Karin Callerud & Karl Velander
The development of the financial system and economic growth in
Sweden
A Granger causality analysis
Economics Bachelor thesis
Term: Spring 2020
Supervisor: Klaas Staal
Sammanfattning
Sambandet mellan det finansiella systemets utveckling och ekonomisk tillväxt i länder är ett till synes utforskat och debatterat ämne. Syftet med denna studie är att studera det kausala sambandet mellan det finansiella systemet och ekonomisk tillväxt i Sverige mellanperioden 1987–2018, med hjälp av tidsseriedata.
Studien kommer att definiera det finansiella systemet genom att avgränsa sig till bankernas utlåning till privata sektorn samt aktiemarknaden. Tidigare forskningsresultat har till stora delar påvisat ett positivt samband mellan den finansiella sektorns utveckling och ekonomisk tillväxt. Varierande resultat har dock uppkommit gällande orsakssambandet mellan dessa två komponenter. Där både enkelriktade och dubbelriktade kausala samband funnits, likaså studier som inte kunnat påvisa något kausalt samband överhuvudtaget. Argumentationer om det är den totala utvecklingen av det finansiella systemets som påverkar ekonomisk tillväxt positivt eller om det är vissa sektorer inom det finansiella systemet som har en större betydelse till ekonomisk tillväxt har visat tvetydiga resultat.
Uppsatsen grundar sig i Vektor Autoregressiva Modeller (VAR) där ett flertal Granger kausalitetstest genomförs för att testa olika riktningar av orsakssamband mellan det finansiella systemet och ekonomisk tillväxt. Resultaten i denna uppsats påvisar ett signifikant kausalt samband mellan ett flertal olika indikatorer av aktiemarknaden och ekonomisk tillväxt i Sverige. Ett signifikant kausalt samband kunde inte fastställas när volatiliteten, mätt som standardavvikelse, granskades på den svenska aktiemarknaden. Inte heller påvisar resultatet ett signifikant kausalt samband mellan bankutvecklingen och ekonomisk tillväxt.
Denna studie fyller en kunskapslucka inom forskningen genom att studera den ekonomiska tillväxten och det finansiella systemet i Sverige med hjälp av olika Granger kausalitetsanalyser. Liknande studier har utformats i andra länder, exempelvis Belgien och Portugal (Nieuwerburgh et al. 2006; Marques et al. 2013).
Resultat gällande det kausala sambandet mellan aktiemarknaden och ekonomisk tillväxt stämmer överens med resultatet från tidigare forskning. Resultat gällande sambandet mellan bankutvecklingen och den ekonomisk tillväxten avviker från resultatet från studien om Belgien men överensstämmer med utfallet från studien om Portugal.
Nyckelord: Granger-Kausalitet, Vektor Autoregressiv Modell, ekonomisk tillväxt, aktiemarknaden, banksektorn
Abstract
The connection between the development of the financial system and economic growth in countries is an apparently explored and debated topic. The purpose of this study is to study the causal relationship between the financial system and economic growth in Sweden during the period 1987–2018, using time series data.
The study will define the financial system by defining the banks' lending to the private sector and the stock market.
Previous research results have shown a positive connection between the financial sector's development and economic growth. However, varying results have emerged regarding the Granger causality between these two components. Where both unidirectional and bidirectional causal relationships exist, as well as no causal relationship at all. Arguments about whether it is the overall development of the financial system that positively affects economic growth or whether certain sectors of the financial system have a greater statistical significance to economic growth have shown ambiguous results.
The thesis is based on Vector autoregressive models where a number of Granger causality tests are conducted to test different directions of causality between the financial system and economic growth. The results of this paper were able to demonstrate a significant causal connection between a number of different indications of the stock market and economic growth in Sweden. A significant causal relationship could not be established when volatility, measured as standard deviation, was examined on the Swedish stock market.
Nor was it possible to demonstrate a significant causal link between bank development and economic growth.
This study fills a gap in research, by studying the economic growth and financial system in Sweden with the help of various Granger causality analyzes. Similar studies have been performed in other countries, such as Belgium and Portugal (Nieuwerburgh et al. 2006; Marques et al. 2013). Results regarding the causality between the stock market and economic growth are consistent with the results of previous studies. Results regarding the causality between the bank development and economic growth differ from the results of the study on Belgium but are consistent with the results of the study of Portugal.
Keywords: Granger-Causality, Vector Autoregression Model, economic growth, stock market, bank sector
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ABEL OF CONTENTS1. INTRODUCTION ... 1
1.1 RESEARCH PROBLEM ... 1
1.2 PURPOSE AND RESEARCH QUESTIONS ... 2
1.3 DELIMITATIONS ... 3
1.4 DISPOSITION ... 3
2. THEORY AND BACKGROUND ... 4
2.1 THEORY ... 4
2.1 PREVIOUS RESEARCH ... 5
3. DATA ... 8
3.1 SECONDARY DATA ... 8
3.2 VARIABLES AND DATA ... 8
3.3 ECONOMIC GROWTH ... 8
3.3.1 Gross domestic product per capita ... 8
3.4 STOCK MARKET DEVELOPMENT INDICATORS ... 9
3.4.1 OMXSPI ... 9
3.4.2 Volatility ... 10
3.4.3 Liquidity ... 11
3.5 BANKING DEVELOPMENT ... 12
3.5.1 Domestic bank credit to private sector ... 12
3.1 DESCRIPTIVE STATISTICS ... 12
4. EMPIRICAL STRATEGY ... 13
4.1 METHODOLOGY ... 13
4.1.2 Choice of method ... 13
4.2 VECTOR AUTOREGRESSION MODEL ... 14
4.3 GRANGER CAUSALITY ... 16
4.4 T-TEST ... 18
4.5 THE BREUSCH-GODFREY TEST ... 19
4.6 DEPENDENT VARIABLE ... 19
4.7 INDEPENDENT VARIABLE ... 19
4.8 R2 ... 20
5. ... 20
EMPIRICAL RESULTS AND ANALYSIS ... 20
5.1 THE CAUSALITY FROM GDP TO OMXSPI AND FROM OMXSPI TO GDP ... 21
5.2 THE CAUSALITY FROM THE STOCK MARKET VARIABLES TO GDP ... 22
5.3 THE CAUSALITY FROM ST.DEV TO GDP, TURNOVER TO GDP AND TURNOVERMSEK TO GDP. ... 22
5.4 THE CAUSALITY FROM GDP TO BANK AND FROM BANK TO GDP ... 24
6. DISCUSSION ... 25
6.1 OMXSPI AND GDP ... 25
6.2. STOCK MARKET VARIABLES AND GDP ... 26
6.3 BANK DEVELOPMENT AND GDP ... 27
7. CONCLUSION ... 28
8. REFERENCES ... 30
1. Introduction
1.1 Research Problem
Economic growth is said to be prerequisite to achieve a higher degree of prosperity within a country (Sida 2009). This makes increased economic growth an important factor for many countries to strive for. For Sweden, and many other countries around the world, the GDP has increased exponentially over the last decades. Sweden's GDP has increased from 140.9 billion in 1980 to 575 in 2019 (The World Bank 2020).
