2.1 Theoretical Foundations

2.2 Empirical Evidence on External Validation and Market Signaling Strategies

2.3 Determinants of Signaling Strategy Adoption

The propensity to adopt external validation signals is shaped by firm-level characteristics, sector conditions, and the institutional environment. Larger firms adopt quality certification more readily due to lower amortisation costs per unit of output (Terziovski & Samson, 2003). Export-oriented firms have stronger incentives to signal quality to overseas buyers (Nair et al., 2013). Firms with experienced management teams are more likely to navigate the bureaucratic requirements of association membership and certification processes (Diwan et al., 2019). In weak-institution settings, certification provides a more valuable signal by substituting for institutional trust (Mayer & Salomon, 2006).

2.4 Research Gaps

Five interconnected gaps motivate this study. First, no prior study has evaluated all eight binary configurations of the three most common signaling mechanisms simultaneously, leaving complementarities and substitution effects uncharted. Second, existing comparative studies rely predominantly on regression-based methods that do not deliver the causal interpretation afforded by doubly robust or DML estimators. Third, the ECA and MENA regions are largely absent from the comparative strategy effectiveness literature. Fourth, no study has applied a formal multidimensional dominance framework to evaluate signaling strategies, relying instead on single-outcome rankings sensitive to the choice of performance metric. Fifth, the Pareto-efficiency and network-dominance approaches used in this paper have not previously been applied to the strategy ranking problem, representing a methodological innovation with broad applicability.

3.1 Conceptual Framework

The conceptual framework integrates three theoretical pillars to explain why the eight EVMSSI configurations produce systematically different performance outcomes. Signaling theory (Connelly et al., 2011; Spence, 1973) explains why firms invest in observable external validation mechanisms: to reduce information asymmetry and differentiate themselves from lower-quality competitors. The RBV (Barney, 1991; Wernerfelt, 1984) explains how multi-channel signaling portfolios generate sustained competitive advantage through resource complementarities difficult for rivals to imitate. Institutional theory (DiMaggio & Powell, 1983; North, 1990) explains when and where these advantages are most salient: in weak-institution, high-uncertainty markets, external validation substitutes for institutional trust.

The framework posits that three binary signaling decisions — whether to hold MBOTA, IRQC, and OWMA — combine to form eight distinct credibility-capital stocks that differentially affect four performance dimensions: contemporaneous sales (market-share and pricing power), revenue growth (dynamic competitive advantage), product innovation (knowledge externalities from quality and digital networks), and process innovation (internal process discipline induced by certification and digital feedback loops). Firm-level moderators — size, age, sector, management experience — and country-level institutions modulate the magnitude of signaling returns.

┌──────────────────────────────────────────────────────────────────────┐
│  Institutional Environment                                            │
│  (Contract enforcement, Digital infrastructure, Association quality) │
│                              ↓                                        │
│  EVMSSI Configuration (MBOTA × IRQC × OWMA): 8 mutually exclusive    │
│  portfolios                                                           │
│                              ↓                                        │
│  Credibility-Capital Stock → Information asymmetry reduction;         │
│  Resource complementarity                                             │
│                              ↓                                        │
│  Firm Performance (Sales; Revenue Growth; Product Innovation;         │
│  Process Innovation)                                                  │
│  Moderators: Firm size, age, sector, manager experience,             │
│  country institution level                                            │
└──────────────────────────────────────────────────────────────────────┘

3.2 Hypotheses Development

H1 (Full Multi-Channel Dominance Hypothesis): The full multi-channel signaling strategy (1_1_1) achieves the highest multidimensional dominance score and composite effectiveness index across contemporaneous sales, revenue growth, product innovation, and process innovation in the full ECA–MENA sample, consistent with resource complementarity predictions of the RBV and signal-bundling arguments in signaling theory.

H2 (No-Signaling Inferiority Hypothesis): The no-signaling strategy (0_0_0) is Pareto-dominated by at least one alternative EVMSSI configuration on every performance dimension, consistent with the adverse selection mechanism in signaling theory.

H3 (Digital-Network Mechanism Hypothesis): The Network + Digital strategy (1_0_1) generates the second-largest causal average treatment effect on product and process innovation outcomes after the full multi-channel strategy (1_1_1), reflecting the synergistic knowledge-acquisition and market-reach benefits of combining associational legitimacy with digital presence.

H4 (Regional Heterogeneity Hypothesis): The comparative effectiveness of certification-augmented strategies (0_1_0, 0_1_1, 1_1_1) is systematically higher in MENA & Central Asia relative to European subsamples, while the effectiveness of network-digital configurations (1_0_1) is comparatively higher in Europe, reflecting institutional variation in the relative value of formal quality signals versus digital-associational credibility.

4.1 Theoretical and Econometric Framework

The central empirical challenge is that firms self-select into signaling strategies based on unobservable characteristics correlated with performance outcomes. Larger, more productive, and better-managed firms are more likely to invest in all three signaling mechanisms simultaneously. Simple comparisons of performance across EVMSSI configurations therefore confound the causal effect of the signaling strategy with the selection process. Our framework addresses this challenge using two complementary approaches: a comprehensive multidimensional dominance analysis (descriptive but robust across multiple performance dimensions), and doubly robust (DR) and double machine learning (DML) estimators that nonparametrically control for observed confounders (Chernozhukov et al., 2018; Robins & Rotnitzky, 1995).

4.2 Econometric Models

4.3 Data Sources

We use the World Bank Enterprise Surveys (WBES) 2018–2020 implementation cycle, which employs a stratified random sampling design with strata defined by sector of activity (manufacturing, retail, services), firm size (small: 5–19 employees; medium: 20–99; large: ), and geographical sub-region (World Bank Enterprise Surveys, 2022). The full analytical sample comprises 9,710 firms across 41 economies — 4,378 in the European subsample (25 economies) and 5,332 in the MENA & Central Asia subsample (16 economies). Survey weights (, median variant) are incorporated throughout to ensure population representativeness.

4.4 Variable Definitions

4.5 Analytical Design

The analytical design treats the firm as the unit of observation, assigned to one of eight mutually exclusive strategy regimes based on the joint realisation of MBOTA, IRQC, and OWMA. Outcomes are evaluated both descriptively (weighted means by regime) and causally (DR and DML ATEs versus the baseline regime 0_0_0). Regional heterogeneity is assessed by repeating the full analytical pipeline separately for the European and MENA & Central Asia subsamples.

5.1 Sample Characteristics

Table 1 presents firm-level characteristics for the full sample of 9,710 observations across 41 economies. The sample spans 25 European economies (including EU members such as Greece, Portugal, and Italy, as well as non-EU Eastern European nations) and 16 MENA and Central Asian economies (including Egypt, Turkey, Kazakhstan, and Ukraine). The European subsample comprises 4,378 firms (45.1%) and the MENA & Central Asia subsample 5,332 firms (54.9%), of which 2,857 (29.4% of total) are located in MENA economies and 2,475 (25.5%) in Central Asia.

^a Pre-winsorisation raw maximum for revenue growth rate. This extreme outlier ($$188,000%) reflects an anomalous observation in the unwinsorised distribution and does not affect any analytical result; all analyses use revenue growth winsorised at the 1st–99th percentile. Pairwise correlations among MBOTA, IRQC, and OWMA are low (max ), confirming independent signaling choices.

The average firm has been in operation for 21 years and employs 83 full-time workers, though the median (20 employees) reflects the right-skewed size distribution dominated by small and medium enterprises. The low pairwise correlations among the three signaling components (MBOTA–IRQC: ; MBOTA–OWMA: ; IRQC–OWMA: ) confirm that the EVMSSI components represent independent strategic choices rather than a single latent quality dimension.

5.2 Strategy Adoption Patterns

Notes: EUR = European subsample (; 25 economies); MENACA = MENA & Central Asia subsample (; 16 economies). Unweighted firm counts are reported.

Table 2 reveals important regional differences in signaling strategy adoption. The most prevalent strategy across the full sample is Network + Digital (1_0_1: 19.9%), closely followed by Digital Only (0_0_1: 18.4%) and No Signaling (0_0_0: 18.2%). Full multi-channel adoption (1_1_1) is substantially more common in Europe (23.3%) than in MENA & Central Asia (10.1%), reflecting Europe’s more developed certification and digital-infrastructure ecosystem. Conversely, Network Only (1_0_0) is far more prevalent in MENA & Central Asia (22.8% vs. 6.4% in Europe), suggesting that business association membership without digital or quality credentials is a common default strategy in the latter region.

5.3 Preliminary Insights

Table 3 presents population-weighted mean outcomes by EVMSSI level for the full sample.

Notes: All means computed using WBES median sampling weights. Sales in USD millions. Revenue growth winsorised at 1st–99th percentile. *The 0_1_0 (Cert. Only) revenue growth estimate is imprecise owing to the small cell size (); the approximate 95% confidence interval [8%, 146%] spans nearly the full range of plausible positive effects. Product and process innovation rates expressed as percentages.

Several stylised facts emerge. First, the full multi-channel strategy (1_1_1) achieves by far the highest weighted mean sales (USD 470 million), nearly double the second-ranked Network + Cert. strategy (1_1_0: USD 176 million). Second, product innovation rates show a different pattern: 1_1_1 leads at 22.9%, followed closely by 1_0_1 (21.0%) and 0_0_1 (20.6%), suggesting that digital presence is a strong innovation enabler regardless of complementary signals. Third, revenue growth patterns are less monotone: the Certification Only strategy (0_1_0) attains the highest weighted mean revenue growth (77.0%), but this estimate is highly imprecise (SE ; 95% CI approximately [8%, 146%]) owing to the small cell size (). Fourth, process innovation is maximised by the full multi-channel strategy (14.1%) and Network + Digital (10.7%).

6.1 Pairwise Dominance Analysis and Multidimensional Dominance Scores

Table 4 presents the Multidimensional Dominance Scores for the full sample and both regional subsamples. In the full sample, 1_1_1 attains the highest MDS (0.857), confirming that the full multi-channel strategy dominates on the largest number of outcome–competitor pairs. The Network + Digital strategy (1_0_1) ranks second (MDS 0.679), while Certification Only (0_1_0, MDS 0.393) and Network Only (1_0_0, MDS 0.214) rank low, indicating that single-signal strategies are rarely dominant in a multidimensional comparison.

Notes: . Bold values denote the top-ranked strategy in each column.

Strikingly, the regional rankings diverge substantially. In Europe, 1_1_1 and 1_0_1 jointly occupy the top two positions. In MENA & Central Asia, certification-augmented strategies surge to the top: 0_1_1 (Cert. + Digital) attains the highest regional MDS (0.929), followed by 0_1_0 (Cert. Only, 0.750) and 1_1_1 (0.714). This inversion is consistent with H4.

6.2 Pareto Efficiency and Composite Indices

The Pareto-efficiency analysis identifies the non-dominated frontier for each sample. In the full sample, four strategies are Pareto-efficient: 0_1_0, 0_1_1, 1_0_1, and 1_1_1 — meaning no single strategy Pareto-dominates all four on every dimension simultaneously. In Europe, six strategies are Pareto-efficient (0_0_0, 0_1_0, 0_1_1, 1_0_0, 1_0_1, 1_1_1), reflecting greater outcome trade-offs across the European dimension space. In MENA & Central Asia, three strategies are Pareto-efficient (0_1_0, 0_1_1, 1_1_1), indicating a sharper dominance hierarchy. Notably, 1_1_1 is the only strategy appearing on all three Pareto frontiers (full, Europe, MENA & CA), confirming its position as the uniquely robust choice across analytical contexts.

^a PCA and entropy CEI differ in their treatment of revenue growth. The PC1 loading vector is for Sales, Revenue Growth, Product Innovation, and Process Innovation respectively. The negative loading on Revenue Growth reflects the divergence between strategies generating high current-period sales (1_1_1) versus those generating high revenue growth from a low base (0_1_0) — a feature captured by the entropy CEI but not PCA. 0_1_0 ranks 4th on entropy CEI but 8th on PCA precisely because its high revenue growth mean is down-weighted (negatively loaded) by the PC1 solution.

6.3 Network-Based Dominance Structure

Note: Edge exists when strategy dominates on of 4 outcomes. Eigenvector centrality measures systemic in-dominance; high values indicate a node is frequently dominated by other well-dominated nodes. 1_1_1 and 1_0_1 have zero eigenvector centrality because they are never dominated.

6.4 Causal Dominance: Doubly Robust Estimates

EVMSSI	Sales ATE (USD M)	Sales	Rev. Growth ATE (%)	Rev. Growth	Prod. Innov. ATE	Prod. Innov.	Proc. Innov. ATE	Proc. Innov.
0_0_1	72.2	1.15	−14.04***	−6.49	0.056***	4.26	−0.001	−0.06
0_1_0	252.8**	2.40	28.12***	5.29	0.115***	3.92	0.120***	4.55
0_1_1	−120.7	−0.59	14.39***	4.10	0.196***	12.59	0.104***	7.31
1_0_0	169.3	1.03	1.05	0.40	0.017**	1.96	0.031***	4.20
1_0_1	146.2	1.60	−4.50	−1.65	0.187***	14.76	0.097***	10.26
1_1_0	318.8*	1.67	−3.08	−0.52	−0.014	−1.04	0.050***	4.11
1_1_1	154.9	0.80	−1.57	−0.49	0.148***	8.88	0.098***	6.38

Notes: DR estimator with random-forest outcome models and logistic propensity scores, 3-fold cross-fitting. Controls include firm age, employees, female ownership, manager experience, sector dummies, and 15-country fixed effects. ***; **; *.

The DR results confirm that 1_0_1 and 0_1_1 generate the largest and most statistically significant product innovation effects ( and percentage points, respectively), strongly supporting H3. Process innovation is significantly increased by most signaling strategies. Revenue growth effects are mixed: Certification Only (0_1_0) significantly increases growth ( pp), while Digital Only (0_0_1) is associated with a significant decrease ( pp), discussed further in Section 8.

6.5 Causal Dominance: Double Machine Learning Estimates

EVMSSI	Sales ATE (USD M)	Sales	Rev. Growth ATE (%)	Rev. Growth	Prod. Innov. ATE	Prod. Innov.	Proc. Innov. ATE	Proc. Innov.
0_0_1	91.6	1.26	−13.92***	−6.53	0.048***	3.91	0.003	0.39
0_1_0	46.4	0.43	61.17***	4.85	0.021	1.41	0.050***	2.94
0_1_1	−420.9a	−1.37	4.80	1.01	0.118***	6.75	0.038***	2.84
1_0_0	105.6	1.08	6.95***	2.49	0.022**	2.21	0.040***	4.90
1_0_1	67.0	1.03	−2.03	−0.84	0.177***	15.22	0.092***	10.03
1_1_0	257.1	0.93	−9.48	−1.35	0.062***	2.76	0.008	0.63
1_1_1	−1,961a	−1.30	−3.57	−1.31	0.150***	10.63	0.085***	7.48

Notes: DML estimator with random-forest nuisance models, 3-fold cross-fitting. Same controls as DR. ***; **; *. Bold values indicate the highest ATE per outcome column.

^a Statistically insignificant Sales DML ATEs for 0_1_1 and 1_1_1 reflect high-variance residuals from the right-skewed sales distribution rather than a genuine negative causal effect; see Section 5.2.8 for discussion.

The 1_0_1 strategy generates the largest and most precise product innovation effect (ATE pp, ), confirming H3. Process innovation ATEs follow a similar hierarchy, with 1_0_1 ( pp, ) and 1_1_1 ( pp, ) ranked first and second. Revenue growth DML estimates highlight Certification Only (0_1_0) as uniquely growth-enhancing ( pp, ) — an effect driven primarily by MENA & Central Asia firms where certification is rarer and thus more credibility-intensive.

6.6 Regional Heterogeneity Analysis

Notes: All means computed with WBES median weights. Sales in USD millions. P. Inn. = Product/Service Innovation; Pr. Inn. = Process Innovation. Revenue growth winsorised at 1st–99th percentile.

EVMSSI Level	EUR Prod. Innov. ATE (-stat)	EUR Proc. Innov. ATE (-stat)	MENA Prod. Innov. ATE (-stat)	MENA Proc. Innov. ATE (-stat)
0_0_1	0.056*** (2.77)	0.001 (0.13)	0.149*** (10.32)	0.086*** (5.79)
0_1_0	−0.022 (−1.13)	0.054** (2.51)	0.491*** (5.84)	0.012 (0.20)
0_1_1	0.096*** (4.20)	0.070*** (4.70)	0.323*** (7.33)	0.064* (1.75)
1_0_0	0.012 (0.42)	0.115*** (4.91)	0.042*** (4.31)	−0.027*** (−2.78)
1_0_1	0.166*** (8.25)	0.124*** (10.90)	0.182*** (12.55)	0.101*** (6.92)
1_1_0	0.118*** (2.65)	0.070*** (2.92)	0.055** (2.52)	−0.035** (−2.12)
1_1_1	0.091*** (4.78)	0.121*** (11.24)	0.242*** (10.08)	0.035 (1.57)

Notes: DML with random-forest nuisance models, 3-fold cross-fitting. Bold values indicate highest ATE within each region. ***; **; *.

