Education Policy and Intergenerational Transfers in Equilibrium

Transcription

1 Education Policy and Intergenerational Transfers in Equilibrium B. Abbott, G. Gallipoli, C. Meghir, G. Violante

2 Introduction Government interventions in markets for higher education are large and complex. We want to understand how these programs have affected long-run outcomes, i.e. efficiency and mobility. e.g. what has been the long-run impact of federal college subsidy/grant programs on GDP There are many papers (some very good) estimating short-run effects of policy on education attainment, but none answer the key policy question of the impact of large scale policy changes on output, inequality and welfare. Through the lens of a general equilibrium framework we are able to address these questions.

3 Introduction Possible reasons for government intervention: Credit constraints Income taxation Imperfect insurance markets Equity

4 Introduction Our model captures: The dependence of college attainment decisions on: Parental transfers, which are possibly conditional The complexity of the existing student finance system with public and private loans and grants that depend on parental wealth/income Liquidity Constraints Both cognitive and non-cognitive skills Gender Intergenerational Transmission: Wealth (parents are altruistic and paternalistic) Cognitive skills (exogenous process) Non-cognitive skills (endogenous because of dependence on parental education)

5 Introduction More on the model: It is a steady-state overlapping generations model with intergenerational links. There are seven factors of production (three levels of education attainment two genders, plus capital). The six human capital aggregates are imperfectly substitutable. Each factor has its own equilibrium price (large economy). idiosyncratic productivity shocks: wage risk varies by gender and attainment.

6 Introduction Empirical Approach We first estimate several components of the model separately: The wage processes The aggregate production function We specify some parameters in advance, e.g. intertemporal elasticity of substitution, Frisch elasticities of labour supply. Given these specifications we then estimate the remaining parameters using a method of moments approach. Effects of cognitive and non-cognitive skills on non-pecuniary ( psychic ) costs of education. Extents of altruism and paternalism

7 Introduction Highlighted Results Current financial aid programs improve welfare and removing them would reduce GDP by over 4% in the long-run. Further expansions of financial aid programs would have only modest effects: Every additional dollar crowds out cents of private investment through reduced parental transfers and student labour supply. Eliminating any credit constraints induces gains through improved sorting, not increased enrollment. A small group of high-ability children from poor families, especially girls, would greatly benefit.

8 Introduction The rest of the talk: 1. Describe the life-cycle 2. Present and discuss Method of Moments Estimation 3. Present counterfactual analyses

9 Model The Life Cycle

10 Model Life cycle: Education The life-cycle - education At age j = 0 an individual receives a transfer from their parents. From then on she/he is independent. She then chooses whether to continue with high school until age j HS or enter the labor market permanently

11 Model Life cycle: Education High-school decision: Vg0 (â, θ, q, κ ɛ) = { } max V g0 (â, θ, q, κ ɛ) κ HS (g, θ, κ ɛ), E z[vg0 LH (â 0, θ, z 0 )], â = (â 0, â CL ). Utility (psychic) costs of high school: κ HS (g, θ, κ ɛ) = ς HS 0 + ς HS 1 1 {g=f } + ς HS 2 log(θ non) + ς HS 3 log(θ cog) + ς HS 4 κ ɛ. We will estimate ς HS by fitting model to the distribution of high school drop-out decisions. We find non-cognitive skills are very important at this stage.

12 Model Life cycle: Education Those who choose not to complete college enter the workforce as singles (will get married later), solve the following problem: V e gj ( aj, θ, z j ) ( ) [ = max u g cj, l j + βez V e ( ) ] g,j+1 aj+1, θ cog, z j+1 c j,l j,a j+1 s.t. (1 + τ c )c j + a j+1 = (1 τ w ) wg e ε e ( ) ( ) gj θcog, z j 1 lj +ψ + [1 + r (1 τ k )] a j a j+1 0, c j 0, l j [0, 1] z j+1 Γgz e ( ) zj+1 z j.

13 Model Life cycle: Education College Completion decision: ) Vg1 (a 1, â CL, θ, q, κ ɛ = ( ) } max {V g1 a 1 + â CL, θ, q κ CL (g, θ, κ ɛ), E z[vg1 HS (a 1, θ, z 1 )]. Utility (psychic) costs of college: κ CL (g, θ, κ ɛ) = ς CL 0 + ς CL 1 1 {g=f } + ς CL 2 log(θ non) + ς CL 3 log(θ cog) + ς CL 4 κ ɛ. We will estimate ς CL by fitting model to the distribution of college graduation rates. We find cognitive skills and preference shocks are relatively more important than at the HS decisions, but non-cognitive still matters.

