Master of Science in Economics
Specialisation International Economics and Globalisation
Faculty of Economics and Business
Supervisor: Dr. D.J.M. Veestraeten
Second reader: N.J. Leefmans
The impact of non-standard monetary policy
on income inequality in the Netherlands
AN EMPIRICAL ANALYSIS
Amsterdam, 23 July 2018
Author
Ahmad Mukhtar Kakar
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Abstract
Studies show that the income inequality in various nations such as Japan, the United Kingdom and Italy increased after the implementation of non-standard monetary policy by the central bank. In order to figure out whether the income inequality in the Netherlands has increased by the unconventional monetary policy, we use a VAR model and impulse-response functions. The time frame we are focusing on is the period between 1980 and 2017. The Granger causality test results show that the ECB’s non-standard monetary policy indeed affected income inequality in the
Netherlands, whereas the impulse-response functions do not present significant results except that ECB’s unconventional monetary policy cause the income disparity to increase when the AMX index and M1 are used in our VAR model instead of AEX index and central bank assets. Our main finding – the ECB’s non-standard monetary policy has no significant impact on the income inequality in the Netherlands – is not robust to the use of different measures of non-standard monetary policy.
Statement of Originality
This document is written by Ahmad Mukhtar Kakar who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
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Table of contents
ABSTRACT ... 2
I. INTRODUCTION ... 4
II. LITERATURE REVIEW ON INEQUALITY AND NON-STANDARD MONETARY
POLICY ... 6
II.1 Definition of inequality ... 6
II.2 Non-standard monetary policy ... 8
II.3 The causation between non-standard monetary policy and income inequality explained ... 10
II.4 Literature on the causation between non-standard monetary policy and income inequality ... 13
III. METHODOLOGY AND EMPIRICAL RESULTS ... 15
III.1 Description of the data ... 15
a. Data summarised ... 15
b. Data transformation to achieve stationarity ... 18
III.2 Vector Auto Regression (VAR) model ... 22
a. VAR model ... 22
b. Lag Length Selection ... 24
III.3 VAR results ... 25
a. Granger causality test results ... 25
a. Impulse-response functions ... 26
III.4 Robustness check ... 32
IV. CONCLUSION ... 36
IV.1 Conclusion ... 36
IV.2 Discussion ... 37
APPENDIX A: GINI COEFFICIENTS ... 38
APPENDIX B: ABBREVIATIONS USED ... 39
APPENDIX C: DESCRIPTION OF THE DATA ... 40
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I. Introduction
One of the slogans of the Occupy Wall Street movement in 2011 was “We’re the 99%” referring to income inequality. According to this movement, the biased distribution of wealth in which the low-income households are relatively poor is absolutely unacceptable. The wide public debate about income and wealth inequality intensified after the publication of “Capital in the Twenty-First Century” (Piketty, 2014). The author of this book states there is an upward trend in a country’s wealth inequality. His reasoning is based on the annual average rate of return on capital - henceforth r - and he argues there is a significant growth in the capital as a percentage of GDP. Piketty studies the relationship between r and the economy’s growth rate g and his forecast shows that in the period from 2012 until 2100 the rise in r will be even larger than the GDP growth rate (Piketty, 2015). Stated differently, the growing income inequality becomes even larger. This can be explained by the effects of the “income composition channel” which is elaborated later on.
Statistics Netherlands (2016) states in a report that the income gap in the Netherlands was relatively stable in the period between 2008 and 2012. This has been invalidated by the Netherlands Scientific Council for Government Policy (hereafter WRR), which statistically provesi that there is an obvious upward trend in income inequality in the Netherlands. The labour earnings held by the highest decile of the income distribution increased with 41% which is considerably faster than the 28% increase in the total earnings held by the top 10% of the income distribution. In addition, the Gini coefficients also increase between 2000 and 2014 (see Figure 1). The Gini coefficient was 0.33 in 2006 and rose to 0.35 in 2014. These coefficients mean everyone has the same income when its value is zero and only one person or household has all the income when the Gini coefficient is 1. The Dutch income equality measured by the Gini coefficient dropped from the 10th place among 31 OECD nations in 2012 to the 12th place among 31 OECD nations in 2013.
To investigate whether the higher income inequality in the Netherlands has increased due to the European Central Bank’s (henceforth ECB) Quantitative Easing (QE), we will answer this research question: “Did the ECB’s non-standard monetary policy in the post-crisisii period affect income
inequality in the Netherlands?” To address this research question a Vector Auto Regression model (a VAR model) will be used. The most recent Gini coefficients are used as dependent variable.
Additional dependent variables which will be added to the VAR model are real GDP in local currency, inflation rates, stock prices and the ratio of the total income of the 20% highest incomes and the total income of the 20% lowest incomes. The central bank assets are used as an independent
i The CBS’s report is mainly based on GINI coefficients, whereas WRR corrects these coefficients for biases and
uses a more detailed version of income inequality. Standardised income is used by the CBS which gives biased results, while WRR uses a corrected version of standardised income.
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variable, but other potentially relevant explanatory variables such as money supply will also be added. This thesis adds value to the literature by focusing on more recent data in order to include the effects of the ECB’s recent unconventional monetary policy.
In order to answer the abovementioned research question, a review of the existing literature will be added in the next chapter. In this chapter, the definitions of the concepts of inequality and non-standard monetary policy will be provided as well. The data will be described in chapter III. The third chapter contains a clarification of the VAR model used and the empirical results are also described here. The fourth and last chapter of this paper contains concluding remarks. Appendices including figures and tables and references are added at the end.
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II. Literature review on inequality and non-standard monetary policy
This chapter of the paper has four parts. Inequality, as it will be used later on, is defined in the first part, followed by the description of non-standard monetary policy by the ECB. There is anexplanation of the causation between non-standard monetary policy and income inequality in the third part. In the last part of this chapter, the extant empirical literature about the causation between non-standard monetary policy and income inequality is discussed.
II.1 Definition of inequality
Generally, there are various types of inequality, namely economic inequality, income inequality, wealth inequality, consumption inequality and social inequality. Economic inequality is a broad concept that includes various specific inequalities such as income inequality, wealth inequality and consumption inequality. Income and consumption inequalities are discussed below. Wealth is equal to the accumulated assets reduced by liabilities. Hence, wealth inequality represents the uneven distribution of accumulated assets minus liabilities. Economic inequality is not the only form in which inequality occur, but inequality can appear in a social form as well. Social inequality can appear if a population is divided into different groups or classes because of the differences in educational achievement, ethnicity, gender and/or sexual orientation. These differences, in turn, lead to the diverging socioeconomic status of the classes or groups (Hurst, Gibbon, & Nurse, 2017).
Whether a higher degree of inequality in each of these types is desirable or undesirable can be viewed from different perspectives. Firstly, Hurst et al. (2017) state that a higher inequality in rewards might be beneficial to the whole society if inequality in rewards guarantees that critical tasks or jobs are done by the individuals with the highest qualifications. In this case, there is an incentive for individuals to work hard, namely higher rewards. The opposite and also the dominant view is that higher inequality in each of the abovementioned types is undesirable since it has mainly negative consequences which are mentioned below. Higher inequality creates frictions between majorities and minorities, men and women and the haves and have-nots which makes the functioning of the society more difficult (Hurst, Gibbon, & Nurse, 2017).
This paper will focus on inequality in the broadest sense of the word, defined as: “the extent of disproportion between each share of things held and the proportion each category or holder constitutes of the total number of categories or holders” (Waldman, 1977). Social and economic inequalities are the broadest concepts since these inequalities consist of various components which are difficult to measure. The remaining three inequalities are more specific and easier to measure. In this paper, the income inequality will be used as there are various reliable measures of this type of inequality. Income inequality is typically represented by the Gini coefficient which shows the income
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distribution of the citizens of a country by comparing their shares of income with the perfectly equal distribution. The data on income inequality will be described in more detail in section III.
