The Determinants of Canadian Provincial Health Expenditures: Evidence from Dynamic Panel PRELIMINARY FIRAT BILGEL * University of Saskatchewan ABSTRACT The aim of this paper is to reveal the magnitude of the income elasticity of health expenditure in Canadian Provinces. Health can be seen as a luxury good if the income elasticity exceeds unity and as a necessity good if the income elasticity is below unity. It can be further postulated that if the income elasticity of health expenditure is less than one, then a high priority has not been given to the public health sector among the goals for social and economic development. Panel data on real per capita GDP, relative price of health care, proportion of publicly funded health expenditure, the share of senior population, life expectancy at birth and real per capita transfers from federal government for 10 provinces have been used to investigate the determinants of Canadian real per capita provincial total, private and government health expenditures for the period 1975- 2002. The evidence in this paper supports that health appears to be a luxury for Manitoba and British Columbia whereas necessity for other provinces. However, from a national perspective health is not a luxury for Canada. Keywords: health expenditure, dynamic panel, income elasticity * e-mail: [email protected]
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The Determinants of Canadian Provincial
Health Expenditures: Evidence from
Dynamic Panel
PRELIMINARY
FIRAT BILGEL*
University of Saskatchewan
ABSTRACT
The aim of this paper is to reveal the magnitude of the income elasticity of health expenditure in Canadian Provinces. Health can be seen as a luxury good if the income elasticity exceeds unity and as a necessity good if the income elasticity is below unity. It can be further postulated that if the income elasticity of health expenditure is less than one, then a high priority has not been given to the public health sector among the goals for social and economic development. Panel data on real per capita GDP, relative price of health care, proportion of publicly funded health expenditure, the share of senior population, life expectancy at birth and real per capita transfers from federal government for 10 provinces have been used to investigate the determinants of Canadian real per capita provincial total, private and government health expenditures for the period 1975-2002. The evidence in this paper supports that health appears to be a luxury for Manitoba and British Columbia whereas necessity for other provinces. However, from a national perspective health is not a luxury for Canada.
Keywords: health expenditure, dynamic panel, income elasticity
* e-mail: [email protected]
2
1. INTRODUCTION
The aim of this paper is to reveal the magnitude of the income elasticity of health
expenditure in Canada. Health can be seen as a luxury good if the responsiveness is
sensitive to income changes (i.e. the income elasticity exceeds unity) and as a necessity
good if the responsiveness is insensitive to income changes (i.e. the income elasticity is
below unity). This concept was introduced by J.P Newhouse (1977). Another
interpretation of this notion can be found in Kyriopoulos and Souliotis (2002):
“If the income elasticity of HE is less than one, then the public health sector does
not have a high priority among the goals for social and economic development.”
1.1 Canadian Literature on Health Expenditures
The analysis of the determinants of health expenditures (henceforth HE) has been
very tempting for both applied econometricians and health economists for the past thirty
years. Nevertheless, there is no consensus on which methods to use, how to proceed and
what type of data to analyze. This may have occurred due to lack of strong theoretical
guidance. The pioneering studies emphasize the importance of national income in
explaining HE along with a selection of non-income variables, some of them are the
relative price of health care, the proportion of the population over 65, urbanization rate
and the publicly funded proportion of HE. While the significance of these non-income
variables depends on the structure of health sector and population, GDP accounts for
most of the variation in health care expenditure – see Parkin et al. (1987).
There exist few studies focused on Canadian health expenditures. Di Matteo and Di
Matteo (1998, henceforth DD) examined the determinants of Canadian provincial
government health expenditures within pooled time-series cross-section framework for
the period 1965-1991. The determinants of provincial government health expenditures
are found to be the real per capita provincial income, the share of senior population and
real per capita federal transfers. Although the issue of stationarity is not addressed, they
reported that the income elasticity of government health care spending is 0.77. Di Matteo
(2000) focused on the public and private Canadian health expenditures over the period
1975-1996. The health expenditures are examined both as total and as sub-expenditure
categories such as hospital, physician and drug spending. His findings of the major
3
determinants of public-private mix are per capita income, the share of individual income
held by the top quintile of the income distribution and federal health transfers.
Di Matteo (2003) compared parametric and nonparametric estimation methods for the
U.S states, the Canadian provinces and the OECD countries. He concluded that
parametric approaches lead to unreliable estimates of the income elasticity of health
expenditure and its magnitude is highly dependent on the level of analysis. In the latter,
national level analyses lead to estimates greater than one. Ariste and Carr (2001,
henceforth AC) used provincial data on real per capita income, the proportion of the
population over the age of 65 and the ratio of the deficit/surplus to GDP to explain the
real per capita government health expenditures by examining the non-stationarity of the
variables and the cointegrating relationships. They have found that variables, both
individually and collectively are non-stationary and possibly non-cointegrated. However,
the coefficient of the aging structure appeared to be insignificant compared to the
significant coefficient that DD found in their study. AC also extended their study to
examine the Baumol effect. They have found that health is a necessity good with income
elasticity of health spending of 0.88.
2. DATA AND METHODOLOGY
I will consider few points that are not considered by DD and AC. First, if the relative
price of health care is known to have an influence on HE (see Bac and Le Pen, 2000 for
example) and the failure to take into account this variable as one of the determinants, will
ultimately lead to specification bias and incorrect estimates due to combined income and
price effects. It should be noted that the income coefficient due to the exclusion of the
health price variable may be biased either upward or downward. Second, the previous
studies on the determinants of Canadian provincial health expenditures can be
characterized by the lack of dynamics. This paper aims to show that the dynamics of
health expenditures should not be neglected for the purposes of modeling and policy
implications. Third, I will examine the determinants of provincial health expenditures
under total, government and private health expenditures. This will enable to see the
differing responsiveness against the income and price changes for government and
private sector as well as total health sector. Fourth, I will incorporate other factors that
4
are not considered in these analyses, such as life expectancy at birth and the public share
of health expenditures.
Finally, concerning unit roots Atkins and Sidhu (2002) state that if the series under
consideration are not weakly stationary (i.e. the series contain at least one unit root)
which is the case in most regional and international comparisons, then the traditional
econometric analysis is not valid. Failure to achieve weak stationarity will cast doubt on
the statistical significance of the coefficients and their reliability. Even if the economic
theory weakly provides guidance on the relationship between HE and its various
determinants, statistical theory shows that the mean and the variance of the underlying
series should be time invariant to make appropriate inferences. On the other hand, if the
series are weakly stationary at level, then the traditional approach can be applied.