14 Model Life cycle: Education College financing sources of funding: 1. grants 2. subsidized loans up to a limit 3. unsubsidized loans underwritten by the government but more expensive than commercial loans 4. Commercial loans (unavailable to poorer students) 5. working 6. Parental transfers means testing based on parental wealth and income, which determine the state variable q 1 student qualifies for subsidized + unsubsidized loan q = 2 student qualifies for unsubsidized loan 3 student qualifies for commercial + unsubsidized loan

15 Model Life cycle: Education A student with wealthy parents (q = 3) has the option to borrow privately and faces the following budget constraint: = (1 + τ c)c j + a j+1 (1 τ w) w g,hs ε g,hs j (θ, z j = 0) ( ) 1 t l j + φ (q, θ) = { [1 + r (1 τk )] a j if a j 0, (1 + r p ) a j otherwise a j+1 a p Private borrowing is less costly than from the government, so wealth students with access choose this route. φ (q, θ) is net tuition (tuition minus grants).

16 Model Life cycle: Education A student who qualifies only for unsubsidized government loans (q = 2) faces the budget constraint: (1 + τ c)c j + a j+1 + b j+1 (1 τ w) w g,hs ε g,hs j (θ, z j = 0) ( ) 1 t l j = { [1 + r (1 τk )] a = φ (q, θ) + j if a j 0, b j = 0 (1 + r u ) b j if a j = 0, b j < 0 a j+1 0 b j+1 b In the time period target (year 2000) government loans could not exceed $23,000, and carried an interest rate prime + 2.6%.

17 Model Life cycle: Education A less advantaged student who qualifies for a subsidized government loan (q = 1) faces the budget constraint: = (1 + τ c)c j + a j+1 + b j+1 (1 τ w) w g,hs ε g,hs j (θ, 0) ( ) 1 t l j + φ (q, θ) = [1 + r (1 τ k )] a j if a j 0, b j = 0 b j if a j = 0, 0 > b j b s b s + (1 + r u ) ( b j + b s) (1) if a j = 0, b j < b s a j+1 0 b j+1 b Subsidized loans are available up to $17,250 do not accrue interest during college. Another $5750 of unbsubsidized loans up to $23,000 also available.

18 Model Life cycle: Education Marriage If individual does not complete college or high school they work as singles until period j col + 1 At that point all individuals draw a match from the empirical distribution of the opposite sex to reproduces matches in the data All characteristics random conditional on education Distribution of Husband-Wife Education Matches (CPS Data ) Wife s Edu HSD HSG CLG Hus- HSD band s HSG Edu CLG

19 Model Life cycle: The Family The Family The life-cycle - work, transfers and retirement After matching, collective model with full commitment and equal weights. There are economies of scale in consumption. Each family has two identical boys or girls, born at age 30. At age 46 the family decides on transfers to their children. Child ability and educational preferences are known at that point. Couples retire at the same time and live to a max age of 100. Perfect annuity markets in retirement, pension income.

20 Model Life cycle: The Family Intergenerational Links (cognitive) There is a known probability that a person of ability θ cog has a child of ability ˆθ cog We estimate this probability matrix from the NLSY We use the AFQT for mothers and the PIAT Maths for children Transition Matrix (cognitive skill bins) Children Mothers

21 Model Life cycle: The Family Intergenerational Links (non-cognitive) The non-cognitive skills of the child also depend on the education of the mother. Thus, the distribution is endogenous and varies with the distribution of education attainment Conditional Probabilities of Non-Cognitive Tercile 1 Child s Cognitive Quintile Mother s Edu HSD HSG CLG Conditional Probabilities of Non-Cognitive Tercile 3 Child s Cognitive Quintile Mother s Edu HSD HSG CLG

22 Model Life cycle: The Family Intergenerational Links (resource transfers) The transfer decisions of parents are as follows: (Brace yourself for notation!)

