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Federal Reserve Bank of Chicago

Accounting for non-annuitization
Svetlana Pashchenko

WP 2010-03

Accounting for non-annuitization
Svetlana Pashchenko

∗

†

University of Virginia
March 25, 2010

Abstract
Why don’t people buy annuities? Several explanations have been provided by
the previous literature: large fraction of preannuitized wealth in retirees’ portfolios; adverse selection; bequest motives; and medical expense uncertainty. This
paper uses a quantitative model to assess the importance of these impediments
to annuitization and also studies three newer explanations: government safety net
in terms of means-tested transfers; illiquidity of housing wealth; and restrictions
on minimum amount of investment in annuities. This paper shows that quantitatively the last three explanations play a big role in reducing annuity demand.
The minimum consumption floor turns out to be important to explain the lack of
annuitization, especially for people in lower income quintiles, who are well insured
by this provision. The minimum annuity purchase requirement involves big upfront investment and is binding for many, especially if housing wealth cannot be
easily annuitized. Among the traditional explanations, preannuitized wealth has
the largest quantitative contribution to the annuity puzzle.

Keywords: annuity puzzle, longevity insurance, adverse selection
JEL Classification Codes: D91, G11, G22

1

Introduction

In the canonical life-cycle model people choose to smooth the marginal utility of consumption throughout their entire lifespan. In the presence of lifespan uncertainty, households
∗

I am grateful to Mariacristina De Nardi, Leora Friedberg, Toshihiko Mukoyama, and Eric Young
for their guidance on this project. I thank Gadi Barlevy, Marco Bassetto, Emily Blanchard, Jeffrey
Campbell, Eric French, John Jones, Alejandro Justiniano, Ponpoje Porapakkarm, Richard Rosen, and all
participants at the Federal Reserve Bank of Chicago Lunch Seminars for their comments and suggestions.
Financial support from the Center of Retirement Research at Boston College, Bankard Fund for Political
Economy, Committee on the Status of Women in the Economics Profession and hospitality of the Federal
Reserve Bank of Chicago is gratefully acknowledged. All errors are my own.
†
Email: sap9v@virginia.edu

1

risk outliving their assets. This risk can be insured by buying life annuities, which are
financial instruments that allow an individual to exchange a lump-sum of wealth for a
stream of payments that continue as long as he is alive. Because annuities cease payment
when a person dies, they offer a higher rate of return in states when a person survives.
Based on this the standard life-cycle model predicts that people should invest in nothing
but annuities.
In practice few people buy annuities. This empirical fact is called the ”annuity puzzle”. The literature seeking to explain the puzzle mainly attributed the lack of interest
in annuities to the following four factors: a substantial fraction of preannuitized wealth
in retirees’ portfolios, actuarially unfair prices, bequest motives, and uncertain health
expenses. It is still an open question, however, what is the relative quantitative importance of different explanations for the annuity puzzle. The goal of this paper is therefore
to provide a quantitative analysis of people’s decision to buy annuities in a model that
nests all major impediments to annuitization.
Most explanations for the annuity puzzle exploit the fact that real world annuities
have two disadvantages. First, an annuity is illiquid, i.e., it entitles a person to a constant
stream of income that cannot be converted back to liquid wealth. Second, the annuity
market suffers from adverse selection because longevity risk is unobservable. In equilibrium, people with higher than average mortality face prices above what is actuarially fair
and lower returns on annuities.
I develop a quantitative model of saving after retirement in which individuals face
lifespan uncertainty that creates demand for longevity insurance. At the same time
the available annuities are illiquid and actuarially unfair. The other key features of the
model are medical expense uncertainty, bequest motives, preannuitized wealth, and, a
government-provided minimum consumption level. Augmented in this way, the life-cycle
model allows for states, when it is not optimal for an individual to lock his wealth in a
constant stream of income.
The model allows for rich heterogeneity of individuals. This is motivated by the fact
that observed annuity demand varies a lot by quintiles of permanent income distribution.
To account for this observation, I include the following dimensions of heterogeneity in the
model: initial wealth, preexisting annuity income, life expectancy and medical expense
risk.
In modeling the annuity market I consider two information structures. In the first,
the insurer and the annuity buyer have the same information about the mortality of the
latter. In the second, there is asymmetric information, and the insurer can only observe
the age of the annuity buyer. The latter scenario creates an environment for adverse
selection. The adverse selection is intensified by the negative correlation between wealth
and mortality. This happens because retirees with low mortality buy more annuities
2

because not only do they expect to live longer but also they are wealthier. I compare
the outcomes of the models with two information setups to identify the effects of adverse
selection on the different group of retirees.
The main quantitative exercise of this paper consists of comparing annuity market
participation rates between the models that incorporate different impediments to annuitization. I start with studying four traditional explanations for the annuity puzzle.
Next, I explore the role of another three factors that have been studied much less: a
government provided social assistance, difficulties with annuitizing housing wealth, and
a minimum purchase requirement set by insurance companies.
The consumption minimum floor, among other things, provides financial support
for people if they outlive their assets and, thus, offer some longevity insurance. This
public longevity insurance may partially substitute for a private annuity, at least for lowincome retirees. In the presence of health uncertainty, the consumption floor can also be
considered as 100 percent tax on annuity income in the states when an individual cannot
finance his medical expenses.
Another possible impediment to annuitization arises because annuities pay off over
a long period of time and, as such, involve a big upfront investment. So when it comes
to buying an annuity, liquidity constraints may become an issue because, first, housing
wealth is not easily annuitized and, second, insurance firms place restrictions on the
minimum amount that can be invested in an annuity.
Housing constitutes a significant portion of retirement wealth. In principle housing
wealth can be annuitized by taking a reverse mortgage. In reality housing and nonhousing wealth differ in terms of costs of annuitization. For example, a 70 year old
woman with $100,000 in liquid wealth can get an annuity that will pay her around $700
every month while she is alive. If on the other hand she has $100,000 worth of housing
wealth and chooses a reverse mortgage with an annuity option, she will get only around
$300 per month1 .
Another consideration is that from the point of view of an economic model, an individual may find it rational to buy $10 worth of annuity. In reality insurance companies
set some restrictions on the minimum amount of investment in an annuity. The minimum premium varies from one firm to another but can go up to $100,000. This minimum
amount of investment constitutes a significant barrier to annuitization for many retirees.
I find that the following four factors play a major role in reducing annuity market
participation rates: preannuitized wealth, consumption minimum floor, minimum annuity purchase requirements, and illiquidity of housing wealth. The consumption minimum
floor affects mostly people in the low and middle quintiles of the permanent income
1
Data for reverse mortgages was taken from the website http://www.reversecalculator.com, and for
annuities - http://www.immediateannuities.com

3

distribution. The other three factors have a big effect on all retirees. Medical expense
uncertainty decreases annuity demand only for people in low income quintiles, while for
higher quintiles it has an opposite effect. Adverse selection has a similar heterogeneous
effect on different income quintiles. Because of this both medical expense uncertainty
and adverse selection have a small overall effect on retirees’ involvement in the annuity
market.
The paper is organized as follows. Section 2 reviews the literature. Section 3 looks
at the data of retirees’ involvement in the annuity market. Section 4 presents the model.
Section 5 describes calibration. Section 6 presents and discusses the results. Section 7
concludes.

