Philippe De Donder (Toulouse School of Economics) CES, Munich, April 2011

Transcription

1 The political economy of social insurance and redistribution Philippe De Donder (Toulouse School of Economics) CES, Munich, April 2011

2 Part 2 The political economy of (early) retirement and public pensions

3 Taxonomy of pension schemes based on 3 distinctions: Funded vs unfunded (or pay-as-you-go, PAYG): in PAYG, aggregate bene ts are nanced by a tax on currently working generations while in a funded system bene ts are nanced by the return on previously accumulated pension funds; De ned bene t (bene t is either xed lump sum or an amount determined by previous earnings, with contribution rates endogenous) vs de ned contribution (contribution rate is exogenous while bene ts are endogenous) Actuarial (bene ts vary with the contribution at the individual level) vs non-actuarial (redistributive). I ll use the terms Bismarck and Beveridge ( at pension). 1

4 One can cross these 3 characteristics and obtain 8 di erent pension systems. Examples: Redistributive de ned bene t PAYG: everybody is promised the same bene t when retiring. Redistributive de ned bene t funded: everybody receives the same pension, based on the nancial return of the average contribution. Actuarial de ned contribution PAYG: notional accounts (Sweden) where each retiree receives a pension based on what he has contributed. Real world system are seldom pure or clear-cut. Example: Non perfectly actuarial, or PAYG with a bit of funded scheme. 2

5 Taxonomy is interesting because each dimension corresponds to an important aspect of program: De ned bene t/contribution: risk sharing. Who supports the rate of return risk (demographic in PAYG, nancial in funded systems) between contributions and bene ts? PAYG vs funded: impact on aggregate saving. Beveridge vs Bismarck: labor market e ciency and redistribution. 3

6 I will consider only PAYG schemes because most often used, and more complex to understand (funded more like saving). Most papers are in steady state ) no di erence between de ned bene t/contribution. I will pay attention to Beveridge vs Bismarck: amount of redistribution in pension system. Remark: Public debt also a means to intergenerational transfer. Many results with pension can be translated in public debt terms. 4

7 Overview 1. Explain emergence/continuation of PAYG. Sjoblom (1985) 2. Seven reasons why decisive agents support PAYG: 2.1. Dynamic ine ciency Reduced time horizon. Browning (1975) 2.3. General equilibrium e ects Altruistic motive. Veal(1986) 2.5. Political power of the old Myopic savers. Cremer et al.(2005) 2.7. Within cohort redistribution. Casamatta-Cremer-Pestieau(2000) 3. Impact of demographic shock on PAYG systems. Casamatta-Cremer-Pestieau(2000) 5

8 1. Explaining emergence/continuation of PAYG. Main problem to explain emergence/continuation of an unfunded social security scheme: why would current workers pay social security contributions now if they only hope to receive much later? So many things can happen in between (30 years later)... We need some way to link tomorrow s pensions to today s contributions, IN A RATIONAL WAY. Idea: SS as implicit contract among successive generations, which de- nes a system of rewards and punishments. Young voters agree to transfer resources to current retirees because they expect to be rewarded with a correspondent transfer in their old age. Failures to comply with the contract are punished with no old age transfer. 6

9 Sjoblom, Voting for social security, Public Choice, 1985: Overlapping generations model (OGM) with repeated elections over social security and trigger strategies. Very nice result: social security may emerge as soon as it is bene cial for the young people. Problems with this approach: Multiplicity of equilibria: high indeterminacy of the sequence of contribution rates. How to choose one? Explains how contract lives on once it is in place, but not how people (across generations!) coordinate on this implicit contract. Reaction to shocks? OK as long as current young bene t from the program compared to no SS. 7

10 Complex setting. So other positive papers on social security take the following short cut: when people vote, they assume that the system will stay in place inde nitely. 8

11 Papers on the political economy of intergenerational redistribution di er according to the following assumptions [Insert Table 1 in Breyer, p 64] 9

