PRELIMINARY
Not for quotation
Health Spending, Health Outcomes, and Per Capita Income in Canada:
A Dynamic Analysis
Kathleen Day*
and
Julie Tousignant**
May 29, 2003
*
Department of Economics, University of Ottawa, 200 Wilbrod Street, Ottawa,
K1N 6N5. e-mail: kmday@uottawa.ca
**
Economic and Fiscal Policy Branch, Department of Finance, 140 O’Connor Street,
Ottawa, K1A 0G5. e-mail: Tousignant.Julie@fin.gc.ca
1. Introduction
While there has been much discussion of the rising cost of the health system in Canada,
there does not seem to be much analysis of the relationship between spending on health
and health outcomes (i.e. population health status) in Canada. Most existing studies of
this relationship use either international cross-section data or time-series data pooled
across countries. Some recent studies have found a positive relationship between
spending on health and health outcomes (Or 2000a,b; Baldacci et al. 2002), but others did
not find a significant relationship between the two variables (Filmer and Pritchett 1999,
Thornton 2002). Still others, such as Baldacci et al. (2002), find that their results depend
on the data set and/or estimation methods used. All studies find a positive and significant
relationship between health outcomes and real per capita income.
To date, it seems that only three papers on the topic have focused on Canada, although
Canada is included in the panel data sets used by Or (2000a,b) and Hitiris and Posnett
(1992). Crémieux et al. (1999) examine the relationship between health indicators such as
infant mortality rates and life expectancy and total (public and private) per capita
spending on health, using pooled time-series cross-section data for the ten provinces for
the period 1978-1992 (Crémieux et al., 1999). Kee (2001) also uses pooled time-series
cross-section data for the ten provinces for the 1975-1996 period. As do Crémieux et al.
(1999), Kee regresses indicators of population health (infant mortality rates, life
expectancy, and age-standardized mortality rates) on a number of variables, including
real per capita public expenditures on health. However, unlike Crémieux et al. (1999),
Kee uses instrumental variables estimation to control for possible simultaneity between
health status and public spending on health. Both studies find a statistically significant
relationship between health status and both health spending and per capita income.
Finally, Deussing (2003), who used microdata from the 1996 National Population Health
Survey for Canada, finds that provincial government spending on health has no impact on
self-assessed health status.
A related strand of literature has examined the determinants of health expenditures
(Gerdtham et al. 1992, Hitiris and Posnett 1992, Di Matteo and Di Matteo 1998). Much
of this literature has focused on the relationship between aggregate health spending and
per capita GDP in OECD countries, with the most recent studies applying unit root and
cointegration tests in an attempt to determine whether per capita health expenditures and
per capita GDP are cointegrated (Hansen and King 1996, 1998; McCoskey and Seldon
1996; Blomqvist and Carter 1997; Gerdtham and Löthgren 2000, 2001; Okunade and
Karakus 2001; Jewell et al. 2003). These studies were motivated by the suspicion that the
counter-intuitive finding of earlier studies that health care was a luxury good, not a
necessity, was a spurious result due to the presence of unit roots in time-series data on per
capita health spending and GDP per capita. However, with the exception of Hitiris and
Posnett (1992) these studies seem to have excluded health outcomes from their analysis.
Furthermore, they focus on the long-run relationship between the variables and do not
explore the short-run dynamics.
2
The exclusion of some indicator of health outcomes from studies of the long-run
relationship between per capita health spending and per capita GDP is surprising given
that several studies of the determinants of health outcomes have pointed to simultaneity
between health outcomes and per capita health spending as a possible source of bias
(Filmer and Pritchet 1999, Kee 2001). In addition, from the point of view of policy
makers, it would be desirable to know more about the short-run dynamics of the
relationship between health outcomes, health spending, and GDP per capita as well as
about the long-run relationship between the variables. For example, they might be
interested in knowing how a permanent increase in per capita health spending is likely to
affect the economy in the short run as well as the long run.
