Retirement and Cognitive Decline: Evidence from Global Aging Data

Retirement and Cognitive Decline: Evidence from Global Aging Data Hiroyuki Motegi Yoshinori Nishimura Masato Oikawa This version: February 15, 2016 Abstract This paper analyses the e ect of retirement on cognitive function in two ways. First, we analyse the e ect of retirement on cognitive function using cross-country variation of pension eligibility age. This method is used in some literatures. The results suggest that the country heterogeneity largely influences the estimated result. The estimated results can lead to precisely the opposite interpretation depending on the analysed countries. We show that the cross-country estimation is not appropriate when we analyse the e ect of retirement on cognitive function. Second, we analyse the e ect of retirement on cognitive function in the U.S. by controlling individual heterogeneity and endogeneity of the retirement behavior. Our estimates indicate that the retirement has a weak e ect on cognitive function just after retirement. However, the negative e ect of retirement on cognitive function becomes stronger as the retirement duration is getting longer. The disincentive of investing cognitive asset becomes stronger as elderly people become closer to the end of life cycle. JEL Classification Numbers: I10, I12, J24, J26 Keywords: mental retirement, cognitive function, social security, pension eligibility age, crosscountry instruments, global aging data Graduate School of Economics, the University of Tokyo, Japan. Email: motegihiro@gmail.com Graduate School of Economics, the University of Tokyo, Japan. Email: nishimura.yy@gmail.com Graduate School of Economics, the University of Tokyo, Japan. Email: masato.oikawa1991@gmail.com 1

1 Introduction The retirement related policy such as a reform of pension system has become important in developed countries to sustain social security system. Many developed countries have faced the same problems of decreasing birthrate and an ing population. As a population ages, the cost of social security and social welfare increases, eroding the country s budget. Many developed countries have reformed pension system to reduce the cost of social security and social welfare. Many developed countries such as the United States, England and Korea have already decided to increase pension eligibility age for some next decades. Japan has already increased pension eligibility age. Pension reforms in developed countries are expected to delay the retirement. When policy makers evaluate the e ect of these reforms, health is a key factor to evaluate the e ect of these policy changes. If working is good for the health of elderly people, it would lead to reductions in medical expenses. However, if working is bad for the health of elderly people, it would lead to increase of medical expenses. Along the growing interest of the e ect of the policies which delay the retirement of elderly people, a number of studies have investigated the relation between retirement and health over the last two decades. 1 In various health indexes, many researchers have examined the relationship between health and retirement. Kerkhofs and Lindeboom (1997) is one of the first papers which suggested endogeneous decision between retirement and health and shed light on the e ect of retirement on health as far as we know. They find that Hopkins Symptom Cheklist (HSCL), which is a health index, can be improved after early retirement in the Netherlands by applying fixed e ect methods. Lindeboom et al. (2002) extends the Kerkhofs and Lindeboom (1997) to other indices such as MMSE (test on cognitive ability), CES-D (test of depressing feelings) and others and applying fixed e ect methods to Dutch data which is di erent from that of Kerkhofs and Lindeboom (1997). Charles (2004) is also one of the first investigations which analyse the causal e ect of retirement on health focusing on subjective well being (SWB) in economic literatures by using instrumental variables. In addition, there are many literatures which study the e ect of retirement on various health indexes. Bound and Waidmann (2007), Coe and Lindeboom (2008), Dave et al. (2008), Neuman (2008), Johnston and Lee (2009), Latif (2011), Coe and Zamarro (2011), Behncke (2012), Bonsang et al. (2012), Mazzonna and Peracchi (2012), Hernaes et al. (2013), Bingley and Martinello (2013), Hashimoto (2013), Insler (2014), Kajitani et al. (2014) and Hashimoto (2015) are other representative papers. There are, however, no unifying views about the impact of retirement on various health indexes. Some studies conclude that retirement has an positive impact on health defined as mental health or physical health, but other studies conclude that retirement has no or negative e ect. In addition, these results depends on characteristics such as sex and education. While the controversial discussion has continued with respect to the estimated results of the various health indexes, the discussion about the e ects of retirement on cognitive function is no exception. In the literatures analysing the e ect of retirement on cognitive function, a controversial discussion has also continued. Adam et al. (2006) confirm the positive e ect of 1 We omit the literatures about the e ect of health on retirement. The representative paper is McGarry (2004). 2

occupational activities on the cognitive function of elderly people in Europe. Rohwedder and Willis (2010) discuss the hypothesis to explain why retirement behaviour decreases cognitive function and they show the negative relationship between retirement and cognitive function by using an elementary regression analysis. However, they do not control basic elements such as age and education. Bingley and Martinello (2013) re-examine the estimated model used by Rohwedder and Willis (2010) adding only years of education variable and gender variable. They conclude that their estimated negative e ect is weaker than the estimated result by Rohwedder and Willis (2010). This implies that we should include the controlled characteristics into the model estimated by Rohwedder and Willis (2010). Furthermore, Coe and Zamarro (2011) find no clear relationship between retirement and cognitive function in Europe. Coe et al. (2012) also find no clear general relationship between retirement duration and cognitive function. 2 On the other hand, Mazzonna and Peracchi (2012) find a negative relationship between retirement duration and cognitive function in Europe. Bonsang et al. (2012) also find a negative relationship between retirement and cognitive function although they control only age factors. Depending on the specifications, the negative relationship disappear. Kajitani et al. (2014) suggests the existence of the heterogeneity of cognitive deterioration depending on the characteristics of occupational type. The goal of this paper is to examine the controversial hypothesis that there exists causal e ect of retirement on cognitive function. We examine two points. First, we examine the influence of country heterogeneity and other heterogeneities on the e ect of retirement on cognitive function. This analysis re-examines the literatures using cross country instruments (e.g. Rohwedder and Willis (2010) and Bingley and Martinello (2013)). Second, we reexamine the e ect of retirement on cognitive function in the U.S. We pay attention to some aspects of heterogeneity of individual characteristics, the heterogeneity of retirement stages (just after retirement or comparatively long time after retirement) and the heterogeneity of the time consumed in leisure time. These are all remaining works or important works remained which the related studies do not analyse. The rest of this paper is arranged as follows. Section 2 describes the data. Section 3 discusses the heterogeneity of the e ect of retirement on cognitive function. Section 4 discusses our estimation methods, identification strategies and the estimated results. Section 5 concludes this research and discusses future extensions. 2 Data This paper uses the Health and Retirement Survey (HRS) 3 and other sister datasets such as the China Health and Retirement Longitudinal Study (CHARLS), the English Longitudinal Survey on ing (ELSA), the Survey on Health, ing, and Retirement in Europe (SHARE), and the Japanese Study of ing and Retirement (JSTAR). They are panel surveys of elderly people aged 50 or older. These family datasets are constructed so that the 2 They find a positive relationship between retirement duration and cognitive function only for blue-collar workers. 3 See the website (http://hrsonline.isr.umich.edu) if you want to know the detail of the HRS. 3

