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

Norges Bank
Oslo, Norway
Jan. 25, 2018
Any opinions expressed here are our own and do not necessarily reflect those of the FOMC.

I NTRODUCTION

E NVIRONMENT

P RODUCTIVITY

C HARACTERIZING THE E QUILIBRIUM

Introduction

I NEQUALITY

C ONCLUSIONS

I NTRODUCTION

E NVIRONMENT

P RODUCTIVITY

C HARACTERIZING THE E QUILIBRIUM

I NEQUALITY

C ONCLUSIONS

I NEQUALITY AND MONETARY POLICY

Interest in income, financial wealth, and consumption inequality
has increased in the last decade.
Some of the discussion has a focus on the role of monetary policy
in promoting or reducing inequality.
Key issues include:
Has global low interest rate policy over the last decade necessarily
exacerbated inequality?
Does low interest rate policy necessarily redistribute toward
borrowers?
Can monetary policy conducted in a way that benefits all
households in a world of substantial heterogeneity?
The answers in this paper are “no,” “no,” and “yes.”

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S OME RECENT LITERATURE

Conference on “Monetary Policy and the Distribution of Income
and Wealth,” held at the St. Louis Fed on September 11 and 12,
2015. Program available online.
Kaplan, Moll, and Violante (AER, 2018 forthcoming): new
Keynesian macro with uninsurable idiosyncratic risk and
multiple assets (“HANK”). Produces reasonable Gini
coefficients. The monetary transmission mechanism is altered
relative to the representative agent case. Also provides a good
discussion of the literature.
This paper also produces reasonable Gini coefficients, and
features incomplete markets due to a friction, with strictly
limited idiosyncratic risk. The policymaker is able to repair the
distortion caused by the friction for all households.

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H OUSEHOLD CREDIT IN A DSGE MODEL

We study an economy with a large private credit market
essential to good macroeconomic performance.
This market has an important friction: Non-state contingent
nominal contracting (NSCNC).
The role of monetary policy will be to keep this large credit
market functioning properly (i.e., complete).
I ignore ZLB issues in this talk. See the companion paper by
Azariadis, Bullard, Singh and Suda (2015), available on my web
page.

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W EALTH , INCOME AND CONSUMPTION INEQUALITY

There is a lot of wealth, income and consumption inequality in
this stylized model.
The role of credit markets, if they work correctly, will be to
re-allocate uneven income profiles across the life cycle into
perfectly equal consumption shares by cohort.
The model equilibrium will naturally rank:
the wealth Gini coefficient > the income Gini coefficient > the
consumption Gini coefficient..

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C ONCLUSIONS

H OW LARGE ARE THESE MARKETS ?

According to Mian and Sufi (AER, 2011), the ratio of household
debt to GDP was about 1.15 before the increase during the 2000s
when it ballooned to 1.65.
In today’s dollars, that would be about $19.5 trillion to about $28
trillion, comprised mostly of mortgage debt.
Disrupting these markets might be quite costly for the economy,
so this friction could be quite important.

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C ONCLUSIONS

T HE MONETARY POLICY IMPLICATIONS

Optimal monetary policy in this model looks like “nominal GDP
targeting”—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 NGDP targeting constitutes “optimal
monetary policy for the masses” in this environment.

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Environment

I NEQUALITY

C ONCLUSIONS

I NTRODUCTION

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C ONCLUSIONS

L IFE CYCLE MODELS

General equilibrium life cycle economy = many-period
overlapping generations.
Key variables are privately-issued debt, real interest rates and
inflation.
Think of privately-issued debt = “mortgage-backed securities.”
This talk has inelastic labor supply. Elastic labor supply can be
added—for more on this, see the companion paper by Bullard
and Singh (2017), available on my web page.

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C ONCLUSIONS

S YMMETRY ASSUMPTIONS
We make a set of important “symmetry assumptions” so that we
can better understand the equilibrium of the model even with
substantial heterogeneity.
These assumptions involve the symmetry of the life cycle
productivity endowment pattern of the households (detailed
below), along with log preferences, no discounting, and no
population growth.
These assumptions help deliver the result that in the equilibria
we study:
The real interest rate is exactly equal to the output growth rate at every
date, even in the stochastic economy.

This in turn creates a set of easy to understand baseline results
for this economy.

