The Impact of the Retirement Decision and Demographics on Pension Sustainability: A Dynamic Microsimulation Analysis

: This paper investigates how retirement decisions, in interaction with demographic changes, impact on pension system sustainability. To do so, we introduce behaviour into a dynamic microsimulation model applied to the Spanish case. Specifically, the retirement decision is modelled using a reduced-form survival model that provides information on retirement hazards, which are then used to calculate times to retirement within the microsimulation model. This model allows us to account for behavioural responses. For example, the behavioural reaction to the 2011 reform improves pension system sustainability, despite individuals opting to retire later to obtain higher benefits. The positive effect (increase in contributions and reduction in time spent in retirement) is greater than the negative effect (increase in pension levels). Additionally, the model allows us to show how the positive effects of the education transition and higher rates of female and older worker participation contribute to reducing the negative impact of population ageing.


INTRODUCTION
Developed countries are facing a population ageing process that threatens the sustainability of their social protection programmes and their governments are seeking ways to uphold their welfare states against a backdrop of rising health and long-term care expenditure and an increasing pension bill.
According to the European Commission (2012) the demographic old-age dependency ratio (people aged 65 or above relative to those aged 20-64) is projected to increase from 28 to 58 in the EU as a whole over the period 2010-60. In this respect, Spain is an extreme example of an abrupt population ageing process, with an old-age dependency ratio rising from 27 to 61 , albeit projected to occur a little later than in other European countries. Sustainability problems are worsened by the fact that the majority of welfare states -among them Spain-are based on a pay-as-you-go (PAYG) nancing system, which means public transfers will be sustained by a proportionally smaller cohort of workers. This is especially true of pension systems in which usual bene ts are covered by raising an earmarked tax (social security contributions).
Concerns for reforms to make pension systems sustainable in the long-term are fully justi ed. Such proposals vary from the complete restructuring of the system -such as making the switch to a true or notional capitalisation system-to marginal adjustments in its legal parameters. 1 Given the expected increase in the ratio of pensioners to contributors, all proposals involve raising contributions and/or reducing pensions. Yet, there remains some scope for improvements on the demographic side. For example, a delay in the retirement age in line with increasing life expectancy is frequently proposed as a way to both boost contributions and reduce expenditure. Other options for raising contributions in a context of an increasingly scarce labour force could involve an increase in fertility (which would have a long-run impact) and migration (with a short-run impact), and an increase in female workforce participation. Finally, the fact that workers will be more educated in the future may also contribute to boosting sustainability. However, we should not ignore the fact that individuals react to reforms, and their behavioural responses may counter to some extent their e fects. For this reason, models are needed to capture the determinants of the retirement decision, since their incorporation in pension simulation models can improve predictions about long-term macroeconomic outputs. Likewise, the design of reform measures requires sound analytical tools. These tools need to be dynamic -to explicitly model lifecycle decisions-and they need to incorporate both macro and micro perspectives. For example, simulation models have recently been developed thanks to the growing availability of high quality databases and computing tools (see Spielauer, 2011, for a description of microsimulation in the social sciences) and the use of microsimulation models in policy evaluation and, especially, pension reforms, has become widespread (see Borella & Moscarola, 2010;Buddelmeyer, Freebairn, & Kalb, 2006;Keegan, 2011;Stensnes & Stølen, 2007;Van Sonsbeek, 2010, for recent examples).
Here, we introduce behavioural responses into a non-behavioural dynamic microsimulation model applied to Spain (DyPeS, see Patxot, Solé, & Souto, 2017). 2 Speci cally, we evaluate how individuals modify their retirement decision in response to the 2011 reform. 3 This decision is estimated using a reduced-form model and the estimated hazards are implemented into the model to analyse the sustainability of the pension system during the demographic transition. The resulting model is one of very few behavioural dynamic microsimulations available. As explained in Section 4, there is a tradeo f between the explanatory power of the econometric analysis provided by the retirement behaviour literature and the feasibility of implementation in behavioural microsimulation models.
The model enables us to identify which e fects of a reform are related to the reactions of individuals to regulatory changes (see O'Donoghue, 2001, for a de nition of behavioural models vs. statistical simulation). Moreover, it allows us to measure the impact of changes concomitant to the demographic transition (for instance, enhanced level of educational attainment and increased female participation) on sustainability.
