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Motivation Data & Estimation Model Results Conclusion
The Effects of Monetary Policy Shockson Inequality in Japan∗
Masayuki Inui Nao Sudo Tomoaki Yamada
10 November, 2017@Gerzensee
∗The views expressed are those of authors and do not necessarily reflectthose of the BOJ/BIS.
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 1 / 45
Motivation Data & Estimation Model Results Conclusion
Table of contents
Motivation
Data & Estimation
Model
Results
Conclusion
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 2 / 45
Motivation Data & Estimation Model Results Conclusion
Motivation: growing interest on inequality
Impacts of monetary easing on inequality have attractedincreasing attention recently
• Cohan (2014): “Mr. Bernanke’s extraordinary QE program,started in the wake of the financial crisis, has only widened thegulf between haves and have-nots.”
• Krugman (2014): “The belief that QE systematically favorsthe kinds of assets the wealthy own is wrong or at leastoverstated.”
• Bernanke (2015): “Monetary policy is a blunt tool whichcertainly affects the distribution of income and wealth,although whether the net effect is to increase or reduceinequality is not clear.”
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 3 / 45
Motivation Data & Estimation Model Results Conclusion
Existing empirical studies
Empirical observations are mixed
• Coibion et al. (2017): Income and consumption inequalityacross U.S. households respond counter-cyclically to monetarypolicy shocks
• Saiki and Frost (2014): The opposite is true when usingJapanese data
• Domanski et al. (2016): Unconventional monetary policy mayhave widened wealth inequality, in particular through anupsurge in stock prices
• Mummtaz and Theophipoulou (2016):
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 4 / 45
Motivation Data & Estimation Model Results Conclusion
Questions raised
Question 1:
• Does a monetary policy affects inequalities?⇒YES
Question 2:
• What transmission mechanism works?
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 5 / 45
Motivation Data & Estimation Model Results Conclusion
What we do
This paper
• Study the distributional effects of monetary policy, using themicro-level data on Japanese households.
• Draw the broad picture of the effects:◦ focusing on inequality measures of income, consumption, and
wealth based on the micro-level data◦ using both the theoretical model and the data◦ using a fairly long-span data sample: periods of conventional
and unconventional monetary policy regimes
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 6 / 45
Motivation Data & Estimation Model Results Conclusion
Potential transmission channels
1. Earnings heterogeneity channel: Japan◦ the response of earnings to a monetary policy shock differs
2. Job creation channel◦ job creation/destruction following a MP shock
3. Income composition channel: US◦ the income composition of different income types differs
4. Portfolio channel◦ the size and composite of asset portfolio differs
5. Saving redistribution channel: Doepke and Schneider (2006)◦ a transfer from lenders to borrowers by a subsequent rise in
inflation caused by monetary easing
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 7 / 45
Motivation Data & Estimation Model Results Conclusion
I. Data & Estimation
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 8 / 45
Motivation Data & Estimation Model Results Conclusion
FIES
Family Income and Expenditure Survey (FIES)
• Monthly survey on household income and expenditures◦ January 1981 – December 2008◦ The number of observations: 8,000◦ Panel data: 6 months◦ Two-or-more household members only
• Focus on full-time employees (household head): 25–59◦ Self-employed, retirees and unemployed are excluded
• Construct quarterly series of variables on economic inequality
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 9 / 45
Motivation Data & Estimation Model Results Conclusion
FIES (cont.)
