The Effect of Different Saving Mechanisms in Pension Saving Behavior: Evidence from a Life-Cycle Experiment

Abstract

We examine how institutional saving mechanisms influence retirement saving decisions under bounded rationality and income risk. Using a life-cycle experiment with habit formation and loss aversion, we test mandatory and voluntary binding savings under deterministic and stochastic income. Voluntary commitment improves saving performance only when income is predictable; under uncertainty, it fails to improve performance. Mandatory savings do not raise total saving, as participants reduce voluntary contributions. These results emphasize the role of income smoothing in enabling behavioral interventions to improve long-term financial outcomes.

1. Introduction

Why do individuals often fail to save adequately for retirement, despite understanding its long-term importance? Canonical economic models assume that people behave as rational planners, dynamically allocating income to smooth consumption over their lifetime (Friedman, 1957; Modigliani & Brumberg, 1954). However, the growing literature shows that individuals systematically deviate from these predictions (Benartzi & Thaler, 2013; Lusardi, 1999; Thaler, 1994). Experimental studies find that even under idealized conditions, individuals often fail to solve dynamic consumption-saving problems optimally (A. L. Brown et al., 2009; Duffy & Orland, 2023; Fenig & Petersen, 2024). Recent experimental evidence reinforces these concerns (Duffy & Orland, 2023; Fenig & Petersen, 2024). These behavioral shortcomings raise important policy questions for pension system design. If saving behavior is systematically suboptimal, what institutional mechanisms can help individuals make better decisions? Should pension systems rely on mandatory contributions, or can voluntary commitment devices enhance outcomes—particularly under income uncertainty, where planning is more difficult?

This paper evaluates the effects of two commonly used mechanisms in pension systems: (i) obligatory savings and (ii) a combination of obligatory and voluntary binding savings. Using a life-cycle experiment, we test how these mechanisms affect individual utility in environments with deterministic and stochastic income. Our goal is to assess whether such mechanisms improve outcomes for participants with bounded cognitive abilities and whether their efficacy depends on income predictability. In a series of laboratory experiments, we examine how different saving mechanisms affect a person’s ability to maximize utility from intertemporal consumption-saving decisions. The decision environment is structured into two phases: a working life (income-generating periods) and a retirement phase (periods with no income). Participants earn utility by “consuming” portions of their income, guided by an induced utility function that incorporates two key behavioral features: loss aversion and habit formation. To investigate the influence of saving mechanisms, we implement a 2 × 3 between-participant design, where we vary the nature of the income stream (deterministic or stochastic), as well as the saving mechanisms available to participants. Here, we differentiate three conditions: (i) Baseline: Participants manage a single account for all savings (“pocket savings”), accessible throughout the experiment. (ii) Obligatory Retirement Contributions: Participants make mandatory payments into a retirement account during their working life, which can only be accessed during the retirement phase, similar to defined contribution pension plans. (iii) Voluntary Binding Savings: Alongside obligatory contributions, participants can set aside additional savings into a third account designated for retirement. These settings allow us to observe how different saving mechanisms affect consumption behavior and utility maximization over time.

Our paper makes three contributions to the literature on savings behavior and pension system design. First, we propose an experimentally implementable formulation of intertemporal utility that incorporates empirically supported features of human preferences—namely, loss aversion and habit formation—while remaining simple and intuitive enough for experimental participants to engage with meaningfully. Second, we experimentally evaluate two savings mechanisms widely used in European pension systems: mandatory contributions and a combination of mandatory and voluntary binding savings. Unlike many prior studies that impose structural constraints on consumption decisions, our design allows participants full flexibility to consume or save their income at any point during the working or retirement stages of the life cycle. This enables us to examine both the demand for institutional saving mechanisms and their behavioral effects on consumption smoothing and welfare outcomes. Our design also reflects recent calls to test the efficacy of such mechanisms in environments where individuals face planning constraints or cognitive limitations (e.g., Bachmann et al., 2023). Third, we contribute to the literature on precautionary saving and behavioral responses to uncertainty by comparing decision making under deterministic and stochastic income. While prior work has shown that income volatility interacts with liquidity constraints and cognitive skills to shape saving behavior, few studies have examined whether the same institutional mechanisms are effective across these environments. By holding preferences and institutional structure constant across income regimes, our experiment isolates the behavioral consequences of income uncertainty and tests the robustness of institutional designs.

Our results replicate key findings from previous life-cycle experiments, including the characteristic hump-shaped pattern of overconsumption/undersaving during the working life and positive effects of learning on saving performance over time. When comparing participants exposed to deterministic vs. stochastic income streams, we find that individuals facing income uncertainty consistently underperform relative to their counterparts with stable income. Notably, voluntary commitment devices—despite their promise as behavioral tools to counteract undersaving—fail to improve outcomes under stochastic income conditions. These findings underscore the importance of income predictability as a prerequisite for the effectiveness of behavioral interventions and suggest that income smoothing may be a necessary complement to commitment-based instruments in the design of modern pension systems.

The paper is organized as follows: Section 2 discusses the relevant literature that inspires the hypotheses in Section 3. Section 4 describes the experimental design. Section 5 presents our results, and Section 6 concludes.

2. Background Literature

2.1. Retirement Planning and Bounded Rationality

The standard literature on household retirement saving builds on the assumption that individuals act as rational planners, allocating their income between consumption and saving to maximize lifetime utility, as proposed in the “life-cycle hypothesis” (Modigliani & Brumberg, 1954). According to this model, individuals aim to smooth consumption over time by saving during high-income periods and dissaving during retirement (Friedman, 1957). However, a growing body of behavioral and experimental research shows that individuals often deviate from these predictions, systematically under-saving for retirement and responding to features of the decision environment that should be irrelevant under full rationality (Benartzi & Thaler, 2013).