The data covers 10 provinces in Canada for the time period 1975-2002 which makes
the total of 280 pooled observations. The provincial total, the provincial private and the
provincial government health expenditures are taken from the Canadian Institute for
Health Information website (www.cihi.ca). These variables are deflated by the provincial
CPI index (1992=100) and divided by the provincial population to obtain real per capita
provincial total (h), real per capita provincial private (pr) and real per capita provincial
government (g) health expenditures. The share of the provincial public health expenditure
(s) is obtained by dividing the real provincial public health expenditures to real provincial
total health expenditures. Transfers from federal government to provinces, provincial
medical CPI (1992=100), provincial proportion of the population over the age of 65
(p65), life expectancy at birth (x) and the provincial GDP are collected from CANSIM.
The provincial GDP and the transfers from the federal government to provinces are
deflated by the provincial CPI index (1992=100) and divided by the provincial
population to obtain the real provincial per capita GDP (y) and the real per capita
transfers from the federal government (f) respectively. The provincial medical CPI is
divided by the provincial GDP implicit price index (1992=100) to obtain the relative
price of health care (r) for each province.
The methodology followed in this paper is as follows: Section 3 provides evidence on
the stationarity of the series with province-by-province and panel unit root tests. Section
4 makes an introduction to dynamic health expenditure models and investigates the
5
reasoning behind the relationship between health spending and its selected determinants.
Section 5 discusses the results and the relevant policy implications and section 6
concludes with directions for future research.
3. PROVINCE BY PROVINCE AND PANEL UNIT ROOT TESTS
Unit root1 is a severe problem in the sense that if the appropriate tests are not
employed, the inferences drawn might possibly be misleading and “seemingly good”
results may occur because of a common trend rather than true economic relationship. I
will first consider Augmented Dickey-Fuller (ADF) unit root test proposed by Dickey
and Fuller (1979) under the null of unit root with its extension to panel by Im et al. (2003,
henceforth IPS) and KPSS test proposed by Kwiatkowski et al. (1992) under the null of
stationarity with its extension to panel by Hadri (2000). See the appendix for technical
discussion on individual and panel unit root tests.
3.3 Unit Root Results
The ADF results show that for most of the series of health expenditures, GDP and
share of public health expenditures, the null hypothesis of unit root cannot be rejected.
Concerning total health expenditures, the null can only be rejected for New Brunswick,
Prince Edward and British Columbia. In the case of GDP, this null can only be rejected
for Prince Edward and British Columbia. The IPS panel tbar-statistics show that all of the
variables can be described as group stationary. The ADF and IPS results are shown in
table 1. It should be emphasized that concerning the IPS test, the chosen lag order or lag
criteria greatly affects the individual unit root statistics in favor of rejecting the null
hypothesis of unit root.
The KPSS individual unit root tests show that for most of the series except the share
of senior population, the null of trend stationarity cannot be rejected. However, Hadri’s
panel unit root tests show that the null hypothesis of either level or trend stationary can be
rejected for all the series at the 5% significance level. This result might be induced from
1 A model should be treated and interpreted over stationary forms of the variables. A common problem in time series is the existence of unit root. Most economic time series are classified as being integrated of order d, denoted as I(d), that is the series must be differenced d times in order to become stationary. Otherwise, a problem known as spurious regression occurs.
6
the fact that the test proposed by Hadri is valid under sequential limit in which ∞→T
followed by ∞→N . The results are displayed in table 2.
The first problem that appears in unit root testing is whether to include a time trend or
not. While Hansen and King (1996) postulated that ADF regression should include a
linear trend, McKoskey and Selden (1998) argued that it should not. This paper argues
that most macroeconomic variables have tendency to increase over time, therefore it may
be more appropriate, where conventional, to include a deterministic component into unit
root testing. However, some variables may not evolve around a trend component at all,
yet may appear stationary. Economic theory does not help so as to whether include a
linear trend or not. At this point, we should rely on the statistical significance of the linear
trend. The decision to include such deterministic components is more or less heuristic.
Karlsson and Löthgren (2000) warn that unit root test such as IPS has high power in
panels with large T therefore researchers might mistakenly conclude that the whole panel
is stationary even though most of individual series are nonstationary and the converse is
true if T is small. This argument is reconciled for both unit root test that I have
undertaken. The decision concerning unit roots is inconclusive. For the IPS test, a
significant fraction of the series is individually nonstationary but they appear to be
stationary as panel. However, for Hadri’s test, a significant fraction of the series is
individually stationary but they all appear to be nonstationary as panel. A careful
assessment of individual and panel unit root tests should be done to identify the order of
integration of the variables with confidence. However, this is beyond the scope of this
paper. It should be underlined that the presence of structural breaks is not considered by
the unit root tests due to short time span of the series.
Our primary concern is whether the relationship between the Canadian HE and its
determinants would be spurious or not if one analyzes this relationship in levels of the
variables. From an economic point of view, shocks to the Canadian health sector have
temporary effects which are quickly absorbed to recover the initial level rather than
effects that alter the level of expenditure permanently. Thus, it is more appropriate to
represent the relationship between HE and its determinants assuming that the panel is
weakly stationary and that the regression is unlikely to be spurious in level. Further, even
7
if this is not the true case, any indication of spurious regression can be captured by the
estimation results.
4. MODELS OF HEALTH EXPENDITURE
4.1 Factors Affecting Health Expenditure
Before introducing the models, this section discusses the reasons behind the inclusion
of the selected factors in the analysis of provincial health expenditures. The early studies
on the determinants of health expenditures concluded that income is the major
explanatory factor of HE. The economic approach argues that other things being equal,
the amount of health expenditure should depend on what an individual is capable of
spending. Therefore, it is expected that provinces with higher income should be able to
spend more on health given other decision factors.
Spending decisions concerning health are not solely affected by the income level but
also by the price of health care. In the case of higher out-of-pocket payments, decisions
rely on the price level. However, health care has special characteristics that are not
similar to those of other “goods”. The government is heavily involved into the delivery
of health and its supervision, attaching health sector a complex working mechanism. On
the other hand, health is a non-storable good and its delivery cannot be delayed. Such
features blur the price-spending relation and pose problems about our expectations of the
magnitude of the price effect and its sign2. This variable is particularly included in the
analysis to separate income and price effects. From the economic point of view, the
failure to include the price variable, if effective, results in misleading inference regarding
policy prescriptions.
With few countries being exception, health care decisions and a considerable volume
of health spending are driven by the governments and public institutions. Therefore, we
expect the share of publicly funded health expenditure to affect health spending.
However, as Roberts (1999) pointed out, both theory and empirical evidence are
contradictory regarding the magnitude and the sign of this effect.
