Models of imperfect rationality and redistribution in the context of retirement


Can individuals provide enough resources for retirement on their own? Does the government optimally support life-cycle savings? And are annuities the optimal savings product for old age? Those are fundamental and pressing questions in times in which publicly financed social security systems are under severe demographic stress. The standard macroeconomic model of old-age savings would answer all those questions with a definite: YES! Yet, two important empirical facts stand in contrast with predictions from this model. First, the vast majority of individuals lag behind their optimal retirement savings pattern. Second, individuals do not annuitize their assets.

The objective of this project is to contribute to the understanding of these phenomena thereby adding to the macroeconomic literature on old-age savings. We will embed incomplete rationality and lifespan heterogeneity into a state-of-the-art overlapping generations setup with idiosyncratic income shocks. We will thus improve the match between a macroeconomic model of life-cycle savings behavior and the corresponding observational data. Using very rich data on the 401(k) program participation and assets accumulation for several birth cohorts in the US, we will identify the dominant mechanisms behind savings patterns of households, which are both highly dispersed across individuals and insufficient to prevent old-age poverty for a considerable share of the population.

Our project builds on three strands of literature. First, we will expand the literature on incomplete rationality in macroeconomic models with a life-cycle dimension, which hints that mandated old-age saving programs improve welfare because they provide a free commitment device. Second, we will contribute to evaluating tax incentives for old-age savings, which suggests that favorable tax treatment may drive individuals to increase their amount of assets at retirement. Third, we will revisit the literature on the annuity puzzle and the intrinsic value of annuities, which hints that mandatory annuitizing raises welfare because it cheaply eliminates the cost of adverse selection in providing insurance against outliving own assets.


Projekt realizowany wspólnie z Szkołą Główną Handlową w Warszawie w ramach polsko-niemieckiej współpracy badawczej zaczynamy badać systemy emerytalne przy założeniu ograniczonej racjonalności podejmowania decyzji. Naszymi partnerami w tym projekcie są Fabian Kindermann oraz Johannes Huber z Universitaet Regensburg.

Źródło finansowania | Financing : Narodowe Centrum Nauki, BEETHOVEN

Projekt realizowany | Timeline : 04/2022 – 03/2025

Budżet łączny | Total budget: 326,193 zł (SGH) + 419,457 zł (FAME)

  • wynagrodzenia dla podstawowych wykonawców | compensation to researchers: 144,000 zł (SGH) + 54,000 (FAME)
  • wynagrodzenia dla asystentów badawczych | compensation to research assistants: 63,000 zł (SGH) + 189,000 (FAME)
  • komputery i oprogramowanie | hardware and software: 8,600 zł (SGH) + 8,600 (FAME)
  • wymiana doktorantów | PhD students exchange: 8,722 zł (SGH) + 17,744 (FAME)
  • konferencje i inne wyjazdy | conference travels: 26,096 zł (SGH) + 28,072 (FAME)
  • koszty pośrednie  | overheads: 53,482 zł (SGH) + 68,776 (FAME)

Our project builds on three strands of the literature. The first one is on incomplete rationality. It has been used in the past as a case for mandatory social security as well as opt-out rather than opt-in for private voluntary pensions. One of the findings in this literature is that mandated systems essentially provide a free commitment device and thus may improve welfare.

The second relevant strand of the literature relates to evaluating tax incentives for old-age savings. Old-age saving schemes with favorable tax treatment have spread to all OECD countries and have been subject to numerous policy and academic debates.. The most frequent concern is that such programs allocate fiscal relief/subsidy to those individuals who otherwise would have no difficulty accumulating wealth for old-age consumption (crowd-out), and at the same time, they do not provide sufficiently meaningful incentives or support for the rest of the society (redistribution).

The third strand of the literature relates to the value of annuity. Numerous studies have shown the theoretical appeal of life annuities. Yet, individuals seem reluctant to buy them – a phenomenon known as an “annuity puzzle”. Behavioral analyses hint that individuals persistently underestimate their life expectancy, thus perceiving annuities as unprofitable. We offer an alternative explanation: differences in life expectancy within a birth cohort bring an important caveat to the intuition that individuals benefit from insurance against the risk of outliving own assets.