23 Model Life cycle: The Family { W j (a j, z f j, zm j, θ f cog, θm cog, ef, e m ; ĝ, ˆθ, ˆκ ɛ) = max u(c m c j m,c j f,lm,l j f j,â 0,âCL j, c f j, lm j, l f j ),a j+1 [ ] +βe z f,z m W j+1 (a j+1, z f j+1, zm j+1, θf cog, θm cog, ef, e m ) +2ω(ĝ)V 0 (â, ĝ, ˆθ, } ˆq, ˆκ ɛ) + 2ξ 1 {ê=cl} (1 + τ c)c j + a j+1 + 2â + 2 âcl 1 + r s.t. = (1 τ w ) w f,e ε f,e j + (1 τ w ) w m,e ε m,e j +ψ + [1 + r (1 τ k )] a j ( ) ( ) θ f, z f j 1 l f j ( ) ( ) θ m, z m j 1 l m j c j = [(c m j ) ρ + (c f j ) ρ ] 1 ρ { } 1 if a j a and max w m,e ε m,e, w f,e ε f,e w j j { } ˆq = 2 if a j a and max w m,e ε m,e, w f,e ε f,e > w j j 2 if a < a j a 3 if a j > a ) ˆθ cog Γ θcog (ˆθcog θ f cog, ˆθnon Γ θnon (ˆθnon ˆθ ) cog, e f

24 Model Life cycle: Retirement Retirement We describe the problem starting backwards. At retirement there is a constant stream of social security and own asset income Annuity markets are perfect. When she retires he annuitizes savings and receives 16.4% of average earnings within the education group in Social Security. { Wj R (a j, e f, e m ) = max u ( c j, 1, 1 ) } + βζ j+1 Wj+1 R (a j+1, e f, e m ) c j,a j+1 s.t. c j + a j+1 = p e,f + p e,m + ψ + ζ 1 j+1 [1 + r (1 τ k)]a j a j+1 0, c j 0.

25 Estimation/Parameterization Estimation/Calibration

26 Estimation/Parameterization Wages Wages and shocks There is a separate wage process for each education and gender group These are specified as (e denotes an education group and θ ability) lnw it = ln(w g,e t ) + f g,e (age) + λ g,e (θ cog,i ) + zit e + m it Note that there is a deterministic return to age (known to the individual). We do not allow for endogenous accumulation of experience. w g,e t is the aggregate (endogenous) price of human capital of type e (6 prices).

27 Estimation/Parameterization Wages The ability Gradient λ g,e Education group Male Gradient Female Gradient Less than HS (0.054) (0.057) HS Graduate (0.030) (0.036) College Ggraduate (0.109) (0.099) Table: Estimated ability gradient λ e (NLSY79)

28 Estimation/Parameterization Wages Productivity Processes z i,j z i,j = ρ g,e z i,j 1 + η i,j, η i,j (0, σ 2 η,g,e) Less than HS HS Graduates College graduates ϱ m (0.010) ϱ m (0.005) ϱ m (0.015) σηm σηm σηm (0.002) (0.001) (0.005) σzm σzm σzm (0.005) (0.003) (0.009) ϱ f (0.023) ϱ f (0.003) ϱ f (0.016) σηf σηf σηf (0.005) (0.001) (0.004) σzf σzf σzf (0.011) (0.003) (0.007)

29 Estimation/Parameterization Production Sector The Production Sector We assume a representative firm supplying goods in a competitive market and hiring labor in a competitive labor market. The Production function is [ Y t = Kt α s LH ( H LH t ) ρ + s HS ( H HS t ) ( ρ ) ρ ] 1 α + s CL Ht CL ρ, (2) where [ Ht e = s e,f ( H e,f t ) χ + (1 s e,f ) ( H e,m ) χ ] 1 χ t. (3)

30 Estimation/Parameterization Production Sector We can then use the first order conditions to estimate the parameters of the production function ( ) ( ),e ϖf t s f,e log ϖ m,e t H f,e = log t s m,e t + χ log t H m,e t ϖ g,e t ( log ϖ CL t /ϖt HS ) = log is factor payment, and H g,e t from PSID. ( s CL t s HS t We use IV and estimate in first-differences. ) + (1 ρ) log ( ) H HS t Ht CL is constructed using the prices estimated We consider lags of the human capital aggregates and total available numbers of individuals in each education group as instruments. We settle on χ = 0.45 and ρ = 0.7 based on the results. We do sensitivity analysis of our main results.

31 Estimation/Parameterization Externally Specified Parameters Preferences Individual: u gj (c, l) = c1 γ 1 γ + ϑg j l 1 νg j 1 ν g j. Frisch elasticities are 1/3, except for women with children have 2/3. (Based on estimates of Blundell et al. (2016)) Inter-temporal substitution elasticity is set to 1/2. Couple: u(c m, c f, l m, l f ) = u m (c m, l m ) + u f (c f, l f ) Economies of Scale: c = [(c m ) ρ + (c f ) ρ ] 1 ρ. with ρ = 1.4 based on Voena (2015).