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13 2. Seven reasons why decisive agents support PAYG system 2.1. Dynamic ine ciency If implicit rate of return on PAYG is bigger than rate of return on savings (compare two technologies). PAYG: Demographic growth n + increase in labor productivity g: Saving: real interest rate r: PAYG better than saving if n + g > r Better technology. In the rest, let s assume that n + g < r: 10

14 2.2. Reduced time horizon In reality, there are more than two cohorts. At each time, when voting, the past contributions cannot be changed. SS contributions are sunk for middle aged workers and retirees Clear that retirees want tax as big as possible. Old + middle aged may support PAYG even if n + g < r 11

15 Illustration of these two e ects: Browning 1975 Assumptions 1-8a + 9b Most crucial: saving exists, and there are 3 generations at any time: young workers, old workers and retirees. Generation t is the cohort of young workers at time t, with size N t : Population grows at rate g t Growth factor of population: G t 1 + g t = N t =N t 1 No technical progress: w is same wage rate at any time t. Labor exogenous (l = 1) so that w is wage income. 12

16 r t+1 is rate at which interest is paid in period t + 1 for savings made in t (s t ) Gross return on saving: R t r t+1 Each (young and old) worker contributes X t in period t to PAYG scheme. The bene t to retirees in period t is given by budget constraint P t = (G t 1 + G t G t 1 )X t = G t 1 (1 + G t )X t : 13

17 Denote by c i;t (i = 1; 2; 3) the i th period consumption at time t and look at generation t: c 1;t = w X t s t c 2;t+1 = w X t+1 s t+1 c 3;t+2 = P t+2 + R t+2 s t+1 + R t+1 R t+2 s t : All individuals of generation t have the same additively separable, strictly monotone and strictly concave utility function U t = u 1 (c 1;t ) + u 2 (c 2;t+1 ) + u 3 (c 3;t+2 ): 14

18 Question: which of the three cohorts (if any) forms the majority at time t? The retirees if G t 1 (1 + G t ) < 1, i.e. if the population shrinks su - ciently fast. If g t is constant, this requires that the population shrinks each generation (20 years) by at least 38.2% The young workers if 1 + G t 1 < G t 1 G t, i.e. if the population grows su ciently fast. If g t is constant, this requires that the population grows each generation (20 years) by at least 61.8% None of the groups forms a majority. Case that is empirically relevant. 15

19 Intermediate results Every voter s preferences over the range of possible contribution rates x X=w 2 [0; 1] is single-peaked. Every pensioner s utility is maximized at x = 1, and the rate x at which an old worker s utility is maximized exceeds the optimal value x for a young worker. Proof at steady state (g t = g 8t): Young prefers x = 0 if real interest rate is higher than rate of return of PAYG: r > g (or R > G). Rate of return of a euro of pension contributions for old workers is (1 + g) + (1 + g) 2 1 = g 2 + 3g + 1 >> g: 16

20 Main results Even if saving is possible, the majority will vote for a positive level of contributions to a public pension system. The size of the system is higher than the socially e cient size which is determined by the preferences of the young workers (who are confronted with its full costs and bene ts over their remaining lifetime). 17

21 Critique If retirees and old workers are convinced that the current tax rate will stay inde nitely in place, the only limit to how much tax they support is due to borrowing constraints. But if they form a majority, they should allow borrowing (remove credit barriers) by creating an institution which made loans to future bene ciaries available. So, an additional reason is needed: incentive e ects of social security 18

22 2.3. Crowding of aggregate savings by SS (Cooley and Soares 1999) General equilibrium e ects SS crowds out private saving ) increases return on capital (because relatively more rare) and decreases return on labor (because relatively more abundant) Redistribution in favor of capitalists and against workers If asset holding and crowding out e ect high enough, young individual may use return-dominated technology (PAYG) to increase return on private assets. 19

