Discussion Paper No. 488
The Pasinetti Index and the Rise of Inequality in theAge of Unconventional Monetary Policy in Japan
Yuki Tada&

Kazuhiro Kurose

April 5, 2024

TOHOKU ECONOMICS RESEARCH GROUP
Discussion Paper

GRADUATE SCHOOL OF ECONOMICS AND

MANAGEMENT TOHOKU UNIVERSITY

27-1 KAWAUCHI, AOBA-KU, SENDAI,
980-8576 JAPANThe Pasinetti Index and the Rise of Inequality in the Age of
Unconventional Monetary Policy in Japan
Yuki Tada*

Kazuhiro Kurose**

Abstract

There are increasing concerns in Japan that unconventional monetary policy (UMP) accelerates
inequality by the asset price mechanism, allowing the higher income group to gain extra capitalincome. The UMP does have limited accounting in creating real wage growth as well as restoring
demand and growth as the overall economy has been stagnant. We revisit the issue of income
inequality in Japan by using Pasinetti’s approach of measuring personal income distribution andalso examine its effect on the effective demand and functional income distribution. We
implement workers’ debt-augmented Pasinetti Index (PI) as a proxy of personal income
distribution, moving away from workers towards rentiers in their interpersonal lending andborrowing relations. Our empirical result with the VAR model for the case of Japan shows 1)
higher PI restrains the effective demand. 2) Higher rentier income also affects the wage sharenegatively through a decrease in capacity utilization.
Keywords: Monetary Policy; Income Distribution; Post-Keynesian Economics; Pasinetti Index.
JEL codes: B50; E12; E52.

* Researcher at Fondation France Japon an l’EHESS** Graduate School of Economics and Management, Tohoku University

11. Introduction:
This paper investigates whether the income flow towards high-income groups from low-income
workers would restrain the effective demand and wage share in the aggregate under the age of
conventional monetary policy in Japan. The country has observed higher income inequality inthe last decades in addition to the stagnant real wage, and several recent empirical studies havefound that unconventional monetary policy (UMP) might have accelerated inequality by the asset
price mechanism, widening wealth and income inequality (Saiki and Frost 2014, Israel et al.
2023). In that sense, despite the fact that UMP might boost the income of the rich, UMP has
limited accounting for creating higher income for the bottom as the real wage has stagnated, andthere is a rise of people with few or no savings and indebtedness, especially among the lowincome group of people. 1 We revisit this issue, focusing on the recent trend of income
distribution and monetary policy and its effect on aggregate demand and functional income
distribution.
While there has been an increasing amount of research to show the effect of UMP and therise of inequality in Japan, there needs to be more studies on how inequality that emerged under
the UMP has affected Japan's overall economic performance and wage share. Following themethodology of Kappes et al. (2023) and Seccareccia and Lavoie (2016), we use the Pasinetti
Index (PI) as a proxy of personal income distribution to take into account the distributionalchange when workers repay their financial liabilities to the rentiers from the wage income.
Pasinetti’s (1981; 1993) fair interest rate rule allows us to measure personal income distribution
by considering the disparity between the income of rentiers and borrowers. As a contribution
from our side, we developed our version of PI by taking into account the rise of inequality
between interest income groups and the labor income group in their interpersonal lending andborrowing relations. This measurement of income distribution boils down to the fact that income
inequality has been rising not only due to the rise of rentiers’ interest income but also due to therise of low-income workers may become indebted from decreasing savings and real wages.
Despite the fact that the UMP by Bank of Japan (BoJ) has been targeting the interest rate at thenegative range to counter economic deflation through massive purchases of securities and yield
curve control of the government 10 years bonds yield, the effect of such UMP is questionable as
the real wage and the effective demand have decreased while allowing the income distribution
favored to the high-income group and also we observed the decrease of wage share.
There are various channels for the distributional effects of monetary policy. The previous
empirical study of the effect of UMP has paid attention to the portfolio channel, which explainsthat the central bank’s asset purchase would cause an increase in the asset price. Expansionary
monetary policy might affect inequality through the heterogeneity in portfolios, which affects
both wealth and income inequality, benefiting financial asset holders more. For example, theempirical research by Saiki and Frost (2014; 2020) and Israel et al. (2023) reveals a rise ininequality, especially since Japan's second phase of UMP due to the rise in asset price. Although
the portfolio channel is related to the rise in asset price and financial asset value which also
affects wealth inequality, Saiki and Frost (2014; 2020) and Israel et al. (2023) measure such
1 The landscape of contemporary income distribution in Japan has changed, especially after the implementationof UMP, while it was limited only to wage inequality, as the top 1% of income source is primarily wage income
Moriguchi and Saez (2008).

2

inequality using specific income survey data to compute wage differential and the Gini
coefficient. The rationale is that there is a positive correlation between the share of securities insavings, and the level of wealth and income level. Another channel is more focused solely toincome inequality, while the previous channel concerns income and wealth inequality. As regards
the impact of monetary policy, there is an income composition channel. As there is heterogeneity
in the source of income, such as labor and capital income, the monetary policy benefits
differently depending on the characteristics of the income composition of households.
Taghizadeh-Hesary et al. (2018) argue that income inequality in Japan since the implementationof UMP in 2001 has widened inequality due to increased capital income related to wage income
as the stock price has hiked, allowing the rich to have higher dividend income.
Nonetheless, we investigate the rise of inequality from the normative monetary policy ruleusing workers' debt-augmented Pasinetti Index (PI), which is a proxy of income distribution
specifically from low-income workers as debtors to rentiers as creditors (see the details in
sections 3 and 4). The PI asserts a normative principle of income distributional neutrality, whichassumes that the long-term nominal interest rate ought to equal the growth rate of nominal wages
to keep the distribution of purchasing power between creditors and debtors unaltered. The
advantage of measuring income distribution in this fashion is that income disparity is embeddedin the PI, which also has normative connotations on whether monetary policy favors rentiers(capital income earning group). Thus, we do not restrict our position only to investigate a
specific channel of the transmission mechanism such as the asset price channel/portfolio channel
in Saiki and Frost (2014; 2020) and Israel et al. (2023) but with the normative point of viewwhich is a combination of income composition channel and portfolio channel.
The previous studies by Taghizadeh-Hesary et al. (2019), Saiki and Frost (2020), and Israel etal. (2023) only focus on the effect of monetary policy on the rise of inequality. As a contribution
from our side, we investigate how higher inequality by UMP would affect growth anddistribution in Japan. While there are many studies about the relationship between effective
demand and functional income distribution, the relationship between the PI, effective demand,and functional income distribution is partially studied. There are few theoretical studies
regarding how PI would affect the dynamic between growth and functional income distribution.
One of the critical post-Keynesian theoretical contributions is the study of the Kaleckian
economic growth and income distribution models (Bhaduri and Marglin 1990; Blecker 1989;
Dutt 1984; Rowthorn 1981; Taylor 1985). Following that research, several authors have analyzed
different economies empirically to identify whether their demand regime is wage- or profit-led.
The aggregative approach uses the estimation of a Vector Autoregressive (VAR) model withcapacity utilization and wage share, showing that these variables are endogenously related. Thisapproach is a theoretical investigation of the neo-Goodwin model, and for the case of the US, theneo-Goodwin pattern is empirically confirmed by Barbosa-Filho and Taylor (2006), Carvalho
and Rezai (2015), and Diallo et al. (2011). These studies find a profit-led demand regime and a
profit-squeeze distribution schedule. In the case of Japan, empirical research by Nishi (2012) has
also revealed that this profit-led and profit squeeze pattern exists in the Japanese economy, using
data from 1985 to 2008.
How the PI would affect the dynamic of growth and distribution has yet to be investigatedsubstantially. If we regard the PI as an indicator of personal income distribution, there is similar
research that can aid us in understanding the relationship between the variables. Lavoie (2017)
argues the effect of overhead labor and its feedback effects on capacity utilization and income
distribution. Income distribution moving towards the overhead labor (higher income group),3which tends to be classified as managers and supervisors receiving not only wage income but
also bonus and remuneration, from the direct labor (lower income group) who received only
wage income, would reinforce the profit-led pattern. 2 For the empirical research of the US
economy, Rolim (2019) confirms the effect of overhead cost on the profit-led pattern. Also, theprofit-squeeze pattern as direct labor only can increase their wage share due to bargaining power.
Also, the VAR model shows that higher income distribution towards overhead labor would
reduce capacity utilization. Recently, there has been empirical research using the VAR model toshow the negative effect of higher PI on capacity utilization and wage share for the case of the
US and Canada (see Kappes et al., 2023).
We conduct a standard VAR model to analyze the questions:• Would a higher income flow due to the UMP toward rentiers restrain the effective
demand and functional income distribution toward workers in Japan?
• What is the relationship between personal income distribution and functional income
distribution under the UMP in Japan?
The main variables we use for this study are the PI, wage share, and aggregate capacity
utilization to see if they are related to each other. Our empirical result with the VAR model
would show 1) Higher PI or income flow moving towards rentiers affects macroeconomic
growth negatively. 2) Higher rentier income flow also affects the wage share negatively, whichindicates that in Japan, under the UMP, the wage share has been indirectly negatively affected by
the higher PI or personal income distribution through the decreasing effective demand.
This paper follows this order: in section 2, we present a brief history of monetary policy
conducted by BoJ and discuss recent literature on the distributional effect of monetary policy andincome inequality. Section 3 explains the basic concept of the Pasinetti Index by analyzing
Pasinetti’s (1981, 1993) interest rule. Section 4 shows the data description and our VAR
approach. Section 5 describes the result of our VAR model. Section 6 is the conclusion.

