Debt Constraints and Employment. Patrick Kehoe, Virgiliu Midrigan and Elena Pastorino

Debt Constraints and Employment Patrick Kehoe, Virgiliu Midrigan and Elena Pastorino

Motivation: U.S. Great Recession Large, persistent drop in employment

U.S. Employment-Population, aged 25-54 82 Employment Rate: Aged 25-54: All Persons for the United States 81 80 79 (Percent) 78 77 76 75 74 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Source: Organisation for Economic Co-operation and Development 2014 research.stlouisfed.org

Motivation: U.S. Great Recession Large, persistent drop in employment Regions with higher HH debt/income in 2007 experienced larger decline in debt larger decline in consumption larger decline in employment Regional employment drop largely due to nontradables

Household Debt/Income, 2007-2009 Change Debt-Income '07-'09 -.2 -.15 -.1 -.05 0.05 TX NY PA OH IL MI NJ USA.8 1.2 1.6 2 Household Debt-Income Ratio 2007 AZ FL CA NV source: Midrigan and Philippon (2011)

Consumption, 2007-2009 TX PA Log Change Consumption '07-'09 -.2 -.15 -.1 -.05 0 NY OH IL MI NJ USA.8 1.2 1.6 2 Household Debt-Income Ratio 2007 AZ FL CA NV source: Midrigan and Philippon (2011)

Employment/Population, 2007-2009 Log Change Empl-Pop '07-'09 -.2 -.15 -.1 -.05 0 TX NY PA OH IL MI NJ USA.8 1.2 1.6 2 Household Debt-Income Ratio 2007 AZ FL CA NV source: Midrigan and Philippon (2011)

Figure 5 Aggregate Demand and Employment across Counties: Geographical Herfindahl-Based Non-Tradable and Tradable Industries This figure presents scatter-plots of county level employment growth from 2007Q1 2009Q1 against the debt to income ratio of the county as of 2006. The le panel examines employment Employment in non-tradable industries based by on geographical sector, herfindahl index and 2007-2009 the right panel focuses on tradable industries based on the same index. The sample includes only counties with more than 50,000 households. Non-Tradable Tradable Non-Tradable Sector Employment Growth 07Q1-09Q1 (based on low geographical concentration) -.2 -.1 0.1.2 Tradable Sector Employment Growth 07Q1-09Q1 (based on high geographical concentration) -.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Debt to Income 2006 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Debt to Income 2006 source: Mian and Sufi (2013)

U.S. Great Recession Popular interpretation: Tightening of HH credit leads to drop in consumption Drop in consumption leads to drop in employment At odds with predictions of standard models Consumption and leisure normal goods Absent relative price changes move together Unless prices or wages are sticky Need to assume lots of stickiness Guerrieri-Lorenzoni, Midrigan-Philippon

We study alternative mechanism Tighter debt constraints less consumption & less employment Idea: large returns to tenure/experience Work is an investment HH debt constraints reduce returns to such investments Make employment less valuable

Alternative mechanism Otherwise standard DMP setup When debt constraints are tighter Consumers discount returns to experience more Firms discount future profits more So surplus from match is reduced Firms create fewer vacancies Do not explicitly impose wage rigidities But arise endogenously due to debt constraints

Model overview Continuum of islands in small open economy. Labor immobile Diamond-Mortensen-Pissarides with on-the-job human capital accumulation idiosyncratic shocks to worker human capital full insurance inside household household debt limit No aggregate uncertainty Study effect of one-time, unanticipated tightening of debt limit 1. economy-wide collateral constraint (U.S. recession) 2. island collateral constraint (predictions for U.S. regions)

Outline 1. Response to economy-wide shock to credit constraint No changes in relative prices No reallocation between tradeable/non-tradeable Identical to those of one good model 2. Island-specific shock to credit constraint Changes in relative prices & terms of trade Labor reallocation from non-tradeable to tradeable More notation, leave for later

One-Good Economy

Household s problem Consists of measure 1 of workers and continuum firms. Income of worker i : y it = wages or home production T t : profits net of vacancy posting costs max t β t u (c t ) s.t. c t + a t+1 = (1 + r)a t + y it di + T t Borrowing constraint: a t+1 d t d t and r t exogenous. Study effect of unanticipated changes

Household s problem Debt constraint binds as long as u (c t )/u (c t+1 ) > β(1 + r) Binds in steady state and our experiments Problem reduces to choosing employment & vacancies Q t = u (c t ): multiplier on date t budget constraint Stochastic OLG structure: φ: worker survival probability

Technology and Human Capital Newborns enter with human capital log(z) N (0, σ 2 z /(1 ρ 2 z))

