The Retirement-Consumption Puzzle and the German Pension System - A Regression Discontinuity Approach

Transcription

1 The Retirement-Consumption Puzzle and the German Pension System - A Regression Discontinuity Approach Hermann Buslei, Peter Haan, Anna Hammerschmid and Pia John December 19, 2017 Preliminary Version In this paper we analyze if the German pension system allows pensioners to maintain their standards of living. We follow Battistin et al. (2009) and use a RDD design based on age-specific retirement rules which allow us to identify the causal effect of retirement on consumption. We focus on different consumption measures and we allow for heterogenous effects by income and wealth. The analysis is based on repeated cross sections from the Sample Survey of Income and Expenditure (EVS) over the period 2003 to For the whole population, we do not find a significant effect of retirement on total non-durable expenditures. When accounting for differences in wealth levels, the study detects significant heterogeneity in retirement effects for all consumption measures. For individuals with a low level of wealth we find a significant reduction in their consumption at retirement. Keywords: retirement age, consumption puzzle, non-durables, age discontinuity. JEL classification: J14; J18; J22; J26, H21. The usual disclaimer applies. DIW Berlin hbuslei@diw.de DIW Berlin, FU Berlin, Netspar, phaan@diw.de DIW Berlin, BERA, ahammerschmid@diw.de 1

2 1 Introduction One central aim of a pension system is to guarantee that pensioners can maintain their standard of living without suffering a significant drop in consumption. Most pension systems include private pension plans, occupational pensions and earnings related state pensions that contribute to the income of pensioners, however the importance of the different pillars strongly varies between countries. Moreover, the entitlements from state pensions or the accumulated wealth from private and occupational pension plans strongly differ between individuals for example by education, working history or family status. In this paper we want to analyze if the German pension system allows pensioners to maintain their standards of living and if specific groups face a particular high risk to suffer a significant drop in consumption. A study of the German pension system is interesting for several reasons. First, in Germany, the earnings related state pension is by far the most important component of pension income. The state pension has a strong contributory link which implies that individuals with a short working history and low lifetime earnings have low entitlements. Second occupational plans are selective and are mostly offered by large firms. Third private pension are not mandatory and although private pension plans are subsidized for the group of low-income individuals only a small fraction of this group has a private old-age pension plan. The previous literature has discussed this research question in the context of the so-called retirement-consumption puzzle which predicts a drop in consumption upon retirement. This is inconsistent with the standard life-cycle hypothesis by Modigliani and Brumberg (1954). The empirical results about the retirement-consumption puzzle are mixed, see e.g. Hurst (2008). For example, Banks et al. (1998) for the UK and Bernheim et al. (2001) for the US show that at ages associated with retirement consumption expenditures significantly decline. In contrast Aguila et al. (2011) for the US, Battistin et al. (2009) for Italy find no significant drop when they use a broader consumption measure and when they account for work related expenses. There exist several reasons why the findings differ. In addition to the different definitions of consumption, country specific institutions of the pension system, and the methodological framework to address the endogeneity of retirement can explain the different results. The empirical studies about the retirement-consumption puzzle face an important endogeneity problem, the endogeneity of retirement. In particular to a large extent retirement is a choice variable which might depend on several unobservable variables and therefore individuals non-randomly select into retirement. We follow Battistin et al. (2009) and use a regression discontinuity design and exploit the age-specific retirement 2

3 rules which allow us to identify the causal effect of retirement on consumption. In line with the previous literature we focus on different consumption measures, including workrelated expenses, food and other non-durable goods, and importantly we concentrate in addition to the average effect on heterogenous effects by income and wealth. The analysis is based on repeated cross sections from the Sample Survey of Income and Expenditure (EVS) over the period 2003 to The empirical analysis presents evidence on wealth heterogeneities in retirement effects. For the whole population, we do not find a significant effect of retirement on the broadest measure of consumption, total non-durable expenditures. Among the categories of non-durables, retirement significantly reduces work-related expenses by about ten percent but has a small and insignificant effect on food consumption. When accounting for differences in wealth levels, the study detects significant heterogeneity in retirement effects for all consumption measures. Individuals with a low level of accumulated wealth reduce their consumption at retirement discontinuously by approximately the same amount as the drop in income. This paper is linked to the literature in several dimensions. First we contribute to the studies that analyze the retirement consumption puzzle, mentioned above. These studies provide different explanations for the puzzle including unanticipated income shocks around retirementbanks et al. (1998) or Bernheim et al. (2001), work related expenses e.g. Banks et al. (1998), Bernheim et al. (2001), Miniaci et al. (2003), Battistin et al. (2009), for Italy and Li et al. (2016) and Luo (2016) for China. Furthermore, a common explanation for the drop in consumption is home production of market-purchased goods and services. Gardening, cooking, laundry and house-cleaning become more advantageous as a result of the increase in leisure time after retiring. Retirees make up for their reduced retirement income by producing consumer goods themselves as the result of having more time. Thus, leisure time used for home production works as a substitute for consumption, see e.g. Aguiar and Hurst (2005) or Lührmann (2010). Smith (2006), Hurd and Rohwedder (2008) and Barrett and Brzozowski (2012) stress involuntary retirement, which represents an unanticipated wealth shock, as another explanation for the observed drop in consumption. In fact Hurd and Rohwedder (2008) and Barrett and Brzozowski (2012) find that there is no retirement-consumption puzzle at the population level but for an important minority for which retirement is involuntary and linked to a negative wealth shock. For Germany there exist two studies on the retirement-consumption puzzle based on the EVS data with mixed evidence. Lührmann (2010), finds a significant decrease of 17 percent of consumption expenditures at retirement, whereas Beznoska and Steiner (2012) do not find any significant effect. The different findings are partly 3