The paper is organised as follows. Section 2 describes the institutional context of the Spanish pension system. Section 3 presents the retirement decision model and the econometric techniques employed.
Section 4 presents the dynamic microsimulation model. Results are presented in Section 5 and, nally, Section 6 concludes.

THE INSTITUTIONAL CONTEXT
The public pension system is the main component of Spain's welfare state. In 2014 spending on the system represented 10.5 of GDP compared to an OECD mean of 7.9 . Besides a non-contributory, means-tested system (a basic and assistance scheme), the pension system is primarily contributory. It is organised on a PAYG basis and includes pension bene ts -retirement, disability and survivalfor those who meet eligibility requirements for age and past contributions to the system. The system comprises a general regime and several special regimes for speci c occupations -self-employed, agriculture, sea, coal mining. Moreover, in the general regime there are di ferent contribution groups, mainly dependent on the workers' level of quali cation. 4 Retirement pensions are the main expenditure, representing around 7.4 of GDP. The bene t depends on the worker's past contributions, which makes the system contributory -or Bismarckianto some extent. Speci cally, the initial pension (IP ) is determined by applying a percentage (p), depending on the number of years of contribution (n), to the regulatory base (BR), de ned as the average contribution base in the past. Moreover, a penalty for early retirement (or a premium in case of delay) can also be applied (cc): Many partial reforms have been made since the system was introduced in 1967. Speci cally, parameters in Equation 1 have been modi ed to make the system more Bismarckian; yet, a fully contributory system has yet to be achieved. Moreover, retirement pensions (and contributions) are subject to upper and lower limits in the pursuit of equity but at the expense of its contributory nature. The latest major reform was implemented in 2011, and was aimed at reducing expenditure in a period of economic crisis characterised by a dramatic drop in contributions. Below, we describe the main measures contained in this reform: 5 (a) The general retirement age was delayed from 65 to 67, although it remained at 65 for those with long working careers, i.e., over 38.5 years of contributions.
(b) The penalty for early retirement and the premium for delayed retirement -cc in Equation 1were modi ed to encourage older workers to continue in the labour market.
(c) To boost the contributory nature of the system, the formula for obtaining the initial pension was modi ed: rst, the number of years of past contributions considered in BR rose from 15 to 25 and, second, the way in which past years of contribution were considered was changed by making p(n) in Equation 1 more linear, and by increasing the number of past years of contribution needed to obtain 100 of BR from 35 to 37.
Given the signi cance of the modi cations, a long transition (2013-27) was established before these reforms took full e fect.

THE RETIREMENT DECISION
Generally, individuals react to changes that impact their living conditions by modifying their decisions.
For example, they can change their behaviour in response to pension system reforms, by modifying their retirement decision to optimize their bene ts. Indeed, given that retirement choices re ect individual balances between present and future income, leisure and risk perceptions, they can be modelled within the theoretical framework of the life-cycle theory of consumption, based on utility maximization. This approach captures the impact of changes in the budget constraint on the retirement decision, given an individual's consumption and leisure preferences as re ected in the utility function. A full structural estimation of this model requires the explicit modelling of all these factors, which in turn implies strong parametric assumptions about these preferences. The approach has the advantage of a fording a clear interpretation of results, but it poses major challenges of feasibility. In this regard, the seminal work of Miller (1984), Pakes (1984, Rust (1987), andWolpin (1984) identi ed the conditions under which these dynamic discrete choice models were both feasible and relevant for solving key economic questions.
An alternative is to use a reduced-form approach -the one opted for here, primarily, because of the nature of the data employed. We use a rich administrative dataset for pensions and work histories, including their (gross) wages and bene ts received. Using a reduced-form model with this rich dataset allows us to obtain a precise picture of reactions to nancial incentives. These administrative records are the result of the interaction between individuals' preferences and constraints, on the one hand, and rms' decisions, on the other. In this sense, the dataset does not capture heterogeneity in preferences and beliefs, but allows us to readily capture detailed changes in nancial incentives and budget constraints. Moreover, a reduced-form hazard model allows for sudden shocks (such as, changes in earnings) to be included in the analysis more readily than is the case with a structural model. Finally, and most importantly, the need to implement the results of the estimation in a microsimulation tool requires a more exible speci cation. The parametric assumptions regarding preferences, beliefs and heterogeneity required in a structural analysis are not easily extrapolated to future periods. In discussing these methodological issues, Stock and Wise (1990) discuss the gains in applicability of both approaches and derive a simpli ed structural model with the advantages of reduced-form models (the option value model). The potential applications of this model are numerous (Casey et al., 2003;Gruber & Wise, 1999, 2005.