There have been discussions relating to which sources that contributes to economic growth and the financial system has been named one important source of growth within a country (Bangake & Eggoh 2011).
Does a well-functioning financial system boost economic growth? The financial system consists of several components such as the central bank, brokerage firms, commercial banks, and stock exchange, to mention a few. The relationship between the financial system and its effect on economic growth has been highly debated (Levine & Zervos 1998; Demirguc-Kunt & Levine 1996 & Caporale et al. 2004). Empirical studies provide different findings about the separate effects of the stock market impact on growth and the bank's impact on growth, as well as the financial systems overall impact on economic growth.
Schumpeter (1934) is one of the first scientists who started to analyze the role of the financial system and argues that a well-developed financial system contributes to higher economic growth. A well-developed financial system according to him has the ability to identify and finance business opportunities, allocate resources, which fosters investments which in turn can increase growth. (Schumpeter 1934) Financial institutions trade in financial instruments such as foreign currency, stock, bonds and domestic currency. If financial institutions are well-developed, it is easier to mobilize savings and deposits and make the exchange of services and goods more efficient. According to Mishkin (2004) well-developed financial institutions can help businesses to increase investment and therefore accelerate economic growth.
In Sweden, the financial system was up until the late 1970th one of the most regulated ones but has since then transformed to one of the least regulated. Which means that the country has opened up to foreign financial interests and that protectionism has been replaced by internationalism. Sweden is classified as a country with a well-developed financial system. A previously less developed financial market has grown strong and the value of stock market and turnover has increased while the banking sector also has increased, in relation to the GDP in Sweden. (Clark et al. 2014) Sweden’s stock exchange has, between the period 1980 to 2019, increased by 29 700 percent which corresponds to an annual increase of 15.8 percent per
year (Petterson et al. 2019). While the foreign ownership in the Stockholm stock exchange also has increased continuously in the last decades (SCB n.d.).
Financial institutions and financial markets are two essential areas required to achieve a certain degree of stability for a country and its economy (Riksbanken 2018). The fact that Sweden's financial markets and institutions have grown larger in relation to the country's GDP (Clark et al. 2014) makes it interesting to study how the financial system has affected the economic growth in Sweden. This study hopes to provide answers to how these areas affect economic growth in Sweden and investigate if there exists Granger causality between these factors.
Over the years, the importance of the financial system and its various parts have varied. During the late 1900th the development of the stock market increased and became more important for the global economy and also became a major subject for both theoretical and empirical studies. The emphasis increasingly shifted to the stock market index and the effect the stock market has on economic growth. Different factors of influences from the stock market has been argued to contribute to economic growth. Obstfeld (1994) argues that through an internationally integrated stock market, the allocation of resources can be more efficient and through that speed up the process of economic growth (Obstfeld 1994). Another aspect is the amount of liquidity on the market. Paudel (2005) states that a more liquid market enables companies to raise capital faster, which facilitates the possibility of capital allocation, growth and investments. The activity on the stock market is therefore an important factor of raising the overall economic activity in a country.
It has been discussions about the various effects of the stock market and the banking sector on economic growth (Levine and Zervos 1998). According to Levine and Zervos (1998), a well-established stock market is not only positive for its ability to diversify risk between market participants and mobilize capital. It also provides a variety of financial services that the bank sector can not offer, which promotes economic growth.
Caporale, Howells and Soliman (2004) states the importance for firms to receive external financing, both through banks and the stock markets. The authors point out some of the differences between financing by banks and by stock markets. Stock markets can finance more productive, risky and innovative investment projects while banks more often only finance well-established, safe borrowers. (Caporale, Howells &
Soliman 2004) From this perspective, the different sectors contribute to economic growth in different ways.
By now it is widely recognized that a well-developed financial system is decisive to economic growth and that the stock market, as a part of the financial system, in many cases plays an important role. But does there exists a predictive causality between the financial system and economic growth in Sweden?
1.2 Purpose and research questions
The purpose of this study is to investigate the causal relationship between the financial system and economic growth in Sweden between the period 1987 to 2019. The aim is to examine whether there is causality
between economic growth and different indicators of the financial market such as volatility, liquidity and turnover within the country. Furthermore, the study will investigate whether there is a causal relationship between the development of the financial sector, development of banks, and economic growth that has taken place in Sweden between this period. The following questions will be answered:
- Is there a causal Granger relationship between OMXSPI and GDP per capita?
- Is there a causal Granger relationship between bank development and GDP per capita?
- Is there a jointly causal Granger relationship between stock market variables and GDP per capita?
- Is there a separately causal Granger relationship between stock market variables and GDP per capita?
1.3 Delimitations
The study is limited to examine the relationship between financial development and economic growth in Sweden, between the time period 1987 to 2018. The study is based on annual data collected from Nasdaq, World Bank and Statistics Sweden. Economic growth is measured by GDP per capita and is referred to as only to GDP further in the text. The OMXSPI index represent the Swedish Stock Exchange market and the data is based on daily closing prices combined with the last closing price for each year. Volatility on the stock market is measured by examining the standard deviation of OMXSPI and the variable liquidity is based on the turnover ratio and total stocks traded on the Stockholm stock exchange each year. The development of the banking sector is measured by examining how domestic credit to the private sector has changed in relation to GDP per capita each year.
The study is based on the Vector Autoregressive model (VAR) and from these regressions, different tests for Granger causality is conducted. The study is limited to examining the Granger causality between the variables OMXSPI and GDP, and the causality between bank development and GDP. The causal relationship is also tested for the variable’s standard deviation (St.dev), turnover ratio (Turnoverratio) and total stocks traded (TurnoverMSEK) to GDP. These three variables are referred to as stock market variables through the essay. Instead of testing the reverse causality, only one direction of causality is checked for. That is, if stock market variables Granger cause GDP. The financial system consists of many different components and sectors which makes it difficult to measure. Because of its complexity, the thesis uses the bank sector and the stock market to represent the financial system in Sweden between the specified years.
