2. Previous research into pension age reforms

The current paper is related to the literature about how social security systems affect retirement decisions. Early studies were mainly motivated by the steady decline in the labour force participation rate among men aged over 60 that prevailed until the 1990s in many industrialised countries (see Gruber and Wise, Reference Gruber, Wise, Gruber and Wise1999). Social security rules were found to have sizable effects on retirement by dynamic life-cycle models in which rational forward-looking individuals choose between labour and leisure (e.g., Burtless and Moffitt, Reference Burtless, Moffitt, Aaron and Burtless1984; Gustman and Steinmeier, Reference Gustman and Steinmeier1985; Rust and Phelan, Reference Rust and Phelan1997). A pension reform was adopted in the US in 1983 that would raise the NRA from 65 to 67 starting from 2003. Gustman and Steinmeier (Reference Gustman and Steinmeier1985) used structural models to predict that this reform would leave the employment rate 3.5–4% higher for the 65–67 age bracket, which translates to a delay of 1.2–1.4 months in the exit age. Mitchell and Fields (Reference Mitchell and Fields1984) used an indirect utility approach to predict a similar rise of 1.5 months in the average labour force exit age.

Empirical studies evaluating the ex post impact of the pension age reforms tend to find the reforms have more impact on labour market outcomes than out-of-sample ex ante estimates referenced above. According to Mastrobuoni (Reference Mastrobuoni2009), the 1983 reform in the US raised the exit age from the labour market by 1 month for 2 months of rise in the NRA on average. This estimate is based on the acceleration of the trend increase in the effective labour market exit age of the cohorts affected by the pension reform compared to the pre-reform cohorts. Analysing the same US reform, Behaghel and Blau (Reference Behaghel and Blau2012) found that the peak in the pension claiming hazard rate observed at the NRA shifted one-to-one with the rise in the pension age, and the peak of exit from employment also shifted. The authors of both papers argued that the reason behind the larger effects found in ex post estimations arises from the signalling effect of the statutory pension age that is added to the effect of financial incentives.

Several empirical studies have employed a difference-in-differences strategy (e.g., Staubli and Zweimüller, Reference Staubli and Zweimüller2013; Vestad, Reference Vestad2013; Atalay and Barrett, Reference Atalay and Barrett2015; Cribb et al., Reference Cribb, Emmerson and Tetlow2016; Rabaté and Rochut, Reference Rabaté and Rochut2020) to estimate the effects of retirement age reforms. This method pins down the immediate effect of the rise in the pension age as a difference in the employment rate with and without pension eligibility given age, the business cycle and personal characteristics. The results obtained from these studies are summarised in the Appendix in Table A1. A common finding that emerges from all these studies is that the pension age reform has a positive effect on the employment rates of those affected but the effect size varies markedly.

At the lower end, Cribb et al. (Reference Cribb, Emmerson and Tetlow2016) estimated that raising the earliest retirement age for women in the UK from 60 to 62 over the years 2010–2014 raised the employment rate at the pre-reform retirement age by 6.3 percentage points. Somewhat larger effects are found by Staubli and Zweimüller (Reference Staubli and Zweimüller2013), who used register data to estimate the effect of a stepwise increase in the ERA in Austria of 2 years for men and 3.25 years for women from 2000 to 2006. They found that the probability of being employed increased by 9.75 percentage points for men and by 11 percentage points for women among those who were no longer eligible for a pension as a result of the reform. In a more recent study on Austria using a regression kink design, Manoli and Weber (Reference Manoli and Weber2016) estimated that the same reforms led to a rise of just under 5 months in the average job exit age for each year the ERA rose by.