Definition of Variables
1. Earnings yL◦ Sum of labor income of all household members
2. Total income y: yL + capital income + private transfer
3. Disposable income yD: y + public transfers - taxes/premiums
4. Nondurable expenditures cND
◦ Housing, purchasing cars and other durables are excluded
5. Total expenditure cT: cND + durables (housing excluded)
• Equivalized by OECD equivalent scale
DETAILS
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 10 / 45
Motivation Data & Estimation Model Results Conclusion
Time path of inequality measures
Variance of log
1980 1985 1990 1995 2000 2005 20100.10
0.15
0.20
0.25
0.30
0.35
Recession yL y yD cT cND
Gini coefficient
1980 1985 1990 1995 2000 2005 20100.20
0.22
0.24
0.26
0.28
0.30
Recession yL y yD cT cND
P90-P10 ratio
1980 1985 1990 1995 2000 2005 20102.50
3.00
3.50
4.00
4.50
Recession yL y yD cT cND
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 11 / 45
Motivation Data & Estimation Model Results Conclusion
Estimation methodology
Estimate the impulse responses of inequality measures to amonetary policy shock, using the LLP by Jorda (2005):
Yt+h︸︷︷︸inequality at t+h
−Yt = αh + Πh(L)Mt + εt+h︸︷︷︸innovation
Mt =
∆TFPt
Factort∆Rt
⇐ Monetary policy variable
• Advantages of LLP:◦ Robustness to model misspecifications:
⇒ choice of explanatory variables and the number of lags◦ Flexibility of model specifications
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 12 / 45
Motivation Data & Estimation Model Results Conclusion
Monetary policy instrument
1980 1985 1990 1995 2000 2005 2010 2015
-8
-6
-4
-2
0
2
4
6
8
10
12
Annualized, %
Ueno (2017)Krippner (2015)JGB-2Y
• Baseline: 1981Q1-1998Q4, Shadow rate: after 1999Q1
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 13 / 45
Motivation Data & Estimation Model Results Conclusion
Monetary policy instrument
1980 1985 1990 1995 2000 2005 2010 2015
-8
-6
-4
-2
0
2
4
6
8
10
12
Annualized, %
Ueno (2017)Krippner (2015)JGB-2Y
• Baseline: 1981Q1-1998Q4, Shadow rate: after 1999Q1
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 14 / 45
Motivation Data & Estimation Model Results Conclusion
Responses of inequality measures: Baseline
0 10 20
-0.005
0.000
0.005
0.010
Variance of log
Earnings
0 10 20
-0.005
0.000
0.005
0.010
Pre-tax income
0 10 20
-0.005
0.000
0.005
0.010
Disposable income
0 10 20
-0.005
0.000
0.005
0.010
Expenditure
0 10 20
-0.005
0.000
0.005
0.010
Consumption
0 10 20-0.004
-0.002
0.000
0.002
0.004
Gini
0 10 20-0.004
-0.002
0.000
0.002
0.004
0 10 20-0.004
-0.002
0.000
0.002
0.004
0 10 20-0.004
-0.002
0.000
0.002
0.004
0 10 20-0.004
-0.002
0.000
0.002
0.004
0 10 20Quarter
-0.050
0.000
0.050
0.100
P90-P10
0 10 20Quarter
-0.050
0.000
0.050
0.100
0 10 20Quarter
-0.050
0.000
0.050
0.100
0 10 20Quarter
-0.050
0.000
0.050
0.100
0 10 20Quarter
-0.050
0.000
0.050
0.100
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 15 / 45
Motivation Data & Estimation Model Results Conclusion
U.S. Economy
• Figure 4 in Coibion et al. (2017)
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 16 / 45
Motivation Data & Estimation Model Results Conclusion
Channel through job creation
0 5 10 15 20
Quarter
-15
-10
-5
0
(1) # of unemployed HH heads
0 5 10 15 20
Quarter
-0.003
-0.002
-0.001
0.000
0.001
0.002(2) The adjusted Gini of earnings
Adjusted Gini
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 17 / 45
Motivation Data & Estimation Model Results Conclusion
Responses of inequality: 1981-2008
0 10 20
-0.005
0.000
0.005
Variance of log
Earnings
0 10 20
-0.005
0.000
0.005
Pre-tax income
0 10 20
-0.005
0.000
0.005
Disposable income
0 10 20
-0.005
0.000
0.005
Expenditure
0 10 20
-0.005
0.000
0.005
Consumption
0 10 20-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
Gini
0 10 20-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0 10 20-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0 10 20-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0 10 20-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0 10 20Quarter