2. Preliminary Consideration
In this section, we present a brief history of the monetary policy conducted by BoJ from 2001 to
2022 and provide a survey of the existing empirical literature on the distributional effect ofmonetary policy. The brief history description would be worthwhile since BoJ has been theforerunner of UMP. BoJ’s UMP was not just Quantitative Easing: it evolved to be followed by
the control of the long-term interest rate, the introduction of negative interest rate, and finally, theyield curve control.

2.1. The brief history of monetary policy by BoJ as the forerunner of UMP
UMP by BoJ has several phases. 3 The first phase started in March 2001. However, it has a prehistory: the ‘zero interest rate policy.’ BoJ encouraged the uncollateralized overnight call rate(call rate, hereafter) to move as low as possible at the monetary policy meeting on 12 February
1999. As a result of this decision, the call rate was stably kept at virtually zero percent. BoJ
As higher personal inequality rises due to the higher income distribution towards the overhead labor, which tends
to have a lower propensity to consume than that of direct labor, Palley (2017) shows there is a high likelihood of a
profit-led regime since it would diminish the stimulus on the consumption of increasing the wage share.
3
The subsection depends on the announcements released by BoJ on the date of the monetary policy meeting, all ofwhich are available in Bank of Japan (1998-2024).
2

4

officially called the policy the ‘zero interest rate policy’ in the announcement on 21 September
1999.
The zero-interest rate policy was terminated at the monetary policy meeting on 11 August
2000, and the call rate was raised to around 0.25%. Montgomery and Volz (2021) argued that thisdecision was premature. The decision was reversed, and UMP started.
【First phase: Quantitative Easing from March 2001】
On 19 March 2001, BoJ announced the new procedure for money market operation andmonetary easing. The main operating target for money market operation was changed from thecall rate to the outstanding balance of current accounts at BoJ, and the amount of the outstandingbalance was increased to around 5 trillion yen. Moreover, it was also decided that the amount of
the outright purchase of long-term government bonds increased to 400 billion yen per month. 4
The first phase of UMP was a bold monetary policy experiment, called the Quantitative
Easing (QE1). In the history of central banking, supplying sufficient liquidity beyond therequired reserves was an unprecedented policy. BoJ purchased large amounts of assets fromcommercial banks to make them more liquid, aiming to lower interest rates on loans forbusinesses and households, which in turn stimulates investment, and economic growth. 5
QE1 was lifted in March 2006. Namely, the operating target was returned from theoutstanding balance of current accounts to the call rate, and the call rate remained at effectively
0 %, although it had been increased to 0.25% at the monetary policy meeting on 15 June 2006.
The monetary policy by BoJ had returned to conventional for the first time in about 5 years.
【Second phase: Quantitative Easing from December 2008】
To respond to the financial turmoil caused by the global financial crisis, at the monetary policy
meeting on 31 October 2008, BoJ decided to decrease the call rate to around 0.3 %, although it
had been increased from 0.25 % to 0.5 % on 21 February 2007. Furthermore, it was decided to
introduce the Complementary Deposit Facility at the meeting on 31 October 2008. It was ameasure to pay interest on excess reserve balances to further facilitate the provision of sufficientliquidity, and a rate of 0.1 % was applied. 6 The BoJ’s initial reaction to the financial crisis wasconventional since the main operating target was the call rate. However, the call rate was further
reduced to 0.1 % at the monetary policy meeting on 19 December 2008. It was also decided at
the meeting that BoJ would add 30-year bonds, floating-rate bonds, and inflation-indexed bonds
to the list of eligible JGBs since the additional measures regarding money market operation werenecessary for the effect of extremely low policy interest rates to prevail in financial markets andcorporate financing.
At the monetary policy meeting on 5 October 2010, BoJ decided to implement the‘Comprehensive Monetary Easing (CME)’ to further enhance monetary easing. It consisted ofthree components:

The amount of the outstanding balance was finally increased to 30–35 trillion yen at the monetary policy meetingon 20 January 2004.
5
See also Fiebiger and Lavoie (2021) with respect to the transmission mechanism of the QE.
6This was initially a temporal measure. However, it was gradually extended and maintained until ‘QQE + NIR’ wasintroduced in 2016, as we will see.
4

5

1.
2.
3.

The reduction of the call rate to virtually zero percent;
The clarification of the policy time horizon, under which the zero-interest rate policy
would be maintained until the price stability is in sight ‘on the basis of theunderstanding of “medium- to long-term price stability”’; 7The establishment of a program on the balance sheet to purchase various financial
assets, such as government securities, commercial papers, exchange-traded funds(ETFs), and Japan real estate investment trusts (J-REITs). The size of the program wasinitially set at 35 trillion.

We term the monetary policy conducted from December 2008 to April 2013 by BoJ‘Quantitative Easing 2 (QE2)’, since BoJ unprecedentedly purchased the financial assets, such as
the long-term JGBs, ETSs, and J-REITs.
【Third phase: Quantitative and Qualitative Easing from April 2013】
At the monetary policy meeting on 4 April 2013, BoJ decided to introduce the ‘Quantitative andQualitative Monetary Easing (QQE)’. This decision was made to achieve the inflation target of
2% in the consumer price index (CPI) within about 2 years. In order to do so, monetary policy
entered a new phase of monetary easing in terms of both quantity and quality. Under QQE, themain operating target was changed from the call rate to the monetary base. QQE was expected to
double the monetary base and the amounts outstanding of Japanese government bonds (JGB) as
well as ETFs in 2 years, and more than double the average remaining maturity of JGB purchases.
More specifically, it was decided:
1.
2.
3.

The monetary base increases at an annual pace of about 60–70 trillion yen.
In order to encourage a further decline in interest rates across the yield curve, BoJ
purchases JGBs so that their amounts outstanding increase at an annual pace of about
50 trillion yen.
JGBs with all maturities including 40-year bonds are made eligible for purchase, andthe average remaining maturity of the JGB purchased by BoJ is extended from slightly
less than three years at present to about seven years.

The third point corresponds to the ‘Qualitative Easing’ in that the central bank massively
purchased the longer-term government bonds.
At the monetary policy meeting on 31 October 2014, the expansion of the QQE wasdecided. In other words, the monetary base increased at an annual pace of about 80 trillion yen,and the average remaining maturity of the JGB purchased by BoJ was extended to about 7–10
years. In addition, it was decided that the outstanding amounts of ETFs and J-REITs increased at
an annual pace tripled compared with the past.
【Fourth phase: QQE + Negative Interest Rate from Jan 2016】
At the monetary policy meeting on 29 January 2016, it was decided to introduce the ‘QQE with anegative interest rate (NIR).’ BoJ applied a negative interest rate of minus 0.1 percent to current

This can be considered to be a sort of forward guidance. In addition, ‘medium- to long-term price stability’ meantthat the inflation rate of the CPI has a positive range of 2 % or lower. See Shirai (2013) on these points in detail.
76

accounts that financial institutions hold at BoJ. 8 Furthermore, it was also announced that the
average maturity of the JGBs purchased by BoJ was extended to 7–12 years. 9 This decision wasmade to pursue monetary easing by making full use of possible measures in terms of three
dimensions, combining quantity, quality, and interest rate. First, ‘QQE + NIR’ will lower the
short end of the yield curve by slashing its deposit rate on current accounts into negative
territory. Second, it will exert further downward pressure on interest rates across the entire yield
curve, in combination with large-scale purchases of JGBs.
【Fifth phase: QQE + Yield Curve Control from Sept 2016】
The new framework for strengthening monetary easing was decided at the monetary policy
meeting on 21 September 2016: the introduction of the ‘QQE with yield curve control (YCC).’
The new framework consisted of two major components:
1.
2.