On the high side among similar studies, Rabaté and Rochut (Reference Rabaté and Rochut2020) found that the rise in the eligibility age from 60 to 61 in France resulted in a large increase of 20.9 percentage points in the employment rate at the age of 60. Vestad (Reference Vestad2013) used register data and found a rather strong effect: had the ERA in Norway not been cut from 64 to 62, more than two out of three early retirement pension recipients would have been employed at the age of 63. Relatively large effect was also reported by Staubli and Lalive (Reference Staubli and Lalive2016) for Switzerland. Using regression discontinuity method, they found that a 1-year increase in the full retirement age for Swiss women (from age 62 to 63 and from 63 to 64 years) induced an average delay in the exit from employment of 4–6 months.

It is not surprising that the size of the effect of the rise in the retirement age varies, because contextual factors also vary. The NBER comparative study Retirement Around the World (see Gruber and Wise, Reference Gruber, Wise, Gruber and Wise1999) covers 12 industrialised countries and suggests that the fall in labour force participation rates at older ages is closely related to the implicit tax on working after the statutory retirement age. In countries where the pension adjustment is less than actuarially neutral, people are inclined to take up a pension as soon as they become eligible and to exit the labour market earlier. Gruber and Wise also argue that pension generosity, measured by the replacement rate, correlates with the employment rates of older people. In countries where pension benefits are generous, people are less motivated to work beyond the retirement age. Some studies have investigated whether liquidity constraints play a role in creating high peaks in the hazard rate for retiring at the early pension age. For instance, Rust and Phelan (Reference Rust and Phelan1997) found that such constraints are indeed significant for medium-income workers without access to private pensions. It follows that in countries in which liquidity constraints matter less, for example, because private savings can be run down, eligibility for the public pension might determine the timing of labour market exit to a lesser degree.

Another contextual feature that might affect benefit claims and the labour supply is the earnings test on pension benefits, which is often applied for those claiming benefits before they reach the NRA. Gruber and Orszag (Reference Gruber and Orszag2003) report that the earnings test in the US becoming less strict increased benefit claims but had no significant effect on the labour supply. By contrast, Hernæs and Jia (Reference Hernæs and Jia2013) found that abolishing the earnings test for early pension claims did increase the labour supply, but mainly through the intensive margin. Laun and Wallenius (Reference Laun and Wallenius2016) pointed out that the availability of disability and unemployment insurance programmes also explains part of the variation in labour market outcomes across countries.

Although there is a fast-growing literature evaluating the effects of pension age reforms, and the pension age has been raised in an overwhelming majority of the Eastern European EU member states, there are very few studies that evaluate the effect of the pension age reforms in these countries. To the best of the authors' knowledge, the only available studies are by Cseres-Gergely (Reference Cseres-Gergely2014), which estimated that a rise in the ERA for Hungarian women had an employment effect in the range of 5.0–7.4 percentage points, and by Komada et al. (Reference Komada, Strzelecki and Tyrowicz2019), which found the effect of the 2009 abolition of the early retirement option for most workers in Poland on labour force participation to be economically small, between one and three percentage points. However, the study found no effect on the employment rate at the NRA. The author explained this unexpected finding as a strong spill-over effect from the concurrent increase in the take-up of disability pensions. Our study complements the literature by analysing the effects of pension age reform in another Eastern European setting.

From the policy perspective, it is relevant not just to estimate the overall effects, but also to assess how sub-groups of the population react to rises in the pension age. Both Rabaté and Rochut (Reference Rabaté and Rochut2020) and Staubli and Zweimüller (Reference Staubli and Zweimüller2013) found that the employment effect of the rise in the NRA increased with health. Staubli and Zweimüller (Reference Staubli and Zweimüller2013) also estimated that a rise in the ERA had heterogeneous effects, with the response increasing with wages. Cribb et al. (Reference Cribb, Emmerson and Tetlow2016) found a somewhat stronger employment response for single women. In this study, we investigate the variation of responses to the increase in the NRA and ERA associated with educational attainment, place of residence and immigrant status. We are interested whether certain vulnerable groups have greater difficulties in adapting their labour market behaviour to changes in pension policy, meaning they need additional policy support if the desired policy aims are to be achieved.

