An examination of health care efficiency in Canada: a two-stage semi-parametric approach

Abstract

Using data envelopment analysis, we examine the efficiency of Canada's universal health care system by considering a set of labour (physicians) and capital (beds) inputs, which produce a level of care (measured in terms of health quality and quantity) in a given region. Data from 2013–2015 were collected from the Canadian Institute for Health Information regarding inputs and from the Canadian Community Health Survey and Statistics Canada regarding our output variables, health utility (quality) and life expectancy (quantity). We posit that variation in efficiency scores across Canada is the result of regional heterogeneity regarding socioeconomic and demographic disparities. Regressing efficiency scores on such covariates suggests that regional unemployment and an older population are quite impactful and associated with less efficient health care production. Moreover, regional variation indicates the Atlantic provinces (Newfoundland, Prince Edward Island, Nova Scotia, New Brunswick) are quite inefficient, have poorer economic prospects, and tend to have an older population than the rest of Canada. Oaxaca-Blinder decompositions suggest that the latter two factors explain about one-third of this efficiency gap. Based on our two-stage semi-parametric analysis, we recommend Canada adjust their transfer payments to reflect these disparities, thereby potentially reducing inequality in regional efficiency.

1. Introduction

As part of their ‘Sustainable Development Goals’, the United Nations has advocated that member states work toward achieving worldwide universal health care coverage by 2030.¹ Given that much of the developed world already provides their citizens with universal health care, and countries like the United States have made some progress toward such a system, understanding the efficiency of its delivery is of key importance to policy-makers. In this paper, we explore the efficiency of health care production in Canada, with particular emphasis on regional disparities.

Using data envelopment analysis (DEA), we investigate how mean levels of regional health in Canada are produced using a set of inputs, and the degree to which inefficiencies are the result of external regional factors. One region may be providing highly efficient care using relatively little input, while another region, of comparable size, may be inefficient in their provision of care. However, DEA alone fails to address the fact that regions are not homogeneous in terms of the demands that are placed on the system. Perhaps individuals in the efficient region tend to be younger or possess more economic opportunity. As a result, we examine the efficiency of health care production in Canada using a two-stage semi-parametric approach, whereby the efficiency of the health care production function (non-parametric) is posited to be impacted by a set of regional characteristics (parametric).²

Two papers have examined health care in Canada using a similar two-stage method. Chowdhury and Zelenyuk (2016) investigate hospital performance in the Canadian province, Ontario, using a technique that couples DEA with a truncated regression analysis. Moreover, Allin et al. (2016) observe health care efficiency for the entirety of Canada, based on differences across health regions – also using a two-stage DEA/regression approach. Among other causes, these articles find that a set of environmental and public health factors impact efficiency. In the former study, a rural location and smaller hospital size predict more efficiency; in the latter, issues such as smoking prevalence, obesity, and hospital re-admissions predict reduced efficiency.

Our analysis differs from these studies in a variety of ways. For starters, we use more recent data (2013–2015) with the previous works analysing data from 2003–2006 and 2007–2009, respectively. More importantly, while Chowdhury and Zelenyuk (2016) and Allin et al. (2016) use quantity-based measures such as impatient days in the former paper and mortality metrics in the latter, we include both a quantity-based outcome, life expectancy, and a quality-based outcome, health utility. As noted in Chowdhury and Zelenyuk (2016), hospitals are ‘indifferent to profit and strive to maximize the quantity and quality of health care services’ (p. 111) and Allin et al. (2016) suggest that quality-based metrics are an avenue of future research.

Our most novel contribution is an examination of how regional-level factors, such as unemployment and population ageing, impact the efficiency of health care production. In particular, we use regression methods that allow for an understanding of the degree to which regional inefficiencies are the result of such circumstances. While other studies have pursued a two-stage approach within the realm of health production, to our knowledge, this is the first paper to explicitly examine the impact of the demand for care on efficiency, while also using decomposition methods to evaluate the relationship between inefficiencies and compositional differences across regions regarding the demand for care. Such insights allow policy-makers to tailor programmes in an effective manner, and given the opportunity cost of public funds, may strengthen the efficiency of a universal health care system.

We posit that regions with poorer health outcomes require additional health care inputs. Accordingly, they are relatively less efficient regarding health care delivery. However, regions with less healthy populations are also more likely to be characterised by poor social determinants of health, implying they have relatively higher levels of demand for care. Consequently, the health care inputs in such regions are less likely to meet desired health care outcomes given heightened demand. This suggests the following transmission mechanism: health deteriorates when a region's primary social determinants of health are worsened, which increases demand for care; therefore, given its current set of inputs, a region's ability to efficiently supply care decreases (compared to regions with more favourable social determinants of health). To illustrate, additional demand for care (without a comparable rise in inputs) will increase waiting times. And, as a larger queue emerges, this would almost certainly reduce the quality of health that is produced in a region – i.e., people must wait longer to receive care, which would negatively impact their quality of health. This implies that there will be a reduction in efficiency.

Our first-stage DEA results suggest that regions in Atlantic Canada (Newfoundland, Prince Edward Island, Nova Scotia, New Brunswick) are typically the least efficient, with Ontario and the Prairies (Manitoba, Saskatchewan, Alberta) producing the highest level of care given the supply of physicians and beds. Our second-stage regression results suggest that regions with higher rates of unemployment, and those with proportionately more senior citizens, are expected to have poorer levels of health care efficiency. Having an ageing population and an unemployment rate well above the national average, Atlantic Canadian provinces are therefore unlikely to achieve efficient health care production. Indeed, results from a series of Oaxaca-Blinder decompositions suggest that these factors explain about one-third (and perhaps as much as two-thirds) of the efficiency gap between Atlantic Canada and the rest of the country.

