The health cost of reducing hospital bed capacity

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Introduction
In the past two decades, most high-income countries have reduced their hospital bed capacity (OECD, 2021).Bed reductions and changes in associated metrics such as length of stay or bed occupancy rates can be regarded as signs of more efficient resource use but could also reflect that health care is decreasingly providing adequate care to patients (Walsh et al., 2022).In this study, we use repeated cross-sections on hospital bed capacity (staffed beds per 1000 people) and population-standardised mortality (deaths per 1000 people) for all 21 Swedish regions between 2001 and 2019 to estimate the potential death toll from bed reductions in Sweden.
Observational studies have found that high bed occupancy rates are associated with higher mortality (Sprivulis et al., 2006;Schilling et al., 2010;Madsen et al., 2014;Boden et al., 2016), lower admission rates (Blom et al., 2014;Af Ugglas et al., 2020a), and higher rates of readmission (Blom et al., 2015;Af Ugglas et al., 2020a).There is also a large literature on emergency department crowding documenting adverse effects in terms of waiting times, delayed treatment, and exposure to medical errors, but with mixed results on mortality (Morley et al., 2018;Turner et al., 2020).Studies of Swedish health care, specifically, have found an association between emergency department crowding and mortality (Af Ugglas et al., 2020b, 2021) but not between occupancy rates and mortality (Af Ugglas et al., 2020a).
Our study differs from previous studies in two important respects.First, by using regional aggregate mortality we avoid problems with selection to sample on hospital admission and capture potential effects of reduced bed capacity for patients that do not seek care via an emergency departmentabout 55% of all hospitalisations (Swedish Agency for Health and Care Services Analysis, 2018) -and individuals who are never hospitalised.Second, we investigate the effect of regions' capacity to admit patient rather than the degree to which they are at capacity, thereby contributing more direct evidence on the benefits of providing additional beds; arguably the most straightforward way in which health policy can target problems associated with crowding in inpatient care.
Between 2001 and 2019, mortality and hospital bed capacity decreased across all Swedish regions but regions that made smaller reductions in beds experienced, on average, greater decreases in mortality.Using ordinary least squares (OLS) with two-way fixed effects (TWFE), we find that a reduction by three beds is associated with about one more death per year.We provide support for a causal interpretation by demonstrating that all factors that we identify as alternate explanations for this association (income, socioeconomics, provision of outpatient care) are balanced with respect to bed capacity and that the estimate is stable or increases when adjusting for these factors.To the extent that selection on observables is informative about selection on unobservables, it therefore seems our estimate may understate the benefits of providing more beds.
The findings of this study have some important policy implications.First, the potential health consequences of bed reductions have so far received limited attention from researchers (note exceptions above).We provide evidence of adverse effects in terms of a hard endpoint, suggesting that decreases in hospital beds per capita are not necessarily indicative of technological advances, which ought to be highly relevant for health policy by substantiating concerns about excessive reductions to a country's capacity for inpatient care.Further, because evidence on the health cost of reducing hospital beds translates to knowledge about the health benefits of providing more beds, our results can also help inform healthcare resource allocation decisions more explicitly.They imply that Swedish health care could generate health gains at a cost of about SEK 400,000 (~US$40,000) per quality-adjusted life year (QALY, the typical outcome used in cost-effectiveness analysis in health care) by providing more hospital beds.This evidence could support decision making about a potential expansion in bed capacity but could alsoconsidering that the capacity to admit patients to hospital constitutes a basic and major function of any health systembe informative about the overall productivity of health care and support more credible estimates of the marginal health benefits of healthcare spending.
The rest of this paper is structured at follows.First, we present an overview of our materials and methods.Next, we report our main findings, several analyses supporting their robustness, and translations of our estimates to QALYs gained per bed.Finally, we discuss the implications and limitations of this study.

