The Impact of Monetary and Tax Policy on Income Inequality in Japan

This paper assesses the effects of the most recent monetary policy behaviour of the Bank of Japan (in particular, zero interest rate policy and negative interest rate policy) and Japanese tax policy on income inequality in this country during the period of 2002Q1 to 2017Q3. The vector error correction model (VECM) that develops in this research shows that increase in money stock (m1) through Quantitative Easing (QE) and Quantitative and Qualitative Easing (QQE) policies of the BOJ significantly increases the income inequality. On the contrary, Japanese tax policy was effective in reducing the income inequality. Variance decomposition results show that increasing of income inequality by monetary policy is larger when comparing to decreasing effects of tax policy on income inequality. Cointegration and VECM results show that monetary policy has both short‐run and long‐run impacts but for tax policy paper could not find any significant short‐run impact on income inequality. In addition, paper found that technological progress only in long‐run can reduce the income inequality by increasing the marginal productivity of labour with positive impacts on employment and wages.


| INTRODUCTION AND THE LITERATURE SURVEY
Growing inequality, especially in advanced economies, has attracted much attention from policymakers and in academics (Bernanke, 2015;Draghi, 2016;Yellen, 2014). Equality is considered a significant value in most societies akin to fairness. Regardless of ideology, culture and religion, individuals acknowledge inequality as unfavourable (Dabla-Norris, Kochhar, Suphaphiphat, Ricka, & Tsounta, 2015). Not only can it become a cause for instability within society, studies have shown it can hinder economic growth.
Recent empirical works found that high levels of inequality are harmful for the pace and sustainability of growth (Ostry, Berg, & Tsangaride, 2014). Also, Cingano (2014) strengthened the finding by demonstrating through an econometric analysis on OECD countries and concluding that income inequality has a negative and statistically significant impact on subsequent growth. The analysis shows that the income distribution itself matters for GDP growth. Specifically, if the income share of the top 20% increases, then GDP growth declines over the medium term. In contrast, an increase in the income share of the bottom 20% is associated with higher GDP growth (Dabla-Norris et al., 2015). Others have argued that increasing inequality may have been a critical contributing factor to the global financial crisis (GFC henceforth). Rajan (2010) argues that increasing inequality led to political pressure for more housing credit, which intensified the falsified lending in the financial sector. Ranciere and Kumhof (2011) present that, in the US, the Great Depression of 1929 and the GFC of 2008 were both anticipated by a rapid rise in income and wealth inequality and by a sharp rise in debt-to-income ratios among low-income households.
In the case of Japan, it is unguarded from the gradual increase in inequality, which is also observed in other OECD countries in the recent years (Hoeller, Joumard, & Koske, 2013). The concerns over income inequality that have grown between the Japanese population and the wide notion that "all Japanese are middle class" have become a concept of the past (Aoyagi, Ganelli, & Murayama, 2015). In their study, they calculated the evidence of increasing income inequality in Japan, showing that the Gini coefficient of Japan has continuously increased over the last three decades. Beginning from the lowest among the G7 countries in the 1980s, it has recently converged to roughly the G7 average of 0.5. Japan's pace of rising inequality has been exceptionally high.
Several reasons have been found by different scholars for the causes of income inequality, including: (i) technology (Bound & Johnson, 1992), (ii) demographics (Karahan & Ozkan, 2013), (iii) globalisation (Feenstra &Hanson, 2008 andFurceri, Loungani, &Zdzienicka, 2016) and (iv) structure of labour market (Jaumotte & Buitron, 2015). Acemoglu and Johnson (2012) and Stiglitz (2015) raised expansionary monetary policy as a possible contributing factor for income inequality. However, the results of the effect of monetary policy on inequality have been ambiguous and sometimes even contradictory. The opinions are often divided among scholars from the results being insignificant to significant and expansionary monetary policy increasing the inequality to reducing inequality.
In the recent study by O'Farrell, Rawdanowicz, and Inaba (2016), the effect of monetary policy on inequality was only limited. They have taken an impact of monetary policy on income and wealth via changes in returns on assets, debt interest payments and asset prices, rather than through its impact on employment and inflation, in selected developed countries and, at the same time, addressing if high inequality has a negative impact on effectiveness of monetary policy.
The effects of monetary policy on income and wealth inequality through financial channels were found to be complex and ambiguous, only giving a limited effect on inequality. The crosscountry difference in size and distribution of income and wealth components was accountable for the ambiguity of the results. As for the second objective, higher inequality did not seem to significantly affect the effectiveness of monetary policy, particularly in boosting private consumption through wealth effects.
