In order to estimate the causal impact of health spending on health outcomes, this study compiles a panel dataset of regional information over a 20-year period. The analyses exploit repeated observations on regions’ health spending and health. Similar to the previous estimation [6], we use regional fixed-effect (FE) models including year-specific dummy variables as regressors. Data from 17 regions and for the period between 2002 and 2022 were compiled.

The 17 regions pertain to the 17 ACs that are responsible for planning and delivering health services to their populations in Spain and which hold over 92% of the overall national health budget. The only areas that are excluded are the two autonomous cities (Ceuta and Melilla) that are centrally managed and together represented under a 0.037% share of the Spanish population. Data were collected from 2002, when the decentralization process that assigned healthcare competencies to ACs was completed. Currently, the latest data published for regional health spending are those of 2021, while regional information on life expectancy (LE) is available until 2022.

The regression model takes the form:

$$log(_)=\alpha +\beta (HCE}_)+}_\theta +_+_+u}_,$$

(1)

where \(_\) is population health observed for region i in time t, \(_\) is healthcare expenditure for region i in time t−1, \(}_\) is a vector of observed control variables for region i in time t−1, \(\theta\) is the associated parameter vector of the vector of observed control variables \(}_\), \(_\) is the time fixed effect, \(_\) is the regional fixed effect, and \(_\) is the idiosyncratic error term.

H and HCE are log transformed and so \(\beta\) can be interpreted as an elasticity: the expected percentage change in health given a 1% change in health spending. Health expenditure, along with the other explanatory variables, are lagged 1 year to allow for the expected delay in accruing a health benefit derived from variations in health spending.

Year and regional FEs account for both unobserved factors that may explain a common national trend in health spending and health as well as for unobserved time-invariant differences between regions. To explore any remaining biases that are not removed by the inclusion of FEs, we include a list of potential covariates, denoted by \(}_\), that captures potential differences in demographic, socioeconomic, lifestyle, contextual, and health factors not amenable to health spending, similar to the approach taken in Siverskog and Henriksson [8]. The potential impact of omitted variable bias in the estimates is often assessed by exploring movements in the coefficients when incorporating additional controls, with limited movements generally being interpreted as a sign of limited omitted variable bias. However, as noted by Oster [20], the lack of coefficient movements alone when controls are added is not sufficient to disregard omitted variable bias. She proposes a method that scales coefficient movements by movements in R-squared, arguing that small coefficient movements could be due to the low explanatory power of these additional covariates. Based on assumptions regarding the importance of the unobservable variables relative to the observable variables in influencing spending (denoted by \(\delta\)) and the share of variance of the dependent variable, which can be jointly explained by observed and unobserved variables (denoted by \(_\)), Oster proposes an approximation of the bias-corrected treatment effect that is derived as follows:

$$^\approx \widetilde-\delta \left[\dot-\widetilde\right]\frac_-\widetilde}-\dot},$$

(2)

where \(\dot\) is the estimate of β from the uncontrolled regression and \(\widetilde\) is the estimate of β from the regression including the control variables. \(\dot\) and \(\widetilde\) are the R-squared values from the uncontrolled and controlled regression, respectively. Oster argues that an appropriate upper bound of \(\delta\) is that of equal selection (i.e., \(\delta =1\)), which implies that the unobservable variables and observable variables are equally related to treatment and affect β in the same direction. The bound when \(\delta =0\) is \(\widetilde\), i.e., the estimate from the controlled regression. Therefore, the unbiased coefficient would lie within the bounds \(\left[^,\widetilde\right]\). The estimate of \(^\) also depends on the selected value of \(_\), the maximum explained variation, which because of idiosyncratic measurement errors Oster assumes to be <1 and proposes a value \(_=1.3*\widetilde\) based on external evidence on randomized studies. This value suggests a bound where the unobservable variables explain somewhat less than the observable variables. This assumption has some intuitive appeal if observable variables are chosen to include the most important factors explaining the outcome [21]. This approach allows us to construct a set of β with two bounds: \(\widetilde\), which is the estimate of β from the controlled regression, and \(^\), which is the effect of health spending on health corrected for omitted variable bias, given a value of δ and \(_\). \(^\) will be the upper bound if the effect of health spending on health is positive and omitted variables generate a downward bias, as it might be expected in the relationship between health and health expenditure. This is because health spending is partly determined by the level of healthcare needs, which in turn causes health outcomes, therefore, we expect models that do not account for omitted variable bias to show a downward bias in the relationship between expenditure and health. We used the Oster methods to estimate \(^\) using Eq. 1 as the controlled model, and we specify the uncontrolled models as:

