offers good asset-liability matching opportunities and is a useful reference point in the sense that it should be used to set the rates of the _marginal_ annuities.<sup>9</sup> With this in mind, the evidence presented in figure 1.B indicates an interesting evolution of the annuity-rate spreads (defined as the annuity rate minus the risk-free 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.<sup>10</sup> 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 interest-rate 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**

<mark>Figure 3</mark> shows the payment profile for a 65-year-old pensioner with no beneficiaries, for a premium of 1,000 UF<sup>11</sup> and a real interest rate of about 5 percent per

> 9 See Data section, Annuity Cost Behavior.

> 10 For example, in the US for 10-year 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 <u>www.bondsonline.com</u> .

> 11 The UF (Unidad de Fomento) is the indexed (inflation-adjusted) 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+ _inf_ t-1), where _inf_ t-1 is the inflation rate of the previous month. The quantity Ch$17,000( _inf_ t-1)/ _n_ , where _n_ is the number of days in a month, is successively added to the previous day’s value of the UF.

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