WPS3972
ANNUITY MARKETS IN CHILE:
COMPETITION, REGULATIONAND MYOPIA?
Eduardo Walker
School of Business Administration
Pontificia Universidad Católica de Chile
Santiago de Chile.
Abstract: We study annuity rates in Chile and relate them with industry competition, finding: a)
that annuity insurance companies paying higher broker commissions paid lower annuity rates; and
b) a structural break of the longrun elasticity of annuity rates to the riskfree rate in 2001.
Moreover, this structural break coincided with the submission of a new draft pension law proposing
greater transparency in annuity markets and a generalized drop in broker commissions. The high
commissions charged in the 1990s were partly returned to annuitants as informal (and illegal) cash
rebates. Myopic pensioners preferred cash rebates over present values. Thus, the legal threat caused
the drop in broker commissions, reduced the illegal practice of cash rebates, increased competition
via annuity rates, and raised the longrun elasticity to one.
JEL Classification Code: G22, G23, G12, L5
Keywords: Annuities, Emerging Markets, Competition, Credit Risk, Myopia
World Bank Policy Research Working Paper 3972, August 2006
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the
exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even
if the presentations are less than fully polished. The papers carry the names of the authors and should be
cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of
the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent. Policy Research Working Papers are available online at http://econ.worldbank.org.
Correspondence details: Eduardo Walker, School of Business Administration, Pontificia
Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile; Phone: (56 2) 354 4002;
Fax: (56 2) 553 1672; email: ewalker@faceapuc.cl
ACKNOWLEDGEMENTS
I thank participants at the Reñaca (Chile) seminar of the Facultad de Ciencias
Económicas y Administrativas, Pontificia Universidad Católica de Chile, for their
comments on this paper, especially Augusto Castillo and Salvador Valdés. Special thanks
are due to Francisco Mellado and Roberto Rocha, who helped significantly improve and
clarify this paper.
ii
Table of Contents
PREFACE...................................................................................................................v
GLOSSARY ..............................................................................................................vi
1. INTRODUCTION AND HYPOTHESES..........................................................1
2. DETERMINANTS OF ANNUITY COSTS ......................................................3
2.1 ModiglianiMiller and the Expected Elasticity ........................................4
2.2 The Case of Chile .....................................................................................5
3. THE DATA ........................................................................................................6
3.1 The Original Data.....................................................................................6
3.2 Annuity Payment Profile ..........................................................................6
3.3 Annuity Cost Behavior.............................................................................7
3.4 Causality Relations...................................................................................7
4. METHODOLOGY AND RESULTS.................................................................7
4.1 LongTerm Elasticity................................................................................8
4.2 Structural Changes....................................................................................8
4.3 Robustness Checks ...................................................................................8
4.3.1 Unadjusted Annuity Rates..............................................................9
4.3.2 Relevant Market Interest Rate........................................................9
5. INTERPRETATION ..........................................................................................9
5.1 Commission Levels ................................................................................10
5.2 Commissions and Adjusted Annuity Interest Rates ...............................10
5.3 Changes through Time ...........................................................................11
5.4 Other Evidence .......................................................................................11
6. SUMMARY AND CONCLUSIONS...............................................................12
REFERENCES .........................................................................................................14
FIGURES:
Figure 1: Annuity Costs, Market Rates, and Interest Rates.....................................15
Figure 2: Annuity Rates (TV) and Adjusted Annuity Rates (TVA)........................16
Figure 3: Annuity Payment Profile..........................................................................17
Figure 4: Estimated Elasticity of Adjusted and Unadjusted Annuity Rates to
Changes in the Reference Riskfree Rate.................................................18
Figure 5: Estimated Monthly Annuity Cost and Internal Rates of Return ..............19
Figure 6: Relationship between Adjusted Annuity Rates and Commissions ..........20
iii
TABLES:
Table 1 Annual Averages and Descriptive Statistics................................................21
Table 2 Empirical Duration and Convexity of Annuities, LongTerm Interest Rates
and Causality Tests......................................................................................22
Table 3 LongTerm Elasticity Estimation ................................................................23
Table 4 LongTerm Elasticity versus Interest Rate and Commission Levels...........24
Table 5 Adjusted Annuity Rates versus Commissions (Panel Regressions)............25
iv
PREFACE
ANNUITY MARKETS IN CHILE: COMPETITION, REGULATIONAND MYOPIA?
Between 1993 and 2003 the longterm riskfree rate in Chile fell by 3.2 percentage
points, while the cost of an annuity increased by less than 12.3 percent, implying a very low
implicit elasticity. This article estimates the longterm elasticity of annuity rates issued by
life insurance companies (defined as the internal rate of return on expected future annuity
payments) to changes in the market riskfree rate. It also examines interactions between the
annuity rates and broker commissions as two alternative instruments of competition and
checks whether there were structural breaks related to key regulatory actions. These
questions are of general interest because, in definedcontribution pension systems, many
pensioners are expected to purchase annuities upon retirement, and elasticities significantly
smaller than one could indicate lack of competition via annuity rates. This result would be
troublesome in the context of a mandatory pension system, because it could reveal failures
in the last link in the long pension chain.
We find several interesting results. First, the estimated longrun elasticity increases
rapidly after 2001, and the hypothesis that it is statistically equal to one cannot be rejected
after that period. Second, this structural change is significantly related to a generalized
drop in broker commissions. Third, both facts coincide with the submission to Congress of
a new draft pension law proposing the creation of an electronic market for pension
annuities and the imposition of a cap on commissions. Fourth, we find evidence that
annuity insurance companies that paid higher commissions also paid lower total annuity
rates. It is likely that higher commissions allowed more room for brokers to provide
informal (and illegal) cash rebates to pensioners. This, in the case of myopic pensioners,
reduced competition via annuity rates and increased competition via advance cash
payments, despite the lower total present value received by the pensioner. The overall
evidence indicates that the threat caused by the draft law (which was only passed in 2004)
caused a generalized drop in broker commissions, which reduced the scope for cash
rebates, increased competition via annuity rates, and caused the elasticity to become
statistically equal to one.
v
GLOSSARY
AR Annuity rate
BC Broker commissions
CRV Annuity cost
IRR Internal rate of return
LICO Life insurance company
PRC20 20year bond issued by the Central Bank of Chile
SAFP Superintendencia de Administradoras de Fondos de Pensiones (Superintendency of
Pension Fund Administrators)
SVS Superintendencia de Valores y Seguros (Superintendency of Securities and Insurance)
TVA Tasa de venta ajustada (commissionadjusted annuity rate)
TV Tasa de venta (annuity rate)
UF Unidad de Fomento (Unit of account of priceindexed contracts)
vi
1. INTRODUCTION AND HYPOTHESES
Many countries have reformed their pension systems in a similar way to Chile's
reform of 1981. This reform was intended to provide reasonable selffinanced pensions
upon retirement, freeing the state from onerous future liabilities, caused in part by
insufficient individual voluntary saving for retirement. The Chilean reform implied the
privatization of social security and the creation of a fully funded, privately managed
pension system with individual (fully portable) savings accounts that can be used
exclusively for retirement purposes.