3. Institutional features

The current Estonian pension system is built on three pillars. The first pillar is the public pay-as-you-go pension scheme. The second pillar is a mandatory pre-funded defined-contribution scheme with individual retirement accounts. The third pillar is a tax-favoured voluntary private scheme. However, the institutional history of the three-pillar pension arrangement is relatively short as Estonia has transformed its pension system in stages from the early 1990s after regaining independence.Footnote ¹

In this paper, we focus on the first pillar, which was the main source of retirement income for the period of our study. The second pillar was launched in 2002 and is mandatory only for cohorts born in 1983 and later. The first payments from the second pillar for cohorts who joined voluntarily were only made in 2009. The coverage of the third pillar remains relatively low at <15% of the labour force. This meant that non-state pensions and other financial assets were of marginal relevance during the period studied of 2001–2011.

The public old-age pension scheme effectively has two tiers, with employment-related old-age pensions paid to people who have an employment history of at least 15 years, and residence-based national pensions paid to people who have been resident for at least 5 years but do not qualify for the employment-related old-age pension. The employment-related pension is financed predominantly from an ear-marked payroll tax called the social tax that is levied on all labour income at the employer level,Footnote ² while the residence-based pension is financed from general revenue transfers. Crucially for this study, the social tax contribution payments were personalised from 1999, meaning the monthly contributions of all employees had to be individually recorded by the tax and social insurance authorities.Footnote ³ The individualised contributions affect one part of the state pension by topping up the flat-rate base component. The net replacement rate of the average old-age pension was in the range of 42–45% in the period studied.Footnote ⁴

The statutory pension age was inherited from the previous Soviet pension system and it remained at 55 for women and 60 for men until 1994.Footnote ⁵ From 1994, the pension age was set to increase gradually in 6-month increments for male cohorts born after 1934 and female cohorts born after 1939, to reach 63 for men by 2001 and for women by 2016.

From April 2000, a general early retirement option was introduced that made it possible to draw an early old-age pension up to 3 years before the NRA, this then becoming the ERA. Claiming the early retirement pension before the NRA permanently reduces the pension received by 0.4% per month. However, the adjustment is less than what would be needed to achieve actuarial neutrality (Medijainen, Reference Medijainen2011). There is a 100% earnings test until the NRA is reached, meaning that the early old-age pension is not paid for the months when there is any work income.Footnote ⁶ In essence, this is a very punitive earnings test.Footnote ⁷ About 17–25% of new claimants of the old-age pension each year opted for the general early retirement pension during the period studied.

Deferring the old-age pension after the NRA has been reached increases the pension received by 0.9% per month and there is no earnings test. However, though this adjustment is higher than actuarially neutral, the option of deferring has been little used, accounting for only about 1% of new pension claims during the period studied.Footnote ⁸ Table 1 shows how the NRA and ERA rose for women during the period studied.Footnote ⁹

Table 1.

Early and normal retirement age in Estonia, women born from 1943 to 1952

Notes: For women in the 1943–1944 birth cohorts, the effective ERA was less than 3 years before the NRA, as they had already reached a higher age by the time the early retirement option was introduced in 2000.

Source: State Pension Insurance Act

There are some exceptional cases when an old-age pension may be drawn before the normal pension age without penalty. The most common special case, covering about 15% of each cohort of women affected by the policy change, is that of parents or guardians who have raised three or more children or a disabled child. Such people have the right to an ‘old-age pension under favourable conditions’. The eligibility starts 1–5 years before the NRA depending on the number of children. About 9% of women in the population are eligible for a pension 1 year ahead of the NRA, 2% for 3 years ahead, and 0.4% for 5 years ahead. Another 4% of those in the cohorts affected receive a special early pension for having worked in specific occupations or branches of the economy that are deemed to be hazardous for health or in specific civil service jobs such as the police and the military. These special cases (women with three or more children or a disabled child, and those receiving a special early occupational pension) are excluded from the analysis to ensure the homogeneity of the study population.