questions of the HRS are reproduced in those of other studies as much as possible. We analyse the e ect of cognitive function in two ways. In the first analysis, we utilise cross-sectional cross-country variation of pension eligibility age. In this analysis, we use the datasets of the HRS, the ELSA and the SHARE at 2004 and we also use the datasets of the HRS, the SHARE, the ELSA at 2010 including the CHARLS at 2011 and the JSTAR at 2009. We cannot use the Korean Longitudinal Study of ing (KLoSA) because the questions with respect to word recall are not comparable with other sister datasets. The reason why we use the JSTAR at 2009 is that the survey year is nearest to other studies at 2010 and the questions of word recall of the JSTAR at 2009 are asked to all respondents. The questions of word recall of the JSTAR at 2011 are asked to only people aged more than 65. As a result, we use the JSTAR at 2009. In second analysis, we utilise both the di erence in pension eligibility age among di erent cohorts in the U.S. and the long-term variation of retirement behaviour. We use only HRS from wave 3 (at 1996) to Wave 10 (at 2010) in the second analysis. They include a rich variety of variables to capture living aspects in terms of economic status, health status, family background, as well as social and work status. We mainly use the harmonised datasets. 4 However, when variables are not available in the harmonised datasets, we use the variables of the original datasets. We use the cognitive function score in the HRS and other sister datasets. In the HRS, we use the scores of Immediate Word Recall, Delayed Word Recall, Serial7 s, Backwards Counting and Word Recall Summary Score. Word Recall Summary Score is the sum of Immediate Word Recall and Delayed Word Recall, which is the score between 0 and 20. In the section 4.2, we use Word Recall Summary Score in all datasets. In the section 4.3 and 4.4, we use all types of scores in the HRS. The Immediate word recall and delayed word recall tests asks the respondent to recall as many words as possible in a list of 10 words. The score of Immediate word recall and delayed word recall are the number of words from 10 word list that were recalled correctly. The Serial7 s test asks the respondent to subtract 7 from the prior number beginning with 100 for five trials. The score of Serial7 s test is between 0 and 5. The Backwards Counting test asks the respondent to count backwards for 10 continuous numbers from 20. The original score of The Backwards Counting is 2 if successful on the first try, 1 if successful on the second, and 0 if not successful on either try. However, we make the indicator which is equal to one when the respondent is successful on the first try. We use only this indicator suggesting whether the respondent succeed on the first try. 5 We summarise the cognitive function scores in the Table 1 and Table 2. In the Table 1, we show the descriptive statistics of the age group from 60 to 64 in all countries and the descriptive statistics of the U.S. in the Table 2. According to Table 1, the cognition cores are not the 4 The Gateway to Global Aging Data (http://gateway.usc.edu) provides harmonised versions of data from the international ing and retirement studies (e.g.hrs, ELSA, SHARE, KLoSA, CHARLS). All variables of each dataset aimed to have the same items and follow the same naming conventions. The harmonised datasets enable researchers to conduct cross-national comparative studies. The program code to generate the harmonised datasets from the original datasets is provided by the Center for Global ing Research, USC Davis School of Gerontology and the Center for Economic and Social Research (CESR). Some variables, such as measures of assets and income, are imputed by this code. 5 We make the indicator suggesting whether the respondent succeed on the first try because we cannot interpret the estimated coe cient on the original score. 4

same level in all countries. 6 All scores in China and European countries are comparatively low compared to other countries. In Table 2, we show the descriptive statistics in the U.S. In Table 2, we can observe the intuitive characteristics of cognitive function. Female people have higher score than male people in Word Recall Score and male people have higher score than female people in Serial 7 s. Highly educated people have higher score than low educated people in all cognition scores. Table 1: Summary Statistics of Cognition Scores (:60-64) at 2010 Obs. Mean S.D. Min Max HRS Word Recall Sum. Score 2774 10.47 3.23 0 20 Immediate Word Recall 2774 5.71 1.57 0 10 Delayed Word Recall 2774 4.74 1.88 0 10 Serial 7 s 2774 3.57 1.63 0 5 ELSA 1 Word Recall Sum. Score 2063 11.50 3.28 0 20 Immediate Word Recall 2062 6.30 1.65 0 10 Delayed Word Recall 2063 5.20 1.91 0 10 SHARE Word Recall Sum. Score 10385 9.72 3.38 0 20 Immediate Word Recall 10401 5.53 1.65 0 10 Delayed Word Recall 10398 4.18 2.04 0 10 Serial 7 s 10199 3.90 1.69 0 5 JSTAR Word Recall Sum. Score 695 10.25 3.02 2 20 Immediate Word Recall 712 5.37 1.47 1 10 Delayed Word Recall 700 4.84 1.91 0 10 Serial 7 s 722 4.17 1.15 0 5 CHARLS Word Recall Sum. Score 2349 7.02 3.12 0 18 Immediate Word Recall 2376 3.98 1.59 0 10 Delayed Word Recall 2359 3.00 1.86 0 10 Serial 7 s 2363 3.16 1.87 0 5 KLoSA Word Recall Sum. Score 2 1131 4.87 1.23 0 6 Immediate Word Recall 2 1131 2.73 0.63 0 3 Delayed Word Recall 2 1131 2.15 0.92 0 3 Serial 7 s 1131 4.00 1.45 0 5 1 : No Serial 7 s Score in ELSA. 2 : KLoSAs Word Recall Scores are not comparable with other dataset. We will explain the pensionable age used in this paper. We use the pensionable age when we produce our instrumental variables. We do the cross-sectional cross-country in the section 4.2. Here, we use the pensionable age in all countries which we analyse. Rohwedder and Willis 6 The maximum score of KLoSA at each test is di erent from other countries. 5