At retirement, most individuals typically have two choices: to withdraw the
accumulated funds over time following a certain rule (programmed withdrawal) or to buy
an annuity, sold in Chile by closely regulated life insurance companies. Each choice carries
different types of risk: a longevity risk, which only an annuity covers, and an investment
risk, which either the pensioner or the insurance company assumes in full.1
Because many pensioners opt for annuities (more than 60 percent in the Chilean
case),2 we need to understand the incentives faced by annuity insurance companies in this
context. In particular, we want to know whether and how changes in the local riskfree rate
are transmitted to annuity rates. In this paper, we define the annuity rate (TV) as the
internal rate of return on expected future annuity payments.3
This is a theoretically simple question, but since the answer depends on the extent of
competition in the insurance industry and the variables used for such competition, it is not
obvious from an empirical perspective. Indeed, figure 1.A shows the time trend of the
estimated inflationadjusted cost of an annuity for a 65yearold pensioner with no
beneficiaries and compares it to a 20year central bank interest rate (PRC20).4 For many
years this was the longest maturity interest rate, and (as we will argue later) it adequately
represents riskfree investment opportunities for the life (annuity) insurance companies
(LICOs). The inverse relationship, as expected, is apparent. However, considering the
starting and ending points, we observe that the PRC20 rate dropped from 7.2 to 4 percent.
With an estimated Macaulay duration of about eight years for the annuity, its cost should
have increased by more than 25.6 percent, but it did only so by 12.3 percent. A simple
regression of the logarithm of the annuity cost on this interest rate level (with several lags)
gives a total coefficient of 3.2, and relating changes in annuity costs to interestrate
changes yields a slope coefficient of 2.6. These coefficients are unexpectedly low. Figure
1.B offers a tautological explanation for these findings: annuity interest rates start below the
1 Lumpsums are restricted in Chile. For a detailed description of the Chilean pension system see
Superintendency of Pension Fund Administrators (2003). For a description of potential pension modalities,
see Edwards and Valdés (1998). Variable annuities were introduced in Chile in 2004.
2 See the website of the pension supervisor (SAFP): www.safp.cl. This number underestimates the
effective proportion of retirees that choose annuities, since it includes disability and survivorship pensioners.
3 These expected payments are based on the (outdated) RV85 mortality table. This implies an
overestimation of the level of annuity rates but should not significantly affect their changes through time.
However, see section Determinants of Annuity Costs, below.
4 In the Data section below, we explain the sources. In every case we use "real" (inflationadjusted)
interest rates.
riskfree rates (with negative spreads) and end above it (positive spreads). Interpreting an
annuity as a longterm (special) bond issued by a LICO, the reported spread behavior is
puzzling.
Here we estimate the longterm elasticity of annuity rates to market riskfree interest
rates and also examine the evolution of this parameter through time. In light of the
preliminary evidence presented, we also look for structural changes.
We believe these questions are important for several reasons. First, the sensitivity of
the annuity cost to changes in market interest rates should partly reflect the degree or form
of competition within the industry. If competition takes place via annuity rates, they should
fully reflect changes in interest rates. In fact, we expect a longterm elasticity close to one.
This implies an interesting question because the preliminary evidence indicates sensitivity
significantly smaller than one. Such result may be a matter of concern for the regulatory
authorities because this is the last link in a mandatory definedcontribution pension system.
On the other hand, the behavior of annuity rates indicates that a structural change may have
occurred, and that the elasticity may have changed. The causes of such a change are
interesting to study. Finally, from a normative perspective, this parameter is important for
determining the kind of investment strategies that, to head off future pension risks, pension
funds should follow as future pensioners approach retirement age.
We find a number of interesting results. First, there is indeed evidence of a
structural break in the longterm elasticity of changes in annuity rates to changes in the
riskfree rate. Until the first quarter of 2001, the elasticity is significantly smaller than one,
and from that point on it becomes statistically equal to one. The parameter change
coincides with a large generalized drop in broker commissions. There is a statistically
significant correlation between the two facts. They also coincide with a discussion in
Congress of a new draft pension law proposing the electronic auctioning of annuities and a
cap on broker commissions. We also find evidence that the LICOs that paid higher broker
commissions paid lower total (adjusted) annuity rates.5 It is therefore likely that higher
commissions allowed more room for brokers and annuitants to liquefy pensions (through
informal cash payments to the pensioner by the broker). This, in the case of myopic
pensioners (forced to save all their lives), reduced competition via annuity rates and
increased competition via commissions and the associated advance cash payments, even
though, in present value terms, the pensioner could be losing money (as evidenced by the
lower total interestrate cost paid by the LICO).
We use the term myopia in the sense of high subjective discount rates, which would
explain both the need for mandatory savings and the preference for advance cash payments
(which partly undo the lifetime mandatory savings). However, we cannot rule out broker
abuse of uneducated consumers, resulting in situations where the annuitants got limited
cash rebates and a large share of the high fees ended up in the brokers' pockets. So, in this
5 Adjusted annuity rates (TVA) correspond to the internal rate of return of expected future payments,
after deducting commissions from the premium paid by the annuitant, so they correspond to the effective
interestrate costs paid by the LICOs.
2
case we need to assume irrationality or lack of education to explain how highcommission
annuities were sold in the first place, when pensioners get no associated extra benefits.
Since the reform, we can safely conclude annuitants today get a much better deal.
The evidence is mostly consistent with the interpretation that a legal threat caused a
generalized drop in commissions. This reduced the slack for pension dilution (or broker
abuse), increased competition via annuity rates, and caused the elasticity to become
indistinguishable from one.
2. DETERMINANTS OF ANNUITY COSTS
From the perspective of a LICO, the process begins when an agent (broker) contacts
a potential pensioner and induces him/her to exchange the balance in the (mandatory)
individual retirement account for an annuity. The agent, who may represent several
different LICOs, gets a commission for this service (usually measured as a percentage of
the initial down payment or premium). Figure 2 shows the nonadjusted and adjusted
annuity rates (TV and TVA, respectively) and the corresponding spread due to
commissions. A fraction of this commission may be returned to the pensioner as an
informal advance cash payment or rebate, implying that the pension is "liquefied." This
marketing practice was illegal, but was apparently common during the 1990s. These
incentives are expected to exist if the pensioner, forced to save during his/her entire active
life, cannot take a lumpsum and is given the opportunity to withdraw informally some of
the money in advance. (Although commissions have fallen, there is no information
regarding how the decrease has changed net of cash payouts to the pensioner.)
Evidently, this transaction generates a longterm liability for the LICO. From this
perspective, the relevant interest rate is the commissionadjusted interest rate (tasa de
venta ajustada, TVA). Regulations require that, in addition to the premium paid by the
pensioner, equity holders in the LICO must put in new equity. This can be achieved in two
ways. First, the maximum leverage ratio is 15. Second, there is a relatively strict norm,
based on assetliability cashflow matching requirements, that the unmatched liability cash
flows must be discounted at rates notably lower than market rates. This implies that the
calculated present value of the liability is larger than the net premium received by the
LICO, which is reflected as an immediate accounting loss in the equity value, meaning that
shareholders must put up additional equity.