BoJ controls short-term and long-term interest rates (yield curve control);BoJ commits itself to expanding the monetary base until the inflation rate of CPI
exceeds the price stability target of 2 percent and stays above the target in a stablemanner (inflation-overshooting commitment).

Under the framework, BoJ initiated to target the yield on 10-year JGB at ‘around zero percent.’
Although the inflation target of 2 %, announced in April 2013, should have been achieved until
2015 at the latest, it could not be achieved in 2016. The inflation-overshooting commitment was
set to raise the inflation expectations.
At the monetary policy meeting on 31 July 2018, it was decided that the commitment toachieving the price stability target is strengthened by the explicit introduction of the forward
guidance for policy rates. The forward guidance implies that BoJ will intend to maintain thecurrent extremely low levels of short- and long-term interest rates for an extended period of time.
No change in YCC was made. 10
To enhance monetary easing in light of the impact of the outbreak of COVID-19, on 16
March 2020, BoJ decided to massively purchase JGBs, ETFs, and J-REITs and establish thespecial program to support financing, while YCC is maintained. 11 On 24 April 2020, it wasannounced that an upper limit of the amount of BoJ’s purchase of JGBs was removed (80 trillion
yen at the past) to control the long-term interest rate.

Following some central banks that introduced a multiple-tier system (e.g., the Swiss national bank), on 29 January
2016, BoJ decided to adopt a three-tier system of the outstanding balance of current accounts that each financial
institution held at BoJ, to each of which a positive interest rate, a zero-interest rate, or a negative interest rate wasapplied, respectively. Regarding the details. The negative interest rate was applied primarily to new excess reserves
each bank hold (Montgomery and Volz 2021).
9
Precisely speaking, this extension had been decided at the monetary policy meeting on 28 December 2015.
10
At the monetary policy meeting on 25 April 2019, the commitment was clarified that the current extremely low
levels of short- and long-term interest rates will be maintained, at least through around spring 2020. At the monetary
policy meeting on 31 October 2019, new forward guidance was decided that BoJ expected short- and long-term
interest rates to remain at the present or lower levels if necessary.
11
The special program to support financing was extended to the end of March 2022 at the monetary policy meetingon 18 June 2021.
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【Sixth Phase: Further Effective and Sustainable Monetary Easing from March 2021】
It was decided at the monetary policy meeting on 19 March 2021 that while YCC wasmaintained the fluctuation of the 10-year JGB yield within ± 0.25 % was allowed. It was the
BoJ’s policy stance to enhance further effective and sustainable monetary easing. It would be
decided, partially because there had been an increasing number of business days when no bids
were submitted in the 10-year JGB market.
At the monetary policy meeting on 20 December 2022, the conduct of YCC was modified to
improve market functioning and encourage a smoother formation of the entire yield curve, while
maintaining accommodative financial conditions. In other words, the range of fluctuation of 10year JGB yield was expanded to ± 0.5 %.

2.2. Related literatures

The effect of monetary policy is one of the important subjects in macroeconomics. The
consensus among economists is that monetary policy stabilizes the fluctuations in output,
investment, prices, interest rates, and employment. Mainstream economists, except Romer andRomer (1999), had paid little attention to the distributional effect of monetary policy in the 20th
Century. Meanwhile, post-Keynesian economists traditionally focused on the distributional
effect, as Lavoie and Seccareccia (1988, 1999) and Rochon (2022) argued.
Although BoJ’s initial reaction was conventional, the global financial crisis in 2008 hadmany central banks implement UMP promptly. The research on the effects of UMP on
macroeconomic stability became popular. For example, Meinusch and Tillmann (2016) showedby using the US 2007–2013 data that UMP (the QE shock) led to a fall in interest rates, anincrease in stock prices, and a rise in real economic activity and inflation. Gambacorta et al.
(2014) demonstrated by using 2008–2011 data from several developed countries that UMP (anexogenous increase in central bank balance sheet at the zero lower bound) led to a temporal risein economic activity and consumer prices. As Dell’ Ariccia et al. (2018) confirmed, most studies
on the macroeconomic effects of UMP indicated that UMP generally had stabilization effects onfinancial markets, prices, and real GDP growth. Hanisch (2017) investigated the effectiveness ofthe monetary policy from 1985 to 2014 implemented by BoJ by using a structural dynamic factor
model and showed that an expansionary monetary policy shock significantly increased real andnominal economic activity. Moreover, he argued that the effectiveness differed depending on thepolicy instrument.
On the other hand, there has been a growing number of debates regarding the rise ininequality of distribution of income/wealth, since Piketty’s (2014) influential book Capital in the
Twenty-First Century. Some academic research revealed that inequality could destabilize growth(Berg et al., 2014; Rajan, 2010) and increase the occurrence of financial crises (Bordo andMeissner, 2012; van Treeck, 2014). Thus, the attention to the relationship between economic
inequality and monetary policy has been growing recently in the economic profession.
Furthermore, central bankers also began to mention the distributional effect of monetary policy.
For example, Kuroda (2017, p. 19), who was the Governor of BoJ, said that monetary policy is
not a policy tool for distributional purposes, but he subsequently stated, ‘this does not mean that
central banks are allowed to ignore the distributional effects of monetary policy, especially if the
distributional effects have an effect on aggregate impact.’
The transmission mechanism of UMP to income distribution is twofold (e.g., Bonifacio et al.,2021). One is the income composition channel. As is pointed out in Section 1, UMP increases
8asset prices and capital income (or capital gain), which is in general beneficial to householdswith higher income. Through this channel, income would be unequally distributed amonghouseholds. The other channel is the earnings distribution channel. UMP stimulates economic
activity, which leads to creating more employment and higher wages, which is in generalbeneficial to households with lower income. This channel would reduce income inequality.
Which effect is greater affects the personal income distribution.
Mainstream empirical studies on the distributional effect of monetary policy have been
actively published. For the US empirical research, for example, Coibion et al. (2017), Davtyan(2017, 2023), and Doepke et al. (2019) analyzed the impact of monetary policy on income
inequality. The UK empirical research is given by Ballabriga and Davtyan (2022), Bunn et al.
(2018), and Mumtaz and Theophilopoulou (2017). Casiraghi et al. (2018) analyzed the
distributional effect of monetary policy in Italy. Guerello (2018), Lenza and Slacalek (2018),
Rupprecht (2020), Creel and El Herradi (2022), and Samarina and Nguyen (2024) analyzed the
distributional effect of monetary policy conducted by the European Central Bank in the selected
countries of the Euro area. El Herradi and Leroy (2021) analyzed the effect in the 12 OECD
countries and Furceri et al. (2018) examined the distributional effect in the case of 32 developed
and developing countries. Hafemann et al. (2018) investigated the effect in the case of six
developed countries. O’Farrell and Rawdanowicz (2017) analyzed the effect of the portfolio
channel in Europe and North America in the 2010s. 12
The sample in some of the above works includes the periods during which conventionalmonetary policy was conducted. As Colciago et al. (2019) and Kappes (2023) argued, thedistributional effect of monetary policy, irrespective of whether it is conventional or
unconventional, yields mixed results. This is because the empirical result depends on various
conditions. 13 However, Kappes (2022, 2023) concluded that an expansionary (contractionary,
resp.) conventional monetary policy tended to decrease (increase) income inequality, and theeffect of UMP was country-specific: it reduced inequality in Europe and increased in Japan.
Post-Keynesian economists also examine the distributional effect of monetary policy. One of
the characteristics of the post-Keynesian studies is to analyze income distribution from thenormative point of view by using PI. PI, whose conceptual explanation is closely made in thenext section, is the index to see whether lenders receive from borrowers a greater purchasing
power compared with the lenders’ contribution in terms of labor when the lenders receive therepayment. If the lenders receive the greater purchasing power, the income distribution turns out