Table 2: Summary Statistics: The U.S. (:60-64) at 2010 Obs. Mean S.D. Min Max Obs. Mean S.D. Min Max Male Female Word Recall Sum. Score 1126 9.87 3.13 1 20 1648 10.87 3.24 0 20 Immediate Word Recall 1126 5.47 1.56 0 10 1648 5.88 1.55 0 10 Delayed Word Recall 1126 4.40 1.81 0 10 1648 4.97 1.90 0 10 Serial 7 s 1126 3.80 1.52 0 5 1648 3.41 1.69 0 5 LTU Univ. Word Recall Sum. Score 2046 9.93 3.12 0 20 727 11.98 3.05 0 20 Immediate Word Recall 2046 5.46 1.53 0 10 727 6.42 1.46 0 10 Delayed Word Recall 2046 4.45 1.83 0 10 727 5.55 1.80 0 10 Serial 7 s 2046 3.29 1.69 0 5 727 4.33 1.15 0 5 White Blue Word Recall Sum. Score 1449 11.31 3.14 1 20 497 9.62 3.03 1 19 Immediate Word Recall 1449 6.07 1.51 0 10 497 5.31 1.49 1 9 Delayed Word Recall 1449 5.22 1.84 0 10 497 4.31 1.77 0 10 Serial 7 s 1449 3.91 1.46 0 5 497 3.41 1.64 0 5 (2010) and Bingley and Martinello (2013) also do the cross-sectional cross-country analysis and use the pensionable age based on the source from Pensions at a Glance (OECD) and Social Security Programs throughout the World: Europe, 2004. However, the pensionable ages in some countries are partly incorrect. We correct these incorrect pensionable ages. We explain this point in Appendix. We also search for the pensionable ages at 2010 of all countries analysed in this paper. In the section 4.3 and 4.4, we use the pensionable age in the U.S. We use the early retirement age and the full retirement age of the U.S. in the section 4.3 and 4.4. 3 Retirement and Cognitive Function Decline The main target of this paper is to discuss the heterogeneity of the e ect of retirement on cognitive function. We would like to discuss this point in this section. We focus on the influence of the country heterogeneity and the individual characteristics heterogeneity on cognitive scores. We will discuss the influence of these heterogeneities depending on the retirement definitions used in the related studies. We show the di erence of the average cognitive function scores between retired people and not retired people. In Figure 3.1, we show the di erence of the average cognitive scores between retired people and not retired people in di erent country. We show the average scores of the Serial 7 s test and the Word Recall Summary in the U.S., The U.K., China, German, Italy and Hungary at 2010. We use the two di erent definition of retire in Figure 3.1 and Figure 3.2. Not work for pay means that a respondent is not working not for pay at 2010. This is the first definition of retire. SR-Retire means that a respondent reports a retired status. We use the r@retemp variable in each Harmonised Data (e.g. Harmonised SHARE, Harmonised ELSA) which is constructed based on the RAND HRS data when we define the retirement status. If the 6

Figure 3.1: The Serial 7 s Score and The Word Recall Summary Score By Country at 2010 (Only China: at 2011) Not work for pay Serial 7's Score US China Germany SR-Retire Serial 7's Score US China Germany 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 Italy Hungary Italy Hungary 0 1 2 3 4 5 Not Graphs by country Not Graphs by country Not work for pay Word Recall Summary Score SR-Retire Word Recall Summary Score US UK China US UK China 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Germany Italy Hungary Germany Italy Hungary 0 5 10 15 20 Not Not Graphs by country Graphs by country variable r@retemp is the value of one or two, we define that a respondent retire at wave @. 7 This is the second definition of retire. Many related studies (e.g. Rohwedder and Willis (2010), Coe and Zamarro (2011), Bonsang et al. (2012), Bingley and Martinello (2013)) use the two definitions of retirement. Generally speaking, the di erence in the cognitive score between retired people and not retired people is very small in all countries. In Figure 3.1, we can observe the di erence in characteristics of some countries depending on the definition of retirement. For example, with respect to the serial 7 s score in the U.S., the score of people based on the definition Not work for pay is lower than Not people based on the definition Not work for pay. On the other hand, the score of people based on the definition reports a retired status is higher than Not people based on the definition reports a retired 7 See the codebook of the Rand HRS data if you want to know the detail of the variable r@retemp which we use. http://hrsonline.isr.umich.edu/modules/meta/rand/randhrsm/randhrsm.pdf. They explain how they construct the variable r@retemp in p.1045. We use the variable r@retemp in all Harmonised Data Sets. 7

Figure 3.2: The Serial 7 s Score and The Word Recall Summary Score in The U.S. at 2010 By Education Level, Gender and Occupational Type Not work for pay Serial 7's Score SR-Retire Serial 7's Score Male LTU White Male LTU White 0 1 2 3 4 5 Not Female 0 1 2 3 4 5 0 1 2 3 4 5 Not Univ 0 1 2 3 4 5 0 1 2 3 4 5 Not Blue 0 1 2 3 4 5 0 1 2 3 4 5 Not Female 0 1 2 3 4 5 0 1 2 3 4 5 Not Univ 0 1 2 3 4 5 0 1 2 3 4 5 Not Blue 0 1 2 3 4 5 Not Not Not Not Not Not Not work for pay Word Recall Summary Score SR-Retire Word Recall Summary Score Male LTU White Male LTU White 0 5 10 15 20 Not Female 0 5 10 15 20 0 5 10 15 20 Not Univ 0 5 10 15 20 0 5 10 15 20 Not Blue 0 5 10 15 20 0 5 10 15 20 Not 0 5 10 15 20 0 5 10 15 20 Not Female 0 5 10 15 20 0 5 10 15 20 Not Univ Blue 0 5 10 15 20 Not Not Not Not Not Not status. Depending on the definition of retirement, the average score is di erent between and Not. In China, people have higher score than Not Retied people depending on the self reported retirement status. Depending on the definition of retirement and the di erence of country, the cognitive function score has a heterogeneous relationship between and Not. There is no general relationship between the cognitive function score of and Not. In the U.S., Serial 7 s score is di erent between and Not. However, Word Recall Summary Score is not so much di erent between and Not. In Hungary, both Serial 7 s score and Word Recall Summary Score is di erent between and Not. Figure 3.2 shows the cognitive function score in the U.S. between and Not depending on the individual characteristics. In Figure 3.2, there is also the di erence depending on the retirement definition which is not ignorable. Serial 7 s score has a di erent characteristics between and Not depending on the retirement definition. According to the self-reported retirement status (The right figure named ), there is only a small gap between and Not in all categories (e.g. Gender, 8