Recent evidence suggests this efficiency gap will persist, as Tombe (2022) notes that health care expenditures in Atlantic Canada are expected to increase at almost twice the national rate over the next two decades. This is largely due to an ageing population that is exasperated by seniors disproportionately moving to Atlantic Canada (Beland and Tombe, 2023). Further, Tombe (2020) suggests that population ageing is expected to dampen economic prospects in Atlantic Canada, which has potential health-related consequences. Thus, policy-makers may wish to adjust health care expenditures to account for socioeconomic status and population ageing. Yet, unlike federal debt, which has trended down since the 1990s, Tombe (2020) notes that provincial debt has steadily risen, and this may pose fiscal challenges given that health care is under provincial jurisdiction.

However, the federal government provides the Canadian Health Transfer (CHT) with the objective of providing equal treatment for all Canadians, regardless of region of residence. The CHT is divided among the provinces on a per capita cash basis, meaning no adjustments are made based on regional composition. Hence, the degree to which factors such as age and economic opportunity impact health inefficiencies across regions, may imply this transfer be amended to account for such heterogeneity; otherwise, health care institutions within many inefficient regions cannot be expected to achieve one of the primary reasons for this transfer – to ensure provinces are meeting a national standard of care to all Canadians.

While a CHT adjustment that allots additional funding to the Atlantic provinces may possibly worsen the efficiency gap, it could be justified based on high levels of demand for care, which obviates much of the Atlantic from being efficient. However, there also remains a sizeable unexplained efficiency gap that is largely the result of ‘group identification’, meaning that there are potential differences in physician quality across regions. This is perhaps due to a self-selection process coupled with the fact that physicians in the Atlantic provinces tend to receive less pay relative to most parts of Canada.³ Therefore, transfer payments could also be used to financially incentivise highly skilled physicians to move to Atlantic Canada, implying potentially significant efficiency gains.

The paper proceeds as follows. Section 2 characterises both first and second-stage methods, while Section 3 presents the results. In Section 4, we examine the regional efficiency gap using Oaxaca-Blinder decomposition techniques. Section 5 concludes.

2. Methods

2.1 First-stage: analysis using DEA

Consider that the production of health care (H) in region j is determined by a set of labour (L) and capital (K) inputs:

(1)$$H_j = f( {L_j, \;K_j} ).$$

We proxy for labour by collecting data on the number of physicians per region,⁴ while proxying for capital based on the number of hospital beds.^{5, 6} To account for regional population differences, these inputs are expressed in per 100,000 person terms.

Defining output is somewhat more complex as we must ask what it is regions are producing in terms of care. For instance, Chowdhury and Zelenyuk (2016) use ‘case-mix adjusted weighted impatient days’ in examining health at the hospital-level – a method ‘designed to identify clusters of acute-care inpatients with similar clinical and resource-utilization characteristics’ (p. 114). Alternatively, Law et al. (2010) measure health at the individual-level as ‘health status after treatment’ (p. 166). Allin et al. (2016) capture output at the regional-level by examining reductions in potential years of life lost from ‘causes of death that are considered to be amenable to health system intervention’ (p. 45). Finally, Asandului et al. (2014) examine health care efficiency based on a set of life expectancy metrics.

There has been an increasing interest in DEA studies that examine health care in terms of quality, as opposed to quantity (Kohl et al., 2019). Therefore, we define output using both quantity and quality factors. In terms of quantity, we observe life expectancy at birth, whereby Statistics Canada determines regional values based on: (i) population estimates and (ii) the observed number of deaths over a given calendar year.

Concerning quality, we use the distinctly Canadian health utility index (HUI). Developed by McMaster University, this individual-level index is a multi-faceted utility function, capturing health-related quality of life (HRQL).⁷ Based on over 30 years of research, and well-grounded in theoretical foundations, the HUI captures a standardised measure of HRQL for those age 5 and up (Horsman et al., 2003). Covering 972,000 unique health states, it provides a reliable and valid HRQL score, given eight health domains (vision, hearing, speech, ambulation, dexterity, emotion, cognition, pain) – each ranging in 5–6 categories of ability. It has been incorporated into several population surveys, including the Canadian Community Health Survey and the National Population Health Survey, and has been used throughout the world (e.g., Canada, USA, Brazil, Cuba, Germany, Sweden, UK, Australia, Israel, Japan, Singapore, Turkey).⁸

In deriving this index, the respondent is asked a series of questions about their usual health status; thus, determining an overall health state. As noted by Horsman et al. (2003), each health state is then mapped to a utility value based on a multi-attribute function developed from community preferences, which accords with von Neumann-Morganstern utility theory. The index is increasing in HRQL, whereby death equals zero and unity captures perfect health. Further, negative HUI scores represent health states considered worse than death. Although we observe this metric at the individual level, it is aggregated such that the mean HUI is determined for each region. Both Drummond (2001) and Grootendorst et al. (2000) suggest that HUI scores that differ by a magnitude of 0.03 (or greater) represent distinct changes in health. This is particularly important given that the standard deviation of regional HUI scores is about 0.03 (see Table 1), which suggests that despite ranging from 0.79 to 0.90, there is notable variation in scores.

