SixtyFour Brown Laschever

When They're Sixty-Four: Peer Effects and the Timing of Retirement

Kristine M. Brown and Ron A. Laschever

Article Citation

Brown, Kristine M., and Ron A. Laschever. 2012. "When They're Sixty-Four:

Peer Effects and the Timing of Retirement." American Economic Journal:

Applied Economics, 4(3): 90115.

DOI:10.1257/app.4.3.90

Abstract

This paper examines the effect of peers on an individual's likelihood of

retirement using an administrative dataset of all retirement-eligible Los

Angeles teachers for the years 1998-2001. We use two large unexpected

pension reforms that differentially impacted financial incentives within and

across schools to construct an instrument for others' retirement decisions.

Controlling for individual and school characteristics, we find that the

retirement of an additional teacher in the previous year at the same school

increases a teacher's own likelihood of retirement by 1.5-2 percentage

points. We then explore some possible mechanisms through which this effect

operates. (JEL H75, I21, J14, J26, J45)

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90

American Economic Journal: Applied Economics 2012, 4(3): 90115 http://dx.doi.org/10.1257/app.4.3.90

When Theyre Sixty-Four: Peer Effects and the Timing of Retirement

By Kristine M. Brown and Ron A. Laschever*

This paper examines the effect of peers on an individuals likelihood of retirement using an administrative dataset of all retirement-eligi-ble Los Angeles teachers for the years 19982001. We use two large unexpected pension reforms that differentially impacted financial incentives within and across schools to construct an instrument for others retirement decisions. Controlling for individual and school characteristics, we find that the retirement of an additional teacher in the previous year at the same school increases a teachers own likelihood of retirement by 1.52 percentage points. We then explore some possible mechanisms through which this effect operates. (JEL H75, I21, J14, J26, J45)

Many countries and US states are reforming insolvent public pension programs by raising retirement ages and cutting benefits.1 The extent to which indi-vidual retirement decisions respond to these reforms will determine their effects on pension viability, labor force composition, and elderly well-being. Cross-country comparisons show that the labor force participation of older workers is strongly aligned with social security rules, and calibrations of macroeconomic models imply large intertemporal labor supply elasticities.2 However, the results of several

1 In 1983, the United States raised the Social Security normal retirement age from age 65 to 67 for those born after 1959. Recently, many European countries have reformed their social security programs: Germany raised the retirement age from 65 to 67 (Wilson 2010); France from 60 to 62; Spain from 65 to 67 (Minder 2011).

2 Gruber and Wise (2004) include several examples of the distinct retirement patterns found across countries. Mastrobuoni (2009) shows (incomplete) shifting toward new normal retirement ages in the US. See Chetty et al. (forthcoming) for an overview of the labor supply elasticity estimates from the macroeconomic literature.

* Brown: Department of Economics and School of Labor and Employment Relations, University of Illinois at Urbana-Champaign, 504 E. Armory Ave., Champaign, IL 61820 (e-mail: [email protected]); Laschever: Department of Economics and School of Labor and Employment Relations, University of Illinois at Urbana-Champaign, 504 E. Armory Ave., Champaign, IL 61820 (e-mail: [email protected]). We thank Rich Akresh, Isabelle Bajeux-Besnainou, Jane Leber Herr, Salar Jahedi, Tobias Klein, Darren Lubotsky, Elizabeth Powers, Deborah Rupp, two anonymous referees, and seminar participants at the 2008 SEA Meetings, 2010 ASSA Meetings, 2010 SOLE Meetings, 2011 Netspar Workshop, Hebrew University, Tel-Aviv University, University of Arkansas, University of Illinois at Chicago, and the University of Illinois at Urbana-Champaign for discussions and comments. Joon Yeol Lew provided excellent research assistance. This research was supported by the US Social Security Administration through grant #10-M-98363-1-01 to the National Bureau of Economic Research as part of the SSA Retirement Research Consortium. The findings and conclusions expressed are solely those of the authors and do not represent the views of SSA, any agency of the federal government, or the NBER. All errors are our own.

To comment on this article in the online discussion forum, or to view additional materials, visit the article page at http://dx.doi.org/10.1257/app.4.3.90.

ContentsWhen Theyre Sixty-Four: Peer Effects and the Timing of Retirement 90I. Pension Plan Details and Data 94II. Empirical Framework 98III. Results 103A. Instrumental Variable Estimates of the Effect of Peers on Retirement 105B. Reduced-Form Results 108IV. Alternative Group Specifications and Robustness Checks 110V. Discussion and Conclusion 113REFERENCES 114

VoL. 4 No. 3 91BroWN ANd LAsChEVEr: pEEr EffECTs ANd ThE TimiNg of rETirEmENT

microeconomic studies imply a small labor supply elasticity with respect to pension program financial incentives.3

The goal of this paper is to examine the role of peer effects in reconciling some of these seemingly contradictory findings. In the presence of peer effects, an indi-viduals change in retirement behavior in response to a pension reform will spill-over and affect the retirement decisions of others, even those that were not directly affected by the reform. The change in individual retirement incentives is then ampli-fied and the resulting social multiplier in retirement may cause the aggregate impact of pension reforms to be larger than would be implied by individual responses to changes in pension financial features.

There are several reasons why peer effects may play a role in the retirement con-text. First, retirement is a complicated financial decision and individuals may rely on others as a source of information or even simply mimic the behavior of oth-ers. Second, individuals may also enjoy retirement more (or enjoy their time at work less) if their long-time colleagues are retired. Further, the growing evidence that peers affect workplace productivity, and other labor market and economic out-comes, suggests that peers may be important in the retirement decision.4, 5

In this paper, we examine the direct effect of peers on the retirement decisions of Los Angeles public school teachers and estimate the causal effect of the number of colleagues retirements in the previous year on a teachers own likelihood of retirement. Using an exogenous reform of the teachers pension plan, coupled with a rich administrative panel dataset of all retirement-eligible Los Angeles school dis-trict teachers in the years 19982001, we employ an instrumental variable strategy to address the main challenges to peer effects estimation. We find that all else equal, an additional peer retirement in the previous year has a positive and statistically significant effect on ones own likelihood of retirement.

While there is some evidence that peers are important for retirement-related deci-sions, there is little work examining the effect of peer behavior on retirement timing. Duflo and Saez (2002, 2003) find that enrollment in retirement plans is affected by the choices of colleagues and Hastings and Tejeda-Ashton (2008) find that peers and family members play a role in providing information for the choice of pension plans in Mexico. These studies do not address the decision of when to retire, but lend support to the importance of coworkers and friends in retirement planning. Our findings, on the other hand, provide some of the first evidence that peers may not only affect retirement decisions indirectly by influencing retirement savings, but also that they have a direct impact on whether or not an individual retires in a given year. Chalmers, Johnson, and Reuter (2008), concurrent with our work,

3 For example, Burtless (1986) and Krueger and Pischke (1992) find that Social Security can explain only a small part of the labor force participation trends of older individuals. Coile and Gruber (2007) find that financial incentives cannot fully explain the high incidence of retirement at ages 62 and 65. Manoli and Weber (2011) provide quasi-experimental evidence of a relatively small response to pension parameters.

4 Peers at the workplace have been shown to have an effect on productivity (e.g., Bandiera, Barankay, and Rasul 2009; Mas and Moretti 2009), and some of the underlying social mechanisms in production may extend to the retirement decision.

5 Researchers have examined peer effects in such settings as welfare take-up (Bertrand, Luttmer, and Mullainathan 2000), drug use among college students (Duncan et al. 2005), social norms and unemployment dura-tion (Stutzer and Lalive 2004), recidivism (Bayer, Hjalmarsson, and Pozen 2009), etc.

92 AmEriCAN ECoNomiC JourNAL: AppLiEd ECoNomiCs JuLy 2012

also examine the effect of coworkers retirement behavior on individual retirement decisions and find that peers play an important role. Whereas they focus on groups at the organization level, with our data we are able to identify all colleagues that work together in the same physical location. Also, the pension reform we examine created multidimensional variation in the incentive to retire across teachers, which is required for our identification strategy.

Incorporating peer effects into any economic decision, including the retirement decision, introduces several challenges to identification and estimation. However, the Los Angeles public school setting and our administrative data offer several advantages for identifying and estimating the causal effect of peer retirements on individual retirement decisions. There are potentially many factors, unrelated to peer effects per se, that could be mistakenly attributed to peer effects. For exam-ple, one might observe a correlation in the retirement outcomes of those who work together because of correlated tastes for leisure among colleagues or as a response to a demanding supervisor.