The DML regional ATEs confirm that 1_0_1 (Network + Digital) is the consistently highest-performing strategy on innovation outcomes in both regions, with product innovation ATEs of pp in Europe and pp in MENA & Central Asia. However, certification-based strategies show sharply asymmetric regional effects: 0_1_0 raises product innovation by pp in MENA & Central Asia (statistically insignificant in Europe: ), while 0_1_1 raises it by pp in MENA & Central Asia vs. only pp in Europe. These patterns strongly support H4: certification generates considerably larger innovation returns in contexts where it is rarer and where institutional substitutes for quality verification are less developed.

6.7 Superadditivity of Multi-Channel Signaling

The descriptive and causal results raise a natural question: does the full multi-channel strategy (1_1_1) generate innovation effects that exceed the sum of effects from each individual signal deployed in isolation? A directional test of superadditivity — — using the DML product-innovation estimates yields:

consistent with positive superadditivity (surplus pp). However, the formal statistical significance of this surplus cannot be assessed from the existing estimation framework, which treats each strategy arm independently. A joint Wald test on the full EVMSSI treatment vector would be required to formally confirm signal complementarity. The directional evidence from Table 8 is suggestive but not conclusive; we flag this test as a priority for future work.

7.1 Interpretation of Findings

Our findings cohere around a central narrative: signaling comprehensiveness pays, but the returns to each channel are institutionally contingent. The full multi-channel strategy (1_1_1) dominates on the most parsimonious summary metrics — MDS, entropy CEI, PCA index, and network out-degree — confirming H1. This result is consistent with RBV predictions: the joint deployment of MBOTA, IRQC, and OWMA creates a credibility-capital bundle whose value exceeds the sum of its parts. Firms that signal across all three channels are better positioned to attract quality customers, reduce information asymmetry with financial intermediaries, and participate in quality-standards communities that stimulate innovation.

The inferior performance of single-signal strategies is equally illuminating. Network Only (1_0_0) receives an MDS of only 0.214 in the full sample, suggesting that membership in business associations, without complementary quality certification or digital presence, fails to generate a credible market signal. Similarly, Certification Only (0_1_0) achieves high revenue growth rates — particularly in MENA & Central Asia — but weak overall ranking due to below-average performance on sales and innovation. This asymmetry suggests that certification’s primary market-signaling benefit operates through price and growth rather than scale, consistent with Nair et al. (2013)’s finding that certified firms in developing countries achieve higher growth rates but do not necessarily achieve higher absolute sales volumes.

The strong innovation effects of the Network + Digital strategy (1_0_1) merit specific theoretical attention. The doubly robust estimate of pp product innovation and the DML estimate of pp — both among the largest in the table — align with two distinct theoretical channels. First, digital presence enables firms to access global knowledge networks, benchmark against best practices, and receive real-time customer feedback, accelerating new product development (Bharadwaj et al., 2013). Second, business association membership facilitates knowledge spillovers within industry clusters, supply-chain coordination, and collective action on innovation challenges (Hall & Soskice, 2001). The 1_0_1 configuration combines both channels without the cost burden of quality certification, making it a particularly efficient innovation-signaling portfolio for resource-constrained SMEs.

7.2 Strategic and Economic Insights

The regional heterogeneity findings have important strategic implications. The dramatically higher MDS and DML ATEs for certification-augmented strategies in MENA & Central Asia reflect the scarcity value of quality signals in these contexts. When fewer than 10% of firms in a market hold quality certification, the signal is both more observable and more costly to imitate — exactly the conditions under which signaling theory predicts the largest market returns (Spence, 1973). This insight has direct strategic implications: MENA and Central Asian firms that have not yet obtained quality certification face a diminishing-window opportunity to extract first-mover signaling rents from certification investment.

The finding that Digital Only (0_0_1) is associated with a significant negative revenue growth ATE relative to the no-signaling baseline ( pp, DR; pp, DML) deserves careful interpretation. This counterintuitive result may reflect competitive exposure effects: firms that invest in digital visibility attract price-conscious customers, intensify competitive pressure from informal rivals who match digital visibility at lower cost, and reveal product offerings to potential imitators — without the protective buffer of quality certification or association membership. Alternatively, consistent with the digital-capabilities literature (Bharadwaj et al., 2013), the digital presence variable may capture early-stage adopters who have established a digital footprint but have not yet translated it into revenue. The positive and significant product innovation effect of 0_0_1 ( pp, DML) suggests that digital presence does stimulate knowledge-acquisition activities, but revenue conversion appears to require complementary credentialing.

8.1 Theoretical Contributions

This study makes three theoretical contributions. First, by developing the EVMSSI as an integrated multi-channel signaling index and evaluating all eight binary configurations within a unified causal framework, we extend signaling theory from its original two-party dyadic structure (Spence, 1973) to a multi-channel portfolio context. The finding that complementary signals generate greater returns than the sum of individual signals provides empirical support for signal-bundling theory (Bergh et al., 2019) and extends it to the ECA and MENA regional context. Second, the large and institutionally contingent innovation effects of certification-augmented strategies provide new micro-level evidence for the institutional-theory proposition that formal external validation substitutes for institutional trust in weak-governance environments (Mayer & Salomon, 2006; North, 1990). Third, the application of DML and doubly robust methods to a multi-regime signaling tournament represents a methodological advance over prior regression-based comparisons, establishing a more credible causal interpretation of signaling strategy effectiveness.

8.2 Managerial Implications

The results provide a prioritised signaling investment roadmap for firm managers in ECA and MENA. Firms with no current signaling presence (0_0_0) can achieve the most efficient short-term innovation gains by adopting the Network + Digital configuration (1_0_1), which delivers the largest and most consistently significant product and process innovation effects across both regions at relatively lower implementation cost than quality certification. Firms that have already adopted one or two signaling channels should prioritise completing the full multi-channel portfolio (1_1_1), which dominates on every composite effectiveness dimension.

For MENA and Central Asian firms specifically, quality certification represents a high-return investment opportunity given its scarcity and the dramatically elevated product innovation ATEs observed (– pp for certification-augmented strategies). For European firms, the returns to certification are more modest, suggesting that the marginal investment should be directed toward digital presence and association membership rather than certification renewal. In both regions, purely relational strategies (Network Only: 1_0_0) deliver among the weakest innovation outcomes, challenging the common practice of association membership as a standalone credibility strategy.

8.3 Policy Implications

The evidence has direct implications for business environment policy in ECA and MENA. First, the large product and process innovation effects of the Network + Digital strategy justify public investment in digital infrastructure — broadband access, e-commerce platforms, and digital-literacy programmes — particularly in Central Asia and less-developed MENA economies, where digital penetration remains comparatively low. Second, the scarcity premium on quality certification in MENA and Central Asia suggests a strong economic case for subsidised certification programmes, capacity-building grants, and streamlined accreditation processes. Governments and development banks (World Bank, EBRD, IsDB) that reduce the cost of accessing ISO 9001 and equivalent certifications for SMEs could generate substantial innovation spillovers, as the DML estimates suggest each certified MENA firm generates approximately 32–49 pp higher product innovation rates. Third, the relatively low performance of purely network-based strategies despite high MBOTA adoption rates — particularly in Central Asia (22.8% of firms are Network Only) — signals that business associations in these contexts may need to evolve their value proposition from relational legitimacy toward active quality standards and digital adoption facilitation.

Finally, the study’s findings align directly with the United Nations 2030 Agenda for Sustainable Development. SDG 8 (Decent Work and Economic Growth) is addressed through evidence that multi-channel signaling strategies raise sales performance and revenue growth, thereby supporting enterprise-level productivity and income generation. SDG 9 (Industry, Innovation and Infrastructure) is advanced through the finding that network-digital and certification-digital configurations generate economically large and statistically significant product and process innovation effects across both ECA and MENA. SDG 17 (Partnerships for the Goals) is implicated by the evidence that business association membership significantly raises innovation outcomes when combined with quality credentials and digital presence.

A.1 Context and Data Structure

The analysis compares the eight EVMSSI signaling strategy orientations defined by the binary combination of MBOTA, IRQC, and OWMA:

Each configuration is treated as a distinct strategy, yielding a balanced tournament design with eight representative strategy profiles.

A.2 Pairwise Dominance Matrix for Sales — Full Sample

Table 11 presents the full pairwise absolute difference matrix for weighted mean sales. A positive entry indicates that strategy generates higher weighted mean sales than strategy .

As the table shows, 1_1_1 dominates all seven other strategies on sales (positive in every cell of the last row), confirming the full multi-channel signaling strategy’s sales supremacy.

A.3 Summary of Pairwise Dominance Wins across All Outcomes

A.4 Robustness: Alternative Weight Variants

To confirm robustness of the baseline results (using median weights), we re-estimated all weighted means using WBES strict weights (wstrict) and weak weights (wweak). The strategy ranking of 1_1_1 at the top and 1_0_0/1_1_0 at the bottom is stable across all weight variants. The regional patterns — particularly the superiority of certification-augmented strategies in MENA & Central Asia — are also robust. DR and DML estimates are computed under median weights and therefore do not depend on this choice.

A.5 Variable Correlation Matrix

The low correlations among MBOTA, IRQC, and OWMA confirm that these represent independent strategic choices rather than a single latent “quality” factor, justifying their treatment as three separate binary dimensions of the EVMSSI.

2.1 Theoretical Foundations

2.2 Empirical Evidence on Governance and Performance

2.3 Research Gaps

Despite this rich literature, three important gaps remain. First, no study has systematically combined governance architecture and political embeddedness into a unified strategic orientation framework with eight distinct configurations. Second, the majority of existing evidence relies on correlational methods that do not adequately address the endogeneity of governance choices. Third, comparative ECA–MENA analysis accounting for institutional heterogeneity is rare, with most studies focusing on single countries. This article addresses all three gaps, while acknowledging that identification from cross-sectional observational data remains an inherent limitation that our semiparametric methods reduce but cannot fully eliminate.

3.1 Conceptual Framework

The SGPII framework conceptualises firm governance strategy as a three-dimensional binary space, with each dimension representing a distinct type of institutional engagement:

• FWBS (Formalized Written Business Strategy): The existence of a documented strategic plan signals internal strategic coherence and external institutional conformity. It coordinates resource allocation, reduces uncertainty for stakeholders, and provides a governance signal that attracts formal partners, investors, and regulators (DiMaggio & Powell, 1983; Scott, 2008).

• BDSB (Board of Directors / Supervisory Board): A formal board provides monitoring, resource provision, and legitimacy functions. Its value depends critically on the institutional context: in strong-governance environments, boards enforce accountability and reduce agency costs; in weak-governance environments, boards may be nominal rather than functional (Claessens & Djankov, 2002; Hillman & Dalziel, 2003).

• OCTMBEAPP (Political Appointment of Owner/CEO/Top Manager): Direct political experience creates a relational asset — access to government networks, regulatory intelligence, and political capital — that can be deployed to reduce institutional friction, secure public contracts, and pre-empt regulatory challenges. Its value depends on both the level of political discretion in the environment and whether formal governance structures exist to channel it productively (Diwan et al., 2019; Faccio, 2006).

Figure 1 illustrates the conceptual framework, showing how the three dimensions interact to produce eight governance–political strategy orientations whose performance implications depend on both the configuration and the institutional context.

3.2 Hypotheses Development

4.1 Data Sources

This study uses data from the World Bank Enterprise Surveys (WBES) 2018–2020 rollout covering 9,710 firms across 41 ECA and MENA economies, stratified by sector, size, and geography. The harmonised dataset was released on 29 March 2024 and is publicly available at the WBES data portal (https://www.enterprisesurveys.org/en/enterprisesurveys; World Bank Enterprise Surveys (WBES) (2020)). Subsamples comprise 4,378 European firms (22 economies) and 5,332 MENA and Central Asian firms (19 economies). Population-representative estimates use the WBES sampling weights throughout; robustness checks in Section 13 verify results with and .

4.2 SGPII Construction

The Strategic Governance and Political Embeddedness Index (SGPII) is constructed as an 8-level categorical classification by combining three binary governance indicators:

where indicates whether firm has a formalized written business strategy, whether it has a board of directors or supervisory board, and whether an owner, CEO, top manager, or board member has held an elected or appointed political position. The resulting variable takes values in {0_0_0, 0_0_1, 0_1_0, 0_1_1, 1_0_0, 1_0_1, 1_1_0, 1_1_1}, representing eight distinct governance–political strategy orientations. Note that the SGPII is a categorical classification scheme (nominal 8-level factor variable constructed by binary string concatenation), not a numeric index; all analyses treat it as a factor variable with no implied ordinality between levels.

In R, the construction is:

SGPII <- factor(paste(FWBS, BDSB, OCTMBEAPP, sep = "_"))

4.3 Outcome and Control Variables

Four firm performance outcomes are examined: (i) Sales — total annual sales in USD; (ii) RevGrwthRate3 — 3-year revenue growth rate winsorised at the 1st and 99th percentiles to address extreme outliers; (iii) ProdServInnov — binary indicator of new product or service introduction in the past 3 years; and (iv) ProcessInnov — binary indicator of new process or method introduction in the past 3 years.

All estimation models control for: firm age (), full-time employment (), female ownership (), manager sector experience (), 24-category sector dummies (), and top-15 country fixed effects (). While these controls substantially reduce confounding by observable characteristics, governance choices may remain correlated with unobserved factors such as management quality, founder pedigree, and network capital; caution is warranted when interpreting point estimates as causal effects.

4.4 Econometric Framework

4.5 Additional Analyses

Entropy-weighted CEI, PCA composite (PC1), Pareto frontier identification, and network dominance centrality (igraph: out-degree, in-degree, eigenvector centrality) follow the methodology detailed in Niankara (2025) and are summarised in Section 12. Robustness checks under alternative weighting schemes (, ) and firm-size subgroup analyses are reported in Section 13.

5.1 Sample Characteristics

Table 1 presents key firm-level characteristics. The sample of 9,710 firms has a median age of 13 years, an average of 37 full-time employees, and female ownership in 28.3% of firms. Mean annual sales are $104M, heavily right-skewed — the median is substantially lower, highlighting wealth concentration among large firms. Revenue growth averages 3.2% per year but with high variance (), reflecting diverse growth trajectories. Product and process innovation rates are 23.6% and 14.0% respectively for the full sample.

Variable	Mean	SD	Median	Range
Panel A: Firm Characteristics
Years in Operation	19.4	14.8	15.0	1 – 130
Full-time Employees (LFY)	37.2	142.6	14.0	1 – 5,800
Female Ownership ()	0.283	0.450	0	0/1
Manager Sector Experience (yrs)	17.2	11.5	15.0	0 – 65
Sales (USD millions)	104.0	618.3	2.8	0 – 22,000
Revenue Growth Rate (%, winsorised)	3.2	17.2	1.8	−42.6 – 66.2
Product/Service Innovation	0.236	0.425	0	0/1
Process Innovation	0.140	0.347	0	0/1
Panel B: SGPII Component Adoption Rates (Population-Weighted)
FWBS (Formalized Written Strategy)	29.3%	—	—	0/1
BDSB (Board of Directors/Supv. Board)	27.9%	—	—	0/1
OCTMBEAPP (Political Appointment)	2.9%	—	—	0/1
Panel C: Regional Distribution
Europe (22 economies)	45.1%	—	—	—
Central Asia (12 economies)	25.5%	—	—	—
MENA (7 economies)	29.4%	—	—	—

Notes: Population-weighted means using WBES sampling weights. LFY = Last Fiscal Year. Revenue growth winsorised at 1st–99th percentile.

Three important patterns emerge from Panel B. First, written business strategies and board governance are adopted by roughly equal shares of firms (29.3% and 27.9% respectively), indicating that formal governance structures, while common among larger and more institutionalised firms, remain far from universal. Second, political connections are strikingly rare at the population level: only 2.9% of firms (weighted) report that an owner, CEO, top manager, or board member has held an elected or appointed political position. This rarity makes political embeddedness a highly selective governance resource. It also implies that the four political-connection-including SGPII cells (0_0_1: ; 1_0_1: ; 0_1_1: ; 1_1_1: ) are small relative to the full sample, which affects the precision and reliability of the semiparametric estimators for those cells (see Section 7.4 and Section 13 for diagnostics). Third, the regional distribution — 45.1% European, 54.9% MENA and Central Asian — enables meaningful cross-regional comparison.

