Nonrivalry and the Economics of Data

Transcription

1 Nonrivalry and the Economics of Data Chad Jones and Chris Tonetti SED 28 June / 42

2 Examples of Data Google, Facebook Amazon Tesla, Uber, Waymo Medical and genetic data Location history Speech records Physical action data Canonical example: data as input into machine learning algorithm. E.g. self-driving car. 2 / 42

3 Data is Nonrival Growth literature: Ideas are nonrival Unlike rival goods, ideas are not depleted by use Data is another nonrival factor of production Bitstrings of ones and zeros Ex: labeled images (cat, house, car,...); driving data; s; speech records Clearly not a blueprint / recipe different from ideas Nonrivalry implies increasing returns to scale: Y = F(D, X) Constant returns to rival inputs: F(D, λx) = λf(d, X) Increasing returns to data and rival inputs: F(λD, λx) > λf(d, X) 3 / 42

4 Data is Nonrival Interesting Questions Do markets produce the right amount of data? Why don t firms (always) sell their data? Who should own data as it s created? Implications of data nonrivalry for antitrust and economic growth? We develop a framework for thinking through these questions 4 / 42

5 Outline Economic environment Allocations: Optimal allocation Firms own data Consumers own data Extreme privacy protection: outlaw data sharing Theory results and a numerical example 5 / 42

6 Basic Setup 6 / 42

7 Overview Representative consumer with a love for variety Innovation endogenous measure of varieties Nonrivalry of data increasing returns to scale How is data produced? Learning by doing: each unit consumed 1 unit of data Alternative: separate PF (Tesla vs Google self-driving car) Any data equally useful in all firms one sector of economy Data depreciates fully each period 7 / 42

8 The Economic Environment Utility e ρt L t u(c t, x it, x it )dt 1 Nt x 2 Nt 2 it di κ 2 Flow Utility u(c t, x it, x it ) = log c t κ 2 ( ) σ Nt σ 1 σ Consumption per person c t = di with σ > 1 Variety resource constraint c σ 1 it c it = Y it /L t Firm production Y it = D η it L it, < η < 1 1 Nt N t x 2 it di Data production J it = Y it Data of firm i used by others D sit x it J it ( Data bundle B t = N 1 ɛ t Nt D ɛ 1 ɛ sit ) ɛ ɛ 1 di with ɛ > 1 Data used by firm i D it αx it J it + (1 α)b t (nonrivalry) Innovation (new varieties) Labor resource constraint Ṅ t = 1 χ L et L et + N t L it di = L t Population growth (exogenous) L t = L e g Lt Creative destruction δ( x it ) = δ 2 x 2 it (equilibrium) 8 / 42

9 Symmetry Simplifications: L pt := L t L et c t = N σ σ 1 t c it = N σ σ 1 Y it t Y it = D η it L it = D η L pt it N t L t Define aggregate output Y t := c t L t. Y t = N 1 σ 1 t D η it L pt 9 / 42

10 The Planner Problem max {L pt,x it, x it } e ρt L u(c t, x it, x it ) dt, subject to ρ := ρ g L c t = Y t /L t Y t = N 1 σ 1 t D η it L pt D it = αx it Y it + (1 α)n t x it Y it Y it = D η it Lpt N t Ṅ t = 1 χ (L t L pt ) L t = L e g Lt 1 / 42

11 Scale Effect from Sharing Data Data: D it = αx it Y it + (1 α)n t x it Y it = [αx it + (1 α) x it N t ]Y it No sharing versus sharing: No sharing: Only the αx t term = no scale effect Sharing: The (1 α) x t N t term = extra scale effect Source of Scale Effect: N t scales with L t Plugging into production function: Y it = ([αx t + (1 α) x t N t ] η L it ) 1 1 η 11 / 42

12 The Optimal Allocation on BGP (asymptotic) ( ) 1 x it = x sp = κ η 1/2 (1) 1 η x it = x sp = α ( ) κ 1 1 α κ κ η 1/2 (2) 1 η L sp i = χρ σ 1 := νsp 1 η (3) N sp L t t = χ ( ) := ψ spl t g L + ν sp (4) L sp pt = νspψspl t (5) Y sp t = ( ν sp(1 α) η x η ) 1 ) 1 1 η sp ψ spl t σ η 1 (6) c sp t = ( ν sp(1 α) η x η ) 1 ) 1 1 η sp ψ spl t σ 1 + η 1 η (7) = Y t L t g sp c = ( 1 σ 1 + η ) g L (8) 1 η D sp i = ((1 α) x spν spψ spl t ) 1 1 η (9) D sp = ND i = ((1 α) x spν sp) 1 1 η (ψ spl t ) η (1) Y sp i = ( ν sp(1 α) η x η ) 1 1 η sp (ψ spl t ) η 1 η (11) 12 / 42

