Life expectancy effects of public and private health expenditures in OECD countries 1970–2012: Panel time series approach

Accepted Manuscript Life expectancy effects of public and private health expenditures in OECD countries 1970–2012: Panel time series approach Mikael Linden, Deb Ray

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Received date : 22 April 2016 Revised date : 16 June 2017 Accepted date : 30 June 2017 Please cite this article as: Linden, M., Ray, D., Life expectancy effects of public and private health expenditures in OECD countries 1970–2012: Panel time series approach. Economic Analysis and Policy (2017), http://dx.doi.org/10.1016/j.eap.2017.06.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

   

LIFE EXPECTANCY EFFECTS OF PUBLIC AND PRIVATE HEALTH EXPENDITURES IN OECD COUNTRIES 1970 - 2012: PANEL TIME SERIES APPROACH

Mikael Linden a* a

University of Eastern Finland (UEF, Kuopio Campus), Department of Health and Social Management (Health Economics), Kuopio, Finland.

Deb Rayb b

University of Eastern Finland (UEF, Kuopio Campus), Department of Health and Social Management (Health Economics), Kuopio, Finland.

__________________________ * Corresponding author. University of Eastern Finland (UEF, Kuopio Campus), Department of Health and Social Management (Health Economics), P.O. Box 162, 70211 Kuopio, Finland. E-mail: [email protected], tel. +358505457699.

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LIFE EXPECTANCY EFFECTS OF PUBLIC AND PRIVATE HEALTH EXPENDITURES IN OECD COUNTRIES 1970 - 2012: PANEL TIME SERIES APPROACH

Abstract Relationships between life expectancy at birth, public and private health expenditures are analysed with econometric panel time series methods for 34 OECD countries between the years 1970 and 2012. The countries are grouped in three clusters depending on size of public health expenditure as a share of GDP. This gives us the possibility to test whether private and public health expenditures have different impacts on life expectancy at different levels of public expenditure as a share of GDP. Panel unit root tests show that all series in clusters are not difference stationary. Co-integration is found for countries with high public expenditure as a share of GDP. The results, augmented with panel VAR models and impulse response analysis, stress the importance of the positive relationship between public health expenditures and life expectancy. Additional results based on private health expenditure as a share of GDP show also the importance of private expenditures for life expectancy, although these are, at the same time, also driven up by public health expenditures.

Keywords: health expenditures; life expectancy; OECD; panel VAR; impulse response JEL codes: I15, I18, H51, C31

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1. Introduction Although OECD countries have less than 20% of the world's population, they accounted for over 85% of world spending on health at the turn of the new century. OECD countries spend the most on health per person globally (Poullier et al., 2002; WHO, 2014). Based on this fact, we ask ‘Can public and private health expenditures explain health status variables, like life expectancy at birth, for the OECD’s 34 countries over 43 years starting in 1970 and ending in 2012?’ The question is non-trivial as health expenditures (HE) in high-income countries bring only marginal improvements in life expectancy today (Poullier et al., 2002; OECD, 2014; Potrafke, 2010, Chansarn, 2010). There are substantial differences in HE even among the relatively homogeneous industrialised market economies, e.g. certain OECD countries like Greece and Mexico have much lesser HE per capita measured by purchasing power parity than say Switzerland, Sweden and the United States. However, this outcome hides the difference in health impacts of public and private health expenditures. We expect them to have different effects as their provision and demand for them are not uniform across the population in different countries. In addition, the nature and the quality of public health services varies in many OECD countries. A major share of HE is publicly financed (i.e. financed through taxes or compulsory social insurance contributions). While some believe that this may raise HE as a result of additional demand resulting from a decrease in the net price of care, others suggest that the public financing of HE serves as a restraining factor. Some researchers even suggest that per capita income is the most relevant variable explaining HE (Newhouse, 1977). Thus, economic policy has effects on health and health inequalities (Drakopoulus, 2011). However the high fraction of public finance in HE creates a problem currently because virtually all countries have deficits in the public sector which have been increasing over time. This increases public debt and interest payments on the debt. These macroeconomic pressures on public budgets spill also over to health budgets. One approach to reducing the extent of public financing is to increase out-of-pocket payments or private insurance. There are, however, major problems with this substitution. First, there is a limit as to how far out-of-pocket payments can be increased if the goal of equity is at stake. Second, private insurance as a means of financing poses a problem because those with the highest potential expenditure also have often the lowest incomes. The public fraction of HE is highest in rich

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countries, which also have the highest total expenditure. Private financing dominates in lower income countries, where direct out-of-pocket payments are more important than private insurance (Gerdtham and Jonsson, 2000). Generally, when one looks into the relationship between HE and health status, one sees broad patterns. Among the lowest spending countries, higher spending appears to be associated with significant improvements in health status. This means that there may be an opportunity for public policy to make a difference. Among high spending countries, additional spending sometimes bears little relationship to improvements in health adjusted life expectancy. This is also one reason behind the concern in wealthier countries over cost containment. Among countries with large public shares of HE, there are few differences in terms of health outcomes stemming from whether public funds are derived from taxes or social security contributions. In this regard, it appears impossible to infer that one type of public financing system is better than the other. Most OECD countries have a mix of all kinds of financing. The commitment of the public sector to health financing can also be inferred from the share of total government spending dedicated to health. Generally, public expenditure on health (HEPUB) as a share of total health spending is poorly correlated with per capita GDP, even if correlation is statistically different from zero. This pattern is consistent with the notion that a lower share of public spending can indicate an active private sector or a policy of limited public involvement. In the highest HE spending brackets, HEPUB is at a relatively high level. Except for a few cases (e.g. the United States and Switzerland), public spending essentially replaces private spending (Poullier et al., 2002; WHO, 2014; Ke et al., 2011; Potrafke, 2010). During most of the second half and especially the last decades of the 20th century, HEPUB has been growing at a faster rate than national income. Empirical studies show that demographic factors, such as population ageing, have a positive effect on expenditure growth, but rather of a second order, when compared with other drivers, such as income, technology, relative prices and institutional settings (Medeiros and Schwierz, 2013). However, after a long period of cost containment, the growth of HEPUB halted after the turn of the century (Maisonneuve and Martins, 2006). Baumol’s (1967) seminal ‘unbalanced growth model’ provides a simple but compelling explanation for the observable rise in HE in the last decades. This model assumes divergent