Education Level). On the other hand, there is a large gap between and Not depending on the definition Not work for pay. In contrast, Word Recall Summary Score do not have a largely di erent characteristics between and Not depending on the retirement definition. In all categories, the gap between and Not is large with respect to Serial 7 s score. With respect or Serial 7 s, there is large gap between and Not depending on the di erence of Educational Level, Gender and Occupational Type. As we can observe in Figure 3.1 and 3.2, we should pay attention to the following points in this paper. (1) The country heterogeneity is not ignorable. (2) The definition of retirement sometimes largely influences the di erence between and to. (3) In the U.S., the individual characteristics is important with respect to Serial 7 s score. 4 Analysis Framework and Results Some related literatures (Rohwedder and Willis (2010), Coe and Zamarro (2011), Bingley and Martinello (2013)) have analysed the e ect of retirement on cognitive function by using the cross-country variation of pension eligibility age. On the other hand, some studies (Bonsang et al. (2012), Coe et al. (2012)) have also analysed the e ect of retirement on cognitive function focusing on the retirement duration by using the HRS. We would like to show that it is di cult to examine the e ect of retirement on cognitive function by the identification strategy to use the cross-country variation of pension eligibility age. We find that the country heterogeneity largely influences the estimated result of the e ect of retirement on cognitive function. We consider that we should analyse the e ect of retirement on cognitive function in only one country. In the first analysis, we want to discuss this point. In the second analysis, we will analyse the e ect of retirement on cognitive function only in the U.S. considering the heterogeneity of individual characteristics. 4.1 Identification Strategy We analyse the e ect of retirement on cognitive function. The target of our identification strategies is to exclude the endogeneity bias on the coe cient of retirement variable as much as possible. We analyse the e ect of retirement of cognitive function in two di erent ways. In the first analysis, we analyse cross-sectional cross-country analysis. When we do this analysis, the identification strategy is to use the variation of pension eligibility ages among di erent countries at a specific year (cross-sectional cross-country analysis). Rohwedder and Willis (2010) analyse the e ect of retirement on cognitive function in this way. We examine the discussion by Rohwedder and Willis (2010) in this paper. When we analyse the e ect of retirement on cognitive function in this way, the problem of this cross-country cross-sectional analysis is that the results are not robust when we change the specification or analysis year. Once we consider unobserved or observed heterogeneity, the results are heterogeneous. We consider that we cannot derive a general conclusion on the e ect of retirement on cognitive function. Rohwedder and Willis (2010) use the pension eligibility ages based on external data 9

sources. 8 We investigate again whether the pension eligibility ages in the analysed countries are correct. We make a modification on the pension eligibility ages which Rohwedder and Willis (2010) use. We explain the detail in the next section. According to our analysis, the e ect of retirement on cognitive function is heterogeneous in di erent countries. We should analyse the e ect of retirement on cognitive function in each country because it is possible that the e ects of retirement on cognitive function are heterogeneous among di erent countries. We choose the U.S. to estimate the e ect of retirement on cognitive function in our analysis because the U.S. has two good properties. In the second analysis, we use the dynamic variation of retirement behaviour on cognitive function. When we analyse the U.S., The first good property is that the HRS has enough waves to analyse the long-term e ect of retirement on cognitive function. The second good property is that we get enough information with respect to leisure time activity. The HRS collects the Consumption and Activities Mail Survey (CAMS). The section A of the CAMS explains that The activities component of the CAMS allows for describing activity patterns and permits the investigation of di erent types of activities and how specific types of activities are a ected by health, family, and economic transitions in later life and, in turn, how activities a ect health and well-being. 9 We use the CAMS data of the time consumed in leisure time of a respondent before retirement and after retirement. Figure 4.1 shows the targets of our analysis describing the goal of each section. We separate our analysis into two parts after the section 4.2. In the first part, we analyse the e ect of the transition from work status to retirement status on cognitive function (short retirement duration analysis). In the second half, we analyse the e ect of retirement duration on cognitive function scores (long retirement duration analysis). In the U.S., we can get enough variation of pension eligibility age among di erent cohorts. This variation of pension eligibility age among di erent cohorts are useful to estimate our model using a panel data. When we do this analysis in the section 4.3 and 4.4, the identification strategy is to use the variation of pension eligibility ages among di erent cohorts at the U.S. We use the panel data from wave 1996 to wave 2010. Finally, we would like to describe some notes. We would like to stress the importance of the heterogeneity of the e ect of retirement on cognitive function. We only analyse the e ect of retirement on cognitive function in the U.S. Therefore, we will not intend to derive the general conclusion with respect to the e ect of retirement on cognitive function. When we change analysis country, it is possible that the result in this paper would be di erent and vice versa. Of course, we can analyse the e ect on retirement on cognitive function at other countries except the U.S. if we can utilise the data variation to identify the e ect of retirement on cognitive function and a panel dataset with enough number of waves to analyse the long-term e ect of retirement on cognitive function. In Korea and other some European countries, pension eligibility ages have already decided to increase. When we can use a panel data with enough number of waves including respondents who have di erent pension eligibility age in these countries, we can analyse the e ect of retirement on cognitive function 8 They use the source from Pensions at a Glance (OECD) and Social Security Programs throughout the World: Europe, 2004. 9 See the website if you want to know the detail. https://ssl.isr.umich.edu/hrs/filedownload2.php?d=522 10

