The impact of neighbouring countries on health
expenditures using dynamic spatial panel approach
Bastiaan Y. Bonnema
*University of Groningen
Supervisor: S.G. See PhD
MSc Economics Thesis (EBM877A20)
June 2020
Abstract
Using a dynamic spatial panel approach and data pertaining to 156 countries over the period 2000-2016, this thesis tests and compares the different spatial econometric models and three matrices describing the mutual relationships among countries to identify the impact of neighbouring countries on public health expenditures. The results show that public health spending measured as a ratio of GDP in one country indeed depends primarily on the public health spending of neighbouring countries, but in a limited number of cases, it also depends on control variables that can be observed in neighbouring countries, among which are the level of GDP, the total population size, the proportion of people aged between 0 to 14 and the proportion of people aged 65 and above. The most likely specification of the matrix describing the relationships among countries is the first-order binary contiguity matrix based on land borders. Finally, the dynamic spatial panel data approaches are preferred over cross-sectional approaches due to their controls for habit persistence, country, and time-period fixed effects.
Keywords: Health Expenditures, Country Spillovers, Dynamic Spatial Panel, Public Finance
JEL Classification: C23, H51, I18, O50
* The author of this thesis would like to thank S.G. See PhD for her helpful comments and guidance during the process of writing this thesis.
2
Table of contents
1. Introduction ...3
2. Background and literature review ...7
2.1 Determinants of health expenditures ...7
2.2 Spatial interactions between countries and regions ... 11
3. Data analysis ...15
3.1 Data retrieval ... 15
3.2 Descriptive statistics ... 16
3.3 Correlation coefficients ... 18
3.4 Stationarity and cointegration ... 19
4. Methodology ...23
4.1 Spatial lags, models and weights ... 23
4.2 Spatial model and weights of health expenditures ... 26
4.3 Dynamics ... 27
4.4 Spatial spillovers ... 28
5. Results ...30
5.1 Country and time-period fixed effects ... 30
5.2 Spatial model comparison ... 31
5.3 Dynamic Spatial model ... 34
5.4 Robustness checks ... 37
6. Conclusion ...40
References ...41
3
1.
Introduction
Individuals consistently rank health as the number one thing they desire in life (WHO, 2002). Generally speaking, health is a state wellness and completeness of a person. It means the state of being fit and mentally balanced to react to changes in the environment (Alleyne & Cohen, 2002). The percentage of GDP (Gross domestic product) spent on healthcare has traditionally been used in evaluating the weight of the health sector within the economy, whereas the percentage of the government’s expenditures spent on healthcare has been used in evaluating the weight of the health sector for a country’s government. These measures are used to analyse how a country’s health sector has evolved over time or to compare the health sectors of different countries at a given point in time (Shmueli & Israeli, 2013). In this thesis, the focus will be on the public health spending measured as a percentage share of the GDP. For most countries, health is one of the highest government expenditures (World Bank, 2019). OECD1 spending on health as a share of GDP – 8.8% on average in 2017 – remained the same since 2013 as overall growth of health spending has closely followed overall economic growth. This stagnation of the percentage of GDP health spending for OECD countries can also be seen in Figure 1 below, in which the annual percentage of GDP health spending for the period 1970-2018 of 20 OECD countries is shown. The highest percentage of GDP spend on health in 2017 was in the United States at 17.1%, which is significantly more than Switzerland (12.3%) and France (11.3%), the second and third highest health spenders. The lowest shares of GDP spend on healthcare were Turkey (4.2%), Luxembourg (5.5%) and Mexico (5.5%) (OECD, 2019). However, this covers only OECD countries, since there are countries with even lower shares of GDP spend on healthcare. The dataset that I compiled, using World Bank data on 156 countries, shows that a staggering 33 countries have spent an even lower share of their GDP on healthcare in 2016 than Turkey, the lowest belonging to Papua New Guinea (2.0%), Laos (2.4%) and Bangladesh (2.4%).
Over the last decades, healthcare expenditures have been increasing in both developed and developing countries and this is causing serious debates and re-evaluation of the benefits and performance of healthcare spending (Hall & Jones, 2007). This growth is clearly depicted for OECD countries in Figure 1 below. Unfortunately, health spending data for such an extensive period (1970-2018) is only widely available for some OECD countries, which are all considered developed countries. This rise in percentage of GDP health spending puts pressure on policymakers and academics to understand the reasons for this rise and assess whether it leads to significant improvements in health and life expectancy (Cutler, Rosen & Vijan, 2006; Murphy & Topel, 2006; Nordhaus, 2002). There are some factors that possibly contribute to the excess growth in healthcare expenditures, which is the growth after controlling for the growth of income and the aging population. These are the spread of
4
insurance, defensive medicine and supplier-induced demand, factor productivity and technology (Chernew & May, 2011; Frogner, Hussey & Gerard, 2011).
Figure 1. Annual percentage of GDP health spending OECD countries
This figure depicts the annual percentage of GDP spend on healthcare for the period 1970-2018 of 20 OECD countries. The country abbreviations are from the OECD Database. Data source: OECD (2020b)
The wellbeing of a nation’s inhabitants is of paramount importance and has a positive correlation with economic growth (Sachs, 2001). Some researchers even argue that a healthy population is a necessary requirement for economic growth. This trend was shown in the study of Fogel (1991), whose research has explained the relationship between body mass and food supply and has shown that this relationship is critical for long-term labour productivity. The relationship between health and economic growth has also been established by other studies on a more modest scale. These studies considered groups of children that were separated according to caloric intakes during their first three years of life. The results clearly show that those with higher caloric intakes generally attain higher incomes 30 years later in life and for this reason they are presumed to be more economically productive (Fuentes, Hernandez & Pascual, 2001). The results of these studies could be one of the rationales behind spending on health. Healthy countries have more favourable conditions to grow economically, especially in a favourable policy environment.
Even though healthcare spending relative to economic growth has stabilized over the last six years for OECD countries (OECD, 2019), healthcare costs around the world are steadily growing faster than general economic growth. Therefore, a majority of countries have seen healthcare spending as a percentage of their gross domestic product (GDP) increase over time
0 2 4 6 8 10 12 14 16 18
% of GDP health spending OECD countries 1970-2018
5
(Kleiman, 1974; Newhouse, 1977; and Hall & Jones, 2007). Healthcare expenditures among countries and even regions such as provinces, states or municipalities vary substantially regardless of how they are measured, limiting cross-country and cross-region healthcare spending analysis. There are several causes for these differences, such as various political factors, budgetary demands, budgetary trade-offs, the business cycle, income inequality and many more. Additionally, international comparisons of healthcare spending suffer from several other shortcomings, such as the characteristics of the population (e.g. age, morbidity, diet, lifestyle, genetic diseases), the characteristics of the health systems (e.g. service availability, insurance coverage, incentives), macroeconomic characteristics and the unique national characteristics (Shmueli & Israeli, 2013).
