Inflation and income inequality in the Eurozone

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Inflation and Income Inequality in the

Eurozone

Robert Wolters

10167226

MSc. Economics, track Monetary Policy and Banking

Supervisor: Christian A. Stoltenberg

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Statement of Originality

This document is written by Robert Wolters who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is 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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Abstract

This paper empirically investigates the relationship between inflation and income inequality from 2005 until 2014 in the Eurozone. As my main result, I find that there is no significant relationship between the ECB’s inflation target and income inequality for the Eurozone as a whole. This insignificance is robust with respect to various measures of income inequality. However, I find a significant relationship for some individual countries. In France, increases in the inflation target decreases income inequality, whereas it increases income inequality in Greece. For the remaining countries, the effect is ambiguous.

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1. Introduction

Since the release of “Capital in the 21st_{century” (Piketty, 2014), income and wealth inequality}

gained importance in the social debate and in policy debates. Piketty claims that the return on wealth exceeds the growth rate of the economy, which will increase inequality on a global level. Piketty was not the first to study the main driving forces behind the dynamics of income inequality. A variety of studies were conducted to identify fiscal policy as the most important factor in the explanation of the dynamics of income inequality. For example, the IMF (2014) describes fiscal policy as the main tool for governments to affect the income distribution. However, there is very little attention for the impact of monetary policy or, more generally, inflation.

Coibion et al. (2012) were among the first to investigate the link between monetary policy and different types of inequality. Whereas they studied this relationship for the United States as a whole, I think it is also important to look at a situation in which a central bank conducts monetary policy for a group of countries. Therefore, I would like to look at the case for the Eurozone, in which the ECB makes an interest rate decision for countries in the Euro area, with a common inflation target in mind. I will try to answer the following research question: What is the relationship between inflation and income inequality in the Eurozone? I will use data for the EU17 group as a proxy of the Eurozone as a whole and data for countries in the EU12 group to look at the effect for individual countries1_.

To answer this question, I estimate the relationship between the inflation tax and the after-tax Gini-coefficient for nominal income, as suggested by Albanesi (2007). After that, I estimate a New Keynesian model proposed by Ireland (2007) , to extract an unobserved inflation target for the Eurozone. Using this inflation target, I use regression analysis to explore the relationship between the inflation target and a variety of income inequality measures.

I will look at the Eurozone as a whole and countries individually. Furthermore, I will use real GDP per capita and government expenditures as percentage of the GDP as control variables. As my main result, I find that there is no relationship between the ECB’s inflation target and income inequality in the Eurozone as a whole. This insignificance is robust to various

1_EU12:_{Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal,}

and Spain.

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measurements of income inequality. However, I find a significant relationship between the inflation target and after taxes income inequality for France and Greece, which is robust to all specifications. The negative relationship for France can be explained by the fact that higher inflation diminishes the real return on savings for a constant nominal interest rate. Since capital income is the main source of income for agents in the upper percentiles of the income distribution, this mechanism reduces income inequality. In the literature, this mechanism is called the “savings-redistribution channel” (Saiki & Frost, 2014). The positive relationship for Greece can be explained by the fact that nominal wages tend to be rigid (Nickell & Quintini, 2003). Thus, an increase in the inflation target decreases real wages. If labor income is the main source of income for those in the lower percentiles of the income distribution, income inequality increases. This mechanism is called the “income composition channel” (Coibion, et al., 2012).

In the first part of this thesis, I provide a review of the literature about income inequality, measurements of income inequality, inflation and monetary policy. In the second part, I explore the relationship between the inflation tax and the pre-tax Gini-coefficient, following Albanesi (2007). In the third part, I explain the method used to estimate the implied unobserved inflation targets over time, using the New Keynesian model and the estimation method as proposed by Ireland (2007). The last part contains the results and concluding remarks.

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2. Literature review

This section provides an overview of the relevant literature and measurements of the variables of interest. As stated earlier, there is not much work done on the link between monetary policy and income inequality or inflation and inequality. First, I briefly discuss different measurements of income inequality. Second, I give an overview on the relation between inflation and income inequality. At the end of this chapter, I look at the research done on monetary policy and income inequality and describe the channels through which monetary policy and inflation might have an impact on income inequality. The combination of the last two topics is essential, because the main part of this thesis combines the former and the latter; it is about the relationship between the unobserved inflation target , which is a measurement of monetary policy, and income inequality.

2.1 Measures of income inequality

The most common way to measure income inequality is to calculate the Gini-coefficient. This coefficient has a range from 0 to 1, or as used later on in this thesis, from 0 to 100. If the Gini-coefficient is 0, income is perfectly equal distributed, while a value of 1 (or 100 respectively) means complete inequality of the income distribution (Piketty, 2014). Despite its common usage, this measure has some shortcomings in telling the story of income inequality at all levels of the distribution. One single number does not tell anything of what is going on at certain points of the distribution, for example the extremes: the bottom 10 % or the top 10 % of the income distribution (Piketty, 2014). To solve this problem, income equality is sometimes measured by calculating the ratio of the income earned by the 9th decile divided by the income earned by the 1st decile. But this raises another problem: data on the mean income at the top of the income distribution is absent most of the times. To deal with this, the ratio of the shares of total income for these two deciles is calculated. If the share of total income earned by the bottom 90% is known, it is possible to calculate the share of total income earned by the top 10%. It is simply the remaining share of total income. Later on in this thesis, I will use the S80/S20 ratio, which is the top 20% share divided by the bottom 20% share

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2.2 Inflation and income inequality

There is some research done on the impact of inflation on income inequality. The most recent contribution has been made by Albanesi (2007). Using a large dataset which contains 51 industrialized countries between 1966 and 1990, she calculates the average inflation tax of this period for each country. The inflation tax is calculated as follows: 𝜋

1+𝜋 , where 𝜋 is the

yearly inflation rate.

After that, she regresses the average inflation tax on the average Gini-coefficient for each country. She finds the following relationship: a higher average degree of income inequality will increase the average inflation tax. This relationship is roughly the same when she uses a different measure of income inequality: the average income per capita of the top 40 % of the population divided by the average income per capital of the bottom 60 %. The most important contribution is the monetary economy model she used to provide an explanation for the found link. In this model, fiscal and monetary policy is determined by a political bargaining game. Excluding countries with an average inflation rate which excess 60% per annum, she concludes that the model is able to explain 41% of the correlation between inequality and inflation (Albanesi, 2007).

2.3 Monetary policy and income inequality

Coibion, et al., (2012) looked at the direct link between monetary policy shocks and several measures of inequality in the US from 1980 till 2008, the year in which the zero lower bound for monetary policy is reached. Because they use detailed micro-data from the Consumer Expenditure Survey (CEX), they were able to distinguish between total income inequality, consumption inequality, labor earnings inequality and expenditure inequality. They find the following relationship: a sudden increase in the policy rate, i.e. a contractionary monetary policy shock, increases all measures of inequality. In order to explain the economic mechanism behind these results, they also looked at the responses of labor earnings in different percentile groups. At the upper end of the distribution, labor incomes increase following a contractionary monetary policy shock. At the same time, labor incomes at the lower end of the distribution fall. The authors conclude that this results point at the need for new elements inside economic models. They argue that monetary policy is mainly conducted through changes in the interest rates (Coibion, et al., 2012). Contractionary monetary policy shocks can be described as a

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sudden increase in the interest rate. This means that investing in additional capital becomes more expensive, which reduces the demand of capital. When I assume that low skilled labor and capital are complements and high skilled labor and capital are substitutes , an increase in the interest rate reduces low skilled labor demand and increases high skilled labor demand. From this point of view, including the substitutability/complementarity of capital with high skilled and low skilled labor in economic models can describe the results found by Coibion et al. (2012).