23 Two problems with this approach: Capitalists aren t numerous enough in a voting model! Disincentives e ects on labor supply go against the adoption of a PAYG system! 20

24 2.4. Altruistic motive PAYG exists because of altruism of young people who care for the old. Illustration: Veal (1986) Two-OLG representative-individual framework Assumptions 1a, 2b, 3c, 4b1, 5-8a, 9b. Saving as an alternative way of providing for old age to receiving transfers. Modelled as a non-cooperative game between two successive generations in working age. Current young decides on their saving (and transfers to current retirees) taking into account the impact this saving will have on how much transfer they will receive from the next generation (Stackelberg game). 21

25 Assume steady-state population growth (G t = G) and the speci c loglinear utility function with ; ; > 0 and G > R: U t = ln c 1;t + ln c 2;t+1 + ln c 2;t Young choose saving s t and transfers X t to maximize V t = ln(w s t X t ) + ln(rs t + GX t+1 (s t )) + ln(rs t 1 + GX t ): First-order condition for saving t t w s t Xt + (R + G@X t+1=@s t ) Rs 0 (=0 if s t > 0). (1) t + GX t+1 First-order condition for transfers t G t w s t Xt + Rs t 1 + GXt 0 (=0 if Xt > 0). (2) 22

26 Assume that there is a solution with transfers and no saving (we ll check later on that it is the case) We can solve equation (2) for the optimal transfer X t as a function of current retirees savings s t 1 : Xt = + w so that the transfer increases with, w and G decreases with, R and s t 1. R + G s t 1; If we assume that, likewise, the next generation will adjust its transfer to the current workers when they retire: X t+1 = + w 23 + R G s t:

27 We now check that no saving is the optimal choice of the current t = = w w X t X t R=( + ) + wg=( + ) + R=G w < 0: Conclusion: altruistic transfers from the workers to the retirees are positive and drive savings to zero in a Stackelberg equilibrium. Main Critique: Why not private transfers instead of PAYG? Not all retirees have children, so PAYG is a way to take care of all retirees. 24

28 2.5. Political power of the old Main idea: Minorities may be decisive in representative democracies. Two reasons: Informational: less free-riding in small groups, so they acquire more information on the quality of the rulers, who pay more attention to them. Larger stake in the outcome: this makes voting worthwhile, while it is not if you have low stake in the outcome; alliances between various groups and multidimensional voting. Illustration: Casamatta (JPET, 2000) 25

29 2.6. Myopic savers Cremer H., Ph. De Donder, D. Maldonado and P. Pestieau, Voting over the Size and Type of Social Security when some Individuals are Myopic, Journal of Public Economics, 2007, 91-10: To my mind, the heart of the context for thinking about Social Security is that it substitutes for poor decision making and for missing insurance opportunities (missing perhaps because poor decision making implies low demand). The various shortcomings in preparation for retirement relate to di erent issues - inadequate overall provision for retirement relates to having a mandatory program (...) P. Diamond, AEA Presidential address, AER

30 A justi cation (for having a mandatory pension system) is based on paternalism: a mandatory system prevents myopic individuals from ending up in poverty in old age.(...) A person of this type is well served by some kind of commitment device, which could consist of a mandatory pension system, that prevents him from procrastinating. So far, however, there does not seem to be any formal political-economy model that explains how such a disciplinary device could be introduced and maintained by collective-decision making. Lindbeck and Persson, JEL,

31 This paper: political economy of pension system design when some individuals are myopic. Questions: Impact of myopic individuals on political support for pension system size (generosity) of system its redistributive character Normative aspects dealt with in companion papers 28

32 Setting Two-period model, with zero interest and population growth rate Two types of individuals myopic, M, (in proportion ) and far-sighted individuals, F, with the same distribution of productivity w satisfying w med < w True preferences `2 U = u(c 2 ) + u(d) where c = rst period consumption, d = second period consumption, ` = labor supply; de ne x = c `2=2: 29

