SWM. The impact of reducing pension generosity on schooling and inequality ECON. Miguel Sánchez-Romero 1,2 and Alexia Prskawetz 1,2

The impact of reducing pension generosity on schooling and inequality Miguel Sánchez-Romero 1,2 and Alexia Prskawetz 1,2 1 Wittgenstein Centre (IIASA, VID/ÖAW, WU) 2 Institute of Statistics and Mathematical Methods in Economics, Research Unit Economics, TU Wien, Austria 12th Global Meeting of the NTA Network, Mexico City, July 23-27 SWM Economics ECON

Motivation: Expected reductions in the generosity of pension systems 100 Old age dependency ratio (in %) 80 60 40 20 Japan Italy Finland Germany Portugal Sweden France Denmark Greece Latvia Estonia United Kingdom Belgium Spain Austria Netherlands EU28 Switzerland Slovenia Czech Republic OECD Hungary Norway Canada New Zealand Australia United States Poland Iceland Ireland Luxembourg Slovak Republic Israel Russian Federation Argentina Korea Chile China Turkey Brazil Mexico India South Africa Indonesia Saudi Arabia Year 2015 0 Figure 1: Old-age dependency ratio across OECD countries 2 / 18

Motivation: Expected reductions in the generosity of pension systems 100 Year 2050 Japan Italy Finland Germany Portugal Sweden France Denmark Greece Latvia Estonia United Kingdom Belgium Spain Austria Netherlands EU28 Switzerland Slovenia Czech Republic OECD Hungary Norway Canada New Zealand Australia United States Poland Iceland Ireland Luxembourg Slovak Republic Israel Russian Federation Argentina Korea Chile China Turkey Brazil Mexico India South Africa Indonesia Saudi Arabia Old age dependency ratio (in %) 80 60 40 20 0 Figure 1: Old-age dependency ratio across OECD countries 2 / 18

Motivation: Increasing longevity gap across socio-economic groups Life expectancy at age 65 (years) 20 15 Education High Low 1990 2000 2010 Year Figure 2: Life expectancy at age 65, US males Source: Own calculations. 3 / 18

Introduction Research interest: What is the impact of reducing the generosity of the pension system on inequality and schooling when individuals differ by longevity? Model: To study this problem, we propose an extension of Pestieau and Ponthiere (2016) by introducing heterogeneity in schooling effort 4 / 18

Individuals budget constraint First period: - stay unskilled (e u ) or become skilled worker (e s ) y(e s ) > y(e u ) - pay social security contributions τ y(e i ) - consumption c - save for retirement s c + s = (1 τ)y(e i ) (1) 5 / 18

Individuals budget constraint First period: - stay unskilled (e u) or become skilled workers (e s) y(e s) > y(e u) - pay social security contributions τy(e i ) - consumption c - save for retirement s c + s = (1 τ)y(e i ) (1) Second period: - For e i π(e i ) - consumption d s d = + f (ei, θ)y(ei ) Rπ(e i ) (2) where f (e i, θ) is the pension replacement rate f (e i, θ) = { ψ if ei = e u, ψ[1 θα(e s)] if e i = e s, (3) where α(e s) = y(e s ) y(e u ) y(e s ) is the relative income advantage of a skilled worker and θ represents the degree of progressivity 5 / 18

Replacement rate Replacement rate, f (e i, θ) 1 ψ Bismarckian θ = 0 θ > 0 Beveridgean θ = 1 y(e u) y(e s ) Labor income Figure 3: Stylized replacement rate function 6 / 18

Individuals preferences The preferences of an individual of type φ are described by the following utility function: V (e i ; φ) = u(c) φ e i + βπ(e i )u(d), (4) where φ R is the effort of attending school and differs across individuals (Oreopolous, 2007; Restuccia and Vandenbroucke, 2013; Le Garrec, 2015; Sánchez-Romero, d Albis and Prskawetz, 2016) Assumption 1: The survival probability positively depends on being a skilled worker, with π(e s ) π(e u) = π > 0. Assumption 2: The elasticity of utility with respect to consumption is between zero and one; i.e. η = xu (x)/u(x) (0, 1) (Hall and Jones, 2007). 7 / 18

