14.461: Technological Change, Lectures 7 and 8 Innovation, Reallocation and Growth

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1 14.461: Technological Change, Lectures 7 and 8 Innovation, Reallocation and Growth Daron Acemoglu MIT September 26 and 30, Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

2 Innovation, Reallocation and Growth Introduction Motivation (I) Recent economic recession has reopened the debate on industrial policy. In October 2008, the US government bailed out GM and Chrysler. (Estimated cost, $82 Billion) Similar bailouts in Europe: Estimated cost 1.18 trillion in 2010, 9.6% of EU GDP. Many think that this was a success from a short-term perspective, because these interventions protected employment, and encouraged incumbents to undertake greater investments. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

3 Innovation, Reallocation and Growth Introduction Motivation (II) More generally, what are the implications of industrial policy for R&D, reallocation, productivity growth, and welfare? Bailouts or support for incumbents could increase growth if there is insuffi cient entry or if they support incumbent R&D. In fact, this is recently been articulated as an argument for industrial policy. They may reduce growth by preventing the entry of more effi cient firms and slowing down the reallocation process. Reallocation potentially important, estimated sometimes to be responsible for up to 70-80% of US productivity growth. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

4 Motivation (III) Innovation, Reallocation and Growth Introduction What s the right framework? 1 endogenous technology and R&D choices, 2 rich from dynamics to allow for realistic reallocation and matched the data (and for selection effects), 3 different types of policies (subsidies to operation vs R&D), 4 general equilibrium structure (for the reallocation aspect), 5 exit for less productive firms/products (so that the role of subsidies that directly or indirectly prevent exit can be studied). Starting point: Klette and Kortum s (2004) model of micro innovation building up to macro structure. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

5 From Micro to Macro Innovation: Klette-Kortum Motivating Facts R&D intensity is independent of firm size. The size distribution of firms is highly skewed. Smaller firms have a lower probability of survival, but those that survive tend to grow faster than larger firms. Among larger firms, growth rates are unrelated to past growth or to firm size. Younger firms have a higher probability of exiting, but those that survive tend to grow faster than older firms. Gibrat s law holds approximately (but not exactly): firm growth rate roughly independent of size, though notable deviations from this at the top and the bottom. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

6 From Micro to Macro Innovation: Klette-Kortum Model I Representative household maximizes U = max e ρt log C t dt 0 All expenses are in terms of labor. Hence C t = Y t. The household owns all the firms including potential entrants. Therefore the total income is Y t = w t L + r t A t where A is the total asset holdings and r t is the rate of return on these assets. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

7 Model II From Micro to Macro Innovation: Klette-Kortum Final good production ln Y t = y j : quantity of intermediate j A fixed mass L of labor 1 0 ln y jt dj L P + S E + S I = L L P : production S E : scientists working for outsiders S I : scientists working for incumbent firms. All workers receive w t Normalize the price of the final good to 1. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

8 Profits I From Micro to Macro Innovation: Klette-Kortum A firm is defined as a collection of product lines. F 3: E F quality level A product line j 0 1 Firm f Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

9 Profits II From Micro to Macro Innovation: Klette-Kortum n will denote the number of product lines that the firm operates. Each intermediate is produced with a linear technology y jt = A jt l jt This implies that the marginal cost is w t /A jt where w t is the wage rate in the economy at time t. Innovations in each product line improves the productivity by λ > 0 such that { (1 + λ) Ajt if successful innovation A jt+ t = otherwise A jt Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

10 Profits III From Micro to Macro Innovation: Klette-Kortum Bertrand competition = previous innovator will charge at least her marginal cost: (1+λ)w t A jt. Hence the latest innovator will charge the marginal cost of the previous innovator p jt = (1 + λ) w t A jt. Recall that the expenditure on each variety is Y t (since P t = 1). Then the profit is π j = y j (p j MC j ) ( A jt Y t (1 + λ) wt = (1 + λ) w t A jt = πy t w ) t A jt where π λ 1+λ. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

