- Original article
- Open Access
A policy for the size of individual unemployment accounts
© The Author(s). 2018
- Received: 6 March 2018
- Accepted: 22 August 2018
- Published: 6 September 2018
Individual unemployment accounts (IUAs) attenuate the moral hazard attached to unemployment insurance. However, the available literature provides no policy recommendation about what percentage of the contributions should go to IUAs. We propose criteria of actuarial neutrality and use a simple job search model to argue that a sizable proportion of the contributions could go to IUAs without changing benefits and contribution rates, and therefore not negatively affecting well-being. We derive this result from a model, first, and then use simulations to show that it also holds in more realistic settings and different labor market dynamics.
- Social security
- Unemployment insurance
- Unemployment accounts
- Moral hazard
The main role for unemployment insurance (UI) is to attenuate liquidity constraints, a market failure that plays against some individuals; while many individuals can save and borrow to smooth their consumption, some cannot when facing unemployment shocks. Holmlund (2015) and Kyyrä et al. (2017) provide a detailed discussion, including the motivation for state rather than private provision of UI.
However, UI introduces by itself a market failure called moral hazard: the unemployed do not take into account the alternative use of the resources when deciding on their labor behavior. Basically, the UI acts as a subsidy for the price of leisure and is distortionary, making unemployment more prevalent than it should be. Most of the numerous empirical literature finds support for the existence of moral hazard attached to UI; a detailed review can be found in Schmieder and Von Wachter (2016). Indeed, most UI systems include several mechanisms to fight moral hazard: a maximum length of unemployment benefits, shrinking the benefit rate as the unemployment spell gets longer, and requiring proof of job search, among others.
In this context, a new mechanism to fight moral hazard emerged around the year 1990: the introduction of a self-insurance component, by means of individual unemployment accounts (IUAs). In this mixed system, an X% of contributions goes to the workers’ IUA, which pays for his/her unemployment benefits, until either they are exhausted (and the risk-pooling component starts to pay the benefits) or the worker finds a job. Any remaining funds from IUAs are withdrawn at retirement or before. The key idea here is that workers experience less moral hazard during the self-financing stage of their unemployment spells while all the consumption smoothing properties are preserved.
This setting has been attracting the attention of developing countries; many are introducing their first UIs, amidst the particularities of their labor markets and institutions (Vodopivec 2013; Robalino and Weber 2013), and the mixed system is already present in Argentina, Austria, Brazil, Chile, Colombia, Ecuador, Jordan, Mauritius, Panama, and Peru.1
Now, policy makers need to set the size of the IA component in their UI systems, but from the academic literature, it is not clear what the right size of the IA component is. This study is the first to propose a right size.
Feldstein and Altman (1998), “the” foundational article for IUAs, perform a simulation based on data from the USA; they conclude that, under different simple scenarios for the impact in moral hazard, UI-associated taxes could be mostly transformed into IUAs. And some articles discuss a wide range of topics related to UI and IUAs in developing countries (notably Robalino et al. 2009, Vodopivec 2013, and Sehnbruch and Carranza 2015). But none of those authors propose a size recommendation for policy makers.
Theoretical models of well-being, based on economic behavioral models applied to mixed systems (Orszag and Snower 2002, Bovenberg and Sørensen 2004, and Jongen 2009 are the available ones), provide a framework to set a value for the optimal X; however, as is also the case for risk-pooling UIs, this theoretic analysis is still somewhat far from policy recommendations about the parameters of the system. Indeed, current UI policy decisions are based mostly on standards and best practices.
A key advancement in the literature is the optimal benefit formula proposed by Chetty (2006), stemming from the work of Baily (1978), who proposed a reduced-form expression for the optimal benefit level based on observable elasticities (rather than a deep primitives).
We explore a standard job search model and found a simple conceptual formula for the actuarially neutral X and then use simulations to add more realistic properties (like risk-heterogeneity across wage levels). We focus on job creation moral hazard, leaving job termination moral hazard for future research2; job creation/termination stands here for all the dynamics underlying the beginning/ending of job relationships.
The only empirical evidence regarding the moral hazard effect of a mixed system is Reyes et al.’s (2011) comparison of aggregated labor market behavior of IUA-financed versus non IUA-financed unemployed individuals in Chile. Nagler (2013) found employment duration effects from the introduction of the UI systems in Chile, although it is not clear what is the pooling-versus-mixed component of this effect. For our study, we take a conservative position, assuming that UIs’ moral hazard is low (setting a − 0.3 “job creation elasticity with respect to UI benefits”), which we discuss after presenting the model.
We first discuss the model and then the simulations.
Define the actuarially fair contribution rate as the one equating expected contributions with expected spending in a stationary setting. Define X as the percentage of the actuarially fair contribution rate that goes to IUAs. The objective of our methodology is to determine the “actuarially neutral X,” i.e., the X where the introduction of IUAs (in an otherwise pure risk-pooling system) has no actuarial impact on the system.