4 related to the definition of consumption and to the different methodology. We extend these papers by using the regression discontinuity design as proposed in Battistin et al. (2009) which allows us to estimate a causal effect of retirement on consumption. Second our paper is linked to studies that exploit age discontinuities in pension eligibility. Following Battistin et al. (2009), Li et al. (2016), Luo (2016) and Dong and Yang (2016) exploit China s retirement policy, which sets 60 as the mandatory retirement age for male individuals to also estimate the effect of retirement on consumption. Exploiting the age cut-off for retirement in France, Stancanelli and Van Soest (2012) analyze the causal effect of retirement on home production. Additionally, Eibich (2015) implements an RD design to estimate retirement effects on health outcomes for Germany making use of the two age thresholds for pension eligibility, age 60 for female and age 65 for male workers. The paper is organized as follows. Section 2 introduces the state pension system in Germany and describes the data and variables used in the paper. The identification strategy and the corresponding econometric model are explained in section 3. Section 4 provides the graphical analysis and section 5 presents the estimation results. Finally, section 6 concludes. 2 Institutions and Data 2.1 The State Pension System in Germany The pension system in Germany is built on three pillars: state pensions, employer-based pensions and private pension insurance. Although policymakers have introduced several reforms since 2001 that aimed at increasing the share of private pension schemes, such as Riester Rente in 2001 and Rürüp Rente in 2005, the state pension scheme is still the most important source of old-age provision. According to the Pension Insurance Report of 2016, a total of 53.3 million people were insured with the German Statutory Pension Insurance Scheme (Deutsche Rentenversicherung) in On average, 63 percent of gross household income of retirees comes from state pensions paid by the German Statutory Pension Insurance Scheme. Employer-based pensions and private pension schemes amount to 22 percent of household income. (Federal Ministry of Labor and Social Affairs, 2016) Eligibility for state pensions depends on two different criteria. As a first requirement for claiming a pension, individuals need to have reached a certain age, the official retirement age. If individuals want to retire at an earlier age than the official retirement age, pensions are decreased by 0.3 percent for each month of early retirement. Second, 4

5 individuals need to have contributed to the pension system for a minimum number of years. These contribution years are accumulated either by paying insurance premiums or through recognition of non-income periods such as unemployment, maternity leave or training. (German Statutory Pension Insurance Scheme, 2016) Historically, the official retirement age in Germany was 70 years at the beginning of the mandatory pension insurance system in Since then, the retirement threshold was first reduced to 65 years and in the following years further relaxed for certain population groups. The first special provision was the introduction of pensions to unemployed from the age of 60 in This was followed by early retirement schemes for women from the age of 60 in 1957, for severely disabled aged 60 and long-term insured aged 63, both in Since the mid-1990s, starting with the pension reform act of 1992 the development of the official retirement age has reversed and gone towards an increase in the retirement age. The amendment act to the statutory pension insurance scheme of 2012 provides a gradual increase in retirement age for individuals born in or after 1947 from currently 65 to 67 years in At the same time early retirement options are restricted. Exemptions will only be made for severely disabled and long-term insured with 45 years of insurance. (Federal Agency of Civic Education, 2016) 5