13 The Optimal Allocation: GDP per person c sp t = Y ( t = ν sp (1 α) η x η sp L ( t 1 σ 1 + η ) g L 1 η g sp c = ) 1 1 η ( ψsp L t ) 1 σ 1 + η 1 η Scale effect: 1 + η σ 1 1 η }{{}}{{} Love of Variety Data More people make more data and all firms use all shared data 13 / 42

14 The Optimal Allocation: Data, Firm Size, Variety ( ) 1/2 1 x sp = κ η 1 η L sp i = χρ σ 1 1 η := ν sp N sp L t t = := ψ sp L t χg L + ν sp Data shared increasing in data production elasticity and decreasing in privacy cost Firm size constant on BGP. N has opposite comparative statics Higher entry cost, time preference, population growth, and elasticity of substitution raise firm size and reduce varieties Higher η raises firm size and reduces varieties: Entry does not create data. 14 / 42

15 Firms Own Data 15 / 42

16 Firms Own Data: Consumer Problem Firms own data, so just choose consumption: U = max {c it } ( Nt s.t. c t = e ρt L u(c t, x it, x it )dt c σ 1 σ it di ) σ σ 1 ȧ t = (r t g L )a t + w t Nt p it c it di 16 / 42

17 Firms own Data: Data Decisions Firms buy D bit data from intermediary at given price p b Firms sell D sit data to intermediary at chosen price p si Perfect competition inconsistent with nonrival data! Monopolistically competitive with own data See the intermediary s downward-sloping demand curve and set price How much data to use / sell? x it : Use all of own data x it = 1 x it : Trade off = selling data versus creative destruction δ( x it ) = Poisson rate transferring ownership of variety 17 / 42

18 Firms own the Data: Incumbent Firm Problem Monopolistically competitive firm takes demand for variety as ( ) 1 ( ) 1 given (from FOC of consumer problem): p it = ct σ c it = Yt σ Y it r t V it = max L it,d bit,x it, x it ( Yt Y it s.t. ) 1 σ Yit w t L it p bt D bit + p st x it Y it + V it δ( x it )V it Y it = D η it L it D it = αx it Y it + (1 α)d bit x it [, 1], x it [, 1] p sit = λ DI N 1 ɛ t ( Bt x it Y it ) 1 ɛ Note: Even if D bit =, then Y it = (α η L it ) 1 1 η Firm sees increasing returns because of data 18 / 42

19 Firms own the Data: Data Intermediary Problem A monopolist takes data purchase price as given and sees the downward sloping demand curve for data p bt (D bit ): max p bt,d sit p bt Nt Nt D bit di p st D sit di s.t. D bit B t = ( N 1 ɛ t Nt D ɛ 1 ɛ sit di ) ɛ ɛ 1 Free entry at zero cost zero profits Problem incorporates data nonrivalry Buys data once from each firm But can sell the same bundle multiple times 19 / 42

20 Entry: Innovation Creates a New Variety χ units of labor needed to create an additional variety Free entry condition: χw t = V it 2 / 42

21 Firms Own the Data: Definition of Equilibrium The equilibrium in which firms own the data consists of quantities {c t, Y t, c it, x it, x it, a t, Y it, L it, D it, D bit, B t, D sit, N t, L pt, L et } and prices {p it, p bt, p sit, w t, r t, V it } such that 1 {c t, c it, a t } solve the Household Problem. 2 {L it, Y it, p it, p sit, D bit, D it, x it, x it, V it } solve the Firm Problem. 3 (D sit, B t ) Data markets clear: D bit = B t and D sit = x it Y it 4 (p bt ) Free entry into data intermediation gives zero profits there (constrains p b as a function of p s ) 5 (L et ) Free entry into producing a new variety leads to zero profits: χw t = V it 6 Definition of L pt : L pt = N t L it di 7 w t clears the labor market: L pt + L et = L t 8 r t clears the asset market: a t = N t V it di/l t 9 N t follows its law of motion: Ṅ t = 1 χ (L t L pt ) 1 Y t := c t L t denotes aggregate output. 21 / 42

22 Firms Own Data: A No Trade Law What if the government, in an attempt to protect consumers privacy, makes data sharing illegal? Government chooses x t (, 1] x t = We call this the Outlaw Sharing allocation 22 / 42

