Knowledge Accumulation, Privacy, and Growth in a Data Economy

Lin William Cong; Danxia Xie; Longtian Zhang

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Knowledge Accumulation, Privacy, and Growth in a Data Economy

Lin William Cong, Danxia Xie, Longtian Zhang

arXiv:2109.10028v1Sep 21, 2021econ.TH

TL;DR

The paper asks how data misuse, digital infrastructure, and privacy regulation affect knowledge accumulation and growth in a dynamic data economy. It develops an endogenous growth model in which consumption generates data used in R&D, and finds that data provision eventually declines but low initial growth can create a new poverty trap. The paper concludes that its findings are first-order benchmark results because it omits some aspects of the data economy.

Problem
The paper addresses limited understanding of how data misuse, digital infrastructure, and privacy regulation affect knowledge accumulation and growth in a dynamic economy.
Method
The paper develops an endogenous growth model in which consumer-generated data enter R&D and knowledge accumulation alongside labor, with privacy concerns and policy-dependent data production.
Results
Data use eventually declines, allaying privacy concerns in the long run, while low-growth economies may face a new poverty trap during the emergence of the data economy.
Takeaways & Limitations
The model identifies transitional growth traps and supports interventions when limited economic activity constrains data generation.
Takeaways & Limitations
The paper leaves out certain aspects of the data economy, so its findings should be treated as first-order benchmark results rather than foregone conclusions.

Abstract

from arXiv · show

We build an endogenous growth model with consumer-generated data as a new key factor for knowledge accumulation. Consumers balance between providing data for profit and potential privacy infringement. Intermediate good producers use data to innovate and contribute to the final good production, which fuels economic growth. Data are dynamically nonrival with flexible ownership while their production is endogenous and policy-dependent. Although a decentralized economy can grow at the same rate (but are at different levels) as the social optimum on the Balanced Growth Path, the R&D sector underemploys labor and overuses data -- an inefficiency mitigated by subsidizing innovators instead of direct data regulation. As a data economy emerges and matures, consumers' data provision endogenously declines after a transitional acceleration, allaying long-run privacy concerns but portending initial growth traps that call for interventions.

1. Introduction

The paper develops an endogenous growth model in which consumer-generated data support innovation and knowledge accumulation while creating privacy concerns. It shows that decentralized growth matches the social optimum in rate on the BGP but differs in welfare, resource allocation, policy responses, and transitional dynamics.

Motivation and contribution: The model makes consumer data a factor in R&D and knowledge accumulation, linking data usage to endogenous growth and privacy concerns.Consumers choose data supplied to intermediate firms, which use raw data to conduct research and produce intermediate goods.
Motivation and contribution: Data are dynamically nonrival and can generate spillovers across periods and users with limited reproduction costs.Data traded among entrants in different periods support knowledge accumulation through new intermediate-good varieties.
Main results: The decentralized economy grows at the same rate as the social optimum on the Balanced Growth Path, but welfare and consumer surplus are lower.The allocation differs because R&D underemploys labor and overuses data, especially during the initial phase of the BGP.
Main results: Monopolistic markups crowd out R&D labor, leading producers to compensate through socially excessive data use.Data overuse occurs even when data are nonrival and consumers own them while accounting for privacy disutility.
Policy implications: Subsidizing R&D wages or intermediate producers is more effective than taxing data overuse at mitigating the social inefficiency.Direct data regulation reduces economic growth and transfers wealth from future generations to current generations.
Transitional dynamics: Consumer data provision can accelerate during transition before declining in the long run, while low initial growth can create a data-generation growth trap.Foreign aid for digital infrastructure can help escape the trap while the data-generating constraint remains binding.
Relation to literature: The paper connects data usage, privacy, knowledge accumulation, and endogenous growth, complementing earlier work that treats data as entering final production directly.It also finds that data play a limited role in long-run growth and is broadly consistent with empirical patterns involving regulation, privacy, and labor income shares.

2. The Model

The model represents a dynamic data economy with consumers, innovative intermediate producers, and a competitive final-good producer. Data are generated through consumption, sold for R&D, transformed into intermediate goods, and linked to innovation, privacy costs, and knowledge spillovers.