We model retirement behaviour by introducing nancial incentives, employing a survival framework.
In line with previous research for the US (Baker, Gruber, & Milligan, 2003;Coile & Gruber, 2001;Gruber & Wise, 2005), survival estimates highlight the role played by the economic incentives for retirement implicit in the pension scheme. Speci cally, in the reduced-form approach retirement hazard is estimated as a function of individual characteristics (age, education, etc.) and retirement incentives.
Still, reduced-form models in form of discrete response or hazard models can be traced back to a utility model as shown by Stock and Wise (1990). Changes in income re ect changes in utility (avoiding to model consumption), while preferences for leisure can be captured by variables expressing impatience to retire. Including this reduced form retirement behavioural equation in our microsimulation model allows us to de ne an 'optimal time of retirement' scenario coherent with current regulations and to compare it with the 'non-behavioural' scenario.
To de ne the incentives for inclusion in our behavioural model, we take as our starting point recent studies for Spain that estimate the e fects of Social Security incentives using the same dataset as the one employed herein (that is, the MCVL). Sánchez, Argimón, Botella, and González (2013) estimate Social Security Wealth (SSW) -the present net value of net bene ts received from the pension system; Social Security Accrual (SSA) -the discounted change in SSW when postponing retirement one year; and the Peak Value (PV), which compares this year's SSW with the maximum SSW that can be attained in the future. The authors report that the coe cients of all three social security variables are statistically signi cant with the expected sign. However, the results regarding the e fect of measures related to SSW appear somewhat mixed for Spain. It is well known (Gruber & Wise, 2005) that SSW might be endogenous and it may not be possible to separate the e fects of nancial incentives and the taste for work -both interacting with age. In this respect, several studies (based on a preliminary experimental version of MCVL) report the limited e fect of retirement incentives on the retirement decision, suggesting that age is the main determinant (Boldrin, Jiménez-Martín, & Peracchi, 2004;Jiménez-Martín, 2006). More recently, García-Pérez, Jiménez-Martín, and Sánchez-Martín (2013) extended the analysis of the MCVL and their results show that, when incentives are properly de ned and problems such as individual heterogeneity are taken into account, incentives have a strong impact on labour market decisions, especially on retirement decisions. We estimated a similar model to that used in Sánchez et al. (2013) and found that the PV has no impact on the probability of retirement (see Appendix A for more details). Thus, in our microsimulation model, we opted to include a set of incentives that are closer to those in García-Pérez et al. (2013). The latter authors specify a model that only considers the current pension bene ts of retirees and changes in their pension rights. We take a similar approach by considering pension rights and the di ference between the expected pension at its The other variables included in our model (apart from retirement incentives) are: level of education, labour status (employed/unemployed), an indicator as to whether the individual is a recipient of unemployment bene t, period of time to obtain the maximum pension, age on reaching the maximum pension, replacement rate, and a time counter that seeks to capture impatience. We also include a proxy for the state of the business cycle (unemployment rate). We expect nancial incentives and variables related to taste for work and impatience to interact, as is commonly assumed by economic theory: people seek to maximize their income, but they prefer leisure to work. The time dimension operates discounting future gains in terms of both leisure time and money (people are assumed to be impatient). The extent of interplay between these contradictory forces and the possible di ferences by group (education and gender, mainly) are the focus of our analysis. People aged over 58 and ful lling the eligibility conditions compute their retirement hazards monthly, and the covariates that determine the retirement decision are also updated monthly. First, individuals are assumed to claim their pension bene t according to a survival model that includes personal characteristics and business cycle indicators, but not nancial incentives (non-behavioural model). These variables are age, age squared, education level, last wage, a dummy variable that takes a value of 1 during the rst year the individual is eligible and 0 otherwise and, nally, the unemployment rate. This set of variables seeks to capture all the factors involved in any retirement decision and under any regulatory framework. This means age, productivity issues and the individual's performance in the labour market, time preferences and business cycle considerations.