2 The first counter argument to its inclusion is that the consumers do never face prices for the health services they receive and therefore this variable may be completely irrelevant for the analysis. The second one is the price of health is heavily subsidized in Canada so that even its effect is not zero, it should be almost zero or negligible.
8
The share of senior population is considered to be another explanatory factor of HE
by the fact that elderly population consume health at a higher rate than others and the
depreciation rate of health is an increasing function of age (Grossman, 1972). Especially
for those of age 65 (regarded as the lower bound of ageing) and over higher and
prolonged periods of cost are involved. The treatment of senior population involves
complexity and is not fully realized in most of the cases. Diabetes, cardiovascular
diseases are few to mention that require relatively technical knowledge and equipment for
treatment and diagnosis. The delivery of health services to elderly population is therefore
associated with higher spending on health.
The relationship between HE and health status indicators is much of a controversy.
The reason to include health status indicator arises from the question whether there is
correlation between expenditure and health level. Life expectancy at birth stands as an
appropriate measure of indicator of health status for Canada which might also capture the
efficiency of necessary health services for elderly population. The previous studies show
that there appears to be no correlation between HE and health status in the OECD
countries (Kyriopoulos and Souliotis, 2002).
The last factor considered is Federal transfers to provincial governments. This
variable is included primarily to reconcile its significance presented by DD. Besides the a
priori expectation that a higher volume of federal transfers increase health expenditures
at the government level, its effect is likely to be smaller than what is found by DD.
4.2 Dynamic Panel Models
This section presents the dynamics of provincial health expenditures. All the models
presented are modeled under one-way error component model due to our focus on the
provincial differences in health expenditures rather than differences across time. It is first
assumed that these differences can be captured by the differences in the endowments. In
this case, these differences in the intercepts cannot be thought as independent of other
variables. I will only consider explicit models for government health expenditures.
The dynamic models considered are of such form:
itittiit Xhh εβρα +++= −'
1, with itiit υµε +=
9
i denotes the provinces and t denotes time, β is a K x 1 vector where K is the
number of explanatory variables, X is a K x NT matrix of income and a selection of non-
income variables, µi is the province specific parameter and υit is the stochastic
disturbance term.
4.2.1 Health Expenditures under Slope Homogeneity
This sub-section starts off by the assumption that the coefficients are constant over
time and homogeneous across provinces. Although some parameters are unlikely to differ
substantially across provinces, the assumption of homogeneity is still strong and
restrictive.
Consider the following model for the government:
ititittiittiitiit prffgyg υββββρβµα ++++++++= −− 65lnlnlnlnln)(ln 541,321,1 (4.1)
where ln denotes the natural logarithm.
Baltagi (2001) demonstrated that under dynamic panel models with fixed effects
(4.1), the lagged dependent variable, lngi,t-1 is correlated with the disturbance even if the
disturbances are not auto-correlated. This problem results in biased and inconsistent OLS
estimates. To overcome this problem, the estimation is done via Instrumental Variables
(IV). Following Arellano (1989), lngi,t-2 is uncorrelated with the error term and
appropriate as an instrument for lngi,t-1.
From (4.1), the respective long-run income and price elasticity of government health
expenditures are:
ρβ−
=Ε1
1, yg
; ρ
β−
=Ε1
4,rg
Whereas the long-run elasticity of government health expenditure with respect to federal
transfers is:
ρββ
−+
=Ε1
32, fg
Equation (4.1) can be written in such form that the estimated parameters are direct
long-run elasticities. This transformation is due to Bewley (1979). Subtracting tig .lnρ on
both sides and reparameterize β vector to give:
10
itititititititiit fgprfyg ωφφφφ +∆Φ−∆Φ+++−+Γ= lnln65lnlnlnln 214321 (4.2)
The constant term in (4.2) can be seen as the steady-state mean for province i, if we let T
go large. The Bewley transformation now includes both level and differenced variables.
However, this transformation also requires IV estimation due to the correlation between
transformed explanatory variables and the error term.
4.2.2 Health Expenditures under Slope Heterogeneity
Currently, most of the studies of health care expenditure are based on the OECD
health data set and some of those studies introduce that there are substantial differences in
the structure of health sectors and demographics in the OECD countries and argue that
imposing slope homogeneity is unrealistic and may lead to misleading coefficients
(Roberts, 1999). Baltagi (2001) discusses briefly that in data field literature where T is
large compared to N, the fixed effects estimation in dynamic panels may lead to large
bias if the parameters are heterogeneous. For the Canadian case, it is argued that some
parameters are unlikely to substantially differ across provinces, but there may be
significant differences in the income parameter due to differences in earnings. To
introduce slope heterogeneity, consider the following dynamic heterogeneous model
analogous to (4.2):
itititiiit zyg υγφ +++Γ= '' lnln (4.3)
where the parameters are the long-run responses as defined earlier, zit consist of variables
with homogeneous parameters and we have introduced the subscript i for φ, allowing the
long-run effects of income to differ randomly across provinces such that:
ii 1ηφφ +=
η1i has zero mean, constant covariance and the average long-run coefficients are:
∑=
=10
1101
iiφφ
Pesaran and Smith (1995, henceforth PS) postulated that the dynamic pooled
estimation, even if the estimation is via IV gives inconsistent, biased and misleading
estimates when the parameters are heterogeneous. The size of this bias depends on ρ, φ,
11
var(φ) and the autoregressive roots of lnyit assuming a stationary AR(1) data generating
process of lnyit given in the appendix of PS. They instead suggested that cross-section
estimation provides consistent estimates of the long-run effects. However in my case, the
cross-section estimation3 will not improve over pooled estimation because N is very
small.
5. RESULTS & POLICY IMPLICATIONS
The estimations based on (4.1) are displayed in table 3. The assumption made about
the differences in the endowments has been incorporated into the models via fixed
effects4. The results show that income, federal transfers and the share of senior
population have statistically significant effects on total HE. The results also show that the
dynamics of HE should not be ignored as they play a significant role in the adjustment
process of explanatory variables. An interesting result, found in total and private health
expenditures models is that the life expectancy at birth has positive, statistically
significant effect on HE.