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productivity growth trends between ‘stagnant’ (personal) services and ‘progressive’ sectors (e.g. manufacturing, ICT-services, and agriculture). Due to technological constraints (e.g. difficulty in automating processes), productivity growth is largely confined to the ‘progressive’ sectors. Assuming that wages grow at the same rate in the ‘stagnant’ and ‘progressive’ sectors of the economy, unit labour costs and prices in the ‘stagnant’ sector rise relative to those in the ‘progressive’ sector. What will happen to the demand for ‘stagnant’ sector products depends on their price elasticity. If it is high, such activities will tend to disappear (e.g. craftsmanship), but if those products are a necessity, with low price elasticities (e.g. health, education), then their expenditure-to-GDP ratios will trend upwards (Baumol, 2012). We address the question of the health impacts of HE with panel time series data for 34 OECD countries over the 1970 - 2012 period. The analysis is conducted for three group of countries with different levels of public health expenditure as a share of GDP. We expect that the health effects depend both on the level and the composition of health expenditures. Thus, we test whether private and public health expenditures have different impacts on life expectancy at different levels of public expenditure as a share of GDP. Data over 43 years help us provide consistent results on HE’s effects on life expectancy. Time lags and reverse causality are handled with dynamic time series methods (co-integration and impulse response analysis). Although we use only three variables (life expectancy at birth, public and private health expenditures) the problem of omitted variables is less severe since the dynamic models include lagged values of variables to be predicted, i.e. they contain all past information that has affected the variable. In addition to this, we use country specific trends and constants (fixed effects) to model the unobserved effects on the modelled variables. Our results show that the relationships between life expectancy and health expenditures are not uniform between three groups of countries with different levels of public health expenditure as a share of GDP. When public expenditure’s share of GDP is large we find positive effects and feedbacks between life expectancy and health expenditures. Contrary to this, when public expenditure’s share of GDP in the country is small, life expectancy and private health expenditures do not always support each other, but a significant positive link between public expenditures and life expectancy is still found. Robustness analysis does not alter these results.

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The paper is divided into five sections. In the following section, we provide a literature review where seminal papers are mainly discussed. In the third section, we describe the data used and give the models applied and the methods involved. The fourth section entails the results. Subsequently, the paper ends with Section 5 containing discussions and conclusions on results.

2. Literature Review 2.1. HE effects on health outcomes Grossman’s health capital model (1972) suggests that health quality significantly influences human capital development through the additional working time and utility derived from leisure. Good health does not only improve individuals’ consumption and production in the short run, but also improves returns from investments in productive activities in the long run. Novignon et al. (2012) provided evidence to show that poor health status has significant negative influence on both current and future welfare of households. Adequate and efficient health related spending is widely considered as necessary for the improvement of health status, at least in low-income countries (Anyanwu and Erhijakpor, 2007). Filmer and Pritchett (1997) provided evidence to show that while health care spending impacted on child mortality, it was not the dominant driver of this health outcome. Factors such as education, technological change, income and cultural differences have been identified by some researchers as major drivers of health outcomes rather than health care spending (Lleras-Muney and Sherry, 2008; Filmer and Pritchett, 1999). While some studies had shown significant positive or negative impacts of health care spending on health outcomes, others have found no significant relationship between the two (e.g. Burnside and Dollar, 1998). So, the extent to which HEPUB also influenced health outcomes depends on the effectiveness of policies and institutions. Musgrove (1996) summarised the few studies conducted before 1995 and concluded that multivariate estimates of the determinants of child mortality suggested that income was always significant, but HE as a share of GDP, the public share of health spending and HEPUB as a share of GDP never were. Hall and Jones (2007) showed that one could generate the growth in health spending and the resulting change in life expectancy solely through growth in income, using a model of endogenous health spending. Instead of modelling other changes simultaneously, they showed that with

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reasonable parameter estimates and implied values of longevity gains, one could generate the rise in health spending and life expectancy. The result was based on the assumption that income elasticity for health is larger than one. Contrary to this, Acemoglu et al. (2013) showed in a more detailed and elaborated analysis that the elasticity is much lower than one. They also remark that identification and measurement of elasticity is a demanding task. Fonseca et al. (2009) followed a similar modelling approach, presenting health spending growth as an optimal response to changing circumstances. They introduced in their framework health insurance and technological change as explicit possible competing alternatives to income growth. Thus, insurance and technological change independently respectively explained 29% and 24% of the total change in health spending and that income explained roughly 10%. The remainder, 37%, was due to synergy effects or interactions created by simultaneously increasing income, the generosity of health insurance and productivity. As for life expectancy, the bulk of the gains was due to productivity. 2.2. Private and public HE effects There are differences in health expenditures (both public and private) amongst OECD countries. However, there are broad patterns in the interconnectivity between health status and HE. Expenditures increase considerably at older ages, as elderly people often require costly medical treatment due to multiple morbidities and chronic illnesses. Improvements in life expectancy often lead to increases in HE and vice versa. There exists quite a large literature looking at how population age profiles affect the HE. However, it is not the age but the proximity to death that determines the expenditures (for partial reviews on the topic, see e.g. Gray, 2005; Felder, 2013; Breyer et al., 2015). The most relevant literature for the approach used in this paper is summarised by Nixon and Ullman (2006) and van Baal et al. (2013). Both survey the literature but pay close attention to 20 different studies that meet basic econometrical standards. Although they mostly review the same articles, their summaries of them are somewhat divergent. Nixon and Ullman resume after survey and with their own estimations for 15 OECD countries over the 1980-1995 period with almost all explanatory variables found in previous literature, that increases in health care expenditure are