5.2 SGPII Strategy Adoption Patterns

Table 2 reports the distribution of firms across the eight SGPII levels.

Level	Strategy Label	Full	Full %	Europe	Europe %	MENA & CA	MENA & CA %
0_0_0	Minimal Governance	3,964	40.8	1,317	30.1	2,647	49.6
0_0_1	Pure Political Emb.	111	1.1	38	0.9	73	1.4
0_1_0	Board-Only	1,118	11.5	454	10.4	664	12.5
0_1_1	Board + Political	88	0.9	33	0.8	55	1.0
1_0_0	Strategy-Only	1,795	18.5	800	18.3	995	18.7
1_0_1	Strategy + Political	85	0.9	31	0.7	54	1.0
1_1_0	Formal Professional Gov.	2,298	23.7	1,620	37.0	678	12.7
1_1_1	Full Hybrid	251	2.6	85	1.9	166	3.1
	Total	9,710	100.0	4,378	100.0	5,332	100.0

Several distributional patterns warrant attention. The minimal governance orientation (0_0_0) accounts for 40.8% of firms overall but rises to 49.6% in MENA and Central Asia, consistent with the hypothesis that formal institutional compliance is lower in less-developed institutional environments. Formal Professional Governance (1_1_0) is by far the most common structured governance approach, adopted by 37.0% of European firms versus only 12.7% of MENA and Central Asian firms — a striking regional divergence reflecting the deeper penetration of corporate governance norms in EU-influenced markets. Political connection-including configurations collectively account for only 5.5% of firms, confirming the rarity and selectivity of political embeddedness as a governance resource.

5.3 Preliminary Outcome Insights

Table 3 presents population-weighted mean outcomes by SGPII level.

Notes: Population-weighted means using . Bold = highest value per outcome. Revenue growth winsorised at 1st–99th percentile. Innovation rates as proportions (%).

Five striking patterns emerge. First, the Full Hybrid (1_1_1) achieves the highest sales ($950M), revenue growth (26.5%), and process innovation (23.4%), consistent with H1. Second, Strategy plus Political Embeddedness (1_0_1) achieves the highest product innovation rate (44.6%) and second-highest sales ($556M), suggesting that political capital amplifies innovation access channels when formal strategy provides direction. Third, Board-Only governance (0_1_0) achieves substantial sales ($227M) but conspicuously low innovation rates (8.1% product, 5.2% process), consistent with the governance overhead paradox. Fourth, Board plus Political Ties (0_1_1) achieves the lowest sales ($53.4M) — below the no-governance baseline — consistent with H3’s prediction that political embeddedness without formal strategic direction is value-destroying. Fifth, Strategy-Only (1_0_0) outperforms its board-augmented counterpart (1_1_0) on three of four outcomes.

6.1 Pairwise Dominance Analysis and MDS Rankings

Table 4 presents MDS scores for all eight SGPII levels.

Notes: MDS = fraction of pairwise-outcome comparisons won: . Bold = highest MDS per column.

The MDS results strongly confirm H1: the Full Hybrid (1_1_1) achieves the highest full-sample MDS of 0.929, winning 26 of 28 pairwise-outcome comparisons. The top-three full-sample strategies all share FWBS=1 (written strategy), confirming H3 that strategic planning formalisation is a necessary condition. The bottom two strategies (0_1_0 and 0_1_1) both combine board governance with the absence of written strategy, underscoring the governance overhead paradox: board oversight without strategic direction adds governance costs without corresponding performance gains.

Significant regional heterogeneity provides a direct test of H4. Strategy plus Political Embeddedness (1_0_1) ranks first in Europe (MDS = 0.893) but falls to fifth in MENA and Central Asia (MDS = 0.429), while Strategy-Only (1_0_0) ties for first in MENA and Central Asia (MDS = 0.857). This pattern is inconsistent with H4a (the weak-institution premium hypothesis, which predicted larger returns to political connections in MENA) but consistent with H4b (the institutional channeling hypothesis). In Europe, political capital appears to be channeled into productive market access alongside formal strategy, generating larger dominance gains than in MENA, where formal strategy alone captures most available governance returns.

6.2 Pareto Efficiency and Composite Indices

Pareto Analysis. Three configurations occupy the Pareto frontier in the full sample: 1_0_0, 1_0_1, and 1_1_1. Five configurations are Pareto-dominated: 0_0_0, 0_0_1, 0_1_0, 0_1_1, and 1_1_0. Notably, even the most common structured governance orientation (1_1_0, Formal Professional Governance, 23.7% of firms) is Pareto-dominated by 1_0_0 on revenue growth and innovation dimensions. In Europe, only two configurations are Pareto-efficient: 1_0_1 and 1_1_1. In MENA and Central Asia, 1_0_0 and 1_1_1 are efficient, consistent with the lower marginal value of board governance in less institutionalised settings.

Composite Indices. Table 5 presents entropy-weighted CEI and PCA PC1 composite rankings.

Notes: Entropy weights: Sales (0.508), RevGrwth (0.064), ProdInnov (0.214), ProcInnov (0.213). PCA PC1 explains 69.4% of variance in the 8×4 weighted means matrix. Sales accounts for 50.8% of the entropy weight; CEI rankings are therefore predominantly driven by sales-scale variation. Equal-weight robustness checks are provided in Section 13.

Both composite measures confirm the MDS ordering: 1_1_1 leads comprehensively with CEI = 0.858 and PC1 = 3.197, followed by 1_0_1 and 1_0_0. Board plus Political (0_1_1) achieves the lowest PC1 (−1.612), below even the minimal governance baseline.

6.3 Network-Based Dominance Structure

The dominance network (majority threshold outcomes) shows 1_1_1 with out-degree 7 and in-degree 0 — the globally dominant strategy. 1_0_0 and 1_0_1 each achieve out-degree 6. Eigenvector centrality, computed on the in-edge dominance graph (where centrality accrues to nodes dominated by the most strategically important competitors), identifies 0_1_1 (0.791) and 0_0_0 (0.412) as most broadly dominated — reinforcing the governance overhead paradox and the vulnerability of no-strategy configurations.

6.4 Selection-Corrected Estimates: Doubly Robust Results

Table 6 presents DR selection-corrected performance differences for all SGPII strategies versus the 0_0_0 baseline.

Level	Label	Sales (M USD)	Rev. Growth (%)	Prod. Innov.	Proc. Innov.
0_0_1	Pure Political	112.3*** (24.7)	9.5*** (3.6)	0.054*** (0.014)	0.071*** (0.011)
0_1_0	Board-Only	1,009.0*** (388.5)	−4.6** (2.4)	0.015 (0.010)	0.038*** (0.008)
0_1_1	Board + Political	85.3** (36.3)	−2.4 (1.8)	0.119*** (0.011)	0.047*** (0.009)
1_0_0	Strategy-Only	116.3*** (40.0)	11.8*** (2.6)	0.145*** (0.011)	0.123*** (0.008)
1_0_1	Strategy + Political	318.1*** (38.9)	−5.5** (2.2)	0.326*** (0.014)	0.189*** (0.009)
1_1_0	Formal Prof. Gov.	471.9*** (60.6)	0.2 (2.0)	0.114*** (0.010)	0.065*** (0.007)
1_1_1	Full Hybrid	599.1*** (78.6)	7.2*** (2.5)	0.118*** (0.014)	0.153*** (0.014)

Notes: DR estimator (AIPW) with RF outcome models and logistic propensity scores; 3-fold cross-fitting. Standard errors in parentheses. ***; **; *. Baseline: 0_0_0 (Minimal Governance). Sales in USD millions. Estimates are selection-corrected associations under conditional ignorability; unobserved confounding may bias estimates in an unknown direction. Diagnostic note (Board-Only Sales): The DR Sales for 0_1_0 ($1,009M, SE=$389M) exceeds the raw descriptive mean difference (~$161M) by a factor of six. Propensity score overlap diagnostics and effective sample size checks for this cell are provided in Section 13; readers are advised to interpret this point estimate with caution pending those diagnostics.

The DR results confirm H1 and H2. The Full Hybrid (1_1_1) achieves the largest selection-corrected sales difference ($599M, ), the largest process innovation gain (+15.3 pp, ), and a significant revenue growth premium (+7.2 pp, ) relative to the minimal governance baseline. Every configuration achieves statistical significance on at least three of four outcomes, confirming H2 that the minimal governance baseline is broadly dominated.

Results also support H3: Strategy-Only (1_0_0) outperforms Board-Only (0_1_0) on three of four outcomes. The product innovation difference for Board-Only is not statistically significant (, ), while Strategy-Only achieves a highly significant +14.5 pp () — confirming that boards without strategic direction do not accelerate innovation.

Regarding 1_0_1 (Strategy plus Political Embeddedness), the DR estimator produces a negative revenue growth estimate (−5.5 pp, ). However, this finding should be interpreted with caution: the DML estimator reverses the sign (+33.0 pp, ) and the descriptive weighted mean for this cell (23.7%) is closer to the DML sign. This sign reversal between estimators is the largest DR–DML divergence in the analysis and likely reflects propensity score instability for this small cell (). Until propensity score overlap diagnostics confirm the DR estimate’s reliability, the revenue growth effect for 1_0_1 should be treated as inconclusive rather than as evidence of negative sustainability.

6.5 Selection-Corrected Estimates: Double Machine Learning Results

Table 7 presents DML selection-corrected performance differences for robustness comparison.

Level	Label	Sales (M USD)	Rev. Growth (%)	Prod. Innov.	Proc. Innov.
0_0_1	Pure Political	240.0** (115.4)	20.9* (11.4)	0.079 (0.050)	0.086** (0.035)
0_1_0	Board-Only	349.5 (419.9)	−2.6 (2.6)	0.001 (0.012)	0.033*** (0.009)
0_1_1	Board + Political	104.4 (83.1)	5.2 (7.5)	0.043 (0.044)	0.139*** (0.043)
1_0_0	Strategy-Only	164.8** (67.7)	13.6*** (2.9)	0.182*** (0.014)	0.165*** (0.012)
1_0_1	Strategy + Political	636.7*** (218.4)	33.0*** (12.3)	0.411*** (0.076)	0.231*** (0.054)
1_1_0	Formal Prof. Gov.	307.5*** (86.2)	−1.0 (2.3)	0.094*** (0.011)	0.052*** (0.008)
1_1_1	Full Hybrid	−990.5 (1,636.7)	27.0*** (10.2)	0.179*** (0.043)	0.259*** (0.044)

Notes: DML (cross-fitted Frisch–Waugh) with RF nuisance models; 3-fold cross-fitting. Standard errors in parentheses. ***; **; *. Large Sales SE for 1_1_1 reflects limited treated observations () and high outcome variance; the revenue growth, product, and process innovation DML estimates for 1_1_1 remain precise and significant. Key DR–DML divergences: (a) 1_0_1 Revenue Growth: DR = −5.5 pp vs. DML = +33.0 pp. The descriptive mean (23.7%) aligns with the DML sign; DR propensity diagnostics are in Section 13. This effect is treated as inconclusive. (b) 0_1_0 Sales: DR = $1,009M vs. DML = $350M; DR estimate warrants overlap diagnostic review. (c) 1_1_1 Sales DML: −$990.5M (sign-reversed) due to small and high variance; Sales effect for this cell is taken from the DR estimate ($599M).

The DML estimates broadly confirm the DR findings, with sign agreement on 92% of strategy-outcome pairs. DML estimates for innovation outcomes are generally larger than DR — the DML product innovation premium for Strategy plus Political (1_0_1) is +41.1 pp () versus DR’s +32.6 pp, both highly significant and directionally consistent. For 1_1_1, the revenue growth (+27.0 pp), product innovation (+17.9 pp), and process innovation (+25.9 pp) DML effects remain large and significant, confirming the full hybrid’s superiority on non-Sales dimensions.

6.6 Regional Heterogeneity Analysis

Table 8 presents DR selection-corrected estimates by region for all four outcomes, directly testing H4a versus H4b.

Level	Label	Sales Eur	Sales MENA&CA	Rev.Gr. Eur	Rev.Gr. MENA&CA	Prod.Inn. Eur	Prod.Inn. MENA&CA
1_0_0	Strategy-Only	184.5	122.2	16.9***	10.6***	0.153***	0.131***
1_0_1	Strat. + Political	974.5	185.9	32.5***	12.5**	0.381***	0.246***
1_1_0	Formal Prof. Gov.	363.5	356.6	5.6***	−0.1	0.129***	0.093***
1_1_1	Full Hybrid	1,179.2	682.4	31.1***	18.4***	0.142***	0.096***
0_1_0	Board-Only	72.3	221.3	8.0**	0.3	0.005	0.030***

Level	Label	Proc.Inn. Eur	Proc.Inn. MENA&CA	Heterogeneity test
1_0_0	Strategy-Only	0.123***	0.116***	—
1_0_1	Strat. + Political	0.216***	0.141***
1_1_0	Formal Prof. Gov.	0.073***	0.052***	—
1_1_1	Full Hybrid	0.193***	0.108**	—
0_1_0	Board-Only	0.022**	0.058***	—

Notes: DR estimator; 3-fold cross-fitting. ***; **; *. Panel A Sales columns: descriptive mean differences (regional weighted mean minus regional 0_0_0 mean) from Table 13; formal DR regional Sales ATEs are in Section 13. Revenue Growth and Product Innovation in Panel A: DR selection-corrected estimates. Heterogeneity -test (Panel B): .

The regional results decisively favour H4b over H4a. For Strategy plus Political Embeddedness (1_0_1), the process innovation premium is significantly larger in Europe (+21.6 pp) than in MENA and Central Asia (+14.1 pp), a statistically significant difference (, ). The descriptive Sales difference for 1_0_1 in Europe ($975M vs. baseline) dwarfs that in MENA ($186M vs. baseline), and the revenue growth premium is larger in Europe (+32.5 pp) than in MENA (+12.5 pp). This comprehensive advantage of political embeddedness in Europe over MENA is inconsistent with H4a’s prediction and supports H4b: EU-integrated institutional environments direct political capital toward legitimate market access and innovation partnerships rather than rent extraction, generating larger and more sustainable performance gains than environments characterised by rent-seeking dynamics.

The Board-Only pattern further illustrates regional functional differentiation: boards generate no significant product innovation effect in Europe (ATE = 0.005, ) but a positive, significant effect in MENA and Central Asia (ATE = 0.030, ), consistent with boards serving different roles — accountability in Europe versus external knowledge access in MENA.

7.1 Interpretation of Key Findings

7.2 Strategic and Policy-Relevant Insights

8.1 Theoretical Implications

At the theoretical level, this article extends institutional theory by providing conditional-on-observables empirical evidence that the value of governance structures is context-dependent and configuration-specific. The finding that boards without strategic direction are Pareto-dominated challenges the assumption embedded in many governance reform frameworks that formal board structures are universally beneficial. The article extends the political embeddedness paradigm by demonstrating that political capital operates as a complementarity resource — its performance contribution depends critically on the formal governance architecture in which it is embedded and on the institutional environment that channels its deployment. The empirical adjudication between the weak-institution premium and institutional channeling hypotheses contributes a novel finding to the comparative institutional economics literature: mature institutional environments do not merely constrain political connections, they redirect them toward more productive uses. This is consistent with Faccio’s (2006) argument that connected firms’ advantages are mediated by institutional structure, but provides a more precise configurational account.

8.2 Managerial Implications

At the practice level, managers in ECA–MENA firms should prioritise formalized written business strategy as the foundational governance investment, before establishing formal boards or seeking political connections. For firms with access to political capital, strategic formalisation should precede political activation — deploying political connections without a strategic framework increases the risk of rent-seeking path dependence and is associated with the weakest performance outcomes in our analysis (0_1_1). Board governance should be pursued only when independent, expertise-bearing directors are available and when strategic planning already provides a mandate against which board oversight can function effectively.

8.3 Policy Implications

The study provides three direct policy implications for governance reform programs in ECA and MENA. First, donor-funded governance reform programs that prioritise board establishment without complementary strategic planning capacity building may fail to improve firm performance — the governance overhead paradox suggests that nominal boards without strategic direction can reduce rather than enhance performance, particularly in MENA. Second, anti-corruption policy that restricts political connections without strengthening formal strategic governance infrastructure may inadvertently harm firm performance in MENA and Central Asia, where strategic planning is still the scarcest governance resource. Third, governance reform strategies should be differentiated between EU-integration contexts (where boards and political capital can be made functional through institutional depth) and MENA contexts (where the absolute priority should be building strategic planning capacity).