Table 1. Descriptive statistics

Notes: The sample consists of 281 observations, based on 95, 91, and 95 health regions examined over the respective years of 2013, 2014, and 2015. Health utility index data were collected from the CCHS and life expectancy data came from Statistics Canada (CANSIM Table 13100389). Physician and bed data were obtained from the CIHI, with population adjustments using Statistics Canada CANSIM Table 17100086. Efficiency scores are derived from calculations by the authors. Unemployment data were obtained from CANSIM Table 14100334 and the remaining data were derived from pooled CCHS datasets.

We assume that each region's health care system wishes to maximise both the quantity of life, and the quality of that life, among it's population. Using this production function, consisting of two inputs and two outputs, we pursue a DEA strategy in order to determine a technological frontier that determines regional health care efficiency.⁹ Initiated in Charnes et al. (1978) and extended by Banker et al. (1984), DEA is a non-parametric optimisation method for efficiency evaluation of decision making units (DMUs), whereby each DMU uses a set of inputs to provide one or more outputs.¹⁰ Given the objective concerning the provision of care is to realise the maximum health that a region can produce for a specific level of resources, we apply an output-oriented DEA model that derives a set of efficiency results ranging from 0 to 1, with a value of unity denoting perfect efficiency (Cooper et al., 2007). Moreover, we assume constant returns to scale (CRS) technology as we do not suspect there to be scale-effects at the regional level (Sherman and Zhu, 2006).

However, as noted in Marques and Carvalho (2013), the distinction between variable returns to scale (VRS) and CRS should not be taken lightly as selection of the incorrect transformation function may significantly distort results in hospital applications. Consequently, we performed a non-parametric test of returns to scale, operationalised by Simar and Wilson (2002).¹¹ This test is based on 999 bootstrap replications of the data, with a test statistic equalling the ratio of the average efficiency score under CRS and VRS assumptions, and a null hypothesis that the technological frontier is globally CRS. Failure to reject the null would imply that the distance between the two frontiers is small (i.e., approaches unity). As an extension, we can also compute the above ratio for each data-point. If the mean of these ratios does not statistically differ from unity, then this provides further credibility that the frontier exhibits CRS. Given our dataset of 281 observations, both test statistics do not statistically differ from unity at conventional levels, which further supports our CRS assumption.¹²

2.2 Second-stage: analysis using OLS

DEA methods determine a level of health care efficiency for each region in Canada. However, the efficiency of such production may also be the result of a set of regional circumstances. For instance, if a particular region is characterised by an ageing population, which presumably demands more health care, the likely result is increased stress on the available inputs, thereby reducing the region's ability to efficiently produce care. Therefore, for region j in time period t, we model efficiency (E) as a function of regional circumstances, such that:

(2)$$E_{jt} = \alpha + SE_{jt}^{\prime} \beta + SD_{jt}^{\prime} \gamma + HS_{jt}^{\prime} \delta + a_t + u_{jt}$$

where SE captures socioeconomic status, SD controls for sociodemographic characteristics, HS denotes a set of health-status issues, a identifies time fixed effects, and u is the error term.¹³

In estimating Equation 2, we proxy for socioeconomic status using the regional unemployment rate, which has been found by Gearhart and Michieka (2018) to be a predictor of less health care efficiency among Californian counties. In terms of demographic characteristics, prevalence of senior citizens and the extent to which each region's sample resided in a rural area are included. Interestingly, Garcia-Lacalle and Martin (2010) observe that, on average, rural hospital performance is on par with those hospitals located in urban settings, in some cases surpassing them on dimensions of quality. This finding is echoed in Athanassopoulos and Gounaris (2001) who suggest that rural hospitals tend to be more efficient than those in urban settings. Afonso and St. Aubyn (2011) note that, among OECD countries, health care efficiency is negatively correlated with obesity and smoking levels. Thus, our health indicators include the average body mass index (BMI)¹⁴ among respondents in each region, along with the percentage of adults who report being a daily smoker. Lastly, as indicated in Khushalani and Ozcan (2017), health care efficiency improved in the United States from 2009 to 2013. As a result, we include a set of time dummy variables with the most recent year in our dataset being the reference category.

3. Empirical analysis

3.1 Data

While health care falls under provincial jurisdiction, we disaggregate to the health region level in order to increase our number of observations for this analysis. Given that a provincial government ministry of health delegates the administration and delivery of health care to ‘health authorities’ who oversee these regions, analysis of a set of DMUs at this level is perhaps more fitting as they are indeed, decision-makers. In 2015, there were 113 health regions in Canada, with almost one-third of those being in the country's most populous province, Ontario.¹⁵

Individual-level data regarding the HUI, along with the determinants of our efficiency scores (excluding the unemployment rate), were collected from the 2013, 2014, and 2015 waves of the Canadian Community Health Survey (CCHS) – an annual cross-sectional survey conducted by Statistics Canada that began in 2001. Taken from their website, this survey aims to ‘support local health units by providing them with the timely information they need to evaluate existing programs and to design new ones suited to their communities’. CCHS collects data on individuals 12 years and older from across all ten provinces and three territories.¹⁶ For each variable, we compute the mean at the health region level. Specifically, the respondent's derived HUI, along with reported age, place of residence,¹⁷ BMI, and smoking behaviour are observed to determine regional means.

Data regarding life expectancy at birth and by health region, came from Statistics Canada (CANSIM Table 13100389) and regional unemployment data were collected from Statistics Canada's Labour Force Survey (CANSIM Table 14100334). Input data – i.e., beds and physicians by health region – were obtained from the Canadian Institute for Health Information (CIHI), a not-for-profit organisation with the mandate ‘to deliver comparable and actionable information to accelerate improvements in health care, health system performance and population health across the continuum of care’. In particular, physician data came from the 2016 edition of Scott's Medical Database, while data on beds were obtained from the Canadian MIS Database. As noted in Section 2, input data are adjusted for regional population levels. Thus, we collected population data from Statistics Canada using CANSIM Table 17100086 such that bed and physician data are per 100,000 people.

