Costly Commuting and the Job Ladder

Costly Commuting and the Job Ladder [preliminary and incomplete] Jean Flemming University of Oxford ESEM Lisbon August 23, 2017

Motivating Facts Job-to-job (J2J) transitions are important for wage growth Topel and Ward (1992), Faberman and Justiniano (2015), Moscarini and Postel-Vinay (2016) Large fraction of jobs are rejected because of commute Rupert et al, 2009 (15%, ECHP), Elabe (23%, France) Jean Flemming (Oxford) Costly Commuting and the Job Ladder 2

What is the Link? Commuting is costly (time and money) High enough costs cause even high-paying jobs to be rejected Mechanism: Workers care about wage and commuting cost Can improve tradeoff by: Making a J2J transition Moving closer to current job High commuting costs lead workers to make Shorter commutes, fewer J2J transitions Less movement from low to high productivity jobs Policy: productivity gains from cheaper commutes? Jean Flemming (Oxford) Costly Commuting and the Job Ladder 3

This Paper Empirical Support Given wage, current commute affects Pr(J2J) and PV of future earnings Add commute and city into Burdett Mortensen (1998) model to Highlight trade-off between wages and commuting costs Model locations of workers and firms, effect on J2J transitions Study effects of changes in commuting and rent costs on productivity Jean Flemming (Oxford) Costly Commuting and the Job Ladder 4

Related Literature Commuting: van Ommeren (1998), Van Ommeren et al (1997, 1998, 1999, 2009,...), Zenou et al (2003, 2005, 2008,...), Glaesar and Rappaport (2006), Rupert et al. (2009), Rupert and Wasmer (2012), Guglielminetti et al. (2015), Roberts and Taylor (2016) This paper: OTJ search with endogenous firm side Migration: Sandell (1977), Mincer (1978), Greenwood (1997), Murphy et al. (2006), Gemici (2011), Kennan and Walker (2011), Guler and Taskin (2013), Kehrig and Ziebarth (2014), Sterk (2015), Schmutz and Sidibé (2016) This paper: daily commuting cost vs one-time moving cost Earnings Losses: Jacobson et al. (1993), Ljungqvist and Sargent (1998), Couch and Placzek (2010), Davis and von Wachter (2011), Jarosch (2016) This paper: due to failure to make J2J transitions Jean Flemming (Oxford) Costly Commuting and the Job Ladder 5

Empirical Support: Description of the BHPS Sample Annual survey, 1992-2009 Information on job histories, wages, housing, commute time Restrict sample to workers between 24-55 No self-employed, report monthly wages & hours worked One-way commute up to 90 minutes ( 0.6% of sample) Summary Stat: J2J Switchers Summary Stat: Commuters Correlation: Wage and Commute Jean Flemming (Oxford) Costly Commuting and the Job Ladder 6

J2J Transition Regressions Dependent Variable J2J t 1 if EE transition between t 1 and t, 0 if stayed in same job Explanatory variables in year t 1: commute (minutes, round-trip) log real hourly wage Controls: Individual, firm characteristics Region and time fixed effects, regional house prices Details Probit Regression Jean Flemming (Oxford) Costly Commuting and the Job Ladder 7

Earnings Regressions Dependent variable: log present value of labor earnings over 2-5 years following nonemployment spell PV over T years using 5% interest rate: T t=1 inc t : reported annual real labor income Explanatory variables: inc t (1.05) t Commute, log of real labor income in year nonemployment spell ended Jean Flemming (Oxford) Costly Commuting and the Job Ladder 8

Earnings Regressions Dependent variable: log present value of labor earnings over 2-5 years following nonemployment spell PV over T years using 5% interest rate: T t=1 inc t : reported annual real labor income Explanatory variables: inc t (1.05) t Commute, log of real labor income in year nonemployment spell ended Controls: Individual, firm characteristics Region and time fixed effects, regional house prices Benchmark Regressions With FE Jean Flemming (Oxford) Costly Commuting and the Job Ladder 8