An important question is whether this additional equity requirement in itself is a
direct cost that should be deducted from the interest rate paid to the annuity holders. If there
is access to capital markets the answer is negative because if the new equity is invested in
financial instruments traded in capital markets at fair prices, the transaction has zero net
present value.
However, from the perspective of a LICO other costs are associated with a new
annuity, which can be categorized as operating or administrative, financial and technical.
Financial costs are associated with eventual mismatching of assetliability cash flow (or
duration); technical costs are related to mortality table risk and consist of systematic
underestimation of life expectancy.
3
Regarding mortality table risk, by definition it is impossible for all pensioners to
live more than the average life expectancy. However, mortality tables may be outdated,
underestimating life expectancy. This means that the estimated (reported) annuity interest
rates, calculated using these outdated mortality tables, will be biased downward.6
2.1 ModiglianiMiller and the Expected Elasticity
From the perspective of a pensioner, whether a homemade annuity is feasible is an
important question. If the age at death is known with certainty, it is feasible using a ladder
of riskfree bonds. If the pensioner cannot build the ladder, the LICO cannot provide one
either without assuming risk. Recognizing the longevity risk, the pensioner should be
willing to give up a fraction of his/her pension in exchange of longevity insurance.
However, if longevity risk is largely diversifiable at no cost, in a competitive annuity
industry the pensioners should not be charged for it.7
An annuity can be interpreted as a longterm bond guaranteed by a LICO. If
annuities are priced (as corporate bonds are) in highly competitive and informationally
efficient markets, the main determinants of their interest rates should be the longterm,
defaultfree rates and LICO credit risk. General creditrisk results should also be directly
applicable to this case. Applying Acharya and Carpenter's analysis of corporate defaultable
bonds (2002), and assuming that longterm matching riskfree assets do exist, the price of
an annuity At should be
At = Bt (1 ct ) (1)
where Bt is the price of a matching defaultfree bond and ct is the value of the default option
held by the LICO equity holders, expressed as a fraction of the value of the defaultfree
bond. It corresponds to the option of buying the riskfree bond with the LICO's assets, so
the underlying asset is the riskless bond and the exercise price is the assets' value. The
default option is valuable if the assetliability ratio is "high", if there is significant
mismatching and/or if assets are risky. However, it is important to note that, given an
assetliability ratio, investing in riskier assets (with higher interest rates or spreads) not
necessarily implies that higher interest rates should be paid on annuities. Modigliani and
Miller (1958) prove that equity absorbs the risks in the first place and that only when risk
becomes "large" is it shared with debt holders.
In any case, determining whether the option to default is valuable is an empirical
matter. Considering that debtequity ratios have been much lower than their legal maximum
(11 versus 15),8 despite mismatching, that LICO portfolios tend to be conservative, and that
riskratings have been in general above (local) AA, we conjecture that the default option is
not significantly valuable.
6 For example, assume constant annual payments for 25 years and an interest rate of 4 percent. If we
wrongly assume that the payments will take place only during 22 years, the reported interest rate will be 3.2
percent.
7 Here we think of diversification at the LICO shareholders' level. We do not mean to say that
longevity risk is diversifiable within each LICO.
8 However, we need to keep in mind that these leverage ratios are calculated with outdated life
expectancy tables such that the true economic leverage may be larger.
4
To model the annuity elasticity with respect to changes in the riskfree interest rate,
let At be the reported annuity cost, which underestimates the true annuity cost by
*
ut = (At  At ) / Bt . We can rewrite equation (1) as
*
At = Bt (1 ct  ut )
* (1')
Thus,
d log At *
= d log Bt d logct + (2)
dy dy (1ct ut)1 dy d logut
dy
where y is the longterm interest rate. Expressing this in terms of interest rates, we
can write
dy * = DBt + 1 dlogct + d logut (2')
dy DAt dy dy
* DAt (1 ct  ut)
*
or
y* DBt + 1 d logct + y (2")
DAt dy dy
* DAt (1 ct  ut)
* d logut
where y* is the reported annuity rate and D· are the corresponding modified durations.
Following Acharya and Carpenter (2002), an interesting implication of (1) is that
when interest rates fall (increase), the value of the riskless reference bond increases
(decreases), but the default option value (to purchase a more valuable underlying asset) also
increases (decreases) (d logct / dy < 0 ), assuming that the assets' value (the exercise price)
increases by less. This is the case if the assets have lower duration or if they are riskier than
liabilities. The implication of the measurement error is similar: when interest rates increase
(decrease) the present value of the farther away cash flows falls (rises). Therefore, from
(2'), if the option to default is valuable or if measurement error is significant, annuity
interest rates should fall (increase) by less than the riskfree rates, and the elasticity may be
lower than one, even if the reference bond and the annuity have the same durations. On the
other hand, an elasticity equal to one should imply no significant default risk or significant
mismeasurement, assuming efficient markets.
In any case, we may expect reported annuity interest rates to be lower than the risk
free rates, even if a small risk premium may have to be added to it, because (1) reported
rates underestimate true annuity rates; (2) operational costs have to be subtracted from asset
returns; and (3) eventual additional premiums, related to mismatching and mortality table
risk, may have to be charged to the annuitant, if they cannot be diversified.
2.2 The Case of Chile
Since 1993, the Chilean fixedincome market has had 20year inflationindexed
bonds issued by the central bank. Its Macaulay duration was about 8 (9) years at the
beginning (end) of the sample period. Given the duration of an annuity, this instrument
5
offers good assetliability matching opportunities and is a useful reference point in the
sense that it should be used to set the rates of the marginal annuities.9
With this in mind, the evidence presented in figure 1.B indicates an interesting
evolution of the annuityrate spreads (defined as the annuity rate minus the riskfree rate):
they were negative by more than 1 percentage point at the beginning of the sample period
and became positive toward the end. Between 1993 and 2003, we find an increase of 169
basis points in the average spreads (table 1.A). Measurement error arguments cannot
explain this; only very significant increases in risk levels could.10 However, even under this
hypothesis, the negative initial spreads are hard to understand. Furthermore, the risk
argument would contradict any unit elasticities that might exist. The explanation may
therefore lie elsewhere.
3. THE DATA
In this section we describe the data that are used for the different estimations, its
sources, and present a few descriptive statistics.
3.1 The Original Data
The original annuities data come from the Superintendencia de Valores y Seguros
(SVS). SVS keeps records of annuity interest rates and also of average market
commissions, which were reported annually until 1999 and quarterly after that. Average
annual rates are presented in table 1.A. The adjusted annuity rates (TVA) represent the
effective interestrate cost for the LICOs. To estimate this cost, we must subtract the broker
commission from the annuity premium and recalculate the internal rate of return with the
new (lower) initial payment. For example, in the case of perpetuities, the cost is equivalent
to dividing the interest rate by one minus the percent commission of the sales agent. To
estimate the TVA, we assume that the average commission is constant throughout the
corresponding reporting periods (annually at first and then quarterly). The same
information is presented in figure 2, but in terms of annuity interest rates before and after
commissions, and the corresponding spread. Table 1.B shows additional descriptive
statistics. The reference interest rate (PRC20) was obtained from transactions data the last
trading day of the month at the Santiago stock exchange (Bolsa de Comercio de Santiago).