We define income inequality as the case in which the highest decile or quintile of the population does not earn the same as the lowest decile or quintile of the population. The same goes for the consumption inequality in which the highest 10 or 20% of the population does not consume the same amount as the lowest 10 or 20% of the population. The consumption inequality measures the skewed distribution in consumption of leisure, durable goodsiii and nondurable goodsiv (Attanasio & Pistaferri, 2016).
Regarding the undesirable consequences, higher income inequality is negatively correlated with the educational attainment level (Mayer, 2001). If the high-income earners earn more and more and the low-income earners earn less, the gap between high and low-income earners will become larger. This rising gap may be associated with poverty which possibly contributes to higher crime rates. The growing gap is also linked with the underinvestment in children’s educational attainment by the parents whose earnings are lower. In this way, households with relatively low income cannot benefit from the increase in returns to schooling by attending additional academic years. In general, the higher the educational attainment, the higher the future earnings of the children. If the
educational attainment level and the parents’ economic status are low, the economic status of the parents may then be inherited by the next generations in view of the positive correlation between educational attainment and the future earnings (Durlauf, 1996).
In addition, an increase in economic inequalityv negatively affects political behaviour of the citizens of a nation and causes economic segregation. For example, the rich are encouraged and able to register their children in private schools rather than in public schools since their income is
relatively high, whereas the poor are mostly unable to enrol their children in private schools. This means families with a high income may have no incentive to support public schools because their children go to private schools. So, if there are national redistributive policies in favour of public schools, then these policies will not be supported by the rich and thus wealthier families will not vote in favour of national redistributive policies (Alesina, Alberto, & Rodrik, 1994).
This change in the political behaviour of the individuals is closely related to economic segregation. Durlauf (1996) states that the place where parents live partly determines the future earnings of their children. High-income earners tend to live in the neighbourhood with lots of positive sociological effects i.e. a neighbourhood which is socially under control. The latter means
iii Durable goods last longer for example vehicles, refrigerators, dryers, (dish)washers and cooking and
entertainment durables.
iv These goods have a relatively short lifespan, e.g. food, fuel, cosmetics products and clothing.
v Which means an increase in income inequality and/or consumption inequality and/or wealth inequality
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there is (almost) no vandalism, trash, drug use and/or graffiti on the streets. At the same time, this kind of neighbourhood is positively affected by its accessibility, good safety, clean and green environment and polite residents who respect each other and pay attention to each other’s properties (Ross, 2000). The living costs in these neighbourhoods with positive sociological effects are relatively high. Therefore, low-income families cannot easily afford to live in these
neighbourhoodsvi. In short, a higher economic and income inequality is undesirable because of the subsequent negative consequences.
II.2 Non-standard monetary policy
Typically, the central bank of a nation is responsible for the monetary unit and the monetary policy of a country, but this is different for the Netherlands. Each euro area country had its own currency before 1 January 1999 when the euro was born. The euro notes and coins started to circulate in 2002. A European Central Bank was needed for the proper functioning of the European Unionvii. All eurozone national central banks participate in the main decision-making body of the ECB, called the Governing Council.
The monetary policy implemented by the ECB is intended to stabilise inflation in a way that the inflation rates remain below, but close to 2% over the medium term. In other words, a year-on-year increase in the Harmonised Index of Consumer Prices (HICP)viii should be below, but close to 2%. The ECB tries to achieve this goal by focussing on three key interest rates: the interest rates on deposits at the ECB and the marginal lending facility and the interest rate on the main refinancing operations. In general, if the inflation is too high, the interest rates are increased by the ECB because higher interest rates make it unattractive to borrow, but attractive to save and vice versa.
In the case of very low inflation the standard monetary policy cannot infinitely be used to lower interest rates because of the zero lower bound. The latter means that the short-term nominal interest rate is already at or close to zero and cannot be decreased further because of the danger of deflation. Here, the Quantitative Easing (QE) and thus a non-standard monetary policy is needed to stimulate economic growth.
After the Global Financial Crisis (henceforth GFC) of 2008, the major central banks introduced non-standard monetary policy measures in an environment of already very low interest rates. The
vi Ross (2000) empirical analysis is based on a sample of 2482 adults in Illinois and even states that living in a
neighbourhood with almost no positive sociological effects is associated with depression. According to the findings of this study, the residents of more advantaged neighbourhoods have lower levels of depression than the residents of low-income disadvantaged neighbourhoods.
vii The economic and monetary union of the EU.
viii The fact that HICP is harmonised means one methodology is used in all the European Union (EU) countries.
The use of the same methodology makes the HICP data of one country easily comparable to other EU members.
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response of the ECB by implementing non-standard monetary policy tools can be divided into three phases.
Firstly, the unconventional monetary policy tools were intended to provide liquidity to the financial intermediaries – for instance banks - and maintain financial stability. This was approached by the fixed-rate full allotment in which infinite credit was provided to banks at a fixed interest rate.
In the second phase, there was a sovereign debt crisis in the eurozone and the ECB
purchased debt securitiesix. The ECB announced the Enhanced Credit Supportx (ECS) which positively affected bank lending and liquidity in the eurozone money market. Very long-term refinancing operations were conducted under the ECSxi.
In the third phase of the ECB’s response to the GFC, the interest rates were historically low and there was the danger of deflation. The interest rate on the deposit facility became negative which meant that banks had to pay for depositing money at the ECB. Simultaneously, financial intermediaries – for instance banks - could borrow almost for free which accelerated the economic growth. In addition, Targeted Longer-Term Refinancing Operations (TLTROs)xii were introduced to increase bank lending through which agents in the private sector could easily borrow and the real economy could be positively affected. Moreover, since March 2015 the ECB purchases public and private sector securities in order to tilt term structure of the interest rates. This became known as the Asset Purchase Programme (henceforth APP)xiii. The APP exists to react to the very low inflation. This programme will be gradually ended in view of an increase in the eurozone inflation to 1,9% in May 2018. Besides the APP, there is also another non-standard monetary policy tool called the
ix This became known as the Securities Markets Programme (SMP) which is no element of monetary policy since
the liquidity effects are to be sterilised. The ECB’s Governing council introduced the SMP on 10 May 2010. There is a so-called sterilisation in the SMP, which means that the central bank liquidity and thus the money supply remained unchanged. The SMP was intended to maintain financial market liquidity without altering the central bank liquidity (European Central Bank, 2018).
x This was announced on 8 December 2011.
xi Two years after the introduction of the SMP on 6 September 2012, the Outright Monetary Transactions
(henceforth OMTs) were undertaken – but have never been used - in order to safeguard the transmission mechanism in all the eurozone countries evenly. Also, the OMTs are not elements of monetary policy, but the OMTs were needed because there were growing differences in the short-term government bond yields of the eurozone countries. The widening differences were also visible in the ten-year government bond yields of the same countries. The OMTs were introduced in order to tackle this issue of growing differences and prevent or lighten the distortions in the government bond markets. However, afterwards, the OMTs are never mobilised.
xii ECB introduced TLTRO I on 5 June 2014 and TLTRO II on 10 March 2016.
xiii The average monthly pace of the net purchases was €60 billion from March 2015 till November 2015, €80
billion from January 2016 till November 2016, once again €60 billion from April 2017 till December 2017 and €30 billion from January 2018 till May 2018. On Thursday 14 June 2018 Mario Draghi, the president of the ECB, announced at a press conference that the net purchases under the APP will be continued at the current average monthly pace of €30 billion till the end of September 2018. Draghi also revealed that the average monthly pace of the net purchases will be €15 billion until the end of December and after that, the ECB will end the APP. This only continues if the incoming data support the ECB’s inflation aim over the medium term.
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Forward Guidance (henceforth the FG) in which the ECB’s expectations regarding the future monetary policy are publicly known.
The concept of standard monetary policy can be captured by interest rates. However, these policy interest rates are virtually constant since 2008. In this paper, we focus on the non-standard monetary policy which at best can be captured by variables such as the money supply, reserves, and the central bank assets. The data and motivation for the sample selection will be described in III.2.