We show, by extending the Partial Population Intervention approach (Moffitt 2001), that a policy reform that exogenously and differentially impacts the finan-cial incentives for retirement across the teaching population can be used to address these challenges and identify the causal effect of others retirement behavior on own likelihood of retirement. The source of our instrumental variable strategy is two pension reforms that created an exogenous, unexpected, and permanent shock to the pension financial incentives for retirement of Los Angeles teachers. The reforms affected individuals differently depending on their age and years of ser-vice at the time of the reform, creating necessary across-school and within-school variation while allowing us to control for the direct effect of the reform on ones own retirement plan. The exogenous and unexpected shock to the pension finan-cial incentives of others is used as an instrument for the number of colleagues that retired in the previous year.

The differential impact of the reform is essential for identification for two rea-sons. First, by affecting individuals differently, it creates variation in the effect of the reform on each peer group due to differences in the composition of teacher charac-teristics. Second, if all teachers in the same school are affected in the same manner, even if the shock is completely exogenous, one cannot identify the effect of peers separately from the direct effect of the shock on an individual.

This differential reform underlies our identification strategy but several features of our data are also beneficial for estimating peer effects. The data include all teach-ers in Los Angeles and their school assignments, so we are able to fully determine and observe each teachers peer group, which we define as retirement-eligible col-leagues working in the same physical location. This is a particularly natural and relevant reference group as workplace colleagues might be a source of information about a work-related pension plan. Because California teachers are not covered by Social Security, their employer-sponsored pension and reforms of this pension are likely to be especially important considerations for retirement planning. We are also able to match teachers to school characteristics that may be correlated with the work environment, such as student test scores. The data allow us to accurately identify the financial incentives that may influence individual retirement decisions, as the


administrative data include salary and other variables that are sufficient to calculate retirement benefits.

Applying our differential instrumental variable strategy and controlling for a host of school characteristics and other teachers characteristics, we find that an additional peer retirement in the previous year increases own likelihood of retire-ment by 1.52.0 percentage points in our preferred specifications. These results are also robust to the inclusion of a school-level fixed effect and an individual-level fixed effect. Several robustness checks indicate that teachers responses to col-leagues retirements in the previous year are not driven by coordinated retirements of spouses, a subsequent increase in workload or a distaste for working with less experienced teachers. We also perform two types of falsification tests, which pro-vide further evidence that our findings are not an artifact of spurious correlations. Using an additional data source, we examine whether the social effect is stronger across sub-networks as defined by race, gender, and subject taught. While there are differences in retirement rates across these characteristics, we find no evidence of a differential response to peers across these characteristics or evidence that peers respond more strongly to those similar to them.

Finally, we further investigate two types of mechanisms through which the social effect may operate. We find little support for the hypothesis that school-specific retirement-age norms play an important role. Because individuals may be affected not only by those who retire, but also by the information provided by those who decide to stay, we examine how teachers are influenced by the change in the financial situation of all of their peers. We find evidence that teachers are not only influenced by others change in financial incentives, but that their response to their own financial incentives is influenced by the change experienced by oth-ers. We also find that the extent to which others maximize their pension benefits affects the degree to which an individual fully maximizes the financial benefits of his or her own pension plan.

Our findings suggest that peers play an important role in influencing the retire-ment decision and are consistent with a social multiplier in retirement. One policy implication is that raising the Social Security normal retirement age for younger cohorts could cause those that are not directly affected by the reform to also delay retirement, while the effect on the target group is mitigated. Our results not only document and estimate the existence of peer effects, but also provide a direct dollar amount estimate of the spillover effect that providing one person with a financial incentive would have on his or her peers. For example, we find that holding all other teachers pension wealth constant, providing an additional unexpected $80,000 of pension wealth to one colleague (the average amount of additional pension wealth gained in the first reform) is equivalent to unexpectedly increasing ones own pen-sion wealth by approximately $6,400.

The next section introduces the retirement plan of Los Angeles teachers as well as the unanticipated pension reforms and describes the data. Section II models the retirement decision and discusses the use of the reform to identify the peer effect. Section III describes the results. We consider alternative specifications and robust-ness checks in Section IV. Section V concludes. Additional details and specifications can be found in the online Appendix.


I. Pension Plan Details and Data

We examine the effect of peer retirement decisions on individual retirement decisions in the Los Angeles Unified School District (LAUSD). This setting is advantageous for several reasons. Small peer groups that are relevant for an individuals retirement decision can be naturally defined as the retirement-eligible teachers working in the same school building. Further, we observe many peer groups because LAUSD, the second largest school district in the country, has over 500 schools. Employment conditions across groups are also more homogenous than they would be across other workplaces. By virtue of working in the same school district, teachers at all schools in our sample share the same salary sched-ule, benefits, and curriculum requirements.

All the teachers in our sample are covered by a statewide defined benefit retire-ment plan administered through the California State Teachers Retirement System (CalSTRS). The characteristics of the California teachers program closely resem-ble those of most employer-sponsored defined-benefit pensions and those of Social Security. Each full-time teacher is required to contribute to the program while work-ing and, upon retirement, receives a lifetime annuity that is determined by his or her salary, retirement age, and years of service.

While many factors will enter an individual teachers retirement decision, includ-ing health, family considerations, and working conditions, the CalSTRS pension is likely to be an important factor for Los Angeles teachers for two reasons. First, CalSTRS members are not simultaneously covered by Social Security, making this pension the only source of employment-based retirement income for career teach-ers. Second, CalSTRS is relatively generous; the average replacement rate for retired teachers is 59 percent of final average salary, compared to a replacement rate of 41 percent for the average Social Security annuitant.6

We exploit two pension reforms to examine how changes to pension financial incentives directly affect individual retirement decisions and also how they indi-rectly affect behavior through the retirement decisions of colleagues. The reforms to the teachers pension are at the heart of our instrumental variable strategy as detailed in Section II. We summarize the effect of the reforms on individual pen-sion financial measures below. The pension plan and reform are further detailed in online Appendix II.

In August 1998 and August 2000, the California State Legislature passed close-of-session bills that substantially increased the generosity of the teachers pension for retirements occurring on or after January 1, 1999 and January 1, 2001, respectively, without any provision to fund the benefit increases.7 The reforms were unexpected and the details were worked out just prior to passage, however, the changes were clearly communicated to all active teachers through the CalSTRS fall newsletters.

The first reform increased pension wealth, the present value of the stream of retirement income, by 1020 percent for those age 60 or older and by 10 percent for younger teachers with at least 30 years of service. The interaction of age and service

6 California State Teachers Retirement System (2006) and Social Security Administration (2006).7 The 1998 legislative bills were AB 1102 and AB 1150 and the 2000 bill was AB 1933.


is important for determining the impact of the reform at the individual level and this interaction created significant variation in the effect of the reform across individuals with similar ages and years of experience. A stylized example of this interaction is illustrated in Figure 1. Panels A and B show pension wealth pre- and post-reform as a function of age, holding service constant at 29 and 30 years, respectively. Panel A shows that the current pension wealth of a 60 year old with 29 years of service is unaffected by the reform, but the unexpected change in pension wealth for an otherwise identical 63 year old colleague is $150,000. Comparing across panels, it is clear that the unexpected change in pension wealth for 60 year olds with just a one year difference in service is also large. The second CalSTRS reform provided a lump sum longevity bonus to teachers at three target service levels. The bonus awarded an additional $2,400 of annual retirement income to teachers with 30 years of service, $3,600 to those with 31 years of service, and $4,800 to those with 32 or more years of service. This reform also affected individuals differently, but only along the service dimension. For the average teacher that was eligible for the bonus at the time of reform, his or her pension wealth increased unexpectedly by 613 per-cent. Such an unexpected increase in pension wealth provides affected individuals with an additional incentive to retire in the current period.

We focus on the impact of the reforms on pension wealth in this section because it is the basis of our IV estimation strategy, however, this was not the only effect of the reform on pension financial incentives. The reform also provided some individuals with an additional incentive to delay retirement. For example, both reforms introduced a discontinuous increase in benefits at 30 years of service,

Figure 1. The Effect of the First Reform on the Pension-Wealth-Age Profile

Note: Salary is fixed at $55,000/year, the individual is assumed to live until age 85, and future income is not discounted.