32 Estimation/Parameterization Externally Specified Parameters Costs of College We consider costs of tuition, fees, books and other non-consumption expenses, and then deduct average private grant amounts (non-progressive), to arrive at $6700/year cost. Depending on parental background we assign annual public grant amounts: Income q amount Low 1 $2,820 Mid 2 $668 High 3 $143

33 Estimation/Parameterization Externally Specified Parameters Remaining Externally Specified Parameters Parameter Value Description γ 2.0 Determines intertemporal elasticity of substitution (0.5) ν m j 5.5 Determines avg Frisch elast. of labour supply for men and non-mother women (0.33) ν f Determines avg Frisch elast. of labour supply for mothers (0.67) a CL 1.36 Limits borrowing of CL households to $75,000 a HS 0.45 Limits borrowing of HS households to $25,000 a LH 0.27 Limits borrowing of LH households to $15,000 b s Limits subsidized loans to $17,250 for q = 1 students b Limits total student loans to $23,000 for q = 1 and 2 students. a p Limits private loans to $23,000 for q = 3 students ι u Interest premium on Stafford loans (0.026 annually) α 0.35 Capital share of GDP δ 0.07 Depreciation rate of capital τ w 0.27 Labor income tax rate τ c 0.05 Consumption tax rate τ k 0.40 Capital income tax rate ζ j varies Mortality rates for retired hh based on US Life Tables 2000.

34 Method of Moments Estimation Method of Moments Estimation There are two blocks of moments/parameters The first relates to psychic costs and observed schooling decisions The second relates to internally calibrated parameters and identifying moments. Parameters are estimated by minimizing an unweighted quadratic distance criterion between data moments and moments implied by the model.

35 Method of Moments Estimation Psychic Costs Estimation Although all moments identify all parameters, we specifically included education attainment rates to help identify psychic cost functions. Table: Attainment Rates - NLSY97 Data High School Drop-Out Rates (Data) Cognitive quintile Non Cognitive tercile College Graduation Rates (Data) Cognitive quintile Non Cognitive tercile

36 Method of Moments Estimation Parameter High School College ς e 0 Constant (0.006) (0.010) ς1 e Female Dummy (0.0150) (0.006) ς2 e log(θ non ) (0.010) (0.011) ς e 3 log(θ cog ) (0.015) (0.012) ς e 4 κ ɛ (0.008) (0.011)

37 Method of Moments Estimation College graduation decisions fit College Graduation Rates (Data) Cognitive quintile Non Cognitive tercile College Graduation Rates (Model) Cognitive quintile Non Cognitive tercile

38 Method of Moments Estimation High school drop out decisions fit High School Drop-Out Rates (Data) Cognitive quintile Non Cognitive tercile High School Drop-Out Rates (Model) Cognitive quintile Non Cognitive tercile

39 Method of Moments Estimation Over 80% of the variation in psychic costs of college is explained by skills. Over 90% for high school. For high school psychic costs non-cognitive skills are 2.5 times as important as cognitive. For college cognitive are 3.25 times as important. If variation in psychic costs is shut down, then 2/3 of the covariance between college and cognitive skills remains. Only 23% of covariance between college and non-cognitive remains.

40 Method of Moments Estimation The Rest of the Parameters Parameter Description Value (s.e.) β Time discount factor (0.006) ϑ g j Male and non-mother female leisure preference (0.004) ϑ f Female with children leisure preference (0.005) ω f Altruism towards sons (0.008) ω m Altruism towards daughters (0.005) ξ Paternalistic utility from a child s college going (0.041) a Wealth upper limit for subsidized loans (group q=1) 2.07 (0.202) a Wealth lower limit for private student loans (group q=3) 2.68 (0.499) ι p Interest premium for private student loans (0.006) ι Basic borrowing wedge that applies to all debt (0.010) ψ Redistributive transfer 0.44 (0.008)

41 Method of Moments Estimation The Rest of the Moments Moment Matched Target Value Model Value Capital-output ratio Average male labour supply Average labour supply of mothers Average IVT to female child $29,096 $29,044 Average IVT to male child $33,164 $33,012 Ratio of college grad. rate in fourth (top) quartile of parental wealth to grad. rate in third quartile HS Fraction of Female Population (cross-section) HS Fraction of Male Population (cross-section) CL Fraction of Female Population (cross-section) CL Fraction of Male Population (cross-section) Fraction of students with subsidized loans Fraction of students with any gov t loans Fraction of students with private loans Fraction of workers with negative net worth Var(log post-tax income)/var(log pre-tax income)

42 Un-targeted Moments Un-targeted Moments We explore the models implications in a number of non-targeted dimensions. e.g. intergenerational earnings mobility (Chetty et al., 2014), life-cycle profiles of income, consumption etc. (Kaplan, 2011).