Summary of Empirical Results Commute is positively correlated with J2J transitions 30 min longer commute at t 1 associated with a 1.5% higher Pr(J2J) Similar effect of a 0.5% decrease in monthly wage at t 1 Commute is positively correlated with future earnings 30 min longer commute at t 1 associated with 4.1 to 5.3% higher PV of earnings after 2-5 years With individual FE, 3.9 to 6.1% higher PV Approximately 3000 in PV over 5 years Jean Flemming (Oxford) Costly Commuting and the Job Ladder 9

Share of Work-Related Movers Citing as Reason for Move New Job, New Employer 37.6% Other Job-Related Reason 20.9% Closer to Same Job 13.6% New Job, Same Employer 10.4% To Seek Work 8.8% Employer Relocated 4.6% Higher Salary, New Home 3.3% Notes: BHPS Sample 1992-2009, annual. Universe: respondents aged 24-55 working full-time in year t. Jean Flemming (Oxford) Costly Commuting and the Job Ladder 10

Model: Set Up Burdett-Mortensen (1998) model with 2 dimensional jobs: wage w, commute ρ Rupert and Wasmer (2012) Closed monocentric city: distance from center d Mills (1967), Muth (1969) Continuous time, discount rate r Ex-ante identical workers Risk neutral, infinitely lived, live in locations - but can move Ex-ante heterogeneous firms Post fixed-wage contracts w At beginning of time, draw fixed productivity y and location Contracts are not contingent on worker locations Assume firms cannot observe where workers are located Jean Flemming (Oxford) Costly Commuting and the Job Ladder 11

Workers Can be employed or unemployed Location is defined by distance to city center, d 0 No asset value, no quantity choice κ(d): exogenous rent, κ (d) < 0 U(d): Unemployed get flow benefit net of rent, b κ(d) E(w, ρ; d): Employed get wage net of commuting costs and rent, w c(ρ) κ(d) Quadratic commuting cost c(ρ) = cρ 2, c > 0 Jean Flemming (Oxford) Costly Commuting and the Job Ladder 12

Job Offers and Moving Opportunities Exogenous separation rate µ Arrival rate of job offer for unemployed (employed): λ 0 (λ 1 ) Job offer is a draw of (w, ρ) F (w, ρ; d) Wage distribution determined endogenously Commute depends on exogenous and fixed firm locations Arrival rate of moving opportunity: ϕ Choose new distance d, no moving cost Stock of locations is exogenous and fixed Jean Flemming (Oxford) Costly Commuting and the Job Ladder 13

Graphical Representation of the Labor Market City Center Jean Flemming (Oxford) Costly Commuting and the Job Ladder 14

Graphical Representation of the Labor Market W 1 d Jean Flemming (Oxford) Costly Commuting and the Job Ladder 14

Graphical Representation of the Labor Market W 1 d d' W 2 Jean Flemming (Oxford) Costly Commuting and the Job Ladder 15

Graphical Representation of the Labor Market W 1 d ρ > 0 F 1 d W 2 Distance, Firm to center: d-ρ ρ' < 0 F 2 Jean Flemming (Oxford) Costly Commuting and the Job Ladder 15

Results: Spatial Determination of Commute Result 1 When rent costs are constant for each distance d from the monocentric city center and housing is homogeneous, the employed worker will always locate on the same ray from the center as her firm. Proposition 1 Given a distance from the firm to the center d ρ, if the employed worker in current job (w, ρ) who lives distance d from the center moves to d, the absolute value of the implied commute is given by ρ(d ) = d d + ρ Jean Flemming (Oxford) Costly Commuting and the Job Ladder 16

