LECTURE 4: JOINT-SEARCH THEORY

Transcription

1 LECTURE 4: JOINT-SEARCH THEORY September 17, 2012 Lecture 4: Joint-Search Theory September 17, / 32

2 Introduction RISE OF DUAL-CAREER COUPLES Female labor force participation rate stands at 60% compared to 75% for males. % of households in which wife provides majority of household income has tripled since Now 1/3 of US households have two main breadwinners. Bottom Line: For many households, job search is increasingly becoming a joint decision process. Lecture 4: Joint-Search Theory September 17, / 32

3 Introduction RISE OF DUAL-CAREER COUPLES FIGURE : Fraction of Household Income Provided by Each Spouse Lecture 4: Joint-Search Theory September 17, / 32

4 Introduction RISE OF DUAL-CAREER COUPLES Female labor force participation rate stands at 60% compared to 75% for males. % of households in which wife provides majority of household income has tripled since Now 1/3 of US households have two main breadwinners. Bottom Line: For many households, job search is increasingly becoming a joint decision process. Lecture 4: Joint-Search Theory September 17, / 32

5 Introduction AIM OF THE PAPER Theoretical characterization of the joint job search problem of a household (i.e., a couple) Same economic environment as in McCall (1970)-Mortensen (1970), and Burdett (1978) We study two cases where joint decision leads to different outcomes from single-agent: 1 Couple has concave utility over pooled income 2 Couple receives job offers from multiple locations, and faces a cost of living apart Systematic comparison to single-agent search problem Lecture 4: Joint-Search Theory September 17, / 32

6 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 of single-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 same environment Lecture 4: Joint-Search Theory September 17, / 32

7 Introduction RELATED LITERATURE Shimer-Rogerson-Wright (2005) s survey: no mention of household search. Burdett-Mortensen (1977): pioneering effort to characterize joint-search problem Danforth (1979): search with risk-free saving Mincer (1978): facts on family migration decisions Dey-Flinn (2007) and Gemici (2007): quantitative search models with two-person households Lecture 4: Joint-Search Theory September 17, / 32

8 Joint-Search Model JOINT-SEARCH MODEL Decision unit: couple, i.e. a pair of infinitely lived symmetric spouses indexed by i = 1,2 Discount rate r, income flows: y i 2{b,w i } Couple pools income (i.e., unitary household ) and there is no storage (relaxed later) Household intra-period utility: u(y 1 + y 2 ) 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) Lecture 4: Joint-Search Theory September 17, / 32

9 Joint-Search Model VALUE FUNCTIONS Flow value for dual-worker couple: rt (w 1,w 2 )=u(w 1 + w 2 ) Flow value for worker-searcher couple: ˆ r (w 1 )=u(w 1 + b)+a max[t (w 1,w 2 ) (w 1 ), (w 2 ) (w 1 ),0]dF (w 2 ) Flow value for dual-searcher couple: ˆ ru = u (2b)+2a max[ (w) U,0]dF (w) Lecture 4: Joint-Search Theory September 17, / 32

10 Joint-Search Model RESERVATION WAGE FUNCTIONS Dual-searcher couple: Accept offer iff w 1 > w s.t. (w )=U Worker-searcher couple (spouse 1 employed): T (w 1,w 2 ) (w 2 ): 2 accepts offer iff w 2 > f(w 1 ) s.t. T (w 1,f(w 1 )) = (w 1 ) 1 does not quit. T (w 1,w 2 ) < (w 2 ): Quit decision: 2 accepts offer iff w 2 > f(w 1 ) s.t. (f(w 1 )) = (w 1 ) 1 quits upon acceptance 1 quits job iff w 1 < y(w 2 ) where y is defined by T (y(w 2 ),w 2 )= (w 2 ) ) y(.)=f(.) Lecture 4: Joint-Search Theory September 17, / 32

11 Joint-Search Model 1. RISK NEUTRALITY: JOINT SEARCH =SINGLE SEARCH Lecture 4: Joint-Search Theory September 17, / 32

12 Joint-Search Model 2. CARA Result I: w < w Trade-off: consumption smoothing vs income maximization Result II: w1 if w f (w 1 )= 1 < w (quit) w if w 1 w (no quit) Because of CARA, the reservation wage of the unemployed spouse is independent of the wage of the employed spouse w 1. Lecture 4: Joint-Search Theory September 17, / 32

13 Joint-Search Model 2. CARA Lecture 4: Joint-Search Theory September 17, / 32

14 Joint-Search Model DYNAMICS WITH BREADWINNER CYCLE Wage Single 1 Spouse Time (weeks) Wage Single 2 Spouse Time (weeks) Lecture 4: Joint-Search Theory September 17, / 32

15 Joint-Search Model 3. GENERAL CHARACTERIZATION FOR HARA: Unemployed couple less choosy than single: w < w 9bw w s.t. for w 1 2 (w, bw): f (w 1 )=w 1 (i.e., 45 0 line) Breadwinner cycle always exists! For w 1 bw : 8 < f 0 (w 1 ) : > 0 if DARA = 0 if CARA < 0 if IARA But Shape/type of region changes depending on DARA, CARA or IARA. Lecture 4: Joint-Search Theory September 17, / 32