Technology and Human Capital Newborns enter with human capital log(z) N (0, σ 2 z /(1 ρ 2 z)) On-the-job human capital accumulation/off-the-job depreciation employed draw z from F e (z z) (drifts up) log z = (1 ρ z )µ z + ρ z log z + σ z ε non-employed draw z from F u (z z) (drifts down) log z = ρ z log z + σ z ε

Matching technology M (u t, v t ) = Bu η t v1 η t Market tightness: θ t = v t /u t Probability firm finds worker λ f,t = M (u t, v t ) v t = ( ut v t ) η = Bθ η t Probability worker finds firm λ w,t = M t (u t, v t ) u t = ( vt u t ) 1 η = Bθ 1 η t

Worker values Match exogenously destroyed with probability σ Discounted lifetime income if currently employed: W t (z) = ω t (z) + βφ Q t+1 (1 σ) max [W t+1 (z ), U t+1 (z )] df e (z z) Q t +βφ Q t+1 σ U t+1 (z ) df e (z z) Q t Discounted lifetime income if currently not employed: U t (z) = b + βφ Q t+1 λ w,t Q t βφ Q t+1 Q t (1 λ w,t ) max [W t+1 (z ), U t+1 (z )] df u (z z) + U t+1 (z ) df u (z z)

Value of filled vacancy J t (z) = z ω t (z) + βφ Q t+1 Q t max [ J t+1 ( z ), 0 ] df e ( z z )

Wages Assume wages renegotiated period by period Nash bargaining: max [W t(z) U t (z)] γ J t (z) 1 γ ω t (z) γ W t (z) U t (z) = 1 γ J t (z)

Free entry condition Firms pay κ units of output to post vacancy Let n u t (z) measure of unemployed, ñ u t (z) = nu t (z) dn u t (z) 0 = κ + βφ Q t+1 λ f,t Q t max [ J t+1 ( z ), 0 ] df u ( z z ) dñ u t (z) pins down θ t

Parameterization Assigned parameters period = 1 quarter β = 0.94 1/4, 1 + r = 0.96 1/4, φ = 1 1/160 Probability of separation: σ = 0.10 (Shimer 2005) Bargaining share and elasticity matching fn: η = γ = 1/2 u(c t ) = c1 α t 1 α, α = 5 so IES = 0.2 Micro-evidence: IES 0.1 0.2 Hall 88, Attanasio et. al. 02, Vissing-Jorgensen 02

Calibrated parameters Vacancy posting cost, κ Efficiency matching function: B Persistence shocks to z: ρ z Std. dev. of shocks to z: σ z Home production, b Returns to work: µ z

Calibrated parameters Vacancy posting cost, κ Normalize steady-state market tightness θ = 1 Efficiency matching function: B Persistence shocks to z: ρ z Std. dev. of shocks to z: σ z Home production, b Returns to work: µ z

Calibrated parameters Vacancy posting cost, κ Efficiency matching function: B Employment-populatio ratio = 0.8 (U.S. all adults 25-54) Persistence shocks to z: ρ z Std. dev. of shocks to z: σ z Home production, b Returns to work: µ z

Calibrated parameters Vacancy posting cost, κ Efficiency matching function: B Persistence shocks to z: ρ z std. dev. of log initial wages = 0.94 (PSID) Std. dev. of shocks to z: σ z Home production, b Returns to work: µ z

Calibrated parameters Vacancy posting cost, κ Efficiency matching function: B Persistence shocks to z: ρ z Std. dev. of shocks to z: σ z std. dev. changes log wages = 0.21 (Floden-Linde 2001) Home production, b Returns to work: µ z

Calibrated parameters Vacancy posting cost, κ Efficiency matching function: B Persistence shocks to z: ρ z Std. dev. of shocks to z: σ z Home production, b b/ median ω = 0.4 (Shimer 2005) Returns to work: µ z

Calibrated parameters Vacancy posting cost, κ Efficiency matching function: B Persistence shocks to z: ρ z Std. dev. of shocks to z: σ z Home production, b Returns to work: µ z returns to tenure & experience data

Returns to work in the data Buchinsky et. al. (2010) estimate log(w it ) = c i + x itβ + f (experience it ) + g(tenure it ) + J it + ε it J it summarizes history previous jobs l = 1 : M it J i,t = M it 4 l=1 k=1 ( φ 0 k + φ s ktenure l i + φ e kexperience l ) i d l k,i