Given the very different living experience of those residing in the Canadian north, we exclude respondents who report living in the three territories, along with those residing in Canada's two most remote northern provincial health regions.¹⁸ Additionally, we exclude the three regions that comprise Canada's three largest metropolitan centres (Montreal, Toronto, Vancouver). Given that many individuals come to Montreal, Toronto, or Vancouver from outside regions to receive care, inputs may not be a reflection of health care production within the region and will thus, bias respective efficiency levels downward.¹⁹ Major research endeavours also take place in each of these three cities, which have far reaching implications that extend beyond regional borders. As such, physicians and beds being used for such initiatives may again create an inaccurate reflection of how health care is being produced within the region.

Further, Statistics Canada derived a series of ‘peer groups’ that cluster health regions based on 24 socioeconomic and demographic determinants. To ensure within group comparison, the algorithm-produced clusters that contained fewer than five regions, were merged with their nearest neighbour. The exception is cluster G (Montreal, Toronto, Vancouver), given that these regions have more in common with themselves than other populations, particularly with respect to their population size. As Statistics Canada (2018) notes, ‘they are too different from the other health regions to be combined with any other peer group’ (p. 9). Hence, it is reasonable to assume these regions are indeed outliers. Notably, our results are robust to their inclusion; however, given their unique peer group classification, we chose to omit them from the analysis.²⁰

In 2014, the province of Nova Scotia updated their regional boundaries, which is reflected in CIHI and Statistics Canada data, but CCHS did not account for this change until 2015. Additionally, only one of the six Nova Scotian pre-2014 regions aligned with the four post-2014 regions. Thus, 2013 and 2014 data pertaining to Nova Scotia are only available for one region, given it was not otherwise possible to accurately merge datasets at the regional level. As a result of the exclusion restrictions and missing data, our sample consists of 281 observations. More specifically, 95 health regions are observed in 2013, along with 91 and 95 regions in 2014 and 2015 respectively.

While the entire population of input data were collected from CIHI, and life expectancy is based on reported mortality statistics from Statistics Canada, all other data were derived from samples. Unemployment data are based on monthly surveys of 56,000 households, and each wave of CCHS data are based on responses from about 60,000 individuals. Labour Force Survey data concerning unemployment are weighted by Statistics Canada, allowing for inference at the population level. Additionally, CCHS provides a vector of population weights to account for their stratified sampling procedure, which we apply in order to allow for accurate regional analysis.

3.2 First-stage results

Descriptive statistics regarding the first-stage, non-parametric, analysis are presented in Table 1. Overall, regions are quite healthy, with a life expectancy of just over 81 years and a mean HUI level of about 0.85. On average, there are about 188 physicians and 280 beds per 100,000 people in each region. However, unlike output variables, there is a large variation in terms of inputs around their respective means. In particular, the number of physicians per 100,000 people ranges from a minimum of just under 60 to almost 425. The variation in beds per 100,000 people is even greater, ranging from about 94 to 1212. That said, one particular health region is an outlier in terms of beds, such that it's removal reduces the range to 94–584. Along with validation from CIHI to ensure these observations are indeed correct, analyses were run both with and without this region and results remained quite stable; thus, we chose to include these data points throughout our analysis.²¹

The mean efficiency score is 0.57. In particular, we find that 7 of the 281 observations have an efficiency value of 1, indicating they are efficient. Notably, one region is efficient in all three years, while another is efficient on two occasions (with the third observation approaching efficiency). The other two regions, while being efficient once, have scores above 0.88 for the remaining years. On the other end of the scale, the minimum efficiency score is 0.21, which is unsurprisingly associated with the health region having the outlier level of hospital beds. While removing this region and re-running the analysis has only a marginal impact on mean efficiency, the minimum value increases to about 0.29. Closer inspection of efficiency scores suggests that inefficient regions tend to be clustered in Atlantic Canada.

3.3 Second-stage results

Descriptive statistics concerning our second-stage explanatory variables (excluding time dummies) are also presented in Table 1. While the average unemployment rate is 7.28 per cent, there is a large amount of heterogeneity across regions, ranging from just over 2 per cent to almost 19 per cent. This is an unsurprising result given a large portion of Canada's economy is resource-based, and thus exposed to cyclical fluctuations in world-market prices. For instance, the time during which these data were collected was largely characterised by high energy prices, which economically benefited the provinces of Manitoba, Saskatchewan, and Alberta. In particular, the lowest regional unemployment rates in our dataset occur exclusively in these Prairie provinces, with the highest values being in Atlantic Canada.

On average, about 20 per cent of a region's residents could be classified as seniors, and about 32 per cent of the residents in each region reside in a rural area. This latter result is prone to a large degree of heterogeneity with some regions being purely urban, and others having about 90 per cent of their population living in rural areas. In terms of our health metrics, the average BMI level across regions is about 26.5. To put this in context, a value between 18.5 and 24.9 is considered ‘normal’, between 25 and 29.9 is deemed ‘overweight’, and 30 or greater is classified as ‘obese’. Thus, it would seem that most Canadian adults are overweight,²² with the minimum regional BMI value being just under 24 and the maximum being slightly above 29. Finally, on average, almost 16 per cent of a region's population reported being daily smokers. However, regions displayed a large degree of heterogeneity whereby smoking prevalence ranged from 5.6 per cent to 27.4 per cent.