Spending on pensions in Estonia has been among the lowest in the EU, ranging from 5.8% to 8.9% of GDP during the study period, with lower values of 5.8–6.1% in the years of fast economic growth in 2001–2007, and a peak at 8.8–8.9% in the years of the economic crisis in 2009–2010. Consequently, the aggregate replacement ratio, which is the ratio of the median individual gross pensions of people aged 65–74 to the median individual gross earnings of people aged 50–59, in Estonia has been below the EU average at 0.45 in Estonia against the EU average of 0.49 in 2008 (European Commission, 2018). However, the flat-rate base amount of the old-age pension, which is about 35% of the average old-age pension, means the individual replacement rate is higher for low wage earners and lower for high wage earners.

At the same time, Estonia has witnessed some of the highest AROP ratesFootnote ¹⁰ in Europe for older people aged 65 and over, though there was a major fluctuation in the AROP rate for older people during the period studied, with values relatively low at below 20% in 2001–2003 and during the peak of the economic crisis in 2009–2011 but reaching over 40% in the years of the economic upsurge in 2006–2008. These sharp fluctuations are explained by the relatively equal distribution of old-age pensions, as a high share of old-age pensioners have pensions that are close to the AROP threshold, implying that even small changes in the ratio of pensions to earnings from work result in quite large changes in the share of pensioners falling below the threshold (Leppik, Reference Leppik, Becker, Schütz and Zimmermann2018).

The flat structure of old-age pensions is confirmed by the relatively low income quintile share ratio of 2.9 for people aged 65 and over in Estonia against the EU average of 4.1 in 2011.Footnote ¹¹ Notably, the income quintile ratio for people under 65 years of age was considerably higher at 5.9 in Estonia than the EU average of 5.2 in 2011 (Eurostat).

At the same time, Estonia has had some of the highest employment rates in Europe for older workers in the 55–64 age group at above 55% from the mid-2000s and reaching 62% in 2008, exceeding the EU average by 10–17 percentage points during the period studied. The institutional features of the pension system contribute to these high employment rates for older workers. Although the reduction that applies if the pension is claimed before the NRA is less than actuarially fair, in light of an extremely punitive earnings test and the low level of pensions, it is not considered a favourable exit route from the labour market. Almost all people claim a pension upon reaching the NRA, but the relatively low replacement rate of the old-age pension gives them a strong incentive to delay their labour market exit and supplement their pension with labour income if possible.

Apart from the old-age pension, there are two main alternative sources of replacement income for financing an exit from the labour market, and these are public unemployment insurance and the disability pension scheme. The unemployment insurance system was introduced in 2002, and those eligible for benefits under it were people who were fully and involuntarily unemployed with at least 12 months of contributions over the preceding 24 months from 2002 to 2006, a qualification period that was extended to 36 months from 2007. The benefit payment period was up to 180 days until 2007, increasing to 270 days from 2007 for people who had paid contributions for 5 years or more. The unemployment insurance benefit is 50% of the former earnings for the first 100 days, after which the rate declines to 40%. For the unemployed who are not eligible for unemployment insurance benefits, a flat rate unemployment assistance was available under less restrictive eligibility criteria. However, the unemployment assistance allowance has been at a very low rate that does not even reach the subsistence level.Footnote ¹²

Another pathway out of economic activity has been the disability benefit scheme. During the period studied, disability pensions were paid to people of working age, which is from 16 to the NRA, who had lost at least 40% of their capacity to work. The amount paid as the disability pension was calculated as the accrued old-age pension subject to a flat-rate minimum, multiplied by the percentage of the work capacity lost. As the pension age rose in the 2000s, the take-up of disability pensions increased markedly (Puur et al., Reference Puur, Leppik and Klesment2015). At the same time, claiming a disability pension did not necessarily mean withdrawing from the labour force, as there was no earnings test for a disability pension and not being employed was not among the eligibility criteria.