2

Related literature

This paper is related to three strands of literature. First, the literature on the annuity
puzzle. Since the seminal work of Yaari (1965), the role of annuities in saving decisions
of consumers with uncertain life spans has been widely studied in economic literature.
Yaari’s famous result is that under certain assumptions an individual should fully annuitize all of his wealth. These assumptions include the absence of a bequest motive,
actuarially fair prices, and no uncertainty except about the time of death.
These theoretical results have been followed by a number of empirical papers measuring the insurance value of annuitization for representative consumers in calibrated life
cycle models (Mitchell et al., 1999; Brown, 2001; Brown et al., 2005). A general finding
of the literature is that there are substantial gains to partial annuitization, though full
annuitization is not always optimal.
The literature seeking to explain the annuity puzzle identified four factors that may
play a major role in reducing the demand for annuities on the part of single retirees. First,
individuals already have a substantial fraction of annuities in their portfolio provided by
Social Security and Defined Benefits (DB) pension plans (Dushi and Webb, 2004).
Second, the prices for annuities are actuarially unfair due to the presence of adverse
selection. Mitchell, Poterba, and Warshawsky (1997) showed that annuity prices in the
U.S. are around 20% higher than implied by the value of an actuarially fair annuity
calculated with population average mortality.
Third, annuitized wealth cannot be bequeathed. Thus individuals with bequest motives should have lower demand for annuities. Lockwood (2008) suggested that bequest
motives play significant role in explaining low annuity demand.
Fourth, the attractiveness of annuities can decrease in the presence of a health uncertainty. The possibility of incurring high medical expenses increases preferences for liquid
wealth as opposed to an illiquid annuity (Turra and Mitchell, 2004). Also big medical
4

expenses coincide with health deterioration, which increases mortality and decreases the
value of an annuity (Sinclair and Smetters, 2004).
The contribution of this paper to the literature on the annuity puzzle is twofold.
First, it extends the list of commonly studied factors contributing to the annuity puzzle.
And second, it provides a relative quantitative assessment of all these impediments to
annuitization.
The second strand of literature this paper is related to studies retirees’ saving decisions
in the presence of medical expense risk. Palumbo (1999), De Nardi, French, and Jones
(2009) analyze decumlation decisions when retirees can only save in bonds. Pang and
Warshawsky (2008) introduce a portfolio choice problem by allowing retirees to save in
bonds, stocks, and annuities. Yogo (2008) studies a more complicated portfolio problem
where retirees can allocate their assets among bonds, stocks, annuities, and housing. At
the same time he treats medical expenditures as endogenous investments in health. I
restrict the portfolio choice of retirees to only two assets - bonds and annuities, and
treats medical expenses as exogenous shocks to income.
The third strand of literature studies equilibrium in the annuity markets in the presence of adverse selection. Hosseini (2009) evaluates the benefits of the mandatary annuitization feature of Social Security. He considers an equilibrium where agents differ
only by their mortality. Walliser (1999) studies the effects of Social Security on the private annuity markets. He constructs the environment where agents are heterogeneous
both by mortality and income and allows for the income-mortality correlation. In this
paper I augment the heterogeneity of individuals by health and medical expenses. This
framework provides a more detailed picture of the effects of adverse selection on different
categories of population.

3

Data

In the U.S. only around 8% of people aged 70 years and older report having income from
private annuities in the HRS/AHEAD dataset. Participation in the private annuities
market varies a lot by quintiles of permanent income distribution (see Table 1). Almost
16% of people in the highest income quintile report having income from private annuities,
while among the bottom quintile this fraction is less than 1%.
To get some idea of what causes such significant variation one can compare life expectancy for people in different income quintiles. Annuities provide longevity insurance
and as such should be more valuable for people who live longer. Indeed, Table 2 shows
that on average at age 70 people in the fifth income quintile expect to live almost four
years longer than people in the first quintile.

5

Table 1: Participation in annuity market for people aged 70 years and older in 2006
Income quintile

Percentage

All

7.8

1

0.8

2

1.5

3

3.7

4

5.7

5

15.9

Annuities not only provide longevity insurance, they are also saving instruments. As
such, they are valued more by people who choose to keep large amounts of assets very late
in life. Table 3 compares asset decumulation rates for single retired individuals in different
income quintiles 2 . More specifically, it shows the percentage change in median assets
between 1995 and 2002 for retirees who were still alive in 2002. For higher permanent
income levels, the decumulation rate is slower than for the lower levels. Since people in
high quintiles spend their wealth more slowly they should be more interested in keeping
part of their assets in annuities as one of the available saving options.

Table 2: Life expectancy at age 70 (Source: De Nardi et al., 2009)
Income quintile

Life expectancy

1

11.1

2

12.4

3

13.1

4

14.4

5

14.7

In general, the observed heterogeneity in saving behavior and life expectancy for different income quintiles should result in significant variation in observed annuity demand.
This heterogeneity should be taken into account when analyzing the annuity puzzle because the reasons for low annuitization may differ by income quintile.
Another dimension to consider is how participation in the annuity market changes
with age. Table 4 presents participation rates for two groups: people aged 70-80 and
those older than 80 in 2006. 10.6% of the older cohort receives private annuity income,
2

In Table 3 the numbers for the bottom income quintile should be taken with caution because people
in this quintile have almost zero assets

6

Table 3: Percentage change in median assets, 1995-2002 (Source: De Nardi et al., 2009)
Income quintile

Ages 72-81

Ages 82-91

1

-83.4

-98.2

2

-33.4

-60.1

3

-23.2

-34.5

4

-27.5

-42.2

5

-7.7

2.7

compared to only 6.2% of the younger cohort. Part of this difference is due to survival
bias: people who buy annuities have higher life expectancy. However, it may also indicate
that people increase annuity purchases as they age. In general, the pattern of annuity
purchase by age is worth exploring because it can convey information about people’s
preferences for financial instruments in retirement and how well annuities meet these
needs.

Table 4: Participation in annuity market for people aged 70 years and older in 2006

4

Income quintile

Age 70-80

Older than 80

All

6.2

10.6

1

1.2

0.0

2

1.3

1.9

3

2.7

5.4

4

4.5

7.5

5

13.0

21.2

Model

Consider a portfolio choice model in which retired people decide how much to save and
how to split their net worth between bonds and annuities. These retirees face uncertain
lifespans and out-of-pocket medical expenses.
Agents have an initial endowment of wealth, part of which is exogenously annuitized.
Preannuitized wealth is the expected present value of the stream of annuities that an
agent is entitled to and consists of Social Security and DB pension wealth.
Agents are heterogeneous by age, health status, and permanent income. Permanent
income is an indicator of the agents’ lifetime earnings and is important for two reasons.
It determines agents’ initial endowment of wealth and affects the survival probability,
7

health evolution and medical expenses. The association between income, health, and
mortality is well documented (Hurd, McFadden, Merrill, 1999) and should be taken into
account in modeling annuity demand.

4.1

Households

4.1.1

Preferences

Denote age of the individual by t, t = 1, ...T, where T is the last period of life. Households
are assumed to have CRRA preferences:
c1−σ
u(ct ) = t
1−σ
and enjoy leaving a bequest. Utility from the bequest takes the following functional form:
υ(kt ) = η

(φ + kt )1−σ
1−σ

with η > 0. Here φ > 0 is a shift parameter making bequests luxury goods, thus allowing
for zero bequests among low-income individuals.
4.1.2

Health, survival, and medical expenses

In specifying medical expenses and survival uncertainty, I follow De Nardi, French, and
Jones (2009) (DFJ). Their framework is well-suited for studying heterogeneity in annutization decisions because they explicitly model the relationship between several factors
affecting demand for annuities: income, life expectancy, and medical expenses.
Each period an individual’s health status mt can be good (mt = 1) or bad (mt = 0).
The transition between health states is governed by a Markov process with a transition
matrix depending on age (t) and permanent income (I). I denote by Pr(mt+1 = 0|mt , t, I)
the probability of being in a bad state tomorrow given current health status.
The individual survives to next period conditional on being alive today with probability st , where sT = 0. Survival is a function of age, permanent income and current
health status: st = s(m, I, t).
Each period, an agent has to pay medical costs, zt , that are assumed to take the
following form:
ln zt = µ(m, t, I) + σ z ψ t ,
where ψ t consists of persistent and transitory components.
ψ t = ζ t + ξ t , ξ t ∼ N (0, σ 2ξ )

8

(1)

The persistent component is modeled as an AR(1) process:
ζ t = ρhc ζ t−1 + εt , εt ∼ N (0, σ 2ε )

(2)

I denote the joint distribution of ζ t , ξ t by F (ζ t , ξ t ). Unconditional mean of medical
expenses is: exp (µ(m, t, I) + 0.5σ 2z ), where
µ(m, t, I) = β h0t + β h1t 1 {mt = 1} + β h2t I + β h3t I 2 .