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significantly associated with large improvements in infant mortality; but only marginally in relation to life expectancy (2006, pp. 9 and 16). Van Baal et al. (2013) argue that it is obvious that health care spending exerts a positive influence on life expectancy, but it is less obvious whether marginal increases in health care spending have resulted in increases in life expectancy. They stress that the strength of effects remains uncertain and that the causal influence of marginal increases in health care spending has been difficult to demonstrate in empirical research (pp. 4243). Both reviews note that cross-section macro data is not the correct approach in this context as health expenditure effects take time to improve health status, and omitted and endogenous variable problems are evident. However even when panel or time series data were used, not a single study using country or region level data addressed all the methodological problems, i.e. time lags, confounders, and reverse causality (van Baal et al., p. 43). Note that the main target of this paper is to test whether public and private HE have the same effect on life expectancy. This question is analysed in very few papers. Only work by Cremieux et al. (2005), Lichtenberg (2000) and Or (2000) provide some information relevant to this question. Cremieux et al. use data on Canadian provinces over the period 1975–1998. They focus on public and private spending on drugs, with many additional variables, by using panel fixed effects regression methods. Results show that life expectancy at birth increases with drug spending and the effect of private spending is somewhat larger than that of public expenditure. Lichtenberg provides time series evidence from the US over the period 1960–1997 for life expectancy in dynamic models where public and private expenditures predict life expectancy, together with GDP and new drug molecular approvals. Public expenditure short and long run effects are positive and statistically significant but private effects are not precise, especially when lagged GDP is added into the model. Or (2000) uses similar methods to Cremieux et al. but predicts premature death in 21 OECD countries in the period 1970-1992 with total HE and the public share of total HE, augmented with public health and environmental factors, and GDP. Although any inference concerning the effects of private HE is not analysed, increases in total HE and the public share of HE have decreasing effects on mortality. Recently, Jaba et al. (2014), Heijink et al. (2013), and Barthold et al. (2014) have analysed life expectancy and mortality effects of HE in OECD countries, albeit not in the form of public and private HE’s, with data starting from the 1990s and ending close to 2010. In all these studies, HE effects are not rejected. Note that Heijink et al. (2013)

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specially control for a large number of variables and for time trends in their analysis, but HE remains a significant determinant of avoidable mortality. On the methodological level, our empirical modelling approach, the panel VAR model, combines aspects of both the panel data and the time series models at the same time in one model. With country fixed effects, time lags, and by treating all variables endogenous allowing for reverse causality, we are able to tackle the methodological problems found in the earlier papers. Thus, the unifying approach presented here has some merit over those approaches found in previous literature.

3. Models, Data and Methods 3.1. Background The argument that income level - either at a person or GDP per capita level - determines the health conditions of individuals and the population is profound in the health economics literature. However, the heterogeneity of health status between both individuals and nations, even at the same income levels, demands for more detailed relationship between health conditions and specific expenditures targeted to promote health and care provision. The distinction between public and private expenditures here is important since the former is mainly a policy variable determined by the political agenda of the state, and the latter reflects the voluntary or individual choice based demand for health care. However, both are determined to a large extent by the general level of income in the country but this does not rule out other - more fundamental - factors affecting both health conditions and (public vs. private) health expenditures. When working with reduced models estimated with times series, the question of confounders is not the primary one like lagged feedback effects and the bidirectional ‘causality’ between healthcare expenditures and health status. Based on these observations, we specify a model for population health status (HS) that is related to private and public health expenditures (HEPRIV, HEPUB). However, we do not argue that health expenditures are exogenously given. In terms of econometrics, this means that all variables here are endogenous. We use panel time series methods to analyse and determine the

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HS  f ( HEPRIV , HEPUB ) relationship. These methods allow for feedback effects from health status to health expenditures, i.e. all three variables HS , HEPRIV and HEPUB are cross-related. 3.2. Data In this context, we use life expectancy data (i.e. life expectancy at birth in total years, LE) as a measure of health status in each country. This has been identified as a standard and valid measure of aggregate health status (Nixon and Ullman, 2006). The data was collected from the World Bank’s World Development Indicators (2015). Total, public, and private health expenditure as a SHARE SHARE , and HEPRIV ) were taken from the OECD (2014). The %-share of GDP (i.e., HESHARE, HEPUB

alternative measures for health expenditures are the level of expenditures per capita in 2005 prices, HEPUB , and HEPRIV . These were calculated as fractions of PPP converted into GDP per capita

values at 2005 constant prices (Penn World Tables, 2012). Note that all the series for the sample countries are upward trending, i.e. typical non-stationary macro time series. The countries are grouped in three clusters depending on the size of public health expenditure as a share of GDP. This gives us the chance to test whether private and public health expenditures have different impacts on life expectancy at different levels of public expenditure as a share of GDP. We choose the public share here as the basis for cluster building because it is a policy variable that corresponds to a large, and much debated, government expenditures in almost all OECD countries. Private expenditures are typically considered to be a non-political issue. The K-means cluster method was used to divide countries into groups depending on their level of public expenditure as a share of GDP in 2012. The clustering method provided the following SHARE variable. Note that large public expenditure as a share of GDP does not results for the HEPUB

necessarily mean low private expenditure as a share of GDP and vice versa (see Appendix, Table A1). In some countries, both shares are large (e.g. USA and Switzerland) and in some countries both shares are small (Estonia, Hungary, Poland)

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SHARE

HEPUB

Cluster

1

2

3

Cluster mean

8.37% (14)

6.40% (12)

4.21% (8)

Table 1. K-means clusters for public health expenditure as a share of GDP in 2012 (number of cluster countries in parenthesis)

3.3. Unit roots in panel data The clear trending behaviour of the series raises the question of non-stationarity and unit roots that conditions the conducted econometric analysis. When all the series have the same order of integration, typically I(1) or I(0), we can proceed then to long-run modelling and to co-integration analysis with a solid foundation. The concept of co-integration refers to the idea that when the series of interest have the same degree of integration, then a linear relation between the variables produces a stationary error term, i.e.  it is I (0) series. Different panel data unit root tests have been proposed in the literature, and we use here the IPS test developed by Im et al. (2003) and the ADF/PP test by Maddala and Wu (1999). These allow SHARE level for the case that individual cross sections, the sample OECD countries in different HEPUB

groups, have different deterministic components and AR(1) terms  i in the unit root testing models e.g. for life expectancy

lnLEit  ci  diTREND   i lnLEit 1  it with vit ̴ iid (0, 2 )

1)

When the unit root properties of the series have been established, we can proceed with balanced series (i.e. all series are I(1)) to test the co-integration properties of the following model that assumes that health expenditures determine life expectancy lnLEit  ( a0  a0i )  it  a1lnHEPRIV ,it  a2lnHEPUB ,it   it .

