Unfunded Pension and Labor Supply: Characterizing the Nature of the Distortion Cost

Unfunded Pension and Labor Supply: Characterizing the Nature of the Distortion Cost Frédéric Gannon (U Le Havre & EconomiX) Vincent Touzé (OFCE - Sciences Po) 7 July 2011 F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 1 / 30

Introduction The unfunded pension schemes play a crucial role by: F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 2 / 30

Introduction The unfunded pension schemes play a crucial role by: controlling the transfers of income between generations (for a better Social Justice) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 2 / 30

Introduction The unfunded pension schemes play a crucial role by: controlling the transfers of income between generations (for a better Social Justice) proposing a relatively low risk -and probably low return- asset class for the long run retirement saving (for a better risk sharing). The aging process compromises the nancing of the unfunded pension promises. Many theoretical and applied analyses using OLG framework -heterogeneity, microeconomic versus macroeconomic shocks, endogenous versus exogenous labor supply, tax analysis- have been proposed since the 80 s to deal with this issue. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 2 / 30

Introduction The hypothesis of endogenous labor supply is particularly interesting because it leads to consider the nancing of the mandatory and unfunded pension schemes (pension rules, contribution rate) as a speci c taxation of labor income. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 3 / 30

Introduction The hypothesis of endogenous labor supply is particularly interesting because it leads to consider the nancing of the mandatory and unfunded pension schemes (pension rules, contribution rate) as a speci c taxation of labor income. The calculus of retirement income induces a particular and implicit tax on the labor income (Browning, 1975; Feldstein and Samwick, 1992). This tax is mainly induced by the fact that : the pension link to earnings might not be strong enough and the rate of return on unfunded pension is generally admitted to be lower than that on funded pension one. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 3 / 30

Introduction Kotliko (1996): he was the rst to show in a computable OLG model calibrated on the US economy that Pareto-improving tax reforms could exist for Social Security. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 4 / 30

Introduction Kotliko (1996): he was the rst to show in a computable OLG model calibrated on the US economy that Pareto-improving tax reforms could exist for Social Security. Brunner (1996) showed that assuming heterogenous agents might compromise such Pareto improving tax reforms. Kotliko et al. (2000) con rmed this property. Nishiyama and Smetters (2007) extended these results to an OLG model with idiosyncratic wage shocks and longevity uncertainty. The redistributive properties of the Social Security pension rules plays as an insurance and they concluded that the e ciency gains of a reform are much reduced. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 4 / 30

Introduction Erosa and Gervais (2002): relying on Chamley (1986), they nd conditions for optimal taxation (second best approach) in an intertemporal framework with OLG. A similar computational optimal growth model has been applied to the US economy by Conesa and Garriga (2008) who contemplate the Social Security policy in a general tax reform. Feldstein (1996, 2005b) proposes to use Harberger (1964) approximation of distortion cost induced by unfunded pension schemes, little has been done to estimate it. Feldstein (1996) estimates "that the deadweight loss due to the net Social Security Tax is about 2.35% of the Social Security payroll tax base" in 1995. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 5 / 30

Introduction AIM OF THE PAPER: This paper relates to Feldstein (1995, 2005) by seeking to estimate analytically this ine ciency (distortion cost). This analytical estimation permits to study precisely the sensitivity of the distortion cost with respect to the parameters, notably, labor supply elasticity, payroll tax and the pension-link-to-earnings coe cient. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 6 / 30

Introduction Plan of the presentation 1. Endogenous labor supply in an OLG model F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 7 / 30

Introduction Plan of the presentation 1. Endogenous labor supply in an OLG model 2. Measuring the E ciency Cost Induced by the Unfunded Pension F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 7 / 30

Introduction Plan of the presentation 1. Endogenous labor supply in an OLG model 2. Measuring the E ciency Cost Induced by the Unfunded Pension 3. Numerical simulations F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 7 / 30

1. Endogenous labor supply in an OLG model 11. Tax administration The intertemporal budget constraint for the tax administration is given by: D + = R D T + (P τ w w l). (1) We suppose P = τ w w l. Hence, D + = R D T. Retired workers receive a pension P + whose a fraction α is linked to the contributive e ort in terms of the personal labor supply (l),the remaining fraction being lump-sum: P + (l) = α l l + (1 α) τ w + w + l +, (2) {z } {z } Tax revenue per worker Pension rule where l and l are respectively the average and individual labor supplies. At the current period, the implicit debt of unfunded pension is equal to amount of promises of pension. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 8 / 30