The disability pension had the advantage over the general early retirement pension of having no earnings test, though it had a lower replacement rate. In addition to being paid without restrictions to working people, even those assessed to suffer full loss of work capacity, the disability pensions were also recalculated annually to reflect the additional pension rights accrued through employment, just like the old-age pensions.

4. Data, variables and descriptive statistics

This study uses individual-level data from administrative registers. The main source of information is the national pension register operated by the Estonian Social Insurance Board (ENSIB). The register data have several important advantages for the purposes of the study, as they cover all Estonian residents who have received pensions or social or family benefits, or have declared labour income or otherwise contributed to social insurance (the register data available for the analysis start from 2001). Furthermore, the data are not affected by non-response or recollection error concerning the labour market status of individuals. The disadvantages of the pension register data are that they do not indicate which individuals form households, and the set of socio-demographic variables is limited.

We use the data on female cohorts born between 1943 and 1952 in our analysis. The cohorts in the sample are chosen so that they reached either the ERA or the NRA or both between 2001 and 2011. We exclude all women who at any point take up a special early occupational pension or a pension on the basis of having raised three or more children or a disabled child. Figure 1 plots the share of old-age and disability pension recipients among those women by age and cohort. Practically all the women who have not already claimed a pension do so at the NRA, which is in line with the very low deferral rate. There is a positive age trend in the take-up of the disability pension, which explains the increase in the share of those receiving a pension before they reach the NRA in subsequent cohorts. The take-up of the disability pension increases from roughly 15% for the 1943 cohort to just above 30% for the 1952 cohort in our sample. This increase is driven not solely by the change in the ERA and the NRA as the proportion of those receiving a disability pension increased with each cohort in ages well before the ERA. Furthermore, the take-up rates of disability pensions increased for men (Puur et al., Reference Puur, Leppik and Klesment2015), who were not affected by the pension age reform in the period from 2001 to 2011.

Figure 1.

The proportion of pension recipients by cohort of women (%).

Notes: The age variable on the horizontal axis is measured in monthly frequency.

Source: Authors' calculations.

The outcome variable that is of primary interest for us is employment, which is available with monthly precision. A person is defined as employed in the given month if social tax was paid on their wages or their income from self-employment. A shortcoming of the administrative data is that individuals who do not receive labour income because they are temporarily absent from their job for holiday or sick leave, and their employer does not therefore make social tax contributions on their behalf, would be coded as inactive. To eliminate the gaps in continuous employment that are generated by regular vacations, we recoded all 1-month periods of inactivity and all 2-month gaps in July and August as employment. Two-month gaps are typical for teachers and affect people with higher education. Another limitation of the data is that the outcome variable only covers declared employment, while informal employment in the shadow economy remains unobserved and is coded as inactivity in our data. Given the relatively large share of working hours for undeclared pay in Estonia, a share which was estimated to be 15% of total hours worked in 2015 (Zukauskas and Schneider, Reference Zukauskas and Schneider2016), this may be a concern. To assess the magnitude of the problem, we compared the employment rates from the register data with those from the labour force survey. The results of the comparison suggest that while there is a noticeable gap in employment rates for men in their prime working age, the difference is quite small for women, particularly for the older age groups examined in this study. Finally, we cannot observe working hours in our data, so adjustments along the intensive margin cannot be studied.

Figure 2 shows the age-specific employment rates for the women included in the final sample by cohort. It can immediately be seen that there is an acceleration in the drop in the employment rate at the ERA and at the NRA, but it is much less pronounced and sharp than the change for pension recipients. For certain cohorts, the effect of the economic recession makes the shifts driven by the pension age reform somewhat difficult to discern. There is also an apparent cohort effect as the employment rate is higher throughout for the younger cohorts. Among the older cohorts (1943–1945), the age–employment profiles closely overlap until reaching the NRA, while the drop in employment rates at the NRA is gradually postponed as the retirement age increases. These cohorts were not affected by the increase in the ERA; the increase in the ERA begins with the 1946 cohort. Although the effect is smaller than that of the NRA, it can be discerned in the figure as the reduction in employment rates that follows the ERA is postponed with each cohort. For the younger cohorts (1950–1952), the age–employment profiles are strongly influenced by the economic boom and recession, which make the effect of the increase in the ERA difficult to visually identify in the figure.