The extent to which one country or region’s government health expenditure affects the spending decisions of neighbouring countries or regions is still relatively unclear. Some research has been done on the impact of health expenditure of a region (Costa-Font & Pons-Novell, 2007) or a state of the United States (Bose, 2015) on that of neighbouring regions or states. However, the impact among countries for health spending in particular has not yet been analysed in the current literature. This literature shows that regions and states indeed impact the health expenditures of their neighbouring regions and states and that this is mainly driven by their own health spending policy. Additionally, Hory (2018) shows that European governments mimic the fiscal policy behaviour of neighbouring governments, which includes health spending. She finds yardstick competition to be the most likely cause for the fiscal interactions in Europe. Yardstick competition is the phenomenon that fiscal policy in one jurisdiction interacts with fiscal policy in neighbouring jurisdictions (Besley & Case, 1995). Therefore, it is very interesting to fill the gap in the existing literature and examine empirically whether a country’s government health expenditure is affected by the government health expenditures and other factors of neighbouring countries on a global scale. This leads to the research question: What is the impact of neighbouring countries on a country’s government health expenditure? To answer this question, this thesis applies a methodological comparison of the Yesilyurt and Elhorst (2017) paper that examines the impact of neighbouring countries on a country’s military expenditures. This method uses a dynamic spatial panel approach, which belongs to a relatively upcoming field in econometrics, namely spatial econometrics.
6
fixed effects as well as the inclusion of dynamic effects, which generally add significant value to the model (Elhorst, 2010).
7
2.
Background and literature review
2.1
Determinants of health expenditures
There is no existing literature on spatial interactions among countries for health spending. However, there is plenty of existing literature on cross-country health spending in general. A body of literature examining the determinants of healthcare expenditures has been developed in an effort to explain why healthcare expenditures have vastly increased in the post-war era and to investigate what variables can be influenced to reduce its costs. Most of this literature has used a determinants approach by regressing (per capita) health expenditures on variables like income, proportion of the population being under the age of 15 or above the age of 65, the public finance share of healthcare spending, amount of foreign aid, urbanization and the number of practicing physicians per capita (Di Matteo & Di Matteo, 1998).
8
years, new methods have been developed in econometrics, allowing to obtain more realistic models of health expenditure and to estimate the income elasticity more accurately (Baltagi et al., 2017). So have Carrion-i-Sevestre (2005) and Hartwig (2008) adopted methods for non-stationary panels with structural breaks and has Chakroun (2010) adopted estimation techniques for heterogeneous panels such as the panel threshold regression. Furthermore, Moscone and Tosetti (2010) as well as Baltagi and Moscone (2010) have adopted panels with spatial correlation (which is not a spatial econometric model) and/or unobserved common factors for health spending.
Despite the extensive literature on the topic, only a few studies have offered a global perspective. A possible reason for this is that these studies have to impose the strong assumption of homogeneity and cross-sectional dependence on the countries examined. In the early studies, the focus was mainly on OECD countries. Later on, in the 1990s, there have been some studies focusing on African countries. In more recent years, there have been studies that examined the income elasticity for healthcare expenditures of Asian countries as well as the whole world. In Table 1 below, an overview is given of the most relevant studies on income elasticity for healthcare expenditures over the last 43 years. It shows that the more recent studies, despite of the continent examined, all find income elasticities below one, which would indicate that healthcare is a necessity.
9 Table 1. Estimated income elasticities for healthcare expenditures from a variety of studies
Study Period Dependent variable(s) Income elasticity
OECD countries
Newhouse (1977) 1970 Per capita HE 1.15-1.31
Leu (1986) 1974 Per capita HE 1.20
Brown (1987) 1978 Per capita HE 1.39
Parkin, McGuire & Yule (1987) 1980 Per capita HE in PPPs & HE share of GDP
1.12-1.18 Gerdtham et al. (1992) 1987 Per capita HE in PPPs 1.39-1.56 Hitiris & Posnett (1992) 1960-1987 Real per capita HE 1.02-1.16 Gerdtham et al. (1998) 1970-1991 Real per capita HE 0.67-0.82 Di Matteo & Di Matteo (1998) 1965-1991 Real per capita HE 0.77 Fogel (1999) 1875-1996 Healthcare Expenditure 1.60 Roberts (1999) 1960-1993 Real per capita HE 1.25-2.00 Okunade & Karakus (2001) 1960-1997 Real per capita HE 1.20-1.46 Freeman (2003) 1966-1998 Healthcare Expenditure 0.81-0.84 Costa-Font & Pons-Novell (2007) 1992-1999 Per capita HE 0.66-0.98 Moscone & Tosetti (2010) 1980-2004 Per capita HE in PPPs 0.36-0.90 Baltagi & Moscone (2010) 1971-2004 Real per capita HE 0.44-0.89 Chakroun (2010) 1975-2003 Per capita HE in PPPs Below 1 Asian countries
Pan & Lin (2012) 2002-2006 Real per capita HE 0.22-0.40 Samadi & Rad (2013) 1995-2009 Per capita HE in PPPs 0.46-0.82 Khan & Mahumud (2015) 1995-2010 Per capita Private and
Public HEs
0.41-0.91 African countries
Gbesmete and Gerdtham (1992) 1984 Per capita HE 1.07
Murthy (2004) 2001 Real per capita HE 1.11
Okunade (2005) 1995 Per capita HE in PPPs 0.60 Jaunky & Khadaroo (2008) 1991-2000 Real per capita Total,
Private and Public HEs
0.75-1.19 Mehara et al. (2012) 1995-2005 Per capita HE 0.94 Lv and Zhu (2014) 1995-2009 Per capita HE 0.98 World
Xu et al. (2011) 1995-2008 Real per capita HE 0.36-1.30 Liang & Mirelman (2014) 1995-2010 Per capita HE in PPPs 0.66-0.94 Fan & Savedoff (2014) 1995-2009 Per capita HE 0.70
10
The time-series literature on the determinants of healthcare expenditures has been criticized on the basis of the problem of stationarity and the applied cointegration approach. Hansen and King (1996) use a model based on that of Hitiris and Posnett (1992) and a balanced data set on 20 OECD countries for the period 1960-1987 to test whether the variables in a standard model of healthcare expenditures are stationary at levels. This is the case when the statistical properties of the variables are constant over time. To test this, they applied the Augmented Dickey Fuller (ADF) test with H0: the data is non-stationary and Ha: the data is stationary, on the data set. They found that two-thirds of the tested variables were nonstationary at levels. This implies that any positive correlation among any of these variables might be false. Additionally, Murthy and Ukpolo (1994) applied cointegration techniques on time-series data for the United States again over the period 1960-1987 and found that income per capita, age of the population, the proportion of public finance spend on healthcare and the number of practicing physicians are important determinants of healthcare spending in the United States. They also applied ADF tests to their variables and found that only half of these were stationary at levels. The results of this study do not differ from the main body of literature where no cointegration techniques are applied, since they found an income elasticity of demand for healthcare spending that is not significantly different from one. Stationarity and cointegration will be more extensively discussed in section 3.4 of this thesis.
These cross-country comparisons of healthcare expenditures have a number of acknowledged problems. Firstly, the definition of what constitutes to healthcare expenditures is not internationally standardized, meaning that some countries will contribute certain expenditures to healthcare and other countries do not (Di Matteo & Di Matteo, 1998). Secondly, when dealing with countries across the world with different currencies, it is difficult to construct exchange rate conversions for the data. Thirdly, countries’ input prices may be correlated with the national income levels of the countries, which may partly cause the high income elasticities for per capita health spending found in the featured studies, since the estimated elasticities may reflect both the pricing as well as quantity or use differences across countries (Leu, 1986). Fourthly, in wealthier countries, health practitioners tend to be paid a higher wage than in poorer countries and income disparities across countries are much greater than the income disparities within countries. In cross-country studies, this may be reflected in high correlations between income and healthcare expenditures, resulting in high income elasticities of demand. Lastly, healthcare has become more subsidized in most countries, making the ability to pay for healthcare a less important determinant of healthcare expenditure.