Value Functions: Workers ru(d) = b κ(d)+λ 0 ρ ρ w w max { 0, E(w, ρ; d) U(d) } df (w, ρ; d) { + ϕ max U(d ) U(d) } d 0 re(w, ρ; d) = w c(ρ) κ(d) + µ(u(d) E(w, ρ; d)) + λ 1 ρ ρ w w max { 0, E(w, ρ ; d) E(w, ρ; d) } df (w, ρ ; d) { + ϕ max E(w, ρ(d ); d ) E(w, ρ; d) } d 0 Jean Flemming (Oxford) Costly Commuting and the Job Ladder 17

Firm Optimality Firms know their distance from center, d F Observe the distributions of E and U: Γ E (w, ρ, d) and Γ U (d) Firm knows d F = d ρ, but not d and ρ separately Firm value depends only on w, y and d F Prob offer w accepted: α(w; d F ), prob worker paid w is poached: P E (w; d F ) Both endogenous, depend on worker distributions Value of vacant firm with productivity y: V (y) rv (y; d F ) = max w {α(w; d F )(J(w, y; d F ) V (y; d F ))} Value of a filled job with productivity y paying w: J(w, y) rj(w, y; d F ) = y w + ( µ + λ 1P E (w; d F ) ) (V (y; d F ) J(w, y; d F )) Jean Flemming (Oxford) Costly Commuting and the Job Ladder 18

Steady State Equilibrium A steady state equilibrium is defined by distributions of offered wage-commute pairs given each distance F (w, ρ; d), of employed workers Γ E (w, ρ; d), and of unemployed Γ U (d), a reservation strategy w U (ρ, d) and optimal moving choice d U (d) for unemployed workers, and a reservation strategy w E (ρ, w, ρ, d) and optimal moving choice d E (w, ρ, d) for employed workers, such that (i) Reservation strategies and moving choices are optimal for all workers (ii) For each level of productivity y and distance d F, the value of posting a vacancy is constant for all wages offered in equilibrium. (iii) The wage offer distribution over d F, and the distributions of employed over (w, ρ, d) and of unemployed over d are constant. Distributions Jean Flemming (Oxford) Costly Commuting and the Job Ladder 19

Reservation Strategy: Employed Proposition 1 Proposition 2 1.3 1.2 w up, ρ down Reservation Wage 1.1 1 0.9 w E (,w,ρ,d) 0.8 w down, ρ up 0.7 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Commuting Offer ρ' Jean Flemming (Oxford) Costly Commuting and the Job Ladder 20

Reservation Strategy: Employed Proposition 1 Proposition 2 1.3 current ρ w E (,w,ρ,d) Reservation Wage 1.2 1.1 1 Accept, Wage Increase Reject, Wage Increase 0.9 Accept, Wage Cut Reject, Wage Cut current w 0.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Commuting Offer ρ' Jean Flemming (Oxford) Costly Commuting and the Job Ladder 20

Firm Optimality Optimal wage posted by firms satisfies y w = α(w;d F ) w α(w; d F ) ( r + µ + λ 1 P E (w; d F ) + α(w; d F ) ) ( r + µ + λ1 P E (w; d F ) ) P α(w; d F )λ E (w;d F ) 1 w More productive firms pay higher wages in equilibrium For high enough commuting cost, high productivity offers are rejected Dependence on d F is ambiguous (numerical exercise in progress) Jean Flemming (Oxford) Costly Commuting and the Job Ladder 21

Policy Implications Probability of acceptance depends on worker s cost of commute Subsidized Commuting Cost: decrease cost from c(ρ) to (1 s)c(ρ) Workers accept longer commutes for all wage offers Fewer wage increases rejected Numerically evaluate effects of other parameters (in progress): Moving arrival rate ϕ Rent function κ(d) Spatial distribution of firms Jean Flemming (Oxford) Costly Commuting and the Job Ladder 22

Conclusion and Next Steps Positive relationship between commute and future earnings Model implies tradeoff between wages and commutes High productivity job offers are rejected for high commuting costs room for policy Next steps: Solve model numerically to study interaction between configuration of firms across city, rent, and worker strategies Externalities in commuting: cost increasing in average commute, social cost not internalized Policy Implications: working remotely, better infrastructure Jean Flemming (Oxford) Costly Commuting and the Job Ladder 23