Similarly, Inui, Sudo, and Yamada (2017) found that both conventional and unconventional monetary policy shocks do not have statistically significant impacts on inequality across Japanese households in a stable manner.
On the other hand, Furceri et al. (2016) have displayed results that the expansionary monetary policy reduces income inequality. They used data on top income shares (top 1%, 5% and 10%) from the World Top Income Databases, the share of wage income in GDP from the OECD and Gini coefficient in 32 advanced and emerging countries. What is unique about their study is that they have incorporated the forecast error of the policy rates. This is implemented to overcome the problem of "policy foresight" (Forni & Gambetti, 2010) and to eliminate the chance of capturing the potentially endogenous response of monetary policy to the condition of the economy. The monetary policy shock effects on inequality are observed through impulse response functions directly from local projections introduced by Jordà (2005). Results showed that an unexpected decline of 100 basis points in the policy rate reduces inequality by approximately 1.25% in the short-term and 2.25% in the medium term. According to their calculations, the effect of policy rates is economically significant as there was a high persistence and limited variation in the Gini. The effect is larger for countries with higher labour share of income and smaller redistribution policies. Likewise, Coibion, Gorodnichenko, Kueng, and Silvia (2012) advocated the significance of the effect and that the expansionary (contractionary) monetary policy reduced (increases) inequality in the US from 1980 to 2008. Under their study, the contractionary monetary policy had significant long-term effects on inequality in consumption, income, expenditure and labour earnings in a statistically significant manner. In their work, the transmission channels are thoroughly examined. Earning heterogeneity channel and income composition channels were especially strong in their outcome. After contractionary monetary policy shocks, higher earnings for high-income earners are observed but lower earnings for low-income earners, demonstrating earning heterogeneity channel. Income composition channel also played a major role as aggregate financial income rose sharply while business income declined after contractionary monetary policy shocks and top 1% of the income distribution received approximately 30% of their income from financial income. The income composition of the low-income earners mostly consists of labour income, thus creating a wider disparity between the income of the top and bottom layers of income distribution. Another research proposing a significance of the monetary policy effect on inequality is by Saiki and Frost (2014). To identify the response of monetary policy shocks to income inequality empirically, a vector autoregression framework and impulse response functions are used. The result makes apparent that the increase in monetary base positively affects the Gini.
In this paper, we shed light on the effect of expansionary monetary policy, in particular, quantitative easing (QE) and quantitative and qualitative monetary easing (QQE) through zero interest rate monetary policy and negative interest rate policy on income inequality across Japan from an empirical point of view. In addition, we also look at the effect of tax policy on income inequality. The effect of tax policy has been clear as it is used as "the primary tool for governments to affect income distribution" (Bastagli, Coady, & Gupta, 2012). Both tax policies and spending policies have the power to alter the distribution of income over the short and medium term. However, the redistributive effects of fiscal policies have been shown less effective in recent past. Our findings show that an increase in monetary stock contributed to an increase in inequality in Japan, demonstrating that an implemented expansionary monetary policy contributed to increasing inequality and, as for the tax policy, it reduced inequality in Japan.

| RECENT MONETARY POLICY OF THE BANK OF JAPAN AND INCOME INEQUALITY TRENDS
As for the most recent monetary policy behaviour of the Bank of Japan (BOJ), on 4 April 2013, they announced the purchase of Japanese government bonds (JGBs). Haruhiko Kuroda made this decision when he first became the governor of the BOJ (Yoshino, Taghizadeh-Hesary, & Miyamoto, 2017). Figure 1 shows the expansion of the monetary base and JGB holdings by the BOJ. Since 2013, there has been a massive increase in the amount of monetary base through the implementation of the QQE 1 in part of the three arrows introduced by Prime Minister Abe. Table 1 depicts the monetary base and government bond purchase data comparison of April 2013 and May 2016. From April 2013 until May 2016, the monetary base of Japan rose from 155 trillion yen to 387 trillion yen, with an average annual increase of about 80 trillion yen. In the same period, in April 2013, assets of the BOJ amounted to ¥175 trillion and, by May 2016, they had enlarged to ¥426 trillion, an increase of almost 2.5 times in 3 years. In the same period, JGBs, which were the major purchase of the BOJ, rose from ¥98 trillion to ¥319 trillion. In other words, the major part of the asset is the purchase of long-term government bonds (Yoshino, Taghizadeh-Hesary, & Tawk, 2017). 1 At the Monetary Policy Meeting held on 20 and 21 September 2016, the Bank decided to introduce a new policy framework of QQE with yield curve control by strengthening the two previous policy frameworks of QQE and QQE with a negative interest rate. The new policy framework consists of two major components: the first is "yield curve control" in which the Bank controls short-term and long-term interest rates through market operations, and the second is an "inflation-overshooting commitment" in which the Bank commits itself to expanding the monetary base until the year-on-year rate of increase in the observed consumer price index exceeds the price stability target of 2% and stays above the target in a stable manner. (https://www.boj.or.jp/en/announcements/education/oshiete/seisaku/b27.htm/). When compared to other countries and other regions of the world, the extremity of Japan's recent monetary easing becomes distinct. In Table 2, the monetary base/GDP ratios of Japan are compared with those of the US and the euro zone. In July 2016, the ratio was 80% in Japan, while 21% in the US, and 20% in the euro zone (Yoshino, Taghizadeh-Hesary and Miyamoto, 2017).