11
in the approaches the earlier studies in the 1980s used to examine the determinants of healthcare, namely single cross-section cross-country studies. The panel data approach might be more appropriate to prevent the aforementioned problems from generating income elasticities greater than one. The interpretation of healthcare as a luxury good, caused by the high income elasticities found in some of these studies, has been heavily criticized because people believe that healthcare is more of a necessity than a luxury good (Culyer, 1988).
2.2
Spatial interactions between countries and regions
As mentioned in subsection 2.1, there is no existing literature on spatial interactions among countries for healthcare spending in particular. However, there is some literature that examines this effect among states of the United States (Bose, 2015) and regions within Spain (Costa-Font & Pons-Novell, 2007). Additionally, there are some studies that examine the spatial interaction effects among regions (Elhorst & Fréret, 2009; Rios, Pascual & Cabases, 2017) and European countries (Hory, 2018) for government expenditures in general (Hory, 2018) as well as the spatial interactions for government military expenditures among countries (Yesilyurt & Elhorst 2017). An overview of the current literature is given in Table 2 below, which includes the type of spatial econometric model used in the studies. All different types of spatial econometric models will be extensively discussed in section 4.1 and the dynamic extension in section 4.3 of this thesis.
Table 2. Overview literature spatial interactions between countries and regions
Study Spatial dimension Period Dependent variable Spatial econ. model Bose (2015) States of the United States 2000-2009 Per capita HE SDM Costa-Font &
Pons-Novell (2007)
Spanish region-states 1992-1998 Per capita HE SEM Elhorst and Fréret
(2009)
French local governments 1992-2000 Gov. expenditures + Taxation
SDM Rios et al. (2017) Spanish municipalities 2000-2012 Gov. expenditures Dynamic SDM
Hory (2018) European countries 1995-2013 Fiscal stance Dynamic SAR
Yesilyurt & Elhorst (2017)
Countries across the world 1993-2007 Share military expenditures of GDP
Dynamic SAR
This table depicts an overview of the current literature on spatial interactions between countries and regions for government (health) expenditures.
12
model has spatial spillovers in the dependent variable through a spatially lagged dependent variable and spatially lagged independent variables, but does not have spatial dependence in the error term. His results show that there are positive spillover effects of health expenditures of one state on the welfare of its neighbouring states, meaning that if one state decides to increase its health spending, neighbouring states will respond with a similar approach. This phenomenon can be explained by both expenditure spillover effects and fiscal competition effects. Some economic, demographic and social factors and their effects on the per capita health expenditure between states are also examined. The results show that a state’s GDP, percentage of population over age 65, proportion of Medicaid expenditures, active physicians per 100,000 people and the poverty rate have significant positive direct effects and varied spillover effects on its neighbouring states’ health spending. On the other hand, the results show that the proportion of health maintenance organizations has a negative direct and spillover effect on per capita health expenditures. The conclusion of Bose is that any policy-driven decision taken by the government that incorporates these variables are likely to limit the growing cost of healthcare in the United States.
Costa-Font and Pons-Novell (2007) examine the determinants of public health expenditure and their spatial interactions between all 17 Spanish region-states during 1992-1998. For their empirical analysis, they examine the per capita health expenditure of every region-state as the dependent variable. They control for economical, demographic and political factors, such as per capita GDP, number of physicians per 1000 habitants, the proportion of people aged 65 and above and several political factors. They use a Spatial Error Panel Model, which includes a spatial interaction effect in the error term. Their results show that there is a spatial interaction effect between region-states for the health expenditures per capita. This means that the health expenditures of one region-state influences the spending decisions of neighbouring states. Additionally, they find that region-states that have more decentralized healthcare are more likely to exhibit higher per capita health expenditure. Furthermore, they provide evidence that the healthcare expenditure of a region-state depends on the political party at power.
13
Rios et al. (2017) examine the determinants and the spatial interactions of local government expenditures of 3032 Spanish municipalities during 2000-2012. They do so by using a Dynamic Spatial Durbin model, which includes both an endogenous and exogenous spatial interaction effects. In their model they control for several economic, demographic and political factors, such as GDP per capita, the unemployment rate, the population density, percentage of the population above the age of 65, election year dummies and whether the sitting local party is regionally or nationally aligned. They provide evidence of significant spatial interaction effects. Additionally, they find that government spending at the local level is mainly explained by economic factors of the municipality and of the neighbouring municipalities and not so much by demographic or political factors. Furthermore, their results support the extension of the static model to a dynamic model as temporal inertia is one of the key drivers of the government spending.
Hory (2018) examines fiscal interactions of 31 European national governments during 1995-2013 by using a Dynamic Spatial Autoregressive model. In her model, she controls for several economic, demographic and political factors. The economic factors are among other things a country’s GDP per capita, unemployment rate, total population size, public debt (% of GDP) and GDP growth rate. The demographic factors are the proportion of people aged 14 and under (in %) as well as the proportion aged 65 and above (in %). Furthermore, the political factors are the political fragmentation scaled from 0 to 1, the political orientation of the government (1 = right-wing, 5= left-wing) and a dummy variable for election years. Her results show that there are significant fiscal interactions in Europe, but that they are delayed by one year. The European governments mimic the behaviour of neighbouring countries on the last year, leading to “delayed mimicking” behaviours as Hory calls it. Furthermore, Hory finds that the most likely cause for this delayed mimicking behaviour is yardstick competition and not so much tax competition. She advocates for more international cooperation and organizations within Europe to improve fiscal policy efficiency.
14
health expenditures and vice versa. Yesilyurt and Elhorst provide evidence that military spending as a ratio of GDP in one country indeed depends primarily on the spending of neighbouring countries. Additionally, they found that in a limited number of cases, it also depends on control variables that can be observed in other countries such as the level of GDP, the occurrence of international wars and the political regime.
After combining the literature on the determinants of government health expenditures and spatial interactions between countries and regions, it is clear that my model needs to be controlled for several economic, demographic and political factors. First, following all the literature on spatial interactions for government expenditures among regions and countries and the determinant literature, my model is controlled for countries’ income in terms of GDP. Additionally, following Elhorst and Fréret (2009), Rios et al. (2017), Yesilyurt and Elhorst (2017) and Hory (2018) my model is controlled for countries’ sizes in terms of population. Similarly to Costa-Font and Pons-Novell (2007), Elhorst and Fréret (2009), Rios et al. (2017), Yesilyurt and Elhorst (2017) and Hory (2018), the model is controlled for a political factor, namely countries’ political system in terms of autocratic or democratic regimes. It is plausible to expect that different political regimes set different spending levels for healthcare (Elhorst & Fréret, 2009). Furthermore, following the approach of Costa-Font and Pons-Novell (2007), Bose (2015), Rios et al. (2017) and Hory (2018), I account for the demographic factor age by controlling for countries’ proportions of people aged 14 and under as well as 65 and above. It is plausible to expect that countries’ with older populations tend to spend more on healthcare and that countries with younger populations tend to spend less. However, countries with a higher share of the inactive population (both young and old people) will have larger public spending relative to tax revenues (Hory, 2018).
15
3.