Some works, such as Coibion et al. (2017) and Mumtaz and Theophilopulou (2017), measured inequality in termsof consumption out of income. McKay and Wolf (2023) also argued the distributional effect of monetary policy interms of consumption across different groups of households. This measure may ignore the increase in higher
consumers due to higher inequality. Setterfield et al. (2016) showed that in Anglo-Saxon countries such as the US
and UK, low-income households are taking higher loans (indebtedness), which contributes to the debt-led growth in
the US; regardless of the income level, the debt-led consumption increases economic instability, which led thefinancial crisis.
13
One of the examples of the conditions is the measure of UMP; some works (e.g., Lenza and Slacalek, 2018) used
the quantitative easing or asset purchase program, while others (e.g., Saiki and Frost, 2014, 2020) used the monetarybase or the size of the central bank’s balance sheet. Second, although the Gini coefficient is often used to measureinequality, the empirical result may change depending on whether the coefficient is derived from gross or net
income. Moreover, El Herradi and Leroy (2021) used the top 1% income share and Taghizadeh-Hesary et al. (2018)used the ratio between the incomes of the top decile and the lowest decile in measuring the inequality. Third, whatkind of econometric technique is used also affects the result, although the vector autoregression or its variants is oneof the representative techniques used to analyze the distributional effect of monetary policy.
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to be unfair. Post-Keynesian economists have analyzed the fairness of income distribution usingPI.
Lavoie and Seccareccia (1988) is the earlier work applying PI to the empirical study ofincome distribution. They analyzed the tendency of the movement of PI and the business cycle in
Canada. Seccareccia and Lavoie (2016) used PI to analyze the income distribution in the US andCanada from 1926 to 2013 and found that the relations of the movement of PI with the growthrate and unemployment rate observed in the US were similar to those in Canada. Seccareccia(2019) analyzed the movement of PI of the selected G7 countries from 1971 to 2017 anddemonstrated that the income was distributed in favor of rentiers from the end of the 1970s to
2008, which was called the era of rentier tranquility. Furthermore, it was argued that the average
unemployment rate was relatively kept higher in the era. Lavoie and Sccareccia (2019) and
Kappes et al. (2023) also examined the income distribution in Canada and the US, respectively,
using PI. Levy-Orlik and Bustamante (2023) utilized PI for several Latin American countries
from 1950 to 2018 and found the inverse relation between the change in the real interest rate andthe real wage growth for the period 1980–2018 although such a relation was not observed from1950 to 1980. Seccareccia and Matamoros (2023) analyzed the income distribution of several
developed countries by using PI and demonstrated that the rentier losses during the post-global
financial crisis decade were primarily reflected in the increased profits of business corporations.
In general, post-Keynesian analyses tend to lead to the result that the net income transfer in favorof rentiers is associated with a negative macroeconomic performance.
Finally, the effect of the monetary policy conducted by BoJ deserves particular attention
since it occupies a special position among those conducted by other central banks, as alreadymentioned in the previous subsection. Moreover, there has been a notable shift in income andwealth distribution in Japan in recent decades. During the period of high economic growth in the
1980s, the inequality in Japan was insignificant as it was the lowest level of inequality among G7
countries. Nonetheless, the recent statistic shows that the poverty rate in Japan is the 7th highest
among the OECD countries, and it has become the highest among G7 (Komiya and Kihara,2021).
Saiki and Frost (2014) is the early work on the effect of BoJ’s UMP and argued that UMP
from 2008 to 2014 conducted by BoJ widened inequality, mainly via the financial market
channel. Saiki and Frost (2020) also analyzed the distributional effect of UMP by BoJ, with thesample periods extended from 2007 to 2017, and derived the same conclusion. Both used the
VAR model. By using the local projections method, Inui et al. (2017) analyzed the distributional
effect of the monetary policy conducted by BoJ from 1981 to 2008. They demonstrated that themonetary expansion shock had a statistically significant impact on inequality across Japanesehouseholds in a stable manner. By using the VAR model, Taghizadeh-Hesary et al. (2018)
analyzed the distributional effect of UMP by BoJ from 2002 to 2017 and showed that themonetary policy increased inequality via the financial market channel. Taghizadeh-Hesary et al.
(2022) also examined the distributional effect of UMP by BoJ from 2000 to 2018 by using theautoregressive distribution lag model and derived similar conclusions to Taghizadeh-Hesary etal. (2018). By using the local projections method, Israel et al. (2023) examined the distributional
effect of UMP from 2007 to 2021 conducted by BoJ and demonstrated that both conventional
and unconventional monetary policy increased income inequality, mainly via the financial

10market channel. 14 Irrespective of the measure of inequality and the econometric method, manystudies pointed out that UMP tended to increase income inequality in Japan.
All the above-mentioned studies regarding the Japanese economy are positive analyses. To
the best of our knowledge, our study is the first one to normatively analyze the distributional
effect of UMP implemented by BoJ using PI.

3. Theoretical understanding of the Pasinetti Index
This section presents the theoretical foundation of this study. First, we review Pasinetti’s (1981,1993) natural rate of interest and define the Pasinetti Index.

3.1 The natural or fair rate of interest
The Pasinetti Index is based on his natural rate of interest, which Lavoie and Seccareccia (1999,2019) called the fair rate of interest to emphasize its normative property. The natural or fair rateof interest is derived from Pasinetti’s (1981, 1993) structural economic dynamics.
Pasinetti’s (1981, 1993) analyzed the economic system in which each sector has a specificgrowth rate of productivity and final demand. The sectoral proportions of outputs, prices, andemployment are ever-evolving, and thus the balanced growth path does not exist in Pasinetti’s(1981, 1993) structural economic dynamics. 15 The natural economic system defines themacroeconomic equilibrium with ever-lasting structural changes and full employment of capitaland employment.
The sectoral differences in the labor productivity imply the emergence of interest. First, let us
consider the property of the natural rate of interest in the simplest case: a pure labor economy
explored by Pasinetti (1993). Although the possibility of saving does not exist in the overall
economic system, it is open to single individuals. An individual can save by postponing
consumption (lending consumption goods) and dissave by forwarding consumption (borrowingthem), even though overall saving is impossible. Those who save are lenders, and those who
dissave are borrowers.
Suppose that the economic system has 𝑚𝑚 commodities, which are indexed in the order asfollows:
𝜌𝜌1 > 𝜌𝜌2 > ⋯ > 𝜌𝜌𝑚𝑚 ,where 𝜌𝜌𝑗𝑗 denotes the growth rate of labor productivity of commodity 𝑗𝑗. The rate of interest
logically consistent with the pure labor economy is a zero rate of interest in terms of labor. It
means that the amount of purchasing power that the lender receives is exactly equal to theamount that was lent. The natural or fair rate of interest is defined as follows:
Definition: The natural or fair rate of interest (Pasinetti, 1993, p. 97)
The natural or fair rate of interest is “the rate of interest which realized through time a
distribution of income among the participants to the production process, which is proportional tothe physical quantities of labour they have contributed”.
14
Israel and Latsos (2020) argued that the expansionary monetary policy from 2003 to 2014 implemented by BoJ
increased labor income inequality. In addition, they showed that the expansionary monetary policy increased theeducational pay gap but diminished the gender pay gap.
15This is a striking difference between Pasinetti’s and the mainstream analysis of structural change. See Kurose(2021) concerning this point.

11

We note that the amount of labor embodied in the same unit of a commodity is decreasingover time because of the growth of labor productivity. This implies that the interest necessarily
emerges to keep the purchasing power in terms of labor unchanged, even though an actual rate ofinterest is zero. The zero rate of interest in terms of labor is a normative criterion of the fair
distribution of income in the pure labor economy, since all contributions to benefits from theproduction process are regulated based on the amount of labor in the economy (Pasinetti, 1981,
p. 166). Therefore, Pasinetti’s natural rate of interest has a normative character.
The numeraire must be set to make a financial contract. Pasinetti (1993, pp. 60–63) indicatedthat the price equations have two degrees of freedom in a dynamic model: the absolute value ofthe numeraire at the initial point of time and its rate of change over time. Letting the evolutionsof the labor coefficient of commodity 𝑗𝑗 and the wage rate be 𝑙𝑙𝑗𝑗 (𝑡𝑡) = 𝑙𝑙𝑗𝑗 (0)𝑒𝑒 −𝜌𝜌𝑗𝑗𝑡𝑡 and 𝑤𝑤(𝑡𝑡) =𝑤𝑤(0)𝑒𝑒 𝜇𝜇𝑤𝑤 𝑡𝑡 respectively, the price equations are generally expressed as follows:
𝑝𝑝𝑗𝑗 (𝑡𝑡) = 𝑙𝑙𝑗𝑗 (𝑡𝑡)𝑤𝑤(𝑡𝑡) = 𝑙𝑙𝑗𝑗 (0)𝑒𝑒 −𝜌𝜌𝑗𝑗𝑡𝑡 𝑤𝑤(0)𝑒𝑒 𝜇𝜇𝑤𝑤 𝑡𝑡 = 𝑙𝑙𝑗𝑗 (0)𝑤𝑤(0)𝑒𝑒 �𝜇𝜇𝑤𝑤 −𝜌𝜌𝑗𝑗�𝑡𝑡 , (1)where 𝑝𝑝𝑗𝑗 (𝑡𝑡) denotes the price of commodity 𝑗𝑗 = 1, ⋯ , 𝑚𝑚.
Since the labor productivity is assumed to grow, the amount of labor embodied in one unit of
a commodity is decreasing at rate of its growth rate of labor productivity over time. It implies
that the interest must emerge to keep the purchasing power in terms of labor unchanged.
Therefore, the own rate of interest is 𝜌𝜌1 in terms of commodity 1, 𝜌𝜌2 in terms of commodity 2,… and 𝜌𝜌𝑚𝑚 in terms of commodity 𝑚𝑚, following the above definition. These are the natural orfair structure of the rates of interest (Pasinetti, 1993, p. 88).
We must consider the numeraire that stipulates all credits and debts and represents thenatural or fair structure of the rates of interest. Choosing the wage rate as the numeraire isequivalent to assuming 𝜇𝜇𝑤𝑤 = 0 in (1). From its definition, the natural or fair rate of interest in∗
this case, denoted by 𝑖𝑖𝑤𝑤
, is given by:∗= 𝜇𝜇𝑤𝑤 = 0. (2)𝑖𝑖𝑤𝑤

