Student Debt and Initial Labor Market Decisions: Wages, Job Satisfaction and Search

Transcription

1 Student Debt and Initial Labor Market Decisions: Wages, Job Satisfaction and Search Mi Luo 1 Simon Mongey 1 1 New York University April 8, 2016

2 Introduction - Student debt Total debt per borrowing student (in 2013 $1,000s) 40 Private 4yr Public 4yr Private 2yr Public 2yr 30 For profit Year Source: NSLDS, reproduced from Yannelis (2015). Inflated to 2013 dollars using the CPI 1. More debt per student 2. Not driven by private for-profit schools 1 / 31

3 Introduction - Overview Aim Investigate the effect of student debt on savings and labor market behavior of graduate; in particular wages, job satisfaction, search 1. Empirically Show that debt causes w, ψ, S - Individual level data on college graduates 2. Simple model Search with asset accumulation Lise (2013) to rationalize facts 3. Full model Rich framework which we can estimate on our data 4. Policy experiments Welfare under changes to repayment schemes 2 / 31

4 Literature Review 1. Student debt and labor market outcomes Rothstein and Rouse (2011), Joensen and Mattana (2014), Oreopoulos, von Wachter, Heisz (2012), Altonji, Kahn, Speer (2016) Liu (2015), Yu (2015), Wang (2015). New: Representative sample. 2. Student debt and borrowing constraints Yannelis (2015), Yannelis and Sun (2015), Lochner and Monge-Naranjo (2011). New: Policy experiments. 3. Search with asset accumulation Lise (2013), Rendon (2006). New: Two assets of normal debt and student debt. 4. Search with non-wage utility Hall and Mueller (2013), Hornstein, Krusell, Violante (2011), Dey and Flinn (2008), Guler, Guvenen, Violante (2012). New: Direct survey measurement of non-wage utility. 3 / 31

5 Introduction - Data 1. Baccalaureate and Beyond Longitudinal Study (NCES) - Restricted-use representative micro-data - Three cohorts: 1993, 2000, and 2008 graduates - Interviews graduates one, four, and ten years after graduation - Administrative - Government - Federal student aid forms (FAFSA, e.g. parental income) - College - Major, GPA - Self-reported - Quantitative - Income, employment - Qualitative - Search, job satisfaction 2. Link to publicly available college level data - Integrated Postsecondary Data System (IPEDS, e.g. grants, loans) - College scorecard data (e.g. SAT scores, default rates) 4 / 31

6 Correlations - Debt and employment decisions Fraction influenced by student debt A. Debt Lower parental income tercile Middle parental income tercile Upper parental income tercile Borrowing quintile Fraction influenced by student debt B. Residual debt Residual borrowing quintile 1. More debt causes increased likelihood of changing employment plans 2. Invariant to parental income Question Has the amount of student loan debt you have from your undergraduate education influenced your employment plans and decisions in any way? Parental income groups defined by over/under the median. Debt quintiles computed within parental income groups. Residual debt is from log d i = ˆβ X i + ê i where X includes age, gender, race, GPA, school dummies 5 / 31

7 Correlations - Debt and job satisfaction 0.70 A. Pay related satisfaction 0.70 B. Non pay related satisfaction Fraction satisfied Fraction satisfied Low income 2. Medium income 3. High income 4. All Debt quartiles Debt quartiles 1. Satisfaction is decreasing in debt within income groups 2. Satisfaction is increasing in income Debt quintiles computed within income quartiles. Zero corresponds to students with no debt (23% of sample). Non-pay related satisfaction equals 1 if answering yes to all questions regarding job (i) security, (ii) career fit, (iii) major relevance, (iv) overall satisfaction, (v) importance in work-place. Full-time workers only where full-time defined as more than 35 hours per week. 6 / 31

8 Correlations - Debt and on-the-job search Fraction of workers searching A. Search by debt and job satisfaction 1. All 2. Low satiscation 3. High satisfaction Fraction of workers searching B. Search by Debt/Income 1. All 2. Low satiscation 3. High satisfaction Debt quintile Debt/Income quintile 1. Search is increasing in debt, decreasing in income within satisfaction groups 2. Search is decreasing in job satisfaction Question Are you currently looking for a job? Zero corresponds to students with no debt (23% of sample). Full-time workers only where full-time defined as more than 35 hours per week. 7 / 31