II.3 The causation between non-standard monetary policy and income
inequality explained
To identify the causation between monetary policy and income inequality, an elaboration of the transmission mechanism of monetary policy is needed. This mechanism is a system in which the impact of monetary policy decisions on the economy and inflation is illustrated (European Central Bank, 2018). The existing literature examines various transmission channels to describe the distributional effects of monetary policy. Coibion et al. (2012) document five channels: (1) the income composition channel, (2) the financial segmentation channel, (3) the portfolio channel, (4) the savings redistribution channel, and (5) the earnings heterogeneity channel. The channels (1), (2) and (3)xiv lead to higher inequality after having expansionary monetary policy. The remaining two channels result in lower inequality after the implementation of expansionary monetary policy.
Regarding the research question of this paper, the financial segmentation channel, the savings redistribution channel and the earnings heterogeneity channel are relatively less relevant but will be briefly described. The financial segmentation channel is based on the connectedness of economic agents to financial markets. Williamson (2008) state there are two types of households, those who are connected to the financial markets because they trade regularly in these markets and others who are unconnected to the financial markets since they participate passively and irregularly in the financial markets. If expansionary monetary policy is announced and implemented, connected households are better off than the unconnected households because the connected economic agents already are actively trading in the financial markets.
The savings and redistribution channel is relevant for the savers and borrowers. One knows that savers benefit from higher interest rates whereas they are hurt by lower interest rates, but the opposite is true for the borrowers. If there is an increase in interest rates unexpectedly, savers will be relatively better off than the borrowers. This provokes increased consumption inequality.
Another transmission channel is the earnings heterogeneity channel which focuses on the way earnings respond to the monetary policy shocks. The response of the income of high- and
xiv However, Coibion et al. (2012) state that the impact of the “income composition channel” is ambiguous if
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income households to monetary policy is not the same, because the income of the low-income households is relatively more sensitive to the monetary policy shocks than the income of the high-income households. This is the case when unemployment rates of high-income households and low-skilled workers decrease disproportionately. The changes in the salaries at the bottom of the distribution are mainly caused by the variations in the business cycle (Heathcote, Perri, & Violante, 2016).
In order to focus on the impact of non-standard monetary policy on income inequality, which is the central notion of inequality in this thesis, the income composition channel and the portfolio channel are the most relevant ones.
Focusing on the income composition channel, there are various types of primary sources of income. Generally, the primary source of income for most of the households is their job, whereas others have also financial income. According to a report by the Statistics Netherlands (CBS) on welfare in the Netherlands, there are more and more millionaires and that 2% of the households in the top 10% of the income distribution had a capital which was more than 90 times as high as that of households in the bottom 10% of the income distribution (Statistics Netherlands CBS, 2016). This report also states that wealthier self-employed workers buy relatively more securities and financial assets than employees. If non-standard monetary policy measures cause a larger increase in profits than in wages, then households with financial income benefit relatively more. At the same time, households with primarily labour earnings are relatively less favoured. Ultimately, this channel leads to higher inequality. Figure 1 on the next page shows an increase in Gini coefficient between 2010 and 2014 which represents higher inequality. At the same time, Figure 2 presents an obvious upward trend in the number of financial assets which especially belongs to the top 50% of the income distribution.
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Figure 1: The 80/20 ratio and the Gini coefficient in the period 2000-2014
The data used in this graph is extracted from Statistics Netherlands (CBS).
Figure 2: Rising number of financial assets Dutch households possess
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The portfolio channel is relevant as well because this channel shows how non-standard monetary policy measures affect inequality via higher asset prices. Erosa and Ventura (2002) study the portfolio holdings and the transaction patterns and state that high-income households tend to hold relatively less cash and comparatively more financial assets than low-income households. They explain: “... high-income families are more likely to perform cash management activities that reduce their exposure to the inflation tax per dollar transacted with money (p.775).” So, the cash held by low-income households may be limited. Households with the lion’s share of positions in their portfolio that are well protected against inflation do not suffer from the inflationary effect of a change in the policy rate and vice versa, households suffer more from inflationary effects of a change in the policy rate if their major share of positions is not protected against inflation. In other words, high-income households with relatively more stocks and financial assets are positively affected by the higher financial asset prices as a result of higher demand since the ECB buys a lot of securities and pays directly. This positive impact on high-income households increases income inequality.
To sum up, in the methodology we follow the theory in the existing literature which states that the shocks in the monetary supply slowly affect inflation and output (Saiki & Frost, 2014). The shocks in prices and output directly affect changes in the monetary policy. Consequently, the income inequality and the stock prices are directly affected by the non-standard monetary policy shocks.
II.4 Literature on the causation between non-standard monetary policy and
income inequality
In general, the existing literature regarding the monetary policy can be divided into two categories. One in which the impact of conventional monetary policies on inequalityxv is analysed and in the other category, the impact of non-standard monetary policy on income inequality is studied. We focus on the last category here, since that is more relevant to the research question of this paper.
Regarding the conventional monetary policy shocks, Coibion et al. (2012) examine the effects of monetary policy shocks to income and consumption inequality in the U.S. since 1980. Their
findings show that in the long run the contractionary monetary policy shocks significantly increase inequality. In the paper of Coibion et al. (2012), the main channel through which this effect
materializes is the income composition channel. This causation between the monetary policy shocks and inequality is also confirmed by the quantitative analysis of Doepke and Schneider (2006).
With respect to standard monetary policy, the first study analysing the effects of non-standard monetary policy measures on inequality is based on the monetary policy shocks
xv Here, we cannot state one specific type of inequality, because there are various papers which analyses the
impact of conventional monetary policies on different types of inequality such as wealth inequality, income inequality, and consumption inequality. For example, Domanski et al. (2016) are interested in wealth inequality whereas Casiraghi et al. (2016) focus on wealth and income inequality.
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implemented by the Bank of Japan (BoJ) after the third quarter in 2008 (Saiki & Frost, 2014). Saiki and Frost (2014) present the results of a Vector Auto Regression (VAR)-analysis and conclude that the unconventional monetary policy in Japan indeed led to higher inequality. Here, the main channel through which this effect unfolds is the portfolio channel.
This empirical evidence from Japan corresponds with the empirical analysis of the effects of Quantitative Easing (hereafter QE) implemented by the Bank of England (BoE) after the GFC. The analysis by Mumtaz and Theophilopoulou (2016) uses data from 1969 to 2012. Mumtaz and Theophilopoulou (2016) find higher income inequality in the United Kingdom after the
implementation of QE by the BoE. This paper can be criticized because the analysis of Mumtaz and Theophilopoulou (2016) is based on the impact of QE on only bond prices and not other public and private sector securities purchased by the BoE. Moreover, the BoE admits that QE provokes higher inequality and states that it is inevitable that there will be some who lose (Bank of England, 2012). At the same time, the BoE stress that the unconventional monetary policy measures in the UK will minimize the negative distributional effects.
Domanski et al. (2016) study the changes in asset prices in fivexvi European countries and conclude that the monetary policy shocks have increased wealth inequality. This is confirmed by Adam and Tzamourani (2016) who study the asset price changes in the whole euro area and also state an increase in wealth inequality.
Moreover, Montecino & Epstein (2015) study the impact of QE on income inequality in the USA using the Federal Reserve’s Survey of Consumer Finances. They compare the pre-QE period between 2008 and 2010 with the post-QE period starting in 2011 until 2013. Their overall results show that QE increases income inequality.
On the other hand, some papers doubt whether income inequality is indeed influenced by the non-standard monetary policy measures. Casiraghi et al. (2016) find that the effect of the ECB’s unconventional monetary policy on income and wealth inequality in Italy is negligibly small. In addition, Colciago et al. (2018) focus on a survey of the existing literature on inequality and central bank policies and also state that it is not yet clear whether QE affects inequality.
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III. Methodology and empirical results
This chapter consists of four parts. In the first part, the data are summarised and transformed in order to achieve stationarity. Secondly, there is a description of the research method and the hypotheses followed by the lag length selection. The last part contains the VAR results including the Granger causality test results and the impulse-response functions. In the end, there is a robustness check.