11 From Micro to Macro Innovation: Klette-Kortum Innovation Technology I Innovations are undirected across product lines. Innovation technology X i = ( ) 1 γ Si n γ ζ where γ < 1, X i is the innovation flow rate, S i is the amount of R&D workers, n is the number of product lines to proxy for the firm specific (non-transferable, non-tradable) knowledge stock. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

12 From Micro to Macro Innovation: Klette-Kortum Innovation Technology II Alternatively, the cost of innovation: C (X, n) = ws i = ζwn = ζwnx [ ] 1 Xi 1 γ n 1 1 γ i where x i X i /n is the innovation intensity (per product line). Let x denote the aggregate innovation rate in the economy. Innovation rate by entrants is x e. Aggregate innovation rate is τ = x i + x e. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

13 From Micro to Macro Innovation: Klette-Kortum Innovation Technology III When a firm is successful in its current R&D investment, it innovates over a random product line j [0, 1]. 1 Then, the productivity in line j increases from A j to (1 + λ)a j. 2 The firm becomes the new monopoly producer in line j and thereby increases the number of its production lines to n + 1. At the same time, each of its n current production lines is subject to the creative destruction τ by new entrants and other incumbents. Therefore during a small time interval dt, 1 the number of production units of a firm increases to n + 1 with probability X i dt, and 2 decreases to n 1 with probability nτdt. A firm that loses all of its product lines exits the economy. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

14 From Micro to Macro Innovation: Klette-Kortum quality level q product line j 0 1 Firm f Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

15 From Micro to Macro Innovation: Klette-Kortum quality level q λ product line j 0 X 1 Firm f Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

16 From Micro to Macro Innovation: Klette-Kortum Value Function I Relevant firm-level state variable: number of products in which the firm has the leading-edge technology, n. Then the value function of a firm as a function of n is nπ t w t ζn 1 γ 1 rv t (n) V t (n) = max +nx i [V t (n + 1) V t (n)] x i 0 +nτ [V t (n 1) V t (n)] This can be rewritten as ρv = π τv + max x i 0 { x i v ωζx 1 1 γ i where v V t (n)/ny t is normalized per product value and ω w t /Y t is the labor share and constant in steady state. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80 }

17 From Micro to Macro Innovation: Klette-Kortum Value Function II First-order condition of R&D choice gives: Or substituting it back: x i = ( ) 1 γ v γ. (1) ηζω v = π 1 ζωx 1 γ i. (2) ρ + τ x i Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

18 From Micro to Macro Innovation: Klette-Kortum Value Function III Proposition Per-product line value of a firm v can be expressed as a sum of production value v P and R&D innovation option value v R : v = v P + v R where v p = v R = π ρ + τ { 1 (ρ + τ) max x i (v R + v P ) ωζx x i 0 i 1 1 γ }. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

19 Entry I From Micro to Macro Innovation: Klette-Kortum A mass of potential entrants. In order to generate 1 unit of arrival, entrants must hire a team of ψ researchers, i.e., production function for entrant R&D is x e = S E ψ. The free-entry condition equates the value of a new entry V t (1) to the cost of innovation ψw t such that Thus, together with (1) and (2) : v = ωψ. x e = π ( ) 1 γ (1 γ) ψ ωψ (1 γ) γ ρ and x i = ζ ( (1 γ) ψ ζ ) 1 γ γ. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

20 From Micro to Macro Innovation: Klette-Kortum Labor Market Clearing I Production workers L P = Y t A j p j = 1 (1 + λ) ω Incumbent R&D workers Entrant R&D workers ( (1 γ) ψ S I = ζ ζ ) 1 γ γ S E = π ( ) 1 γ (1 γ) ψ ω ζ γ ψρ ζ Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