As for the income inequality in Japan, the indicator we used for empirical survey in this research is the average households' income of top 10% (rich) over average households' income of bottom 10% (poor).   Figure 2, the index of inequality shows a drastic upward trend, especially during the last decade, meaning increasing income inequality. This ratio was 10.14 when BOJ had first implemented QE, which was removed in March 2006 as the inflation rate turned positive and the economy seemed to be recovering. However, when the GFC hit in 2008 and the economy went into a tailspin, BOJ lowered its interest rate to almost zero. In 2010, they executed comprehensive monetary easing policy and the ratio increased to 10.48. In 2013, as Prime Minister Abe took power for the second time and released his Abenomics' three arrows, 2 which included QQE, was executed as a remedy to combat the prolonged deflation in Japan. The inequality during this period marked the highest. In this period, the inequality ratio reached 10.60, and this phase is covering the negative interest rate from 29 January 2016. 3

| Channels for transmission of monetary policy to inequality
In order to capture the distributional effects of monetary policy on inequality, we will need to review the potential transmission channels. There are four major channels introduced by Coibion et al. (2012), Nakajima (2015) and Inui et al. (2017), in which monetary policy affects the income inequality.
1. Earnings heterogeneity channel-proceeds when the response of earnings to monetary policy shock differs across different households' income groups. This channel is affected by the level of labour unionisation, stickiness of nominal wage or labour market flexibility. According to the research done by Mumtaz and Theophilopoulou (2016), this channel works countercyclically to a monetary policy shock. However, this channel works procyclically among Japanese households, according to Inui et al.'s (2017) study. Under the assumption that the high-income households have more capital income and less wage income when expansionary monetary policy is implemented, their capital income increases. However, because of the stickiness of nominal wage, the income of the poor which is mostly wage income will not change. Thus, this contributes to the widening of income inequality across households. 2. The job creation channel-arises with job creation and job destruction, which resulted from the implementation of monetary policy. This channel generates a countercyclical response of labour income inequality since an accommodative (contractionary) monetary policy shock creates (reduces) jobs and decreases (increases) the number of households with zero earnings according to Bernanke (2015). 3. The portfolio channel-becomes apparent when the size and composition of asset portfolios differ across households. Also, under the assumption of the rich holding most of their assets in financial assets and poor in cash, income inequality widens as the result of monetary easing. This situation occurs due to equity prices elevating, resulting in an increase in income of the richer households, and the result of inflation depreciates cash, in which case the disparity of the rich and poor widens. 4. The savings redistribution channel-emerges from the fact that a decline in the policy rate set by the central bank and the rising inflation leads to transfer from lenders to borrowers. According to quantitative theory of money (MV = PY), when expansionary monetary policy is implemented, the price level increases. Due to the Taylor rule, the interest rate eventually increases, and, as a result, inequality increases as borrowers (the low-income households) will need to pay higher interests to lenders (high-income households).
As the top 20% of Japanese hold 15.4% of their assets in stocks and bonds, which is 5 times as much as the second top quintile, the possibility of the earnings heterogeneity channel and the portfolio channel is suggested. In the economic severity, the unconventional monetary policy was put in place, which resulted in higher asset prices. Higher asset prices benefited the high-income households, who held a larger amount of overall savings in securities, and, thus, benefited from greater capital income, hence increasing the income inequality among the households.

| Impact of tax policy on inequality
In this section, we are going to glance at the impacts of fiscal policy, especially putting emphasis on the tax policy, on inequality. In the research by Bastagli et al. (2012), fiscal policy is defined as "the primary tool for governments to affect income distribution." And its three main objectives are described as "to support macroeconomic stability, provide public goods and correct market failures, and redistribute income." Both tax policies and spending policies have the power to modify the distribution of income over the short and medium term.