$$log(_)=\alpha +\beta (HCE}_) +_+_+u}_.$$

(3)

The uncontrolled regression includes only the key variable of interest (in our case, healthcare spending) and observed covariates whose correlation with the key explanatory variable of interest is not informative about selection bias; this is the case of the regions and year FEs, which are fully captured and do not have unobserved counterparts [22]. We calculate \(^\) using the formula in Eq. 2, where \(\widetilde\) and \(\dot\) are the β estimated from Eqs. 1 and 3, respectively, and \(\widetilde\) and \(\dot\) are the within R-squared values from Eqs. 1 and 3, respectively. Following Oster’s suggestions, we use \(\delta =1\) and \(_=1.3*\widetilde\) to compute the upper bound estimate. In a supplementary analysis, we explored the assumption that \(_=1\) and applied the Stata command psacalc to estimate the Oster bias-corrected coefficients.

The main models are estimated using FE estimators. Population weightingFootnote 2 and adjustment of standard errors for clustering at the regional level are applied in all models. P-values lower than 0.1 are considered weakly significant, and p-values lower than 0.05 are considered strongly significant. A number of robustness checks are conducted including the use of different functional forms and lag structures. The impact of health spending on mortality and on QoL alone is also explored, as well as the changes on the estimated effect when recent years of data are added in the models. Analyses are conducted in Stata software v16.

Population health is measured using average quality-adjusted LE (QALE). Quality-adjusted LE is derived by combining information on LE and QoL. Information on region-year-specific LE can be obtained from life tables [23], which provide information on the number of years a cohort is expected to live if exposed, from birth through death, to the mortality rates observed at year t. This information is generally routinely available in most settings.

To estimate the system-wide incremental cost per QALY, QoL data are required on a QALY scale at population level. Unfortunately, there is not routinely, nor regionally representative data collected on QoL in Spain, which might also be the case in other settings. In Spain, the only source of nationally and regionally representative data on a relevant QoL instrument is the Spanish Health Survey conducted in 2011/12, which collected EQ-5D data from a sample of over 21,000 Spanish residents aged 15 years and older. The Spanish Health Survey is conducted every 4–5 years (available in 2003/04, 2006/07, 2011/12, and 2016/17) [24]. The European Health Survey in Spain is an additional source of regionally representative health data, which is also conducted every 5 alternate years (i.e., in 2009/10, 2014/15, and 2019/2020) [25]. Using the same approach as in the previous estimation [6], we predict age-gender-region-specific EQ-5D values based on a common set of health and socioeconomic variables included in all these surveys (see Appendix 1 of the Electronic Supplementary Material [ESM]). EQ‐5D models were stratified by gender and age groups (15–44, 45–64, and 65 or more years). Predicted EQ-5D scores by age-gender groups and by region and year were then applied to adjust LE, so that we obtain values of QALE using the approach described in Gaminde and Roset [26]. Predicted EQ-5D scores were assigned to each corresponding year when a health survey was conducted (either the Spanish Health Survey or the European Survey in Spain). For years in which predicted EQ-5D scores were not available (none of the surveys was conducted in 2005, 2008, 2013, 2018, and 2021), we used the values from the nearest year to adjust LE.

