Myopia and pensions in general equilibrium

As in similar studies, we assume myopia is the primary rationale for the existence of a social security program. We abstract from the other roles that social security programs play in insuring against longevity risk and redistributing income among the elderly.

Cremer and Pestieau’s (2000) position is that “majority voting typically results in overspending on social security.”

Additionally, the way we handle endogenous retirement follows Cremer et al. (2004).

This literature is too large to cite properly here, but see the many references in Findley and Caliendo (2009) and Caliendo and Gahramanov (2009) for background, and also see the surveys by Findley and Caliendo (2008) and Cremer and Pestieau (2009). The many papers from this literature systematically examine whether various forms of myopia, such as standard discounting (Feldstein 1985; Andersen and Bhattacharya 2008; Cremer et al. 2009), hyperbolic discounting (İmrohoroğlu et al. 2003; Caliendo 2009), short planning horizons (Findley and Caliendo 2009), temptation preferences (Bucciol 2006, 2008; Kumru and Thanopoulos 2008), and limited computational ability (Caliendo and Findley 2009) are able to rationalize a program as large as the one in the US. The present assumption that a fraction of the population live hand-to-mouth is the most extreme description of myopia and therefore should bias the results in favor of a large social security program.

We direct readers to Andersen and Bhattacharya (2008) for a careful theoretical treatment of the limits of myopia as a rationale for social security. In particular, if myopia takes the form of a discount rate used in decision making that is less than the one used in welfare calculations, then myopia must be paired with another friction (such as pessimism or borrowing constraints) or must be studied in general equilibrium in order to rationalize social security in a dynamically efficient economy. Basically, Andersen and Bhattacharya show that if the analysis is in partial equilibrium, then myopia needs to be severe enough that the individual is observationally hand-to-mouth (meaning the borrowing constraint always binds) or there must be enough pessimism (as in Feldstein 1985). In general equilibrium, if social security reduces capital accumulation and hence raises the interest rate, a forward looking consumer will choose a steeper consumption profile with social security than without, and the steeper profile is more in line with the profile that maximizes true utility. Hence, Andersen and Bhattacharya make it clear that both hand-to-mouth behavior and general equilibrium effects can act as channels to help rationalize social security. Both of these channels are present in our study.

In addition to the US, many countries in the OECD have social security programs in which b ^′(T) > 0. Cremer et al. (2004) ask the normative question of whether this is a good way to design a pension system. It is the redistributive feature of the program that may be welfare improving in their paper, since they abstract from myopia. Also see Cremer and Pestieau (2003) and Casamatta et al. (2005).

Note that the hand-to-mouth consumer just makes a single choice, unlike the LCPI consumer who solves a dynamic problem.

Problem (8)–(10) is time consistent.

Another simple way to introduce a motive for retirement is found in Cremer et al. (2004). They modify the period utility function directly so that disutility from work gets larger with age. Also see Gustman and Steinmeier (2005).

Retiring after the age of 70 does not generate any additional increases in the social security annuity.

The Gourinchas and Parker (2002) estimate of earnings over the life cycle is hump shaped, but as explained above, it is the downside of the hump that drives the retirement decision. So what matters for our calibration is that our efficiency profile declines at the same rate as the downside of their earnings profile. (Note that efficiency units and earnings share the same slope over the life cycle in our model.)

If in addition to sleep time we also take out time spent eating and commuting to work, then a 40 h work week would imply a lower value for l ₋ (such as 55% in Ortiz 2009).

Cremer and Pestieau (2000) summarize a literature which illustrates how, under majority voting, a social security program can naturally grow bigger than is socially desirable. Basically, everyone who experiences an internal rate of return on social security that beats the market, from the perspective of where they are currently standing in the life cycle, will vote for a large program. Those near or at retirement, together with low income individuals match this description and they form a majority. See Cremer et al. (2007) for more on voting.

Note that the predictions of our general equilibrium model are consistent with the vast empirical evidence suggesting that growth in the generosity of social security programs across the world may be responsible for part of the tendency toward earlier retirement. Yet, the LCPI retirement age doesn’t change much because we have simply scaled down the size of the program, and as in Samwick (1998), the LCPI retirement choice has more to do with the benefit formula b(T) than the magnitude of the tax. A change in the benefit rule b(T), such as setting z ₁ = 0, can have a very large effect on the retirement choices of both consumers in the model.

The optimal timing of benefit collection is the subject of much debate in the household finance literature, though it is emphasized far less in the typical macro models with social security (Coile et al. 2002).

This simplified modeling approach could potentially be justified on the grounds that, in reality, delayed claiming is “far less prevalent than theory predicts” (Coile et al. 2002). Also Casamatta et al. (2005) argue that a bias towards early retirement in the design of social security is both desirable in a utilitarian sense and supportable by majority voting. Also see Cremer et al. (2004).

Collecting benefits before retirement is possible in reality but is not considered here. See Ortiz (2009).

The shape of this graph is consistent with Coile et al.’s (2002) calculation that anything less than a 6% discount rate argues for delayed claiming (our discount rate is much lower than 6%).

The alternative equilibrium in Fig. 6 may be particularly relevant for other industrialized countries. Gruber and Wise (1997) summarize the large NBER project “Social Security Programs and Retirement Around the World”, which is a compilation of 11 country-specific studies, and they conclude that postponing collection of benefits does not typically increase the present value of the social security benefit annuity. Thus, while many countries do provide incentives to compensate people for postponing collection of benefits, the incentives are generally not strong enough to make our baseline assumption about synchronization too problematic in the international context.