Optimal schooling and the proportion of skilled workers The optimal schooling decision satisfies e i = { e u if φ φ, e s if φ > φ, (5) where the parameter φ denotes the threshold utility cost of schooling for which an individual is indifferent between continuing unskilled and becoming a skilled worker i.e, V (e u ; φ ) = V (e s ; φ ), φ = u(c (e s )) u(c (e u)) + β[π(e s )u(d (e s )) π(e u)u(d (e u))]. (6) Probability density function, g(φ) Proportion of skilled workers q := G ( φ) = φ g(x)dx skilled 0 φ unskilled Utility cost of schooling, φ Figure 4: Stylized probability density function of the utility cost of schooling 8 / 18

The implicit tax on work The impact of pensions on inequality Combining (1) and (2), the intertemporal budget constraint is c + Rπ(e i )d = (1 τ E (e i ))y(e i ) (7) 9 / 18

The implicit tax on work The impact of pensions on inequality Combining (1) and (2), the intertemporal budget constraint is c + Rπ(e i )d = (1 τ E (e i ))y(e i ) (7) Implicit tax on work the effective social security tax/subsidy rate on work, τ E (e i ), is given by: τ E (e i ) = τ f (e i, θ)rπ(e i ) (8) 9 / 18

The implicit tax on work The difference in the effective social security tax rate between unskilled and skilled workers, τ (θ) = τ E (e u ) τ E (e s ), is with ε(e s ) = π(e s ) π(e u ) π(e s ) τ (θ) = ψπ(e s ) [ε(e s ) θα(e s )] R (9) Proposition 1: Assuming a constant longevity across skill groups, π(e s ) = π(e u), a pension system with (a) a flat replacement (θ = 0) does not redistribute resources among skill groups (b) a progressive replacement rate (θ > 0) redistributes resources from skilled workers to unskilled workers 10 / 18

The implicit tax on work The difference in the effective social security tax rate between unskilled and skilled workers, τ (θ) = τ E (e u ) τ E (e s ), is with ε(e s ) = π(e s ) π(e u ) π(e s ). τ (θ) = ψπ(e s )α(e s ) [p θ] R (9) Proposition 1: Assuming a constant longevity across skill groups, π(e s ) = π(e u), a pension system with (a) a flat replacement (θ = 0) does not redistribute resources among skill groups (b) a progressive replacement rate (θ > 0) redistributes resources from skilled workers to unskilled workers Proposition 2: Assuming that π(e s ) > π(e u) and defining p = ε(e s ) α(e as the ratio of the s ) relative mortality to the relative income advantage of skilled workers, a pension system with (a) a flat replacement rate (θ = 0) transfers resources from short-lived and unskilled workers to long-lived and skilled workers (b) a progressive replacement rate (θ > 0) redistributes income (i) from skilled workers to unskilled workers when θ > p and (ii) from unskilled workers to skilled workers when θ < p 10 / 18

The implicit tax on work τ E ( ) p = ε(es ) α(es ) skilled (ε 1 ) implicit tax unskilled (ε 1 ) implicit subsidy p 1 Degree of progressivity, θ Figure 5: Effective social security tax/subsidy rate (τ E ) for each educational group by degree of progressivity (θ) 11 / 18

Impact of reducing the pension replacement rate on pension inequality To study the effect of a decrease in the replacement rate (ψ) on pension inequality, we calculate the sign of the derivative of Eq. (9) with respect to ψ { τ > 0 if θ > p = π(es )α(es ) (θ p) R (10) ψ < 0 if θ < p τ E ( ) implicit tax Lower pension inequality p = ε(e s ) α(e s ) Higher pension inequality skilled (ψ 1 ) skilled (ψ 2 ) unskilled (ψ 1 ) unskilled (ψ 2 ) implicit subsidy p 1 θ Figure 6: Impact of a fall in the replacement rate (ψ 1 > ψ 2 ) on the effective social security tax/subsidy rate (τ E ) for each educational group by degree of progressivity (θ) 12 / 18