3.2 Annuity Payment Profile
Figure 3 shows the payment profile for a 65yearold pensioner with no
beneficiaries, for a premium of 1,000 UF11 and a real interest rate of about 5 percent per
9 See Data section, Annuity Cost Behavior.
10 For example, in the US for 10year bullet bonds, such an increase would be associated with a drop
in risk ratings from significantly above to significantly below investment grade. See for example
www.bondsonline.com .
11 The UF (Unidad de Fomento) is the indexed (inflationadjusted) unit of account. It is calculated as
follows: given an initial value expressed in pesos for the day 9 of a given month (say, Ch$17,000) the ending
value of the UF for day 9 of the following month is calculated as Ch$17,000(1+inft1), where inft1 is the
inflation rate of the previous month. The quantity Ch$17,000(inft1)/n, where n is the number of days in a
month, is successively added to the previous day's value of the UF.
6
year. Such a profile is obtained from the official mortality tables (RV85) used by the LICOs
until 2003. Considering this payment profile and the annuity interest rates, we obtain
estimated annuity costs.
3.3 Annuity Cost Behavior
With the adjusted annuity rates (TVA) and the profile just described, we estimated
an index representative of the annuity cost (CRV). For descriptive purposes, it can be
related to the TVA. Considering that interest rates changed significantly in the sample
period, we estimated the durations in a slightly unconventional way, as a function of
interestrate levels, and by doing so we take into account that durations change with
interestrate levels. Notice that we do not assume an adjustment lag or anything of that sort.
It is just an ad hoc definition. Table 2 shows empirical estimations of the annuities'
modified duration and (marginal) convexity.
Given the relationship that (by definition) exists between the annuity cost and the TVA, the
regression adjustment is almost perfect. The (empirical) modified duration (which measures the
percentage change in the annuity cost given a 1 percent change in its interest rate) turns out to be
1044TVAt1. For example, for an adjusted interest rate of 4 percent, the modified duration is 8.24.
The (empirical marginal) convexity (which accompanies the quadratic term) is 22. For comparison,
we perform the same exercise for a PRC20 total return wealth index, which assumes monthly
investment in a new PRC20. We get a modified duration of 9.7232PRC20t1. With 4 percent
interest rates, the modified duration is 8.44. The empirical or residual convexity of this instrument is
marginally larger than that of the annuity.
We can thus conclude that the PRC20 may be a reasonable instrument for matching LICO
assets and liabilities, at least in the case of 65yearold male. However, it is important to keep in
mind that many of the annuities paid by insurance companies actually correspond to early retirees,
and for that purpose the duration of the PRC20 is too short.
3.4 Causality Relations
As part of the descriptive information, it will prove useful to perform Granger
causality tests. Considering the full sample and the interestrate levels, several statistical
criteria indicate an optimal lag of about 3 months. Considering changes in interest rates, the
optimal lag is 2. Table 2.C shows the results. As expected, they indicate that PRC20
interestrate levels and changes "cause" the levels and changes in annuity interest rates. The
inverse relation does not exist, implying that annuity interestrate levels and changes do not
anticipate future interest rates. These results do not change much considering other sample
periods.
4. METHODOLOGY AND RESULTS
Here we estimate the longterm elasticity of annuity interest rates to changes in the
risk free rates, look for structural changes and present robustness checks.
7
4.1 LongTerm Elasticity
One purpose of this study is to determine the longterm elasticity of the annuity cost
to the relevant longterm interest rate (equation [1']). This is equivalent to estimating the
annuity interestrate elasticity to the same variable (equation [2']). We use the second
alternative, since the interpretation is clearer. Our hypothesis is that the elasticity is equal to
one, which would be true if the chosen riskfree rate adequately represents the marginal
cost of an annuity and if risk or mismeasurement considerations are unimportant.
Because some time must elapse between the sale of the annuity and the official
recording and reporting of the sale, a lag is to be expected, particularly if we use month
end, riskfree interest rates. It may also take time for the LICOs to adjust their business
strategies to changing market conditions. We thus estimate the following equation:
TVAt = a + TVAt +b0PRC20t +b1PRC20t +...+bPRC20t
1 1  +t (3)
With this specification, to have at least part of the changes in the riskfree interest rate
transmitted to the annuity interest rate in the long term, we needb > 0. In addition, to have unit
l
l=0
1
elasticity, we require1 b =1 or equivalently
l b l=1 .
l=0 l=0
Results are presented in table 3. We used two lags, given the results presented in the
previous section. If we also include the contemporaneous market rate, the coefficient is
essentially zero and does not affect the results. The sum of the coefficients b1 and b2 is 0.3;
it is highly and significantly different from zero (table 3.B). The coefficient of the lagged
dependent variable is 0.34522, which gives a longterm elasticity of 0.466, which is
significantly smaller than 1 (table 3.B). Thus, the evidence so far contradicts the hypothesis
that changes in the longterm interest rate are fully transmitted to the annuity cost.
4.2 Structural Changes
Given the observed evolution of the spreads between the annuity costs, of the risk
free interest rate and of the reported commissions (figures 1.B and 2.A) a reasonable doubt
arises about whether longterm elasticity has changed. With this in mind, equation (1) was
estimated with rolling 36month samples. With each estimation, we verified the hypotheses
b1 + b2 = 0 and b1 + b2 = 1 with likelihood ratio tests. Our results, shown in figure 4.A,
are eloquent. The sum of the coefficients b1 and b2 is always significantly different from
zero. Furthermore, after mid2001 the longterm elasticity (b1 + b2)/(1 ) becomes
statistically indistinguishable from one. This means that evidence of a structural change is
clear and that all of the market interest changes were fully transmitted to the annuity costs
during the last three sample years.
4.3 Robustness Checks
Here we present robustness checks of our results, by considering alternative dependent
(unadjusted annuity rates) and independent (termstructureadjusted risk free rates) variables.
8
4.3.1 Unadjusted Annuity Rates
We repeated the rolling estimation exercise using the (unadjusted) annuity interest
rate received by the pensioner. Results are presented in figure 4.B. They are essentially
similar to those found using the adjusted interest rate or TVA. It even looks as if these
unadjusted interest rates began their adjustment earlier.
4.3.2 Relevant Market Interest Rate
LICOs might consider a different interest rate as the relevant one for determining
the annuity cost considering that the payment schedule of the PRC20 is flat and biannual,
whereas expected annuity payments are monthly and decreasing.
To consider this possibility, we performed the following exercise. First, we
estimated the endofmonth term structure of interest rates between 1993 and 2003 using
bonds issued by the central bank of Chile, based on the Nelson and Siegel (1987)
parametric representation. With the estimated termstructure parameters, we obtained a full
set of monthly zerocoupon prices. Then, we used these prices to determine the monthly
present value of the annuity and the corresponding series of internal rates of return.12 Figure
5.A shows the evolution of the estimated annuity cost and Figure 5.B its internal rate of
return (IRR). The regression R2 of running the IRR against the PRC20 rate is 0.99, and the
slope coefficient is insignificantly different from one with a pvalue of 15 percent. Thus, for
the purposes of this study, no termstructurerelated errors seem to affect the results.
