Nonrivalry and the Economics of Data

Transcription

1 Nonrivalry and the Economics of Data Chad Jones and Chris Tonetti UCLA 19 November / 44

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. 1 / 44

3 Data is Nonrival Data is infinitely usable Contrast with rival goods: coffee, computer, doctor Multiple engineers/algorithms can use same data at same time (within and across firms) Key ways that data enters the economy: Nonrivalry social gain from sharing data Privacy Firm: competitive advantage ( moat ) Social planner and consumers only care about the first two. But firms care a lot about the last one inefficiency 2 / 44

4 Policies on Data Are Being Written Now What policies governing data use maximize welfare? European General Data Protection Regulation (GDPR) Privacy vs. social gain from sharing The protection of natural persons in relation to the processing of personal data is a fundamental right The right... must be considered in relation to its function in society and be balanced against other fundamental rights... The California Consumer Privacy Act of 2018 Allows consumers to opt out of having their data sold 3 / 44

5 Nonrivalry of Data Increasing Returns 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) When firms hoard data, a firm learns only from its own consumers But when firms share data, all firms learn from all consumers Firms, fearing creative destruction, will not do this But if consumers own the data, they appropriately balance data sharing and privacy 4 / 44

6 Data Property Rights Matter Key point: allocations with different degrees of data sharing different output, welfare, etc. To illustrate, we assume (plausibly?) the Coase theorem fails Consumers can t commit to selling data to just one firm Firms can t commit to not using data they acquire Useful for showing the role of data sharing How do different property rights affect the use of data? Firms own data versus consumers own data 5 / 44

7 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 6 / 44

8 Outline Economic environment Allocations: Optimal allocation Firms own data Consumers own data Extreme privacy protection: outlaw data sharing Theory results and a numerical example 7 / 44

9 Basic Setup 8 / 44

10 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 9 / 44

11 The Economic Environment Utility 0 e ρt L t u(c t, x it, x it )dt 1 Nt x 2 Nt 2 0 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 Data production Variety resource constraint J it = c it L t c σ 1 0 it c it = Y it /L t Firm production Y it = D η it L it, η (0, 1) Data used by firm i D it αx it J it +(1 α)b t (nonrivalry) 1 Nt N t x 2 0 it di Data of firm i used by others D sit x it J it ( Data bundle B t = N 1 ǫ t Innovation (new varieties) Labor resource constraint Ṅ t = 1 χ L et Nt D ǫ 1 ǫ 0 sit L et + N t 0 L it di = L t Population growth (exogenous) L t = L 0 e g Lt ) ǫ ǫ 1 di with ǫ > 1 Creative destruction δ( x it ) = δ 0 2 x 2 it (equilibrium) 10 / 44

12 The Planner Problem (using symmetry of firms) max {L pt,x it, x it } 0 c t = Y t /L t Y t = N 1 e ρt L 0 u(c t, x it, x it ) dt, ρ := ρ g L σ 1 t subject to 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 0 e g Lt More sharing negative utility cost but more consumption Balance labor across production and entry/innovation 11 / 44

13 Scale Effect from Sharing Data D it = αx it J it +(1 α) ( N 1 ǫ t Nt 0 ( x it J it ) ǫ 1 ǫ di ) ǫ ǫ 1 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 12 / 44

14 The Optimal Allocation on BGP (asymptotic) ( ) 1 x it = x sp = κ η 1/2 1 η (1) x it = x sp = α ( ) κ 1 1 α κ κ η 1/2 1 η (2) L sp it = χρ σ 1 1 η := ν sp (3) N sp L t t = χ ( ) := ψ sp L t g L +ν sp (4) L sp pt = ν spψ sp L t (5) Y sp t = ( ν sp (1 α) η x η ) 1 ) 1 1 η sp ψ sp L t σ η 1 (6) c sp t = ( ν sp (1 α) η x η ) 1 ) 1 1 η sp ψ sp L t σ 1 + η 1 η (7) = Y t L t g sp c = ( 1 σ 1 + η 1 η ) g L (8) D sp i = ((1 α) x sp ν sp ψ sp L t ) 1 1 η (9) D sp = ND i = ((1 α) x sp ν sp ) 1 η(ψ 1 sp L t ) 1+ 1 η 1 (10) Y sp it = ( ν sp (1 α) η x η ) 1 1 η sp (ψ sp L t ) η 1 η (11) 13 / 44