in these countries. We would like to expect the future work considering the importance of the heterogeneity of the e ect of retirement on cognitive function in the countries except the U.S. Cogni,ve Func,on Figure 4.1: The Analysis Targets (Target 1) Sec,on 4.3: Short Re,rement Dura,on Analysis Work (Target 2) Sec,on 4.4: Long Re,rement Dura,on Analysis Not Work Re,rement 4.2 Validation Analysis on Cross-sectional Cross-country Analysis 4.2.1 Analysis Framework Rohwedder and Willis (2010) estimate the following model. They use the HRS, the SHARE and the ELSA at 2004. They restrict the analysed sample between age 60 and age 64. As you see, they do not control any variable. notwork i is a indicator which is equal to one when arespondentisnotworkingforpayatthesurveyyear. cognition score i is a score of word recall question (minimum 0, maximum 20). age i is the variable which is a respondent s age. cognition score i = 0 + 1 notwork i + 1i (1) notwork i = 0 + 1 1{age i A eb i } + 2 1{age i A fb i } + 2i A eb i :theearlyretirementbenefiteligibilityage A fb i :thefullretirementbenefiteligibilityage We control some other control variables. Bingley and Martinello (2013) estimate the same model as (1) additionally including only years of schooling variable. However, it is not enough 11

to control only educational characteristics based on the discussion of section 3. We estimate the following model considering the heterogeneity of a respondent s cognitive function. cognition score i = 0 + 1 notwork i + 0 x i + 1i (2) notwork i = 0 + 1 1{age i A eb i } + 2 1{age i A fb i } + 0 x i + 2i A eb i :theearlyretirementbenefiteligibilityage A fb i :thefullretirementbenefiteligibilityage In the model (1), the individual characteristics x i are unobserved. These characteristics x i, which are the source of the di erence of cognitive function and also can correlate with the variable networki, can change the final conclusion. As we discuss in the next section, we find three points in this framework. The e ect of other control variables cannot be ignorable and the magnitude with respect to the e ect of retirement on cognitive function are small compared to the related literatures. We sum up this point in the section 5. We also examine the e ect of changing the analysed sample (e.g. changing the analysed countries). The e ect of changing the analysed sample is not also ignorable. This suggests that the e ects of retirement on cognitive function are also heterogeneous among di erent groups. The instrumental variables which we correct does not so much influence the final results of Rohwedder and Willis (2010) and Bingley and Martinello (2013). The e ect of correcting the instrumental variables is weak. We explain in detail these points in the next section. 4.2.2 Results First, we restrict the sample aged from 60 to 64 following Rohwedder and Willis (2010) and Bingley and Martinello (2013). We examine the e ect of including the other control variables and changing the instrumental variables (Table 3). The columns of IV1 means the analysis results when we use the instrumental variables used by Rohwedder and Willis (2010) and Bingley and Martinello (2013). The columns of IV2 means the analysis results when we use the our own instrumental variables in section 2.2. We present the result of OLS when the DWH test is not rejected in the specification to use the instrumental variables. When the DWH test is rejected, we support the result of the OLS. The column (1) in Table 3 is the result of the same specification in Rohwedder and Willis (2010). The column (3) in Table 3 is the result of the same specification in Bingley and Martinello (2013). 10 The column (2) 10 Bingley and Martinello (2013) impute the value of the years of schooling of the ELSA. However, we do not impute the value of the years of schooling of the ELSA. We omit the sample of the ELSA in the column (3) in Table 1. 12

in Table 3 is the result of the specification only changing the variable of education in Bingley and Martinello (2013). We also check the e ect of the di erence in the education variables on the e ect of the estimated coe cients in the columns (2) and (3). Form the column (4) to the column (6), we add some basic characteristics variables which Rohwedder and Willis (2010) and Bingley and Martinello (2013) do not include. For example, in the columns (4), we add country dummies into the specification (3). In the columns (5) and (6), we add the other characteristics variables into the specification (4). The are some important properties in Table 3. The Di erence in the Instrumental Variables: The e ect of changing the instrumental variables gradually influences the value of the coe cients more as we add other characteristics variables. However, the e ect is not large when we compare the specifications between IV1 and IV2. In the specifications (5) and (6), the results of the OLS are almost the same. In the specifications from (1) to (4), the magnitude of the coe cients are not di erent so much. The specification (1), which is the same specification of Rohwedder and Willis (2010), reports a small di erence between IV1 and IV2. In the specification (3) (IV2), the coe cient is not significant while the coe cient of the specification (3) (IV1) is significant. In other specifications, the e ect is weak. The Di erence in the Control Variables: When we include the country dummies, the change in the magnitude of the coe cients are very large. When we compare the specifications (2) and (4), the sign of the coe cients changes in the opposite direction. Finally, the direction of the coe cient is negative in the specification (6) while the absolute value of the coe cient is very small (the OLS result in the specification (6):-0.459). The value of the coe cients of the specification (2) is -6.831 (IV2). As a result, the omitted variable bias is very large in the specification (2). The country s heterogeneity of the e ect of retirement on cognitive function is very large. In Table 3, we can find that the e ect of the country s heterogeneity is not weak. In the specification (6), the coe cients of Spain (the OLS:-2.233) or Italy (the OLS:-1.244) are negative while the coe cient of the U.S. (the OLS:2.080) is positive. Finally, we comment on Table 3 with respect to the di erence in the education variables. We estimate the same specification by Bingley and Martinello (2013) 11 in the column (3) of Table 3. The e ect of omitting the ELSA is large. Bingley and Martinello (2013) reports -3.014 in the specification All in Table 3 of the paper by Bingley and Martinello (2013). However, when we estimate the same model in our paper, the coe cients are -4.433 (IV1) and -5.177 (IV2). Please note that we do not impute years of schooling variable of the ELSA We omit the samples of the ELSA. The heterogeneity of the e ect of retirement on cognitive function is large in each country. On the other hand, when we use the dummy variable indicating people with more than college degree, the di erence in the value of coe cient is not large. We use the dummy variable indicating people with more than college degree in all the columns except the column (3) because the education variable indicating people 11 See the specification All in Table 3 of Bingley and Martinello (2013). 13

