Health expenditure refers to the financial resources allocated by governments, private actors, households, and international partners to maintain and improve population health. ²⁴ It is an all-encompassing factor covering expenses for health issues, prevention, pharmaceutical costs, diagnostic costs, and health-related programmes, including training, research, awareness, and development. ⁷ From a broad perspective, health spending covers basic infrastructure, services, and supplies to deliver health care but not the expenditure on informal care and capital purchase of big items. ¹ In a socially sustainable approach Sentürk et al., ²⁶ averred that health spending is not only an input into the provision of services but a system that guarantees equity, resilience, and long-term intergenerational well-being. Social sustainability in health, therefore, is the ability of a system to achieve fair access, minimize exposure to poverty and catastrophe shocks, and support long-term duration in a fashion that maintains welfare in the long term in. ^{20, 22} Framing health spending in the broader sustainability framework helps scholars in the subsequent empirical reviews to examine the question of whether increased investment translates into long-lasting welfare improvements or whether inefficiencies, inequities, and frail institutions sabotage results.

Adegoke et al., ⁷ with the assistance of ARDL and causality tests of a panel dataset of Nigeria (1995-2020) uncover that while health outcomes in the first phase are beneficial from the expenditure, falling returns are quick to emerge and shed light on inefficiencies and inappropriateness between priorities and needs. The result highlights the significance of the health expenditure composition and the systems of governance through which it is channeled in the quest to achieve social sustainability. Disaggregated evidence for Nigeria strengthens this observation. Nnamdi and Ngwu ⁸ find that while private expenditure has a positive impact on life expectancy, public expenditure delivers detrimental weaker effects, reducing longevity while increasing mortality. These findings reveal that financing structure, rather than sheer volume, determines social sustainability. Voto et al. ⁶ also confirm that almost 30% of West Africans are pulled into poverty each year because of OPHS, widening inequities and undermining the sustainability of health gains. Such findings support Rahman et al., ¹⁷ utilizing panel cointegration and causality to document the mediating effect of governance in BRICS countries (1995-2021): functional government strengthens returns from spending, while faltering institutions weaken them. In Nigeria, where health spending is routinely fragmented and governance issues are rampant, such evidence explains why increased expenditures failed to shut sustainability gaps.

The broader SSA and developing comparative evidence provides additional methodological and conceptual refinement. Owusu et al., ¹¹ employing quantile regression of a panel (2000-2017), uncover heterogeneous effects across the health outcomes range and find that spending decreases infant and maternal deaths but with disparate advantages. Beşer et al. ¹⁶ also find using System-GMM of a panel (1990-2020) that health investment increments are associated with life expectancy increments in Africa but tenuous when fiscal and environmental sustainability are excluded from the picture. These confirm the necessity of policy arrangements that synthesize efficiency, governance, and sustainability principles in health systems financing. They also reinforce the extension of Grossman’s ¹² model from an individual-level stock of health capital to a system-level dynamic shaped by policy and macroeconomic institutions.

Outside Africa, evidence also highlights expenditure composition, efficiency, and institutional context. Onofrei et al., ¹⁰ analysing EU developing countries using panel regression (2000-2018), demonstrate that public spending is positively associated with improved outcomes, but fiscal discipline and institutional quality determine the scale of benefits. Polcyn et al. ²⁷ show, using CS-ARDL methods for Asian economies panel data (1995-2019), that higher health spending increases life expectancy, but effects are asymmetric and contingent on demographic pressures. Also, Gillani et al. ²⁴ establish lagged reactions in Asian panel datasets (1980–2018), and long-run equilibria are very different from short-run impacts—an empirical result very relevant to Nigeria’s policy environment. Magida et al. ²⁵ in South Africa using quantile regressions on the data (1994-2020) report that the spending effect varies across the mortality level and therefore verify Nigeria’s heterogeneous health finance outcomes. In general, the studies verify that the relationship between health finance and outcomes is nonlinear and not universal but is shaped by context, system efficiency, and governance architecture.

