1 ))) are solutions as functions of policies. Social welfare is now just total revenue: max T {τ,s} T t=1 t=1 ( 1 R )t 1 (τ t E(π ti ) s t E(M t (r ti ))) Aggregate (or cross-sectional averages): r t = E(r ti ) and π t = E(π ti )

32 32 35 Optimal Formulas as Function of Sufficient Statistics with Formulas valid even if other instrument not optimally set. Useful to evaluate reforms. Could use structural or reduced-form (sufficient stats) approach. Fiscal externality from one tax on other tax base. τ t = 1 + s t 1ε 1 τ r t 1 r,t 1 π t 1 + ε 1 τ π,t ε 1 τ r,t 1 = de(m(r t 1i)) 1 τ d(1 τ) r t 1 st = 1 + τ tε s 1 π,t π t r t 1 + ε s 1 r,t ε 1 τ π,t = dπ t 1 τ d(1 τ) π t ε s 1 π,t = dπ t s 1 d(s 1) π t ε s 1 r,t = de(m(r ti)) d(s 1) s 1 r t

33 33 35 Optimal Size and Age-Independent Policies Same Formula and same sufficient stats different estimation required in data. τ = 1 + sε1 τ r 1 + ε 1 τ π r π s = 1 + τεs 1 π π r 1 + ε s 1 r π = T ( ) 1 t 1 T ( ) 1 t 1 π t r = t=1 R r t 1 t=1 R ε 1 τ r = ε s 1 π = T ( ) 1 t 1 ε 1 τ r t 1 r,t 1 t=1 R r T t=1 ( 1 R ) t 1 ε s 1 π t π,t π ε 1 τ π = ε s 1 r = T ( 1 t=1 R T t=1 ( 1 R ) t 1 ε 1 τ π t π,t π ) t 1 ε s 1 r t r,t r

34 Outline 1 Model 2 Optimal Unrestricted Mechanism 3 Simpler Policies and Sufficient Statistics 4 Conclusion

35 35 35 Conclusion Model of R&D investments and endogenous growth with heterogeneous firms, private information, and spillovers. Use mechanism design to solve for constrained efficient allocations. Characterize using wedges. Optimal to subsidize R&D investments because of externality. Asymmetric info: could tend to reduce R&D subsidy if very complementary to firm quality. But optimal R&D subsidy is nonlinear. Simple sufficient stats formula for R&D subsidy and corporate tax in linear, age-dependent or age-independent cases. Next step: estimate model using patent + compustat data.