23 Consumers Own Data 23 / 42

24 Consumers own Data: Consumer Problem Consumers own data, so now choose how much to share (x it, x it ): U = s.t. c t = max {c it, x it, x it } ( Nt c σ 1 σ it di e ρt L u(c t, x it, x it )dt ) σ σ 1 Nt Nt Nt ȧ t = (r t g L )a t + w t p it c it di + x it p a stc it di + x it p b stc it di Nt = (r t g L )a t + w t q it c it di where q it := p it x it p a st x itp b st is the effective price of consumption 24 / 42

25 Consumers own the Data: Incumbent Firm Problem Monopolistically competitive firm takes demand for variety as given (from FOC of consumer problem): ( ) 1 ( ) 1 q it = ct σ c it = Yt σ Y it = p it x it p a st x itp b st Firm buys data on its own variety (D ait ) and data on other firms varieties (D bit ) r t V it = max L it,d ait,d bit [ ( Yt Y it ) 1 ] σ + p a st x it + p b st x it Y it w t L it p at D ait p bt D bit + V it δ( x t )V it s.t. Y it = D η it L it D it = αd ait + (1 α)d bit D ait, D bit 25 / 42

26 Consumers own the Data: Data Intermediary Problem The DI chooses the price at which it sells a firm its own data and the price of other firms data, given its purchase price max p ait,p bit,d a cit,db cit Nt (p ait D ait + p bit D bit )di s.t. D ait D a cit D bit B t = i ( N 1 ɛ t Nt Nt (p a std a cit + pb std b cit )di (D b cit ) ɛ 1 ɛ di ) ɛ ɛ 1 i Can not sell more data on firm i than it buys from consumers Can sell all data purchased as type-b data to each firm (nonrivalry) 26 / 42

27 Consumers own the Data: Equilibrium An equilibrium in which consumers own data consists of quantities {c t, Y t, c it, x it, x it, a t, Y it, L it, D it, D ait, D bit, D a cit, Db cit, B t, N t, L pt, L et } and prices {q it, p it, p ait, p bit, p a st, pb st, w t, r t, V it } such that 1 {c t, c it, x it, x it, a t } solve the Household Problem. 2 {L it, Y it, p it, D ait, D bit, D it, V it } solve the Firm Problem. 3 (q it ) The effective consumer price is q it = p it x it p a st x itp b st 4 D a cit, Db cit, B t, p ait, and p bit solve the Data Intermediary Problem (with zero profits). 5 p a st clears the data market: Da cit = x itc it L t. 6 p b st clears the data market: Db cit = x itc it L t. 7 (L et ) Free entry into new varieties leads to zero profits: χw t = V it 8 Definition of L pt : L pt = N t L it di 9 w t clears the labor market: L pt + L et = L t 1 r t clears the asset market: a t = N t V it di/l t 11 N t follows its law of motion: Ṅ t = 1 χ (L t L pt ) 27 / 42

28 Results: Comparing Allocations 1. Planner Problem 2. Firms Own Data 3. Outlaw Data Sharing 4. Consumers Own Data 28 / 42

29 Data Sharing Own Firm Data x sp = α κ 1 α κ ( 1 κ η 1 η ) 1/2 x sp = x f = 1 x f = Sharing with Other Firms ( 1 κ ( Γρ ) 1/2 η 1 η ) 1/2, (2 Γ)δ Γ := η(σ 1) ɛ ɛ 1 ση x ns (, 1] x ns = ( ) 1/2 ( ) 1/2 x c = α κ 1 η σ 1 1 x 1 α κ κ 1 η σ c = η σ 1 κ 1 η σ Firms fear creative destruction and share less than planner (δ ) Consumers share less than planner because of mark up. No sharing law restricts data even more (privacy vs. output?) 29 / 42

30 GDP [ Y sp t = ν sp (1 α) η x ] 1 η 1 η ( ) σ σ 1 sp ψsp L + η 1 η t Y f t [ν = f (1 α) η x ] η 1 1 η ( ) σ σ 1 f ψf L + η 1 η t Y ns t = [ν ns α η x η 1 1 η ns] (ψ ns L t ) σ σ 1 Two source of increasing returns to scale: Standard variety effect: σ Data sharing: η Recall x t > from data sharing scale effect 3 / 42

31 GDP per person and Growth c sp t = Const 1 L 1 t σ 1 + η 1 η c f t = Const 2 L 1 σ 1 + η 1 η t c ns σ 1 t t = Const 3 L 1 which implies per capita growth of ( g sp c = g f 1 c = g ns c = σ 1 + ( 1 σ 1 ) g L η ) g L 1 η 31 / 42