5

6

7

8

9

10

Pen

sion

wea

lth ($

100k

)

Age

5

6

7

8

9

10

55 56 57 58 59 60 61 62 63 64 65

Pen

sion

wea

lth ($

100k

)

Age

Pre-reform pension wealthPost-reform pension wealth

Panel A. Holding service fixed at 29 years Panel B. Holding service fixed at 30 years

55 56 57 58 59 60 61 62 63 64 65


providing individuals with 29 years of service at the time of the reforms with a clear incentive to delay retirement for a year. We do not detail this aspect of the reforms here (see online Appendix II for further technical details), but we intro-duce a variable in Section II that captures the financial option value of delaying retirement and include it in our analysis.

data.In this study we use individual-level administrative data for the com-plete population of teachers age 45+ that were employed by the LAUSD.8 The data include an annual census of active teachers for each of the academic years 19972003 and all retirement episodes during this time period. We focus on retire-ment-eligible teachers, those age 55 or older in academic years 19982001. Each person-year observation (N = 24, 444) includes age, years of service, salary, gen-der, retirement date (if applicable) and school assignment. School assignment is the key variable with which we are able to identify each teachers colleagues and a teacher-specific identifier allows us to follow teachers over time. Two measures of the pension financial incentives, pension wealth and peak value, are calculated for each teacher in each academic year using the salary, service, and age informa-tion available from the administrative data. These measures are described in Section II and further calculation details can be found in Appendix II. The administrative teacher-level data has also been matched to school-level characteristics.9 These school characteristics include the average age, service, and education of all teach-ers (regardless of age) in the school, as well as student characteristics, such as test scores and grade level of the school.

We use an academic year as the time unit of analysis. The academic year is defined as starting in September and ending the following August (e.g., academic year 1998 covers the period September 1, 1998August 31, 1999). Although we know the exact date of all retirement occurrences and could look at retirement decisions in finer units of time, such as months or even days, an annual measure is more natural for the LAUSD context. Retirements are not spread evenly across the year as over 80 percent of retirements occur during the summer months with over 70 percent occurring in June alone.10 Teachers are also required to formally announce their retirements at least 30 days in advance (and they may be encour-aged to do so even earlier by administrators for staff planning purposes). These two facts make the window in which teachers are able to respond to observed retirements of other teachers at their school by immediately retiring in the same academic year very small, though it does not rule out peer consultation that results in simultaneous retirements. In Section IV, we show that our results are robust to looking at shorter and longer peer retirement windows, as well as at contempora-neous peer retirements.

8 These data were compiled with the assistance of the Office of Personnel Research and Assessment in LAUSD.9 We use the publicly available CBEDS data from the California Department of Education (http://www.cde.

ca.gov/ds/).10 This is not surprising as teachers may be reluctant to leave their classes mid-year. Finishing out the contract

year is also important for maximizing retirement service credits.


Summary statistics for LAUSD teachers are shown in panel A of Table 1. Each year 9.4 percent of teachers age 55 and over retire. The retirement-eligible LAUSD teachers are, on average, just short of 60 years old and have 21 years of service within LAUSD, and over 70 percent are women. As a group they have an average pension wealth of $518,000. The peak value measure, fully described in the next section, suggests that these teachers could increase their pension wealth by up to 20 percent, on average, with continued work. For those individuals that had an unex-pected gain in pension wealth due to the reforms in academic years 1998 and 2000, the average gain in pension wealth was $81,200.

If coworkers are affecting individual retirement decisions, then it is not only own characteristics that matter, but the characteristics of ones group. For each teacher,

Table 1Summary Statistics for Academic Years 19982001

panel A. Teacher-level (Teacher year); N = 24,444

panel B. school-level (school year); N = 2,270Statistics of the school-mean

Variable Mean SD Median Mean SD Median

Retired during this academic year 0.094 0.292 0.093 0.117 0.063Pension wealth ($100k) 5.180 3.238 4.626 5.217 1.508 5.171Peak value ($10k) 10.106 8.596 10.135 10.393 3.721 10.241Unexpected change in pension wealth ($100k)a 0.812 0.342 0.844 0.828 0.201 0.839Unexpected change in peak value ($10k)b 3.230 3.849 3.103 2.474 2.768 2.805Salary ($10k) 5.837 0.738 6.062 5.822 0.367 5.842Age 59.920 3.912 59.030 59.859 1.675 59.788Service 21.240 11.048 20.960 21.216 5.060 21.473Female 0.725 0.446 0.805 0.206 0.857Average peers pension wealth ($100k) 5.023 1.287 4.994 5.055 1.496 5.010Average peers peak value ($10k) 10.098 2.923 9.879 10.285 3.380 10.169Total of peers unexpected change in pension wealth ($100k)c

5.841 4.860 4.384 3.520 3.501 2.558

Average of peers unexpected change in pension wealth ($100k)c

0.343 0.188 0.318 0.356 0.217 0.334

Total of peers unexpected change in peak value ($10k)c

36.434 52.883 13.357 22.590 35.464 8.090

Average of peers unexpected change in peak value($10k)c

2.167 2.390 0.927 2.277 2.488 1.489

Number of peers age 55+ at school 18.176 13.181 14.000 10.660 9.378 8.000Number of full-time equivalent teachers at school

80.736 44.759 72.580 56.746 35.129 48.000

Average age of all teachers at school 43.946 3.267 44.100 43.071 3.681 42.918Average teaching experience of all teachers at school

12.917 2.697 12.800 12.396 3.067 12.140

Pupil to teacher ratio 21.698 3.273 21.000 20.290 3.340 19.608Math test ranking at school level 5.567 2.608 5.500 5.506 2.659 5.367Fraction of all teachers with at least an MA at school

0.286 0.089 0.286 0.266 0.098 0.257

Elementary school 0.513 0.500 0.722 0.448Middle school 0.187 0.390 0.125 0.330High school 0.250 0.433 0.086 0.281

Note: The sample includes, for each academic year 19982001, all teachers age 5575 in the given year. a Observations are included conditional on having a nonzero value of the unexpected change in pension wealth

at the individual level (5,144 individual-year observations).b Observations are included conditional on having a nonzero value of the unexpected change in peak value at the

individual level (8,126 individual-year observations).c These include only observations in the years 1998 and 2000 (11,846 individual-year observations).


we define the relevant peer group for retirement to be all teachers age 55 or older that are working in the same school.11 There are 585 unique schools observed in LAUSD over this time period, and the average number of teachers age 55 or greater working in each school is 10.77. However, there is substantial variation across schools.

Panel B of Table 1 provides summary statistics for the schools. The table treats each school-by-year average as an observation, and reports the mean, median, and standard deviation of the average-within-school teacher characteristics. The standard deviation illustrates the amount of variation in peer characteristics across schools. The variables central to our estimation are the school-level retirement rate and the unexpected change in pension wealth that is used as the instrument for school-level retirements. The average retirement rate across school-by-year observations is 9.3 percent but the standard deviation is 11.7 percent. The mean total unantici-pated change in peers pension wealth (our primary instrument) in the reform years is $352,000. There is also significant variation in this variable across schools. As indicated in Table 1, the standard deviation in the average total unexpected change in pension wealth across schools is $350,100. We discuss this measure, used as an instrument, in further detail in the next section.

II. Empirical Framework

The focus of this paper is the identification and estimation of the effect of peers on ones own likelihood of retirement. We highlight this in our model by expand-ing on the core feature of all retirement decision models, utility maximization over lifetime consumption and leisure (years in retirement), to explicitly incorporate both the effects of the school environment and the characteristics and behavior of ones peers. Given that our focus is not the estimation of the price and income elasticities of labor supply for comparison with the existing retirement literature, a reduced-form approach is more suitable for our purposes.12

The econometric specification we use is derived from a utility-based choice framework (McFadden 1974). Let u i, s, t * be the latent utility that individual i, in school s gets from retirement in year t. We specify the latent utility as an addi-tively separable function of work-related financial incentives, other individual characteristics, and school characteristics. Allowing for an individual fixed effect i , the econometric framework of the retirement decision y = 1, can be written as Pr( y i, s, t = 1 | i, s, t) = Pr( u i, s, t * > 0 | i, s, t). To keep our discussion and illustration of the identification strategy tractable we focus, as the bulk of the literature has, on the linear-in-means specification:13

(1) y i, s, t = X i, s, t + m( _ y i, s ) + Z s, t + s + t + i + i, s, t ,

11 We chose 55 since, in almost all cases, that is the earliest retirement-eligible age. However, our results are robust to defining the group as those 45 and older.