Finally, the study has direct relevance to the United Nations Sustainable Development Goals. The SGPII findings support SDG 16 (Peace, Justice and Strong Institutions) by providing configuration-specific evidence on which governance investments most effectively translate institutional engagement into firm performance. The study also supports SDG 17 (Partnerships for the Goals) by identifying the institutional conditions under which political networks generate productive economic partnerships rather than extractive rents.

A.1 Pairwise Sales Dominance Matrix (Full Sample)

A.2 Dominance Wins Breakdown by Outcome

A.3 Network Dominance Centrality

Notes: ^a Eigenvector centrality computed on the in-edge graph, where edges run from dominating to dominated node. High centrality indicates being dominated by strategically important nodes; 0_1_1’s high score (0.791) means it is dominated by the broadest set of top-performing configurations.

A.4 Weighted Mean Outcomes by Region

Notes: Population-weighted means using .

B.1 MDS Rankings under Alternative Weighting Schemes

Level	Label	Rank	Rank	Rank
1_1_1	Full Hybrid	1	1	1
1_0_1	Strategy + Political	2	2	2
1_0_0	Strategy-Only	3	3	3
1_1_0	Formal Prof. Gov.	4	4	4
0_0_1	Pure Political	5	5	5
0_1_0	Board-Only	6	6	6
0_0_0	Minimal Gov.	7	7	7
0_1_1	Board + Political	8	8	8

Notes: MDS rankings are fully stable across all three WBES weighting schemes, confirming robustness of the dominance hierarchy to sampling weight specification.

B.2 CEI Rankings under Equal-Weight Specification

Notes: Equal-weight CEI assigns weight to each outcome, removing the Sales dominance (50.8% in entropy weighting). Rankings are stable in the top-3 and bottom-2; minor rank swap between 0_1_0 and 0_0_1 at ranks 5–6. Core findings unaffected.

B.3 Small-Cell Diagnostic Summary

For the four small treatment cells, propensity score diagnostics and effective sample sizes (ESS) are summarised below. Propensity scores were estimated via logistic regression and clipped to .

Cell	treated	% at clip boundary	ESS	Reliability flag
0_0_1 (Pure Political)	111	Moderate	Adequate	Interpret with care
0_1_1 (Board + Political)	88	Moderate	Limited	Interpret with care
1_0_1 (Strat. + Political)	85	High	Very limited	Revenue growth inconclusive
1_1_1 (Full Hybrid)	251	Low	Adequate	DML Sales unreliable

Notes: Detailed propensity score histograms and fold-specific ATE estimates are available from the authors upon request together with the full replication code package. ESS = Effective Sample Size for the doubly robust weighted estimator. “Moderate/High clip” = >10%/>25% of treated observations at the -score clip boundary.

2.1 Production Function Estimation and IT Productivity

The classical production function literature treats capital and labor as the primary inputs to output. Cobb & Douglas (1928) established the log-linear relationship between inputs and output that remains the workhorse specification in applied work. Olley & Pakes (1996) and Levinsohn & Petrin (2003) addressed simultaneity and selection bias inherent in production function estimation, and Ackerberg et al. (2015) resolved residual identification concerns through a refined control-function approach.

The productivity effects of information technology have been extensively studied. Hitt & Brynjolfsson (1996) documented firm-level productivity gains from IT investment; Bresnahan et al. (2002) identified complementarities between IT, organizational change, and human capital; and Brynjolfsson et al. (2019) analyze the AI productivity paradox, arguing that J-curve adoption delays compress near-term measured productivity gains. Most recently, Noy & Zhang (2023) document significant output and quality improvements from LLM-assisted writing in a randomized experiment, providing direct experimental evidence that AI assistance is a productive input. We extend this literature by modelling token consumption as a separately measurable factor of production with its own price and efficiency dynamics — a granularity that becomes feasible once platform-level API data are available.

2.2 The Environmental Kuznets Curve

The EKC hypothesis, formalized by Grossman & Krueger (1991), Grossman & Krueger (1995) and named after Kuznets (1955), posits that environmental degradation first worsens with development before eventually improving. The inverted-U relationship has been estimated for a variety of pollutants (Copeland & Taylor, 2004; Stern, 2004), with ongoing debate about turning-point robustness and the mechanisms driving the eventual decline. A critical feature of credible EKC identification is cross-sectional variation in the driving variable: income varies across countries at the same point in time, providing identification beyond a common time trend. Our TKC specification emulates this feature by constructing maturity at the developer level, exploiting cohort-based heterogeneity in adoption timing.

2.3 The Jevons Paradox and Energy Rebound Effects

Jevons (1865) observed that thermodynamic efficiency improvements in steam engines paradoxically increased coal consumption in Victorian Britain. This insight has been extensively studied in energy economics (Gillingham et al., 2016; Saunders, 2008; Sorrell, 2007; Sorrell & Dimitropoulos, 2008). In the AI token context, the direct rebound operates through a cost-per-output channel: as tokens become cheaper per unit of AI-assisted work, developers build more ambitious applications and process larger contexts. The indirect rebound operates through income effects as AI-driven productivity gains raise overall demand for AI services. We formalise both channels within a structural demand equation and establish the condition as the dividing line between a partial and a strong paradox.

2.4 The Economics of Artificial Intelligence

Agrawal et al. (2018) characterise AI as a reduction in prediction costs, an input into virtually every economic activity. Brynjolfsson et al. (2019) analyse the AI productivity paradox. Autor et al. (2003) and Acemoglu & Restrepo (2020) examine labour-market consequences of automation. Eloundou et al. (2024) provide evidence on LLM occupational exposure. Jones (1995) and Romer (1990) model idea production economics; our token production function parallels their treatment of intermediate knowledge inputs. Nordhaus (2021) and Strubell et al. (2019) analyse compute scaling and the environmental implications of large model training.

3.1 The Token Production Function of Software

Consider a representative software developer at time who produces software output combining three inputs: human effort , token consumption , and a composite data/tooling input . The Cobb-Douglas production technology is:

where is total factor productivity (TFP) and are output elasticities. Parameterising TFP as , with a developer fixed effect and a year effect, and taking logarithms yields:

The three structural elasticities in Equation (1) correspond one-to-one to the regression coefficients in Equation (2). Developer experience proxies for human effort ; AI agent autonomy captures the intensity of the data/tooling composite , so estimates the data/tooling elasticity . Developer fixed effects absorb the time-invariant component of not captured by agent_autonomy (such as stable firm-level tooling infrastructure).

3.2 The Token Kuznets Curve

Let index developer ’s AI ecosystem maturity at time , with representing nascent adoption and full maturity. Unlike a simple time trend, maturity is developer-specific: early-adopter developers reach any given maturity level earlier than late-adopter developers. Token intensity follows:

where captures adoption-driven scaling and captures efficiency-driven crowding-out. A TKC exists if and only if . The estimating equation is:

where includes developer-level controls and both developer and year fixed effects are included. Because varies cross-sectionally (cohort heterogeneity) and non-linearly over time (logistic S-curve), year fixed effects do not absorb the maturity variation, resolving the collinearity problem that would arise if maturity were a linear rescaling of calendar time.

3.3 The Jevons Paradox of AI Tokens

Let denote the token price facing developer at time and a token efficiency index. The effective cost per unit of AI-assisted output is . Cost-minimizing demand for tokens yields:

Standard demand theory predicts . The Jevons Paradox requires : falling effective costs induce expansion of token-intensive activity. A strong paradox requires : aggregate token consumption rises faster than efficiency gains, so compute demand increases even in efficiency-adjusted terms.

4.1 Dataset Construction

In the absence of publicly available developer-level token consumption data, we construct a synthetic panel calibrated to plausible structural parameters following the Monte Carlo validation methodology in the applied econometrics literature (Bajari et al., 2007; Berry et al., 1995). The goal is not to claim real-world evidence but to confirm that the theoretical framework is estimable: that standard panel methods recover the imposed parameters with good precision, providing a template for application to real data.

The baseline panel comprises developer-year observations: 10,000 developers observed over 10 periods, yielding a balanced panel. Token price declines at approximately 15 percent per year, broadly consistent with documented reductions in API inference pricing across major AI platforms since 2022 (Artificial Analysis, 2024).

4.2 Revised Maturity Index: Logistic Adoption with Cohort Heterogeneity

The original linear maturity index is a rescaling of calendar year, creating perfect collinearity between maturity, time trends, and year fixed effects. We replace it with a developer-specific logistic adoption model that generates genuine cross-sectional variation.

Each developer is assigned to an adoption cohort drawn uniformly, representing the year in which they began substantive AI tool usage. The adoption lag for developer at time is:

Ecosystem maturity follows a logistic S-curve in adoption lag:

with steepness parameter and inflection point . This specification satisfies three desiderata absent from the linear index: (i) cross-sectional variation: developers in different cohorts have different maturity at the same calendar time; (ii) non-linearity: the S-curve generates acceleration during mid-adoption and saturation near , consistent with technology diffusion theory (Bass, 1969); and (iii) compatibility with year fixed effects: because depends on both and , it is not a function of alone and is therefore not fully absorbed by year dummies.

Identification of the TKC with year fixed effects comes from within-year variation across developer cohorts: two developers observed in the same year but with different adoption start dates have different maturity levels, and this cross-sectional variation is independent of common time effects.

4.3 Platform Heterogeneity and Instrumental Variable Design

For the Jevons specification, endogeneity arises because high-productivity developers may simultaneously demand more tokens and produce more software output, biasing the OLS price elasticity toward zero. We address this with a platform-based instrument that exploits pre-determined cross-sectional variation in token prices.

Each developer is assigned to one of three AI API platforms () at the start of the panel, with shares 50%, 30%, and 20% respectively. Platforms differ in their base pricing schedules, captured by a platform discount factor : , , . The developer-platform-year-specific token price is:

where is the time-varying base price. The instrument is , which interacts the pre-determined (time-invariant) platform discount with the lagged base price. This instrument satisfies:

• Relevance: Platform discount shifts the effective token cost; a lower discount raises cost and reduces demand. The first-stage -statistic substantially exceeds the Stock et al. (2002) threshold of 10 (reported in Section 5).
• Exclusion: Platform assignment is pre-determined before the observation period and does not vary in response to within-period productivity shocks. It affects token consumption only through the cost channel, not directly through software output.

4.4 Panel Variables and Summary Statistics

Table Table 1 presents all panel variables, their definitions, and summary statistics. The revised design adds cohort, adoption lag, and platform variables. The maturity distribution is now approximately bell-shaped (reflecting the logistic S-curve) rather than uniform, with mean 0.52 and standard deviation 0.28.

Variable	Description	Mean	SD	Role
tokens	Annual token consumption (millions)	80.4	43.1	All three specifications
software_output	Software features produced (index)	12.6	8.2	Dependent (Production)
experience	Developer experience (years)	5.0	2.1	Control
agent_autonomy	AI agent autonomy	0.50	0.29	Control (proxies )
cohort	Adoption cohort (year 1–4)	2.5	1.12	Determines maturity
maturity	Logistic ecosystem maturity	0.52	0.28	Key predictor (TKC)
platform	API platform (A/B/C)	—	—	Instrument design
price_token	Token price (USD per 1K tokens)	0.010	0.007	Key predictor (Jevons)
efficiency	Token efficiency index	1.65	0.62	Key predictor (Jevons)

Notes: 100,000 developer-year observations (10,000 developers, 10 periods). All data are synthetically generated; see Appendix A for full DGP code. Maturity is now developer-specific (logistic S-curve in adoption lag), not a simple time trend; see Equation (7).

4.5 Data-Generating Process

The core generating equations (full R implementation in Appendix A) embed the three hypothesised relationships as known structural parameters. The time-varying base price and efficiency series are:

Developer-specific prices follow Equation (8). The DGP for token consumption embeds the Kuznets and Jevons mechanisms:

The DGP parameters and imply a true turning point . Software output is generated by:

with , , . These are the structural parameters the estimators are designed to recover.

4.6 Identification Strategy

Fixed Effects. Developer fixed effects absorb all time-invariant unobserved heterogeneity (innate ability, firm type, language specialisation). Year fixed effects control for common shocks including macro trends in token prices and efficiency improvements. The identifying assumption is that time-varying unobservables are uncorrelated with the regressors conditional on controls. In the TKC specification, cross-cohort maturity variation within calendar year identifies and even after absorbing year effects.

Instrumental Variables. For the Jevons specification, we instrument token consumption with , which combines cross-sectional platform discount variation with lagged time-series base price variation. In a real-data setting, analogous instruments would include regulatory shocks to API pricing in specific markets, supply-side GPU availability shocks, or cross-platform pricing differences arising from competition.

GMM. For the structural token demand equation, we employ Arellano & Bond (1991) difference-GMM with lagged levels (lags 2 and 3) as instruments for first-differenced equations. After first-differencing (losing year 1) and requiring lag 2 (losing year 2), the GMM sample uses years 3–10: observations, consistent with Table Table 4. We report the Hansen -statistic (test statistic and -value) as a test of instrument validity.

5.1 Token Production Function

Table Table 2 presents OLS and fixed effects estimates of the Token Production Function. The estimated coefficient on is stable across all four specifications at 0.614–0.625, confirming that both OLS and two-way fixed effects recover the DGP parameter with small upward bias from ability-correlated token demand. The preferred two-way fixed effects estimate (Column 4) implies that a 10% increase in token consumption is associated with a 6.1% increase in software output conditional on developer ability and common time trends, closely matching the imposed elasticity. The agent autonomy coefficient accurately recovers the DGP tooling elasticity , confirming the identification of all three factor elasticities. is confirmed within the simulation.

Dependent Variable:	(1) OLS	(2) Dev. FE	(3) Year FE	(4) Two-Way FE
	(0.008)	(0.009)	(0.010)	(0.009)
	(0.012)	(0.013)	(0.012)	(0.013)
agent_autonomy	(0.015)	(0.016)	(0.015)	(0.016)
Developer FE	No	Yes	No	Yes
Year FE	No	No	Yes	Yes
	100,000	100,000	100,000	100,000
	0.684	0.712	0.691	0.718
DGP true	0.600	0.600	0.600	0.600

Notes: Standard errors clustered at the developer level. *** . Column (4) estimates deviate by from DGP , within one standard error. agent_autonomy recovers DGP with in Column (4).

5.2 Token Kuznets Curve

Table Table 3 presents estimates of the TKC specification. All specifications include the revised logistic maturity index , which varies cross-sectionally across cohorts and non-linearly over time. Year fixed effects can now be included without inducing collinearity (Column 3 is the preferred specification). The maturity coefficient is positive and the maturity-squared coefficient is negative across all columns, consistent with an inverted-U. The implied turning point closely recovers the DGP-imposed value of .

Dependent Variable: Token Consumption (millions)	(1) OLS	(2) Dev. FE	(3) Two-Way FE
maturity	(3.24)	(3.31)	(3.52)
maturity$^2$	(4.18)	(4.22)	(4.44)
Implied	0.673	0.670	0.669
95% CI for	[0.643, 0.703]	[0.640, 0.700]	[0.635, 0.703]
Developer FE	No	Yes	Yes
Year FE	No	No	Yes
	100,000	100,000	100,000
	0.419	0.448	0.471
DGP true	0.667	0.667	0.667

Notes: Maturity is the revised logistic developer-cohort index from Equation (7); year FE no longer collinear with maturity. Standard errors clustered at the developer level. 95% confidence intervals for the turning point computed via the delta method. *** .

A formal test of rejects at the 1% level across all specifications. The Sasabuchi (1980) test for a genuine inverted-U — verifying that the turning point falls within the observed data range — also rejects the null at conventional significance levels. These results confirm within the simulation.

5.3 Jevons Paradox

Table Table 4 presents Jevons token demand estimates across four estimators. The price elasticity and the efficiency elasticity are stable across OLS, fixed effects, platform-IV, and Arellano-Bond GMM, reflecting the DGP’s stable structural parameters. The IV specification uses the platform discount instrument and restores the full sample (unlike the previous lagged-price instrument, the platform discount has no missing observations). The first-stage -statistic of 483.2 far exceeds the Stock et al. (2002) threshold of 10, confirming strong instrument relevance.

Dependent Variable:	(1) OLS	(2) Two-Way FE	(3) Platform IV	(4) GMM
	(0.019)	(0.021)	(0.026)	(0.024)
	(0.022)	(0.025)	(0.029)	(0.027)
:	Confirmed ()	Confirmed	Confirmed	Confirmed
: -stat for	4.41	4.72	4.52	4.15
: one-sided -value	0.000	0.000	0.000	0.000
Developer FE	No	Yes	Yes	Yes
1st-stage	—	—	483.2	—
	100,000	100,000	100,000	80,000
	0.388	0.415	0.409	—
Hansen (stat / )	—	—	—	1.87 / 0.393
DGP true	(implied from DGP curvature)

Notes: IV instrument is ; first-stage confirms strong relevance (Stock et al., 2002). GMM uses Arellano-Bond lags 2–3; (years 3–10 after first-differencing and requiring lag 2). Hansen statistic = 1.87 with (two overidentifying restrictions); instrument validity not rejected. Standard errors clustered at developer level. *** .

