1

The Zero Bias in Target Retirement Fund Choice

Xiao Liu, Wei Zhang, and Ajay Kalra1

EXTENDED ABSTRACT Despite the importance of retirement savings, people often make suboptimal decisions, especially under-diversification and insufficient balancing over time. An increasingly popular investment vehicle, Target Retirement Funds (TRFs), has been created to help consumer alleviate these problems. With TRFs, the asset allocation decision is made for the investors, with the allocation automatically rebalancing to become more conservative as one gets closer to retirement. The major decision people have to make is to estimate their planned retirement year and select one of the TRFs. TRFs has been advocated to be an appropriate retirement vehicle for consumers who do not want to actively manage their retirement savings. Despite the appeal of TRFs, in this research, we want to investigate, do consumers also make systematic mistakes when choosing among target retirement funds? Or is there any bias associated with TRF choices? If so, what is the impact of this bias on consumers' investment contributions as well as risk exposure? Moreover, what factors can predict the bias? And finally, how can we solve the problem? Using a large data of people who hold Target Retirement Funds, we find a strong “zero” bias in that investors base their choices of TRFs not on the age of 65 at which they are likely to retire but rather on a zero ending calendar year. Specifically, they exhibit a strong preference for TRFs which end with zero (2030, 2040) as compared to TRFs that end with five (2035, 2045). The intended retirement time appears to be driven by the use of rounding heuristics. This bias is not all-encompassing but more provincially manifests itself based on the year an individual is born. In particular, the bias manifests for people born in years ending between 8 and 2 (e.g., 1968-1972), with people whose birth year ending is 0,1 or 2 selecting TRFs that imply they intend to retire at 70 whereas those born in years ending in 8 and 9 select TRFs aspiring to retire at 60. The bias is costly for those born in years ending between 0 and 2 as it significantly lowers their wealth accumulated by decreasing the amount they contribute towards the retirement and exposing them to excessive risk. We further explore some factors where the likelihood of observing the zero bias is stronger and find that demographics, firm interactions and fund expense ratios have the strongest prediction power. Interestingly, other financial behavioral abnormalities, for instance, overreaction to the stock market is also highly correlated with the zero bias. We also observe that investors who participate in a simple 30-minute financial training program are less likely to exhibit the zero bias tendency. The zero bias effect has clear implications for policymakers and fund providers. 401(k) plan menu designers should take this bias into consideration, emphasize the implications of the choices made at the point of decision, and nudge investors into making selections that maximize financial well-being. Theoretically, our findings are consistent with the literature that observes a preference for round numbers. In contrast to this literature that shows round numbers in the context of an ambition or aspiration point, we find that bias is an outcome of either rounding when using computational heuristics or may show an affinity for landmark years. Keywords: retirement savings, computational estimation, cognitive bias, behavioral finance

1 Xiao Liu, Stern School of Business, New York University, xliu@stern.nyu.edu; Wei Zhang, College of Business, Iowa State University, wtzhang@iastate.edu; Ajay Kalra, Jones Graduate School of Business, Rice University, ajay.kalra@rice.edu.

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Consumers are profoundly influenced by numbers (e.g. Bagchi and Davis 2016). In many

purchase decisions, consumers mentally solve numerical problems requiring the use of

mathematical operations. For example, estimating the cost of a vacation entails adding up the

various components (airfare, hotel, meals, entertainment, and other expenses), as does

determining the total cost of a wedding (catering, flowers, liquor, etc.). Sometimes, consumers

may also have to perform subtractions – for example, the percentage off the regular price to

arrive at the promoted price – or use multiplication when buying multiple units. How do

consumers make these simple mental arithmetic calculations and what is the impact of the

process they use?

A common decision that requires simple mental arithmetic is an individual’s decision

about when to retire. This question has to be addressed by approximately half of the American

population who save for retirement using a defined contribution plan such as a 401(k) or 403(b)

as part of their financial planning goals. We examine the decision using the data from people

selecting Target Retirement Funds (TRFs) where they are explicitly required to choose their

likely retirement year. TRF, named for targeting a specific year a person anticipates retiring,

involve selection from a menu of choices with five-year intervals (e.g. 2030, 2035, 2040, etc.).

There are several possible routes to determine one’s retirement year, including adding one’s

desired age of retirement to the his or her birth year, adding how many more years one desires to

remain the workforce to his or her current age, or estimating with more complex heuristics.

Regardless, all involve the use of mental arithmetic.

Using a large dataset from a global financial investment management firm that offers

retirement plans, we identify a systematic “zero” bias in individuals’ retirement investment

decisions, which is a tendency to select zero-ending TRFs as compared to five-ending TRFs. The

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preference for zero-ending TRFs implies that some individuals intend to retire either at the age of

60 or 70, rather than 65. The bias is consistently evident for people born in the 1950s through the

1980s. The selection of the TRF is based on the birth-year, with those born in years ending 8 or 9

(e.g. 1968, 1969) project to retire at 60, whereas those born in years ending in zero, one, or two

(e.g. 1960, 1971) chose TRFs consistent with retiring at 70. We find evidence of the use of

rounding heuristics with rounding-up being more prevalent than rounding-down.

We find that the bias affects investors in two substantial ways. First, it may lead to an

investment portfolio with an incompatible level of risk. Second, the choice of the TRF appears to

impact the amount people contribute towards their retirement savings. This suggests that it may

perceptually alter the perceived number of earning years left before retirement. Together, these

two results can significantly lower total wealth accumulated at the time of retirement for a

segment of risk-averse investors, specifically for those who are born in years ending in zero, one,

and two who tend to select later TRFs. On the other hand, the bias is beneficial to the risk averse

consumers born in 8- and 9-ending years who are more likely to select earlier TRFs. Our

simulations find that approximately half the investors who select a mismatched TRF

(inconsistent with retiring at 65) are financially worse off compared to choosing the matching

TRF.

We replicate the zero bias in an experimental setting and find evidence that suggests that

choice of TRF can influence contribution rates of retirement savings. We further explore

demographic factors where the likelihood of observing the zero bias is stronger and find that

males, higher income, and older people are more likely to demonstrate the bias. We also observe

that investors who participate in a simple 30-minute financial training program are less likely to

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exhibit the zero bias tendency. Finally, results using an experimental approach suggest that

nudging consumers to select a TRF compatible with a retirement age of 65 is effective.

Our findings have substantive policy implications. When designing retirement plan

menus, policymakers or fund providers should take the zero bias into consideration, emphasize

the implications of the choices made at the point of decision, and nudge investors into making

selections that maximize financial well-being.

We contribute to three literature streams. First, our findings add to the literature that

observes a preference for round numbers (e.g. Allen et al. 2016). In contrast to this literature,

which shows round numbers in the context of a reference or aspiration point, in this context the

zero bias is an outcome of rounding-up or rounding-down when using computational heuristics.

We also contribute to the literature on computational estimation (Lemaire and Lecacheur 2001;

Lemaire and Arnaud 2008) by examining the use of mental arithmetic in a substantive problem

and find that people choose rounding-up heuristics more than rounding-down in this class of

problem. Finally, we contribute to the literature in behavioral finance by identifying a strong bias

in the selection of one of the most popular retirement investment vehicles.

