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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
The Bank of Finland Monetary Policy Webinar:
New Challenges to Monetary Policy Strategies
Nov. 24, 2020
Any opinions expressed here are our own and do not necessarily reflect those of the FOMC.
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
Introduction
2
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
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.”
3
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
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.
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.
4
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
O PTIMAL MONETARY POLICY
We construct a stylized economy with considerable wealth, income and consumption
inequality.
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.
5
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
K EY THEMES
Monetary policy is part of the general equilibrium and therefore has effects on
income, financial wealth and consumption inequality.
The role of monetary policy when credit markets play an important role is to “induce
the correct real interest rate period-by-period”—this real interest rate is the one that
would occur if there were no nominal frictions.
The life cycle contributes importantly to Gini coefficients for income, consumption
and wealth in this model.
The model equilibrium features both poor-hand-to-mouth and
wealthy-hand-to-mouth households with high marginal propensity to consume
(MPC).
The model accommodates arbitrarily rich and arbitrarily poor households.
6
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
Environment
7
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
G ENERAL - EQUILIBRIUM LIFE - CYCLE ECONOMY
Each period, a new cohort of households enters the economy, makes economic
decisions over the next 241 quarters, then exits the economy.
Households have log-log preferences defined over consumption and leisure.
Households are randomly assigned one of many possible personal productivity
profiles 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.
Productivity units determine the value of an hour worked in a competitive labor
market.
No capital, no discounting, no population growth, no default, no borrowing
constraints, no government spending and no taxes; no ELB and no money demand
(see Azariadis et al. JEDC, 2019).
8
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
L IFE - CYCLE PRODUCTIVITY PROFILES
Households entering the economy draw a scaling factor x ∼ U ξ −1 , ξ and receive a
life-cycle productivity profile that is a scaled version of the baseline profile, es :
es,i = x · es ,
where ξ ≥ 1 determines the within-cohort dispersion and
"
#
s − 120 4
.
es = f (s) = 2 + exp −
60
All idiosyncratic risk is borne by agents at the beginning of the life cycle.
Huggett, Ventura and Yaron (AER, 2011) argue that differences in initial conditions
are more important than differences in shocks.
We also consider ln (x) ∼ N µ, σ2 , creating an economy with arbitrarily rich and
poor households.
9
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
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.
10
I NTRODUCTION
T HE MASS
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
OF LIFE - CYCLE PRODUCTIVITY
F IGURE : The mass of endowment profiles: es,i
4
−1
s−120
∼ es · U ξ , ξ , es = 2 + exp −
, ξ = 6.5.
60
11
I NTRODUCTION
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P OLICY
C ONCLUSIONS
N OMINAL INTEREST RATE CONTRACTS
The overlapping-generations structure creates a large private credit market essential
to good macroeconomic performance.
Loans are dispersed and repaid in the unit of account—that is, in nominal terms—and are not
contingent on income realizations.
Households meet in a large competitive credit market where they contract by fixing
the nominal interest rate one period in advance.
The non-state contingent nominal interest rate is given by
ct (t)
P (t)
−1
n
R (t, t + 1) = Et
.
(1)
ct (t + 1) P (t + 1)
This rate can be understood as expected nominal GDP growth.
In the equilibria we study, this expectation is the same for all households, even for
those born at different dates or with different levels of productivity.
12
I NTRODUCTION
E NVIRONMENT
H OUSEHOLDS ’
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
PROBLEM
The problem of households i entering the economy at date t is
T
max
{ct,i (t+s),`t,i (t+s)}Ts=0
Et
∑ [η ln ct,i (t + s) + (1 − η ) ln `t,i (t + s)]
s=0
subject to the budget constraint
at,i (t + s)
≤ es,i [1 − lt,i (t + s)] w (t + s) +
P (t + s)
a (t + s − 1)
+Rn (t + s − 1, t + s) t,i
, s = 0, . . . , T
P (t + s)
ct,i (t + s) +
at,i (t − 1) = at,i (T ) = 0.
13
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
L INEAR PRODUCTION TECHNOLOGY
Aggregate real output Y (t) is given by
Y (t) = Q (t) L (t) ,
(2)
where L (t) is the aggregate labor input and Q (t) is the level of productivity.
Productivity grows at a stochastic rate λ (t, t + 1) ,
Q (t + 1) = λ (t, t + 1) Q (t) ,
(3)
λ (t, t + 1) = (1 − ρ) λ̄ + ρλ (t − 1, t) + σe (t + 1) ,
(4)
where λ̄ > 1 represents the average gross growth rate, ρ ∈ (0, 1) , σ > 0, and e (t + 1)
is a truncated normal with bounds ±b, b > 0, such that the ZLB is avoided.