(3)

Here β h0t , β h1t , β h2t , β h3t are time-varying coefficients.
4.1.3

Government transfers

An agent who doesn’t have enough assets to pay his medical expenses receives a transfer
from the government in the amount τ t . This transfer maintains the agent’s consumption
at a minimum level guaranteed by the government cmin .
4.1.4

Portfolio choice

Individuals have two investment options - a risk-free bond with return r and an annuity
- and cannot borrow. As usually assumed in the literature, once the annuity is bought,
it cannot be sold. The annuity is modeled in the following way: by paying the amount
qt ∆t+1 today, an individual buys a stream of payments ∆t+1 that she will receive each
period, conditional on being alive. I denote the total annuity income an agent receives
at age t by nt .
4.1.5

Optimization problem

Each period an individual decides how to distribute her current wealth between consumption (ct ) and investments in bonds (kt+1 ) and annuities (∆t+1 ), given that he has to pay
medical expenses. I denote as Xt the set of state variables I, t, nt , kt : Xt = (I, t, nt , kt ) .
The recursive formulation of the optimization problem can be represented in the following
form:
Z


u(ct ) + βst Pr(mt+1 = 0|mt , t, I) V (Xt+1 , 0, ζ t+1 , ξ t+1 )dF (ζ t+1 , ξ t+1 )+





ζ,ξ
R
V (Xt , mt , ζ t , ξ t ) =
max
βst Pr(mt+1 = 1|mt , t, I) V (Xt+1 , 1, ζ t+1 , ξ t+1 )dF (ζ t+1 , ξ t+1 )+
ct ,kt+1 ,∆t+1 


ζ,ξ



β(1 − st )υ(kt+1 )
(4)

s.t. the budget constraint:

9















ct + zt + kt+1 + qt ∆t+1 = kt (1 + r) + nt + τ t ,
government transfers
τ t = min {0, cmin − kt (1 + r) − nt + zt } ,
the annuities evolution equation
nt+1 = ∆t+1 + nt ,
borrowing and annuity illiquidity constraints: kt+1 , ∆t+1 ≥ 0, and initial conditions
k0 , n 0 , m 0 .

4.2

Insurance sector

A common approach in the literature is to model annuities as non-exclusive insurance
contracts (Chiappori, 2000). Individuals are free to buy an arbitrary number of contracts
from different insurance companies, which makes it impossible to condition the contract
design on the amount purchased. I assume contracts are linear: to purchase ∆ units of
annuity coverage, an individual pays q∆ in premiums. This assumption rules out market
separation through menus of contracts.
I assume insurance firms set a restriction on the minimum amount than can be invested in annuities equal to ∆. This minimum purchase requirement can be rationalized
as follows. From the point of view of an insurance company, what matters is not only
how many annuities are sold, but also how many accounts are open. Keeping track of
too many small accounts is costly, so insurance companies need to put some limits on
the number of small customers.
Another restriction that annuity buyers face is the maximum issue age t . Individuals
older than t cannot buy annuities. This restriction reflects the fact that in most states
insurance companies are prohibited from selling annuities to individuals beyond a certain
age (Levy et al., 2005).
In terms of information structure, I consider two scenarios. Under the first scenario
insurance firms are allowed to observe all state variables of the individual that are relevant
for forecasting her survival probability. I call this setup the “full information scenario”.
In the second scenario the insurers know the aggregate distribution of individuals over
states, but they cannot observe any characteristics of the annuity purchaser except age.
I call this setup the “asymmetric information scenario”. In this environment all people
of the same age buy annuities at a uniform price. This outcome resembles the current
situation in the market for longevity insurance in the U.S. - annuity prices are usually
conditioned only on age and gender.
10

I assume insurance firms act competitively: they take the price of annuity qt as given.
Expected payout per unit of insurance sold to an individual of age t can be expressed as
follows:
TX
−t
sbt+i
π t (Ωt ) = qt (Ωt ) − γ
,
(1 + r)i
i=1
where γ ≥ 1 is the administrative load, assumed to be proportional to the total expected
payment for the contract. Ωt is the information available to the insurer about an individual of age t, and sbt+i is the insurer’s expectation of the future survival probability of
the individual buying the annuity. It can be expressed as follows:
sbt+i = Et (st+i |Ωt ).
In the full information case, the insurer and annuity buyer have the same information.
Thus, Ωt includes all variables relevant for determining the survival probability of a person
of a given age:
Ωt = (mt , I).
In the asymmetric information case the firm does not know anything about the individual except the age and the fact that he bought an annuity, so:
Ωt = (∆t+1 (k, n, m, I, t, ζ, ξ) ≥ ∆ ).
In this case sbt+i is the firm’s belief about the probability that an individual who buys
an annuity will survive untill period t + i. In equilibrium, sbt+i has to be consistent with
the individual’s behavior.
Firms chooses the amount of annuity to sell (Nt ) by solving the following maximization
problem:
max Nt π t .
Nt

4.3

(5)

Competitive equilibrium

Before defining the competitive equilibrium, denote the distribution of individuals of age
t over states by Γt (k, n, m, I, ζ, ξ), where k ∈ K = R+ ∪ {0}, n ∈ N = R+ ∪ {0} ,
m ∈ M = {0, 1}, I ∈ {I1 , I2 , I3 , I4 , I5 }, ζ ∈ R, ξ ∈ R.
The competitive equilibrium for the asymmetric information case can be defined as
follows:.
Definition 1 A competitive equilibrium is
11

(i) a set of belief functions {b
st+i , i = 0, .., T − t}Tt=1
(ii) a set of annuity prices {qt }Tt=1
(iii) a set of decision rules for households
©

∗ (k, n, m, I, t, ζ, ξ), ∆∗ (k, n, m, I, t, ζ, ξ), m ∈ M, I ∈ I, k ∈ K, n ∈ N
c∗t (k, n, m, I, t, ζ, ξ), kt+1
t+1

and for insurance firms {Nt∗ }Tt=1
such that
1. Each annuity seller earns zero profit:
Nt∗ π t = 0
2. Firms’ belief functions are consistent with households’ decision rules:
R
∆∗t+1 (k, n, m, I, t, ζ, ξ)Γtt+i (k, n, m, I, ζ, ξ)
K,N ,M,I,ζ,ξ
R
sbt+i =
∆∗t+1 (k, n, m, I, t, ζ, ξ)Γt (k, n, m, I, ζ, ξ)
K,N ,M,I,ζ,ξ

where Γtt+i (k, n, m, I) is the measure of people of age t + i who bought an annuity in
the amount ∆∗t+1 (k, n, m, I, t, ζ, ξ) at age t. It can be defined recursively in the following
way:
Γtt+1 (k, n, m, I, ζ, ξ) = s(m, I, t)Γt (k, n, m, I, ζ, ξ)
Z
Γtt+i (k, n, m, I, ζ, ξ)

s(m,
e I, t + i − 1)Γtt+i−1 (k, n, m, I, ζ, ξ, m)
e

=

m∈M
e

Here Γtt+i−1 (k, n, m, I, m)
e is the distribution of people aged t + i − 1 who bought an
∗
annuity in the amount ∆t+1 (k, n, m, I, t, ζ, ξ) at age t across their current health status
m.
e It can be recursively expressed as follows:
Γtt+1 (k, n, m, I, ζ, ξ, m)
e = Pr(m|m,
e
t, I)s(m, I, t)Γt (k, n, m, I, ζ, ξ)
Z
e
Γtt+i (k, n, m, I, ζ, ξ, m)

Pr(m|m,
e
t+i−1, I)s(m, I, t+i−1)Γtt+i−1 (k, n, m, I, ζ, ξ, m)

=
m∈M

3. Given annuity prices {qt }Tt=1 , households’ decision rules solve optimization problem
4 and Nt∗ solves equation 5.
4. The market clears
Z
Nt∗

∆∗t+1 (k, n, m, I, t, ζ, ξ)Γt (k, n, m, I, ζ, ξ)

=
K,N ,M,I,ζ,ξ

12

ªT
t=1

The definition of the competitive equilibrium for the full information scenario is similar, with the following modifications: the annuity prices now depend on mt and I; and
the second condition for the equilibrium takes the form:
sbt+i = Et (st+i |mt , It ).

5
5.1

Data and calibration
Mortality, health and medical expenditures

The parameters governing the evolution of health, survival, and medical expenses come
from papers of French and Jones (2004) and De Nardi, French, and Jones (2009) (DFJ)
which use the AHEAD dataset. These parameters include coefficients from the relationship (3), σ z and characteristics of the stochastic component of medical expenses process
(2): ρhc and σ 2ε .
In the DFJ model an additional state variable affects health uncertainty and mortality
- gender. My model does not have gender, so, when using the DFJ estimates, the effect
of gender on all the variables was averaged out.
French and Jones (2004) found that the AR(1) component of health costs is quite
persistent: ρhc = 0.922. They found that the innovation variance of the persistent component σ 2ε is equal to 0.0503 and the innovation variance of the transitory component is
0.665. Thus 66.5% of the cross sectional variance of medical expenses comes from the
transitory component and 33.5% from the persistent component. The variance of the log
medical expenses σ 2z is equal to 2.53.