III.1 Description of the data
In this first part of chapter three, there is an elaborate description of the data used in our VAR model. To begin with, the data are summarised. Then, the data transformation is discussed and eventually stationary variables are presented.
a. Data summarised
Table 1 (see Appendix C) contains the averages, standard deviations, minimum and maximum values of all the variables used in this paper. The main variables of interest are the Gini coefficients
representing the income inequality and the central bank assets as a measure of non-standard monetary policy.
Firstly, the World Bank estimate of the Gini coefficient
xviii xvii is used as a measure of income inequality in the Netherlands. Italian statistician Corrado Gini developed his coefficient and published its approach and the formulae in 1912 in an Italian book called “Variabilità e Mutabilità” . This coefficient shows how much the income distribution of households or individuals deviate from the completely equal income distribution (see Figure 4). Stated differently, the Gini coefficient is equal to half the relative mean difference, represented by the function below:
𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝐺𝐺𝑐𝑐𝐺𝐺𝑐𝑐𝐺𝐺𝑐𝑐 =
2µα=
N21 ∑i=1N .∑Nj=1�xi−xj�2µ (1)
with μ the average income of the population, N the population and xi the income of
household i. In the numerator of the equation above, there is the sum of the absolute values of the income differences. The smaller these differences (i.e. the smaller the sum in the numerator), the smaller the income inequality. Complete inequality is represented by the denominator. If one household has all the income, then the numerator equals 2µ. It means the value of the Gini coefficient is between 0 representing complete equality and 1 showing complete inequality.
xvii The Gini coefficients for the Netherlands from 2004 till 2015 are derived from the World Bank database. The
missing observations of the Gini coefficients are filled by the Gini coefficients extracted from various other sources such as the World Income Inequality Database of the United Nations and Luxembourg Income Study (LIS).
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This approach is visualised by the Lorenz curve, which plots the cumulative percentages of income on the vertical axis and the cumulative percentage of the population on the horizontal axis. The horizontal axis goes from the number of recipients with low-income to high-income. The line of equality or the 45-degree line corresponds to a Gini coefficient with the value 0 meaning that everyone has the same income. In case there is inequality, then the Gini coefficient is computed by measuring the area between the Lorenz curve and the equality line divided by the maximum area under the equality line. So, G𝐺𝐺𝐺𝐺𝐺𝐺 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝐺𝐺𝑐𝑐𝐺𝐺𝑐𝑐𝐺𝐺𝑐𝑐 =total area OBAshaded area C . (2)
Figure 4: The Gini coefficient visualised
The mean of the Gini coefficients from 1981 until 2016 is 0.27. Its lowest value is 0.236 in 1987 and its highest value is 0.3 in 2006 (see Figure 5). Altogether, there is an obvious trend of rising income inequality in the Netherlands. Also, the Gini coefficient slightly increases after 2009. This pattern of rising income inequality corresponds to the results of the study by Salverda (2014)xix who analyses the development and consequences
of inequality. At the end of the 1980s, the income of the lowest decile rose with 1000 euros while that of the top decile rose with more than 24000 euros.
Figure 5: Rising income inequality in the Netherlands since the 1980s
xix Source: Salverda, W. (2014). De tektoniek van de inkomensongelijkheid in Nederland. In M. Kremer, M.
Bovens, E. Schrijvers, & R. Went (editors), Hoe ongelijk is Nederland? Een verkenning van de ontwikkeling en gevolgen van economische ongelijkheid (p. 39-58). (WRR Verkenningen; Nr. 28). Amsterdam: Amsterdam University Press.
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Besides the Gini coefficient, there are various other measures of income inequality e.g. the 80/20 ratioxx, the relative interquartile rangexxi, the Robin Hood indexxxii and the Atkinson index . xxiii The Gini coefficient is used in this paper as a measure of income inequality instead of those other measures because the Gini coefficient meets more conditions in order to qualify for a reliable measure than those other abovementioned standards of income inequality. For example, the Gini coefficient has a lower bound, namely 0, and an upper bound of 1 which makes the coefficient easily interpretable and comparable, whereas the lower and upper bounds of the 80/20 ratio and the relative interquartile range are unlimited and vary enormously. Moreover, the Gini coefficient fulfils the Pigou-Dalton criterion, which requires the inequality measure to change if income is
redistributed. More accurately expressed, the inequality measure should become higher if the degressive tax system is introduced and implemented. On the contrary, the inequality measure must decrease if a progressive tax system enables redistribution of income from high-income households to low-income households in a way that the income of the rich does not become lower than the income of the low-income households. The 80/20 ratio, the interquartile range and the Robin Hood index do not satisfy the Pigou-Dalton criterion, but the Gini coefficient meet this condition (Bos, Marion, & Ferdy, 2018).
Furthermore, Montecino & Epstein (2015) use the Gini coefficient as a measure of the income inequality and state that the QE significantly affects the Gini coefficients. It implies there is higher income inequality after the QE is implemented. In addition, the Gini coefficients are used in the structural Vector Auto Regression model and counterfactual analysis by Mumtaz &
Theophilopoulou (2016). Mumtaz and Theophilopoulou (2016) also conclude that there is a significant impact of the QE on income inequality.
Secondly, in this paper, the total assets of the Dutch central bank - called De Nederlandsche Bank (henceforth DNB) - as a percentage of Dutch GDP are used as a measure of monetary policy shocks. Often, the monetary base or the interest rates are used as a measure of monetary policy shocks, but these measures do not sufficiently represent non-standard monetary policy which is implemented after the collapse of Lehman Brothers. The reason for this is that many central banks, including the ECB, partly sterilised the effects of non-standard monetary policies on base money. It
xx The 80/20 ratio is the ratio of the top 20% of the individuals in the income distribution to the bottom 20% of
individuals with low income.
xxi Interquartile Range (IQR) = Q
3 – Q1. It is the difference between the 75th and 25th percentiles.
xxii The Robin Hood index - which is also known as the Hoover Index – measures the income inequality by
determining the proportion of income that should be redistributed from high-income households to low-income households to accomplish complete equality. A lower Robin Hood index corresponds to lower low-income inequality.
xxiii The Atkinson index is a measure of income inequality which provides additional information on which group
of the population – i.e. the highest quintile or the fourth or third quintile – contributed most to the income inequality (Allison, 1977).
18
means, the monetary base does not plainly reflect the non-standard monetary policy measures, whereas the total assets of the balance sheet of the central bank do clearly reflect the
unconventional monetary policy measures (Gambacorta & Hofmann, 2012). Not only the panel VAR analysis by Gambarcorta and Hofmann (2012) use the central bank assets as a measure of non-standard monetary policy during the crisis, but also Saiki and Frost (2014) include central bank assets as a percentage of GDP to study the effects of unconventional monetary policy.
The fact that in this paper the total assets of DNB are used as a measure of monetary policy shocks and not the balance sheet total assets of the ECB does not have to be controversial.
Plotting the total assets of the balance sheets of the ECB and DNB in the same graph yields a reasonably matching pattern (see Figure 6). The sample coefficient of correlation between these two types of total assets is 0.8119 which is large enough to explain and confirm the matching pattern in Figure 6.
Figure 6: Rising total assets of the balance sheets of the ECB and the DNB The data used in this graph is extracted from the ECB and DNB.
b. Data transformation to achieve stationarity
The VAR model used in this paper and described in the next subsection III.2 contains five variables. These variables are: the Gini coefficient (0 = complete equality; 1 = complete inequality), the Dutch GDP in billions of dollars, Consumer Price Index as a measure of inflation rate, the AEX index, the AMX index - which is only used later on to check for robustness – and the DNB balance sheet total assets as a percentage of GDP. These variables are plotted in Figure 7. Since the units of these five variables vary enormously from Gini coefficient with a range of [0; 1] to the Dutch GDP in billions of
19
dollars, it is useful to standardise all the values of these variables so that the empirical results are more easily interpretable.