At the frontier of theory, Bala et al. ¹³ put Grossman’s demand-side health capital framework in perspective with a concurrent supply-side model and reveal that health outcomes result not just from private investment but also from health system financing and institutional mechanisms. Such theoretical refinement is consistent with empirical evidence from SSA and Nigeria where institutional frailties and dispersed financing systems vitiate health sustainability in the face of increased expenditure. Vărzaru ⁹ contributes a predictive angle where only nations applying sustainability values in health finance will realize stable welfare improvements. These results resonate with Pitkänen et al. ²⁰ and Adler, ²¹ who argue that social sustainability requires financing schemes that reduce inequalities while ensuring longevity and intergenerational welfare.

Confirmatory studies from other regions strengthen these conclusions. In India, Pradhan and Behera ²⁸ document catastrophic OPHS between 2000 and 2017, which mirrors the Nigerian experience of expenditure-induced traps of poverty. Sayuti and Sukeri ²⁹ similarly show, using time-series regression (2000-2018), how high OPHS undermines health outcomes of Malaysia, reinforcing that household-dominated financing models are unsustainable. In OECD countries, Silva et al. ³⁰ emphasize with panel regression (1995-2020) that private health expenditures interact with fiscal capacity, determining long-run sustainability. In China, Liang et al. ³¹ demonstrate using panel regression (2000-2016) that resource allocation: specifically health worker density, has stronger effects on mortality than raw spending volumes, highlighting the role of efficiency. Studies by Xiu et al.’s ³² and Gani’s ³³ continue the discussion and relate natural resource rents and wealth with health outcomes and reveal the constraint that fiscal space places on the success of spending. Despite the circumstances differing between the studies, they steadfastly verify the fundamental finding that without consistency of the structure of financing to institutional ability and sustainability principles, health spending is not achieving sustainable social outcomes.

Despite an expanding empirical base, critical gaps remain that this study addresses. Much of the SSA literature emphasises aggregate spending without disaggregating financing streams, limiting insight into how public, private, out-of-pocket and external components differently affect social sustainability. ^{2, 6, 16} Nigeria-specific analyses similarly prioritise aggregate trends, leaving the distinct roles of private versus public financing and the poverty-inducing effects of OPHS under-specified. ^{7, 8} Further, cross-sections or short-panels cannot reveal long-run equilibria, structural breaks, and lagged adjustment important for sustainability assessment in the long term. ^{1, 24, 34} Empirically, threshold and interaction terms are under-estimated in the case of Nigeria although with implications of their relevance in regional and BRICS applications. ^{7, 17} Therefore, the lacuna calls for robust time-series analysis that disaggregates spending and models nonlinearity and structural change to inform policy consistent with SDG3. This study uses ARDL and cointegration methods on long-run Nigerian series to explicitly estimate policy-relevant thresholds.

The current study follows an ex post facto research design grounded in Grossman’s health-capital model, extended to the macro level and embedded within a social-welfare (social-sustainability) interpretation. The presentation proceeds in four steps: (i) Grossman’s micro health production, (ii) the macro reformulation, (iii) the social-welfare (social-sustainability) function, and (iv) the empirical reduced form and dynamic specification used in this study. Grossman ¹² models health as a stock that individuals produce using a vector of inputs. In reduced form: H = f ( X ) (1) where H is the individual health stock and X is a vector of inputs (medical care, nutrition, education, time invested in health, and environmental and innate endowments). ²³ Health naturally depreciates at rate δ and evolves according to: H t + 1 = ( 1 − δ ) H t + I t , (2) where I t is gross investment in health (healthcare consumption, preventive measures, etc.). This formulation motivates viewing health as an accumulable capital stock that responds to flows of public and private inputs. ²³

Empirical and policy analyses extend Grossman to the aggregate (country) level. ^{35– 37} Fayissa and Gutema ³⁸ offer a compact macro specification that organises determinants into economic, social, environmental and health-service blocks: H = f ( Y , S , V , D ) (3) where at the national level H denotes aggregate health outcomes (e.g., life expectancy, infant/under-5 mortality), Y is a vector of economic variables (GDP per capita, public health spending, employment), S denotes social variables (education, demographic structure), V stands for environmental conditions (sanitation, disease burden, water access), and D captures health-service and system variables (coverage, facility capacity, immunization). In scalar (expanded) form this is: H = f ( y 1 , … , y n ; s 1 , … , s n ; v 1 , … , v n ; d 1 , … , d n ) (4)