5.2

Parameters calibration

Parameters of the model that need to be calibrated include: r, γ, t, ∆, β, σ, η, φ, and
cmin . The annual interest rate r was set to 2%, which corresponds to the historical mean
of twenty-year U.S. government bonds. The administrative load γ was assumed to be
equal to 10%. This number is based on the study of Mitchell et al. (1997) who showed
that, on average, U.S. insurance companies add 10% to the annuity price because of
administrative costs. The maximum issue age was set to be equal to 88 years. In general
the maximum issue age varies by insurance companies and ranges from 80 years old to
the mid-90s.
The minimum purchase requirement was set to $2,500. This means in order to buy
an annuity, the individual should be willing to initiate a contract that will bring him at
least $2,500 per year or $208 per month. Given prices produced by the model, this is
13

equivalent to a minimum initial premium (q∆) of $25,000 for a 70 year old and $11,000
for an 88 year old. The minimum premium for a life annuity varies across insurance
companies and can go up to $100,000. For example, two big annuity distributors, Vanguard and Berkshire-Hathaway, put restrictions of $20,000 and $40,000, respectively, on
the minimum premium for a life annuity.
The discount factor β was set to 0.96, which is a standard value for calibrated lifecycle models. For preference parameters σ, η, and φ, and the minimum consumption
floor cmin I used structural estimates from the DFJ study. Later on I report results for
several alternative values of the coefficient of risk aversion and the discount factor. Table
5 summarizes all the parameter values.

Table 5: Parameters of the model

5.3

Parameter

Value

Risk aversion σ

4

Discount factor β

0.96

Strength of bequest motive η

2360

Shift parameter φ

$273,000

Interest rate r

2%

Administrative load γ

10%

Consumption floor cmin

$2,663

Maximum issue age t

88 years

Minimum premium ∆

$2,500

Initial distribution

Initial wealth (k0 ) and preexisting annuity holdings (n0 ) that individuals start their
retirement with are calibrated from the AHEAD dataset. Individuals in the model start
their retired life at age 70, so I used the cohort aged 69-76 in 1993 to calibrate initial
wealth. The sample used for calibration includes only retired individuals who were single
(divorced, separated or never married) at the time of the survey. The total number of
observations is 1,114.
Initial financial wealth (k0 ) includes the value of housing and real estate, vehicles,
value of business, IRAs, Keoghs, stocks, bonds, checking, and saving and money market
accounts, less mortgages and other debts. Preexisting annuity holdings (n0 ) correspond
to annuity-like income that an individual is entitled to receive during his retirement
years. To measure annuity-like income, I sum the values of Social Security benefits, DB
14

pensions, and annuities that individuals receive each year and then take the average over
all years that individuals are observed in the data. This measure of preexisting annuity
income also proxies permanent income (I). Since both Social Security benefits and DB
payments are closely linked to lifetime earnings, this provides a good approximation of
permanent income.
The joint distribution of retirees over k0 and n0 was estimated using two-dimensional
kernel density.

6

Results

This section presents results for different versions of the model above. It starts with
the analysis of a model without medical expenses (zt = 0 for ∀ t), bequest motives
(η = 0), or minimum annuity purchase requirements (∆ = 0) and with full information
annuity pricing. This simplified model is used to study annuitization decisions for people
in different income quintiles, given heterogeneity in life expectancy and initial wealth
holdings.
This simplified version of the model is then augmented with, first, deterministic and,
second, uncertain medical expenditures. The model with uncertain medical expenditures
is the baseline for further comparisons.
The following features of the baseline model are then changed one at a time. First, I
drop full information assumption and require insurance firms to price annuities according
to scenario two, the asymmetric information scenario. Second, I allow for a bequest
motive. Third, I increase the consumption minimum floor. Fourth, I assume housing
wealth is completely illiquid. Fifth, I consider the effect of the restrictions on minimum
annuity purchase.

6.1

Simplified version of the model: no medical expenses

The model considered here only allows for lifespan uncertainty and preannuitized wealth
coming from Social Security and DB pension plans. There are no medical expenses,
bequest motives, minimum annuity purchase requirements, or unfair annuity pricing.
To illustrate the intertemporal decision process, Figures 1 and 2 show the general
pattern of annuity purchases for individuals who were given initial wealth and annuity holdings that correspond to the median values in the initial distribution for each
permanent income quintile. Several things can be noticed in the graph.
First, people buy annuities only once in the first period. It can be shown (see
Pashchenko, 2010) that, under certain conditions, the one-time purchase of annuities
in the first period is a general result. The conditions under which this result holds are
15

Annuity purchased at each age

Annuity purchased at each age

5

5
1st quintile
2d quintile
3d quintile
4th quintile
5th quintile

4.5

3.5

4

annuity income, thousands

annuity income, thousands

4

3

2.5

2

3.5

3

2.5

2

1.5

1.5

1

1

0.5

0.5

0
70

75

80

85

90

0
70

95

1st quintile
2d quintile
3d quintile
4th quintile
5th quintile

4.5

age

75

80

85

90

95

age

Figure 1: Annuities purchased by people in good
initial health

Figure 2: Annuities purchased by people in bad
initial health

the following:
- There is no uncertainty except the time of death
- Medical expenditures are constant
- β(1 + r) < 1
- n0 − z > cmin or k0 + n0 − z > q1 (cmin − n0 − z), where z is value of medical
expenditures that doesn’t change over time.
The last condition insures that an individual is already guaranteed income net of
medical expenditures that exceeds the minimum consumption floor or can afford to get
the equivalent stream of income by buying an annuity in the first period.
The intuition behind this theoretical result is as follows. There are two ways to finance
an annuity purchase: using financial wealth or existing annuity income. The second way
would imply increasing consumption profile, which is not optimal given β(1 + r) < 1.
Thus, if an individual buys an annuity, he will use his financial wealth. If the individual
waits to buy annuities, he has to save in bonds. But this strategy is dominated by buying
annuities from the start, because over the long-run an annuity brings a higher return.
Second, the amount of annuity purchased is increasing with income quintile. People
in the highest income quintile who start their retirement in good health buy a stream of
annuity income equal to almost $2,500 per year. People in the second income quintile
buy a stream of annuity income equal to only $700. The median annuity purchases of
retirees in the lowest quintile is almost zero.
Third, people who start their retirement in bad health invest less in annuities than
people whose initial health is good. While healthy retirees in the highest income quintile
buy annuity income equal to almost $2,500, retirees in bad health in the same income
quintile buy annuity income of only $1,700. This difference is explained by two factors.
16

First, people in bad health have lower life expectancy. Second, people in bad health start
their retirement with lower wealth.
To isolate the effect of the survival probability on annuity demand, I run two counterfactual experiments. In the first experiment, an individual who starts his retirement
in good health was given the survival probability of a person whose health is always bad
without changing initial wealth. In the second experiment, the survival probability was
set to be that of someone who is always in bad health and in the lowest income quintile.
The results of these experiments are presented in the first column of Table 6 for retirees
in the top income quintile (the results for other quintiles are similar)
Table 6: Impact of survival probability on annuity demand, top PI quintile
Survival probability

Annuity purchased, thousands
Price is fixed Price is adjusted

Own

2.50

2.50

Always in bad health

1.50

3.50

Always in bad health and lowest income quintile

0.25

5.00

Everything else being equal, the reduction in survival probability decreases demand
for annuities: in the first experiment, the annuity purchase decreases from $2,500 to
$1,500 and in the second experiment, to $250. It is important to note, however, that
in these experiments, the change in the survival probability did not have any effect on
price, which was fixed at the level of a price for a retiree whose initial health is good.
In another set of experiments, I allow the annuity price to adjust to changes in the
survival probability. The results are presented in the second column of Table 6. In this
case, the decrease in survival probability actually increases demand for annuities: in
the first experiment, the amount of annuity bought increases from $2,500 to $3,500 and
in the second, to $5,000. This is explained by the fact that a decrease in the survival
probability triggers two effects: it increases the effective discount factor, making people
care less about future consumption, and it decreases the price for annuities, making
future consumption more affordable. The income effect from decreasing price turns out
to be more powerful.
Given that insurance firms have full information about the annuity buyer in the simplified version of the model considered in this subsection, prices are based on individual
survival probabilities. Individuals who start their retirement in bad health, face lower
annuity prices and this should increase their demand for annuities. Lower demand for
annuities on the part of this group results from the fact that they have less initial wealth,
not a lower survival probability.
17

Apart from the amount of annuity purchased, another dimension to consider is how
many people do invest in annuities. The first column of Table 7 shows the percentage
of retirees in each income quintile who have non-zero investments in annuities. The first
thing to notice is that the overall participation rate is very high: 75.3% of retires invest in
annuities, despite the fact that they already have part of their wealth annuitized through
Social Security and DB pension plans.