While many standard saving experiments focus on one-shot or short-horizon decisions—often isolating particular mechanisms or incentives—life-cycle experiments require individuals to solve dynamic optimization problems across multiple periods, typically involving planning under constraints, uncertainty, and feedback. These tasks impose higher cognitive demands and more closely reflect the structure of real-world retirement planning. Importantly, life-cycle experiments allow researchers to compare observed behavior against normative benchmarks derived from backward induction, making them well suited for assessing the degree and structure of suboptimality in saving behavior.

Existing life-cycle experiments consistently show that individuals tend to overconsume early in life and fail to accumulate sufficient retirement savings, even when such plans are feasible and optimal (Duffy & Li, 2019). These deviations are often attributed to limited cognitive ability, myopic preferences, and difficulties in planning across multiple stages of life (Ballinger et al., 2011; Harris & Laibson, 2001; Lusardi, 1999). Recent studies reinforce this view; Fenig and Petersen (2024) and Duffy and Orland (2023) find persistent departures from theoretical optima even in deterministic environments with full information.

In an extensive replication study, Bachmann et al. (2023) confirm that life-cycle decisions remain suboptimal even in simplified task designs adapted for broader populations. These findings support the view that bounded rationality is a key constraint in retirement saving and must be explicitly addressed in policy and experimental design.

2.2. Saving Decisions in Different Environments

Experimental evidence shows that institutional design plays a central role in shaping retirement saving behavior, particularly when individuals face cognitive or informational constraints. Commitment devices—such as restricted-access accounts or early withdrawal penalties—have been shown to increase savings by helping individuals overcome self-control problems (Ashraf et al., 2006; Beshears et al., 2015a, 2020). However, their effectiveness depends on how they are embedded in broader institutional settings and how they interact with individual preferences and planning ability.

A related line of research focuses on the role of framing and default rules in retirement decision making. Experimental studies demonstrate that annuitization, asset allocation, and retirement timing decisions are highly sensitive to how options are presented. Framing effects can lead to substantial deviations from normative benchmarks even when underlying incentives remain constant (Agnew et al., 2008, 2015; J. R. Brown et al., 2008). Davidoff et al. (2005) show that relatively small institutional frictions can account for low annuity take-up, challenging the explanatory power of standard models. Fatás et al. (2013) and Card and Ransom (2011) likewise find that the form of benefit payments and default structures can meaningfully alter behavior.

Bachmann et al. (2023) replicate several of these institutional effects using larger and more diverse samples. They confirm that matching contributions are more effective than tax rebates and that annuity framing influences retirement timing. However, they also document that increased task complexity and ambiguity can substantially dampen responsiveness to institutional incentives, particularly when cognitive demands are high. This highlights the importance of designing interventions that are both behaviorally effective and cognitively accessible.

2.3. Saving Decisions Under Stochastic Income

The empirical relevance of precautionary saving under income uncertainty remains contested. Standard theory predicts that income risk should lead to higher savings (Gourinchas & Parker, 2002; Zeldes, 1989), but the experimental results are mixed. Some studies find support for increased saving in the presence of volatility (Carbone & Hey, 2004), while others do not (Meissner, 2016). Cognitive constraints may partly explain this inconsistency. The recent work confirms that income unpredictability reduces the effectiveness of saving mechanisms. Duffy and Orland (2023) show that while participants respond directionally to shocks, their behavior remains systematically off the theoretical benchmark. Kappes et al. (2023) find that scarcity and income predictability interact to determine consumption smoothing success.

Our study contributes to this literature by testing how voluntary and mandatory saving mechanisms perform under deterministic vs. stochastic income profiles in a controlled life-cycle experiment. In contrast to previous studies that typically examine income uncertainty or institutional mechanisms in isolation, our study combines both dimensions in a unified life-cycle experiment with an induced behavioral utility function. This design allows us to evaluate whether mechanisms that are effective under certainty retain their efficacy under income risk, thereby providing new evidence on the interaction between institutional design and bounded rationality in retirement saving behavior.

3. Hypotheses

Drawing on the literature reviewed in Section 2, we derive the following hypotheses, focusing on typical deviations from optimal saving behavior, the role of income uncertainty, and the impact of institutional mechanisms.

3.1. Hypothesis I: Undersaving/Overconsumption

A wide range of empirical and experimental studies reports consistent undersaving, often attributed to bounded rationality, cognitive constraints, or behavioral biases. Repetition has been found to mitigate such effects by allowing participants to learn (for a review, see Duffy, 2008). We therefore expect that (i) retirement savings will initially be lower than optimal and (ii) this behavior improves with repeated exposure to the task.

H Ia:

Participants achieve less than optimal utility due to inadequate retirement savings.

H Ib:

Repeating the task leads to higher utility due to reduced undersaving/overconsumption.

3.2. Hypothesis II: Income Uncertainty

Income uncertainty can influence saving behavior in opposing ways. Theoretically, risk should lead to increased precautionary saving (Gourinchas & Parker, 2002; Skinner, 1988; Zeldes, 1989), which may help reduce overconsumption and raise utility. Conversely, if individuals tend to undersave, then due to loss aversion, negative income shocks could lower utility more than positive ones improve it. We therefore propose two competing hypotheses:

H IIa:

Participants earn higher utility under stochastic income conditions due to increased precautionary savings.