21 From Micro to Macro Innovation: Klette-Kortum Labor Market Clearing II Therefore labor market clearing determines the normalized wage rate L = = ω = 1 (1 + λ)ω + ζ ( (1 γ) ψ + π ω ζ ( (1 γ) ψ ζ 1 L + ρψ ζ ) 1 γ γ ) 1 γ γ ψρ Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

22 From Micro to Macro Innovation: Klette-Kortum Equilibrium Growth I Recall the final good production function ln Y t = = = ln ln y jt dj ln A jt l jt dj Y t (1 + λ)w t + = ln L + ρψ 1 + λ ln A jt dj ln A jt dj Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

23 From Micro to Macro Innovation: Klette-Kortum Equilibrium Growth II Define Thus ( 1 Q t exp ln Q t = ln A jt dj g = Ċt C t = Q t Q t ) ln A jt dj Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

24 From Micro to Macro Innovation: Klette-Kortum Equilibrium Growth III Moreover ln Q t+ t = 1 0 [τ t ln(1 + λ)a jt + (1 τ t) ln A jt ] dj + o( t) = τ t ln(1 + λ) + ln Q t + o( t) g = τ ln(1 + λ) Hence g = [ ( ) λ L 1 + λ ψ + 1 γ γ ( (1 γ) ψ ζ ) 1 γ γ ] ρ ln(1 + λ) 1 + λ Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

25 Moments From Micro to Macro Innovation: Klette-Kortum Consider a firm with n product lines. The approximate growth rate is R&D spending/intensity n t+ t = n t + nx i t nτ t = ṅ t n t = x i τ R&D Sales = ζwnx n 1 1 γ i = ζwx 1 1 γ i Both of these are independent of firm size (consistent with Gibrat s law ). Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

26 From Micro to Macro Innovation: Klette-Kortum Firm Size Distribution Firm size distribution: fraction of firms with n leading-edge products, µ n, given by: Outflow Inflow entry&exit: µ 1 τ = x e 1-product: (x i + τ) µ 1 = µ 2 2τ + x e n-product: (x i + τ) nµ n = µ n+1 (n + 1) τ + µ n 1 (n 1) x i This implies the following simple firm size distribution: µ 1 = x e /τ µ 2 = x e 2τ 2 x i µ 3 = x ex i 3τ 3... =... µ n = x ex i nτ n Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

27 From Micro to Macro Innovation: Klette-Kortum Firm Size Distribution F 4: F S D Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

28 Reallocation What s Missing? A nice and tractable model, but: no reallocation (all firms that previous in equilibrium are equally good at using all factors of production); no endogenous exit of less productive firms; limited heterogeneity (see next slide). All of these together imply very little room for endogenous selection which could be impacted by policy. We now consider a model that extended this framework to introduce these features. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

29 Reallocation Why Heterogeneity Matters 1A: T R 1B: R&D I 1C: S G 1D: E G Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

30 Simplified Model Baseline Model: Preferences Preferences Simplified model (abstracting from heterogeneity and non-r&d growth). Infinite-horizon economy in continuous time. Representative household: U = exp ( ρt) C (t)1 θ 1 dt. 0 1 θ Inelastic labor supply, no occupational choice: Unskilled for production: measure 1, earns w u Skilled for R&D: measure L, earns w s. Hence the budget constraint is C (t) + Ȧ (t) w u (t) + w s (t) L + r (t) A (t) Closed economy and no investment, resource constraint: Y (t) = C (t). Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

31 Simplified Model Preferences Final Good Technology Unique final good Y : ( Y = N ) ε y ε 1 ε 1 ε j dj. N [0, 1] is the set of active product lines. The measure of N is less than 1 due to 1 exogenous destructive shock 2 obsolescence Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

32 Simplified Model Preferences Intermediate Good Technology As usual, each intermediate good is produced by a monopolist: y j,f = q j,f l j,f, q j,f : worker productivity, l j,f : number of workers. Marginal cost : MC j,f = w u q j,f. Fixed cost of production, φ in terms of skilled labor. Total cost TC j,f (y j,f ) = w s φ + w u y j,f q j,f. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

