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O PTIMAL M ONETARY P OLICY
FOR THE M ASSES
James Bullard (Federal Reserve Bank of St. Louis)
Riccardo DiCecio (Federal Reserve Bank of St. Louis)

Center for Research on the Wisconsin Economy
University of Wisconsin-Madison
March 28, 2019
Madison, Wis.
Any opinions expressed here are our own and do not necessarily reflect those of the FOMC.

I NTRODUCTION

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C ONCLUSIONS

Introduction

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I NTRODUCTION

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I NEQUALITY AND MONETARY POLICY

Interest in income, financial wealth and consumption inequality has increased in the
last decade.
Can monetary policy be conducted in a way that benefits all households even in a
world of substantial heterogeneity?
The answer in this paper is “yes.”

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S OME RECENT LITERATURE

Kaplan, Moll and Violante (AER, 2018):
NK model with heterogeneous households (HANK); reasonable Gini coefficients.
The monetary policy transmission mechanism is substantially altered relative to the
representative agent model (RANK).

Bhandari, Evans, Golosov and Sargent (Working paper, NBER, 2018):
Incomplete markets, nominal friction, heterogeneous households (HAIM); reasonable
Gini coefficients.
Optimal monetary-fiscal policy (Ramsey) substantially altered relative to the standard
model.

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A DDITIONAL RECENT LITERATURE

Bullard and DiCecio (Working paper, St. Louis Fed, 2019):
Incomplete markets, nominal friction, heterogeneous households (HAIM); reasonable
Gini coefficients.
Optimal monetary policy repairs the distortion caused by the friction for all households.

See also the conference on “Monetary Policy and the Distribution of Income and
Wealth,” held at the St. Louis Fed on Sept. 11-12, 2015. See the program.

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W EALTH , INCOME AND

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CONSUMPTION INEQUALITY

There is a lot of financial wealth, income and consumption inequality in this stylized
model.
The role of credit markets, if they work correctly, is to reallocate uneven income
across the life cycle into perfectly equal consumption shares by cohort, appropriately
scaled by life-cycle productivity.
The model equilibrium generates realistic Gini coefficients.

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O PTIMAL MONETARY POLICY

The role of monetary policy in this model is to make sure private credit markets are
working correctly (i.e., complete).
Optimal monetary policy in this model looks like “nominal GDP targeting”—that is,
countercyclical price-level movements.
This result continues to hold even when there is “massive” heterogeneity—enough
heterogeneity to approximate income, financial wealth and consumption inequality
in the U.S.
Hence, the main result is that nominal GDP targeting constitutes “optimal monetary policy
for the masses” in this environment.

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Environment

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L IFE - CYCLE MODELS

General-equilibrium life-cycle economy.
Each period, a new cohort of households enters the economy, makes economic decisions
over the next 241 periods, then exits the economy. The model is therefore “quarterly.”
Households have log preferences defined over consumption and leisure.
Households are assigned a personal productivity profile when they enter the model.
The profile is symmetric—it begins low, rises and peaks exactly in the middle of life, then
declines back to the low level. There will be many of these, as discussed below.
Productivity units determine the value of an hour worked in a competitive labor market.
There is no population growth in this version.

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H OUSEHOLD CREDIT

The overlapping-generations structure creates a large private credit market essential
to good macroeconomic performance.
Relatively young households want to borrow to move consumption forward in the
life cycle, while middle-aged households wish to save for retirement. So households
in the middle of life lend to the relatively young.
The key variable is therefore privately issued household debt. Household debt
outstanding in the U.S. is on the order of GDP, around $20 trillion.
As practical motivation, think of privately issued debt = “mortgage-backed
securities.”

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N ON - STATE CONTINGENT

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NOMINAL CONTRACTING

There is a friction in the credit market: Non-state contingent nominal contracting
(NSCNC).
NSCNC: Loans are dispersed and repaid in the unit of account—that is, in nominal
terms—and are not contingent on income realizations.
There are two aspects to this friction:
The non-state contingent aspect means that real resources are misallocated via this friction.
The nominal aspect means that the monetary authority may be able to fix the distortion to
the equilibrium.