9 IV estimation - Framework 1. Estimating equation y i,j,c = α + βd i,j,c + ΓX i,j,c + δw j,c + λ c + ε i,j,c i, j, c Individual, College, Cohort d i,j,c Total borrowing from all student loan sources X i,j,c W j,c ε i,j,c Age, gender, race, SAT score, major Within-region tercile of average SAT scores (College scorecard data) Standard errors clustered to (j, c)-level 2. Potential endogeneity - ε i,j,c and d i,j,c are correlated - Instrument for d i,j,c using IPEDS data Z j,c = grant j,c grant j,c + loan j,c [0, 1] Data: Variation in instrument c Z j,c 8 / 31

10 IV estimation - Sample restrictions and 2008 cohorts - Age under 30 upon graduation - Attended a four year college - Only attended one college - Working more than 35 hrs/week at the time of interview - Colleges: C = Students: N = 3, / 31

11 IV estimation - Estimates of β Dependent variable log(wage) Satisfaction OTJ Search Teaching (1) (2) (3) (4) OLS * (0.001) (0.001) (0.001) (0.001) OLS *** *** (0.001) (0.001) (0.001) (0.000) OLS 2001/ ** ** 0.002*** (0.000) (0.000) (0.000) (0.000) IV 2001/ *** * 0.011* * (0.007) (0.005) (0.006) (0.004) 1. Conditional on positive debt, $10,000 more debt increases wage by 12% 2. Rothstein and Rouse (2011) estimate an effect of 6-8% 3. OLS vs IV consistent with ability, debt i.e. selection is negative as found by Yannelis (2015) 10 / 31

12 Simple model - Motivation 1. Empirical results Increases in student debt cause graduates to sort into jobs with Result 1. higher wages, Result 2. lower job satisfaction, and Result 3. conditional on employment search more on the job. 2. Theoretical model - Simple model to rationalize Result 1 and Result 2 - Lise (ReStud 2013) - On the Job Search and Precautionary Savings - McCall model with exogenous w F (w), job-destruction, a risk-free asset - Add job satisfaction ψ - Remove on-the-job search - Prove Lower assets induce a trade-off between w and ψ 11 / 31

13 Simple model - Problems 1. Unemployed problem [ U(a) = max u(c) + β λ c a = (1 + r)a + b c a Γ { } max W (a, w, ψ ), U(a ) df (w, ψ ) ] + (1 λ)u(a ) 2. Employed problem W (a, w, ψ) = max c a = (1 + r)a + w c a Γ where lim ψ 0 v(ψ) = and lim ψ v(ψ) = 0 [ ] u(c) v(ψ) + β δu(a ) + (1 δ)w (a, w, ψ) 12 / 31

14 Simple model - Comparative statics a 1. Substitution effect: Black rotates outwards to Blue 2. Income effect: Blue shifts inwards to Red 13 / 31

15 Quantitative model - Setup 1. Modelling aims - Quantitatively assess changes in (i) repayment policies, (ii) initial conditions - Precisely estimate on the BB2009 data 2. New state variables - Outstanding student debt - d - Student loan repayment period remaining - t - States - s U = (a, d, t), s E = (a, d, t, w, ψ) 3. Student debt - Initial balance d i,0 H(d), fixed interest rate r d - A repayment policy is a tuple of functions R = {ρ,, τ} - Baseline R S : Stafford Loans under Standard Repayment - Experiment R I : Stafford Loans under Income-Based Repayment 4. Further additions - On-the-job search (Result 3): λ U λ E, κ H(κ) - Borrowing constraints: (E) a γw, (U) a min{a, 0} 14 / 31

16 Quantitative model - Unemployed problem subject to U(a, d, t) = max c c λ U log(c) + β [ (1 λ U )U(a, d, t ) +... ] { } max W (a, d, t, w, ψ ), U(a, d, t ) df (w, ψ ) Case I - Repayment - (1 + r a (a))a + b + Γ U (a) c ρ(d, t) a = (1 + r a (a))a + b c ρ(d, t) d = (1 + r d ) d ρ(d, t) t = t + 1 Case II - Delinquency - (1 + r a (a))a + b + Γ U (a) c < ρ(d, t) a = Γ U (a) d = (a, d, t, b) t = τ(d, t) 15 / 31