Appendix Region: Local Authority Districts Back

Appendix Details on BHPS Regressions Back Control for age, age 2, sex, race, tenure in current job, homeownership, housing expenditures, full or part time job, education, employment status of spouse/partner, number of children, and a dummy for whether mode of commute and job has changed Also include year, region, mode of commute, industry, and occupation fixed effects Use cross sectional in regressions of job-finding probability, no weights in earnings regressions (Jenkins, 2010) Earnings Regressions: Earnings: annual labor income (inc t ) Initial commute reported after being U or N for at least 1 week Individuals must show up in survey for the next 5 years

Appendix Summary Statistics, J2J Transitions Back J2J No J2J N 9,048 36,096 Age 35.9 39.4 % Low Skilled/% High Skilled 11%/55% 17%/48% % Male 45% 43% Real Individual Labor Income 12,970 13,578 Weekly Hours 44.7 43.3 Commute (minutes R/T) 47.3 42.1 Years of Tenure - 5.8 % Full Time 85% 78% % Unemp last year 7% 4% % Married 57% 65% % Moved house last year 15% 8% % Homeowners 79% 83% % in London/ SE England 31% 27%

Appendix Summary Statistics, Commuters Back Commute 30 min 30<Commute 180 N 22,870 22,274 Age 39.1 38.1 % Low Skilled/% High Skilled 20%/42% 11%/56% % Male 38% 49% Real Individual Labor Income 11,173 15,775 Weekly Hours 43.0 44.2 Commute (minutes R/T) 19.2 67.7 Years of Tenure 5.2 4.3 % Full Time 73% 86% % Unemp last year 4% 5% % Married 66% 60% % J2J last year 18% 22% % Moved house last year 8% 10% % Homeowners 81% 84% % in London/ SE England 24% 33%

Appendix Summary Statistics, Regression Sample vs All Respondents Back 24-55, Employed All N 45,144 116,683 Age 38.7 46.5 % Low Skilled/% High Skilled 16%/49% 32%/34% % Male 43% 40% Real Individual Labor Income 13,454 6,659 Weekly Hours, Employed 43.7 42.7 Commute (minutes R/T) 43.1 24.1 Years of Tenure, Employed 4.8 7.7 % Full Time, Employed 79% 71% % Unemp last year 5% 6% % Married 63% 53% % Moved house last year 9% 8% % Homeowners 82% 73% % in London/ SE England 28% 27%

Appendix Regressions of Wage on Contemporaneous Commute, Controlling for Average Regional House Price Real log Wage t Commute t 30 0.015*** (0.004) Ind. characteristics Ind. FE Region, Time, Commute Method, Size, Industry& Occupation FE R 2.616 N obs 11,395 N ind 2,200 Back

Appendix Marginal Effects: Commuting and Transition Probability J2J t J2J t Commute t 1 30 0.022*** 0.015*** (0.003) (0.004) Real log Wage t 1-0.075*** -0.038*** (0.011) (0.012) Individual Characteristics Region, Time, Commute Method Size, Industry & Occ FE Pseudo R 2.058.096 N obs 12,731 11,471 Back 24-65 Excluding London

Appendix Marginal Effects: Commuting and Transition Probability, Age 24-65 J2J t J2J t Commute t 1 30 0.020*** 0.013*** (0.003) (0.003) Real log Wage t 1-0.073*** -0.036*** (0.010) (0.012) Individual Characteristics Region, Time, Commute Method Size, Industry & Occ FE Pseudo R 2.058.104 N obs 13,939 12,559 Back

Appendix Marginal Effects: Commuting and Transition Probability, Regional Subsamples Excluding London J2J t England only J2J t Commute t 1 30 0.023*** 0.022*** (0.004) (0.004) Real Wage t 1-0.070** -0.080*** (0.012) (0.011) Individual Characteristics Region, Time, Commute Method Size, Industry & Occ FE Pseudo R 2.059.061 N obs 11,423 12,021 Back

