Artificial intelligence and technological unemployment

Wang and Wong develop a continuous-time labor-search model to assess the dynamic effects of generative AI (GenAI) on labor productivity and unemployment. The paper is motivated by conflicting empirical evidence: micro studies find productivity gains of 14% (Brynjolfsson, Li, and Raymond 2025) and 55.8% faster coding (Peng et al. 2023), while macro estimates suggest modest TFP gains of at most 0.064% annually (Acemoglu 2024), and occupation-level evidence shows a 13% relative employment decline in AI-exposed jobs (Brynjolfsson, Chandar, and Chen 2025).

The model distinguishes GenAI from earlier automation technologies by its learning-by-using mechanism: AI capability grows at rate µ per employed worker (law of motion dAt/At = µHt − δ), raises employed workers’ productivity, and creates a displacement threat through renegotiation. When renegotiation fails, AI replaces the worker, generating technological unemployment. Firms renegotiate wages at a rate ρµAt proportional to AI’s learning rate and the job’s exposure ρ. The joint surplus condition governs whether replacement occurs: AI replaces a worker if and only if πA (AI’s net present value per output) exceeds the post-renegotiation joint surplus St.

The model admits three steady states: (i) a some-AI steady state with finite AI capability, persistent AI adoption (It = 1), expanded job creation but declining employment at H∞ = δ/µ; (ii) an unbounded-AI equilibrium with sustained endogenous growth, no displacement (It = 0), and employment at H∞ = α/(α+σ); and (iii) a no-AI equilibrium reverting to the Mortensen-Pissarides benchmark. In the benchmark model (exogenous job-finding rate, AI-augmented productivity), multiple steady states can coexist—global indeterminacy—when condition (28) holds. In the full model (endogenous job creation via free entry), both global and local indeterminacy are possible, and a continuum of oscillatory transition paths converge to the some-AI steady state.

Calibrated to U.S. data, targeting a pre-AI unemployment rate of 5%, AI elasticity of productivity εy = 1.069 (from Czarnitzki et al. 2023), initial AI productivity boost of 14% (Brynjolfsson et al. 2025), worker exposure ρ = 0.618 (Brynjolfsson et al. 2018’s machine learning suitability index), AI replacement cost ϕ = 0.0043 (from U.S. business GenAI spending), AI learning rate µ = 0.632, and AI error rate δ = 0.462 (Moore’s law half-life of 1.5 years), the model converges to a some-AI steady state. The long-run results are: a 23% employment loss (H∞ = 0.732 vs. H0 = 0.95), AI capability improvement of 321%, and labor productivity gain of 366%. Approximately half of the employment loss—11.5 percentage points—occurs within the first five years, alongside a 49.3% output gain and 45.5% AI capability improvement over that period.

Untargeted moments are validated: the model implies 7.08% labor productivity growth over the first 10 years (consistent with Briggs and Kodnani 2023) and an AI elasticity of vacancies averaging 0.16 over the first five years (consistent with Acemoglu et al. 2022).

On welfare, equilibria are inefficient even when the Hosios condition holds. AI introduces four externalities beyond standard matching frictions: job destruction via displacement, productivity enhancement for employed workers, feedback from AI learning depending on employment, and direct effects on matching surpluses. A constrained-optimal subsidy to jobs at risk of AI displacement is 26.6% in the short run and exceeds 50% in the long run. In the full model, the Hosios condition requires fixing firm bargaining power θ to the vacancy elasticity of matching ξ, but an additional per-output transfer T = µApωA to firm-worker matches is necessary to correct AI adoption inefficiency.

Q: What is the core mechanism by which AI generates unemployment in this model? A: AI capability grows through a learning-by-using process (dAt/At = µHt − δ), improving as it observes employed workers. As capability rises, firms gain a displacement option that arrives at rate ρµAt per matched pair. When renegotiation over wages fails—i.e., when the AI’s NPV πA exceeds the joint surplus—firms replace workers with AI, causing unemployment. This creates a feedback loop: higher employment accelerates AI learning, which increases displacement pressure and reduces employment.