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L INEAR PRODUCTION TECHNOLOGY

Output is produced using a technology that is linear in the labor input.
In the equilibrium we study, the labor input (hours worked) will be constant.
The level of technology (aka “aggregate productivity”) grows at a stochastic rate.
The technology growth rate is bounded so that the zero lower bound is avoided.

The real wage grows at the same stochastic rate as aggregate productivity.

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T IMING PROTOCOL

Period t

Nature

Policymaker

Households

growth rate of
aggregate productivity
=⇒ real wage

price level

labor/leisure
consumption/saving

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N OMINAL INTEREST RATE DETERMINATION

Households meet in a competitive market for nominally denominated, non-state
contingent loans.
The non-state contingent nominal interest rate, “the contract rate,” that clears this
market is given by expected nominal GDP growth.
In the equilibrium we study, this expectation is the same for all households, even
those born at different dates or with different levels of personal productivity.

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T HE EQUILIBRIUM MONETARY POLICY CREATES
The monetary policymaker follows a nominal GDP targeting rule that delivers
complete-markets consumption allocations—similar to Sheedy (BPEA, 2014) and
Koenig (IJCB, 2013).
That is, low inflation in response to a high realization of the aggregate productivity
growth rate, and vice versa.

Given this policy rule, households consume equal amounts of available production
conditional on their productivity; this is called “equity share contracting,” and it is
optimal under homothetic preferences.
This means that any two households that share the same personal productivity
profile will consume the same amount at each date.
The nominal GDP targeting rule perfectly insures the household against future
shocks to income.
Income, consumption and asset holdings fluctuate from period to period but in
proportion to the value of the real wage.
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T HE W ICKSELLIAN NATURAL REAL RATE OF INTEREST

The equilibrium we study has the following property:
The real interest rate is exactly equal to the output growth rate at every date, even in the stochastic
economy.

One could think of this as “the Wicksellian natural real rate of interest.”
This in turn creates a set of easy-to-understand baseline results for this stylized
economy.

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Life-Cycle Productivity

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L IFE - CYCLE PRODUCTIVITY PROFILES
Households entering the economy draw a scaling factor and receive a life-cycle
productivity profile, which is a scaled version of the baseline profile.
Life-cycle productivity profiles, once assigned, are deterministic.
This process is a stand-in for the human capital development that takes place before
age 20 in actual economies, including schooling, parenting and any pre-age 20 job
experience.
Huggett, Ventura and Yaron (AER, 2011) argue that differences in initial conditions
are more important than differences in shocks.
We also consider a lognormal distribution for the scaling factor, creating an economy
with arbitrarily rich and poor households.

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B ASELINE LIFE - CYCLE PRODUCTIVITY
4
3
2
1
0

0

60

120

180

240

quarters
F IGURE : Baseline endowment profile. The profile is symmetric and peaks in the middle period of
the life cycle.

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T HE MASS

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OF LIFE - CYCLE PRODUCTIVITY

F IGURE : The mass of endowment profiles.

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Characterizing the Equilibrium

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I NTRODUCTION

H OURS

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WORKED OVER THE LIFE CYLE

1

0.5

0

0

60

120

180

240

quarters
F IGURE : Cross section: Leisure decisions by age (green), labor supply by age (blue), and fraction of
work time in U.S. data, 19% (red). The labor/leisure choices depend on age only. High-income
households work the same hours as low-income households at each age.
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L ABOR INCOME MASS

F IGURE : Cross section: Labor income profiles. Personal productivity peaks at the middle of the life
cycle, and households work more at that time as well, making income even more concentrated in
the peak earning years.
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C ONSUMPTION MASS

F IGURE : Cross section: Consumption mass (red) and labor income mass (blue) along the
complete-markets balanced growth path. Under optimal monetary policy, the private credit market
reallocates uneven labor income into perfectly equal consumption for each productivity profile. The
consumption Gini is 31.8%, similar to values calculated from U.S. data.
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N ET

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ASSET HOLDING MASS

F IGURE : Cross section: Net asset holding mass. Borrowing, the negative values to the left, peaks at
stage 60 of the life cycle (age ˜35), while positive assets peak at stage 180 of life (age ˜65). The
financial wealth Gini is 72.7%, similar to values calculated in U.S. data.
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T HREE NOTIONS

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OF INCOME

Three notions of income:
1
2
3

Labor income (Y1 ).
Labor income plus non-negative capital income (Y2 ).
The non-negative component of total income (Y3 ).