We begin our second-stage, parametric, analysis with a simple linear regression model of efficiency scores on the unemployment rate and iteratively add controls for sociodemographic characteristics, health, and year of observation. Regressions are run using ordinary least squares (OLS) and results are presented in Table 2. Collectively, inclusion of all variables explains almost 25 per cent of the variation in efficiency scores across regions. Moreover, given that efficiency is measured on a 0 to 1 scale, a ceteris paribus one unit increase in any of our continuous explanatory variables can be interpreted as a ‘proportion-point’ increase in efficiency. Additionally, our results regarding year of observation are in reference to 2015.

Table 2. Regression results

Notes: Estimation method: ordinary least squares with robust standard errors in parentheses. The sample consists of 281 observations, based on 95, 91, and 95 health regions examined over the respective years of 2013, 2014, and 2015. Unemployment data were obtained from CANSIM Table 14100334 and the remaining data were derived from pooled CCHS datasets.

*** p < 0.01, ** p < 0.05, * p < 0.1.

An increase in the unemployment rate is predicted to reduce health care efficiency. The parameter estimate remains fairly consistent across specifications and suggests that a one percentage point increase in the regional unemployment rate is associated with about a 0.022–0.025 point reduction in efficiency. It is also worth noting that in the simple linear regression model, unemployment explains over 13 per cent of the variation in regional efficiency.

Moreover, the prevalence of senior citizens in a region is associated with lower efficiency. Fairly consistent across specifications, a one-point increase in the per cent, age 65 and over in a given region, is associated with a 0.009–0.011 point decrease in efficiency. Our results also suggest that efficiency decreases, at a decreasing rate, as a region has a more rural populace. However, the minimum efficiency point occurs below 20 per cent of the population being rural, suggesting that relatively rural regions are associated with more efficient health care production. To fully appreciate this result, one must keep in mind that both unemployment and senior controls are quite positively correlated with rural living. Thus, factors often considered a part of rural living, and predictive of lowered health care efficiency, likely explain why this result is not ‘more negative’ than perhaps anticipated.²³

Regions that have a more overweight population are associated with greater levels of health care inefficiency. More specifically, a one-point increase in a region's mean level of BMI is associated with a 0.026–0.029 decrease in efficiency. However, with a p-value above 0.05, but less than 0.1, this result is only weakly statistically significant. Surprisingly, the percentage of daily smokers does not appear to impact efficiency. It may be possible that once we control for the unemployment rate, factors like smoking and obesity are no longer (or less likely to be) significant predictors of efficiency – especially given the multicolinearity of such variables.

As a test, we estimated two simple linear regression models, where we separately regressed regional efficiency on: (i) mean BMI and (ii) daily smoking prevalence. Although results in both cases are statistically significant at the 10 per cent level, parameter estimates are quite small, with a simple linear regression of efficiency on the unemployment rate producing a coefficient that is over 5 times larger relative to the prevalence of daily smoking. Thus, while obesity and smoking rates do impact efficiency, and such relationships are jointly determined by the socioeconomic status of the region, these impacts, regardless of the degree of multicolinearity, are quite small. Lastly, while time dummies have the hypothesised direction of effect, magnitudes are quite small, and results are statistically insignificant at conventional levels. Presumably technological developments produce higher rates of efficiency over time; however, within this small time frame, such a result is not apparent.

Finally, we perform two robustness checks that account for the bounded nature of the efficiency index, along with concerns over serial correlation. Specifically, DEA results are bounded between 0 and 1, and our OLS method does not take this into account. Secondly, as noted in Simar and Wilson (2007), efficiency scores may be serially correlated given that results are based on relative performance; hence, observations cannot be considered independent and a particular region may only appear efficient as a result of the sampling design. Results, which are available from the lead author upon request, suggest that accounting for these factors has little impact on our key findings – an unsurprising outcome given predicted scores occur between 0 and 1, and we observe the bulk of the population.

4. Oaxaca-Blinder decomposition: Atlantic Canada efficiency

Presented in Table 3, our DEA results suggest that Atlantic Canadian regions are typically less efficient at producing health care given the availability of physicians and hospital beds. While the rest of country has an efficiency score of about 0.56–0.61, Atlantic Canada lags well behind with a value of about 0.41. Of particular note, this value is more than two-standard deviations below the mean values within Ontario, the Prairie provinces, and British Columbia. Moreover, the most efficient health region in Atlantic Canada has a score of 0.57, which is only marginally higher than the mean level in Quebec of 0.56.

Table 3. DEA results across Canada

Notes: Atlantic Canada consists of Newfoundland, Prince Edward Island, Nova Scotia, New Brunswick; the Prairies include Manitoba, Saskatchewan, Alberta.

However, regions across Canada are certainly not homogeneous in their composition, with those in Atlantic Canada often characterised by elderly populations and a dearth of economic opportunity – notably, the two most impactful factors in our second-stage analysis. Descriptive statistics in Table 4 suggest that the Prairie provinces, on average, have the lowest unemployment rate (4.53 per cent), and proportionately, the fewest individuals age 65 and over (17.63 per cent).²⁴ Moreover, Atlantic Canadian health regions typically have an unemployment rate that is well over 7 percentage points above that of the Prairies, along with having a prevalence of senior citizens that is about 3.5 percentage points higher.

Table 4. Second-stage means across Canada

ATL, Atlantic Canada provinces; PQ, Quebec; ON, Ontario; PR, the Prairie provinces; BC, British Columbia.

