Multidimensional spatial inequality in China and its relationship with economic growth

The paper addresses how spatial inequalities across multiple development dimensions manifest and evolve in China, and whether these inequalities relate to economic growth following Williamson’s inverted U-shaped hypothesis. Spatial inequality undermines cohesion and sustainable development, and persists both between and within countries. Beyond income, disparities span education, healthcare, housing, infrastructure, digital access, and environmental burdens such as air pollution and carbon emissions. The COVID-19 pandemic further exacerbated multidimensional inequalities. The study asks: What are the levels of spatial inequality across economy, society, environment, infrastructure, and innovation in China? How have they evolved since 1990? Has rapid growth narrowed regional gaps? Do these inequalities follow inverted U-shaped dynamics with economic growth? The purpose is to provide a comprehensive, policy-relevant assessment that extends the inequality-growth relationship beyond income.

Classic work by Williamson (1965), building on Kuznets, posits an inverted U-shaped relationship between regional inequality and development: disparities widen early and narrow as economies mature, with links to Solow’s convergence hypothesis. Empirical studies offer mixed evidence: support in OECD countries and European case studies; challenges include lack of convergence (Baumol), inverted N-shaped or rising inequalities at high GDP per capita in some regions. In China, extensive research documents significant spatial economic disparities using CV, Gini, and Theil indices, evolving from east–west to north–south gaps, influenced by geography, transport, globalization, urbanization, technology, migration, and policy interventions (e.g., Western Development Strategy). Beyond income, studies show persistent inequalities in housing, digital access, secondary education, healthcare concentration, and evolving patterns in carbon intensity, car ownership, energy burdens, and innovation agglomeration. However, comparative multidimensional analyses remain scarce, and the applicability of Williamson’s hypothesis beyond economic indicators, particularly within China, is insufficiently tested.

Study scope: 31 provincial-level units in mainland China, 1990–2021 (Hong Kong, Macau, and Taiwan excluded). Indicators: 13 measures aligned with SDGs and China’s 14th Five-Year Plan/2035 goals, spanning five dimensions—economy (GDP per capita, disposable income per capita), society (rate of high school graduates and above, density of physicians, unemployment rate, living space per capita), environment (PM2.5 concentration, carbon emissions per capita, urban green space per capita), infrastructure (road density, internet penetration rate), and innovation (granted patents per capita, R&D expenditure per capita). Data sources: China Statistical Yearbook, Population and Employment Statistical Yearbook, China Census Yearbook, China Science and Technology Statistical Yearbook; internet penetration from China Internet Development Report; carbon emissions from MEIC; PM2.5 from Washington University in St. Louis. GDP converted to constant 1990 prices. Due to data constraints, living space, PM2.5, green space, road density, and internet penetration are available from 2000 onward.

Inequality and spatial analysis: The study employs the population-weighted coefficient of variation (WCV) to account for population size differences across provinces, alongside the Gini coefficient to corroborate inequality trends. Spatial autocorrelation and clustering are assessed using global Moran’s I (contiguity and inverse-distance weight matrices) to capture spatial patterning (clustering vs dispersion) not reflected in dispersion-only indices.

Growth–inequality coupling: To test relationships between inequality and economic growth, per capita GDP is used as the growth proxy. Log-linear, quadratic, and cubic models are estimated with WCV, Gini, and Moran’s I as dependent variables against ln(GDPpc), [ln(GDPpc)]^2, and [ln(GDPpc)]^3. Log transformations mitigate outliers and heteroscedasticity. Best-fit specifications are selected via goodness-of-fit, and curve types (monotonic, U, inverted U, N, inverted N) and turning points are inferred from estimated coefficients. Robustness is checked by substituting Gini for WCV and by alternative spatial weights for Moran’s I.