While monetary policy shocks are more of a temporary nature, Coibion, et al., (2012) also investigated whether this relationship holds for a more structural change in the monetary policy regime. To do so, they used two methods to estimate the Fed’s target rate of inflation. For the first method, the Fed’s reaction function was estimated using real forecasts of each Federal Open Market Committee (FOMC) meeting from the Greenbook. The second method uses an estimation method introduced by Ireland (2007). This method consists of a New-Keynesian model with Taylor rule, which is estimated using Maximum Likelihood using actual values for GDP, its deflator and the Federal Fund Rate. I will explain more about this method in chapter 4, since I use it myself to answer the research question. Using these two methods, the conclusion remains the same: a decrease in the unobserved inflation target increases all inequality measures.

One limitation of the analysis by Coibion, et al. (2012), is that it does not include the zero lower bound period in which the Fed introduced quantitative easing and other extraordinary measures. Saiki and Frost (2014) tried to look at the relationship between unconventional monetary policy and income inequality in Japan. Using quarterly data from 2008Q4 till 2014Q1, they conducted a VAR analysis with the top20%/bottom20% - ratio as inequality measure. Their results suggest that unconventional monetary policy increases this measure of income inequality, mainly via the portfolio channel. Because of the short time-horizon used in this paper, it is questionable whether this relationship holds for a longer time span.

Channels through which monetary policy and inflation might have an impact on income inequality

In this thesis, I will focus on the relationship between inflation and income inequality. The relationship between inflation and wealth inequality is also interesting to explore, but it is beyond the scope of this thesis. Therefore, I will only discuss the ways in which inflation might

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influence income inequality. The most important and direct one is the savings redistribution channel (Saiki & Frost, 2014). If inflation increases, the real return on savings (assuming that the nominal return remains the same) will decrease. Thus, the real income from savings will be smaller. In the US and France, the share in total income of the fraction of capital income is larger for the upper part of the income distribution than it is for the lower part of the income distribution (Piketty, 2014, pp. 271-303). This means that the people in the highest deciles receive a greater percentage of their total income from return on savings. As a consequence, a higher rate of inflation diminish a substantial part of top-incomes and decreases inequality.

Another channel following from this mechanism is the income composition channel (Coibion, et al., 2012). As said before, the income composition differs among the income distribution. Higher incomes rely mostly on returns on savings, while labor income tends to be the primary source of income for lower incomes. As we know from the literature (for example, (Nickell & Quintini, 2003)), wages tend to be rigid, for example: because wages are negotiated by labor unions and are part of labor contracts. As a result, when inflation suddenly increases, real wages will decrease. Given the fact that lower incomes rely relatively more on labor income than higher incomes, this mechanism has a positive effect on income inequality: an unexpected rise in inflation will increase income inequality.

There are also channels which describe the effect of monetary policy on income inequality. The most direct channel is the portfolio channel (Saiki & Frost, 2014). The idea behind this channel is that monetary policy influences asset prices. For example, if the central bank wants to lower the interest rate because of poor economic forecasts, the board of directors will decide to buy assets, which will lead to a price-increase of these assets. This price increase in turn leads to a lower rate of return on these assets, but also in a capital gain for asset holders. If asset-holdings are mostly concentrated in the upper part of the income distribution, expansionary monetary policy as described above, will increase income inequality because of the increase in capital gains.

Related to the portfolio channel is the financial segmentation channel (Coibion, et al., 2012). This channel describes the importance of access to financial markets. It predicts that agents who are more frequently in contact with the financial market will benefit more from increases in the money supply (Coibion, et al., 2012). If these agents are assumed to be in the upper part of the income distribution, the higher incomes benefit more than the lower incomes. Thus, this mechanism increases income inequality.

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3. The long-run relationship between inflation and income

inequality in the Eurozone

In the literature review, I discussed the paper by Albanesi (2007), which explores the long run relationship between the average inflation tax and the average degree of income inequality before taxes. In this chapter, I will investigate this relationship for the Eurozone and compare the results with the findings of Albanesi (2007).

3.1 The relationship between average inflation tax and average

Gini-coefficient

Albanesi (2007) found the following relationship through a simple OLS regression: in the long run, a higher average degree of income inequality (before taxes) is associated with a higher average inflation tax. In order to compare my results with the results she found, I will follow her methodology for the group countries which are together called the EU12. This group consists of the following countries: Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal and Spain.

Because of data availability problems, I will use after-taxes Gini-coefficients (on a scale of 0-100) for total income, or in Eurostat terminology: equivalised and disposable income. These Gini-coefficients and inflation rates (HICP) for EU12 countries from 1999 till 2014 can be found at Eurostat. 2 Before-taxes Gini-coefficients are only available from 2005 till 2014: using these coefficients in a regression gives insignificant results. It could be the case that there is no significant relationship at all. Another problem is the short time horizon : Albanesi (2007) investigated the long run relationship between inflation tax and income inequality. This relationship might not exist in the short run. Therefore, if I do the same regression for the EU17 countries, I encounter the same problem. Summary statistics of the data I use in the regression can be found in appendix A1.

The results are listed in appendix A1. I find a positive significant relationship between the inflation tax and the degree of income inequality. The standard deviation for the mean Gini-coefficient is 3.24, which is tabulated in table A1 in appendix A1. I interpret the result in table A2 in appendix A1 as follows: for a 1 standard deviation increase in the average

2_{HICP: http://ec.europa.eu/eurostat/web/hicp/data/database}

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coefficient, the inflation tax will increase with approximately 0.01923 percentage points in the long run. Compared to what Albanesi (2007) found for 51 countries over the period between 1966 and 1990 , this effect is much smaller. This could be explained by the shorter time horizon of my analysis. Besides that, it could be caused by the fact that all countries in my sample are all developed countries which are member of the same monetary union. Albanesi (2007) also performed the same regression for 15 developing countries, with a non-significant result and a similar value for R-square. It could be the case that there is no relationship between inflation tax and income inequality at all for a sample of countries with roughly the same levels of inequality and inflation.

In the total sample used by Albanesi (2007), the standard deviation of the mean-Gini coefficients is approximately 7: this is much higher than the standard deviation in my sample (see table A1). This supports the reasoning that the countries in my sample are more similar than the countries in Albanesi’s (2007) sample.

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4. Estimating the New Keynesian Model

In the Eurozone, the ECB conducts monetary policy for the Eurozone as a whole. It has one inflation target for all countries in the Eurozone. To answer the research question, I explore the relationship between the ECB’s inflation target and income inequality. However, the inflation target of the ECB is “below, but close to 2 %”3_{. This means that the information about the}

observable inflation target does not change over time, which makes it impossible to explore any relationship. Therefore, I use a New Keynesian model to estimate the unobserved inflation target. I use these estimates to investigate whether there is a relationship between the ECB’s inflation target and income inequality.

In this section, I discuss and explain the New Keynesian model proposed by Ireland (2007) and the estimation method I use to obtain the coefficients of the model. I will start with a description of the model and the assumptions for each sector in the model. After that, I will describe how the model is estimated. Moreover, I present the estimation results and give the implications of these results.

4.1 Description of Ireland(2007)’s model

Ireland (2007) describes a standard New Keynesian model. It consists of a representative household, a representative finished producing firm and a group of intermediate goods-producing firms. The last description means that there are many intermediate goods-goods-producing firms, each producing a different intermediate good.