12 See Lumsdaine and Mitchell (1999) for a survey of the structural retirement literature.13 However, the reduced-form specifications were also estimated using the logit functional form and the results

are qualitatively and quantitatively similar. See online Appendix Table A8.


where _ y i, s , Z s, t , and s are school-level measures that may affect retirement. The

individuals observable financial incentives, such as salary, and the pension variables pension wealth (p W i, s, t ) and peak value (p K i, s, t ), are included in X i, s, t . Observable personal characteristics that may affect the disutility of working, such as age and years of service, are also included in the vector X i, s, t , while unobservable character-istics are captured by an individual-level fixed effect i and individual shock i, s, t . For the purpose of calculating the pension variables, retirement and pension claim-ing are treated as coincident, and we assume it is an absorbing state.14 We describe the pension variables briefly below as they are important for capturing individual financial incentives and are central to our identification strategy.

Pension wealth, p W i, s, t , is the present discounted value of the stream of pen-sion income for the individual if he or she retires in year t and it can be written as

a=t T a | t ( 1 _ 1 + r ) at B(t), where B(t) is annual pension income; a | t is the prob-ability of living to year a, given having lived to year t; and r is the real interest rate.

The peak value measure, introduced by Coile and Gruber (2001), succinctly captures the financial return to work or the price of retirement in terms of pen-sion wealth when pension wealth accrual is nonlinear.15 This measure of the finan-cial option value of delaying retirement is the difference between pension wealth associated with retirement in the current year and the expected pension wealth for retirement at the future age that maximizes pension wealth. It can be written p K i, s, t = p W i, s, r max p W i, s, t , where p W i, s, t is pension wealth in year t, and r max is the retirement year in [t + 1, T ] in which pension wealth is maximized.16

The effects of the school environment as well as the characteristics of ones peers are summarized in equation (1) by: m( _ y i, s ) + Z s, t + s . We consider three possible types of group-level effects. The first type of measure is the retirement behavior or outcomes of all others,

_ y i, s , where the notation i denotes that own

behavior is excluded. The second type of measure is the observable school charac-teristics summarized by the vector Z s, t , such as the student body or the age compo-sition of other teachers in the school. The third type of measure is the unobserved school-level effect, such as a friendly and supportive school principal, which is denoted by s .

We are first and foremost concerned with correctly identifying the effect of others behavior from alternative explanations, such as workplace environment, however, there are many mechanisms through which the peer effect could operate. One rea-son individuals may be affected by others retirement is that they derive utility from

14 Teachers that have started receiving CalSTRS pension payments are eligible to work again only in California school districts that face a shortage of qualified teachers, but they will not accrue wealth under CalSTRS and they face an earnings limit.

15 Peak value does not capture the structure of these benefits precisely, but this would only be crucial if one were trying to estimate structural parameters, such as retirement elasticity. For example, Blomquist and Newey (2002) develop a nonparametric estimate in the presence of nonlinear budget constraints. We adapted this method and found that the peak value approach captured the essential features of the pension program well enough given the focus of our paper.

16 Coile and Grubers (2001) peak value is similar to the Stock and Wise (1990) utility option value. Peak value has been used extensively in other work including a volume of international retirement studies edited by Gruber and Wise (2004) and Asch, Haider, and Zissimopoulos (2005). Similarly, Samwick (1998) calculated the individual option value and used this variable directly in a regression.


acting in accordance with others (social norms). Alternatively, increased retirement behavior among others may increase own likelihood of retirement for other reasons. Deciding when to retire is complex so individuals may mimic the behavior of others in order to reduce the computational burden of the decision. Brock and Durlauf (2001) discuss utility-based models in which own behavior depends on the utility and behavior of others, and distinguish between own utility increasing in group-level outcomes, and own utility depending on the distance from the group-level outcome. In online Appendix III, we explore two possible types of mechanisms: conforming to retirement-age norms, and the effect of others response to financial incentives on own response to financial incentives.

identification strategy.The growing body of literature on identification and estimation of peer effects has recognized several threats to validity and problems associated with the family of specifications that includes equation (1).17 First, because assignment to schools (or groups) is not random, a concern is that teachers with an unobservable taste for work might select their working environment based on the characteristics (observable or unobservable) of other teachers. Second, like in the nonpeer case, an omitted variable problem may exista common unobserv-able-to-the-econometrician factor in a school, such as the school principal, may be affecting all teachers retirement decisions.

Additionally, two types of reflection problems (Manski 1993) could exist in our setting, and would cause us to mistakenly attribute the observed social effect to others retirement behavior. First, peer unobservables may be correlated with the observables of those peers resulting in one type of reflection problem. Second, because we are using the linear-in-means specification, even if assignment were random, and there were no school-unobservable components, a reflection problem would still exist, namely the inability to separately identify and . In our context, for example, we would want to distinguish and identify whether peer retirements were directly affecting own retirement, or whether teachers were affected by the years of service of their colleagues. Teachers may prefer to work with (and thus be less likely to retire when surrounded by) more experienced colleagues, but at the same time, the average years of service among colleagues is positively correlated with colleagues retirements.

Our identification strategy makes use of three features of our setting and avail-able data to address these potential sources of bias. We use the exogenous changes induced by the pension reform to derive instrumental variables to address any bias for group-level retirement outcomes as well as own pension financial incentives. We also exploit the panel data nature of our sample to difference out any individual or school-level, fixed-over-time unobservable component. Finally, the richness of the individual- and school-level data allows us to distinguish among various school-level effects on teacher retirement, such as student test scores or an increase in work-load due to colleagues retirements.

17 The interested reader is referred to Brock and Durlauf (2001) and Moffitt (2001) for a more thorough discus-sion of some of these issues.


In the case of peer effects, a valid instrument, i.e., one that is correlated with the endogenous group outcomes and uncorrelated with own unobservables, is not suf-ficient, as noted for instance, by Brock and Durlauf (2001) and Krauth (2006). An additional requirement of the instrument is that it has a differential effect across and within schools. The intuition behind this requirement is straightforward. Consider a case in which a reform exposes all group members to the same exogenous incentive to retire. This new incentive will enter each individuals retirement decision and so should be included directly in the regression. Therefore, it can not also be used as an instrument for the groups retirement behavior, as it would be identical to the own-incentive measure. In this case, it will not be possible to distinguish an individuals response to his or her own change in incentives from his response to the groups reform-induced change in behavior, even though the instrument was not correlated with individual unobservables.

Moffitt (2001) discusses a Partial Population Intervention strategy that can be used when some individuals in each group are assigned a treatment (e.g., in Miguel and Kremer (2004) only some children in every class receive a deworming treat-ment; in Cipollone and Rosolia (2007) the treatment only directly affected boys in each class). In online Appendix I, we extend this approach to allow for different treatments to individuals within a group, which we denote as a differential popula-tion intervention (DPI). For example, the reform caused an unanticipated change in pension wealth, and did so differently for each teacher, according to their age and years of service. In turn, this generates sufficient variation across and within groups. This allows us to instrument both own and others measures simultaneously (e.g., Acemoglu and Angrist (2000) instrument own schooling and state-level schooling using different instruments).

The differential IV addresses concerns regarding the endogeneity of the group retirement measure as well as own financial measures. However, a common concern in the retirement literature is that in addition to the pension variables, other variables of interest may be correlated with individual-level unobservables that also affect the retirement decision. This would lead to biased estimates even if peer effects played no role. The fact that all California teachers are covered by the same pension alleviates a usual concern that individuals may select into retirement programs with features that match their tastes for work, however, it is still possible that teachers with relatively poor health or greater demands outside of work may be less attached to the labor force and have systematically lower pension wealth.

In addition to using the pension-reform-derived instrumental variables to address the endogeneity of own pension plan financial variables, our panel data allow us to use fixed effects to address other systematic unobservable character-istics, such as health or marital status. Note that the case of an individual-level unobservable fixed component encompasses the less general case of an unob-served school-level fixed component when teachers do not change schools.18 We extend our DPI approach to the case where there is an unobservable individual-level and school-level fixed effect, and show that identification is possible even

18 As discussed in Section III, our results are robust to the inclusion of teachers who moved across schools, as they represent a very small portion of the sample.


if there is a differential reform in only some of the periods. As discussed in the empirical specifications, the inclusion of an individual fixed effect allows us to address unobserved health, marital status, and external wealth resources. Further, in Section V, we provide evidence that our peer effect estimates are not driven by the joint retirement decisions of couples working at the same school.