17 Quantitative model - Employed problem W (a, d, t, w, ψ) = max log(c + c) v(ψ) + β c 0 W S (a, d, t, w, ψ) = λ E +(1 δ) [ δu(a, d, t )... { } ] max κ + W S (a, d, t, w, ψ), W (a, d, t, w, ψ) dh(κ) } max {W (a, d, t, w, ψ), W (s E ) df (w, ψ ) subject to +(1 λ E )W (a, d, t, w, ψ) Case I - Repayment - (1 + r a (a))a + w + Γ E (w) c ρ(d, t) a = (1 + r a (a))a + w c ρ(d, t) d = (1 + r d ) d ρ(s E ) t = t + 1 Case II - Delinquency - (1 + r a (a))a + w + Γ E (w) c < ρ(d, t) a = Γ E (w) d = (a, d, t, w) t = τ(d, t) Extension: Endogenous college decision 16 / 31

18 Quantitative model - Parameters and functional forms 1. Externally calibrated θ 1 = {β, δ, r a +, ra, γ, b, c} 1. Rate of time preference β = /12 2. From SCF Kaplan-Violante sample restricted to college graduates r a + = 0.02, ra = 0.12, γ = Lise (2013) calculation using NLSY 1979 for college graduates δ = Federal poverty level c = $ Good approximation to SCF reported unemployment benefits b = c/2 = $495 Fig. Data: γ and r a by age and education (SCF 2001) 17 / 31

19 Quantitative model - Parameters and functional forms 2. Internally estimated θ 2 = {H(κ), v(ψ), F (w, ψ), λ U, λ E } - Assume κ U[κ, κ] - Assume v(ψ) = 1/ψ - Assume ψ {ψ L, ψ H } - Assume F (w, ψ) described by ( ) and ( ) log w ψ k N(µ k, σk s { ) ψ ψ k = H w.p. p H ψ L w.p. 1 ph s ( ) ( ) - Gives 11 parameters to estimate θ 2 = {κ, κ, ψ L, ψ H, p H, µ L, µ H, σ L, σ H, λ U, λ E } Extension: Adding additional heterogeneity 18 / 31

20 Quantitative model - Estimation 1. Data - Graduated unemployed with zero debt n = 1, Construct ψ i from non-pay satisfaction questions - Construct Xn data = {u i, h i, j i, s i, w i, ψ i } n i=1 12 months after graduation 2. Moments [ ] - Means E[h i ], E[j i ], E[s i ], E 1 [ψi =ψ H ] - Wages E[log w i ψ i = ψ k ], V[log w i ψ i = ψ k ], k {L, H} - ML estimates { } ˆβ w, ˆβ ψ, ˆσ e from auxiliary model ( ) s i = β 0 + β w log w i + β ψ 1 [ψi =ψ H ] + e i, e i N 0, σe 2 3. Indirect inference - Initialize sample of n unemployed workers - With probability p a = 0.35 draw log a i,0 N (µ a, σ a ) - Simulate to 12 months, construct Xn model = {u i, h i, j i, s i, w i, ψ i } n i=1 - Compute moments m n (θ 2 ), repeat 5,000 times and average m n (θ 2 ) ( - MDE of ˆθ 2 by arg min θ2 m data n m n (θ 2 ) ) ( Wn m data n m n (θ 2 ) ) - Construct W n = Cov [ m data ] n by bootstrap Data: Observed distributions of w i ψ i Data: Initial asset distribution a i 19 / 31

21 Quantitative model - Target moments Mean Std. Deviation Moments (12) Data Model Data Model A. Means (1) (2) (3) (4) Duration E[h i ] Number of jobs E[j i ] Search E[s i ] Probability of ψ H E[1 [ψi =ψ H ]] B. Wage distribution Mean log w for ψ L E[log w i ψ L ] Mean log w for ψ H E[log w i ψ H ] Variance log w for ψ L V[log w i ψ L ] Variance log w for ψ H V[log w i ψ H ] C. Regression coefficients Wage ($000) coefficient ˆβ w High satisfaction coefficient ˆβ ψ Std. dev. residuals ˆσ e Column (1) Mean of moment estimates from 5,000 bootstrap samples from Xn data with n = 1, 439 obs. - Column (2) Mean of moment estimates from 5,000 samples of Xn model with n = 1, 439 obs. - Column (3) Std. dev. of moment estimates from 5,000 bootstrap samples from Xn data - Column (4) Std. dev. of moment estimates from 5,000 samples of Xn model 20 / 31