In both the behavioural and non-behavioural models, we estimate a piecewise constant exponential model in which the hazard is assumed constant within pre-speci ed survival time intervals but the constants may di fer for di ferent intervals. This kind of semi-parametric model is commonly used in a continuous time framework -the approach we adopt to exploit the richness of our dataset-to avoid the assumptions about the shape of the hazard function implied by parametric models. Then, the exponential model can be de ned by: where the baseline hazard rate theta is constant within each of the K intervals but di fers between intervals, X is a vector of variables ( xed or, if time-varying, constant within each interval) representing personal characteristics, working careers and macro-indicators that are relevant for our model, beta is the vector of parameters we wish to estimate, and t represents time. We use a monthly panel dataset covering the period 2005-10, derived from the MCVL. It includes all individuals eligible for retirement during this period, excluding those who retired due to collective agreements or forced to do so by regulation (unemployed who reach the minimum retirement age). Table 1 shows the results of the behavioural model. As expected, the retirement hazard increases with age (at a decreasing rate), but the most powerful e fect is that associated with the variable ' rst year of eligibility', which increases the hazard for both genders. This is consistent with the fact that between 55 and 60 of people (depending on the year considered) retire as soon as they can (via the "ordinary" retirement pathway). The unemployed and those receiving unemployment bene t tend to retire later.
As discussed, individuals are forced to retire (via the "ordinary" pathway) if they are unemployed at the legal retirement age. In our estimation we eliminated these enforced retirement events as they do not re ect real choices. Hence, the unemployed present in our sample are mostly people eligible for early retirement, observed before their ordinary retirement age. Variables related to nancial incentives behave as expected (see explanation above) and the e fects of the replacement rate (individual ratio of pension to last wage) and the minimum pension are especially strong. The e fect of the PV proxy is I J M (2018) 11(2) 84-108 92 also very strong in the case of women (we compute changes in one euro). These results are in line with those reported by García-Pérez et al. (2013), who show that greater accrued pension rights are, as expected, associated with lower re-entry rates and higher retirement rates. The e fect of the economic crisis (measured using the unemployment rate) is associated with delayed retirement for both genders. Men with higher education tend to remain less time in the labour market after becoming formally eligible for retirement (the same e fect is observed for women but it is not signi cant). In contrast, the less educated are more likely to be a fected by periods of unemployment and non-participation, above all during years of crisis. This e fect, combined with lower wages, may reduce their entry pension level, obliging them to work longer to achieve nancial security. As explained, the retirement choice re ects heterogeneous tastes for work and leisure, and di ferent budget constraints. Longer working careers may re ect work and leisure preferences more aligned to remaining in the labour market (associated with the more highly educated and those earning higher wages). But retirement decisions also re ect budget constraints, supposedly more so for the less educated, and thus, they work in the opposite direction.
We should mention at this point some of the limitations of our retirement model. Some variables that may be relevant when explaining retirement decisions are not included in our estimations. This is the case of marital status (as emphasized by Blau & Riphahn, 1999) and the partner's incentives to retire, health status (as discussed in the seminal paper by Anderson and Burkhauser (1985)), private savings, and expectations about anticipated inheritances. The inclusion of these variables is not possible for two main reasons: on the one hand, problems of data availability (no data source combines work histories, retirement transitions and pensions with any of these variables for Spain); and, on the other hand, the design of the microsimulation model. We opted to project individuals instead of households (pensions rights are, in Spain, individual), which complicates the modelling of the partner's incentives.
Yet, even if information had been available on health status and savings, projecting these variables into the future is beyond the scope of DyPeS given its current stage of development. However, to test the extent to which health status (disability) and marital status (living with a person of similar age) might in uence the retirement decision, we have estimated our model including these variables (see Appendix E for an explanation). Other circumstances (that is, rm agreements or regulations) that force people to retire are eliminated from the model. Our model only includes voluntary retirements, excluding those a fected by collective agreements ( rms and employees) and those with the obligation to retire due to unemployment status or other circumstances. In the microsimulation model, those forced to retire for legal requirements retire automatically, with no intervention of the behavioural model.