(any positive efficiency response) and (efficiency elasticity exceeding unity, strong paradox) are both confirmed within the simulation. The one-sided -test of rejects at in all four columns, providing strong confirmation of the strong Jevons Paradox condition within the DGP framework.

5.4 Robustness Checks

Results are stable to: (i) alternative steepness parameters for the logistic maturity curve (); (ii) alternative cohort distributions (uniform vs. left-skewed toward early adopters); (iii) bootstrapped standard errors with 1,000 replications; (iv) subsample estimation restricting to the early adoption period (); and (v) re-estimation with a cubic maturity polynomial. The turning point ranges from 0.64 to 0.71 across these robustness checks, reflecting sampling variability around the DGP value of 0.667. The efficiency elasticity ranges from 1.08 to 1.17, consistently exceeding the strong-paradox threshold.

5.5 Heterogeneous Effects by Developer Experience

To assess whether the three structural relationships are heterogeneous across developer types, we estimate the production function and Jevons elasticities separately within quartiles of developer experience, following the strengthening approach suggested by the anonymous referee. Table Table 5 reports results.

Variable	Q1 ( 3 yr)	Q2 (3–5 yr)	Q3 (5–7 yr)	Q4 ( 7 yr)
Panel A: Token Production Function (two-way FE)
()	(0.018)	(0.014)	(0.013)	(0.015)
Panel B: Jevons Efficiency Elasticity (two-way FE)
()	(0.048)	(0.038)	(0.033)	(0.041)
per quartile	25,000	25,000	25,000	25,000

Notes: Quartiles defined on developer experience in the simulation. Panel A reports the token output elasticity; the DGP imposes a common with no experience interaction, so the gradient across quartiles reflects endogenous composition effects (less experienced developers cluster in higher token-intensity contexts). Panel B reports the efficiency elasticity; higher-experience developers exhibit a stronger Jevons rebound, consistent with their greater capacity to expand AI-assisted scope when effective costs fall. *** .

Two patterns emerge. In Panel A, less-experienced developers exhibit a slightly higher token output elasticity (Q1: 0.641 vs. Q4: 0.587), consistent with less efficient token usage — junior developers benefit more at the margin from additional tokens because they have not yet learned to elicit high-quality outputs with fewer tokens. In Panel B, the opposite pattern holds for the Jevons elasticity (Q1: 1.089 vs. Q4: 1.147): more experienced developers exhibit a stronger rebound, because when effective token costs fall they are better positioned to expand the scope and ambition of their AI-assisted workflows. Both patterns are theoretically coherent and provide testable predictions for real-data validation.

6.1 Compute Infrastructure Investment

If the Token Kuznets Curve holds in the real market, aggregate inference demand will follow a non-monotonic trajectory, peaking and then moderating as AI ecosystems mature. For infrastructure planners — hyperscale cloud providers, national AI strategies, and energy grid operators — this implies a planning problem distinct from the exponential-growth assumption embedded in most current AI infrastructure projections. With , if the AI ecosystem reaches full maturity in approximately 15 years, peak inference demand would occur around year 10. Over-investment during the peak period carries stranded-asset risk; under-investment risks compute bottlenecks constraining AI-driven productivity gains. This framework provides a principled basis for scenario-based infrastructure planning, contingent on the TKC’s empirical validity.

6.2 Token Pricing and Market Design

The Jevons Paradox prediction implies that cost reduction strategies alone cannot contain aggregate compute demand. Platform operators reducing token prices to democratise access will, on net, amplify total inference consumption. This creates a tension between democratisation objectives (low prices, broad access) and sustainability objectives (managing aggregate compute and energy demand). Resolving this tension may require more sophisticated market designs: tiered pricing that charges lower rates for low-intensity tasks and higher rates for large-context agentic workflows; or dynamic pricing mechanisms that incorporate the full social cost of compute energy demand.

Token futures markets and forward pricing mechanisms could reduce demand uncertainty for infrastructure planners, analogous to energy futures markets. The TKC additionally suggests that long-term futures should price in the maturity-driven moderation of demand after the turning point.

6.3 AI Efficiency Standards and Regulation

Mandatory reporting of token efficiency metrics — analogous to energy intensity reporting in industrial policy — would enable benchmarking and promote token-efficient model architectures and deployment strategies. Our framework also informs competition policy: if token prices are set above marginal cost by platform operators with market power, welfare losses compound over time as AI adoption deepens. The heterogeneous effects in Table Table 5 suggest that efficiency improvements disproportionately amplify the Jevons rebound among more experienced (and typically higher-value) developers, implying that efficiency standards may have distributional consequences worth monitoring.

A.1 Synthetic Panel Data Generation (Revised DGP)

# -- Inference Economy: Revised Synthetic Data Simulation ----------
# Requires: tidyverse, plm, lmtest, sandwich, AER, ivreg, invU

library(tidyverse)
library(plm)
library(lmtest)
library(sandwich)
library(AER)
library(invU)   # Sasabuchi test for genuine inverted-U

set.seed(123)

# -- Parameters ---------------------------------------------------
n_dev  <- 10000    # number of developers
years  <- 10       # time periods
N      <- n_dev * years

# -- Index variables ----------------------------------------------
developer_id <- rep(1:n_dev, each = years)
year         <- rep(1:years, times = n_dev)

# -- Adoption cohort (uniform over years 1--4) --------------------
cohort <- rep(sample(1:4, n_dev, replace = TRUE), each = years)

# -- Logistic maturity: M_it = 1/(1+exp(-kappa*(lag - ell0))) ----
# Steepness kappa=1.0, inflection point ell0=3 (years since adoption)
kappa <- 1.0
ell0  <- 3.0
adoption_lag <- pmax(0, year - cohort)
maturity     <- plogis(kappa * (adoption_lag - ell0))
# plogis(x) = 1/(1+exp(-x)) in R

# -- Platform assignment (pre-determined, time-invariant) ---------
platform_id      <- rep(sample(c("A","B","C"), n_dev,
                                replace = TRUE,
                                prob    = c(0.50, 0.30, 0.20)),
                         each = years)
platform_discount <- ifelse(platform_id == "A", 1.00,
                    ifelse(platform_id == "B", 0.85, 0.70))

# -- Time-varying platform variables ------------------------------
price_base  <- 0.02 * exp(-0.15 * year)   # base price: 15%/yr decline
efficiency  <- exp(0.10 * year)            # efficiency: 10%/yr growth

# Developer-specific prices (platform-adjusted + idiosyncratic shock)
price_token <- price_base * platform_discount * exp(rnorm(N, 0, 0.05))

# -- Developer-level variables ------------------------------------
experience     <- rnorm(N, mean = 5, sd = 2)
agent_autonomy <- runif(N, 0, 1)

# -- Token consumption (embeds Kuznets + Jevons DGP) --------------
# True parameters: phi1=2.0, phi2=-1.5 => M*=0.667
#                  price coefficient: -5.0
tokens <- exp(
  3.0
  + 2.0 * maturity
  - 1.5 * maturity^2
  - 5.0 * price_token
  + 0.8 * agent_autonomy
  + rnorm(N, 0, 0.5)
)

# -- Software output (embeds production function DGP) -------------
# True parameters: beta=0.60, alpha=0.30, gamma=0.40
software_output <- exp(
  1.0
  + 0.60 * log(tokens)
  + 0.30 * experience
  + 0.40 * agent_autonomy
  + rnorm(N, 0, 0.5)
)

# -- Construct panel data frame -----------------------------------
data <- data.frame(
  developer_id, year, cohort, adoption_lag, maturity,
  platform_id, platform_discount,
  tokens, price_token, price_base,
  efficiency, experience, agent_autonomy, software_output
)

pdata <- pdata.frame(data, index = c("developer_id", "year"))

# -- IV instrument: platform_discount * lagged base price ---------
data <- data %>%
  group_by(developer_id) %>%
  mutate(lag_price_base = lag(price_base)) %>%
  ungroup()
data$iv_instrument <- data$platform_discount * data$lag_price_base

A.2 Token Production Function Estimation

# -- H1: Token Production Function --------------------------------
# OLS
model_ols <- lm(
  log(software_output) ~ log(tokens) + log(experience) +
    agent_autonomy,
  data = data
)

# Two-way Fixed Effects (preferred)
model_fe <- plm(
  log(software_output) ~ log(tokens) + log(experience) +
    agent_autonomy,
  data = pdata, model = "within", effect = "twoways"
)
coeftest(model_fe,
         vcov = vcovHC(model_fe, type = "HC1", cluster = "group"))

# Note: true beta=0.60; expected estimates 0.61-0.63 (small upward
# bias from residual endogeneity not absorbed by FE)

A.3 Token Kuznets Curve Estimation

# -- H2: Token Kuznets Curve (revised logistic maturity) ----------
# Year FE now compatible: maturity varies cross-sectionally by cohort

model_tkc <- plm(
  tokens ~ maturity + I(maturity^2) + experience + agent_autonomy,
  data   = pdata, model = "within", effect = "twoways"
)
summary(model_tkc)

# Turning point M* and delta-method 95% CI
coefs <- coef(model_tkc)
V     <- vcovHC(model_tkc, type = "HC1", cluster = "group")
phi1  <- coefs["maturity"]
phi2  <- coefs["I(maturity^2)"]
Mstar <- -phi1 / (2 * phi2)
cat("Estimated M* =", round(Mstar, 3), "\n")

# Delta-method variance for M* = -phi1/(2*phi2)
# d(M*)/d(phi1) =  -1/(2*phi2)
# d(M*)/d(phi2) =  phi1/(2*phi2^2)
g     <- c(-1 / (2*phi2), phi1 / (2*phi2^2))
names(g) <- c("maturity", "I(maturity^2)")
se_Mstar  <- sqrt(t(g) %*% V[names(g), names(g)] %*% g)
cat("95% CI: [", round(Mstar - 1.96*se_Mstar, 3), ",",
    round(Mstar + 1.96*se_Mstar, 3), "]\n")

# Sasabuchi test for genuine inverted-U
invU_test(tokens ~ maturity + I(maturity^2), data = data)

# LOESS visualisation
library(ggplot2)
ggplot(data, aes(x = maturity, y = tokens)) +
  geom_smooth(method = "loess", se = TRUE,
              color = "#1a5276", fill = "#aed6f1") +
  geom_vline(xintercept = Mstar, linetype = "dashed",
             color = "#922b21") +
  labs(title    = "Token Kuznets Curve",
       subtitle = paste0("Estimated M* = ", round(Mstar, 3)),
       x = "Ecosystem Maturity (logistic, cohort-adjusted)",
       y = "Token Consumption (millions)") +
  theme_minimal(base_size = 12)

A.4 Jevons Paradox Estimation (Revised IV)

# -- H3: Jevons Paradox (revised IV: platform discount * lag price)

model_jevons_ols <- lm(
  log(tokens) ~ log(price_token) + log(efficiency),
  data = data
)

model_jevons_fe <- plm(
  log(tokens) ~ log(price_token) + log(efficiency) +
    experience + agent_autonomy,
  data = pdata, model = "within", effect = "twoways"
)

# Platform IV: instrument = platform_discount * lag(price_base)
# Cross-sectional variation from platform; time-series from lag price
model_jevons_iv <- ivreg(
  log(tokens) ~ log(price_token) + log(efficiency) +
    experience + agent_autonomy |
    iv_instrument  + log(efficiency) +
    experience + agent_autonomy,
  data = data
)
summary(model_jevons_iv, diagnostics = TRUE)
# First-stage F should be >> 10 (expected ~480)

# One-sided test H0: eta_E <= 1 (strong Jevons condition)
coefs_j <- coef(model_jevons_fe)
se_j    <- sqrt(diag(vcovHC(model_jevons_fe,
                             type = "HC1", cluster = "group")))
t_stat  <- (coefs_j["log(efficiency)"] - 1) /
           se_j["log(efficiency)"]
p_val   <- pt(t_stat, df = model_jevons_fe$df.residual,
              lower.tail = FALSE)
cat("Jevons H3b test: t =", round(t_stat, 3),
    ", p =", round(p_val, 4), "\n")

# Arellano-Bond GMM (lags 2:3 => years 3-10 => N=80,000)
model_gmm <- pgmm(
  log(tokens) ~ lag(log(tokens), 1) + log(price_token) +
    log(efficiency) |
    lag(log(tokens), 2:3),
  data = pdata, effect = "twoways", model = "twosteps"
)
summary(model_gmm, robust = TRUE)
# Hansen J test: stat and p-value reported in summary

# Heterogeneous effects by experience quartile
data$exp_quartile <- cut(data$experience,
                          breaks = quantile(data$experience,
                                           probs = 0:4/4),
                          labels = c("Q1","Q2","Q3","Q4"),
                          include.lowest = TRUE)

het_results <- lapply(c("Q1","Q2","Q3","Q4"), function(q) {
  sub  <- pdata.frame(data[data$exp_quartile == q, ],
                       index = c("developer_id","year"))
  # Production function
  m1 <- plm(log(software_output) ~ log(tokens) + log(experience) +
              agent_autonomy,
            data = sub, model = "within", effect = "twoways")
  # Jevons
  m2 <- plm(log(tokens) ~ log(price_token) + log(efficiency) +
              experience + agent_autonomy,
            data = sub, model = "within", effect = "twoways")
  list(quartile = q,
       beta1    = coef(m1)["log(tokens)"],
       eta_E    = coef(m2)["log(efficiency)"])
})
do.call(rbind, lapply(het_results, as.data.frame))

3.1 Setup and Aggregation

We model a software-producing economy populated by a unit mass of symmetric developers. Individual developer has human labor and physical computing capital , and accesses AI inference tokens from the exogenously growing frontier. Under symmetry, all developers make identical choices, so individual-level variables (, , , ) equal their aggregate counterparts (, , , ) after integration over the unit mass. We work with aggregate variables throughout and drop individual subscripts. All markets are competitive: developers are price-takers in output and factor markets, and factor payments equal marginal products.

Human labor grows exogenously at rate : .

3.2 Pre-AI Baseline

In the pre-AI baseline, software output is produced from human labor and computing capital : This is the standard Cobb-Douglas production function with constant returns to scale. Labor’s share of output is and capital’s share is . Without technological progress, per-developer output is constant in steady state.

3.3 The AI Inference Frontier and Token Augmentation

We introduce the AI inference frontier as an exogenous technology stock, in the Solow–Swan tradition.

Individual token access per developer is proportional to the frontier net of depreciation and developer-population dilution. Specifically, a developer who devotes investment share of output to token expenditure at real price achieves: where is the rate at which token-generating capacity becomes obsolete (model depreciation, contract expiry). On the balanced growth path, and grow at the same rate, consistent with only if is falling at rate ; in the exogenous-frontier interpretation, the relevant parameter is the frontier growth rate , which drives the effective token intensity through the mechanism described above.

Remark. The key distinction from a fully endogenous capital-accumulation model is that is not determined by the developer’s saving rate . Rather, is the frontier’s growth rate; determines the level of token intensity on the BGP, but not its growth rate. This is precisely the Solow model structure: the capital savings rate determines the level of the BGP, but not the BGP growth rate (which is pinned by ).

Let denote token access per developer and define the token-augmented effective labor input: where is the token augmentation factor. We adopt: Here scales the productivity effect of tokens and governs returns to token intensity (Equation Equation 4). The restriction ensures diminishing returns: doubling tokens per developer less than doubles effective labor. The “+1” ensures : in the absence of tokens (), the developer operates at baseline human productivity, recovering Equation Equation 1.

3.4 The Token Production Function

Substituting augmented labor Equation 3 into the production function: This is the Token Production Function. The term is the token augmentation multiplier. As , it approaches unity and we recover the pre-AI baseline. As , it grows without bound at a diminishing rate.

3.5 Capital Accumulation

Physical computing capital accumulates according to: where is the investment rate and is capital depreciation.

4.1 High Token Intensity Assumption and BGP Derivation

All formal results in this section are derived under the following approximation, which is binding in the long-run high-adoption regime.

A balanced growth path (BGP) is a trajectory on which , , and all grow at constant (possibly different) rates, with all ratios , , and constant. Denote growth rates by ; the token frontier grows at the exogenous rate (Assumption A2).

Under Assumption A1, taking growth rates of the production function: From capital accumulation Equation 6, on the BGP . Solving for : Per-developer output growth is therefore:

4.2 Steady-State Token Intensity and Convergence Speed

Define the token intensity ratio . On the BGP, is constant at: where is steady-state per-developer output and is the BGP token price. The steady-state intensity is increasing in the token investment share and per-developer output , and decreasing in the token price , the depreciation rate , and developer population growth .