22 Quantitative model - Parameter estimates ˆθ 2 Parameters (12) Value Std. Dev. A. Search costs (1) (2) Lower bound κ Upper bound κ B. Job offer arrival rates Unemployed λ U Employed λ E C. Disutility of labor Low satisfaction High satisfaction D. Sampling distribution parameters ψ 1 L ψ 1 H Probability of ψ H p H Mean log w for ψ L µ L Mean log w for ψ H µ H Variance log w for ψ L σl Variance log w for ψ H σh Results: Sampling and observed distributions of w ψ under θ 2 21 / 31

23 Quantitative model - Other moments Mean Std. Deviation Moments Data Model Data Model A. Unemployment, consumption and assets (1) (2) (3) (4) Unemployment E[u i ] Mean log consumption E[log c i ] Consumption - Labor income ratio E[c i ]/E[w i ] Mean log assets E[log a i ] Variance log assets V[log a i ] Coef. var. of log assets V[log ai ]/E[log a i ] B. Other regression moments Regression R-squared R Std. dev. residuals ˆσ e Column (1) Mean of moment estimates from 5,000 bootstrap samples from Xn data with n = 1, 439 obs. - Column (2) Mean of moment estimates from 5,000 samples of Xn model with n = 1, 439 obs. - Column (3) Std. dev. of moment estimates from 5,000 bootstrap samples from Xn data - Column (4) Std. dev. of moment estimates from 5,000 samples of Xn model 22 / 31

24 Quantitative model - Low vs High assets Unemployment rate Solid - Positive assets Dashed - Zero assets Mean monthly wage Fraction high satisfaction Months Months Sampling probability ph Months Job offer acceptance rate Employed Unemployed Employed fraction searching Mean assets Employed Unemployed Months Months Months - Low asset cohort is 100,000 individuals with a i,0 = 0 - High asset cohort is 100,000 individuals from top quartile of F (a 0 ) 23 / 31

25 Student debt - Baseline repayment policy - R S (ρ,, τ) modelled after the Federal Stafford Loan repayment policy - Grace period of T G = 6 months - Repayments amortize loan over T = 120 months - Missed repayments accrue a penalty φ = 18.5% - If not repaid at T 6 then renegotiate t to T G + 1 ρ f (d, t) = { 0, if t TG [ ] r d 1 (1+r d ) (T +1 t) d, if t T G + 1 [ ] (a, d, t, y) = (1 + r d )d ρ p (a, y) + φ ρ f (d, t) ρ p (a, y) { } ρ p (a, y) = max (1 + r a )a + y + Γ c, 0 τ(d, t) = { T G + 1, if d > 0 and t = T 6 t + 1, otherwise 24 / 31

26 Student debt - Model fit 0.78 A. Satisfaction by Debt/Income 0.6 B. Search by Debt/Income Fraction high satisfaction Model - High income Model - Medium income Model - Low income Data - Average Debt/Income quintile Fraction of workers searching Debt/Income quintile - Simulated with 100,000 individuals initialized with a i,0 N (µ a, σ 2 a ) - Debt/Income quintiles are computed within income terciles 25 / 31

27 Student debt - Comparing cohorts Wage Satisfaction Offer Acceptance Rate Unemployed (solid) Employed (dashed) Zero debt Medium debt High debt Months Months Months Emp: Frac searching Debt Repayments Value Months Months Months - Simulated with 100,000 individuals initialized with a i,0 = 0 - High debt d i,0 = $85, 000, medium debt d i,0 = $40, / 31

28 Experiment - Income based repayment policy - R IBR (ρ,, τ) introduced by Obama administration in Repayments are a fraction ζ of disposable income - Government covers interest payments if delinquent in first 3 years - Leave all other details the same as the Stafford Repayment Policy (R S ) ρ f (w, t) = { 0, if t TG { } max ζ (w 1.50c), 0, if t T G + 1 This is an active and evolving policy - Congressional approval Implemented July 1, 2009 with ζ = executive action lowered ζ = 0.10 for loans originated after July 1, executive action changed this date to Jan 1, 2013 No students in our data are on IBR plans. 27 / 31

29 Experiment - Welfare Initital life-time utility Ui, A. Student welfare under R S and R I Standard repayment policy Income-based repayment policy B. Distribution of student debt d i,0 Solid - logd N(ˆµ d,ˆσ d) Dashed - Smoothed data Initital student debt d i,0 (units of $10,000) Initital student debt d i,0 (units of $10,000) - Welfare measured as average value of unemployment with a = 0 and t = 1 W = U(0, d, 1)dH(d) - Result Welfare 1.3% higher and 89.9% of borrowing students prefer R I 28 / 31