Table 7: Participation in annuity market: model without medical expenses
Income quintile

Percentage
With preannuitized wealth

Preannuitized wealth removed

All

75.3

91.0

1

51.0

85.3

2

86.7

100.0

3

78.6

100.0

4

81.3

100.0

5

75.5

100.0

For comparison, the second column of Table 7 presents results for the case where
individuals do not have any preannuitized wealth. More specifically, initial wealth k0
was increased by the amount q1 n0 and annuity holdings n0 were set equal to zero. In
other words, retirees were given additional liquid wealth which corresponds to the market
value of the annuity income they are entitled to. In this case the overall participation
rate increases to 91%. Except for the bottom income quintile, all retirees buy annuities.
The fact that around 15% of people in the first quintile do not invest in annuities is
explained by the fact that they rely on the minimum consumption floor provided by the
government. The comparison between the first and second columns of Table 7 shows that
preannuitized wealth has a significant effect on the annuity market participation rate.
However, even in the presence of Social Security and DB pension plans, the interest in
private annuities is still high.
Another important observation is that in the model with preannuitized wealth and no
medical expenses, we do not see the monotonic relationship between the annuity market
participation rate and the income quintile that can be observed in the data. On the
contrary, the participation rates are lowest for people in the highest (fifth) and the lowest
(first) income quintiles. Around 75% of the retirees in the fifth income quintile choose
to invest in annuities and among those in the first income quintile, the rate is 51%. For
comparison, among people in the second income quintile, participation is around 87%.
The relatively low participation rate of the highest income quintile is not surprising in
18

this environment. People in the highest income quintile have a considerable amount of
annuity income already and, given the absence of precautionary motives, they choose not
to invest ny more in annuities.

Table 8: Share of annuity-like income in available resources
Quintile

Retirees who
bought annuity

Retirees who
didn’t buy annuity

1

20.9

36.3

2

36.6

94.7

3

33.8

90.8

4

32.3

91.4

5

24.6

88.1

In general what matters for annuity demand in the environment with no uncertainty
except the time of death, no bequest motives, and actuarially fair prices is the combination of liquid and annuitized assets that people have (see Pashchenko, 2010). The
necessarily conditions for a retiree to invest in an annuity are that the annuity income
he is entitled to is relatively small and the amount of liquid wealth is relatively big. Tan0
ble 8 shows the share of annuity income in total amount of available resources
k0 + n 0
separately for people who bought annuities and those who did not. Those retirees in the
top four income quintiles who decide not to invest in annuities have few resources except from annuity income: the ratio of annuity income to total available funds is around
90%. For people who chose to invest in annuities this ratio is much lower: it does not
exceed 40%. The only quintile where this is not true is the bottom one. Even those
people who choose not to invest in annuities have this ratio below 40%. It is important
to note that for this quintile, the actual annuity income that they take into account is
the income from the government-provided means-tested transfers. The majority of this
group (around 68%) cannot afford to buy an annuity that will guarantee them income
higher than the consumption minimum floor3 .

6.2
6.2.1

The effect of medical expenditures
Deterministic medical expenditures

The next question is how the pattern of annuity holdings changes when medical expenditures are introduced. Figures 3 and 4 show the results for the case when retirees are
3

Note, that to buy income equal to the minimum consumption floor, people have to pay upfront
around $26,000.

19

facing medical expenditures that are deterministically increasing over time. That is to
say, ψ t in expression (1) is set to zero and the mean of medical expenditures is adjusted
to match the mean in the stochastic case4 .
Annuity purchased at each age

Annuity purchased at each age

5

5
1st quintile
2d quintile
3d quintile
4th quintile
5th quintile

4.5

3.5

4

annuity income, thousands

annuity income, thousands

4

3

2.5

2

3.5

3

2.5

2

1.5

1.5

1

1

0.5

0.5

0
70

75

80

85

90

0
70

95

age

1st quintile
2d quintile
3d quintile
4th quintile
5th quintile

4.5

75

80

85

90

95

age

Figure 3: Deterministic medical expenses: annu-

Figure 4: Deterministic medical expenses: annu-

ities purchased by people in good initial health

ities purchased by people in bad initial health

The pattern of annuity purchases changes significantly compared to the case of no
medical expenditures. People still buy annuities at the beginning of retirement but they
also increase annuity holdings towards the end of life. The retirees now have to save more
because they have to finance not only their consumption but also medical expenditures
that are increasing steeply over time. In this case, retirees use their annuity income
to buy more annuities. The survival probability and, thus, the price of an annuity are
decreasing with age and, as annuities become cheaper, they are more actively used to
finance medical expenses.
The fraction of retirees involved in the annuity market increases in the presence of deterministic medical expenses. The second column of Table 9 presents participation rates
in the beginning of retirement and the second column of Table 10 present participation
rates in the last period when individuals are allowed to buy annuities (88 years). The
participation rate at age 70 goes up from 75 to 86% and the participation rate at age 88
increases from 0 to 77%.
Thus, if anything, the presence of deterministic medical expenditures increases demand for annuities in a significant way. This means that medical expenditures by themselves cannot be an explanation for the annuity puzzle. The next section will consider
how the stochastic component of medical expenditures affects annuity demand.
4

The term ”deterministic” was chosen to emphasize the absence of the stochastic component. There
is still some degree of uncertainty in medical expenses due to the uncertainty of health status.

20

Table 9: Participation in annuity market at age 70: effect of medical expenses
Medical expenses
Deterministic Uncertain

Income quintile

None

All

75.3

86.1

76.3

1

51.0

32.4

40.7

2

86.7

90.2

80.7

3

78.6

100.0

83.8

4

81.3

100.0

85.9

5

75.5

99.6

84.8

Table 10: Participation in annuity market at age 88: effect of medical expenses
Medical expenses

6.2.2

Income quintile

None

Deterministic

Uncertain

All

0.0

77.2

72.1

1

0.0

0.9

11.1

2

0.0

63.8

58.9

3

0.0

50.5

76.3

4

0.0

99.4

81.9

5

0.0

99.2

85.8

Uncertain medical expenditures

Introduction of the uncertain medical expenditures enforces the pattern of annuity purchases observed in the previous experiment: the demand for annuities increases substantially in the advanced ages (see Figures 5 and 6). To understand why retirees now buy
even more annuities in advanced ages, one has to remember that the stochastic component of medical expenditures is highly persistent. Thus, with some probability retirees
will face much higher medical expenses than in the deterministic case.
The participation rate drops compared to the case of deterministic medical expenditures but still stays higher than in the case of no medical expenditures (see third columns
of Table 9 and Table 10). Thus, uncertainty in medical expenses results in two things.
Some retirees, mostly in the lower income quintiles, give up on fully financing their health
costs and decrease participation in the annuity markets. At the same time, retirees who
choose to self-insure against medical shocks increase their annuity holdings.
One interesting result is that in the first retirement period, the introduction of deterministic medical expenses increases participation in the annuity market in each quintile
21

Annuity purchased at each age

Annuity purchased at each age

5

5
1st quintile
2d quintile
3d quintile
4th quintile
5th quintile

4.5

3.5

4

annuity income, thousands

annuity income, thousands

4

3

2.5

2

3.5

3

2.5

2

1.5

1.5

1

1

0.5

0.5

0
70

75

80

85

90

1st quintile
2d quintile
3d quintile
4th quintile
5th quintile

4.5

0
70

95

75

80

age

85

90

95

age

Figure 5: Uncertain medical expenses: annuities

Figure 6: Uncertain medical expenses: annuities

purchased by people in good initial health

purchased by people in bad initial health

except the bottom one, where participation actually decreases. Introduction of uncertain medical expenses decreases participation rates in each quintile except the bottom
one, where participation increases. This behavior of people in the bottom quintile is
explained by their reliance on government transfers. The introduction of deterministic
medical expenses makes it easier to qualify for the means-tested transfers. If medical expenses have a persistent stochastic component, some groups of people may not meet the
requirements for receiving government transfers in case their realized medical shocks are
small. Thus, they have to finance their old age consumption themselves so they increase
annuity market participation.
Another dimension to consider is the share of annuity investment in retirees’ portfolios. Table 11 shows this percentage for individuals with median wealth holdings at the
beginning of retirement for three cases: no medical expenses, deterministic, and uncertain
medical expenses.