To this end, we explore the dynamic relationship between three variables: real per capita
income (as measured by GDP or GNP), real per capita spending on health and an
indicator of health outcomes, using time-series data for Canada. With data from the
Historical Statistics of Canada we explore this relationship for the longest time period
possible. In order to do this, we examine different subsets of variables during the periods
1926-1999 and 1950-1997. For purposes of comparison with earlier studies that used
post-1960 panel data for OECD countries we also carry out an analysis for the period
1960-1997. Although other studies provide evidence that other variables (eg.,
demographic structure, tobacco and alcohol consumption, environmental quality) also
influence per capita health care spending and health outcomes, in this paper we restrict
our attention to a three-variable system because it is not possible to find extensive timeseries on many of these other variables. We also experiment with three different health
indicators: the infant mortality rate, age-standardized mortality rate, and a composite of a
group of standard health indicators constructed using principle components analysis. Unit
root and cointegration tests are used to help identify the appropriate dynamic model. Our
econometric analysis differs from that of previous studies in that we make use of a
relatively new unit root test proposed by Elliot, Rothenberg, and Stock (1996), and a new
lag selection criterion for unit root tests proposed by Ng and Perron (2001). The results
indicate that the dynamic relationship between the three variables may be more complex
than what previous studies have indicated.
2. Econometric Methods
The objective of this paper is to build a simple dynamic model of the relationship
between three variables. Since the choice of specification for a dynamic model depends
on whether or not the included variables have unit roots, we begin our analysis by testing
for the presence of unit roots in the data during each of the time periods considered.
Many different unit root tests have been proposed and it is well-known that many of them
suffer from a lack of power.1 Previous studies of the relationship between per capita
health expenditures and per capita GDP have used a variety of different tests, including
the augmented Dickey-Fuller (ADF) test (Hansen and King 1996, Okunade and Karakus
2001, Gerdtham and Löthgren 2001) the Phillips-Perron (PP) test (Blomqvist and Carter
1
See Maddala and Kim (1998) for a recent survey of unit root tests and their properties.
3
1997, Okunade and Karakus 2001), the Im, Pesaran, and Shin (IPS) (2003) panel unit
root test (McCoskey and Selden 1998, Gerdtham and Löthgren 2001, 2001; Okunade and
Karakus 2001), and the Im, Lee, and Tieslau (ILT) (2002) panel unit root test that allows
for an unknown structural break (Jewell et al. 2003). Because we are restricting our
attention to Canada alone, panel unit root tests are out of the question. Instead, we use the
ADF test with GLS detrending, called the ADF-GLS test, proposed by Elliot,
Rothenberg, and Stock (1996). Elliot et al. show that the power of the ADF test in the
case of series with a constant mean and/or a deterministic trend is improved considerably
by the method they propose to estimate the coefficients of the deterministic terms.
Usually the coefficients of these terms are estimated simultaneously with the test statistic
by including a constant or a constant and trend in the test equation. Elliot et al. suggest
estimating these coefficients before estimating the test statistic, using OLS applied to
quasi-differences of the original series and the deterministic terms. Then these estimated
coefficients are used to detrend the original series, and the ADF test is applied to the
detrended residuals.
To be more precise, the ADF-GLS test is based on the equation
k
∆~
yt = β 0 ~
yt −1 + ∑ β j ∆ ~
yt − j + ε tk ,
(1)
j =1
where yt is the series to be examined, εtk is a random error term, ~
y t = y t − ψˆ ′z t , zt is a p
by 1 vector of deterministic terms, ψˆ is the OLS estimator of the vector y in the
regression of ya = (y1, y2 - a y1 , …, yT - a yT −1 )′ on za = (z1, z2 - a z1 , …, zT - a zT −1 )′ , and
a = 1 + c / T . Elliot et al. (1996) recommend that c be set equal to –7 when zt consists
solely of a constant and equal to –13.5 when zt includes a constant and a trend. The test of
the null hypothesis of a unit root is based on the t ratio of β̂ 0 , the estimated coefficient of
~
y t −1 . In the case where zt includes a constant term only, the critical values for the test are
identical to those for the standard ADF test with neither constant nor trend. Elliot et al.
(1996) provide asymptotic critical values for the case where zt includes a constant and a
trend, as well as critical values for 50, 100, and 200 observations. The standard ADF test
should be used in cases where yt is believed to have a zero mean (in which case no
deterministic terms are necessary).
Like the standard ADF test, the ADF-GLS test is sensitive to the choice of k, the number
of lagged terms to be included in the test equation. Recently Ng and Perron (2001) have
demonstrated that additional gains in the power of the ADF-GLS test can be achieved by
using a modified version of the AIC criterion, which they call the MAIC. We therefore
use this criterion to choose k for the ADF-GLS test.2
When data series are found to contain unit roots, the next step in the analysis is to test for
cointegration between the variables. Most econometric analyses of cointegration have
focused on the case where all variables are I(1), or integrated of order 1. In this case, we
2
Both the ADF-GLS unit root test and automated lag length selection based on the MAIC have recently
been implemented in EViews 4.1, which we used to carry out our analysis.