1.4 Disposition
In the second section of this thesis, the theory and background are introduced. In this section
previous research is presented with the aim of obtaining an overview of previous studies on the subject and how research has varied over time. Section three presents the variables and data.
Thereafter, the empirical strategy is presented which contains of choice of method, regression models and different tests that the study is based on. Empirical results and analysis are presented in section five. The results, from the performed tests, is then discussed in section six where past research and models are linked to answer the study’s hypotheses. In the last part of the paper, the results and analysis are summarized into a conclusion which is the final part of the thesis.
2. Theory and Background
2.1 Theory
In the 19th century, Hicks (1969) claims, for the first time in history, that investments and projects had become too expensive to be funded by individuals or by the profits received by firms. Revolutionary technological inventions, such as the steam engine, had been invented earlier, but the implementation of these industrial inventions had to wait for well-developed financial market due to the lack of financial means. A financial system was required, in the industrial age, to provide companies with long-term financing which could be used for investments, and further lead to increased economic growth. (Hicks 1969) Another researcher, Schumpeter (1934), also determine the importance of a developed financial system when countries strive for economic growth. According to Schumpeter, a well-developed financial system contributes to higher economic growth. A developed financial system has the ability to identify and finance business opportunities as well as allocate resources, which promotes investments and increase economic growth.
Financial markets enable more efficient financing of public and private investment projects (Levine 1997) In the beginning of the 1990th, Levine examined the importance of financial markets, mainly through stock markets. Levine (1991) argues that stock markets can affect economic growth in two ways. The first way is that companies, through stock markets, have the opportunity to increase their resources within the company, through the stock market's ability to eliminate premature capital withdrawals from companies.
The second way that stock markets can affect growth is to increase the liquidity of the company's investments by encourage investments and reduce productivity-risk which improves efficiency. Both of these factors are, according to Levine (1991), contributing factors that accelerate economic growth and increases the rate of growth for production per capita and human capital.
The direction of Granger causality can according to Nieuwerburgh et al. 2006 be central for economic policy decision making. By evaluating relevant factors of the financial system and the causal relationship to economic growth, conclusions can be drawn of which financial sectors that are most important for a country. Decisions on how, what and why a country should focus on specific parts of the financial sector can then be based on these evaluations. (Nieuwerburgh et al. 2006)
2.1 Previous research
The relationship between the financial system and economic growth have for a long time been a controversial topic. Historically, economists have had a big focus on banks but after the second half of the 1900th century the focus moved to the link between stock markets and economic growth. This created more theoretical literature on the subject, but the empirical evidence was still limited.
Levine and Zervos (1998) published the work “Stock Markets, Banks and Economic Growth”, studying the empirical relationship between several measures of banking development, stock market and long-run economic growth. The study is conducted in 47 countries between the time period 1976 to 1993 and was an expansion of recent cross-section research between financial intermediation and growth written by King and Levine (1993) and includes measures of stock market indicators. Levine and Zervos (1998) used several numbers of indicators as measures of banking development, stock market development and growth. The result of the study showed, after controlling for political and economic factors, that banking development and stock market liquidity both were positively and robust correlated with capital accumulation, productivity improvements and growth. The result is consistent with the notion that a greater ability to trade ownership of productive technologies of an economy will favor efficient resource allocation and faster economic growth. The paper also established that international integration, stock market size and volatility are not positively robust with growth. Thus, the paper finds strong positive link between economic growth and financial development and also that different services from financial markets and institutions are crucial for long-run growth. (Levine and Zervos 1998)
In the paper “Stock market development and economic growth in Belgium” Nieuwerburgh, Buelens and Cuyvers (2006) analyze how the financial market, bank development and stock market affect economic growth in Belgium between the years 1832–2002. The authors calculated their results by using a Vector Autoregression Model. From these regressions, tests for Granger causality were conducted to establish different directions of relationships. (Nieuwerburgh, Buelens and Cuyvers 2006) To measure the development of the stock market the paper analyzes market capitalization of the Belgium stock market and data about savings and deposits was collected to represent the development of the banking sector. To measure the economic growth in Belgium the authors are using the GDP. Lagged terms (five years) are then used in the Vector Autoregression Model to see how the past values affects the results. The results presented indicates that the financial development, especially the stock market development, have had a significant effect on the economic growth between 1873–1935, i.e. Granger caused GDP and that the effect is bidirectional. The outcome of the Granger causality test also indicates that the bank development Granger caused GDP, but the direction in this case is unidirectional. (Nieuwerburgh et al. 2006) Another study by Caporale, Howalles and Soliman (2004) examined the causality between banking development and
economic growth in seven countries. The result of the study indicates that there existed a bi-directional causality between banking development and economic growth in two of the seven countries (Caporale et al. 2004).
Demirguc-Kunt and Levine (1996) also examined the relationship between financial intermediary development and stock market development. Using data from four developed and developing countries from 1976 to 1993. The result displayed that countries with better developed stock markets also tends to have better financial intermediaries. Their conclusion is that the stock market goes hand-in-hand with the financial intermediary development. (Demirguc-Kunt and Levine 1996)
The article of Marques, Fuinhas and Marques (2013) “Does the stock market cause economic growth?
Portuguese evidence of economic regime change” essentially examined the causal relationship between the stock market and economic growth, but the relationship between growth and bank financing is also investigated. In order to study the direction of causality, the Granger causality, they use a Vector Autoregressive Model. The time period studied was between 1993 to 2011 in Portugal. They found strong evidence that the stock market development causes economic growth, but they also found evidence, albeit weak (10 percent significance) that growth causes development of the stock market. (Marques et al. 2013) The latter performance is inconsistent with previous literature, which usually have only identified a Granger unidirectional causality, that is, causality running from stock market to economic growth (Tsouma 2009).
The study did not find any evidence of Granger causality running from bank financing to economic growth.
During the period of investigation, the main factor for driving economic growth in Portugal was not the banking system, but the stock market. Instead, the bank financing has been a net beneficiary of the growth.