30 Student debt - Comparing cohorts - R I Wage Satisfaction Offer Acceptance Rate Unemployed (solid) Employed (dashed) Zero debt Medium debt High debt Months Months Months Emp: Frac searching Debt Repayments Value Months Months Months - Simulated with 100,000 individuals initialized with a i,0 = 0 - High debt d i,0 = $85, 000, medium debt d i,0 = $40, / 31

31 Additional results - Valuing high satisfaction High satisfaction annual wage ($000): wh Low assets High assets Low assets - κ = 0 High assets - κ = Low satisfaction annual wage ($000) w L - Wage on y-axis solves: W ( w (w, a), a, ψ H ) = W (w, a, ψ L ) - As a at a given w willing to w by more - As w at a given a willing to w by increasingly more - For any (a, w) when search is free, willing to w by more 30 / 31

32 Conclusion This paper... - Empirical: finds that higher student debt induces graduates to choose jobs with higher wages but lower satisfaction, and to search more on the job. - Theory: extends McCall search model to jobs with two dimensions. - Quantitative: policy experiment indicates a 1.3% welfare increase under Income-based Repayment Plan. Future work: - Backward looking: Ability and decisions for college choice and debt take-up. - Forward looking: Wage growth; government policies incorporating student choice responses. 31 / 31

33 Thank-you!

34 Quantitative model - Credit limits: a γw Median ratio of limit to annual income No college College A. Credit limit Age Median interest rate (% p.a.) B. Interest rate Age 1. Credit limits are almost constant in age 2. Variation due to college education larger than variation due to age - Source SCF 2001, sample selection as in Kaplan and Violante (2014). Income includes wage income, unemployment benefits, child benefits, TANF and other. Values represent medians within a cell, approx. 1,000 observations per cell Back - Estimation

35 Extension - Additional heterogeneity Baseline 1. No unobservables: component of wages, or other - E.g. Initial assets a 0,i, constraints r a i, γ i, search costs κ i 2. Parameters Θ are constant across individuals 3. No correlation of debt d i with other unobservables Heterogeneity 1. Allow parameters Θ i to be correlated with initial states 2. Initial states include an unobserved fixed-effect ε i which is potentially correlated with debt d i ε i G (ε d i ) 3. Wages a function of (i) ε i, (ii) productivity draw (z i, ψ i ) F (z i, ψ i ) log w i = γ z log z i + γ ε log ε i Back - Estimation

36 Quantitative model - Initial assets log a i,0 N(µ a, σ a ).5.4 Kernel smoothed estimate Log normal fit Exponential fit Density Summer job savings ($000) - Source BB2009, standard estimation sample. Back - Indirect Inference

37 Extension - Pre-college decision - Aim Use continuation values to estimate discrete choice problem - State Observed assets a and skills s, unobserved pref η i - Decision (i) College or Labor Force, (ii) college choice c C - College A college is a tuple c = (ω c, h c, X c ) 1. Cost of tuition ω c 2. Stochastic skill technology s s 0 h c (s s0) 3. Observed and unobserved give W i,c = ξ c + γ 1 X c + γ 2 X i,c - Costs Takes T periods - Wages Function of skill and match prod. w(s, z) - Heterogeneity Can allow η i to be correlated within (a, s) max { U i (s i, a i ) + η i, max c C { }} s W i,c + β T U i (a i ω c, s ) dh c (s s 0 ) s Back - Employed worker problem

38 Quantitative model - log w i ψ i N(µ(ψ i ), σ(ψ i )).4 Low satisfaction (n=545) High satisfaction (n=894).3 Density Wage ($000, monthly) Solid is a kernel smoothed estimate using an Epanechnikov filter. Dashed is log normal fit with parameters estimated by maximum likelihood Back - Indirect inference

39 IV estimation - Variation in instrument 1 A and 2009 Grant/Loan Ratios 20 B. Change in Grant/Loan ratio Grant/Loan ratio, Percent of institutions Grant/Loan ratio, Value of instrument Back - IV framework

40 Quantitative model - Distributions of (w, ψ) A. Low satisfaction jobs Population distribution wi ψl log N(µL, σl) Observed distribution wi ψl log N(ˆµL, ˆσL) B. High satisfaction jobs Population distribution wi ψh log N(µH, σh) Observed distribution wi ψh log N(ˆµH, ˆσH) Wages ($000s) Wages ($000s) - Sampling probability of ψ H p H = Observed probability of ψ H p H = Back - Parameter estimates