2)

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The panel co-integration tests developed by Pedroni (1999, 2004) and Kao (1999) focus on the unit properties of error term  it depending on the deterministic parts of the proposed co-integrated model. We use a test model developed by Pedroni, augmented with country specific constants and trends, and a Kao test that uses only country specific constants. 3.4. Impulse response analysis (IRF) IRF analysis is a convenient method for analysing how random shocks in different series errors (innovations) impact all series in the Vector Autoregressive–model (VAR) framework. For example, if we estimate the following VAR(1) model for series lnLEt , lnHEPRIV ,t , and lnHEPUB ,t  lnLEt   a1   11      lnHEPRIV ,t    a2     21  lnHEPUB ,t   a3    31

12  22  32

13   lnLEt 1   1,t       23  lnHEPRIV ,t 1    2,t  33   lnHEPUB ,t 1   3,t 



3) yt  a  Byt 1   t

with

E[ t  t ']= ,

and have at time t = 0 a random shock, we have y0*  y0  a =  0 . This means that at time t = 1 the shock size is y1* = By0*  B 0 , and at time t we have yt* = B t  0 . Alternatively, we can start the process today, t*  t and inject one time random shocks (impulses) per series in  t* and analyse their series specific responses into future values of yt  i . Note the magnitudes of these responses or deviances from the long run mean values of y  [ I  Bˆ ]1 a are determined directly by the original VAR(1) coefficient estimates Bˆ . That is

yˆ t* i  y  Bˆ i t* for i  0,1, 2,3,....

4)

By summarising these responses, we get the accumulated impulse responses over some future period T* for which the response effects typically decay away (i.e. Bˆ T *  0 )

yˆ t*T *  y   i 0 Bˆ i t* . T*

5)

For VAR(2) and higher order processes, similar impulse response presentation can be derived (see Lutkepohl, 2005; Section 2.3.2). All this can also be put in the panel framework (for more details,

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see e.g. Canova and Ciccarelli, 2013). In this context, the starting point is the country fixed effect panel VAR model for different countries in HEPUB share clusters. We use the STATA code developed by Cagala and Glogowsky (2015). 4. Results 4.1. Panel data model results for three clusters of OECD countries We start the analysis with panel unit root testing. Table 2 reports the relevant results. The results give quite a strong indication that the panels of series are not uniformly I(0)–series across the country clusters, with country specific linear trends and constants. The 5% level of rejections of unit root hypotheses are marked with bold font, and the 10% level are in italics. The life expectancy

A: test value, B: p-value, C: number of cross sections, D: number of observations SERIES TESTS lnLE IPS ADF PP SHARE lnHEPRIV

IPS ADF PP SHARE lnHEPUB

IPS ADF PP

lnHEPRIV IPS ADF PP

lnHEPUB IPS ADF PP

CLUSTER 1

CLUSTER 2

A -2.012 56.035 55.480 A

B 0.022 0.001 0.001 B

C 14 14 14 C

D 587 587 588 D

A -1.692 52.629 49.572 A

-0.645 30.871 30.696 A

0.259 0.322 0.330 B

14 14 14 C

573 573 588 D

-2.530 42.945 39.540 A

0.005 0.010 0.023 B

-1.455 40.816 35.974 A

0.072 0.055 0.143 B

14 14 14 C

582 582 588 D

-2.506 44.019 34.113 A

0.006 0.007 0.082 B

-1.298 37.566 39.207 A

0.097 0.106 0.077 B

14 14 14 C

578 578 588 D

-1.824 34.643 37.839 A

585 585 588

-1.922 37.388 32.471

-1.307 38.902 28.891

0.095 0.082 0.418

14 14 14

B 0.045 0.001 0.002 B

C 12 12 12 C

CLUSTER 3 D 496 496 504 D

A 0.9148 26.970 18.6394 A*

B 0.819 0.041 0.287 B*

C 8 8 8 C

D 320 320 336 D

12 12 12 C

496 496 504 D

-1.534 32.382 19.827 A

0.062 0.008 0.228 B

8 8 8 C

328 328 336 D

12 12 12 C

490 490 504 D

-4.171 101.82 107.628 A

0.000 0.000 0.000 B

8 8 8 C

334 334 336 D

0.034 0.073 0.036 B

12 12 12 C

501 501 504 D

-0.822 21.499 13.061 A

0.205 0.160 0.668 B

8 8 8 C

328 328 336 D

0.027 0.040 0.115

12 12 12

499 499 504

-3.683 79.665 62.197

0.000 0.000 0.000

8 8 8

334 334 336

*) test with country effects

Table 2. Panel unit root test. Years: 1970 – 2012 for country clusters 1, 2 and 3. (Exogenous variables: country effects, country linear trends. Automatic lag length selection based on SIC. Variance estimation: Newey-West automatic bandwidth selection and Bartlett kernel).

13    SHARE series lnLE is, with high probability, trend stationary in high HEPUB countries. In low share

countries (cluster 3), the stationarity around the trend is not obtained. For expenditure share series SHARE SHARE in clusters 2 and 3, stationarity dominates test results but less so for lnHEPRIV and lnHEPUB

cluster 1. For the expenditure level series lnHEPRIV and lnHEPUB results are mixed. For low share countries (cluster 3), public expenditures are stationary but private expenditures are not. The results for cluster 1 countries are opposite to this and for middle level countries (cluster 2) both expenditure series are with high probability stationary. Some general patters are observable from the test results. The stationary results are most wellfounded in cluster 2. In cluster 1, results are also balanced if series lnLE is excluded but for cluster 3 the results support the unbalanced series outcome, i.e. series having different orders of integration. To interpret these results, we observe that in cluster 2, where the levels of public and private health expenditure as a share of GDP are close to each other, their growth rates are constant and their movements around the trend revert to the mean. Contrary to this, especially in high share countries (cluster 1), these types of stationarity results are not obtained. Life expectancy is trend stationary but expenditure series are less mean reverting. This may be the outcome of a strong policy orientation towards public health expenditures in cluster 1 countries. Opposite arguments may be valid for cluster 3 countries, where public expenditures are smallest and policy supports the private expenditures. From the viewpoint of co-integration, the obtained unit root testing results are mixed. For cluster 2, stationary errors for co-integration model 2 are trivially true since the related model series are stationary. For cluster 1, co-integration depends on the trend included in the test model and how expenditure series may show pairwise stationarity dependence. For cluster 3, it is hard to say much about possible co-integration. For these reasons, we conducted the panel co-integration test with and without country specific trends and retaining the country fixed effects. Table 3 gives a summary of panel co-integration tests. Detailed results can be obtained from the authors upon request. CIC,TR and CIC mark the cases where a null hypothesis of no co-integration is rejected at a 5% level for all tests with and without a trend. If the test outcomes are in parentheses

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the test significance level is 10%. The obtained test results show that co-integration is more evident when HEPUB as a share of GDP is high (cluster 1). Contrary to this, in low share countries (cluster 3) no co-integration is found. In cluster 2, no co-integration is rejected also with test models including a trend.