Agents and environment: The economy contains representative consumers-workers, innovative intermediate producers, and a competitive final-good producer in continuous time.Consumers supply labor to either R&D or final-good production.
Consumers: Consumers generate data as consumption by-products, sell them to intermediate producers, and account for privacy leakage and misuse in utility.The baseline lets data fully depreciate each period, although this assumption is relaxed in the online appendix.
Consumers: The data-provision constraint bounds data growth by consumption growth and implies that data cannot exceed a fixed proportion of consumption.The constraint reflects data’s status as a by-product of economic activity.
Final-good production: The final-good producer combines labor with one-period-use intermediate-good varieties, whose quantities and prices are determined by first-order conditions.Intermediate varieties are used only in final-good production for one period.
Intermediate producers and innovation: Potential intermediate producers conduct R&D using researchers and consumer data, paying data-processing costs before research success grants monopoly rights over a new product.The innovation frontier depends on data, R&D labor, innovation efficiency, and knowledge spillovers.
Intermediate producers and innovation: Data enter R&D as an input to creating intermediate goods, distinguishing the model from studies where data enter only final-good production.The innovation process tracks data supplied by consumers, R&D labor, and the fraction of labor employed in R&D.
Data properties: Dynamic nonrivalry lets entrants and incumbents benefit from the same data across periods without high reproduction costs.Data generate knowledge spillovers to future periods through new intermediate-good varieties.
Data properties: Consumers may own and sell data, while privacy regulation and digital infrastructure affect their endogenous production and use.This ownership structure and policy dependence distinguish data from labor and capital.

3. Data Economy on the Balanced Growth Path

On the Balanced Growth Path, the model characterizes growth, labor allocation, and data provision in a data-driven endogenous growth economy. Decentralized growth matches the planner’s rate but exhibits persistent misallocation, with policy and ownership shaping data use and transitional dynamics.

Framework: The analysis solves the model on the Balanced Growth Path, where all variables grow at the same constant rate, then identifies inefficiencies and policy remedies.It also examines data nonrivalry and ownership.
Data provision and labor: Consumers’ per-capita data contributions steadily decrease in the long run, although aggregate data use can continue to grow.The decentralized labor share in R&D is constant on the BGP and becomes zero when growth is zero.
Growth: BGP growth rates are ultimately driven by the exogenous population growth rate n and become zero when n becomes zero.The model restricts attention to parameter ranges ensuring existence and uniqueness of a BGP equilibrium.
Growth: Data contribute positively to the innovation possibility frontier, so growth depends on population growth, knowledge accumulation, and data’s innovation contribution.The model does not exhibit a population scale effect, and its growth rate can exceed Jones (1995)’s under the same parameters.
Growth: When γ > 1, BGP growth increases with ξ and with σ, while increasing γ lowers growth because consumers prefer lower growth and production.Higher privacy concerns raise the growth rate required to compensate consumers for information-leakage disutility.
Decentralization and misallocation: The decentralized economy grows at the same BGP rate as the social planner’s solution, but its output and welfare are lower because data usage differs through the decentralized data-price markup.The planner’s labor share is constant, while decentralized equilibrium underemploys R&D labor and overuses data.
Decentralization and misallocation: R&D labor is underallocated and data are overused in the decentralized economy, with data usage four to five times higher than under the planner’s solution.These distortions are more severe when data matter more for innovation and knowledge accumulation is slower.
Decentralization and misallocation: Intermediate producers compensate for R&D labor underemployment by using more data, creating a crowding-in of data usage relative to the socially optimal level.The mechanism differs from settings where labor is the only input to innovation because data enter the innovation possibility frontier.

4. Transitional Dynamics: A Numerical Analysis

The numerical analysis traces how economies transition toward balanced growth when data generation is endogenous and potentially constrained. Data provision initially accelerates, but later declines as data become less productive for innovation, while low initial growth can create prolonged traps.

Methodology and Calibration: The planner’s transitional dynamics are derived from differential equations for three state-like variables and solved using reverse shooting.The numerical exercise illustrates possible transitional dynamics rather than calibrating any particular country’s data.
Results and Discussions: Consumption growth and variety growth converge to steady-state levels from different starting points, with relatively rapid transition once growth becomes nontrivial.The simulations report robust convergence patterns across initial conditions.
Results and Discussions: Data provision initially rises rapidly to support intermediate-good variety accumulation, then its growth rate turns negative as the economy approaches balanced growth.As data become less productive for innovation, the economy substitutes labor for data use and focuses more on exploiting existing data.
Results and Discussions: Labor shifts from production toward R&D during the transition, causing temporary declines in output and consumption before growth becomes positive.The simulations also show periods of negative consumption growth during adjustment.
Results and Discussions: When data provision is binding, declining data provision reduces the cost of reallocating labor away from production, eliminating the temporary pain found in the unconstrained case.The data constraint binds from time 0 to 400 in the illustrated case.
Results and Discussions: Data constraints do not affect balanced-growth rates but can substantially alter transitional dynamics, including prolonged near-zero growth and delayed output recovery.An economy starting near zero growth may take almost 200 additional periods to reach balanced growth, with permanently lower output from the delay.
Results and Discussions: Interventions that improve digital infrastructure or relax privacy regulation can help economies escape growth traps earlier, while long-run data use declines as privacy concerns remain.The paper suggests focusing regulation on excessive R&D data use rather than directly restricting data provision.