4
apply Johansen’s trace test and maximum eigenvalue tests, described in Johansen
(1995a). Prior to the application of the tests we use a system AIC to choose a lag length
for each unrestricted VAR model. The analysis of systems with I(2) variables is left to
future research.
3. Data
For the purposes of this study, we need data on three variables: a measure of the
population’s health, a measure of real per capita spending on health, and a measure of
real per capita income. As there is no general agreement as to what is the best measure of
the overall health of the population, we use several different measures, all of which are
discussed in section 3.1. In addition, in order to obtain long time series of data on health
spending and income per capita, certain assumptions had to be made about how to link
overlapping data series. Further details about data sources and the construction of the data
are provided in the data appendix, while the behaviour of the data over the sample period
is discussed in sections 3.2 and 3.3.
3.1 Measures of population health
Health status, which refers to the level of health of an individual, group or population, is
difficult to estimate and there is no universally accepted indicator that captures all the
aspects of health. Different measures of health status are available but they provide only a
partial perspective on the population’s level of health. The most commonly used
indicators are based on mortality data. These indicators capture the decrease in mortality
and therefore provide an indication of improvement in the quantity of life, not in the
quality of life. This means that even if these measures show an improvement in longevity,
they are not sufficient to indicate that health status has improved. The following is a list
of commonly used measures:3
1) Potential Years of Life Lost (PYLL) consists of the number of years of life “lost”
when a person dies before age 70 or age 75. It provides an indirect estimate of
how many deaths could be potentially avoided. The rate per 100,000 population is
more useful because it takes into account the effect of the size of the population.
2) The Infant Mortality Rate (IMR) refers to the number of deaths per 1,000 live
births. It generally reflects the level of mortality and the effectiveness of
preventive care and the attention paid to maternal and child health.
3) The Perinatal Mortality Rate (PMR) consists in the count and rate of fetal deaths
of 28 or more weeks gestation and infant deaths under 1 week per 1,000 total
births. This indicator reflects standards of obstetric and pediatric care, as well as
the effectiveness of public health initiatives.
3
This list is taken from http://www.statcan.ca/english/freepub/82-221-XIE/free.htm .
5
4) The Age-Standardized Mortality Rate (ASM) is the number of deaths per 100,000
of total population, standardized for the age composition of the population. The
use of a standard population adjusts for variations in population age distributions
over time and across different geographic areas.
5) Life Expectancy (LE) is the number of years a person would be expected to live,
starting from birth (for life expectancy at birth) or at age 65 (for life expectancy at
age 65), on the basis of the mortality statistics for a given observation period. It
measures quantity rather than quality of life.
6) Probability of Survival from Birth to Age 80 is the probability of a newborn infant
surviving to age 80, if subject to prevailing patterns of age specific mortality
rates. This measure is recent and not widely used. Statistics Canada provides it for
the period 1986 to 1996.
Recently, other measures have been developed that aim at measuring the quality as well
as the quantity aspect of life associated with health, such as Health-Adjusted Life
Expectancies (HALEs) and Disability-Adjusted Life Years (DALY).4 Essentially, these
measures adjust life expectancy for quality of life mainly by using years of life without
any activity limitation.
In this study, only five of the indicators will be used as measures of health status because
of the absence of data for a long period of time. These measures are the infant mortality
rate (IMR), the perinatal mortality rate (PMR), the age-standardized mortality rate
(ASM), life expectancy at birth (LEB), and life expectancy at 65 (LE65). The infant
mortality rate is used for our analysis because it is available for the 1926-1999 time
period. The IMR and the ASM are both used in our analysis of the 1950-97 and post1960s periods.
Figure 1 shows the evolution of IMR, PMR, ASM, LEB and LE65 between 1950 and
1997. All the indicators show an improvement in health status between 1950 and 1997.5
The greatest improvements (in percentage terms) over the 1950-1997 period have been in
IMR and PMR, while LEB and LE65 improved the least. The improvements in IMR and
LEB reflect observations made in previous work which suggest that life expectancy at
birth has increased primarily as a result of the reduction in infant mortality rates, since the
effect on life expectancy is larger when mortality rates fall at younger ages. The
percentage improvement in ASM lies between that of the other four measures over the
period 1950-1997.
4
See Jee and Or (1998) for a discussion of these and other alternative health indicators.
The indicators have been converted to indexes with their first year equal to 100, thus any improvement in
the measure reflects improvement in the population health status. IMR, ASM, PYLL and PMR would
ordinarily show an improvement in the health status of the population through a decline in their levels (i.e,
a decline in mortality means children are healthier), but to make them comparable to life expectancy in the
figures their growth rates were multiplied by –1.
