The Impact of Consumer Credit Access onUnemployment

Kyle F. HerkenhoffNBER Working Paper (2018)

Macroeconomics Reading GroupMorteza Ghomi

March 6, 2019

Outline

Introduction

ModelHouseholdsSaving and Lending InstitutionsFirms

Stochastic Steady StateCalibration1977 vs. 2010

Exploring the Model’s MechanismsIR Experiment

Main Quantitative ExperimentFixed vs. Fluctuating accessTrend vs. Cycle

Conclusion

2 / 32

Introduction

I Unemployed households’ access to unsecured revolving creditmore than tripled over the last three decades

I Low asset unemployed households replace approximately 15%of lost income through unsecured borrowing

I 40% of households self-report defaulting on non-mortgagepayments in response to job loss

I The ability to borrow significantly prolongs unemploymentdurations and raises replacement wages (Herkenhoff et al2015)

3 / 32

Main Question

”How growth and fluctuations in households’ access to creditmarkets since the 1970s have affected the way employment evolvesover the business cycle?”

Main features

I Trying to answer this question both theoretically andquantitatively

I Using a general equilibrium search and matching model withdefaultable debt and searching in two markets

I Taking into account saving and lending institutions

I Both aggregate and idiosyncratic shocks, heterogeneity inemployment outcome and credit histories and interactionbetween them

4 / 32

Main Question

”How growth and fluctuations in households’ access to creditmarkets since the 1970s have affected the way employment evolvesover the business cycle?”

Main features

I Trying to answer this question both theoretically andquantitatively

I Using a general equilibrium search and matching model withdefaultable debt and searching in two markets

I Taking into account saving and lending institutions

I Both aggregate and idiosyncratic shocks, heterogeneity inemployment outcome and credit histories and interactionbetween them

4 / 32

Main Contributions

I The paper develops a general equilibrium search and matchingmodel with defaultable debt

I The paper measures the mechanisms through which creditaccess impacts unemployment over the business cycle

I The paper constructs aggregate time series for unemployedhouseholds’ access to credit and use of credit from 1970onwards

5 / 32

Main Results

I Credit fluctuations have contributed to moderately deeper andlong lasting recessions over the last 40 years

I As more individuals obtained credit access from 1977 to 2010,credit fluctuations became more important determinants ofemployment dynamics

I Even though business cycles are more volatile, newbornsstrictly prefer to live in the economy with growing, butfluctuating, access to credit markets

I In the absence of procyclical credit fluctuations, slow-movingtrend credit growth may actually dampen business cycledynamics

6 / 32

ModelNotation

I Time is discrete

I T ≥ 2 overlapping generations of risk averse HH facing bothidiosyncratic and aggregate shocks

I Each household lives T periods deterministically

I ct : consumption, ht : indivisible labor, and η: leisure

I x(D): penalties of default (fraction of debt defaulted upon)

I χc : cost of searching in credit market

I States:I HH:

e ∈ W ,U, a ∈ C ,N,w ∈W , z = γw ∈ Z , b ∈ B, t ∈ NT

I Aggregate state: Ω = [y ,A, µ]I µ : W ,U × C ,N ×W ∪ Z ××B × NT → [0, 1]

7 / 32

ModelNotation

I Time is discrete

I T ≥ 2 overlapping generations of risk averse HH facing bothidiosyncratic and aggregate shocks

I Each household lives T periods deterministically

I ct : consumption, ht : indivisible labor, and η: leisure

I x(D): penalties of default (fraction of debt defaulted upon)

I χc : cost of searching in credit market

I States:I HH:

e ∈ W ,U, a ∈ C ,N,w ∈W , z = γw ∈ Z , b ∈ B, t ∈ NT

I Aggregate state: Ω = [y ,A, µ]I µ : W ,U × C ,N ×W ∪ Z ××B × NT → [0, 1]

7 / 32

Household ProblemTiming

Each period consists of three stages:

1. HH participate in asset market, search for borrowingopportunities and make accumulation and default decision

2. HH enter labor market and make job search decision

3. Expense shocks are realized

8 / 32

Household Problemfirst stage

I HH choose whether or not to look for credit, cost = χc

I w.p AψU,t(z , b, ; Ω) they will match and bargain over terms ofloan (A is matching efficiency)