Materials and methods
Swedish health care is organised into 21 autonomous regions.Here, we use data from the municipality and region database (KOLADA) on the annual average number of staffed inpatient care beds in each region between 2001 and 2019 to estimate the potential effect of reduced bed capacity on population mortality.The regional business statistics classify hospital beds as provided within either somatic care (internal medicine, surgery, geriatric care, other) or psychiatric care (Swedish Association of Local Authorities and Regions, 2018).Fig. 1 shows that there was an absolute reduction in the number of staffed beds across all these areas of inpatient care between 2001 and 2019.This has been primarily attributed to technological advances that have substituted outpatient care (e.g., day surgery) for inpatient care or made procedures in inpatient care less invasive, but also nursing staff shortages (National Board of Health and Welfare, 2018).In our main analysis, we investigate the association between mortality and total beds per 1000 people.The association between mortality and beds in different types of inpatient care is explored as part of our robustness checks, detailed later.As our main outcome, we use population-standardised mortalityage-sex-specific mortality rates weighted by their corresponding national population shares in 2019 -to remove variation in mortality that is due to variation in the age-sex composition of the population.Mortality rates are calculated using data on the number of dead by year, birth year, region, and sex from Statistics Sweden.
Fig. 2 plots the evolution of bed capacity and standardised mortality over our sample period.In 2001, Sweden had 3.27 hospital beds per 1000 peopleone of the lowest numbers of beds per capita in the OECD (OECD, 2021) -and by 2019, only 2.07 beds were provided per 1000 people.During the same period, mortality decreased from 11.8 to 8.6 deaths per 1000 people, which at first glance gives little cause for concern that bed reductions have been harmful to population health.However, the decline in mortality can potentially be explained by other factors that coincide with the reduction in bed capacity.
Our strategy in this study is to exploit repeated observations on regions to compare within-region trends in bed capacity and mortality.By using OLS with TWFE, we account for both unobserved factors that may explain a common national trend in beds and deaths as well as unobserved time-invariant differences between regions.Fig. 3 illustrates the gist of this strategy and the variation upon which it relies.The relationship between the change in mortality and change in bed capacity for each region between 2001 and 2019 suggests that regions that made smaller reductions in beds experienced larger decreases in mortality.Retaining one more bed is associated with 0.38 fewer deaths per year (standard error [s.e.] = 0.21; throughout this paper, we report robust standard errors, clustered on region in case of more than one observation per region).
This observation forms the motivation for this paper, but by itself does not imply that reductions in bed capacity have caused increases in mortality since regions may have experienced different trends in other determinants of mortality that either coincide with or affect bed capacity.We consider two alternate explanations for why bed capacity could be negatively associated with mortality.First, higher population income could mean that regions are able to afford more beds due to increased tax revenue, and these increases could be driven by changes in the socioeconomic make-up of the population, which also affects population mortality.Second, more hospital beds could go along with more of other healthcare services due to variation in either the budget constraints or input prices that regions face.It may be these services rather than the number of beds that reduce mortality.From a conservative point of view, confounding that induces a spurious negative association is the most serious threat to validity, but bias from population composition and the provision other healthcare services could also mean that the observed association understates the effectiveness of beds.If certain groups have a greater need for healthcare, regions may choose to provide more beds when these groups grow.Even though such need can be expected to go along with lower income, high-need regions could be able to afford more beds, either by increasing their tax rate or due to the workings of Sweden's regional redistribution system.That is, the Swedish central government redistributes funds between the regions based on income and transfers additional funding based on demographic and socioeconomic factors (Swedish Agency for Public Management, 2014).Further, conditional on budget constraints and input prices, a region providing more beds should be expected to provide less, not more, of other healthcare services.
To assess potential confounding from these factors, we use a set of 39 covariates on the share of the population at the beginning of each year by age, sex, and socioeconomic status, population income (current and lagged), the number of nurses and physicians per capita employed in different parts of the healthcare sector and municipal residential/social care sector, spending per capita in different areas of healthcare, and the number of outpatient surgeries per capita (see Table 1 for all variables and Table B.1 in Supplement for data sources).Specifically, we check for balance in these covariates and adjust for them in our regressions of mortality on bed capacity.In addition, we carry out a number of other robustness checks which are detailed below.