If the specific commodity, say ℎ, is chosen as the numeraire, 𝑝𝑝ℎ (𝑡𝑡) = 1 holds over time.
From (1), it implies that 𝑝𝑝ℎ (𝑡𝑡) = 𝑙𝑙ℎ (0)𝑤𝑤(0)𝑒𝑒 (𝜇𝜇𝑤𝑤 −𝜌𝜌ℎ )𝑡𝑡 = 1, which mean that 𝜇𝜇𝑤𝑤 = 𝜌𝜌ℎ holds overtime. In other words, choosing commodity ℎ as the numeraire is equivalent to assuming that thewage rate grows at rate of 𝜌𝜌ℎ . Therefore, the natural or fair rate of interest in this case, denotedby 𝑖𝑖ℎ∗ , is given by:𝑖𝑖ℎ∗ = 𝜇𝜇𝑤𝑤 = 𝜌𝜌ℎ . (3)∗If the standard dynamic commodity is chosen as the numeraire, 𝑝𝑝𝐷𝐷 (𝑡𝑡) = ∑𝑚𝑚
𝑖𝑖=1 𝑝𝑝𝑖𝑖 (𝑡𝑡)𝛼𝛼𝑖𝑖 (𝑡𝑡) =∗1 holds, where 𝑝𝑝𝐷𝐷 (𝑡𝑡), 𝛼𝛼𝑖𝑖 (𝑡𝑡) denote the price of the dynamic standard commodity and the weightof commodity 𝑖𝑖 in the commodity basket constituting the standard dynamic commodity at period𝑡𝑡, respectively. 16 By the same token, this case is equivalent to assuming that 𝜇𝜇𝑤𝑤 = 𝜌𝜌∗ , where 𝜌𝜌∗Based on Sraffa’s (1960) standard commodity, Pasinetti (1993, pp. 70–72) invented a special composite
commodity, called the dynamic standard commodity. Its property is that the labor productivity grows at the weighted
average growth rate of labor productivities of all commodities. Thus, the labor productivities of the half ofcommodities grow faster and the labor productivities of the other half grow slower than the labor productivity of the
dynamic standard commodity. It means that the dynamic standard commodity can be the numeraire that keeps thegeneral price level constant over time. In other words, the dynamic standard commodity serves as the Ricardianinvariable measure of value in that the value is invariant to technical progress, leaving aside the possibility of a16

12

is the weighted average growth rate of labor productivities of all commodities (i.e., the growthrate of labor productivity of the dynamic standard commodity). Therefore, the natural or fair rateof interest in this case, denoted by 𝑖𝑖𝐷𝐷∗ , is given by:
𝑖𝑖𝐷𝐷∗ = 𝜇𝜇𝑤𝑤 = 𝜌𝜌∗ .

(4)Note that (2) – (4) are the equivalent expressions in terms of labor.
In any case, the natural or fair rate of interest, denoted by 𝑖𝑖 ∗ , is expressed by:𝑖𝑖 ∗ = 𝜇𝜇𝑤𝑤 .

(5)This is the most general and the simplest expression of the natural or fair rate of interest
independent of the choice of the numeraire.
Furthermore, Pasinetti (1981, pp. 171–173) considered the case in which production needs
not only labor but also physical capital goods as its inputs. The natural economic system in
Pasinetti (1981) defines a specific equilibrium with structural changes. In the system, eachvertically integrated sector receives the amount of profits just equal to the amount of its
equilibrium investments since the natural rates of profit are valid. Thus, no production agent
needs to borrow or lend in the natural economic system, and thus total consumption is equal tototal wage. As in the pure labor economy, therefore, single individuals can save by postponing
consumption (lending consumption goods) and dissave by forwarding consumption (borrowingthem) in Pasinetti’s (1981) case. Therefore, there is no need to make an essential modification to(5) even in Pasinetti’s (1981) case. In other words, the rate of interest that keeps the purchasing
power unchanged in terms of labor exists irrespective of whether the economic system is thepure labor one.
We can derive the implication on income distribution from the concept of the natural or fairrate of interest. Recall that it is defined as the rate of interest which keeps purchasing power interms of labor unchanged through time. Therefore, if the actual rate of interest is not equal to thenatural or fair rate, the income is redistributed through time among debtors and creditors. Moreprecisely, if the actual rate of interest is higher than the natural or fair rate, the income isredistributed from debtors to creditors. In this case, the creditors receive a purchasing power
greater than that justified by the amount of labor that the creditors contributed. 17 Moreover, thedebtors are deprived of a part of the purchasing power originally obtained by the amount of laborthat the debtors contributed. The deprivation by the creditors can be regarded as “exploitation”(Pasinetti, 1993, pp. 98–99).

3.2 The Pasinetti index
In order to analyze the effects of monetary policy on income distribution, the post-Keynesian
economists invented the PI using the implication on income distribution derived from the naturalor fair rate of interest. It is the index to see whether income distribution is fair in terms of labor
contribution to production processes.
In fact, it is difficult to directly apply Pasinetti’s natural or fair rate of interest to analysis of
the real economy. This is because the concept is based on the specific macroeconomicchange in factor income distribution. See Kurose and Yoshihara (2019) on the generalization of the Ricardianinvariable measure of value.
17
The purchasing power that the creditors receive in this case shall be called ‘usury’, not ‘interest’. See Pasinetti(1993, p. 93) concerning this respect.

13equilibrium, as is argued in Subsection 3.1. The functional income distribution changes throughtime. Therefore, we need the approximate methods to apply it to empirical research, as Lavoie
and Seccareccia (2019) examined.
Lavoie and Seccareccia (1988, 2019), Seccareccia (2019), and Seccareccia and Lavoie(2016) defined the PI in the real terms as follows:
𝑃𝑃𝑃𝑃 ≡ 𝑖𝑖𝑀𝑀 − 𝜎𝜎𝑀𝑀 − 𝜆𝜆, (6)where 𝑖𝑖𝑀𝑀 , 𝜎𝜎𝑀𝑀 , 𝜆𝜆 denote the nominal rate of interest, the inflation rate, and the average growth rateof labor productivity, respectively. The PI is defined as the real rate of interest minus the average
growth rate of labor productivity. If 𝑖𝑖𝑀𝑀 − 𝜎𝜎𝑀𝑀 > (<, resp. ) 𝜆𝜆, then income distribution ischanging in favor of creditors (debtors).
In contrast, we define the PI in the real terms, denoted by 𝑃𝑃𝑃𝑃𝑤𝑤 , as follows:
𝑃𝑃𝑃𝑃𝑤𝑤 ≡ 𝑖𝑖𝑀𝑀 − 𝜎𝜎𝑀𝑀 − 𝜎𝜎𝑤𝑤 , (7)where 𝜎𝜎𝑤𝑤 denotes the growth rate of real wage. In other words, the 𝑃𝑃𝑃𝑃𝑤𝑤 is the real rate of interest
minus the growth rate of the real wage. 18 If 𝑖𝑖𝑀𝑀 − 𝜎𝜎𝑀𝑀 > (<, resp. ) 𝜎𝜎𝑤𝑤 , then income distribution
is changing in favor of creditors (debtors). We choose the version with the growth of real wage
instead of growth of labor productivity because 𝑃𝑃𝑃𝑃𝑤𝑤 would allow us to connect the issue of therecent rise in inequality in Japan during the unconventional monetary policy with the fact that
there is a trend of increasing income inequality shown in the higher Gini coefficient, as Figure 1
indicates. Figure 2 shows that there has been an increase in the share of households with nofinancial assets since 2007 around the beginning of the second phase of UMP. Furthermore,
Figure 3 shows that increasing debt to personal income has been noticeable for all wage-earning
households compared with all households.
Insert Figures 1, 2, and 3 here.