5. Conclusion

The paper develops an endogenous growth model in which consumer-generated data support innovation and long-run growth, while privacy and ownership shape data provision. Decentralized growth matches the social optimum on the Balanced Growth Path, but resource allocations differ and transitional dynamics can generate privacy concerns and growth traps.

Main findings: Decentralized growth equals the socially optimal rate on the Balanced Growth Path, but R&D underemploys labor and overuses data.The decentralized equilibrium is therefore inefficient despite matching the planner’s growth rate.
Privacy and welfare: Consumers are inadequately compensated for potential information leakage and privacy violation when providing data.The paper links consumer welfare concerns to the compensation and privacy consequences of data provision.
Privacy and welfare: When consumers own data, privacy concerns become allayed in the long run because data use eventually declines.The model therefore predicts declining long-run data use despite data’s role in innovation.
Transitional dynamics: Less developed economies with low growth at the dawn of the data economy may face a new form of poverty trap.The conclusion identifies this transitional risk as potentially warranting intervention.
Transitional dynamics: Different starting points and privacy policies generate different pre-Balanced-Growth-Path trajectories, including paths under looser or fully relaxed privacy regulation.The comparison includes a privacy policy with s = 0.078 and the limiting case s →∞.
Model contribution: The model treats data as an input alongside labor for creating intermediate-good varieties that support final-good production and long-run growth.Data are generated endogenously as by-products of economic activity, dynamically nonrival, and subject to flexible ownership.
Scope: The paper excludes final-goods differentiation for tractability and presents its findings as first-order benchmark results rather than foregone conclusions.This scope boundary limits the interpretation of the model’s conclusions.

1. Proofs of Lemmas and Propositions

The proofs establish properties of labor allocation, growth, and the social planner’s problem in the model. They show constant sectoral labor shares on the Balanced Growth Path, derive growth expressions, and compare decentralized and socially optimal outcomes under stated conditions.

Labor allocations: Labor shares in production and R&D remain constant on the Balanced Growth Path because labor-market clearing bounds both shares between zero and one.If one share grew persistently, either it would exceed one or force the other share to grow positively.
Labor allocations: The proof uses the labor-market-clearing condition lE(t) + lR(t) = 1 to establish the Balanced Growth Path labor-share result.The shares satisfy 0 ≤ lE(t), lR(t) ≤ 1.
Growth-rate derivations: The paper derives growth rates for consumption, data, information, varieties, patent value, and per-capita output from equilibrium and Euler conditions.These derivations combine free-entry, production, innovation-frontier, and asset-pricing relationships.
Social planner: The social planner’s problem is formulated with a current-value Hamiltonian and necessary conditions for consumption, information, production labor, and varieties.The shadow prices λ(t) and µ(t) correspond to the model’s constraints.
Social planner: The social planner’s Balanced Growth Path growth rate is the same as in the decentralized model.The proof derives the planner’s growth rate and then equates it with the decentralized expression.

2. Extended Discussions

The extended discussions examine Balanced Growth Path existence, data accumulation, and transitional dynamics. They report conditions for a unique Balanced Growth Path and show that data provision can peak during transition before declining while cumulative provision plateaus.

Balanced Growth Path existence: A unique Balanced Growth Path exists when the model’s stated conditions on the growth rate and spillover parameters are satisfied.The conditions include positive growth and the transversality condition.
Balanced Growth Path existence: The transversality condition reduces on the Balanced Growth Path to g* + n − r* < 0.The proof also uses r* = γg* + n + ρ.
Data accumulation: When data used in innovation can accumulate, the model replaces contemporaneous information with total accumulated data governed by a depreciation rate κ.Φ(t) denotes total data accumulated in R&D activities, while κ measures how quickly data become out of date.
Data accumulation: With accumulated data, information growth equals the growth of total accumulated data on the Balanced Growth Path.The extended formulation preserves similar derivations by replacing the relevant information growth rate with accumulated-data growth.
Transitional dynamics: Under σ = 1.5, data provision peaks and then declines rapidly to a low level while cumulative data provision remains on a plateau.The figures illustrate transitional dynamics under alternative values of the disutility parameter and data-provision constraints.
Transitional dynamics: The economies undergo long but relatively steady transitional states before reaching the Balanced Growth Path endpoints.This result is reported for the illustrated transitional dynamics without the data-provision constraint.