Standardising the values of the abovementioned five variables takes place in two steps. Firstly, we subtract the average from the value for every case which results in a zero mean. In the second place, the outcome of the first step is divided by the standard deviation which yields in a standard deviation of 1. In formulae, it means standardised value of 𝑥𝑥 =x − µσ ~𝑁𝑁(0, 1). Here, µ is the mean and σ is the standard deviation. The descriptive statistics of all the standardised values are reported in Table 1, Appendix C. Focusing on GDP, for example, the mean of the standardised GDP is -2.20e-09 which is approximately zero. Here, we assume 10-9 is close enough to zero to call it zero. The standard deviation of the standardised GDP is 1. Moreover, Table 2 in Appendix C contains correlation matrices of the original variables with its standardised values. These correlation matrices show a perfect correlation between the original and the standardised values.
20
Figure 8: Variables included in the VAR model standardised
21
Empirical analysis of the time series data requires the variables to be stationary. The Augmented Dickey-Fuller test is used to detect a stochastic trend and subsequently state whether the variables are stationary or not. Regarding the sample in this paper, the time series GDPt in the VAR model is stationary if its probability distribution remains the same over time. Under the null hypothesis, GDPt has a stochastic trend and under the alternative hypothesis there is no stochastic trend and, thus, GDPt is stationary.
More explicitly, the variables in our VAR model are covariance stationary in case the first two moments of these variables exist and are, in addition, independent of time. Firstly, it implies that E[Yt]xxiv, E[πt], E[CBAt], E[St] and E[Gt] are finite and also independent of time. In the second place, Var[Yt], Var[πt], Var[CBAt], Var[St] and Var[Gt] are also finite and independent of time. Thirdly, the covariances between the values at any two points in time are a finite function of |t – s| but not of s or t alone.
The test statistics of the Augmented Dickey-Fuller tests with respect to the standardised data are reported in Table 3. All variables are nonstationary without the consumer price index which is stationary since the absolute value of its test statistic is larger than the absolute value of the 5% critical value, meaning |-3.216| > |-1.950|. So, the null hypothesis is rejected. It means data should be transformed further before performing VAR regression.
Table 3: Augmented Dickey-Fuller test for a unit root with respect to the standardised data
Interpolated Dickey-Fuller Critical values
Standardised variables Test Statistic 1% 5% 10% N** Stationary at 10%?
Gini Coefficient -1.426 -2.658 -1.950 -1.600 26 No GDP -0.403 -2.647 -1.950 -1.603 33 No Inflation -3.216 -2.646 -1.950 -1.604 34 Yes AEX Index -1.487 -2.650 -1.950 -1.602 31 No AMX Index -1.056 -2.650 -1.950 -1.602 31 No DNB* 0.243 -2.650 -1.950 -1.602 31 No
*DNB: Balance sheet Total assets of the Dutch Central Bank DNB **N: number of observations.
We take the first differences in order to have stationary variables and tackle the unit root problem. The VAR analysis by Saiki and Frost (2014) is also performed after taking the first differences. Given the time series {𝐺𝐺𝐺𝐺𝐺𝐺𝑡𝑡}0𝑇𝑇, we create the following first-differenced series:
𝐺𝐺𝐺𝐺𝐺𝐺𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑡𝑡 𝑑𝑑𝑓𝑓𝑓𝑓𝑓𝑓𝑑𝑑𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑, 𝑡𝑡= 𝐺𝐺𝐺𝐺𝐺𝐺𝑡𝑡− 𝐺𝐺𝐺𝐺𝐺𝐺𝑡𝑡−1. (3)
with t indicating years. The other variables are transformed in the same way. The descriptive statistics of all first-differenced variables are reported in Table 1, Appendix C. Table 4 below shows that virtually all variables are stationary except for GDP which is stationary at a significance level of 10%. So, all variables of our VAR model – graphed in Figure 9 - are stationary at least at 10% level.
22
Table 4: Augmented Dickey-Fuller test for a unit root with respect to the first-differenced data
Interpolated Dickey-Fuller Critical values
Variables Test Statistic 1% 5% 10% N** Stationary at 10%?
Gini Coefficient -2.760 -2.660 -1.950 -1.600 25 Yes
GDP -1.861 -2.647 -1.950 -1.603 33 Yes
Consumer Price Index -3.111 -2.647 -1.950 -1.603 33 Yes
AEX Index -3.145 -2.652 -1.950 -1.602 30 Yes
AMX Index -3.097 -2.652 -1.950 -1.602 30 Yes
DNB* -2.658 -2.652 -1.950 -1.602 30 Yes
*DNB: Balance sheet Total assets of the Dutch Central Bank DNB **N: number of observations
III.2 Vector Auto Regression (VAR) model
There are two subsections in this second part of chapter three. In the beginning, the VAR model is presented. The second subsection discusses the lag length selection in our VAR model.
a. VAR model
The research question is: “Did the ECB’s non-standard monetary policy in the post-crisis period affect income inequality in the Netherlands?”. We expect to find a positive relationship between the non-standard monetary policy and the income inequality, since – as mentioned in the literature review – there is rising income inequality in the Netherlands simultaneously in the period in which non-standard monetary policy is introduced and implemented.
In our baseline VAR model, we consider the time series {𝑌𝑌𝑡𝑡}0𝑇𝑇xxv , {𝜋𝜋𝑡𝑡}0𝑇𝑇 , {𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡}0𝑇𝑇 , {𝑆𝑆𝑡𝑡}0𝑇𝑇 and
{𝐺𝐺𝑡𝑡}0𝑇𝑇 which contain data for Dutch GDP in millions of euros, annual CPI headline inflation, DNB
balance sheet total assets as a percentage of GDP, AEX stock prices and Gini coefficient respectively. A VAR representation of these five series is the following: (4)
⎣
⎢
⎢
⎢
⎢
⎡ 𝑌𝑌
𝑡𝑡𝜋𝜋
𝑡𝑡𝐶𝐶𝐶𝐶𝐶𝐶
𝑡𝑡𝑆𝑆
𝑡𝑡𝐺𝐺
𝑡𝑡⎦
⎥
⎥
⎥
⎥
⎤
=
⎣
⎢
⎢
⎢
⎡
𝛼𝛼
𝛼𝛼
12𝛼𝛼
3𝛼𝛼
4𝛼𝛼
5⎦
⎥
⎥
⎥
⎤
+ � 𝐶𝐶
𝑓𝑓⎣
⎢
⎢
⎢
⎢
⎡
𝑌𝑌
𝜋𝜋
𝑡𝑡−𝑝𝑝 𝑡𝑡−𝑝𝑝𝐶𝐶𝐶𝐶𝐶𝐶
𝑡𝑡−𝑝𝑝𝑆𝑆
𝑡𝑡−𝑝𝑝𝐺𝐺
𝑡𝑡−𝑝𝑝⎦
⎥
⎥
⎥
⎥
⎤
+
⎣
⎢
⎢
⎢
⎡
𝜀𝜀
𝜀𝜀
𝜋𝜋,𝑡𝑡𝑌𝑌,𝑡𝑡𝜀𝜀
𝐶𝐶𝐶𝐶𝐶𝐶,𝑡𝑡𝜀𝜀
𝑆𝑆,𝑡𝑡𝜀𝜀
𝐺𝐺,𝑡𝑡⎦
⎥
⎥
⎥
⎤
𝑃𝑃 𝑓𝑓=1In this VAR representation of the abovementioned five series, Ai is the matrix of coefficients and the shocks are depicted by ε which is the independent and identically distributed error term. It
represents the following VAR in standard form:
Y
t= α
1+ a
11Y
t-p+ a
12π
t-p+ a
13CBA
t-p+ a
14S
t-p+ a
15G
t-p+ ε
Y,t (5)π
t= α
2+ a
21Y
t-p+ a
22π
t-p+ a
23CBA
t-p+ a
24S
t-p+ a
25G
t-p+ ε
π,t (6)CBA
t= α
3+ a
31Y
t-p+ a
32π
t-p+ a
33CBA
t-p+ a
34S
t-p+ a
35G
t-p+ ε
CBA,t (7)
23
S
t= α
4+ a
41Y
t-p+ a
42π
t-p+ a
43CBA
t-p+ a
44S
t-p+ a
45G
t-p+ ε
S,t (8)G
t= α
5+ a
51Y
t-p+ a
52π
t-p+ a
53CBA
t-p+ a
54S
t-p+ a
55G
t-p+ ε
G,t (9)The ordering of the variables in the VAR model is as written down above. Here, the
assumption used is that the monetary policy of the ECB or DNB acts in a way that is influenced by the changes in the CPI headline inflation and the GDP, as described in chapter II. Subsequently, we assume the AEX index directly reacts to changes in monetary policy. Eventually, we also assume that the variations in the AEX index affect the income distribution by means of the portfolio channel.
