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I NCOMPLETE C REDIT M ARKETS AND
M ONETARY P OLICY WITH
H ETEROGENEOUS L ABOR S UPPLY
James Bullard (FRBSTL)

Aarti Singh (U. Sydney)

Bank of Korea 2016 Conference
Employment and Growth
Seoul, Korea
May 30, 2016
Any opinions expressed here are the authors’ and do not necessarily reflect those of the FOMC.

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Overview

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T HIS TALK
This is an academic talk.
In the model presented here, monetary policy has an important
role to play, but not because of “sticky prices.”
Households will supply labor endogenously, and household
labor supply will differ across households.
Nevertheless, monetary policymakers will be able to carry out an
optimal monetary policy without reference to household labor
supply.
I see this result as helping to inform the debate on whether U.S.
monetary policy needs to worry about declining labor force
participation.
The bottom line of this talk is that the answer is “no”.

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Labor Force Participation
and Monetary Policy

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D EPRESSED U.S. LABOR FORCE PARTICIPATION

U.S. labor force participation (LFP) has been depressed since the
large 2007-2009 recession.
Portions of the current U.S. monetary policy discussion have
been focused on reviving labor force participation to higher
levels.
Key questions: Can monetary policy substantially affect labor
force participation? If so, should it?
Important: For this presentation, I will think of “labor force
participation” and “household labor supply” interchangeably.

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T WO VIEWS
Traditional view: Aaronson et al. (BPEA, 2006) built a
demographically-based LFP model and successfully predicted
the post-crisis 2013 LFP rate.
“Different demographic groups tend to have different LFP.”
Consideration of longer-term trends in labor force participation
seems to be consistent with the traditional view, as reviewed in
Bullard (StLFedRev, 2014).
Alternative view: Erceg and Levin (JMCB, 2014) argued that a
large portion of the post-crisis fall in LFP was cyclical, and built a
New Keynesian model in which an “LFP gap” becomes a
component of optimal monetary policy after large recessions.

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T HE TRADITIONAL VIEW : A ARONSON ET AL . (2006)

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T HE TRADITIONAL VIEW :

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LONGER RUN

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T HE E RCEG AND L EVIN (2014) VIEW

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T HIS PAPER

The argument in this paper is that the traditional view is more
nearly correct.
The model economy includes heterogeneous households that
will supply different amounts of labor at every date.
Monetary policy will be conducted optimally to repair a friction
in household credit markets.
The optimal monetary policy can be conducted independently of
household labor supply decisions.
Demographic factors—time-varying population growth—will
affect measured labor supply of households.

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Credit Market Friction

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T HE RETURN OF HOUSEHOLD CREDIT MARKETS

The 2007-2009 financial crisis increased attention on household
credit markets.
Could monetary policy be used to help keep household credit
markets working well?

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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 mostly to keep this large
credit market functioning properly (i.e., complete).
When large and persistent negative shocks hit the economy, the
zero lower bound (ZLB) will threaten.
The monetary authority can maintain a smoothly operating
credit market even when the ZLB threatens.

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I NCOME AND WEALTH INEQUALITY

There is a lot of income and wealth inequality in this stylized
model.
The role of credit markets, if they work correctly, will be to
reallocate uneven income across the life cycle into perfectly equal
consumption by cohort.
The model equilibrium will naturally rank the wealth Gini
coefficient as the highest, the income Gini coefficient as
somewhat lower, and the consumption Gini coefficient as the
lowest.

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H OW LARGE ARE THESE MARKETS ?

According to Mian and Sufi (AER, 2011), the ratio of household
debt to GDP in the U.S. was about 1.15 before it ballooned to
1.65 during the 2000s.
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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What We Do

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W HAT WE DO
Simple, stylized, endowment DSGE T-periods (quarterly)
life-cycle model of private debt, real interest rates and inflation.
The economy has a large credit sector and a small cash sector.
Friction: Non-state contingent nominal contracting (NSCNC).
Labor productivity growth is the only source of uncertainty.
Monetary policy can substitute for the missing state-contingent
contracts by choice of the price level.
For certain shocks, the ZLB threatens to bind.
Monetary policy can continue to complete credit markets in this
situation.
Labor supply will be heterogeneous but independent of
monetary policy choices.

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T HE MONETARY POLICY IMPLICATIONS

In ordinary times, optimal monetary policy looks like “nominal
GDP targeting”—countercyclical price level movements.
When the ZLB threatens, the monetary authority should
generate a one-time increase in the price level.
There is no role for forward guidance—staying at the ZLB would
be associated with incomplete credit markets.
Household labor supply is driven by non-monetary factors.
These results may help inform the debate on monetary policy in
a low nominal interest rate environment.