5
6
When we consider a longer time horizon, between 1926 and 1997, the greatest
improvements (in percentage terms) are again observed for IMR and PMR, while LEB
and LE65 improved the least (Figure 2). However, the improvement in LEB is greater
when 1926 serves as the base year, while the evolution remained comparable for the
other three variables. Lise (2000) notes that prior to the mid 1960s, the increase in life
expectancy at birth was the result of more people surviving childhood and early working
years and living to old age. Since the mid 1960s, while falling childhood mortality has
continued to be an important factor, there have also been increased gains resulting from
falling mortality rates over age 55, leading to increased years of old age. However, the
total improvement in LEB since the mid 1960s has been only about half of the gain
during the previous 40 years.
Finally, for the 1950-1997 and 1960-1997 periods we also use a composite indicator
constructed from five of the individual measures. While the health status indicators
discussed above provide different perspectives on population health, they are all derived
from vital statistics data on death rates and are highly correlated. A summary indicator
that could account for a high proportion of the variation in the group of indicators
considered may serve as a good overall indicator of health status.
To construct a summary indicator, principal components analysis was used.6 This
mechanical procedure produces a single indicator of health status (the first principal
component) summarizing the information contained in multiple measures using a linear
function that applies a different weight to each variable. An indicator summarizing IMR,
ASM, PMR, LEB and LE65 was computed (Figure 3). Its behaviour throughout the 1950
and 1997 period shows a clear improvement in population health status. Other indicators
can be computed for different time periods and different subsets of the individual
indicators.
3.2. Public/Private Health Spending in Canada
Figure 4 presents a brief portrait of the evolution of health spending in Canada. Since
1975, public health spending (real per capita, age-adjusted, internal calculations)7 has
fluctuated somewhat but has increased overall from approximately $9,000 in 1976 to
$12,000 in 2001. Private health spending (real per capita, age-adjusted) over the same
period increased from $3,000 to $5,000.
Between 1975 and 1991, public sector spending grew rapidly but between 1993 and 1997
it decreased in real per capita terms. This reduction coincides with the period in which
Established Programs Financing (EPF) and the Canada Assistance Plan (CAP) were
consolidated into the Canada Health and Social Transfer (CHST) and total cash payments
under this program were reduced.
6
For more information, see chapter 7 of Morrison (1967).
The authors would like to thank Harriet Jackson and Alison McDermott, economists at Finance Canada,
Fiscal Policy Division, for providing these numbers.
7
7
Since real per capita age adjusted expenditures are only available for a short period of
time, total real health expenditures per capita, i.e. the sum of private and public spending,
will be used. This is done to capture the variation in spending between the two sectors
and because the breakdown is not available historically as far as we would like.
Since 1945, total real health expenditures per capita have increased (Figure 5), aside from
the 1993 to 1997 period where they remained stable, reflecting the public sector spending
period mentioned above.
3.3 Real income per capita
Real income per capita is measured by GDP per capita in most studies of the
determinants of health spending and health outcomes. However, real GDP is not available
for Canada for the entire 1926-1999 period. Therefore we use real GDP per capita only
for the 1950-1997 and 1960-1997 periods. For the 1926-1999 period, we use real GNP
per capita. Figure 6 illustrates the behaviour of the two series, in millions of 1997 dollars,
over the 1926-1999 period. It can be seen that the two series behave in a very similar
fashion and increased overall throughout time.
4. Results
In this section we report the results of unit root and cointegration tests for the three
different time periods analyzed: 1960-1997, 1950-1997, and 1926-1999. All tests were
applied to the natural logs of the variables.
4.1 1960-1997
As noted in the introduction, recently a number of authors have tested for unit roots and
cointegration between real per capita health expenditures and real per capita GDP in
OECD countries, using different unit root and cointegration tests. The sample period
covered by these studies varies, but all begin in 1960. Their results for Canada are
summarized in Table 1.
A glance at Table 1 reveals substantial disagreement between the previous studies on the
order of integration of real per capita health expenditures and real per capita GDP in
Canada. Even studies which appear to use the same data (they cite the same sample
period and data source) obtain different results. In some cases these differences may be
due to the fact that not all studies tested explicitly for the order of integration; of the four
studies that used data for the period 1960-1997, only Okunade and Karakus (2001) and
Gerdtham and Löthgren (2000) provide the results of unit root tests for both the levels
and the first differences of variables, which may help to explain why Okunade and
Karakus (2001) are the only ones to conclude that for Canada, health expenditures were
8
integrated of order 2 (using both the ADF and PP tests).8 The ADF tests (but not the PP
tests) carried out by Okunade and Karakus also implied that per capita GDP was
integrated of order 2. Jewell et al. (2003), on the other hand, using a panel unit root test
that allows for the possibility of structural break, found that per capita GDP was trendstationary (with no breaks) for Canada.