Data analysis
3.1
Data retrieval
To be able to analyse whether neighbouring countries affect a country’s government health expenditure, the use of annual data on countries across the world is required. In the spatial econometric model I use to conduct the empirical analysis, the dependent variable is the government health expenditure as a percentage of countries’ GDPs. For the explanatory variables, I consider three categories: economic, demographic and political. The economic factors are the gross domestic product (GDP) of countries and their population sizes. The demographic factors include the percentage of the total population aged between 0 to 14 and the percentage of the total population aged 65 or above. Lastly, the political factor is the political regime of a country, which often functions as a determinant of government health expenditures. Data about the countries’ government health expenditures as a percentage of their GDP is retrieved from the World Bank and is available for 176 countries covering the period 2000-2016. Additionally, data on these countries’ GDPs (denoted in constant 2010 US Dollars) is also retrieved from the World Bank, which covers the period 1960-2018 and is used to control for economic conditions. Data on the countries’ total population sizes is again collected from the World Bank, which also covers the period 1960-2018 and is used to control for countries’ population sizes. Data on countries’ GDPs and total population sizes is available for 215 countries. The data required to control for countries’ age structures is also retrieved from the World Bank and again covers the period 1960-2018, but for 191 countries. Lastly, to control for countries’ political regimes, data is retrieved on the Polity2 variable from the Polity IV project dataset and covers the period 1800-2018 for 168 countries (Marshall, 2014). This indicator ranges from -10 to +10, where -10 indicates a strongly autocratic country and +10 a full democracy. Since percentage of GDP health spending data on most countries is only widely available for the period 2000-2016, the empirical analysis in this thesis will be based on this period. All countries that have health spending data available also have data available on the other variables retrieved from the World Bank (GDP, population size and age structure). Therefore, the data from the World Bank consists of 176 countries and is (nearly) fully balanced. This World Bank data is merged with the Polity2 variable, for which 168 countries are available, to construct one complete dataset of all variables required for the empirical analysis. After this merging process, the dataset that is used for empirical analysis results in annual data for 156 countries, which are depicted in Table A1 in the appendix. Additionally, a full overview of the data collection process is given in Table A2 in the appendix.
16
Elhorst, 2017). Data on the government health expenditure as a percentage of countries’ GDPs contains 23 missing observations among 6 countries. Furthermore, the dataset of the Polity2 variable contains 29 missing observations among 5 countries. However, the datasets of the population sizes, percentages of the populations aged between 0 to 14 and percentages of the populations aged 65 and above are fully balanced. Lastly, the dataset of the countries’ GDPs is nearly balanced and only misses the observations of Afghanistan for the years 2000 and 2001. To make the panel fully balanced, the total of 54 missing observations are replaced by the expected values of the linear trend consisting of the known data points of the same unit, using the least squares method.
3.2
Descriptive statistics
The descriptive statistics of the level series for the period 2000-2016 can be found in Table 3 below. Additionally, the sample means per year of these variables can be found in Table A3 in the appendix and their corresponding standard deviations in Tables A4 to A9 in the appendix. Every variable has 2,652 observations (N = 156, T = 17), since the panel contains no missing observations anymore. All variables except POLREG are skewed to the right, as their means are greater than their medians. This is also shown in Figures 2 to 7 below, where the variables’ percentile shares are depicted in graphs. For example, as displayed in Figure 3, nearly 80% of the worldwide GDP is produced by only 10% of the countries. Additionally, the percentile shares and Gini coefficients per year are shown in Tables A4 to A9 in the appendix. The Gini coefficient is a widely used measure for statistical dispersion, ranging from 0 to 1. Where a coefficient of 0 means a perfectly equal distribution and 1 means a perfectly unequal distribution.
Table 3. Descriptive statistics
Variable Obs. Mean Median Std. Dev. Min Max
HEALTH 2,652 6.108 5.769 2.500 1.025 20.415 GDP 2,652 398.808 37.790 1412.743 0.462 16972.348 POP 2,652 42.591 10.029 146.000 0.413 1378.665 YOUNG 2,652 29.995 29.712 11.026 12.289 50.264 OLD 2,652 7.589 5.183 5.448 0.686 26.592 POLREG 2,652 3.932 6 6.194 -10 10
17
Figure 2. Percentile shares distribution of HEALTH Figure 3. Percentile shares distribution of GDP
Figure 4. Percentile shares distribution of POP Figure 5. Percentile shares distribution of YOUNG
Figure 6. Percentile shares distribution of OLD Figure 7. Percentile shares distribution of POLREG
18
The average percentage of a country’s GDP spend on healthcare during 2000-2016 is 6.11%, with a minimum of 1.03% (Timor-Leste in 2006) and maximum of 20.42% (Sierra Leone in 2015). A country’s GDP is on average 399 billion US Dollars, while the minimum GDP of a country is 462 million US Dollars (Solomon Islands in 2002) and the maximum being 17 trillion US Dollars (United States in 2016). The average number of people living in a country is 42.6 million, while the lowest amount of country inhabitants in my data set is 412,660 (Solomon Islands in 2000) and the highest amount being 1.38 billion (China in 2016). On average, 30.00% of a country’s population is aged between 0 to 14 and 7.59% aged 65 and above. Furthermore, the minimum shares of young and old people are 12.29% (Singapore in 2016) and 0.69% (United Arab Emirates in 2010) respectively, while the maximum shares are 50.26% (Niger in 2013) and 26.59% (Japan in 2016) respectively. Lastly, the average score of the Polity2 variable is 3.93. This means that countries are on average on the democratic side of an anocracy, which is a regime that mixes democratic with autocratic features (Fearon & Laitan, 2003).
The variables GDP, POP and POLREG have high standard deviations compared to the mean, suggesting that these variables are widely spread among countries. The variables HEALTH, YOUNG and OLD have more moderate standard deviations. The variables GDP and POP will be log-transformed for the empirical analysis because of their high values and relatively high standard deviations. The log-transformation will decrease their values and standard deviations to that of the log-normal distribution. One of its properties is that it has a proportionality of the standard deviation to the mean. Additionally, if there is strong evidence of a skewed distribution (see Figures 3 and 4) of the levels series, a log-transformation of the series is usually preferable.
3.3
Correlation coefficients
19
where +1 indicates a perfect positive relationship, -1 indicates a perfect negative relationship, and a 0 indicates that no relationship exists. If the Pearson’s coefficient value lies between ±0.5 and ±1, it is seen as a strong correlation. In general, a coefficient value above 0.7 or below -0.7 indicates the presence of multicollinearity. Additionally, if the value lies between ±0.3 and ±0.5, then it is said to be a moderate correlation, and below ±0.30, it is said to be a low degree of correlation (Kirch, 2008).
Table 4. Pearson’s correlation matrix
Variable HEALTH GDP POP YOUNG OLD POLREG HEALTH 1.000 GDP 0.358 1.000 POP -0.072 0.429 1.000 YOUNG -0.316 -0.255 -0.063 1.000 OLD 0.515 0.289 -0.002 -0.678 1.000 POLREG 0.418 0.141 -0.037 -0.337 0.528 1.000
This table depicts the Pearson’s correlation matrix for the variables for the 156 countries examined in this thesis over the period 2000-2016. Where HEALTH is the government health expenditure as a percentage of countries’ GDPs; GDP is the country’s gross domestic product; POP is the country’s total population size; YOUNG is the percentage of the total population between ages 0 to 14; OLD is the percentage of the total population aged 65 and above; and POLREG represents a country’s political regime.