SERIES lnLE, HE

SHARE PRIV

, HE

SHARE PUB

lnLE, lnHEPRIV , lnHEPUB

CLUSTER 1 CIC,TR, (CIC), (CIC (Kao))

CLUSTER 2 (CIC,TR)

CLUSTER 3

CIC,TR, CIC, CIC (Kao)

CIC

CIC (Kao)

Table 3. Pedroni and Kao co-integration test results for cluster 1, 2 and 3 countries.

Although these results already now have some relevance for health policy, clearer implications should become evident with impulse response function analysis (IRF), conducted with a simultaneous VAR model for all three series. Note also that IRF results do not depend on any model error and test distribution assumptions, or on the assumption of co-integration. The 95% confidence intervals of IRF’s are derived with consistent VAR model coefficient estimates in a bootstrap resampling setting. 4.2. Impulse response analysis (IRF) Next, we present panel IRF analysis for country clusters based on HEPUB as a share of GDP. In VAR models, we used the expenditures series lnHEPRIV and lnHEPUB because the results with these are easier to understand. The estimation results with share series were similar to ones obtained with expenditure series. The IRF analysis is conducted with a fixed effects panel VAR model with 10 lags and a forecasting horizon of 10 periods (years). For clusters 1 and 2, the non-detrended series were used but for cluster 3 the analysis was based on detrended series, following the results from unit root and co-integrated analysis. This supports a more balanced (stationary) presentation for the series. The 95% confidence intervals (CI’s) were calculated with bootstrap methods (200 replications). Figures 1, 2 and 3 graph the IRF’s. Note that non-converging IRF’s are typical for I(1) series.

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The first row in each figure gives the lnLE impulse responses on lnHEPRIV and lnHEPUB , i.e. we let an exogenous shock happen in model innovations of lnLE (the first component in  t* ), and detect how it affects all model variables. In cluster 1, the long run response to 1 standard deviation positive shock in lnLE is a positive long run effect on private and public health expenditures. In cluster 2 (Figure 2), the responses are statistically insignificant, except for a lag value of 10 for the lnHEPUB series. In cluster 3 (Figure 3), a positive shock in lnLE leads to negative effects on private

health expenditures in the long run. Long run public expenditure responses are positive. This result is interesting since cluster 3 contains the countries where HEPUB as a share of GDP is smallest. Although this does not mean that cluster 3 countries have the largest private expenditures as a share of GDP, the result shows that rising life expectancy leads to increases in public health care, not in private care.

FIGURE 1

FIGURE 2

FIGURE 3

                     

In conclusion, the IRF results indicate that the larger is HEPUB as a share of GDP in a country, the more evident are the positive effects and feedbacks between life expectancy and health expenditures. Contrary to this, when HEPUB as a share of GDP in a country is small, life expectancy and HEPRIV do not sustain each other. However, a positive long run response of public expenditures to life expectancy shock is also observed in cluster 3.

16   

The 10 year accumulated responses in Table 4 indicate that a 10% shock in life expectancy leads to a 1.2% increase in private health expenditures in cluster 1 but has a -2.2% effect in cluster 3. The corresponding public effects are 0.5% and 1.2%. Note that life expectancy effects from lnHEPUB (i.e. lnHEPUB  lnLE) are always positive, albeit small. In cluster 3, the cross responses

to lnHEPUB and lnHEPRIV are negative, in cluster 2 they are positive. Interestingly, in cluster 1 lnHEPRIV drives lnHEPUB up but the reverse response is negative. However, all these responses

are very imprecise in the long run.

IMPULSE    RESPONSE  lnLE  lnHEPRIV

CLUSTER  1  0.121 

CLUSTER  2  (0.062) 

CLUSTER 3  ‐0.225 

lnLE  lnHEPUB

0.056 

(‐0.009) 

0.122 

lnHEPRIV  lnLE

0.004 

(0.003) 

‐0.011 

lnHEPRIV  lnHEPUB

(0.029) 

(0.082) 

(‐0.096) 

lnHEPUB  lnLE

0.006 

(0.004) 

0.006 

lnHEPUB  lnHEPRIV

(‐0.048) 

(0.052) 

(‐0.062) 

Table 4. 10 year accumulated responses to 1 standard deviation shock: HEPUB as a share of GDP clusters (results in parentheses when 95% CI’s include zero).

Our test hypothesis concerned the difference in health impacts of public and private expenditures. The obtained results indicate that there is a difference in the long run contribution of expenditure types that depends on the level of a country’s public health expenditure as a share of GDP. The private and public expenditure shocks have different responses in Figures 1, 2 and 3. The reported values were not sensitive to the de-trending of the series. We know that most of the expanding life expectancy in OECD countries comes from other things like better food, health oriented life habits, and decreasing mortality risks not related to illness. If the trend in life expectancy counts for these effects, and public health expenditures support life expectancy for the most vulnerable persons among the population (the children and the elderly), then the results above indicate that higher private health expenditures will not necessarily increase life expectancy at birth.

17   

4.3. Robustness analysis The above analyses were based on K-means cluster results with public health expenditure as a share of GDP from 2012. Three clusters were identified with different levels of HEPUB as a share of GDP. The focus of analysis was on HEPUB level effects on life expectancy, conditioned with last sample year information on HEPUB as a share of GDP. Sample year 2012 can be considered as outcome of policy options that the different countries had during the sample years with respect to health expenditures. Evidently, this research strategy is quite specific and some alternative approaches are needed here to check the robustness of the derived results. Thus, we first provide findings with K-means cluster results for private health expenditure as a share of GDP from 2012, and secondly we conduct the analysis with two 10 country panels, where the countries are selected on the basis of the largest increases in HEPUB and HEPRIV as a share of GDP during the years 1970– 2012. Table 5 provides the clusters for HEPRIV shares of GDP in 2012. Appendix A gives the details of the clusters. Interestingly, the largest share cluster contains only one country, the USA. We derived the generalised IRF’s for it with a VAR(2) time series model with non-correlated residuals.