6 Table 1: Overview of the state pension system in Germany Type of Pension Minimum Early Retirement Age Official Retirement Age Insurance Period Regular Old-Age Pension 5 65, since 2012 gradual increase from 65 to 67 for individuals born in or after , since 2012 gradual increase from 65 to 67 for individuals born in or after 1947 Pension for Long-Term Insured , since 2012 gradual increase from 65 to 67 for individuals in or after 1949 Pension for Exceptionally Long- Term Insured , since 2013 gradual increase from 63 to 65 for individuals born in or after 1953 Pension for Severely Disabled 35 60, since 2012 gradual increase from 60 to 62 for individuals born in or after , since 2013 gradual increase from 63 to 65 for individuals born in or after 1952 Pension after Unemployment or 15 60, 65 Part-Time Employment* since 2013 gradual increase from 60 to 63 for individuals born in or after 1952 Pension for Women* * Since 2012 this type of insurance is omitted. The state pension system does not distinguish between men and women any longer. Source: German Statutory Pension Insurance Scheme (2016). 6

7 Currently, the German Statutory Pension Insurance Scheme distinguishes between six different types of old-age pensions targeted at different population subgroups for which the eligibility criteria vary. Table 1 lists the eligibility criteria: minimum insurance period, early and normal retirement age for the six different pension plans. It can be inferred from the table that there are three major age thresholds in the German pension system: age 60, pensions for women (until 2012), unemployed and severely disabled individuals, age 63, pensions for long-term and exceptionally long-term insured and age 65, the standard old-age pension. In the empirical analysis the threshold at age 65 is exploited because most of the individuals included in the sample retire at the official retirement age: male household heads are used and the data do not give information about the individual s work history (to assess the years of contribution). Also, severely disabled individuals are excluded from the analysis because the behavioral response of disabled might differ from nondisabled retirees. 2.2 Survey Information The data for the empirical analysis of the retirement-consumption puzzle is obtained from the Sample Survey of Income and Expenditure (Einkommens- und Verbrauchsstichprobe, EVS), a repeated cross-section of German consumption survey data. The EVS is the largest and most informative data source on consumption for Germany. It consists of a representative sample, covering roughly 60,000 households (about 0.2 percent of all German households), including households of all social groups. Households are requested to supply data on household income and expenditures, savings, durable consumer goods and their housing situation. The large size of the survey makes the EVS well suited to display the income situation, the living standard and the consumer relations of the population in total and various groups. The data is supplied on a voluntary basis. The survey includes the following four components: General data, which provide information on the housing situation and durable consumer goods of households and individuals in addition to basic socio-demographic and socio-economic data. Financial and non-financial asset data, which provide information on the financial situation of households and individuals including consumer loans and mortgage debts. The book of household accounts, in which a quarter of all participating households write down their income and expenditures for a period of three months. 7

8 The household s detailed information booklet on food, beverages and tobacco, in which every fifth household covered by the EVS lists all expenses for one month. For our analysis, we review the three most recent survey waves (2003, 2008 and 2013). Earlier waves are not suitable for the analysis because of a major conceptual change after the 1998-wave regarding the collection of asset information. Asset information is needed in the later analysis when wealth heterogeneity is taken into account Sample Selection For the analysis all individuals within a ten year band from retirement eligibility at the age of 65 are included. This corresponds to individuals from 55 to 75 years. With smaller bands (such as five-year bands) estimates are affected by outliers, with larger bands (15-year and more) composition effects start playing an important role because of increasing mortality. Individuals that are exactly at the threshold of age 65 are excluded from the analysis. This is done to avoid a mixture of pre- and post-retirement consumption as the question on consumption for those who retire at age 65 covers pre- and post-retirement periods. Furthermore, individuals are restricted to male household heads. In the EVS the household head is defined as the main earner. The analysis focuses on male household heads because the retirement legislation for women provides more options concerning the age of retirement eligibility through early retirement schemes. Self-employed individuals are excluded because they often decide against state pension insurance and rely on private pension provisions instead. All monetary variables are noted per quarter values, adjusted to the price level of 2003 using the consumer price index and equivalized by the square root of household size according to OECD publications 2 to account for economies of scale. Eventually, male household heads between 55 and 75 are left. 1 Up until 1998 asset data acquisition took place on four different dates. This procedure caused distortions and methodological problems when combining the four values into one average value. From 2003 onwards asset information is collected on one certain date and separately released as an additional component. (Federal Statistical Office, 2005) 2 Monetary values are divided by the square root of household size according to (Organisation for Economic Co-operation and Development, 2012). 8