1. Endogenous labor supply in an OLG model 12. Households The individual utility function writes: U c, z +, l = u c, z + v (l) where v (l) = β l 1+ 1 ε with β, ε > 0 and u (c, z + ) = c s z 1+ 1 +1 s with s > 0. ε The household s intertemporal budget constraint writes: c = (1 τw ) w l T S (when young) z + = R + S + P +. (3) (l) (when old) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 9 / 30

1. Endogenous labor supply in an OLG model 12. Households Each household maximizes his intertemporal welfare w.r.t savings and labor supply. The F.O.C. are respectively: S : uc = R + u z l : v 0 (l) = (1 τ w ) w u c + P +0 (l) u z. (4) where the LHS and the RHS are respectively the marginal cost and the marginal bene t of the two components of utility. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 10 / 30

1. Endogenous labor supply in an OLG model 12. Households These two conditions lead to: ( S = s (1 τ w ) w l (1 s) P + R + l = v A 0 1 (R +, w) 1 τ w 1 P +0 (l)/(τ w w ). (5) R + where A (R +, w) = (1 s) 1 s s s R +s w. The marginal tax rate induced by the unfunded pension scheme is equal to: τ w 1 P +0 (l) / (τ w w) R + (6) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 11 / 30

1. Endogenous labor supply in an OLG model 12. Households The indirect welfare function W associated with a tax system (τ w, α, T ) and marginal factor productivities (R +, w) is then given by: W τ w, α, T, R +, w = A R +, w {z } Marginal utility of consumption 2 l {z} Optimal labor supply P 1 τ w 1 + (l )/(τ w w l ) T R + w l {z } 6 4Life-cycle net income per unit of gross labor income v (l ) A(R +,w + )l {z } Relative e ort cost of labor supply (7) 3. 7 5 F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 12 / 30

1. Endogenous labor supply in an OLG model 13. Productive Sector We consider a linear technology of production where R and w are respectively the marginal factor productivities. R is certain and stationary and denoted thereafter R. We assume that w increases according to the constant growth factor Γ = w + w. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 13 / 30

1. Endogenous labor supply in an OLG model 14. Welfare Characterization at the General Equilibrium Proposition 1: If the tax system is stationary then the stationary growth factor of labor income w + l + w l is equal to Γ 1+ε. From proposition 1 and FOCs, we deduce: ε l = l (τ w, α, w, R) = 1 β A 1 τ w 1 α Γ1+ε R, (8) and W = W (τ w, α, τ f, w, R) = β ε A 1+ε 1 τ w 1 1+ε h1 τ w 1 α Γ1+ε R 1 Γ 1+ε R (1 + ε (1 α)) ε (9) i τ (1 + ε). F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 14 / 30

1. Endogenous labor supply in an OLG model 14. Welfare Characterization at the General Equilibrium Without distortionary taxation (τ w = 0 = α, τ 0), we have: and l = l max (w, R) = l (0, 0, w, R) = 1 β Aε, (10) W = W max (τ, w, R) = β ε A 1+ε 1 1+ε [1 τ (1 + ε)]. (11) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 15 / 30

2. Measuring the E ciency Cost Induced by the Unfunded Pension 21. De nition Monetary cost: We evaluate the amount of scal surplus that a virtual lump-sum tax might generate by paying back the implicit debt of unfunded pension sustaining a Pareto-equivalence principle (Diamond & MacFadden, 1974 ; Green & Sheshinski, 1978). De nition 1: A lump-sum tax is Pareto equivalent (PE) i it sustains the same welfare dynamics as the unfunded pension scheme. Hence, its corresponding rate τ pe must check: W (τ w, α, 0, w, R) = W max (τ pe, w, R). (12) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 16 / 30