SHARE

HEPRIV

Cluster

1

2

3

Cluster mean

8.86% (1)

3.00% (18)

1.63% (15)

Table 5. K-means clusters for private health expenditure as a share of GDP in 2012 (number of cluster countries in parentheses). However, the IRF’s in Table 6 show that for the USA only, the impulse response lnHEPRIV  lnHEPUB is significant in statistical terms and that the 10 year accumulated response is 0.121. This

means that large private health expenditures drive up the public expenditures in the USA and this complementary effect is one-sided as the lnHEPUB  lnHEPRIV response is non-significant. In

18   

cluster 2, both the private and public heath expenditure responses to life expectancy (i.e. lnHEPRIV

 lnLE and lnHEPUB  lnLE) are positive, with almost equal size. Note that we find a significant positive lnHEPUB  lnHEPRIV effect for this cluster. Life expectancy drives public health expenditures up with a value of 0.046, but there are no significant responses from private health expenditures.

IMPULSE    RESPONSE  lnLE  lnHEPRIV

CLUSTER  1  (‐0.005) 

CLUSTER  2  (0.118) 

CLUSTER 3  (0.031) 

lnLE  lnHEPUB

(0.002) 

0.046 

0.072 

lnHEPRIV  lnLE

(0.117) 

0.004 

0.006 

lnHEPRIV  lnHEPUB

0.121 

(0.018) 

(0.098) 

lnHEPUB  lnLE

(0.101) 

0.005 

(0.005) 

lnHEPUB  lnHEPRIV

(0.107) 

0.073 

(0.015) 

Table 6. 10 year accumulated responses to 1 standard deviation shock HEPRIV as a share of GDP clusters (results in parentheses when 95% CI’s include zero).

Cluster 3, with the smallest HEPRIV shares, provides only significant lnLE  lnHEPUB and lnHEPRIV  lnLE responses. Note that these responses are close values in Table 4 for cluster 1

having the largest HEPUB GDP shares. As there is not a clear one-to-one correspondence with large HEPUB and small HEPRIV shares (and vice versa), the results in Tables 4 and 6 stress the importance of a positive two-way link between life expectancy and public health expenditures that is missing from private expenditures. This outcome is partly over-ruled when we build two samples of 10 countries with the largest differences in HEPUB and in HEPRIV as a share of GDP between 2012 and 1970, and estimate the corresponding IRF’s for these panels. In Table 7, response lnLE  lnHEPUB is negative with statistical significance, implying that in the countries with the largest HEPUB as a share of GDP,

19   

the increased life expectancy reduces public health expenditures. However, this is not found in countries with the largest HEPRIV as a share of GDP. In other respects, the results in Table 7 are close to results found in other tables. Note that some additional analysis showed that results in Table 7 were not sensitive to the number of countries selected for the panels.

  IMPULSE    RESPONSE 

Countries with 10 largest HEPUB as a share of GDP increases

Countries with 10 largest HEPRIV as a share of GDP increases 

lnLE  lnHEPRIV

(0.111) 

(0.025) 

lnLE  lnHEPUB

‐0.029 

(0.012) 

lnHEPRIV  lnLE

0.004 

0.011 

lnHEPRIV  lnHEPUB

(‐0.031) 

(‐0.006) 

lnHEPUB  lnLE

0.008 

0.008 

lnHEPUB  lnHEPRIV

0.067 

0.026 

Table 7. 10 year accumulated responses to 1 standard deviation shock: 10 largest HEPUB and 10 largest HEPRIV as share of GDP countries (results in parenthesis when 95% CI’s include zero).

At a general level, the obtained results are not in conflict with the earlier ones found in the literature. Our significant results imply that larger public expenditures mean increasing life expectancy and that public health expenditures drive up private expenditures, except in the USA, where we found a reverse relationship. Panel and times series model results elsewhere (e.g. Cremieux et al. 2005, Lichtenberg 2000, Or 2000) indicate that public expenditures generally improve health but for private expenditures the results are not so clear. Note that the macroeconomic results presented here, with life expectancy responses to health expenditure shocks, are hard to find in the literature.

20   

5. Conclusions The relationship between life expectancy at birth and private and public health expenditures was analysed with panel time series methods, in the context of a panel for 34 OECD countries for the years 1970 – 2012. Countries were grouped in three clusters depending on the size of their public health expenditure by share of GDP. We found that private and public health expenditures had similar positive effects on life expectancy in the highest public share cluster. However, these effects disappear in lower share clusters and private effects even turn negative in the smallest share cluster. The exogeneity of expenditures is clearly ruled out as life expectancy has significant effects on both health expenditures in high and low share clusters. However, it is only in high public share countries where extensions in life expectancy drives both private and public health expenditures upward. Conducting robustness analysis with alternative data configurations did not change our main finding, that larger public health expenditures increase life expectancy. In addition, we found that larger public health expenditures lead to higher private expenditures except in USA. From the health policy perspective, the obtained results are interesting. In OECD countries, there is still room for public and private health expenditures to improve health if the public expenditure by share of GDP is above 7.5%, but in countries where such expenditure is a lower share of GDP (less than 5.0%) only public expenditures seem to have positive effects on life expectancy. This could be the result of the different goals of private and public health expenditures in these countries. The former focuses on a diversified health market goods not consumed by the lower income families that rely on public health services. Alternatively, the health care system is built on the needs of the working population and the private providers do no serve the non-active population equally. Thus, best policy option would be to boost the public health expenditures in these countries. As a higher level of public expenditure also means higher life expectancy and private health expenditures in countries with high private expenditure as a share of GDP, the level of public expenditures is important in these countries. Before more complex policy options can be developed, we must know in detail to what extent private and public health care services are complements to each other. Also, more research is needed to get a detailed picture of the different contributions to health made by private and public health expenditures across the income and wealth distributions, between and within countries.