5. INTERPRETATION
Summarizing, so far we have documented the following facts: first, at market
interest rates the annuity costs increased by 30 percent, whereas the total price charged to
pensioners increased only by 12 percent. This happened because spreads between the
adjusted annuities interest rates and the reference rates (PRC20) were negative at the
beginning of the sample period and became positive toward its end (figure 1.B).13 Second,
reported commissions have dropped (table 1 and figure 2). Third, the annuity interestrate
elasticity to market interest rates was significantly smaller than one and turned statistically
indistinguishable from one. Thus, we should see what changes in the industry might explain
these noteworthy adjustments in the annuity parameters.
12 Calculation details are available from the author upon request.
13 Given the reasoning presented in the previous sections, it is hard to understand why annuity rates
end above the riskfree rates, especially if they are underestimated in outdated mortality tables. It is as if
competition may have taken annuity rates "too far." The evidence analyzed in James, Song, and Vittas (2001)
is consistent with the idea that annuity rates in Chile are "too high" toward the end of the sample period.
There are several possible explanations for this: (1) risk is much higher than what we assume it to be; (2))
irrationality (or agency problems) influence LICO behavior; (3) there are generalized (markettiming) bets on
interestrate increases (which itself may be rational or irrational, depending on the efficiency of the local
financial market); (4) some LICOs may also be assuming conscious losses in order to acquire dominant
market shares. This needs further study. However, even if, from the LICO's perspective, annuities are sold
with negative net present value, this need not imply bankruptcy or be reflected as negative margins in the
financial statements.
9
The drop in commissions coincides with the date the elasticity became statistically
equal to one, and both changes coincide with a generalized drop in interest rates. Jointly,
these facts probably indicate that these changes reflect intensified competition via interest
rates in the annuity industry. The very fact that commissions fell is likely to indicate more
competition. We now analyze the evidence further to check this conjecture.
5.1 Commission Levels
A potential indicator of the degree of competition is the commission level. It may be
argued that if part of these commissions is returned to pensioners it may be a bad indicator.
However, in view of the generalized drop in interest rates, it is likely that LICOs may have
to compete more actively through annuity rates. To verify this, we regressed the (log of) the
longterm elasticity reported in figure 4.A against commissions, measured as interestrate
spreads (figure 2). We also included the interestrate level as an additional regressor to see
whether the drop in interest rates alone explained the structural change. Results, presented
in table 4, confirm the latter conjecture. The effect of interest rates on the longterm
elasticity is not significant, but the level of commissions is.14
5.2 Commissions and Adjusted Annuity Interest Rates
Whether the pensioner ends up with a worse deal (lower net present value) with an
advance cash payment when the commission is increased is also of interest.15 One way to
check this is to verify whether LICOs that paid higher commissions (partly returned to the
annuity buyer) obtained cheaper financing, by paying a lower total interestrate cost on
their annuities. To study this, we need detailed information at the LICO level, which has
been available since 2001.
We performed the following exercise. First, we estimated the adjusted interest rates
(TVA) using LICOlevel annuity interest rates (TV) and broker commissions (C),
controlling for market share (p), for each month and for each LICO, considering a 65year
old pensioner with no descendants. Using a panel data specification we estimated the
following:
TVAit  PRC20it 2 = co( + c1pit + c2(TVAit TVit)+ eit
i) (4)
and
TVAit  PRC20it 2 = co( + c1pit + c2Cit +uit
i) (5)
Market share was used as an additional control variable, to consider the possibility
of systematic differences. In any case, given eventual endogeneity problems, we also
estimated the equations using lagged market shares and excluding this variable altogether.
Results do not change much.
We used several panel data specifications (common constant for all panel members,
lagged dependent variable, fixed effects, and random effects). Results are presented in table
14We tried with one interest rate and several different lags (one at a time due to multicolinearity),
and the results did not change significantly.
15See footnote 6.
10
5. Part A shows the results of estimating (4) and part B, of (5). Results are quite consistent
with each other, and in this sense they seem robust. In every case, we verify the hypothesis
that higher commissions are associated with lower adjusted interest rates. Depending on the
specification, an additional percentage point in commissions is related to a lower interest
rate cost between 9 and 18 basis points.16
To further understand the importance of this result, assume for example that the
annuitant pays 1, 1c is received by the LICO and c by the broker. To simplify, let us work
with perpetuities and assume that they are a function of this commission, A(c). We find
that that the adjusted annuity rate R(c)=A(c)/(1c) decreases with c (dR(c)/dc<0).
Differentiating we find
dR(c) 1 dA(c) + A(c) = 1 dA(c)
(6)
dc 1 c dc 1 c 1 c dc + R(c) < 0
implying that
dA(c) < R(c)dc (7)
Therefore, even if annuitants get all of the higher commissions back as rebates, it is
actuarially unfair, since the annuity falls by more than the interest rate times the additional
commission. In other words, from the perspective of the pensioner, higher commissions
definitely are associated with lower net present values.
5.3 Changes through Time
Considering the possibility that our results are driven only by the significant drop in
commissions, we reestimated (2) in successive rolling quarters. Because these are
essentially crosssectional regressions, we did not subtract the PRC20 interest rate, and we
used a common constant. Results are presented in figure 5, together with the LICOlevel
commissions. We do find that the significantly negative relationship between commissions
and adjusted annuity rates exists only until mid2001 and then disappears.
5.4 Other Evidence
Additional evidence is consistent with the idea that the reported structural changes
are due to changes in competition levels or attributes. Indeed, in November 28 of 2000
begins the official Senate discussion of a new draft pensions law to implement a mandatory
system of electronic annuity auctions, which would also impose a cap on commissions.
Among other things, this new law would have established that "(pension fund) affiliates
may select one of the three best pension offers or any other offer which is at least equal to
the average of the top three [annuity rates] minus 2 percent", which would indirectly limit
the maximum pension dilution. In addition, it "forbids insurance companies, brokers, sales
agents and other people intervening in the process of selling annuities to offer incentives or
benefits other than those established in the law, with the purpose of contracting pensions
using this modality".17
16For the specification with the lagged dependent variable, we divided the commission coefficient (
0.0304) by one minus the average coefficient on the lagged dependent variable.
17See Diario de sesiones del senado, publicación oficial legislatura 343ª. See references.
11
The commission levels (figures 2 and 5) had already dropped in the first quarter of
2001. Thus, it seems likely that the industry used the reduction as a "selfregulation signal"
(or first move) to influence the legislative debate.18 Because this legal change also meant
changes in competition mechanisms, the reduction may have been an attempt to accelerate
sales. An indirect indicator of this probability is the crosssectional dispersion in monthly
market shares, which peaked first in 2001 (and then more permanently in 2003, indicating a
more permanent market concentration).