Various researchers found the outcome through regression-based studies that greater reliance on income taxes and higher spending on welfare reduces inequality (Martínez-Vázquez, Vulovic, & Moreno-Dodson, 2012;Muinelo-Gallo & Roca Sagalés, 2013;Niehues, 2010;and Woo, Bova, Kinda, & Zhang, 2013). The bulk of these studies provides evidence that direct taxes, such as income tax, corporate tax and wealth tax, are more redistributive than indirect taxes, such as sales tax and service tax, and social protection spending lowers inequality.
However, recently, a reduction in the social benefits and less progressive taxation in most OECD member countries has resulted in a decrease in the redistributive impact of fiscal policy. Fiscal reforms in many economies since the mid-1990s are accountable for the decline in the redistributive power of fiscal policy (Gupta, 2014). These reforms reduced the generosity of unemployment and social assistance benefits, as well as income tax rates, particularly for high-income earners (OECD, 2011a(OECD, , 2011b. The main reasons for the reduction in the distributive impact of fiscal policy were the cost and efficiency. As for means tested social benefits, it provided disincentives for low-skilled workers to look for job opportunities (OECD, 2011b). Progressive income tax can have disincentives for the higherincome individuals. However, recent research has argued that the efficiency cost of progressive taxation may be much less than previously thought (Bastagli et al., 2012). As opposed to productivity boosting, increases in top incomes were achieved at the expense of lower-income groups, showing no correlation between the rising top incomes and per capita GDP growth (Stantcheva, Saez, & Piketty, 2012). On the grounds of that, more progressive taxation on high-income groups was called for (Tanzi, 2011).
As previously stated, tax policies intend on reducing inequality, and, generally, they have a diminishing effect on inequality. For example, the inheritance tax in Japan is very high, up to 55% (Table 3). Moreover, after the revision of the inheritance tax in January 2015, the total deduction was calculated by adding ten million yen per heir to the basic deduction of 70 million yen. However, after being revised, the basic deduction declined to 42 million yen and only seven million yen per heir. This can be seen as the attempt to mitigate Japan's widening income inequality since one of the major causes of inequality in Japan is explained by inheritance.
Japan's income tax is also effective in combating the growing inequality. As seen in Table 3 below, the income tax for low-income households is very low, gradually rising as income rises, and elevates quickly for high-income households. This is unique compared with other advanced countries, such as the US, the UK and France (Figure 3). The well-established tax system in Japan is one of the major reasons that historically inequality has not widened as much as other advanced countries.
Fiscal policy is for stabilisation as well as redistribution objectives. There is a built-in fiscal stabiliser role created by progressive tax rate system. A more progressive income tax policy that offered by the Japanese tax system could offer a stabilising alternative. It could result in more revenue, more countercyclical policy and more income equality and thus more stable demand growth.   On the other, income redistribution could be applied to weaker sectors such as to farmers through agricultural subsidies. The tax policy's effectiveness in reducing the inequality in Japan will be examined empirically in section 4.

| Model development
Here, we provide a simple theoretical model in order to show the impact of monetary policy and tax policy on income inequality. First, the two distinct income groups are presented in the form of their income and tax. Then, the relationship between the macroeconomic factors and inequality is depicted: (1) In Equations (1) and (2), we are considering the earning of two income groups, which are the high-income group and low-income group, denoted as E H and E L , respectively. The rich receive the wage income w H L H , where w H is the wage rate per hour, for the high-income group, and L H shows how many hours they work. The second source of income for the high-income group is the interest income from their deposit, r D D H , where r D denotes the deposit interest rate and D H denotes amount of deposits of the high-income group. The high-income group is also investing in the capital market, so they receive dividends from the stock market as their third income source (π d P S S H ) where π d shows the dividend (as percentage), P S shows the price of stock, and S H the number of shares the high-income group is holding. In addition to the dividend gain, the highincome group also have capital gains from changes in the stock price indexes shown in Equation (1) by π c P S S H , where π c shows the percentage of capital gain. The low-income group receives labour income w L L L and also interest from their deposit r D D L . w L , L L and D L are, respectively, the wage rate per hour for the low-income group, how many hours the low-income group works, and deposits of the low-income group, the difference in their income emanates from the wage income, deposit income and also whether they can invest in the capital market or not.