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E NVIRONMENT DETAILS

Standard T + 1-periods (quarterly) DSGE life-cycle endowment
economy.
Each period, a new cohort of households enters the economy at
age 20, makes economic decisions over the next 241 periods, then
exits the economy.
There is one asset in the model, privately-issued debt
(consumption loans).
The monetary authority controls the nominal price level P (t)
directly. For a money demand version, see Azariadis et al. (2015).
All households have log preferences with no discounting.
Other assumptions: No population growth, inelastic labor supply,
no capital, no default, flexible prices, no borrowing constraints.

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C ONCLUSIONS

K EY FRICTION : 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 assumption.
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.

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C ONCLUSIONS

S TOCHASTIC STRUCTURE
We model a growing economy in which a linear technology is
improving over time.
The real wage w (t) is then exogenously given by
w (t + 1) = λ (t, t + 1) w (t) ,

(1)

where w (0) > 0, and λ (t, t + 1) is the gross rate of aggregate
productivity growth between date t and date t + 1, and where
λ (t, t + 1) = (1

ρ) λ + ρλ (t

1, t) + ση (t + 1) ,

(2)

where λ > 1 represents the average gross growth rate, ρ 2 (0, 1) ,
σ > 0, and η (t + 1) N (0, 1) .
For sufficiently large, negative draws of η, the ZLB may threaten.
We ignore this issue in this paper and refer readers to Azariadis
et al. (2015).

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T IMING PROTOCOL

At the beginning of date t, nature moves first and chooses
λ (t 1, t) , which implies a value for w(t).
The policymaker moves next and chooses a value for P (t) .
Households then decide how much to consume and save.

C ONCLUSIONS

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C ONCLUSIONS

N OMINAL INTEREST RATE

Households contract by fixing the nominal interest rate one
period in advance.
The non-state contingent nominal interest rate, “the contract
rate,” is given by
Rn (t, t + 1)

1

= Et

ct ( t )
P (t)
.
ct ( t + 1 ) P ( t + 1 )

(3)

This rate depends on the expected rate of consumption growth
and the expected rate of inflation.
In the equilibria we study, this expectation is the same for all
households, even those born at different dates or with different
levels of productivity.

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W HAT MONETARY POLICY DOES
The countercyclical price level rule delivers complete markets
allocations:
Rn (t 1, t)
P (t) = r
P (t 1) ,
(4)
λ (t 1, t)
where λr indicates a realization of the shock and Rn is the
expectation given in the previous slide.
This is a similar result to Sheedy (BPEA, 2014) and Koenig (IJCB,
2013).
Given this policy rule, households consume equal amounts of
available production, given their productivity, “equity share
contracting,” which is optimal under homothetic preferences.
This price level rule renders the households’ date-t decision
problem deterministic because it perfectly insures the household
against future shocks to income.
Consumption and asset holdings fluctuate from period to
period, but in proportion to the value of w (t) .

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Life-Cycle Productivity

I NEQUALITY

C ONCLUSIONS

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C ONCLUSIONS

L IFE - CYCLE PRODUCTIVITY PROFILES
Households entering the economy draw one of N + 1 life-cycle
productivity profiles

es =

where ξ

8
>
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
>
:

ẽs
ξ

w.p. 1/ (N + 1)
..
.

..
.

1

1ξ 1
ξ N/2

ẽs

ẽs
1+

ξ 1
N/2

..
.
ξẽs

ẽs

w.p. 1/ (N + 1)
w.p. 1/ (N + 1) ,
w.p. 1/ (N + 1)
..
.
w.p. 1/ (N + 1)

1 determines the within-cohort dispersion.

Productivity profiles are deterministic.
Huggett, Ventura and Yaron (AER, 2011) argue that differences in
initial conditions are more imporant than differences in shocks.

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AVERAGE LIFE - CYCLE PRODUCTIVITY

The average profile, ẽs , is given by:
(
ẽs = f (s) = exp

(s

120)
80

4

)

,

such that f (0) = f (240) > 0 and f (120) = 1.
Profiles begin at a low value, rise to a peak in the middle period
of life, and then decline to the low value.
The productivity profiles are symmetric.
Agents can sell productivity units available in a particular period
in the labor market at the competitive wage.

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T HE RANGE OF LIFE - CYCLE PRODUCTIVITY
2

1.5

1

0.5

0
0

50

100

150

200

F IGURE : The range of productivity endowment profiles for credit market
participant households (N = 2). Profiles are symmetric and peak in the
middle period of the life cycle.