Table 11: Percentage of annuity investment in retiree’s portfolio at age 70
Medical expenses
Deterministic Uncertain

Income quintile

None

1

0.0

0.0

0.0

2

100.0

100.0

73.0

3

100.0

100.0

92.5

4

100.0

100.0

81.8

5

61.4

100.0

86.9

22

The median retiree in the bottom income quintile does not invest in annuities in all
three cases. Among other quintiles, only retirees in the fifth quintile did not save entirely
in annuities in the case of no medical expenses. This means that since people in this
quintile are entitled to big annuity income already, they prefer to decumulate part of
their financial wealth in several years as opposed to a lifetime investment in annuity. In
the case of deterministic medical expenses, annuities clearly dominate bonds for each
income quintile. Finally, in the case of uncertain medical expenses, individuals prefer to
hold part of their wealth in liquid form in order to be able to finance transitory medical
shocks.
6.2.3

Summary of the effect of medical expenses

In general, if anything uncertain medical expenditures make the annuity puzzle harder
to explain. Uncertain medical expenditures do decrease the annuity market participation
rate in the lower income quintiles but, in the aggregate, this is more than compensated
for by the increase in the demand for annuities from the high income quintiles. People
who can afford to finance their medical expenses will do it at least partially through
buying annuities. The annuity pays out in a state when the individual is old and alive,
and it coincides with the state when he is likely to have high medical expenses. Thus,
insuring medical expense risk and insuring longevity risk become complementary. This
result is consistent with the conclusion of Pang and Warshawsky (2008) that medical
expenses increase retirees’ investment in annuities.
The version of the model with uncertain medical expenses, fair prices, and no bequest
motives is the baseline for comparison for all further experiments. The pattern of annuity
purchased we observed in Figures 5 and 6 is robust to all subsequent changes in the
baseline model, so I omit graphs of annuity purchase in retirement in the rest of the
analysis.

6.3

Effect of adverse selection

In this section, I consider a version of the model in which insurance firms price annuities
according to the asymmetric information scenario. This means they do not observe any
characteristics of the annuity buyer except age. In this case, there exists one pooling price
that is above what is actuarially fair for people with high mortality and below what is
actuarially fair for people with low mortality. Since mortality is negatively correlated with
permanent income, this means that in the pooling equilibrium, higher income quintiles
will face better prices and thus get an implicit subsidy from low income quintiles. Table
12 provides a quantitative assessment of this subsidy. For people in the lowest income
quintile and bad health, the pooling equilibrium price is around 73% higher than the
23

price they face if the insurance firms observe their mortality. On the other extreme,
people in the highest quintile and in good health pay 13% less for annuities than in the
full information equilibrium.

Table 12: Percentage change in price in pooling equilibrium compared to full information
equilibrium
Income quintile

Bad health

Good health

1

73.2

25.7

2

53.5

14.0

3

35.7

3.7

4

20.1

-5.3

5

6.8

-13.1

As a result, the participation of high income quintiles in the annuity market increases
and the participation of low quintiles decreases. Table 13 compares the participation rates
with the baseline model. In the bottom income quintile, the fraction of people buying
annuities at age 70 drops from 40.7% to 30.8%. In the highest quintile, this number
increases from 84.8% to 93.5%. The decline in participation rates among low income
quintiles is partially offset by the increase in participation rates among low quintiles.
Thus, the overall effect of the adverse selection is quite small: in the pooling equilibrium
the percentage of people involved in the annuity market at age 70 decreases by less than
4% compared to the baseline model.

Table 13: Participation in annuity market at age 70: baseline model vs. model with
adverse selection
Income quintile
Baseline
Adverse selection

6.4

All

76.3

72.5

1

40.7

30.8

2

80.7

63.1

3

83.8

74.7

4

85.9

89.9

5

84.8

93.5

Effect of bequest

24

An annuity is a financial instrument that pays out only in a state when the individual
is alive. Bequest motives make individuals care about a state when they are not alive
and thus decreases the attractiveness of annuities. In theory very strong bequest motives
can drive demand for annuities to zero. However, the empirical evidence suggests that
a bequest is a luxury good; moreover, only saving decisions of people in the highest
income quintile get affected by bequest motives in a significant way (De Nardi, French,
and Jones, 2009).
To get some idea of the effect of bequest motives, this section uses recent estimates
of De Nardi, French, and Jones (2009). Using the AHEAD dataset, DFJ found that the
strength of the bequest motive (η) is equal to 2360 and the shift parameter (φ) is equal to
$273,000. The easiest way to understand the intuition behind these parameters’ values is
to consider a two-period deterministic model where an agent lives for one period and dies
with certainty in the second period. In this case, using the estimated values for η and φ,
one can compute that only individuals with wealth above $38,000 will leave a bequest.
Once the bequest motive becomes operative, its effect is very strong: 88 cents of every
additional dollar of wealth will be bequeathed (see DFJ, 2009).
Table 14 illustrates the effect of bequest motives on participation rates: overall the
percentage of retirees involved in the annuity market decreases by around 4%. This
decrease mostly comes from the highest income quintile. While participation rates for
individuals in the first four quintiles are hardly affected, the fraction of people buying
annuities in the fifth income quintile decreases by almost 16%, from 85.8 to 69%. This is
not surprising given the high value of the shift parameter φ: only people in the highest
income quintile are significantly affected by a bequest motive.
Table 14: Participation in annuity market at age 70: baseline model vs. model with
bequest motives

6.5

Income quintile

Baseline

Bequest motive

All

76.3

71.9

1

40.7

40.6

2

80.7

79.7

3

83.8

83.2

4

85.9

85.7

5

84.8

69.0

Effect of minimum consumption floor

The consumption minimum floor provides alternative annuity income, and the question is
how well does it substitute for a private annuity. In the baseline model of this study, the
25

government guaranteed consumption minimum floor was set to be equal to $2,663. This
number is on the low side of what is commonly used in the literature (see Kitao and Jeske,
2009, and Kopecky and Koreshkova, 2009). Table 15 demonstrates how participation in
the annuity market changes when the consumption floor is raised to $6,000.

Table 15: Participation in annuity market at age 70: baseline model vs. model with
cmin = $6000
Income quintile
Baseline
cmin = $6000
All

76.3

53.1

1

40.7

8.6

2

80.7

28.8

3

83.8

61.5

4

85.9

73.5

5

84.8

82.9

The increase in the consumption minimum floor has a significant effect on the overall
participation rate: it drops from 76.3 to 53.1%. This decrease mainly comes from the
three bottom income quintiles - the top two quintiles are affected much less. While in
the first quintile, an increase in the consumption minimum floor leads to a decline in
the participation rate from 40.7 to 8.6%, in the highest quintile the participation rate
goes down from 84.8 to 82.9%. This asymmetric effect is not surprising. People in the
highest quintile start their retirement with annuity income that is significantly higher
than the consumption minimum floor. For them, the probability of qualifying for meanstested government transfers is low: it happens only if they get hit by a bad sequence of
medical shocks. Hence, the size of the consumption minimum floor has a small effect on
their decision to annuitize. People in the lower quintiles have more chances to rely on
government transfers and the increase in public longevity insurance has a big effect on
their demand for private annuities.

6.6

Effect of illiquid housing

In the next version of the model, I assume that housing wealth is completely illiquid.
In other words, each person’s total initial wealth is replaced with his total non-housing
wealth. The assumption that retirees cannot use their housing wealth even to finance
medical expenses is the other extreme from the assumption maintained before that households can consume out of their housing wealth. It has been shown (Walker, 2004) that
housing wealth in retirement is not used to finance consumption; however, it may be
26

used to finance catastrophic medical expenditures. Given computational difficulties with
treating housing wealth as a separate state variable, this paper considers two alternative
assumptions of perfect liquidity and absolute illiquidity of housing wealth. This may give
some idea about the magnitude of the bias of imposing any assumption of this sort. What
is important for this study, however, is that housing wealth is not equal to non-housing
wealth in terms of the cost of converting it into annuity.
Table 16 shows the percentage of retirees involved in the annuity market if housing
wealth is assumed to be illiquid. The ban on using housing wealth decreases the participation rate though the effect is not big; on average only around 3% of retirees leave the
market. Illiquidity of housing wealth uniformly affects all quintiles, though the biggest
effect it has is on retirees in the bottom quintile: their participation rate drops by 10%.
This big effect is explained by the fact that for this group of people housing constitutes a
major part of their retirement wealth. In the next section, I will show that the illiquidity
of housing wealth has a much bigger effect on the participation rate once a minimum
annuity purchase requirement is introduced.

