Education Policy and Intergenerational Transfers in Equilibrium Education Policy and Intergenerational Transfers in Equilibrium B. Abbott, G. Gallipoli, C. Meghir, G. Violante
Education Policy and Intergenerational Transfers in Equilibrium 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.
Education Policy and Intergenerational Transfers in Equilibrium Introduction Possible reasons for government intervention: ◮ Credit constraints ◮ Income taxation ◮ Imperfect insurance markets ◮ Equity
Education Policy and Intergenerational Transfers in Equilibrium 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)
Education Policy and Intergenerational Transfers in Equilibrium 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.
Education Policy and Intergenerational Transfers in Equilibrium 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
Education Policy and Intergenerational Transfers in Equilibrium 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 60-70 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.
Education Policy and Intergenerational Transfers in Equilibrium Introduction The rest of the talk: 1. Describe the life-cycle 2. Present and discuss Method of Moments Estimation 3. Present counterfactual analyses
Education Policy and Intergenerational Transfers in Equilibrium Model The Life Cycle
Education Policy and Intergenerational Transfers in Equilibrium 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
Education Policy and Intergenerational Transfers in Equilibrium Model Life cycle: Education High-school decision: V ∗ g 0 ( ˆ a , θ, q , κ ǫ ) = � � a , θ, q , κ ǫ ) − κ HS ( g , θ, κ ǫ ) , E z [ V LH g 0 (ˆ max V g 0 ( ˆ a 0 , θ, z 0 )] , a CL ) . a = (ˆ a 0 , ˆ ˆ Utility (psychic) costs of high school: κ HS ( g , θ, κ ǫ ) = ς HS + ς HS 1 1 { g = f } + ς HS log ( θ non ) + ς HS log ( θ cog ) + ς HS 4 κ ǫ . 0 2 3 ◮ 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.
Education Policy and Intergenerational Transfers in Equilibrium 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 V e � � � � � a j , θ, z j = c j ,ℓ j , a j + 1 u g max c j , ℓ j + β E z a j + 1 , θ cog , z j + 1 gj g , j + 1 s . t . ( 1 − τ w ) w e g ε e � � � � ( 1 + τ c ) c j + a j + 1 = 1 − ℓ j θ cog , z j gj + ψ + [ 1 + r ( 1 − τ k )] a j a j + 1 ≥ 0 , c j ≥ 0 , ℓ j ∈ [ 0 , 1 ] Γ e � � z j + 1 ∼ z j + 1 | z j . gz
Education Policy and Intergenerational Transfers in Equilibrium Model Life cycle: Education College Completion decision: � � V ∗ a CL , θ, q , κ ǫ a 1 , ˆ = g 1 � � � � a CL , θ, q − κ CL ( g , θ, κ ǫ ) , E z [ V HS max a 1 + ˆ V g 1 g 1 ( a 1 , θ, z 1 )] . Utility (psychic) costs of college: κ CL ( g , θ, κ ǫ ) = ς CL + ς CL 1 1 { g = f } + ς CL 2 log ( θ non ) + ς CL 3 log ( θ cog ) + ς CL 4 κ ǫ . 0 ◮ 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.
Education Policy and Intergenerational Transfers in Equilibrium 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
Education Policy and Intergenerational Transfers in Equilibrium 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 1 − ¯ ( θ, z j = 0 ) � � t − ℓ j + φ ( q , θ ) = j � [ 1 + r ( 1 − τ k )] 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).
Education Policy and Intergenerational Transfers in Equilibrium 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 1 − ¯ � � ( θ, z j = 0 ) t − ℓ j = j � [ 1 + r ( 1 − τ k )] a j if a j ≥ 0 , b j = 0 = φ ( q , θ ) + ( 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%.
Education Policy and Intergenerational Transfers in Equilibrium 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 1 − ¯ ( θ, 0 ) � � t − ℓ j + φ ( q , θ ) = j [ 1 + r ( 1 − τ k )] a j if a j ≥ 0 , b j = 0 0 > b j ≥ − b s = b j if a j = 0 , (1) − b s + ( 1 + r u ) b j + b s � b j < − b s � if a j = 0 , 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.
Education Policy and Intergenerational Transfers in Equilibrium 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 - 2000) Wife’s Edu HSD HSG CLG Hus- HSD 0.107 0.030 0.002 band’s HSG 0.027 0.498 0.042 Edu CLG 0.002 0.056 0.236
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