H IIb:

Participants earn lower utility under stochastic income conditions due to the negative effects of income shocks outweighing any positive effects.

3.3. Hypothesis III: Savings Mechanisms

Many European pension systems rely on obligatory contributions to reduce undersaving (Hinrichs, 2021), but it remains debated whether such mechanisms increase total savings or simply displace voluntary ones (Duffy & Li, 2019). Moreover, their impact on life-cycle utility is unclear. This leads to the following hypothesis:

H IIIa:

Participants earn higher utility in the presence of an obligatory contribution mechanism than in its absence.

In contrast, commitment devices and awareness-enhancing interventions have shown promise in supporting self-control and improving saving outcomes (Karlan et al., 2016; Rha et al., 2006; Rodríguez & Saavedra, 2015). Voluntary but binding mechanisms combine both elements. Their use in real-world pension systems—alongside mandatory contributions—has been expanding (Ebbinghaus, 2021; Rudolph, 2016). We therefore state the following:

H IIIb:

Participants earn higher utility when a voluntary but binding saving mechanism is available, as it will reduce undersaving compared to settings with only mandatory or non-binding voluntary contributions.

4. Experimental Design

4.1. The Consumption-Saving Task

Our experimental design builds on the standard life-cycle consumption framework (Modigliani & Brumberg, 1954), where participants optimize the sum of immediate and future consumption utility based on expected lifetime income. All participants live for T periods.1 In each period, they earn utility by consuming part of their income. Since we are interested in an individual’s ability to sustain themselves during retirement, we divide the individual’s lifetime into working periods (t = 1, …,$\tau$) and retirement periods (t = $\tau$ + 1, …, T), with consumption during retirement financed by prior savings. While working, the individual receives labor income $y_t$ in each period, which can be used for immediate consumption or saved for consumption in later periods. No labor income is earned during retirement when all consumption has to be financed by savings from previous periods. Participants cannot consume more than their current actual income plus prior savings. Borrowing is excluded to simplify the task. For the same reason, the savings rate is set to zero, following, e.g., Ballinger et al. (2011, 2003); Feltovich and Ejebu (2014); Gechert and Siebert (2022). The optimization problem is expressed as

$$\begin{array}{ccc}\hfill \underset{c_t}{\max }& E\left[\sum _{t=1}^T{u}_t\right]\hfill & \\ \hfill \mathrm{s}.\mathrm{t}.& s_t=y_t+s_{t-1}-c_t\hfill & \hfill t\in [1,\tau ], s_0=0\\ & s_t=s_{t-1}-c_t\hfill & \hfill t\in [\tau +1,T], s_T=0\end{array}$$

(1)

Here, $s_t$ represents savings, $y_t$ is income, and $u_t$ is the utility in period t.

4.1.1. Consumption Utility

While individual preferences may vary, controlled experiments allow us to induce a uniform consumption utility structure, enabling the derivation of optimal consumption paths despite the heterogeneity of actual individual preferences (Hey & Dardanoni, 1988). Using an induced utility function is an established and essential practice in experimental economics (see Bachmann et al. (2023) for a replication survey.), as it ensures a controlled environment where participants’ consumption choices can be analyzed. The induced utility structure reflects average consumer behavior derived from prior experimental and empirical research (e.g., Carroll et al., 2000; Fehr & Zych, 1998). This approach is necessary because we lack detailed knowledge of each participant’s unique utility function. By employing the parameters validated in previous studies, we create a standardized model that captures realistic decision-making patterns while allowing comparisons between participants’ observed and optimal behavior. Implementing an induced utility function also motivates participants to distribute their consumption over time, which is critical in experiments without interest on savings or periodic payoffs (Bachmann et al., 2023). Without such a structure, participants may concentrate their consumption in select periods, diminishing the realism of the data generated. Furthermore, this design maintains external validity by retaining common, influential features in real-world decision making, such as (i) loss aversion and (ii) habit formation, which complicate consumption–saving decisions in practice. To simplify participant engagement and avoid framing effects tied to economic terminology, we refer to the induced utility function as “points” rather than explicitly using the term “utility”. This wording encourages participants to focus on strategic decisions related to saving and consumption within the experiment, thereby aligning their decisions with intuitive behavioral responses rather than economic concepts.

4.1.2. Loss Aversion

Loss aversion in our setting refers to the heightened sensitivity of individuals to consumption falling below the current habit level. To model loss aversion, we build on the utility function proposed by Bowman et al. (1999):

$$u_t(h_t,c_t)=\left\{\begin{array}{cc}\alpha \times {\displaystyle \frac{h_t}{\overline{y}}}+{\left({\displaystyle \frac{c_t-h_t}{\overline{y}}}\right)}^{\alpha },\hfill & c_t>h_t,\hfill \\ \alpha \times {\displaystyle \frac{h_t}{\overline{y}}}-\beta \times {\left({\displaystyle \frac{h_t-c_t}{\overline{y}}}\right)}^{\alpha },\hfill & c_t\le h_t,\hfill \end{array}\right.$$

(2)

where $c_t$ is the level of consumption, and $h_t$ is the consumption habit in period t. $\alpha$ and $\beta$ are parameters for risk aversion and loss aversion, respectively.

This formulation is a variation of the value function introduced in prospect theory (Tversky & Kahneman, 1992). Based on a comprehensive review of empirical evidence on parameter values (Camerer & Ho, 1994; Tversky & Fox, 1995; Wu & Gonzalez, 1996), we select $\alpha =0.85$ and $\beta =2$, which are widely supported across studies.