Returns to work in the data log(w it ) = c i + x itβ + f (experience it ) + g(tenure it ) + J it + ε it Cumul. returns to experience: 5 yrs 10 yrs 15 yrs College graduates 0.43 0.66 0.76 High School graduates 0.28 0.40 0.44 High School dropouts 0.24 0.36 0.41 Cumul. returns to tenure: 5 yrs 10 yrs 15 yrs College graduates 0.29 0.48 0.62 High School graduates 0.28 0.48 0.62 High School dropouts 0.30 0.51 0.68

Returns to work in the data log(w it ) = c i + x itβ + f (experience it ) + g(tenure it ) + J it + ε it Our approach: Simulate paths for experience and tenure for our model Use BFKT estimates (high school grads) to evaluate log (ŵ it ) = f (experience it ) + g(tenure it ) + J it Minimize distance mean log(ŵ it ) & log(w it ) model 5.2% per year

Moments used in calibration Data Model fraction employed 0.80 0.80 mean growth rate wages 0.052 0.052 home production/ median wage 0.40 0.40 std. dev. wage changes 0.21 0.21 std. dev. initial wages 0.94 0.94

Returns to work: model vs. data 1.5 Our model BFKT estimates 1 0.5 0 0 2 4 6 8 10 12 14 16 18 20 experience (years) Initialize w/ 0 experience, mean z it exp = 0, no shocks

Parameter values B 0.595 steady state match probability ρ z 0.952 1/4 persistence human capital σ z 0.112 std. dev. efficiency shocks µ z 2.82 returns to work b 1.75 home production / mean z new entrant

6 Steady state measures measure workers 8 x 10 3 log( z) log(b) 4 2 0 3 2 1 0 1 2 3 4 5 6 log(z) measure unemployed 2.5 x 10 3 2 1.5 1 0.5 0 3 2 1 0 1 2 3 4 5 6 log(z)

1 0.5 Policy and value functions firm profits 4 3 ω b wages 0 0.5 10 1 2 3 4 log(z) J 2 1 10 1 2 3 4 log(z) W U 5 5 0 1 2 3 4 log(z) 0 1 2 3 4 log(z)

Model implications fraction workers with w < b 0.181 prob. job destroyed endogenously 0.002 prob. worker matches, λ w 0.595 fraction matches with positive surplus 0.724 drop in w after non-employment spell 1.9% drop in w if not employed 1 year 6.1% drop in w if not employed 2 years 8.8%

Experiment: economy-wide credit crunch Binding debt limit: c t = d t (1 + r)d t 1 + y t Assume unanticipated tightening debt limit d t Choose path for d t so c t falls 5% then mean-reverts c t = 0.90c t 1 + 0.10 c ( ) α Implies future discounted more: Q t+1 /Q t = ct+1 c t

Credit crunch 0 0.01 Consumption 1.005 1 0.995 Discount factor 0.02 0.99 0.03 0.985 0.04 0.98 0.05 0 10 20 30 40 quarters 0.975 0.97 0 10 20 30 40 quarters

Employment 0 0.005 0.01 0.015 0.02 0 5 10 15 20 25 30 35 40 quarters

Employment vs. Consumption 0 0.01 0.02 0.03 0.04 Consumption Employment 0.05 0 5 10 15 20 25 30 35 40 quarters

Employment response Maximal drop employment 2.0% vs. 5.0% drop in C Employment drop much more persistent Cumulative impulse responses: 2 years: 10 years: overall: CIR E = 0.44 CIR C CIR E = 0.69 CIR C CIR E = 0.92 CIR C

Why does employment drop? Drop in Q t+1 /Q t reduces surplus W t (z) U t (z) + J t (z) Reduces returns to learning by doing for workers Reduces returns to posting vacancies for firms Employment drops because Some existing matches endogenously destroyed Fewer vacancies posted Fewer matches have positive surplus

Job separations 0.107 0.106 0.105 0.104 0.103 0.102 0.101 0.1 0 5 10 15 20 25 30 35 40 quarters

Market tightness 1 0.95 0.9 0.85 θ t λ w,t 0 5 10 15 20 25 30 35 40 quarters

Probability match accepted 0.73 0.725 0.72 0.715 0.71 0.705 0.7 0 5 10 15 20 25 30 35 40 quarters

Employment decomposition Shimer 2012 approach E t+1 = (1 s t )E t + λ w,t a t (1 E t ) s t : separation rate λ w,t : worker matching probability a t : acceptance rate Construct three counterfactual employment series: Vary s t, λ w,t, a t in isolation Leave others at steady state values

Employment decomposition 0 0.005 0.01 0.015 actual vary separation rate vary matching rate vary acceptance rate 0.02 0 5 10 15 20 25 30 35 40 quarters