Each households enters the period with money holdings for transactions and savings in bonds from the previous period. In the period itself, it obtains dividends from intermediate goods firms and it receives income from labor. The last source of income for the household, is a nominal transfer from the central bank. With these sources of income, the household makes a decision on how much to consume, how many labor hours to supply, how much to invest in bonds and on the amount of money holdings for transactions. The households choose these amounts in order to maximize the expected utility function (21) and to satisfy the budget constraint (20) . The finished goods firms decides how much of the intermediate good it uses in its production technology to maximize its profits. Intermediate goods firms act under monopolistic competition, which means they are able to set prices above marginal costs in

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order to receive a markup. The intermediate goods firm determines its price and the amount of labor to hire from the household, to maximize its expected real market value. Furthermore, the model includes a social planner, which decides upon the efficient output level and the amount of labor supplied by households. More details on the behavior of households, finished goods firms, intermediate goods firms, the social planner and the equilibrium conditions can be found in appendix A2.

4.2 The central bank and the inflation target

An important extension compared to the basic New Keynesian model is a central bank which follows a modified Taylor-rule (Taylor, 1993). This Taylor-rule is specified as follows:

ln(𝑅_𝑡) = ln(𝑅𝑡−1) + 𝜌Πln(Π𝑡⁄Π𝑡∗) + 𝜌𝑔𝑦ln(𝑔𝑡 𝑦

𝑔𝑦

⁄ ) + ln(𝑣_𝑡) (𝟏) where 𝑅_𝑡 is the nominal interest rate, Π_𝑡 actual inflation, and Π_𝑡∗_{the inflation target. 𝑔}

𝑡 𝑦

and 𝑔𝑦

represent the actual output growth and the steady state output growth respectively. In this equation, 𝜌_Π and 𝜌_𝑔𝑦 are response coefficients, chosen by the central bank. 𝜌_Π is assumed to be positive, while 𝜌𝑔𝑦 is assumed to be non-negative. Hence, the central bank lowers its policy

rate if inflation (Π_𝑡) is below its steady state value. The same holds for the growth rate of output 𝑔_𝑡𝑦, if 𝜌_𝑔𝑦 is non-zero. The transitory policy shock 𝑣_𝑡 is described by the following autoregressive process:

ln(𝑣_𝑡) = 𝜌𝑣ln(𝑣𝑡−1) + 𝜎𝑣𝜀𝑣𝑡 (𝟐)

with 0 ≤ 𝜌𝑣 < 1 ,𝜎𝑣 ≥ 0 and 𝜀𝑣𝑡 is a serially uncorrelated innovation which follows the

standard normal distribution with mean zero.

The inflation target Π_𝑡∗_{follows a random walk and responds to shocks to the variables}

for cost-push shocks (𝜃_𝑡), technology shocks (𝑍_𝑡) and to standard normal distributed (mean zero) inflationary shocks (𝜀_𝜋𝑡). Thus, the inflation target follows a random walk:

ln(Π_𝑡∗) = ln(Π_𝑡−1∗ _{) − 𝛿}

𝜃𝜀𝜃𝑡−𝛿𝑧𝜀𝑧𝑡 + 𝜎𝜋𝜀𝜋𝑡 (𝟑)

where all response coefficients (𝛿_𝜃, 𝛿_𝑧 and 𝜎_𝜋) are non-negative. According to this specification, the inflation target increases if there are inflationary shocks or positive shocks to the habit formation variable. The inflation target decreases if there is a cost-push shock or a technology shock. Besides its appearance in equation (1), the inflation target also enters in the

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profit function of intermediate goods firms. As I describe in appendix A2, it is assumed that intermediate goods firms incur price adjustment costs. It depends on the parameters of the models whether intermediate goods firms can adjust prices in line with the current inflation target or in line with the inflation rate from the previous period.

4.3 Log linearizing the model around the steady state

In the steady state, every variable in the stationary model, which consists of (44)-(59) in appendix A2, is at its long rung equilibrium and every shock in the model is equal to its mean: 𝑦_𝑡 = 𝑦, 𝑐_𝑡= 𝑐, 𝜋_𝑡 = 𝜋, 𝑟_𝑡 = 𝑟, 𝑞_𝑡 = 𝑞, 𝑥_𝑡 = 𝑥, 𝑔_𝑡𝑦 = 𝑔𝑦, 𝑔_𝑡𝜋 = 𝑔𝜋,

𝑔_𝑡𝑟 = 𝑔𝑟, 𝑟_𝑡𝑟𝜋 = 𝑟𝑟𝜋 , 𝜂𝑡 = 𝜂, 𝑎𝑡 = 𝑎, 𝜃𝑡 = 𝜃, 𝑧𝑡 = 𝑧 , 𝑣𝑡 = 𝑣 𝑎𝑛𝑑 𝜋𝑡∗ = 𝜋∗𝑓𝑜𝑟 𝑒𝑣𝑒𝑟𝑦 𝑡

I apply the steady state conditions to each equation of the stationary system in appendix A2, starting with (45), (48), (49), (58) and (59) to obtain the following steady state values: 𝑎 = 1, 𝜃 = 1, 𝑧 = 1, 𝑣 = 1 𝑎𝑛𝑑 𝜋∗= 1.

With these steady state values and from equation (57), it follows that 𝜋 = 1. Using this information and equations (44), (51), (52) and (53), I obtain the following steady state conditions: 𝑐 = 𝑦, 𝑔𝑦 _{= 𝑧, 𝑔}𝜋 _{= 1 𝑎𝑛𝑑 𝑔}𝑟 _{= 1}

Then I solve equation (50) for 𝜂 in the steady state: 𝜂 = 𝜃 (𝜃 − 1)⁄ Using steady state values and 𝑐 = 𝑦, I solve (46) for y:

𝑦 = (𝜃 − 1 𝜃 ) (

𝑧 − 𝛽𝛾 𝑧 − 𝛾 ) From (55),I find the steady state solution for q :

𝑞 =𝑧 − 𝛽𝛾 𝑧 − 𝛾

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𝑥 =𝜃 − 1 𝜃 As a final step, I am able to simplify (47) towards:

𝑟 = 𝑧/𝛽

Since the inflation rate in the steady state is equal to one, the same holds for 𝑟𝑟𝜋.

In order to analyze how the economy reacts to shocks according to the model, I have to log-linearize the model around the steady state. The first step is to define log linearized variables, which measure the deviation of its steady state value in percentages:

𝑦̂_𝑡 = ln(𝑦_𝑡⁄ ) ,𝑦 𝑐̂ = ln(𝑐_𝑡 _𝑡⁄ ) ,𝑐 𝜋̂_𝑡 = ln(𝜋_𝑡⁄ ) = ln(𝜋𝜋 _𝑡) , 𝑟̂_𝑡= ln(𝑟_𝑡⁄ ), 𝑟 𝑞̂ = ln(𝑞𝑡 𝑡⁄ ) , 𝑥̂𝑞 𝑡 = ln(𝑥𝑡⁄ ) , 𝑔̂𝑥 𝑡 𝑦 = ln (𝑔_𝑡𝑦/𝑔𝑦), 𝑔̂𝑡𝜋 = ln (𝑔𝑡𝜋⁄𝑔𝜋) = ln (𝑔𝑡𝜋), 𝑔̂_𝑡𝑟_{= ln (𝑔} 𝑡𝑟), 𝑟̂𝑡𝑟𝜋 = ln (𝑟𝑡𝑟𝜋⁄𝑟𝑟𝜋) , 𝜂̂𝑡= ln (𝜂𝑡/𝜂), 𝑎̂𝑡 = ln (𝑎𝑡/𝑎) = ln (𝑎𝑡), 𝜃̂_𝑡 = ln (𝜃_𝑡/𝜃), 𝑧̂_𝑡= ln (𝑧_𝑡/𝑧) , 𝑣̂_𝑡= ln (𝑣_𝑡) and 𝜋̂_𝑡∗ _{= ln (𝜋} 𝑡∗)