Gini coefficients of the various income distributions: GY1 = 56.2%, GY2 = 51.6%,
GY3 = 59.6%.

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L ABOR INCOME + NON - NEGATIVE CAPITAL INCOME

F IGURE : Cross section: Profiles of labor income and non-negative capital income.

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N ON - NEGATIVE TOTAL INCOME

F IGURE : Cross section: Profiles of non-negative total income.

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Inequality

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D ATA ON INEQUALITY IN THE U.S.

Consumption (Heathcote, Perri and Violante, RED, 2010): GC,U.S. = 32%.
Income (CBO, 2016): pre-taxes/transfers GY,U.S. = 51%; post-taxes/transfers
GY,U.S. = 43%.
Financial wealth (Davies, Sandström, Shorrocks and Wolff, EJ, 2011): GW,U.S. = 80%.

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I NEQUALITY IN THE MODEL

There is a large amount of heterogeneity that depends in part on life-cycle
productivity dispersion.
Financial wealth is defined as the non-negative part of net assets.
We also consider lognormal productivity:
This allows for arbitrarily rich and arbitrarily poor households.
All distributions (wealth, income and consumption) are mixtures of lognormals (and δ
functions).
Gini coefficients can be computed with “paper and pencil.”

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G INI COEFFICIENTS
Wealth
W

Y1

Income
Y2

Y3

51%

Consumption
C

U.S. data

80%

32%

Uniform

72.7%

56.2%

51.6%

59.6%

31.8%

Lognormal

72.4%

55.7%

51.1%

59.0%

32%

TABLE : Gini coefficients in the U.S. data and in the model with uniform and lognormal productivity.

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Policy

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I NTERPRETING MONETARY

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POLICY

The nominal GDP targeting rule characterizes policy by “countercyclical price-level”
movements.
But the policy can also be interpreted more conventionally in interest rate terms.
Nominal interest rates are determined in a private market, understanding policy ...
And policy is made understanding nominal interest rate determination ...
Nominal interest rate policy is a fixed point of this process.

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P OLICY CHARACTERIZATION

The nominal rate is determined one period in advance as the expected rate of
nominal GDP growth.
Wicksellian natural real rate = aggregate productivity growth rate, λ.
The nominal rate is always ratified ex post by the policymaker.
This makes the real rate = aggregate productivity growth rate = Wicksellian natural
real rate of interest.
“Just like the simple NK model.”

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N OMINAL GDP

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TARGETING

How can we interpret these results as nominal GDP targeting?
No persistence in productivity growth: The expected rate of nominal GDP growth never
changes, and the economy never deviates from the nominal GDP path. “Perfect nominal
GDP targeting.”
Persistence in productivity growth: The expected rate of nominal GDP growth fluctuates
persistently with the shock, and it takes longer to return to the balanced growth nominal
GDP path.
Nominal and real rates fall in a recession.

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E FFECTS

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OF A SHOCK
1.06
1.02
1.04
1
1.02
0

5

10

0

quarters

5

10

quarters

1.4

1.06

1.2

1.04
1.02

1
0

5

quarters

10

0

5

10

quarters

F IGURE : Monetary policy responds to a decrease in aggregate productivity growth by increasing the
inflation rate in the period of the shock. Subsequently, inflation converges to its long-run
equilibrium value from below. The nominal interest rate drops in the period after the shock.
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Conclusions

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S UMMARY
This paper attributes observed levels of U.S. inequality to life-cycle effects in
conjunction with heterogeneous life-cycle productivity profiles.
All households in this model, regardless of their assigned life-cycle productivity
profile, face a problem of smoothing life-cycle consumption in a world with a credit
market friction, “non-state contingent nominal contracting.”
The monetary authority can remove this impediment to life-cycle consumption
smoothing for all households: “optimal monetary policy for the masses.”
Does monetary policy affect inequality? Yes, it improves consumption allocations,
alters the asset holding distribution and alters the income distribution by altering
hours worked.

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