4.1.3. Habit Formation

In dynamic consumption-saving decisions, habits form endogenously based on past consumption. Empirical studies show that consumption utility depends on both current and past consumption (Carroll et al., 2000; Fuhrer & Klein, 1998; Marshall, 2005). Moreover, habit growth slows asymptotically (Lally et al., 2010). To capture this, we modify the habit formation model of Carroll (2000) to incorporate diminishing habit growth:2

$$h_t=\overline{y}\times {\left({\displaystyle \frac{\lambda \times h_{t-1}+(1-\lambda )\times c_{t-1}}{\overline{y}}}\right)}^{\varphi },$$

(3)

where $c_t$ and $h_t$ denote the levels of consumption and habit at time t, and $\lambda$ and $\varphi$ are parameters. We choose $\varphi$ = 0.85, which implies moderate concavity.3 Again, we divide by $\overline{y}$ to impose homogeneity, yielding relative values for consumption and habit.

4.2. Treatment Conditions

4.2.1. Baseline

In our baseline setting, one life cycle consists of fifteen consecutive consumption-saving decisions, where the first ten periods represent the working life and the last five constitute retirement. Using this setting, we implement a 2 × 3 experimental design where (i) participant income during the working life is either deterministic or stochastic, and (ii) participants have the choice among different saving mechanisms.

4.2.2. Deterministic vs. Stochastic Income

We implement two variants of participants’ working income, $y_t$: (i) deterministic income and (ii) stochastic income. In treatments with deterministic income (Det), participants receive 100 experimental currency units (ECU) in each of the first ten periods. This is commonly known. In treatments with stochastic income (Stoch), the per-period income is randomly drawn from the set $\{80,100,120\}$ with equal probabilities. The random draws in each period are independent of the draws in any other period. This income structure was completely revealed to the participants during the introduction of the experiment and therefore common knowledge. To control for path dependence but still keep observations comparable, we randomly generate two income paths (Path 1 and Path 2) before conducting the experiment. Half of the participants in stochastic income treatments faced Path I in their first and Path II in their second life cycle, and vice versa for the other half. This procedure is important to allow for the calculation of optimal behavior conditional on the actual realization of the income stream.

Using the life-cycle model outlined above, we calculate the optimal saving and consumption paths, which serve as a benchmark for evaluating the participants’ decision making. We solve the optimization problem in equation (1) using backwards induction, allowing us to derive consumption paths under both deterministic and stochastic income conditions. This benchmark helps assess how closely the participants’ behavior aligns with optimal decision making in the presence of behavioral constraints.

Figure 1 illustrates the optimal absolute consumption paths for both deterministic and stochastic income conditions (for more information on differences between the two stochastic paths, please check

Table A1. Realized income paths This table reports the income paths that are realized for the participants in the respective treatments. In stochastic treatments, half of the participants faced stochastic path I in life cycle 1, resp. path II in life cycle 2; for the other half of participants, it was the other way around.

Treatment/Period	1	2	3	4	5	6	7	8	9	10	Sum
Deterministic	100	100	100	100	100	100	100	100	100	100	1000
Stochastic I	120	80	100	120	80	80	100	80	120	120	1000
Stochastic II	80	120	100	80	120	100	120	120	80	80	1000

in Appendix C). Despite minor differences, the optimal paths for both stochastic income scenarios remain relatively close to the deterministic path, indicating that uncertainty has limited effects on the theoretical benchmark for consumption.

For the given income paths, the optimal saving and consumption decisions are feasible throughout the experiment. Importantly, optimal savings exceed obligatory contributions, suggesting that from a rational planner perspective, neither mandatory nor voluntary saving mechanisms bind the participants’ choices. Consequently, any deviations from optimality observed in the experiment can be attributed to behavioral factors, such as loss aversion or habit formation, rather than institutional constraints.

4.2.3. Saving Mechanisms

Pension systems vary widely, particularly in the types of available saving mechanisms and the level of access to funds prior to retirement.4 However, many European systems share common features, including mandatory contributions to a pension account and the option of a voluntary savings account dedicated to retirement savings (Hinrichs, 2021). Our experiment aims to analyze these core elements in a simplified way (e.g., neglecting tax rules).

To do so, we implement three distinct institutional environments, each offering the participants different saving mechanisms. We summarize them in

Table 1. Treatment overview. A + symbol signals that a savings mechanism is available.

Session	Treatment	Income ${\mathit{y}}_{\mathit{t}}$ per Period (ECU)	Setting	Pocket Savings	Obligatory Savings	Voluntary Savings
1	S1Det	always 100	1	+
2	S2Det	always 100	2	+	+
3	S3Det	always 100	3	+	+	+
4	S1Stoch	80, 100 or 120	1	+
5	S2Stoch	80, 100 or 120	2	+	+
6	S3Stoch	80, 100 or 120	3	+	+	+

In each case, savings $s_t$ can be accumulated through one or a combination of the following mechanisms: pocket savings, obligatory savings and voluntary savings. To distinguish these combinations while avoiding any confusion with real-world pension systems, we will call them settings 1–3.