21   

Appendix A Private and public health expenditure shares of GDP in OECD countries, 2012

COUNTRY Australia Austria Belgium Canada Chile Czech Republic Denmark Estonia Finland France Germany Greece Hungary Iceland Ireland Israel Italy Japan Luxembourg Mexico Netherlands New Zealand Norway Poland Portugal Slovakia Slovenia South Korea Spain Sweden Switzerland Turkey United Kingdom United States of America

HE

SHARE PRIV

3,02 2,68 2,70 3,27 3,72 1,21 1,56 1,17 2,27 2,63 2,62 2,92 2,98 1,76 2,88 2,84 2,08 1,84 1,19 3,04 1,66 1,78 1,39 2,05 3,53 2,47 2,67 3,47 2,63 1,80 3,91 1,25 1,49 8,86

HE

SHARE PUB

6,11 8,42 8,19 7,66 3,60 6,34 9,42 4,63 6,82 8,98 8,64 6,22 4,98 7,28 6,00 4,39 7,10 8,44 5,99 3,12 9,93 8,50 7,90 4,67 5,92 5,68 6,70 4,16 6,67 7,78 7,52 4,14 7,79 8,04

SHARE HEPRIV

SHARE HEPUB

cluster 2 2 2 2 2 3 3 3 3 2 2 2 2 3 2 2 3 3 3 2 3 3 3 3 2 2 2 2 2 3 2 3 3 1

cluster 2 1 1 1 3 2 1 3 2 1 1 2 3 2 2 3 2 1 2 3 1 1 1 3 2 2 2 3 2 1 1 3 1 1

Table A1. Private and public health expenditure shares of GDP in 2012 with share cluster indicators

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

22   

References Acemoglu, D., Finkelstein, A., Notowidigdo, M., 2013. Income and Health Spending, Evidence form Oil Price Shocks. Review of Economics and Statistics. 95(4), 1079–1095. Anyanwu, C.J., Erhijakpor, E.O.A., 2007. Health Expenditures and Health Outcomes in Africa. Economic Research Working Paper No 91. African Development Bank. Barthold, D., Nandi, A., Rodriguez, J.M., Heymann, J., 2014. Analyzing Whether Countries Are Equally Efficient at Improving Longevity for Men and Women. American Journal of Public Health. 104(11), 2163–2169. Baumol, W., 2012. The cost disease – why computers get cheaper and health care doesn't. New Haven: Yale University Press. Baumol, W., 1967. Macroeconomics of Unbalanced Growth, the Anatomy of Urban Crisis. American Economic Review. 57(3), 415–426. Breyer, F., Lorenz, N., Nichel. T., 2015. Health Care Expenditures and Longevity, Is There a Eubie Blake Effect? European Journal of Health Economics. 16(1), 95–112. Burnside, C., Dollar, D., 1998. Aid, the Incentive Regime and Poverty Reduction. Policy Research Working Paper. Washington D.C.: The World Bank. Cagala, T., Glogowsky, U., 2014. Panel Vector Autoregressions for Stata (xtvar). Canova, F., Ciccarelli, M., 2013. Panel Vector Autoregressive Models, Survey. ECB-wp 1507. Chansarn, S., 2010. Labor Productivity Growth, Education, Health and Technological Progress: A Cross-Country Analysis. Economic Analysis & Policy. 40(2), 249 – 261. Cremieux, P.-Y., Meillur, M.-C., Quellette, P., Petit, P., Zelderm, M., Potvin, K., 2005. Public and Private Pharmaceutical Spending as Determinants of Health Outcomes in Canada. Health Economics. 14, 107–116. Drakopoulos, S.A., 2011. Economic Policies, Political Considerations and Overall Health. Economic Analysis & Policy. 41(3), 273 – 286. Felder, M., 2013. Managing the Healthcare System, The Impact of Demographic Change on Healthcare Expenditure. CESinfo Report, 1/2013, 3–6. Munich: Centre for Economic Studies (CES). Filmer, D., Pritchett, L., 1999. The Impact of Public Spending on Health, Does Money Matter? Social Science and Medicine. 49(12), 1309–1323.

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Filmer, D., Pritchett, L., 1997. Child Mortality and Public Spending on Health, How Much Does Money Matter. World Bank Policy Research Working Paper No 1864. Washington D.C.: The World Bank. Fonseca, R., Michaud, P.C., Galama, T., Kapteyn, A., 2009. On the Rise of Health Spending and Longevity. IZA Discussion Paper No. 4622. Bonn: Institute of Labor Economics. Gerdtham, U.G., Jonsson, B., 2000. International Comparisons of Health Expenditure, Theory, Data and Econometric Analysis. In Culyer, A.J., Newhouse, J.P. (Eds.), Handbook of Health Economics, Vol. 1A, (pp. 11–53). Netherlands: Elsevier. Gray, A., 2005. Population Ageing and Health Care Expenditure. Ageing Horizons. 2(1), 15–20. Grossman, M., 1972. On the Concept of Health Capital and the Demand for Health. Journal of Political Economy. 80(2), 223–255. Hall, R.E., Jones, C.I., 2007. The Value of Life and the Rise in Health Spending. The Quarterly Journal of Economics. 122(1), 39–72. Heijink, R., Koolman, X., Westert, G.P., 2013. Spending More Money, Saving More Lives? The Relationship between Avoidable Mortality and Healthcare Spending in 14 Countries. European Journal of Health Economics, 14(5), 527–538. Im, K. S., Pesaran, H.M., Shin, Y., 2003. Testing for Unit Roots in Heterogeneous Panels. Journal of Econometrics. 115(1), 53–74. Jaba, E., Baln, C.B., Robu, I.-B., 2014. The Relationship between Life Expectancy at Birth and Health Expenditures Estimated by a Cross-country and Time-series Analysis. Procedia Economics and Finance. 15(2), 108–114. Kao, C.D., 1999. Spurious Regression and Residual-Based Tests for Co-integration in Panel Data. Journal of Econometrics. 90(1), 1–44. Ke, X., Saksena, P., Holly, A., 2011. The Determinants of Health Expenditure, A Country-Level Panel Data Analysis WHO Working paper. Geneva: Results for Development Institute, WHO. Lichtenberg, F., 2000. Sources of U.S. longevity increase, 1960–1997. CES-info wp-405. Munich: Centre for Economic Studies (CES). Lleras-Muney, A., Sherry, G., 2008. Health Inequality, Education and Medical Innovation. Demography. 45(3), 741–761. Lutkepohl, H., 2005. New Introduction to Multiple Time Series Analysis. Berlin: Springer. Maddala, G. S., Wu, S., 1999. A Comparative Study of Unit Root Tests with Panel Data and A New Simple Test. Oxford Bulletin of Economics and Statistics. 61(6), 631–52.