The second step is to replace each variable 𝑑_𝑡 by 𝑑 ∙ 𝑒𝑑̂𝑡_{(where 𝑑 is the steady state value) and} to apply a first-order Taylor approximation to all equations. Following these steps for equation

(44) gives: 𝑐̂𝑡 = 𝑦̂𝑡. If I do the same for the remaining equations, the system of equations

becomes: 𝑐̂𝑡 = 𝑦̂𝑡 (𝟒) 𝑎̂_𝑡= 𝜌_𝑎𝑎̂_𝑡−1+ 𝜎_𝑎𝜀_𝑎𝑡 (𝟓) (𝑧 − 𝛾)(𝑧 − 𝛽𝛾)𝜂̂𝑡 = 𝛾𝑧𝑦̂𝑡−1− (𝑧2+ 𝛽𝛾2)𝑦̂𝑡+ 𝛽𝛾𝑧𝐸𝑡𝑦̂𝑡+1+ (𝑧 − 𝛾)(𝑧 − 𝛽𝛾𝜌𝑎)𝑎̂𝑡− 𝛾𝑧𝑧̂𝑡 (𝟔) 𝜂̂𝑡 = 𝑟̂𝑡+ 𝐸𝑡𝜂̂𝑡+1− 𝐸𝑡𝜋̂𝑡+1 (𝟕) 𝑒̂_𝑡 = 𝜌_𝑒𝑒̂_𝑡−1+ 𝜎_𝑒𝜀_𝑒𝑡 (𝟖) 𝑧̂𝑡 = 𝜎𝑧𝜀𝑧𝑡 (𝟗) (1 + 𝛼𝛽)𝜋̂𝑡= 𝛼𝜋̂𝑡−1+ 𝛽𝐸𝑡𝜋̂𝑡+1− 𝜓𝜂̂_𝑡+ 𝜓𝑎̂𝑡− 𝑒̂𝑡− 𝛼𝜋̂𝑡∗ (𝟏𝟎) 𝑔_𝑡𝑦 = 𝑦̂𝑡− 𝑦̂𝑡−1+ 𝑧̂𝑡 (𝟏𝟏) 𝑔_𝑡π = 𝜋̂_𝑡− 𝜋̂_𝑡−1+ 𝜋̂_𝑡∗_(𝟏𝟐)

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14 𝑔_𝑡𝑟 _{= 𝑟̂} 𝑡− 𝑟̂𝑡−1+ 𝜋̂𝑡∗ (𝟏𝟑) 𝑟𝑡𝑟π = 𝑟̂𝑡− 𝜋̂𝑡 (𝟏𝟒) 0 = 𝛾𝑧𝑞̂𝑡−1− (𝑧2 + 𝛽𝛾2) ∙ 𝑞̂𝑡+ 𝛽𝛾𝑧𝐸𝑡∙ 𝑞̂𝑡+1+ 𝛽𝛾(𝑧 − 𝛾)(1 − 𝜌𝑎) ∙ 𝑎̂𝑡− 𝛾𝑧𝑧̂𝑡 (𝟏𝟓) 𝑥̂_𝑡 = 𝑦̂_𝑡− 𝑞̂_𝒕 (𝟏𝟔) 𝑟̂_𝑡 = 𝑟̂_𝑡−1+ 𝜌_π𝜋̂_𝑡+ 𝜌_𝑔𝑦𝑔̂_𝑡𝑦−𝜋̂_𝑡∗+ 𝑣̂_𝑡 (𝟏𝟕) 𝑣̂𝑡 = 𝜌𝑣𝑣̂𝑡−1+ 𝜎𝑣𝜀𝑣𝑡 (𝟏𝟖) 𝜋̂_𝑡∗ _{= 𝜎} 𝜋𝜀𝜋𝑡− 𝛿𝑒𝜀𝑒𝑡−𝛿𝑧𝜀𝑧𝑡 (𝟏𝟗) where 𝜓 = (𝜃 − 1)/𝜙, 𝑒̂𝑡 = (1 𝜙⁄ )𝜃̂𝑡, 𝜌𝑒= 𝜌𝜃, 𝜎𝑒= 1

𝜙𝜎𝜃, 𝛿𝑒= 𝛿𝜃 and 𝜀𝑒𝑡 follows the standard

normal distribution.

I use actual data for the outcomes of equations (11), (12) and (14) to estimate the parameters of the model, which consists of equations (4)-(19), with maximum likelihood estimation. More details on the estimation method can be found in appendix A3.

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15

4.4 Estimation procedure

Ireland (2007) has written a Matlab-code in which the growth rates of output, inflation and the ratio of the nominal interest rate to inflation are used as input4. Given the availability of inequality measures, I will estimate the model for two groups: the EU12 group in the period 2014 and the EU17 group between 2005 and 2014. The EU12 group in the period 1999-2014 consists of the following countries: Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, and Spain. The EU17 group between 2005 and 2014 consists of the same countries as the EU12 with five additional countries: Cyprus, Estonia, Malta, Slovenia and Slovakia.

For output, I use quarterly data for real gross domestic product in 2010 prices (seasonally adjusted and adjusted data by working days) divided by the population. To obtain a measure of the price level, I compute the implicit price deflator by dividing the nominal measure of GDP by the real measure of GDP in 2010 euros to obtain the GDP deflator in 2010 prices, following the procedure of Ireland (2007). These datasets are available at Eurostat5. For the short-term nominal interest rate 𝑅_𝑡 I use data on the 3 month EURIBOR rate6.

In order to get growth rates, I take the log of these variables and I calculate the difference between periods:

log(𝑥𝑡) − log (𝑥𝑡−1).

With this data as given, the first step is to calculate values for 𝑧 and 𝛽 to make sure that the steady state in the model matches the steady state values of output growth and the ratio of nominal interest to inflation in the data: 𝑔𝑦 = 𝑧, 𝑟𝑟𝜋 = 𝑧/𝛽. These values for the EU12 and the EU17 group can be found in table 1. In order to compare my results with Ireland’s (2007) findings, I will make the same assumption regarding the coefficient on real marginal costs and the degree of price adjustment costs. Thus, I assume 𝜓 to be 0.10, which implies that goods prices remain fixed for an average of 3.7 quarters (Ireland, 2007). Ireland (2007) made this

4_{Which can be found at: https://www2.bc.edu/peter-ireland/programs.html}

5_{GDP data : http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=namq_10_gdp&lang=en}

Population: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=namq_10_pe&lang=en

6_{Which can be found at the ECB’s Statistical Data Warehouse (SDW):}

http://sdw.ecb.europa.eu/quickview.do?trans=QF&start=&submitOptions.y=0&submitOptions.x=0&end=&SE RIES_KEY=143.FM.M.U2.EUR.RT.MM.EURIBOR3MD_.HSTA&periodSortOrder=ASC

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assumption, because when he estimates this coefficient freely along with the other 14 coefficients, he found very small estimates of 𝜓. This implies very high adjustment costs and, as a consequence, a very high degree of price stickiness for intermediate goods firms, which is not realistic.