2. Measuring the E ciency Cost Induced by the Unfunded Pension 21. De nition Welfare cost: We determine the additional welfare induced by a virtual lump-sum tax refunding exactly the implicit debt of unfunded pension. This approach is based on the conventional (or primal) consumer s program. This approach is similar to Levhari and Sheshinski (1972) and Chamley (1981) who calculate the intertemporal welfare gain induced by a capital income tax suppression. However, to be precise, we can qualify this gain as maximum since it supposes that the distortive tax does not nance any public expenditure. Here, we assume the distortive tax nances the implicit public debt induced by the pension promises and we measure the gap between a rst best lump-sum tax and the implicit tax. Notice that according to Harberger (1964), the latter can be quali ed as "n th best". F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 17 / 30

De nition 2: A lump-sum tax is tax revenue equivalent (TRE) i it refunds exactly the implicit amount of public debt induced by the unfunded pension scheme. Hence, its corresponding rate τ tre must check: τ tre w l max (w, R) R R Γ 1+ε = τ w w l (τ w, α, 0, w, R). (13) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 18 / 30

2. Measuring the E ciency Cost Induced by the Unfunded Pension 22. Monetary Distortion Cost Proposition 2: The PE lump-sum tax rate is equal to: ε τ pe = 1 1+ε h1 1 τ w 1 α Γ1+ε (14) R i 1 τ w 1 (1 + ε (1 α)) Γ1+ε. R F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 19 / 30

2. Measuring the E ciency Cost Induced by the Unfunded Pension 22. Monetary Distortion Cost Proposition 2: The PE lump-sum tax rate is equal to: ε τ pe = 1 1+ε h1 1 τ w 1 α Γ1+ε (14) R i 1 τ w 1 (1 + ε (1 α)) Γ1+ε. R Proposition 3: The monetary distortion cost (MDC) of unfunded pension income writes: MDC = R R Γ 1+ε w l max (w, R) τ pe τ tre. (15) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 19 / 30

2. Measuring the E ciency Cost Induced by the Unfunded Pension 22. Welfare Distortion Cost Proposition 4: The TRE lump-sum tax rate refunding the implicit public debt is given by: ε τ tre Γ = τ w 1 1+ε 1 τ R w 1 α Γ1+ε R. (16) Proposition 5: The welfare distortion cost (WDC) of unfunded pension writes: WDC = β ε A 1+ε 1 1+ε τpe τ tre. (17) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 20 / 30

2. Measuring the E ciency Cost Induced by the Unfunded Pension 22. Welfare Distortion Cost Proposition 4: The TRE lump-sum tax rate refunding the implicit public debt is given by: ε τ tre Γ = τ w 1 1+ε 1 τ R w 1 α Γ1+ε R. (16) Proposition 5: The welfare distortion cost (WDC) of unfunded pension writes: WDC = β ε A 1+ε 1 1+ε τpe τ tre. (17) If the marginal tax rate τ w 1 α Γ1+ε is small enough, the R di erence τ pe τ tre f f can be approximated well by a simple expression: τ pe τ tre 2 ' ε2 1+ε τ w 1 α Γ1+ε R. (18) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 20 / 30

2. Measuring the E ciency Cost Induced by the Unfunded Pension 23. Comparing with the Harberger s triangle approximation The monetary cost computed at each period (in per cent of w l max ) is measured by: τ pe τ tre 2 ' ε2 1+ε τ w 1 α Γ1+ε R. (19) The approximation of Feldstein (1996, 1999) (in per cent of w l max ) is given by: 2 1 2 τ ε w 1 α Γ1+ε R. (20) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 21 / 30

2. Measuring the E ciency Cost Induced by the Unfunded Pension 23. Comparing with the Harberger s triangle approximation The di erence between the two expressions evolves as follows : ε 1 2 2 ε 1+ε τ w 1 α Γ1+ε R. (21) From a relative point of view, the di erence w.r.t ε evolves as follows: 1 2 1 ε 1. (22) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 22 / 30

3. Numerical simulations We assume: ε = 1.0; τ w = 20%; α = 80%; s = 0.5, R = (1 + 6%) 40 ; Γ = (1 + 1.5%) 40 ; w 0 = 1. WDC /W max (0, w, R) = 2.21% and MDC / (w l max (w, R)) = 1.63%. 3.5 2.8 3.0 2.4 2.5 2.0 2.0 1.6 1.5 1.2 1.0 0.8 0.5 0.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Relative welfare cost (%) Relative monetary cost (%) 18.7 16.6 14.5 12 10.4 8 6 Pareto equivalent Tax revenue equivalent.3.2 4 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2.1 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Lump sum tax rate (%) Ratio labor income growth factor / interest factor Fig. 1. Sensitivity to ε F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 23 / 30

