Multidecadal dynamics project slow 21st-century economic growth and income convergence

The paper addresses the central question of how global and regional GDP per capita may evolve over the 21st century and the extent of income convergence across countries. Economic growth trajectories shape poverty reduction, demographic change, technological progress, environmental pressures, and geopolitical dynamics. Existing projections span an order of magnitude by 2100, creating deep uncertainty for climate and development planning. The Shared Socioeconomic Pathways (SSPs), widely used in climate research, illustrate divergent futures—from rapid growth and strong convergence (SSP5) to slow growth and persistent inequality (SSP3). The authors note that such high-growth scenarios imply very different societal and environmental outcomes (including additional warming if unmitigated) and are used with limited guidance about plausibility. Motivated by longstanding empirical patterns linking GDP per capita levels to their growth rates, the study investigates whether historical multidecadal dynamics constrain plausible 21st-century growth paths and whether simpler empirically grounded models can provide consistent, informative long-run forecasts.

Prior work includes statistical long-run growth forecasts, expert elicitations, and scenario frameworks (e.g., SSPs) that collectively imply wide uncertainty, with 2100 world GDP per capita varying by an order of magnitude. Slow-growth outlooks are associated with limited trade/cooperation and weak convergence; faster-growth outlooks with strong innovation and rapid convergence. Many scenarios and forecasts do not directly include damages from climate change or other disruptions. SSP5 envisions very high growth and convergence, while SSP3 is much slower with persistent inequality; these differences alone can drive about 1 °C additional warming under no-policy conditions. Recent studies suggest: linear (additive) rather than exponential productivity growth; potential overstatement of growth in autocracies; and limited cross-country income convergence in recent decades. Expert and statistical projections (e.g., Christensen et al., Müller-Stock-Watson, Startz, Rennert et al.) span outcomes from SSP4-like to SSP5-like, with substantial uncertainty bands.

The study employs two complementary approaches: (1) a simple empirically fitted differential-equation model (DEM) capturing the observed hump-shaped relationship between GDP per capita (G) and its growth rate, and (2) the complex International Futures (IFs) integrated assessment modeling platform.

Differential-Equation Model (DEM):

• Empirical pattern: GDP per capita growth rises at low/middle income levels and declines at higher income levels, peaking around 5,000–15,000 (2005 USD PPP). This pattern is linked to structural factors such as demographic aging, shifts from manufacturing to lower-productivity-growth services, and institutional/developmental constraints in poorer economies.
• Functional form (non-asymptotic DEM): Ġ(t) = a + b ln(G(t)) + c [ln(G(t))]^2, estimated by least squares using 1960–2020 data aggregated at World Bank income-group level (conversions to 2005 USD PPP). Annual growth is measured as 100[ln G(t) − ln G(t−1)].
• Asymptotic DEM: Ġ(t) = [1/G(t)](a + b ln(G(t)) + c [ln(G(t))]^2), allowing growth to approach zero asymptotically as G → ∞.
• Projection: Set Ġ(t) = 100 dG/dt / G and solve numerically using 2020 income-group initial conditions. Correct for variance and heteroskedasticity in growth rates due to lognormal compounding by adding σ^2(G)/2 to the projected instantaneous growth rate. σ(G) is estimated with an Empirical Dynamic Modeling-inspired weighting scheme and interpolated via spline; for out-of-range G, hold σ at σ(G_max).
• Uncertainty exploration: Bootstrap the DEM fits 1,000 times by resampling observations within income groups to generate ranges of 2100 outcomes. Also produce historical projections starting in 1980, 1990, 2000, 2010, and 2020 to test stability.
• Comparison with IMF: Compile IMF World Economic Outlook country forecasts (2004–2020; 1–5-year horizons), aggregate to income groups, and compare to DEM hindcasts to assess relative predictive performance.

International Futures (IFs) model:

• A dynamic, annually recursive, data-rich integrated assessment framework with a general equilibrium economic core linked to demographic, energy, agriculture, environment, health, and poverty modules. It tracks >700 variables and draws on >5,500 data series.
• Economics: Production based on capital, labor, and multifactor productivity with extensive drivers; SAM-based tracking of financial flows; partial equilibrium detail in energy and agriculture; income distribution (lognormal) and poverty representation using Gini.
• Demography: Cohort-component model with endogenous fertility (driven by GDP per capita at PPP, contraception, infant mortality, education) and mortality by cause, age, and sex.
• Energy and emissions: Partial-equilibrium energy system (oil, gas, coal, hydro, nuclear, renewables), with technology, resource dynamics, prices, energy intensity convergence, and fuel-specific carbon contents determining CO2 emissions.
• Implementation: Run IFs base case and SSP scenarios within IFs for consistency; convert GDP per capita outputs to 2005 USD PPP. Use UN Medium population for aggregation where needed. Compare IFs base and SSP markers on population, extreme poverty (<$1.90/day 2011 PPP), primary energy, and CO2 emissions.

Data sources include World Bank Databank conversions and indicators, UN Population Division, IIASA SSP database, and other cited datasets. Figures summarize fits, projections, and comparisons across models and scenarios.