The dependent variable HEALTH has mostly moderate degrees of correlation with the independent variables with the exclusions of OLD, which value is greater than 0.5, and POLREG, which value is nearly 0. However, these coefficients are only included for a more comprehensive overview of the data and are not relevant for the problem of multicollinearity. Looking at the correlation coefficients of the independent variables, there are two variables with a high degree of correlation, namely YOUNG & OLD (-0.678) and POLREG & OLD (0.528). This means that the percentage of the total population aged 65 and above has a strongly negative relationship with the percentage of the total population between ages 0 to 14 and a strongly positive relationship with a country’s political regime. However, both these high degrees of correlation are above/below the threshold of ±0.7 at which the problem of multicollinearity is present.
3.4
Stationarity and cointegration
20
statistic nearly 1 or >1), meaning it is non-stationary, and Ha: the panel variable is stationary (test statistic << 1). This stationarity test assumes that the number of panels tend to infinity while the number of time periods is fixed, making it suited for my dataset with a large number of countries and relatively few time periods. The Harris-Tzavalis unit-root test results are shown in Table 5 below.
Table 5. Harris-Tzavalis unit-root test results Variable Test statistic
value p-value HEALTH 0.791 0.001 GDP 1.034 1.000 POP 0.989 1.000 YOUNG 0.940 1.000 OLD 1.043 1.000 POLREG 0.778 0.000
This table depicts the Harris-Tzavalis unit-root test statistic values and corresponding p-values of the variables for the 156 countries examined in this thesis over the period 2000-2016. Where HEALTH is the government health expenditure as a percentage of countries’ GDPs; GDP is the country’s gross domestic product; POP is the country’s total population size; YOUNG is the percentage of the total population between ages 0 to 14; OLD is the percentage of the total population aged 65 and above; and POLREG represents a country’s political regime.
21 Figure 8. Ln(GDP) Germany and neighbours Figure 9. Ln(POP) Germany and neighbours
Figure 10. YOUNG Germany and neighbours Figure 11. OLD Germany and neighbours
The Figures 8 to 11 depict the non-stationary variables, namely GDP, POP, YOUNG and OLD for Germany and its 9 neighbouring countries over the period 2000-2016. Where GDP is the country’s gross domestic product; POP is the country’s total population size; YOUNG is the percentage of the total population between ages 0 to 14; and OLD is the percentage of the total population aged 65 and above. Both GDP and POP are log-transformed. And where AUT = Austria, BEL = Belgium, SWI = Switzerland, CZE = Czech Republic, DEU = Germany, DNK = Denmark, FRA = France, LUX = Luxembourg, NLD = Netherlands and POL = Poland.
24 25 26 27 28 29 30 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Ln(GDP) Germany and neighbouring countries
AUT BEL SWI CZE DEU DNK FRA LUX NLD POL 12.5 13.5 14.5 15.5 16.5 17.5 18.5 2000 2002 2004 2006 2008 2010 2012 2014 2016
Ln(POP) Germany and neighbouring countries
AUT BEL SWI CZE DEU DNK FRA LUX NLD POL 10 12 14 16 18 20 22 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
% of population aged 65 and above Germany and neighbouring countries
AUT BEL SWI CZE DEU DNK FRA LUX NLD POL 12 13 14 15 16 17 18 19 20 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
% of population aged 14 and under Germany and neighbouring countries
22
However, Kao (1999) as well as Phillips and Moon (2000) show that in a panel-data setting, which is used in this thesis, the regression stops being spurious and estimates of the structural parameter binding two non-stationary independent variables converge to zero, whereas it is a random variable in the case of time-series analysis. This means that non-stationary panel data may lead to biased standard errors, but the estimations of the parameters are still consistent. Given this fact, the variables YOUNG and OLD are not transformed to deal with the non-stationarity issue. This is done in order to keep the levels information of these variables in the regressions, while the GDP and POP variables are already log-transformed for the empirical analysis. These log-transformations deal with the issue of non-stationarity somewhat, but it still remains present in a weaker form.
Non-stationary variables might be cointegrated with each other, meaning that there exists a stable long-run relationship between them (Kao, 1999). I use the cointegration test of Kao (1999) for the four non-stationary variables (GDP, POP, YOUNG and OLD) with H0: there is no cointegration among the variables, and Ha: all variables are cointegrated. The five test statistics and corresponding values of the Kao cointegration test are shown in Table 6 below.
Table 6. Kao cointegration test results
Test statistic Test
statistic value p-value Modified Dickey-Fuller 11.184 0.000 Dickey-Fuller 15.200 0.000 Augmented Dickey-Fuller 9.148 0.000 Unadjusted Modified D-F 11.077 0.000 Unadjusted Dickey-Fuller 14.912 0.000
This table depicts the five test statistics and its values of the Kao cointegration test performed on the four non-stationary variables: GDP, POP, YOUNG and OLD. Where GDP is the country’s gross domestic product; POP is the country’s total population size; YOUNG is the percentage of the total population between ages 0 to 14; and OLD is the percentage of the total population aged 65 and above.
23
4.
Methodology
4.1
Spatial lags, models and weights
Due to the nature of the research objective, the research method should contain a model which is able to detect spatial spillovers. There are three main types of spatial lags that can be used to explain the government health expenditure of a country (LeSage & Pace, 2009; Elhorst, 2014b). The first type is an endogenous spatial lag, which measures whether the percentage of GDP spend on healthcare of country i depends on the percentage of GDP spend on healthcare of country j (j ≠ i), or vice versa. Including only this spatial interaction effect in an econometric model, results in the Spatial Autoregressive (SAR) model, which is commonly used in spatial econometrics literature. Secondly, there is the spatial lag among the error terms, which may be appropriate if countries face similar unobserved institutional environments or share similar unobserved characteristics. An econometric model that includes only the spatial lag among the error terms is the Spatial error model (SEM), but remains rather unpopular. Beck, Gleditsch and Beardsley (2006) argue that this is the case because the model is very odd to use in many applications, as space matters in the error process, but not in the essential portion – that is the dependent and explanatory variables – of the model. Lastly, there are exogenous spatial lags, which measure whether the percentage of GDP spend on healthcare of country i depends on the explanatory variables of other countries j (j ≠ i). The number of exogenous spatial lags equals the number of explanatory variables K. Including only exogenous spatial interactions in an econometric model, results in the Spatial lag of X (SLX) model. Models including exogenous spatial lags are widely used, but less common in the existing spatial econometric literature (Elhorst, 2014b). In addition to the SAR, SEM and SLX models that include only one type of spatial lag, alternative models combine two or even all three types of spatial lags. Overall, the number of possible spatial lags equals K + 2 if all three spatial interaction effects are included in the model. In the existing spatial econometric literature, too many studies only consider one type of spatial lag and thus estimate the SAR, SEM or SLX model without testing model specifications against one another or considering whether the more extensive models with two or even all three types of spatial lags are more appropriate (Yesilyurt & Elhorst, 2017). Including all three spatial lags yields the General Spatial Nesting (GNS) model and has the form given in Equation 1 below (LeSage & Pace, 2009):
𝑌 = 𝜌𝑊𝑌 + 𝛼0𝜄𝑁+ 𝑋𝛽 + 𝜃𝑊𝑋 + 𝑢 (1a) 𝑢 = 𝜆𝑊𝑢 + 𝜀 (1b)
24
Where 𝑌 denotes an N x 1 vector that represents the dependent variable for every unit in the sample, 𝜄𝑁 is an N x 1 vector of ones associated with the constant parameter 𝛼0, 𝑋 denotes an N x K matrix of exogenous explanatory variables associated with the K x 1 vector parameters 𝛽, 𝜀 denotes the disturbance term, where 𝜀𝑖 are identically and independently distributed
error terms for every 𝑖 with mean zero and diagonal variance-covariance matrix 𝜎2𝐼, which has a constant variance and zero covariance between observations. W denotes the N x N matrix of spatial weights 𝑤𝑖𝑗 , which describes the spatial interaction between country 𝑖 and
𝑗. This matrix is shown in Equation 2 below, in which the row elements exhibit the impact on a particular unit by all other units and the column elements exhibit the impact of a particular unit on all the other units.