• Setting 1 (S1): All unspent income automatically becomes pocket savings ($p{s}_t$), which can be accessed at any time. Total retirement savings ${\sum }_{t=1}^{\tau }{s}_t$ equal $p{s}_{\tau }$.
• Setting 2 (S2): Participants must contribute 10% of their work life income each period to an obligatory pension savings account ($o{s}_t$), which cannot be accessed until retirement starts in Period 11. During the working phase, obligatory savings increase by 0.1 × $y_t$ per period. Participants can still accumulate pocket savings by spending less than their disposable income, i.e., up to 0.9 × $y_t$ per period. At retirement, total savings $s_{\tau }$ are the sum of pocket and obligatory savings: ${\sum }_{t=1}^{\tau }{s}_t=p{s}_{\tau }+{\sum }_{t=1}^{\tau }0.1y_t$.
• Setting 3 (S3): In addition to the obligatory and pocket saving mechanisms from S2, participants can also make voluntary pension savings ($v{s}_t$). Like obligatory savings, voluntary savings cannot be accessed before retirement. There is no interest advantage for holding funds in obligatory or voluntary accounts compared to pocket savings. Hence, total retirement savings are the sum of all three accounts: ${\sum }_{t=1}^{\tau }{s}_t=p{s}_{\tau }+{\sum }_{t=1}^{\tau }0.1y_t+{\sum }_{t=1}^{\tau }v{s}_t$.

4.3. Implementation

The experiment was programmed in oTree (Chen et al., 2016) and conducted at the WiSo Experimental Laboratory in Hamburg. We ran six sessions with a total of 180 student participants. Participants spent approximately 60 min in the laboratory. Each treatment consisted of five parts: (1) questions to test cognitive abilities; (2) the BRET task; (3) questions to control for understanding of the main experiment (one treatment); (4) two life cycles of this treatment; (5) a demographic questionnaire.

The cognitive abilities of the participants were measured using the memory span task proposed by Conway et al. (2005). Before running the main part of the experiment, we asked participants multiple-choice questions to see whether they understood the main features of the experiment (the habit formation process, the utility function, etc.). If participants answered incorrectly, they were given a warning to rethink their answers. After finishing the life-cycle decision task, participants went through a short questionnaire asking for information about their age, gender and educational background. After the experiment, participants were paid for their participation, receiving an average payment of 11 EUR (see Appendix B for detailed information).

To reduce the computational burden on participants, we provided them with a table displaying various combinations of habit and consumption along with the corresponding utility values. Additionally, at the decision stage, a calculator was available to compute utility based on the participants’ chosen input values. Before starting the experiment, we ensured that all participants fully understood the task through comprehension checks. Since the utility function is complex and decreases sharply when choices deviate from the optimum, participants who failed to grasp the task would experience significantly lower utility. After identifying outliers, we excluded five participants (out of 180) who clearly did not understand the task, resulting in 175 fully independent observations for our analysis. The sample size—approximately 30 individuals per treatment cell—conforms to conventions in similar laboratory-based life-cycle experiments (for a review, see Bachmann et al., 2023) and provides adequate statistical power to detect medium-sized treatment effects in a between-participants design (Cohen, 1988).

The external validity of student samples has been examined in several studies. While students may differ from general populations in baseline behavior, their relative treatment responses are often consistent with those of non-students. For example, Cleave et al. (2013) show that selection effects exist but do not substantially distort treatment effects. Fréchette (2015) similarly finds that students and professionals respond comparably to experimental manipulations, even when their absolute behavior differs.

Falk and Heckman (2009) argue that the primary value of laboratory experiments lies in identifying behavioral mechanisms, not in generating population-level estimates, and that student samples are appropriate for this purpose. This rationale is particularly relevant in our context, as life-cycle consumption–savings models presuppose substantial cognitive capacities for solving dynamic optimization problems. Student samples may thus provide a conservative test of behavioral biases under bounded rationality, since participants are arguably better equipped to understand and engage with abstract intertemporal decision tasks. In that sense, the experimental design offers a favorable benchmark for evaluating deviations from rational behavior.

5. Results

5.1. Sample Characteristics

Table 2. Distribution of characteristics in our sample.

Parameter	Description	Fraction	${\mathit{\chi }}^{\mathbf{2}}$
Gender	Female/Male	61%/39%	0.51
Education	High School/Bachelor/Master/PhD/Other	3%/50%/35%/11%/1%	0.40
Age	Below 20/20–25/25–30/Above 30	3%/56%/28%/13%	0.13
Cognitive abilities	Fewer than 4 correct answers/4–8/8–16	1%/13%/86%	0.39
Background	No /A bit/Some/Sufficient	89%/8%/1%/2%	0.64
Task Understanding	None correct/All Correct	18%/82%	0.32

summarizes descriptive statistics for our sample. There were more female than male participants, aged mostly between 20 and 30 years, and the vast majority of them hold a Bachelor’s or a Master’s degree. The background check reveals that only 2% of participants had already taken a course on pension decisions, whereas almost 90% did not have any prior specific knowledge in pension finance. A majority of participants (82%) successfully demonstrated their understanding of the experimental task at the first try in a quiz. Furthermore, most of the participants showed high cognitive abilities: 86% answered more than half of the logical questions correctly. We checked whether the distribution of these characteristics varies across treatments. Based on the results of a Chi-squared test, we found no significant differences across treatments with regards to gender, education, cognitive abilities, age of participants or their understanding of the experimental task (see Table 2).

5.2. Hypotheses Ia and Ib: Undersaving/Overconsumption

Figure 2 shows the average levels of consumption in each period across settings and life cycles together with the corresponding optimal consumption paths.5 On aggregate, we observe a (suboptimal) hump-shaped consumption pattern in all our treatment conditions in both the first and the second life cycles. Participants undersaved (overconsumed) during their working lives (periods 1–10), thus having to cut back on consumption during retirement. The tendency toward overconsumption decreased from the first to the second life cycle, indicating that the participants learned and adjusted their consumption choices toward the optimal path when the experiment was repeated.