Main results
Table 1 reports our covariates regressed on the number of beds per 1000 people by OLS with TWFE.The results reveal no apparent imbalances that would lead us to suspect that these factors are an important source of confounding for the effect of bed capacity on mortality.For all covariates, the coefficient on bed capacity is small in relation to its standard error.
Table 2 reports regressions of mortality on bed capacity with TWFE, adjusting for different subsets of our covariates.Without adjustment for covariates, we find that one additional bed is associated with 0.3 fewer deaths per year (s.e.= 0.08).Introducing covariates for income and the share of the population by age, sex, and socioeconomic groups leads to an estimate of 0.41 deaths averted per bed (s.e.= 0.12), with a movement in R 2 from 0.03 to 0.11.This suggests that confounding from population composition may lead us to underestimate the effectiveness of beds, but there is no indication that covariate adjustment brings the estimate closer to zero.
Next, we consider a subsample, excluding 2001-2004 and the region Gotland, which allows us to introduce covariates for the provision of other healthcare services.The unadjusted coefficient on beds in this  sample is almost the same as in the full sample (− 0.32, s.e.= 0.08) and adjusting for age, sex and socioeconomics affects the estimate in the same way as before.Adjustment for resource use in non-inpatient care leads to a modest improvement in R 2 (0.04-0.1) but has very little effect on the coefficient for beds (− 0.3, s.e.= 0.08).In other words, we find no evidence that our estimate captures the effect of providing more or less of other healthcare services.Since it has been advanced as an explanation for bed reductions in Sweden, it is interesting to note specifically that the estimate is stable to adjustment for the number of surgical outpatient visits.In fact, without conditioning on other factors, day surgeries and bed capacity are weakly positively correlated (see Table 1), which is inconsistent with the notion that differences in the degree to which regions have substituted outpatient surgery for inpatient surgery is an important determinant of differences in how many beds they have retained (however, it should be noted that the National Board of Health and Welfare cautions that the reliability of this variable may be poor due to improved reporting).Finally, we adjust for inpatient staffing and secondary care spending.This takes into account that a large secondary care or inpatient care sector would tend to provide more beds but could be generating health benefits in some other way.However, it might also remove some of the identifying variation in bed capacity if some is due to more spending or staffing.We find that the estimate is virtually unaffected by the addition of these covariates.Adjusting for all covariates, we end up with an estimate of 0.45 deaths averted per bed (s.e.= 0.12) and R 2 = 0.18.

Robustness checks
In addition to our main analysis, we perform several robustness checks which are summarised in Table 3; the full results of these analyses are reported in the supplement.First, there may be reason to believe that a reduction from 3 to 2 beds per 1000 people would have a greater impact than a reduction from 4 to 3 beds.However, using a loglog specification leads to similar results (e.g., for 11.8 deaths and a reduction from 3.27 to 2.27 beds, an elasticity of − 0.07 implies 0.3 additional deaths) with no apparent improvement in goodness of fit.Further, when including a quadratic term for beds in our linear specification, it is close to zero with only a small change in the coefficient on the linear term (− 0.27, s.e.= 0.08).By virtue of its simple interpretation, we therefore favour a linear specification.
The robustness of our results is further supported by that they are stable to the introduction of more detailed covariates (age groups by sex and socioeconomics by age group: <65, ≥65) and to weighting by population size.When weighting by population size, it could be relevant to also consider the effect of beds on non-standardised mortality, since its interpretation may come closer to that of an average treatment effect (Angrist and Pischke, 2009) of exposing individuals to higher capacity in inpatient care.The population-weighted estimate is 0.39 deaths averted per bed (s.e.= 0.19) and including the full set of covariates, it increases   2005, 2007, 2010, 2013, 2016, and 2019).See Table 2 for further notes.
to 0.53 deaths averted (s.e.= 0.12) with a movement in R 2 from 0.05 to 0.5.To provide some intuition for what kind of variation we draw on in our analyses, we have offered the interpretation that regions that made smaller bed reductions experienced greater decreases in mortality on average.Also intuitively, however, the TWFE estimator (unlike the twoperiod first difference illustrated in Fig. 3) utilises both short-run and long-run variation in the outcome and treatment variable.In an attempt to explore the contribution of short-run and long-run variation to our results, we propose a novel decomposition of the TWFE estimator into a variance-weighted average of a long-run and a short-run component (see Appendix A), which shows that 51% of our estimate comes from different long-term trends in beds and deaths between regions.Discarding this variation by introducing region-specific linear trends yields an estimate of − 0.22 (s.e.= 0.13) and shows that we would come to a similar conclusion (albeit with marginal significance) if we were to rely on short-run variation only.This robustness can be further supported by another decomposition of our TWFE estimate as a variance-weighted average of all possible two-period first-difference estimates in our sample (Ishimaru, 2022).Our results are reasonably stable to restricting estimation to the use of a single length of difference, ranging between − 0.18 with one-year differences and − 0.40 with nine-year differences (see Table B.22 in Supplement).
On a related note, we also consider that repeated cross sections for every year may not contribute a lot of additional information.Estimating with data for every third year (n = 147) produces larger estimates and values of R 2 , both with TWFE and in differences with fixed effects for years.A possible interpretation of these findings is that measurement error in the regressor biases estimates towards zero (e.g.Ashenfelter and Krueger, 1994).Since we exploit downward trends in bed capacity, we would expect the size of potential measurement error to shrink relative to the actual change in bed capacity from one year to another as we consider changes over longer periods.
Next, we investigate whether clustered standard errors could be misleading due to a small number of clusters (i.e., there are only 21 regions).We find that the wild cluster bootstrap, which has been shown to perform well with as few as six clusters (Cameron et al., 2008), leads to only slightly larger confidence intervals and do not affect our inferences.For example, a bootstrapped 95% confidence interval on our base case estimate is − 0.47 to − 0.13 deaths per additional bed compared with − 0.45 to − 0.14 deaths per bed using regular clustered standard errors (see Fig. B1 in Supplement).
In our main analysis, we make no distinction between beds in different areas of inpatient care.Regressing mortality on both beds in somatic care and beds in psychiatric care per 1000 people suggests that our overall estimate reflects the effect of somatic beds, which make up about 80% of the total bed count.One more bed in somatic care is associated with 0.3 deaths averted (s.e.= 0.08) and a bed in psychiatric care with 0.55 deaths averted per year (s.e.= 0.3).Further splitting up somatic care into internal medicine, surgery, and geriatric or other care shows that all three have about the same association with mortality, but that it is less stable and precise for beds in surgical care (see Tables B.12-B.14 in Supplement).Although the same is true of the association between mortality and psychiatric beds, it is interesting to note that our findings are at least suggestive of bed reductions in psychiatric care having a comparable or even larger mortality effect than bed reductions in somatic care.
Finally, we note that if bed capacity has an effect on mortality, we should be able to observe that capacity is associated with providing more or better care in some way.Regressing inpatient care utilisation on bed capacity shows that more beds are indeed strongly associated with more hospitalisations (20.92 per bed, s.e.= 3.98) and lower occupancy rates (− 14.63 percentage points per bed per 1000 people, s.e.= 3.74) (see .