The sample consists of 286 observations, based on 95, 91, and 95 health regions examined over the respective years of 2013, 2014, and 2015. Unemployment data were obtained from CANSIM Table 14100334 and the remaining data were derived from pooled CCHS datasets.

A visual representation of the relationship between health care efficiency and unemployment, along with the prevalence of seniors, is provided in Figures 1 and 2. Notably, scatterplots emphasise regions in Atlantic Canada. In both cases, and as confirmed in Table 2, it is apparent that a negative correlation exists. Additionally, with Atlantic Canadian regions typically clustered in the bottom-right quadrants of both figures, there is evidence to suggest that such factors may be negatively impacting the degree to which Atlantic Canadian health regions can provide efficient care. Therefore, we ask, to what degree do such factors explain the above regional differences in efficiency scores?

Figure 1. Efficiency and unemployment scatterplot.

Figure 2. Senior population and efficiency scatterplot.

Presented in the first column of Table 5, a simple linear regression of regional efficiency scores on an Atlantic Canada dummy variable, suggests that these provinces are about 0.19 proportion points less efficient than the rest of Canada. Adding controls for regional unemployment and the percentage of seniors (column 2), reduces the magnitude to about 0.13 – i.e., about a 30 per cent reduction in relative inefficiency. Inclusion of the additional controls from Table 2 does not change this result. Therefore, among our control variables, economic prospects and population ageing are quite impactful, and disproportionately affect Atlantic Canadian health regions.

Table 5. Regression results

Notes: Estimation method: ordinary least squares with robust standard errors in parentheses. The sample consists of 281 observations, based on 95, 91, and 95 health regions examined over the respective years of 2013, 2014, and 2015. The Atlantic Canadian region consists of Newfoundland, Prince Edward Island, Nova Scotia, and New Brunswick. Unemployment data were obtained from CANSIM Table 14100334 and the remaining data were derived from pooled CCHS datasets.

*** p < 0.01, ** p < 0.05, *p < 0.1.

We further address regional disparities using Oaxaca-Blinder methods of decomposition (Blinder, 1973; Oaxaca, 1973), dividing the mean outcome gap into two categories: the explained and unexplained. More specifically, the gap is decomposed into: (i) group differences in magnitudes of the independent variables, and (ii) group differences in the impacts of these variables. Thus, we examine the degree to which Atlantic Canada inefficiency can be explained by compositional differences in unemployment and age, and the extent to which differences in the returns to these variables (along with differences in the constant term) comprise the unexplained gap.

Decomposing the gap can be done by applying Atlantic Canada parameter estimates to the means derived from the rest of Canada, or by applying the latter's parameter estimates to Atlantic Canadian means. Both produce a similar yet different result, with no technical reason for preference of one versus the other. Given the arbitrariness of an anchor point, alternative methods have been developed that focus on a weighted parameter estimate $( \hat{\beta }^\ast )$. This would incorporate results from Atlantic Canada parameter estimates $( \hat{\beta }^{ATL})$, along with those pertaining to the rest of Canada $( \hat{\beta }^{CAN})$.

Reimers (1983) suggests using the mean of the two decompositions, such that: $\hat{\beta }^\ast{ = } ( \hat{\beta }^{ATL} + \hat{\beta }^{CAN}) /2$, while Cotton (1988) proposes that weights be adjusted for the sample size of each group: $\hat{\beta }^\ast{ = } \bar{n}^{ATL}\hat{\beta }^{ATL} + \bar{n}^{CAN}\hat{\beta }^{CAN}$, where $\bar{n}^i$ is the proportion of the total sample comprised of group i. Additionally, both Neumark (1988) and Oaxaca and Ransom (1994) suggest using parameter estimates derived from a model that pools both groups. However, as noted in Fortin et al. (2011) and Jann (2019), pooled estimation may lead to an over-estimation of the explained portion of the decomposition. As such, Fortin (2008) recommends the inclusion of a dummy variable, which captures group identification, in order to correct this bias.

Decompositions, using the weighted parameter estimate techniques, are presented in Table 6. Given a predicted efficiency score of about 0.407 for Atlantic Canada and 0.598 for the rest of Canada, the difference to be decomposed equals 0.191. The proportion of the gap that is explained by unemployment and a senior population varies by method, from about 0.27 to almost 0.61. However, as noted above, this upper limit value may possess an upward bias, which seems quite apparent as the next highest value is about 0.43.

Table 6. Oaxaca-blinder decompositions

Notes: Each column presents a set of results based on a parameter estimate weighting mechanism proposed by the respective author. Robust standard errors in parentheses. In the case of the third and fourth columns, Oaxaca and Ransom (1994) suggest an equivalent method. The first column of estimates is based on a 50% weighting of each group's parameter estimates. The second column adjusts the weights based on observation totals. The third and fourth columns are the result of parameter estimates obtained from a pooled regression consisting of both groups – the difference being the inclusion of a group dummy variable in the former column.

*** p < 0.01, ** p < 0.05, * p < 0.1.

That said, the average of the more conservative estimates suggests that about one-third of the gap is the result of these two variables. Although not presented in Table 6, the bulk of the explained gap is the result of regional unemployment and the unexplained gap is due to group membership (i.e., differences in the constant term). For instance, it is possible that highly skilled physicians self-select into regions they deem more desirable (e.g., proximity to a major urban centre), thus contributing to the unexplained gap.