On 29 January 2016, Bank of Japan policy board introduced QQE with a negative interest rate to achieve the price stability target of 2% at the earliest possible time. Since February 2016, the short-term interest rate (call rate-overnight uncollateralised interest rate) has been negative (Yoshino, Taghizadeh-Hesary, & Tawk, 2017). Although the short-term interest rate became negative, however the interest rate on deposits is positive but very low and near to zero. On July 2018, average interest rate for 10 million yen or more deposits for 1-year maturity was 0.010, for 5-year maturity was 0.015 and for 10-year maturity was 0.017 per cent per annum. 4 At this moment, although in Japan, the interest rate on deposits is very low, but still 51.5% of the financial assets held by Japanese households is in form of currency and deposits. This ratio is 13.4% in the US and 33.2% in the euro area (BOJ, 2017). However, we expect that r D in Equations 1 and 2 do not have significant correlation with the earning of the high-income group and low-income group, as presently interest rate is near to zero: Equation (3) shows the relationship between the stock price, P S , and dividends, π d1 ; π d2 ; π d3 ; . . .. The present stock price depends on the present discount value of dividend and future expected price of stocks. So we have to discount the dividend by 1 + r, (1 + r) 2, (1 + r) 3 and (1 + r) n : M"! r# and r D #! r D D#; (4) M"! r# P S ": Explanation (4) shows the impact of money supply on deposits. If the money supply goes up, M↑, the interest rate declines, r↓, and that will reduce the deposit rate of interest, r D ↓. As far as their asset return is concerned, the deposit interest rate will go down and their money in deposit will be reduced, r D D↓. Also, if the monetary policy works well, the interest rate goes down, which leads stock prices to recover and future prices of the stocks increase because of monetary easing (Explanation (5)). Then, the total return from the capital market investment goes up for the higherincome group. However, for the lower-income group, they are only putting their money in their deposit, so when the deposit interest rate goes down, their total asset does not increase. Rich people are affected strongly from easing monetary policy and lower income or poor people are outside of those influences, which will diversify the income distribution.
Next, we add taxes to Equations (1) and (2); results are found in Equations (6) and (7), stated as below: where t H w denotes wage income tax for high-income group and t L w denotes the wage income tax for low-income group and t H C denotes tax on capital. As it is clear in terms of tax, there are two kinds of tax, which are wage income tax and tax on capital.
Next, in order to capture the impact of monetary policy on each income-group's income, we get the first-order conditions of E H in Equation (6) and E L in Equation (7) with respect to M, or the money supply; the results of first-order conditions are found in Equations (8) and (9): Therefore, ∂E H ∂M = ∂E L ∂M > 1, which means the money supply, will increase the earning of the highincome group more, compared to the low-income, which means increasing the income inequality among the different income groups. According to our theoretical model, monetary policy has the power to widen the income distribution.
On the other hand, if the tax ratios are progressive, the higher-income group needs to pay much higher wage taxes, while the poor only need to pay a small amount of tax, equalising the income between the rich and the poor. For the capital income, the rich people will have to pay more capital income. This shows that, based on our model, the tax policy could be in favour of reducing the income inequality.
In the next step, in order to find the empirical model, we write E H E L as in Equation (10): Equations (11)- (17) show that each of the variables in Equation (10) are functions of certain variables: π c ¼ π c ðr; M; YÞ: Equation (11) shows that wage rate is a function of price level and GDP (income level). Equation (12) shows that the price of stock is a function of interest rate, money supply and GDP (income level). As stated earlier in Equation (3), when interest rate goes down, the present discount value of stock will increase and the discounted present value of dividends (π d1 ; π d2 ; π d3 . . .) is a function of monetary policy and economic conditions (GDP), and this is the reason that as in Equation (12), the stock price is a function of the interest rate (r), money supply (M) and GDP (Y). Equation (13) shows that deposit interest rate is a function of interest rate, money supply and GDP (income level). Deposit interest rate depends on how banks manage their assets (r) and how households change their deposit supply which depends on their income and monetary condition. That is why as in Equation (13), the deposits interest rate is a function of interest rate (r), money supply (M) and GDP (Y). Equation (14) shows that labour supply is a function of interest rate, money supply, GDP (output level) and wage rate. Production function depends on capital and labour. Capital stock depends on the level of interest rate, which also affects the employment, and this is the demand supply of the labour market. And on the supply side of the labour market, labour supply depends on the wage rate and the economic conditions (GDP). From Equation 11, the wage rate is depending on the price (P) and economic conditions (Y). Companies' dividend is shown in Equation (15), which is a function of interest rate of the companies' borrowing from bank, money supply (monetary policy) and the economic conditions (GDP). Deposits depend on interest rate and income level. The interest rate on deposit as shown in Equation (13) is a function of r, M and Y. Therefore, in Equation (16), deposits are mentioned as a function of interest rate, money supply and GDP (income level). As in Equation (17), the number of shares is a function of price of stock, interest rate, money supply, and GDP (income level). Equation (18) shows that the capital gain is a function of interest rate of the companies' borrowing from bank, money supply (monetary policy) and the economic conditions (GDP). If people are considering stocks and deposits as two types of assets, they compare the deposits interest rate and stock price and then deposit interest rate depends on interest rate (r) and economic conditions (Y). Then, we write the linearised E H E L as in Equation (19), according to Equations (11)-(18), by considering that each variable is a function of other variables: Equation (19) shows that E H E L which is the indicator of inequality in this study, is a function of M (money supply), t (tax rate), r (interest rate) and Y (GDP).