The result of the directions of causality in this study lead to a number of valuable effects. That is, if policy makers want to stimulate growth, the act should be to develop the stock market. (Marques et al. 2013)
In another study by Bangake and Eggoh (2011), “Further evidence on finance-growth causality: A panel data analysis” the causal relationship between financial development and economic growth is also investigated. The study consisted of seventy different countries, both developed and developing countries, between the period 1960 to 2004. The results show that there is a bidirectional causality between economic growth and financial development in the long run, however, in the short run the situation was different.
Results between countries differed depending on the time horizon. In the short run there is no evidence for a relation between financial development and economic growth in developing countries (low-middle income countries). In developed countries however (high income countries) there is an indication of a relationship between economic growth and financial development. The result of this implies that developing countries should implement long run policies. The study also determined that to gain sustainable growth in developing countries, it would be worthwhile to undertake financial reforms in forms of liberalization of the financial sector. (Bangake & Eggoh 2011)
There has been a growing interest in stock market’s impact on economic growth. Research has determined that several stock market indicators have been a factor of explanation to the variation of growth in countries (Atje & Jovanovic 1993; Levine & Zervos 1998). Another study by Arestis et al. (2001) also examined the relationship between financial development and economic growth, with focus on the stock market and bank development. Variables with strong connection to the stock market sector such as volatility and liquidity are used in the analysis to see how they affected the relationship between economic growth and stock market. The study is conducted in four developed countries between the time period 1972 to 1998 (Arestis et al., 2001). The empirical analysis states that the development of stock markets and banks for each country are an important factor for economic growth. However, the contribution of the stock market is not as big compared to the effect that the banking system has on economic growth. The result showed that high values of volatility had negative effects on economic growth, mostly because it creates a higher level of uncertainty on the market. Furthermore, the volatility tends to be smaller on larger stock exchanges than on smaller stock exchanges. The paper concludes that the effect of liquidity on the stock market has on the growth rate is not distinct, but that the relationship can be both negative and positive. (Arestis et al., 2001)
Boubakari and Jin (2010) argue that there is a positive link between economic growth and stock market for several countries where the stock market is liquid and highly active. Levine (1991) and Bencivenga, Smith and Starr (1995) also argues that a liquid stock market makes financial assets less risky because this gives people the opportunity to quickly and easily sell and buy assets. More liquidity means a lower market risk, as people do not need to invest their capital in only one investment over a longer period. At the same time, companies have access to capital through share issues. A more liquid market can also be seen to contribute to increased acquisition of information about companies. Hence, a liquid market provides better conditions for allocation of capital, which is an important channel to promote economic growth. (Boubakari & Jin, 2010)
From empirical research it can be found that there is a strong link between economic growth and the stock market (Nieuwerburgh et al. 2006; Obstfeld 1994). Researchers have also argued that an internationally integrated stock market can accelerate the allocation of resources and thus the process of economic development (Obstfeld 1994). In the same way, Korajczyk (1996) concludes that through an international integrated stock market, capital accumulation can be magnified and thus have a positive correlation between economic growth and stock market integration.
3. Data
3.1 Secondary data
The main theoretical information used in this study is obtained mainly from academic sources, such as books and articles. Research articles are retrieved from Google Scholar, Karlstad University database and through citation information. In order to achieve high quality and a high degree of credibility of the articles, the ones with “peer reviewed” is used. Articles that have many citations, i.e. used as references in other studies, are also taken into account. The thesis is supplemented by two underlying studies of Nieuwerburgh, Buelens and Cuyvers (2006) and one of Arestis, Demetriades and Luintel (2001).
3.2 Variables and data
The study is based on secondary data, collected from websites such as The World Bank, Statistiska Centralbyrån (SCB) and Nasdaq's website. The study uses annual data for Sweden over the time period 1987- 2018, with a total of 32 observations. The chosen time period, 31 years, provide the survey with a better basis for illustrating the development of the selected variables. Which also gives a higher credibility to the results. Cross-sectional data can be used in studies, which is data that is collected for one or more variables at a specific time. Panel data can also be used, this is when data is collected for multiple survey units and for several time periods. In this study annual time series data is used, which means that observations of the same variables are collected over a longer period of time (Gujarati & Porter 2009).
Times series data is used because the survey is conducted in one specific country. The collected data is processed in Excel and the main regressions and econometric tests is performed in SPSS.
To be able to assess the relationship and causality between economic growth, banking development and stock market development, the study requires: (1) a measure of economic growth; (2) a measure of banking development and; (3) empirical indicators of stock market size, liquidity and volatility. By using more than one single indicator of the change in the stock market the research can provide a richer picture of the link between economic growth and the stock market. The section below defines the different variables that are used in this research.
3.3 Economic Growth
3.3.1 Gross domestic product per capita
Gross domestic product per capita is used in this study to represent economic growth in Sweden. GDP is a measurement used to capture how the overall economic activity of a country looks like over a given period of time. That is, the sum of the value of all services and goods produced. Comparing countries total GDP
can give an estimate of how big respective countries' economies are. With that said, the measurement of GDP does not say anything about how rich a country is. To be able to measure the” well-being” and the richness of a country, one must take into account the nation’s population. The measure GDP per capita is calculated by dividing GDP by a country’s population development. To be able to compare countries GDP per capita, a transformation of each country’s currency (Purchasing Power adjustment) is needed. The transformation is done with the help of purchasing power parities such as PPP (Purchasing Power Parity) where a shopping basket in a country is compared to an average shopping basket for a larger area, for example Europe, the OECD. A correction for countries that have a large difference between domestic and foreign trade, that is the current account balance, is also made. By using GDP per capita and taking PPP into account we can convert different GDP values and compare it with other countries or/and over different time periods. (Weil 2013) The Figure below show the development in GDP per capita in Sweden between 1987 and 2019.
Figur 1. Change in GDP per capita in Sweden between 1987 and 2019.
3.4 Stock Market Development Indicators
3.4.1 OMXSPI
A stock index represents the average development of a market by measuring the weighting of the change of specific shares. How individual shares affect an index depends on the size and the value of the company.
An index is market weighted, for example, the fluctuations of a larger company affect an index more than fluctuations of a small company. The OMXSPI index reflects all the companies on the Stockholm Stock Exchange. As this study investigates the relationship between the entire stock market and the economic growth in Sweden between 1987-2018, the index OMXSPI is used as a stock market development indicator and thereby reflect how the stock market has changed. As the work examines the annual impact, closing rates for the last trading day each year have been collected and the value is measured in Swedish kronor (SEK). (Nasdaq 2018) Figure 2 shows the development of OMXSPI between 1987 and 2018.