32 Numerical Example: How large is η? Error rate is proportional to M η. Productivity = 1/(error rate) ERROR RATE.34 From 4b, with fine tuning ERROR RATE From 4a, no fine tuning Estimated eta = -.33 Doubling data lowers error by -2.3 percent NUMBER OF IMAGES (MILLIONS) Estimated eta = Doubling data lowers error by -1.4 percent NUMBER OF IMAGES (MILLIONS) ERROR RATE From 4b, no fine tuning Estimated eta = Doubling data lowers error by -8.2 percent NUMBER OF IMAGES (MILLIONS) ERROR RATE Facebook data Estimated eta = -.8 Doubling data lowers error by -5.7 percent NUMBER OF IMAGES (MILLIONS) Average η =.8. Double data, 6% reduction in error rate. η 1 η g L g y is about.1 pp higher b/c of data sharing. 32 / 42

33 Numerical Example: Other Parameters Description Parameter Value Importance of data η.8 Elasticity of substitution (goods) σ 3 Elasticity of substitution (data) ɛ 5 Weight on privacy κ = κ.1 Population level L 1 Population growth rate g L.1 Rate of time preference ρ.2 Labor cost of entry χ.1 Creative destruction δ.2 Weight on own data α 1/2 33 / 42

34 Numerical Example: Consumption Equivalent Welfare ( ) log c alloc c. U alloc ss = 1 ρ κ 2 x2 alloc + galloc ρ Let Uss alloc (λ) denote steady-state welfare when we perturb the allocation of consumption by some proportion λ: Uss alloc (λ) = 1 ρ ( log(λc alloc ) κ 2 x2 alloc + galloc c ρ ). Define consumption equivalent welfare as λ alloc : U sp ss (λ alloc ) = Uss alloc (1) with log λ alloc = log c alloc log c sp κ ( ) x 2 alloc }{{} 2 x2 sp }{{} Level term Privacy term + galloc c g sp c ρ }{{} Growth term Note: The x it terms drop out because scaled by 1/N 34 / 42

35 Allocations Firm Cons- Creative size Variety Privacy umption Growth Destruction ν N/L = ψ x c g δ Social Planner Consumers Own Data Firms Own Data Outlaw Sharing Consumers share more than firms, which leads to high creative destruction and low N Firms share less than consumers, taking less advantage of data nonrivalry Planner takes advantage of data nonrivalry and δ irrelevant 35 / 42

36 Consumption Equivalent Welfare Welfare Level Privacy Growth Allocation λ log λ term term term Optimal Allocation Consumers Own Data Firms Own Data Outlaw Sharing Level effect dominates welfare differences Variety effect dominates level effect Neither ownership regime close to planner Outlawing data sharing has huge negative consequences. Variety effect is strong. 36 / 42

37 Allocations: With Entry Subsidy Firm Cons- Creative size Variety Privacy umption Growth Destruction ν N/L = ψ x c g δ Social Planner Consumers Own Data Firms Own Data Outlaw Sharing Use subsidy to entry to fix variety margin Isolates data ownership/sharing at center of this paper 37 / 42

38 Consumption Equivalent Welfare: With Entry Subsidy Welfare Level Privacy Growth Allocation λ log λ term term term Optimal Allocation Consumers Own Data Firms Own Data Outlaw Sharing Consumers own data very close to optimal Much better than firms own data, which is way better than outlawing sharing Big gains from taking advantage of data nonrivalry 38 / 42

39 Implications for IO Firms that use data might grow fast compared to those that don t Firms would like to merge into one single economy-wide firm Implications for antitrust Targeted mandatory sharing? E.g., airplane safety (after a crash) What are the costs of forced sharing? Disincentive to create data (in MS, data is aggregate, good approx?) Data as a barrier to entry (extension to quality ladder model) 39 / 42

40 The Boundaries of Data Diffusion: Firms and Countries How does data diffuse across firms and countries? Ideas eventually diffuse across firms or countries, so no country scale effect (e.g. HK vs China) What about data? Intellectual property rights Scale effects and country size Larger countries may have an important advantage as data grows in importance Scale effects and institutions What if China mandates data sharing across Chinese firms and U.S. has no such policy 4 / 42

41 Appendix 41 / 42

42 Data versus Ideas Both nonrival Ideas: blueprint, algorithm, production function Data: factor of production Interesting differences in excludability Maybe technologically easier to transmit data than idea (usb key vs. education)... But data can be encrypted and monitored Data seems highly excludable Idea: use machine learning to train self-driving car algorithm ML needs lots of data. Each firm gathering own data 42 / 42