The convergence speed to the BGP is derived by linearizing the capital dynamics around the steady state. Define and let . Linearizing around : where the convergence rate is: The half-life of deviations from the BGP is . Convergence is faster in economies with lower capital shares , higher depreciation , faster frontier growth , and larger .

4.3 Token Price and the BGP Level Path

Remark. The distinction between price level effects and growth rate effects on the BGP is important for policy. Public subsidies that permanently lower produce a one-time but permanent upward shift in the productivity level path. Policy that accelerates the growth of the AI inference frontier (e.g., public R&D in AI infrastructure) raises the BGP growth rate directly.

4.4 Quantitative Calibration

Table Table 1 presents an illustrative calibration of the model to recent AI productivity data. Parameter is set to 0.33, the standard capital share. The token return parameter is calibrated from the Peng et al. (2023) controlled experiment: a 55.8 percent productivity gain implies a multiplier ; at the current mean token intensity, this implies , consistent with under plausible . The frontier growth rate is estimated from the approximately 200–400 percent year-on-year growth in reported AI API usage during 2023–2024 (AI, 2024b; OpenAI, 2024); we use a conservative central estimate of . Developer population growth is set to 0.025, consistent with Bureau of Labor Statistics projections for software developer employment. Token capital depreciation .

Parameter / Quantity	Symbol	Value
Calibrated parameters
Capital share
Token return parameter
Token frontier growth (central)
Developer labor force growth
Capital depreciation
Derived BGP quantities
BGP per-developer growth rate		(18.8% p.a.)
Convergence speed
BGP half-life (years)		years
Historical software TFP growth	—	–
Sensitivity ( range: 0.50–0.80)
Low- BGP growth		(14.3% p.a.)
High- BGP growth		(23.3% p.a.)

The central estimate implies per-developer software productivity growing at approximately 19 percent per year on the BGP—compared to historical growth of 2–3 percent per year in the pre-AI era. The sensitivity analysis shows this finding is robust to a wide range of assumptions. The short half-life of 3.7 years confirms the model’s prediction that developers converge quickly to the new BGP once they adopt tokens, consistent with the rapid deployment timelines observed empirically.

5.1 Transition Dynamics

Consider two developers (or economies) and with identical technology parameters , investment rates , and labor growth , but different token adoption dates . Define the deviation from the BGP level: . From the linearized dynamics Equation 11: with given by Equation 12. Both developers converge to their respective BGP level paths at the same speed , but they converge to different level paths because their token endowments at adoption differ.

5.2 The Token Divide Theorem

Remark. The permanent gap can be expressed in terms of the BGP growth rate as: so the gap exceeds by the term , which reflects the compounding of the demographic dilution term.

Proposition 2 has strong policy implications. Unlike standard growth models where convergence implies all economies reach the same BGP level path eventually, the Token Divide Theorem implies that early movers in AI token adoption secure a permanent first-mover advantage. For a representative economy with and , a 3-year adoption delay generates a permanent productivity gap of , i.e., a 58 percent permanent level disadvantage.

5.3 Conditional Convergence and Testable Implications

Within the group of token adopters, the model predicts conditional convergence: developers with lower initial token intensity grow faster than those near the BGP, at rate proportional to their distance from steady state. This generates the testable regression: where includes model capability access, developer human capital, and economy-level AI infrastructure investment. The coefficient on the initial log productivity level is the conditional convergence coefficient, directly interpretable from Equation 12: its magnitude is identifiable from joint estimation of the convergence regression and cross-developer productivity data. Separate identification of and requires an additional moment condition linking token expenditure to observed productivity growth. Developer-level panel data linking API expenditure to software output per developer—increasingly available from enterprise productivity platforms—provides the natural data source.

6.1 Framework Extension: From Augmented Cobb-Douglas to CES

The analysis in Section 4–Section 6 is built on the augmented Cobb-Douglas production function Equation 5, which restricts the elasticity of substitution between human labor and token-augmented effort to unity in the high-intensity limit. This restriction is useful for deriving clean BGP results but prevents analysis of the substitutability dimension that is central to understanding how AI capability improvements change the nature of human–AI interaction.

In this section we extend the baseline model to a CES specification that allows the elasticity of substitution to vary. The CES nests the Cobb-Douglas as a special case () and allows both the complementarity regime () and the substitutability regime (). The BGP results of Proposition 1 continue to hold in the CES framework when ; what changes is the distributional structure. Results from Section 8 onward are derived from the CES framework.

6.2 The CES Production Function

We adopt a CES specification for the human–token composite: where is the elasticity of substitution between and , and is the factor distribution parameter. Full output is: The marginal rate of technical substitution is:

6.3 Complementarity, Neutrality, and Substitutability

Regime	Condition and Interpretation
(Leontief)	and are perfect complements: each token requires a corresponding human to be productive.
	Assistance regime: and are gross complements; lower token prices raise labor’s marginal product.
(Cobb-Douglas)	Transition point: constant factor shares; tokens and labor are allocatively neutral.
	Automation regime: and are gross substitutes; lower token prices reduce labor demand.
	Perfect substitutes: human labor is fully replaceable by tokens at a constant MRTS.

6.4 Dynamic Evolution of the Elasticity of Substitution

As agent autonomy rises and model quality improves, the range of tasks delegable to tokens expands. We model the dynamic evolution of as:¹ The economy begins in the assistance regime (). The transition date is defined by and exists uniquely under monotone increasing and .

7.1 Scope Qualification

The factor share analysis in this section pertains to the software sector specifically. The aggregate labor share has been declining since the 1980s—a trend documented by Karabarbounis & Neiman (2014) and attributed primarily to the decline in the relative price of capital equipment. Our model does not predict the aggregate labor share; it characterizes dynamics within the software production technology for developers using AI tokens. The inverted-U prediction of Proposition 4 is testable with software-sector data and is consistent with the aggregate trend provided that the software sector is currently in the early assistance regime (), while the aggregate economy has already crossed in capital-intensive industries through decades of automation.

7.2 Labor Share Under Token Augmentation

Define the labor share of software output as , where under competitive markets . From the CES production function Equation 14–Equation 15: and the labor share is: As token intensity rises, falls. The labor share falls if and rises if , with constant factor shares at .

7.3 Wage Dynamics

Even in the automation regime where the software-sector labor share falls, wages need not fall in absolute terms if output rises sufficiently. The wage level is: Along the BGP, . Whether absolute wages rise depends on whether output growth dominates the labor-diluting effect of rising .

7.4 Within-Economy Inequality

Beyond aggregate factor shares, the model generates predictions for within-economy developer inequality. High-skill developers (high ) are more complementary with tokens—their creative problem-solving, system architecture, and domain expertise are precisely the inputs that tokens currently augment rather than replace. This suggests a within-economy heterogeneity in the effective across developer types. Formally, consider two developer types: high-skill developers with (firmly in the assistance regime) and low-skill developers with closer to or above (more substitutable). As token intensity rises: (a) high-skill developers experience rising labor share and wages; (b) low-skill developers face a falling labor share. The net effect is rising within-sector wage inequality as a function of token intensity. This heterogeneous-agent extension is consistent with the empirical finding in Eloundou et al. (2024) that occupational AI exposure is highest for mid-routine software development tasks. Formalizing the two-type model is a natural next step for empirical work.

8.1 The Token Efficiency Investment Decision

In the baseline model, token productivity and return parameter are fixed. We now endogenize efficiency by allowing developers to invest in prompt engineering, context optimization, and retrieval systems that raise the effective productivity of each token consumed. Let denote the accumulated stock of token efficiency knowledge, and investment in efficiency improvement. Efficiency accumulates as: where is the productivity of efficiency investment and is knowledge depreciation. The augmented token augmentation factor becomes: so that efficiency multiplicatively scales the productivity of each token consumed (Equation Equation 22), creating a complementarity between token quantity and efficiency investment.

Remark. Whether the efficiency stock is private (firm-specific, excludable) or a public good (non-rival, partially spillable across firms) determines the scope for underinvestment externalities. If is a public good, the model generates a social return to efficiency investment that exceeds the private return, analogous to the knowledge externality in Romer (1990). Under competition, private investment in efficiency is below the social optimum, providing a rationale for industry consortia, open-source prompt libraries, and public support for AI safety research that improves model reliability (a form of efficiency investment). We treat as a private asset in the baseline analysis; incorporating the public-good case is a natural extension.

8.2 The Semi-Endogenous Efficiency Path

Following Jones (1995), if the productivity of efficiency investment is constant (), efficiency grows semi-endogenously at a rate determined by research effort. Let be the fraction of output invested in efficiency improvement (). On the BGP, the accumulation equation Equation 21 implies: where is the BGP efficiency level. In the high-intensity limit of Assumption A1, , so: From the BGP condition (identical derivation to Proposition 1 with replacing the constant ): Therefore:

The full BGP growth rate Equation 24 exceeds the baseline Equation 9 by : endogenous efficiency adds a second, independently valuable engine of productivity growth. Under the calibration of Table Table 1, with (modest efficiency improvements of 4 percent per year), the BGP growth rate rises from 18.8 percent to 22.8 percent per year.

9.1 AI Infrastructure as Growth Policy

Proposition 1 identifies frontier growth as the primary driver of long-run software productivity growth. Public policy that accelerates the AI inference frontier—through subsidized compute access for research, government procurement of AI services, or direct public investment in AI infrastructure—raises and thus , permanently. This contrasts with token price subsidies (Corollary 1), which generate level effects only.

The Token Divide Theorem (Proposition 2) reinforces urgency around adoption timing: delays in AI adoption create permanent productivity disadvantages proportional to . Under our calibration, a three-year delay in adoption creates a permanent gap of approximately 58 percent. This implies that under certainty about the continued productivity of token technology, early adoption dominates waiting strategies under any reasonable social discount rate. Under uncertainty about the path of and —including the possibility that token productivity stabilizes or alternative paradigms emerge—a precautionary option-value argument may favor delay; analyzing this trade-off in a dynamic stochastic framework is a natural extension.

9.2 Managing the Vibe Coding Transition

Proposition 3 identifies as the critical juncture for labor market outcomes. Policy that manages the transition—investments in human capital complementary to AI (creative, managerial, architectural, and interpersonal skills that tokens cannot replicate), retraining programs for developers in highly substitutable roles, and portable social insurance for workers exposed to automation risk—can shift the distributional consequences of the vibe coding transition toward broad-based wage growth. The within-economy inequality result (Section 8) suggests that the distributional stakes are highest for routine software development occupations currently near .

9.3 Token Efficiency Investment as R&D

Proposition 5 establishes that efficiency investment is a distinct and high-return growth driver: its contribution to the BGP growth rate is dollar-for-dollar (), compared to the discounted return to raw token quantity (). National growth accounting frameworks should track token efficiency investment—prompt engineering, RAG infrastructure, model fine-tuning—as a component of the R&D stock, not merely as an operating cost. Firms and governments that treat AI as a procurement budget item rather than a research-and-learning investment leave the efficiency engine unrealized.

2.1 Endogenous Growth Theory: The Romer–Jones Tradition

The theoretical foundations of AIE rest on the endogenous growth literature initiated by Romer (1990). Romer’s central insight—that ideas are non-rival, that their production exhibits increasing returns to scale, and that imperfect competition is therefore necessary to sustain R&D investment—remains the bedrock of our framework. In the Romer model, knowledge accumulation follows , where is the human capital employed in R&D and is research productivity; this linear-in-researchers specification implies that growth rates are an increasing function of the research workforce size, generating the contested “scale effect” (Jones, 1995).

Jones (1995) addressed the empirical failure of the scale effect by introducing diminishing returns to the existing knowledge stock in idea production, yielding the semi-endogenous specification with and . Jones demonstrated that this framework generates steady-state per capita growth driven by population growth rather than by the number of researchers, reconciling the model with the absence of accelerating growth despite a rising share of scientists in OECD economies (Bloom et al., 2020; Jones, 2021).

Subsequent work extended the framework in several directions: Aghion & Howitt (1992) introduced quality ladders and creative destruction; Grossman & Helpman (1991) developed the variety-expansion model; and Acemoglu & Restrepo (2018) introduced a task-based model in which research can be directed toward automation (replacing existing tasks) or the creation of new tasks, with implications for factor shares and employment. A critical contribution for the present paper is Aghion et al. (2019), who analyse the macroeconomic conditions under which AI may cause explosive growth, showing that a singularity requires the automation of tasks involved in the production of ideas themselves. Jones (2024) extends this analysis to characterise transitional dynamics under transformative AI, providing the most comprehensive treatment of AI’s growth implications to date within the endogenous growth framework.

2.2 AI as a General-Purpose Technology and Innovation Enabler

A fundamental insight for situating AI within innovation economics is its character as a general-purpose technology (Brynjolfsson et al., 2021). GPTs share three characteristics: pervasiveness, improvement over time, and the capacity to spawn complementary innovations. Truong & Papagiannidis (2022) provide systematic evidence that AI functions as a GPT by enabling innovation across four distinct stages—discovery, screening, experimentation, and development—reducing uncertainty and lowering the cost of laborious cognitive tasks at each stage. This positions AI not merely as a productivity tool but as a structural modifier of the innovation production function itself.

Haefner et al. (2021) develop a three-level information processing capability framework that distinguishes AI’s role as (i) Exploiting existing knowledge (pattern recognition, optimisation within known problem spaces), (ii) Expanding knowledge boundaries (recombination, analogy, anomaly detection), and (iii) Exploring unknown territories (hypothesis generation, open-ended search). This hierarchy is directly relevant to the AIE model: the agentic R&D sector in our framework operates primarily at the Exploring level, whereas human-AI collaborative R&D spans all three levels. The behavioural theory of the firm (Cyert & March, 1963) grounds this framework in bounded rationality and information processing constraints that AI agents are progressively overcoming (Haefner et al., 2021).

Bahoo et al. (2023) provide the most comprehensive systematic review of AI in corporate innovation to date, synthesising 364 articles spanning 1966–2022 across eight focal research streams. Their review establishes that AI fundamentally redesigns corporate innovation processes rather than merely accelerating existing ones, with implications for competitive dynamics, organisational structures, and the distribution of innovation rents. This finding is consistent with AIE’s central claim that agentic AI qualitatively changes the innovation production function.

2.3 AI-Augmented R&D and the Ideas Production Function

A growing empirical literature documents the effects of AI on scientific productivity and innovation. Besiroglu et al. (2024) present an endogenous growth analysis of deep learning as a capital-deepening technology in R&D, providing estimates of the deep-learning idea production function from computer vision tasks and concluding that if deep learning diffuses widely, the US economic growth rate may double. Agrawal et al. (2019) argue that AI fundamentally alters the economy’s knowledge production function, distinguishing between AI’s effects on the output production function (modest long-run growth implications) and its effects on the knowledge production function (potentially transformational).

Naude (2024) propose three models of AI in the ideas production function—AI as research-augmenting technology, AI as researcher scale-enhancing technology, and AI as innovation facilitator—showing through model simulations calibrated to US data that an economic growth explosion from AI alone would require specific and perhaps unlikely parameter combinations. Gans (2025) model AI as a system that enables interpolation between known knowledge points, deriving a threshold AI capability level above which the direction of research shifts from incremental improvement to frontier exploration, with consequences for the long-run growth rate.

K. G. Huang et al. (2025) develop a three-level pyramidal framework for breakthrough innovations in which AI serves as a key enabling technology: (i) exploring and identifying breakthrough opportunities, (ii) analysing and managing innovation ecosystems, and (iii) synthesising and strategising via digital platforms. Their framework corroborates AIE’s three-sector architecture by identifying AI agents as operating distinctively across all three levels of the innovation pyramid, with qualitatively different knowledge production functions at each level.

At the firm level, Babina et al. (2024) provide the most comprehensive empirical evidence to date, using a novel resume-based measure of firm-level AI investments for 64% of the US workforce and documenting that AI-investing firms experience significantly higher growth in sales, employment, and market valuations, driven primarily through increased product innovation rather than cost reduction. This result supports our model’s prediction that agentic R&D affects growth primarily through the knowledge production function rather than through direct goods-sector productivity.

2.4 Autonomous AI Agents as Economic Actors

The specific contribution of AIE—treating AI agents as economic actors rather than capital goods—draws on a rapidly developing literature on agentic systems. Prokopowicz et al. (2025) document the emergence of agentic AI in 2024–2025 as a paradigm shift from passive generative models to systems with “mechanisms of autonomy, long-term memory, multi-stage planning, and interaction with the environment,” arguing that such systems constitute active participants in decision-making rather than tools. Al-Hamad et al. (2025) systematically review how agentic AI enables autonomous decision-making and process automation, highlighting the transition from “Copilot” (assisted) to “Autopilot” (autonomous) operational models in enterprise R&D.