16 Joint-Search Model DARA: Lecture 4: Joint-Search Theory September 17, / 32

17 Joint-Search Model CARA Lecture 4: Joint-Search Theory September 17, / 32

18 Joint-Search Model IARA Lecture 4: Joint-Search Theory September 17, / 32

19 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 (w 1,w 2 ) 3 Working on one job at wage w 1, while searching for the second job and producing only b at home If wage offer on the second job is high enough, worker quits her first job and searches for a better secondary job Lecture 4: Joint-Search Theory September 17, / 32

20 Joint-Search Model THREE EXTENSIONS Symmetric on-the-job search (a e = a u ) 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. Strengthens breadwinner cycle. Lecture 4: Joint-Search Theory September 17, / 32

21 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 and SD(log w)=0.1 Offer arrival rates a u set to match u = 5.5% Value of leisure b = 0.40 Lecture 4: Joint-Search Theory September 17, / 32

22 Numerical Example COMPARISON OF SINGLE VERSUS JOINT SEARCH r = 0 r = 2 Single Joint Single Joint Mean wage Mm ratio Unemp. rate 5.5% 5.5% 5.4% 7.6% Unemp. duration Dual-searcher Worker-searcher Quits/separations 0% 11.1% EQVAR- income 0% 1.1% Lecture 4: Joint-Search Theory September 17, / 32

23 Numerical Example COMPARISON OF SINGLE VERSUS JOINT SEARCH r = 0 r = 2 Single Joint Single Joint Mean wage Mm ratio Unemp. rate 5.5% 5.5% 5.4% 7.6% Unemp. duration Dual-searcher Worker-searcher Quits/separations 0% 11.1% EQVAR- income 0% 1.1% Lecture 4: Joint-Search Theory September 17, / 32

24 Numerical Example COMPARISON OF SINGLE VERSUS JOINT SEARCH r = 0 r = 2 Single Joint Single Joint Mean wage Mm ratio Unemp. rate 5.5% 5.5% 5.4% 7.6% Unemp. duration Dual-searcher Worker-searcher Quits/separations 0% 11.1% EQVAR- income 0% 1.1% Lecture 4: Joint-Search Theory September 17, / 32

25 Numerical Example COMPARISON OF SINGLE VERSUS JOINT SEARCH r = 0 r = 2 Single Joint Single Joint Mean wage Mm ratio Unemp. rate 5.5% 5.5% 5.4% 7.6% Unemp. duration Dual-searcher Worker-searcher Quits/separations 0% 11.1% EQVAR- income 0% 1.1% Lecture 4: Joint-Search Theory September 17, / 32

26 Numerical Example NON-MONOTONIC BEHAVIOR IN RRA r = 2 r = 4 r = 8 Single Joint Single Joint Single Joint w /w E (w) Mm U rate 5.4% 7.6% 5.4% 7.7% 5.3% 5.6% U duration D-S W-S Quits 11.1% 5.55% 0.74% EQ-cons. 4.5% 14% 26% E- income 1.1% 2.8% 0.7% Lecture 4: Joint-Search Theory September 17, / 32

27 Two-Location Model TWO-LOCATION MODEL Risk-neutrality Inside location (i) and outside location (o) Offers arrive at rate a and a o, drawn from the same distribution F Fixed cost of living apart k (in consumption units) for the couple No cost of migration across locations Lecture 4: Joint-Search Theory September 17, / 32

28 Two-Location Model VALUE FUNCTIONS Dual-worker and Separate dual-worker couple: rt (w 1,w 2 ) = w 1 + w 2 rs(w 1,w 2 ) = w 1 + w 2 k Worker-searcher couple r (w 1 )=w 1 +b+a i ˆ + a o ˆ max[t (w 1,w 2 ) (w 1 ), (w 2 ) (w 1 ),0]dF (w 2 ) max[s(w 1,w 2 ) (w 1 ), (w 2 ) (w 1 ),0]dF (w 2 ) Dual-searcher couple ˆ ru = 2b + 2(a i + a o ) max[ (w) U,0]dF (w) Lecture 4: Joint-Search Theory September 17, / 32

29 Two-Location Model RESERVATION WAGES: INSIDE AND OUTSIDE OFFERS Outside Offers Inside Offers Lecture 4: Joint-Search Theory September 17, / 32

30 Two-Location Model TIED-MOVERS AND TIED-STAYERS Lecture 4: Joint-Search Theory September 17, / 32

31 Two-Location Model ILLUSTRATIVE SIMULATION: 9LOCATIONS k = 0 k = 0.3 Single Joint Joint Reservation wage w /w Mean wage Unemployment rate 5.5% 5.5% 13.7% Unemployment duration Dual-searcher Worker-searcher 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% Lecture 4: Joint-Search Theory September 17, / 32

32 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 richer model based on this framework. Lecture 4: Joint-Search Theory September 17, / 32