-0.050
0.000
0.050
P90-P10
0 10 20Quarter
-0.050
0.000
0.050
0 10 20Quarter
-0.050
0.000
0.050
0 10 20Quarter
-0.050
0.000
0.050
0 10 20Quarter
-0.050
0.000
0.050
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 18 / 45
Motivation Data & Estimation Model Results Conclusion
Changes in responses of earnings inequalityover time
1996 1998 2000 2002 2004 2006 2008End point of sample period
-0.002
0.000
0.002
0.004
0.006
0.008
0.010
0.012(1) Variance of log
1996 1998 2000 2002 2004 2006 2008End point of sample period
-0.001
0.000
0.001
0.002
0.003
0.004(2) Gini coefficient
1996 1998 2000 2002 2004 2006 2008End point of sample period
-0.020
0.000
0.020
0.040
0.060
0.080
(3) P90-P10 ratio
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 19 / 45
Motivation Data & Estimation Model Results Conclusion
Empirical observations
Observation 1:
• Impact of expansionary monetary policy on income inequalityis procyclical, arises mainly from procyclical response ofearnings inequality. ⇒ Earnings heterogeneity channel
• Once-prevailing distributional effects diminish during 2000s
• Possibility that a decline in earnings inequality due to jobcreation channel counters its rise from earnings heterogeneitychannel
Observation 2:
• Transmission of income inequality to consumption inequality isless than one-to-one
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 20 / 45
Motivation Data & Estimation Model Results Conclusion
Accounting for observations
To address to these observations, we employ three toolkits:
1. Two-sector DSGE model with attached labor inputs◦ illustrate how the distributional effects of monetary policy
change with the structure of the economy
2. Industry-level aggregate data sets
3. Micro-level data on households’ financial assets and liabilities◦ check whether the model’s predictions accord with the data
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 21 / 45
Motivation Data & Estimation Model Results Conclusion
II. Model
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 22 / 45
Motivation Data & Estimation Model Results Conclusion
Literature: Theory
Models of inequality:
• Monetary policy shock:◦ Guerrieri and Lorenzoni (2012), Gornemann et al. (2014),
Auclert (2015), McKay et al. (2016)
• Fiscal policy:◦ Oh and Reis (2012), McKay and Reis (2015)
• Income inequality and Pareto distribution:◦ Gabaix et al. (2016)
• Business cycle and heterogeneity:◦ Challe, Matheron, Ragot, and Rubio-Ramirez (2015)
• Mechanism behind earnings inequality in HANK⇒ idiosyncratic risks (stochastic, but exogenous)
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 23 / 45
Motivation Data & Estimation Model Results Conclusion
Our model
• Two production sectors (X and Z )◦ each of which has final goods firms and intermediate goods
firms◦ consumption composite consists of goods X and goods Z
• Two households (X and Z )◦ each of which has two types of members: “attached” and
“mobile”◦ “Attached” supplies its labor inputs to one of two sectors◦ “Mobile” can supply its labor inputs to both sectors
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 24 / 45
Motivation Data & Estimation Model Results Conclusion
Objectives of households
• Each type of households (X and Z ) maximizes:
Us,t = Et
[∞
∑q=0
βqu(Cs,t+q,Cs,t+q−1,Ns,t+q,Hs,t+q)
]
u(·, ·, ·, ·, ) = log(Cs,t+q − bCs,t+q−1)− θN
1+ηs,t+q
1+ η− ϕ
H1+ηs,t+q
1+ η
◦ N: attached labor input, H: mobile labor input◦ β: discount factor, C : consumption, b: habit
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 25 / 45
Motivation Data & Estimation Model Results Conclusion
Budget constraint
• For s = X ,Z , the budget constraint:
Cs,t +Bs,t
Pt≥
Ws,tPt
Ns,t +WtPt
Hs,t
+(
ΠX ,t+ΠZ ,tPt
)γΠs +
(RX ,tKX+RZ ,tKZ
Pt
)γKs
+Rt−1Bs,t−1Pt
+ κB
(Bs,tPt
)2
,