We first review the relevant literature on retirement savings behaviors and the round

number bias. Our main results about the zero bias are presented next. We then use simulations to

quantify the economic impact of the zero bias. Next, we discuss the possible mechanisms. Then

we examine heterogeneity and explore predictors of the zero bias and finally conclude and

discuss the implications of our findings.

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BACKGROUND AND LITERATURE REVIEW

Retirement Savings

Currently, US retirement assets total approximately $28.3 trillion dollars (Investment

Company Institute 2018). According to the Federal Reserve’s Report on the Economic Well-

Being of U.S. Households (Board of Governors of the Federal Reserve System 2017), in 2016,

50% of the American population saved for retirement using a defined contribution plan such as a

401(k) or 403(b). With a 401(k), employees control how much to save and employers typically

match this contribution, often with a 100% matching rate. Additionally, employees control how

the money is invested. Most plans offer a spread of mutual funds composed of stocks, bonds, and

money market investments. To oversee the accounts, employers usually hire a financial

administrator such as Fidelity Investments. Then, based on the options made available by the

administrator, employees decide their own investment portfolio and the specific allocation. As

401(k)s put much of the burden on individual choices, the quality of investment decisions plays a

crucial role in people’s future standard of living.

Target Retirement Funds

Target Retirement Funds, or TRFs, are funds named for a target retirement date. For

example, Vanguard offers the Target Retirement 2060 Trust, BlackRock offers the LifePath 2030

Investor Fund, and Manning and Napier offers the Target 2035 R Fund. Generally, TRFs assume

that employees retire at the age of 65. This is consistent with surveys identifying that

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approximately 80% of employees anticipate retiring at 65 (Nationwide 2017). TRFs are funds

that hold many underlying stocks, bonds, and money market assets that help employees become

fully diversified. For those opting to invest in TRFs, the choice of the funds is between

alternatives with years ending in zero (e.g. 2030, 2040) or ending in five (e.g. 2035, 2045). An

important benefit accorded by TRFs is that they automatically rebalance the portfolio over time,

with the goal of decreasing the percentage invested in stocks and increasing the percentage

invested in bonds. In other words, they follow a so-called glide-path to reallocate the percentage

in each type of asset class.

For example, in a Vanguard TRF, a 20-40 year old investor follows a glide-path where

almost 90% of retirement savings are invested in either international or US stocks. Then, in the

next period between 40 and 65, the percentage in stocks gradually decreases while the

percentage in bonds gradually increases. When the investor turns 65, only 50% of the assets

remains in stocks. This ratio for stocks further decreases in the early retirement period and finally

reduces to less than 30% after age 72 (Please see Web Appendix for examples of glide-paths).

Due to the “set it and forget it” approach which alleviates the pain for those who are not

comfortable navigating financial decision making, TRFs have become a very popular investment

choice. According to a joint study by the Employee Benefit Research Institute and the

Investment Company Institute (VanDerhei, Holden, Alonso, and Bass 2012), in 2015, 72% of the

401(k) plans offered Target Retirement Funds, 50% of 401(k) investors held TRFs, and 20% of

all 401(k) assets were invested in TRFs. More importantly, TRFs are growing rapidly. From

2008 to 2018, TRFs increased from $160 billion to $1.19 Trillion in assets (Morningstar 2018).

In addition, they are especially popular among young employees. Seventy percent of recently

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hired employees in their 20s invested in TRFs. According to Fidelity, 42% of all their clients and

68% of millennials are entirely invested in this fund group (Fidelity 2018).

Round Number Bias

As described, individuals have a choice of selecting between zero-ending and five-ending

TRFs. Prior findings suggests an affinity and preference for round ending number (zeros).

First, literature across different domains has recorded the tendency to self-report using

round numbers. For example, it has been observed that people use round numbers to self-report

physical characteristics such as their own heights (Bopp and Faeh 2008), measurements such as

beer-cask volumes and beer-bottle contents (Cunliffe 1976) as well as to report behaviors such as

the number of cigarettes smoked daily (Klesges, Debon, and Ray 1995). A robust finding in

finance and economics literature is price clustering around round prices (zero and five) in

financial markets such as in stocks (Sonnemans 2006), gold (Lucey and O’Connor 2016), and

bitcoins (Urquhart 2017).

People are also more likely to respond using round numbers when estimating or guessing.

For example, Plug (1977) found that when asked to provide estimates of breadth-to-height ratios

of geometrical figures, respondents used round numbers. It has been speculated that preferences

for round numbers occur because they are likely more fluently processed than non-round

numbers. Additionally, round numbers occur more in the environment (e.g., in texts (see

Coupland 2011) thereby leading to a familiarity-based effect (Zajonc 2001)).

Round numbers are also utilized by people as benchmarks or reference points against

which to judge their own performance. For example, SAT takers set goals at round scores like

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1,300, professional baseball players aim for batting averages at numbers like 0.300 (Pope and

Simonsohn 2011), and marathon runners aspire to full hours (e.g. four hours) as completion

times (Allen et al. 2016).

In contrast to these findings where round numbers are used as a goal towards which

people expend effort, the “zero” bias in investment decisions suggests that the affinity for using a

round ending calendar year as a time to retire is a result of a rounding bias in mathematical

calculations.

Findings in the computational estimation literature, defined as determining approximate

answers to simple arithmetic problems, show the use of rounding-down or rounding-up strategies

to arrive at solutions (Siegler and Lemaire 1997; Lemaire and Lecacheur 2001). For example,

people mentally compute 136 + 59 + 48 to be 250 by rounding up operands (150 + 50 + 50) or

calculate 63 × 12 to be 600 by rounding down operands (60 × 10). In a comparison of strategies

used by younger and older people, Lemaire and Arnaud (2008) found greater use of columnar

retrieval by older people. For instance, in a problem of adding 12 + 46, columnar retrieval is

defined as first adding the units and then the decades ([2+6]+[10+40]) indicating more reliance

on round numbers. The computational estimation literature finds that multiple strategies are used

to solve different problems based on the characteristics of the problem (Campbell and Xu 2001),

the situation (Trbovich and LeFevre 2003), and individual differences (Gandini, Lemaire and

Michel 2009). This literature also concludes that individuals often use multiple strategies for the

same problems (Dowker et. al. 1996).

All these findings across different domains suggest that in investment choice decisions,

there is likely a preference for zero ending years in the choice of TRFs. To gather preliminary

evidence, we collected the total net asset information of all the TRFs in the market from the

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Center for Research in Security Prices (CRSP) database. We use data from 3,289 TRFs of 443

TRF fund families and 64 providers in 2014. We define a provider to be a firm (e.g., Vanguard).