To gain a more in-depth understanding, we calculate the total (cumulative) savings over the first 10 periods for each of the participants and analyze the averages across treatments (see

Table 3. Average savings at the end of working life across life cycles I and II (ECU).

	Deterministic Income				Stochastic Income
	S1Det	S2Det	S3Det	Opt	S1Stoch	S2Stoch	S3Stoch	Opt
Total	308	281	369	384	264	250	329	379
Std. Dev.	10.63	11.99	11.42	5.39	10.55	9.73	11.70	7.03

). In all treatments, participants had less savings at the end of working life than they optimally should, with the highest savings—closest to the optimum—in S3.

However, total savings at the end of working life are only one important factor to compare. Another question is how the savings accumulated over time. For example, if a participant started out with too high a level of consumption while savings were very low, she needed to save relatively more later, whereas the optimal strategy would have been to start by consuming more modestly and increasing consumption smoothly over time. Therefore, in Table 3, we also report the standard deviation of savings per working period for each of the treatments. In general, the level of savings in all treatments varied more than it should optimally. The variation of per-period savings was the smallest for the S1 when income was deterministic and for S2 when income was stochastic.

To support our graphical analysis, we report results from statistical tests in

Table 4. Statistical tests: Total savings (p-values).

		Deterministic Income			Stochastic Income
Test	Comparison	S1Det	S2Det	S3Det	S1Stoch	S2Stoch	S3Stoch
Mann–Whitney U	Observed vs. Optimal	0.07	0.00	0.63	0.00	0.00	0.02
Wilcoxon-Signed-Rank	Life cycle I vs. II	0.00	0.00	0.17	0.00	0.00	0.04

. A Mann–Whitney U-test allows us to analyze whether participants saved significantly less compared to the optimal path.6 We found that at the 5% level of significance, participants undersaved (overconsumed) before retirement relative to the optimal path in all treatments except for treatment S1Det, which is only slightly significant with a p-value of 0.07, and treatment S3Det, which is insignificant. Savings between the two life cycles are compared using a Wilcoxon-Signed-Rank test that shows that participants saved more in the second life cycle compared to the first in all treatments except for treatment S3Det.

To test for statistical significance we start with a regression explaining participants’ performance (as measured in total points achieved per life cycle) with dummy variables for Settings 2 and 3, as well as a dummy for stochastic income:7

$$\mathrm{Total}\mathrm{points}\mathrm{I}/\mathrm{II}\hspace{1em}=\hspace{1em}\alpha +{\beta }_1\times \mathrm{S}2+{\beta }_2\times \mathrm{S}3+{\beta }_3\times \mathrm{Stochastic}+\epsilon ,$$

(4)

where Total points I/II is the number of total points collected by the participant during Life cycle I (II); S2, S3 and Stochastic are treatment dummies for our treatment dimensions.

We run two specifications of the regression model for Life cycle I, for Life cycle II, and for the differences between the life cycles. The results of the regressions are reported in

Table 5. Total points collected—Life cycle I and II.

	Dependent Variable:
	Total Points I		Total Points II		Δ Total PointsI,II
	(1)	(2)	(3)	(4)	(5)	(6)
Constant	1111.259 ***	948.928 ***	1162.206 ***	1096.978 ***	50.956 **	148.050 ***
	(29.491)	(66.566)	(21.347)	(51.644)	(20.441)	(54.061)
Stochastic	−70.925 **	−70.772 ***	−59.611 ***	−61.741 ***	11.314	9.031
	(28.382)	(27.291)	(20.477)	(19.770)	(21.262)	(20.837)
Setting 2	−12.671	−28.050	2.983	−12.389	15.654	15.661
	(29.591)	(30.106)	(25.719)	(24.730)	(21.980)	(21.997)
Setting 3	−32.104	−45.677	8.199	−3.924	40.304	41.753
	(39.313)	(37.242)	(25.829)	(24.497)	(28.241)	(27.907)
Logic		15.134 ***		8.996 **		−6.137
		(5.311)		(3.678)		(4.215)
Female		−41.167		−67.969 ***		−26.801
		(29.121)		(20.213)		(22.920)
Observations	175	175	175	175	175	175
R2	0.032	0.101	0.048	0.133	0.015	0.043

Note: * p < 0.1; ** p < 0.05; *** p < 0.01.

. One specification includes only treatment dummies (columns (1), (3) and (5)) while the other also controls for participant characteristics (columns (2), (4) and (6)).8

For the first specification, the intercept in columns (1) and (3) corresponds to the total number of points collected under Setting 1 with deterministic income. With regard to Hypotheses Ia and Ib, we find no significantly higher or lower performance of Setting 2 or 3 in comparison to Setting 1 within this specification. An interesting question is what drives individual performance in our experiment. To this end, we augment the regression Equation (4) by cognitive ability and gender as additional explanatory variables, which have been found in the previous literature to affect the performance in similar tasks (columns (2), (4) and (6)). In line with previous studies, we observe that participants with relatively higher cognitive abilities earned significantly more points, and the intercepts in columns (5) and (6) indicate learning, i.e., participants performed better in the second life cycle. Surprisingly, we find women to perform worse in the repetition of the task.

While risk aversion is induced through the $\alpha$ parameter in our utility function and should not affect behavior in the deterministic condition, individual risk attitudes of participants may arguably affect their behavior in the stochastic treatments. To test for behavioral patterns relating to individual risk attitudes, we run all regressions with risk aversion as an additional control variable. We have tested and derived it individually for each participant by using the bomb risk elicitation task (Crosetto & Filippin, 2013). We neither find any significant effect of individual risk aversion nor do any of the other factors change markedly.