𝑊 = (
𝑤11 . 𝑤1𝑁
. . .
𝑤𝑁1 . 𝑤𝑁𝑁) (2)
Hence, the W represents the spatial weight matrix that captures the spatial dependence among the spatial units in the sample. Since it is assumed that spatial units cannot influence themselves, the diagonal elements of the matrix will be zeros. In spatial econometrics, determining how to construct the spatial weight matrix W is very crucial, but can be difficult. The elements of the matrix can depend on geographical, economic or political distances between countries (Yesilyurt & Elhorst, 2017). Several methods have been developed to construct the spatial weight matrices, the most common one being the binary contiguity matrix, in which the elements take a value of 1 if the spatial units have something in common, like a border, and otherwise have the value 0. Another common spatial weight matrix is the distance-based binary matrix, in which the elements take a value of 1 if the distance between the two units is less than a certain threshold cut-off distance and take the value 0 otherwise. Additionally, there is a non-binary distance matrix, in which the elements won’t be assigned zeros and ones, but will be based on the distance between the two units that an element represents. A good example of this is the inverse distance matrix that will assign higher values the smaller the distance is between two units.
25 Table 7. Spatial econometric models
Model Spatial
interaction effects
Restrictions Flexibility and country spillovers
OLS, Ordinary least squares model - 𝜃=𝜌=𝜆=0 Zero by construction SAR, Spatial autoregressive model WY 𝜃=𝜆=0 Constant ratios, global SEM, Spatial error model Wu 𝜃=𝜌=0 Zero by construction SLX, Spatial lag of X model WX 𝜌=𝜆=0 Fully flexible, local SAC, Spatial autoregressive
combined model
WY, Wu 𝜃=0 Constant ratios, global SDM, Spatial Durbin model WY, WX 𝜆=0 Fully flexible, global SDEM, Spatial Durbin error model WX, Wu 𝜌=0 Fully flexible, local GNS, General nesting spatial model WY, WX, Wu - Fully flexible, global
This table depicts an overview of the different types of spatial econometric models, each with a different combination of spatial interaction effects. Source: Yesilyurt and Elhorst (2017)
For the spatial autoregressive model (SAR) and the spatial autoregressive combined model (SAC), a proportionality relationship arises between the direct and spillover effects. This means that the ratio of spillover to direct effects is the same for all variables in the model, which is not very likely from an empirical perspective (Elhorst, 2010). Only spatial econometric models that include exogenous spatial interaction terms can have different ratios of spillover to direct effects across variables. These are the spatial lag of X model (SLX), the spatial Durbin model (SDM), the spatial Durbin error model (SDEM) and the general nesting model (GNS).
Finally, the country spillover effects could be either local or global. The local spillover effect occurs when ρ = 0 and θ ≠ 0, and countries are connected through the spatial weight matrix W. If in a spatial econometric model with a local spillover effect two countries i and j are not connected ( 𝑤𝑖𝑗 = 0), a change in an exogenous variable of country i cannot affect the
dependent variable of country j and vice versa. On the other hand, the global spillover effect occurs when ρ ≠ 0 and θ = 0, regardless of whether the countries are connected or not. Thus, in a spatial econometric model with a global spillover effect, a change in an exogenous variable of country i gets transmitted to all other countries even if 𝑤𝑖𝑗 = 0 (Yesilyurt & Elhorst,
26
4.2
Spatial model and weights of health expenditures
The literature in section 2 suggests the presence of spatial spillovers for health spending between regions and states, but in the current literature this effect has not yet been established for countries. To estimate these spatial spillovers among countries, a spatial econometric model is estimated, which will result in estimates for both the direct and indirect (spillover) effects of the dependent and the explanatory variables. In the empirical analysis of this thesis, the focus will be on the spillover effects. How the estimations of these vary among the different types of spatial econometric models will be discussed later in section 4.4. The specific spatial econometric model for health spending that includes all three spatial lags as well as spatial and time-period fixed effects is shown in Equation 3 below.
𝐻𝐸𝐴𝐿𝑇𝐻𝑖𝑡 = 𝛽0+ 𝛽1𝑙𝑛𝐺𝐷𝑃𝑖𝑡+ 𝛽2𝑙𝑛𝑃𝑂𝑃𝑖𝑡+ 𝛽3𝑌𝑂𝑈𝑁𝐺𝑖𝑡+ 𝛽4𝑂𝐿𝐷𝑖𝑡+ 𝛽5𝑃𝑂𝐿𝑅𝐸𝐺𝑖𝑡+ 𝛽6∑𝑁𝑗=1𝑤𝑖𝑗𝐻𝐸𝐴𝐿𝑇𝐻𝑗𝑡 + 𝛽7∑𝑁𝑗=1𝑤𝑖𝑗𝑙𝑛𝐺𝐷𝑃𝑗𝑡+ 𝛽8∑𝑁 𝑤𝑖𝑗 𝑗=1 𝑙𝑛𝑃𝑂𝑃𝑗𝑡+ 𝛽9∑𝑁𝑗=1𝑤𝑖𝑗𝑌𝑂𝑈𝑁𝐺𝑗𝑡 + 𝛽10∑𝑁𝑗=1𝑤𝑖𝑗𝑂𝐿𝐷𝑗𝑡+ 𝛽11∑𝑁 𝑤𝑖𝑗 𝑗=1 𝑃𝑂𝐿𝑅𝐸𝐺𝑗𝑡+ 𝜉𝑡+ 𝜇𝑖 + 𝑢𝑖𝑡 (3a) 𝑢𝑖𝑡= 𝜆 ∑𝑁𝑗=1𝑤𝑖𝑗𝑢𝑗𝑡+ 𝜖𝑖𝑡 (3b)
Where 𝐻𝐸𝐴𝐿𝑇𝐻 represents a country’s health expenditure as a percentage of its GDP; 𝐺𝐷𝑃 captures a country’s gross national product (GDP) and 𝑃𝑂𝑃 captures a country’s total population size. 𝑌𝑂𝑈𝑁𝐺 indicates a country’s population between ages 0 to 14 as a percentage of the total population and 𝑂𝐿𝐷 indicates a country’s population aged 65 and above as a percentage of the total population. 𝑃𝑂𝐿𝑅𝐸𝐺 represents a country’s political regime on a scale from -10 to 10, where -10 indicates a strongly autocratic country and +10 a full democracy. The country fixed effects and time fixed effects are captured by 𝜇 and 𝜉, respectively. The 𝑤 represents the row-normalized spatial weight matrix that captures the spatial linkages between country 𝑖 and 𝑗.
Consequently, a spatial weight matrix should be constructed. The chosen specification of the spatial weight matrix matters a lot as it influences both the values and the significance levels of the estimated parameters in the spatial model. For this reason, it is recommended to use different spatial weight matrices to examine whether the results are sensitive to the specification of the spatial weight matrix (Elhorst & Halleck Vega, 2017).