Figure 2.

Employment rates by cohort of women (%).

Notes: The age variable on the horizontal axis is measured in monthly frequency.

Source: Authors' calculations.

On top of the social security contributions from employment, those made by the state on behalf of the registered unemployed can also be observed in our data. We use contributions of this type to proxy for a second outcome state, unemployment. However, only those who are under the NRA are eligible to register as unemployed, which means that unemployment registration drops to zero as the NRA is reached. This implies that our study is only able to estimate how raising the ERA affects unemployment, but not how raising the NRA does. Before 2007, an average of 50% of the females aged 55 and over who were registered as unemployed could be identified in our database.Footnote ¹³ Those registered as unemployed who exhausted their insurance benefits or had too little work history to qualify for unemployment assistance could not be observed. From 2007, the coverage ratio of unemployed persons rose to 95%.Footnote ¹⁴ The change represents a structural break in our data that we account for in the multivariate analysis. If a person was neither employed nor unemployed, they were classified as economically inactive.

Figure 3 shows the age profiles for the proportion of registered unemployment among the cohorts included in our study. Although the profiles are modulated to varying degrees by exogenous macro-economic factors, a common pattern can be discerned for most of the cohorts. At the beginning, the profiles tend to exhibit a moderate downward trend that reflects the period of economic growth prior to 2008. The break in the time series of registered unemployment noted above is hardly visible, as it occurred at a time of low unemployment and its effect was spread over a period of 12 months for each cohort. The downward trend is subsequently replaced by an increase in the proportion of unemployed. This is an outcome of the financial crisis, which affected Estonia more severely than most of the other European countries from 2008 to 2010. Unemployment increased for all cohorts under the NRA at that time, but especially for the 1951 and 1952 cohorts, which were under the ERA. After reaching the NRA, the level of registered unemployment drops to zero, but that drop occurs at older ages with each cohort.

Figure 3.

The proportion of registered unemployed by cohort of women (%).

Notes: The age variable on the horizontal axis is measured in monthly frequency.

Source: Authors' calculations.

For this study, the pension register was merged with the population census database of 1989 and additional data on educational attainment, type of settlement, immigrant status, language proficiency in a second language and marital status were obtained. All these characteristics are time-fixed, measured at the census date. Table 2 presents the characteristics of the birth cohorts from 1943 to 1952. The marked increase in the proportion of immigrants that starts after the birth cohort for 1945 reflects the emergence of the second generation of immigrants, who were the descendants born to immigrants from the former USSR who started to arrive in Estonia in large numbers after the Second World War.

Table 2.

Labour market status and socio-demographic characteristics of the study population, women by birth cohort, Estonia

Note: Women who were granted a pension on the basis of having raised three or more children or a disabled child, having worked in specific occupations or branches of the economy deemed to be hazardous to health, or in specific civil service occupations such as the police or military are excluded.

Source: Authors' calculations based on data of the ENSIB register.