3. Numerical simulations 32. Sensitivity to the labor productivity growth factor 3.5 3.0 2.5 2.0 1.5 1.0 0.5 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 18 16 14 12 10 Relative welfare cost (%) 8 Pareto equivalent 6 Tax revenue equivalent 4 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Lump sum tax rate (%) 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Relative monetary cost (%).8.7.6.5.4.3.2.1.0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Ratio labor income growth factor / interest factor Fig. 2. Sensitivity to Γ F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 24 / 30

3. Numerical simulations 33. Sensitivity to the capital return factor 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 12 11 10 9 8 7 6 5 4 3 Relative welfare cost (%) Pareto equivalent Tax revenue equivalent 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 Lump sum tax rate (%) 1.60 1.55 1.50 1.45 1.40 1.35 1.30 1.25 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 Relative monetary cost (%).9.8.7.6.5.4.3 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 Ratio labor income growth factor / interest factor Fig. 3. Sensitivity to R F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 25 / 30

3. Numerical simulations 34. Sensitivity to the Social Security tax rate 24 20 16 12 8 4 0.0.1.2.3.4.5 35 30 25 20 15 10 5 Relative welfare cost (%) Pareto equivalent Tax revenue equivalent 0.0.1.2.3.4.5 Lump sum tax rate (%) 16 14 12 10 8 6 4 2 0.0.1.2.3.4.5 Relative monetary cost (%).340.335.330.325.320.315.310.305.300.0.1.2.3.4.5 Ratio labor income growth factor / interest factor Fig. 4. Sensitivity to τ w F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 26 / 30

3. Numerical simulations 35. Sensitivity to the contributive pension share 4.4 4.0 3.6 3.2 2.8 2.4 2.0 1.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13.5 13.0 12.5 12.0 11.5 Relative welfare cost (%) 11.0 Pareto equivalent Tax revenue equivalent 10.5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Lump sum tax rate (%) 3.2 2.8 2.4 2.0 1.6 1.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Relative monetary cost (%).340.335.330.325.320.315.310.305.300 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Ratio labor income growth factor / interest factor Fig. 5. Sensitivity to α F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 27 / 30

Conclusion Paper related to the works of Feldstein (1996, 2005) F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 28 / 30

Conclusion Paper related to the works of Feldstein (1996, 2005) We propose an analytical modelling of the distortion cost induced by unfunded pension based on endogenous labor supply in a simple OLG framework. We propose an alternative estimation to Harberger approximation of the intergenerational social deadweight loss induced by unfunded pension by providing new analytical insights. We nd tractable expressions of welfare and monetary costs which express as linear functions of the di erence between "Pareto equivalent" and "tax revenue equivalent" lump-sum tax rates. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 28 / 30

Conclusion Main limit & extansion: F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 29 / 30

Conclusion Main limit & extansion: 1. The linear production technology leads to the independence of factors productivity with respect to capital accumulation. That means we do not measure the impact of a lower capital accumulation on the welfare cost. Developing a pure analytical approach seems di cult. However, our approach could be easily implemented in a CGE framework. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 29 / 30

Conclusion Main limit & extansion: 1. The linear production technology leads to the independence of factors productivity with respect to capital accumulation. That means we do not measure the impact of a lower capital accumulation on the welfare cost. Developing a pure analytical approach seems di cult. However, our approach could be easily implemented in a CGE framework. 2. Our evaluation of the distortion cost is limited to a single implicit taxation of unfunded pension scheme. It could be interesting to apply it to a multi-tax framework. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 29 / 30

Conclusion Main limit & extansion: F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 30 / 30

Conclusion Main limit & extansion: 3. The objective of the paper does not directly focus on tax reform which would imply to consider equity linked to heterogeneity of agents. However, whenever a strong distortion cost is evidenced, tax reform and the adoption of a more e cient tax system are at stake. This issue is treated implicitly by Erosa and Gervais (2002) and Conesa and Garriga (2008) in a context of optimal growth. F. Gannon & V. Touzé (Welf. econ. congr.) Unfunded Pension & Distortion Cost 7 July 2011 30 / 30