250000 300000 350000 400000 450000 500000
1985 1990 1995 2000 2005 2010 2015 2020
GDP per Capita
(SEK)
Figure 2. The development of OMXSPI between 1987 and 2018
3.4.2 Volatility
Volatility is a measure that shows how the fluctuations of a specific asset or portfolio, such as an index, have changed in relation to its mean value. Volatility can also represent the risk of an asset or an aggregate portfolio. (Bodie et al. 2018) In this thesis, the variable volatility represents the fluctuations that have taken place on the Stockholm Stock Exchange (OMXSPI) between 1987-2018 and a comparison of how this may have affected economic growth in Sweden will be made. Volatility is represented by the standard deviation for OMXSPI each year. The values of standard deviation are based on collected data of the closing rates for OMXSPI each trading day every year between 1987-2018. A high value of standard deviation indicates large fluctuations, which means that the value of how the Stockholm Stock Exchange (OMXSPI) has changed significantly. A low value of standard deviation indicates smaller fluctuations and a miner change in the value of the Stockholm Stock Exchange. (Kissell 2014) Figure 3 presents the development of the standard deviation of OMXSPI between 1987 and 2018.
Figure 3. The development of the standard deviation of OMXSPI between 1987 and 2018
0 100 200 300 400 500 600
1985 1990 1995 2000 2005 2010 2015 2020
OMXSPI (SEK)
0 10 20 30 40 50 60
1985 1990 1995 2000 2005 2010 2015 2020
Standard deviation of
OMXSPI
3.4.3 Liquidity
The turnover ratio is used as a measure of market liquidity on the stock market. The measurement of the turnover ratio shows the percentage of the existing shares that have been traded on the Stockholm Stock Exchange, in relation to the total value of shares available on the market. In other words, the trading volume of the stock market relative to its own size (Datar et al. 1998). Another variable that is used as a measurement for liquidity is turnover, total stocks traded. The turnover shows the total value of all the stocks traded on the Stockholm stock exchange between a specific time period. Previous models have made predictions that countries with more illiquid markets will create disincentives for investments in the long run because of the difficulty of selling shares in specific firms. In contrast, a liquid market provides better incentives for long-run investments. This can promote more efficient allocation of resources and faster economic growth. (Levine 1991; Bencivenga, Smith, & Starr 1995) Figure 4 and figure 5 shows the development of the turnover ratio and total stocks traded on the Stockholm stock exchange between 1987 and 2018.
Figure 4. Turnover ratio of OMXSPI between 1987 and 2018
Figure 5. Total stocks traded on Stockholm stock exchange (OMXSPI) between 1987 and 2018
0 20 40 60 80 100 120 140 160
1985 1990 1995 2000 2005 2010 2015 2020
Turnoverratio OMXSPI
0 2000 4000 6000 8000
1985 1990 1995 2000 2005 2010 2015 2020
Turnover OMXSPI (Total stocks traded in
MSEK)
3.5 Banking Development
3.5.1 Domestic bank credit to private sector
The measurement “Domestic bank credit to the private sector” refers to the proportion of financial resources provided to the private sector by depository corporations. This through loans, trade credits, purchases of non-equity securities and other receivables that have a claim for repayment (The World Bank 2020). Thus, this measure describes the capital flow and other financial corporations that exist between the private sector and banks. Banks in this case indicate all banks, except the Central Bank, and other financial institutions who run under the government (Finansinspektionen 2019). The study uses this measure to capture the development of the banking system in Sweden and figure 6, below, shows the evolution of the bank system between 1987 and 2018.
Figure 6. Evolution of the banking system between 1987 and 2018
3.1 Descriptive statistics
The main purpose of descriptive statistics is to describe and summarize the collected data set. Descriptive statistics can be divided into two fundamental categories: measures of variability or spread and measures of central tendency. Measures of variability include variance, standard deviation and the maximum and minimum values of a variable. Measures of central tendency contains of the median and mean. (Agresti, et al. 2017) Table 1 shows maximum, minimum, mean and standard deviation for the selected variables in the study.
0 20 40 60 80 100 120 140
1985 1990 1995 2000 2005 2010 2015 2020
Bank development
(% av GDP)
Table 1. Descriptive statistics of the collected data
Variable N Minimum value Maximum value Mean Std.Deviation GDP per capita 32 288500,00 475100,00 377968,750 64466,6928
Bank Development 32 31,52 131,85 82,6195 39,77244
OMXSPI 32 38,62 568,80 253,5153 161,96596
Stdev. 32 3,03 49,85 17,9444 11,24068
Turnover Ratio 32 15,00 152,00 80,6563 40,55312
TurnoverMSEK 32 103,60 6523,70 2620,4844 1841,760
Valid N 32
4. Empirical strategy
In this chapter the thesis regression models and tests are presented and explained. All variables included in the different regression models are measured in annual figures dated from the year 1978 to 2018. The chosen method of this study is also presented in the chapter.
4.1 Methodology
The chosen method for this study is an empirical analysis which examine if there exists a predictive Granger causality between economic growth and financial development. This, by analyzing and determining different directions of causality between indicators of the stock market development, banking development and economic growth. The study is based on the Vector autoregression model (VAR) and from these regressions, tests are conducted to test for Granger causality.
4.1.2 Choice of method
The main purpose of this study is to determine the Granger causality and different directions of causality between the stock market, banking system and economic growth. To be able to answer the thesis purpose, a quantitative study is conducted. Where tests are carried out, using collected data, to investigate the relationship between selected variables. A quantitative study is based on a number of testable hypotheses, were both empirical and quantifiable data are collected and compiled into statistical forms (Nationalencyklopedin n.d.). The results are then analyzed to be able to answer the research questions. A qualitative study, based on the collection and interpretation of non-numeric data, (Nationalencyklopedin n.d.) would not have been feasible in order to answer this thesis purpose. Usually there is a distinction between two different approaches, deductive and inductive approach. A study has deductive features when it starts from a frame of reference and then a hypothesis is formulated which is tested against reality. An
inductive approach, on the other hand, starts with an investigation of the phenomenon before a problem formulation is established. (Thuren 2007) Since this study is based on examining a number of specific research issues this thesis is based on a quantitative method with a deductive approach.
4.2 Vector Autoregression Model
Looking at times-series analysis, one basic model often used is the Vector Autoregression (VAR) Model.