3.1. Policy Implications on BGP

On the Balanced Growth Path, constant data taxes preserve growth but do not correct decentralized labor and data-use allocations. Direct data-usage taxes alter transitions only, whereas constant subsidies to R&D labor or intermediate-producer profits can align labor allocations with the social planner without changing BGP growth.

Taxing Data Usage: Privacy-policy regulation that reduces s lowers growth and cannot improve welfare without sacrificing growth, if it improves welfare at all.The policy discussion therefore restricts attention to interventions that preserve growth rates.
Taxing Data Usage: Data-usage taxes alter transitional data use and labor employment but ultimately return the decentralized economy to its original BGP path.Consequently, taxing data collection does not bring decentralized BGP allocations closer to the social planner’s solution.
Taxing Data Usage: Constant data taxes leave BGP growth rates unchanged.The tax rate must be constant over time for growth to remain at the baseline level.
Subsidizing R&D Labor: A constant subsidy on R&D labor can move decentralized labor allocations toward the social-planner solution without changing BGP growth rates.The required subsidy rate is determined by the condition stated in Proposition A.4.
Subsidizing Innovators: A constant profit subsidy to intermediate-good producers can likewise align decentralized labor allocations with the social planner while preserving BGP growth rates.Proposition A.5 specifies the required rate as τ′(t) = (τ′)* > 1.

3.2. Data Nonrivalry and Creative Destruction

The model treats data as dynamically nonrival: entrants combine newly collected consumer data with depreciating historical data traded by incumbent producers. Despite creative-destruction effects and data-market trading, the extended setting preserves baseline BGP growth rates and labor allocations under the reported conditions.

Data Trading: Potential entrants combine new consumer data with historical data purchased from incumbent intermediate producers, which depreciates at rate δ.Entrants choose new collection, historical-data purchases, and future sales over a finite entry horizon.
Data Trading: Consumers take future resale proportions as given, while incumbent producers endogenously determine them; firms use all newly collected data.Consumers cannot resell historical data under the model’s ownership assumptions.
Creative Destruction: Entrants’ profit includes innovation benefits, wage and new-data costs, future data-sale revenue, historical-data purchase costs, and expected creative-destruction losses.Selling data to future entrants can make an incumbent’s patent valueless according to a Poisson process.
Balanced Growth Path: The extended model yields the same BGP growth rates as the baseline model.The result follows from the derived growth-rate relationships for variety and data provision.
Balanced Growth Path: Labor allocations and R&D employment also remain the same as in the baseline model.Historical-data trading therefore changes data-market arrangements without changing the reported BGP labor allocation.
Data Trading: With the stated parameterization, the nonzero historical-data-sharing solution is dS = 0.53.The alternative numerical result dD = 3.70 exceeds the feasible proportion range and is omitted.

3.3. Data Ownership: Firms versus Consumers

Data ownership and processing costs affect firms’ incentives and, in some cases, BGP growth, while consumer ownership with positive processing costs preserves baseline growth and labor allocations under the stated condition. Binding data-provision constraints lower growth, and firms owning data leads them to use all available data.

Ownership Scope: The firm-ownership analysis focuses on positive processing costs because zero processing cost makes ownership trivial and the alternative consumer-payment case is intractable.The processing-cost friction represents firms’ cost of handling data.
Consumer Ownership: With positive data-processing cost and consumer data ownership, BGP growth rates and labor allocations remain unchanged from the baseline under the stated condition.The condition is σ(2−ζ) + (ξ + φ)(γ −1) > 0.
Consumer Ownership: Under standard parameter values, consumption grows faster than data provision before a tighter constraint binds in BGP.Tightening the provision limit by reducing s produces the lower-growth constrained case.
Firm Ownership: When firms own data, the BGP growth rate differs from the baseline, although labor allocations retain the same form as in Proposition 2.In this ownership regime, firms are inclined to use up all the data they have.
Consumer Ownership: A binding per-capita data-provision constraint lowers the BGP growth rate because firms require excessive data.The constraint binds when 2−ζ > ξ + φ.