6. SUMMARY AND CONCLUSIONS
The objective of this paper has been to estimate the longterm elasticity of annuity
interest rates to changes in market interest rates, but this investigation disclosed several
other interesting facts. We believe this is an important question in the first place because
this elasticity partly reflects the degree of competition or the attributes used to compete in
the annuities industry.19
From a public policy perspective, it would be worrisome to find that annuity rates
do not reflect financial market conditions. That would mean that, after a long accumulation
phase in the mandatory pension system, pensioners at the beginning of the payout phase
would leave a significant portion of their lifetime savings in the hands of brokers and
annuity insurance companies in the form of "excessive profits" (reflected in cheap
financing costs). This absurdity might be due to myopia ("the original sin") on the part of
the pensioners, accepting advance cash payments in exchange for actuarially unfavorable
annuity payments.
This study indicates that, between 1993 and 2003, annuity costs measured by market
interest rates increased by 30 percent, while the actual cost charged to pensioners by LICOs
increased only by 12 percent. This happened because annuity interestrate spreads with
respect to the riskfree rate (PRC20) were negative at the beginning of the sample period
and turned positive at the end of it.
Results also indicate that annuities have always been sensitive to market interest
rates, but until 2000 only a small fraction of interestrate changes was transmitted to
annuity interest rates (with a longterm elasticity between 20 and 40 percent). From that
point on, we cannot reject the hypothesis of a unitary elasticity, which means that changes
in market rates are fully reflected in annuity interest rates. This structural change is
significantly related to a generalized drop in broker commissions. The higher elasticity and
the lower costs coincided with the discussion in Congress of a draft law that would have
forced an electronic auction of annuities and imposed a cap on commissions. In addition,
we find evidence that companies that paid higher commissions also paid lower total
(adjusted) interestrate costs on annuities.
18The softer version of this law approved in 2004, indeed imposed a cap on fees, and created a fairly
transparent information system of annuity quotations for potential pensioners, but without the obligation of
choosing among the top three. See references.
19 This elasticity is also important for determining the investment policies that that pension funds
should follow to immunize pensions (Walker 2003).
12
An explanation that is consistent with all the combined evidence is that higher
commissions allow more room to liquefy pensions (advance cash payments or rebates to
the pensioner by the broker), which in the case of myopic pensioners reduces competition
via pensions and increases it via advance cash payments, even though the total net present
value received by the pensioner is lower. In summary, our results are consistent with the
interpretation that the legal threat caused a generalized drop in broker commissions,
reducing the slack for pension dilution, increasing competition via annuity rates, and
causing the elasticity to increase and become equal to one.
There are two competing explanations, coming from very different angles. First, we
cannot rule out that annuitants got modest cash rebates and that a large part of the higher
fees just ended up in the broker's handsbroker abuse of uneducated consumers. This
story uses irrationality or lack of education to explain how highcommission annuities were
sold in the first place, when pensioners got no compensatory extra benefits. In this case, we
can conclude that today's annuitants almost certainly get much better deals.
Another possible explanation is risk: that spreads increase due to higher credit risk
of life insurance companies. There may be some truth to this, since a generalized drop in
interest rates significantly increases LICO debt and debttoequity ratios, if assets and
liabilities have been mismatched. However, this explanation is hard to reconcile with the
initial negative spreads and with the fact that since 2001 the longterm annuity rate
elasticity to changes in the riskfree rate has become equal to one, something that should
happen only if risk is relatively low. Risk can neither explain why life insurance companies
that paid higher commissions also paid lower adjusted annuity rates. We thus believe the
evidence is more consistent with our interpretation of myopic incentives.
13
REFERENCES
Acharya, V., and J. Carpenter (2002) Corporate bond valuation and hedging with stochastic interest
rates and endogenous bankruptcy, Review of Financial Studies 15: 135583.
Edwards, G., and S. Valdés (1998). Jubilación en los sistemas pensionales privados. El Trimestre
Económico 65(1), No. 257, Marzo.
James, Estelle, Xue Song, and Dimitri Vittas (2001). Annuities Markets Around the World.
American Economic Association Meetings, January.
Modigliani, F., and M. Miller (1958). The Cost of Capital, Corporation Finance and the Theory of
Investment. American Economic Review 48 (June): 26197.
Nelson, C.R., and A.F. Siegel (1987). Parsimonious Modeling of Yield Curves. Journal of Business
60(4): 47389.
Senado de la República de Chile (2000). Diario de sesiones del senado, publicación oficial
legislatura 343ª, extraordinaria. Sesión 13ª, en martes 28 de noviembre de 2000.
http://sil.senado.cl/docsil/diar3620.doc/: 1113.
Senado de la República de Chile (2004). Law 19934, February 21, 2004.
http://sil.senado.cl/pags/index.html, Bulletin number 114805.
Superintendency of Pension Fund Administrators (2003). The Chilean Pension System. Fourth
Edition, Santiago, Chile. Publisher: Superintendencia de Administradoras de Fondos de Pensiones.
http://www.safp.cl/sischilpen/english.html.
Superintendencia de Valores y Seguros (2002). El sistema chileno de pensiones, Fifth Edition.
Chapter 6: Principales resultados. http://www.safp.cl/sischilpen/espanol.html.
Walker, Eduardo. (2003). Determinación de la cartera de inversión óptima de una AFP. Mimeo,
Business School, Pontificia Universidad Católica de Chile.
14
Figure 1: Annuity Costs, Market Rates, and Interest Rates
A. Annuity Costs and Market Rates
115
110
)02 105
CR Annuity
100 co
(Petrae .09 stindex
.08 95
fre .07
skiR .06 (CRV)
.05
.04
.03
93 94 95 96 97 98 99 00 01 02 03
CRV PRC20
Note: The annuity cost index (CRV) is calculated as the scaled present value of expected future
payments, using the RV85 mortality table for a 65yearold male pensioner with no beneficiaries, and
"adjusted" annuity rates (TVA). Adjusted rates correspond to the effective internal rate of return paid by life
insurance companies, which excludes from the premium paid by the annuitant the commissions paid to the
brokers. PRC20 corresponds to the Central Bank longterm indexed bond interest rate.
B. Interest Rates
.02
.01
d
an)AVT(yti .00
.01
.09 Sp
.02
nu .08 read
an setartsreetni)02CR .03
.07
edt (Pe
usdjA rre .06
skri .05
.04
.03
93 94 95 96 97 98 99 00 01 02 03
TVA PRC20(2) TVAPRC20(2)
Note: TVA corresponds to the "adjusted" annuity rate using the RV85 mortality table for a 65year
old male pensioner with no beneficiaries. Adjusted rates correspond to the effective internal rate of return paid
by life insurance companies, which excludes from the premium paid by the annuitant the commissions paid to
the brokers. PRC20 corresponds to the Central Bank longterm indexed interest rate.
15
Figure 2: Annuity Rates (TV) and Adjusted Annuity Rates (TVA)
.009
.008
.007
.006
setratsreet .070
.005
.065
.004 Spread
.060
In .003
.055
.050
.045
.040
93 94 95 96 97 98 99 00 01 02 03
TVA TV TVATV
Note: TVA corresponds to the effective internal rate of return paid by insurance companies, which excludes
from the premium paid by the annuitant the commissions paid to the brokers. TV is the effective interest rate
(IRR) obtained by the annuitant, calculated using the total premium paid and the expected future payments
received. In all cases, we use the RV85 mortality table for a 65yearold male pensioner with no beneficiaries.