The model is used for the analysis of multivariate time series and the basis behind the model is that each time series, variable in the system affects each other. Each variable in the model is explained by its past, or its lagged, value(s) and also the past values of all other variables. In other words, past values are used to predict and forecast the current and future value of the time series. The reason why the model is called a Vector Autoregression Model is because it consists of a vector of several (two or more) variables and it is an autoregression model because of the dependent variable lagged value(s). (Gujarati & Porter 2009) With multiple time series that influence each other, there will be a system of equations, depending on how many time series is chosen to be included.
One important decision that has to be made when constructing the Vector Autoregression Model is the lag length, k. The lag length shows how many past values of each variable that should be included in the model.
Lags are used to describe the effect each variable lagged value has on the dependent variable. Including too few lagged values can lead to specification error, which can lead to incorrect conclusions being drawn from the regressions. Including too many lagged values can reduce the amount of degrees of freedom. It can also lead to problems with multicollinearity, which means that two or several independent variables in the regression is correlated with each other. (Gujarati & Porter 2009)
Each variable in the VAR-model is constructed as a linear combination of each past value of itself and also the past values of the other variables included in the model. The amount of regressions depends on how many variables, and lagged terms of each variable, that is included in the model. (Studenmund 2017) The VAR-models in this thesis consists of six different variables. The structure of the models look as follows:
X!"= β!#+ % β!!$
%
$&!
+ X!"'$+ % β!($
%
$&!
+ X("'$+ % β!)$
%
$&!
+ X)"'$+ % β!*$
%
$&!
+ X*"'$+ % β!+$
%
$&!
+ X+"'$+ % β!,$
%
$&!
+ X,"'$+ u!$
(1.1)
X("= β(#+ % β(!$
%
$&!
+ X!"'$+ % β(($
%
$&!
+ X("'$+ % β()$
%
$&!
+ X)"'$+ % β(*$
%
$&!
+ X*"'$+ % β(+$
%
$&!
+ X+"'$+ % β(,$
%
$&!
+ X,"'$+ u($
(1.2)
….
X,"= β,#+ % β,!$
%
$&!
+ X!"'$+ % β,($
%
$&!
+ X("'$+ % β,)$
%
$&!
+ X)"'$+ % β,*$
%
$&!
+ X*"'$+ % β,+$
%
$&!
+ X+"'$+ % β,,$
%
$&!
+ X,"'$+ u,$
(1.3)
where k stand for number of lags included in the Vector Autoregression Model and 𝑋!-= GDP per capita, 𝑋(-= OMXSPI, 𝑋)-= Bank development, 𝑋*-= Std. dev, 𝑋+- = Turnoverratio, 𝑋,- = TurnoverMSEK
Equation 1.4 is of order one, where the dependent variable, GDP, depends on its past value and also on the other time series past values. Depending on the direction of the Granger causality test similar models are created for each affected variable. For example, the GDP equation of the VAR (1) model look like the following:
GDP"= α#+ β!!,!GDP"'!+ β!(,!OMXSPI"'!+ β!),!Bank"'!+ β!*,!Std. dev"'!
+ β!+,!Turnoveratio"'!+ β!,,!TurnoverMSEK"'!+ εt (1.4)
The Granger causality test is also performed using two lagged values. This model includes both the first and second lagged values of each time series in the regression. The VAR (2) model includes all variables like in equation 1.4. But in equation 1.5 the dependent variable, GDP, depends on two lagged values of itself and also two lagged values of the other time series included in the study. This is replicated for every variable included in the model. For example, the GDP equation of the VAR (2) model look like the following:
GDP"= α#+ β!!,!GDP"'!+ β!!,(GDP"'(+ β!(,!OMXSPI"'!+ β!(,(OMXSPI"'(+ β!),!Bank"'!
+ β!),(Bank"'(+ β!*,!Std. dev"'!+ β!*,(Std. dev"'(+ β!+,!Turnoveratio"'!
+ β!+,(Turnoverratio"'(+ β!,,!TurnoverMSEK"'!+ β!,,(TurnoverMSEK"'(+ ε"
(1.5)
4.3 Granger Causality
A statistical method which is used to examine the relationship between two or more variables, where a dependent variable is affected or dependent on one or more independent variables, is a regression analysis.
A regression analysis does not necessarily test for causality between variables or the direction of causality between them. To be able to analyze the direction of the causality, one can use a Granger causality test.
Granger causality analysis is a statistical hypothesis test which investigate the direction of causality between variables to find the direction of a potential causal relationship. The null hypothesis of the Granger causality test states that there is no causality between two variables while the alternative hypothesis says that there is a causality.
The basic idea of a Granger causality test is to determine whether future values of a time series X can be predicted by the use of past values of an additional variable, for example, time series Y and identify which variables occur first. If time series Y can be predicted using past values of both Y and X, the result can be expressed as variable X is Granger causing variable Y. Granger causality tests observe two time series to be able to discern whether series Y occurs earlier than series X or if the movements of the variables occur simultaneously. (Studenmund 2017) Granger causality does not identify direct causality and does not analyzing if there are other influencing factors, the causality test only determines if one variable precedes another or not. By using annual data this thesis is not analyzing direct causality, instead the purpose of this work is to analyze in which order the different variables occurs, therefore a Granger causality analysis is used. An example of the Granger causality analysis is how meteorologists predict the weather through weather forecasts, these forecasts precede the actual weather. This does not mean that the meteorologist's forecast is causing the current weather, this is an example of Granger causality, how to interpret it and how it can be misleading. Granger causality only shows which variable that occurs first, but one cannot determine if the variable that occurs first is the cause of the change. However, one can determine that it’s not the other way around (Leamer 1985).
Granger causality tests can be applied through the technique of VAR. Equation 1.1 and 1.2 states that 𝑋!-
and 𝑋(- are related to past values of the other as well as the past value of itself. By running the Granger- test, conclusions about causality can be established. That is, if 𝑋!- Granger causes 𝑋(-or if 𝑋(- Granger causes 𝑋!-. If the result of the Granger test states that both 𝑋(- and 𝑋!- causes each other there is a bidirectional causality running between them and one can not identify which variables precedes another. If only one variable causes the other, there is a so-called unidirectional causality. There can also be a case of independence, that is, when the two variables coefficients are not statistically significant in either of the
In this section, focus is to determine a number of directions of Granger causality between selected variables.
The direction of causality that are investigated is presented in table 2. The study investigates the causal relationship between OMXSPI and GDP and the causal relationship between Bank development and GDP.