I They remains matched until the HH defaults, D > 0, or thematch is destroyed exogenously (with rate s)

I Breakup probability:

s(D) =

1 if D > 0

s if D = 0

I BE for employed and unemployed agent:

Ut(z , b, ; Ω) = maxAψU,t(z , b, ; Ω)UCt (z , b, ; Ω) + (1− AψU,t(z , b, ; Ω))

UNt (z , b, ; Ω)− χC ,U

Nt (z , b, ; Ω) ∀t ≤ T

Wt(z , b; Ω) = maxAψW ,t(w , b; Ω)W Ct (w , b; Ω) + (1− AψW ,t(w , b; Ω))

WNt (w , b; Ω)− χC ,W

Nt (w , b; Ω) ∀t ≤ T

9 / 32

Household Problemsecond stage

I Asset market closes and aggregate state is realized

I Unemployed agents enter the labor market looking for jobspaying w ∈W

I Each submarket is indexed by a wage and age pair (w , t)

I pt(w ,Ω′): Pr. of matching with an employer paying w

10 / 32

Household Problemthird stage

I Labor market closes and expense shock is realized

I This shock is designed to disconnect default from employmentstatus

I With probability px , they begin the next period with anadditional debt burden of x

I For each BE V ∈ W ,W c ,U,UC :

V (w , b′; Ω′) = pxV (w , b′ − x ; Ω′) + (1− px)V (w , b′; Ω′)

I LOM for aggregate state:

Ω′ = (µ′,A′, y ′) µ′ = Φ(ω,A′, y ′)y′ ∼ F (y ′|y) A′ ∼ G(A′|A)

11 / 32

Household ProblemBellman Equation

For an unemployed with access to credit:

UCt (z, b, ; Ω) = max

b′∈B,D∈[0,1]u(c)− x(D) + η

+(1-s(D))βEΩ′

[maxw∈W

pt+1(w ; Ω′)(W Ct+1(w , b′; Ω′))+(1−pt+1(w ; Ω′))UC

t+1(z, b′, ; Ω′)

]+s(D)βEΩ′

[maxw∈W

pt+1(w ; Ω′)(Wt+1(w , b′; Ω′)) + (1− pt+1(w ; Ω′))Ut+1(z, b′, ; Ω′)

]

UCT+1(z, b; Ω) = 0

subject to the budget constraint:

c + qU,t(z, b′,D,Ω)b′ ≤ z + (1− D)b

12 / 32

Household ProblemBellman Equation

For an unemployed without access to credit:

UNt (z, b; Ω) = max

b′≥0,D∈[0,1]u(c)− x(D) + η

+βE

[maxw∈W

pt+1(w ; Ω′)(Wt+1(w , b′; Ω′)) + (1−pt+1(w ; Ω′))Ut+1(z, b′, ; Ω′)

]∀t ≤ T

UNT+1(z, b; Ω) = 0

subject to the budget constraint:

c + 11+rf

b′ ≤ z + (1− D)b

13 / 32

Household ProblemBellman Equation

For an employed household:

W Ct (w , b; Ω) = max

b′∈B,D∈[0,1]u(c)− x(D) + βE

[(1− δ)(Wt+1(w , b′; Ω′)) +

δmaxw∈W

pt+1(w ; Ω′)(Wt+1(w , b′; Ω′)) + (1−pt+1(w ; Ω′))Ut+1(γw , b′, ; Ω′)]∀t ≤ T

subject to:

c + qW ,t(w , b′,D; Ω)b′ ≤ w + (1− D)b

WNt (w , b; Ω) = max

b′≥0,D∈[0,1]u(c)− x(D) + βE

[(1− δ)(Wt+1(w , b′; Ω′)) +

δmaxw∈W

pt+1(w ; Ω′)(Wt+1(w , b′; Ω′)) + (1−pt+1(w ; Ω′))Ut+1(γw , b′, ; Ω′)]∀t ≤ T

subject to:

c + 11+rf

b′ ≤ w + (1− D)b

14 / 32

Saving Institutions and Lending Institutions

I Unit measure of risk neutral saving institutions and a unitmeasure of risk neutral lending institutions

I Saving institutions accept deposit each period in a frictionlessmarket offering the risk free rate (rf ) on saving