Table 3: The e ect of instrumental variables and other control variables (without the coe cients of country dummies) (1) (2) (3) (4) (5) (6) IV1 IV2 IV1 IV2 IV1 IV2 IV1 IV2 OLS IV1 IV2 OLS IV1 IV2 IV-early 0.183 0.132 0.170 0.115 0.190 0.078 0.083 0.089 0.010-0.009 0.014-0.004 (0.013) (0.011) (0.014) (0.011) (0.016) (0.013) (0.015) (0.015) (0.017) (0.018) (0.017) (0.018) IV-normal 0.160 0.199 0.130 0.143 0.161 0.160 0.038 0.049 0.054 0.049 0.055 0.052 (0.011) (0.013) (0.012) (0.014) (0.013) (0.016) (0.020) (0.022) (0.020) (0.021) (0.020) (0.021) Not work for pay -3.346-3.181-5.208-6.831-4.433-5.177-0.893-2.389-0.531-1.697-3.761-0.459-1.503-3.837 (0.319) (0.433) (0.421) (0.690) (0.404) (0.766) (0.952) (1.032) (0.071) (2.246) (3.272) (0.072) (2.114) (3.125) Univ 1.121 0.887 1.613 1.401 1.607 1.450 1.173 1.473 1.374 1.153 (0.120) (0.154) (0.158) (0.169) (0.082) (0.314) (0.450) (0.086) (0.219) (0.312) Years of schooling 0.239 0.221 (0.014) (0.021) Female 1.693 1.893 1.569 1.648 1.076 1.278 1.111 1.274 1.562 1.097 1.238 1.554 (0.096) (0.126) (0.093) (0.120) (0.143) (0.154) (0.067) (0.319) (0.461) (0.067) (0.292) (0.427) 14 1.851 2.152 2.684 2.235 2.462 2.970 (2.385) (2.491) (2.777) (2.390) (2.460) (2.750) squared -1.568-1.774-2.138-1.877-2.028-2.365 (1.923) (1.993) (2.210) (1.927) (1.972) (2.196) Mariage 0.586 0.601 0.626 0.344 0.405 0.542 (0.082) (0.088) (0.099) (0.089) (0.154) (0.208) Nofchildren -0.100-0.100-0.098-0.085-0.086-0.089 (0.021) (0.021) (0.022) (0.021) (0.021) (0.023) Income 0.129-0.014-0.023 (0.056) (0.016) (0.018) Own house 0.603 0.563 0.473 (0.093) (0.124) (0.157) Total wealth 0.006 0.003 0.002 (0.006) (0.002) (0.002) Observations 8838 8838 8620 8620 7352 7352 8620 8620 8558 8558 8558 8463 8463 8463 R 2-0.071-0.057-0.261-0.591-0.046-0.158 0.186 0.127 0.197 0.172 0.007 0.208 0.189 0.008 DWHchi2 57.548 30.350 140.490 120.335 102.651 41.531 0.112 3.338 0.354 1.243 0.293 1.487 DWHpval 0.000 0.000 0.000 0.000 0.000 0.000 0.738 0.068 0.552 0.265 0.588 0.223 Standard errors in parentheses p<.1, p<.05, p<.01 All economic variables (e.g. Total wealth, Income) are measured in dollars. In the specification (6), (country dummy) (economic variable). (e.g. (Total wealth) (the U.S. dummy)) variables are also included. The estimated coe cients of these cross terms are not presented. The Belgium dummy is omitted.

Table 3: (continue) The e ect of instrumental variables and other control variables (only the coe cients of country dummies) (1) (2) (3) (4) (5) (6) IV1 IV2 IV1 IV2 IV1 IV2 IV1 IV2 OLS IV1 IV2 OLS IV1 IV2 2.US 1.842 1.308 2.138 1.696 0.915 2.080 1.691 0.823 (0.369) (0.396) (0.148) (0.866) (1.248) (0.183) (0.809) (1.177) 3.UK 1.930 1.517 1.991 1.664 1.086 1.649 1.418 0.901 (0.310) (0.328) (0.156) (0.657) (0.935) (0.203) (0.519) (0.732) 11.Austria 0.793 0.875 0.798 0.852 0.946 1.008 1.047 1.134 (0.238) (0.243) (0.232) (0.254) (0.288) (0.324) (0.336) (0.366) 12.Germany 0.631 0.444 0.616 0.456 0.174 0.568 0.452 0.193 (0.220) (0.230) (0.183) (0.362) (0.489) (0.235) (0.333) (0.426) 13.Sweden 1.036 0.346 1.157 0.615-0.344 1.176 0.817 0.015 (0.474) (0.509) (0.184) (1.063) (1.532) (0.306) (0.787) (1.114) 14.Netherlands 0.708 0.608 0.685 0.600 0.450 0.923 0.846 0.675 (0.205) (0.211) (0.194) (0.257) (0.315) (0.290) (0.328) (0.377) 15 15.Spain -1.751-2.004-1.694-1.903-2.272-2.233-2.399-2.770 (0.267) (0.283) (0.213) (0.459) (0.630) (0.284) (0.444) (0.590) 16.Italy -1.128-1.208-1.176-1.250-1.381-1.244-1.264-1.311 (0.193) (0.199) (0.186) (0.237) (0.284) (0.228) (0.232) (0.250) 17.France -0.126-0.145-0.111-0.131-0.166 0.240 0.205 0.127 (0.204) (0.212) (0.201) (0.209) (0.229) (0.260) (0.272) (0.303) 18.Denmark 1.254 0.893 1.351 1.068 0.567 1.297 1.161 0.857 (0.329) (0.350) (0.232) (0.597) (0.835) (0.306) (0.419) (0.540) 19.Greece 0.026-0.221 0.080-0.110-0.448-0.531-0.653-0.926 (0.250) (0.264) (0.193) (0.419) (0.579) (0.275) (0.369) (0.473) 20.Switzerland 1.042 0.461 1.146 0.692-0.112 1.623 1.298 0.573 (0.462) (0.493) (0.285) (0.922) (1.311) (0.427) (0.775) (1.062) Observations 8838 8838 8620 8620 7352 7352 8620 8620 8558 8558 8558 8463 8463 8463 R 2-0.071-0.057-0.261-0.591-0.046-0.158 0.186 0.127 0.197 0.172 0.007 0.208 0.189 0.008 Standard errors in parentheses p<.1, p<.05, p<.01 All economic variables (e.g. Total wealth, Income) are measured in dollars. In the specification (6), (country dummy) (economic variable). (e.g. (Total wealth) (the U.S. dummy)) variables are also included. The estimated coe cients of these cross terms are not presented. The Belgium dummy is omitted.