A unidirectional causal relationship is examined from St.dev, Turnover ratio and Turnover MSEK to GDP, jointly and separately.
Table 2. The directions of causality being investigated
OMXSPI→ GDP GDP → OMXSPI OMXSPI ↔ GDP Bank → GDP GDP → Bank Bank ↔ GDP Stock market variables →
GDP St.dev → GDP
Turnoverratio → GDP
TurnoverMSEK → GDP
In order to conduct a Granger causality test some steps need to be implemented in advance. First: each variable’s lagged terms are computed for regressing the unrestricted and restricted models. In the unrestricted models, each variable is regressed on lagged terms of itself and on the other variables in the system. The unrestricted model contains of all parameters. In the restricted model the variables are also regressed on its past values, but it excludes the lagged value of the investigated variable in the model. Both these models are needed to perform an F-test. (Gujarati & Porter 2009)
A restricted and an unrestricted model is created to be able to conduct the F-tests, to test for Granger causality. The unrestricted and restricted model can be determined from the equation 1.1 and 1.2. When testing for the direction of causality from 𝑋!- (GDP) to 𝑋(-(OMXSPI) equation 1.1 is the unrestricted model. By exclude, the variable 𝑋(- and all the lagged values connected to 𝑋(-, from equation 1.1, one get the restricted model which means that all 𝛽-values related to 𝑋(- is equal to zero. By exclude several variables simultaneously, one can analyze the jointly causality between more than two variables. For example, by exclude the variables 𝑋*-, 𝑋+- and 𝑋,- in equation 1.1 and all lagged values connected to each variable, the 𝛽-values related to this three variables is equal to zero and the outcome will be a restricted model. These steps, to create restricted and unrestricted models, are applied to analyze direction of causality between several variables.
The null hypothesis states that one variable does not Granger cause another. To test whether the null hypothesis is true or false, a F-test is conducted. In the tests both the restricted and unrestricted regression models are required to receive the restricted and unrestricted residual sum of squares. The residual sum of
squares, both restricted and unrestricted, is needed to be able to calculate the F value used in the F-test.
(Gujarati & Porter 2009)
𝐹 = 𝑅𝑆𝑆/− 𝑅𝑆𝑆0/ / 𝑚 𝑅𝑆𝑆0/ (𝑛 − 𝑘)
(1.6)
𝑅𝑆𝑆0/ : residual sum of squares from the unrestricted regression model 𝑅𝑆𝑆/ : residual sum of squares from the restricted regression model k: number of parameters estimated in the unrestricted regression n: number of observations
m: number of terms that is lagged n-k: the degree of freedom
From the F-test a computed F-value is received, at a chosen level of significance, and is then compared with the critical F-value. The critical value of F is obtained from the F-distribution which is based the degrees of freedom. The null hypothesis can be rejected if the observed F-value exceed the critical F-value, at the chosen level of significance. If the computed F-value does not exceed the critical F-value the null hypothesis can not be rejected. Alternatively, the p-value can also be used which determines whether the null hypothesis can be rejected or not depending on the specified level of significance. If the p-value of the computed F-value is lower than the chosen level of significance the null hypothesis can be rejected. To check different directions of Granger causality all the steps above are applied in all cases. (Gujarati & Porter 2009)
4.4 T-test
In addition to an F-test, this thesis uses a t-test to answer some of the hypotheses. The use of a t-test is needed for testing individual significance, i.e. how one variable affect another given that the other variables in the regressions are kept constant. The t-test uses a certain level of significance to see if a hypothesis can be rejected or not by comparing an observed t-value with a critical t-value. The critical t-value is determined from the t-table where the difference between the number of observations and parameters determines which degree of freedom to use to find the correct critical value. Another way to interpret the result of the regression without using the observed t-value is to analyze the p-value. The p-value determines whether the null hypothesis can be rejected or not depending on the specified level of significance. A high p-value indicates that the null hypothesis can not be rejected, and a low p-value indicates that the null hypothesis can be rejected i.e. the p-value tells the probability that the null hypothesis can be true. (Gujarati & Porter 2009)
4.5 The Breusch-Godfrey Test
In studies of time series analysis, it is important to test whether the residuals in the regression are correlated over different time periods. Serial correlation, autocorrelation, is when the error term for one period of time, is correlated with the error term for the subsequent time period. If this occurs in regressions, there can be misspecifications and incorrect conclusions. In order to test for serial correlation, in autoregressive models, a Breusch-Godfrey (BG) test is conducted. The Breusch-Godfrey test analyzes how the lagged residuals can explain the residuals from the original equation that also includes the lagged values of the independent variables. If the lagged residuals are insignificant in explaining this time’s residuals, one can not reject the null hypothesis, which means that there is no autocorrelation. The null hypothesis, of no first order serial correlation looks like 𝐻#: 𝑝! = 0 and can be rejected if the lagged residuals are significant.
(Studenmund 2017)
With the help of the Breusch-Godfrey tests, decisions can be made of how many lagged values the Vector Autoregression Model should contain of. Testing for first-order serial correlation, that is lag equal to 1.
Testing for second-order serial correlation, indicates that the lag equals to 2 and so on. Different orders of serial correlation are tested, because there can be correlation in different orders of serial correlation. From the results of the Breusch-Godfrey tests decisions about how many lagged values that should be included in the Vector Autoregression Model can be made. (Studenmund 2017)
4.6 Dependent variable
The part of the regression analysis is the dependent variable and how the changes in it is influenced by the change in the independent variables. The aim of a regression analysis is therefore to see how the dependent variable is affected by the change of the independent variables. (Studenmund 2017)
4.7 Independent variable
An independent, or explanatory, variable is a variable that is likely to affect the outcome of another, in other words the dependent variable. The value of the independent variable does not depend on anything, i.e. is not affected by other variables. (Studenmund 2017) The change in the dependent variable in this study is based on different independent variables and lagged terms independent variables.
In this study the VAR model is used to be able to test for Granger causality. This model requires every variable to be set as both independent and dependent variables, i.e. the variables GDP, bank development, OMXSPI, turnover ratio, standard deviation, and total stocks traded are interpreted as both independent and dependent variables in the regression model.