Impact of reducing the pension replacement rate on pension inequality Progressivity a Ex ante progressive relative mortality advantage of skilled workers p= relative income advantage of skilled workers 0.9 0.6 0.3 a Ex ante regressive HUN LVA FIN SWE AUT POL TUR ITA FRA CHL SVN θ = p θ < p θ > p CZE NOR AUS DNK USA UK CAN NZL 0.0 SVK MEX 0.0 0.4 0.8 Degree of progressivity, θ Figure 7: Empirical values of p = ε(e s)/α(e s) and θ for 21 selected OECD countries Source: Values obtained from OECD (2017), Murtin (2017), and authors calculations. 13 / 18

Impact of reducing the pension replacement rate on education To study the impact of a decrease in ψ on education, we differentiate the proportion of skilled workers, q, with respect to ψ [ q ψ = g( φ)u (c τ (e s ))y(e s ) ψ + (Φ 1) τ ] E (e u), (11) ψ with Φ = u (c (e u ))y(e u ) u (c (e s ))y(e s ) Less skilled workers More skilled workers Less skilled workers More skilled workers τe ( ) skilled (ε 1 ) τe ( ) skilled (ε 1 ) implicit tax implicit tax unskilled (ε 1 ) unskilled (ε 1 ) implicit subsidy p 1 θ implicit subsidy p 1 θ (a) Case: Φ < 1 (b) Case: Φ > 1 Figure 8: Impact of a reduction in the replacement rate on the proportion of skilled wokers by degree of progressivity of the pension system (θ) 14 / 18

Impact of reducing the pension replacement rate on education Impact of a fall in the replacement rate Impact of a fall in the replacement rate Less skilled workers Less skilled workers relative mortality advantage of skilled workers p= relative income advantage of skilled workers 0.9 0.6 0.3 More skilled workers SWE HUN LVA FIN AUT POL TUR ITA FRA CHL SVN DNK USA NOR CZE CAN AUS UK NZL relative mortality advantage of skilled workers p= relative income advantage of skilled workers 0.9 0.6 0.3 More skilled workers SWE HUN LVA FIN AUT POL TUR ITA FRA CHL SVN DNK USA NOR CZE CAN AUS UK NZL 0.0 SVK MEX 0.0 SVK MEX 0.0 0.4 0.8 Degree of progressivity, θ 0.0 0.4 0.8 Degree of progressivity, θ (a) Relative risk aversion = 0.5 Φ < 1 (b) Relative risk aversion = 1.5 Φ > 1 Figure 9: Impact of a reduction in the replacement rate on the proportion of skilled workers by degree of progressivity of the pension system (θ) in 21 selected OECD countries Source: OECD (2017), Murtin (2017), and authors calculations. Calculations done assuming each period lasts forty years, a power marginal utility function u (x) = x γ, where γ is the relative risk aversion coefficient, a constant annual real interest rate of 3 percent, a productivity growth rate of 1.5 percent, and a subjective discount factor of 1 percent. 15 / 18

The combined effect of a reduction in pension generosity More skilled workers & lower pension inequality Less skilled workers & higher pension inequality τe ( ) τe ( ) implicit tax Less skilled workers & lower pension inequality More skilled workers & higher pension inequality implicit tax Less skilled workers & lower pension inequality More skilled workers & higher pension inequality implicit subsidy p 1 θ implicit subsidy p 1 θ (a) Case: Φ < 1 (b) Case: Φ > 1 Figure 10: Impact of a reduction in the replacement rate (ψ) on the proportion of skilled workers (q) and on pension inequality ( τ ) by degree of progressivity of the pension system (θ) 16 / 18