These three strands of literature leave several theoretic and at the same time policy-relevant issues unaddressed. First, we offer a novel take on incomplete rationality in retirement decisions. The literature on incomplete rationality is dominated by time-inconsistency whereas this form of incomplete rationality implies challenges for normative inference. In addition, recent research suggests that a typical individual has approximately six different biases, not merely singled out myopia or hyperbolic discounting. Existing overlapping generations models are unable to match the patterns of life-cycle savings observed in the data. Second, we propose to formalize the implications of incomplete rationality for wealth inequality and old-age poverty. Typically models of retirement decisions focus on macroeconomic implications, leaving aside the implied redistribution, resulting wealth inequality and ability to accumulate savings for consumption at old age. Third, the literature typically views social security as beneficial due to the unambiguous value of annuities. We provide novel insights on the annuity puzzle and novel mechanisms for normative inference regarding mandated annuitization of old-age savings. Finally, the political economy literature thus far substantiated mechanism behind social security, but not the voting mechanism behind tax-favored old-age saving schemes. We will fill this gap by proposing a novel voting framework, with stable and suboptimal equilibrium in terms of the pension system.

Systemy emerytalne, Społeczne

Our proposed project has multiple objectives. First, we intend to develop a novel class of overlapping generations models (OLG) with income uncertainty, heterogeneity in life expectancy and incomplete rationality. The neoclassical assumption of rationality fails to explain the patterns observed in the data with respect to the life-cycle profile of wealth and accumulation of old-age savings, see for example Angeletos et al. (2001). Indeed, a median individual has as many as 7 behavioral biases in decision-making, of which at least three relevant for inter-temporal optimization (Stango and Zinman 2020), as well as persistently misguided perception of longevity (Gottlieb and Mitchell 2020).

The crucial challenge for this objective is to develop an OLG model in which households exhibit heterogeneous behavioral patterns and life expectancies that replicates the actual patterns of old-age savings. In the case of the US, the availability of data in the Survey of Income and Program Participation (SIPP) allows to track old-age savings in 401(k) accounts and Individual Retirement Accounts (IRA). There are several possible deviations from rationality, like temptation, quasi-hyperbolic discounting, habit formation or cognitive discounting. All these result in insufficient savings for old age, but for different reasons and, therefore, may require different policies to remedy them. We will study these imperfections in the OLG model context. We plan to enrich the state-of-the-art calibrated OLG model solved by value function iteration with an endogenous grid-point method and a simulated method of moments estimation. This will allow us to adequately match the observational data from SIPP and thus enable us to embed an adequate amount of heterogeneity in behavioral patterns into the OLG model. In doing so, we will verify the following hypotheses:

(H1) Accounting for imperfect rationality improves the match of the OLG model to observational data in terms of old-age savings patterns. We will investigate several types of imperfect rationality existing in the theoretical literature and compare them to the patterns observed in SIPP data using a simulated method of moments. The key objective here is to develop a method of matching the model to the data that would go as far as possible with the current state of numerical methods. The final intended outcome is an OLG model with idiosyncratic income shocks, ex ante heterogeneity and different life expectancies within a birth cohort.

We will subsequently use this framework to conceptualize the effects of tax-incentivized old-age savings schemes. These plans should be designed for people who save too little for retirement. As such, they should reduce wealth inequality. However, with voluntary participation and favorable tax treatment, participation may be a poor indicator of whether the instruments achieve their objectives. For example, if inappropriate design makes participation beneficial mostly for rational agents, tax-incentivized old-age saving schemes exacerbate wealth and consumption inequality rather than attenuate them. The empirical literature tends to evaluate tax incentivized schemes based on participation rates and cross-sectional measures of crowd-out. Using our structural macroeconomic model will allow us to study if these measures are indeed informative of welfare effects. In the course of such an analysis, we will shed light on the following hypothesis:

(H2) Participation in 401(k) programs and cross-sectional measures of crowd-out, commonly used in the literature, are not informative about the benefits of tax-incentivized old-age savings schemes. The fundamental premise behind favorable tax treatment is to increase savings for retirement, and not to crowd-out other savings that households would have made anyway. As multiple mechanisms are at work here, we need a simulation model to disentangle the partial equilibrium, general equilibrium and composition effects. Thus, we use the macroeconomic structural model to verify if schemes such as 401(k) in fact lead to higher savings at retirement, and for which groups of the population they do provide such savings incentives. Note that whether or not an individual participates in these programs is not necessarily an indication for a savings increase. On the one hand, retirement savings might only crowd out other liquid savings. On the other hand, an empirically observed low amount of crowd-out might also originate from a change in the timing of savings rather than an increase in total assets at retirement. Having investigated the savings incentives of different population groups in our model, we will be able to clarify whether 401(k) programs may even increase rather than attenuate wealth inequality.