A fund family denotes a particular share class of a fund. For example, “Vanguard TRF A shares”

is a fund family. Within it, there are 12 funds from 2005-2060 that are divided into 5 year

increment funds. With the data from the entire universe of all TRFs, we present the distribution

of total net assets by TRF Year in Figure 1. The y-axis represents the total net asset in millions of

dollars. The purple boxplots represent the five-ending TRFs and the yellow boxplots represent

the zero-ending TRFs. Consistently across all decades, the yellow boxes are higher than the

purple boxes, for both the median and the 3rd quartile, revealing that the total net asset in the

zero-ending TRFs is higher than that in the five-ending ones. This plot suggests that consumers

prefer the zero-ending TRFs to the five-ending TRFs.

Figure 1. Distribution of Total Net Asset by TRF Year

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While the aggregate data from total assets held by the population indicates a general

tendency for a preference of round-ending years, a limitation of the data is that when TRFs were

first introduced, some of them only offered the zero-ending TRFs. To verify the preferences and

better understand the underlying process, we obtained individual level data of investors’ choices

including birth year.

We next describe the data. We first discuss the analysis of how birth years shape the

choice of the TRFs. We then examine the implications of the choices. First, we investigate

whether the choices impact wealth accumulated at the time of retirement. To do so, we run

simulations using data on every investor’s choice and their past returns. Second, we use choice

of the TRF to examine if the choices correlate with other financial behaviors. We then discuss

the findings from a natural experiment on whether the “zero” bias we identify in our analysis can

be mitigated. Next, we use participants from CINT to get a better understanding of the how the

TRF choices impact saving contribution rates and finally discuss the implications of our findings.

DATA AND FINDINGS

Zero Bias

To study individual investor choices among TRFs, we obtained data from a global

financial investment management firm that offers retirement plans. Our 2016 proprietary data

includes 84,600 individual accounts from 52 employer-defined contribution plans. For

confidentiality reasons, we were not provided the names of the employees or the employers. On

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a typical website, the TRFs’ targeting retirement years are listed chronologically (e.g. 2020 –

2065). As the commission rates are quite similar, the focal firm has no incentive to promote any

TRF of a specific year. Rather, the focal firm’s main goal is to increase investment amounts in

the 401(k) plans.

Nearly half of the sample (40,848) invest in TRFs (e.g., Vanguard Target Retirement

2050 Investment Fund). In total, our data contain 91 different TRFs from six fund providers. We

observe the investor’s fund choice, monthly contribution amounts, and some demographic

characteristics (e.g., age, gender, marital status, etc.). Out of those who invest in TRFs, 33,876

(82.9%) invest their entire 401Ks in only one TRF. We use only these in our analysis. Among

them, 2,484 (7.3%) customers started investing before both 5-ending TRFs and 0-ending TRFs

became available. We deleted those observations with a final dataset consisting of 31,392

customers.

We also have information on the interactions between these consumers and the

investment firm. For example, when a consumer visits the company’s website or receives an

email from the company, the information is recorded. Table 1 provides the summary statistics of

the demographics.

We first examine the choice of the TRFs. In Figure 2, the solid blue line depicts the

number of investors choosing each of the TRFs (aggregated across all providers). As easily

observed, the number of investors who choose any of the 2020/2030/2040/2050 ending dates is

much greater than the number of investors who opt for any of the 2025/2035/2045/2055 ending

dates. This confirms a “zero bias” in that investors choose more TRFs with years ending in zero

than those ending in five.

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Table 1. Distribution of Demographic Variables

Sample Size Mean Median Std Min Max Age 31,386 47.0 47 10.8 26 86

Female 30,174 0.495 0 0.5 0 1 Income 30,034 $65,495 $60,000 $29,589 $15,000 $373,000 Married 1,036 0.67 1 0.6 0 1

Tenure (Years) 31,392 11.0 9 6.0 2 50 Deferral % 31,392 4.1% 3% 5.5% 0.01% 21%

Number of Cities 4,356 Number of States 50

Number of NAICS 43 Number of Sectors 14

We first conduct a robustness check to rule out that the zero bias is due to an unbalanced

distribution of investor age. It is plausible that more people in our sample potentially retire

around the zero-ending years rather than five-ending years. To investigate this possibility, we

plot the predicted number of investors choosing each TRF in Figure 2, using the dashed orange

line. To obtain the predicted number of investors choosing each TRF, we assume the typical

retirement age of 65 and use each investor’s birth year plus 65 to calculate their “predicted”

retirement year and hence the associated TRF; for example, for those born in 1978, the predicted

retirement year is 1978+65=2043, leading to the 2045 fund. The orange line in Figure 2 reveals

that the distribution of investors’ predicted target retirement years is almost uniform, ranging

from 2020 to 2050. This confirms that the random sample of investors is representative.

However, the observed number of investors for each fund shows a strong zigzag pattern, as

displayed by the blue line.

We conduct two robustness checks to verify whether the pattern was driven by the

presence of a default fund. It is possible that some firms suggest default choices when their

employees are deciding their 401(k) portfolios. One default could be the recommendation of a

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TRF matching the employees’ retirement age of 65. Another default is that a firm recommends a

0-ending TRF. Our data consist of 52 firms. Due to confidentiality issues, we cannot pinpoint

which employers offer default funds. However, we are able to conduct analysis at the firm level

to rule out these alternative explanations. If an employer offers age-appropriate default TRF, we

should observe fewer people deviating from the matching choice. Therefore, for each employer,

we calculate the percentage of the investors that are “deviators”, i.e. their choice of fund is

different from the matching TRF. Seven firms have a relatively low percentage of deviators, i.e.

<10%. We consider them as potential firms that offer age-appropriate TRF as the default. We

delete these seven firms (7736 observations, 22.8% of the sample). Our main results still hold.

There are also six firms where the zero bias is exhibited by more than 90% of the employees,

suggesting that it is possible that there could be a zero ending default TRF. After removing these

six firms, we still find that the zero bias in the remaining data is strong. Please see the detailed

results in the Web Appendix B.

Figure 2. Actual versus Predicted Frequency of Target Retirement Funds

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To decipher the origin of the zigzag pattern in Figure 2, we depict the choices made by

investors of each birth year in figures 3a-3d. The different colors in figures 3a-3d represent funds

with different target dates, while the height of the bar represents the number of investors. For

example, for those investors born in 1958, 32.11% choose 2020 (orange), 57.01% selected 2025

(gray), and 7.64% picked the 2030 fund (yellow).

Figure 3a plots the choice of fund for each investor born between 1953 and 1962.

Consistent with data that indicates that most people retire at 65, we will henceforth refer to the

appropriate fund (retirement at 65) as the matching fund. For easy exposition, we group birth

years that should lead to the selection of the same TRF. Assuming the retirement age of 65, for

people born in the 1955 birth group {1953,1954,1955,1956,1957}, the 2020 fund is the matching

fund, whereas those in the 1960 birth group {1958,1959,1960,1961,1962}, the 2025 fund

matches the retirement year. Given that TRFs have only zero-ending and five-ending

alternatives, investors with birth years not ending with zero or five are required to perform

computations that involve some form of rounding. For example, investors born in 1956 ought to

plan to retire in 2021 (at age 65) and choose the 2020 TRF by rounding down (1956+65=2021),

whereas those born in 1958 ought to select 2025 by rounding up (1958+65 = 2023).