• Cross-sectional inequality: Innovation exhibits the highest spatial inequality (WCV for granted patents and R&D per capita typically >1 through much of the period), while social indicators show the lowest inequality (average WCV ≈ 0.33) with a declining trend. • Temporal evolution since 1990: Most indicators show decreasing spatial inequality. Exceptions include unemployment rate and carbon emissions per capita, which display rising inequality in the past decade and U- or N-shaped dynamics. • Regional patterns: Economic development and innovation remain concentrated in eastern coastal provinces, widening gaps with central and western regions. Conversely, inequalities in housing, healthcare access (physician density), roads, and digitalization have narrowed as central and western regions experienced faster growth in these indicators. Northeast China underperforms national averages in economy, education, roads, and innovation, with rising unemployment. Provinces such as Xizang and Guizhou show relatively high growth in several indicators due to transfers and strategic sectoral development (e.g., big data, tourism). • Spatial clustering (Moran’s I): Environmental indicators (PM2.5 and carbon emissions) show the strongest spatial clustering (Moran’s I often >0.15), indicating pollution concentration. Clustering in unemployment and green space declines to nonsignificance over time; innovation shifts from nonsignificant to significant clustering. Education’s clustering declines; GDP, income, housing, and physicians first rise then fall in clustering, suggesting movement toward spatial balance. Road density and internet penetration show increasing clustering, pointing to a spatial Matthew effect in infrastructure. • Growth–inequality relationships (WCV models): Inverted U-shapes are found for GDP per capita, disposable income, education, physician density, road density, internet penetration, granted patents, and R&D expenditure (turning points typically below about 28,000 RMB per capita GDP). Unemployment rate shows a U-shape. Living space per capita shows a monotonic decline in inequality with growth, implying turning point before 1990. Carbon emissions per capita follows an N-shape (turning points around 0.18 and 1.85×10^4 RMB), suggesting potential future increases in inequality. PM2.5, green space, and patents per capita exhibit inverted N-shapes; with China beyond the second turning point, inequality in these may continue to decline. • Growth–clustering relationships (Moran’s I models): GDP, income, housing, carbon emissions, and roads follow inverted U-shaped clustering with growth; physician density approximates an inverted U (formally inverted N with an early small first inflection). PM2.5 shows a U-shaped clustering trend with a turning point around 24,100 RMB (circa 2009). Internet penetration exhibits a positive linear rise in clustering despite declining inequality (WCV). Education shows a negative linear trend in clustering. • Robustness: Substituting Gini for WCV preserves curve shapes with minor shifts in turning points; Moran’s I trends are generally robust to alternative spatial weights (inverse distance), with road density being a noted exception.

Findings confirm that rapid economic growth in China is associated with declining spatial inequalities across many human-wellbeing dimensions, extending Williamson’s inverted U-shaped pattern beyond income to education, healthcare, infrastructure, and digitalization. However, environmental indicators behave differently: PM2.5 and carbon emissions exhibit strong spatial clustering, and carbon emissions inequality can rise again at higher development levels (N-shape), underscoring dynamic trade-offs between economic and environmental goals that vary by development stage. The results also reveal growing spatial concentration (clustering) in infrastructure (roads, internet) and innovation resources, even as dispersion measures decline, pointing to a spatial Matthew effect that may hinder balanced regional development. Regionally, eastern coastal provinces consolidate advantages in economy and innovation, while central and western regions catch up in social services and infrastructure; the Northeast’s underperformance and Xinjiang’s lagging trajectory require targeted interventions. Together, these outcomes address the study’s questions by quantifying the extent and evolution of multidimensional inequalities, demonstrating stage-dependent inequality–growth couplings, and highlighting domains where policy must reconcile efficiency with equity.

China shows the highest spatial inequality in innovation and the lowest in social indicators. Since 1990, most inequalities have declined, but unemployment and carbon emissions inequalities have risen recently. Environmental indicators display the greatest spatial clustering, while education, healthcare, and housing are trending toward more balanced spatial distributions. Infrastructure exhibits increasing spatial clustering despite declining dispersion. Regional gaps in economy and innovation have widened between eastern coastal and central–western regions, and the Northeast lags across multiple dimensions.

Williamson’s inverted U-shaped hypothesis extends in China to income, education, healthcare, infrastructure, and digitalization, but not consistently to environmental metrics, housing, or innovation. Spatial clustering of GDP, income, housing, carbon emissions, roads, and healthcare also follows inverted U-shaped patterns with growth. Nonlinear relationships among economic and environmental indicators suggest the need for stage-specific, dynamic policy mixes. Future research should unpack mechanisms behind innovation clustering, expand cross-country validations of multidimensional inequality–growth relationships, and integrate longer and finer-grained datasets to corroborate turning points and dynamics.

Data limitations constrain some indicators to post-2000, shortening time series and potentially affecting reliability of inferred turning points. While qualitative historical context suggests similar pre-2000 trends for several indicators, full validation is limited. The analysis is statistical and does not deeply investigate causal mechanisms, particularly regarding innovation clustering’s benefits and drawbacks. Findings are limited to China; external validity requires comparative studies in other countries and regions.