9 2.4 Definition of Variables Retirement status Before analyzing the effect of retirement it is necessary to define the treatment. Retirement implies that an individual leaves the workforce and exits the labor market permanently in old age. This generally coincides with the individual s eligibility to receive retirement provisions such as old age pensions. The retirement status is defined on the basis of two questions. In each survey wave, individuals are asked for their employment status. In particular respondents can choose among the following possible states: not working, working full-time, part-time and marginal employed. In a second question respondents are asked to self-assess their occupational status. Among others, possible choices are self-employed, civil servant, white or blue collar worker, pensioner and inactive. In this paper, we consider an individual as retired if he self-reports to be not working and the social status is either pensioner, if previously employed in the private sector or civil servant pensioner if previously employed as a civil servant in the public sector. Several studies (for example, Smith (2006) and Barrett and Brzozowski (2012)) distinguish between voluntary and involuntary retirement to take into account heterogeneity between these two groups. But unfortunately in the EVS there is no information available to differentiate between voluntary and involuntary retirement. Covariates In the estimation dummies for survey year and quarter are included to account for time effects and seasonal differences in consumption. To control for differences between birth cohorts, dummy variables for five-year birth cohorts are added. Further variables are used to control for heterogeneous effects of individual and household characteristics. Variables for region, education, household size, children in the household, marital status and retirement status of the partner are included in the analysis. The regional dummy equals one if the household is located in East Germany and zero otherwise. Education is measured by a dummy variable which equals one for individuals who obtained a university degree. The dummy variable Household with Children covers children up to the age of 27 that live together with their parents. It equals one if there are children in the household and zero otherwise. Household Size reflects the number of individuals living in a household. The dummy variable for marital status is one if the individual is married and lives together with the partner and zero otherwise. Additionally, the analysis takes into account the partner s retirement status which is 9

10 obtained by matching the self-reported retirement status of spouses to each other. The choice of covariates is in line with existing studies about the retirement-consumption puzzle, for example Li et al. (2016) and Moreau and Stancanelli (2015). A list of all covariates including definitions and mean values is documented in table 2. Comparing retired to not yet retired individuals, the table indicates that the means of covariates are of similar sizes. Approximately 20 percent of individuals out of the sample live in East Germany, nearly 40 percent have a university degree. The average household size amounts to two persons and more than 80 percent are married. Only the presence of children in the household and the retirement status of the partner changes markedly between households with retired and not yet retired household heads. The proportion of households with children of up to 27 years of age decreases from 27 percent to less than ten. Looking only at individuals who have a partner, four percent of not yet retired household heads have retired partners. This value increases by more than 20 percent for retired household heads. The sharp increase in the probability of having a retired partner can be explained by the age difference between couples 3 and the fact that women had been allowed to retire at age 63 until Hence, in the sample couples oftentimes retire at the same time. 3 In fact, in the sample wives are on average three years younger than their husbands. 10

11 Table 2: Definitions and means of covariates Variables Definition Mean Mean of non-retired of retired Survey year (Base category: 2003) Year 2008 Dummy Year 2013 Dummy Survey quarter (Base category: 1st quarter) nd quarter Dummy rd quarter Dummy rd quarter Dummy Birth cohort (Base category: ) Cohort Dummy Cohort Dummy Cohort Dummy Cohort Dummy Cohort Dummy East (Base category: West Germany) Dummy Education (Base category: no university degree) Dummy HH with Kids (Base category: no kids) Dummy HH Size No. of Persons Married (Base category: not married) Dummy Retired Partner (Base category: no partner) Dummy Not yet retired partner Dummy Retired partner Dummy

12 Wealth measure One important advantage of the EVS data is that it contains high-quality wealth information observed on the household level. Following Beznoska and Steiner (2012), the wealth measure for the analysis includes net housing wealth (gross housing wealth minus debts), which forms the largest part of wealth for the majority of households, and financial wealth, including deposits, stocks, bonds and life and pension insurance wealth. Social security wealth, i.e. entitlements to the pay-as-you-go public pensions system due to previous contributions, is not included. As for consumption and income, wealth is equivalized by the square root of household size. To account for the potential endogeneity of the level of household wealth in the consumption equation, a procedure suggested by Bernheim et al. (2001) is applied to eliminate the component from observed individual wealth that is correlated with an individual s retirement status. In a first step, this is done by taking a sub-sample of individuals not yet eligible for retirement and not yet retired. Then, their total wealth is regressed on variables that are correlated with life-time wealth but do not change abruptly as individuals become eligible for retirement. The specification includes a set of dummy variables for education, housing situation, region, employment status and an age variable. On the basis of this equation (that explains approximately 15 percent of the variation in the dependent variable) a predicted wealth value for each sample observation, whether retired or not, is assigned. In the last step, the lowest quarter of the adjusted wealth distribution is selected as the poverty subsample. This variable is used when extending the RD estimation to account for wealth heterogeneity in retirement effects in section 5.3. Consumption measures In this study three different consumption measures are considered to analyze the retirementconsumption puzzle. The overall measure of consumption is total non-durable expenditures. It includes all frequently bought goods such as food, clothing, personal care utilities, entertainment costs and leisure activities as well as rents and imputed rents for owner-occupied housing. All expenditures on non-frequently bought goods, such as cars and furniture, are excluded. Additionally, two detailed consumption categories are included in the analysis: food consumption at home and work-related expenses. Food consumption consists of expenditures on food, non-alcoholic drinks, alcoholic drinks and tobacco 4. Following the 4 I tested different compositions of the measure for food consumption (e.g. leaving out alcoholic drinks 12

