lecture4: joint-searchtheoryusers.econ.umn.edu/~guvenen/handout4_jointsearch.pdf · l ecture 4: j...

LECTURE 4: JOINT-SEARCH THEORY

September 17, 2012

Lecture 4: Joint-Search Theory September 17, 2012 1 / 32

Introduction

RISE OF DUAL-CAREER COUPLES

Female labor force participation rate stands at 60% compared to 75% formales.

% of households in which wife provides majority of household income hastripled since 1970.

Now 1/3 of US households have two main breadwinners.

Bottom Line: For many households, job search is increasingly becominga joint decision process.


Introduction


FIGURE : Fraction of Household Income Provided by Each Spouse


Introduction


Female labor force participation rate stands at 60% compared to 75% formales.

% of households in which wife provides majority of household income hastripled since 1970.

Now 1/3 of US households have two main breadwinners.

Bottom Line: For many households, job search is increasingly becominga joint decision process.


Introduction

AIM OF THE PAPER

Theoretical characterization of the joint job search problem of ahousehold (i.e., a couple)

Same economic environment as in McCall (1970)-Mortensen (1970), andBurdett (1978)

We study two cases where joint decision leads to different outcomes fromsingle-agent:

1 Couple has concave utility over pooled income

2 Couple receives job offers from multiple locations, and faces a cost of livingapart

Systematic comparison to single-agent search problem


Introduction

PREVIEW OF RESULTS

1 Risk-aversion (HARA): New opportunities

Joint-search similar to on-the-job search

reservation wage of unemployed couple is lower than reservation wage ofsingle-agent

endogenous quits into unemployment ) couple climbs up wage ladder(“breadwinner-cycle”)

Extension to nonparticipation

2 Multiple locations: New frictions (even with risk neutrality)

Joint-search process generates “tied-movers” and “tied-stayers” (Mincer,1978)

Couple misses job opportunities grabbed by single-agent facing sameenvironment


Introduction

RELATED LITERATURE

Shimer-Rogerson-Wright (2005)’s survey: no mention of householdsearch.

Burdett-Mortensen (1977): pioneering effort to characterize joint-searchproblem

Danforth (1979): search with risk-free saving

Mincer (1978): facts on family migration decisions

Dey-Flinn (2007) and Gemici (2007): quantitative search models withtwo-person households


Joint-Search Model

JOINT-SEARCH MODEL

Decision unit: couple, i.e. a pair of infinitely lived symmetric spousesindexed by i = 1,2

Discount rate r , income flows: y

i

2 {b,wi

}

Couple pools income (i.e., “unitary household”) and there is no storage(relaxed later)

Household intra-period utility: u(y1 + y2)

Search only during unemployment (relaxed later)

At rate a unemployed draw offer from F(w), exogenous

Wage constant during employment spell

No exogenous separation into unemployment (relaxed later)


Joint-Search Model

VALUE FUNCTIONS

Flow value for dual-worker couple:

rT (w1,w2) = u(w1 +w2)

Flow value for worker-searcher couple:

r⌦(w1) = u(w1 +b)+aˆ

max [T (w1,w2)�⌦(w1) ,⌦(w2)�⌦(w1) ,0]dF (w2)

Flow value for dual-searcher couple:

rU = u (2b)+2aˆ

max [⌦(w)�U,0]dF (w)


Joint-Search Model

RESERVATION WAGE FUNCTIONS

Dual-searcher couple:

Accept offer iff w1 > w

⇤⇤ s.t. ⌦(w⇤⇤) = U

Worker-searcher couple (spouse 1 employed):

T (w1,w2)� ⌦(w2):

2 accepts offer iff w2 > f(w1) s.t. T (w1,f(w1)) = ⌦(w1)1 does not quit.

T (w1,w2)< ⌦(w2):

2 accepts offer iff w2 > f(w1) s.t. ⌦(f(w1)) = ⌦(w1)1 quits upon acceptance

Quit decision:

1 quits job iff w1 < y(w2) where y is defined by T (y(w2),w2) = ⌦(w2)

) y(.) = f(.)


Joint-Search Model

1. RISK NEUTRALITY: JOINT SEARCH = SINGLE SEARCH


Joint-Search Model

2. CARA

Result I: w

⇤⇤ < w

⇤

Trade-off: consumption smoothing vs income maximization

Result II:

f (w1) =

⇢w1 if w1 < w

⇤ (quit)w

⇤ if w1 � w

⇤ (no quit)

Because of CARA, the reservation wage of the unemployed spouse isindependent of the wage of the employed spouse w1.


Joint-Search Model

2. CARA


Joint-Search Model

DYNAMICS WITH BREADWINNER CYCLE

0 20 40 60 80 100 120 140 160 180 200

0.4

0.6

0.8

1

1.2

Time (weeks)

Wag

e

0 20 40 60 80 100 120 140 160 180 200

0.4

0.6

0.8

1

1.2

Time (weeks)

Wag

e

Single 2

Spouse 2

Single 1Spouse 1


Joint-Search Model

3. GENERAL CHARACTERIZATION FOR HARA:

Unemployed couple less choosy than single: w

⇤⇤ < w

⇤

9bw � w

⇤ s.t. for w1 2 (w⇤, bw):

f (w1) = w1 (i.e., 450 line)

Breadwinner cycle always exists!