Equation (3) organises potential inputs so that empirical work can test which blocks—and which specific inputs within blocks—drive population health. According to Sentürk et al.’s ²⁶ findings, population health is both an outcome and a fundamental component of social sustainability: health improvements support equity, resilience and intergenerational welfare. ³⁹ The current study, thus, formalise social sustainability (SS) as a social welfare function in line with Adler ²¹ that depends on health and complementary social goods: SS = g ( H , E , I , P ) , (5) where E is education/human capital, I is institutional inclusiveness and governance, and P denotes poverty reduction and equity. Under Equation (5), improvements in H raise SS ceteris paribus; conversely, persistently weak health undermines long-run social sustainability. ^{17, 21, 22, 26} Substituting the macro health production Equation (3) into Equation (5) gives the structural relation that guides empirical identification: SS = g ( f ( Y , S , V , D ) , E , I , P ) (6)

Equation (6) clarifies that health expenditures (part of Y and D ) influence social sustainability indirectly by changing H , consistent with the Grossman ¹² health production framework. ^{14, 23} The empirical strategy therefore examines whether disaggregated health financing (per-capita spending, recurrent, capital, out-of-pocket) yields durable improvements in the health stock that translate into higher social sustainability.

For operational clarity, the current study treats two observed SS health outcomes models: life expectancy at birth (LEX) and infant mortality rate (IMR), as proximate measures of H (and, by extension, of social sustainability). The baseline reduced-form relations are: LE X t = α 0 + α 1 HEXP c t + α 2 RHE X t + α 3 CHE X t + α 4 OPH S t + Γ Z t + ε t , (7) and IM R t = β 0 + β 1 HEXP c t + β 2 RHE X t + β 3 CHE X t + β 4 OPH S t + Λ Z t + μ t , (8) where HEXPc = health expenditure per capita, RHEX = recurrent health expenditure, CHEX = capital health expenditure, OPHS = out-of-pocket spending; Z t is a vector of control variables drawn from the Y , S , V blocks (e.g. GDP per capita, female literacy, sanitation coverage); ε t , μ t are disturbances. The current study’s a priori expectation is thus: α 1 , 2 , 3 > 0 and β 1 , 2 , 3 < 0 ; signs on α 4 , β 4 are ambiguous because OPHS can reflect both access and financial burden. ^{4, 6}

Because health is a stock and adjustments take time, a dynamic specification is required. We adopt the ARDL-Error Correction (ECM) approach ⁴⁰ to estimate short-run and long-run effects while allowing regressors of mixed integration orders. The ARDL form for LEX (Model 1) is: Δ LE X t = ϕ 0 + ∑ i = 1 p ϕ 1 i Δ LE X t − i + ∑ j = 0 q ϕ 2 j Δ HEXP c t − j + ∑ k = 0 r ϕ 3 k Δ RHE X t − k + ∑ l = 0 s ϕ 4 l Δ CHE X t − l + ∑ m = 0 u ϕ 5 m Δ OPH S t − m + λ ( LE X t − 1 − θ ′ X t − 1 ) + η t (9) and analogously for IMR (Model 2): Δ IM R t = ψ 0 + ∑ i = 1 p ψ 1 i Δ IM R t − i + ∑ j = 0 q ψ 2 j Δ HEXP c t − j + ∑ k = 0 r ψ 3 k Δ RHE X t − k + ∑ l = 0 s ψ 4 l Δ CHE X t − l + ∑ m = 0 u ψ 5 m Δ OPH S t − m + γ ( IM R t − 1 − ϕ ′ X t − 1 ) + ν t (10) where X t = [ HEXP c t , RHE X t , CHE X t , OPH S t ] ′ ; λ , γ are error-correction coefficients (expected negative); short-run dynamics are given by the Δ terms and the long-run multipliers by the normalized cointegrating vector θ (or ϕ ).