with more than college degree is available in the Harmonised Data Set made by the code which the Global Aging Data provides. 12 We comment on Table 4. Table 4 shows the results of the same specification (6) in Table 3. However, we show the results of the di erent cohort groups. The columns in 2004 presents the estimated result using the samples aged from 60 to 64 at 2004. The columns in 2010 presents the estimated result using the samples aged from 60 to 64 at 2010. The analysed cohort groups are di erent between the column 2004 and the column 2010. The analysed countries are the same in both the column 2004 and the column 2010. We analyse the same countries in Table 4. According to Table 4, the e ect of the di erence in the cohort groups is very weak. The DWH tests in both the column 2004 and the column 2010 are rejected. The OLS results in both the column 2004 and the column 2010 are almost the same (-0.472 (2004) and -0.631 (2010)) after controlling the heterogeneity of the analysed countries. After controlling the heterogeneity of the analysed countries, the coe cient of the other control variables are also similar between the OLS result of 2004 and that of 2010. Table 5 reports the result when we change the analysed countries. The specification is the same as that of the column (6) in Table 3. All results are estimated by using only the dataset at 2010. 13 We change the analysed countries in each result. 2004 Ori. shows the estimated result including only the countries (e.g. the U.S., England, France and Germany) which Rohwedder and Willis (2010) analysed. Table 5 shows the estimated coe cients of the country dummies in each specification. Western includes only the European countries which are both the European countries analysed by Rohwedder and Willis (2010) and the countries added to the SHARE by 2010 (e.g. Czechia, Poland and Hungary). 2004 Ori.+EA includes the European countries analysed by Rohwedder and Willis (2010), China and Japan. ALL countries includes all countries. As we can see, the degree of the heterogeneity of the estimated results are very large in Table 5. When we analyse only the European countries, the coe cients are significantly negative ( 2004 Origi. :-0.631(OLS), Western :-0.653(OLS) while the coe cients of 2004 Ori.+EA or ALL countries are significantly positive or not significant ( 2004 Ori.+EA :5.554(IV2)(not significant), ALL countries :3.912(IV2)). We separate the samples into two parts in ALL countries. Not Attend Social Act indicates the samples who do not participate any social activity at 2010 which we explain in the section 2. Attend Social Act indicates the samples who participate at least one social activity at 2010. Table 5 also shows the importance of separating the samples depending on the heterogeneity of activity. According to Table 5, in the samples who participate at least social activity, the e ect of retirement on cognitive function is negative while the e ect is not significant in the samples who do not participate any social activity ( Attend Social Act. :-0.415(OLS), Not Attend Social Act. :-0.020(OLS)(not significant)). However, with respect to the heterogeneity of activity, we have to be careful of interpreting the result. We use the cross sectional information here. As a result, the e ect of the change in social interaction on remaining cognitive function after retirement is unclear. We do not consider any transition pattern before and after retirement. 12 See the website. http://gateway.usc.edu 13 The JSTAR is the data at 2009. The CHARLS is the data at 2011. 16

17 Table 4: The e ect of the di erence in the cohort groups 2004 2010 OLS IV1 IV2 OLS IV2 IV-early 0.019-0.003 0.000 (0.017) (0.018) (0.018) IV-normal 0.045 0.062 0.053 (0.021) (0.022) (0.019) Not work for pay -0.472-0.278-3.956-0.631-3.372 (0.074) (2.327) (2.697) (0.072) (2.770) Univ 1.461 1.480 1.120 1.385 1.080 (0.088) (0.245) (0.283) (0.081) (0.319) Female 1.131 1.106 1.579 1.140 1.460 (0.068) (0.306) (0.353) (0.066) (0.326) 3.345 3.287 4.387 1.387 2.647 (2.455) (2.556) (2.868) (2.366) (2.862) squared -2.775-2.734-3.508-1.116-2.017 (1.980) (2.042) (2.291) (1.909) (2.258) Mariage 0.369 0.359 0.559 0.211 0.352 (0.092) (0.159) (0.180) (0.086) (0.172) Nofchildren -0.090-0.089-0.095-0.037-0.044 (0.021) (0.022) (0.024) (0.022) (0.024) Income 0.012-0.009-0.023 0.183-0.003 (0.040) (0.017) (0.017) (0.099) (0.016) Own house 0.598 0.606 0.458 0.426 0.340 (0.095) (0.134) (0.150) (0.088) (0.127) Total wealth -0.005 0.003 0.002-0.002-0.001 (0.002) (0.002) (0.002) (0.003) (0.003) 2004 2010 OLS IV1 IV2 OLS IV2 2.US 2.078 2.151 0.785-0.102-0.685 (0.183) (0.883) (1.017) (0.202) (0.623) 3.UK 1.644 1.687 0.871 1.212 0.920 (0.203) (0.561) (0.645) (0.226) (0.378) 11.Austria 1.009 1.002 1.134 0.333 0.610 (0.324) (0.334) (0.361) (0.285) (0.417) 12.Germany 0.561 0.583 0.175-0.401-1.003 (0.235) (0.349) (0.389) (0.458) (0.776) 13.Sweden 1.169 1.236-0.030 0.348-0.627 (0.306) (0.858) (0.975) (0.439) (1.086) 14.Netherlands 0.919 0.933 0.664 0.089-0.422 (0.290) (0.336) (0.360) (0.279) (0.600) 15.Spain -2.238-2.207-2.789-2.619-2.676 (0.284) (0.466) (0.534) (0.287) (0.320) 16.Italy -1.249-1.245-1.317-1.529-1.411 (0.228) (0.232) (0.249) (0.304) (0.339) 17.France 0.240 0.247 0.122-0.606-0.333 (0.260) (0.271) (0.301) (0.265) (0.397) 18.Denmark 1.294 1.319 0.840 0.784 0.082 (0.306) (0.430) (0.502) (0.365) (0.825) 20.Switzerland 1.616 1.677 0.530 0.905-0.186 (0.427) (0.833) (0.945) (0.284) (1.140) Observations 8095 8095 8095 9299 9299 R 2 0.208 0.207-0.004 0.151 0.018 DWHchi2 0.005 2.142 1.392 DWHpval 0.944 0.143 0.238 Standard errors in parentheses p<.1, p<.05, p<.01 All economic variables (e.g. Total wealth, Income) are measured in dollars. In the specification (6), (country dummy) (economic variable) (e.g. (Total wealth) (the U.S. dummy)) variables are also included. The estimated coe cients of these cross terms are not presented. The Belgium dummy is omitted.