Before analyzing the precise effects of those variables, we should confine ourselves
to the reparameterized models we made use of, based on Bewley (1979) to directly
estimate the average long-run effects of the explanatory variables. This
reparameterization enables to assess the significance of long-run effects and their
standard errors. Table 4 reports the results. Income, federal transfers, the share of senior
population and life expectancy at birth has positive significant long-run effects on total
HE. However, the long-run effect of the relative price of health care appeared to be
insignificant in the preliminary estimation and therefore removed from the equations. The
insignificance of price effect might have occurred to due the fact that, discarding private 3 Since the number of cross sections is 10 and the number of explanatory variables is 6, the law of large numbers is invalid and some tests are not computable. Due to this problem, the mean group estimation suggested by PS, which involves estimating separate regressions for each province when T is large and averaging the coefficients over provinces, is used as an alternative method and a benchmark to compare with the average long-run effects obtained from pooled estimation. The pooled estimator slightly overestimates the average long-run effects of income compared to the mean group estimator. The results are available upon request. 4 We have performed F-test to test the joint significance of the individual fixed effects under the null hypothesis, Ho: µ1 = µ2 = ..... = µ10 = 0. The F-test turned out to be 5.26, 7.83 and 35.85 for total, government and private HE respectively, resulting in favor of rejecting the null hypothesis. Therefore, the models can be characterized by allowing the intercept to differ across provinces. For all models, the explanatory power and the Durbin-Watson statistics are fairly high.
12
sector, health care is free of charge in Canada and therefore price may be irrelevant to the
consumer. In his seminal work, Newhouse (1977) argued that for this reason, price may
not be an important factor in explaining health expenditures. The long-run income
elasticity of total health expenditure is 0.61 whereas the long-run elasticity of total health
expenditures with respect to federal transfers is 0.077. The effect of the share of senior
population appeared to be very small, even negligible.
Concerning the government HE, all long-run effects are significant. The long-run
income elasticity of government health expenditure is 0.78. On the contrary of the
previous studies, the evidence suggests that the effect of the share of senior population is
neither high as it is previously realized by DD5, nor insignificant as argued by AC. If the
proportion of the population over the age of 65 goes up by 1 percent, the government
health expenditures increase on average only by 0.018 percent.
The estimation for private health expenditures has given the most sensible results.
The long-run income elasticity of private health expenditures is found to be 0.46, being
much lower than those of total and government HE. For the relative prices, the long-run
price elasticity turned out to be significant and positive. This result requires explanation.
A possible argument supports the changing role of both public and private health sectors
and the shifting needs of patients. The lags in the adaptation of new technology, the time
spent between diagnosis and treatment and the concern for long-term care have led the
Canadians to shift the growing demand toward alternatives. The Canadian Medical
Association-sponsored poll on user fees reported that 57 percent supported user fees
(Irvine and Ferguson, 2002). These may explain the positive relation between prices and
private health expenditures. However, the provincial governments face the full price of
health services even though this cost is not projected on patients through billings.
Regardless of this fact, the provision of health care is not free and there are long-term
issues in financing of public health (see Brown, 1991).
The share of public HE is included into the analysis of private sector to evaluate a
potential trade-off between private and public health expenditures and its size. Our
findings indicate a significant, negligible negative trade-off between the share of public
5 According to DD, the impact of the share of the population over the age of 65 on government health expenditures is found to be 0.81 whereas AC found no evidence on its significance.
13
HE and private HE. However, this negative trade-off does not tell us about whether this
shift toward spending more on public services is due to changes in the quality of services
or not. Therefore, the evidence of this negative trade-off is of low quality.
A distinction should be made between the effects of variables that represent
demographic structure and health status. An increasing share of senior population implies
increasing health expenditures due to rising costs of treatment of the elderly. However,
increasing life expectancy or health status in this matter implies increasing health
expenditures due to rising needs for long-term care. As mentioned at the beginning of this
section, the interesting result found was the significance of life expectancy at birth on
health expenditures. But the magnitude of health status effect is very small. In case of a
one year increase in life expectancy, the private health expenditures increase by
3.5/10000. This suggests that there is a positive but negligible effect on health
expenditures resulting from the rising needs for long-term care. In this case, the analysis
confirms that these long-term needs are to be met by spending on private medical
services rather than public services. These findings are consistent with the evolving
medical needs of the Canadians for alternative treatments that are “neglected” by the
public health sector (see Klatt, 2000).
There appears to be substantial differences in the long-run elasticities if we allow the
income parameter to be heterogeneous. Figure 1 displays this variation.
Figure 1: The long-run income elasticity of health expenditure under slope heterogeneity
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.802.00
NF PE NS NB QC ON MN SK AB BC
Government Total Private
14
The long-run income elasticity of government HE is higher than the income elasticity of
total HE for most of the provinces. After allowing for heterogeneity, the income elasticity
of total HE for Quebec, Saskatchewan and Alberta appeared to be insignificant. The
findings show that the fixed effect estimator after allowing for heterogeneity
overestimates the average long-run effects in comparison to homogenous models.
The evidence in this paper suggests that health appears to be a luxury for Manitoba
and British Columbia whereas necessity for other provinces. However, from a national
perspective the evidence supports that health is not a luxury for Canada and the
determination of health spending in that matter is dominated by the needs rather than the
ability to pay. This is what Culyer (1988) was referring to as “the Bioengineering view”.
The “according to needs” argument supported by our results is also consistent with the
fact that physicians have a high-degree of control over the decisions about the medical
services that their patients need.
6.CONCLUSION
This study aimed at revealing the magnitude of income elasticity and the impact of
non-income determinants of health expenditures in Canadian provinces using panel data
on per capita GDP, relative price of health care, the share of public health expenditures,
share of senior population, per capita federal transfers and life expectancy at birth, over
the period 1975-2002.
The main differences captured in this study are summarized as follows:
• The relation between health expenditure and its determinants is of dynamic
structure.
• The relative price of health appears to have influence on private health
expenditures.
• The effects of non-income variables on health spending are very small, even
negligible.
• There appears to be a trivial correlation between health spending and health
status.
• After allowing the effect of income to be heterogeneous, health is a luxury for
some provinces and necessity for others.
15
The models showed that most of the variation in provincial health expenditures can
be explained by the current values of the explanatory variables as well as lags of health
expenditures. Under the assumption of homogenous parameters, the income elasticity of
health expenditure is below unity. This result is consistent with the previous studies at the
point that the regional or national estimates are usually below one.
The first difficulty encountered in this paper was the indecision whether the panel can
be described as stationary or not. The IPS and Hadri’s panel unit root tests have given
contradictory result regarding the unit root problem. Most of the panel unit root tests are
based on and therefore valid only under joint or sequential limit theory and I have
presented evidence on the fact that these tests are known to render the researcher with
conflicting results due to their high/low power in certain cases. Based on this fact, I have
argued that the effects of shocks to Canadian public sector can be best characterized as
temporary rather than permanent. Furthermore, our results following the approach which
can be seen as “traditional” appeared to be sensible and viable. However, a thorough and
careful assessment of panel unit root problem is needed to be addressed.