Wages and Productivity 1.015 1.01 mean wage productivity 1.005 1 0.995 0.99 0.985 0 5 10 15 20 25 30 35 40 quarters

Consumer vs. firm debt constraints Our benchmark model: firms owned by households debt constraints change discount rate of workers & firms Separate role of each only let discount rate of workers change only let discount rate of firms change

Worker vs. firm debt constraints 0 0.005 0.01 0.015 Benchmark Worker discount rate change Firm discount rate change 0.02 0 5 10 15 20 25 30 35 40 quarters

Consumer vs. firm debt constraints Employment drops mostly because of worker discounting Worker retains most human capital after separation Longer horizon, surplus more sensitive to discount rate

Role of returns to work Employment falls much less absent returns to work Illustrate by setting µ z = 0 & σ z = 0 Similar results with heterogeneity: σ z > 0

No returns to work 0 0.005 0.01 0.015 Benchmark No returns to work 0.02 0 5 10 15 20 25 30 35 40 quarters

Comparison with Hall 2014 Results consistent with Hall 2014 Studies effect of increase discount rate in DMP model Steady state effects of change in discount rate small: r from 10% to 20%: U up from 5.8% to 5.88% Wage rigidities amplify effects

Intuition from simple model First, suppose no learning by doing ρw (z) = ω(z) σ (W (z) U (z)) ρu (z) = b + λ w (W (z) U (z)) ρj(z) = z w(z) σj(z)

Intuition from simple model First, suppose no learning by doing ρw (z) = ω(z) σ (W (z) U (z)) ρu (z) = b + λ w (W (z) U (z)) ρj(z) = z w(z) σj(z) Surplus: S(z) = W (z) U (z) + J(z) S(z) = z b ρ ρ = ρ + σ + 1 2 λ w not sensitive to ρ since λ w and σ much larger

Intuition from simple model Next, suppose dz = gzdt if employed, 0 otherwise ρw (z) = ω(z) σ (W (z) U (z)) + zgw (z) ρu (z) = b + λ w (W (z) U (z)) ρj(z) = z w(z) σj(z) + zgj (z)

Intuition from simple model Next, suppose dz = gzdt if employed, 0 otherwise ρw (z) = ω(z) σ (W (z) U (z)) + zgw (z) ρu (z) = b + λ w (W (z) U (z)) ρj(z) = z w(z) σj(z) + zgj (z) Surplus: S(z) = W (z) U (z) + J(z) S(z) = z b ρ + gz ( ρ g) ρ ρ = ρ + σ + 1 2 λ w ( ) g = g 1 + λw 2ρ : sensitive to ρ

Many-Good Economy

Many-Good Economy Multi-sector economy Each island produces tradable and nontradable goods Labor cannot move across islands but can switch sectors Study response to island-specific shocks evaluate model against Mian and Sufi (2013) evidence Firms owned by consumers on all islands

Preferences Household on island s: (βφ) t u (c t (s)) t=0 Consumption is an aggregate of tradeables (m) and non-tradables (n): c t (s) = ] [τ 1 σ (c n t (s)) µ 1 µ + (1 τ) 1 σ (ct m (s)) µ 1 µ Tradables imported from all other islands, s ( ct m (s) = c m t (s, s ) ν 1 ν ds ) ν ν 1

Prices Price of goods produced in s: p n t (s) and p m t (s) Price of composite imported good in s ( Pt m (s) = p m t ( s ) ) 1 1 ν 1 γ ds = Pm Aggregate price index in s P t (s) = [ ( ) τ (pt n (s)) 1 µ 1 µ ] 1 1 µ + (1 τ) Pm

Demand for goods Assume non-employed produce b units of composite good Let b t (s) = b(1 e t (s)): total home production Only c t (s) b t (s) purchased on the market Demand for non-tradeables ( ) p ct n n µ (s) = τ t (s) ( ct (s) P t (s) b t (s) ) Demand for variety s tradeables: ( p ct m (s, s m ) = (1 τ) t (s ) ν ( ) µ ) Pm ( ct (s) P m P t (s) b t (s) )

Technology Two sectors: tradeables (x) and non-tradeables (n) y = z in both sectors Matching technology: Mt x = B x (u t ) η (vt x ) 1 η and Mt n = B n (u t ) η (vt n ) 1 η λ x w,t = M t x u t λ n w,t = M t n u t ( v = B x x t u t ( v = B n n t u t ) 1 η = B x (θ x t ) 1 η ) 1 η = B n (θ n t ) 1 η