Table 4 shows that in one setting, S3Det, consumption seems to be closer to the optimum than in the other settings. We therefore refine our analysis and make two additional changes to Equation (4) (on top of the addition of Logic and Female dummies). First, we restrict the treatment dummies to a single dummy variable S3Det to compare this treatment to all others. Second, a visual inspection of results indicated that participants who performed worse showed higher variability in their saving behavior. To test whether smoothness in individual saving behavior indeed explains performance differences, we add a corresponding proxy variable. A natural candidate is the standard deviation of the marginal savings, i.e., of the increase in total savings in each period:

$$\begin{array}{c}\mathrm{Total}\mathrm{points}\mathrm{I}/\mathrm{II}=\alpha +{\beta }_1\times \mathrm{S}3\mathrm{Det}++{\beta }_2\times {\sigma }_{\mathrm{Marginal}\mathrm{savings}}+{\beta }_3\times \mathrm{Logic}+\hfill \\ \hfill +{\beta }_4\times \mathrm{Female}+\epsilon .\end{array}$$

(5)

The results in

Table 6. Total points collected—Life cycle I and II using Equation (5).

	Dependent Variable:
	Total Points I		Total Points II
Constant	1253.44 ***	1136.03 ***	1207.71 ***	1128.50 ***
	(33.164)	(74.812)	(27.118)	(58.04)
S3_Deterministic	46.38 **	37.98 *	24.75	11.90
	(20.47)	(20.39)	(20.85)	(20.42)
St.deviation_marginal savings	−10.91 ***	−10.44 ***	−5.106 ***	−5.20 ***
	(−1.91)	(2.04)	(1.56)	(1.54)
Logic		8.92 *		9.20 **
		(4.84)		(3.80)
Female		−9.99		−60.73 ***
		(26.84)		(19.92)
N	175	175	175	175
R-squared	0.293	0.311	0.084	0.161

Note: * p < 0.1; ** p < 0.05; *** p < 0.01.

show that participants earned significantly more points in treatment S3Det, roughly 3.7%. This effect disappeared in the second life cycle. We also find that the smoothness of savings is indeed a highly significant explanatory variable. The smoother the savings path (low SD), the higher the performance.

Result I: Participants made suboptimal saving decisions in all treatments, except for the one with deterministic income and saving mechanisms setting 3. They consumed too much before retirement and consequently did not have sufficient money to sustain their utility level after retirement. In all treatments, participants saved more when the task was repeated. Therefore, we accept Hypothesis Ia for all treatments except for S3det, and we accept Hypothesis 1b for all treatments.

5.3. Hypotheses IIa and IIb: Income Uncertainty

In order to assess Hypotheses IIa and IIb, we revisit Table 5. We find significantly negative coefficients for the stochastic treatment dummy in both life cycles. Figure 2 shows clear overconsumption during the working life. This left only a little to save, and these savings were not sufficient to secure a high utility path when negative income shocks occurred. We will present more detailed information about the time structure of savings in the next section. We conclude that participants performed generally worse when income was stochastic.

Result II: We found that participants achieved lower utility when income was stochastic. Therefore, we reject Hypothesis IIa and accept Hypothesis IIb.

5.4. Hypotheses IIIa and IIIb: Pension Systems/Saving Mechanisms

Optimal saving decisions are essential in real-world pension planning and so they are in this experiment. We have shown in Section 5.2 that the participants behaved non-optimally in all settings except for S3Det. In this section we analyze their savings in more detail. Figure 3 presents the means of marginal savings for each treatment during the working life and compares them to the optimal marginal savings. Note that differences observed across the treatments cannot be explained by individual rationality, as the optimal consumption and savings paths are feasible in all treatments.

We find that savings in S1 and S2 do not differ much over time. There was a tendency of participants to save more in S1 at the beginning (first two periods) and at the end of the working life (last three periods). This, however, did not lead to significant differences in total utilities, as we see in Table 5. For S3, when a voluntary saving mechanism was available, we observe higher savings (closer to the optimum) in all periods in the deterministic as well as in the stochastic income treatments compared to the other settings.

Depending on the setting, different saving mechanisms were available. This calls for a more thorough investigation into the use of the additional saving mechanisms available in Settings 2 and 3, respectively. In order to understand potential substitution dynamics, we analyze the structure of savings in each treatment. Figure 4 and Figure 5 illustrate graphically the reason for the differences between setting and the other two settings. We find that participants saved almost the same total amount in S1 and S2. In S2, they reduce their pocket savings (blue) approximately by the amount they were obliged to save (red). Hence, compared to S1 (pocket savings only), the main effect of introducing the mechanism of obligatory savings only crowded out pocket savings. However, introducing voluntary pension savings as a self-commitment mechanism led to significantly higher total savings despite their illiquidity relative to pocket savings. In the settings where the voluntary (dedicated) pension saving mechanism was available (green), total savings increased because of a large amount allocated to voluntary pension savings.9 To summarize, we find a crowding-out effect between obligatory pension savings and pocket savings. In contrast, the availability of voluntary pension savings increased total savings significantly.

Another observation from Figure 3 is that in the case of stochastic income (right-hand graph), participants adjusted their savings asymmetrically to income shocks. In periods 6 and 7, income shocks occurred in both paths of the stochastic income treatments: a negative shock in period 6, followed by a positive shock in period 7. As a reaction to the negative income shock in period 6, the observed reduction in savings was of about the same magnitude as the corresponding reduction on the optimal paths. This means that participants still undersaved, but the extent of undersaving remained roughly constant relative to the optimal savings path. On the other hand, when a positive income shock occurred in period 7, participants failed to adjust their savings accordingly and saved about the same as in the periods without income shock (periods 3–5). This effect was far less pronounced for Setting 3.

