Behavioral Biases and Annuity Choice

To study status-quo bias, we introduce a treatment that removes the status quo of not owning an annuity. Unlike the control group, where participants have an endowment without an annuity and can choose to “buy” an annuity, in the no-status-quo group the annuity choice is presented using a neutral framing (people choose between taking an annuity or not, without either choice being the default).

Within the no-status-quo framing, we study four treatments that address people’s potential failures to think through how they would condition their savings choices on their choice of acquiring an annuity. In the first treatment, respondents first choose their level of savings in each of the two contingencies—having an annuity and not having annuity—and then they make the decision of whether to acquire an annuity or not. In other words, the first treatment encourages respondents to think through the dynamic decision using backwards induction. Because this treatment highlights how savings choices might optimally vary with the annuity decision, we call this the “savings salient” treatment.

The second treatment eliminates the need to solve the problem using backwards induction by showing the corresponding level of savings, as previously chosen by the respondent. We refer to this treatment as “explicit contingencies” because all consequences of choosing the annuity or not are fully explicit in this treatment. The third treatment is nearly identical, but presents the same choice without context—i.e., without discussing “savings”, “income,” or “annuities.” In other words, the choice is presented solely in terms of tokens corresponding to each of the two choices. We refer to this treatment as “explicit contingencies, no context.” The fourth treatment is like the third but ensures that the annuity stochastically dominates by adjusting the savings decision for the annuity such that the resulting tokens in stage 2 are identical with and without the annuity (and the resulting tokens in stage 1 are higher for the annuity).

Finally, we study a potential heuristic aversion to allocating income to states of the world in which there is both high marginal and high absolute utility from money. We do this by constructing a nearly identical setting where the impact of annuitization and feasible savings levels are identical, but where the state of the world in which the “annuity” pays off is actually the state with a lower absolute level of utility. We do this by reframing people’s decisions as being about insuring the loss of stage-2 income. Our hypothesis is that people find it more natural to insure states of the world with lower absolute utility than with high absolute utility. Because this treatment reverses the correlation between marginal utility and absolute utility relative to the standard positive relationship in the annuity context, we call this the “reverse correlation” treatment.

2021-01-01

2021-04-30

Take-up of the annuity option (or its equivalent when framed as insurance or Social Security)

Experimental savings decisions

To summarize the interventions listed above, we have a total of 9 experimental groups.


• The control group (“G0”), which is constructed to best resemble the conditions of annuity choice that people typically face. These annuities are worse than actuarially fair, the status quo is not owning an annuity, respondents are not induced to think about savings nor are the reminded of their savings plans for each contingency, and the annuity choice uses natural wording such as “annuities”, “insurance” or “Social Security.”

Five treatments investigate the three mechanisms of primary interest:
• One treatment group which is like the control group but where the status quo of not owning an annuity is removed (“G1”)
• Four treatments that increase proper accounting for contingent savings decisions, leading to the following groups:
o Savings salient group (“G2”)
o Explicit contingencies group (“G3”)
o Explicit contingencies, No context, group (“G4”)
o Explicit contingencies, No context, Dominance, group (“G5”)
• The reverse correlation treatment group (“G10”)

Two treatment groups to help us gauge the magnitude of the response:
• The low-price group (“G20”)
• A combined treatment group (“G35”), which combines a low price, the treatment in G5, and reverses the correlation as in G10.

We randomize subjects such that the expected number of observations in each of these 9 groups is expected to be equal.

Each respondent makes 6 decisions, and the decisions are divided into three blocks. The order of the blocks varies across respondents.

Savings block (3 decisions):
• The desired amount of savings if the respondent does not have an annuity
• The desired amount of savings if the respondent has a better-than-fair annuity (low price)
• The desired amount of savings if the respondent has a worse-than-fair annuity (high price)

Regular annuity decisions (2 decisions):
• Annuity choice if the annuity has a low price (i.e., is better than fair)
• Annuity choice if the annuity has a high price (i.e., is worse than fair)

One of the three “Explicit contingencies” decisions:
• Annuity choice if the contingencies are made for the treatment (i) explicit contingencies, (ii) explicit contingencies, no context, or (iii) explicit contingencies, no context, dominance. Because contingencies can only be made explicit if the respondent has already made their savings choices, this block necessarily comes after the savings block.


The primary randomization allocates annuity decisions (not respondents, because respondents each make three annuity decisions) into one of the 9 experimental groups described above. Decisions are randomized into these 9 groups with equal probability.

All decisions of a given respondent are either randomized into “regular correlation” groups (in columns A or C of Figure 1 in the uploaded "Full summary of experimental design" ) or into “reverse correlation” groups (in columns B or D of Figure 1 of Figure 1 in the uploaded experimental design summary).

There are five secondary randomizations:
• Wording. In the explanation of the experiment and in the some of the annuity decisions (the ones with context), the annuity choice is described either in terms of “annuities,” “insurance,” or “Social Security.” One of these three wordings is selected with probability 1/3 for each of the respondents whose annuity decisions are randomized into “regular correlation” groups. Only the insurance wording is used for respondents whose annuity decisions are randomized into “reverse correlation” groups (the other two wordings would be unnatural).
• When there is no status quo, we randomize (with equal probability) which option is presented on the left or the right.
• If the savings block is asked first, the order of the two annuity blocks is randomized.
• The order of the 3 savings decisions in the savings block is randomized
• The order of the two annuity decisions in the regular annuity decision block is randomized

Pseudo-random number generator on office computer.

Our treatments are randomized both between and within participants.

Yes

3000 participants

3,000 participants, at 3 annuity and 3 savings decisions per participant, meaning 9,000 annuity decisions and 9,000 savings decisions.

We randomize subjects such that the expected number of observations in each of these 9 cells described above is expected to be equal.

Analysis+plan.pdf