The ARDL approach is parsimonious, accommodates small samples, and yields straightforward long-run elasticities. ⁴¹ All estimations and diagnostic tests in the current study were conducted using EViews 12 econometric software, as it is well suited for handling dynamic models. ^{8, 25} Empirical identification relies on cointegration tests (ARDL bounds), for with EViews provides built-in routines that facilitate lag selection criteria, and robustness checks including alternative control sets, log-specifications, and tests for structural breaks and residual diagnostics (serial correlation, heteroskedasticity, stability).

To ensure empirical consistency and clarity, Table 1 provides the operational definitions, measurement units, and data sources for all variables employed in the study.

Table 2 shows the summary statistics of the study variables. It provides a snapshot of their central values and distribution.

Table 2 shows that LEX has an approximate average of 49.5 years, ranging from 45.49 (minimum) to 55.75 (maximum), with a standard deviation of 3.06 years. IMR on the other hand, averages at 15.7 deaths per 1,000 live births, which ranges from 10.99 to 18.87 (standard deviation = 2.33). HEXPc has a mean of US$58.0 per person, with values spanning US$15.2 to US$106.1 (standard deviation = 27.8). RHEX averages ₦134.5 billion, but varies widely between ₦0.15 billion and ₦459.3 billion (standard deviation = 148.8). CHEX is lower on average, at ₦22.7 billion, with a range of ₦0.38-53.9 billion (standard deviation = 19.1). OPHS averages at 62.3%, ranging from 9.44% to 77.27%, with a standard deviation of 22.0%. Also, Table 2 depicts the skewness coefficient that measures asymmetry degree the distribution. Most variables exhibit near-symmetry (skewness values close to zero), except RHEX (positively skewed) and OPHS (negatively skewed). The kurtosis values indicate that for LEX, IMR, HEXPc, RHEX, and CHEX, these are platykurtic (<3), while OPHS is leptokurtic (>3). The Jarque-Bera’s test of normality reveals that majority of the variables are normally distributed (p > 0.05).

4.2.1 Unit root results

Testing for unit roots is essential in time-series analysis to avoid spurious regression; a situation where non-stationary variables falsely appear related. ⁴² The Augmented Dickey-Fuller (ADF) test was applied to evaluate the null hypothesis of a unit root, ⁴³ with results presented in Table 3.

Table 3 ADF root tests reveals that all the variables (LEX, IMR, HEXPc, RHEX, and CHEX) except and OPHS are integrated of order one, or I ( 1 ) , indicating that each of them becomes stable after taking its first differences. However, OPHS was stationary at level. The purpose of testing for the stationarity properties of the variables in bounds approach to cointegration is because the ARDL bounds testing approach becomes applicable only in the presence of I ( 1 ) , I ( 0 ) variables or a mixture of both. This means that the assumption of bounds testing will collapse in the presence of I ( 2 ) variable. The ADF unit root results presented implies that the bounds testing approach is applicable in the current study, as the variables are integrated of order one, or I ( 1 ) and order zero, I ( 0 ) .

4.2.2 Co-integration results

The variables were found to be integrated of order zero, I ( 0 ) , and order one, I ( 1 ) , consistent with the requirements of the ARDL bounds testing approach, which allows for regressors with mixed integration orders provided none is integrated of order two, I ( 2 ) (Pesaran et al., 2001). The bounds test in Table 4 evaluates the null hypothesis of no long-run relationship among the variables, with co-integration confirmed if the calculated F-statistic exceeds the upper-bound critical value.

Table 4 presents the bounds test results for both models. In the case of Model 1, the F-statistic (14.22) is well above the 5% upper bound (3.49), while for Model 2, the F-statistic (6.22) also exceeds the critical values, although marginally. In both cases, the null hypothesis of no long-run relationship is rejected, confirming the existence of co-integration and thereby supporting the use of the ARDL error-correction framework.

Based on the co-integration from the bound tests, the second step is to predict the ARDL model to account for both the short-run adjustment as well as the long-run associations between health financing variables and social sustainability indicators (LEX and IMR). Table 5 presents the regression results for Model 1, including the error-correction estimates and the corresponding long-run coefficients.

