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More research on MWRs is merited, because price dispersion in March of 2005 still seemed significant, and a closer inspection of the sample revealed several cases where the annuitants’ age, gender, premium, and terms of the annuity purchased were similar, but MWRs were different. As mentioned before, there is separate evidence that the new quotation system has enhanced the transparency of the Chilean annuities market and has ensured that pricing is effectively based on the best quotes. The systematic computation of MWRs would provide further evidence as to whether the new quotation system is indeed eliminating market inefficiencies and reducing differences that cannot be explained by individual risk characteristics.

# **6. Comparisons with Other Empirical Studies**

# **_6.1. Comparisons with MWR Estimates for Other Countries_**

Comparing MWRs in Chile with those estimated by other researchers for other countries provides many additional insights into the performance of the Chilean annuities market. Such a comparison is done in two steps. The first involves a comparison of MWRs calculated with cohort annuitant tables and the risk-free rate. As mentioned before, this is the measure that reflects most accurately the value of the annuity to the average consumer (the annuitant), and the one most commonly used for international comparisons. The second step involves a comparison of MWRs also calculated with the cohort annuitant table, but discounted with the corporate bond rate. This measure captures more accurately the cost of the annuity to providers.

Table 15 shows a selected number of MWRs in Chile, estimated for annuities issued in March 2004. The MWRs are computed with the most updated cohort annuitant table (the cohortized RV-04) and two discount rates – the risk-free rate and the corporate bond rate.<sup>13</sup> Tables 16 and 17 summarize the results obtained for other countries by other researchers, using similar parameters. Most MWRs computed for other countries are nominal, i.e., they related to nominal annuities. This reflects the absence of indexed annuities in most countries – the UK is the only country in this sample that has developed indexed annuities as well. Table 16 also shows indexed MWRs for the US, based on quotations of indexed annuities by a life insurance company (ILONA). These annuities have not been sold in the US market, but are also shown for purposes of illustration.

As shown in Tables 15 and 16, the average MWRs estimated for Chile are higher than the average nominal MWRs estimated for all other countries, across all classes of annuitants. The differences between the Chilean MWRs and the MWRs of indexed annuities in the UK and the US are striking, amounting to 20 percent. The average MWRs in the US and UK decline with age, unlike in the Chilean case. The MWRs for males and females tend to be very similar in other countries, unlike in the Chilean case. MWRs of joint annuities are very similar or lower than single annuities, more similar to the pattern in Chile.

> 13 The year 2004 was chosen because it was the last year for which MWRs were computed both with the risk-free rate and the higher corporate bond rate.