5. Discussion

This paper examines health care efficiency in Canada using a two-stage semi-parametric method. First-stage results are derived using DEA – a non-parametric approach, where the number of physicians and beds (per 100,000 people) are posited to interact; thus, producing a level of health among those residing in that region. Regions are specified using Canada's health region boundaries and input data come from CIHI. Using the 2013, 2014, and 2015 waves of CCHS data, health is defined in quality terms using McMaster University's health utility index, which is comprised of a set of self-reported assessments of the respondent's health and we compute the mean index value per region. Additionally, life expectancy at birth data (collected from Statistics Canada) is included as a quantity-based output. First-stage results suggest more efficient regions are clustered in the central (Ontario) and western (Manitoba, Saskatchewan, Alberta, British Columbia) portions of the country.

In the second-stage, we conjecture that a region's ability to efficiently produce health care is impacted by a set of external circumstances, including socioeconomic, demographic, and health factors. Using OLS, along with more sophisticated techniques that account for serial correlation and the bounded nature of our efficiency scores, results suggest regional unemployment and the per cent of seniors within a region are indeed impactful and reduce efficiency. Explaining as much as 25 per cent of the variation in efficiency scores across regions, we also note that high levels of unemployment and seniors tend to exist more so in Atlantic Canada – i.e., Newfoundland, Prince Edward Island, Nova Scotia, and New Brunswick.

Given regional discrepancies, we examine the extent to which higher levels of unemployment and senior citizens in Atlantic Canada explain the gap in efficiency scores. Using a set of Oaxaca-Blinder methods of decomposition, we find that about one-third, and perhaps as much as two-thirds, of the relative inefficiency observed in Atlantic Canada is attributable to more unemployment and seniors. The remainder of this gap appears to be the result of differences in ‘group membership’ – i.e., the unexplained gap is largely due to differences in the intercept parameter estimate. It is possible that highly skilled physicians may have more employment opportunities across Canada and self-select into more desirable locations – e.g., some may be compelled to live in closer proximity to a major urban centre. Additionally, 2013–2015 CIHI data, obtained from the National Physician Database, suggests that physicians in Atlantic Canada are among the lowest paid, along with those in Quebec – the next least efficient locale in Canada. And, if higher than average demands are being placed upon the health care system, this too would incentivise physicians to seek employment elsewhere – particularly if socioeconomic factors reduce the province's ability to fund physicians and hospitals.

The primary limitation of this study concerns ‘separability’ of stages. Simar and Wilson (2011) argue that those variables included in the second-stage regression be exogenous in terms of impacting the first-stage frontier. If this exogeneity assumption is violated, then first-stage results may be biased, leading to erroneous inferences in the second-stage. While a covariate such as the regional unemployment rate is undoubtedly correlated with the health of a region, the question is whether such a variable belongs in the first-stage of health care production (in addition to current inputs). Dario et al. (2018) suggest a method for testing separability; however, they also note that a ‘dishonest researcher might be tempted to split the sample repeatedly until the desired result is obtained’ (p. 187) – hence, a robust test has not been developed. While we leave a test of separability to future research, we did test one of our key findings: that a sizeable portion of the Atlantic Canadian efficiency gap would be reduced had the region been endowed with less unemployment and a younger population. By including these two variables in our first-stage analysis, we determined a set of efficiency scores using DEA, and results are very much in line with our original findings – i.e., Atlantic Canadian health regions tend to be less efficient. We then replaced the Atlantic Canada unemployment and senior variable values with Canadian averages (that excluded this part of the country), and re-ran our first-stage estimation procedure. Results suggest that while Atlantic Canada still lags behind the rest of the country, the efficiency gap drops by 34 per cent – a value that is comparable to our Oaxaca-Blinder decomposition findings.

Further, with a standard DEA model, there is neither consideration of the DMU internal structure, nor the intervening steps (e.g., patients entering the model as part of the production function). On the other hand, a network DEA model, opens the ‘black box’ and considers different aspects of a health region. Thus, the production of health care presented by a network DEA model may contain the entire health care market, including patient characteristics. In addition to the efficiency of the entire health care production model, it enables efficiency calculations of separate sub-processes (Lewis and Sexton, 2004; Tone and Tsutsui, 2009; Podinovski, 2021; Afonso et al., 2023). Such a multi-stage DEA model would be an avenue for future research, and could increase the discriminatory power regarding the efficiency of health care production in regions across Canada.

Another limitation is that we are unable to observe where individuals receive their health care; instead, we assume that care is provided in the respondent's region of residence. This is not always the case. For instance, a very sick individual may not be able to receive the care they need within their region, and is therefore required to travel elsewhere.²⁵ As a result, we are erroneously attributing their region's inputs to the betterment of their health. Moreover, regions that receive these sick individuals require more inputs, which causes them to appear more inefficient. Indeed, Canada's three largest cities – Montreal, Toronto, Vancouver – have efficiency scores that are far lower than anywhere else in the country. While we remove these three outliers from the analysis, as well as the two very northern/remote regions (which likely require care from such urban centres), the extent of interregional travel for health purposes is not directly observed in our analysis and something future studies may wish to examine.