Table 5 (ARDL regression results) reports the estimated short- and long-run effects of health financing variables on LEX in Nigeria. The study’s a priori expectations, given in Equation (7), are α 1 , 2 , 3 > 0 and an ambiguous sign for α 4 . In line with these priors, the short-run results indicate that HEXPc (β = 0.012, p < 0.05), RHEX (β = 0.008, p < 0.01), and CHEX (β = 0.015, p < 0.01) significantly raise life expectancy, both contemporaneously and with lags, highlighting the immediate and lagged benefits of public health financing. In the long run, HEXPc (β = 0.049), RHEX (β = 0.021), and CHEX (β = 0.063) remain positively associated with LEX, further reinforcing the view that sustained and well-targeted health investments improve social sustainability outcomes. By contrast, OPHS shows a mixed effect (β = –0.003 in the short run; β = –0.017 in the long run, both p > 0.1), which aligns with the ambiguous theoretical expectation that out-of-pocket spending can enhance access but also impose financial risks. The error correction term (CointEq(–1)) is significant and negative (β = –0.577, p < 0.01), in line with the assertion that about 58% of short-run disequilibrium is corrected each year, thus assuring convergence to long-run equilibrium. Overall, the model explains 95% variation in the level of LEX (R ² = 0.948; Adj. R ² = 0.893), while the DW-statistic (2.15) renders serial correlation absent, therefore affirming the robustness in the estimates towards policy use.

Table 6 presents the ARDL regression results for Model 2, with IMR as the dependent variable. The theoretical priors, following Equation (8), expect β 1 , 2 , 3 < 0 and an ambiguous sign for β 4 , since higher public health financing should reduce infant mortality, while OPHS may work in either direction. Consistent with these priors, the short-run results show that lagged HEXPc significantly reduces IMR (β = –0.011, p < 0.01; β = –0.007, p < 0.05), consistent with priors, while RHEX (β = 0.003–0.005, p < 0.01) and CHEX (β = 0.014–0.019, p < 0.01) unexpectedly increase IMR, pointing to short-run inefficiencies or misallocations. OPHS exhibits mixed behavior, simultaneously negative (β = –0.010, p < 0.05) but positive in lags (β = 0.008–0.012, p < 0.05), in line with performing simultaneously as cost burden as well as channel to access. Long-run coefficients for HEXPc (β = 0.049), RHEX (β = –0.007), CHEX (β = –0.163), and OPHS (β = –0.086) are statistically insignificant in the long run, which implies that mortality-reduction from health spending may depend on structural change rather than spending alone. The adjustment coefficient (CointEq(–1)) is significant and in the expected negative direction (β = –0.162, p < 0.01), validating sluggish correction of disequilibrium, with approximately 16% of short-run deviations being corrected in the long run, annually. The model explains 93% of IMR variation (R ² = 0.932; Adj. R ² = 0.836), while DW statistic (2.14) verifies lack of serial correlation, validating reliability in the model.

Diagnostic tests were carried out to examine the validity as well as the strength in the models in the ARDL. Following standard econometric practice, ⁴⁰ normality, serial correlation, as well as tests for heteroskedasticity were applied to the residuals. Results are summarized in Table 7.

Table 7 shows that for both models, the p-values exceed 0.05 in all tests, implying that the null hypotheses cannot be rejected. Hence, the models satisfy normality, are free from serial correlation, and exhibit homoscedastic residuals.

This research poses the health financing paradox in Nigeria as a question: spending is on the increase while health social sustainability is patchy, why? Like Grossman’s ¹² health capital theory that stipulates that increased spending will yield better health stocks, in Nigeria, we find systematic barriers to good health as well as weak governance inhibiting this effect. The theory is partially supported, especially in the case of life expectancy, while refuted in the application to infant mortality, weak governance, and systematic inefficiencies. The current study therefore both confirm and extend Grossman’s theory by locating spending in institutional as well as macroeconomic limitations.

The long-run impacts affirm that recurrent (β = 0.0099, p < 0.01) and capital spending on health (β = 0.1074, p < 0.01) raise life expectancy significantly, in line with interpreting health as durable capital stock. ²³ Corresponding results by Polcyn et al. ²⁷ in Asia and by Onofrei et al. ¹⁰ in the EU imply that Nigeria is in line with broader world trends in longevity increases. Yet, infant mortality has no significant long-run reaction to recurrent (β = –0.0070), capital (β = –0.1628), or out-of-pocket spending (β = –0.0856; all p > 0.1). This contrasts with Owusu et al., ¹¹ who report significant negative mortality impacts from health spending in 177 nations. Such divergence implies that institutional bottlenecks, rather than expenditure volumes, drive Nigeria’s underperformance.