It is useful to think about the role of fixed effects when combined with instrumen-tal variables. First, the inclusion of fixed effects would address any concern about a fixed group-level unobservable effect. However, it would not suffice in the case where unobservable characteristics are (systematically) changing over time. This is especially a concern when studying retirement that explicitly alters group mem-bership, since group characteristics are based on the composition of its members. Similarly, even a constant setting may lead to group responses to shocks that would not be captured by the fixed effect. For example, even if the principal did not change during a reform year, she might influence teachers to respond to and think of the reform in a certain way. For these reasons, fixed effects would not eliminate the need for instrumenting the group effects, and we employ both strategies simultaneously.

In regard to own characteristics, we view the use of individual fixed effects as addressing many of the potential biases due to unobservables such as wealth and health. Controlling for an individual fixed effect, the pension reform is not likely to be correlated with any yearly shocks to health or nonpension wealth. Unlike the case of group-level measures, when controlling for the fixed effects changes to own financial measures are not likely to be correlated with the taste for retirement. Therefore, once fixed effects are included, instrumenting own characteristics is not likely to be needed. For completeness, we present our fixed effects results with and without instrumenting own characteristics.

The derivation of the DPI identification with fixed effects in online Appendix I follows the setup of many papers in the literature on peer effects by examining the effect of others contemporaneous outcomes. One disadvantage of contempo-raneous timing is the need to assume the existence of a social equilibrium (e.g., Manski 1993) or that individuals have the correct expectations about group behav-ior.19 The detailed panel data at our disposal allows us to also examine how lagged (and therefore observable to teachers) retirements of others affect individuals. Our preferred specification for equation (1) is to use the lagged, and therefore actual, realization of the group outcome: m( _ y i, s ) = _ y i, s, t1 (others retirement in the previous period, self excluded), instead of m( _ y i, s ) = E[ y j, t | j s ]. The results we present in Section IIIA focus on lag-outcomes specifications as they are more consistent with the institutional detail discussed in Section I. However, our deriva-tions in online Appendix I emphasize that the source of the identification is not the use of lagged outcomes. Note that using lagged outcomes does not eliminate the simultaneity problem of the group decision and requires us to use the identifica-tion strategy discussed in this section.20 We find similar results in Section IV when

19 See Angrist and Pischke (2008, 19498) for a concise treatment of the drawbacks to using same-period outcomes of others.

20 For example, if there is an important observable or unobservable group-level variable ( Z s or s ) that deter-mines retirement, it is likely to affect previous year retirements of others just as strongly as it affects (planned) current-year retirements of others.


we examine alternative group-effect-timings that consider the contemporaneous retirement of others.

The above discussion assumed that all peers have an equal weight on ones own outcomes. We relax this assumption in Section IV by considering various group partitions, such as gender, race, and teaching subject.

III. Results

In Section II, we examined the advantages of a differential instrumental variable (IV) strategy. The IV for colleague retirements is constructed from measures of the reform-induced change in pension financial incentives faced by each individual. For both the first and second reforms, individual i s unanticipated change in pen-sion wealth (and similarly for peak value) is the pension wealth for individual i at time t calculated under the post-reform benefit formula minus the pension wealth for individual i at time t calculated under the pre-reform benefit formula: pW_i V i, t = p W i, t post p W i, t pre . The unexpected changes in pension wealth are completely driven by differences in the pre-reform and post-reform calculation of pension benefits. The individual characteristics that enter the pension formulaage, years of service, and salaryare held constant at their values in year t. We use this individual-level shock as an instrument for own pension financial incentives.

The main IV for colleague retirements in year t at school s is calculated as the sum of colleagues unanticipated change in pension wealth, self excluded:

peer_pW_i V i, s, t = js, ji

p W_i V j, t .

Similarly, in some specifications we also make use of the unexpected change in peak value, the shock to the option value of delaying retirement, which is calculated in the same way. The measures of the unanticipated change in financial incentives will be zero in nonreform years.

There are several conditions that must hold for this IV to be valid for estimat-ing peer effects in retirement. As motivated in Section II, crucial for identification, the reforms must have a differential effect on teachers within and across schools. There is large variation in pW_i V i, t both within and across schools (see Table 1) that allows us to identify and estimate the peer effect. This allows us to use both own shock and shock to others in the same specification. In addition to having a differential effect, our instrument should be correlated with the variable of inter-est. Since each individual is affected by the unanticipated change in their financial incentives, it is likely their outcomes as a group would be affected by a change in the groups incentives. We show empirical support for this below. Finally, the most crucial question in any IV setting is whether the instrument is uncorrelated with the unobservable component. We argue that, in this case, two features make this more likely to hold. First, the pension reform was unanticipated. Second, we are able to observe all the factors that affect our IV. In particular, the IV is solely a function of the age, service, and salary composition of teachers in a given school, all of which are measures we fully observe and can control for in the analysis.


In Table 2, we show estimates of equation (1), excluding peer retirements to first provide empirical support for our instrument at the individual level. Columns 13 show that individual financial incentives are strongly correlated with the retire-ment decision after controlling for age, years of teaching experience, salary, and additional individual and school characteristics. The coefficients of both pension wealth and peak value are of the expected sign and statistically significant at the 1 percent level. The estimates are also in line with estimates from other studies that use this model of retirement (e.g., Gruber and Wise 2004). The integer age dummies (not reported in the table) also have the expected sign. The coefficient on salary is positive in most specifications, but is only statistically different from zero in the 19982001 sample. The expected sign of the salary coefficient in this setting is ambiguous because the salaries of LAUSD teachers are a strict function of service (which we also control for directly) and education, and are negotiated at the district level. In addition, several omitted variables, including nonpension wealth and taste for work, may be correlated with salary. Our results both for own pension measures and the peer effects discussed in the next section are robust to controlling for every possible location on the salary schedule rather than salary directly (see online Appendix Table A8).

Table 2Determinants of Retirement Excluding Peers Retirement Behavior

All LAUSD teachers, ages 5575; Linear probability model; Dependent variableRetirement

(1) (2) (3) (4) (5) (6) (7) (8)Specification OLS OLS OLS 2SLS OLS 2SLS OLS 2SLS

Pension wealth ($100k) 0.013*** 0.013*** 0.013*** 0.022** 0.014*** 0.022* 0.038*** 0.036***(0.004) (0.005) (0.005) (0.011) (0.005) (0.011) (0.008) (0.014)

Peak value ($10k) 0.006*** 0.005*** 0.005*** 0.001 0.005*** 0.001(0.001) (0.000) (0.000) (0.001) (0.001) (0.001)

Peak value is positive 0.088*** 0.682(0.020) (0.596)

Salary ($10k) 0.009** 0.005 0.006 0.006 0.004 0.007 0.023 0.029(0.004) (0.004) (0.004) (0.008) (0.004) (0.008) (0.016) (0.021)

Years of service in LAUSD 0.003*** 0.003*** 0.002*** 0.005*** 0.003*** 0.005***(0.001) (0.001) (0.001) (0.001) (0.001) (0.001)

Years of service (squared) 0.000*** 0.000*** 0.000*** 0.000** 0.000*** 0.000** 0.001*** 0.000(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001)

Fixed-effects level School School Teacher TeacherAcademic years 19982001 19992001 19992001 19992001 19992001 19992001 19992001 19992001 r2 0.10 0.11 0.11 0.11 0.12 0.12 0.19 0.06

Sample size 24,444 21,296 21,296 21,296 21,296 21,296 21,296 21,296

Notes: Standard errors, in parentheses, are clustered at the school level, allowing any correlation across individuals and years within school. All specifications control for gender, and include age dummies and year fixed effects. Peer group measures (self-excluded) include number of retirement-eligible (age 55+) teachers and the average age and service of those 55+. School-level measures include pupil-to-teacher ratio, fraction of teachers with a masters degree or higher, fraction of teachers that are female, and aver-age rank on students standardized math test scores. Specifications without teacher or school fixed effects also include the number of full-time-equivalent teachers and school grade-range (elementary, high school, etc.). The specifications in columns 1 and 2 do not include peer group or school-level measures. In column 1, the sample includes, for each academic year 19982001, all teach-ers age 5575 in the given year. In the remaining columns, the sample includes all teachers that are age 5575 during at least one of the academic years 19992001 and that do not change schools. Given the sample, teacher fixed effects also capture school fixed effects. There are 585 unique schools. The p-values of the f-test for the excluded instruments in columns 4, 6 and 8 (with f-statistics adjusted for multiple endogenous variables using Angrist and Pischke 2008) are 0.001 or less in all cases. See online Appendix Table A2 for first stage summary.