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Environment

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S EGMENTED MARKETS
Standard T-periods (quarterly) DSGE life-cycle endowment
economy with segmented markets. Any T 3 will work; I prefer
T = 241 (quarterly); odd values are convenient; T ! ∞ is
continuous time.
Households are divided into two types, “participants” in the
credit markets and “non-participants”.
There are two assets in the model, privately-issued debt
(consumption loans) and currency.
Participants can hold either asset but, in the stationary equilibria
we study, they will not hold currency as it is dominated in rate of
return.
Non-participants can only hold currency.

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P REFERENCES
All participant households have log preferences with no
discounting
T

Vt = Et ∑ [η ln ct (t + j) + (1

η ) ln `t (t + j)]

j=0

where η 2 (0, 1] , ct (t + j) > 0 is the date t + j consumption of the
household born at date t, and `t (t + j) 2 (0, 1) represents the
fraction of a unit time endowment per period devoted to leisure
activities.
Other assumptions: Within-cohort agents are identical, no
population growth, no capital, no default, flexible prices, no
borrowing constraints.

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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.

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S TOCHASTIC STRUCTURE
Labor supply with η 2 (0, 1) will turn out to be independent of
the real wage.
The real wage w (t) is exogenously given by
w (t + 1) = λ (t, t + 1) w (t) ,

(1)

where w (0) > 0, and
λ (t, t + 1) = (1

ρ) λ + ρλ (t

1, t) + σe (t + 1) ,

(2)

where λ > 1 represents the average gross growth rate, ρ 2 (0, 1) ,
σ > 0, and e (t + 1) N (0, 1) .
For sufficiently large, negative draws of e (t + 1) , the ZLB will
threaten.

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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 the price
level, P (t) .
Households then decide how much to consume and save.

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L IFE - CYCLE PRODUCTIVITY

All participant households are endowed with an identical
productivity profile over their lifetime.
The profile begins at a low value, rises to a peak at the middle
period of life, and then declines to the low value.
Agents can sell productivity units in the labor market at the
competitive wage.
The productivity profile is symmetric.

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L IFE - CYCLE PRODUCTIVITY
1 .0

0 .8

0 .6

0 .4

0 .2

50

100

150

200

F IGURE : A schematic productivity endowment profile for credit market
participant households. The profile is symmetric and peaks in the middle
period of the life cycle. About 50 percent of the households earn 75 percent of
the labor income in the credit sector for η = 1.

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L ABOR INCOME CHANGES
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50

10 0

15 0

20 0

F IGURE : How labor income changes across cohorts when the real wage
increases 10 percent for η = 1.

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Money and Nominal Interest Rates

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N ON - PARTICIPANTS

Completely precluded from credit markets.
Inactive in the first period 0.
Productivity endowment is γ “small” in every odd period of life 1,
3, 5, ..., T 2.
These households consume in every other subsequent period 2, 4,
6, ..., T 1.

There is no life-cycle aspect to productivity or consumption.
Conclude: Non-participants work only intermittently and save all
income by holding currency.

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C URRENCY PROVISION

The central bank can print currency and sell it to non-participant
households who value it.
Currency demand at date t is a simple function of real wages in
the cash sector.
The central bank completely controls the date t price level via the
gross growth rate of currency creation.
The choice of the price level characterizes equilibrium for the
cash sector.
Seigniorage revenue is rebated lump sum to even-dated cash
users.

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N OMINAL INTEREST RATE
Participant 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

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

(3)

This rate depends on the expected rate of consumption growth
and the expected rate of inflation.
We study stationary equilibria in which the ZLB is never
breached.

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T HE CENTRAL BANK MANDATE

The central bank has a hierarchical mandate.
First and foremost, the central bank mandate calls for a smoothly
operating credit market, i.e., a form of “financial stability.”
Secondarily, the central bank is expected to maintain an
exogenously given inflation target.
We assume an inflation target of zero for convenience.
Because of the lump-sum rebate assumption, the policy outlined
here will be first-best for both participant and non-participant
households.

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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.
The key condition is that aggregate asset holding A (t) = 0 8t.

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Non-Stochastic Balanced Growth

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N ET ASSET HOLDING
15
10
5

50

100

5
10
15

F IGURE : Net asset holding by cohort along the complete markets balanced
growth path with η = 1. 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). About 25 percent of the population holds about 75 percent of
the assets.

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C HANGE IN NET ASSET HOLDING
20

10

50

100

150

200

10

20

F IGURE : How net asset holding changes by cohort when the wage increases
by 10 percent when η = 1.

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C ONSUMPTION
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F IGURE : Schematic representation of consumption, the flat line, versus labor
income, the bell shaped curve, by cohort along the complete markets
balanced growth path with w (t) = 1 and η = 1. The private credit market
completely solves the point-in-time income inequality problem.