Table 16: Participation in annuity market at age 70: baseline model vs. model with
illiquid housing

6.7

Income quintile

Baseline

Illiquid housing

All

76.3

73.2

1

40.7

30.5

2

80.7

74.9

3

83.8

78.6

4

85.9

80.3

5

84.8

77.5

Effect of minimum purchase requirements

In this section, I assume the insurance firms set a minimum annuity purchase requirement
equal to $2,500. The results of introducing a minimum purchase requirement in the
baseline model are presented in Table 17. The decline in participation rates is very
noticeable; the percentage of people involved in the annuity markets drops from 76.3 to
39.9%. The effect of a minimum purchase requirement on the participation rate becomes
even bigger once housing wealth is assumed to be totally illiquid (third column of Table
17). The participation in annuity market at age 70 drops to 24.2%.

27

Table 17: Participation in annuity market at age 70: baseline model vs. model with
minimum purchase requirement
Income quintile

Baseline

Minimum purchase
Liquid housing Illiquid housing

All

76.3

39.9

24.2

1

40.7

23.9

11.2

2

80.7

32.5

16.1

3

83.8

35.4

18.6

4

85.9

43.1

23.7

5

84.8

57.4

36.4

The large effect of the restriction on minimum investment in annuity on the participation rates results from the fact that a lot of retirees involved in the annuity market
invest only small amounts. Even in the highest income quintile, for a considerable group
of retirees the optimal amount of investment in annuities is below the minimum one:
the participation in this quintile decreases from 84.8 to 57.4% in the case with liquid
housing. This reduction is accounted for by people whose financial wealth is relatively
small compared to their preexisting annuity income.
Given that on average retirees are willing to participate in the annuity market but are
not willing to invest a lot, one question to ask is: how much do individuals value access to
the annuity market? Table 18 shows how much a median retiree has to be compensated
in terms of the percentage of consumption if he loses access to the annuity market.

Table 18: Value of annuity market for median retiree in each income quintile (in percentage of consumption)
Income quintile

Good health

Bad health

1

0.0

0.0

2

2.4

0.7

3

2.3

0.3

4

6.3

2.8

5

8.9

7.3

Not surprisingly, the value of the annuity market for retirees increases with income
quintile and health status. If a median retiree in the lowest income quintile is indifferent
between having access to the annuity market or not, for a retiree in good health and in
the highest income quintile the loss of opportunity to invest in annuities is equivalent to
28

8.9% of consumption. In general for people in good health and in high income quintiles
the opportunity to have access to the annuity market is very valuable. Annuities bring
higher returns over the long run and can help to finance medical expenses late in life.
However, the amount of money that retirees can actually spare to invest in annuities is
not big. The issue of liquidity constraints is accentuated by the need to keep part of the
wealth as a buffer stock against medical shocks and the impossibility of using housing
wealth.

6.8

Summary

The quantitative effect of the different explanations for non-annuitization is summarized
in Table 19. In terms of overall participation rates, three factors have the largest effects:
preannuitized wealth, minimum purchase requirement and consumption minimum floor.
In terms of participation rates by quintile, the consumption minimum floor affects mostly
people in low quintiles while the impacts of minimum purchase requirement and preannutized wealth are approximately uniform. Bequest motives have a significant effect only
on people in the highest income quintile. The impact of illiquidity of housing wealth
is large only in combination with a minimum purchase requirement. Adverse selection
and medical expenses have significant effects on participation rates in each quintile, but
these effects have the opposite sign for low- and high-income group. For people in low
income quintiles, both medical expenses and adverse selection reduce participation in the
annuity markets, while for people in high income quintiles the effect goes the other way.
Table 19: Quantitative importance of different factors behind non-annuitization
Factors

Impact on low quintiles

Impact on high quintiles

Overall effect

Preannuitized wealth

Big (negative)

Big (negative)

Big (negative)

Medical expenses

Big (negative)

Big (positive)

Small (positive)

Adverse selection

Big (negative)

Big (positive)

Small (negative)

Bequest

None

Big (negative)

Small (negative)

Consumption floor

Big (negative)

Small (negative)

Big (negative)

Illiquid housing

Small (negative)

Small (negative)

Small (negative)

Minimum premium

Big (negative)

Big (negative)

Big (negative)

6.9

Combined effect

Now that the separate effects of different factors behind non-annuitization are quantified,
the next step is to evaluate how much all these factors combined can contribute to the
29

annuity puzzle. To do this I consider the full version of the model: in this version
insurance firms are assumed to price according to the asymmetric information scenario
and restrict the minimum amount of annuity purchase. Retirees face stochastic medical
expenses, have bequest motives, and cannot use their housing wealth. The consumption
floor guaranteed by the government is set to be equal to $6,000 per year. Table 20
compares annuity market participation rates at age 70 produced by the full model with
the baseline model and with participation rates observed in the data for people aged from
70 to 80 years old.
Table 20: Participation in annuity market at age 70: baseline model vs. model with all
impediments to annuitization
Income quintile

Baseline

Full version

Data

All

76.3

19.6

6.2

1

40.7

1.9

1.2

2

80.7

6.5

1.3

3

83.8

12.8

2.7

4

85.9

20.8

4.5

5

84.8

35.3

13.0

As can be seen the model, combining different factors behind non-annuitization goes
a long way in explaining low participation rates in the annuity market compared to the
baseline model. However, the predicted participation rates are still higher than those
observed in the data.
Another way to look at the performance of the model is to compare prices it produces
with the ones observed in the data. Figure 7 shows that prices in the model line up well
with what we see in the data5 , though the model underpredicts the real prices.
There are at least three explanations for this downward bias of the prices in the model.
First, the model considers only single individuals, while real prices are based on the
aggregate statistics that include couples. Second, the AHEAD dataset underrepresents
wealthy individuals. Given that wealth is negatively correlated with mortality and that
rich individuals tend to buy more annuities, the lack of wealthy individuals in the model
biases the prices downwards6 . Third, this paper makes assumption that insurance firms
are perfectly competitive and sets administrative load to 10%. It may be that the markup
5

The observed price corresponds to the price of a lifetime annuity with fixed income payment with
inflation adjustment. The quotes were obtained from Vanguard at www.aigretirementgold.com.
6
This problem is accentuated by the fact that for the calibration of the initial distribution, the second
wave of the AHEAD dataset was used. This wave tend to significantly underreport asset holding ( see
Rohwedder, Haider, and Hurd, 2004).

30

Price for unit of insurance contract ($)
13
Model
Data
12

11

10

9

8

7

6

5

4
70

72

74

76

78

80

82

84

86

88

age

Figure 7: Prices in the model and in the data
insurance firms actually have is more than 10% due to higher administrative expenses or
violation of the perfect competition assumption.

7

Conclusion

This study considers different explanations for the annuity puzzle in a quantitative heterogeneous agent model. It shows that, in the absence of any impediments to annuitization, all but the poorest retirees buy annuities. Social Security and DB pension plans
significantly decrease the annuity market participation rate but it still remains high.
Uncertain medical expenses increase demand for annuities because health expenditures are increasing with age: the state of being old and alive coincides with the state of
being old and having to pay high medical costs. Thus, insurance against longevity risk
and insurance against medical costs uncertainty compliment each other.
Adverse selection decreases demand for annuities for people in low income quintiles
because their mortality is high and in equilibrium they face unfair prices. However, the
equilibrium price is not high enough to completely crowd high mortality types out of the
market. Thus, in pooling equilibrium people in high-income quintiles face lower prices,
which increases their demand for annuities.
The quantitative effect of bequest motives is not big because it affects the demand
for annuities only for those in the highest income quintile. Public longevity insurance
provided through various means-tested transfers plays a big role in reducing demand for
private annuities from the low and middle income quintiles.
In general, people place a high value on the opportunity to invest in annuities. However, the amount of annuities retirees are actually buying is small. This is because

31

annuities bring returns for many years and the upfront investment even when buying a
small stream of annuity income is not trivial. When insurance firms restrict the minimum
amount an individual can invest in an annuity, it substantially decreases the number of
retirees in the market, especially if housing wealth cannot be annuitized.