A second point for future research lies in more advanced econometric techniques to
reconsider the soundness of macroeconomic health policies. Regarding policy
implications, AC argued that if health is a luxury (i.e. the income elasticity is greater than
one), the health sector will consume a larger share of national income therefore
governments will allocate a larger share of their revenues to health expenditures, at the
expense of other sectors. However, the last part of this argument cannot be reconciled
based on this type of study due to the unknown nature of the relationship among various
sectors in Canada. This paper argues that if health is a luxury, a multi-equation
framework6 may serve for the purpose of revealing whether a greater allocation of
government revenues will take place at the expense of other sectors.
What are not needed are further studies of the effects of quantitative measures on
health expenditures. The standard measures appeared to be the determinants of health
expenditures are so far, known to every researcher in this area. What is not known is the
6 Such analysis, for instance, may examine the determinants of expenditures of various sectors within a system of equations to conclude that there is a trade-off between those sectors.
16
precise effect of measures that are indicators of the quality of life and health. Therefore,
the next generation of international or regional comparisons of health expenditure should
base their analysis on the effects of qualitative measures that are truly responsible for the
persistent increase or disparities in health expenditures.
REFERENCES
Arellano, M. (1989) “A Note on the Anderson-Hsiao Estimator for Panel Data”, Economics Letters, 31: 337-341 Ariste, R. and Carr, J. (2001) “New Considerations on the Empirical Analysis of Health Expenditures in Canada: 1966 – 1998”, Health Canada Applied Research and Analysis Directorate
Atkins, F. and Sidhu, N. (2002) “Unit Roots and Alternative Hypotheses in Health Care Econometrics”, University of Calgary, Department of Economics working papers
Bac, C. and Le Pen, Y. (2002) “An International Comparison of Health Care Expenditure Determinants”, 10th International Conference on Panel Data, Berlin
Baltagi, B. H. (2001) “Econometric Analysis of Panel Data”, Second Edition, Wiley & Sons
Bewley, R.A. (1979) “The direct estimation of equilibrium response in a linear model”, Economics Letters, 3: 357-361
Brown, M.C. (1991) “Health economics and Policy: Problems and prescriptions”, Toronto, McClelland & Stewart
Culyer, A.J. (1988) “Health Care Expenditures in Canada: Myth and Reality; Past and Future”, Canadian Tax Paper no: 82 (Canadian Tax Foundation) Di Matteo, L. (2000) “The Determinants of the Public-Private Mix in Canadian Health Care Expenditures: 1975 – 1996”, Journal of Health Policy, 52: 87-112
Di Matteo, L. (2003) “The Income Elasticity of Health Care Spending: A Comparison of Parametric and Nonparametric Approaches”, European Journal of Health Economics, 4: 20-29
Di Matteo, L. and Di Matteo, R. (1998) “Evidence on the Determinants of Canadian Provincial Government Health Expenditures: 1965-1991”, Journal of Health Economics, 17: 211-228
17
Dickey, D.A, Fuller, W.A (1979) “Distribution of the estimators for auto-regressive time-series with a unit root”, Journal of the American Statistical Association”, 74: 427-431 Grossman, M. (1972) “On the Concept of Health Capital and the Demand for Health”, Journal of Political Economy, 80: 223-255
Hadri, K. (2000) “Testing for Stationarity in Heterogeneous Panel Data”, Econometrics Journal, 3: 148-161 Hansen, P. and King, A. (1996) “The Determinants of Health Care Expenditure: A Cointegrating Approach”, Journal of Health Economics, 15: 127-137
Im, S.K., Pesaran, M.H., Shin, Y. (2003) “Testing for Unit Roots in Heterogeneous Panels”, Journal of Econometrics, 115: 53-74
Irvine, B., Ferguson, S. (2002) “Background Briefing: The Canadian Health Care System”, online: http://www.civitas.org.uk/pdf/Canada.pdf Karlsson, S. and Löthgren, M. (2000) “On the power and interpretation of panel unit root tests”, Economics Letters, 66: 249-255 Klatt, I. (2000) “Understanding the Canadian Health System”, online: http://www.cfp-ca.org/pdf/understanding_canadian_healthcare.pdf Kyriopoulos, P. and Souliotis, K. (2002) “Health Care Expenditures in the OECD Countries”, Reading Module, National School of Public Health, Greece Kwiatkowski, D., Phillips, P., Schmidt, P., Shin, Y. (1992) “Testing the null hypothesis of stationarity against the alternative of unit root”, Journal of Econometrics, 54: 159-178 McCoskey, S.K. and Selden, T.M. (1998) “Health Care Expenditures and GDP: Panel Data Unit Root Test Results”, Journal of Health Economics, 17: 369-376 Newhouse, J.P. (1977) “Medical Care Expenditure: A Cross National Survey” Journal of Human Resources, 12: 112-125 Parkin D., McGuire A., Yule B. (1987) “Aggregate Health Expenditures and National Income: Is Health Care a Luxury Good”, Journal of Health Economics, 6 :109-127 Pesaran, M.H. and Smith, R. (1995) “Estimating Long-run Relationships from Dynamic Heterogeneous Panels”, Journal of Econometrics, 68: 79-113 Roberts, J. (1999) “Sensitivity of Elasticity Estimates for OECD Health Care Spending: Analysis of a Dynamic Heterogeneous Data Field”, Health Economics, 8: 459-472
18
Tab
le 1
: Pro
vinc
e by
Pro
vinc
e A
DF
τ-st
atis
tics a
nd IP
S Pa
nel t
-bar
stat
istic
Prov
ince
To
tal H
ealth
Exp
endi
ture
G
over
nmen
t Hea
lth E
xpen
ditu
re
Priv
ate
Hea
lth E
xpen
ditu
re
Tran
sfer
from
the
Fede
ral G
ov.