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Figure 3a. Fund Choice Distribution for Investors Born Between 1953 and 1962

Figure 3b. Fund Choice Distribution for Investors Born Between 1963 and 1972

0

200

400

600

800

1,000

1,200

1953 1954 1955 1956 1957 1958 1959 1960 1961 1962

Num

ber o

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rs

Birth yearTRF 2020 TRF 2025 TRF 2030 TRF 2035 TRF 2040TRF 2045 TRF 2050 TRF 2055 TRF 2060

0

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1,000

1,200

1963 1964 1965 1966 1967 1968 1969 1970 1971 1972

Num

ber o

f Inv

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rs

Birth year

TRF 2020 TRF 2025 TRF 2030 TRF 2035 TRF 2040TRF 2045 TRF 2050 TRF 2055 TRF 2060

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Figure 3c. Fund Choice Distribution for Investors Born Between 1973 and 1982

Figure 3d. Fund Choice Distribution for Investors Born Between 1983 and 1992

0

100

200

300

400

500

600

700

800

900

1973 1974 1975 1976 1977 1978 1979 1980 1981 1982

Num

ber o

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Birth yearTRF 2020 TRF 2025 TRF 2030 TRF 2035 TRF 2040TRF 2045 TRF 2050 TRF 2055 TRF 2060

0

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1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

Num

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Birth year

TRF 2020 TRF 2025 TRF 2030 TRF 2035 TRF 2040TRF 2045 TRF 2050 TRF 2055 TRF 2060

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We now discuss the specific patterns that emerge in the choice of TRFs. The first is that

the zero bias originates primarily from investors born in the zero-ending birth groups—those

who should choose the five-ending appropriate TRFs. However, instead of choosing the

matching five-ending funds, they select the zero-ending ones. Figure 3a illustrates the shift in

behavior for this group. Although 87.9% of the investors born in the 1955 birth group

({1953,1954,1955,1956,1957}) pick the matching 2020 date, only 57.0% of the investors born in

the 1960 birth group ({1958,1959,1960,1961,1962}) choose their matching 2025 TRF. We

observe similar patterns in other birth-year groups (1950, 1970, and 1980) as well, as shown in

figures 3b–3d. The pattern is clearly visible in all the figures. For brevity, we do not report all the

numbers. Overall, the percentage of people selecting the appropriate matching fund is

significantly lower in the zero-ending birth groups (59.7%) as compared to the five-ending birth

groups (86.9%) (𝜒𝜒12 =2,920.0, p < .0001).

Second, the zero bias is asymmetric: investors with birth years ending with eight or nine

tend to choose an earlier date (retire at 60), whereas investors with birth years ending with zero,

one, or two tend to pick a later date (retire at 70). For instance, 57.0% (gray bars) of the investors

in the 1960 birth group selected the matching 2025 date, leaving the rest 43.0% as deviators

(figure 3a). Within the deviators born in 1958 or 1959, the majority or 71.8% (29.9% of the total,

shown in orange) deviate to the earlier 2020 TRF. Also, the majority or 83.9% (36.8% of the

total, shown in yellow) of the deviators born in 1960, 1961, or 1962 deviate to the later 2030

TRF. Across all the data, within the deviators born in years ending with eight and nine, 81.6%

(32.9% of the total) select the earlier fund, whereas among the deviators born in zero-, one-, and

two-ending years, 77.1% (31.5%) choose the later fund. Comparing those born in eight- or nine-

ending years with those born in zero-, one-, or two-ending years, we find that the pattern of

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choices significantly differs for these subgroups born across the four decades (all p’s < .0001).

The systematic pattern of selecting earlier or later TRFs based on the birth year confirms some

use of mental arithmetic in solving the retirement age estimation problem.

The third noteworthy effect the data show is that individuals round up more than round

down. For instance, the matching fund for those people born in 1970 is the 2035 fund as it is

precisely matching their retirement age. Any deviation implies a choice between rounding down

to 2030 or rounding up to 2040. The data show that 72.8% (262 out of 360) of the investors that

deviate round up to 2040, suggesting a strong rounding-up tendency. Similarly, for people born

in 1960, 79.0% (298 out of 377) round up to 2030, and for people born in 1980, 67.1% (200 out

of 298) round up to 2050. The use of the rounding-up heuristic by those born in the zero years is

consistent for all age groups. If we sum over deviators born in 1960, 1970, and 1980, 73.43%

round up.

To further investigate whether there are any differences in the tendency to round up or

round down, we next compare only the cohort born in eight- or nine-ending years with those

born in one- or two-ending years. Of the total 6,292 individuals born in eight/nine, 2,133 (33.9%)

round down, whereas out of the 5,963 consumers born in one/two, 2,177 (36.5%) round up. The

difference between the frequency of rounding up and rounding down is significant (𝜒𝜒12 =

9.1349, p <0.01). Together, the data indicate strong evidence for use of rounding up relative to

rounding down.

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ECONOMIC IMPLICATIONS

We now discuss the implications of the zero bias for investors’ welfare in terms of the

accumulated wealth over their life cycle. The choice of the TRF can potentially serve as an

anchor point to determine the number of working years left before retirement. It may therefore

impact the rate at which the consumer saves for post-retirement, with people saving more if the

retirement looms early or saving less if retirement appears far away. We quantify the welfare

impact of the zero bias and decompose the effect to the amount contributed towards retirement

and exposure to risk.

First, we find that individuals are more likely to contribute less if they select a later fund

date as compared to selecting the matching TRF. Figure 4 shows the average contribution,

measured as percentage of income, by the birth year of the individual. The three lines—blue,

gray, and orange—represent the average contribution when investors choose an earlier date, the

appropriate TRF that reflects the retirement age of 65, and a later fund. For example, for

investors born in 1970, the fund that matches the retirement age of 65 is the 2035 TRF. Within

these investors, those who choose the 2035 fund on average contributed 4.38% of their income

towards their retirement, whereas those who choose the 2030, the earlier fund, on average

contributed 4.57% (which is significantly higher than that of investors who choose the 2035

fund, t =13.82, p < 0.001), and those who choose the 2040, the later fund, on average contributed

4.21% (which is significantly lower than that of investors who choose the 2035 fund, t = 11.26, p

< 0.001). The downward trend in Figure 4 simply indicates that older people contribute a higher

percentage. Summarizing over all age groups, we find that people who select a later retirement

date contribute 4.63% less than those who pick the matching fund.