Appendix Regression: Log PV of Earnings on Initial Commute and Labor Income 2 Years 3 Years 4 Years 5 Years Initial Commute 30 0.051*** 0.052*** 0.043*** 0.046*** (0.011) (0.011) (0.012) (0.012) Initial Real log Income 0.322*** 0.296*** 0.269*** 0.256*** (0.016) (0.015) (0.016) (0.017) Region, Time, Commute Method, Industry, Occ FE R 2.738.759.762.761 N obs 2,241 1,892 1,635 1,387 Back With House Prices

Appendix Regression: Log PV of Earnings on Initial Commute and Labor Income, Individual FE 2 Years 3 Years 4 Years 5 Years Initial Commute 30 0.066*** 0.052*** 0.047*** 0.053*** (0.016) (0.015) (0.013) (0.013) Initial Real log Income 0.014-6.00e-05-2.74e-04-0.006 (0.017) (0.016) (0.015) (0.014) Region, Time, Commute Method, Industry, Occ FE Individual FE R 2.436.488.530.545 N obs 1496 1284 1092 923 N ind 589 511 439 375 Notes: Controlling for coarse regions due to small sample size when including individual FE. Back

Appendix Regression: Log PV of Earnings on Initial Commute and Labor Income, Individual FE, 2.65% Interest Rate 2 Years 3 Years 4 Years 5 Years Initial Commute 30 0.066*** 0.051*** 0.047*** 0.053*** (0.016) (0.015) (0.014) (0.013) Initial log Income 0.020 0.006 0.007 0.003 (0.017) (0.016) (0.015) (0.015) Region, Time, Commute Method, Industry, Occ FE Individual FE R 2.440.493.537.558 N obs 1,496 1,284 1,092 923 N ind 589 511 439 375 Notes: Controlling for coarse regions due to small sample size when including individual FE. Back

Appendix Steady State Distributions I Back In steady state, distributions F (w), Γ U (d), and Γ E (w, ρ; d) are constant F (w) is determined by the condition that V is constant for all w offered in equilibrium y w = α(w;d F ) w α(w; d F ) ( r + µ + λ 1 P E (w; d F ) + α(w; d F ) ) ( r + µ + λ1 P E (w; d F ) ) P α(w; d F )λ E (w;d F ) 1 w u is determined by setting the flow into unemployment equal to the flow out µ w ρ w ρ = λ 0 ρ dγ E (w, ρ; d) dρdw ρ w w U (ρ, d) df (w, ρ; d) + γ U ( d)1{d U ( d) d}

Appendix Steady State Distributions II In steady state, distributions F (w), u, and H(w, ρ) are constant Back Γ E (w, ρ; d) is determined by the condition that the flow into employment at any ( w, ρ) and distance d is equal to the flow out = λ 0 γ U ( d) w ρ w ρ ρ w ρ w U (ρ, d) df (w, ρ; d) + Φ I ( w, ρ, d) Γ E (w, ρ; d)1{d E (w, ρ, d) d} dρdw+φ O ( w, ρ, d) where γ U is the associated pdf of Γ U and Φ I ( w, ρ, d) and Φ O ( w, ρ, d) represent respectively the inflow and outflow of employed workers to Γ E ( w, ρ; d) through job-to-job transitions.

Appendix Results I: Employed Proposition 2 The reservation wage for the employed worker w E (ρ, w, ρ, d) is (a) Increasing in the absolute value of the offered commute, ρ (b) Increasing in the current wage, w (c) Decreasing in the absolute value of the current commute, ρ Result 2 For all d, w E (ρ, w, ρ, d) = w. Back

Appendix Results II: Unemployed Proposition 3 The reservation wage for the unemployed worker w U (ρ, d) is strictly increasing in the absolute value of the current commute, ρ. Back