5. Empirical methodology

The estimation strategy used in this article to evaluate the impact of a rise in the pension age is a difference-in-differences approach similar to that employed by Vestad (Reference Vestad2013), Staubli and Zweimüller (Reference Staubli and Zweimüller2013), and Cribb et al. (Reference Cribb, Emmerson and Tetlow2016). Since there were parallel shifts in the ERA and the NRA, we use one equation to estimate their effect on employment. The treatment variables are thus below the ERA and below the NRA. For unemployment and inactivity, we are only able to estimate the effect of the ERA. Each individual in the sample is treated at some point in time and non-treated at another. We identify the effect of the treatment by comparing the labour market outcomes at the same age for different cohorts for whom pension eligibility starts at different times, but that are otherwise similar after adjustment for observable characteristics. The assumption underlying the model is that once the effects of the business cycle and individual characteristics are controlled for, the treatment and control groups would share a common age trend in the outcome variable without treatment, and the change or difference in the labour market behaviour would be attributable solely to the treatment variable. To eliminate the effect of fluctuations in labour demand that also impact labour market outcomes, we add quarterly time dummies to our model. The number of women in the treated and non-treated groups is shown in the Appendix (Tables A2 and A3).

For the employment outcome, the comparison between the groups is made by estimating linear probability models in the following form:

(1)$$y_{ict} = \alpha BERA_{ict} + \beta BNRA_{ict} + \mathop \sum \limits_t \delta _tT_t + \mathop \sum \limits_a \delta _aA_a + \mathop \sum \limits_c \delta _cC_c{\rm \;} + \gamma X_i + \varepsilon _{ict}.$$

For unemployment and inactivity it is:

(2)$$y_{ict} = \alpha BERA_{ict} + \mathop \sum \limits_t \delta _tT_t + \mathop \sum \limits_a \delta _aA_a + \mathop \sum \limits_c \delta _cC_c{\rm \;} + \gamma X_i + \varepsilon _{ict}.$$

The outcome variable of main interest on the left-hand side y _it in equation (1) is an indicator for employment that takes the value 1 if a social tax payment was made for the person in the given month. In equation (2) the outcome variable is unemployment, defined as claiming unemployment benefits or being a registered unemployed in the given month, with inactivity as the residual status. On the right-hand side, BNRA _ict denotes the treatment variable of being below the NRA in the given month and BERA _ict is that of being below the ERA.

Control variables are added to the models in a stepwise fashion. The first model (M1) includes controls for the business cycle and quarterly age dummies. To control for business cycle effects, a series of quarterly time dummies (T _t) is employed. Doing this means the effects of the business cycle are assumed to be similar across the individuals observed in the same quarter, which is a standard assumption in the difference-in-differences approach. To control for age effects, quarterly age dummies (A _a) are included. In the second model (M2), a control for the effects associated with the birth cohort (C_c) is added. To avoid perfect linearity between age, time and cohort, we use a 2-year specification for the birth cohort variable. Further, model M3 adds controls for individual characteristics of educational attainment, immigrant status, rural or urban place of residence, marital status and language proficiency (X _i). Model M4 loosens the standard assumption about the similarity of the effects of the time variable across individuals. To allow for variation in the time trend, we add the interactions of our quarterly time dummies with educational attainment and place of residence. The thinking behind model M4 is that the global economic recession, which began in 2008, hit people with low educational attainment and rural residents harder. Finally, model M5 introduces individual fixed effects in order to maximise the control of differences between individuals in the population studied.

To make sure that the groups are sufficiently similar, equation (1) is estimated on a narrow age group of 56–61 years and equation (2) is estimated on 56–59 years. In addition, only those birth cohorts that reached the NRA or ERA within the period studied are considered. Technically, we estimate the equations as a panel data GLS random-effects linear probability model with robust standard errors to take account of the panel structure of our data, where disturbance terms may not be independent within individuals. A linear probability model was selected because it provides a straightforward interpretation of the estimates in terms of the change in employment, unemployment and inactivity rates.

To provide an insight into how the response to the pension age reform has varied across sub-groups, we estimate additional models for employment that interact the treatment variables with three individual characteristics of educational attainment, place of residence and immigrant status. The purpose of the interaction models is to ascertain whether the more vulnerable sub-groups of the population, which are people with low educational attainment, people of immigrant origin and rural residents, have experienced greater difficulty in adapting to the rise in the statutory pension age.