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Figure 4. Average Contribution as a Percentage of Income by Birth Year

Table 2. Regression of Percentage Contributed

DV: Contribution Percentage Estimate Standard Error

Intercept 1.105467488*** 0.06096842

Birth Year -0.000537638*** 0.00003091

Income 0.000000129*** 0.00000001

Female -0.002430144*** 0.00065761

Late TRF -0.006961999*** 0.00099075

Early TRF 0.007825348*** 0.00099088

N =31,392 R2=0.026

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

53 57 61 65 69 73 77 81 85 89

Aver

age

cont

ribu

tion

as p

erce

ntag

e of

inco

me

(%)

Birth yearEarly Exact Late

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To verify the intuition in Figure 4, we regressed the percentage contributed on age,

income, gender, and choice of TRF. The results are provided in Table 2. The analysis shows that

those who select late (early) TRFs are more likely to contribute a lower (higher) percentage as

compared to those who select the appropriate TRFs. Additionally, we find that, not surprisingly,

older and richer individuals contribute more of their income. Interestingly, women contribute a

lower percentage than men.

Besides contributions, we require information on returns and risk of the portfolios to

determine the welfare implications. The zero bias also exposes investors to different risk-return

trade-offs; choice of a later date generally implies higher risk than the normative TRF that

matches a retirement age of 65. To understand the impact of risk preferences on consumers’

welfare, we follow the approach in Poterba et al. (2009) to simulate the retirement wealth.

The notion behind the simulation is to construct the path of contributions over an

investor’s life before retirement and combine these contributions with information on asset

returns. For each investor, we simulate future retirement wealth using data from past monthly

contributions and past returns. Using these contribution trajectories, we extrapolate the data to

obtain the yearly contributions until the age of 65 for each investor, regardless of the chosen

TRF.

For each investor i, let Ci(a) be her contribution at age a, Ri(a) be the return of TRF

chosen by investor i at age a, and Si be the age when investor i starts to invest for retirement. The

retirement wealth at age 65 is therefore given by

∑ ∏−

= =

−−+=iS

ti

t

jii tCjRW

65

0 0

)65(})]65(1[{)65( (1)

This equation implies that the retirement wealth is the sum of the cumulative returns from

each contribution over the course of the working life. Because Ri(a) is the return of a TRF whose

22

mix of stocks and bonds varies with time, we collect data on the glide-paths and underlying

holdings of each TRF in our sample. The glide-paths inform us of the weights of stock and bond

holdings. We obtained each fund’s historical holdings and its returns from Morningstar. Because

Morningstar does not have the holdings information for trusts such as Vanguard Target

Retirement Trust Funds, our simulation analysis excludes investors who hold trusts. There are 18

trusts out of the 91 TRFs in our sample. After excluding trust holders, 14,824 investors are left in

the simulation analysis. We obtain the returns of the TRFs by varying portfolio weights over

time according to the glide-paths. Note that Target Retirement Funds continue to accept monthly

contributions and invest in various asset classes even after maturity. For ease of comparison, we

simulate retirement wealth only up until the age of 65.

Because asset returns are stochastic in nature, we simulate consumers’ retirement wealth

using the following algorithm: for each individual i at age 𝑎𝑎𝑖𝑖, in each iteration h, a sequence of

65 – 𝑎𝑎𝑖𝑖 stock and bond returns is drawn from the empirical return distribution of the holdings in

the TRF chosen by the specific investor. Then the sequence of returns of the entire TRF span is

calculated by applying the weights obtained from the glide-path of the TRF. Next, we use

equation (1) to calculate the terminal wealth at age 65. For each investor, we simulate the

retirement wealth 20,000 times. To understand the impact of asset returns on consumers’ well-

being, we calculate consumers’ expected utility associated with the distribution of these

simulated terminal wealth values. Following Poterba et al. (2009), we use the utility function

with a constant relative risk aversion parameter.

Because we do not observe individual risk aversion values, we follow Poterba et al.

(2009) and compare the results at four different risk aversion values, 𝛼𝛼 ∈ {0, 1,2,4}, with higher

values indicating more risk aversion.

23

As a result, the utility of investor i for the return history h (one iteration in the simulation)

is given by

(2)

We then obtain the expected utility as the probability-weighted average of these utility

outcomes. Given that the expected utility is a function of consumers’ risk tolerance, we construct

a certainty equivalent measure; that is, the total certain wealth that can provide utility at the same

level as the expected utility. Specifically, the certainty equivalent of the accumulated wealth is

αα −−= 11

)]1(*)([ ihihi WUEZ (3)

The notion of a certainty equivalent suggests that an investor with a higher level of risk

aversion has a lower expected utility for a later TRF because the later TRF puts investors in

excess risk. However, an investor with a low level of risk aversion will have a higher expected

utility for the later TRF, due to better expected returns.

We use equation (1) to (3) to simulate the retirement wealth (certainty equivalent) for all

investors in our sample. We use each investor’s TRF choice observed in the data to find the

corresponding glide-path. To make comparison easier, we assume all the investors save between

age 30 and 65.

Figures 5a-5d plot the results for the simulation assuming risk averse (𝛼𝛼 =4) investors,

each panel representing those born between birth years ending 3 through ending 2 in each

decade. For example, Figure 5a illustrates expected accumulated wealth for those born between

1953-1962. Similarly, Figures 6a-6d plot the simulation results for risk neutral (𝛼𝛼 =0) investors.

The simulation incorporates changes in the riskiness of the portfolio as well as contribution rates.

α

α

−=

−

1)(

1ih

ihihW

WU

24

Figure 5a illustrates the simulated accumulative wealth for risk averse investors (alpha =

4) born between 1953 and 1962. We use three colors (green, grey, and red) to represent three

choices: the earlier TRF, the matching TRF, and the later TRF, respectively. The height of a bar

represents the accumulative expected wealth and the width represents the number of investors as

in the sample. For example, for investors born in 1959, more investors selected the earlier TRF

(2020) as compared to the later one (2030). Please note there are no earlier TRFs for birth year

1953-1957 because fund providers do not offer the matching 2015 fund.

Figure 5a clearly shows that the expected accumulated wealth becomes significantly

lower when people deviate from the matching TRF to the later TRF while it becomes higher

when deviating to the earlier TRFs. Aggregating across the panel, the average accumulative

wealth for investors choosing the matching TRF is $195,508 while that for investors choosing

the later TRF, it is $163,455, 16.3% lower. A similar pattern can be observed in Figures 5b, 5c,

and 5d. Across all the four decades, the accumulated wealth of investors choosing the later TRF

($168,634) is 13.3% lower (t = -172.76, p < 0.0001) than that of investors choosing the matching

TRF ($194,443). The birth year effect is also readily apparent. For example, comparing birth

years 1959 and 1961 show the sharp change in the number of people selecting the later/earlier

TRFs.

Figures 5a-5d reveal that for risk averse investors, deviating to the earlier TRFs increases

accumulated expected wealth. Aggregating across all years, we find that wealth can be 14.2%

greater when selecting the earlier TRF as compared to the matching TRF ($222,068 vs.

$194,443, t = 169.82, p < 0.0001).

Interestingly, in Figures 6a through 6d, we find that for risk neutral investors (𝛼𝛼 =0),

deviating to the later TRF decreases accumulated wealth by 2.1% as opposed to selecting the

25

matching TRF ($319,746 vs. $326,688, t =-73.7, p < 0.0001). On the other hand, deviating to

the earlier TRF increases accumulated wealth by 0.2%, which is significantly higher than

selecting the matching TRF ($327,330 vs. $326,688, t =4.4, p < 0.0001). Note that in some birth

years (e.g. 1970-72), individuals suffer financially either way they deviate from the matching

fund. This is caused by the combination of the risk effect and the contribution rates effect.