15 The Optimal Allocation: Data, Firm Size, Variety ( ) 1/2 1 x sp = κ η 1 η L sp it = 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 / 44

16 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 15 / 44

17 Firms Own Data 16 / 44

18 Firms Own Data: Consumer Problem Firms own data and choose one data policy (x it, x it ) applied to all consumers Consumers just choose consumption: U 0 = max {c it } ( Nt s.t. c t = 0 0 e ρt L 0 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 0 p it c it di 17 / 44

19 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 18 / 44

20 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 [0, 1], x it [0, 1] p sit = λ DI N 1 ǫ t ( Bt x it Y it ) 1 ǫ Data Intermediary (p bt, p st, D bit ) and Free Entry complete eqm. 19 / 44

21 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 0 Nt D bit di p st D sit di s.t. D bit B t = p bt p bt ( N 1 ǫ t 0 Nt 0 D ǫ 1 ǫ sit di ) ǫ ǫ 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 20 / 44

22 Entry: Innovation Creates a New Variety χ units of labor needed to create an additional variety Free entry condition: χw t = V it + Nt 0 δ( x it )V it di Ṅ t The value of a new variety and the per-entrant share of business stealing from creative destruction 21 / 44

23 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 ++ Nt δ( x 0 it )V it di Ṅ t 6 Definition of L pt : L pt = N t 0 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 0 V it di/l t 9 N t follows its law of motion: Ṅ t = 1 χ (L t L pt ) 10 Y t := c t L t denotes aggregate output. 22 / 44

24 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 it (0, 1] x it = 0 We call this the Outlaw Sharing allocation 23 / 44

25 Consumers Own Data 24 / 44

26 Consumers own Data: Consumer Problem Consumers own data, so now choose how much to share (x it, x it ): U 0 = max {c it, x it, x it } ( Nt s.t. c t = 0 0 c σ 1 σ it di e ρt L 0 u(c t, x it, x it )dt ) σ σ 1 ȧ t = (r t g L )a t + w t Nt 0 Nt Nt p it c it di+ x it p a stc it di+ x it p b stc it di 0 0 Firm problem similar to before, but now takes x, x as given, can t sell data, and has to buy own data 25 / 44

27 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 0, D bit 0 26 / 44

28 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 0 (p ait D ait + p bit D bit )di s.t. D ait D a cit D bit B t = i ( N 1 ǫ t Nt 0 Nt 0 (p a std a cit + pb std b cit )di (D b cit )ǫ 1 ǫ di ) ǫ ǫ 1 i p ait p ait and p bit p bit 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) 27 / 44

29 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 ++ Nt δ( x 0 it )V it di Ṅ t 8 Definition of L pt : L pt = N t 0 L it di 9 w t clears the labor market: L pt + L et = L t 10 r t clears the asset market: a t = N t 0 V it di/l t 11 N t follows its law of motion: Ṅ t = 1 χ (L t L pt ) 12 Y t := c t L t denotes aggregate GDP. 28 / 44

30 Key Forces: Consumers vs. Firms vs. Outlaw Sharing Firms use all data on own variety, ignoring consumer privacy restrict data sharing because of creative destruction Consumers respect their own privacy concerns sell data broadly, ignoring creative destruction Outlaw sharing maximizes privacy gains missing scale effect reduces consumption 29 / 44

31 Results: Comparing Allocations 1. Planner Problem 2. Firms Own Data 3. Outlaw Data Sharing 4. Consumers Own Data 30 / 44

32 Results Preview of Scale Effect Recall: Role of data sharing D it = αx t Y it +(1 α)n t x t Y it = [αx t +(1 α) x t N t ]Y it Plugging into production function: Y it = ([αx t +(1 α) x t N t ] η L it ) 1 1 η Scale Effect from Data Sharing: (1 α) x t N t from data sharing and N t scales with L t Unless x t = 0 (outlaw sharing) 31 / 44

