Abstract
In this paper, we explore the links between pension reform, early retirement, and the use of unemployment as an alternative pathway to retirement. We use a dynamic rational expectations model to analyze the search and retirement behaviour of employed and unemployed workers aged 50 or over. The model is calibrated to reproduce the main reemployment and retirement patterns observed between 2002 and 2008 in Spain. It is subsequently used to analyze the effects of the 2011 pension reform in Spain, characterized by 2-year delays in both the early and the normal retirement ages. We find that this reform generates large increases in labour supply and sizable cuts in pension costs, but these are achieved at the expense of very large welfare losses, especially among unemployed workers. As an alternative, we propose leaving the early retirement age unchanged, but penalizing the minimum pension (reducing its generosity in parallel to the cuts imposed on individual pension benefits, and making it more actuarially fair with age). This alternative reform strikes a better balance between individual welfare and labour supply stimulus.
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Notes
See de la Fuente and Doménech (2012) for a complete description of the reform.
At the Normal Retirement Age, workers who have contributed in full during their working lives enjoy full pension benefits. However, workers are usually allowed to collect penalized benefits at earlier ages, starting at the Early Retirement Age.
Regarding the literature on reduced-form econometric analysis, see Samwick (1998), and for the Spanish case, Jiménez-Martín and Sánchez-Martín (2004), Boldrin et al. (2004), or, more recently, Cairó (2010) and García-Pérez et al. (2013); while Jiménez-Martín and Sánchez-Martín (2007), or the classic works by Rust and Phelan (1997) or French (2005), or more recently, Van der Klaauw and Wolpin (2008) or Haan and Prowse (2014), as good examples of the use of structural econometrics.
Also to make room for the young, under the “lump of labour fallacy”, as discussed in, for example, Munnnell and Yanyuan Wu (2012), pp. 136–137.
See, for example, Manuelli et al. (2012).
Both Lammers et al. (2013), for the Netherlands, and Kyyrä and Ollikainen (2009), for Finland, analyze whether or not it is best for older workers to search when unemployed. Lammers et al. (2013) finds that an increase in the search requirements for older unemployed workers significantly increases workers’ entry into employment. However, practically no substitution is found between UI benefits and early retirement benefits. This is because penalties on early retirement were increased in the Netherlands at the same time.
This administrative dataset includes information on the complete labour histories of more than one million Spanish workers. We focus here on a relatively narrow sub-sample of 21,902 male workers selected to guarantee that the economic incentives of individuals are clearly identified. These workers are all affiliated to the General Regime of the Spanish Social Security System, and are also entitled to receive contributory unemployment benefits and pensions upon retirement. We have all their employment and unemployment spells during the 2002–2008 period. A complete description of the database, along with a detailed reduced-form econometric analysis can be found in García-Pérez et al. (2013).
Modelling the objective and constraints of firms and their interactions with workers and their representatives is a very complex task, and a long-term target for this strand of the literature. Hutchens (1999) offers a first approach to these issues within the implicit contract literature.
The robustness of our findings for some of these assumptions is discussed in “Appendix 3
In Spain, successive legislative changes have delayed the Early Retirement Age from the age of 60 to 61 and 63, but the value in force during our simulation was still 60.
Pension payments cannot exceed a legislated maximum (which we also include in the simulations), but whose empirical relevance in our sample is very small.
The real world formula is approximated in our simulations with \(\hat{w}_{\tau +1}=\hat{w}_{\tau }+\frac{w-\hat{w_{\tau }}}{D}\). Otherwise, solving the model would require a much larger vector of state parameters (including all previous wages between age \(\tau -D\) and \(\tau -1\)).
The real values are 70 % during the initial six months and 60 % for the rest of the spell. We work with the 65 % average.
We implemented different linear structures for retirees, employees, and the unemployed who engaged in the effort to search. In principle, we considered differences in both the level and growth rate of \(\nu \) with age, for each group. Nevertheless, the final specification is very parsimonious, including a baseline leisure value of 0 for employees, different initial leisure levels for retirees and the unemployed (0 & 0.45 respectively), and just one common 6 % growth rate for both groups (which, for retirees, is operative only after the ERA). We have checked that these values are well-aligned with those used in other structural retirement papers (eg, French 2005).
Strictly speaking, all behavioural and labour supply parameters have some influence on each one of the dimensions of labour supply (retirement of employees and the unemployed, and re-entry rates and wages of the unemployed). Nonetheless, extensive simulation of the model uncovered an approximate partition of the parameter space for calibration purposes: retirement is largely controlled by the parameters in the utility function, while re-entry wages and re-entry rates are disproportionately associated to the properties of job offers.
The model solution provides evidence to support our standpoint, as the optimal firing patterns by age (from the perspective of the employees) are very different from the empirically observed ones. This can be appreciated in the bottom-left panel in Fig. 3.