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Maisonneuve C., Martins, J., 2006. The Drivers of Public Expenditure on Health and Long-term Care, an Integrated Approach. OECD Economic Studies. No 43, 116–154. Medeiros, J., Schwierz, C., 2013. Estimating the Drivers and Projecting Long-term Public Health Expenditure in the European Union, Baumol's Cost-disease Revisited. European Economy: Economic Papers. 507(1), 1–52. Musgrove, P., 1996. Public and Private Roles in Health Theory and Financing Patterns. World Bank Discussion Paper No. 339. Washington D.C.: The World Bank. Newhouse, J.P., 1977. Medical Care Expenditure, a Cross-National Survey. Journal of Human Resources. 12(2), 115–125. Nixon, J., Ulmann, P., 2006. The Relationship between Health Care Expenditure and Health Outcomes. Evidence and Caveats for a Causal Link. European Journal of Health Economics. 7(1), 7–18. Novignon, J., Olakojo, S.A., Nonvignon, J., 2012. The Effects of Public and Private Health Care Expenditure on Health Status in Sub-Saharan Africa, New Evidence from Panel Data Analysis. Health Economics Review. 2(1), 1–8. OECD. (2014). Health Spending - OECD Data. Paris: OECD. Or, Z., 2000. Determinants of Health Outcomes in Industrialized Countries, A pooled, Crosscountry, Time Series Analysis. OECD Economic Studies. 30(1), 53–77. Pedroni, P., 1999. Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors. Oxford Bulletin of Economics and Statistics. 61(5), 653–70. Pedroni, P., 2004. Panel Co-integration; Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis. Econometric Theory. 20(6), 597–625. Penn World Table. 2012. PWT/Version 7.3. Center for International Comparisons of Production, Income and Prices. Philadelphia: University of Pennsylvania. Potrafke, N., 2010. The Growth of Public Health Expenditures in OECD Countries, Do Government Ideology and Electoral Motives Matter? Journal of Health Economics. 29(6), 797– 810. Poullier J.P., Hernandez, P., Kawabata, K., Savedoff, D.W., 2002. Patterns of Global Health Expenditures, Results for 191 Countries. WHO Discussion Paper No 51. Geneva: WHO. Van Baal, P., Oqbulqasim, P., Brouwer, P., Nselder, W., Mackenbach, J., 2013. The Influence of Health Care Spending on the Life Expectancy. NETSPAR panel paper 35. Tilburg: Tilburg University. WHO. 2014. Who Global Health Expenditure Atlas. Geneva: WHO.

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World Bank. 2015. Indicators - World Bank Data - World Bank Group. Washington D.C.: The World Bank  

1   

.04

.016

.03

.012

.02

.008

.01

.004

.00

.000

-.01

-.004

-.02

-.008 1

2

3

4

5

6

7

8

9

10

11

1

IMPULSE: lnLE, RESPONSE: lnHEpriv

3

4

5

6

7

8

9

10

11

IMPULSE: lnLE, RESPONSE: lnHEpub

.0010

.012

.0008

.008

.0006

.004

.0004

.000

.0002

-.004

.0000

-.008

-.0002

2

-.012 1

2

3

4

5

6

7

8

9

10

11

1

IMPULSE: lnHEpriv, RESPONSE: lnLE .0012

2

3

4

5

6

7

8

9

10

11

IMPULSE: lnHEpriv, RESPONSE: lnHEpub .02

.0010 .01 .0008 .00

.0006 .0004

-.01

.0002 -.02 .0000 -.0002

-.03 1

                     

2

3

4

5

6

7

8

9

10

IMPULSE: lnHEpub, RESPONSE:lnE

11

1

2

3

4

5

6

7

8

9

10

11

IMPULSE:lnHE_pub, RESPONSE:lnHEpriv

Figure 1. Impulse response functions with 95% CI’s for Cluster 1.

1   

. .05

.025

.04

.020

.03

.015

.02

.010

.01 .005 .00 .000

-.01

-.005

-.02

-.010

-.03 -.04

-.015 1

2

3

4

5

6

7

8

9

10

11

1

IMPULSE:lnLE, RESPONSE:lnHEpriv

2

3

4

5

6

7

8

9

10

11

IMPULSE: lnLE, RESPONSE: lnHEpub

.0016

.020

.0012

.015

.0008

.010

.0004

.005

.0000

.000

-.0004

-.005

-.0008

-.010 1

2

3

4

5

6

7

8

9

10

11

1

IMPULSE: lnHEpriv, RESPONSE:lnLE

2

3

4

5

6

7

8

9

10

11

IMPULSE:lnHEpriv, RESPONSE:lnHEprub

.0016

.04 .03

.0012

.02 .0008

.01

.0004

.00 -.01

.0000

-.02 -.0004

-.03

-.0008

-.04 1

                          

2

3

4

5

6

7

8

9

10

IMPULSE:lnHEpub, RESPONSE:lnLE

11

1

2

3

4

5

6

7

8

9

10

11

IMPULSE:lnHEpub, RESPONSE: lnHEpriv

Figure 2. Impulse response functions with 95% CI’s for Cluster 2

1   

.03

.05

.02

.04

.01 .03 .00 -.01

.02

-.02

.01

-.03 .00 -.04 -.01

-.05 -.06

-.02 1

2

3

4

5

6

7

8

9

10

11

1

IMPULSE:lnLE, RESPONSE:lnHEpriv

2

3

4

5

6

7

8

9

10

11

IMPULSE: lnLE, RESPONSE:lnHEpub

.002

.02

.001

.01

.000

.00

-.001

-.01

-.002

-.02

-.003

-.03

-.004

-.04 1

2

3

4

5

6

7

8

9

10

11

1

IMPULSE:lnHEpriv, RESPONSE:lnLE

2

3

4

5

6

7

8

9

10

11

IMPULSE: lnHEpriv, RESPONSE:lnHEpub

.0020

.04 .03

.0015

.02 .0010

.01

.0005

.00 -.01

.0000

-.02 -.0005

-.03

-.0010

-.04 1

2

3

4

5

6

7

8

9

10

IMPULSE:lnHEpub, RESPONSE:lnLE                                                                   

11

1

2

3

4

5

6

7

8

9

10

11

IMPULSE:lnHEpub, RESPONSE:lnHEpriv

Figure 3. Impulse response functions with 95% CI’s for Cluster 3