• Historical growth dynamics: A robust hump-shaped relationship links GDP per capita levels to their growth rates, with peaks around 5,000–15,000 (2005 USD PPP). High-income regions exhibit declining per-capita growth consistent with demographic aging and shifts to services.
• DEM projections (world): From starting points as early as 1980, the DEM consistently projects 2100 world GDP per capita of roughly 35,000–45,000 (2005 USD PPP), similar to SSP4 (“Inequality”).
• DEM projections (income groups, non-asymptotic): By 2100, low-income ~25,000–35,000; lower-middle-income ~30,000–45,000; upper-middle-income ~35,000–50,000; high-income ~35,000–55,000 (all in 2005 USD PPP). Relative to SSP4: slightly faster growth in low-income, slower in high- and upper-middle-income groups, similar in lower-middle-income.
• Upper bounds: The non-asymptotic DEM implies an upper limit near ~55,000 (2005 USD PPP) where growth goes to zero. The asymptotic DEM removes this cap and yields qualitatively similar outcomes but allows the high-income group to reach ~100,000 by 2100.
• Timing sensitivity to SSP5-like growth: If the world follows DEM growth through 2030 then switches to SSP5 rates, 2100 GDP per capita is ~33% below SSP5 (≈110,000), akin to SSP1; switching in 2050 yields ~54% below SSP5 (~75,000), similar to SSP2; switching in 2075 results in outcomes similar to SSP4/asymptotic DEM. Achieving SSP5 by 2100 would require immediate and sustained departures from historical dynamics.
• Forecast accuracy vs IMF: In high-income group, DEM (1980 start) mean error ≈ −0.37 percentage points per year in growth, with a 2020 level error of 14% after 40 years; asymptotic DEM bias ≈ +0.6 p.p./y. IMF median 3-year forecast error in the 2010s ≈ +0.76 p.p./y. DEMs show positive bias in upper- and lower-middle-income groups (+1.0 and +1.5 p.p./y). In low-income group, DEM biases are large (+3.5 p.p./y from 1980; +2.0 p.p./y from 1990), slightly larger than IMF’s (~+1.9 p.p./y for 2-year forecasts), suggesting DEM projections may be best-case for low-income growth.
• IFs base vs DEM and SSPs: IFs base broadly aligns with DEMs for low-, lower-middle-, and upper-middle-income groups and with the asymptotic DEM for high-income. High-growth SSPs (SSP1, SSP5) require rapid, unprecedented increases in productivity and sustained growth, inconsistent with historical structural transitions (e.g., services share).
• Development and environmental implications (IFs base): • Population: Trajectory between SSP3 and SSP4, close to UN 2019 Medium; higher than in SSP1/2/5 due to slower income-driven fertility declines. • Poverty and inequality: Higher poverty and between-country inequality versus high-growth SSPs, similar to SSP4 (more poverty early, less later). • Energy and CO2: Mid-range primary energy demand and CO2 emissions among SSP marker scenarios; CO2 path similar to SSP2-4.5, implying ~2–3.5 °C warming by 2100 without additional policy.
• Overall implication: SSP4 may better represent a realistic best-case for growth and convergence, while high-convergence pathways (SSP5/SSP1) would demand immediate and large deviations from entrenched historical patterns.

Findings indicate that entrenched multidecadal dynamics—aging populations and structural shifts toward services—are likely to continue suppressing per-capita growth at higher income levels, limiting the pace of global income convergence. Both a parsimonious DEM and the comprehensive IFs model point toward a slow-growth, slow-convergence future similar to SSP4. This challenges the common practice of treating SSP4 as a pessimistic edge case for development and suggests recalibrating scenario plausibility assessments in climate and development research. The observed predictive stability of the DEM since 1980 and its comparative accuracy against IMF short-term forecasts underscore the utility of simple, empirically anchored models for long-horizon, large-aggregate forecasting. At the same time, results highlight the risks of overestimating growth in low-income regions and the need for improved modeling there. Policy-wise, a slower-growth world implies higher poverty and population, potentially less innovation and adaptive capacity, and mid-range energy and emissions outcomes—raising the importance of targeted development, efficiency, and decarbonization strategies. High-growth, rapid-convergence futures would require transformative, near-term departures from historical relationships, potentially via breakthroughs (e.g., AI, energy) and changes in structural transition patterns, whose scale and likelihood remain uncertain.

The study demonstrates that incorporating the historical hump-shaped relationship between GDP per capita and its growth yields consistent, robust 21st-century projections of slow growth and modest convergence, aligning with SSP4. A simple DEM and the complex IFs model independently converge on this outlook, and the DEM would have outperformed IMF near-term forecasts at aggregate levels while still overpredicting low-income growth. These results suggest that research and policy should devote greater attention to slow-growth, slow-convergence scenarios and reconsider the plausibility assigned to high-growth SSPs. Future work should: refine forecasting for low-income regions; examine conditions enabling sustained deviations from historical dynamics (e.g., technological breakthroughs, structural policy changes); integrate explicit climate damage and shock modules; and compare across empirical/statistical and structural models to better characterize uncertainty and drivers of divergence in long-run economic projections.

• Deep uncertainty: Analyses are exploratory and do not capture the full range of possible long-run growth outcomes or structural breaks (e.g., pandemics, conflicts, transformative technologies). Bootstrap intervals reflect fit variability, not comprehensive scenario probabilities.
• Model scope: DEM is intentionally simple and suited to large aggregates over long horizons; performance at country or short horizons is not guaranteed. Positive bias in low-income forecasts indicates missing mechanisms (e.g., governance, conflict, data quality).
• Out-of-sample extrapolation: High-income projections extend beyond historical ranges used for fitting, especially for the asymptotic DEM, increasing uncertainty.
• Structural assumptions: Reliance on historical relationships (aging, sectoral shifts) may understate potential future deviations due to policy or technology. Many external damages (e.g., climate impacts) are not directly modeled in most scenarios/forecasts.
• Data/reporting issues: Potential biases in national accounts (e.g., autocracy overreporting) may affect historical fits and validation.
• Unit conversions and aggregations: Use of PPP conversions, income-group aggregations, and UN population pathways can affect projected aggregates and convergence assessments.