13 literature (Li et al., 2016; Luo, 2016), work-related expenses include expenditures for eating out, transportation, telecommunication (including phone service, postal service and others) and clothing (including clothes, shoes and others). The importance of analyzing subcomponents of consumption is emphasized by Aguiar and Hurst (2013). The authors provide evidence that life-cycle consumption patterns are mainly driven by work-related expenses and goods that can potentially be produced at home. 2.5 Descriptive Statistics In table 3, average levels of the three consumption measures for retired and not yet retired individuals as well as the difference between the two groups are given. Levels and differences of net household income and wealth are also reported for comparison. All variables are measured in real euro equivalized for household size. Consumption and income is given per quarter, wealth is a stock value. The table shows that consumption is lower for individuals that are already retired. While average total non-durable consumption of retired individuals is 9.2 percent below the average amount observed for those not yet retired and average food consumption changes by 7.3 percent, work-related expenses are even 21.7 percent lower for retired individuals compared to those not yet retired. As expected, there is a substantial differential in average net income of more than 30 percent. This is likely to result from income replacement rates of less than one upon retirement. The observed differences in average consumption and income between retired and not yet retired individuals provide only suggestive evidence of how consumption and income change at the time of retirement. The role of retirement needs to be assessed more formally because the two groups may differ by other factors correlated with both consumption and retirement. One such factor is the level of household wealth. The table shows that the equivalized stock of wealth of those retired is by 12.6 percent smaller than the average stock of those not yet retired. As discussed by Bernheim et al. (2001), the consumption discontinuity may be the larger the smaller the accumulated level of wealth is at retirement. It is therefore interesting to estimate heterogeneous retirement effects conditional on the level of household wealth. Hence, in section 5.3 the analysis is extended by taking into account wealth heterogeneity. and tobacco) which led to similar results. 13

14 3 Methodology This study aims at determining the causal effect of a change in the retirement status on consumption. The standard approach is to estimate the following regression equation by ordinary least squares (OLS): ln(c i ) = α + βretire i + X iγ + u i (1) C is a measure of consumption and Retire is a dummy variable for the retirement status which equals one if the individual is retired and zero otherwise. The estimated coefficient on the retirement dummy, β, measures the average effect of retirement on consumption, provided the retirement status can be treated as exogenous, conditional on the set of control variables X. Problem of endogeneity There are severe reasons why there might be a problem of endogeneity concerning the retirement status in the consumption equation. In particular, a problem arises from self-selection into retirement. Due to the fact that retirement is not mandatory in Germany, individuals might retire before the official retirement age or continue to work after they reach retirement eligibility. Individuals self-select into retirement either based on unobserved factors such as unexpected health problems or based on expected gains in connection with retirement - those who enjoy working least might retire early, those who expect large drops in income at retirement might tend to retire later. In this case, individuals non-randomly select into retirement and the OLS estimate is subject to a selection bias. Another aspect why the retirement status might be endogenous depends on the choice of control variables in the consumption equation. An omitted variable bias might be induced through unobserved individual characteristics, which influence both the retirement decision and consumption. If, for example, wealth was not controlled for the results would be biased because wealth affects consumption and is also likely to be correlated with the individual retirement status. However, simply including wealth in the consumption equation and thereby treating it as exogenous might bias the retirement effect. According to Bernheim et al. (2001), income shocks prior to retirement induce a correlation between consumption and wealth at the time of retirement which leads to the bias. If any of this is the case, OLS estimates of β are biased and do not display the correct size of the retirement effect on consumption. Thus, to identify the causal effect of 14