43 Un-targeted Moments Un-targeted Moments We explore the models implications in a number of non-targeted dimensions. e.g. intergenerational earnings mobility (Chetty et al., 2014), life-cycle profiles of income, consumption etc. (Kaplan, 2011). One thing that is new in the revision is the models ability to capture attainment by ability and parental wealth College Attainment Rate parental net worth quartile 1 parental net worth quartile 2 parental net worth quartile 3 parental net worth quartile θ cog Quartile

44 Counterfactual Experiments Counterfactual Experiments

45 Counterfactual Experiments Counterfactuals compare steady-state equilibria with labour income tax rates adjusted to balance the government budget.

46 Counterfactual Experiments Unconstrained Economy The first experiment sets a benchmark for what policy might accomplish regarding the effect of credit constraints on schooling. Here all debts must be paid at retirement, but otherwise agents are unconstrained and borrow at prime. Efficiency gains are driven by improvement of selection into college by ability, more so than increases in college enrollment. We are leaving the federal grant program in tact when we do this.

47 Counterfactual Experiments Unconstrained Economy Unconstrained Economy Benchmark G.E. Long-run Men College Women Graduation Men - top 1/3 of cognitive skills Rates Women - top 1/3 of cognitive skills Total - top 1/3 of parental wealth Total - bottom 1/3 of parental wealth Crowding out of IVTs - Male -$3,932 Other Crowding out of IVTs - Female -$3,774 Statistics Student labor supply -33.7% Aggregate output +1.16% Welfare gain +0.42% Crowding out is the average change in IVTs given to children who are college non-switchers (college graduates in both cases).

48 Counterfactual Experiments Grant Removal Next we eliminate the federal grants program. Grants are a subsidy that may be beneficial for both easing credit constraints and undoing distortions of risk and income taxes. We find substantial effects on both selection and enrollment (particularly for women).

49 Counterfactual Experiments Grant Removal Removal of Public Tuition Grants Benchmark P.E. Short-run G.E. Long-run Men College Women Graduation Men - top 1/3 of cognitive skills Rates Women - top 1/3 of cognitive skills Total - top 1/3 of parental wealth Total - bottom 1/3 of parental wealth Crowding out of IVTs - Male +$596 -$2,723 Other Crowding out of IVTs - Female +$253 -$3,157 Statistics Student labor supply +13.4% +4.47% Aggregate output -1.95% Welfare gain -0.68%

50 Counterfactual Experiments Loan Removal Next we eliminate the federal student loans program. Except for the very richest few (q = 3), no borrowing is possible to finance college. Again, substantial efficiency and welfare effects are mostly driven by changes in sorting.

51 Counterfactual Experiments Loan Removal Removal of Student Loans Benchmark P.E. Short-run G.E. Long-run Men College Women Graduation Men - top 1/3 of cognitive skills Rates Women - top 1/3 of cognitive skills Total - top 1/3 of parental wealth Total - bottom 1/3 of parental wealth Crowding out of IVTs - Male +$2,837 +$3,740 Other Crowding out of IVTs - Female +$2,099 +$2,199 Statistics Student labor supply +38.3% +5.84% Aggregate output -2.95% Welfare gain -0.65%

52 Counterfactual Experiments Grant Expansions We also experiment with general, means-tested and ability-tested grant expansions. We find that means-tested performs somewhat better on efficiency and welfare improvements. An optimal means-tested expansion (paid by labor income taxes) is 195%. Under such an expansion college is free for q = 1 (plus a bit more money).

53 Counterfactual Experiments Conclusions We set up a rich policy framework for the analysis of education policy We put particular emphasis on modeling the sources of funding for education, both through parents and institutions existing federal grants and loans programs improve welfare and output. Distortions reducing the ex-ante return are still important, particularly for low background students. Credit constraints are less important.