33 Simplified Model Preferences Definition of a Firm A firm is defined as a collection of product qualities as in Klette-Kortum Firm f = Q f { q 1 f, q2 f,..., qn f }. n f Q f : is the number of product lines of firm f. quality level q product line j 0 1 Firm f Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

34 Relative Quality Simplified Model Preferences Define aggregate quality as ( Q N ) 1 qj ε 1 ε 1 dj. In equilibrium, Define relative quality: Y = C = Q, ˆq j q j w u. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

35 R&D and Innovation Simplified Model R&D Innovations follow a controlled Poisson Process X f = n γ f h1 γ f. X f : flow rate of innovation n f : number of product lines. h f : number of researchers (here taken to be regular workers allocated to research). This can be rewritten as per product innovation at the rate x f X ( ) 1 γ f hf =. n f Cost of R&D as a function of per product innovation rate x f : n f w s G (x f ) w s n f x 1 1 γ f. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

36 Simplified Model R&D Innovation by Existing Firms Innovations are again undirected across product lines. Upon an innovation: 1 firm f acquires another product line j 2 if technology in j is active: q (j, t + t) = (1 + λ) q (j, t). 3 if technology in j is not active, i.e., j / N, a new technology is drawn from the steady-state distribution of relative quality, F ( ˆq). Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

37 Simplified Model R&D Entry and Exit A set of potential entrants invest in R&D. Exit happens in three ways: 1 Creative destruction. Firm f will lose each of its products at the rate τ > 0 which will be determined endogenously in the economy. 2 Obsolescence. Relative quality decreases due to the increase in the wage rate, at some point leading to exit. 3 Exogenous destructive shock at the rate ϕ. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

38 Static Equilibrium Simplified Model Equilibrium Drop the time subscripts. Isoelastic demands imply the following monopoly price and quantity ( ) ( ) ε 1 ε 1 ε pj,f = and cj = ˆq j Y ε 1 ˆq j ε Gross equilibrium (before fixed costs) profits from a product with relative quality ˆq j are: ( ) π (ˆq j,f ) = ˆq ε 1 j (ε 1) ε 1 ε ε Y. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

39 Simplified Model Implications for Firm Size Distribution 0 q ˆ= q w Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

40 Simplified Model Implications for Firm Size Distribution 0 q qˆ= w Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

41 Simplified Model Implications for Firm Size Distribution 0 q qˆ= w Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

42 Simplified Model Implications for Firm Size Distribution Without a fixed cost 0 q ˆ= q w Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

43 Simplified Model Implications for Firm Size Distribution exit With fixed cost φ > 0 0 ˆq min q ˆ= q w Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

44 Simplified Model Implications for Firm Size Distribution 0 qˆ ˆq min Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

45 Dynamic Equilibrium Simplified Model Dynamic Equilibrium In equilibrium, Y = C = Q and w u = ε 1 Q. ε Let us also define normalized values as Ṽ V Y, π (ˆq j,f ) = π (ˆq j,f ), w u w u Y Y and w s w s Y. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

46 Simplified Model Dynamic Equilibrium (continued) Dynamic Equilibrium r Ṽ ( ) ˆQ f = ˆqj,f ˆQ f { ˆQ f max xf π (ˆq jf ) w s φ j Ṽ ˆq jf ˆq jf Ṽ w u (t) + w u (t) t +τ [ Ṽ ( ˆQ f \ { ˆq jf } ) Ṽ ( + )] ˆQ f [ wg (x f ) +x f E ˆq Ṽ ( ) ˆQ f (1 + λ) ˆq ( )] j,f Ṽ ˆQ f +ϕ [ 0 Ṽ ( )] ˆQ f } τ: creative destruction rate in the economy. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