In order to correctly interpret the VAR model estimates, it is required that the VAR model estimates satisfy the stability condition. If our baseline VAR model is indeed stable, then it should have an infinite-order vector moving-average representation. This corresponds to the conclusion of Lütkepohl (2005) who states that the estimated VAR model is stable in case the modulus of every eigenvalue of the matrix A is strictly less than 1. This is confirmed by Hamilton (1994) who also analyses the stability condition of VAR estimates. Table 5 contains eigenvalues and the modulus of the eigenvalues. Here, the matrix eigenvalues are used to obtain eigenvalues. The modulus of the eigenvalue r + ci is √𝑟𝑟2+ 𝑐𝑐2. Table 5 shows that our VAR satisfies the stability condition since all the eigenvalues lie inside the unit circle. Hence, the modulus of every eigenvalue of the matrix A is strictly less than one. The associated matrix is as follows:
𝐶𝐶 = ⎝ ⎜ ⎛ 𝐶𝐶1 𝐼𝐼 0 ⋮ 0 𝐶𝐶2 0 𝐼𝐼 ⋮ 0 ……… ⋱ … 𝐶𝐶𝑝𝑝−1 0 0 ⋮ 𝐼𝐼 𝐶𝐶𝑝𝑝 𝐼𝐼 0 ⋮ 0⎠ ⎟ ⎞
Table 5: Eigenvalue stability condition Figure 10: Eigenvalue stability condition graphed
Eigenvalue Modulus -.9488315 .948832 .1565951 + .8782887i .89214 .1565951 - .8782887i .89214 .7073804 + .4840676i .857151 .7073804 - .4840676i .857151 -.4239621 + .7042345i .822004 -.4239621 - .7042345i .822004 .4221757 + .656916i .780878 .4221757 - .656916i .780878 .07370568 + .5274663i .532591 .07370568 - .5274663i .532591 -.4993888 + .09715831i .508752 -.4993888 - .09715831i .508752 .4957695 .495769 -.05577025 .05577
24
b. Lag Length Selection
It is important to correctly select the order p – the number of lag terms - of an autoregression since valuable information is omitted when the number of lags is too low. On the contrary, if the number of lags is too high, there will be too many coefficients estimated than necessary. There are various information criteria to base the lag length selection choice on them e.g. the likelihood ratio (LR) test statistics, the Final Prediction Error (FPE), the Akaike information criterion (AIC), Hannan-Quinn information criterion (HQIC) and the Bayes information criterion (BIC)xxvi. Liew (2004) examines various information criteria and states that AIC and FPE are superior to other selection-order criteria regarding studies with a relatively small sample i.e. at most 60 observations. This applies to our sample. So, we determine the number of lag terms mainly based on the AIC. The AIC values can be calculated as follows:
𝐶𝐶𝐼𝐼𝐶𝐶(𝑝𝑝)
xxvii= ln �
SSR(p)T
� + (𝑝𝑝 + 1)
2
𝑇𝑇 (10)
with p the number of lag terms, SSR(p) the sum of squared residuals and T indicating the period. Regarding the first term
ln �
SSR(p)T�
, the sum of squared residuals decreases after adding an additional lag term. The second term(𝑝𝑝 + 1)
𝑇𝑇2depicts the number of lag terms p plus one
intercept multiplied by
𝑇𝑇2. The second term goes up if an additional lag term is added. In
other words, the AIC trades off between these two terms which ultimately result in the
number of lag terms that minimise the AIC, making this information criterion a consistent
estimator of the true number of lag terms. Calculating the AIC(p) for p = 0, 1, 2 and 3 yields
the AIC values in the table below.
Regarding the AIC and FPE selection-order criteria, three lag terms should be chosen. The LR and HQIC confirm the choice of three lags (see the values with an asterisk in Table 6).
xxvi BIC is also known as Schwartz information criterion (SIC) which is sometimes abbreviated as SBIC.
xxvii Source: Stock, J. H., & Watson, M. W. (2015). Introduction to Econometrics. London: Pearson Education
Limited.
Table 6: Selecting Lag Length
Selection-order criteria Sample: 1991-2016 Number of observations = 26
Lag LL LR df p FPE AIC HQIC SBIC
0 62.4948 8.3e-09 -4.42267 -4.353 -4.18073*
1 90.6912 56.393 25 0.000 6.7e-09 -4.66855 -4.25053 -3.2169
2 127.396 73.409 25 0.000 3.5e-09 -5.5689 -4.80253 -2.90754
3 171.698 88.604* 25 0.000 1.7e-09* -7.05367* -5.93895* -3.18261
Endogenous: GDP, CPI Headline inflation, Central Bank Assets, AEX index and Gini coefficient Exogenous: _cons
25
III.3 VAR results
The VAR results are presented in two subsections. The first subsection contains the Granger causality test results followed by the impulse response analysis.
a. Granger causality test results
Since there are six variables in our VAR model with three lag terms, the vector autoregression output table contains 3 ∗ 62= 108 coefficients. Because of this large number of coefficients, we focus on
the informative postestimation statistics of the Granger causality test (see Table 7).
The Granger causality statistic tests the hypothesis that the coefficients on all the values of one of the variables in equation (11), (12), (13), (14) or (15) are zero. The null hypothesis implies these regressors have no predictive content for (11) Yt, (12) πt, (13) CBAt, (14) St or (15) Gt. Roughly said, there is no causal relationship between the variables and the lag terms of the variables. The alternative hypothesis implies the coefficients are larger than zero i.e. there is causality between the variables and the lag terms of the variables.