THE MICROSIMULATION MODEL
Microsimulation models that include behaviour in the retirement decision are scarce and heterogeneous in their modelling approach, since there is an inevitable trade-o f between the explanatory power of the econometric analyses found in the retirement behaviour literature and their feasibility of implementation in behavioural microsimulation models. Indeed, the latter can be intractable if there is no empirical correspondence for the many free parameters that would need to be speci ed in the model.
As a result, microsimulation models are preferably endowed with simple -non-behavioural-rules for retirement: for example, assuming that individuals retire as soon as they are eligible (Borella & Moscarola, 2010) or aligning the transitions to the observed patterns (Dekkers et al., 2009;Leombruni & Richiardi, 2006). Recently, Tikanmäki, Sihvonen, and Salonen (2015) use dynamic microsimulation techniques to analyze the distributional impact of the forthcoming Finnish pension reform.
Similarly to those mentioned before, it is a model without behavioural adjustments in which the agegender-speci c behaviour is obtained from a macro model and the di ferences in transition probabilities between educational groups are extrapolated from the register data. In turn, the econometric literature on retirement behaviour accounts for the role played by the nancial incentives embedded in the pension rule by integrating empirical evidence with life-cycle theory -see, for example, Baker et al. (2003) for Canada, Blundell, Meghir, and Smith (2002) for the United Kingdom, Coile and Gruber sible. The retirement decision is modelled by estimating a probit model and the main money's worth measures used are the present value of pension bene ts (PVB) and the peak value (PV), de ned as the maximum forecasted accrual at each age. In Van Sonsbeek (2010), the retirement decision is modelled using the option value (OV) approach, rst suggested by Stock and Wise (1990), which combines individual data on wages and on state and private pension entitlements with individually varied option value parameters (time and leisure preferences and risk aversion). In the microsimulation model of Stock and Wise (1990), the retirement decision is taken de nitively at the age of 60, which does not allow the agent to update the changes observed in their nal working period. This is crucial for us to simulate changes in mature workers' participation. In contrast, in our model, agents update expected pensions monthly until they retire, taking into account changing labour market conditions. Bianchi, Romanelli, and Vagliasindi (2003)  after the baseline and whose working careers are fully simulated. The rst step in the simulation is to assign individuals with a level of education. For those present in the MCVL born before 1991 the level of education level is recorded, but for "future" individuals (born after 1991), the level attained is assigned randomly so as to reproduce the educational distribution observed and foreseeable by the Spanish Ministry of Education (MEC, 2010) for the Spanish population (see Section 5). Second, once individuals reach the age of 16, they are exposed to the probability of entering the labour market by age, gender, education and initial quali cation level (obtained from the MCVL).
Third, when individuals enter the labour market, they are exposed to labour market transitions (based on those observed in the MCVL). Wages grow according to a Mincer equation (estimation results provided in Appendix B,

RESULTS
This section reports the results of the microsimulator DyPeS together with the behavioural reactions of individuals estimated in the previous section. The baseline situation is characterised (Section 5.1) and the impact of behavioural responses to the 2011 pension reform in Spain is analysed (Section 5.2).
Di ferent counterfactual scenarios are estimated in order to evaluate the impact of demography on pension sustainability.

Baseline scenario
Our baseline scenario incorporates behaviour in the retirement decision and the e fects of the 2011 reform. It seeks to reproduce the "real" situation insofar as the 2011 reform had already been implemented when our projections were made, based on the behavioural model that best replicates the retirement decision. In this respect, other scenarios -without behaviour, without reform-act as counterfactuals. Figure 1 shows the evolution of wages and pensions over recent decades and their projected growth rates. The average growth rate of wages between 1995 and 2008 was 3.5 and their projected future growth is 3 . Remarkably, pensions have grown at a rate higher than that of wages: 4.7 between 1995 and 2008, which has been corrected for the period 2008-60 (with an average growth rate of 3.1 ).