I Lending institutions send out credit offers to potentialborrowers with cost κC and are guaranteed a minimumproportional service fee τ

I After being matched, households have full bargaining powerand send take-it-or-leave-it bond price offer

qe,t(w , b′,D; Ω)=

sE [1− Da′e′,t+1

(w ′, b′; Ω′)] + (1− s)E [1− DCe′,t+1

(w ′, b′; Ω′)]

1 + rf + τif b′ ∈ B−and D = 0

0 if b′ ∈ B−and D > 0

1

1 + rfif b′ ∈ B+

15 / 32

Firms

I Firms post fixed wage contracts (w,t) with cost κL

I The posted wage w is fixed once an employee is found

I Vacancy filling rate: ft(w ; Ω)

I BE for a firm:

Jt(w ; Ω) = y − w + βE[(1− δ)Jt+1(w ; Ω)

]∀t ≤ T

I Free entry of firms:

κL = ft(w ; Ω)Jt(w ; Ω) iff θt(w ; Ω) > 0

16 / 32

Equilibrium

I We will focus on Block Recursive Competitive Equilibria

I Under relatively weak assumptions, a block recursiveequilibrium exists

I Under more restrictive conditions, the equilibrium is unique

17 / 32

Stochastic Steady Statespecifying the functions

I Preferences:u(c) + η(1− h)− x(D) = c1−σ−1

1−σ + η(1− h)− κD D1−D+εD

I Matching function in both labor and credit market:M(u, v) = u.v

(uζ+vζ)1ζ∈ [0, 1)

I Aggregate productivity deviations:ln(y ′) = ρln(y) + ε1 ε1 ∼ (0, σ2

e )

18 / 32

Stochastic Steady stateCalibration

19 / 32

Stochastic Steady state1977 vs. 2010

Same calibration, different matching efficiency: A1977 = 0.48 andA2010 = 0.72

20 / 32

Exploring the Model’s Mechanismstwo effects

When credit access expands:I Expansion Effect

I In the short run, acts like a safety net and households feelmore secure

I HH optimally search for better-paying but harder-to-find jobsI If credit grows coming out of a recession, this may lead to

elevated unemployment in the short run and a slower recovery;

I Level EffectI With greater long-run levels of credit access, more individuals

dissave and enter recessions indebtedI With a tighter labor market in a recession, indebted agents

avoid default by cutting their reservation wagesI Tends to dampen employment volatility over the business cycle

21 / 32

IR Experiment of a productivity shockcredit expansion: before vs. after recession

22 / 32

IR Experiment of a productivity shockthe level matters!

Larger Fraction Borrowing Amplifies Credit Shocks

23 / 32

Main Quantitative Results

I Credit growth coming out of the 1990, 2001, and 2007recessions increases the severity of each downturn

I In the 2001 and 2007 recessions, credit growth reduces thespeed of recovery

I At every point along the transition path, newborns prefer tolive in the world with fluctuating, but growing, credit access,even though the unemployment rate is more volatile, and lastly

I Credit fluctuations, as opposed to trend credit growth, areprimarily responsible for generating slower recoveries

24 / 32

Main Quantitative Resultsfixed access vs. expanding and fluctuating access

25 / 32

fixed access vs. expanding and fluctuating access

26 / 32

fixed access vs. expanding and fluctuating access

27 / 32

Main Quantitative ResultsWelfare Gains from 1977 to 2010

I During the late 2000s, individuals are willing to give up moreto live in an economy with greater credit access, even thoughbusiness cycles are more volatile

I Credit is more valuable during recessions, welfare gains arehigher for cohorts born during the 2007-2009 crisis

28 / 32

Main Quantitative ResultsTrend vs. Cycle

29 / 32

Trend vs. Cycle

30 / 32

Trend vs. Cycle

31 / 32

Conclusion

I Unemployed households’ access to credit has grownremarkably, but how it affects business cycles and welfare?

I Credit fluctuations have contributed to moderately deeper andmore protracted recessions over the last 40 years

I As more individuals obtained credit access, credit fluctuationsbecame more important determinants of employmentdynamics

I Even though business cycles are more volatile, newbornsstrictly prefer to live in the economy with growing, butfluctuating, access to credit markets

I In the absence of procyclical credit fluctuations, trend creditgrowth may actually dampen business cycle dynamics

32 / 32