Q: What are the three steady states and what distinguishes them? A: The some-AI steady state features finite AI capability, persistent displacement (It = 1), and long-run employment H∞ = δ/µ; it involves technological unemployment. The unbounded-AI steady state features infinite AI capability, no displacement (It = 0), endogenous productivity growth, and employment H∞ = α/(α+σ) as in the standard Mortensen-Pissarides model. The no-AI steady state has A∞ = 0 with the same H∞ = α/(α+σ) but no AI contribution. Employment is higher in the unbounded-AI equilibrium than in the some-AI equilibrium.

Q: What does the calibration imply for long-run employment and productivity? A: The calibrated full model converges to a some-AI steady state with a 23% employment loss (H∞ = 0.732), a 321% improvement in AI capability, and a 366% gain in labor productivity. The parameters yield a unique equilibrium under the baseline calibration (πA = 1.949 > sAI = 0.8735 confirms some-AI existence). These results reflect a large worker replacement effect under the calibrated AI learning and error rates, while the job creation effect is relatively modest.

Q: How fast does technological unemployment materialize? A: Approximately half of the total 23% employment loss occurs within the first five years; specifically, employment falls by 11.5 percentage points over that period. Over the same five years, AI capability improves by 45.5% and output rises by 49.3%. Over the first 10 years, AI capability improvement accumulates to 94.0% and output gain to 103% (approximately double the five-year output gain).

Q: How does the full model differ from the benchmark model in transition dynamics? A: In the full model, job-finding rates are endogenous: firms post vacancies until a free-entry condition (κyt = ftΠt) is satisfied, tying job-finding rate αt to the surplus ratio st via αt = α(st). This endogeneity implies that as AI raises labor productivity, firms create more vacancies, slowing the employment decline relative to the benchmark model with a fixed job-finding rate. At the same time, AI capability grows faster in the full model because higher employment accelerates AI learning.

Q: What is global indeterminacy and when does it arise? A: Global indeterminacy occurs when both the some-AI and unbounded-AI steady states coexist, so the long-run outcome depends on initial conditions or expectations. In the benchmark model this requires condition (28): 0 < r + σ + α(1−θ) − (1−b)/πA ≤ εy(µα/(α+σ) − δ). In the full model, global indeterminacy is plausible when firm bargaining power rises to θ = 0.95 given the baseline AI replacement cost ϕ = 0.0043. The region of global indeterminacy is larger when firm bargaining power is higher.

Q: What is local indeterminacy and what does it imply for transition paths? A: Local indeterminacy means there is a continuum of equilibrium paths converging to the some-AI steady state in the neighborhood of that steady state, rather than a unique saddle path. In the full model, under alternative parameters (θ = 1, ξ = 0.765, εy = 6), the eigenvalues feature a negative real root and two complex roots with negative real parts, yielding oscillatory local dynamics in employment and AI capability. This implies short-run cycles in productivity and unemployment, consistent with the wide range of empirical findings on AI’s labor-market effects.

Q: Why does the Hosios condition fail to deliver efficiency in this model? A: The Hosios condition eliminates the standard matching externality by setting firm bargaining power to the vacancy elasticity of matching. But AI introduces four additional externalities: (i) job destruction through displacement, (ii) productivity enhancement for employed workers, (iii) feedback from AI learning that depends on aggregate employment, and (iv) direct effects on matching surpluses and job-finding rates. These externalities mean the standard Hosios rule alone is insufficient; additional instruments are required.

Q: What is the constrained-optimal policy response? A: In the simple model, the constrained optimal AI adoption threshold differs from the equilibrium threshold because firm bargaining power θ distorts adoption decisions: AI is over-adopted when πA > (1−b)/(r+σ+α(1−θ)) and under-adopted when (1−b)/(r+σ+α) < πA ≤ (1−b)/(r+σ+α(1−θ)). In the full model, constrained optimality requires setting θ = ξ (Hosios) plus a per-output subsidy T = µApωA to firm-worker matches exposed to AI displacement. This targeted subsidy is 26.6% in the short run and exceeds 50% in the long run.

Q: How does AI compare to computers in this model’s counterfactual? A: The paper reports that exogenous productivity growth from computers reduced unemployment only modestly—by 0.16 percentage points. By contrast, AI’s learning-by-using and displacement features imply a nearly 20% long-run employment loss in a comparable counterfactual. The key distinction is that computers lack the self-learning improvement and associated renegotiation-triggered displacement that characterize GenAI in this model.