The main reason for the past increase is the so-called substitution e fect -new pensioners obtained systematically higher pay-outs. Moreover, the minimum pension has also grown at a rate above the average. The

Behavioural responses to reform measures
We report the results obtained from simulating the e fects of the 2011 pension reform (see Section 2 for more details) in which the baseline scenario includes behaviour and the impact of the crisis. Besides  sider the future bene ts of waiting for a higher pension. Second, the e fect of the crisis on working careers seems marked, pointing to the notable bene ts to be gained from continuing to work after the crisis.   lower wages) are weaker. The delay in the retirement age causes, as expected, fewer retirements during the rst part of the simulation, but is o fset during the period 2042-53. Unsurprisingly, the only measure that has an e fect on the time of retirement in the non-behavioural scenario is the "compulsory" one: delay in retirement age from 65 to 67. In this scenario, agents are not allowed to use retirement time to react to the changes in nancial incentives. Consequently, other measures produce no changes. The most general indicator, which summarises the di ferent e fects of the pension reform, is the ratio between total pension expenditure and the wage bill. Figure 5 shows the percentage changes in this ratio and the contribution of each measure. In the behavioural scenario, the ratio falls due to the introduction of the reform over the whole period, except for the period 2014-32. As expected, the change in the computation of the BR is -except during the initial years-associated with a higher ratio, as is the increase in the retirement premium for delayed retirement, whereas the delay in retirement age cuts this ratio, and is the only measure that signi cantly improves sustainability (changes in p(n) operate in the same direction, but their e fects are weak).

The role of demographics
Demographics play a key role in the evolution of the pension systems. Besides ageing, the role of the education transition (i.e., a progressively higher educational attainment) and the increase in female labour market participation are increasingly relevant. Below, to evaluate their respective roles, we present the results of two counterfactual scenarios.

Education
Educational attainment is modelled in two di ferent ways: for individuals already in the starting population and born after 1978 (who supposedly have nished their studies by 2007, the year of the sample) the information is recorded as a variable; for future generations, the distribution of population by education level is imputed according to o cial data and projections from the Instituto de Evaluación, Ministerio de Educación y Ciencia (MEC). Figure 6 shows Spain's education transition (ending with the cohort born in 1978), with rates of university studies close to 45 for women and 35 for men.
Our projections assume these high rates will be maintained in the future (given that supposing further improvements would be unrealistic). Yet, despite this increase in the educational attainment of Spanish youth, its impact on wages and future pensions is not direct as it is mediated by labour market performance. Indeed, it is quite plausible that the labour market will not translate this increase in human capital into better working careers (higher labour force participation and higher wages). In our model, educational attainment, labour force participation and working careers are closely linked so that a level of educational attainment is rst assigned to individuals (as described above); second, entry contribution groups are assigned according to observed hazards by level of education and sex; and, nally, unemployment and re-employment hazards are held dependent on the level of quali cation. Thus, the more highly educated rise faster to reach higher occupation levels and are more likely to end up in the highest contribution groups. To verify the impact of changes in education on the pension system, two counterfactual scenarios are simulated. The rst supposes that the observed education transition did not occur, so the education distribution of those born in 1950 (observed in our starting subsample) applies to all subsequent generations (lower education, LE-scenario). This distribution implies rates of 11, 41 and 48 for university, secondary and below secondary studies, respectively, for women, and rates of 15, 48 and 37 for men.
In contrast, the second scenario supposes that the increase in human capital is fully translated into higher occupation rates in the highest contribution group, that is, the scenario supposes that all workers with university education rise to the highest contribution group in the second transition (absence of over-education, AO-scenario).
Not unexpectedly, the results of these two scenarios present opposing pictures of the average pension evolution and its relation to wages. Panels A and B in Figure 8 show the e fects of lowering educational attainment on the average pension and the ratio of pension expenditure to the wage bill. During the rst period of this projection, lower education levels translate into lower wages, weakening the sustainability of the pension system. After 2045, the situation is reversed, as less educated workers retire with lower pension bene ts (lower wages during their careers results in lower pensions from 2035 on).
The e fects of the second scenario point in the opposite direction and are more sizable (panels C and D in Figure 8). The "pure" e fect of Spain's education transition involves an increase in the average pension, reaching growth rates close to 8 in 2050. The initial improvement in the system's sustainability is even more notable, with reductions in the ratio of total pension expenditure to total wages close to 16 during the initial period of simulation. As in the rst scenario, the situation is reversed after 2045, when the more highly educated cohorts -who have been in the highest contribution group with the highest wage levels-retire.

Female labour participation
In the DyPeS model, labour force participation is the result of various interactions: entry hazards by education, sex and contribution group; changes in contribution groups by contribution group Figure 8: The e fect of education on pensions ( change).