The real wage w (t) grows at the same rate as productivity,
w (t + 1) = λ (t, t + 1) w (t) .
(5)
14
I NTRODUCTION
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I NEQUALITY
P OLICY
C ONCLUSIONS
T IMING PROTOCOL
Period t
Nature
Policymaker
Households
λ (t − 1, t)
=⇒ w(t)
P (t)
labor/leisure
consumption/saving
15
I NTRODUCTION
E NVIRONMENT
W HAT MONETARY
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
POLICY DOES
The countercyclical price-level rule delivers complete markets allocations:
P (t) =
Rn (t − 1, t)
P (t − 1) ,
λ (t − 1, t)
(6)
where λ is the realized productivity shock and Rn is the contract rate—similar to
Koenig (IJCB, 2013) and Sheedy (BPEA, 2014).
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 shocks to income.
Consumption and asset holdings fluctuate from period to period but in proportion to
the real wage, w (t) .
16
I NTRODUCTION
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C ONCLUSIONS
S TATIONARY EQUILIBRIA
We let t ∈ (−∞, +∞) .
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.
∞
A stationary equilibrium is a sequence {R (t) , P (t)}t+=−
∞ such that markets clear,
households solve their optimization problems, and the policymaker credibly adheres
to the stated policy rule.
The key condition is that aggregate asset holding A (t) = 0 ∀t.
17
I NTRODUCTION
E NVIRONMENT
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I NEQUALITY
P OLICY
C ONCLUSIONS
O PTIMALITY
T HEOREM
Assume a planner who places equal weight on all households for all time and discounts forward
and backward in time at the stochastic rate of growth of the economy.
(a) If the planner can constrain the assignment of productivity profiles to a single baseline profile
as defined earlier, then the planner will conclude that the competitive equilibrium described
above is a social optimum.
(b) If the planner cannot constrain the assignment of productivity profiles, the planner will
conclude that the competitive equilibrium described above is a constrained social optimum.
18
I NTRODUCTION
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E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
Characterizing the Equilibrium
19
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
S TATIONARY EQUILIBRIA
T HEOREM
Assume symmetry as defined above. Assume the monetary authority credibly uses the price-level
rule (6) ∀t. Then the gross real interest rate is equal to the gross rate of aggregate productivity
growth, and hence the real growth rate of the economy, λ (t − 1, t) , ∀t.
C OROLLARY (E QUITY SHARE CONTRACTING )
Any two households that share the same productivity profile consume the same amount at each
date, and consumption growth is equalized for all households.
C OROLLARY
Desired labor supply over the life cycle depends on the shape of the productivity profile alone and
not on the scaling factor x.
20
I NTRODUCTION
H OURS
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
WORKED OVER THE LIFE CYLE
1
0.5
0
0
60
120
180
240
quarters
F IGURE : Leisure decisions (green), labor supply (blue) and fraction of work time in U.S. data, 19%
(red). The labor/leisure choice depends on the current-to-lifetime average productivity ratio.
Productivity profiles of the form es,i = x · es imply labor/leisure choices depend on age only.
21
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I NEQUALITY
P OLICY
C ONCLUSIONS
C ONSUMPTION MASS
F IGURE : Cross section: Consumption mass (red) and labor income mass (blue). 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.
22
I NTRODUCTION
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P OLICY
C ONCLUSIONS
C ONSUMPTION EVOLUTION
F IGURE : Time series: Evolution of the distribution of log consumption (shaded area) and examples
of individual log consumption profiles (colored lines). Under optimal monetary policy, individual
consumption profiles share the same stochastic trend as aggregate consumption.
23
I NTRODUCTION
N ET
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
ASSET HOLDING MASS
F IGURE : Cross section: Net asset holding mass by cohort. 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 72.7%, similar to values calculated in U.S. data.
24
I NTRODUCTION
E NVIRONMENT
T HREE NOTIONS
1
E QUILIBRIUM
OF INCOME
I NEQUALITY
P OLICY
C ONCLUSIONS
F IGURES
Labor income,
Y1 = es,i [1 − `t (t + s)] w (t + s) ,
2
Labor income plus non-negative capital income,
Y2 = es,i [1 − `t (t + s)] w (t + s) +
a (t + s − 1)
,0 ,
+ max [λ (t + s, t + s − 1) − 1] t,i
P (t + s − 1)
3
The non-negative component of total income,
(
)
es,i [1 − `t (t + s)] w (t + s) +
Y3 = max
.
a (t+s−1)
+ [λ (t + s, t + s − 1) − 1] Pt,i(t+s−1) , 0
Gini coefficients of income distributions: GY1 = 56.2%, GY2 = 51.6%, GY3 = 59.6%.