The resulting multidimensional grid is the Cartesian product of the following sets (as always, values are in thousands of 2008 euros): \(\Pi =\{ 8.0 \, 12.4 \, 16.4 \, 20.6 \, 25.1 \, 29.5\, 33.1 \, 36.7 \} \quad \hat{W}=\{ 7.1 \, 10.3 \, 13.1 \, 16.1 \, 19.0\, 21.8 \, 24.8\, 28.0 \}\). \(\Pi \) is used for both the unemployed and employees’ wages. See García-Pérez and Sánchez-Martín (2013) for a more detailed description of the numerical solution procedure.
Note that, in every year between 65 and 69, we need a minimum sample size on each of our 8 \(\times \) 8 \(\times \) 3 “cells” defining the state of the unemployed. For employees, the constraint is less demanding, as there are “only” 8 \(\times \) 8 cells to be covered.
The bottom-right panel of Fig. 3 shows the raw transition data (blue line) and its approximation in the model with the exogenous firing model described in Sect. 2.2.3 (red dashed line). It also represents (green dotted line) the transitions from employment to unemployment optimal from the workers’ viewpoint (ie, the endogenous model prediction in terms of voluntary dismissals).
This restriction is reasonable in a world in which most savings are held in an illiquid form (eg, a property or other forms of fixed assets).
A detailed theoretical analysis is included in García-Pérez and Sánchez-Martín (2013).
Haan and Prowse (2014), who calibrate a life cycle model retirement with search (among a number of other features), also find strong effects on labor supply but with somehow alternative welfare implications.
Recall that we keep to the assumption that all firing is done by employers. The results on voluntary non-participation are only for informative purposes.
This is done to facilitate comparison with the welfare measure introduced later in the section.
After the reform, the average costs in the 65/67 age range increase. This is explained by the change in behaviour previously discussed in combination with the cost patterns by age in Figure. Note, in particular, that the relative position of unemployed workers and pensioners shifts at the NRA.
As with the previous cost measures, a detailed description of the welfare measure can be found in García-Pérez and Sánchez-Martín (2013).
Strictly speaking, we should compare welfare on an individual basis, but the usual problems with interpersonal welfare comparisons are somewhat less acute in our simulation, as our individuals are assumed to have identical utility functions (at each age).
Since November 2006, all Eurobarometer surveys (www.ec.europa.eu/public_opinion) clearly illustrate how, of all the solutions proposed for resolving the pension crisis, increasing the retirement age is the one generating the most opposition among European citizens.
Workers may simply ignore the option of earlier retirement offered by the reform. Yet note that, for the small group of workers entitled to minimum pensions at or after 63, the pension payment under the new system would be smaller than under the pension reform.
The labor impact of the reform is not reproduced to save space, but we also find very similar results in absence of hysteresis to those in the main text.
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We are grateful for the support from the Spanish Social Security through FIPROS 2007 and projects ECO2011-30323-C03-02 and SEJ2006-04803/ECON. Our thanks to the Editor and alto to the audience at the conferences ESPE 2013 (Aarhus) and “The labour market for older workers: Mechanisms and Institutions” (CPB, The Hague). The usual disclaimer applies.
Appendices
Appendix 1: A Optimal Behavior
This section presents an illustrative summary of the policy functions of employees and unemployed workers in the three institutional environments considered in the paper. Figure 8 starts with benchmark economy, showing the optimal choices of short-term unemployed (\(\hbox {h}=1\)), long-term unemployed (\(\hbox {h}=3\)) and employees in a number of selected ages. The changes created by the delay of the statutory pension ages (pension reform) are illustrated in Fig. 9, while the changes resulting from allowing early retirement (with penalized minimum pensions) are shown in Fig. 10.
Optimal labor decisions by age in the benchmark employment. Code of choices for unemployed: 1 search; 0 retirement; N non-participation. Code for employees: 1 stay employed; 0 retirement; V voluntary unemployment
Change in the optimal labor decisions of employed and unemployed workers in the reformed environment (ERA = 63; NRA = 67) versus the benchmark economy. Code of changes for the unemployed: 1 = N1; 2 = 01; 4 = N0; 5 = 10; 7 = 0N; 8 = 1N; Code of changes for employees: 1 = V1; 2 = 01; 4 = V0; 5 = 10; 7 = 0V; 8 = 1V
Change in the optimal labor decisions of employed and unemployed workers in the environment with Voluntary Early Retirement (ERA = 60) versus the reformed environment (ERA = 63). Code of changes for the unemployed: 1 = N1; 2 = 01; 4 = N0; 5 = 10; 7 = 0N; 8 = 1N; Code of changes for employees: 1 = V1; 2 = 01; 4 = V0; 5 = 10; 7 = 0V; 8 = 1V
The structure of the arrays is the same in all figures, but the information presented depends of the environment considered. For the unemployed, each cell is defined by a combination of the wage enjoyed in the preceding employment spell, \(\pi \), and of the level of accrued pension rights, \(\hat{w}\). These variables take values in the discretized sets \(\Pi \times \hat{W}\) reproduced in footnote 18. Previous wages are arranged in an increasing fashion from the top down, while accumulated pension rights growth with the column from left to right. For the employees, each cell in an array reflects a combination of current wage \(w\) and accrued pension rights \(\hat{w}\) belonging to the same \(\Pi \times \hat{W}\) space.
