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From this aspect, a higher annuity premium should lead to lower annuity rates (when annuity rates are measured with the same mortality table, as is the case). However, life insurance companies value customers with larger annuity premiums, just like commercial banks value customers with larger deposits, because they involve lower unit costs and higher unit profits for the providers. Therefore, annuity providers may be willing to pay higher annuity rates for larger premiums, just like banks pay higher interest rates for larger deposits. In fact, some annuity providers seem to specialize in the upscale annuity market, just like some banks specialize in the corporate sector or in the upscale consumer market, avoiding the higher costs associated with retail banking, for the same levels of scale, and being able to pay higher rates for higher income consumers.<sup>11</sup> The variable CR measures the commission rate, defined as the ratio of broker commissions to the premium. In Chile as in other countries, annuities can be sold either by sales staff, which are employees of an insurance company, or by independent brokers. As shown in section 2, commission rates increased continuously in the 1990s and then declined rapidly in the early 2000s as a result of political and supervisory pressures. An increase in the commission rate has an unambiguously negative impact on the annuity rate, due to several factors operating both on the side of demand and the side of supply of annuities—under the heuristic model outlined above a higher commission rate leads simultaneously to an expansion in the demand and a contraction in the supply of annuities. These effects are further elaborated below.

The level of commissions reflects the broker’s efforts to search for new customers and induce eligible workers to retire. In general, it is likely that the intensity of broker activity replaces the annuity rate as marketing device, leading eligible workers to buy an annuity without a complete market search. In some cases the broker may provide services which are valued by the consumer, such as the verification of the conditions for retirement and all the required paperwork. The eligible worker may be more willing to sacrifice market search when these services are provided. There is an even more direct and powerful substitution effect between the commission rate and the annuity rate when the commission is partly shared with retiring workers. The illegal practice of sharing the commission was a loophole in the system that allowed workers _de facto_ access to a modest lump-sum. Several of these workers were probably willing to accept a lower annuity rate in exchange for such an informal lump-sum.

An increase in commission leads to a contraction in supply because it implies an increase in company’s costs. The company needs to issue an annuity based on a smaller premium net of commissions. If interest rates, operating costs, and all other variables remain constant, the only way to preserve profit margins is to reduce annuity payments and the annuity rate. From another angle, the company will try to maintain constant the adjusted annuity rate, which is the annuity rate plus the capitalized value of the commission.

Finally, the variable HER captures the degree of industry concentration, as measured by the Herfindahl index. An increase in the Herfindahl index due to a reduction in the number of market participants should reflect the greater monopoly power of incumbents

> 11Most studies of economies of scale in banking and other areas of the financial sector involve the estimation of a cost function that includes a measure of scale such as assets or the number of accounts, complemented by a variable measuring the average balance.  Average costs are shown to decline both with larger scale and larger average balances.