𝑌𝑌𝑡𝑡= 𝛼𝛼1+ 𝛽𝛽11 𝑌𝑌𝑡𝑡−1+ 𝛽𝛽12 𝑌𝑌𝑡𝑡−2+ 𝛽𝛽13 𝑌𝑌𝑡𝑡−3+ 𝛾𝛾11 𝜇𝜇𝑡𝑡−1+ 𝛾𝛾12 𝜇𝜇𝑡𝑡−2+ 𝛾𝛾13 𝜇𝜇𝑡𝑡−3+ 𝛿𝛿11 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−1+ 𝛿𝛿12 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−2+ 𝛿𝛿13 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−3 + 𝜁𝜁11 𝑆𝑆𝑡𝑡−1+ 𝜁𝜁12 𝑆𝑆𝑡𝑡−2+ 𝜁𝜁13 𝑆𝑆𝑡𝑡−3+ 𝜂𝜂11 𝐺𝐺𝑡𝑡−1+ 𝜂𝜂12 𝐺𝐺𝑡𝑡−2+ 𝜂𝜂13 𝐺𝐺𝑡𝑡−3+ 𝜀𝜀𝑌𝑌,𝑡𝑡 (11) 𝜋𝜋𝑡𝑡= 𝛼𝛼2+ 𝛽𝛽21 𝑌𝑌𝑡𝑡−1+ 𝛽𝛽22 𝑌𝑌𝑡𝑡−2+ 𝛽𝛽23 𝑌𝑌𝑡𝑡−3+ 𝛾𝛾21 𝜇𝜇𝑡𝑡−1+ 𝛾𝛾22 𝜇𝜇𝑡𝑡−2+ 𝛾𝛾23 𝜇𝜇𝑡𝑡−3+ 𝛿𝛿21 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−1+ 𝛿𝛿22 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−2+ 𝛿𝛿23 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−3 + 𝜁𝜁21 𝑆𝑆𝑡𝑡−1+ 𝜁𝜁22 𝑆𝑆𝑡𝑡−2+ 𝜁𝜁23 𝑆𝑆𝑡𝑡−3+ 𝜂𝜂21 𝐺𝐺𝑡𝑡−1+ 𝜂𝜂22 𝐺𝐺𝑡𝑡−2+ 𝜂𝜂23 𝐺𝐺𝑡𝑡−3+ 𝜀𝜀𝜋𝜋,𝑡𝑡 (12) 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡= 𝛼𝛼3+ 𝛽𝛽31 𝑌𝑌𝑡𝑡−1+ 𝛽𝛽32 𝑌𝑌𝑡𝑡−2+ 𝛽𝛽33 𝑌𝑌𝑡𝑡−3+ 𝛾𝛾31 𝜇𝜇𝑡𝑡−1+ 𝛾𝛾32 𝜇𝜇𝑡𝑡−2+ 𝛾𝛾33 𝜇𝜇𝑡𝑡−3+ 𝛿𝛿31 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−1+ 𝛿𝛿32 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−2+ 𝛿𝛿33 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−3 + 𝜁𝜁31 𝑆𝑆𝑡𝑡−1+ 𝜁𝜁32 𝑆𝑆𝑡𝑡−2+ 𝜁𝜁33 𝑆𝑆𝑡𝑡−3+ 𝜂𝜂31 𝐺𝐺𝑡𝑡−1+ 𝜂𝜂32 𝐺𝐺𝑡𝑡−2+ 𝜂𝜂33 𝐺𝐺𝑡𝑡−3+ 𝜀𝜀𝐶𝐶𝐶𝐶𝐶𝐶,𝑡𝑡 (13) 𝑆𝑆𝑡𝑡= 𝛼𝛼4+ 𝛽𝛽41 𝑌𝑌𝑡𝑡−1+ 𝛽𝛽42 𝑌𝑌𝑡𝑡−2+ 𝛽𝛽43 𝑌𝑌𝑡𝑡−3+ 𝛾𝛾41 𝜇𝜇𝑡𝑡−1+ 𝛾𝛾42 𝜇𝜇𝑡𝑡−2+ 𝛾𝛾43 𝜇𝜇𝑡𝑡−3+ 𝛿𝛿41 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−1+ 𝛿𝛿42 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−2+ 𝛿𝛿43 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−3 + 𝜁𝜁41 𝑆𝑆𝑡𝑡−1+ 𝜁𝜁42 𝑆𝑆𝑡𝑡−2+ 𝜁𝜁43 𝑆𝑆𝑡𝑡−3+ 𝜂𝜂41 𝐺𝐺𝑡𝑡−1+ 𝜂𝜂42 𝐺𝐺𝑡𝑡−2+ 𝜂𝜂43 𝐺𝐺𝑡𝑡−3+ 𝜀𝜀𝑆𝑆,𝑡𝑡 (14) 𝐺𝐺𝑡𝑡= 𝛼𝛼5+ 𝛽𝛽51 𝑌𝑌𝑡𝑡−1+ 𝛽𝛽52 𝑌𝑌𝑡𝑡−2+ 𝛽𝛽53 𝑌𝑌𝑡𝑡−3+ 𝛾𝛾51 𝜇𝜇𝑡𝑡−1+ 𝛾𝛾52 𝜇𝜇𝑡𝑡−2+ 𝛾𝛾53 𝜇𝜇𝑡𝑡−3+ 𝛿𝛿51 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−1+ 𝛿𝛿52 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−2+ 𝛿𝛿53 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡−3 + 𝜁𝜁51 𝑆𝑆𝑡𝑡−1+ 𝜁𝜁52 𝑆𝑆𝑡𝑡−2+ 𝜁𝜁53 𝑆𝑆𝑡𝑡−3+ 𝜂𝜂51 𝐺𝐺𝑡𝑡−1+ 𝜂𝜂52 𝐺𝐺𝑡𝑡−2+ 𝜂𝜂53 𝐺𝐺𝑡𝑡−3+ 𝜀𝜀𝐺𝐺,𝑡𝑡 (15)
Table 7 contains the Granger causality test results of all the equations (5), (6), (7), (8) and (9). It is commonly known that monetary policy of the ECB is adjusted to the inflation level since ECB’s main goal is to make sure the inflation rates remain below, but close to 2% over the medium term. At the same time, the results in the 22nd row in Table 7 show that the three lagged variables of the central bank assets affect the stock prices since its p-value is 0.025 which is lower than 0.05. Here, the relevant null hypothesis is rejected at the 5% level. Simultaneously, the regression output in the 29th row presents the fact that the movement of the stock prices influence the income inequality because its p-value is much lower than the critical p-value of 0.05.
The ordering of the variables in our baseline VAR model is based on the assumptions
discussed earlier. Since the ordering of the variables affects the vector autoregression output and the relevant Granger causality test results, we, in addition, look to an alternative ordering presented below. Saiki and Frost (2014) argue that the monetary policy of the ECB reacts to the changes in the
26
stock market when the stock markets are vulnerable and financial stress dominates. This implies for the ordering that St comes to the place of CBAt.
𝐼𝐼𝐺𝐺𝐺𝐺𝑐𝑐𝐺𝐺𝐼𝐼𝐼𝐼 𝑐𝑐𝑟𝑟𝑜𝑜𝑐𝑐𝑟𝑟𝐺𝐺𝐺𝐺𝑜𝑜 =
⎣
⎢
⎢
⎢
⎢
⎡ 𝑌𝑌
𝑡𝑡𝜋𝜋
𝑡𝑡𝐶𝐶𝐶𝐶𝐶𝐶
𝑡𝑡𝑆𝑆
𝑡𝑡𝐺𝐺
𝑡𝑡⎦
⎥
⎥
⎥
⎥
⎤
= ⋯
xxviii𝐶𝐶𝐼𝐼𝑐𝑐𝑐𝑐𝑟𝑟𝐺𝐺𝐼𝐼𝑐𝑐𝐺𝐺𝐴𝐴𝑐𝑐 𝑐𝑐𝑟𝑟𝑜𝑜𝑐𝑐𝑟𝑟𝐺𝐺𝐺𝐺𝑜𝑜
⎣
⎢
⎢
⎢
⎢
⎡ 𝑌𝑌
𝑡𝑡𝜋𝜋
𝑡𝑡𝑆𝑆
𝑡𝑡𝐶𝐶𝐶𝐶𝐶𝐶
𝑡𝑡𝐺𝐺
𝑡𝑡⎦
⎥
⎥
⎥
⎥
⎤
= ⋯
Table 8 contains the Granger causality test results with an alternative ordering of variables in our VAR model. The results in the 22nd row in Table 8 show that the lagged stock prices do not cause the central bank assets to change since its p-value 0.402 is much larger than the critical p-value of 0.05. In other words, the null hypotheses cannot be rejected at the 5% level.