La
g or
der
τ-sta
tistic
La
g or
der
τ-sta
tistic
La
g or
der
τ-sta
tistic
La
g or
der
τ-sta
tistic
New
foun
dlan
d 2
-1.8
41
3 -1
.859
4
-1.9
39
3 -2
.622
Prin
ce E
dwar
d Is
land
2
-3.4
10**
* 4
-1.7
40
2 -3
.586
***
2 -2
.979
Nov
a Sc
otia
2
-2.0
12
3 -2
.126
3
-2.1
76
2 -3
.002
New
Bru
nsw
ick
3 -3
.419
***
3 -2
.821
2
-4.0
62**
1
-2.3
87
Que
bec
4 -2
.551
1
-2.5
47
2 -2
.207
2
-3.5
55**
*
Ont
ario
2
-2.3
91
3 -2
.361
3
-2.5
53
2 -2
.136
Man
itoba
3
-2.8
70
3 -2
.947
3
-2.4
67
1 -2
.241
Sask
atch
ewan
2
-1.7
74
3 -2
.882
2
-3.7
26**
4
-2.0
51
Alb
erta
2
-2.4
42
2 -2
.417
3
-2.7
78
2 -2
.580
Brit
ish
Col
umbi
a 4
-3.8
32**
3
-3.2
01
2 -2
.067
2
-2.8
53
Pane
l t –
bar
stat
istic
-2.6
54**
-2.5
39**
*
-2.7
56**
-2.6
40**
Not
e: A
DF
regr
essi
ons i
nclu
de li
near
tren
d. *
, **
and
***
repr
esen
t 1%
, 5%
and
10%
sign
ifica
nce
leve
ls re
spec
tivel
y. T
he 1
%, 5
% a
nd 1
0% c
ritic
al v
alue
s of t
he IP
S t-b
ar te
st sta
tistic
are
-2.7
9, -2
.60
and
-2.
51 re
spec
tivel
y T
able
1: P
rovi
nce
by P
rovi
nce
AD
F τ-
stat
istic
s and
IPS
Pane
l t-b
ar st
atis
tic (c
ont’
d)
Prov
ince
G
DP
Rel
ativ
e Pr
ice
of H
ealth
Li
fe E
xpec
tanc
y at
Birt
h Sh
are
of S
enio
r Pop
ulat
ion
Shar
e Pu
blic
Hea
lth E
xpen
ditu
re
La
g or
der
τ-sta
tistic
La
g or
der
τ-sta
tistic
La
g or
der
τ-sta
tistic
La
g or
der
τ-sta
tistic
La
g or
der
τ-sta
tistic
New
foun
dlan
d 3
-2.3
64
3 -3
.956
* 2
-4.0
31**
1
-0.0
52
3 -2
.828
Prin
ce E
dwar
d Is
land
0
-3.5
16**
* 3
-4.4
02*
1 -3
.486
***
2 -1
.711
2
-3.3
95**
*
Nov
a Sc
otia
3
-1.7
23
1 -4
.767
* 1
-3.0
41
2 -3
.904
* 3
-1.9
74
New
Bru
nsw
ick
0 -3
.071
1
-2.1
01
1 -2
.380
2
-2.9
21
3 -3
.739
**
Que
bec
2 -2
.547
1
-1.2
64
1 -2
.864
2
-1.6
67
2 -2
.647
Ont
ario
2
-2.9
00
2 -1
.796
1
-2.7
76
3 -2
.749
2
-1.5
38
Man
itoba
3
-2.3
47
1 -1
.522
2
-1.8
05
3 -2
.904
2
-2.2
55
Sask
atch
ewan
2
-1.1
86
4 -1
.852
1
-1.5
72
3 -1
.521
3
-2.8
51
Alb
erta
1
-2.0
78
2 -2
.242
3
-3.2
20
2 -0
.857
2
-2.1
78
Brit
ish
Col
umbi
a 3
-4.0
82**
2
-1.8
92
3 -3
.480
***
3 -1
.619
2
-3.6
32**
Pane
l t –
bar
stat
istic
-2.5
82**
*
-2.5
79*
-2
.865
*
-1.9
905*
*
-2.7
13**
Not
e:
re
pres
ents
that
the
AD
F re
gres
sions
do
not i
nclu
de li
near
tren
d. *
, **
and
***
repr
esen
t 1%
, 5%
and
10%
sign
ifica
nce
leve
ls re
spec
tivel
y. T
he 1
%, 5
% a
nd 1
0% c
ritic
al v
alue
s of t
he IP
S t-b
ar te
st
statis
tic a
re -2
.21,
-1.9
9 an
d -1
.89
resp
ectiv
ely.
19
Tab
le 2
: Pro
vinc
e by
Pro
vinc
e K
PSS
η-st
atis
tics a
nd H
adri
’s P
anel
Tes
t sta
tistic
und
er st
atio
nari
ty
Prov
ince
To
tal H
ealth
Exp
endi
ture
l 4 =
3
Gov
. Hea
lth E
xpen
ditu
re
l 4 =
3
Priv
ate
Hea
lth E
xpen
ditu
re
l 4 =
3
Tran
sfer
s fro
m th
e Fe
dera
l Gov
.
l 4 =
3
η τ
η µ
η τ
η µ
η τ
η µ
η τ
η µ
New
foun
dlan
d 0.
112
0.78
0**
0.08
9 0.
779*
* 0.
112
0.21
9 0.
112
0.37
2
Prin
ce E
dwar
d Is
land
0.
066
0.79
0**
0.07
4 0.
771*
* 0.
066
0.67
5**
0.09
1 0.
244
Nov
a Sc
otia
0.
140
0.76
7**
0.12
5 0.
741*
* 0.
131
0.78
6**
0.09
2 0.
231
New
Bru
nsw
ick
0.17
3**
0.77
1**
0.16
1**
0.76
5**
0.15
8**
0.76
0**
0.12
6 0.
126
Que
bec
0.09
8 0.
791*
* 0.
113
0.74
5**
0.09
5 0.
776*
* 0.
074
0.47
0**
Ont
ario
0.
155*
* 0.
774*
* 0.
151*
* 0.
697*
* 0.
126
0.80
6**
0.12
6 0.
287
Man
itoba
0.
115
0.77
6**
0.10
8 0.
734*
* 0.
091
0.77
1**
0.14
3 0.
290
Sask
atch
ewan
0.
132
0.76
2**
0.13
3 0.
686*
* 0.
091
0.74
7**
0.13
6 0.
215
Alb
erta
0.
128
0.67
2**
0.13
0 0.
463
0.05
7 0.
794*
* 0.
148*
* 0.
327
Brit
ish
Col
umbi
a 0.
100
0.79
5**
0.09
1 0.
778*
* 0.
054
0.79
4**
0.11
2 0.
302
Had
ri Pa
nel S
tatis
tic
4.97
3**
12.7
8**
4.51
6**
11.8
8**
2.97
3**
12.4
0**
3.76
**
2.86
**
Not
e: η
τ and
ηµ a
re th
e tre
nd a
nd th
e le
vel s
tatio
narit
y ca
ses r
espe
ctiv
ely.
The
5%
crit
ical
val
ue o
f the
Had
ri Pa
nel s
tatis
tic is
1.6
45. *
* de
note
s 5%
sign
ifica
nce
leve
l.