15 retirement on consumption and to account for the potential endogeneity of the retirement status, the consumption equation is estimated using an RD design. 3.1 Regression Discontinuity Design In the existing literature there are several studies that apply RD methods to investigate the retirement effect on consumption. One of the first papers by Battistin et al. (2009) evaluate the change in consumption that accompanies retirement by exploiting the exogenous variability in pension eligibility to correct for the endogenous nature of the retirement decision. Among others, Luo (2016), Li et al. (2016), Moreau and Stancanelli (2015) and Stancanelli and Van Soest (2012) follow this approach and implement an RD design to solve the retirement-consumption puzzle. The present study exploits the retirement legislation in Germany that sets age 65 as the official retirement age for the average male worker to instrument the effect of retirement on consumption. The existence of a legal retirement age creates a discontinuity in the probability of retirement as a function of age that enables to apply an RD approach. As stated earlier, the main advantage of an RD design over other approaches is that it comes close to a natural experiment because individuals marginally above and below the discontinuity are likely to be very similar in observed as well as unobserved individual characteristics. Thus, the causal effect of retirement, instrumented with the age discontinuity, on consumption can be identified. The validity of the analysis relies on two main assumptions. First, local continuity is assumed. Individuals slightly above and below the official retirement age of 65 need to be comparable in their individual characteristics so that it can be seen as random whether they are retired or not around the age cut-off. To this end, this study checks for discontinuities in predetermined variables and other covariates. If there was a discontinuity in one of the variables this would cast doubt on the identification strategy since the results might be driven by the discontinuity in other covariates. Second, it is assumed that the running variable cannot be manipulated near the threshold which is not possible with age. As a result of the German retirement legislation and self-selection into retirement, some individuals retire earlier than the official retirement age due to early retirement schemes and sector specific arrangements. Others retire later than the age cut-off because retirement is not mandatory after 65 and some individuals decide to keep on working. This implies that the retirement probability jumps discontinuously at the age cut-off and that the size of the discontinuity is less than one. It follows that this setup fits a fuzzy RD design. 15

16 3.1.1 Estimation Equations The fuzzy RD design can be estimated by specifying a 2SLS model of the retirement effect on consumption. In the first stage the endogenous retirement status is instrumented by the age cut-off. In the second stage the effect of retirement (using the fitted values from the first stage) on consumption is estimated. The intuition behind the approach is that the estimated retirement status contains the part of the variation in the retirement status which is induced by crossing the age threshold. The estimated effect should be interpreted as a local average treatment effect because a fuzzy RD design is by construction a 2SLS estimation which only captures the average treatment effect for those who retire at the point where they reach the official retirement age 5. Retire is the dummy variable for the retirement status of the male household head that equals one if the individual is retired and zero otherwise. To instrument the retirement status the age indicator, I[Age 65], is specified. It equals one if the individual is above the official retirement age of 65 and zero if it is aged below. As shown in the graphical analysis of section 4, I[Age 65] is a strong predictor for retirement and is very unlikely to suffer from manipulation or selection bias. For generalization, the running variable Age is redefined as the difference of the individual s age to the official retirement age of 65 and represents the years to (or from) age 65. Negative values of the standardized running variable imply that eligibility for retirement has not yet been attained. Positive values measure the time from the first year of eligibility. 5 Note that the group of compliers includes both, individuals who choose to retire as well as individuals who are forced to retire due to working contracts. Unfortunately, the data does not allow to distinguish between the two. 16

17 First stage regression The first stage regresses the endogenous retirement status Retire on the instrument I[Age 65] and exogenous covariates. The retirement-age profile is modeled with a piecewise linear trend 6. To this end, an interaction term of the running variable and the age cut-off is included in the equation. This allows not only for a jump at the age cut-off but also for the possibility that consumption follows a different trend on either side of the cut-off. The equation is specified as follows: Retire i = α R + β R Age i + γ R I[Age i 65] i + δ R Age i I[Age i 65] i + X iλ R + vi R (2) Second stage regression In the second stage, consumption expenditures C are regressed on the fitted values of the retirement status from the first stage, Retire, and on exogenous covariates X. In the literature there are two approaches to account for differences in the trend of the data and thereby to increase the flexibility of the estimation. The first approach allows the slope to follow a different trend on each side of the age cut-off not only in the first but also in the second stage. To this end, it includes an interaction term of the running variable and the age cut-off from the first stage as an additional exogenous control variable in the second stage. 7 For version 1, the following equation is estimated: ln C i = α C + β C Age i + γ C Retire i + δ C Age i I[Age i 65] i + X iλ C + v C i (3) The second version assumes that the change in the retirement status not only causes a one-time drop in consumption but also effects the age trend in consumption. Thus, an interaction between the running variable and the fitted retirement status from the first stage is included in the second stage which needs to be estimated in an additional first stage equation. 8 For version 2, the second stage equation is as follows: ln C i = α C + β C Age i + γ C Retire i + δ C Age i Retire i + X iλ C + v C i (4) Both versions are estimated. The results are reported and interpreted in section 5. 6 As a robustness check, I also implement a higher order polynomial in section For a paper that implemented version 1 in the context of retirement effects see Eibich (2015). 8 The following papers that analyzed the retirement-consumption puzzle implemented version 2: Li et al. (2016) and Luo (2016). 17