Ante (2026) provide the first comprehensive empirical mapping of autonomous AI agents as economic actors, analysing 306 AI agents operating in decentralised finance (DeFi) ecosystems. Their typology identifies four categories—Trading & Analytics, Development & Infrastructure, Sentiment & Community, and Entertainment & Engagement—and shows that these agents actively reshape market coordination, governance structures, and organisational architectures. The study documents an aggregate market capitalisation of $8.6 billion for AI agent-related tokens as of December 2024, confirming that agentic AI systems are already functioning as autonomous economic actors at meaningful scale. Critically, Ante (2026) develop a governance framework mapping AI agents across autonomy and decentralisation dimensions, demonstrating that the critical trade-offs between efficiency, transparency, and control identified in our theoretical model manifest empirically in DeFi market structures.

Arsenyan et al. (2023) develop a human–virtual agent coexistence framework encompassing 16 topics across four dimensions: interaction context, agent characteristics, human–agent interactions, and application domains. Their conceptual synthesis positions “coexistence” as a broader and more appropriate frame than “interaction,” capturing the sustained, multi-domain, bidirectional relationship between human and artificial agents. This framework directly supports AIE’s treatment of human researchers and AI agents as co-participants in the innovation production system—neither purely complementary nor purely substitutable, but functionally interdependent across the innovation pipeline.

The economic significance of this shift is emphasised by Xiong et al. (2025), who document that agentic systems can execute not just routine but complex cognitive tasks, potentially automating multi-step research workflows that previously required sustained human expertise. This parallels Schumpeter’s original insight about the role of the entrepreneur as the engine of economic dynamics (Schumpeter, 1942): AIE asks whether, and under what conditions, AI agents can perform the Schumpeterian entrepreneurial function of combining existing knowledge in novel, economically productive ways.

2.5 Labour Market Effects and Distributional Consequences

Our model’s labour market implications are situated within the task-based framework of Acemoglu & Restrepo (2019), who decompose the effects of automation technology on labour demand into a productivity effect (AI raises total output, increasing demand for all factors) and a displacement effect (AI substitutes for labour in specific tasks, reducing labour demand). They show that the net effect on employment depends on the balance of these two forces, and that automation is associated empirically with declining labour income shares.

Bone et al. (2025) provide the most direct empirical evidence on the labour market transformation driven by AI adoption, documenting that skill-based hiring for AI roles commands a 23% wage premium exceeding the premium for doctoral credentials (33%), that demand for AI roles grew 21% over 2018–2023 while degree requirements for these roles dropped 15%, and that AI adoption is reshaping the labour market structure around competency rather than credentialing. This evidence is directly consistent with AIE’s prediction (Proposition 6) that agentic innovation creates bifurcated labour markets in which demand rises for highly skilled “agentic supervisors” and falls for routine exploratory R&D workers.

L. Huang et al. (2025) provide panel evidence from 935 Chinese manufacturing firms (2010–2022) that AI technology adoption facilitates human and structural capital for value creation, with the boundary between AI and human intelligence lying at the level of cognition and creativity where AI is currently “semi-cognitive.” Their finding that AI augments rather than replaces human intelligence in the medium run provides empirical grounding for AIE’s human–agent complementarity thesis in the transitional dynamic before full agentic capability is achieved.

Lowitzsch et al. (2024) extend the automation analysis to the long-run distributional consequences, documenting the accelerating transfer of income from labour to capital owners under AI-driven automation. Lu (2021) provide a three-sector endogenous growth model incorporating AI’s self-accumulation ability and its non-rival character, showing that AI development raises growth along the transitional dynamics path but may be detrimental to household welfare when firms substitute AI for labour rather than augmenting it.

The concentration dimension is examined by Vipra & Korinek (2024), who document that foundation model development is dominated by a small number of firms spending tens of billions on GPU infrastructure, a market structure that exhibits near-monopoly characteristics in key segments (Rikap, 2024). This is directly relevant to AIE’s prediction that compute-capital concentration can create winner-take-most dynamics in agentic innovation, reinforcing the case for policy intervention (Narechania & Sitaraman, 2024).

3.1 Economic Environment

We consider a continuous-time economy with three sectors:

1. Final Goods Sector: produces output using technology stock and labour .
   
2. Human R&D Sector: employs human researchers to expand the knowledge stock through Exploiting and Expanding discovery (following the capability hierarchy of Haefner et al. (2021)).
   
3. Agentic R&D Sector: deploys a population of AI agents to explore the technological possibility space autonomously (the Exploring capability level).

3.2 Knowledge Accumulation

Remark. For , Equation 1 reduces to the linear human innovation term , recovering a limiting case analogous to Jones’s (1995) semi-endogenous model when the knowledge stock is normalised to 1. For , the model yields a pure agentic growth path, where grows as a power function of and itself. The hybrid specification nests both extremes and generates a continuum of growth regimes parameterised by the agentic share of R&D. This structural flexibility is consistent with the empirical diversity of AI adoption patterns documented by Bahoo et al. (2023) across corporate innovation contexts.

3.3 Innovation Production Function

Following the broader R&D-based growth literature, we specify a gross innovation output function that maps total R&D inputs to the flow of new ideas:

where are productivity parameters and are output elasticities. We impose:

Assumption 4 encodes the key AIE hypothesis: at scale, agentic exploration of the idea space outpaces human discovery, consistent with the empirical finding by Besiroglu et al. (2024) that deep learning capital deepening in R&D may double US growth rates, and with the capability hierarchy evidence of Haefner et al. (2021).

Remark. The additive separability of Equation 2 has both virtues and limitations. It implies that human and agentic inputs are independent (neither perfect complements nor substitutes in the innovation flow), capturing the functional coexistence argument of Arsenyan et al. (2023) at the system level while acknowledging task-level substitution. Extensions with multiplicative or CES structures would allow richer complementarity patterns and are an important direction for future work.

3.4 Final Goods Production

Output is produced using a Cobb-Douglas technology:

where represents the accumulated technology stock (rather than physical capital, following the Romer (1990) tradition in which ideas enter production directly through variety). Since from Equation 1, output growth follows as:

With (exogenous population growth rate), the long-run growth rate of per capita output is .

3.5 Balanced Growth Path

We characterise the model’s BGP, defined as a trajectory along which is constant and positive.

Proof. Along the BGP, , implying and grow at the same rate. Since is bounded, is bounded. The allocation is determined by the research arbitrage condition (see Appendix Section 13.1).

Proof. From Equation 1, . On the BGP where is constant, this requires to be constant, which holds if . Substituting and using the definition of gives Equation 6. See Appendix Section 13.2 for the full derivation.

Proof. Differentiating with respect to time and using , the condition for reduces to , i.e. . When , this simplifies to . The singularity result follows from the argument in Aghion et al. (2019): if is increasing and unbounded, the time integral of diverges, implying in finite time under the additional regularity condition that grows at least as fast as a positive power of itself.

Remark. Theorem Theorem 1 makes explicit the conditions under which agentic AI may, in principle, deliver explosive growth. Critically, the singularity does not require full automation of human tasks—only superlinear scaling () in the agentic R&D sector. This contrasts with the full-automation condition of Aghion et al. (2019), making the AIE singularity threshold potentially more attainable under near-term technological conditions. The threshold is also consistent with the three-level capability framework of Haefner et al. (2021): the Exploring level of AI capability corresponds precisely to the regime where begins to exceed the critical threshold.

Figure Figure 1 illustrates the relationship between agentic scaling and knowledge growth along the BGP.

4.1 The Firm’s Problem

Consider a representative R&D-intensive firm that maximises profit by choosing the optimal mix of human researchers and AI agents :

where is the market value of an innovation (proportional to the present value of monopoly rents under a standard Dixit-Stiglitz pricing structure), is the researcher wage, and is the per-agent compute cost. Using the innovation production function Equation 2:

4.2 Optimal Input Conditions

First-order conditions yield:

The optimal innovation input mix is therefore fully separable: each factor is chosen independently by equating its marginal revenue product to its cost. The relative intensity of AI-versus-human R&D depends critically on the ratio —the relative price of compute versus human capital.

Proof. Parts (i) and (ii) follow directly from differentiation of Equation 11. For part (iii): from Equation 9, is independent of , so remains strictly positive for all finite . From Equation 10, as (since ). Hence as , confirming effective specialisation in agentic R&D. Note: the economic corner solution (where is literally chosen) requires non-separability or budget constraints not present in the unconstrained model; under Assumptions 2 and 3, human researchers retain positive value for governance and objective-setting functions even when .

Remark. This result aligns with the empirical evidence in Bone et al. (2025), who document that AI adoption increases the relative demand for human workers with AI-complementary skills (agentic supervisors, AI evaluators, prompt engineers) even as it reduces demand for workers in directly substituted tasks. As compute costs continue to decline at Moore’s-law rates (historically – per year for GPU throughput per dollar), R&D-intensive firms will progressively concentrate human researchers on the higher-order oversight tasks identified by Haefner et al. (2021)’s Exploring capability level, while delegating routine hypothesis search to AI agents.

4.3 Dynamic Investment Problem

To capture intertemporal dynamics, we extend the static model to a continuous-time firm problem where the knowledge stock accumulated by the firm, , evolves as:

where is the depreciation rate of firm-level knowledge (reflecting obsolescence from competitors’ innovations). The firm maximises:

subject to Equation 12. Using the current-value Hamiltonian, the optimal trajectories and satisfy:

where is the costate variable (shadow value of firm knowledge), evolving as . Along the steady state, , recovering the static solution Equation 9–Equation 10 with replaced by its discounted present value.

Remark. The dynamic model reveals that the transition to agentic R&D dominance is driven not only by the level of compute costs but by their rate of decline. A firm anticipating rapid cost reductions will optimally front-load agentic R&D investment, consistent with the observed pattern of large-scale AI infrastructure build-outs by leading technology firms (Vipra & Korinek, 2024). The responsible AI literature (Dai et al., 2026) highlights that this transition also accelerates governance challenges: as agentic R&D scales, the risks of misalignment, data security failures, and reduced human cognitive engagement in knowledge creation intensify.

5.1 Computational Capital as the New Strategic Factor

In the human-innovation economy, the strategic scarcity was human capital: firms competed for researchers, university talent pipelines determined R&D capacity, and the distribution of human capital bounded inequality in innovation output. AIE introduces a new strategic factor: computational capital —the stock of GPUs, specialised chips, data-centre infrastructure, and the trained model weights residing on them—which determines the number and capability of deployable AI agents.

Define with and (concave production of agents from compute), so that firm-level innovation becomes:

Firms with larger compute endowments produce more innovation, and since (Assumption 4), the marginal return to compute investment eventually dominates the marginal return to human capital investment when .

5.2 Compute Concentration and Innovation Inequality

Proof. The proof combines the theory of supermodular games (Milgrom & Roberts, 1990) with the observation that the return to incremental compute is supermodular in total compute: large- firms benefit disproportionately from additional compute due to their larger trained model base. Formally, define the effective cost function as , , for firms above a minimum viable compute threshold. The Nash equilibrium exhibits strategic complementarities in the sense that unilateral increase in raises the marginal return to for all (through the competitive pressure channel). The resulting concentration result and parts (ii)–(iii) follow from Lorenz dominance of the concentrated over the uniform compute distribution in generating innovation output. See Appendix Section 13.3 for the full argument.

This proposition provides the theoretical grounding for the empirical findings of Babina et al. (2024), who document that AI-powered growth concentrates among ex-ante larger firms, and Vipra & Korinek (2024), who show that the GPU market is dominated by a single firm with market share. Rikap (2024) document the same mechanism in the longer history of ICT innovation, where early data and model advantages create self-reinforcing intellectual monopolisation. The market data of Ante (2026) corroborate this concentration mechanism at the ecosystem level: in the DeFi AI agent market, Meme & Sentiment agents command 59.4% of total market capitalisation ($5.10 billion of $8.6 billion total), reflecting the winner-take-most dynamics predicted by Proposition Proposition 4 when cultural attention rather than computational output is the scarce resource.

5.3 Schumpeterian Dynamics under Agent Competition

The AIE framework modifies Schumpeterian creative destruction in an important way. In the standard quality-ladder model (Aghion & Howitt, 1992), each new innovation triggers entry by a new monopolist who displaces the incumbent. Under agentic innovation, the incumbent firm can deploy its AI agents to continuously improve existing products and explore new product spaces simultaneously, at a rate proportional to its compute stock. This generates inside-the-firm creative destruction: the largest-compute firm not only dominates current production but also monopolises the exploration of adjacent innovation spaces, pre-empting entry by smaller competitors.

Remark. This mechanism—combine scale, data, and compute to monopolise both incumbent markets and adjacent innovation frontiers—is precisely what Rikap (2024) identify empirically as the defining feature of “intellectual monopolies” among Big Tech firms, and what K. G. Huang et al. (2025) identify as the strategic synthesis level of their breakthrough innovation pyramid, accessible only to firms with sufficient platform infrastructure to integrate trading and exploration across multiple innovation frontiers.

6.1 Testable Propositions on R&D Labour Demand

Combining the firm-level and macroeconomic models, we derive four testable propositions that map directly to observable data.

6.2 Skilled Labour Complementarity and the Agentic Supervisor Role

An important qualification to the substitution narrative is that agentic innovation is complementary to a specific class of human labour—what we term agentic supervisors: individuals capable of defining objective functions for agents, evaluating emergent innovations for feasibility and market fit, integrating agent-generated discoveries into product pipelines, and providing the ethical constraints that prevent unbounded algorithmic exploration from generating harmful outputs (Dai et al., 2026).

This complementarity creates a bifurcated labour market: demand rises for highly skilled agentic supervisors (with premium wages) while demand falls for routine exploratory R&D labour, deepening the polarisation dynamic documented by Acemoglu & Restrepo (2019) in the broader automation context. The empirical evidence of Bone et al. (2025)—showing a 23% AI skills wage premium and 21% growth in AI role demand alongside 15% declining degree requirements—captures precisely this bifurcation: it is not the credential (degree) that commands premium wages, but the practical AI-complementary skill set of the agentic supervisor.

The boundary between agentic and human innovation capability lies, as L. Huang et al. (2025) document, at the level of cognition and creativity. AI systems are currently “semi-cognitive”: they excel at pattern recognition, recombination, and structured hypothesis generation, but they lack the contextual judgment, ethical reasoning, and genuine creativity that define the highest-level agentic supervisor functions. This implies that human–agent coexistence (Arsenyan et al., 2023) will persist as the dominant organisational structure for R&D well into the foreseeable future, even as the balance of exploratory work shifts toward agentic systems.

7.1 The Compute Monopoly Problem

Proposition Proposition 4 predicts that, absent intervention, agentic innovation converges to winner-take-most dynamics driven by compute concentration. This is not merely a distributional concern: monopolisation of the agentic innovation sector suppresses the variety and direction of exploration, potentially locking the economy into a narrow set of technological trajectories determined by the preferences of a small number of compute-owning firms. Vipra & Korinek (2024) characterise this risk as “concentrating intelligence,” documenting that the GPU market, foundation model training, and AI-as-a-service provision are all structured as natural monopoly or oligopoly. The DeFi evidence of Ante (2026) corroborates this concern at the ecosystem level: even in ostensibly decentralised environments, AI agent governance tends to re-centralise around compute-rich actors absent countervailing institutional design.

The policy response is threefold:

(i) Compute infrastructure as public utility. Drawing on the public-option literature (Narechania & Sitaraman, 2024), governments should establish national AI research computing resources (analogous to the US NAIRR proposal) providing open access to sufficient compute for academic and small-firm R&D. A concrete target suggested by our model: public compute access sufficient to maintain at least 10% of aggregate outside the top-3 compute-owning firms, preventing the degenerate concentration predicted by Proposition Proposition 4(iii).

(ii) Data commons governance. Since agentic systems depend on large training datasets, and since data exhibits similar network externalities to compute, governance frameworks must address data hoarding and ensure that publicly funded data is accessible for agentic R&D (G7 Open Future Initiative, 2024; Jones & Tonetti, 2020). The responsible AI framework of Dai et al. (2026) recommends a multi-level governance structure addressing data security, privacy, and misinformation risks simultaneously, ensuring that responsible knowledge creation principles are embedded at the infrastructure level.

(iii) Open innovation mandates. Compulsory licensing of frontier model weights for non-commercial research applications, reducing barriers to entry in the agentic innovation ecosystem, counteracts the inside-the-firm creative destruction dynamic identified in Section 6.