33 In rst period, myopic individuals discount the future too much U M = u(c with o <. For simplicity o = 0: `2 2 ) + o u(d); Self control problem: they cannot help themselves and resist the temptation to consume too much and save too little. They know they will regret when they retire, but it will be too late. Myopic individuals see the pension system as a commitment device that will force them to save. ) When voting over pension system, the myopic individuals use their true preferences ( état de grâce ) 30

34 Pension system Financed by a linear payroll tax on labor income w`. Pension bene t p i of individual i is given by p i = (w i`i + (1 )Ew`); with Ew` the average income and the contributory parameter: = 1: purely contributory (Bismarckian) pension. = 0: at rate (Beveridgean) pension. 31

35 Collective and individual decisions Two characteristics of the pension system (; ) are chosen by majority voting Sequential procedure: 1. type of system = 0 or = 1 2. size (generosity), 32

36 Myopic individuals use their true preferences (use = 1) when voting, anticipating that they will lose self control (use 0 = 0) when choosing how much to work and save. Individuals choose labor supply and savings (s 0; no borrowing allowed) for a given pension system 33

37 Main results If homogenous society: all far-sighted or all myopic (but di ering in productivity): at pension bene ts, Beveridgean system =) redistributive system. Intuition: A majority of people gain from redistribution ( med < ) If both types coexist: a Bismarckian system may arise. Intuition: Beveridgean tax is a compromise between far-sighted and myopics ) it gets less support, in each group, than in the corresponding homogenous society. Generosity is not necessarily an increasing function of proportion of myopics 34

38 Numerical example u = ln x M Support F Support Total Support V V ( V ; ) for Beveridge for Beveridge for Beveridge /

39 2.7. Within cohort redistribution Individuals di er inside a cohort. Three reasons why may have redistribution Financing: non linear with income (may be progressive or, in the US, capped) Pension: may not be linked to contributions (income) Di ering life expectancies Most common: linear SS tax + at pension (ex: UK) redistributes from high to low income Then, a young with low income may bene t from SS even if average return of PAYG lower than saving 36

40 Illustration 1: Tabellini 2000 Two generations (young workers, parents as retirees) in a static model: the young may transfer money to old, but no link between young future pensions and current transfers. Each parent has the same number G of working-age children. Mutual altruism between parents and children, but weak enough that no private transfer is made: altruism will only play a role when voting over social security. Workers can save and even borrow against their future pension bene ts. Assumptions: 1b, 2b,3a, 4b2, 5b1, 6b, 7-8a, 9b 37

41 Workers di er in wage income, so that a at-bene t proportionalcontribution social security scheme involves two di erent kinds of transfers: from workers to pensioners; from high-income to low-income. If voted upon in isolation: rst kind of transfer would be accepted by all pensioners and rejected by all workers (because altruism is too weak) second kind of transfer accepted by families with below-average income earners and rejected by above-average. Trick: these transfers are available only in combination in pension system! 38

42 Among workers: Mean income will refuse system; Below a certain threshold (lower than mean) income, workers will favor positive contribution rate; The lower the income, the higher the most-preferred contribution rate. Among parents: The parent of a child with mean-income favors a positive contribution rate. Contribution rate is decreasing with the children s income, and is zero above a threshold. 39

43 Majority voting: there exists a positive tax rate such that exactly half the voters (more than 50% of the retirees and less than 50% of workers) would prefer a higher and half would prefer a lower level. Due to single-peakedness of individual preferences, this value is the Condorcet winning contribution rate. Comparative statics: the Condorcet winning contribution rate increases with pre-tax income inequality and children s altruism; decreases with population growth rate and parents altruism. 40

