Does club convergence matter? Empirical evidence on inequality in the human development index among Indian states

The paper addresses whether HDI levels across Indian states and union territories converge over time and, if so, whether they do so to a common steady state or into distinct convergence clubs. HDI, introduced by UNDP in 1990, encompasses health, education, and standard of living and is a prominent alternative to income-based measures of development. Despite global poverty reduction, inequalities in health, education, and income persist, affecting human development outcomes and social stability. In India, large interstate disparities and the impacts of events such as COVID-19 on health and education underscore the importance of assessing HDI convergence. The study tests the null hypothesis that HDI does not converge across states/UTs, using methods that allow for heterogeneous dynamics and club formation. Findings have policy relevance: if convergence patterns differ across groups, uniform national policies may be less effective than strategies tailored to clubs with similar transition paths.

Prior research on India has examined human development and income convergence using classical econometric approaches. Dholakia (2003) found causality between economic and human development with declining HDI inequality across major states despite persistent income disparities. Ghosh (2006) reported regional convergence in human development among 15 major states. Studies using beta and sigma convergence (Mukherjee and Chakraborty, 2007, 2011; Roy, 2012; Banerjee and Kuri, 2015) yielded similar convergence evidence. At finer spatial scales, Das et al. (2015) observed weak conditional convergence and absolute divergence among districts. Other works indicate multiple steady states and club convergence in income due to heterogeneity in initial conditions, human capital, technology, demographics, and institutions (Ghosh, 2008; Bandyopadhyay, 2011; Ghosh et al., 2013; Mishra and Mishra, 2018; Hembram and Haldar, 2019; Hembram et al., 2019). Health expenditure convergence analyses highlight non-income determinants and political factors (Apergis and Padhi, 2013; Youkta and Paramanik, 2020). While club convergence in HDI has been studied across countries and for Spanish provinces, a Phillips and Sul-based club convergence analysis of HDI for Indian states and UTs has been lacking, which this study addresses.

Data and sources: Annual HDI data for 36 Indian states and union territories from 1990–2019 are obtained from the Global Data Lab (GDL), which provides subnational HDI consistent with UNDP national HDI methodology. Missing years are interpolated/extrapolated from survey and census-based indicators; subnational indicators are population-weighted to match national values.

HDI construction: HDI is computed as the geometric mean of three indices: health (life expectancy at birth indexed between 20 and 85 years), education (average of indices for mean years of schooling, capped at 15 years, and expected years of schooling, capped at 18 years), and income (index based on logarithm of GNI per capita between 100 and 75,000). UNDP’s post-2014 categorization is used (low: <0.550; medium: 0.550–0.699; high: 0.700–0.799; very high: ≥0.800).

Inequality measures: Cross-state dispersion is tracked using standard deviation and coefficient of variation (sigma convergence), and inequality is assessed using Gini and Theil indices for both population-unweighted and population-weighted distributions at selected years (1990, 1995, 2000, 2005, 2010, 2015, 2019).

Convergence framework: The Phillips and Sul (2007, 2009) “log t-test” is applied to assess overall convergence and to identify endogenous clubs. The model decomposes HDI into a common component and time-varying idiosyncratic loadings; convergence is tested via the relative transition parameter and a log t regression with critical value -1.65 (one-sided). If overall convergence is rejected, a four-step clustering algorithm orders units by terminal-period HDI, selects a core group maximizing the t-statistic above -1.65, sequentially adds states passing the threshold, and repeats for remaining states to form initial clubs. Club merging tests are then conducted to determine if clubs can be combined. The magnitude of the estimated beta parameter provides a scaled measure of the speed of convergence. Kernel density estimation is used to examine distribution dynamics across benchmark years, revealing stratification, polarization, or unimodality patterns.

Spatial visualization: Clubs and HDI levels are mapped to examine geographic patterns, using GIS software for cartographic presentation.