The results of the ADF-GLS tests for real per capita total health expenditures (LTHE),
real per capita public health expenditures (LPHE), real GDP per capita (LGDP), and
three alternative indicators of health outcomes (the composite indicator, age-standardized
mortality rate, and the infant mortality rate) are presented in Table 2. To determine the
order of integration of each variable for each time period, we apply the ADF-GLS test to
the levels, first differences, and if necessary, the second differences of the series. Since
the graphs in section 3 indicate that all the data series exhibit clear trends, for tests on the
levels of all variables, zt is assumed to consist of a constant and a trend; for the first
differences, only a constant term is included in zt; and for the second differences, which
appear to have a zero mean, the standard ADF test with neither constant nor trend is used.
In all three cases the MAIC was used to select the appropriate number of lagged terms to
include in the test equation.
While for most of the variables the results with respect to the order of integration during
the 1960-1997 period are clear, in the case of total health expenditures it is not entirely
clear whether the series is I(1) or I(2). We can reject the null hypothesis of a unit root in
the first difference of LTHE, but only at the 10% level of significance. The second
difference of LTHE is definitely stationary, at even the 1% level of significance. Public
health expenditures, however, are clearly I(2), and as in most of the previous studies, per
capita GDP is found to be I(1). Of the three indicators of health outcomes, only the agestandardized mortality rate (LASM) is I(1), while the infant mortality rate (LIMR) and
the composite indicator (LHS) are both I(2).
These findings have important implications for cointegration testing. If in fact the orders
of integration of total health expenditures and GDP are different, then they cannot be
cointegrated in a bivariate model. This would contradict the findings of Blomqvist and
Carter (1997) and Gerdtham and Löthgren (2000, 2001). Furthermore, cointegration
would also be impossible in a trivariate model including LTHE, LGDP, and LASM since
such a model would include only one I(2) variable. The possibility remains that
cointegration might exist in a trivariate model in which either LHS or LIMR were used as
the indicator of health outcomes, but the most widely-used tests for cointegration,
Johansen’s trace and maximum eigenvalue tests, would not be valid in this I(2) model. It
is also possible that public health spending may be cointegrated with LGDP and either
LHS or LIMR.
8
In footnote 15 of their paper Gerdtham and Löthgren (2000) note that ADF tests applied to the first
differences of the log of per capita health expenditures (with a constant but no trend included in the test
equation) led to the conclusion that this variable was I(1) in all but four of the 21 countries they examined.
However, they do not indicate the countries in which per capita health spending was I(2).
9
If instead LTHE is I(1), then we can use Johansen’s trace and maximum eigenvalue tests
to test for cointegration between the I(1) variables LTHE, LGDP, and LASM, or between
any pair of these variables. Table 3 presents the results of cointegration tests for I(1)
vector error correction models (VECM) involving these three variables. Except where
indicated, the tests were carried out under the assumption that both a constant and a trend
appear in the cointegrating equations.
For the trivariate model including per capita total health expenditures, per capita GDP,
and the age-standardized mortality rate, it is possible to reject the null hypothesis of no
cointegrating vectors at the 10% level of significance. However, the test statistics are
only marginally significant; if we were to apply the degrees of freedom correction
proposed by Reimers (1992) it would be impossible to reject the null hypothesis.9
Similarly, when a trend is included in the cointegrating equation we do not find
cointegration in any of the bivariate models analyzed. With respect to the bivariate model
that includes per capita total health spending and per capita GDP, our results thus
contradict the earlier findings of Blomqvist and Carter (1997), and Gerdtham and
Löthgren (2000, 2001). This finding raises the possibility that the results of previous
studies of the relationship between these variables that did not test for cointegration may
not be reliable.
4.2 1950-1997
For the 1950-1997 period, the results of the ADF-GLS tests are presented in Table 4. For
all of the variables the results with respect to the order of integration during the period are
clear: the series are I(2). The second differences of all variables are definitely stationary
at the 1% level of significance, but neither the levels nor first differences are stationary at
even the 10% level of significance.