18 4 Graphical Analysis The graphical analysis is an integral part of an RD analysis because it visualizes the identification strategy of the approach. A standard way of graphing the data is to divide the running variable into a number of bins with a certain bandwidth. The EVS data measures the age of individuals in years. This means that the running variable is of discrete nature and provided only on a yearly basis. This simplifies the problem of bin width choice: a bin width of one year is used to show the graphic fit. The average value of the outcome variable can be computed for each bin and graphed against the mid-points of the bins. To increase visual clarity local polynomial smoothed lines with 95 percent-confidence intervals 9 are added on either side of the threshold. 4.1 Density of the Running Variable To evaluate the credibility of the RD strategy it is useful to inspect several graphs. The first plot of interest shows the distribution of the running variable to assess the possibility of manipulation. A concern is that there is a discontinuity in the distribution of the running variable at the threshold which would indicate that the value of the running variable was manipulated by the individuals. This would invalidate the RD results. Figure 1 is a histogram of the running variable for male household heads. As one can see, the distribution of the variable is rather even over the range of negative and positive values. Only in the rightmost part of the 20 year-window one can observe a decrease in the density. This is most probably caused by an increase in mortality rates in later life. Additionally, a function of kernel density estimates is included as suggested by Lee and Lemieux (2010). The bin-to-bin jumps provide an indication of unusually large jumps at the threshold. 10 Looking at the kernel density estimates, the bin-to-bin jumps are of equal size and the jump at the threshold is not unusual. This supports the assumption that the running variable is not subject to manipulation or selection bias. 4.2 Covariates by Running Variable The next set of plots compares average values of additional covariates on either side of the age cut-off. The graphs can be used to inspect whether there are other changes 9 This is done via the STATA command lpoly. 10 A more formal test of a discontinuity in the density can be found in McCrary (2008). 18

19 Table 3: Consumption and income levels before and after retirement Not retired Retired Difference in % Total non-durable consumption Food consumption Work-related expenses Net household income Wealth stock All levels are real equivalent values in euro and prices of The levels are evaluated at the mean and equivalized by the square root of household size. Figure 1: Density of the running variable Frequency Years to / from age 65 19

20 apart from a change in the treatment probability at the same cut-off point. Such changes might affect the outcome and these effects may falsely be attributed to the treatment. 20

21 In order to fulfill the assumption of local continuity, the graphs of individual and household characteristics should not show any evidence of a discontinuous jump around the cut-off point. Figure 2 shows indeed rather smooth graphs for clearly predetermined variables, such as East and Education. Regarding the other covariates, there is a slightly different picture. The variables Household Size and Household with Kids also show smooth trends. But the variable Married exhibits a clear jump at age 65, though very small in size (from 0.83 to 0.86). This implies that the probability of being married changes discontinuously at the age cut-off. A possible explanation is that couples that might not have been married before retirement, decide to get married after they retire, for example for income tax reasons. Furthermore, the partner s retirement status also jumps at the threshold. The presence of a discontinuity in the partner s retirement status can be explained by the fact that couples oftentimes retire at the same point in time. The pre-assumption test in section further evaluates this finding. 21

22 Figure 2: Impact of being older than 65 on covariates Probability East Years to / from age 65 Probability Education Years to / from age 65 Number of persons HH size Years to / from age 65 HH with kids Married Retired partner* Probability Probability Probability Years to / from age Years to / from age Years to / from age 65 * For this graph only individuals that have a partner are included (15 percent do not have a partner). 22

23 In the case of a fuzzy RD design, it is also useful to plot the mean values of the treatment variable to make sure that there is indeed a jump in the probability of treatment at the cut-off point. As one can see in figure 3, there is a sudden jump in the probability of retirement at the age of 65. Individuals already start to retire before 65. This proportion gradually increases until a discrete large jump of apparently more than 20 percent occurs from age 64 to 66. After that the proportion of retirees is close to one. It is also important to investigate whether the household income decreases at the age cut-off. If this was not the case, the potential smoothness of consumption (if one expects consumption smoothing over the life-cycle) could simply be due to unchanged income. As expected, figure 4 indicates that there is a drop in income at the age cut-off. The abrupt fall are likely to results from income replacement rates of less than one after retirement. 4.3 Outcomes by Running Variable The last set of plots graphs average values of the outcome variables for different values of the running variable. The question is whether there is evidence of a jump in the mean of the outcomes around the threshold. If the plots do not show evidence of a discontinuity, there is little chance that an RD analysis will lead to robust and credible estimates of statistically significant sizes. Figure 5 shows average values of the three consumption measures used in the analysis. The graphs for total non-durable expenditures as well as for the two subcomponents, food consumption and work-related expenses, exhibit a downward jump in expenditures. Whether these observed discontinuities are significant in size is to be estimated in the next section. 5 Estimation Results 5.1 Ordinary Least Squares As a benchmark, in a first step an OLS estimation is implemented in which the individual retirement status is treated as exogenous, conditional on the set of control variables. Under this assumption, the estimated coefficient of the retirement dummy measures the average effect of retirement on consumption. Table 4 reports the results from regressions of the log of the three consumption measures on the retirement dummy, dummy variables for survey year, survey quarter and 23