The effectiveness of hospital beds
In economic evaluation of health care, the effectiveness of new healthcare interventions is typically measured in terms of life years or QALYs gained.We now attempt to cast our results in such terms.To this end, we use remaining life expectancy by age and sex from Statistics Sweden discounted at a 3% rate (Dental and Pharmaceutical Benefits Agency, 2017) and health-related quality-of-life weights for age-sex groups elicited from a large sample of the Swedish general population (Burström et al., 2014).The average remaining discounted life expectancy for the population in 2019 was 22.3 years or 18.2 QALYs.A crude translation of 0.3 deaths averted per hospital bed would mean that 6.6 life years or 5.4 QALYs are gained per additional bed.
However, it may not be realistic to assume that mortality reductions are independent of age.Table 4 reports results from three of the specifications in our main analysis by age group.These results show that more beds are primarily associated with lower mortality in the older population; 1.19 (s.e.= 0.35) fewer deaths per 1000 people 65 years and older and 0.06 (s.e.= 0.05) fewer deaths per 1000 people below 65.Weighting the estimates 20:80, which closely corresponds to the population shares of these groups, leads to almost the same overall figure on deaths averted per bed as before (0.29, s.e.= 0.08) but implies instead 3.83 life years (s.e.= 1.19) or 2.94 QALYs (s.e.= 0.94) gained per bed.Including all covariates in the subsample, we find 3.59 QALYs gained per bed (s.e.= 1.3) due almost entirely to deaths averted in the older population.
As an alternative approach to translation, we use the elasticity of standardised mortality with respect to bed capacity from our log-log specification and evaluate the impact of a permanent increase from 2.07 to 2.08 beds per 1000 people on age-sex-specific life expectancies extrapolated from mortality rates in 2019.This assumes that additional beds lead to the same relative risk reduction for all age-sex groups but translates to larger effects in the older population because of higher absolute risk.The permanent increase in bed capacity implies that a total of 0.22 additional beds (discounted future bed years) per 1000 people have to be provided over remaining and added life years with a gain of 0.82 life years or 0.61 QALYs per 1000 people; that is 2.76 QALYs gained per bed.Including all covariates in the full sample and the subsample, the estimates translate to 4.26 and 3.75 QALYs gained per bed, respectively.

Table 4
Standardised mortality (deaths per 1000 people) regressed on beds per 1000 people by age group (0-64 years, 65+ years) with translation of effects to life years and quality-adjusted life years (QALYs).