The combined effect of a reduction in the pension generosity More skilled workers & lower pension inequality Less skilled workers & higher pension inequality τe ( ) τe ( ) implicit tax Less skilled workers & lower pension inequality More skilled workers & higher pension inequality implicit tax Less skilled workers & lower pension inequality More skilled workers & higher pension inequality implicit subsidy p 1 θ implicit subsidy p 1 θ (a) Case: Φ < 1 (b) Case: Φ > 1 Figure 10: Impact of a reduction in the replacement rate (ψ) on the proportion of skilled workers (q) and on pension inequality ( τ ) by degree of progressivity of the pension system (θ) If we pursue avoiding pension inequality, then a reduction in the generosity of the pension system will lead to an ambiguous result on the number of skilled workers 16 / 18

The combined effect of a reduction in pension generosity Impact of a fall in the replacement rate θ = p Impact of a fall in the replacement rate Less skilled workers and lower inequality Less skilled workers and lower inequality θ = p relative mortality advantage of skilled workers p= relative income advantage of skilled workers 1.0 0.5 More skilled workers and lower inequality More skilled workers and higher inequality HUN CZE LVA FIN SVN NOR AUS SWE CHL DNK UK FRA USA AUT CAN NZL POL TUR ITA relative mortality advantage of skilled workers p= relative income advantage of skilled workers 1.0 0.5 Less skilled workers and higher inequality More skilled workers and higher inequality HUN CZE LVA FIN SVN NOR AUS SWE CHL DNK UK FRA USA AUT CAN NZL POL TUR ITA 0.0 SVK MEX 0.0 SVK MEX 0.5 0.0 0.5 1.0 Degree of progressivity, θ (a) Relative risk aversion = 0.5 Φ < 1 0.5 0.0 0.5 1.0 Degree of progressivity, θ (b) Relative risk aversion = 1.5 Φ > 1 Figure 11: Impact of a reduction in the replacement rate (ψ) on the proportion of skilled workers (q) and on pension inequality ( τ ) by degree of progressivity of the pension system (θ) in 21 selected OECD countries Source: See figs. 7 and 9. 17 / 18

Conclusions We have developed a model for analyzing the impact of a reduction in the generosity of the pension system on inequality and schooling Within this framework we study the impact of a reduction in the generosity of the pension system on schooling and inequality when there exists differential mortality across groups We show that when there exists ex ante mortality differences, it is necessary to introduce a progressive pension system to avoid that pension system becomes regressive 18 / 18

Thank you! We would like to thank David de la Croix, Michael Freiberger, Bernhard Hammer, Michael Kuhn, Ronald Lee, Klaus Prettner,Timo Trimborn, Stefan Wrzaczek for valuable comments. This project has also received fundings from the Austrian National Bank (OeNB) under Grant no. 17647. 18 / 18

US OAI pension system (DB-II) Replacement rate, ψ(p) 0.900 p:= y:= Pension earnings or Average Indexed Monthly Earnings (AIME) Average Labor Income 0.417 0.283 0 y/6 y 2y p (or AIME) Figure 12: Old-Age Insurance replacement rate in the US Note: AIME is calculated as 1/12 of the mean of the 35 highest labor incomes over the working life, measured in real terms. 18 / 18

The impact of an increase in π and in α e on the implicit tax on work skilled (α 2 ) τe ( ) skilled (ε 1 ) τe ( ) skilled (α 1 ) implicit tax skilled (ε 2 ) implicit tax unskilled (ε 2 ) unskilled (ε 1 ) unskilled (α 1 ) unskilled (α 2 ) implicit subsidy ε 1 ε 2 1 α 1 α 1 θ implicit subsidy ε 1 α 2 ε 1 α 1 1 θ (a) Increasing longevity gap (ε 1 < ε 2 ) (b) Increasing income gap (α 1 < α 2 ) Figure 13: Effective social security tax/subsidy rate (τ E ) for each educational group by degree of progressivity (θ) 18 / 18