Study of the most recent literature revealed that there are other variables that might have impact on income inequality, among which technology and globalisation are the most cited variables. Mehic (2018) used a panel of 27 countries from 1991 to 2014 in order to see whether there is any relationship between technological development through industrial employment with income inequality. The analysis showed that technological development through industrial employment is significantly negatively associated with income inequality. Additionally, the results suggest that it is the middle earners that have borne the largest burden in terms of inequality increases. Baiardi and Morana (2018) found strong evidence in favour of a euro area wide steady-state financial Kuznets curve and of ongoing convergence across euro area members towards a common per capita income turning point level. By means of a counterfactual analysis, they also point to worsening economic and income inequality conditions for all the EA countries, although the level of financial integration and globalisation raised. Therefore, in order to capture the impact of these two variables on income inequality, we included them. For technology, we used gross domestic expenditures on research and development (R&D), expressed as a percentage of GDP. It includes both capital and current expenditures in the four main sectors: business enterprise, government, higher education and private non-profit. R&D covers basic research, applied research and experimental development. As for globalisation, we used the financial globalisation index 5 based on Cordella and Ospino Rojas (2017). The variables we used for the empirical study and their definitions are summarised in Table 5. 5 Cordella and Ospino Rojas (2017) computed a new financial globalisation index for a large sample of countries for 1992-2016. Unlike other measures, their financial globalisation index corrects for the heteroscedasticity of global volatility. This leads to a downward adjustment of financial globalisation trends for developed, emerging and frontier markets. They also showed that that financial globalisation reduces market volatility (measured by the volatility of stock returns) in tranquil times and increases it in turbulent ones. On average, the first effect dominates so that financial globalisation leads to a decrease in market volatility, which is more pronounced in frontier markets.

| EMPIRICAL ANALYSIS
Although the Gini index might be a better definition for representing the level of inequality in a country, due to the lack of data for Japan, in this paper, the definition of inequality is the average household earning of top 10% (rich) over the average household earning of the bottom 10% (poor) as our inequality measure, and the original data were collected from FIES, conducted by Statistics Japan.

| Unit root tests
In order to evaluate the stationarity of all series, we performed unit root tests on all variables using three tests: (i) the augmented Dickey-Fuller (ADF) test; (ii) the Phillips-Perron (PP) test; and (iii) the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. The ADF has the null hypothesis of a unit root. The Schwarz information criterion (SIC) with a maximum of 10 lags was used. The PP test also has the null of a unit root. The Bartlett kernel spectral estimation method and Newey-West bandwidth were used. The KPSS has the null of stationarity, and it was performed with the Bartlett kernel spectral estimation method and Newey-West bandwidth. Securing a robust assessment of the effective characteristics of the series is the main reason to use the three complementary tests. The results for both level and first difference are summarised in Table 6. Our results imply that with the exception of E H E L which is stationary based on all three tests, all series have unequivocally a unit root therefore non-stationary. These results demonstrate that the short-term interest rate, total tax, real GDP, money stock (M1), Financial globalisation index and technology variable each contain a unit root and non-stationary. However, in the first differences, we were able to reject the null hypothesis of presence of unit root for those variables. Since six of the variables were non-stationary at level and stationary at first differences, they are integrated of order 1 or I (1). Due to the non-stationary series, the next step is to apply a cointegration analysis to examine whether the series are cointegrated, meaning that long-run relationships are present among these variables or not.

| Cointegration analysis
One of the main issues in VAR/VEC models is lag order selection. Ivanov and Kilian (2005) presented six criteria for lag order selection, which are the SIC, the Hannan-Quinn criterion (HQC), the Akaike information criterion (AIC), the general-to-specific sequential likelihood ratio (LR) test, a small-sample correction to LR (SLR) and the Lagrange multiplier (LM) test. In this research, we used AIC standards, which suggested two lags.