Discussion
This study finds a large and relatively precisely estimated negative association between hospital bed capacity and population mortality.During our study period, Swedish health care reduced its bed capacity from 3.27 to 2.07 beds per 1000 people.For Sweden's population in 2019 (~10 million), our base case estimate implies that this reduction is associated with about 3600 additional deaths per year.When adjusting for a large set of potential confounders and performing a variety of other robustness checks, there is no indication that this association is due to confounding, which supports a causal interpretation.This evidence contributes to our so far limited understanding of the consequences of Sweden's great reduction in bed capacity and should be highly relevant to health policy on this issue.
Perhaps more importantly, our results can be directly helpful in healthcare resource allocation.Because we show how many QALYs one additional bed could produce, a statement about the cost effectiveness of providing more beds is straightforward, at least in principle.By way of illustration, assuming it would take one additional physician, nurse, and assistant nurse to staff six more beds, the monetary cost of providing one additional bed would be SEK 1.3 million per year (see supplement for details and alternative calculations) and health gains could be generated at a cost of about SEK 400,000 (~US$40,000) per QALY (this implies 3.25 QALYs gained per bed; we report estimates in the range of 2.76-4.26QALYs per bed).
In theory, cost-effectiveness evidence allows decision makers to maximise QALYs subject to a budget constraint (Weinstein and Zeckhauser, 1973) but in practice, cost-effectiveness analysis has long struggled with how to determine a cost-per-QALY threshold at which new interventions should be considered cost effective (Gafni and Birch, 2006).Recent research has attempted to bridge the gap between theory and practice by estimating a health system's marginal cost of producing a QALY (Martin et al., 2008(Martin et al., , 2012(Martin et al., , 2021;;Claxton et al., 2015;Vallejo-Torres et al., 2018;Edney et al., 2018;Siverskog and Henriksson, 2019;Stadhouders et al., 2019;Lomas et al., 2019;Edoka and Stacey, 2020;Ochalek et al., 2020), which could function as an expectation on the opportunity cost of funding new interventions (Culyer, 2016;Thokala et al., 2018;Siverskog and Henriksson, 2021).
We suggest that the cost per QALY gained by providing more hospital beds can be interpreted in two ways.For Swedish health care, the marginal cost of producing a QALY has been estimated at SEK 180,000 (Siverskog and Henriksson, 2019).Judged against this threshold, an expansion in hospital bed capacity would be an inefficient use of resources.However, the approach to estimating the marginal cost per QALY in Sweden and other countries has essentially been to regress mortality on health spending with adjustment for potential confounders (Edney et al., 2022).Our study addresses two shortcomings with such an approach and can therefore complement past research to arrive at more credible estimates of a health system's marginal cost of producing a QALY.
First, if population health improves in response to an increase in health spending, then this must be because spending goes towards the provision of some form of care.Therefore, estimates of the productivity of specific uses of resource are necessary to underpin the credibility of a potential link between spending and mortality.Although this study does not formally link bed capacity to health spending, we can expect hospital bed reductions to be one way in which healthcare budgets accommodate new, cost-increasing interventions.Studies on the potential displacement of current healthcare services have found that very few distinct services are discontinued to finance new ones (Appleby et al., 2009;Wammes et al., 2020).This is unsurprising, because financing a new intervention by explicitly denying care to other patients may not be politically expedient.If the reimbursement of new interventions is crowding out other healthcare services, then it seems plausible that it is doing so by diluting rather than denying care (Klein, 2010;Siverskog and Henriksson, 2020) and a creeping reduction in hospital bed capacity seems a good example of what form such healthcare rationing might take.
Second, relying on covariate adjustment to identify the effect of health spending on mortality assumes that available covariates account for all confounding.This is hard to argue convincingly.Siverskog and Henriksson (2019) find that their estimate of the health spending elasticity of life expectancy in Sweden decreases by more than half when additional covariates are introduced.This should bring their estimate closer to the truth but also raises concerns that their findings could be as sensitive to adjustment for factors that they do not observe.In comparison, we are able to show that confounding from observed factors appears to be limited and, to the extent that it does matter, probably leads us to underestimate the effectiveness of beds.This does not mean that we can rule out confounding from unobserved factors.We might have found evidence of bias in our estimate had we been able to adjust in more detail for time-varying differences between regions in terms of, e. g., healthcare need or the provision of different forms of outpatient and inpatient care.Still, the fact that our findings are insensitive to adjustment for a fairly large set of covariates should inspire some confidence that the negative association between bed capacity and mortality is not spurious.
In this way, our study does not directly estimate the number of QALYs that we can expect to forgo when new interventions are funded but can neverthelessif we adopt an incremental approach to empirical knowledge (Angrist and Pischke, 2010) -be seen as building towards such an estimate by reporting relatively credible evidence on the productivity of one important use of healthcare resources.
The major limitation of this study is that we, unlike with an experimental or a quasi-experimental design, do not identify the source of variation in bed capacity.We rely instead on the assumption that, after including fixed effects, variation in capacity is as good as random.Our results could be made more credible if we were able to explain why some regions have retained more beds than others.We do investigate the potential role of nurse staffing in explaining variation in bed capacity (see subsection B.3 in Supplement) but are unable to provide precise enough estimates that could support that bed reductions are caused by staff shortages.
Our ability to argue that there is no or limited confounding after including fixed effects is also limited by the quality of our covariates in several ways.First, we have argued that a regional aggregate outcome is a strength since it avoids selection to sample on who is admitted to hospital or visits an emergency department, but a lack of individuallevel covariates makes it much harder to be certain which covariates are appropriate to adjust for.Therefore, when adjusting for a covariate, we could be introducing bias if the covariate is an outcome of bed capacity and subject to a different set of confounders (Angrist and Pischke, 2009).Second, our covariates are not perfect measures of the potential confounding factors that we aim to adjust for.In particular, we are only able to adjust for other aspects of hospital care in terms of spending and the number of nurses and physicians.Had we been able to measure the adoption of new surgical procedures, patient-safety routines, or other aspects of the quality of care that is provided or how hospitals are organised, we could have been more certain that our findings were due only to variation in bed capacity.Third, if the covariates are not good measures of confounding factors, they may not be good predictors of mortality either.Therefore, small coefficient movements when adjusting for covariates do not necessarily mean that there is limited confounding (Oster, 2019).We should have liked to see small coefficient movements coupled with larger movements in R 2 to be more confident in our findings in this respect.However, this last concern is to some extent mitigated by that the direction of coefficient movements (regardless of their size) imply that we under-rather than overestimate the number of deaths averted per bed.
Finally, although our estimate of the number of deaths averted per bed is relatively precise and stable, there is an added uncertainty when making statements about the number of QALYs gained per bed from our assumptions that bed reductions do not affect the quality of life of patients and that average remaining life expectancy and quality of life are applicable to averted deaths.