Quality-adjusted LE values provide the expected remaining number of healthy years individuals at a given age cohort x are expected to live (e.g., \(_=\) at birth, 1 year, 5 years, 10 years, …, 95 years). The average QALE of a given population can be computed as the population-weighted mean QALE across age cohorts:

where \(_\) is the share of the population in age group x. We use average QALE (\(_)\) as our main dependent variable.

The explanatory variable of interest is per capita annual public health expenditure. We have information on per capita region-year-specific annual health spending incurred annually by the ACs. This information is publicly available in Spain through the “key indicators of the NHS” website [27]. We used current expenditure for each year. The same coefficient estimates were obtained when using real values computed using gross domestic product deflator estimates for Spain. We denote our explanatory variable of interest, annual healthcare expenditure per capita, by \(HCE.\)

Using primarily the “key indicators of the NHS” website [27], we also compiled a set of control variables based on routine sources from the Information System of the Spanish NHS and data sources managed by other official organizations. These indicators are published by the Spanish Ministry of Health in the “key indicators of the NHS” website immediately after the data are published in the original source. Some indicators are updated annually, while some others are updated according to the periodicity of the original source, for example, some indicators are retrieved from the health surveys conducted every 2–3 years. A series of indicators were also obtained from data published by the National Institute of Statistics (INE, Spanish acronym) of Spain, which offers a large amount of freely accessible statistical information from official sources [28,29,30,31].

The set of potential confounders was carefully chosen to incorporate factors falling into five predefined categories: demographic factors (age and gender profile, population size, population density); socioeconomic factors (gross domestic product per capita, unemployment rate, immigration rate, and out-of-pocket spending on healthcare), lifestyle factors (smoking, sedentarism, obesity prevalence), contextual factors (labor cost and floor space price), and health factors non-amenable to health spending (traffic accident victims and labor accident rates). The latest variables were selected following the conceptual model proposed by Siverskog et al. [7], which emphasises that “we should be careful when controlling for morbidity, since measures of morbidity that are affected by (amenable to) healthcare will block the path between expenditure and life expectancy”. Table 1 summarizes the variables used in this study, their data sources, and their availability by year. When data were not available for a given year, information from the nearest year was used.

As noted, the estimated \(\beta\) in Eqs. 1–3 measure the spending elasticity of health, interpreted in our case as the expected percentage change in the average remaining QALE of the population given a 1% increase in annual healthcare spending. To translate this into the incremental cost per QALY, we use the following formulae:

$$Cost\, per \,QALY=\frac_}}_}}=\frac_}\frac_}}=\frac_}}_}}}} }=\frac_}}}}\frac_}},$$

(5)

where \(_\) is the average remaining LE of the population, computed using the same formulae as for \(_\) (Eq. 4). As noted by Siverskog and Henriksson [7], deriving the incremental cost per QALY based on these models that measure the impact of annual health spending on a measure of (quality-adjusted) LE, can be understood in two ways. First, as the average number of years left to live times the additional expenditure during each year (for a €1 increase in expenditure, this becomes simply the mean of \(_\)), divided by the change in QALYs due to the increase in health expenditure (for a €1 increase in expenditure, this is the marginal effect of health spending on health denoted by \(\frac_}\)). Second, and shown next in Eq. 5, it can alternatively be computed and understood as the additional expenditure per year (i.e., €1 increase) divided by the change in QALYs owing to the increase in expenditure allocated equally across remaining life-years (for a €1 increase, this is the marginal effect of health spending on health divided by the remaining LE, i.e., \(\frac_}\frac_}\)). The last two terms in Eq. 5 show how this is computed using the input from our regression models, where the \(\beta\) estimate is expressed as an elasticity rather than the marginal effect (i.e., \(\beta =\frac_}\times \frac }_}}\)). Using Eq. 5, we estimate the incremental costs per QALY corresponding to the estimated set of \(\beta :\) \(\left[^,\widetilde\right]\).