In the next step, in order to identify the cointegrating vectors among FGI, TECH, M, r, t, Y and E H E L we conduct a cointegration analysis using Johansen's cointegration test by assuming a linear deterministic trend and in two cases, with intercept no trend and with intercept and trend. The results of the cointegration test summarised in Table 7.
As we can see from Table 7, results for intercept and no trend indicate 4 cointegrating equations and for intercept and trend indicate 5 cointegrating equations at 5% significance level. This means that variables are cointegrated, and there is a long-run association among variables; thus, they move together in the long term. Therefore, we should run a vector error correction model (VECM).

| Vector error correction model (VECM)
We estimate Model (19) by incorporating FGI (financial globalisation index) and TECH (Technology) in a VECM setting, including the seven variables: inequality variable ( E H E L ), financial globalisation index (FGI), technology or R&D expenditures (TECH), money stock (M), the short-term interest rate (r), total tax (t), real GDP (Y). We define all variables except interest rate in their logarithmic forms. The VECM is defined as: where where D is the first differences, L is the lag operator, and ε is an error term. Q can be written as Q = ab', where "a" is a loading matrix defining the adjustment speed of the variables in V to the long-run equilibrium defined by the cointegrating relationship and "b" is a vector of the cointegrating relationship. (Yoshino, Taghizadeh-Hesary, Hassanzadeh, & Prasetyo, 2014). The rank of Q is expressed by r. As mentioned in the previous subsection, the AIC standard suggested two lags for these series. In our VECM, we used all aforementioned 7 variables as endogenous variables in order to find if there is any significant association between FGI, TECH, M, r, t, Y with the E H E L . Section 4.2.2 and 4.2.3 analysed the possible long-run and short-run relationships.

| Long-run relationship
Johansen cointegration test results revealed that there is a long-run association among variables; thus, they move together in the long term. Based on Johansen's technique, the normalised long-run cointegration relationships are as follows: : Values in the parentheses are the standard errors. The normalised long-run cointegration relationship is very revealing. The observed signs are as anticipated and consistent with our expectation. There is negative long-run relationship between tax and E H E L , and this means that the Japanese tax system is effective in reducing the income inequality. On the other hand, there is a positive long-run relationship between monetary policy and E H E L , and this means in the long-run, increase of the money stock or reduction of the policy interest rate, the income inequality ( E H E L ) will be increased. The GDP in long-run contributes to reduction of the income inequality. Finally, more R&D expenditures will reduce the income inequality in long-run. High level of R&D expenditures as a percentage of GDP will result in more technological progress; therefore, marginal productivity of labour will increase and the wage rates increase which will reduce income inequality, and this is in line with the findings of Mehic (2018) who used a panel of 27 countries from 1991 to 2014.
All variables except interest rate are in logarithmic form; therefore, we can interpret the estimated coefficients as long-run elasticities. Results show that a 1% increase in the M1 over GDP ratio will result in a 0.22% increase in the average household earning of the top 10% (rich) over average household earning of the 10% bottom (poor) ratio, a 1% increase in the total government tax receipts over GDP ratio will reduce the average household earnings of the top 10% (rich) over average household earnings of the 10% bottom (poor) ratio by 0.37%, and finally, a 1% increase in the real GDP will reduce the average household earning of the top 10% (rich) over average household earning of the 10% bottom (poor) ratio by 1.01%. Table 8 shows the VEC model estimates. Based on Johansen cointegration results, cointegrating equation set at 4 with intercept without trend. The presence of cointegration requires at least one of the coefficients of the error correction terms (ECT) to be statistically significant. This condition is observed throughout the VEC model. For the ECT1, value of E H E L is negative and statistically highly significant, as expected, signalling that the system is stable and converges to the equilibrium track after some disturbance in the system. With a 95% confidence interval, for E H E L , the value of ECT1 is not different from 1, and therefore, the value of ECT1 being slightly higher than 1 is deemed acceptable. In addition, when looking at values of E H E L ðÀ1Þ row, for M the coefficient value is 0.29 and statistically significant, and for r, the coefficient value is −1.33 and statistically significant, that shows the short-term positive impact of increase in money supply and lower interest rates on increasing the income inequality. On the other hand for Y, the coefficient is −0.24 and statistically significant, that is another evidence that higher economic growth will reduce the income inequality. As for t (Tax), Table 8 results do not find any significant association with income inequality. In another words, tax policies have a more long-run impact on income inequality as we showed in the previous section; however, monetary policy has both short-run and long-run impact on enlarging the income inequality.

