# **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 self-financed 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.<sup>1</sup> Because many pensioners opt for annuities (more than 60 percent in the Chilean case),<sup>2</sup> 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 risk-free 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.<sup>3</sup> 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, <mark>figure 1.A</mark> shows the time trend of the estimated inflation-adjusted cost of an annuity for a 65-year-old pensioner with no beneficiaries and compares it to a 20-year central bank interest rate (PRC20).<sup>4</sup> For many years this was the longest maturity interest rate, and (as we will argue later) it adequately represents risk-free 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 interest-rate changes yields a slope coefficient of –2.6. These coefficients are unexpectedly low. <mark>Figure 1.B</mark> offers a tautological explanation for these findings: annuity interest rates start below the

> 1 Lump-sums 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” (inflation-adjusted) interest rates.