Again, these results have important implications for cointegration testing. Since all
variables are of the same order of integration, cointegration may exist in either a trivariate
or a bivariate system. However, the most widely-used tests for cointegration, Johansen’s
trace and maximum eigenvalue tests, are not valid in an I(2) model. The problem of
testing for cointegration in I(2) systems with a deterministic trend has recently been
discussed by Rahbek et al. (1999), but we have not applied their tests in this paper.10
4.3 1926-1999
For the 1926-1999 period, the results of the ADF-GLS tests for real GNP per capita and
the infant mortality rate are presented in Table 5. As in the shorter sample periods, the
9
The results of the trace and maximum eignevalue tests assuming a constant but no trend for the other
models are not reported here, as they either were the same as for the case reported or indicated that the
variables were stationary. The latter conclusion conflicts with the results of the unit root tests and can be
regarded as a sign of model misspecification.
10
Testing and estimation in I(2) systems is also addressed in Johansen (1995b).
10
results indicate that the infant mortality rate is integrated of order 2, as we can reject the
null hypothesis that the second difference of LIMR has a unit root at the 1% level of
significance. In the case of real GNP per capita, the results indicate that we can reject the
null hypothesis of a unit root in the level of LGNP at the 5% level of significance, which
suggests that real GNP per capita is trend stationary with no unit roots. This result is
somewhat surprising, since real GDP per capita was found to have a unit root in the
shorter sample periods. The fact that the orders of integration of the two variables are
different means that LGDP and LIMR cannot be cointegrated in a bivariate model. Thus
no further analysis of this long time period is possible without the addition of more
variables to the system.
5. Conclusion
Despite considering three different health indicators and two different measures of health
spending, in this paper we have not managed to achieve our objective of building a
simple dynamic model of the relationship between per capita health spending, per capita
GDP, and health outcomes. But several conclusions can be drawn from the analysis. First
of all, the results of the unit root tests are clearly sensitive to the choice of sample period.
For example, real per capita GDP was found to be integrated of order 2 and integrated of
order 1, depending on the sample period. Similarly, the order of integration of some
health indicators and measures of per capita health spending seems to depend on the
choice of sample period.
Second, we found little evidence of cointegration between per capita health spending, per
capita GDP, and health outcomes during the 1960-1997 period. Furthermore, the infant
mortality rate and per capita GDP do not seem to be cointegrated during the longer 19261999 time period. Cointegration tests were not carried out for the 1950-1997 period
because during this period, all the variables examined appeared to be integrated of order
2. Further testing and estimation of a more complex model for I(2) variables along the
lines proposed by Rahbeck et al. (1999) is required to pinpoint the number of
cointegrating vectors and analyze the dynamic behaviour of the variables.
What do these results imply regarding the relationship between per capita health
spending, per capita GDP, and health outcomes? Although on the surface the results seem
to suggest the lack of a long-run relationship between the variables, in fact what they may
really imply is that the simple bivariate and trivariate models analyzed in this paper are
inadequate. There are at least two possible directions for further research worth pursuing.
First, it may be the case that as Jewell et al. (2003) conclude, the variables we have
examined are in fact stationary around a broken deterministic trend. Although a break is
not obvious in the plots of the data, both public and private health spending are likely to
have been affected by such major policy changes in the funding of health care medicare
in Canada. The application of unit root and/or cointegration tests that allow for the
possibility of unknown structural breaks would therefore be a good idea.11
11
Recently Peron and Rodriguez (2003) have extended the unit root tests of Elliot et al. (1996) and Ng and
Perron (2001) to the case of single unknown structural break.
11
Second, the observed lack of cointegration between the I(1) variables examined may be
an indication of model misspecification rather than the absence of any long-run
relationship between the variables. If so, it would be worthwhile to develop a more
complete structural model of the interactions between per capita health spending, per
capita GDP, and health outcomes (in addition to estimating an I(2) model for the 19501997 period). While the sample period available for the estimation of such a model would
necessarily be more restricted than that employed here, it is possible that cointegration
might in fact exist in a properly specified model.
12
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15
Data Appendix
1. The data for Age-Standardized mortality rate per 100,000 population comes out of the
Statistics Canada’s Health Indicators 1999 CD-ROM.
2. The data source for Infant Mortality Rate for 1921 and 1990 is the Selected Mortality
Statistics, Canada, 1921-1990, Catalogue 82-548, while the data source for 1990 to 1999
is Cansim II table 102-0030, Statistics Canada.