Conclusion
Both hospital bed capacity and mortality decreased in all Swedish regions between 2001 and 2019, but regions that made smaller reductions in beds experienced larger decreases in mortality on average.This association does not disappear when taking into account alternate explanations for it.In fact, covariate adjustment leads to a slightly stronger negative association.This evidence supports the interpretation that hospital bed reductions are not solely signs of increased efficiency but have come at the cost of population health.We suggest that the cost effectiveness of providing more beds can be a relatively credible piece of a larger puzzle for determining the marginal health benefits of healthcare spending.

Fig. 1 .
Fig. 1.Number of staffed hospital beds in Swedish inpatient care in 2001 and 2019, by area of inpatient care.

Fig. 2 .
Fig. 2. Hospital beds and deaths per 1000 people in Sweden between 2001 and 2019.Age-sex specific mortality rates for each year are weighted by their corresponding population shares in 2019 to produce a measure of standardised mortality (there were 10.5 actual deaths per 1000 people in 2001).

Fig. 3 .
Fig. 3.The association between change in number of hospital beds and change in standardised mortality (deaths per 1000 people) for 21 Swedish regions between 2001 and 2019.Retaining one more bed is associated with 0.38 fewer deaths per year (standard error = 0.21).

Table 1
Potential confounders regressed on hospital beds per 1000 people.
Notes: coef.= difference in covariate value associated with a one-bed increase per 1000 people.s.e.= robust standard error, clustered on region.All regressions are estimated by ordinary least squares with fixed effects for regions and years.

Table 2
Standardised mortality (deaths per 1000 people) regressed on beds per 1000 people, adjusting for potential confounders.=coefficienton beds per 1000 people.s.e.= robust standard error, clustered on region.Results are reported for the full sample and a subsample (excluding 2001-2004 and the region Gotland) based on data availability.All regressions are estimated by ordinary least squares with fixed effects for regions and years.R 2 is calculated after residualising with respect to the fixed effects.See Table1for covariate numbers.

Table 3
Alternate specifications of regressions in main analysis.
Notes: * and † indicate analyses using data for every third year (in the subsample,