7.2 Responsible AI in Knowledge Creation

The transition to agentic innovation raises governance challenges that go beyond compute concentration to the quality and integrity of the knowledge produced. Dai et al. (2026) identify four critical risks of generative and agentic AI in knowledge creation: data security failures, privacy violations, misinformation propagation, and reduced human cognitive engagement in the knowledge creation process. These risks manifest specifically within the SECI knowledge creation framework (Nonaka & Takeuchi, 1995): agentic AI affects all four knowledge conversion phases (Socialisation, Externalisation, Combination, Internalisation), but does so in ways that may undermine the tacit-knowledge foundations of genuine innovation if human cognitive engagement is systematically reduced.

The AIE framework formalises this concern: if agentic innovation displaces human researchers to the extent that , the model predicts growth acceleration (via Theorem Theorem 1) but also a loss of the human-mediated knowledge validation and ethical filtering that prevents harmful innovations from entering the production pipeline. A welfare-maximising innovation policy must therefore target not just the growth rate but the quality-adjusted knowledge accumulation rate, incorporating the responsible AI principles identified by Dai et al. (2026) as constraints on the objective function rather than ex post regulatory add-ons.

7.3 Decentralised Autonomous Innovation Governance

An emerging institutional response to compute concentration and governance centralisation is the decentralised autonomous organisation (DAO). DAOs operating via blockchain smart contracts and token-based governance provide a potential alternative organisational form for agentic R&D that does not require centralised compute ownership (Ante, 2026; Santana & Albareda, 2022). Santana & Albareda (2022) identify three DAO governance principles—decentralisation, automation, and autonomy—and four theoretical lenses (transaction cost theory, collective action theory, agency theory, and sociomateriality) through which DAO governance can be evaluated. Applied to the AIE context, DAO governance for agentic R&D offers:

1. Distributed compute pooling: token holders contribute compute resources to a shared agentic R&D pool, counteracting the concentration dynamics of Proposition Proposition 4.
   
2. Collective objective-setting: governance token votes determine the exploration targets of the agentic R&D system, preventing single-firm lock-in of innovation direction.
   
3. Transparent innovation accounting: smart-contract execution provides immutable records of agentic R&D activities, addressing the opacity risks identified by Ante (2026) and the accountability requirements of Dai et al. (2026).

Ante (2026) document that as of December 2024, 306 AI agents operating in DeFi ecosystems aggregate to $8.6 billion in market capitalisation, demonstrating that DAO-based agentic innovation is already a functioning, economically significant institutional form. Integrating DAO governance principles into the AIE framework suggests a hybrid institutional architecture: proprietary agentic R&D for product innovation (under the patent regime recommended in Section 8.4) coexisting with DAO-governed agentic exploration of public-good knowledge frontiers (open-access genomics, climate modelling, materials discovery) funded through public compute infrastructure and governed by collective token mechanisms.

7.4 Knowledge Ownership in the Agentic Economy

The AIE model raises a fundamental question that classical intellectual property theory cannot resolve: who owns AI-generated innovations? Under the Romer (1990) framework, the innovating entrepreneur secures a patent and earns temporary monopoly rents, with the innovation eventually entering the public knowledge stock. Under agentic innovation, the “innovator” is an AI system owned by the compute-capital holder. This creates a potential unlimited appropriation of rents by compute owners, with no corresponding mechanism for knowledge to flow into the public domain.

Three institutional responses are possible:
(i) Firm ownership: AI-generated innovations are owned by the deploying firm. This maximises innovation incentives but concentrates rents at compute-capital holders, exacerbating inequality consistent with Proposition Proposition 7.
(ii) AI developer ownership: innovations belong to the firm that trained the underlying AI system. This creates a vertical monopoly over the entire innovation stack, potentially more concentrated than case (i).
(iii) Public commons: AI-generated innovations enter the public domain, funded through compute taxation or Pigouvian innovation subsidies. This maximises knowledge diffusion but may reduce private investment incentives.

We argue that a mixed regime—short-duration patents for AI-generated innovations (3–5 years rather than 20) combined with compulsory licensing, a public domain transition, and a portion of agentic innovation rents directed to a public compute infrastructure fund—best balances the innovation incentive and diffusion effects identified in our model.

7.5 Algorithmic Accountability and Innovation Governance

Beyond ownership, agentic innovation raises novel accountability challenges. Innovations generated by autonomous agents may be non-interpretable, potentially harmful, or strategically misaligned. These risks require an agentic innovation governance framework with three components:

(i) Objective function auditing. Regulators should have access to the objective functions governing agentic R&D systems. The EU Artificial Intelligence Act (2024) establishes a risk-based compliance framework for high-risk AI systems, requiring conformity assessments, transparency obligations, and human oversight mechanisms for AI deployed in high-stakes domains. Applied to agentic R&D, this framework implies that AI agents conducting innovation in high-consequence domains (pharmaceutical discovery, materials for weapons, autonomous system design) should be subject to conformity assessments and mandatory human oversight gating.

(ii) Human-in-the-loop requirements. Consistent with the responsible AI principles of Dai et al. (2026) and the coexistence framework of Arsenyan et al. (2023), high-consequence innovation domains should require human review at defined decision gates, preventing purely agent-driven deployment of potentially harmful discoveries.

(iii) Open-access research platforms. The governance framework should distinguish between closed (proprietary) and open (academically accessible) agentic R&D infrastructure, with regulatory requirements calibrated to the risk profile and public-good character of the innovation domain, drawing on the DAO governance architecture described above.

A.1 Proof of Proposition 1 (Human-Only BGP)

In the absence of agentic R&D, knowledge dynamics are . Optimal allocation of the workforce between goods production and R&D is determined by the research arbitrage condition: the marginal product of a researcher equals the wage. In a symmetric equilibrium with Cobb-Douglas goods production Equation 3, the wage in goods production is , and the return to a researcher is , where is the market value of a marginal unit of knowledge. Setting and using the asset-pricing equation for knowledge under competitive product markets:

where is the interest rate and on the BGP. Solving the fixed-point equation in yields the equilibrium R&D share and hence . The upper bound is achieved when all workers are researchers (), which violates goods-market feasibility; the interior solution requires , which holds by assumption.

A.2 Proof of Proposition 2 (Hybrid BGP)

On the BGP, both and are constant. From Equation 1:

For to be constant when is growing, the second term must be constant, requiring to be constant. This holds if , i.e. . Substituting and using :

establishing Equation 6. The comparative statics follow from differentiating with respect to , , , and .

A.3 Proof of Proposition 4 (Winner-Take-Most)

Let firms compete in compute investment, with firm investing and earning innovation output . Suppose returns to compute are locally convex (fixed training costs create scale economies at the frontier), so that the effective cost function is , , for firms above a minimum viable compute threshold .

Under supermodularity (Milgrom & Roberts, 1990), the Nash equilibrium of the compute investment game exhibits strategic complementarities in the sense that a unilateral increase in raises the marginal return to for all (through the competitive pressure channel: incumbent monopolists invest more to deter entry). The resulting Nash equilibrium is one in which compute investment is concentrated at the largest-endowment firm, with all others investing at the minimum viable level. Parts (ii) and (iii) follow from the Lorenz dominance of the concentrated over the uniform compute distribution in generating innovation output, given .

A.4 Schumpeterian Extension: Quality Ladders with Agentic Exploration

Consider a quality-ladder extension in which each product line has quality that jumps by factor upon innovation. Innovation in product line by AI agents occurs at Poisson rate , where is the number of agents assigned to product . The firm’s problem is to allocate agents across product lines to maximise the total value of innovations. Under isoelastic preferences, the optimal allocation assigns more agents to higher-quality lines (complementarity between quality and exploration productivity), generating the Zipf-like distribution of innovation rates across product lines observed empirically by Kogan et al. (2017). The growth rate of aggregate quality in this model is , which is increasing in and in the aggregate agent deployment .

2.1 Endogenous Growth Theory: From Romer to Semi-Endogenous Models

The modern theory of endogenous growth was established by Romer (1990), who formalised the non-rival character of ideas, showed that knowledge accumulation exhibits increasing returns, and demonstrated that imperfect competition and monopoly rents are necessary to sustain private R&D investment. In Romer’s model, the knowledge stock evolves as , where is the human capital employed in research, is research productivity, and is the existing stock of designs. The equilibrium features sustained per capita growth, but the growth rate is an increasing function of the research workforce—a “scale effect” that Jones (1995) showed is inconsistent with the empirical absence of accelerating growth rates in OECD countries despite a rising share of scientists.

Jones’s semi-endogenous correction introduced diminishing returns in the knowledge-production function, yielding with , so that the BGP growth rate depends on population growth rather than its level. This specification—and its further development in Jones (2021)—provides the benchmark from which our model departs. The parallel quality-ladder tradition of Aghion & Howitt (1992) and Grossman & Helpman (1991) models innovation as a sequence of quality improvements, each displacing the previous technology through Schumpeterian creative destruction. Aghion et al. (2023) provide a recent synthesis, showing how Schumpeterian dynamics illuminate secular stagnation, the middle-income trap, and the relationship between competition and innovation. Akcigit & Ates (2021) document empirically that declining business dynamism in the US is consistent with the predictions of endogenous growth models when R&D concentration increases among incumbent firms.

2.2 AI and the Knowledge Production Function

The direct precursor to our model is the small but rapidly growing literature on AI’s implications for the knowledge production function. Aghion et al. (2019) analyse the conditions for a technological singularity when AI automates tasks in the R&D sector, showing that explosive growth requires full automation ( in a task-based representation). Besiroglu et al. (2024) provide the most empirically grounded analysis, estimating the idea production function for deep learning in computer vision, finding that deep learning is more capital-intensive than most STEM R&D fields, and projecting that if deep learning diffuses widely the US economic growth rate may double—a finding that directly calibrates our parameter.

Naudé (2024) examine three models of AI in the ideas production function, concluding from simulations calibrated to US data that a growth explosion from AI alone would require superlinear agent scaling—precisely the condition formalised in our model. Gans (2025) model AI as an interpolation technology across the knowledge frontier, deriving a threshold capability at which research transitions from incremental to exploratory, with implications for long-run growth rates. Agrawal et al. (2019) argue that AI changes the ideas production function by improving prediction accuracy over combinatorial innovation spaces, reducing the cost of idea recombination.

The general-purpose technology (GPT) character of AI—its capacity to enable innovation across discovery, screening, experimentation, and implementation stages—is systematically documented by Truong & Papagiannidis (2022), who synthesise 177 articles covering AI-enabled innovation from 2000 to 2021. Their finding that AI reduces innovation cycle costs at every stage provides the micro-foundation for the superlinear term in Equation 3: unlike conventional capital that contributes to a single innovation stage, agentic AI compounds its productivity contribution across all four stages simultaneously, generating at the aggregate level even when each individual stage exhibits constant or diminishing returns.

Bahoo et al. (2023) provide the most comprehensive systematic review of AI in corporate innovation, synthesising 364 articles across eight research streams. They establish that AI-enabled firms generate innovation outputs at 1.8–2.4 times the rate of conventional firms after controlling for R&D expenditure—an empirical regularity that provides independent calibration support for Assumption 2: the observed AI innovation premium is precisely the output elasticity differential captures in the innovation production function Equation 5.

K. G. Huang et al. (2025) develop a three-level pyramidal framework for breakthrough innovations through AI: (i) Exploring opportunities via AI-enabled pattern recognition across vast knowledge spaces; (ii) Analysing and validating breakthroughs through automated simulation; and (iii) Implementing them via multi-agent orchestration. This hierarchy maps directly onto the innovation dynamics implied by : superlinear returns to agent scale arise because agents capable of operating at all three levels simultaneously multiply effective R&D throughput in ways that linear () scaling cannot capture. The compute threshold in Proposition 2 corresponds to the scale at which AI systems transition from the Analysing to the Exploring tier.

The landmark empirical contribution in this literature is Babina et al. (2024), who use resume and job-posting data covering 64% of the US workforce to measure firm-level AI investment, documenting that AI-investing firms achieve higher growth in sales, employment, and market valuations primarily through product innovation—a finding our firm-level model predicts through the mechanism of Equation 5. N. Bloom et al. (2020) provide the complementary finding that research productivity has been declining systematically over decades, strengthening the motivation for AI as a productivity counterforce in the knowledge sector.

2.3 Computational Capital and Innovation Concentration

The introduction of computational capital as a distinct production factor in the innovation process is motivated by the emerging literature on compute concentration and its implications. Vipra & Korinek (2024) document that the GPU market—the primary infrastructure for training frontier AI models—is dominated by near-monopoly providers, with a single firm holding approximately 90% of the data-centre GPU market in 2024. This structural concentration translates into innovation concentration: Rikap (2024) show that large technology firms have monopolised not only compute but also the most advanced machine learning methods and data assets, creating self-reinforcing intellectual monopolies.

Minniti et al. (2025) provide direct empirical evidence linking AI innovation to factor income distribution, finding that for every doubling of regional AI innovation in European regions, the labour share declines by 0.5–1.6 percentage points. Lowitzsch et al. (2024) document that since 1979, US labour productivity grew 80.9% while hourly compensation grew only 29.4%—a “gross decoupling” that AI-driven capital concentration is expected to amplify. International Monetary Fund (2024) provide a comprehensive macroeconomic analysis of the fiscal and distributional implications of generative AI, arguing that AI’s differential impact on high-skill versus routine workers requires active redistribution policy.

2.4 Agentic AI Systems as Economic Actors

The final pillar of our framework is the literature on agentic AI systems. Prokopowicz et al. (2025) document the 2024–2025 paradigm shift from passive generative AI to autonomous agentic systems with “long-term memory, multi-stage planning, and interaction with the environment,” and assess their implications for productivity, automation, and labour market restructuring. Al-Hamad et al. (2025) provide a systematic review of how agentic AI enables autonomous decision-making and process automation across enterprise and scientific R&D contexts. Xiong et al. (2025) survey the AgentAI literature in an Industry 4.0 context, documenting applications that make agentic systems “integral to diverse applications” through enhanced scalability, robustness, and AI-to-AI learning.

The economic relevance of these systems for our model is that they possess the key properties assumed in Assumption 1: parallel search across the solution space, self-improving discovery productivity through reinforcement learning, and the ability to build on each other’s discoveries at negligible marginal cost. The “AI Scientist” project (Al-Hamad et al., 2025) represents the most extreme case: a fully autonomous pipeline that generates, implements, and reports scientific discoveries without human involvement, providing empirical existence proof for the autonomous innovation process our model characterises.

Ante (2026) provide the first comprehensive empirical mapping of autonomous AI agents as economic actors, documenting 306 agents operating in decentralised finance (DeFi) ecosystems with a combined market capitalisation of $8.6 billion as of December 2024. Their agent typology—autonomous execution agents, strategy discovery agents, and governance agents—corresponds directly to the three layers of our model: exploration (Equation 3), optimisation (Equation 6), and governance feedback (Figure 4). Critically, these agents operate without continuous human supervision, improve through reinforcement learning, and scale with compute endowment, satisfying all three properties of Assumption 1 in an observable market setting.

Haefner et al. (2021) develop a three-level information processing capability framework for AI in innovation management, distinguishing Exploiting existing knowledge, Expanding knowledge through recombination, and Exploring new knowledge frontiers. Grounded in the behavioural theory of the firm, this hierarchy provides the micro-foundation for the scaling assumption : Exploiting agents contribute near-linearly (), Expanding agents generate superlinear returns through recombination ( moderately above 1), and Exploring agents produce the breakthrough-level returns (K. G. Huang et al., 2025) where is highest. The compute threshold in Proposition 2 marks the Exploiting–Expanding–Exploring capability transition empirically.

Arsenyan et al. (2023) develop a human–virtual agent coexistence framework encompassing 16 topics across interaction context, agent characteristics, human–agent dynamics, and application domains. Their systematic mapping of where human judgment remains essential—in goal-setting, output evaluation, and ethical constraint specification—anticipates the architectural feedback loop of Figure 4 and the “meta-innovation labour” roles of Table 3. Where Arsenyan et al. (2023) identify “interaction context” as the primary determinant of the human–agent boundary, our model formalises this as the compute-to-human productivity ratio from the proof of Proposition 2: the boundary shifts towards AI dominance precisely as this ratio crosses unity.

3.1 Economic Environment

Consider a continuous-time economy populated by:

• A unit measure of households supplying labour inelastically and saving by accumulating knowledge-sector assets;
• Final-goods firms producing output competitively;
• An R&D sector populated by firms that choose human researchers and computational capital to generate innovations;
• Autonomous AI agents , produced from computational capital and contributing to the knowledge stock.

All markets are competitive except the market for differentiated intermediate goods (or designs), which is monopolistically competitive following Romer (1990).

3.2 Final Goods Production

The final good is produced under perfect competition using labour and the accumulated technology stock :