Artificial intelligence and religious freedom: divergent paths converging on economic expansion

The paper investigates how technological change via artificial intelligence (AI) and institutional context via religious freedom interplay with traditional growth drivers (labor and capital) to shape economic growth. Motivated by historical links between technology and growth since the Dartmouth conference (1956) and the growing societal footprint of AI (including its interactions with religion), the study examines 26 countries over 2000–2021. It asks whether AI advancement and religious freedom contribute to economic performance alongside labor and capital. The study aims to fill a gap by jointly analyzing AI and religious freedom within a unified empirical framework and to assess their dynamic interactions using panel vector autoregression (PVAR). Contributions include: (1) documenting positive relationships among AI, religious freedom, and growth; (2) employing a combined PVAR and forecast-error variance decomposition (FEVD) approach to describe dynamics and predictive relevance; and (3) reaffirming the enduring importance of labor and capital while validating results via Toda–Yamamoto Granger causality.

On AI and growth: Early views (Aghion et al., 2017) likened AI to prior technologies with potentially transitory effects, while later work (Walton & Nayak, 2021; Borrellas & Unceta, 2021) emphasized AI’s adaptive learning and transformative potential. Concerns include job displacement (Liang et al., 2022; Osoba & Welser, 2017; Vermeulen et al., 2017), but productivity gains and innovation creation are highlighted (Damioli et al., 2021; Czarnitzki et al., 2023; Cockburn et al., 2018; Åström et al., 2022). Distributional issues may arise (Makridakis, 2017; Lim, 2022). A meta-view (Berdiyeva et al., 2021) suggests effects are context-dependent. On religious freedom and growth: Studies suggest links between religious liberty and prosperity, trade, finance, investment, and entrepreneurship (Gill & Owen, 2017; Gill, 2013, 2021; Qayyum et al., 2020; Cao et al., 2019; Squicciarini, 2020; Prasadh & Thenmozhi, 2019; Mavelli, 2020; Kim et al., 2021; Shahzad et al., 2014; Gutsche, 2019; Oyekan, 2023). Results are generally supportive though heterogeneous across contexts. On labor and capital: Extensive literature underscores their centrality to growth, via labor force dynamics, capital formation, productivity, skills, and capital deepening (Shahbaz et al., 2019; Abbas et al., 2020; Azenui & Rada, 2021; Topcu et al., 2020; Ahmed et al., 2020; Han & Lee, 2020; Alshubiri, 2022; Curtin et al., 2019; Liotti, 2020; Nordhaus, 2021). Overall, prior work indicates AI and religious freedom may affect growth, but joint empirical analyses remain limited, motivating this study.

Data and variables: Panel of 26 countries (limited by AI data availability) from 2000–2021. Measures: AI (number of AI-related patents, log; OECD), religious freedom (index 0–1; World Bank), economic growth (GDP, constant 2015 US$, log; World Bank), labor input (employment-to-population ratio, 15+ total %, ILO modeled estimate; World Bank), capital input (gross capital formation, constant 2015 US$, log; World Bank). Theoretical framework: Extends a production function grounded in Solow (1956) and Romer (1990), adding AI (technology) and religious freedom (institutional quality, Robinson & Acemoglu, 2012). The baseline log-linearized form: log eg_it = log A + a log li_it + b log ci_it + c log ai_it + d log rf_it + ε_it, with constant returns to scale (a + b + c + d = 1). Econometric approach: Panel vector autoregression (PVAR) treating ai, rf, eg, li, ci as endogenous: y_it = μ_i + α(L) y_it + α + δ_t + ε_it. Estimation via system-GMM after removing country and year fixed effects (Helmert/mean differencing). Lag selection: Schwarz information criterion for PVAR; Toda–Yamamoto causality uses maximum lag of one selected via AIC. Diagnostics: Cross-sectional dependence assessed using Pesaran (2021) CD-type tests; panel unit root tests that allow for cross-sectional dependence (Pesaran, 2007; Smith et al., 2004). Results show strong cross-sectional dependence and I(1) behavior; stationarity holds in first differences. Westerlund (2006) panel cointegration tests (with bootstrapped p-values) indicate failure to reject the null of no cointegration. Impulse response functions (IRFs) and forecast-error variance decomposition (FEVD): Orthogonalized IRFs via Cholesky decomposition (ordering: AI, religious freedom, labor input, capital input, economic growth), with 10,000 bootstrap iterations to construct confidence intervals; effects traced over a decade. FEVD computed at horizons 5, 10, 15, 20 periods to apportion forecast-error variance of economic growth to shocks in each variable.