The first spatial weight matrix that I consider is a first-order binary contiguity matrix W1, which captures border-linkages between spatial units. This means that if country 𝑖 shares a land border with country 𝑗, then 𝑤𝑖𝑗 = 1 and consequently if countries do not share a
27
to interact with each other than countries that do not share a common border. The average number of “neighbours” per country is 3.46 for W1.
Secondly, I consider a second-order binary contiguity matrix W2, since a country might influence countries beyond her order neighbours. This means that on top of the first-order neighbours, second-first-order neighbours will have 𝑤𝑖𝑗 ≠ 0 in the spatial weight matrix. The
W2 matrix is constructed by the matrix multiplication of W1 times W1. Consequently, the diagonal elements are made zero, since countries cannot be their own neighbours. This results in an average number of 10.01 “neighbours” per country for W2.
Thirdly, I consider a third-order binary contiguity matrix W3, since a country may influence countries even further away. This means that on top of the first- and second-order neighbours, countries that are third-order neighbours will have 𝑤𝑖𝑗 ≠ 0 in the spatial weight
matrix. The W3 matrix is constructed by the matrix multiplication of W2 times W1 and afterwards the diagonal elements are made zero again. This results in an average number of “neighbours” per country of 18.71 for W3.
All the binary contiguity matrices W1, W2 and W3 will be row-normalized, which means that the weights are transformed using Equation 4. All elements in a row will be divided by the sum of the row. This will result in the sum of each row being equal to one, while the zero elements will remain zero, since dividing zero by something will still be zero.
𝑤𝑖𝑗𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 = 𝑤𝑖𝑗
∑𝑁𝑗=1𝑤𝑖𝑗
(4)
4.3
Dynamics
Like in the paper of Yesilyurt and Elhorst (2017), this thesis extends the static spatial econometric models to dynamic spatial econometric models to examine the spatial spillovers of government health expenditures between countries. The dynamic models will include the temporal lag of the dependent variable, 𝑌𝑡−1, to control for habit persistence. This means that the government health expenditure measured as a percentage of a country’s GDP is subject to budgetary inertia, because spending depends on decisions made in previous years and it might be subject to bureaucratic institutions (DiGiuseppe, 2015). Korniotos (2010) examines the use of spatial dynamic models for explaining the consumption growth of the United States over the period of 1966-1998 and interprets the coefficients of the space-time and temporal lags of the dependent variable as measures of the relative strength of external (𝜂𝑊𝑌𝑡−1) and
28
as the Dynamic General Spatial Nesting (GNS) model (Costa da Silva, Elhorst & Silveira Neto, 2017).
𝑌𝑡 = 𝜏𝑌𝑡−1+ 𝜌𝑊𝑌𝑡+ 𝜂𝑊𝑌𝑡−1+ 𝛼0𝜄𝑁+ 𝑋𝑡𝛽 + 𝜃𝑊𝑋𝑡+ 𝜉𝑡+ 𝜇 + 𝑢𝑡 (5a) 𝑢𝑡= 𝜆𝑊𝑢𝑡+ 𝜀 (5b)
𝜀 ~ 𝑁(0, 𝜎2𝐼) (5c)
4.4
Spatial spillovers
Spatial econometric models generally focus on the spillover effects between countries, regions or municipalities, such as whether a change to the level of GDP in a particular country affects the government health expenditures in neighbouring countries. Comparing the estimates of non-spatial econometric models that do not account for spatial interactions with spatial econometric models, may lead to erroneous conclusions. This also goes for comparing different types of spatial econometric models with one another (Yesilyurt & Elhorst, 2017). LeSage and Pace (2009) show that a partial derivative interpretation allows for easier interpretation of the spillover effects, but only for cross-sectional data. However, Elhorst (2014b) developed a method to compute the partial derivatives of the Dynamic GNS model based on spatial panel data. He shows that the matrix of partial derivatives of the expected value of the dependent variable with respect to the kth independent variable for i = 1, … , N is given by the N x N matrix of Equation 6 below.
[𝜕𝐸(𝐷) 𝜕𝑥1𝑘 … 𝜕𝐸(𝐷) 𝜕𝑥𝑁𝑘 ] = [(1 − 𝜏)𝐼 − (𝜌 + 𝜂)𝑊]−1[𝛽𝑘𝐼𝑁+ 𝜃𝑘𝑊] (6)
29
elements. The calculation of the direct effects reflects the marginal effects of each
30
5.
Results
5.1
Country and time-period fixed effects
Following the approach of Elhorst (2014a), I investigate whether country fixed effects are jointly significant or random effects can replace them and whether time-period fixed effects should be included. The models without any spatial interaction effects are estimated in order to test this. An overview of these non-spatial panel data models for cross-country percentage of GDP health spending is given in Table 8 below.
Table 8. Estimation results non-spatial panel data models Determinants Pooled OLS Country fixed
effects
Time fixed effects
Country and time fixed effects Ln(GDP) 0.069 (1.53) -0.259** (-2.04) 0.078* (1.73) -1.048*** (-6.95) Ln(POP) -0.068 (-1.39) 1.017*** (4.05) -0.085* (-1.75) -0.220 (-0.78) YOUNG 0.080*** (9.54) -0.033** (-2.25) 0.086*** (10.29) -0.003 (-0.17) OLD 0.320*** (21.08) 0.378*** (13.64) 0.327*** (21.60) 0.151*** (4.13) POLREG 0.063*** (8.06) 0.026** (2.55) 0.060*** (7.75) 0.013 (1.23) Intercept 0.433 (0.56) R2 0.325 0.118 0.336 0.160 Log-likelihood 3412.44 3346.84 Observations 2,652 2,652 2,652 2,652
This table depicts the estimation results of the non-spatial panel data models with different combinations of country and time-period fixed effects. The t-values are reported in the parentheses and *, ** and *** represent the 10%, 5% and 1% significance levels, respectively.
31
(heteroscedastic). The test results (chi2 = 13720.08, df = 1, p = 0.0000) provide strong evidence that the null hypothesis of homoscedastic error variances must be rejected and Pooled OLS is preferred over random effects. The combination of these test results justify the extension of the model with country fixed effects in all further regressions.
To examine whether time-period fixed effects should also be included in the model, a simple Wald test of joint-significance is performed on the time fixed effects. This test has H0: the time-period fixed effects are jointly insignificant, and Ha: the time-period fixed effects are jointly significant. Using the fixed effects model with robust standard errors, the test results (F = 8.81, df = 155, p = 0.0000) indicate that the null hypothesis must be rejected and time-fixed effects should be included. Additionally, I test for the significance of time-period time-fixed effects by using the Likelihood-ratio (LR) test. This test is based on minus two times the difference between the value of the log-likelihood function in the restricted model and the value of the log-likelihood function of the unrestricted model and is given in Equation 5 below. The restricted model is always nested within the unrestricted model, meaning that it has the same properties but with one or multiple restrictions imposed. The test hypotheses are H0: the restricted model is the best model, and Ha: the unrestricted model is the best model. The test statistic has a chi2 distribution with degrees of freedom equal to the number of restrictions imposed.
𝐿𝑅𝑇 = −2 (𝑙𝑜𝑔𝐿𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑− 𝑙𝑜𝑔𝐿𝑢𝑛𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑) (5)
In this case, the restricted model is the fixed effects model and the unrestricted model is the fixed effects model including time-period fixed effects. The results (LR chi2 = 131.20, df = 16, p = 0.0000). The combination of these test results justify the extension of the model with time-period fixed effects in all further regressions.