Tab
le 2
: Pro
vinc
e by
Pro
vinc
e K
PSS
η-st
atis
tics a
nd H
adri
’s P
anel
Tes
t sta
tistic
und
er st
atio
nari
ty (c
ont’
d)
Prov
ince
G
DP
l 4 =
3
Rel
ativ
e Pr
ice
of H
ealth
l 4 =
3
Life
Exp
ecta
ncy
at B
irth
l 4 =
3
Shar
e of
sen
ior p
opul
atio
n
l 4 =
3
Shar
e of
Pub
lic H
ealth
Exp
endi
ture
l 4 =
3
η τ
η µ
η τ
η µ
η τ
η µ
η τ
η µ
η τ
η µ
New
foun
dlan
d 0.
089
0.67
7**
0.18
1**
0.53
4**
0.08
8 0.
624*
* 0.
098
0.80
5**
0.08
7 0.
527*
*
Prin
ce E
dwar
d Is
land
0.
110
0.66
0**
0.17
1**
0.61
5**
0.10
1 0.
604*
* 0.
185*
* 0.
737*
* 0.
067
0.07
8
Nov
a Sc
otia
0.
167*
* 0.
625*
* 0.
182*
* 0.
576*
* 0.
133
0.64
3**
0.20
7**
0.79
1**
0.09
4 0.
740*
*
New
Bru
nsw
ick
0.11
3 0.
652*
* 0.
123
0.63
3**
0.16
6**
0.62
6**
0.20
2**
0.79
6**
0.10
0 0.
648*
*
Que
bec
0.07
6 0.
628*
* 0.
101
0.71
7**
0.12
7 0.
643*
* 0.
153*
* 0.
807*
* 0.
098
0.74
6**
Ont
ario
0.
066
0.58
8**
0.13
9 0.
709*
* 0.
117
0.64
4**
0.19
3**
0.79
8**
0.14
3 0.
690*
*
Man
itoba
0.
106
0.59
7**
0.12
6 0.
597*
* 0.
153*
* 0.
605*
* 0.
205*
* 0.
751*
* 0.
097
0.46
5**
Sask
atch
ewan
0.
158*
* 0.
450
0.17
0**
0.58
5**
0.14
0 0.
585*
* 0.
147*
* 0.
773*
* 0.
124
0.21
5
Alb
erta
0.
122
0.22
3 0.
177*
* 0.
566*
* 0.
145
0.63
2**
0.12
2 0.
763*
* 0.
143
0.62
4**
Brit
ish
Col
umbi
a 0.
046
0.63
7**
0.14
5 0.
459
0.11
0 0.
643*
* 0.
185*
* 0.
749*
* 0.
085
0.36
4
Had
ri Pa
nel S
tatis
tic
4.05
1**
11.8
7**
7.93
2**
9.01
**
4.68
**
9.72
**
8.43
**
13.1
4**
2.29
7**
8.40
6**
Not
e: η
τ and
ηµ a
re th
e tre
nd a
nd th
e le
vel s
tatio
narit
y ca
ses r
espe
ctiv
ely.
The
5%
crit
ical
val
ue o
f the
Had
ri Pa
nel s
tatis
tic is
1.6
45. *
* de
note
s 5%
sign
ifica
nce
leve
l.
20
Tab
le 3
: Dyn
amic
Reg
ress
ion
Resu
lts, [
1977
– 2
002]
M
etho
d: In
strum
enta
l Var
iabl
es, o
ne-w
ay fi
xed
effe
cts e
rror
com
pone
nt m
odel
Var
iabl
e
Tota
l Hea
lth E
xpen
ditu
res
Gov
ernm
ent H
ealth
Exp
endi
ture
s Pr
ivat
e H
ealth
Exp
endi
ture
s
Coe
ffici
ent (
s.e)
P –
valu
es
Coe
ffici
ent (
s.e)
P –
valu
es
Coe
ffici
ent (
s.e)
P –
valu
es
GD
P 0.
20 (0
.024
)0.
0000
0.27
(0.0
40)
0.00
000.
141
(0.0
34)
0.00
01Pr
ice
of H
ealth
Car
e
0.
144
(0.0
23)
0.00
00Fe
dera
l Tra
nsfe
rs
0.02
5 (0
.009
)0.
0101
0.04
9(0
.014
)0.
0008
Shar
e of
Pub
lic H
.E
-0.0
29 (0
.001
2)0.
0000
Shar
e of
Sen
ior P
opul
atio
n 0.
011
(0.0
03)
0.00
130.
006
(0.0
03)
0.06
100.
030
(0.0
05)
0.00
00Li
fe E
xpec
tanc
y at
Birt
h 0.
008
(0.0
03)
0.00
61
0.02
6 (0
.004
)0.
0000
Lagg
ed G
DP
0.20
(0.0
33)
0.00
00La
gged
Dep
ende
nt V
aria
ble a
0.
67 (0
.030
)0.
0000
0.64
2 (0
.043
)0.
0000
0.24
7 (0
.028
)0.
0000
Con
stan
ts
New
foun
dlan
d -0
.461
5 0.
0640
-0
.535
6 0.
0211
1.
2213
0.
0001
P
rince
Edw
ard
Isla
nd
-0.4
990
0.04
18
-0.5
879
0.01
16
1.13
36
0.00
02
Nov
a Sc
otia
-0
.502
8 0.
0408
-0
.603
3 0.
0100
1.
1036
0.
0004
N
ew B
runs
wic
k -0
.493
6 0.
0460
-0
.585
9 0.
0123
1.
1460
0.
0002
Q
uebe
c -0
.501
3 0.
0434
-0
.585
7 0.
0125
1.
1221
0.
0004
O
ntar
io
-0.5
117
0.03
93
-0.6
100
0.00
98
1.05
93
0.00
09
Man
itoba
-0
.512
4 0.
0372
-0
.599
6 0.
0109
1.
0913
0.
0005
S
aska
tche
wan
-0
.544
8 0.
0271
-0
.613
6 0.
0091
1.
0174
0.