*** Significant at the 1 percent level. ** Significant at the 5 percent level. * Significant at the 10 percent level.


In column 4, we instrument own pension wealth and peak value with individual-level reform-induced shocks, pW_i V i, t and pK_i V i, t . The standard errors increase, but the coefficient on pension wealth is still of the expected sign, somewhat larger in magnitude and statistically significant at the 5 percent level. This lends support for the use of the shock in pension wealth at the group level to instrument for retire-ments of the group. The peak value, however, is no longer statistically significant. This result is also consistent with our finding below that the unexpected change in peers pension wealth is better suited than the unexpected change in peers peak value as an instrument for peer retirements. In columns 5 and 6, we include school fixed effects. The f-test of the joint significance of the school-level fixed effects rejects the null at the 1 percent level, suggesting that the existence of school-level peer effects is plausible. In column 6, we also instrument own pension financial incentives and the results are similar to column 4. In columns 7 and 8, an individual fixed effect is included and the effect of pension wealth on retirement, even after instrumenting, remains statistically significant at the 1 percent level.

A. instrumental Variable Estimates of the Effect of peers on retirement

We estimate the effect of others retirement behavior on ones own retirement using the unanticipated change in financial incentives of own and others as IVs. The specification we estimate is

(2) y i, s, t = X i, s, t + Z s, t + y i, t1, s + t + s + i + i, s, t .

The variable of interest is y i, t1, s , the lagged retirement of others. In Table 3, we use the number of retirements in the previous year. We obtain similar results when we examine the lagged average retirement rate of others in the same school, self excluded (see Section IV).

The peer effect results are presented in Table 3. The first column of Table 3 includes the nave OLS estimate. The number of retirements of others is found to have a posi-tive and statistically significant effect on the likelihood of own retirement. Using the point estimate of column 1, one additional retirement of a colleague would increase ones own likelihood of retirement by 0.6 percentage points. Since peer retirement measures are lagged one year and include a host of individual, year, and school level controls, we view these results as instructive. However, to address any lingering concern regarding these group measures, we turn to the IV estimates in columns 28. The performance of the group-level instrument is detailed in panel B of Table 3. The individual-level IVs are detailed in online Appendix Table A2. Column 2 is the same as 1, but now the peer-retirement measure is instrumented by the unantici-pated change in pension wealth of others. The results for the peer measure are sta-tistically significant at the 1 percent level. As might be expected, the standard errors are larger. Using the point estimate of column 2, one colleague retirement increases the individuals likelihood of retirement by an additional 1.5 percentage points. The second-stage goodness of fit and the f-statistic for the excluded instrument (28.59) illustrate the strength of our instrument.


The group-IV is solely a function of the age, service, and salary composition of teachers in a given school, all of which are measures we fully observe. In all specifi-cations, we control for the average age, size, and years of service of those eligible to retire (age 55 or older). The results are robust to instead using the lagged values of

Table 3Two-Stage-Least-Squares Estimates of Peer Effects

All LAUSD teachers ages 5575; 2SLS (columns 28); Dependent variableRetirement (1) (2) (3) (4) (5) (6) (7) (8)

specification OLSIV peer

retirementIV peer

retirementIV peer

retirementIV peer

retirementIV peer

retirement

IV peer retirement and own financials

IV peer retirement and own financials

panel A

Number of retirees among 0.006*** 0.015*** 0.015** 0.026** 0.015* 0.020** 0.021** 0.017** peers 55+ in previous year

(0.002) (0.006) (0.007) (0.010) (0.008) (0.010) (0.010) (0.008)Pension wealth ($100k) 0.011** 0.011** 0.011** 0.012** 0.021* 0.013*** 0.021* 0.035***

(0.006) (0.006) (0.006) (0.006) (0.012) (0.005) (0.011) (0.014)Peak value ($10k) 0.006*** 0.006*** 0.006*** 0.006*** 0.005*** 0.001

(0.001) (0.001) (0.001) (0.001) (0.001) (0.001)Own peak value is positive 0.124*** 0.575

(0.024) (0.606)Number of peers age 55+ 0.000 0.000 0.000 0.003* 0.000 0.000 0.000 0.000

(0.000) (0.000) (0.000) (0.002) (0.001) (0.000) (0.000) (0.001)Average age of peers 55+ 0.003* 0.003* 0.003* 0.013*** 0.004 0.002 0.002 0.004

(0.002) (0.002) (0.002) (0.004) (0.004) (0.001) (0.001) (0.004)Average service of peers 0.000 0.000 0.001 0.002 0.000 0.000 0.000 0.000 55+ (0.001) (0.001) (0.001) (0.001) (0.001) (0.000) (0.000) (0.002)Additional peer service categories

Yes

Fixed-effects level School Teacher Teacher

Academic years 1999,2001 1999,2001 1999,2001 1999,2001 1999,2001 19992001 19992001 19992001

r2 of second stage 0.11 0.11 0.11 0.11 0.21 0.11 0.11 0.10

Sample size 14,150 14,150 14,150 14,150 14,150 21,296 21,296 21,296

panel B. first stage for number of retirees among those 55+ in previous year (see notes for additional coefficients)Lag total unanticipated 0.185*** 0.170*** 0.158*** 0.153*** 0.087*** 0.087*** 0.151*** change in pension wealth of peers ($100k)

(0.034) (0.039) (0.055) (0.061) (0.026) (0.026) (0.049)f-statistic for excluded IVa 28.59 19.48 8.19 6.18 11.43 11.40 4.80

p-value for the above test 0.0000 0.0000 0.0044 0.0132 0.0008 0.0008 0.0085

r2 of first stage 0.45 0.46 0.12 0.11 0.40 0.40 0.13

Notes: Standard errors, in parentheses, are clustered at the school level. All specifications control for own pension wealth, peak value, salary, years of service, service squared, gender, and include age dummies and year fixed effects. Peer group measures (self-excluded) include number of retirement-eligible (age 55+) teachers and the average age and service of those 55+. School-level measures include pupil-to-teacher ratio, fraction of teachers with a masters degree or higher, fraction of teachers that are female, and average rank on students standardized math test scores. Specifications without teacher or school fixed effects also include the number of full-time-equivalent teachers and school grade-range (elementary, high-school, etc.). The sample includes all teachers that are age 5575 during at least one of the academic years 19992001 and that do not change schools. Given the sample, teacher fixed effects also capture school fixed effects.

a The f-statistic in case of multiple endogenous variables (columns 7 and 8) was adjusted using Angrist and Pischke (2008). In column 8, the first-stage coefficient of the 2-year lag unexpected change in others pension wealth on peer retirements is 0.137*** (0.048). The first-stage coefficient of the effect of unexpected change in pension wealth on own pension wealth is 1.126*** (0.023) in column 7 and 0.889*** (0.007) in column 8. The first-stage coefficient of the effect of unexpected change in peak value on peak value is 1.789*** (0.027) in column 7, and the first-stage effect of unexpected change in peak value on peak value is positive is 0.003*** (0.001) in column 8.



these variables or defining the peer group as those 45 and older (see online Appendix Table A8). Column 3 includes additional measures of the school-level service com-position (fraction of other teachers with 1519, 2024, 2529, and 30 or more years of service) as well as average salary of others. The coefficient of the group measure remains statistically significant at the 5 percent level and is of the same magnitude. Column 4 illustrates the results are robust to the inclusion of a school fixed effect. In column 6, we expand the sample to include academic year 2000 (between the two years used in columns 15). The additional year allows us to instrument own pension financial measures (columns 78). The peer effect is still of similar magni-tude but now has a larger standard error (significant at the 5 percent level), and the instrument is weaker. This is likely due to the fact that for the added year, the peer group IV takes the value of zero as there was no reform during that year.