16
Figure 3: Annuity Payment Profile
Expected monthly payment (UF)
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0

0 5 10 15 20 25 30 35 40
Year
Note: The profile is for a male, age 65, no descendants, premium of 1000 UF (see footnote 10),
market rate 5.07 percent, using the RV85 mortality table.
17
Figure 4: Estimated Elasticity of Adjusted and Unadjusted Annuity Rates to Changes in the
Reference Riskfree Rate
A. Adjusted Annuity Rates (TVA)
1.0
0.8
0.6
0.4
0.2
0.0
93 94 95 96 97 98 99 00 01 02 03
LT_ELAST P1 P2
Note: Estimated equation: TVAt = a + TVAt 1+b1PRC20t +b2PRC20t
1 2+t . The figure
shows rolling estimations of (b1 + b2 ) /(1 ) (LT_ELAST), pvalues of the restriction (b1 + b2 ) = 0 (P1)
and of the restriction (b1 + b2 ) = (1 ) (P2)
B. Unadjusted Annuity Rates (TV)
1.0
0.8
0.6
0.4
0.2
0.0
93 94 95 96 97 98 99 00 01 02 03
LT_ELAST P1 P2
Note: Estimated equation: TVt = a + TVt 1+ b1PRC20t +b2PRC20t
1 2 +t . The figure
shows rolling estimations of (b1 + b2 ) /(1 ) , pvalues of the restriction (b1 + b2 ) = 0 (P1) and of the
restriction (b1 + b2 ) = (1 ) (P2)
18
Figure 5: Estimated Monthly Annuity Cost and Internal Rates of Return
A. Estimated Monthly Annuity Cost
140
130
120
110
100
90
93 94 95 96 97 98 99 00 01 02 03
CRV CRV_E0
Note: Calculations of the indexes representing the cost of an annuity are based on the full term structure of
interest rates (CRV_E0) and on the effective interest rates paid by LICOs (CRV).
B. IRR of the Estimated Annuity Cost (TVA_E0) versus PRC20
.09
.08
.07
.06
.05
.04
.03
93 94 95 96 97 98 99 00 01 02 03
TVA_E0 PRC20
Note: Internal rates of return of the annuity cost for LICOs estimated using the full term structure of interest
rates (TVA_E0) versus the long term risk free rate.
19
Figure 6: Relationship between Adjusted Annuity Rates and Commissions
6
4
2
V) 0
TA C2
2
(TVnoissimoC 1.0
4
0.8 andttest
0.6
0.4
0.2
2001:01 2001:07 2002:01 2002:07 2003:01 2003:07
AGF_TVAAGF_TV INTERR_TVAINTERR_TV
BICE_TVABICE_TV ISELA_TVAISELA_TV
CDS_TVACDS_TV MAPF_TVAMAPF_TV
CHILCON_TVACHILCON_TV METL_TVAMETL_TV
CIGNA_TVACIGNA_TV OHIO_TVAOHIO_TV
CNA_TVACNA_TV PRINC_TVAPRINC_TV
CNLIFE_TVACNLIFE_TV RNAC_TVARNAC_TV
CONSO_TVACONSO_TV SANTA_TVASANTA_TV
CONSTR_TVACONSTR_TV COM_COEF (C2)
EUROAM_TVAEUROAM_TV COM_TESTT
ING_TVAING_TV
Note: Moving Quartlerly Panel Regression of the equation TVAit = c0+c1pit+c2(TVAitTVit). The
acronym before the symbol "_" represents a specific life insurance company. In each case the difference
between "adjusted" (TVA) and unadjusted (TV) annuity rates is plotted. "COM_COEFF" and
"COM_TESTT" represent the regression slope coefficient (c2) and the corresponding ttest, respectively.
20
Table 1: Annual Averages and Descriptive Statistics
A. Annual Averages (percent)
Annuity Adjusted
rate  Commission annuity rate  PRC20
Year TV (1) (1) TVA (2)
1993 5.17 4.26 5.74 6.83
1994 4.77 4.26 5.33 5.93
1995 4.84 4.84 5.48 6.20
1996 5.10 4.98 5.77 6.17
1997 5.01 5.33 5.72 6.45
1998 5.56 5.28 6.29 7.32
1999 5.33 5.95 6.15 6.54
2000 5.37 5.90 6.19 6.42
2001 5.24 3.94 5.77 5.53
2002 4.93 2.67 5.28 4.56
2003a 4.18 2.70 4.51 3.91
Average 5.07 4.61 5.56 6.05
a.Until August.
Sources: (1) Superintendencia de Valores y Seguros; (2) Bolsa de Comercio de Santiago.
B. Descriptive Statistics
TVA
Statistic PRC20 TVA PRC20(2) TVATV
Mean 0.060256 0.056862 0.003916 0.006229
Median 0.061400 0.057390 0.004960 0.006664
Maximum 0.084600 0.065279 0.010017 0.008786
Minimum 0.036700 0.043670 0.019999 0.003266
Standard 0.009409 0.004881 0.005597 0.001623
deviation
Skewness 0.790931 0.790634 0.222732 0.560318
Kurtosis 3.631803 3.578910 3.054669 2.217609
JarqueBera 15.11179 14.76848 1.049101 9.728959
Probability 0.000523 0.000621 0.591821 0.007716
Sum 7.532000 7.107753 0.489547 0.778576
Sum of squared 0.010979 0.002954 0.003884 0.000326
deviations
Observations 125 125 125 125
Note: TV corresponds to the internal rate of return obtained by the annuitant. TVA is the adjusted
annuity rate paid by the insurance companies, which deducts broker commissions from the premium. Both
rates are estimates using the RV85 mortality table for a 65yearold male with no descendants. PRC20 is the
interest rate of an indexed central bank annuitytype bond.
21
Table 2: Empirical Duration and Convexity of Annuities, LongTerm Interest Rates
and Causality Tests
A. Annuity Duration and Convexity
Dependent variable: DLOG(CRV)
Variable Coefficient tstatistic
D(TVA) 10.009 1610.78
D(TVA)*TVA(1) 44.042 411.10
D(TVA)^2 21.950 69.919
C 8.98E09 0.0196
B. Duration and Convexity of a Total Return (index of investing in PRC20)
Dependent variable DLOG(IPRC20)
Variable Coefficient tstatistic
D(PRC20) 9.7152 71.321
D(PRC20)*(PRC20(1)) 32.047 15.668
D(PRC20)^2 27.597 5.7995
C 0.0048 70.483
C. Granger Causality
Sample: 1993:01 2003:12
Hypotheses Obs FStatistic Probability
PRC20 n.c. TVA (Lags: 3) 124 34.9951 3.2E16
TVA n.c. PRC20 0.40836 0.74728
D(PRC20) n.c. D(TVA) (Lags: 2) 123 49.0612 2.9E16
D(TVA) n.c. D(PRC20) 0.41652 0.42634
Note: TVA corresponds to the "adjusted" annuity rate using the RV85 mortality table for a 65year
old male pensioner with no beneficiaries. Adjusted rates correspond to the effective internal rate of return paid
by life insurance companies, which excludes from the premium paid by the annuitant the commissions paid to
the brokers. PRC20 corresponds to the Central Bank longterm indexed interest rate.