Since those wage-earning households are likely to earn their income solely from wage, 𝑃𝑃𝑃𝑃𝑤𝑤 issuited to focus on the circumstance of such households, who can be categorized as debtors who
repay to rentiers. In other words, the adoption of the 𝑃𝑃𝑃𝑃𝑤𝑤 gives us the possibility to focus on thestate of lower-income households; thus, we use the 𝑃𝑃𝑃𝑃𝑤𝑤 as the proxy of the personal income
distribution.
Insert Figure 4 here

Figure 4 shows the time series trend of the movements of the 𝑃𝑃𝑃𝑃𝑤𝑤 , the capacity utilization,
and wage share from the second period of UMP. The 𝑃𝑃𝑃𝑃𝑤𝑤 during the period of 2008-2022 islocated in the positive range except during the time of global financial crisis and the recent
COVID-19 crisis when the government transfer might have allowed the higher wage growth. It
implies that the UMP might lead to a massive transfer of income away from low-income workers
and in favor of rentiers. Figure 4 also indicates the trend that the wage share has been declining
during the period of UMP except for the global financial crisis and the COVID-19 crisis.
Lavoie and Seccareccia (2019) used the “adjusted PI”, defined as the real rate of interest minus the growth rate ofreal wage (the proxy of the growth rate of all-industry real total labor compensation), as well as the PI. They
compared the former with the latter and showed that the two series had remarkably similar patterns from 1970 to2017 in Canada.
18

14

Furthermore, we can observe the interesting trend of the capital utilization (the proxy of
aggregate demand), which would decrease when the 𝑃𝑃𝑃𝑃𝑤𝑤 is in the positive range, meaning thatthe monetary policy would be favoring the rentiers. The possibility to analyze the relationshipamong the changes in personal income distribution, capital utilization, and aggregate demand is
the advantage of the adoption of the 𝑃𝑃𝑃𝑃𝑤𝑤 .
In the next section, we conduct an econometric analysis with a standard VAR model
methodology using the 𝑃𝑃𝑃𝑃𝑤𝑤 as proxy of change in personal income distribution to confirm thisphenomenon. The main variables we use for this study are the 𝑃𝑃𝑃𝑃𝑤𝑤 , income distribution (wageshare), and aggregate demand (capacity utilization rate) to see if they are connected, and the data
we used is quarterly data from 2008 to 2022.

4. Data and Empirical Strategy
In this section, we explain the data source and present our econometric model.

4.1 Data
The data periods that we use in our model are the quarterly time series data from Q1 2008
through Q1 2022 (see the time series trend of the main variables in Figure 4). Recall that themain variables that we use in the empirical analyses are the following:•••

Pasinetti Index: 𝑃𝑃𝑃𝑃𝑊𝑊 = 𝑖𝑖𝑀𝑀 − 𝜎𝜎𝑀𝑀 − 𝜎𝜎𝑤𝑤 where;𝑖𝑖 𝑀𝑀 as the long-term interest rate for ten years government bond, 19
𝜎𝜎𝑀𝑀 as the inflation rate, and𝜎𝜎𝑤𝑤 as real wage growth.
Capacity Utilization: 𝐶𝐶𝐶𝐶𝐶𝐶
Wage Share: OMEGAThe QE2 started in 2008, and the time frame would include the BoJ’s CME which started in
December 2010 and its even larger-scale QQE which began in Q2 2013. Thus, our empiricalanalysis covers both CME and QQE. This allows us to conduct our study, which uses the 𝑃𝑃𝑃𝑃𝑤𝑤 as
the proxy of personal income distribution in our study parallel to the study conducted by Saikiand Frost (2014; 2020) and Israel et al. (2023), which employ personal income ratio and Gini
coefficient as a measurement of the personal income distribution. 20 As we use 𝑃𝑃𝑃𝑃𝑤𝑤 , our study
implements the normative rule of monetary policy to see how the current long-term government
bond rate targeted by the BoJ is fair for the wage earners in debt repayment and might allow
income for moving towards the rentiers. While 𝑃𝑃𝑃𝑃𝑤𝑤 can be applied for any monetary policy
evaluation, we use the data set specifically since the second phase of UMP to evaluate the trendof income distribution associated with such monetary policy.
The appropriate choice of interest rate is also discussed by Lavoie and Seccareccia (2019). Despite the fact thatmortgage loans are the appropriate target of a fair rate of interest when we think about the income distribution thatarises from the debt/credit relation from workers (wage earners) to lenders (rentiers); however, it comes with somerisk premier. Thus, we chose the 10-year government bonds rate as Lavoie and Seccareccia (2019) suggest being
royal to the notion of Keynes’ ‘classical rentier asset’.
20
Saiki and Frost (2014; 2020) used the data from Q4 2008 to Q1 2014 and from Q4 2010 to Q2 2018 while Israel etal. (2023) used the data from Q1 2007 to Q2 2021.
19

15

The definitions of the following variables and the manner in which they have been estimatedare given: 21- The capacity utilization (CAP) is the output gap (GAP) as a percentage of potential output,
and the source of the data is from BoJ.
- The wage share (OMEGA) is constructed by dividing the compensation of employees by thenational income from National Account. The data was downloaded from the Economic andSocial Research Institute website, and the data source is from the Cabinet Office of theGovernment of Japan.
- The Pasinetti index with real wage growth rate (𝑃𝑃𝑃𝑃𝑤𝑤 ) is composed of the following threevariables: 𝑖𝑖 𝑀𝑀 as nominal interest rate; 𝜎𝜎𝑀𝑀 as the inflation rate, and 𝜎𝜎𝑤𝑤 as real wage growth(see eq. 4).
• For the 𝑖𝑖 𝑀𝑀 , we use the data constructed by the Japanese Ministry of Finance for 10-Year
Government Bond Yields.
• For 𝜎𝜎𝑀𝑀 we downloaded the consumption price index (CPI) data from the Cabinet Office,Japanese Statistics Bureau.
• For 𝜎𝜎𝑤𝑤 we use the data of real wage indices growth from the Japanese Ministry of Health,Labour, and Welfare. The data is originally downloadable as quarterly time series data,
and thus we haven’t modified other frequent data into quarterly. This data is for all typesof industries; the size of the establishment is more than 30 employees. Also, this data
does not contain the bonus.

4.2 VAR Model
To examine how income flow towards rentier would affect income distribution in terms of wage
share and the growth and demand in an empirical manner, we use a VAR model. The main
premise of the VAR model is its ability to provide a coherent and credible approach to data
description, forecasting, structural inference, and policy analysis. 22 The VAR model has beenused widely in the post-Keynesian literature, most notably to empirically investigate the relation
between effective demand, income distribution, and unemployment for the USA, UK, and France(Stockhammer and Onaran, 2004). Also, the long debate of post-Keynesian literature regarding
the wage-led or profit-led growth regime is empirically investigated by Barbosa-Filho and Taylor(2006) with the VAR model. Recently, the debt-led and debt-burdened demand analysis areinvestigated with VAR model for the case of Germany and the U.S. by Hein and Schoder (2011)
and Japan by Nishi (2012).
For our study we conduct three variable VAR model:
3-variable VAR model:𝒑𝒑

𝒚𝒚𝒕𝒕 = 𝜶𝜶 + � 𝝓𝝓𝒋𝒋 𝒚𝒚𝒕𝒕−𝒋𝒋 + 𝒆𝒆𝒕𝒕
𝒋𝒋=𝟏𝟏

21
The Pasinetti Index and the choice of real wage growth instead of labor productivity growth can be explained byleaving the assumption that the profit rate and the capital-to-output ratio (inverse of the capacity utilization rate in a
simplistic manner) are constants; we do not assume a condition of Harrod’s neutral technical progress. This is thereason why Lavoie and Seccareccia (2019, p. 98) emphasize the alternative way to compute the Pasinetti index
which does not rely on labor productivity growth.
22
See the detail of VAR model in the paper: Stock and Watson (2001)