C ONCLUSIONS

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C ONCLUSIONS

S TATIONARY EQUILIBRIA

We let t 2 ( ∞, +∞) .
We only consider stationary equilibria under perfectly credible
policy rules governing P (t) .
We let R (t) be the gross real rate of return in the credit market.
Stationary equilibrium is a sequence fR (t) , P (t)gt+=∞ ∞ such that
markets clear, households solve their optimization problems,
and the policymaker credibly adheres to the stated policy rule.
Key condition is that aggregate asset holding A (t) = 0 8t.

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C ONCLUSIONS

S TATIONARY EQUILIBRIA

T HEOREM
Assume symmetry as defined above. Assume the monetary authority
credibly uses the price level rule 8t. Then the general equilibrium gross real
interest rate, R (t 1, t) , is equal to the gross rate of aggregate productivity
growth, and hence the real growth rate of the economy, λ (t 1, t) , 8t.

C OROLLARY
For any two households that share the same productivity profile,
consumption is equalized at each date t.

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Characterizing the Equilibrium

C ONCLUSIONS

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C ONCLUSIONS

C ONSUMPTION
2

1.5

1

0.5

0
0

50

100

150

200

F IGURE : Consumption (flat lines) versus income (bell shaped curves) profiles,
by cohort along the complete markets balanced growth path with w (t) = 1.
Under optimal monetary policy, the private credit market reallocates uneven
income into perfectly equal consumption for each productivity profile. The
consumption Gini is 35.9%, similar to values calculated from U.S. data.

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C ONCLUSIONS

N ET ASSET HOLDING
50

0

-50
0

50

100

150

200

F IGURE : Net asset holding profiles by cohort along the complete markets
balanced growth path. Borrowing, the negative values to the left, peaks at
stage 60 of the life cycle (age ~35), while positive assets peak at stage of life
180 (age ~65). The financial wealth Gini is 74.4%, similar to values calculated
in U.S. data.

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Inequality

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C ONCLUSIONS

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I NEQUALITY

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,
2010): gW,U.S. = 80%.

C ONCLUSIONS

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C ONCLUSIONS

I NEQUALITY IN THE MODEL
Large amount of heterogeneity which depends in part on how
many productivity profiles N we include.
There are N
levels.

121 income (wealth) levels, and N consumption

We measure inequality by the Gini coefficient, g.
Financial wealth is defined as the non-negative part of net assets.
Denote by gW (gY , gC ) the wealth (income, consumption) Gini
coefficient.
For ξ = 2.5 and nine possible income profiles (i.e., N = 8)
gW = 72% > gY = 50% > gC = 31%,
versus U.S. data
gW,U.S. = 80% > gY,U.S. = 51% > gC,U.S. = 32%.

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P RODUCTIVITY DISPERSION AND G INI COEFFICIENTS
1

= 2.5: model Gini coefficients
repo rted in previou s slide.

0.8

0.6

0.4

W ealth
Incom e
Consum ption

0.2

0
1

2

3

4

5

F IGURE : As the dispersion of productivity profiles, ξ, increases, the Gini
coefficients increase. The ordering gW > gY > gC is preserved.

C ONCLUSIONS

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Conclusions

I NEQUALITY

C ONCLUSIONS

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C ONCLUSIONS

A LL HOUSEHOLDS FACE A CONSUMPTION SMOOTHING
PROBLEM

The relationship between monetary policy and inequality has
been a topic of increased research interest.
This paper attributes observed levels of inequality to life-cycle
effects in conjunction with heterogeneous life-cycle productivity
profiles.
The productivity profiles are exogenous to the model, but they
could be interpreted as representing the output of an
unmodelled human capital accumulation process.
All households in this model face a problem of smoothing
life-cycle consumption in a world with non-state contingent
nominal contracting (the NSCNC friction).

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C ONCLUSIONS

Monetary policy can eliminate the distortion coming from the
NSCNC friction for all households, even when there is
substantial heterogeneity.
All households benefit from eliminating this distortion.
The monetary policymaker is not operating by helping financial
wealth holders or borrowers, but by repairing the distortion
caused by the NSCNC friction.
To the extent optimal monetary policy affects inequality in this
model, it is mostly through helping households smooth lifetime
consumption, and therefore the largest effects are likely on the
consumption Gini as opposed to those associated with income or
financial wealth.