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and be accompanied by a contraction in aggregate supply and ultimately a lower annuity rate.

# **4. The Data**

The sample is based on pooled quarterly data of active annuity providers over the 19932003 period. The sample starts in the first quarter of 1993 and ends in the third quarter of 2003, yielding a total of 43 quarters. The number of active providers ranged from 17 to 24 during the period under examination. This yields a total of 693 observations. The time unit is the quarter because of some limitations on monthly data. First, balance sheet data on the providers such as the portfolio composition, reserves, and leverage are only available quarterly. Second, some series such as annuity rates and commissions are available monthly, but suffer from discontinuities, due to the fact that many active providers do not sell annuities every month. All the flow variables were constructed by computing averages of the monthly figures within the quarter. The stock variables are end of quarter figures. The Insurance Supervisory Agency ( _Superintendencia de Valores y Seguros_ - SVS) was the source of most of the raw data used in the analysis. Market interest rates were obtained from the Central Bank of Chile.

ARj,t is the average annuity rate of each company during the quarter, computed by the average of monthly rates, weighted by the premiums. Each company needs to calculate the annuity rate of every annuity issued (the _tasa de venta_ ), based on a regulated mortality table (which was the RV-85 during the sample period).<sup>12</sup> The SVS databank provides a breakdown of annuity rates by type of policy, i.e., early retirement, normal age retirement, disability, and survivors of deceased members. The empirical analysis focuses on the annuity rates for early retirement policies AR(EARLY), and normal age retirement policies, AR(OLD).

The risk-free rate, RF, was measured by the interest rate on 20 year indexed bonds issued by the Central Bank of Chile (PRC-20). The instrument was discontinued in 2002, but secondary market quotations are available after that date and were used to complete the series. Monthly data on interest rates on corporate and mortgage bonds are available from the SVS, but only since 1995, and reflecting instruments with varying maturities, possibly resulting in some consistency problems. Estimates of the returns of other risky assets such as equity can be obtained, but there are no direct data on the returns on foreign assets held by annuity providers.

The share of other fixed income assets, SOFI was measured by the combined share of corporate bonds, mortgage bonds, endorsable mortgages, and other fixed income assets in the total fixed income portfolio. The share of other assets, SOA, was measured by the combined shares of variable income and foreign assets in the total portfolio. Leverage, LEV, was measured by the ratio of technical reserves to equity. The duration mismatch, MIS, was measured by a coefficient reported by companies to the supervisor, under capital rules.<sup>13</sup> Market share, MSHARE, was measured by dividing the technical reserves of each

> 12Companies are free to use their own mortality tables for pricing annuities, but they have to report annuity rates based on regulated mortality tables.  During the period of analysis annuity rates were calculated and reported with the RV-85.  The calculation of annuity rates with the updated RV-04 would produce primarily a level effect and would not change the results significantly.

> 13 Capital rules for annuity providers penalize duration mismatches, as mentioned before. See Rocha and Thorburn (2006) for a detailed description of capital rules.