The arrays in Fig. 8 display the optimal decision rules of employees and unemployed workers at some particular ages. The decision shown in the cell defined by the \(i\)-row and \(j\)-column, \(d_{i,j}\), is the optimal behavior for the individual whose previous wage is the i-th element of \(\Pi \) and whose pension rights are given by the j-th element of \(\hat{W}\). For the unemployed, \(d_{i,j}\) takes the value “1” when search is the optimal choice; “0” if it is optimal to retire; and “N” if non-participation is best. For the employees, \(d_{i,j}\) takes the value “1” when staying employed is best; “0” if it is optimal to retire; and “V” if a transition to unemployment is the most valuable alternative.
The arrays in Fig. 9 display the changes in the optimal choices resulting from the pension reform. In this case, \(d_{i,j}\) takes the value “1” to represent a change from non-participation into search and “2” for a change from retirement to search. Codes “4” and “5” indicate similar changes into retirement (“4” for a change from initial non-participation and “5” for a previously searching unemployed). Finally codes “7” and “8” reflect transitions into non participation from retirement and search, respectively. For the employees the number of possible changes is smaller and the code is simpler: \(d_{i,j}\) is “1” when the best options shifts from voluntary unemployment in the benchmark to staying employed under the reform. “2” is for changes from retirement to employment; “4” and “5” for changes into retirement (from voluntary unemployment and employment, respectively) and “7” and “8” for changes into voluntary unemployment (from previous choices of retirement and employment, respectively).
Appendix 2: Net Pension/Unemployment Costs
This appendix completes the information in the main text regarding the net costs (to the pension and unemployment system) of workers/unemployed with different characteristics. Figure 11 displays the average net costs that employees and unemployed of different ages represent for the combined pension/unemployment protection system. It illustrates the differences resulting from the introduction of the pension reform (delay of the ERA to 63 and of the NRA to 67). The main text reproduces the differences in net pension costs in both systems (ie, the cost savings resulting from the reform).
Average net annual cost of employees (left panel) and unemployed workers (right panel) in two institutional environments: the benchmark economy (blue continuous line) versus the pension reform economy (dashed, red line). All figures are in thousand Euros in 2008
Figure 12 disaggregates the net pension cost by age according to the labor state/optimal choice of the considered individual. Note that in this set of graphs we represent one particular individual (previous wage and accrued pension rights of 16 thousand euros) rather than weighted values. The top panel of Fig. 12 displays the structure observed in the benchmark economy, while the middle and the bottom panels illustrate the pension reform and voluntary ER environments, respectively.
Net pension and unemployment costs for a representative individual in four labor states (employed (Emp), retired (Ret), unemployed without searching (UnemNS) and unemployed and searching (UnS). Three institutional settings are displayed: the base simulation (top panel), pension reform (middle panel) and Voluntary-ER (bottom panel) environments
Appendix 3: Robustness Check: Age-Independent Rate of Arrival
The process of arrival of job offers is a key input in our model of labor supply behavior for unemployed workers. In this final section of the Appendix we test the robustness of our findings to the specification of this process. Specifically, we consider an alternative specification characterized by the absence of hysteresis: all unemployed workers have the same probability of receiving a job offer, independently of the duration of the unemployment spell. Obviously, this specification does not perform as well as the one in the main text, but we can get a very reasonable adjustment if we simultaneously adjust the general rate of arrival of job offers. The alternative parameter values selected for the simulation are 60 % for workers with high pension rights and 40 % for the rest (vs 80 and 65 % in the main text). After the age of 60, these rates still suffer a 30 % drop (25 % in the main text). The resulting fit to the empirical data is shown in Fig. 13. It is apparent that ability of the model to capture variation with age in the basic labor supply patterns is not a result of the assumed discrete drop in reemployment opportunities for the long term unemployed.
Sensitivity analysis: model performance versus empirical data in absence of hysteresis. Analogous to Fig. 3 when the arrival rate of job offers is independent of unemployment duration
The main simulations results (cost savings and welfare impact of the reforms) in this alternative environment are presented in Table 5.Footnote 32 Qualitatively, this table is almost indistinguishable from Table 3 in the main text. There are some quantitative differences, specially among the unemployed (the pension reform generates bigger savings in costs without imposing larger welfare costs and the voluntary ER reform fails to produce any extra cuts in costs). But we can clearly conclude that the main findings from our experiments are robust in this dimension.
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Sánchez-Martin, A.R., García-Pérez, J.I. & Jiménez-Martín, S. Delaying the Normal and Early Retirement Ages in Spain: Behavioural and Welfare Consequences for Employed and Unemployed Workers. De Economist 162, 341–375 (2014). https://doi.org/10.1007/s10645-014-9235-7
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DOI: https://doi.org/10.1007/s10645-014-9235-7