Table 1: Pre-estimation steady state values

While these three parameters are fixed beforehand, I will use maximum likelihood estimation to obtain estimates for the remaining 14 parameters of the model. More information on this estimation method can be found in appendix A3. To obtain estimates and standard errors, I use a parametric bootstrapping method (Ireland, 2007). This method first generates 1000 artificial samples for the growth rates of output and inflation and the nominal interest rate to inflation rate ratio, with the same number of observations as the real dataset. After that, these 1000 artificial data samples are used to estimate the model with the maximum likelihood method, which generates 1000 possible estimates. These 1000 estimates form a sample, which has a mean and standard deviation. The last step is to calculate the mean and standard deviation, which will lead to an estimate and a bootstrapped standard error (Johnson, 2001). The results for this estimation method, together with the value of the log-likelihood function, can be found in table 2.

Group 𝑧 𝑧/𝛽 𝛽 EU 12 1.0019 1.0021 0.9998

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Table 2: Maximum Likelihood estimates and Bootstrapped standard errors, rounded to four digits. L denotes the maximized value of the log-likelihood function.

The estimation results show that the degree of backward looking (𝛼) is equal to zero. In other words, it is costless for intermediate goods firms to adjust their prices in line with the current period inflation target. The habit formation coefficients (𝛾) range between 0.42 and 0.59. When I compare this to what Ireland (2007) found in the US, relative consumption is more important in the Eurozone than it is for the US (Fuhrer, 2000). Similar to Ireland (2007), 𝜌𝜋 and 𝜌𝑔𝑦 are both significant, which means that inflation and output growth are significant

in the Taylor-rule. For both groups, the preference shock seems to be persistent, since 𝜌_𝑎 is close to one and significant. The persistence of cost push shocks and transitory monetary policy shocks (measured by 𝜌_𝑒 and 𝜌_𝑣) are significant in the EU12 group, whereas they are not in the EU17 group. Moreover, the inflation target can be determined by inflationary shocks (𝜎𝜋𝜀𝜋𝑡),

cost push shocks (𝛿_𝑒𝜀_𝑒𝑡) or technology shocks (𝛿_𝑧𝜀_𝑧𝑡). For the EU12 group, only inflationary shocks are important in the process of inflation targeting, while the inflation target for the EU17 group is mainly determined by cost push shocks.The volatilities of all shocks are roughly the same for both groups, with the exception of the volatility of the inflationary shock (𝜎_𝜋). In the EU12 group, this volatility is estimated to be 0.0004, whereas the estimate for the EU17 group turns out to be zero.

Parameter EU12 estimate EU12 bootstrapped std. error

EU17 estimate EU17 bootstrapped std. error 𝛾 0.5872 0.0606 0.4211 0.0598 𝛼 0.0000 0.0548 0.0000 0.0263 𝜌𝜋 0.3271 0.0356 0.3857 0.0237 𝜌𝑔𝑦 0.1638 0.0210 0.1183 0.0086 𝜌𝑎 0.8545 0.0448 0.8456 0.0369 𝜌_𝑒 0.3741 0.1227 0.0000 0.0001 𝜌_𝑣 0.2058 0.0797 0.1520 0.0813 𝜎𝑎 0.0168 0.0026 0.0183 0.0022 𝜎_𝑒 0.0002 0.0004 0.0005 0.0003 𝜎𝑧 0.0124 0.0013 0.0122 0.0011 𝜎_𝑣 0.0009 0.0001 0.0007 0.0000 𝜎_𝜋 0.0004 0.0002 0.0000 0.0001 𝛿𝑒 0.0000 0.0001 0.0003 0.0001 𝛿_𝑧 0.0000 0.0001 0.0000 0.0001 L 919.266 514.052

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5. The relationship between income inequality and the

unobserved inflation target

In this section, I will analyze whether the dynamics of income inequality can be explained with the unobserved inflation target, a variable which summarizes the behavior of the central bank. In order to do so, I will first estimate the unobserved inflation target for the Eurozone as a whole . After that, I regress different measures of income inequality on the estimated inflation target through simple OLS and draw conclusions from these regressions.

5.1 Estimates of the unobserved inflation target

In section 4.4, I estimated the model using the maximum likelihood method. In this section I use the estimated coefficients to obtain values for the unobserved inflation target. In order to do so, I have to estimate the unobserved state vector first, which is given by:

𝜉𝑖 = [𝑎̂𝑡 𝑒̂𝑡 𝑧̂𝑡 𝑣̂𝑡 𝜋̂𝑡∗]

To estimate this vector, I use the method used by Ireland (2007) and described in more detail by Hamilton (1994). This method exploits the information contained in the actual data to generate data on the unobserved inflation target. In appendix A3, I give more information about this method.

In figure 1 , I plot the unobserved inflation target 𝜋∗_{against the actual inflation rate 𝜋}

(measured by the implicit GDP deflator, which I calculated in section 4.4 ) over time for the EU12 and the EU17 group as a whole.

Figure 1: Actual inflation and inflation target for EU12 and EU17 in %

0 0,5 1 1,5 2 2,5 3 3,5 4 1999Q 1 1999Q 4 2000Q 3 2001Q 2 2002Q 1 2002Q 4 2003Q 3 2004Q 2 2005Q 1 2005Q 4 2006Q 3 2007Q 2 20 08 Q 1 2008Q 4 2009Q 3 2010Q 2 2011Q 1 2011Q 4 2012Q 3 2013Q 2

Inflation targets and actual inflation

Actual inflation EU12 Inflation Target EU17 Inflation Target

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5.2 After-taxes Gini coefficients

In order to estimate the effect of changes in the unobserved inflation target of the central bank on income inequality, I will estimate the following equation using OLS:

𝑖𝑛𝑒𝑞𝑢𝑎𝑙𝑖𝑡𝑦𝑚𝑒𝑎𝑠𝑢𝑟𝑒_𝑖 = 𝛼_𝑖 + 𝛽_𝑖 ∙ 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑡𝑎𝑟𝑔𝑒𝑡 + 𝜀_𝑖

All measurements of income inequality are for equivalised total income. Thus, it includes all sources of income, such as labor income and capital gains. This is one drawback of my thesis: I cannot diversify between sources of income, like Coibion et al. (2012) did. I can only differentiate between before and after taxes inequality measures: more about this in section 5.4.

I will start with after-taxes measurements of income inequality, since this corresponds the most with reality. Yearly data on the after-taxes Gini coefficients for all countries in the EU12 group and for the EU17 group as a whole is available on Eurostat from 2005 until 2014

7_{. Because of the yearly frequency of the data on inequality, I aggregate the quarterly estimates}

of the unobserved inflation target to yearly data. In figures 2 and 3, I plot the values for the after tax Gini-coefficients for all countries over time, with the after tax Gini-coefficient for the EU17 group as a whole as a reference point.

When I look closely at the plot for the EU17 as a whole in figure 3, I see an upward trend. From figure 1 on the previous page, I conclude that the data on the inflation target contains a downward trend.

7_{Source: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=ilc_di12&lang=en} 26 27 28 29 30 31 32 33 34 35 36 37 38 39 2005 2006 2007 2008 2009 2010 2011 2012 2013

After taxes Gini-coefficients (1)

EU17 France Greece Ireland Italy Spain Portugal 24 25 26 27 28 29 30 31 2005 2006 2007 2008 2009 2010 2011 2012 2013

After taxes Gini-coefficients (2)

EU17 Austria Belgium Finland Germany Netherlands Luxembourg

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Therefore, if I perform an OLS regression with this data, it will give spurious results. The correlations found in this regression can be caused solely by both trends. As a consequence, the estimates will be invalid. The results from this procedure can be found in table 3. “GiniEU17” is the after taxes Gini-coefficient (0-100) for the EU17 group as a whole, “pistar” is the inflation target measured in %, “ycap” the real GDP per capita in thousands of Euros and “gtogdp” the government expenditures to nominal GDP ratio in % 8_{. As expected from both}

trends, the relationship is negative, but as I said before, these results are invalid.