In our model, labour and capital are specified in terms of number of physicians and hospital beds. This is not a comprehensive list of inputs. Additional matters such as the number of nurses and specialists, along with the quality of the physicians and/or infrastructure, may shed further light on the production process. However, this would require access to several datasets, some of which are not publicly available. Consequently, data restrictions limited our selection of inputs. As noted above, several other papers have used a similar set of inputs (i.e., number of physicians and beds); nonetheless, we suggest that future DEA research examine the extent to which these efficiency results are robust to the inclusion of additional inputs.²⁶

5.1 Conclusion and policy implications

Although unemployment benefits are paid out federally, provincial governments are also impacted by rising levels of unemployment. In particular, the unemployed do not contribute to provincial-level revenues to the same extent as those who are working. Consequently, this puts additional strain on the provision of publicly-funded health care (which is under provincial jurisdiction). Although the CHT is designed to equalise per capita health care services,²⁷ given that the unemployed tend to be less healthy (McKee-Ryan et al., 2005; Dorling, 2009; Halliday, 2014), which presumably increases their demand for health care, there are resulting inefficiency implications concerning the provision of care. As a result, budgets may need to be adjusted downward in light of rising levels of unemployment – e.g., salaries may be frozen and modernised capital may no longer be affordable. This would imply that health regions in provinces with above average levels of unemployment are less likely to provide quality care given a dearth of new technology and updated infrastructure, along with concerns that non-competitive salaries may incentivise care providers (particularly those most efficient) to look elsewhere. Consequently, the efficiency of health care provision in these regions is reduced. Therefore, we argue that transfer payments be adjusted to account for factors, such as an ageing population and unemployment, to better equalise health care efficiency across Canada. While this may be particularly helpful to Atlantic Canada, where the unemployment rate has historically exceeded the national average, it would also benefit those provinces that are prone to boom-and-bust cycles that arise from resource price fluctuations.

Although health care is among the largest provincial expenditures, Canada's federal government provides the CHT to each province, which typically accounts for as much as 20 per cent of provincial spending on health. For instance, the Government of Canada reported that, in 2014–15, just over 32 billion Canadian dollars was transferred among the provinces, more than the other two major transfers – the Canada Social Transfer and Equalization – combined.²⁸ This transfer is justified on the basis of ensuring provinces maintain a certain standard of care as identified by the Canadian Health Act.²⁹

Beginning 2014–15, the Conservative government began allotting the CHT to each province on an equal per capita cash basis – a policy that continues under the Liberal party. This policy change was in addition to a downward revision of the previous 6 per cent escalator, such that annual CHT growth is, as of 2017–2018, based on nominal GDP growth with a 3 per cent floor.³⁰ However, this increase applies to the total CHT allotment; not the amount transferred to each province. As Di Matteo (2017) notes, given different population growth rates, this has led to CHT growth in Atlantic Canada lagging behind the rest of the country.

Prior to this policy change, the CHT included both cash and tax point transfers, meaning the per capita cash transfers had previously differed across provinces. Many have argued this policy change has increased the amount of fiscal stress placed on provinces with below-average incomes.³¹ More specifically, tax point transfers allowed for a more redistributive system with ‘have-not’ provinces receiving more per capita pay outs. Thus, provinces with larger tax bases see a greater benefit from an equal per capita cash model. Certainly, an equalised per capita allotment appears fair given fiscal discrepancies across provinces; however, such a policy fails to address other notable differences, including age and socioeconomic status – issues that our results suggest, reduce a region's ability to produce efficient health care.

Mou (2021) argues that the CHT be age-adjusted to reduce between-province health inequities. Likewise, Marchildon and Mou (2014) suggest that the CHT formula be adjusted using a ‘needs-based’ allocation system that accounts for both an ageing population and geographic dispersion within each province. Their findings suggest that the Atlantic provinces would gain under this new formula, even when compared to the previous policy that blended both cash and tax point transfers. While our results argue in favour of an adjustment based on population ageing and socioeconomic differences, the latter would be the responsibility of the Equalization transfer – and such an amendment would likely be ‘politically challenging’ (Mou, 2021).³² However, as noted in Section 4, our results do suggest a high degree of correlation between regional unemployment and rural living. Hence, our paper presents further support for a CHT model that accounts for factors that put pressure on a province's ability to efficiently produce health care – even if such amendments operate through indirect channels such as geographic dispersion. It is also akin to policies used in several other countries, including the United Kingdom, where a risk-adjusted capitation model accounts for, among other factors, regional demographic diversity.

More resources do not necessarily entail hiring more physicians and/or purchasing more hospital beds – this would yield more inefficiency based on our model. Nevertheless, the current demands placed on the health care system do require additional inputs, which ultimately suggest that the Atlantic provinces are less efficient than the rest of Canada. Therefore, elevated levels of inefficiency may be justified on account of the demands that are being placed on the system – i.e., these regions are inefficient partially because socioeconomic and demographic factors reduce their ability to achieve high levels of health utility and life expectancy with their current set of resources. However, given our decomposition results suggest there is a potential unexplained efficiency gap regarding ‘group identification’, this implies that additional resources could also be used to attract a highly skilled talent pool of physicians. Thus, a larger transfer may help provinces incentivise physicians to practice in regions of need.

Additionally, more advanced capital could be afforded. Barua and Moir (2019) find that New Brunswick, Nova Scotia, and Prince Edward Island have some of Canada's longest wait times in terms of referrals to specialists and technology. Likewise, Esmail and Wrona (2008) note that Canada compares poorly with the OECD countries in terms of access to medical technology. However, their findings also suggest a large degree of disparity across provinces, which may certainly be exasperated in light of an equal per capita cash funding model that does not adjust for external factors.

Given unemployment and an ageing population put downward pressure on health care efficiency, adjustments to the CHT for regional heterogeneity may allow regions in Atlantic Canada to meet their relatively high levels of health care demand, while still having adequate resources that are broadly in line with those used throughout the rest of the country. Further, such a policy amendment would also be in line with Canada's 1982 Charter of Rights, which promotes ‘equal opportunities for the well-being of Canadians’. As such, a needs-based transfer model would better allow Canada to sustain high-level universal health care, while improving upon equity among the so-called ‘have’ and ‘have-not’ provinces.