• National HDI performance: India’s HDI rose from 0.429 (1990) to 0.494 (2000), 0.579 (2010), and 0.646 (2019), with average annual growth rates of approximately 1.42%, 1.60%, 1.22%, and 1.42% for 1990–2000, 2000–2010, 2010–2019, and 1990–2019, respectively. Growth accelerated in 2000–2010 and slowed thereafter.
• Inequality trends (Table 2): Cross-sectional dispersion declined over time, indicating sigma convergence. Population-unweighted Gini fell from 0.102 (1990) to 0.046 (2019) and Theil from 0.0158 to 0.0032; population-weighted Gini fell from 0.115 to 0.047 and Theil from 0.0039 to 0.0015. Standard deviation and coefficient of variation also declined.
• Overall convergence test (Table 3): The full-sample log t statistic is -15.2339 (< -1.65), rejecting overall convergence, implying heterogeneous transition paths and absence of a single steady-state for all states/UTs.
• Initial club formation (Table 3): Three convergent clubs identified: Club 1 (5 units: Andaman and Nicobar, Goa, Kerala, Lakshadweep, Puducherry; β=1.559; t=3.860), Club 2 (24 units; β=0.261; t=5.816), Club 3 (7 units: Assam, Bihar, Chhattisgarh, Jharkhand, Madhya Pradesh, Odisha, Uttar Pradesh; β=2.270; t=9.727).
• Club merging (Table 3): Club 1+2 merge test: β=0.2227; t=4.9388 (not merged per authors’ criterion). Club 2+3 merge test: β=-0.4874; t=-10.4350 (reject convergence), leading to two final clubs after merging decisions.
• Final clubs (Table 3): Two clubs emerge. Club 1 (29 units): Andaman and Nicobar, Andhra Pradesh, Arunachal Pradesh, Chandigarh, Dadra and Nagar Haveli, Daman and Diu, Goa, Gujarat, Haryana, Himachal Pradesh, Lakshadweep, Jammu and Kashmir, Karnataka, Kerala, Maharashtra, Manipur, Meghalaya, Mizoram, Nagaland, Delhi, Puducherry, Punjab, Rajasthan, Sikkim, Tamil Nadu, Telangana, Tripura, Uttarakhand, West Bengal (t=4.939). Club 2 (7 units): Assam, Bihar, Chhattisgarh, Jharkhand, Madhya Pradesh, Odisha, Uttar Pradesh (t=9.727).
• Convergence speeds (Table 4): Club 1 converges at approximately 0.112% and Club 2 at approximately 1.135%; average across clubs 0.624%. Lower-HDI states (Club 2) converge faster than higher-HDI states (Club 1).
• Distribution dynamics (Kernel density): 1990 exhibits stratification; 2000 and 2010 show polarization (twin peaks); by 2019 the distribution becomes more unimodal around the mean, indicating movement toward a common steady state despite club heterogeneity.
• Spatial patterns: Higher- and medium-HDI states cluster geographically distinct from the low-HDI group (Assam, Bihar, Chhattisgarh, Jharkhand, Madhya Pradesh, Odisha, Uttar Pradesh).

The study’s convergence tests show that Indian states and UTs do not converge to a single steady-state HDI but rather form distinct convergence clubs. This addresses the research question by demonstrating heterogeneity in development trajectories: higher and medium-HDI regions cluster into one club, while persistently lower-HDI regions form another. The faster convergence rate among the lower-HDI club suggests potential catch-up, consistent with conditional convergence in capabilities; however, overall non-convergence indicates persistent structural differences across regions. The kernel density evidence of stratification transitioning to polarization and then to a more unimodal distribution by 2019 supports the view that dispersion has decreased and that many states are moving toward a common central tendency, even as club structures remain. The significant declines in Gini and Theil indices corroborate reduced interstate inequality in HDI. Policy relevance is clear: uniform interventions may have limited impact where convergence paths differ. Tailored strategies acknowledging club-specific constraints and opportunities—particularly targeted investments in health, education, and income-generating capabilities in the low-HDI club—are essential to accelerate convergence and reduce disparities.

The paper contributes by providing the first Phillips and Sul-based club convergence analysis of HDI for all 36 Indian states/UTs over 1990–2019, integrating distributional analysis via kernel density estimation and inequality metrics. It documents two final convergence clubs with distinct speeds, a general decline in HDI inequality, and evolving distribution dynamics toward unimodality. Policy implications include designing regionally differentiated human development strategies aligned with each club’s convergence path to achieve horizontal equity. Future research could investigate spatial clustering mechanisms and drivers behind club formation, including institutional, demographic, and technological factors, and explore spatial econometric approaches to assess spillovers and neighbourhood effects.