8
8.1

Appendix
Robustness check

This section checks the sensitivity of results to changes in two parameters: discount factor
(β) and risk aversion (σ). Table 21 compares participation rates in the annuity market
with the baseline model when β is first raised to 0.98 and then decreased to 0.8. Note,
that in the first experiment β was increased to the point when β(1 + r) = 1.
Table 21: The sensitivity of participation rates to change in discount factor
Income quintile

Baseline

β = 0.98

β = 0.80

All

76.3

81.2

43.0

1

40.7

43.9

26.4

2

80.7

85.1

44.1

3

83.8

90.4

45.8

4

85.9

90.1

47.2

5

84.8

89.9

48.3

Not surprisingly, an increase in the discount factor raises annuity market participation
rates and a decrease in the discount factor has the opposite effect. Patient individuals
save more and so they are more interested in annuities as one of the available saving
options. The overall increase in the participation rate due to a higher discount factor is
equal to 5%. When the discount factor goes down to 0.8, the participation rate drops
almost twice. In general, an increase in the discount factor makes the annuity puzzle
harder to explain, though the effect is not big for ranges where β(1 + r) ≤ 1.
In the next experiment, risk aversion was first set to 2 and then raised to 4. Table 22
compares the results of these experiments with the baseline model. When risk aversion
decreases, agents want to save less and, thus, they buy less annuities. An increase in risk
aversion has the opposite effect. Higher risk aversion makes the annuity puzzle harder to
explain, but again, the effect is not big.

32

Table 22: The sensitivity of participation rates to change in risk aversion

8.2

Income quintile

Baseline

σ=2

σ=6

All

76.3

69.3

77.4

1

40.7

32.8

44.8

2

80.7

69.2

83.3

3

83.8

74.1

82.6

4

85.9

81.5

88.6

5

84.8

81.6

82.6

Computation

I solved the model using backward induction. In the last period (t = T ), the value
function (and policy functions) can be solved for analytically. For every age t prior to T
and for each point in the state space, I optimize with respect to bonds and annuities. I
solve the two-dimensional optimization problem by applying, first, a coarse grid search
and then the Brent method along both dimensions. The numerical integration of tomorrow’s value function was performed using Gauss-Legendre quadrature. This numerical
integration was complicated by the fact that the value function is not concave. The
non-concavity arises because each period, the agent can run out of assets due to medical
expense shocks. The probability of getting into this state is endogenous. To address
this problem, in numerical integration “kink point”for each grid of tomorrow’s assets is
identified. The “kink point”is a value of tomorrow’s medical shock that lets the agent
finance her medical expenses and be left exactly with an amount equal to the consumption minimum floor. Then the value function was integrated separately to the left and to
the right of the “kink point”. I evaluate the value function for points outside the state
space grid using a linear interpolation.

References
[1] Ameriks J., Andrew Caplin, Steven Laufer, and Stijn Van Nieuwerburgh (2007),
“Annuity valuation, long-term care, and bequest motives,” WP 2007-20, Pension
Research Council, Wharton.
[2] Brown Jeffrey R. (1999), “Private pensions, mortality risk, and the decision to annuitize,” NBER WP 7191.
[3] Brown Jeffrey R. (2007), ”Rational and Behavioral Perspectives on the Role of
Annuities in Retirement Planning”, NBER WP 13537.

33

[4] Brown, Jeffrey R., Olivia S. Mitchell and James M. Poterba (2001), “The Role of
Real Annuities and Indexed Bonds in an Individual Accounts Retirement Program,”
in J. Campbell and M. Feldstein, Risk Aspects of Investment-Based Social Security
Reform, University of Chicago Press: Chicago, IL, pp. 321-360.
[5] Brown Jeffrey R. and Warshawsky (2001), “Longevity insured retirement distributions from pension plans: market and regulatory issues”, NBER WP 8064.
[6] Chiappori Pierre-André (2000), “Econometric Models of Insurance under Asymmetric Information”, in Dionne George, “Handbook of Insurance”
[7] Davidoff, Thomas (2008) “Housing, Health, and Annuities”, Haas School of Business
[8] Davidoff, Thomas, Jeffrey R. Brown and Peter A. Diamond (2005), “Annuities and
Individual Welfare,” American Economic Review, 95(5), 1573 – 1590.
[9] De Nardi Mariacristina, Eric French, and John Bailey Jones (2009), Why do the
Elderly Save? The Role of Medical Expensess,” forthcoming in Journal of Political
Economy
[10] Dushi, Irena and Anthony Webb (2004), “Household Annuitization Decisions: Simulations and Empirical Analysis,” Journal of Pension Economics and Finance, 3 (2),
109–143.
[11] Eichenbaum, Martin and Dan Peled (1987), “Capital accumulation and annuities in
an adverse selection economy”, Journal of Political Economy, 95(2):334{354).
[12] Friedman, Benjamin M. and Mark J. Warshawsky (1990), “The Cost of Annuities:
Implications for Saving Behavior and Bequests,” The Quarterly Journal of Economics, 105 (1), 135–154.
[13] French, Eric, Jones B. John (2004), “On the distribution and dynamics of health
care costs,” Journal of Applied Econometrics 19, 705–721.
[14] Johnson, Richard W., Leonard E. Burman, and Deborah Kobes (2004), “Anuitized
Wealth at Older Ages: Evidence from the Health and Retirement Study”, Washington DC: The Urban Institute.
[15] Hosseini Roozbeh (2007), “Adverse selection in the annuity market and the role for
Social Security”, mimeo, University of Minnesota.
[16] Hurd, Michael, Daniel McFadden and Angela Merrill (1999), “Predictors of Mortality Among the Elderly,” NBER Working Paper 7440.
[17] Kitao, Sagiri and Karsten Jeske (2009) “U.S. Tax Policy and Health Insurance Demand: Can a Regressive Policy Improve Welfare?” Journal of Monetary Economics,
Vol. 56, No.2
[18] Kopecky, Karen A. and Koreshkova, Tatyana (2009) “The Impact of Medical and
Nursing Home Expenses and Social Insurance Policies on Savings and Inequality”

34

[19] Levy Robert A., William Riley, Mary Gabay, John Nyman, Roger Feldman (2005),
”Analysis of the Use of Annuities to Shelter Assets in State Medicaid Programs”,
The CNA Corporation
[20] Lockwood, Lee (2008), “Bequest Motives and the Annuity Puzzle”, mimeo, University of Chicago.
[21] Love, David, Michael Palumbo, and Paul Smith (2008), “The Trajectory of Wealth
in Retirement”, mimeo, Federal Reserve Board.
[22] McGarry , Kathleen and Jonathan Skinner (2008), “Out-of-Pocket Medical Expenses
and Retirement Security”, NBER.
[23] Michelangeli, Valentina (2008) “Doest It Pay To Get a Reverse Mortgage? ” Boston
University
[24] Milevsky, Moshe Arye and Virginia R. Young (2007), “The timing of annuitization:
investment dominance and mortality risk,” Insurance: Mathematics and Economics,
40, 135-144.
[25] Mitchell, Olivia S., James M. Poterba, Mark J. Warshawsky and Jeffrey R. Brown
(1999), “New Evidence on the Money’s Worth of Individual Annuities,” American
Economic Review, 89(5): 1299-1318.
[26] Murtaugh, Christopher, Brenda Spillman and Mark J. Warshawsky (2001), “In Sickness and in Health: An Annuity Approach to Financing Long-Term Care and Retirement Income.,” Journal of Risk and Insurance, Vol. 68, No. 2, Pp. 225 – 254.
[27] Pang, Gaobo and Mark J. Warshawsky (2008), “Optimizing the Equity-BondAnnuity Portfolio in Retirement: The Impact of Uncertain Health Expenses”, Pension Research Council Working Paper No. 2008-05.
[28] Pashchenko, Svetlana (2010), “Annuitization in retirement: some theoretical results”, mimeo, University of Virginia.
[29] Rohwedder, Susann, Steven Haider and Michael Hurd (2004), “Increases in wealth
among the elderly in the early 1990s: How Much Due to Survey Design?” PNBER
Working Paper 10862.
[30] Sinclair, Sven H. and Kent A. Smetters (2004), “Health Shocks and the Demand for
Annuities,” Technical Paper Series 2004-9, Congressional Budget Office.
[31] Turra, Cassio M. and Olivia S. Mitchell (2004), “The Impact of Health Status and
Out-of-Pocket Medical Expenditures on Annuity Valuation,” Working Paper, Pension Research Council WP 2004-2.
[32] Walker, Lina (2004) “Elderly Households and Housing Wealth: Do They Use It or
Lose It? ” University of Michican Retirement Research Center, WP 2004-070
[33] Walliser, Jan (2000), “Adverse selection in the annuities market and the impact of
privatizing Social Security”, Scandinavian Journal of Economics, 102(3).
35

[34] Yaari, Menahem E. (1965), “Uncertain Lifetime, Life Insurance, and the Theory of
the Consumer,” Review of Economic Studies, 32, 137.
[35] Yogo Motohiro (2008), “Portfolio Choice in Retirement: Health Risk and the Demand for Annuities, Housing, and Risky Assets,“ mimeo, University of Pennsylvania

36

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