47 Simplified Model Dynamic Equilibrium (continued) Dynamic Equilibrium r Ṽ ( ) ˆQ f = π (ˆq jf ) w s φ j ˆqj,f ˆQ f + Ṽ ˆq jf w u (t) ˆq jf w u (t) t Ṽ +τ [ Ṽ ( ˆQ f \ { ˆq jf } ) Ṽ ( + )] ˆQ { f ˆQ f wg (x max f ) xf [ +x f E ˆq Ṽ ( ) ˆQ f (1 + λ) ˆq ( )] j,f Ṽ ˆQ f +ϕ [ 0 Ṽ ( )] ˆQ f } τ: creative destruction rate in the economy. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

48 Simplified Model Dynamic Equilibrium Franchise and R&D Option Values Lemma The normalized value can be written as the sum of franchise values: Ṽ ( ˆQ f ) = ˆq ˆQ f Υ (ˆq), where the franchise value of a product of relative quality ˆq is the solution to the differential equation (iff ˆq ˆq min ): rυ (ˆq) Υ (ˆq) ˆq ˆq w u (t) w u = π (ˆq) w u φ + Ω (τ + ϕ) Υ (ˆq), (t) t where Ω is the R&D option value of holding a product line, { Ω max w s ( G (x f ) + x f E ˆq Ṽ ( ) ˆQ f (1 + λ) ˆq ( ))} j x f 0 f Ṽ ˆQ f, Moreover, exit follows a cut-off rule: ˆq min π 1 ( w s φ Ω). Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

49 Simplified Model Dynamic Equilibrium Equilibrium Value Functions and R&D Proposition Equilibrium normalized value functions are: ( π (ˆq) ˆqmin Υ (ˆq) = 1 r + τ + ϕ + g (ε 1) ˆq + Ω [ w s ( ) r +τ+ϕ ] φ ˆqmin g 1, r + τ + ϕ ˆq and equilibrium R&D is [ x (ˆq) = x (1 γ) E ˆq Υ (ˆq) = w s ] 1 γ γ ) r +τ+ϕ+g (ε 1) g. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

50 Entry Simplified Model Dynamic Equilibrium Entry by outsiders can now be determined by the free entry condition: { ( )} max w s φ + x entry EV entry (ˆq, θ) w s G x entry, θ E = 0 x entry 0 ( ) where G x entry, θ E, as specified above, gives a number of skilled workers necessary for a firm to achieve an innovation rate of x entry (with productivity parameter θ E ). X entry mx entry is the total entry rate where m is the equilibrium measure of entrants, and x entry innvation rate per entrant. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

51 Simplified Model Dynamic Equilibrium Labor Market Clearing Unskilled labor market clearing: 1 = N (t) l j (w u ) dj. Skilled labor market clearing [ ( )] L s = [φ + h (w s )] dj + m φ + G x entry, θ E. N (t) Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

52 Simplified Model Dynamic Equilibrium Transition Equations Finally, we need to keep track of the distribution of relative quality stationary equilibrium distribution of relative quality F. This can be done by writing transition equations describing the density of relative quality. These are more complicated than in Klette-Kortum because there is no strict Gibraltar s law anymore. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

53 Full Model Preferences and Technology Preferences and Technology in the General Model Same preferences. Introduce managerial quality affecting the rate of innovation of each firm. Some firms start as more innovative than others, over time some of them lose their innovativeness. Young firms are potentially more innovative but also have a higher rate of failure. Introduce non-r&d growth (so as not to potentially exaggerate the role of R&D and capture potential advantages of incumbents). Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

54 Definition of a Firm Full Model R&D A firm is again defined as a pair of technology set and management quality θ: Firm f (Q f, θ f ), where Q f { q 1 f, q2 f,..., qn f }. n f Q f : is the number of product lines owned by firm f. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

55 Full Model R&D R&D and Innovation Innovations follow a controlled Poisson Process. Flow rate of innovation for leader and follower given by X f = (n f θ f ) γ h 1 γ f. n f : number of product lines. θ f : firm type (management quality). h f : number of researchers. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