44 Illustration 2: Casamatta-Cremer-Pestieau 2000 Two-period OLG model, with saving, intra-cohort heterogeneity and without any altruism. Assumptions: 1a1, 2a, 3a, 4a, 5b1, 6a, 8a, 9b Both exogenous and endogenous labor supply considered. Small open economy with given interest rate r t : Two cohorts: L t workers and L t growth (L t = L t 1 (1 + n t )). 1 retirees, n t the rate of population Individuals di er according to their wage w 2 [w and median w m < w. ; w+] with mean w All vote for contribution rate (once for all). 41

45 Pension has a at part and a contributory part. Bismarckian factor gives fraction of pension bene t linked to contribution. The pension bene t a current worker in period t expects to receive next period is p t+1 (w) = (1 + n t+1 ) t+1 (w + (1 ) w): Workers choose their saving and, for the moment, supply labor exogenously. Questions: Majority voting equilibrium level of contribution rate for a given : How does this level vary with? 42

46 Step 1: Optimal choice of saving for given t = t+1 and such that s A t = arg max U t = u(c t ) + u(d t+1 ) c t = w(1 t ) s t d t+1 = (1 + r t+1 )s t + p t+1 (w) We obtain the indirect utility function V t ( t ; t+1 ; w) = u(w(1 t ) s A t ) + u((1 + r t+1 )s A t + p t+1 (w)) where we can from now on forget the subscript t since we look at the steady state. 43

47 Step 2: Most preferred contribution rate for a given The retirees want R =1, because it is the level that maximizes their pension (absent incentives e ects). Result 1 A worker will always be in favor of a zero tax if 1 + r > ( + (1 ) w=w)(1 + n); i.e. return from private saving is higher than implicit return from PAYG. ) zero tax rate and positive saving above threshold ^w, positive tax rate and no private saving below this threshold. 44

48 Result 2 Most preferred value of increases with w for w < ^w when the intertemporal elasticity of substitution < 1. Intuition: in extreme case where =0, individuals want to equalize consumption in two periods, and since the rate of return of PAYG decreases with income, richer individuals want a higher contribution rate. Result 3: the most preferred value of is always strictly lower than R =1 (because even richest wants to consume in rst period) 45

49 Step 3: Majority voting solution for contribution rate Denote by ~w the identity of the decisive, median voter (not the voter with the median wage!) Ends-against-the-middle result: See Figure 1 46

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51 Comparative statics with respect to the Bismarckian factor Table: Social security replacement ratios as a function of income Income/average Half One Twice Regime % GNP Canada Beveridge 5.4 France Bismarck 12.5 Germany Bismarck 12.8 Italy Bismarck 15.6 Japan Mixed 6.6 Netherlands Beveridge 5.2 New Zealand Beveridge 5.4 UK Mixed 4.4 USA Mixed 4.6 It seems that Beveridgean systems are smaller than Bismarckian system. Can we explain that regularity with the current model? 47

52 We obtain A ( ~w(); A ( ~w(); ~w() ; the rst term (positive) measures the increase in the most preferred tax rate of the decisive voter when is increased (because he has less than average income and low intertemporal substitution); the second term (negative) measures the impact of the change in the identity of the decisive voter: as increases, the PAYG becomes less attractive to low wage workers. The more productive among those who supported PAYG now switch to private saving, and the decisive voter becomes poorer. He then prefers less tax. 48

53 If r = n, the identity of the median voter is not a ected by, so that only the rst impact exists and CW increases with (as in Table). If r > n, the net impact of on CW is ambiguous. When r > n > 0 and close to 1, the equilibrium tax rate jumps discontinuously to zero. Impact of n on CW is also ambiguous, for the same reasons. 49

54 3. Impact of demographic shocks on PAYG Illustration: Casamatta Cremer Pestieau 2000 Same model as above, but instead of focusing on steady state ( t = t+1 ), look at impact of demographic shock. It is now necessary to separate current variables from next period s variable (whose values are only expected): p e t+1(w) = (1 + n t ) t w + p 0 t+1; (3) with the noncontributory (Beveridgean) part, obtained from the government budget constraint in the next period as the residual p 0 t+1 = (1 + n t+1 ) t+1 w (1 + n t ) t w: Important: the pension you expect to receive in t + 1 depends on t+1 an n t+1. 50