Notes: LE represents the "lower education" scenario and AO the "absence of over-education" scenario as explained in the text. of origin and sex; and unemployment and re-employment hazards by sex and contribution group.
The modelling is conducted using observed hazards for 2007. Insofar as no alignments are made in this baseline scenario to adjust results to any reference scenario, the resulting employment and participation rates are the "pure" result of interacting the increase in human capital with labour market transitions.
Before assigning individuals to a contribution group, DyPeS assigns them an educational level based on o cial data, capturing in the process the signi cant increase in Spain's educational attainment.
This increase in human capital has an e fect on labour force participation. In particular, the increasing educational levels of women (surpassing those of men) have their counterpart in relatively high female employment rates (see panel A of Figure 9). While these rates are strongly a fected by the increase in human capital and remain similar to or even higher than those for men throughout almost the whole period, unemployment rates also remain signi cantly higher for women (see panel B of Figure   9). This re ects the fact that women are more likely to be a fected by periods of unemployment, although this is partly o fset by their increasing labour force participation in the form of transitions from non-participation to employment (note, employment rates are calculated over the total population of young people, including non-participants, while unemployment rates are calculated considering only the active population).
The impact of this situation is analysed in a hypothetical scenario in which women present the same unemployment and re-employment hazards as men. Figure 10 shows that the e fects of this scenario on the pension system's sustainability are sizable. However, while the impact on the average pension paid is only relevant at the end of the simulation period, the e fect on the ratio of total pension expenditure to the wage bill (re ecting the higher contributions associated with increased female participation) are notable from the outset. As in the case of improved labour market performance, the situation is reversed at the end of the simulation, when women with longer careers (and higher average contributions) retire. Figure 10: The e fect of higher female participation on pensions (changes in ).

FINAL REMARKS
The sustainability of pension systems in most industrialised countries is threatened by demographic ageing. However, in parallel, other demographic characteristics are changing and may have a counter e fect on sustainability. Two obvious examples are shifts in the labour market caused by an increase in the participation of older workers and women and the improvement in education levels. Similarly, the behavioural reaction of these heterogeneous agents to policy adjustments may well modify the impact of policies.
As such, there is an undoubted need for sound simulation models that can project pension expenditure and evaluate the e fects of potential reforms. In this regard, the necessity of capturing the behaviour of agents that present di ferent characteristics requires the use of microsimulation models.
With the progressive availability of longitudinal microdata and enhanced computation methods, the most innovative models can aim at capturing the behavioural response of individuals to retirement The model also allows us to evaluate the impact of other demographic characteristics on pension system sustainability. Speci cally, the role of changes in educational attainment and female participation can be analysed. In relation to the former, we examine two hypothetical scenarios, one that reverses the education transition and another that assumes all quali ed workers nd employment in the highest contribution group. Results show that education and, more speci cally, the capacity of the labour market to absorb quali ed workers, do matter. Higher levels of educational attainment mean higher wages in the short and medium term, reducing signi cantly the pension expenditure to wage bill ratio until 2050. Yet, they also imply higher pension bene ts in the distant future, but with a limited impact on sustainability. In contrast, the lower education scenario produces a marked increase in the ratio until 2042, given the lower wages nancing pensions. Sustainability only improves when the lower educated workers retire on correspondingly lower pensions.
In the case of female participation, we examine a hypothetical scenario in which women have the same unemployment and re-employment hazards as men. Again, the e fects on pension sustainability are notable, showing that the labour market plays a critical role in the evolution of pension sustainability. and Peak Value (PV) as main nancial incentives. These variables are commonly used in the literature (Gruber & Wise, 2005) and particularly in previous studies for Spain (Sánchez, Argimón, Botella, & González, 2013). These authors use SSW, the Social Security Accrual (SSA) and PV and nd that all the coe cients of these social security variables are statistically signi cant with the expected sign. Increases in the total present value of the ow of pensions that a person will receive from the year she retires to the year she dies, i.e. a rise in SSW, increase the hazard. Increases in the di ference of this amount derived from postponing the retirement (either one or more years) reduce the hazard, irrespectively of whether SSA or PV is used to capture the substitution e fects. By contrast, after controlling from other variables we nd that the e fects of the SSW and PV variables are very weak, being non-signi cant in the case of the PV. Hence, we opted for discarding this model and used the one explained in Section 3 to describe the social security incentives involved in the retirement decision. Two di ferent kinds of reasons might explain why our results di fer from those found in Sánchez et al. (2013): (2013) is de ned in years, and ours is de ned in months. Finally, models are not identical. For example, Sánchez et al. (2013) use control variables -such as regional dummies-that we do not include in our model. Note that in our modelling framework we can only include the variables that we are going to reproduce for future periods in our microsimulation model. Table B.1 shows the wage estimations used in our microsimulation model. All the variables behave as predicted by the theory. Variables related to productivity -education, experience-increase wages, and more quali ed and non-manual jobs are better paid. Also, wage increases with age but at a decreasing rate and immigrants are worse paid than Spaniards. We introduced cohort e fects -assuming a linear relation-through the variable 'year of birth', whose impact on wages is strong and positive.