For w1 � bw :

f 0 (w1)

8<

:

> 0 if DARA

= 0 if CARA

< 0 if IARA

But Shape/type of region changes depending on DARA, CARA or IARA.


Joint-Search Model

DARA:


Joint-Search Model

CARA


Joint-Search Model

IARA


Joint-Search Model

AN ISOMORPHISM: MODEL OF MULTIPLE JOB HOLDING

Suppose unit of active time can be divided into two subperiods: e.g.,day-shift and night-shift

Single worker can be either:

1 Searching for first job, while producing 2b at home

2 Holding two jobs with wages (w1,w2)

3 Working on one job at wage w1, while searching for the second job andproducing only b at home

If wage offer on the second job is high enough, worker quits her first job andsearches for a better secondary job


Joint-Search Model

THREE EXTENSIONS

Symmetric on-the-job search (ae

= au

)

Joint-searching reduces to single-agent search

CARA with saving and “loose enough” borrowing limit

Joint-searching reduces to single-agent search

Exogenous separation

In the CARA and DARA cases, f (w) is strictly increasing. Strengthensbreadwinner cycle.


Numerical Example

ILLUSTRATIVE SIMULATION: SINGLES VS COUPLES

Period: one week [discount rate r = 0.001]

CRRA (DARA) with risk aversion coefficient r 2 {0,2,4,8}

Yearly exogenous separation rate 25%

Wage distribution: Log-normal, with mean wage normalized to zero andSD(logw) = 0.1

Offer arrival rates au

set to match u = 5.5%

Value of leisure b = 0.40


Numerical Example

COMPARISON OF SINGLE VERSUS JOINT SEARCH

r = 0 r = 2Single Joint Single Joint

Mean wage 1.06 1.06 1.07 1.10Mm ratio 1.04 1.04 1.09 1.47Unemp. rate 5.5% 5.5% 5.4% 7.6%Unemp. duration 9.9 9.9 9.7 12.6

Dual-searcher � 6 � 4.7Worker-searcher � 9.8 � 14.2

Quits/separations � 0% � 11.1%EQVAR- income � 0% � 1.1%


Numerical Example







Numerical Example

NON-MONOTONIC BEHAVIOR IN RRA

r = 2 r = 4 r = 8Single Joint Single Joint Single Joint

w

⇤/w

⇤⇤ 0.98 0.75 0.81 0.58 0.60 0.48E (w) 1.07 1.10 1.01 1.05 1.001 1.01Mm 1.09 1.47 1.23 1.81 1.67 2.10U rate 5.4% 7.6% 5.4% 7.7% 5.3% 5.6%U duration 9.7 12.6 9.8 13.3 9.6 10.0

D-S � 4.7 � 7.7 � 7.1W-S � 14.2 � 13.6 � 9.6

Quits � 11.1% � 5.55% � 0.74%EQ-cons. � 4.5% � 14% � 26%E- income � 1.1% � 2.8% � 0.7%


Two-Location Model

TWO-LOCATION MODEL

Risk-neutrality

Inside location (i) and outside location (o)

Offers arrive at rate a and ao

, drawn from the same distribution F

Fixed cost of living apart k (in consumption units) for the couple

No cost of migration across locations


Two-Location Model

VALUE FUNCTIONS

Dual-worker and Separate dual-worker couple:

rT (w1,w2) = w1 +w2

rS(w1,w2) = w1 +w2 �k

Worker-searcher couple

r⌦(w1)=w1+b+ai

ˆmax [T (w1,w2)�⌦(w1) ,⌦(w2)�⌦(w1) ,0]dF (w2)

+ao

ˆmax [S(w1,w2)�⌦(w1) ,⌦(w2)�⌦(w1) ,0]dF (w2)

Dual-searcher couple

rU = 2b+2(ai

+ao

)

ˆmax [⌦(w)�U,0]dF (w)


Two-Location Model

RESERVATION WAGES: INSIDE AND OUTSIDE OFFERS

Outside Offers Inside Offers


Two-Location Model

TIED-MOVERS AND TIED-STAYERS


Two-Location Model

ILLUSTRATIVE SIMULATION: 9 LOCATIONS

k = 0 k = 0.3Single Joint Joint

Reservation wage w

⇤/w

⇤⇤ 1.02 1.02 0.94Mean wage 1.058 1.058 1.045Unemployment rate 5.5% 5.5% 13.7%Unemployment duration 9.9 9.9 13.0

Dual-searcher � 6.5 3.0Worker-searcher � 9.3 28.0

Movers/Population 0.52% 0.52% 1.16%Stayers/Population 1.12% 1.12% 3.4%Tied-movers/Movers � 0% 60%Tied-stayer/Stayers � 0% 23%Job quit rate � 0% 50%EQVAR-cons � 0% �6.5%


Two-Location Model

FUTURE WORK

Theoretical: Explore

asymmetries between spouses

asymmetries in locations (i.e., size of cities or labor markets)

Quantitative:

We plan to use Danish data (IDA) for a structural estimation of a richermodel based on this framework.


lecture4: joint-searchtheoryusers.econ.umn.edu/~guvenen/handout4_jointsearch.pdf · l ecture 4: j...

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