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C HANGE IN CONSUMPTION
1.0

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0.2

0

50

100

F IGURE : How labor income and consumption change by cohort when the
wage increases by 10 percent with η = 1.

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H OUSEHOLD LABOR SUPPLY

F IGURE : Schematic hump-shaped labor supply and U-shaped leisure by
cohort under log-log preferences. Participant households in peak earning
years work more, and those at the beginning and end of the life cycle work
less, independent of consumption choices. The vertical axis is percent of
available household time per period.

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H ETEROGENEOUS HOUSEHOLD LABOR SUPPLY

Household labor supply is heterogeneous—middle-aged
households work more. This is independent of monetary policy
choices.
As shocks hit the economy, labor supply by cohort remains the
same.
Key implication: Hours worked and population growth should
be highly correlated.
Key implication: An economy with more older workers would
have a lower aggregate labor supply than a similar economy
with an even age distribution.

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L ABOR SUPPLY AND POPULATION IN THE U.S. DATA

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K EY FEATURE OF THE NON - STOCHASTIC STEADY STATE

By careful choice of assumptions, the general equilibrium gross
one-period real interest rate is equal to the gross real output
growth rate in the steady state; that is,
R = λ.
All households have an “equity share” in the economy—this is the
optimal contract under homothetic preferences.

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M ONETARY GROWTH IN THE NON - STOCHASTIC STEADY
STATE

The pace of currency creation θ = λ along the complete markets
balanced growth path with an inflation target of zero.
The gross nominal interest rate
Rn = λ > 1,
so the net nominal interest rate would always be positive.
This is an important part of the non-stochastic benchmark.

(4)

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Complete Markets

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C OMPLETE MARKETS WITHOUT NSCNC

Now allow aggregate shocks, under the price stability policy
P (t) = 1 8t.
Set the NSCNC friction aside for this slide only.
Conjecture and verify a stationary equilibrium with
R (t) = λr (t 1, t) , where λr (t 1, t) is the realized value of the
stochastic process governing growth.
Participant households again consume equal amounts of
available production in the credit sector.
Consumption and asset holdings fluctuate from period to
period, but in proportion to the value of w (t) .

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C OMPLETE MARKETS WITH NSCNC
Now include NSCNC. The countercyclical price level policy rule
delivers complete markets allocations:
1, t)]
1 [ λ (t
P (t 1)
λr (t 1, t)
(1 ρ) λ + ρλ (t 2, t 1)
=
P (t
(1 ρ) λ + ρλ (t 1, t 2) + σe (t)

P (t) =

Et

(5)
1) .

Similar to Sheedy (BPEA, 2014) and Koenig (IJCB, 2013).
Households again consume equal amounts of available
production in the credit sector.
Consumption and asset holdings fluctuate from period to
period, but in proportion to the value of w (t) .

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T HE NATURE OF COMPLETE MARKETS POLICY

This policy involves countercyclical price level movements.
Heuristically:
π (t)

π ? = Et

1

[∆y (t)]

∆y (t)

where π (t) is the net inflation rate and ∆y (t) is the net output
growth rate.
On average, an inflation target could still be maintained.
This can be interpreted as nominal income targeting.
It works well, but what happens when the ZLB is encountered?

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Zero Lower Bound

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E NCOUNTERS WITH THE ZERO LOWER BOUND

The economy grows over time at gross rate λ, and the inflation
target is zero.
The ZLB threatens when expected net consumption growth is
negative.
If the nominal interest rate were allowed to be zero, the saver
segment of participant households would want to hold currency.
We do not analyze this possibility, but it would entail a
significant transition.
How can complete credit markets be maintained?

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PRICE LEVEL ADJUSTMENT

The central bank in this situation would wish to keep the
nominal interest rate positive.
The central bank can promise a one-time increase in the price
level for the following period sufficient to keep the nominal rate
positive.
This must be part of a credible commitment to a policy rule.

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T HE PRICE LEVEL METHOD

Knowing this policy is in place, the credit sector households will
contract using a positive nominal interest rate.
Consumption will again be equalized among participant
households alive at date t, and credit markets will be complete.

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Conclusions

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C ONCLUSIONS

The desire behind many actual policy choices over the last
several years has been to help credit markets perform better.
This paper features a credit market that is essential to good
macroeconomic performance, in which the friction is NSCNC.
This paper suggests a method of conducting monetary policy
when the ZLB threatens: Credibly promise a one-time increase in
the price level.

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B OTTOM LINE

Here one would want to keep nominal interest rates positive, not
at zero.
This result is in stark contrast to common policy
recommendations in recent years—forward guidance
committing to stay at the ZLB even longer, or quantitative easing
justified as “keeping longer-term nominal interest rates low.”
Household labor supply is heterogeneous, but independent of
monetary policy choices, consistent with the traditional,
demographically-based view of labor force participation.
This may help inform the debate during this conference.

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