Figure 5a-5d. Accumulated Wealth for Risk Averse Individuals

26

27

Figure 6a-6d. Accumulated Wealth for Risk Neutral Individuals

28

29

To summarize the economic impact, we first estimate the proportion of people who

choose the mismatched TRF who are worse off. The table below shows the percentage of the

consumers who choose the early (or late) TRF that end up worse under different risk aversion

scenarios. Table 3 shows that as the risk aversion increases from 0 to 4, a lesser proportion of

consumers who choose early TRFs end up financially worse off. In contrast, a larger proportion

of consumers who choose late TRFs end up worse.

As the simulation demonstrates, consumers are not universally worse off by choosing the

“mismatched” (earlier or later) TRF. These results are driven by two factors: contribution rates

and risk profile. As discussed earlier, consumers who choose early TRFs are likely to contribute

more than consumers who choose the matching or later TRFs. Purely from the contribution

perspective, consumers who choose a later TRF end up worse. From the risk perspective only,

30

as risk aversion decreases, we see more investors who choose the early TRF end up worse off.

Together, while higher expected returns of the late TRF are more likely to make investors’

wealthier, their lower contribution rate negatively influences their well-being.

Across all the consumers in our sample who choose the mismatched TRF, 46.9% choose

the early TRF and 53.1% choose the late TRF. As can be seen in Table 3, across all the different

risk aversion scenarios, approximately 50% of the investors who choose the mismatched TRF

end up worse.

Table 3. Percentage of Investors Worse Off

Risk Aversion Percentage of Individual Impacted

0 1 2 4

Percentage of Consumer Who Choose Earlier TRF and End Up Worse-off 43.1% 33.7% 23.9% 2.8%

Percentage of Consumer Who Choose Later TRF and End Up Worse-off 56.0% 68.3% 74.8% 100%

Percentage of Consumer Who Choose Mismatched TRF and End Up Worse-off 49.9% 52.1% 50.9% 54.4%

Another perspective on quantifying the economic impact of the decision is to calculate

the number of months the additional wealth accumulated from the matching TRF can sustain a

retiree’s life. We use Finke, Ho, and Houston (2017) ’s estimate of $1,456 average monthly

spending per-retiree (based on data from the Health and Retirement Study and CAMS survey

collected by the University of Michigan). We also consider that a retiree receives social security.

According to the Health and Retirement Study and CAMS survey, the average monthly social

security retirement payment is $1,413. Assuming a 20% of tax rate leaves a disposable income of

$1,130. Therefore, a retiree’s monthly shortfall of $326 ($1456-1130) needs to be covered by

retirement savings. As discussed earlier, the difference between the wealth of an average investor

choosing the matching TRF and later TRF is $25,809 ($194,443 - $ 168,634). This implies that a

31

retiree can use the additional wealth by choosing the matching TRF for 79 months

($25,809/$326), approximately six and a half years. From the perspective of a retiree meeting

living expenses, the difference in savings alone is quite consequential. We now turn to

examining the relationship between the choices of TRF’s and saving rates.

CHOICE OF TRF AND CONTRIBUTIONS TO RETIREMENT

The patterns in Figure 2 that show an association between TRF choice and savings

contribution rates (as a percentage of income) can be rationalized by two alternative

explanations. First, if an investor can afford to save at a high rate now, she can choose to retire

early while another investor who cannot save adequately for retirement has to retire later. In

other words, a consumer may first decide how much to save, then choose the retirement age and

TRF accordingly. Second, there may be some other alternative third unidentified factor that

drives both retirement age and contribution rate. In contrast, we suggest and provide evidence

that it is likely that consumers first choose the retirement age and the associated TRF, then plan

contributions accordingly. We do so using the real-world data supplemented with an experiment.

The data casts doubt on the two alternative explanations. Our intuition is that if it is true

that consumers’ contribution percentage decisions is made prior to the TRF choice, then the

contribution percentage choice should not be connected to the zero bias, i.e., the contribution

percentage choice should not be associated with whether her birth year is around 0 or around 5.

Similarly, if factors other than birth year are driving the contributions, we should have no reason

to believe the distribution of contribution for each segment differs by birth year. Therefore, we

32

should observe a similar distribution of contribution percentage for those around birth years 0

and birth years around 5.

In Figure 7, we plot the standard deviations of contribution percentage for each birth

year. As can be easily observed, the standard deviations of contribution percentage is much

larger for birth years around 0. This pattern occurs because when an individual's birth year is

around 0, she is more likely to deviate to non-matching (not 65) TRFs, leading to a higher

standard deviation of the contribution percentage. However, a consumer whose birth year is

around 5 is less likely to deviate by selecting the matching TRF, resulting in a small standard

deviation of the contribution percentage. Also, in particular, there are interesting changes in

standard deviations in specific years: they sharply increase from year ending 7 to year ending 8

year and then sharply decrease from year ending 2 to year ending 3. Please note that the standard

deviations are similar for those the two groups born after 1983 – here the sample sizes are very

small compared to the other groupings.

The contrasting contribution percentage distribution patterns for birth years around 0

versus around 5 suggest that the contribution choice likely stems from the choice of the TRF.

33

Figure 7. Standard Deviation of Contribution Percentage by Birth Year

It is possible that there may be systematic differences between the segments of those who

belong to different birth years. To further investigate whether the choices and contribution rates

are driven by factors other than birth year, we run the Kolmogorov–Smirnov test on gender and

income to determine if these distributions are the same for different birth ending years. We run

the test on two observed variables that are very likely to influence contribution rates, gender

and income, and find no significant differences. However, we find the difference in the

distribution of the contribution rates across these groups to be significantly different. Detailed

results are provided in the Web Appendix C. We next describe an experiment that provides

additional evidence that the TRF choices may impact retirement contribution rates.

0

0.0005

0.001

0.0015

0.002

0.0025

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92

Stan

dard

Dev

iatio

n of

Def

eral

Per

cent

age

Birth Year

34

EXPERIMENT

The experiment serves three purposes. First, our goal is to examine if the zero bias

replicates in an experimental setting. Second, we want to investigate if it is possible to nudge

investors to select the default TRF that matches the retirement age of 65. Third, we want to

obtain insights as to whether the distribution of the retirement contribution rates change after

people are nudged to the default TRF. If the distribution of contribution rates shifts after the

nudge, it provides additional evidence that the choice of the TRF can impact contribution rates.

Two hundred and thirteen participants were recruited from CINT. The average age of

participants was 46.7 (range 30-66). They all held retirement savings in 401(K) plans. The

household income distribution was as follows: $25,000-$49,999 (12%), $50,000-$79,999 (32%),

$80,000-$99,999 (13%), $100,000-$149,999 (24%), $150,000-$199,999 (9%), > $200,000

(10%). There were two conditions in the experiment where either the participants were given a

default TRF or not (No-Default versus Default). In the No-Default condition (n= 107),

participants were first asked to imagine that they were investing in a TRF for their retirement.