If we consider this point, we have to use a panel data. We analyse this point in detail in next section. Finally, Table 6 shows the results analysing the e ect of changing the surveyed age-group and the definition of retirement. The columns of Not Work is the analysis defining the retirement as not working for pay. The columns of is the analysis defining the retirement as a respondent reports a retired status. This is the same definition of the second retirement definition in the section 3. See footnote. The & Not Work is the analysis defining the retirement as not working for pay and a respondent reports a retired status. According to Table 6, the e ect of changing the age group is not strong while the e ect of changing the retirement definition is very strong. In the columns & Not Work, the result of OLS are not significant in both age groups. In addition, in the columns Not Work, the result of OLS is significantly negative. In addition, in the columns, the result of OLS is significantly positive except the age group 60-64 at 2004. Whether a respondent or not depends on the self-reported information. Some respondent retire according to the definition of although they work for pay. This is the reason that the di erence in the definitions influences the di erence in the final conclusions. We summarise this section. What we find from our analysis in this section is the followings. The unobserved heterogeneity largely influences the estimated result when we omit the important control variables (Table 3). The heterogeneity of the analysed countries largely influences the estimated result. When we change the analysed country, we can get the di erent conclusion. As a result, we should care the heterogeneity of each country when we analyse the e ect of retirement on cognitive function (Table 3, 5). The definition of retirement also largely influences the result. Sometimes, the results derives di erent conclusion depending the definition of retirement (Table 6). Other factors, which are the di erence in age-groups or the di erence in the cohort groups, are not important (Table 4, 6). According to our analysis, the country heterogeneity largely influences the estimated result and the cohort or age group heterogeneity do not largely influences. When we use the identification strategy in this section (cross-sectional cross-country analysis), we cannot omit the unobserved heterogeneity which can correlate the other control variables and can be the source of bias on the coe cient of the retirement variable. We consider that we should analyse the e ect of retirement on cognitive function in only one country and omit the unobserved heterogeneity when we estimate the e ect of retirement on cognitive function. In next section, we analyse only the U.S. by using the HRS. We also analyse the influence of the heterogeneity of the behaviour transition pattern before and after retirement and individual characteristics. 18

Table 5: The e ect of the di erence in the analysed countries (without the coe cients of country dummies) 2004 Ori. Western 2004 Ori.+EA ALL countries Full sample Not Attend Social Act. Attend Social Act. OLS IV2 OLS IV2 OLS IV2 OLS IV2 OLS IV2 OLS IV2 IV-Early 0.000-0.010 0.017-0.000 0.081-0.020 (0.018) (0.014) (0.017) (0.014) (0.043) (0.017) IV-Normal 0.053 0.048 0.042 0.046 0.060 0.034 (0.019) (0.013) (0.018) (0.013) (0.026) (0.015) Not work for pay -0.631-3.372-0.653-0.727-0.396 5.554-0.465 3.912-0.020 3.923-0.415 0.456 (0.072) (2.770) (0.063) (1.943) (0.065) (3.465) (0.058) (2.331) (0.127) (2.908) (0.072) (2.725) Univ 1.385 1.080 1.380 1.371 1.392 2.049 1.386 1.872 1.188 1.154 1.334 1.433 (0.081) (0.319) (0.072) (0.227) (0.080) (0.398) (0.071) (0.272) (0.193) (0.222) (0.083) (0.321) Female 1.140 1.460 1.081 1.089 0.908 0.172 0.914 0.397 0.497-0.035 0.912 0.805 (0.066) (0.326) (0.057) (0.224) (0.059) (0.434) (0.052) (0.280) (0.112) (0.409) (0.064) (0.339) 1.387 2.647 1.462 1.509 1.599-0.313 1.558-0.691 0.859-3.121 1.275 1.030 (2.366) (2.862) (2.025) (2.370) (2.138) (3.055) (1.877) (2.511) (4.035) (5.522) (2.264) (2.391) 19 squared -1.116-2.017-1.169-1.204-1.295 0.016-1.254 0.387-0.763 2.327-1.027-0.868 (1.909) (2.258) (1.634) (1.871) (1.725) (2.415) (1.514) (1.982) (3.254) (4.405) (1.826) (1.895) Mariage 0.211 0.352 0.144 0.149 0.207 0.005 0.138-0.106 0.146-0.026 0.051-0.010 (0.086) (0.172) (0.072) (0.155) (0.080) (0.158) (0.068) (0.153) (0.155) (0.217) (0.083) (0.208) Nofchildren -0.037-0.044-0.051-0.051-0.054-0.020-0.064-0.043-0.093-0.063-0.041-0.036 (0.022) (0.024) (0.020) (0.020) (0.020) (0.034) (0.019) (0.025) (0.039) (0.050) (0.023) (0.027) Income 0.183-0.003 0.519 0.079 1.074-0.023 0.520 1.113 4.163 1.524 0.677 0.284 (0.099) (0.016) (0.397) (0.473) (0.175) (0.020) (0.396) (0.570) (1.746) (1.282) (0.375) (0.636) Own house 0.426 0.340 0.314 0.313 0.374 0.595 0.287 0.421 0.191 0.530 0.085 0.082 (0.088) (0.127) (0.077) (0.090) (0.080) (0.168) (0.072) (0.111) (0.157) (0.314) (0.088) (0.089) Total wealth -0.002-0.001 0.030 0.016 0.001 0.006 0.023 0.023-0.235 0.081 0.024 0.016 (0.003) (0.003) (0.010) (0.006) (0.006) (0.004) (0.026) (0.007) (0.141) (0.062) (0.009) (0.006) Observations 9299 9299 12938 12938 11365 11365 15004 15004 3287 3287 9918 9918 R 2 0.151 0.018 0.161 0.161 0.231-0.346 0.208-0.092 0.345 0.142 0.169 0.157 DWHchi2 1.392 0.038 4.950 4.243 2.439 0.017 DWHpval 0.238 0.845 0.026 0.039 0.118 0.897 Standard errors in parentheses p<.1, p<.05, p<.01 All economic variables (e.g. Total wealth, Income) are measured in dollars. In the specification (6), (country dummy) (economic variable) (e.g. (Total wealth) (the U.S. dummy)) variables are also included. The estimated coe cients of these cross terms are not presented. The Belgium dummy is omitted.