Table 3: EU17 regressions

To obtain results which are statistically valid, I have to remove the trend from the data. To do this, I use the Hodrick-Prescott (HP) filter (Hodrick & Prescott, 1997), with smoothing parameter 400 to capture the annual frequency of the data. It filters the trend component out of the data, and returns the stationary part as output. Thus, the result of applying this filter to all variables is that the data becomes stationary. Hence, using this data in my regressions gives results which are statistically valid. The results can be found in table 4.

8_{For real GDP per capita, I use data from footnote 4. Readings on government expenditures to GDP can be}

found at Eurostat: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=gov_10a_main&lang=en (1) giniEU17 (2) giniEU17 (3) giniEU17 (4) giniEU17 pistarEU17 -1.389*** (0.297) -1.643*** (0.251) -1.745** (0.679) -1.504 (0.716) ycapEU17 0.266* (0.132) 0.525 (0.457) gtogdpEU17 -0.0816 (0.0812) 0.0991 (0.185) constant 32.04*** (0.366) 24.68*** (3.779) 36.50*** (4.630) 12.15 (21.53) N adj. R-sq 9 0.712 9 0.784 8 0.582 8 0.609 Robust standard errors in parentheses, * p<0.10, ** p<0.05, *** p<0.01

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Table 4: EU17 regressions. All variables are treated with the HP-filter

From table 4, it becomes clear that when I correct for both time trends, the relationship in table 3 disappears. I can draw the following conclusion: for the EU17 group as a whole, a change in the inflation target has no effect on after taxes income inequality. I find these insignificant results to be robust to the filtering of the data: applying other methods to filter out the time trend also gives insignificant coefficients. To explore the relationship for separate countries, I perform the same regressions for all countries in the EU12 group. Again, I use the HP-filter with smoothing parameter 400 for all variables to remove the trend from the time series. The coefficients on the inflation target in these regressions can be found in table 5.

without controls robust std. error GDP per capita robust std. error GtoGDP robust std. error Both controls robust std. error gini-austria -6.819*** (1.795) -9.089** (2.480) -10.49* (5.125) -8.448 (5.103) gini-belgium -0.798 (2.574) -0.336 (2.122) 0.283 (1.990) 0.395 (2.388) gini-finland 0.696 (1.091) -0.240 (1.172) -0.913 (1.134) -10.99** (2.731) gini-france -8.733*** (2.444) -11.45** (3.795) -13.83*** (4.183) -16.37*** (3.092) gini-germany 3.117 (5.390) -2.528 (5.297) -7.353 (7.523) -3.860 (12.80) gini-greece 6.918*** (0.929) 6.827*** (1.025) 6.579*** (1.001) 5.959*** (1.117) gini-ireland 5.266 (3.662) 11.82* (5.470) 9.025 (4.847) 16.83 (9.276) gini-italy 3.657** (1.316) 5.845** (1.870) 4.654 (2.408) 3.950* (1.830) gini-luxembourg 2.441 (4.955) 4.484 (4.526) 8.440 (5.344) 11.97 (6.905) gini-netherlands 0.0191 (3.238) -0.318 (3.021) -3.410 (7.138) -1.082 (4.851) gini-spain -3.150** (1.137) -2.192 (1.605) -1.657 (3.833) -0.174 (13.37) gini-portugal 5.594* (2.518) 4.479** (1.327) 5.338 (3.271) 1.315 (17.42)

Table 5:Estimated coefficients on inflation target EU12, after taxes Gini . All variables are treated with the HP filter. * p<0.10,** p<0.05, *** p<0.01

The results for the regressions without controls shows that there are five countries within the EU12 group which have a significant relationship between income inequality and the inflation target. For Austria, France and Spain, this relationship is negative: a sudden

(1) giniEU17hp (2) giniEU17hp (3) giniEU17hp (4) giniEU17hp pistarEU17hp -0.554 (1.120) -1.575 (0.940) -2.206 (1.886) -0.660 (1.931) ycapEU17hp 0.261* (0.129) 0.431 (0.249) gtogdpEU17hp -0.0965 (0.110) 0.0911 (0.148) constant -1.64e-10 (0.0859) 2.83e-09 (0.0764) 0.0203 (0.0972) -0.0238 (0.0910) N adj. R-sq 9 -0.121 9 0.114 8 -0.194 8 -0.143 Robust standard errors in parentheses

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increase of the inflation target reduces after taxes income inequality. The coefficients for Greece and Italy are positive, which means that a sudden increase of the inflation target increases after taxes income inequality. If I include real GDP per capita or the government expenditures to GDP ratio, the relationship for Spain becomes insignificant, while including government expenditures to GDP gives an insignificant coefficient for Italy. When I look at the results for all regressions , including the regressions with both control variables, the relationships for France and Greece are robust to the different specifications I use. If the ECB increases its inflation target with one percent, the after taxes Gini-coefficient for France decreases with 8.73 to 16.37 points, whereas the after taxes Gini-coefficient for Greece increases with 5.96 to 6.92 points. The inclusion of government expenditures to GDP leads to a smaller coefficient for Greece and a larger coefficient for France (in absolute terms). This can be explained by the fact that government expenditures to GDP can be seen as a measurement of social transfers. As described by the IMF (2014), most governments conduct policies to influence the income distribution. Therefore, the coefficient for Greece after controlling for social transfers decreases, whereas the coefficient for France becomes more negative.

5.3 S80/S20 ratio

As pointed out in section 2.1, Piketty (2014) stresses the importance of having different measurements of inequality. Therefore, I perform the same regressions as I did in the previous section for a different after-tax inequality measure: the S80/S20 ratio. This measure is constructed by Eurostat by calculating the share of total income received by the top 20% of the income distribution divided by the share of total income received by the bottom 20% of the income distribution 9. In other words, this measurement gives some information about what happens at the extremes of the income distribution. If the Gini-coefficient used in the previous section gives the right image about the income distribution, the results from this procedure should be the same in terms of significance and signs. Since I expect to encounter the same problem with trends in the data, I also apply the HP filter with the same smoothing parameter on the time series for the S80/S20 ratio. The results from the regressions for the EU17 group

9_{http://ec.europa.eu/eurostat/web/gdp-and-beyond/quality-of-life/s80s20-income-quintile. Data for this ratio}

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as a whole can be found in table 6. I plot the S80/S20 ratio in figures A1 and A2 in appendix A4.

The results are similar to what I have found in section 5.2. For the EU17 as a whole, there is no significant relationship between the inflation target and income inequality, as measured by the S80/S20 ratio. Thus, this insignificance is robust to different measurements of inequality.To see whether there is a difference for separate countries between these regressions and those in the previous section, I also run the regressions for individual countries in the EU12. The results from this procedure can be found in table 7.