2.1 The model
The model is based on a standard setup (see a complete review on Rogerson et al. 2005): workers contribute an actuarially fair rate c of their wages to UIs and randomly terminate their labor relationships at a job termination rate that for simplicity is set fixed at λ. The actuarially fair level of c is defined as the level where the expected inflow equals the expected outflow of cash into the system. In the case of unemployment, workers receive a replacement rate of b of their previous wage, without time limit, until they start a new labor relationship, which depends on receiving a job-wage offer whose present value is superior to the present value of not accepting it. From there, a job creation rate emerges. This rate can be further explored on the grounds of the individual’s search effort and, relatedly, at the rate of arrival and distribution of job-wage offers. These parameters can be further extended to add worker-firm matching and bargaining, all common elements in this literature. For the purposes of this study, however, it suffices to summarize the job creation behavior in two single parameters: α, the job creation rate before the introduction of IUAs, and F, the proportional increase in α during the self-financeable stage of the unemployment spell. F captures the effect of IUAs on moral hazard. We assume no behavioral impact of IUAs outside the self-financeable stage of the unemployment spell. Administration costs are not included in the model.
Since λ is exogenous, and we want to keep c constant, any actuarially neutral change must keep the same expected total cost per unemployment spell. Therefore, we focus on that expected cost.
Underlying Eq. 2, there are two opposite actuarial components: on one hand, unemployment spells are shorter and therefore cheaper, but on the other hand, a new benefit is added (the withdrawals from IUAs), making them more expensive. By the nature of the problem, as X grows, the second effect starts to dominate over the first one.
The actuarially neutral size of IUAs depends only on F, the percentage increase in the job finding rate during the self-financeable stage of the unemployment spell. It is not a function of job creation or termination rates, and therefore, it is not a function of average duration of employment or unemployment, nor is it a function of the level of benefits, and therefore, it is not a function of the risk-pooling UI actuarially fair contribution rate. Simply, if F lays between 20 and 40%, the actuarially neutral X lays between 17 and 29%. If F goes to infinity, i.e., everybody finds a job immediately after losing a job, the actuarially neutral X is 100%.
Figure 1 shows the case of F = 30%.
It is important to mention that even relatively large changes in the “job-finding behavior” will have little impact on the employment rate, because the unemployed are a minority; from there, the growth in total contributions associated with the introduction of UIAs could be extremely small. In our modeling for simplicity, we assume that total contributions stay the same regardless of X, and, along the same lines, our simulations show that they stay very constant, indeed.
In order to explore the actuarial balance in more realistic settings (maximum duration of benefits at 6 months, maximum and minimum level of benefits, involuntary/voluntary job termination ratio, withdrawals of funds from the IUAs only at retirement, and job termination rates that change as the employment spell progress), we code a simulation of a stable group of 5000 individuals. We assume that the job creation rate is constant across the UI covered stage.4 We add a 5% monthly change in the job termination rate (as the employment spell progresses, following one of the few international articles in this topic: Hobijn and Sahin 2007, which includes developed countries only, though). We assign lifetime wages randomly from the observed wage distribution in the formal labor market of Indonesia (taken from the Indonesian Labor Market Survey, Sakernas). As the maximum and minimum level of benefits, we use the value of the sixth and first decile of income, without attaching behavioral changes to them. We do not try a decaying rate of benefits because the empirical literature gives them a small role in labor behavior.
The simulations start with a risk-pooling UI system and everyone with an employed status. The simulation loop is applied until it reaches its stationary level. This level is reached at about 300 months (25 years) after the introduction of IUAs. The same seed was used for all the trajectories of random numbers. We report the actuarial balance, which is the average difference between the inflow rate per worker (namely the contribution rate) and the average outflow per worker (total benefits and withdrawals from IUAs, over total wages).
For the following results, du is set to 6 months and the duration of employment (the inverse of λ) is set to 60 months. A sensitivity analysis covers other values.
Figure 2 shows that the predictions from the simple model, regarding the actuarially neutral X, holds well in more realistic settings. If F is 30%, for example, the actuarially neutral X is approximately 23%. Figure 2 shows the same inverted U shape as Fig. 1, because at low levels of X, the positive impact (less moral hazard, i.e., more job creation) is greater than the negative impact (withdrawals of money from the IUAs), but at higher levels of X, the opposite is true.
In Fig. 2, it is possible to see the direct implication from Eq. 3: the higher the F, the higher the actuarially neutral X, i.e., the higher the impact of IUAs on moral hazard, the higher the amount that can be directed to them without causing an actuarial imbalance in the system. Regarding an empirical value for F, the literature does not have a clear estimation of elasticities of unemployment duration to UIAs’ benefits, but the more “classical” case of elasticities of unemployment duration to UI benefits lie in the [0.3–1] range (Kyyrä et al. 2017; Schmieder and Von Wachter 2016). For our study, under any discounting of future benefits, F should be smaller than the elasticity to UI benefit cuts; as a “base case” scenario, F = 0.3 could be sufficiently lower than the elasticity to UI benefit cuts, which as a base case could lie around 0.7. With F = 30%, then, even at X = 40%, the actuarial imbalance will be low: 0.15% of wages.