Table 7: Granger causality Wald tests
(1) (2)
Equation Excluded chi2 (3) (4) df Prob > chi2 (5) Row number (6)
GDP 1
CPI headline inflation 4.1823 3 0.242 2 Central bank assets 7.8049 3 0.050 3 Stock prices (AEX index) 86.182 3 0.000 4 Gini coefficient 10.428 3 0.015 5
ALL 123.83 12 0.000 6
CPI headline inflation 7
GDP 3.5983 3 0.308 8
Central bank assets 10.388 3 0.016 9 Stock prices (AEX index) 8.7761 3 0.032 10
Gini coefficient 17.573 3 0.001 11
ALL 37.762 12 0.000 12
Central bank assets 13
GDP 40.131 3 0.000 14
CPI headline inflation 3.2591 3 0.353 15 Stock prices (AEX index) 2.9306 3 0.402 16 Gini coefficient 5.1318 3 0.162 17
ALL 139.92 12 0.000 18
Stock prices (AEX index) 19
GDP 14.928 3 0.002 20
CPI headline inflation 6.7326 3 0.081 21 Central bank assets 9.3852 3 0.025 22 Gini coefficient .90986 3 0.823 23
ALL 28.924 12 0.004 24
Gini coefficient 25
GDP 13.55 3 0.004 26
CPI headline inflation 3.581 3 0.310 27 Central bank assets 8.802 3 0.032 28 Stock prices (AEX index) 16.953 3 0.001 29
ALL 26.663 12 0.009 30
27
Table 8: Granger causality Wald tests
Here, we use an alternative ordering, namely:
GDP, inflation rate, stock prices, central bank assets and Gini coefficient instead of the initial ordering in our VAR model:
GDP, inflation rate, central bank assets, stock prices and Gini coefficient.
(1) (2)
Equation Excluded chi2 (3) (4) df Prob > chi2 (5) Row number (6)
GDP 1
CPI headline inflation 4.1823 3 0.242 2
Stock prices 86.182 3 0.000 3
Central bank assets 7.8049 3 0.050 4
Gini coefficient 10.428 3 0.015 5
ALL 123.83 12 0.000 6
CPI headline inflation 7
GDP 3.5983 3 0.308 8
Stock prices 8.7761 3 0.032 9
Central bank assets 10.388 3 0.016 10
Gini coefficient 17.573 3 0.001 11
ALL 37.762 12 0.000 12
Stock prices (AEX index) 13
GDP 14.928 3 0.002 14
CPI headline inflation 6.7326 3 0.081 15
Central bank assets 9.3852 3 0.025 16
Gini coefficient .90986 3 0.823 17
ALL 28.924 12 0.004 18
Central bank assets 19
GDP 40.131 3 0.000 20
CPI headline inflation 3.2591 3 0.353 21
Stock prices 2.9306 3 0.402 22
Gini coefficient 5.1318 3 0.162 23
ALL 139.92 12 0.000 24
Gini coefficient 25
GDP 13.55 3 0.004 26
CPI headline inflation 3.581 3 0.310 27
Stock prices 16.953 3 0.001 28
Central bank assets 8.802 3 0.032 29
ALL 26.663 12 0.009 30
a. Impulse-response functions
In order to know more about the interconnectedness between the endogenous variables in our VAR model, we also use impulse-response functions since these functions specifically show how a variable responds to an impulse in another variable in a VAR model that contains a number of further
variables as well. In case there is a response of one variable to an impulse in another variable, then there is obviously a causal relationship and the latter causes the former one. On the other hand, the impulse response lines are horizontal and the impulse responses are zero if there is no causal relationship between variables.
Since the variables included in our baseline VAR model have various scales, we consider responses to innovations of one standard deviation (henceforth SD) instead of responses to unit
28
shocks. The horizontal axis for all the impulse-response graphs presented below is in the units of time that our VAR is estimated in, namely years. So, the impulse-response graphs on the next pages show the effect of a one standard deviation innovation over a 10-year period. The units of the
vertical axis in all panels in the figures below correspond to the Gini coefficient which has values from 0 complete equality to 1 complete inequality.
Table 9: The covariance matrix of the estimated residuals
Variable GDP CPI headline inflation Central bank assets Stock prices Gini coefficient
GDP .0005907
CPI headline inflation .0055294 .113691
Central bank assets -.0015739 -.026812 .0445262
Stock prices -.0048607 -.0773592 -.0072738 .1142499
Gini coefficient .0000511 .0003462 .0000837 -.0002099 .0000307
In all the relevant impulse-response figures, the orthogonalised impulse-response functions are graphed in order to mitigate the endogeneity bias. Also, the 95% confidence interval is sketched. One of the shortcomings of our baseline VAR model is that the residuals are correlated across equations, but this correlation is negligibly small (see Table 9). The orthogonalised impulse-response functions are used to completely eliminate this problem of the correlated estimated residuals. Our main purpose of using impulse-response functions is to examine how an equation is affected by a shock while at the same time all other shocks are kept constant. The orthogonalised impulse-response functions are impulse-impulse-response functions which correct for the correlation between the estimated residuals by taking Cholesky decomposition into consideration.
Figure 11: Impulse responses of Gini coefficient, cumulative response
29
Figure 11 shows three panels including the effect of a one-standard-deviation impulse to the AEX index, CPI headline inflation and central bank assets equation. We expected that monetary policy shocks – in this case, an increase in balance sheet total assets held by De Nederlandsche Bank - increase the income inequality. The response of Gini coefficient to a one-standard-deviation
innovation in central bank assets is graphed in the third panel in Figure 11, which shows income disparity falling by 0.116 percentage points to its lowest level over the year following the shock. It implies that in the short run monetary policy shocks decrease income disparity e.g. because central banks with a high degree of credibility fully concentrate on maintaining price stability which in turn helps economic agents who do not need to increase their prices for fear of higher inflation. In the long run, the income inequality passes the lowest level and there is even a slight increase, but it does not get higher than the initial level. Altogether, the Gini coefficient decreases over time. This result is not statistically significant since zero is always within the confidence band.
Table 10: Cumulative orthogonalised impulse responses and 95% confidence interval
This table belongs to Figure 11.
(1) AEX index (2) CPI headline inflation (3) Central bank assets
Step 0 1 2 3 4 5 6 7 8 9 10
Coirf* Lower** Upper S.E.***
.001399 -.000485 .003283 .000961 .001295 -.000549 .003139 .000941 .001348 -.001418 .004115 .001412 .00127 -.001908 .004448 .001622 .000949 -.002706 .004603 .001865 .001571 -.002401 .005543 .002026 .000676 -.003251 .004604 .002004 .00093 -.002881 .004742 .001945 .000727 -.003125 .004578 .001965 .001211 -.002512 .004934 .0019 .001035 -.002533 .004603 .00182
Coirf Lower Upper S.E.
-.000533 -.002498 .001433 .001003 -.001092 -.003197 .001013 .001074 -.000227 -.003011 .002558 .001421 .001148 -.001987 .004283 .0016 .00022 -.003246 .003686 .001769 .000805 -.002728 .004338 .001803 .000641 -.002778 .00406 .001744 .000555 -.002638 .003747 .001629 .000258 -.002913 .003429 .001618 .000628 -.002354 .003611 .001522 .000077 -.002988 .003143 .001564
Coirf Lower Upper S.E.
.000996 -.000945 .002938 .00099 -.00116 -.003141 .00082 .00101 -.000412 -.003353 .002529 .0015 -.000383 -.003981 .003214 .001835 .000605 -.003665 .004875 .002179 .000695 -.003959 .005348 .002374 .001156 -.003556 .005868 .002404 .00075 -.003756 .005256 .002299 .001149 -.003141 .005439 .002189 .000709 -.003174 .004592 .001981 .000771 -.002737 .004278 .00179
(1) irfname = varbasic, impulse = AEX index, and response = Gini coefficient
(2) irfname = varbasic, impulse = CPI headline inflation, and response = Gini coefficient (3) irfname = varbasic, impulse = Central bank assets, and response = Gini coefficient *Coirf: cumulated orthogonalised impulse-response function.
**Lower: 95% lower and upper bounds are reported. ***S.E.: Standard Error
Focusing on the materialisation of the portfolio channel, an unexpected impulse of one-standard-deviation to the AEX index is associated with a relatively stable movement of the Gini coefficient which very slowly rises for about 5 years, peaking at a 0.1571 percentage points increase 5 years after the impulse to the stock prices (see the first panel in Table 10). In the long run, the income inequality approaches the initial level. By and large, the stable movement of the widening income disparity prevails. It implies that an increase in stock prices does not necessarily result in a widening gap between high- and low-income earners. This could be explained by the fact that a very small majority in the top 10% or even in the top 1% benefit from higher stock prices which cannot directly be translated into a widening gap in the entire income distribution. The less widening income