22
Table 3: LongTerm Elasticity Estimation
A. Relationship between Interest Rate Changes
Dependent variable: D(TVA)
Sample 1993:05 2003:08
Observations: 124
Variable Coefficient Standard error tstatistic Probability
D(TVA(1)) () 0.3452 0.0657 5.2542 0,0000
D(PRC20(1)) (b1) 0.1599 0.0218 7.3078 0,0000
D(PRC20(2)) (b2) 0.1449 0.0245 5.9108 0.0000
CONSTANT (a) 0.0000 5.28E05 0.0828 0,9341
Rsquared 0.5922 Average Dependent 0.000118
Variable
Adjusted Rsquared 0.5820 Standard deviation of 0.000895
dependent variable
Regression standard 0.0005 Akaike information 12.04
error criterion
Sum squared residuals 4.01E05 Schwarz criterion 11.95
Log likelihood 750.56 Fstatistic 58.10
DurbinWatson 2.1469 Probability(Fstatistic) 0.0000
Note: Results of estimating TVAt = a + TVAt 1+b1PRC20t +b2PRC20t
1 2 +t .
TVA corresponds to the "adjusted" annuity rate using the RV85 mortality table for a 65yearold male
pensioner with no beneficiaries. Adjusted rates correspond to the effective internal rate of return paid by life
insurance companies, which excludes from the premium paid by the annuitant the commissions paid to the
brokers. PRC20 corresponds to the Central Bank longterm indexed interest rate.
B. Hypotheses
b1+b2 = 0
Test statistic Value DF Probability
Fstatistic 97.235 (1. 120) 0.0000
Chisquare 97.235 1 0.0000
b1+b2 = 1
Test statistic Value DF Probability
Fstatistic 30.212 (1. 120) 0.0000
Chisquare 30.212 1 0.0000
23
Table 4: LongTerm Elasticity versus Interest Rate and Commission Levels
Dependent variable: LOG(LT_ELAST)
Method: Generalized Method of Moments
Sample: 1995:02 2003:08
Observations: 103
Variancecovariance adjusted using a Bartlett kernel with fixed bandwidth (4),
no prewhitening
Simultaneous weighting matrix and coefficient iteration
Instruments: PRC20(2) TVATV C
Variable Coefficient Standard error tstatistic Probability
PRC20(2) 9.5417 6.0331 1.5815 0.1169
TVATV 154.47 30.911 4.9972 0.0000
C 0.6744 0.2191 3.0773 0.0027
Rsquared 0.7288 Average Dependent 0.8796
Variable
Adjusted Rsquared 0.7234 Standard deviation of 0.4132
dependent variable
Regression standard 0.2172 Sum squared residuals 4.7216
error
DurbinWatson 0.2953 Jstatistic 4.15E29
Note: Results from regressing the rolling coefficient (b1+b2)/(1) against longterm interest rates
and commissions. TVA (TV) corresponds to the "(un)adjusted" annuity rate using the RV85 mortality table
for a 65yearold male pensioner with no beneficiaries. Adjusted rates correspond to the effective internal rate
of return paid by life insurance companies, which excludes from the premium paid by the annuitant the
commissions paid to the brokers. PRC20 corresponds to the Central Bank longterm indexed interest rate.
Unadjusted rates correspond to the internal rate of return received by the pensioners.
24
Table 5: Adjusted Annuity Rates versus Commissions (Panel Regressions)
Simple period: 2001:1  2003:10 (34 months)
Different LICOs: 21
Total number of obs. (unbalanced panel): 553
A. Explanatory Variable: Broker Commission (X=C)
Regression Type
Simple* Lagged Dependent* Fixed Effects* Random Effects
Constant 0.7888 0.2103 0.7713
ttest 20.5494 5.5699 13.8779
Comission (C) 0.1429 0.0304 0.1810 0.1778
ttest 18.2339 3.6939 25.1292 22.2234
Market share (p) 0.0797 0.2547 2.4068 2.1209
ttest 0.3564 1.4179 7.9998 6.7970
TVAit1PRC20t3 0.6670
ttest 22.977
Rsquared 0.3197 0.6318 0.5990 0.5976
Adj. Rsquared 0.3172 0.6297 0.5823 0.5962
Regression standard
error 0.2600 0.1797 0.2033 0.1999
Log likelihood 38.1528 160.1250 107.9990
DurbinWatson 0.6531 2.0471 1.0969 1.0846
Avg. Dep. Var. 0.3019 0.3241 0.3019 0.3019
Std. Dev. Dep. Var. 0.3146 0.2954 0.3146 0.3146
Sum of Squared Resids. 37.1687 16.3587 21.9088 21.9821
F Statistic. 129.2222 40.4762 35.9848
Prob(Fstatistic) 0.0000 0.0000 0.0000
B. Explanatory Variable: X=TVATV
Regression Type
Variable Simple* Lagged Dependent* Fixed Effects* Random Effects
Constant 0.7816 0.2110 0.7604
ttest 21.0700 5.6590 13.9642
Commission (TVATV) 1.2117 0.2608 1.5346 1.5098
ttest 18.8536 3.7694 25.8782 23.6732
Market share (p) 0.1224 0.2472 2.3835 2.1123
ttest 0.5615 1.3745 8.1120 6.9687
TVAit1PRC20t3 0.6620
ttest 22.396
Rsquared 0.3385 0.6321 0.6236 0.6224
Adj. Rsquared 0.3361 0.6301 0.6080 0.6210
Regression Standard 0.1796
Error 0.2563 0.1970 0.1937
Log likelihood 30.3765 160.40 125.5211
DurbinWatson 0.6735 2.0423 1.1618 1.1504
Avg. Dep. Var. 0.3019 0.3241 0.3019 0.3019
Std. Dev. Dep. Var. 0.3146 0.2954 0.3146 0.3146
Sum of Squared Resids. 36.1379 17.043 20.5635 20.6296
F Statistic. 140.7520 302.51 39.9151
Prob(Fstatistic) 0.0000 0.0000 0.0000
*Variancecovariance matrix adjusted by heteroskedasticity and autocorrelation using White
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Note: results of estimating the equation TVAit  PRC20t 2= co( +c1pit +c2Xit +uit with two
i)
specifications for X: broker commission as percentage of the insurance premium and expressed as the
difference between adjusted and unadjusted annuity rates. TVA (TV) corresponds to the "(un)adjusted"
annuity rate using the RV85 mortality table for a 65yearold male pensioner with no beneficiaries. Adjusted
rates correspond to the effective internal rate of return paid by life insurance companies, which excludes from
the premium paid by the annuitant the commissions paid to the brokers. PRC20 corresponds to the Central
Bank longterm indexed interest rate. Unadjusted rates correspond to the internal rate of return received by the
pensioners.
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