3. The Perinatal Mortality Rate data was taken from the Selected Infant Mortality and
Related Statistics, Canada 1921-1990, Catalogue 82-549 for 1921 to 1990, while the data
source for 1990 to 1999 is the Statistics Canada’s Health Indicators 1999 CD-ROM.
4. Because the data for Life Expectancy going back to 1920 is only presented for fiveyear intervals, life expectancy for Canada used in this article was computed using internal
calculations on a yearly basis.12 Calculations were made using data on death rates and
population numbers provided by Statistics Canada’s Life Tables.
5. Total health expenditures uses data from the 1945 to 1975 series B513, Total Health
Expenditures, of Statistics Canada’ Historical Statistics and from the 1975 to 1999 series
Total Health Expenditures from a publication13 of the Canadian Institute for Health
Information (CIHI).
6. Public health expenditures used the following data sources:
a) Series H307, All governments, gross general expenditure on health
from Statistics Canada’s Historical Statistics, 1965 to 1975
b) Series H150, All governments, net general expenditures on health, also
from the Historical Statistics, 1945 to 1969
c) Series Total Public Sector Health Expenditures from the CIHI
publication14, 1975 to 1999
7. Total population is the result of merging three series:
a) Series A1, from Statistics Canada’s Historical Statistics , 1926 to 1961
b) Population series from the Statistics Canada’s Health Indicators 1999
CD-ROM, 1961 to 1970
c) Series V466668, Total population, from Cansim II Table 051-0001,
Statistics Canada, 1971 to 2000
12
The authors would like to thank Allan Pollock, economist at Finance Canada, Economic Studies and
Policy Analysis Division, for computing these numbers.
13
National Health Expenditures Trends, 1975-2001._ Canadian Institute for Health Information, Ottawa,
2001, p.77, Table A.2.1.
14
National Health Expenditures Trends, 1975-2001._ Canadian Institute for Health Information, Ottawa,
2001, p.77, Table A.2.1.
16
8. Implicit price index for government current expenditure uses data from the price index
available through Statistics Canada’s Historical Statistics (1945 to 1975) and the price
index available through CIHI’s publication15 (1975 to 1999).
9. GDP data was taken from Finance Canada’s economic forecasting model. This GDP
measure is equal to Statistics Canada’ Series V1992067, Gross Domestic Product at
market prices, from Cansim II Table 380-0002.
8. GNP uses the following data sources:
a) Series F13, Gross National Product at market prices, from Statistics
Canada’ Historical Statistics, 1926 to 1975
b) Series V499688, Gross National Product at market prices, from
Cansim II Table 380-0015, 1961 to 1999.
9. GNP and GDP’s price deflator uses data from Series K172, Implicit Price Indexes of
Gross National Expenditures at market prices, from Statistics Canada’ Historical
Statistics (1926 to 1975) and from Series V1997756, Implicit Price Indexes, Gross
Domestic Product at market prices from Cansim II Table 380-0003 (1961 to 1975).
15
National Health Expenditures Trends, 1975-2001._ Canadian Institute for Health Information, Ottawa,
2001, p.B-1, Table B.1.
17
Figure 1
Infant Mortaility Rate, Perinatal Mortaility Rate, Age-Standardized Mortality Rate, Life
Expectancy at 65 and Life Expectancy at birth , Canada, 1950 to 1997 (1950=100)
210
190
IMR
ASMR
PMR
LEB
LE65
170
150
130
110
90
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
Figure 2
Infant Mortality Rate, Perinatal Mortality Rate, Life Expectancy at Birth and Life Expectancy at
65, Canada, 1926 to 1997 (1926=100)
210
190
170
IMR
PMR
LEB
LE65
150
130
110
90
1926 1930 1934 1938 1942 1946 1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994
18
Figure 3
Summary Indicator of Health Status for Canada, 1950 to 1997
160
150
140
130
Summary indicator
120
110
100
90
1950
1954
1958
1962
1966
1970
1974
1978
1982
1986
1990
1994
Figure 4
Public/Private Health Expenditures, Real per Capita, Age-Adjusted, (1975 dollars), Canada,
1976 to 2001
14,000
12,000
8,000
Public Sector
Private Sector
6,000
4,000
2,000
0
19
76
19
77
19
78
19
79
19
80
19
81
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
(In 1975$ )
10,000
19
Figure 5
Total Real Health Expenditures per Capita, (1997 dollars), Canada, 1945 to 1999
3,500
3,000
(In 1997$)
2,500
2,000
1,500
1,000
500
0
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
Figure 6
Real GNP per Capita and Real GDP per Capita, 1997 dollars, Canada 1926 to 2000
35,000
30,000
20,000
Real GNP per Capita
Real GDP per Capita
15,000
10,000
5,000
0
19
26
19
29
19
32
19
35
19
38
19
41
19
44
19
47
19
50
19
53
19
56
19
59
19
62
19
65
19
68
19
71
19
74
19
77
19
80
19
83
19
86
19
89
19
92
19
95
19
98
(In 1997 dollars)
25,000
20
21
Table 1. Unit root test results for Canada: Results of previous studies
Study
Unit root
test
Sample
period
Hansen and King (1996)
Blomqvist and Carter (1997)
McCoskey and Selden (1998)
Gerdtham and Löthgren
(2000)
Okunade and Karakus (2001)
ADF
PP
IPS
ADF, IPS,
KPSS
ADF, PP,
IPS
ADF, IPS
1960-1987
1960-1991
1960-1987
1960-1997
I(0)
I(1)
I(0)
I(1)
I(1)
I(1)
I(1)
I(1)
1960-1997
I(2)
I(2), I(1)
1960-1997
I(1)
I(1)
Gerdtham and Löthgren
(2002)
Jewell et al. (2003)
Order of integration
HE
GDP
Im et al.