◦ γΠs : share of dividends, γKs : share of capital stock◦ κB : adjustment costs of bond holding
• Capital stock is fixed at some level
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 26 / 45
Motivation Data & Estimation Model Results Conclusion
Firm’s price setting and gross output
• In sector X , the intermediate firm i choose the prices to solve:
maxPX ,t (i)
E
[∞
∑q=0
βt+q Λt+q
Λt
Πt+q,X (i)
Pt+q
]
• subject to
ΠX ,t+q,X (i) = PX ,t+q(i)xt+q(i)−MCX ,t+q(i)xt+q(i)
− κX2
(PX ,t+q(i)
PX ,t+q−1(i)− 1
)2
PX ,t+qXt+q,
xt(i) = ANX ,t(i)αµUX ,t(i)
α(1−µ)KX ,t(i)1−α
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 27 / 45
Motivation Data & Estimation Model Results Conclusion
Rest of the model
• Production technology of gross output:
Xt =
[∫ 1
0xt(i)
1− 1ε di
] εε−1
• The aggregator constructs the composite of consumptiongoods using the aggregate technology
Ct = Xρt Z
1−ρt
• Monetary policy:
logRt = ρn logRt−1 + (1− ρn)φ log πt + ϵR,t
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 28 / 45
Motivation Data & Estimation Model Results Conclusion
Setup
• Assume that ρ > 1− ρ and κX > κZ• Other parameters are symmetric
• Then,◦ X receives higher earnings than Z at steady state◦ Monetary policy affects two sectors differently around steady
state
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 29 / 45
Motivation Data & Estimation Model Results Conclusion
Expansionary monetary policy shock
0 5 10 15 20-0.010
0.000
0.010
0.020
0.030
0.040
%
(1) Value-added
Sector XSector Y
0 5 10 15 20-0.025
-0.020
-0.015
-0.010
-0.005
0.000
%
(2) Relative price
0 5 10 15 200.000
0.010
0.020
0.030
0.040
%
(3) Earnings
Household XHousehold Y
0 5 10 15 20Quarter
0.000
0.010
0.020
0.030
0.040
%
(4) Consumption
Household XHousehold Y
0 5 10 15 20Quarter
0.000
0.005
0.010
0.015
0.020
0.025
0.030
%
(5) Earnings inequality
0 5 10 15 20Quarter
0.000
0.005
0.010
0.015
0.020
0.025
0.030
%
(6) Consumption inequality
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 30 / 45
Motivation Data & Estimation Model Results Conclusion
Labor market flexibility: µ ∈ {0.4, 0.6, 0.8}
0 5 10 15 200.00
0.01
0.02
0.03
0.04(1) Earnings of household X
highmidlow
0 5 10 15 200.00
0.01
0.01
0.02
0.02
0.03
0.03(2) Earnings of household Z
highmidlow
0 5 10 15 200.00
0.01
0.02
0.03
0.04
0.05
0.06(3) Earnings inequality
highmidlow
0 5 10 15 20-0.01
0.00
0.01
0.02
0.03
0.04
0.05(4) Consumption of household X
highmidlow
0 5 10 15 20-0.01
0.00
0.01
0.02
0.03(5) Consumption of household Z
highmidlow
0 5 10 15 200.00
0.01
0.02
0.03
0.04
0.05
0.06(6) Consumption inequality
highmidlow
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 31 / 45
Motivation Data & Estimation Model Results Conclusion
Labor market flexibility in Japan
1985 1990 1995 2000 2005 2010 2015Year
10
12
14
16
18
20
22
24
26
%
(1) Proportion of temporary workers
Labor force surveyMonthly labor surcey
1985 1990 1995 2000 2005 2010 2015Year
3.0
3.2
3.4
3.6
3.8
4.0
%
(2) Labor turnover ratio
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 32 / 45
Motivation Data & Estimation Model Results Conclusion
Transmission to consumption inequality
• Why didn’t consumption inequality increase as much asincome inequality?◦ Responses of consumption of households are all weak?◦ Or other possible explanations?
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 33 / 45
Motivation Data & Estimation Model Results Conclusion
Responses of consumption and the MPC
0 5 10 15 20-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025(1) Consumption responses
0-20%80-100%
0 5 10 15 20-0.02
-0.02
-0.01
-0.01
0.00
0.01
0.01
0.02
0.02
0.03
0.03(2) MPC responses
0-20%80-100%
• by income quintiles
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 34 / 45
Motivation Data & Estimation Model Results Conclusion
Transmission to consumption inequality
• Why is the MPC conditional on monetary policy shocks higherin the low income quintile?