The coefficients for France and Greece are significant again, which means that the results I found in the previous section, are robust to different measures of after-taxes income

(1) ratioEU17hp (2) ratioEU17hp (3) ratioEU17hp (4) ratioEU17hp pistarEU17hp 0.208 (0.345) -0.0289 (0.380) -0.419 (0.452) -0.413 (0.620) ycapEU17hp 0.0606* (0.0257) 0.00183 (0.0612) gtogdpEU17hp -0.0369 (0.0211) -0.0361 (0.0406) constant -1.20e-10 (0.0185) 5.76e-10 (0.0158) 0.00674 (0.0168) 0.00656 (0.0207) N adj. R-sq 9 -0.079 9 0.214 8 0.229 8 0.037 Robust standard errors in parentheses

* p<0.10, ** p<0.05, *** p<0.01

Table 6 : EU17 regressions, all variables treated with HP-filter (see section 5.2)

Table 7:Estimated coefficients on inflation target EU12, after taxes S80/S20 ratio. All variables are treated with the HP filter (see section 5.2). * p<0.10,** p<0.05, *** p<0.01

without controls

robust std.

error GDP per capita

robust std. error GtoGDP robust std. error Both controls robust std. error ratio-austria -1.459*** (0.246) -1.889** (0.569) -1.839 (1.197) -1.242 (1.090) ratio-belgium 0.116 (0.443) 0.00475 (0.466) -0.101 (0.463) -0.103 (0.556) ratio-finland -0.0410 (0.274) -0.385 (0.282) -0.617* (0.273) -2.555** (0.825) ratio-france -1.232** (0.372) -1.826** (0.611) -2.209** (0.643) -2.568*** (0.480) ratio-germany 1.070 (1.291) -0.435 (1.135) -1.748 (1.565) -0.865 (2.858) ratio-greece 2.852*** (0.790) 2.648** (0.724) 2.959** (0.807) 2.506** (0.865) ratio-ireland 1.034 (1.005) 2.271 (2.278) 1.528 (1.579) 2.948 (3.125) ratio-italy 1.446** (0.466) 1.923* (0.848) 1.371 (0.973) 1.157 (0.927) ratio-luxembourg 0.665 (0.915) 1.106 (0.803) 1.790 (1.001) 1.904 (1.458) ratio-netherlands -0.389 (0.539) -0.433 (0.536) -1.319 (0.991) -1.040 (0.872) ratio-spain -1.040* (0.473) -0.857 (0.586) -0.335 (1.240) -0.0456 (1.035) ratio-portugal 2.238** (0.848) 1.761*** (0.242) 3.653** (1.081) 2.160** (0.550)

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inequality. However, for Spain and Portugal, it matters how income inequality is measured. In the previous section, the relationship for Spain was significant, while the relationship for Portugal was insignificant. Using the S80/S20 ratio as inequality measure, the results indicate that it is the other way around: the coefficients for Spain are insignificant, while the coefficients for Portugal are significant and robust to all specifications.

I can explain the negative relationship for France with the savings redistribution channel (Saiki & Frost, 2014). If the ECB increases its inflation target, actual inflation will increase. This diminishes the real return on savings, if I assume the nominal return to be constant. Piketty (2014, pp. 271-303) shows that in France, agents in the upper percentile of the income distribution rely relatively more on income from savings than agents in the lower percentiles of the income distribution. This means that total income for the upper percentiles deteriorates relatively more than the total income for the lower percentiles of the income distribution. As a consequence, income inequality decreases.

Moreover, I can explain the positive relationship for Greece using the income composition channel (Coibion, et al., 2012). If the ECB conducts inflationary policy, real wages suddenly decrease. Since nominal wages are mostly negotiated through a collective wage agreement, nominal wages will not adjust immediately to compensate for inflation. If I assume that the lower percentiles of the income distribution rely relatively more on labor income than the upper percentiles, this mechanism increases income inequality.

5.4 Before-taxes Gini-coefficients

As said before, most governments in developed countries use fiscal policy to make changes in the income distribution (IMF, 2014). Therefore, it is useful to look at inequality measures of the income distribution before governments intervene, by using before-taxes measurements of inequality. There are two before-taxes measurements of income inequality available at Eurostat: coefficients with or without pension transfers. I will indicate these Gini-coefficients with “ginibt” and “ginibtwp”. The first abbreviation stands for “before transfers”, while the latter means “before transfers with pensions”. Thus, the first measurement does not account for pension transfers while the latter one does.

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25 Gini-coefficients before transfers

First, I use Gini-coefficients which exclude taxes and pension incomes 10_{. In table 8, I} present the results for the EU17 group as a whole. In figures A3 and A4, which can be found in appendix A4, I graph the before taxes Gini-coefficients.

Table 8: EU17 regressions, all variables treated with HP-filter (see section 5.2)

In the regression without control variables, the effect of a change in the inflation target on the before taxes Gini-coefficient is positive and significant. This can be explained by fact that governments conduct policies to affect income inequality. When I control for real GDP per capita and government expenditures to GDP, the significant relationship disappears. This corresponds with the results I found in the previous sections. In table 9, I list the coefficients on the inflation target from the regressions for the countries in the EU12 group.

10_{Source: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=ilc_di12b&lang=en} (1) ginibtEU17hp (2) ginibtEU17hp (3) ginibtEU17hp (4) ginibtEU17hp pistarEU17hp 5.314** (2.091) 4.260 (2.259) 1.419 (2.964) -0.0864 (3.184) ycapEU17hp 0.270 (0.266) -0.420 (0.333) gtogdpEU17hp -0.230 (0.148) -0.413 (0.201) constant 1.24e-09 (0.154) 4.34e-09 (0.157) 0.0379 (0.164) 0.0808 (0.162) N adj. R-sq 9 0.267 9 0.237 8 0.299 8 0.192 Robust standard errors in parentheses

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26 without controls robust std. error GDP per capita robust std. error GtoGDP robust std. error Both controls robust std. error ginibt-austria -4.360 (2.717) -6.469** (2.039) -7.358** (2.772) -5.190 (3.457) ginibt-belgium 1.347 (5.298) 5.024 (4.135) 9.344** (3.467) 9.895* (4.029) ginibt-finland 4.074* (1.997) 4.533 (2.491) 4.763 (2.901) -1.806 (11.69) ginibt-france 5.902*** (1.520) 8.200* (3.454) 8.675* (4.156) 8.597 (5.169) ginibt-germany 5.398 (4.115) -2.092 (5.621) -3.881 (9.643) 9.356 (15.57) ginibt-greece 25.73** (7.991) 23.19** (6.582) 29.69*** (3.889) 26.92*** (4.702) ginibt-ireland -6.373 (5.593) 5.560 (13.93) -2.332 (8.538) 11.20 (21.13) ginibt-italy 5.679** (1.884) 7.567** (2.782) 5.291 (3.216) 4.428 (2.306) ginibt-luxembourg 0.463 (4.647) 4.937 (3.102) 11.67*** (3.005) 12.01* (4.795) ginibt-netherlands 0.399 (3.052) 0.245 (2.988) -7.102 (3.753) -6.359 (3.610) ginibt-spain 4.988 (5.076) 7.247 (5.225) -5.165 (11.71) -1.860 (9.422) ginibt-portugal 15.05** (5.066) 11.56*** (1.912) 17.64 (10.42) 5.259 (5.275)

Table 9: Estimated coefficients on inflation target EU12, before taxes Gini-coefficient. All variables are treated with the HP filter (see section 5.2). * p<0.10,** p<0.05, *** p<0.01

The results in table 9 show that if government intervention is absent, as it is in these regressions, the impact of monetary policy on income inequality is much larger for Greece. The relationship for France changes from negative to positive. A change in the ECB’s inflation target increases before taxes income inequality in France, whereas it decreases after taxes income inequality in France. It could be the case that the pension system changes the impact of monetary policy. In the next subsection, I will look at the role of the pension system.

Gini-coefficients before transfers with pensions

To investigate whether the pension system has an influence on the relationship between the inflation target and income inequality, I perform the same regressions using the Gini-coefficients which excludes taxes but includes pension income11_{. To explore this influence, I}

compare the results presented here with the results from the previous section. The only difference between the inequality measure used here and the measure in the previous section, is that the measure used here accounts for pension transfers. Thus, by comparing these two sets of results, I am able to isolate the effect of pension transfers. Moreover, I can compare the results found here with the results in section 5.2 to isolate the effect of taxes. I list the results for the EU17 as a whole in table 10. In figures A5 and A6, which can be found in appendix A4, I graph the before taxes with pensions Gini-coefficients.