Worker values Discount factor: S t = ( ct+1 c t ) α Pt P t+1 W x t (z) = ωt x (z) + βφs t (1 σ) max [ Wt+1 x (h, z ), U t+1 (z ) ] df e (z z) +βφs t σ U t+1 (z ) df e (z z) U t (z) = P t b + βφs t λ x w,t βφs t λ n w,t max [ W x t+1 (1, z ), U t+1 (z ) ] df u (z z) + max [ W n t+1 (1, z ), U t+1 (z ) ] df u (z z) + +βφs t ( 1 λ x w,t λ n w,t) U t+1 (z ) df u (z z)

Firm values No change in discount factor since owned by all islands Jt x (z) = pt x z ωt x (z) + βφ (1 σ) max [ J x t+1 (z ), 0 ] df e (z z) Jt n (z) = pt n z ωt n (z) + βφ (1 σ) max [ J n t+1 (z ), 0 ] df e (z z) Free entry: P m κ n = βφλ n f,t P m κ x = βφλ x f,t max [ J n t+1 (z ), 0 ] df u (z z) dñ u t (z) max [ J x t+1 (z ), 0 ] df u (z z) dñ u t (z)

Non-tradeables Equilibrium prices ( p n ) µ τ t (c t b t ) = P t zdn e,n t (z) Tradeables ( ξ: vacancy posting costs + interest on debt) ( p x ) ν t (1 τ) P m ( Pm P ) µ ( c b ) + ξ = zdn e,x t (z) Idea: drop in c t reduces pt n (more so when µ is low) labor flows to x, reduces pt x (more so when ν is low)

Additional parameters Preferences: τ = 0.831 (2/3 employment non-traded Mian-Sufi) µ = ν = 1.5 (Backus-Kehoe-Kydland) Choose B x and B n so that: 80% employment-population steady state p x = p n Choose κ x s.t. θ x = 1, κ x /B x = κ n /B n Implies θ n = 1 and ω x (z) = ω n (z) Steady state predictions = one-sector model

Employment responses absent returns to work 0.02 0.01 Total Tradable Nontradable 0 0.01 0.02 0 5 10 15 20 25 30 quarters

Wage responses absent returns to work 0 0.05 0.1 Average Tradable Nontradable 0 5 10 15 20 25 30 quarters

Our model: employment 0 0.005 0.01 0.015 0.02 Our model No returns to work 0.025 0 5 10 15 20 25 30 quarters

Our model: nontradable employment 0 0.01 0.02 0.03 Our model No returns to work 0 5 10 15 20 25 30 quarters

Our model: tradable employment 0.02 Our model No returns to work 0.01 0 0.01 0 5 10 15 20 25 30 quarters

Our model: wages 0 0.05 Our model No returns to work 0 5 10 15 20 25 30 quarters

Experiment motivated by Mian-Sufi 2013 Differentially tighten debt constraint on 20 islands Island 1: consumption falls 1% after 2 years... Island 20: consumption falls 20% after 2 years

Employment vs. consumption: data Log Change Empl-Pop '07-'09 -.2 -.15 -.1 -.05 0.05 NV Slope = 1/2 AZ OH FL CA USA NY NJ IL MI -.2 -.15 -.1 -.05 0.05 Log Change Consumption '07-'09 PA TX source: Midrigan and Philippon (2011)

Employment vs. consumption: model 0 0.05 ln(e) 0.1 0.15 Slope = 0.61 0.2 0.2 0.15 0.1 0.05 0 ln(c)

Summary DMP model with returns to work predicts: employment sensitive to HH debt constraints as debt constraints reduce these returns so reduce match surplus and employment Predictions consistent with Mian-Sufi evidence

Figure 3 Aggregate Demand and Employment across Counties: Non-Tradable and Tradable Industries This figure presents scatter-plots of county level employment growth from 2007Q1 2009Q1 against the debt to income ratio of the county as of 2006. The left panel examines employment in non-tradable industries excluding construction and the right panel focuses on tradable industries. The sample includes only counties with more Employment than 50,000 households. The thin black line by in the left panel sector, is the non-parametric 2007-2009 plot of non-tradable employment growth against debt to income. Non-tradable (excluding construction) Tradable Non-Tradable Employment Growth 07Q1-09Q1 (excludes construction) -.2 -.1 0.1.2 Tradable Employment Growth 07Q1-09Q1 -.6 -.4 -.2 0.2 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Debt to Income 2006 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Debt to Income 2006 source: Mian and Sufi (2013)

Our model: non-traded wages 0 0.05 0.1 Our model No returns to work 0 5 10 15 20 25 30 quarters

Our model: traded wages 0.03 0.02 Our model No returns to work 0.01 0 0.01 0.02 0.03 0 5 10 15 20 25 30 quarters