Lastly, I tested the model for cross-sectional dependence, which is used in the computation of the spillover effects. I used Pesaran’s (2004) CD test that has H0: there is no cross-sectional dependence, and Ha: there is cross-sectional dependence. The fixed effects model is tested and the results (CD = 9.843, p = 0.0000) indicate that he null hypothesis of no cross-sectional dependence must be rejected.
5.2
Spatial model comparison
32
W2 and W3 are tested against each other by looking at the log-likelihood function values of the different spatial econometric models as shown in Table 9 below.
Table 9. Log-likelihood function values for use of the different spatial weight matrices
Spatial weight matrix Log-L SAR (WY) Log-L SEM (Wu) Log-L SLX (WX) Log-L SAC (WY, Wu) Log-L SDM (WY, WX) Log-L SDEM (WX, Wu) Log-L GNS (WY, WX, Wu) W1 3314.15 3312.13 3340.76 3312.33 3306.97 3308.78 3306.38 W2 3339.80 3338.98 3337.48 3338.75 3329.99 3329.86 3330.50 W3 3342.78 3342.06 3341.67 3341.90 3337.00 3336.33 3336.98
This table depicts the log-likelihood function values of the different spatial econometric models for cross-country percentage of GDP health spending with different combinations of the spatial interaction effects (WY, WX and Wu) for the use of the three spatial weight matrices W1, W2 and W3. Every model includes country and time-period fixed effects.
The general approach would be selecting the W matrix with the highest log-likelihood function values, but the table shows that these values are positive, even though the log-likelihood functions only contain terms with a minus sign. However, since σ2<1, we have –log(σ2)>0. Furthermore, since it is usually the positive term that is used, the positive values of the Log-likelihood are displayed (Elhorst, 2014a). Therefore, the lower the value of these functions – as displayed in Table 9 – the better the data and spatial weight matrix describe the data. The table shows that the log-likelihood function values are generally much higher (and thus lower in Table 9) for the spatial econometric models estimated with the first-order binary contiguity matrix W1 compared to those of the second and third-order binary contiguity matrices W2 and W3. Only the log-likelihood function value for the SLX model is higher (and thus lower in Table 9) when using W2, but this model has the lowest likelihood anyhow. Thus, the most likely specification of the spatial weight matrix is the first-order binary contiguity matrix based on land borders. Therefore, this first-order binary contiguity matrix W1 is used in the remainder of the empirical analysis of this thesis.
33 Table 10. Estimation different spatial econometric models for health spending
Determinants SAR (WY) SEM (Wu) SLX (WX) SAC (WY, Wu) SDM (WY, WX) SDEM (WX, Wu) GNS (WY, WX, Wu) Ln(GDP) (β) -0.949*** (-6.61) -0.976*** (-6.53) -0.970*** (-5.83) -0.975*** (-6.54) -0.965*** (-6.12) -0.956*** (-6.21) -0.956*** (-5.96) Ln(POP) (β) -0.211 (-0.79) -0.288 (-1.01) -0.790** (-2.22) -0.280 (-0.97) -0.697** (-2.07) -0.604* (-1.85) -0.786** (-2.27) YOUNG (β) -0.004 (-0.27) -0.006 (-0.37) -0.012 (-0.65) -0.005 (-0.32) -0.014 (-0.81) -0.011 (-0.61) -0.019 (-1.05) OLD (β) 0.142*** (4.08) 0.172*** (4.76) 0.177*** (4.30) 0.166*** (4.34) 0.195*** (4.98) 0.195*** (4.96) 0.196*** (5.07) POLREG (β) 0.012 (1.27) 0.010 (1.07) 0.013 (1.30) 0.011 (1.09) 0.012 (1.21) 0.013 (1.26) 0.010 (1.02) W x HEALTH (ρ) 0.210*** (8.42) 0.037 (0.30) 0.219*** (8.62) 0.365*** (5.47) W x Ln(GDP) (θ) -0.269 (-1.18) 0.053 (0.24) -0.106 (-0.47) 0.167 (0.78) W x Ln(POP) (θ) 0.829 (1.61) 0.679 (1.39) 0.744 (1.46) 0.720 (1.51) W x YOUNG (θ) 0.004 (0.17) 0.011 (0.45) 0.002 (0.09) 0.017 (0.72) W x OLD (θ) -0.064 (-1.06) -0.109* (-1.89) -0.048 (-0.79) -0.143** (-2.43) W x POLREG (θ) 0.036 (1.63) 0.024 (1.16) 0.022 (1.02) 0.027 (1.33) W x u (λ) 0.218*** (8.56) 0.189 (1.61) 0.211*** (8.19) -0.173** (-2.14) R2 0.0029 0.0001 0.1642 0.0004 0.0013 0.0002 0.0035 Log-likelihood 3314.15 3312.13 3340.76 3312.33 3306.97 3308.78 3306.38 Observations 2,652 2,652 2,652 2,652 2,652 2,652 2,652
This table depicts the estimation results of the different spatial econometric models for cross-country
percentage of GDP health spending with different combinations of the spatial interaction effects (WY, WX and Wu). Every model includes country and time-period fixed effects and W is the pre-specified first-order binary contiguity matrix (W1). The t-values are reported in the parentheses and *, ** and *** represent the 10%, 5% and 1% significance levels, respectively.
34
with the null hypothesis H0: λ = 0. The results (LR chi2 = 1.17, df = 1, p = 0.2787) indicate that the null hypothesis cannot be rejected and the SDM model is preferred over the GNS model. Overall, the SDM is preferred over the GNS, SDEM and SAC models.
Subsequently, I test whether the Spatial Durbin Model can be simplified to a spatial econometric model that has only one spatial interaction effect, namely the Spatial Error model (SEM), the Spatial Autoregressive model (SAR) or the Spatial lag of X model (SLX). When testing whether the SDM can be simplified to the SEM, the null hypothesis looks as follows: H0: θ + λβ = 0. The test results (LR chi2 = 10.23, df = 2, p = 0.0057) indicate that the null hypothesis must be rejected and the SDM is preferred over SEM. Similarly, when testing whether the SDM can be simplified to the SAR model, the null hypothesis looks as follows: H0: θ = 0. The test results (LR chi2 = 14.37, df = 5, p = 0.0134) indicate that the null hypothesis must be rejected and the SDM is preferred over the SAR model. Lastly, the test whether the SDM can be simplified to the SLX model has H0: ρ = 0. The test results (LR chi2 = 67.58, df = 1, p = 0.0000) indicate that the null hypothesis must be rejected and the SDM is preferred over the SLX model. This implies that all the three models, namely the SEM, SAR and SLX, must be rejected in favour of the Spatial Durbin Model. This is a convenient outcome, since only the SLX, SDM and SDEM models, i.e. the models that include WX variables, produce reliable results. The SEM model produces spillover effects that are zero by construction, while more general models show that the spillover effect of the GDP and population aged 65 and above are significant. The SAR and SAC model suffer from the problem that the ratio between the spillover effect and the direct effect is the same for every explanatory variable and therefore explanatory variables can get a wrong and significant sign. Lastly, the GNS model is often overparameterized, as a result of which the t-values of the coefficients tend to go down. Additionally, the coefficient of the spatial lag and the spatial error term have opposite signs and are therefore difficult to interpret, which can been seen from the negative coefficient for W x u (λ) of the GNS model in Table 9.