55 Main assumption: the noncontributory part can be adapted more easily than the Bismarckian (entitlement) part. 51

56 Majority voting in steady state Idem above. Demographic Shock Unanticipated shock from n b = r to n a < r. Shock occurs at beginning of period 1 with generation 0 young before shock and old after, while generation 1 is born after the shock. If no entitlement: new majority in period 1 votes to stop PAYG ( a = 0) and the retirees in period 1 are left without resources (reminder: without distortions, either PAYG or saving). Question: how to protect this transition generation? Entitlements vs Minimum pension 52

57 First mechanism: entitlements The retirees feel entitled to the contributory part of their pension bene t: retirees in t + 1 with past earning w should receive a pension of at least t+1 w, with the replacement ratio t+1 obtained from (3) t+1 = (1 + n t ) t : So, in a generic period t, the tax rate that is necessary to pay the entitlements of the retirees in that period is c t = 1 + n t n t t 1 The shock happens at the beginning of period 1. We then have c 1 = 1 + n b 1 + n a b; c 2 = 1 + n a 1 + n a 1 + n b 1 + n a b = 1 + n b 1 + n a 2 b 53

58 The tax rate implemented in a generic period t 1 is then c t = 1 + n b 1 + n a t b The pension received at time t by a retiree with past earning w is Conclusions: p t (w) = (1 + n b ) t bw: The PAYG system slowly disappears (at a rate 1 ). Entitlements help protect the transition generation by smoothing the impact of the demographic shocks on future generations. 54

59 Second mechanism: Basic Pension A minimum pension of p 0 is guaranteed to everybody. The minimum tax rate in period t 1 is then given by c p 0 t = w(1 + n a ) : The main di erence with entitlements is that PAYG never disappears with a minimum pension. 55

60 Choosing the parameters and p 0. The analysis made up to now assumes that and p 0 are exogenous. Question: What would be the optimal values of and p 0? We need optimality criterion: Rawlsian, i.e. maximize the utility of the worst o individual. 56

61 1. Entitlements: choosing The worst o individual has the lowest wage w, but to which generation does he belong? max min V t (w ) t with V t (w ) = V t ( t ; t+1 ; w ): Can show that worst o individual belongs to the transition generations (those a ected by shock): V 0 (w ) = u((1 b)w ) + u( b(1 + n b )w ) V t (w ) = maxu((1 c t)w ) + u( c tw + s(1 + r)); t = 1; 2; ::: s 57

62 Can show that utility increases after period 1, and t (w )=@ c t < 0: because PAYG pension systems o ers a return < 1 and is not redistributive anymore, individuals would be better o with no pension at all and relying only on private saving. )With c t decreasing overtime, the worst o individual belongs either to generation 0 or 1. Rawlsian problem is then to max min(v 0(w ); V 1 (w )): Casamatta et al. show that there exists at least one (may be several) value of that equalizes V 0 (w ) and V 1 (w ), and that this value is strictly between 0 and 1. 58

63 Conclusion: A positive value of protects the poorest in the transition generations, even though it makes the system less redistributive. Intuition: the entitlement part is associated to the value of. So there is a trade o, since a higher : decreases redistribution (bad for low income); increases the entitlements (good for low income). 59

64 2. Minimum pension: choosing and p 0 : With two instruments, one can tackle both intergenerational and intragenerational redistribution. Main result: optimal Rawlsian system involves a zero value of (maximum intragenerational redistribution) together with a minimum pension (some intergenerational redistribution). See Figure 4: shows the trade-o at hand. With another criterion than Rawlsian, may choose entitlements rather than minimum pension if weight put on future generations high enough. 60

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