56 Full Model R&D Innovation Realizations With R&D Innovations are undirected within the industry. After a successful innovation, innovation is realized in a random product line j. Then: 1 firm f acquires product line j 2 technology in line j improves q (j, t + t) = (1 + λ) q (j, t). Without R&D Firms receive a product line for free at the rate ϱ. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

57 Full Model R&D quality level q qˆ ~ F( qˆ) λ product line j 0 X 1 With R&D Without R&D Firm f Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

58 Entry and Exit Full Model R&D There is a measure of potential entrants. Successful innovators enter the market. At the time of initial entry, each firm draws a management quality θ : ( ) Pr θ = θ H = α ( Pr θ = θ L) = 1 α, where α (0, 1) and θ H > θ L > 0. Exit happens in three ways as in the baseline model. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

59 Maturity Shock Full Model R&D Over time, high-type firms become low-type at the rate ν > 0 : θ H θ L. Convenient to capture the possibility of once-innovative firms now being ineffi cient (and the use of skilled labor). Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

60 Equilibrium Full Model Equilibrium Equilibrium definition and characterization similar to before (with more involved value functions and stationary transition equations). Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

61 Estimation Methodology Data: LBD, Census of Manufacturing and NSF R&D Data Sample from combined databases from 1987 to Longitudinal Business Database (LBD) Annual business registry of the US from 1976 onwards. Universe of establishments, so entry/exit can be modeled. Census of Manufacturers (CM) Detailed data on inputs and outputs every five years. NSF R&D Survey. Firm-level survey of R&D expenditure, scientists, etc. Surveys with certainty firms conducting $1m or more of R&D. USPTO patent data matched to CM. Focus on continuously innovative firms : I.e., either R&D expenditures or patenting in the five-year window surrounding observation conditional on existence. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

62 Estimation Methodology Data Features and Estimation 17,055 observations from 9835 firms. Accounts for 98% of industrial R&D. Relative to the universal CM, our sample contains over 40% of employment and 65% of sales. Important small firms also included: of the new entrants or very small firms that later grew to have more than 10,000 employees or more than $1 billion of sales in 1997, we capture, respectively, 94% at 80%. We use Simulated Method of Moments on this dataset to estimate the paremeters the parameters of the model. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

63 Estimation Methodology Creating Moments from the Data We target 21 moments to estimate 12 parameters. Some of the moments are: Firm entry/exit into/from the economy by age and size. Firm size distribution. Firm growth by age and size. R&D intensity (R&D/Sales) by age and size. Share of entrant firms. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

64 Estimation Methodology RESULTS Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

65 Results Parameters T 1. P E # Parameter Description Value 1. ε CES φ Fixed cost of operation L S Measure of high-skilled workers θ H Innovative capacity of high-type firms θ L Innovative capacity of low-type firms θ E Innovative capacity of entrants α Probability of being high-type entrant ν Transition rate from high-type to low-type λ Innovation step size γ Innovation elasticity wrt knowledge stock ϕ Exogenous destruction rate ϱ Non-R&D innovation arrival rate Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

66 Results Parameters T 2. M M # Moments model data # Moments model data 1. Firm Exit (small) Sales Gr. (small) Firm Exit (large) Sales Gr. (large) Firm Exit (young) Sales Gr. (young) Firm Exit (old) Sales Gr. (old) Trans. large-small R&D/Sales (small) Trans. small-large R&D/Sales (large) Prob. small R&D/Sales (young) Emp. Gr. (small) R&D/Sales (old) Emp. Gr. (large) year Ent. Share Emp. Gr. (young) Aggregate growth Emp. Gr. (old) Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

67 Results Parameters 2A: T R 2B: R&D I 2C: S G 2D: E G Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

68 Results Parameters Non-Targeted Moments T 3: N - M Moments Model Data Corr(exit prob, R&D intensity) Exit prob of low-r&d-intensive firms Exit prob of high-r&d-intensive firms Corr(R&D growth, emp growth) Share firm growth due to R&D Ratio of top 7.2% to bottom 92.8% income Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