4.8 R
2R-squared describes how strong the relationship is between the dependent and independent variables. The value explains how much the dependent variable changes in proportion to the independent variables. The value ranges from 0 to 1, where 1 indicates that a change in the dependent variable is explained by 100 percent of a change in the independent variables and 0 indicates that the dependent variable does not change as the independent variables change. (Agresti, et al. 2017)
5. Empirical results and analysis
The aim of this study is to investigate the causal relationship between the financial system and economic growth. By using different measures of indicators of the stock market development and banking development. Thus, in order to establish different channels through which finance can affect economic growth and causal relationships between variables.
The study is based on two previous research studies done by Nieuwerburgh, Buelens and Cuyvers (2006) and one by Arestis, Demetriades and Luintel (2001), who also examined Granger causality. It is a combination of both previous reports as different variables were taken from both articles to examine the relationship between the financial sector and economic growth. The aim is to investigate whether their results regarding causal relationship between variables also holds in Sweden.
To determine how many lagged terms the VAR model should consist of, the Breusch-Godfrey test is conducted. The tests are performed on all six variables by including one lagged value in the first test, two lagged values in the second test and three lagged values in the third test. This to identify if serial correlation would be a problem or not when including different numbers of lagged terms. The result from the Breusch- Godfrey test showed that the degree of serial correlation was lowest at the first and second preceding periods, i.e. when including one and two lagged terms. Therefore, the results and answers to the hypotheses are based on the outcome from regression models which includes one and two lags.
The paper examines the separate direction of causality between different variables as well as jointly direction of causality between variables. In the section below, a t-test is used to test the directions of causality when including one lagged term of each variable in the VAR model. When the model consists of two lagged terms of each variable the F-test is used to determine the causality between different variables. The F-test is also used when testing the hypothesis with jointly causality, using only one lag in the VAR model. The unrestricted and restricted regressions are created to be able to implement the F-test.
5.1 The causality from GDP to OMXSPI and from OMXSPI to GDP
To test the direction of causality between GDP and OMXSPI and the reverse direction with only one lag in the regression model, a t-test is conducted. Two different null hypotheses are determined to be able to test for reverse causality between GDP and OMXSPI. The first null hypothesis is: ΔGDP does not Granger cause ΔOMXSPI, i.e. the parameter of lagged ΔGDP equals zero, and the reverse is: ΔOMXSPI does not Granger cause ΔGDP, i.e. the parameters of lagged ΔOMXSPI equals zero. Table 1.2 shows the results from the GDP and OMXSPI Granger causality test. Based on the Breusch-Godfrey test one lag is included in the VAR-model.
Table 1.2 Granger causality between GDP to OMXSPI and OMXSPI to GDP with one lag.
1 Lag t-statistic R2 p-value Hypothesis
GDP → OMXSPI 3,541 0,951 0,0002 H0 is rejected
OMXSPI → GDP 6,191 0,994 0,000 H0 is rejected
The critical value for the t-test statistic is obtained from the t-distribution with 24 degrees of freedom at the 5 percent significance level. The critical value of t is 2,06. In both cases, the t-statistic exceed the critical value, which indicates that the null hypotheses can be rejected. Hence, there is evidence for Granger causality from GDP to OMXSPI and from OMXSPI to GDP.
The direction of causality between GDP and OMXSPI is also investigated using two lagged terms in the VAR model. When testing for two numbers of lags an F-test is performed. To conduct the F-test an unrestricted and a restricted model are created. Thereafter the first null hypothesis is stated, ΔGDP does not Granger cause ΔOMXSPI. This means that lagged terms of ΔGDP do not belong in the regression.
The second null hypothesis tests the reverse direction, ΔOMXSPI does not Granger cause ΔGDP per capita, i.e. lagged ΔOMXSPI does not belong in the regression. Table 1.3 presents the results from the GDP and OMXSPI Granger causality test. Based on the Breusch-Godfrey test two lags are included in the VAR-model.
Table 1.3 Granger causality between GDP to OMXSPI and OMXSPI to GDP with two lags
2 Lags F-statistic
R2
(unrestricted regression) Hypothesis
GDP → OMXSPI 6,347 0,967 H0 is rejected
OMXSPI → GDP 25,538 0,998 H0 is rejected
The critical value of F-test statistics is obtained from the F-distribution with 2 and 17 as the degrees of freedom at the 5 percent significance level. The critical value of F is 3,59. The F-statistics exceeds the critical
value, which indicates that the null hypotheses can be rejected. Hence, there is evidence for Granger causality from GDP to OMXSPI and from OMXSPI tom GDP.
5.2 The causality from the Stock market variables to GDP
When testing for the joint significance of Granger causality from several stock markets variables to GDP, the F-test is performed and the Vector Autoregression model consists of one lag and two lags. Thus, two F-test are conducted. One, when the Autoregression Model consists of one lagged value of each time series and a second time when the model includes two lagged values of each time series. The overall significance from stock market variables, standard deviation, turnover ratio and total stocks traded, to GDP are tested.
Before conducting the F-test the unrestricted and restricted model are created. The null hypothesis is thereafter stated; ΔStock market variables do not Granger cause ΔGDP, lagged Stock market variables do not belong in the regression. Table 1.4 presents the results from the stock market variables and GDP Granger causality test. Based on the Breusch-Godfrey test one regression is made up of one lag and the other with two lags.
Table 1.4 Granger causality between stock market variables to GDP with one and two lags
Number of lags Direction F-statistic R2
(unrestricted regression) Hypothesis
1 Stock market variables →
GDP 6,828 0,998 H0 is rejected
2 Stock market variables →
GDP 12,079 0,994 H0 is rejected
The critical value for the F-test statistics is obtained from the F-distribution. With one lag the degree of freedom is 3 and 24 and with two lags the degree of freedoms is 6 and 17. The critical value of F are 3,01 with one lag and 2,7 with two lags. The F-statistics exceeds the critical values in both cases, which indicates that the null hypotheses can be rejected. Hence, there is evidence for Granger causality from stock market vairables to GDP in both the tests.
5.3 The causality from St.dev to GDP, Turnover to GDP and TurnoverMSEK to GDP.
The Granger causality between the stock market variables to GDP is also tested separately, and only through one direction. The t-test is applied on all hypotheses using one lag in the regression model. The first null hypothesis is: ΔSt.dev does not Granger cause ΔGDP, i.e. the parameter of lagged ΔSt.dev is equal to zero.
The second is: ΔTurnoverratio does not Granger cause ΔGDP, i.e. the parameter of lagged ΔTurnoverratio is equal to zero. The last null hypothesis is: ΔTurnoverMSEK do not Granger cause ΔGDP, i.e. the