| Variance decomposition analysis
In the VAR/VEC framework, variance decomposition clarifies which one of the macroeconomic factors provides explanatory power for a variation in our inequality measure over different periods (Lutkepohl, 2005).
The result of the variance decomposition for the E H E L using Cholesky is shown in Table 9. Monte Carlo error (MCE) implemented using 100 repetitions. The variance decomposition makes it possible to determine the magnitude of each variable in creating fluctuations in other variables. Results show that after ten periods, first, almost 48.20% of forecast error variance of the E H E L is accounted for by its own innovations; in other words, the lagged inequality made the current and will make the future Inequality. Second, 9.30% of the forecast error variance can be explained by exogenous shocks to monetary policy shock-the money stock (M1). The short-term interest rate and financial globalisation also account for the increase in inequality by 2.32% and 18.22%. On the other hand, the total tax, real GDP and technology contributed in reducing the inequality measure, respectively, by 3.77%, 12.35% and 5.80% after ten periods. Then, when looking at the variance decomposition in 20 th period, the contributions changed drastically. Contribution of own innovations of E H E L reducing to 36.06%. The ratio for FGI and Y reduced to 14.55% and 12.06%, respectively. However contribution of TECH, M, r and t raised to 12.19%, 15.83%, 4.65% and 4.62%, respectively.

| CONCLUSION
In this paper, we used our original calculation of inequality measure using Japanese statistics to study how monetary policy shock and tax policy affected inequality in Japan. We constructed quarterly series of inequality measures of income by calculating average household earning of the top 10% over average household earning of the bottom 10% from 2002Q1 to 2017Q3 and estimated their response to monetary shocks and the tax policy implemented. We found that the zero and negative interest rate policy of the Bank of Japan increased income inequality through a rise in the price of the financial assets that just benefited the rich income groups, which resulted in widening the income gap among different income groups.
Further breaking down our results, variance decomposition results show after 10 periods (2.5 years) almost 48.20% of forecast error variance of the inequality is accounted for by its own innovations; in other words, the lagged inequality made the current and will make the future Inequality. However, this percentage is reducing to 36.06% in the 20th period (after 5 years). In addition, variance decomposition results show that that increasing of income inequality by monetary policy is larger when comparing to decreasing effects of tax policy on income inequality. Cointegration and VECM results show that monetary policy has both short-run and long-run impacts on inequality. However, taxes have only long-run impact on income inequality and we could not find any short-run relationship between taxes and income inequality. In addition, paper found that technological progress can reduce the income inequality only in long-run by increasing the marginal productivity of labour with positive impacts on employment and wages.
The Japanese economy has been in a stagnant situation, often described as the "lost decade," and monetary policy could not promote the economic growth nor create jobs. Only those households holding financial assets and investing in the capital market, which are the high-income households, are gaining benefit, contributing to the rise of the inequality Yoshino and Taghizadeh-Hesary (2017b).
One theory to explain the ineffectiveness of the monetary policy is mentioned by Yoshino and Sakakibara (2002), Yoshino and Taghizadeh-Hesary (2015b) and Yoshino, Taghizadeh-Hesary, & Tawk (2017). The investment-saving curve (IS) became vertical due to low level of marginal productivity of capital; therefore, when the monetary policy changed the liquidity preference and money supply curve (LM), private investment does not grow despite very low interest rates. Depressed investment in Japan means that the economy is not able to recover by the means of monetary policy (Yoshino & Taghizadeh-Hesary, 2016). Since the burst of the asset price bubble in Japan in the 1990s that put the Japanese economy into a tailspin and reduced investments, the corporate restructuring to reduce idle capacity and input new investments was not pursued (Yoshino and Taghizadeh-Hesary, 2017b). And greater importance placed on monetary policy instead of accelerating corporate restructuring .
Under the unconventional monetary policy, while the high-income households gain from appreciating price of the financial assets, low-income households, who do not hold significant financial assets, are unable to see the rise in their income.
Although this unconventional monetary policy in Japan has been taken as the last measure to combat the long-lasting stagnation, it may bring about an unwanted side effect. As inequality already rising, following with this policy, it will not achieve a desirable result to the Japanese economy and, furthermore, to the nation itself.
On the bright side, the tax policy implemented had been successful in reducing inequality, as there is a progressive income tax system existing in Japan, as shown in Figure 3, besides other types of taxes (inheritance tax, sales tax, capital tax, etc.).
Beyond its pertinence for Japan, this study paves a way for other countries tackling economic turmoil and initiating unconventional measures. Its extensive history of unconventional monetary policy has the potential to enlighten other regions of the world in terms of the monetary policy's future and, hence, for future growth.