16

The VAR model above shows autoregressive, which means that the presence of the lagged
values of the dependent variable on the right-hand side of the equation. In our model, we first
specify the following order: the Pasinetti Index (PI_w), capacity utilization (CAP), wage share(OMEGA). 𝒚𝒚𝒕𝒕 = [𝑃𝑃𝑃𝑃𝑡𝑡𝑤𝑤 , 𝐶𝐶𝐴𝐴𝐴𝐴𝑡𝑡 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑡𝑡 ]′ represents a column vector (3 × 1). 𝝓𝝓𝒋𝒋 is the coefficientmatrix for lagged explanation variables. The parameter 𝜶𝜶 = [𝛼𝛼1 , 𝛼𝛼2 , 𝛼𝛼3 ]′ is a constant vector. The
dash mark represents transposition of the vector. The parameters, 𝒆𝒆𝑡𝑡 is an error vector for which
we suppose that the variance-covariance matrix is constant, the mean is zero, and there is noserial correlation.
In the baseline model, we use Cholesky decomposition, which allows the decomposition ofresiduals in a triangular fashion in VAR (or the so-called recursive system, i.e.), and the order ofthe variables must be set based on the degree of exogeneity. Regarding the decision of theordering of the variables, the Granger causality test described below posits that capacity
utilization would precede wage share, and capacity utilization would precede wage share. Thus,
it is not possible to determine the order uniquely using the exogeneity test. However, the focus is
the 𝑃𝑃𝑃𝑃𝑤𝑤 shock to the rest of the variables, and we set the 𝑃𝑃𝑃𝑃𝑤𝑤 as the most exogenous variable.
Then the result of the Granger causality test shows that the movement of capacity utilization canbe predicted by the 𝑃𝑃𝑃𝑃𝑤𝑤 but the same result cannot be assumed when we apply the movement ofwage share to see if it is affected by 𝑃𝑃𝑃𝑃𝑤𝑤 . Thus, regarding the order of profit share and capacity
utilization, we set capacity utilization is the variable to be set the second exogenous. We set thewage share the in the third variables in the order meaning that the wage share could be affectedindirectly by the Pasinetti index; 𝑃𝑃𝑃𝑃𝑤𝑤 affects capacity utilization, and then capacity utilization
would affect functional income distribution. However, we use generalized order in the robustness
check to see if the results would be the same in the impulse response function to see theconsistency of the result if we change the order.
To define the lag structure of the model, we set eight quarters as the maximum length andcomputed Akaike (AIC) and Schwarz (SBIC) information criteria for all specifications. From theresults in Table 1, we set the appropriate lag as 3.
Insert Table 1 here.
The inverse roots of the AR characteristic polynomial are used to check the stability of the VAR
or stationarity. The estimated VAR is stable if all inverse roots of the characteristic AR
polynomial have a modulus less than one and lie inside the unit circle. From Figure A.1 in the
Appendix, all lie inside the unit circle; therefore, the VAR model is stationary.

5. Result
In this section, we show the results of Granger causality test and the impulse response.
Subsequently, we derive the implications from results.

5.1 Granger causality test
First, we check the Granger-causality statistics to examine whether lagged values of one variable
help to predict another variable in the VAR (3) model. Table 2 shows that when the dependent
variable is capacity utilization (CAP), with a 10% significance level, we can reject the null17

hypothesis that the Pasinetti index (PI_w) and wage share (OMEGA) would Granger cause thecapacity utilization. When the dependent variable is wage share, the p-value of the capacity
utilization rate is only significant, and the p-value of the Pasinetti Index is insignificant. Capacity
utilization Granger causes the wage share showing the validity of ordering the variables in the
VAR model specified in the previous section. When we have the Pasinetti Index as the dependent
variable, only the p-value of the wage share is significant. Higher wage share Granger causes the
𝑃𝑃𝑃𝑃𝑤𝑤 . Taking these results into consideration, all variables must be included in the VAR analysis.
Insert Table 2 here.

5.2 IRF and AIRF
We investigate the effect of the Pasinetti index on the capacity utilization and functional income
distribution in the Japanese economy using the VAR (3) with innovation accounting. First, we
conduct the Impulse Response Function (IRF) with Cholesky ordering as our baseline model
estimation in order to investigate the dynamic characteristics among the variables but not tosearch the equilibrium relation among the variables. Figures 5 and 6 illustrate IRF and
Accumulated Impulse Response Functions (AIRF), respectively, derived from VAR (3), showing
the first 10th quarter.
Insert Figures 5 and 6 here.
First, from the IRF and the AIRF we can confirm that both capacity utilization and wage
share are negatively affected by the Pasinetti index from Figures 5 and 6. On the other hand,from the Granger causality test in Table 2, we could not reject the hypothesis at the 10%
significance level that the Pasinetti index Granger causes the wage share despite that IRF and
AIRF confirming the negative influence of the Pasinetti index on wage share. Thus, we assume
that the higher Pasinetti index would only affect the capacity utilization directly. Also, the IRF
and the AIRF, with regard to the distribution schedule, suggest that the wage share is positively
affected by a shock in capacity utilization, which indicates some profit-squeeze outcome. At thesame time, the demand schedule suggests a negative impact of the wage share on capacity
utilization, which shows profit-led demand corresponding to the previous empirical results by
Nishi (2012). The IRF shows the nonlinear effect of higher capacity utilization on the Pasinetti
index; in the first 2 quarters and between the 8th and 10th quarters, it would affect negatively, butfrom the 2nd and 7th quarters, it would affect positively. The AIRF shows that during the 10thquarter, higher capacity utilization would induce a higher Pasinetti index, but from the Granger
causality test (Table 2), we could not reject the hypothesis at the 10% significance level that thecapacity utilization Granger causes the Pasinetti index. Thus, there is an ambiguity in the
feedback effect between 𝑃𝑃𝑃𝑃𝑤𝑤 and capacity utilization. The increase in the wage share shows anonlinear effect on the Pasinetti index in the IRF; from the 1st and 5th quarters, it would
decrease the Pasinetti index, but from the 6th to the 10th quarter, it affected positively. The
Granger causality test (Table 2) also shows that wage share Granger causes the Pasinetti index.
As a robustness check, we conduct different ordering with generalized impulse response
functions. This is because impulse response analysis comes with the price: the result can dependon the ordering of variables in VAR. To make our work robust, we see how our results are
sensitive to the ordering, by using a generalized AIRF (Pesaran and Shin, 1998), which does notdepend on the ordering. The results with generalized AIRF (see Figure 7) show that they are18

consistent to our results with Cholesky ordering (in Figure 6). With the general IRF we canconfirm that capacity utilization continuously decreases after an increase of 1 standard deviationin the Pasinetti index.
Insert Figure 7 here.
With regards to the direction of the shock, our results confirm that 𝑃𝑃𝑃𝑃𝑤𝑤 can be the initialshock of the dynamic between the three variables. From the Granger causality test, themovement of wage share is not predictable when the 𝑃𝑃𝑃𝑃𝑤𝑤 is an independent variable, but only
capacity utilization can be predicted by 𝑃𝑃𝑃𝑃𝑤𝑤 . Thus, we set capacity utilization as the more
directly affected by the shock of 𝑃𝑃𝑃𝑃𝑤𝑤 . The capacity utilization also Granger causes wage share,
and from IRF, we also observe a profit squeeze. Thus, the identification of the causal ordering is
captured as below:
𝑃𝑃𝑃𝑃𝑤𝑤  Capacity utilization  Wage share

We can discuss our findings from the theoretical perspective following our empirical results.
The preexisting economic growth and income distribution model, such as the neo-Goodwin
pattern (utilization/wage share cycles), can be observed in our findings; there is a profit squeeze
and a profit-led demand pattern. In terms of the personal income distribution (𝑃𝑃𝑃𝑃𝑤𝑤 ) and how it
affects the dynamics of capacity utilization and wage share, there are some new findings. First,
from the Granger causality test, 𝑃𝑃𝑃𝑃𝑤𝑤 , only Granger causes capacity utilization. The dynamic of
capacity utilization and wage share is driven by higher 𝑃𝑃𝑃𝑃𝑤𝑤 ; higher 𝑃𝑃𝑃𝑃𝑤𝑤 first causes lower
capacity utilization. Due to the profit squeeze, lower capacity utilization can cause a lower wage
share. However, the story might continue, and there are nonlinear outcomes from the interactionsof the three variables. As the Granger causality test shows, the wage share Granger causes
capacity utilization and also 𝑃𝑃𝑃𝑃𝑤𝑤 . Lower wage shares due to the profit-led demand pattern cause
capacity utilization to increase, and the AIRF, IRF, and 𝑃𝑃𝑃𝑃𝑤𝑤 also get increased by the higher
wage share. The rest of the outcome depends on the dominance of the effect of wage share on
𝑃𝑃𝑃𝑃𝑤𝑤 and capacity utilization. Higher 𝑃𝑃𝑃𝑃𝑤𝑤 can diminish capacity utilization, but the higher
capacity utilization due to the lower wage share can offset the overall reduction of capacity
utilization. Thus, using our empirical findings, we need to formalize the dynamic of the threevariables. The PK literature on how PI affects utilization (and growth) was modeled by Rochonand Setterfield (2012); however, they do not produce endogenous cycles.