Q: How is AI exposure parameterized and what does it capture? A: The exposure parameter ρ captures the degree to which a job is subject to AI-driven replacement risk. It is calibrated using Brynjolfsson et al. (2018)’s suitability for machine learning (SML) index: on a 1–5 scale, SML averages 3.47 across 964 O*NET occupations, translating to (3.47−1)/(5−1) = 61.8%, so ρ = 0.618. The effective exposure measure is ρµ, which is higher when facing a faster-learning AI.

Q: What is the predator-prey analogy in the model’s dynamics? A: The dynamical system for AI capability (At) and employment (Ht) in the simple model resembles the Lotka-Volterra predator-prey system. Employment (prey) feeds AI learning; as AI capability (predator) grows, it displaces workers faster, reducing employment; lower employment then slows AI learning, causing capability to decay; and the cycle repeats with diminishing magnitude until the steady state is reached. This mechanism operates only when the AI learning rate µ is neither too high nor too low, with the convergence path being a spiral when µα < 4δ²(1 − δ(α+σ)/(µα)).

Q: What is the labor-share implication of the unbounded-AI equilibrium? A: In the unbounded-AI steady state, employment is higher than in the some-AI steady state (H^AJJ > H^AI) and labor productivity grows without bound. However, the labor share is lower in the unbounded-AI equilibrium if the firm’s bargaining power θ is sufficiently low. This implies that while workers are not fully displaced and rising AI-augmented productivity sustains employment, workers’ income share may still decline even in the more favorable unbounded scenario.

Technological unemployment: A phenomenon in which AI adoption raises labor productivity and expands job creation, yet still causes sizable employment losses because the worker displacement effect (driven by renegotiation failure when AI’s NPV πA exceeds the joint surplus) dominates the job-creation effect. In the calibrated model this amounts to a 23% employment loss despite a 366% productivity gain.

Learning-by-using AI: The model’s representation of GenAI as a technology whose capability At grows through reinforced learning from employed workers at rate µ per worker, so aggregate AI growth is µHt, offset by deterioration at rate δ. This distinguishes GenAI from earlier automation technologies (computers, robotics) that do not self-improve through usage.

Some-AI steady state: A long-run equilibrium with finite AI capability (gA∞ = 0), persistent AI adoption (It = 1), and employment pinned at H∞ = δ/µ—the ratio of AI’s error rate to its learning rate. Characterized by expanded job creation but lower employment than the no-AI benchmark, constituting the model’s primary calibrated outcome.

Unbounded-AI steady state: A long-run equilibrium with infinite AI capability (A∞ = ∞), no displacement (It = 0), and endogenous growth at rate gA = µH^AJJ − δ. Employment equals the Mortensen-Pissarides level H∞ = α/(α+σ), and labor productivity grows without bound, complementing Aghion, Jones, and Jones (2019)’s idea production framework.

Global indeterminacy: Coexistence of multiple steady states (some-AI and unbounded-AI) such that the long-run equilibrium depends on initial conditions or expectations rather than being uniquely determined. Arises in the benchmark model when condition (28) holds and becomes more likely with higher firm bargaining power θ.

Local indeterminacy: A continuum of equilibrium transition paths converging to a single steady state from nearby initial conditions, rather than a unique saddle path. Arises in the full model under certain parameter configurations (e.g., θ = 1, ξ = 0.765, εy = 6), implying oscillatory short-run dynamics in employment and AI capability.

AI exposure (ρ): A firm-level parameter capturing the degree to which a job-match is subject to AI-driven displacement risk. The displacement option arrives at rate ρµAt per matched pair; ρ is calibrated at 0.618 using the average suitability-for-machine-learning score across O*NET occupations. The effective exposure measure is the product ρµ.

Renegotiation-proof displacement: Proposition 1’s result that the joint surplus Snt is independent of the renegotiation round n, so the AI adoption decision It is also round-invariant. This simplifies the model to a single indicator function: AI replaces the worker if and only if πA exceeds the joint surplus St, regardless of how many renegotiation rounds have occurred.