1960-1997
I(1)
I(0)
(2002)
Only Hansen and King (1996), Blomqvist and Carter (1997), and Okunade and Karakus
(2001) test explicitly for the order of integration by testing both first and second
differences of the variables for unit roots.
22
Table 2. Results of unit root tests, 1960-1997
Variable
k
T
ADF-GLS
LGDP
∆ LGDP
0
0
37
36
-1.060
-4.154c
LTHE
∆ LTHE
∆2 LTHE
1
1
2
36
35
33
-1.914
-1.789a
-2.531b
LPHE
∆ LPHE
∆2 LPHE
2
8
1
35
28
34
-1.016
-0.003
-7.146c
LHS
∆ LHS
∆2 LHS
0
6
0
37
30
35
-1.382
0.065
-12.702c
LASM
∆ LASM
1
1
36
35
-2.075
-4.414c
LIMR
∆ LIMR
∆2 LIMR
a
significant at the 10% level
b
significant at the 5% level
c
significant at the 1% level
0
4
0
37
32
35
-1.116
-0.856
-10.551c
23
Table 3. Results of Johansen tests for cointegration, 1960-1997
H0
λTrace
H0
λmax
LGDP, LTHE, LASM k = 1, n = 37; constant and trend in cointegrating equations
r=0
39.664a
r=0
21.381a
18.282
r=1
12.586
r≤1
5.697
r=2
2.697
r≤2
LGDP, LTHE k = 1, T = 37; constant and trend in cointegrating equation
r=0
19.498
r=0
3.177
r=1
r≤1
16.321
3.177
LGDP, LTHE k = 1, T = 37; constant, no trend in cointegrating equation
r=0
19.312b
r=0
a
3.016
r=1
r≤1
16.296b
3.016a
LGDP, LASM k = 2, T = 36; constant and trend in cointegrating equation
r=0
19.498
r=0
3.177
r=1
r≤1
16.321
3.177
LASM, LTHE k = 3, T = 35; constant and trend in cointegrating equation
r=0
19.498
r=0
r=1
3.177
r≤1
a
significant at the 10% level
b
significant at the 5% level
c
significant at the 1% level
24
16.321
3.177
Table 4. Results of unit root tests, 1950-1997
Variable
k
T
ADF-GLS
LGDP
∆ LGDP
∆2 LGDP
1
9
0
46
37
45
-1.566
-0.924
-8.643c
LTHE
∆ LTHE
∆2 LTHE
0
7
0
47
39
45
-1.063
-1.532
-10.817c
LHS
∆ LHS
∆2 LHS
1
6
0
46
40
45
-1.599
-0.980
-16.422c
LASM
∆ LASM
∆2 LASM
1
7
0
46
39
45
-1.808
-0.641
-16.067c
LIMR
∆ LIMR
∆2 LIMR
a
significant at the 10% level
b
significant at the 5% level
c
significant at the 1% level
0
5
0
47
41
45
-1.432
-0.666
-10.689c
25
Table 5. Results of unit root tests, 1926-1999
Variable
k
T
ADF-GLS
LGNP
∆ LGNP
1
4
72
68
-3.566b
-3.266 c
LIMR
∆ LIMR
∆2 LIMR
a
significant at the 10% level
b
significant at the 5% level
c
significant at the 1% level
4
8
0
69
64
71
-1.627
-0.634
-16.816c
26