5.3 UMP and income distribution
From the policy perspective, the more the monetary policy favors the rentier, making the income
distribution moving from rentiers and workers, the more it would induce lower capacity
utilization, and it follows the diminishing wage share. The results shown in the previous
subsection postulate a question that attempts income flow towards workers (lower income
earning group) compared to the financial asset holders/rentiers (higher income groups) would
have been more effective in order to restore the effective demand and economic growth. As
workers spend a more significant proportion of their income than wealthier ones, a policy that
redistributes toward workers may encourage greater growth. In this sense, a permanent policy of
low-nominal and even zero interest rates under the UMP has been, in fact, by the BoJ might haveaccelerated economic downturn despite zero interest rates QE was intended to induce the19demand and restore the growth stability. There is always a percussion of monetary policy thatcauses some distributional change when the monetary policy deviates from the normative
position. Our result could also contribute an additional story in Japan's unconventional monetary
policy age and higher income inequality. Higher inequality in comparison to rentiers and workers
also contributes to the sluggish effective demand growth, higher income inequality has been
detrimental to the macroeconomic performance in Japan.

6. Concluding Remarks:
This paper sheds light on Pasinetti’s work on a distributional aspect of interest rate, later
formalized as the Pasinetti index, the normative rule of monetary policy by Lavoie andSeccareccia (2019). The Pasinetti index allows us to measure the income flow movement either
towards rentiers or workers. Thus, we investigate the fairness of the monetary policy using the
Pasinetti index to measure the higher income flow toward rentiers for the Japanese economy
under the UMP. We conduct the VAR model to investigate whether higher income inflow
towards rentiers would restrain the effective demand and wage share toward works under UMP
in Japan. The stylized fact is that the country has observed higher income inequality in the last
decades, and it has been revealed that UMP accelerates inequality by the asset price mechanism,
widening wealth and income inequality (Israel et al., 2023). Before the UMP in the early 2000s,
the basic consensus was that the analysis of Japanese income inequality was insignificant,according to Moriguchi and Saez (2008), as the top 1% of income source is primarily wage
income. However, after almost 20 years, new research results show rising inequality, especiallybetween wage earners and rentiers. 1) Our empirical result confirms that the rise of rentier
income at the age of UMP affects macroeconomic demand growth negatively. 2) Higher rentier
income flow also affects the wage share negatively.
Such a policy of zero-nominal interest rates must be reconsidered when it comes to the
distributional aspect: the last fifteen years since the BoJ accelerated the unconventional monetary
policy with even control of the rate of the long-term government bond (since 2013) have shown
the fragility of our economic system when monetary policy is not accommodative to workers. In
other words, monetary policy has acted as an income policy that protected rentiers. The monetary
policy does not protect workers who tend to hold fewer financial assets, will not see an impact on
wages, and may even be negatively impacted by lower deposit interest rate earnings on saving
accounts.
Another factor affecting income distribution is the real wage growth, given that our PI uses thegrowth rate of real wage. As is already shown, the real wage growth has been sluggish for manyof the periods our study covers. It is attributable to the sluggish nominal wage growth, which isaffected by Japanese firms’ behavior. One of the characteristics of Japanese firms is that they
overall hold a larger amount of cash equivalent (i.e., cash and deposit). The tendency of theJapanese firms to increase the cash equivalent holding after the global financial crisis and thetendency was reinforced after the COVID-19 pandemic, as Oku et al. (2018) shows. It also
reveals that many of listing Japanese firms hold cash equivalent beyond the appropriate levels,and thus they cannot increase their corporate values. The productive spending of cash could
increase employment and wage, and thus contribute to the reduction of income inequality.
Lastly, it is worth noting that the post-Keynesian literature has contributed historically to thestudy of growth and distribution: the relationship between wage/profit share and its implication
on growth. However, there needs to be more clarity regarding the functional and personal income
20

distribution and its implication for growth. The former has accounted for growth and distribution
with macroeconomic variable data, but the latter has employed microeconomics measurement(such as wage differential and Gini coefficient). The complementarity of the two methodologies
can be reconciled and strengthened by the endorsement of the Pasinetti Index methodology,
which employs the income flow between wage earners and rentiers (lenders) by decomposing the
traditional capitalists and workers into smaller segments.

Acknowledgements
The authors thank Monetary Policy Institute, Louis Philippe Rochon, Sylvio Kappes, Pedro
Hugo Clavijo Cortes, Marc Lavoie, Mario Seccareccia, Mark Setterfiled, Sebastien Lechevalierand also those who gave valuable comments in the FMM 27th Conference and 1st Lille postKeynesian Conference. The usual disclaimers apply.

Disclosure statement
No potential conflict of interest was reported by the authors.

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Appendix
Insert Figure A.1 here

27

Lag
AIC
SBIC

0
1.80
1.91

1
-2.18
-1.72

2
3
4
5
6
*
-2.48 2.90
-2.73
-2.9 -2.65*-1.67 1.75
-1.33 -1.05 -0.45
Table 1: Information Criteria

7
-2.87
-0.32

8
-2.67
0.23

Notes: AIC and SBIC represent Akaike information criteria and Schwartz information criteria, respectively. * denotes
the minimum information values.

Dependent variable: CAP
ExcludedChi-sq

df

Prob.

OMEGA

19.5812330.0002

PI_w

7.218963

3

0.0552

All

22.74079

60.0009Dependent variable: OMEGA
ExcludedChi-sq

df

Prob.

CAP

11.69818

30.0085

PI_w

3.695604

30.2963All

14.56411

60.0239Dependent variable: PI_w
ExcludedChi-sq

df

Prob.

CAP

2.923617

30.4036

OMEGA

10.23378

30.0167

All

18.82830

60.0045

Table 2: Granger Causality Test
Note: chi-sq and df represent chi-square statistic and the degree of freedom, respectively.

Figure 1: Gini coefficient for Japan
Data source: Japanese Ministry of Health, Labour and Welfare, Income redistribution survey (所得再分配調査)
Note: The Gini coefficient is computed using pre-tax income = (after tax) income + tax + social security fee.
The Gini coefficient after-tax redistribution is computed using after-tax and redistribution income = after-tax income – social security
fee + social security benefit (such as pension, medical, etc.).

Figure 2: Share of Households with No Financial Assets from 2008 to 2022
Data source: 金融広報中央委員会

Figure 3: Household debt to personal income ratio for Japan
Data source: Statistic Bureau of Japan, Annual Household Survey Report: Savings-Debt Edition (家計調査年報: 貯蓄・負債編）
Note: All wage-earning households only include those who heard of households earning wage income. All wage-earning households aredefined as the head of the household working at a company, government office, school, factory, store, etc. However, households where
the head of the household is a member of the board/executive officer of a corporate organization, such as a company president, director,
managing director, etc., are excluded from the definition.

Figure 4: The capacity utilization (CAP); Wage share (OEMGA); and the Pasinetti Index (with real
wage growth) using the Japanese macroeconomics data from Q1 2008 to Q1 2022 (horizontal axis).
*For the value of OMEGA, see the right-hand side axis.
*See the data description section for the source of data and details in subsection 4.1.

Figure 5: Impulse responses of VAR (3)Figure 6: Accumulative impulse responses of VAR (3)Figure 7: Accumulative generalized impulse responses of VAR (3)Appendix

Figure A.1: The AR root graph of the baseline model, 𝑌𝑌𝑡𝑡 = [𝑃𝑃𝑃𝑃𝑡𝑡𝑤𝑤 , 𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡 , 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑡𝑡 ] with 3 lags