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27 (1) ginibtwpEU17hp (2) ginibtwpEU17hp (3) ginibtwpEU17hp (4) ginibtwpEU17hp pistarEU17hp -0.372 (1.376) -1.266 (1.300) -3.217* (1.464) -3.236 (2.000) ycapEU17hp 0.229 (0.147) -0.00522 (0.337) gtogdpEU17hp -0.171** (0.0588) -0.174 (0.128) constant -3.85e-10 (0.0765) 2.24e-09 (0.0686) 0.0143 (0.0685) 0.0149 (0.0712) N adj. R-sq 9 -0.130 9 0.092 8 0.283 8 0.103 Standard errors in parentheses

* p<0.10 ** p<0.05 *** p<0.01

Table 10: EU17 regressions, all variables treated with HP-filter (see section 5.2)

For the Eurozone as a whole, proxied by EU17, the relationship between the inflation target and the Gini-coefficient before taxes with pensions is insignificant. In table 11, I list the coefficients from the regressions for all countries in the EU12 group.

without controls robust std. error GDP per capita robust std. error GtoGDP robust std. error Both controls robust std. error ginibtwp-austria -5.719** (2.124) -7.555*** (1.873) -10.38*** (2.622) -9.862** (3.139) ginibtwp-belgium -1.171 (3.938) 0.677 (3.414) 3.761 (3.628) 4.549 (4.172) ginibtwp-finland 2.172 (1.545) 1.791 (1.736) 1.449 (2.037) -10.52 (6.987) ginibtwp-france -7.129*** (1.644) -10.90*** (1.785) -12.54*** (1.429) -13.67*** (1.325) ginibtwp-germany 5.435 (4.199) 0.0782 (3.747) -2.538 (4.540) 4.437 (9.777) ginibtwp-greece 8.243*** (0.695) 8.089*** (0.806) 7.995*** (0.703) 7.297*** (0.837) ginibtwp-ireland -6.708 (4.890) -1.252 (9.564) -0.968 (6.008) 6.151 (15.55) ginibtwp-italy 3.808** (1.202) 5.998** (2.000) 4.712 (2.444) 3.999* (1.964) ginibtwp-luxembourg 0.362 (5.147) 4.286 (4.291) 11.06** (4.270) 14.66** (5.429) ginibtwp-netherlands -0.225 (1.867) -0.317 (1.851) -4.444 (2.756) -3.989 (2.977) ginibtwp-spain -5.161* (2.648) -3.385 (3.162) -9.204 (6.838) -6.550 (6.329) ginibtwp-portugal 4.348** (1.274) 3.323** (0.927) 7.518* (3.812) 4.333 (2.588)

Table 11:Estimated coefficients on inflation target EU12, before taxes with pensions Gini-coefficient. All variables are treated with the HP filter (see section 5.2). * p<0.10,** p<0.05, *** p<0.01

The introduction of pensions decreases the impact of a change in the inflation target for Greece. Compared with the results in section 5.2, the effect is still bigger. This indicates the reducing effect of fiscal policy. The positive relationship for France, which I found in the previous subsection, changes into a negative relationship. This makes sense because pensions are in fact savings. If I assume that the upper percentiles of the income distribution save

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relatively more for their retirement, an increase in the inflation target deteriorates pension incomes at the upper part of the income distribution more than at the lower part. Thus, this mechanism decreases income inequality. However, the after taxes results for France in section 5.2 indicate that an increase in the inflation target reduces income inequality more after the French government intervenes. This corresponds with the view that fiscal policy is used to reduce income inequality.

Thus, I conclude that there is no relationship between the unobserved inflation target and income inequality for the Eurozone as a whole. This result is robust to different measurements of inequality. I used the Hodrick-Prescott filter to remove the trends from the data. Using other methods to obtain stationary data yields similar results. Thus, the non-significant relationship is also robust to the filtering of the time series. For some individual countries, there is a significant relationship, which is most visible for France and Greece.

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6. Conclusion

In this thesis, I investigated the link between income inequality and inflation, and vice versa. I began with an exercise similar to Albanesi (2007). I calculated the average after-tax Gini-coefficient for the EU12 countries for the period between 1999-2014. Moreover, I calculated the average inflation tax for these countries for the same period and regressed it on the average Gini-coefficient. The results of this procedure show that a higher average inflation tax increases income inequality by a small amount on average.

After that, I estimated the unobserved inflation target, using a New Keynesian model as specified by Ireland (2007). I used this inflation target to see whether it could explain the dynamics of income inequality between 2005-2014. I used before and after taxes Gini-coefficients and the after tax S80/S20 ratio as measurements of income inequality to check the robustness of my results . I did this procedure for the Eurozone as a whole, proxied by the EU17 group, and for separate countries in the EU12 group. From the results, I conclude that there is no relationship between the ECB’s inflation target and income inequality for the Eurozone as a whole. This result is robust for all measures of income inequality and for the filtering of the time series. In the individual country regressions, I found a significant relationship for France and Greece, which is robust to various measures of income inequality. An increase in the inflation target increases income inequality in Greece, whereas it decreases income inequality in France.

The mechanism driving the results for France is the savings redistribution channel. When inflation suddenly goes up, the real return on capital is reduced. If the upper part of the income distribution relies more on benefits from savings as primary source of income than the lower part of the income distribution, it reduces income inequality. In Greece, the income composition channel might be the main mechanism. However, I cannot be sure about this, since all the inequality measures used here include total income. I was not able to make a distinction between sources of income. Moreover, I have no detailed information about the primary income sources for each part of the income distribution for each country. The inequality measures which exclude taxes and pension transfers allowed me to say something about it, but more detailed information about the sources of income for each income level and the wealth distribution is needed to give more informative conclusions.

There are many possibilities for further research. One possibility is to obtain more detailed information about the income distribution for labor income and capital income. With

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this information, it is possible to investigate the effect of inflation on the distribution of labor and capital income. Another possibility is to use micro-data to increase the frequency of the dataset from yearly to quarterly data to get more reliable results. Moreover, with the introduction of Quantitative Easing (QE) in the Eurozone , it is important to find out whether this relationship changes with the introduction of QE over a larger period.

Another element, which is beyond the scope of this thesis, is the relationship between inflation and wealth inequality. One mechanism I described in this thesis is that inflation lowers the real return on capital, and it decreases income inequality through the savings redistribution channel. But inflation is an increase of prices. If wealth is held mainly in assets by the upper percentiles of the distribution, wealth increases for asset holders. This increases wealth inequality (Piketty, 2014, p. 452). It is interesting but difficult to investigate which effect is stronger.

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Perspective. Journal of Economic Literature, Issue 37, pp. 1661-1707.

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Appendix A1: Tables chapter 3

Mean-GINI Austria 26.533 Belgium 27.336 Finland 25.687 France 28.58 Germany 27.825 Greece 33.65 Ireland 30.521 Italy 31.408 Luxembourg 27.586 Netherlands 26.679 Portugal 35.938 Spain 32.48 St.dev 3.241 mean 29.520

Table A1 : summary statistics of Gini’s

Table A2 : regression average inflation tax on average Gini

Inflationtax (average) Gini (0-100, average) 0.00641** (0.00228) constant 0.498*** (0.0705) N adj. R-sq 12 0.258 Standard errors in parentheses * p<0.10, ** p<0.05, *** p<0.01

Inflation and income inequality in the Eurozone