69 Results Comparison to Micro Estimates Parameters Estimates of the elasticity of patents (innovation) to R&D expenditures (e.g., Griliches, 1990): [0.3, 0.6] This corresponds to 1 γ, so a range of [0.4, 0.7] for γ. Our estimate is in the middle of this range. Use IV estimates from R&D tax credits. US spending about $2 billion with large cross-state over-time variation. Literature estimates: log(r&d i,t ) = α i + β t + γ log(r&d_cost_of _Capital i,t ) Bloom, Griffi th and Van Reenen (2002) find (0.024) on a cross-country panel. Similar estimates from Hall (1993), Baily and Lawrence (1995) and Mumuneas and Nadiri (1996). In the model, ln R&D = γ 1 γ ln (c R&D ) +constant. So approximately γ 0.5, close to our estimate of γ = Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

70 Baseline Results Policy Experiments T 4. B M x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Note: All numbers except wage ratio and welfare are in percentage terms. g : growth rate Φ high : fraction of high p. lines x out : entry rate ˆq l,min : low-type cutoff quality x low : low-type innv rate ˆq h,min : high-type cutoff quality x high : high-type innv rate wel : welfare in cons equiv. Φ low : fraction of low p. lines Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

71 Density Policy Experiments Relative Quality Distribution F Low Type High Type qhat Explains why very little obsolescence of high-type products. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

72 Policy Experiments Policy Analysis: Subsidy to Incumbent R&D T 4. B M x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Use 1% and 5% of GDP, resp., to subsidize incumbents R&D: T 5A. I R&D S (s i = 15%) x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel T 5B. I R&D S (s i = 39%) x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

73 Policy Experiments Policy Analysis: Subsidy to the Operation of Incumbents T 4. B M x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Use 1% of GDP to subsidize operation costs of incumbents: T 6. O S (s o = 6%) x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Now an important negative selection effect. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

74 Policy Experiments Policy Analysis: Entry Subsidy and Selection T 4. B M x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Use 1% of GDP to subsidize entry: T 7. E S (s e = 5%) x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

75 Density Density Policy Experiments Understanding the Selection Effect F 4. P P D.. L T 0.6 Baseline High Type Entry Subsidy High Type 0.7 Baseline Low Type Entry Subsidy Low Type qhat qhat Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

76 Policy Experiments Social Planner s Allocation T 4. B M x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel What would the social planner do (taking equilibrium markups as given)? T 8. S P x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

77 Policy Experiments Optimal Policy (I) T 4. B M x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Optimal mix of incumbent R&D subsidy, operation subsidy and entry subsidy: T 9. O P A W I & E P (s i = 17%, s o = 246%, s e = 6%) x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

78 Policy Experiments Optimal Policy (II) T 4. B M x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Optimal mix of incumbent R&D subsidy and operation subsidy: T 9. O P A W I P (s i = 12%, s o = 264%) x entry x l x h m Φ l Φ h ˆq l,min ˆq h,min g Wel Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

79 Policy Experiments Summing up Industrial policy directed at incumbents has negative effects on innovation and productivity growth though small. Subsidy to entrants has small positive effects. But not because R&D incentives are right in the laissez-faire equilibrium. The social planner can greatly improve over the equilibrium. Similar gains can also be achieved by using taxes on the continued operation of incumbents (plus small R&D subsidies). This is useful for encouraging the exit of ineffi cient incumbents who are trapping skilled labor that can be more productively used by entrants and high-type incumbents. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80

80 Policy Experiments Robustness These results are qualitatively and in fact quantitatively quite robust. The remain largely unchanged if: γ = 0.5. ϱ = 0. entry margin much less elastic. Daron Acemoglu (MIT) Innovation, Reallocation and Growth September 26 and 30, / 80