25
I NTRODUCTION
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E QUILIBRIUM
M ARGINAL PROPENSITY
I NEQUALITY
P OLICY
C ONCLUSIONS
TO CONSUME
T HEOREM
The marginal propensity to consume out of income depends on age but is independent of the scaling
factor draw. In particular, the MPC out of labor income is
MPC1 (s) =
ηē
dc
.
=
dy1
es − (1 − η ) ē
26
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
M ARGINAL PROPENSITY
8
I NEQUALITY
C ONCLUSIONS
TO CONSUME
wealthy
hand-to-mouth
consumers
poor
hand-to-mouth
consumers
6
P OLICY
4
2
1
0
0
60
120
180
240
quarters
F IGURE : Cross section: Marginal propensity to consume out of labor income by cohort. Young and
old households are not very productive and have a high MPC. Young households are accumulating
debt and can be thought of as “poor hand-to-mouth.” Older consumers are relatively wealthy and
can be thought of as “wealthy hand-to-mouth.”
27
I NTRODUCTION
E NVIRONMENT
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I NEQUALITY
P OLICY
C ONCLUSIONS
Inequality
28
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P OLICY
C ONCLUSIONS
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%.
29
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
I NEQUALITY IN THE MODEL
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, ln (x) ∼ N µ, σ2 :
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.”
Details
30
I NTRODUCTION
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P OLICY
C ONCLUSIONS
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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C ONCLUSIONS
P RODUCTIVITY DISPERSION AND G INI COEFFICIENTS
1
0.653
0.5
0.443
0.32
0
0
0.5
1
1.5
2
2.5
3
3.5
F IGURE : As the dispersion of productivity profiles, σ, increases, the Gini coefficients increase. The
ordering GW > GY > GC is preserved.
32
I NTRODUCTION
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C ONCLUSIONS
Policy
33
I NTRODUCTION
E NVIRONMENT
I NTERPRETING MONETARY
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
POLICY
The price-level rule characterizes policy by countercyclical price-level movements.
But the policy can also be interpreted more conventionally in interest rate terms.
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.”
34
I NTRODUCTION
E NVIRONMENT
N OMINAL GDP
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
TARGETING
No persistence in productivity growth, ρ = 0: The expected rate of NGDP growth
never changes, and the economy never deviates from the NGDP path. “Perfect
NGDP targeting.”
Persistence in productivity growth, ρ > 0: The expected rate of NGDP growth
fluctuates persistently with the shock, and it takes longer to return to the balanced
growth NGDP path.
Nominal and real rates fall in a recession.
35
I NTRODUCTION
E FFECTS
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
OF A SHOCK
1.06
1.02
1.04
1
1.02
0
5
0
10
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, λ, by increasing the
price level in the period of the shock. Subsequently, inflation converges to its BGP value, π ∗ , from
below. The nominal interest rate drops in the period after the shock.
36
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C ONCLUSIONS
Conclusions
37
I NTRODUCTION
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C ONCLUSIONS
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 consumption in a world with a credit market
friction, “non-state contingent nominal contracting.”
The monetary authority can remove this impediment to 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.
38
L ABOR INCOME MASS
F IGURE : Cross section: Labor income profiles es,i (1 − `) w.
0
L ABOR INCOME + NON - NEGATIVE CAPITAL INCOME
F IGURE : Cross section:
Profiles of labor income and non-negative capital income
es,i (1 − `) w + max (λ − 1) Pa , 0 .
0
N ON - NEGATIVE TOTAL INCOME
F IGURE : Cross section: Profiles of non-negative total income max es,i (1 − `) w + (λ − 1) Pa , 0 .
Back
0
L OGNORMAL PRODUCTIVITY: G INI
COEFFICIENTS
Distribution of consumption, income and wealth
ln c ∼ N µ + ln (w) + ln (ηē) , σ2 ,
240
FY1 =
∑
s=0
FY1,s
241
,
Y1,s ∼ ln N µ + ln (w) + ln [(es − (1 − η ) ē)] , σ2 ,
240
FWs
,
s=0 241
ln N µ + ln (w) + ln ∑sk=0 ek − ē , σ2 ,
Ws ∼
δ
FW =
∑
s = 120, ..., 239
s = 0, ..., 119; s = 240
L OGNORMAL PRODUCTIVITY: G INI
COEFFICIENTS
Consider a mixture of N lognormal distributions, ln Xi ∼ N µi , σi2 :
N
ln (x) − µi
σi
σ2
m = E (X) = ∑ wi exp µi + i
2
i=1
!
X ∼ F (x) =
∑ wi Φ
i=1
N
,
.
The Gini coefficient is given by (Young, unpublished manuscript, LSE, 2011):
2
N N wwm
σi + µi − µj
i j i
2Φ q
− 1 .
G=∑∑
m
σ2 + σ2
i=1 j=1
i
Back
j