33 Key Allocations: alloc {sp, f, c, ns} Firm size: L alloc i = L pt /N t = ν alloc ν sp := χρ σ 1 1 η σ 1 ν os := χρ 1 ση ρ+δ( x c ) ν c := χg L g L +δ( x c ) σ 1 1 ση ρ+δ( x f ) ν f := χg L g L +δ( x f ) σ 1 1 ση ǫ 1 ǫ Number of firms: N alloc t = ψ alloc L t 1 ψ alloc := χg L +ν alloc 32 / 44

34 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 0 Γ := η(σ 1) ǫ ǫ 1 ση x os (0, 1] x os = 0 ( ) 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 0 ) Consumers share less than planner because of mark up No sharing law restricts data even more Firms use more own-variety data compared to consumer/planner 33 / 44

35 Output For alloc {sp, c, f}: Y alloc t = [ ν alloc (1 α) η x η alloc ] 1 1 η (ψ alloc L t ) 1+ 1 σ 1 + η 1 η For Outlaw Sharing: Y os t 1 = [ν os α η x α 1 η os] (ψ os L t ) 1+ 1 σ 1 Two source of increasing returns to scale: Standard variety effect: Data sharing: η 1 η σ σ 1 Recall x t > 0 from data sharing scale effect 34 / 44

36 Consumption per person and Growth Consumption per person: For alloc {sp, c, f}: For outlaw sharing: c alloc t = Const alloc L 1 c os σ 1 t t = Const os L 1 σ 1 + η 1 η t Per capita growth: ( g sp c = g f 1 c = g c c = σ 1 + η ( ) 1 g os c = g L σ 1 1 η ) g L Intuition: No sharing means you learn from 10 workers (constant firm size), sharing means you learn from the entire population 35 / 44

37 Numerical Example: How large is η? Error rate is proportional to M η. Productivity = 1/(error rate) ERROR RATE From 4b, no fine tuning Estimated eta = Doubling data lowers error by 8.2 percent NUMBER OF IMAGES (MILLIONS) Average η = Double data 6% reduction in error rate 36 / 44

38 Numerical Example: Other Parameters Description Parameter Value Importance of data η 0.08 Elasticity of substitution σ 5 Weight on privacy κ = κ 0.20 Population level L Population growth rate g L 0.02 Rate of time preference ρ 0.03 Labor cost of entry χ 0.01 Creative destruction δ Weight on own data α 1/2 Use of own data in NS x 1 37 / 44

39 Numerical Example: Consumption Equivalent Welfare ( ) log c alloc c. U alloc ss = 1 ρ 0 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 0 ) κ 2 x2 alloc + galloc c ρ ). Define consumption equivalent welfare as λ alloc : ss(λ alloc ) = Uss alloc (1) with logλ alloc = log c alloc 0 log c sp 0 κ ( ) x 2 alloc }{{} 2 x2 sp }{{} Level term Privacy term U sp + galloc c g sp c ρ }{{} Growth term Note: The x it terms drop out because scaled by 1/N 38 / 44

40 Allocations Data Sharing Firm Consu- Creative own others size Variety mption Growth Destruct. Allocation x x ν N/L = ψ c g δ Social Planner % Consumers Own Data % Firms Own Data % Outlaw Sharing % 0 Firms overuse their own data and undershare with others Consumers share less data than planner, but not by much Growth rate scale effect is modest, level differences are large 39 / 44

41 Consumption Equivalent Welfare Welfare Level Privacy Growth Allocation λ log λ term term term Optimal Allocation Consumers Own Data Firms Own Data Outlaw Sharing Outlaw sharing: particularly harmful law (66 percent worse!) Firms own data: substantially lower welfare (11 percent worse) Consumers own data: nearly optimal (1 or 2 percent worse) 40 / 44

42 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) 41 / 44

43 Data versus Ideas: 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 / 44

44 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 43 / 44

45 Conclusion Nonrival data large social gain from sharing data If firms own data, they may: privately use more data than consumers/planner would share less data across firms than consumers/planner would Nonrivalry Laws that outlaw sharing could be very harmful Consumers owning data good at balancing privacy and sharing 44 / 44