It is interesting to note that heterogeneity in labor risk rates could have a low impact on the finances of the UIA system, because workers of high performance (low risk of job destruction and high risk of job creation) will be at the same time more costly (because they withdraw larger amounts from their UIAs) and less costly (because the higher the UIAS, the lower the moral hazard and so the lower the spending in unemployment benefits) than workers of low performance. From there, an association between wages and performance will also have a low impact on the finances of the systems, to the extent that benefits are indexed to wages. We replicated the calculus behind Fig. 2 but assuming a linear relation between wages and hazard rates such that higher wage quintile has about 2.5 (0.5) times the employment (unemployment) duration of lower wages, and results are closely the same.
We also replicated the calculus behind Fig. 2 but assuming that withdrawals of funds from the IUAs have to wait until retirement, instead of occurring right after the end of each unemployment spell (as the model assumes). Results barely change. As withdrawals are referred until retirement, (A) more of the UI benefits are paid out of IUAs and less out of the risk-pooling component, but those effects counteract each other almost perfectly, and (B) while withdrawals are lower, the influence of lower moral hazard is longer, so IUAs are increased and then withdrawals increase; those effects counteract each other almost perfectly.
As unemployment insurance (UI) systems slowly spread throughout the developing world, the issue of moral hazard gains attention and so does one relatively new mechanism to fight it: individual unemployment accounts (IUAs). The available literature, however, provides no policy recommendation about what percentage of the contributions should go to IUAs. We propose here an “actuarially neutral” rule and use a simple job search model to argue that even if the “lower moral hazard” effect of IUAs is low, even a sizable UIA component (like 40% of the contributions, for example) will fight moral hazard while preserving the original contributions and benefit rates. This result holds under our simplified model, although we use simulations to add more realistic assumptions.
It is interesting to note that heterogeneity in labor risk rates could have a low impact on the finances of the UIA system, because workers of high performance will be at the same time more costly (greater withdrawals from UIAs) and less costly (less UI benefits). From there, an association between wages and performance will also have a low impact on the finances of the systems, to the extent that benefits are indexed to wages.
Our model assumes early withdrawals of funds while the common rule of at-retirement withdrawals is explored by simulations (most authors, like Feldstein and Altman 1998 and Stiglitz and Yun 2002 analyze withdrawals at retirement, although some countries allow early withdrawals). The actuarially fair contribution rate of those two options appeared as basically the same. Therefore, if it happens that early withdrawals have a greater “low moral hazard” effect, then this policy could be a better alternative than previously thought (in our modeling, early and at-retirement configurations have the same effect on moral hazard).
Our study has some important limitations that are left for future research. First, there is almost no evidence regarding the impact of UIAs on behavior. In our base case scenario, we assume the impact is half of the impact of UI on behavior, for which there is much available literature, but future empirical research could focus on the distinctive impact of UIA and UI systems. Also, we assume independence between the size of the UAIs (the percentage of the contributions that go into IUAs) and the level of benefits, but the social planner objective function should jointly include both the level of benefits and the size of UIAs. Chetty’s (2006) optimal benefit formula, for example, suggests that larger sizes (and thus lower moral hazard) are associated with greater benefits. Moreover, we do not add heterogeneity, other than random components in the model and simulations. We also focus solely on job creation moral hazard.
Chile introduced in the year 2002 the first mixed system in the world (Acevedo et al. 2006, describe the introduction process). Ferrer and Riddell (2009) describe outcomes from mixed systems across Latin American countries.
The evidence regarding risk-pooling UI’s effect on job termination is rather limited (Tatsiramos and van Ours 2012) but points to the existence of such effects.
Take Equation 25 on Rogerson et al. (2005) and express the rates as the inverse of the average durations.
The literature discusses two effects of UI exhaustion which has two components (Schmieder et al. 2012, 2016; Card et al. 2007): (A) leaving the unemployment state to the employment state, where a small spike is found, and (B) leaving the UI administrative records without moving to the employment state, where a big spike is found. Therefore, the actual job creation rate (the risk of leaving unemployment towards employment) could be more or less constant during the UI-covered stage.
Without IUAs in the model, unemployment is about 9% and, in the highest IA case, with X = 100%, is about 6% (setting F at 30%).
The authors thank Truman Packard and Milan Vodopivec for many useful discussions and Juan Tapia for revising the final version. The authors would also like to thank the anonymous referee and the editor for the useful remarks.
Responsible editor: Denis Fougère
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