0012
A
lber
ta
-0.5
278
0.03
91
-0.6
392
0.00
84
1.08
98
0.00
10
Brit
ish C
olum
bia
-0.5
147
0.03
70
-0.5
787
0.01
29
1.05
53
0.00
09
R2 =
0.9
9
R2 =
0.9
9
R2 =
0.9
9
a:
two-
perio
d la
gged
val
ue in
leve
l is u
sed
as a
n in
strum
ent
21
Tab
le 4
: Dire
ct L
ong-
run
Estim
ates
usin
g Be
wle
y tra
nsfo
rmat
ion,
[197
7 –
2002
]
M
etho
d: In
strum
enta
l Var
iabl
es, o
ne-w
ay fi
xed
effe
cts e
rror
com
pone
nt m
odel
Var
iabl
e
Tota
l Hea
lth E
xpen
ditu
res
Gov
ernm
ent H
ealth
Exp
endi
ture
s Pr
ivat
e H
ealth
Exp
endi
ture
s
Coe
ffici
ent (
s.e)
P –
valu
es
Coe
ffici
ent (
s.e)
P –
valu
es
Coe
ffici
ent (
s.e)
P –
valu
es
GD
P 0.
61 (0
.055
)0.
0000
0.78
(0.0
57)
0.00
000.
46 (0
.023
)0.
0000
Pric
e of
Hea
lth C
are
0.
192
(0.0
30)
0.00
00Fe
dera
l Tra
nsfe
rs
0.07
7 (0
.028
)0.
0069
0.13
8(0
.036
)0.
0002
Shar
e of
Pub
lic H
.E
-0
.039
(0.0
01)
0.00
00Sh
are
of S
enio
r Pop
ulat
ion
0.03
6 (0
.010
)0.
0011
0.01
8 (0
.008
)0.
0466
0.04
0 (0
.006
)0.
0000
Life
Exp
ecta
ncy
at B
irth
0.02
7 (0
.008
)0.
0016
0.
035
(0.0
05)
0.00
00C
hang
e in
GD
P a
-0
.274
(0.0
41)
0.00
00C
hang
e in
Dep
ende
nt V
aria
ble b
-2
.09
(0.2
87)
0.00
00-1
.79
(0.3
34)
0.00
00-0
.328
(0.0
48)
0.00
00C
onst
ants
New
foun
dlan
d -1
.426
4 0.
0487
-1
.497
9 0.
0131
1.
6224
0.
0002
P
rince
Edw
ard
Isla
nd
-1.5
424
0.02
94
-1.6
442
0.00
62
1.50
58
0.00
03
Nov
a Sc
otia
-1
.554
0 0.
0284
-1
.687
2 0.
0052
1.
4661
0.
0005
N
ew B
runs
wic
k -1
.525
8 0.
0329
-1
.638
6 0.
0067
1.
5224
0.
0003
Q
uebe
c -1
.549
5 0.
0308
-1
.638
0 0.
0070
1.
4906
0.
0050
O
ntar
io
-1.5
815
0.02
73
-1.7
061
0.00
50
1.40
72
0.00
10
Man
itoba
-1
.583
9 0.
0256
-1
.677
0 0.
0057
1.
4498
0.
0005
S
aska
tche
wan
-1
.683
8 0.
0174
-1
.716
2 0.
0046
1.
3516
0.
0013
A
lber
ta
-1.6
314
0.02
72
-1.7
876
0.00
41
1.44
77
0.00
11
Brit
ish C
olum
bia
-1.5
907
0.02
54
-1.6
186
0.00
72
1.40
19
0.00
10
R2 =
0.9
9
R2 =
0.9
9
R2 =
0.9
9
a:
one
-per
iod
lagg
ed v
alue
in le
vel i
s use
d as
an
instr
umen
t
b:
two-
perio
d la
gged
val
ue in
leve
l is u
sed
as a
n in
strum
ent
22
APPENDIX:
3.1 Test of Null of Unit Root
The Augmented Dickey-Fuller test can be shown by the following model:
∑=
−− +∆+−++=∆iK
jitjtijitiiiiit xxtx
1,,1,)1( εβρδα εit C i.i.d (0, σ2)
where variable t is time trend, t = 1,……,T and j = 1,......,K. K is the number of lags,
determined such that the error term is autocorrelation free.
IPS proposed a fixed T, fixed N panel unit root test based on the average of the ADF test statistics:
∑=
=N
iiNT N
t1
1 τ i = 1,.….,10
where τi is the ADF test statistic for ith province.
The test statistic has a non-normal distribution and the critical values are supplied by IPS. The null
hypothesis that all series contain unit root is tested against the alternative that some series are
stationary.
Ho: ρi = 1 for all i
HA: ρi < 1 i = 1, 2, …, N1 where N1 is a subset of N
A particular lag order is determined for each of the series instead of choosing a common lag order to
avoid misleading ADF statistics resulting from autocorrelation.
3.2 Test of Null of Stationarity
The KPSS unit root test unlikely the ADF, constructs the null hypothesis of stationarity against the
alternative of unit root. This ensures that the null will be rejected only when there is strong evidence
against it. Due to Kwiatkowski et al. (1992), a time series can be decomposed into three components, a
deterministic trend, a random walk and a stationary error:
titiiti rtx ,,, εθ ++= (1)
where t captures the deterministic trend and ri,t is a random walk:
tititi urr ,1,, += − ui,t C i.i.d (0, σu2) (2)
The test statistic is a one-sided LM statistic under the null of level stationary (Ho: θi = 0) with the
errors being iid in eq. (1). The LM test statistic is defined as:
23
)(ˆ/1 2,
1
2,2 lS
T i
T
ttii εση ∑
==
where T is the sample size, )(ˆ 2 liσ is the estimate of the error variance, l is the lag truncation parameter7
and Si,t is the partial sums of the residuals, ∑=
=t
jjitiS
1,, ε̂ . The KPPS test makes a nonparametric
correction of the estimate of the error variance such that:
∑∑∑+=
−==
+−+=
T
ststiti
l
s
T
ttii lTT
l1
,,11
2,
2, ˆˆ
12121)(ˆ εεεσε
The extension of the KPSS test for panel data has been realized by Hadri (2000). The panel LM
test statistic is defined as the mean of the individual test statistics under the null of level stationary:
∑=
=N
iiN
ML1
1ˆ ηµ
The null hypothesis of level or trend stationarity is tested against the alternative of unit root in panel.
Under the assumptions that E[ui,t] = E[εi,t] = 0, ui,t and εi,t are i.i.d across i and over t, the test statistic
has the following limiting distribution:
)1,0()ˆ(
NMLN
Z ⇒−
=µ
µµµ ζ
ξ
where ⇒ represents weak convergence in distribution, ξµ , ζµ are mean and variance of the standard
Brownian bridge ∫1
0
2 )( drrV . The computed numerical values of ξµ, ζµ are 1/6 and 1/45 for the level
case and 1/15 and 11/6300 for the trend case respectively. The major shortcoming of Hadri’s panel unit
root test is that, the test statistic does not remain valid under small N and moderate T.
7 Lag truncation is set to integer [4(T/100)1/4] to correct the estimate of the error variance.
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