In a recent newsletter I scratched out a simple growth model showing how “regulation” (broadly defined) could be conducive to economic growth by facilitating innovation.
The basic intuition is this: a portion of labor focuses on things like scientific research and discovery which produces the new ideas which we call innovation. But in a new emergent field, a portion of these PhDs and other high-skilled workers have to spend time reconciling different methods and terminology so those new ideas can maximally recombine and build on each other to produce the next innovative iteration. A form of regulation can reduce this “translation drag” as a coordination mechanism: defining terms, establishing common measurement rubrics, facilitating interoperability, and so on.
Nobel-laureate Paul Romer’s canonical endogenous growth theory provides a tractable model on which to scaffold this idea. His includes a variable to account for specialized labor devoted to discovery of new ideas which is a core driver of economic growth in his story.
Below I briefly restate his base model before explaining two extensions introducing regulation as a variable in different ways.
Here regulation is a broadly applicable term, and later allows for non-governmental regulation such as self-regulatory organizations or quasi-private institutions.1
Base Romer model (w/ knowledge spillover)
Narrative description: labor devoted to adding to the stock of knowledge is the source of innovation-driven growth. Beyond the actual amount of labor, this is subject to the effectiveness of this work (research), and degree to which new ideas feed into and interact with other ideas.
Formal description:
A = knowledge stock, LA = total pool of skilled R&D labor, δ = research productivity, β = knowledge-spillover parameter.2
Implication: growth depends on A which increases in level one-time through an increase in R&D labor if β < 1, or in growth rate if β = 1.
Extension 1 — regulation as coordination
Narrative description: in the absence of regulation, a portion of skilled R&D labor gets peeled off to work on interpretation, translation of existing ideas in lieu of producing new ones, creating translational drag on growth potential. Regulation can reduce translational drag but imposes it’s own cost (compliance). The effect of regulation is a priori ambiguous.
Formal description: instead of R&D labor (LA) going entirely to production of the knowledge stock, some is peeled off into resolving knowledge frictions. The diverted R&D labor (LR) then is characterized as:
θ = share of skilled labor (LA) going to knowledge production, bounded by θ(R) ∈ [0,1]. R is the regulatory level: at R = 0 no regulation and maximum translational drag; at R = 1, maximum regulatory drag.
Effective knowledge-producing labor is the remainder, LA − LR = θ(R)LA, giving:
θ(R) can be further decomposed as:
T(R) = translational drag (decreasing in R), C(R) = compliance drag (increasing in R). Optimal R* maximizes θ(R):
Implication: Regulation’s effect on growth (via innovation) is optimally ambiguous, but non-zero. At R = 0, some of LA is occupied with reducing translational drag. Adding regulation from zero frees more labor into direct knowledge production faster than it adds compliance burden. There is an optimal R* where the two marginal effects exactly offset which is an improvement in innovation from the baseline no regulation case.
Extension 2 — government v. industry regulation
Narrative description: There are now two types of regulatory regimes. (1) government-issued OR (2) industry-issued, via a Self-Regulatory Organization (SRO) or similar standards-setting body.3 One regime is chosen exclusively.
Government rules lead to 100 percent adoption across the industry, but will be further from a theoretical ideal set of rules (being more intermediated by political incentives and other frictions). SRO regulation is closer to the ideal in substance, but has only partial adoption (never fully reaching 100 percent).4
Formal description: Regulation R is now split into government (Rg) and voluntary (Rv). Both are subject to different coefficients for adoption level a and substantive quality (fidelity) φ. Under either regime, the other is set to zero.
Adoption: av(Rv) ∈ [0, ā], ā < 1; ag= 1
Fidelity: φg, φv ∈ [0,1], φv > φg (note: phi renders slightly differently in LaTeX below)
Adoption and fidelity both discount the effective quantity of regulation entering a single shared drag-reduction function τ, which is common to both channels, lower-bounded by 0, characterized by decreasing marginal returns.
Only one regulatory regime operates (government-issued OR SRO-issued):
Under government regulation, translation and compliance costs are given by:
So total combined effect is:
Which optimizes at Rg* such that (same as Extension 1, before expanding):
Under voluntary regulation, translation and compliance costs are given by:
Combines as:
Optimizes such that (requiring cross-partials since adoption is now also a factor):
First-order conditions for each given by:
Rg:
Rv
Government is optimal when:
Voluntary is optimal when:
Implication: Government regulation is preferable when the translational drag it removes, net of what it costs to comply, exceeds what the best voluntary standard could net after accounting for the same tradeoff. Because of universal compliance, every dollar of Cg is paid, and every unit of τ is realized.
Voluntary regulation is preferable when it’s fidelity advantage (φv>φg) is sufficient to compensate for adoption holdouts.
Empirical question: to what degree is SRO/industry-developed regulation higher quality than mandatory government-issued regulation. We assume it is higher-quality to some degree in the model but the magnitude is important here. It has to compensate for what’s lost to non-adoption (free-riders).
If you suppose the policy regime is such that industry-developed rules are “voluntary” in the sense of how they are developed and who can participate, but nonetheless legally binding, then this approach will always be superior.
Hypothetical Illustration: (assuming baseline growth ≈ 3%, δ = 0.08, LA = 1, Aβ-1 = 1)
gA(Rg) / gA(Rv) / gA(0)
The author is Nonresident Senior Fellow at the Foundation for American Innovation
Most people think of onerous command-and-control rules when they hear the word regulation. But in the federal government a continuum of forms constitute what could reasonably thought of as regulation. At the least restrictive end there are government entities explicitly engaged in developing measurement criteria and technology (“metrology”), best practices, testing methodologies, and certification criteria—all on a purely voluntary basis. NIST is the best known of these, and CAISI most pertinent for AI. Why call it regulation? Well it is a margin of government output: funding, staffing, prominence in interagency processes is a policy choice, and while industry is free to ignore any of it, the government is also free to use it as a basis for internal policies such as agency technology protocols and procurement rules. Further, CAISI’s predecessor has been accused of imposing a counterproductive policy agenda on the country (just ask the Senate Commerce Cmte Chair) so fair or not important policymakers treat it as having effectively regulatory authority.
From there we can walk through guidance, Dear Colleague letters, advisories, all the way up to 553 rulemakings. A taxonomy distinct from strictly legal definitions (on which I have a lot to say and experience). Another way to think of “regulation” in this article’s context is a means of answering the question “Should the government have a role in AI innovation?” and then determining the level of that policy margin.
The knowledge spillover is a modification from Jones (1995) based on theoretical and empirical findings.
You can think of this as structurally entirely emergent from industry coordination or resulting from affirmative government policy choice like PCAOB or FINRA. The model does not lose generality of the implication by including such hybrid institutions in the voluntary variable.
This is a necessary assumption to distinguish between the two regimes, otherwise voluntary would strictly dominate.