The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
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
Monetary Policy and Heterogeneity
Federal Reserve Board Virtual Conference
October 15, 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 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
E NVIRONMENT
T HE MASS
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
OF LIFE - CYCLE PRODUCTIVITY
F IGURE : The mass of endowment
profiles: es,i ∼ es · U ξ −1 , ξ ,
4
es = 2 + exp − s−60120
, ξ = 6.5.
11
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
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
P (t)
ct ( t )
Rn (t, t + 1)−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
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
H OUSEHOLDS ’ 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
E NVIRONMENT
T IMING
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
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:
Rn (t − 1, t)
P (t − 1) ,
(6)
P (t) =
λ (t − 1, t)
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
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
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
E QUILIBRIUM
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 above, 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
E NVIRONMENT
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
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
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
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
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
E QUILIBRIUM
T HREE NOTIONS
1
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) +
at,i (t + s − 1)
+ max [λ (t + s, t + s − 1) − 1]
,0 ,
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
E NVIRONMENT
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
ηē
dc
=
MPC1 (s) =
.
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
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
Inequality
28
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
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
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
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.
31
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
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
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
Policy
33
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NTERPRETING MONETARY
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 NVIRONMENT
E FFECTS
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
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
C ONCLUSIONS
Conclusions
37
I NTRODUCTION
E NVIRONMENT
E QUILIBRIUM
I NEQUALITY
P OLICY
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
FW =
Ws ∼
FWs
,
s=0 241
∑
s = 120, ..., 239
ln N µ + ln (w) + ln ∑sk=0 ek − ē , σ2 ,
δ
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):
N N wwm
σi2 + µi − µj
i j i
− 1 .
2Φ q
G=∑∑
2 + σ2
m
σ
i=1 j=1
i
Back
j