Next to this first set of research questions, we will study the implications of heterogeneity in life expectancy for individual returns and take up rates of tax-favored old-age savings accounts. In particular, we will ask how mandatory annuitization at the average cohort life table affects take up rates of tax-favored retirement plans across the income distribution and, if take up were mandatory, what were the welfare consequences for different income groups. In particular, we will verify the following hypotheses:

(H3) The life expectancy gap between richer and poorer households contributes to low take-up rates of tax-favored old-age savings schemes at the lower end of the income and wealth distribution. Understanding the relationship between life expectancy and investment in tax-favored retirement plans is a crucial insight when designing private tax-incentivized pension products. There might be multiple reasons why low-income individuals shy away from tax-favored retirement plans. Those plans are typically illiquid and, hence, households cannot withdraw funds from them to buffer adverse labor productivity shocks. In addition, the tax advantage is obviously small for those households who do not pay a lot of taxes in the first place. As multiple mechanisms are at work here, we need a simulation model to disentangle the impact of life expectancy differences on program participation.

(H4) Mandatory contributions to tax-favored old-age savings schemes and mandatory annuitization can lead to welfare losses for low-income individuals. Over the course of substantial reforms to public social security systems, the political discussion in many countries has centered around substituting part of the public pay-as-you-go pension system by mandatory contributions to a private system. There are even countries, like the Netherlands, that organize their old-age income provision purely on a capital market investment basis with mandatory annuitization. It is therefore crucial to understand the welfare consequences of such policies in light of the fact that individuals will experience different returns to mandatory annuitization when there is a substantial life expectancy gap along the income distribution.

The results from these proposed investigations will be informative in multiple ways. On the one hand, they can contribution to a long debate in the literature called the “annuitization puzzle”. It is a well-known fact that households typically do not annuitize their retirement wealth, see amongst others Reichling and Smetters (2015) for a discussion. Differences in returns to annuity products triggered by systematic differences in life expectancies might be one reason for this phenomenon. On the other hand, they can deliver valuable insights for the optimal design of third-pillar pension-savings products. Should contributions to these products be mandatory? Does strengthening the role of occupational private pensions make sense? Is mandatory annuitization a good option? The answer to such questions is to a large part shaped by the answers to the aforementioned research questions.

In the final steps we pursue a positive line of inquiry and study the origins of tax incentivized saving in a political economy setting. We will employ a voting mechanism in the OLG framework to see how societal preferences shape voluntary, tax-incentivized retirement savings schemes. In the process, we will verify the following hypothesis:

(H5) With imperfectly rational agents, equilibrium tax incentives are suboptimal, and this equilibrium is stable. For imperfectly rational agents, subsidies to savings reduce the under-saving problem that results from either temptation or time-inconsistent preferences. If the median voter's degree of imperfection is larger than that of the average voter in society, policies are suboptimal. We will also explore alternative voting mechanisms, reflecting empirical regularities in the model setup.

Our proposed analysis will help us understand how imperfect rationality shapes the design of tax incentives aimed at stimulating retirement savings. There is hardly any literature on this topic. This analysis will contribute to the literature on the design of tax incentives in retirement savings. The work that we will do here will be, to a large extent, affected by the results obtained from the research questions presented above.

We had our first team meeting, in Warsaw, on Nov 4th-6th. 

Both teams presented the developments so far. Krzysztof talked about temptation preferences in an OLG setup, Fabian showed a model with endogenous choice of tax favored asset.

We discussed the tasks for the nextt step. The proximate goal for the subsequent work periods is to compare the evolution of variables within the simple, stylized OLG model with temptation preferences and Beta, Delta preferences. Gamma parameter should be manipulated in order to inspect behavior of the model with temptation preferences. Such evolution with respect to consumption and savings paths in respective periods, the influence of taxation, the influence of social system contributions, should be compared to models with both rational and hyperbolic discounting agents.

Subsequently we should investigate the crowd-out effect of different contribution schemes in the model with temptation preferences and compare it to results from previous models. As temptation preferences allow for welfare inference, the relative welfare effect of various schemes should also be checked. Of particular interest is the influence of temptation preferences on the Euler equation (and the possible channels of this influence - mainly those that do not come from hitting liquidity, or other constraints), which could lead to asset paths differing qualitatively from the asset path of rational agents with no pension scheme. A model can be augmented with additional types of agents (and its interactions) such as: financially illiterate, hand to mouth etc.