• Cross-sectional dependence: Tests reject cross-sectional independence at 1% across variables and lags (Table 3). Variables are integrated of order one and stationary in first differences per Pesaran (2007) and Smith et al. (2004) tests (Table 4). Westerlund cointegration tests yield bootstrapped p-values of 0.168–0.447, failing to reject no cointegration (Table 5).
• PVAR(1) estimates (Table 6; coefficients with t-stats): • Effect on economic growth (Δeg): Δai−1 = 0.177** (2.118); Δrf−1 = 0.078** (1.973); Δli−1 = 0.383*** (5.124); Δci−1 = 0.584*** (4.498); own lag Δeg−1 = 0.864*** (8.791). This indicates AI and religious freedom positively and significantly contribute to growth alongside strong contributions from labor and capital. • Dynamic interactions: Δeg−1 positively affects Δai (0.291**, 2.053) and Δrf (0.205**, 2.022), suggesting feedback from growth to AI activity and religious freedom scores. Additional positive links include Δci−1 on Δli (0.717***, 3.231) and Δeg−1 on Δli (0.314**, 1.972) and Δci (0.352*, 1.779).
• Toda–Yamamoto causality (Table 7): • AI ↔ Economic growth: bidirectional causality (eg → ai: χ² = 9.556**, p = 0.028; ai → eg: χ² = 8.412***, p = 0.000). • Religious freedom → Economic growth: not significant at conventional levels in TY test (rf → eg: χ² = 4.053, p = 0.103), though PVAR lagged coefficients show a positive significant effect of rf on eg. • Labor ↔ Economic growth: bidirectional (li → eg: 12.564***, p = 0.000; eg → li: 8.978**, p = 0.024). • Capital ↔ Economic growth: bidirectional (ci → eg: 9.111***, p = 0.008; eg → ci: 11.906***, p = 0.000).
• Impulse response functions (Fig. 1): A one-standard-deviation shock to AI leads to a statistically significant, persistent increase in economic growth over a 10-period horizon. Shocks to religious freedom, labor input, and capital input also elicit significant positive responses in economic growth, consistent with theory and prior literature.
• Forecast-error variance decomposition (Table 8; percentage of eg variance explained): At horizon 20, AI accounts for 3.052%, religious freedom 2.267%, labor 13.107%, and capital 10.317% (own shocks of eg decrease from 80.541% at 5 periods to 69.258% at 20). The shares of AI and religious freedom increase with horizon, indicating growing long-run relevance. Overall, results indicate robust positive dynamic linkages among AI, religious freedom, and growth, while reaffirming the dominant roles of labor and capital. AI and growth reinforce each other, and RF exhibits positive dynamic associations with growth within the PVAR/IRF framework.

The findings address the central question by demonstrating that AI progress and religious freedom are positively associated with economic growth dynamics in a panel of 26 countries, even after accounting for traditional inputs. PVAR estimates and IRFs show that shocks to AI and religious freedom raise growth, suggesting these factors act as complementary engines alongside labor and capital. Bidirectional causality between AI and growth indicates feedback loops: stronger economies stimulate AI activity, while AI-driven technological change further accelerates growth. Labor and capital maintain strong, statistically significant effects on growth and exhibit bidirectional causality with output, consistent with established growth theory. Although Westerlund tests do not support long-run cointegration among the variables, short-run dynamics captured by PVAR and FEVD are economically meaningful, with AI and religious freedom gaining explanatory power at longer horizons. These results align with theories of endogenous growth, institutional economics, and human-capital augmentation, underscoring that technological and institutional environments jointly shape macroeconomic performance.

The study shows that AI development and religious freedom are positively linked with economic growth dynamics across 26 countries (2000–2021), complementing the enduring roles of labor and capital. FEVD indicates rising long-horizon contributions from AI and religious freedom to growth variance, and IRFs confirm positive growth responses to shocks in these variables. Policy implications include: (1) prioritize AI R&D, diffusion, and skills development; (2) protect and promote religious freedom to foster social trust, stability, and a conducive business environment; and (3) continue strengthening labor market policies and capital formation to support complementary effects with new growth catalysts. Future research could expand country coverage and time horizons, explore non-linearities and heterogeneity, employ alternative methods (e.g., machine learning, network models), and examine sub-domains and moderators (political, social, cultural) to refine mechanisms and context-specific policy guidance.

• Sample limited to 26 countries due to AI data availability, constraining generalizability across cultural, religious, and economic contexts.
• PVAR may not fully capture complex non-linearities among AI, religion, and growth; aggregation can mask within-domain heterogeneity.
• Focus on aggregate measures (AI patents, broad religious freedom index, GDP) may overlook sectoral and micro-level mechanisms.
• Potential moderating variables (political, social, cultural) are not explicitly modeled; cointegration tests suggest no long-run equilibrium relationships, focusing inference on short-run dynamics. Future directions include enlarging and diversifying samples; extending the time span; using non-linear, ML, and network approaches; studying sub-domains within AI, religion, and growth; and incorporating institutional, political, social, and cultural moderators for context-sensitive insights.