Short-run dynamics enrich this paradox. Both recurrent (β = 0.0030–0.0047, p < 0.01) and capital spending (β = 0.0142–0.0189, p < 0.01) impact on infant mortality in positive directions—in contradiction to expectations. This can imply misallocation or lags in the effectiveness of spending, in that funds are not delivered to frontline primary health care services in time to affect mortality outcomes. Liang et al. ³¹ point out that health worker density and allocative efficiency are more important than aggregate spending, a lesson applied all too poorly in Nigeria’s urban-biased capital projects that leave rural infant health needs unaddressed.

The picture is complicated by out-of-pocket spending (OPHS). In the short term, this decreases infant mortality in the same period (β = –0.0098, p < 0.01), but later lags reverse the trend (β = 0.0116; 0.0085, p < 0.05). Long term, OPHS is not statistically significant (β = –0.0856, p = 0.1672). This is indicative of short-term access gains lost to regressive financial charges, as found by Voto and Ngepah ⁴ and Derkyi-Kwarteng et al., ⁵ who indicate that in Sub-Saharan Africa, OPHS worsens poverty. Similar evidence from India ²⁸ and from Malaysia ²⁹ finds that household financing leads to catastrophic spending that is anti-equity.

Theoretically, these findings challenge the sufficiency of Grossman’s model. While the theory explains increases in life expectancy, the theory underestimates institutional capacity, spending composition, as well as the composition’s contribution to outcomes. Sepehri ¹⁴ criticizes Grossman model’s individualism, and our evidence also agrees that spending effectiveness is conditioned by systemic situations. Rahman et al. ¹⁷ as well as Langnel and Buracom ¹⁸ also show that spending outputs are amplified by governance in BRICS as well as SSA.

The relevance of the findings also applies to the third Sustainable Development Goal (SDG 3) that places emphasis on “good health and well-being.” Albeit increased spending, Nigeria remains off-target in achieving SDG targets. ⁷ This buttresses Micah et al.’s ¹ conclusion that isolated funding is insufficient; judicious allocation, institutional reform, and sustainability principles are inevitable. Without judicious allocation and reform in the structure of government, increased spending in health can solidify inefficiencies rather than yield social sustainability.

The findings carry important policy implications. Firstly, Nigeria must reduce the overdependence on out-of-pocket spending on health, which still thrusts households into poverty while defeating progressive access to services. Scaling up pooled public funding instruments, such as national health insurance, is essential in insulating all those who are most vulnerable. Secondly, spending structure in health has to change. Recurrent spending and capital spending have to be directed towards primary health care, maternal and child health services, as well as rural health facilities rather than administrative overhead or urban-biased capital projects. Thirdly, government reforms in the form of transparency, accountability, and institutional capacity have to accompany spending. Without all these, increased spending will not translate into improved service delivery. Sustainable health systems are not merely about spending, but also about equity and resilience in distribution and management of resources.

Despite its contribution, the research has weaknesses. Its use in applying to Nigeria limits generalisability to other countries with divergent health system organisation and profiles in governance. Moreover, while the ARDL model captures dynamic relationships effectively, it does not explicitly include governance or institutional quality variables, which are increasingly recognised as critical mediators in health financing effectiveness. The research also does not address the impact from any potential nonlinearities or threshold impacts that can interfere in the interaction between health financing and outcome.

Future research should supplement these findings by integrating measures of institutional quality and governance into empirical models. Interaction terms such as “expenditure × governance” would provide insight into how institutional performance shapes the health financing impact. Nonlinear as well as threshold impacts may also be estimated through more advanced econometric techniques such as quantile ARDL or threshold regression to uncover spending impacts that change with health outcome levels or institutional advancements. Other SSA countries can increase generalisability as well as comparative understanding by expanding the analysis. Additionally, micro as well as spatial data: such as household surveys or regional health indicators, can provide nuanced understanding into equity, access, as well as distribution impacts from health financing.