They were provided a description of a TRF including an example of a glide-path. They were

asked to choose from the set of TRFs ranging from 2015-2070 (given vertically in that specific

order). Next, they were asked to provide their savings contribution rate (as a percentage of

income on a sliding scale anchored between 0 and 15%). Finally, age and other demographics

were elicited. In the Default condition (n=106), we first asked the participants their age. Then

they read the descriptions of the TRFs. Next, they were asked to select from the same menu of

TRFs and were told what her matching TRF was (“Based on your age, 20xx is the TRF fund that

35

matches your retirement age of 65). Following the choice of the TRF, participants indicated

their retirement contribution rate finally followed by demographic information.

The results of the TRF choice are provided in Table 4. First, the results of the No-Default

condition show that the zero bias replicates in an experimental setting with 65.4% of the

participants selecting a zero ending TRF. Figure 8 plots the data that shows the identical zig-zag

pattern observed in the real-world choices. Next, Table 4 shows that providing the default

matching TRF has a strong impact on choices with only 47.2 % of the participants selecting the

zero-ending TRF. Approximately 81.1% of the participants in the Default condition selected the

matching TRF as compared to 66.4% in the No-Default condition. The average ages we impute

from the TRF choices that participants want to retire are at 65.4 (Default condition) and 63.8

(No-Default condition).

We next turn our attention to the standard deviation of the contribution rates. The

standard deviations of the saving rates are provided in Table 5 and plotted in Figure 9. The

results of the choice condition mimic the standard deviations observed in the real-world: the

standard deviation of the contribution rates are significantly higher (F= 1.604, p =0.044) in the

zero-birth groups as compared to the five-birth groups. Importantly, in the default condition,

where participants were nudged to the matching TRF, the standard deviation of the savings

contributions shrink from 2.48 to 1.92, leaving the difference of standard deviations in the two

samples insignificant (F= 1.058, p = 0.416) thereby providing additional evidence that the

choice of the TRF impacts the savings contributions rates. We now turn back to the data to

examine if there are any demographic markers associated with the zero bias.

36

Table 4. TRF Choices in Experiment 1

No-Default Condition Default Condition Zero-

Ending TRF

Five-Ending TRF

Total Zero-Ending TRF

Five-Ending TRF

Total

Matching TRF Year

Zero-Ending 81.5% 18.5% 50.5% 81.3% 18.8% 45.3% Five-Ending 49.1% 50.9% 49.5% 19.0% 81.0% 54.7% Total 65.4% 34.6% 47.2% 52.8%

Figure 8(a). Fund Choice Distribution in the No-Default Condition of Experiment 1

02468

101214161820

2020 2025 2030 2035 2040 2045 2050 2055

Num

ber o

f Inv

esto

rs

Target Retirement Fund YearData Predicted

37

Figure 8(b). Fund Choice Distribution in the Default Condition of Experiment 1

Table 5. Contribution Rates in Experiment 1

Condition

Choice Default Mean Std Mean Std

Birth Year Group Five-Ending 4.72 1.96 5.23 1.97 Zero-Ending 5.49 2.48 5.16 1.92

Figure 9. Standard Deviations of Contribution Rates in Experiment 1

0

5

10

15

20

25

2020 2025 2030 2035 2040 2045 2050 2055

Num

ber o

f Inv

esto

rs

Target Retirement Fund YearData Predicted

0.00

0.50

1.00

1.50

2.00

2.50

3.00

Choice Default

Stan

dard

Dev

iatio

n of

C

ontri

butio

n Pe

rcen

tage

Birth Year 5 Birth Year 0

38

HETEROGENITY IN THE ZERO BIAS

We now explore some factors that can explain the heterogeneity in the zero bias.

Specifically, we examine whether any demographic variables are predictive of the zero bias.

Table 1 presents the summary statistics of the demographic variables. The average age of the

investors is 47.0, with the share of females at 49.5%. 67% of the sample is married and the mean

income is $65,495. The average tenure with the company is 11.0 years. The average deferral

percentage is 4.1%. The investors are geographically diverse, with the sample containing

individuals from each of the 50 states of the US. The employment also span a wide range of

industries or sectors.

Combining all the demographic variables, we run a logistic regression to predict the zero

bias. Table 6 presents the results. We control for geographical location and employment sector

random effects (denoted as Yes). We find that older individuals, males, those longer tenure with

the firm, and those who earn higher income are predictors of the zero bias.

Table 6. Effects of Demographics on Zero Bias (Logistic Regressions)

Variables Estimate Std Age 0.00833*** 0.00262 Female -0.0467* 0.0262 Tenure 0.0457*** 0.00447 Income 1.619E-6** 9.446E-7 Location Yes Employment Yes AIC 11,191.45 Pseudo R2 0.33 N = 12,480

*, **, *** indicate 0.10, 0.05, 0.01 significance levels, respectively.

39

We next examine other behaviors associated with the choices of non-matching TRF

choices.

BEHAVIORAL IMPLICATIONS

Is the zero bias associated with other behaviors such as information search? We

conducted post-hoc analysis to examine browsing behavior. We began by examining how the

zero bias is associated with information search by analyzing responses to the firm’s emails and

web visits during the period from January 1, 2012 to December 30, 2014. First, we found that as

compared to those who do not exhibit the zero bias, individuals who exhibit the bias open

significantly more emails sent by the firm (MBias = 7.13, MNoBias = 3.91; t = 8.68, p < .001) as

well as a larger percentage of emails received (MBias = 48.00%, MNoBias = 39.75%; t = 4.39, p <

.0001). Consumers with the zero bias were more likely to visit the company’s website (MBias =

14.85, MNoBias = 10.48; t = 5.85, p < .0001), visit more unique webpages (MBias = 26.48, MNoBias

= 24.24; t = 5.14, p < .0001), and stay longer on the site (MBias = 5006 seconds, MNoBias = 4362

seconds; t = 2.24, p < .0251).

These findings are puzzling as it is plausible that investors who spend a longer time on

their portfolios are more attentive and more careful. To resolve this puzzle, we explored the

content of the webpages. We found that investors exhibiting the bias are more likely to visit

webpages with loan information (MBias =45.88%, MNoBias =40.94%; 𝜒𝜒12=8.79, p < 0.01). These

loans are offered as a special service by the company for consumers to borrow against their

401(k)s. This action is generally acknowledged to be financially unwise, as taking this loan

shrinks retirement savings and reduces growth rates, compounded, or tax-deferred. Those

40

exhibiting the zero bias are potentially associated with those who are likely to be financially

distressed or financially unsophisticated. To examine financial lack of sophistication, we next

looked at the use of the website calculator and Q&A pages.