24 Figure 3: Impact of being older than 65 on retirement Probability of retirement Years to / from age 65 24

25 Figure 4: Impact of being older than 65 on household income Net HH income (per quarter, in euro) Years to / from age 65 25

26 Figure 5: Impact of being older than 65 on consumption expenditures (per quarter, in euros) Total non-durable consumption expenditures Years to / from age 65 (per quarter, in euros) Expenditures on food at home Years to / from age 65 (per quarter, in euros) Work-related expenditures Years to / from age 65 26

27 birth cohort as well as a set of additional covariates which control for observed heterogeneity in individual and household characteristics. Also included is the constructed wealth measure (wealth adjusted for the correlation with an individual s retirement status). Column (1) shows the OLS results for the broadest consumption measure: total non-durable expenditures. A reduction of non-durable consumption by approximately seven percent at retirement is identified. This effect is statistically significant at the one percent level. In column (2) and (3) the estimation results for the two expenditure components are reported. Both subcomponents also experience a highly significant decrease upon retirement. Food consumption drops by three percent, whereas work-related expenses drop by even 16 percent. Contrasting these results, a study by Beznoska and Steiner (2012) finds insignificant coefficients on the retirement dummy when implementing an OLS regression using the same data source. The main explanation (apart from different sample selection criteria) is that the authors use a broader consumption measure in their main specification, the flow of durables consumption. In a robustness check they in fact estimate a significant negative effect on retirement on food consumption of similar magnitude. Looking at included control variables, most covariates are highly significant and the effects are as expected: Individuals in Eastern Germany have comparatively lower consumption whereas those with a university degree have higher consumption expenditures than the base category. The adjusted wealth variable is also highly significant and the estimated coefficient indicates that accumulated wealth is associated with an increase in consumption. 27

28 Table 4: OLS estimation results (1) (2) (3) VARIABLES ln(non-durables) ln(food) ln(work-related) Retired *** *** *** ( ) ( ) (0.0117) East *** *** *** ( ) ( ) (0.0118) Education 0.127*** *** 0.251*** ( ) ( ) ( ) HH with Kids *** *** ( ) (0.0122) (0.0183) HH Size *** ( ) ( ) (0.0110) Married *** 0.191*** 0.163*** ( ) (0.0118) (0.0187) Retired Partner *** *** *** ( ) ( ) (0.0129) ln(adjusted Wealth) 0.169*** ** 0.142*** ( ) ( ) ( ) Constant 5.909*** 5.986*** 4.442*** (0.0520) (0.0546) (0.0974) Observations 28,141 28,141 28,124 R-squared Year, quarter, cohort dummies Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 28

29 5.2 Regression Discontinuity Design The RD design is implemented to examine whether there is a drop in total non-durable expenditures and in the two sub-components caused by the transition into retirement. The approach exploits the exogenous variation in retirement eligibility around the threshold of age 65 and accounts for the endogeneity of the retirement status Pre-Assumption Tests Before estimating the retirement effect on consumption, the results from the graphical analysis are more formally examined to validate the design specifications. The effect of retirement on income and on additional control variables is estimated in an RD framework. The graphical analysis has already shown an obvious downward jump of household income at age 65. This observation is confirmed by the regression results shown in table Column (1) reports results of a 2SLS estimation with net household income as the dependent variable. The estimated coefficient on being retired (using the age indicator for being older than 65 as the instrument) is and statistically significant at the one percent level. This suggests that net household income drops by more than 20 percent upon retirement of the household head. In columns (2) to (7) the continuity of individual and household characteristics is investigated. The estimated coefficients on Retired indicate whether the variables are correlated with the jump in the probability of retirement at the age of 65. The coefficient is not significant for the variables East, Education, Household Size and Household with Kids. This implies that these covariates do not jump when the household head s age reaches 65 years. However, the probability of being married increases significantly by 6.5 percent and having a retired partner also increases significantly even though small in size upon retirement. This is in line with the graphical findings. The results of the RD design might be of limited validity due to the discontinuity in the marital status and the retirement status of the partner. To take this into consideration, the results of the RD estimation are reported for three different sets of control variables. In the first specification dummy variables for year, quarter and birth cohorts are included to control for time, seasonal and cohort effects. In the second specification a set of covariates that do not exhibit a jump at retirement is added (East, Education, HH with Kids, HH Size). In the third specification the variables exhibiting a discontinuous jump at retirement are additionally included to examine whether they influence the effect of retirement on consumption significantly. These two variables are Married and Retired 29