1. Distributional effects via financial asset holdings2. Difference in consumption behavior across households
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 35 / 45
Motivation Data & Estimation Model Results Conclusion
Distribution of financial assets matters
0 5 10 15 200.00
0.01
0.01
0.02
0.02
0.03
0.03(1) Earnings inequality
highmidlow
0 5 10 15 200.00
0.01
0.01
0.02
0.02
0.03
0.03(2) Consumption inequality
highmidlow
0 5 10 15 20-0.01
0.00
0.01
0.02
0.03
0.04
0.05(3) Consumption of household X
highmidlow
0 5 10 15 20-0.01
0.00
0.01
0.02
0.03(4) Consumption of household Z
highmidlow
• γKX∈ {0.4, 0.5, 0.6}
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 36 / 45
Motivation Data & Estimation Model Results Conclusion
Conclusion
Empirically and theoretically study how monetary policyshocks are transmitted to inequality.
• Findings:◦ Distributional effects of monetary policy were once present, but
have become statistically insignificant during the 2000s◦ Transmission of income inequality to consumption inequality is
minor
• Takeaways:◦ Labor market flexibility is central to the dynamics of income
inequality after the monetary policy shocks◦ Distributions of financial assets and liabilities don’t play a
significant role
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 37 / 45
Motivation Data & Estimation Model Results Conclusion
Danke schon!
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 38 / 45
Motivation Data & Estimation Model Results Conclusion
Appendix Figures
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 39 / 45
Motivation Data & Estimation Model Results Conclusion
Responses of macro variables
0 5 10 15 20-2
0
2
4
6(1) GDP
0 5 10 15 20-5
0
5
10
15(2) Investment
0 5 10 15 20-1
0
1
2
3(3) Consumption
0 10 20-0.4
-0.2
0
0.2
0.4
0.6
0.8(4) Price Level
0 5 10 15 20Quarter
-10
0
10
20(5) Stock Price
0 5 10 15 20Quarter
0
1
2
3(6) Labor Income
0 5 10 15 20Quarter
-2
0
2
4
6(7) Capital Income
0 5 10 15 20Quarter
-10
-5
0
5
(8) Unemployed
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 40 / 45
Motivation Data & Estimation Model Results Conclusion
Cross-firm heterogeneity to earningsinequality: baseline
0 5 10 15 20-0.004
-0.002
0.000
0.002
0.004
0.006
0.008(1) Value-added
0 5 10 15 20-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0.004(2) Earnings per employee
0 5 10 15 20-0.001
0.000
0.001
0.002
0.003
0.004(3) Earnings per working hour
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 41 / 45
Motivation Data & Estimation Model Results Conclusion
Cross-firm heterogeneity to earningsinequality: 1981-2008
0 5 10 15 20-0.004
-0.002
0.000
0.002
0.004
0.006
0.008(1) Value-added
0 5 10 15 20-0.004
-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0.004
0.005(2) Earnings per employee
0 5 10 15 20-0.005
-0.004
-0.003
-0.002
-0.001
0.000
0.001
0.002(3) Earnings per working hour
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 42 / 45
Motivation Data & Estimation Model Results Conclusion
Data Details
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 43 / 45
Motivation Data & Estimation Model Results Conclusion
Data Details
Definition of Variables
• Labor income y :◦ sum of monthly labor income of household members, which
include household head, his/her spouse and other householdmembers
• Nondurable expenditure c :◦ food; repair and maintenance of houses; fuel, light and water
charges; domestic utensils, non-durable goods, and services;clothing and footwear; medical care; transportation andcommunication, excluding purchase of vehicles and bicycles;education; culture and recreation, excluding recreational durablegoods; and other consumption expenditure, excludingremittance
RETURN
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 44 / 45
Motivation Data & Estimation Model Results Conclusion
Adjusted Gini
Adjusted Gini coefficient
G ∗ ≡∑N
i=1 ∑Nj=1 |xi − xj |
2N ∑Ni=1
= GN
N+
N − N
N
• Assumption: earnings of unemployed = 0
RETURN
The Effects of Monetary Policy Shocks on Inequality in Japan M. Inui, N. Sudo and T. Yamada 45 / 45