The calculator or worksheet is helpful for users to compute contribution percentages. For

instance, it translates the percentage of salary that should be contributed to the 401(k) any year to

reach a specific amount (e.g, $5,000). This calculator helps with very basic math. Consumers

with the zero bias are more likely to use this calculator (MBias =9.25%, MNoBias =7.33%; 𝜒𝜒12=4.55,

p < 0.05). Investors with the zero bias are also more likely to visit the Q and A pages (MBias

=21.46%, MNoBias =16.28%; 𝜒𝜒12=16.49, p < 0.0001), which reflects that they might not have

much knowledge about finance or saving.

The browsing behavior points to those demonstrating the zero bias to be more naïve

decision makers is consistent with the literature that novices differ from experts in several

dimensions including information search (e.g., Brucks 1985, Jacoby et al. 2001). We next

describe a natural experiment conducted by the focal firm that examines the impact of a financial

educational program.

REDUCING THE BIAS – A NATURAL EXPERIMENT

We consider whether it is possible to assuage the zero bias problem using an educational

program. We therefore leverage a natural experiment. Unlike the experimental approach, the

natural experiment provides an investigation on the specific segments that are more likely to be

influenced by financial education. During the sample period, the firm offered a financial

educational program that was a 30-minute, one-on-one meeting where retirement professionals

41

helped investors identify their personal goals and needs. The professionals answered questions

such as “Are we saving enough?” and “How do I select my investment?” To gauge effectiveness,

at the initial stage, the meetings were offered only to a select sample of investors. In this testing

period, we find that investors who receive the financial education are significantly less likely to

have the zero bias than those without training (MBias = 45.63%, MNoBias = 27.97%; 𝜒𝜒12 =457.94, p

< .0001). This analysis is far from conclusive, because we are not privy to the content discussed

in these meetings. However, it appears that the financial education training is helpful for

softening the zero bias.

Interestingly, we find that the effect of this training program is not homogeneous. To see

how the treatment effect varies for different investors, we use the causal tree model in Athey and

Imbens (2016) to quantify the heterogeneous treatment effect. The model builds on a regression

tree model (Breiman et al. 1984; Armstrong and Andress 1970; Homburg, Steiner, and Totzek

2009) and allows us to partition the entire sample of consumers into subgroups that differ in the

magnitude of their treatment effect of receiving the financial education. Please note that the

regression tree model recursively partitions data according to a relationship between the X and Y

values, creating a tree of partitions. It finds a set of cuts or groupings of X values that best

predicts a continuously distributed Y value. It does this by exhaustively searching all possible

cuts or groupings. These splits (or partitions) of the data are done recursively, forming a tree of

decision rules until the desired fit is reached. This is a powerful platform, because it chooses the

optimum splits from a large number of possible splits. For a more complete description of the

regression tree model, please see Breiman et al. (1984). Here we consider demographic

heterogeneity. The final output for the causal tree is fairly complex. Simply put, we find that the

program is most effective (with a treatment effect of 0.151, p < 0.001) for female investors

42

(mean treatment effect =-0.151, p<0.001) than for males (mean treatment effect = -0.129, p <

0.007). This intervention heterogeneity is consistent with the notion that women prefer lower

levels of investment risk and an educational intervention is helpful in informing them that they

are taking on more risk by investing in a farther dated fund. In contrast, the male investors may

have a preference for the greater risk associated with the long-dated fund in the first place and so

may not need correcting. The program is also more effective for lower income (less than $

47,000) investors (mean treatment effect =- 0.138, p < 0.001) than for higher income investors

(greater than $ 47,000).

CONCLUSION

We document that investors (specifically those born in years ending eight, nine, zero,

one, and two) are subject to the zero bias in their target retirement choices, where they are more

likely to choose zero-ending TRFs than five-ending TRFs. Those born in years ending in zero,

one, or two select TRFs that imply that their goal is to retire at 70, whereas those born in years

ending in eight and nine select TRFs that suggest that they plan to retire at 60.

The bias has far-reaching implications for the total wealth accumulated at the time of

retirement. First, the incorrect choice of TRFs can expose investors to risk that is incompatible

with their profile. Second, the research show that the savings rates are associated with the choice

of the TRF year with people selecting later (earlier) TRFs contributing less (more) to their

savings rates than those who select the matching TRFs. Overall, our simulations show that most

extremely risk averse consumers who choose later TRFs are more likely to be financially worse

off at the time of retirement. However, as investors’ tolerance towards risk increases, fewer

43

people who choose later TRFs are less likely to be worse off. Across all risk aversion scenarios,

we find that half of the investors who choose mismatched TRFs end up financially worse off.

The evidence we gathered suggests that the choice of the year of the TRF potentially

serves as an anchor against which people conjecture the number of working years left.

People (born in zero through two-ending years) who buy later TRFs save at a

significantly lower rate than those who buy the matching TRFs. Fortunately, people born in years

ending in eight and nine self-correct by contributing more. However, those born in years ending

in zero, one, and two suffer a double whammy by contributing less and potentially bearing

unnecessary risk.

The paradigm in the computational estimation literature examines how people solve

problems using simple mathematical problems. In contrast to this paradigm, we examine how

people make estimations using mental arithmetic. The estimations for retirement year

conceptually differ from standard problems, as multiple starting points are available (birth year,

current year, age). Additionally, rather than arrive at one solution, consumers have to determine

the best fit among the alternatives. We therefore add to the computational estimation literature by

investigating a different class of problems. We also add to the literature in computational

estimation by examining the use of mental arithmetic in the real world and observe more

evidence of the heuristic of rounding up than of rounding down.

Despite the recognized importance of retirement savings decisions, several findings in

finance, marketing, and economics literature have observed that investors often make sub-

optimal decisions. For example, it has been found that 401(k) participation rates are heavily

influenced by the default option (Madrian and Shea 2001), with participation much higher with

automatic enrollment. The asset allocation decision has also been observed to be quite extreme,

44

with either 100% invested in stocks or 100% in bonds (Ameriks and Zeldes 2004; Agnew,

Balduzzi, and Sunden 2003). Investors also do not diversify enough. Many invest almost 20% of

their discretionary 401(k) contributions in their own company’s stocks (Brown, Liang, and

Weisbenner 2007). Even though some investors are familiar with the principle of diversification,

they follow a naïve 1/N diversification heuristic where they divide their contributions evenly

across funds (Benartzi and Thaler 2001). This heuristic leads to a suboptimal outcome in that the

proportion invested in stocks depends strongly on the proportion of stock funds available in the

plan. Finally, there is limited portfolio reshuffling, in sharp contrast to discount brokerage

accounts (Agnew et al. 2003). Our article contributes to this stream of literature by investigating

the quality of investment decisions in the choice of Target Retirement Funds.

A question that we cannot completely address with the empirical data is the precise

nature of the computational estimation used in the choice process. As most people select TRFs

that project them to retire when they are between 60-70 years old, they are clearly using

computational heuristics that include rounding. What is unclear is how and why the starting point

between different starting points (date of birth, current age, or current year) is selected.

Identification of the zero bias effect has clear and actionable implications for consumers

and fund providers. The designers of 401(k) who plan menus should take this bias into

consideration, educate investors on the long-term consequences of the choices made at the point

of decision, and nudge investors into making selections that increase their financial well-being.

45

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