A third observation is that participants’ first-period saving decisions were quite close to the optimal values, with some oversaving observable especially in S3. Despite this cautious start, the effect of overconsumption set in quickly in settings 1 and 2 and prevented participants from saving enough already as early as in period 2 (3) in the stochastic (deterministic) income case. In S3, this effect set in somewhat later, i.e., in period 4 (5) in the stochastic (deterministic) income case.

Result IV: We find savings are not necessarily higher in the presence of an obligatory contribution mechanism than in its absence, whereas the additional availability of voluntary savings makes participants save more for their retirement. Therefore, we reject Hypothesis IIIa and accept Hypothesis IIIb.

6. Conclusions

This paper has examined the effectiveness of institutional saving mechanisms in shaping retirement saving behavior under bounded rationality and income uncertainty. Using a novel life-cycle experiment, we analyzed how individuals make intertemporal consumption and saving decisions when facing deterministic or stochastic income and when subject to different combinations of mandatory and voluntary saving rules. To ensure comparability and tractability, we induced a utility function that incorporates key behavioral features relevant for pension decisions—loss aversion and non-linear habit formation.

Across all treatments, we find that participants tend to overconsume in the early stages of the life cycle and undersave for retirement, resulting in substantial utility losses in the retirement phase. This tendency is most pronounced in the baseline condition without any commitment mechanism. The only setting in which participants approximate the optimal consumption path is the one combining deterministic income with both obligatory and voluntary binding savings. This finding suggests that a mix of structure and choice can improve retirement outcomes but only under conditions of income stability.

Contrary to the precautionary savings argument, we do not observe higher saving under stochastic income. Participants exposed to income risk perform consistently worse than those with deterministic income. They neither accumulate precautionary buffers nor respond effectively to positive or negative income shocks. However, this result is consistent with the theoretical benchmark in our setting, which features moderate risk aversion and relatively low income volatility. Hence, the absence of precautionary savings in our data aligns with the optimal strategy under these conditions, though this may not generalize to environments with higher uncertainty or more risk-averse preferences.

The analysis of saving structures shows that obligatory savings alone are ineffective in raising total saving, as participants offset them by reducing voluntary contributions. In contrast, voluntary but binding savings significantly increase overall saving—but only under deterministic income. Under stochastic income, these mechanisms lose effectiveness, likely due to increased planning complexity. This suggests that while commitment devices can support savings, their success depends on the broader decision environment. Income predictability may be a prerequisite for individuals to benefit fully from such instruments.

While our experiment offers new insights into savings behavior under different institutional and income conditions, it has several limitations. First, the experiment was conducted with a student sample, which—despite being relatively homogeneous and cognitively able—limits external validity. Future studies should examine more diverse populations, particularly older individuals or those with lower financial literacy. Second, our experimental design deliberately balances internal and external validity. To isolate the behavioral effects of institutional saving mechanisms, we abstracted from several real-world features of pension systems—such as employer matching, taxation, and annuitization. This simplification enhances causal identification but necessarily limits the external realism of the setting. Moreover, we did not examine commitment devices in isolation, as purely voluntary binding mechanisms do not exist independently in any pension system we are aware of. Instead, we studied combinations that reflect institutional practice, which limits our ability to disentangle the effect of mechanism type from the number of mechanisms available. Nonetheless, this design choice strengthens the policy relevance of our findings by reflecting realistic institutional configurations. Third, income volatility in our stochastic treatment was moderate and systematic. Different degrees of income risk or uncertainty could elicit different responses, including precautionary saving. Finally, the stylized nature of the experiment and the relatively short planning horizon may limit how well the experiment captures long-term behavior. These limitations suggest several avenues for future research. Field experiments or panel studies could test the robustness of our findings in real-world pension contexts. Varying the intensity of income risk, the nature of commitment mechanisms, small changes in the mechanisms and the role of defaults or advice could further clarify the boundary conditions under which individuals benefit from saving interventions.

Our findings can inform ongoing debates in pension design. First, voluntary but binding retirement accounts—such as third-pillar products with restricted access—can help individuals improve retirement readiness, provided the income environment is stable and transparent. Policymakers may consider introducing or expanding retirement accounts that restrict early withdrawals while allowing individuals some level of choice in their contributions. Such a mechanism could stimulate individuals to save effectively for their retirement. Second, policymakers should recognize that behavioral interventions alone may fail under income volatility. Complementary policies aimed at improving earning predictability or providing stabilizing income floors may be necessary for individuals to realize the benefits of long-term saving tools. Third, our evidence reinforces the value of financial education and experiential learning. Individuals improved significantly in their second life cycle, regardless of treatment. This reemphasizes the need for policy interventions that simulate decision making such as interactive and gamified savings simulators that could help individuals to make their retirement savings timely and wisely. Similarly, introducing financial education programs focused on teaching the basics of financial literacy at school and at work could help people better grasp the long-term implications of their savings decisions, especially in a stochastic income real-world environment.

Overall, our study highlights some of the potential and limits of behavioral design in pension systems. While institutional mechanisms matter, their success depends on the interplay between individual capabilities and environmental features. Designing effective retirement systems thus requires attention not only to incentives and defaults but also to the cognitive and informational conditions under which people make long-term financial decisions.