The IV estimates in columns 26 address potential concerns regarding the peer-retirement measure, but the results may still be biased if the individual unobserv-able component is important in determining retirement and is correlated with own pension measures. In column 7, we use the shock to own financial incentives to instrument own pension wealth and own peak value. Similar to the results in Table 2, own pension wealth is still statistically different from zero at the 10 percent level, though own peak value is no longer statistically significant. This is likely due to two reasons. First, given the timing of the reforms, the IV measures have a value of zero in two of the three years in the sample.21 Second, the IV for peak value is likely to be quite weak as the peak value measure is a function of pension wealth, and therefore highly correlated with it. The effect of others retirement behavior remains unchanged in magnitude and statistically significant at the 5 percent level.22

Though the individual-level IVs allow us to address potential bias in own pen-sion financials, this would not address any concerns about biased estimates of other measures, such as education and the associated salary, that could result from unob-servables, such as baseline health condition or marital status. The rich dataset at our disposal allows us to link teachers over time, and thus purge any individual fixed effect. We implement the strategy discussed in Section II. Columns 5 and 8 of Table 3 include an individual-level fixed effect, corresponding to i in equation (2). The samples in Table 3 condition on those who have not changed schools, so the indi-vidual fixed effect also controls for any fixed school unobservable.23 The individual-level fixed-effect specification only includes those variables that change over time (both for self and at the school level). In addition, the pension wealth and peak value measures are colinear in this case. We therefore include only pension wealth as our

21 When we adjust the standard errors for the fact that IVs are nonbinding in some years the statistical signifi-cance remains the same.

22 The results in columns 27 of Table 3 include a single IV for peer retirements. We obtained almost identi-cal results both for the point estimates and the significance levels when we used two group-level instruments: the unanticipated change in pension wealth (as before), as well as the unanticipated change in peak value. Appendix Table A3 contains the full set of those results and the results of the overidentification teststhe null is never rejected at the 10 percent level. Becasue the peak value group-IV is weaker in each of the specifications our preferred speci-fications use only the group-level pension wealth IV.

23 The results in the previous sections and for this specification are the same whether or not we exclude teachers who moved between schools, as only a small proportion of teachers move between schools this late in their career. For example, see columns 7 and 8 in online Appendix Table A8. In our sample, on average, less than 160 teachers over the age of 55 move between schools every year.


measure. As an alternative measure of peak value, we include an indicator for those who have not yet reached their maximum pension wealth.

With the individual fixed effect, the effect of others previous year retirements remains positive and statistically significant at the 10 percent level or better. In col-umn 5, where we do not instrument own financial measures, own pension wealth has a positive coefficient, and the coefficient for the peak value measure is negative, as expected. Both are statistically significant at conventional levels. In column 8, pen-sion wealth and the peak value measure are instrumented with the pension wealth and peak value shocks. The result for the peer effect remains very similar. The stan-dard error for own peak value is now very large, likely due to the relative weakness of the additional IV. The coefficient on pension wealth remains positive and statisti-cally significant at the 10 percent level. We view the fixed effect approach in this setting as addressing most if not all of the concerns that instrumenting own pension measures would address, but column 8 of Table 3 illustrates that our peer effects finding is very similar when these strategies are combined.

Taken together, our findings of peer effects remain after using three strategies at the same time. We control for any individual-level fixed effect, we examine the lag rather than the contemporaneous peer retirement measure, and we instrument that lag measure using the unanticipated change in financial incentives experienced by others.

B. reduced-form results

In this section, we use the unanticipated change in financial incentives both for self and peers as predictors of change in retirement behavior. In addition to being a direct test of the IV (e.g., Chernozhukov and Hansen 2008), in this particular setting the direct estimates have a meaningful and straightforward economic inter-pretation. An unanticipated shock to financial incentives is likely to be a central feature of most pension reforms and the shock we study is denominated in dol-lars. For the different specifications we use, we control for an individuals own pension wealth and peak value to include the reform-induced shocks to their own financial measures. Hence, we focus on the unanticipated shocks for all others, self excluded.

The results of the reduced-form specification, examining the shocks directly, are presented in Table 4. For example, columns 13 of Table 4 correspond to the IV estimate in columns 35 in Table 3 that were discussed above. The full set of reduced-form results corresponding to Table 3 can be found in online Appendix Table A3. In all cases, the lagged total unanticipated change in pension wealth of all other teachers age 55 or older in ones school, self excluded, has a positive and statistically significant effect on own likelihood of retirement. The point estimates suggest that an additional $100,000 of pension wealth to all others (in total, not each) increases ones own likelihood of retirement by 0.2 to 0.4 percentage points. In columns 48, we replace own pension wealth and peak value with the unex-pected change in each, and column 5 also includes the unanticipated change in the peak value of others. The coefficient on others pension wealth does not change and remains statistically significant at the 10 percent level. The unexpected change in own pension wealth is statistically significant at the 10 percent level and of the


same magnitude as the coefficient on pension wealth when it was instrumented in Table 3. However, neither own nor others unexpected change in peak value is significantly different from zero in many of the specifications. Columns 3, 7, and 8 all include individual (and school) fixed effects. The coefficient on others unex-pected change in pension wealth remains the same and is statistically significant at the 10 percent level or lower.

Column 8 in Table 4 is the reduced form corresponding to column 8 in Table 3. The additional sample year (2000) allows us to include an additional group-level IV, the 2-year lag unexpected shock to the pension wealth of others.24 The measure is statistically significant at the 10 percent level (compared to the 1 year lag which is statistically significant at the 1 percent level). For comparison, column 7 of Table 4

24 Additional specifications incorporating this IV can be found in online Appendix Table A4.

Table 4The Effect of Peers Unanticipated Change in Financial Incentives on Own Retirement (reduced form)

All LAUSD teachers ages 5575; Linear probability model; Dependent variableRetirement (1) (2) (3) (4) (5) (6) (7) (8)Lag total unanticipated 0.003** 0.004*** 0.002* 0.002*** 0.002*** 0.001* 0.001** 0.003** change in pension wealth of peers, self excluded ($100k)

(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)

Unexpected change in own 0.024* 0.025* 0.024* 0.033*** 0.033*** pension wealth ($100k) (0.013) (0.013) (0.013) (0.011) (0.011)Lag total unanticipated 0.000 change in peak value of peers, self excluded ($10k)

(0.000)

Unexpected change in own 0.003* 0.003* 0.002 0.002 0.002 peak value ($10k) (0.002) (0.002) (0.002) (0.002) (0.002)2-year lag total 0.002* unanticipated change in pension wealth of peers, self excluded ($100k)

(0.001)

Pension wealth ($100k) 0.011** 0.013** 0.019(0.006) (0.006) (0.012)

Peak value ($10k) 0.006*** 0.006***(0.001) (0.001)

Own peak value is positive 0.121***(0.024)

Fixed-effects level School Teacher School Teacher Teacher

Academic years 1999,2001 1999,2001 1999,2001 19992001 19992001 19992001 19992001 19992001

r2 0.11 0.12 0.22 0.11 0.11 0.11 0.19 0.19

Sample size 14,150 14,150 14,150 21,296 21,296 21,296 21,296 21,296

Notes: Standard errors, in parentheses, are clustered at the school level. All specifications control for own salary, years of service, service squared, gender, and include age dummies and year fixed effects. Peer group measures (self-excluded) include number of retirement-eligible (age 55+) teachers and the average age and service of those 55+. School-level measures include pupil-to-teacher ratio, fraction of teachers with a masters degree or higher, fraction of teachers that are female, and average rank on students standardized math test scores. Specifications without teacher or school fixed effects also include the number of full-time-equivalent teachers and school grade-range (elementary, high school, etc.). Column 1 includes additional peer service categories. The sample includes all teachers that are age 5575 during at least one of the academic years 19992001 and that do not change schools. Given the sample, teacher fixed effects also capture school fixed effects.



includes only one group-level IV, as well as the two IVs that capture the shock to ones own financial measures.

The point estimates in Table 4 suggest that the effect of an unanticipated change to own pension wealth is roughly 13 times larger than the effect of others receiving an unanticipated shock of the same amount (in total, not each). The point estimate suggests that other colleagues receiving an extra $100,000 in pension wealth (in total, not each) has the same effect on ones own retirement as receiving an addi-tional $8,300 to ones own pension wealth.