B WAGE ESTIMATIONS
This variable tries to capture changes (supposed to be improvements over time) in individual skills and productivity, mainly related to changes in education system and access to education, health system improvements with e fects on individual health (and productivity).

C THE EFFECTS OF THE ECONOMIC CRISIS
As a result of changes in unemployment and re-employment rates -simulated following FEDEA to 2026, we observe more retirements in the scenario with crisis than in the baseline one. All these results show that there is a reaction in retirement decisions due to the big movements in labour status that the current crisis produces. In a behavioural model such as the one considered here, agents can exit the labour market through early retirement, escaping penalties, and then avoid a higher reduction in entry pension level. As we will see in the next section it seems that, when behaviour is incorporated into the model, workers e fectively tend to retire later, coping in this way with the e fect of the crisis on their labour careers. As shown in panels C and D of Figure C.3, the total e fect of the crisis in terms of increasing total expenditure and ratio of pensions to wage bill is huge, despite the sizeable delay in entry pensions shown in Figure C.2. It is mostly the consequence of the dramatic fall in wages due to the crisis, which has permanent e fects (see panel B of Figure C.3) This sensitivity analysis shows the potentially strong impact of the crisis and illustrates the di culties in projecting the future evolution of wages and in designing the interplay between the micro and macro modules of the model.    However, the di ferences between the estimations in the case of women are remarkable. Whereas previously the e fect of age had been linear and negative, it is now quadratic and strongly positive.
In fact, the results are now similar to those for men. The reasons for this may be linked to the impact of the crisis (that is, more women needing to work longer). Also, the coe cient for unemployment changes its sign, due to extreme changes in the value of unemployment rates.  As for the link between the omitted health variable and some of our included variables (such as, education) and its joint impact on retirement, the international evidence is abundant. However, studies of the Spanish case are scarce. No data base reports both health status and nancial incentives to retire.
In fact, the MCVL is the only work history database that includes a variable related to health status, namely, disability. Therefore, we have re-estimated the same model including this time the degree of disability and a dummy variable for disability. The results indicate that the inclusion of this variable does not alter substantially the impact of the other variables. Its impact on retirement is signi cant for men (reducing retirement hazards) but not for women. This nding is in line with that obtained by Sánchez et al. (2013Sánchez et al. ( ) et al. (2013, who also use the MCVL to explain retirement behaviour and include a dummy variable for disability in their model. Those receiving disability bene ts the year before retirement show a lower hazard, probably re ecting the fact that, besides having a poorer health, they will probably be the ones receiving retirement disability pensions when they turn 65, the only age at which pensions of this type can be awarded, so they will tend to wait until they reach that age. In the case of marital status we also perform an estimation controlling for this omitted variable, to the extent that this is possible. Speci cally, we include a dummy variable that takes a value of 1 if the individual lives with a person of a similar age. The results show that the e fect of including this variable does not alter the impact of the other variables.    observed and in the model (behaviour and non-behaviour). Panel C and D present the ratio between the number of pensions/entry pensions and the population aged 65 or older. As expected, the behavioural model reproduces more precisely the observed behaviour. Only for the ratio of new pensioners to population aged 65 or older the simulation describes a sizeable di ferent pattern compared to the observed ratio. Nevertheless, this trend is corrected and, for the last year with available observations (2016), there is no appreciable di ference between the behavioural model and the actual rates.