IV. Alternative Group Specifications and Robustness Checks

We examine alternative group specifications, including contemporaneous timing, as well as summarize the results of two falsification tests. These results are reported in Table 5. In column 1, we examine the average retirement rate of others (lagged,

Table 5Alternative Group Specifications and Falsification Tests

All LAUSD teachers ages 5575; Dependent variableRetirement (columns 17), Salary (column 8)(1) (2) (3) (4) (5) (6) (7) (8)

Specification 2SLS 2SLS 2SLS 2SLS 2SLS OLS OLS OLS

panel ARate of retirement in 0.182** previous year (0.091)Period during which group Previous Previous Current & Current retirements are measured (25)

summer spring & summer

previous year

year

Number of retirees during 0.019*** 0.015*** 0.010*** 0.027*** period listed above (25) (0.007) (0.006) (0.003) (0.006)Lead unanticipated change 0.002 0.003 in pension wealth of peers ($100k) (0.002) (0.002)Lag unanticipated change 0.004*** 0.000 in pension wealth of peers ($100k) (0.001) (0.002)Academic years 1999,2001 1999,2001 1999,2001 1999,2001 1999,2001 1999 1999 1999,2001

r2 of second stage 0.11 0.11 0.11 0.11 0.10 0.10 0.10 0.50

Sample size 14,145 14,145 14,145 14,145 14,145 7,653 7,653 14,145

panel B. first stage of the above specifications (first stage reported for variable listed above) Unanticipated change in pension wealth of peers ($100k)

0.198*** (0.021)

0.158***(0.032)

0.186***(0.033)

0.290***(0.049)

0.104***(0.039)

f-statistic for excluded IV 81.85 24.23 31.31 34.19 7.20

r2 of first stage 0.12 0.40 0.43 0.63 0.53

Notes: Standard errors, in parentheses, are clustered at the school level. All specifications control for own pension wealth, peak value, salary, years of service, service squared, gender, and include age dummies and year fixed effects. Peer group measures (self-excluded) include number of retirement-eligible (age 55+) teachers and the average age and service of those 55+. School-level measures include pupil-to-teacher ratio, fraction of teachers with a masters degree or higher, fraction of teachers that are female, average rank on students standardized math test scores, number of full-time-equivalent teachers and school grade-range (elemen-tary, high school, etc.). The sample includes all teachers that are age 5575 during at least one of the academic years 19992001 and that do not change schools. In columns 25, all other own and group-level measures are computed for the academic year.



self excluded) rather than the number of other retirees. As an instrument (first stage results reported in panel B), we use the average unanticipated change in pension wealth of others. The result for the average-measure is statistically significant at the 5 percent level and is quantitatively the same as the result for number of retirements.

We demonstrate in columns 25 that our findings are robust to using alterna-tive windows of time to define the peer group. Though our preferred specification focuses on the effect of others retirements in the previous academic year, one might be concerned that this definition is too exclusive, omitting the effect of contempo-raneous peer decisions, or too inclusive. Each column examines a different set of peers, while holding the effect of own characteristics and other school-level mea-sures the same as in the previous specifications. In columns 24, we examine the effect of others retirements in the previous summer, previous spring and summer, and current and previous year. In all cases, the peer effect remains statistically sig-nificant at the 1 percent level and the magnitudes of the effect are similar to the one-year case. In column 5, we examine the effect of only current-period retirements and find a statistically significant effect at the 1 percent level. To make the results comparable, column 5 examines the same years as column 1 in Table 3. The IV for current number of retirees is therefore the unanticipated shock to pension wealth among all others in the previous period.

In columns 6 and 7 of Table 5, we present the results of a reduced-form fal-sification test in which the lead (future) shock to the pension wealth of others is considered. By exploiting the specific timing of the two reforms, we are able to include both the lag and future unexpected shocks to others financial measures.25 We find that the lag-retirement of others remains statistically significant, whereas the future-retirement of others has a smaller point estimate, and is not statistically significant. When we include only the lead measure (column 6), we find an even smaller and statistically insignificant effect. These findings are consistent with the retirements of others having an actual causal effect on individual retirements, rather than merely being a proxy for the work-conditions in a given school. Last, in column 8, we examine an identical specification to the ones in the previous section, but as a falsification test, the dependent variable is salary rather than retirement. While own characteristics, such as years of service and age, are found to affect ones own salary, the shock to others pension wealth (self excluded) no longer has a statistically sig-nificant effect (and the point estimate is 0.00007). Since teachers have very little control over their own salary (beyond years of service or education), this finding is consistent with our group instrument having a true effect on own retirement, rather than picking up a spurious correlation in the attributes of teachers in schools. The results of additional robustness checks, described below, can be found in more detail in online Appendix Section III.

As an additional robustness check, we address the concern that while the retire-ment of others directly affects individuals retirement decisions, the peer effect we estimate may be driven by the coordinated retirements of married couples working in the same school. Note that due to the lag structure of our main specification,

25 The reforms were two years apart, and so we examine the retirement behavior of those in the year after the first reform and before the second reform.


the peer effect would pick up couples that retire in consecutive years rather than together. We test whether individuals are less sensitive to the retirements of same-sex colleagues. To do this we include the total number of same-sex retirees in ones school in the previous year in our main specification. This variable is instru-mented with the lag total unanticipated change in pension wealth of same-sex peers. While the coefficient on the retirements of same-sex colleagues is negative, it is half the magnitude of the coefficient on all retirements and is not statisti-cally different from zero (e.g., column 8 in online Appendix Table A5). Further, in online Appendix IV1, we show that there is little change in the peer effect when we estimate our specifications excluding randomly assigned coworker couples. This result is robust to 1,000 iterations of random couple assignment where the number of excluded couples is derived from the US Census 2000 teacher-married-to-teacher marriage rates.

We explore the potential heterogeneity in the retirement peer effect across teach-ers with different observable characteristics. First, we consider that the peer effect may not be homogenous across teachers by sex, race/ethnicity, and teaching assign-ment. For example, we may expect individuals that can more easily calculate their pension benefits (e.g., science or math teachers) to be less influenced by their peers. We find that the positive effect of number of colleague retirements on own retire-ment is robust to this specification. Women are more likely to retire, all else equal, but we find no evidence that individuals are differentially impacted by their peers as a function of their own characteristics. Second, we may expect that individuals are more likely to respond to the behavior of those that are more similar or with whom they interact more. Here we relax the implicit assumption in Section IIIA that all coworkers are weighted equally as peers and test whether individuals respond differently to similar peers. We find no evidence that individuals respond differently to peer retirements if peers are of the same race/ethnicity or if they teach the same subject area. As discussed above, we only find a small effect of shared gender. The full set of results are presented in online Appendix Table A5.

Finally, we examine possible mechanisms through which the peer effect may operate. While our instrumental variable strategy addresses threats to validity due to unobservable differences in school quality, it is possible that retirements of colleagues cause a change in working conditions at the school and that it is this change, and not the retirement of others per se, that is affecting individuals retirement decisions in the following year. Specifically, schools may fill the teaching positions vacated by retirees with less experienced teachers or, if teachers are in short supply, they may hire teach-ers that are not fully credentialed or even leave positions unfilled, altering the work-place climate or workload faced by returning teachers. The change in the experience, credentials, or number of teachers at a school has no discernible effect on individual retirement decisions, but the effect of lag retirements remains virtually unchanged and statistically significant in every specification, even when school fixed effects are included. The results are available in online Appendix Table A6.

In online Appendix Sections III4 and III5, we further examine two possible mech-anisms through which the peer effect may operate: a retirement-age norm, and how individuals response to own financial incentives is modified by others response to their own pension financial incentives. We find little evidence that individuals are


affected by the retirement age of others, but we do find that the financial response of others affects the way individuals interpret their own financial incentives.

V. Discussion and Conclusion

We use a unique dataset and features of reforms of the California State Teachers Retirement System to identify and estimate the effect of ones peers on ones own retirement decision and find a statistically and economically significant peer effect. Our results suggest that for each additional peer retirement that is observed, a teach-ers own likelihood of retirement increases by an additional 1.52.0 percentage points. The reforms, which consisted solely of a change in pension financial incen-tives allow us to directly calculate, in economic terms, the effect of unexpectedly changing others pension wealth on ones own likelihood of retirement.

Our identification strategy highlights that peer effects can be identified using a natural experiment that has a differential effect on members of each group. This identification strategy could be used in other settings, where a program has a dif-ferential effect on group members. Further, in contrast to many studies that exploit exogenous assignment to groups, we are able to examine the impact of an unan-ticipated reform on existing networks of peers. In turn, such a setting may be more relevant for cases in which changing the nature of networks and associations among peers may be harder to accomplish.

Peer effects will play a role in shaping how individuals understand and respond to both recent and future Social Security reforms and to changes to other retirement savings programs, such as 401(k)s. Changes to benefits or program rules will have both a direct effect on those targeted by the reform, and also an indirect effect on those affected by the retirement decisions of others. To properly predict the effect of a reform it is important to accurately estimate both the direct effect and the spill-over effectthe behavior of one individual affects the behavior of his or her peers, and so on. For example, when we extrapolate our results to the 2008 US population of social-security-eligible workers

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