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company by total technical reserves in the system. Note that technical reserves account for a large share of the balance sheet and also constitute a good proxy for scale.

The average premium for each company, AP, is directly available from the SVS databank, broken down by class of annuity, including old age AP(OLD) and early retirement policies, AP(EARLY). The quarterly figure is simply the average of the monthly figures. The commission rate was computed by dividing the payments to brokers by the total premium. Finally, the Herfindahl index was constructed on the basis of company premia (or annuity sales). As in the case of average premium, the Herfindahl index was also constructed separately for early retirement policies, HER(EARLY), and normal old age policies, HER(OLD).

# **5. Econometric Results**

The econometric analysis of the annuity rate involves the following preliminary steps. First, the series are tested for non-stationarity through a set of unit root tests, and a solution to deal with non-stationarity is elaborated. Second, several specification tests are conducted, involving pooled OLS versus Fixed Effects, pooled OLS versus Random Effects, and Fixed versus Random Effects. Third, after identifying the best estimating model, a test of autocorrelation is performed to select an appropriate robust variancecovariance matrix estimator and conduct inference about estimated coefficients.

# 5 **_.1. Unit Root Testing_**

Table 4 presents a summary of the unit root tests performed for each series. All the tests considered have a unit root process as the null hypothesis, either a common one for all the companies or a specific process for each company. The figures in Table 4 correspond to asymptotic p-values for each test statistic. Therefore, a number lower than 0.05 means that the null hypothesis of a unit root is rejected at the 5 percent significance level.

The first test statistic (LLC) is due to Levin, Lin, and Chu (2002). In this case, the null hypothesis is a common unit root process for all the cross-section units. The statistic is based on a basic ADF (Augmented Dickey-Fuller) specification for each cross-section, but with the same AR(1) coefficient for all of them. The test is a modified t-statistic for the coefficient of interest (1 minus the autoregressive parameter) from a pooled regression involving standardized variables. For the specification of the ADF regressions, an information criterion is required (such as AIC or BIC) to select the optimum number of lags and capture the autocorrelation in the series. In addition, to modify the standard t- statistic, a kernel-based spectral density estimator at frequency zero is computed (by using the corresponding bandwidth truncation selection method). Under the null of a common unit root process, the final test statistic is asymptotically distributed as N(0,1).

The second statistic (IPS) was proposed by Im, Pesaran, and Shin (2003). In this case, the null hypothesis is a specific unit root process for each individual cross-section unit. To compute the unit root test statistic, an ADF regression is specified for each cross-section, and then the average t-statistic for the individual coefficients is adjusted by using the expected mean and variance of the individual t-statistics. As in the previous test, an optimum lag order is required for the construction of the ADF regressions. The IPS test also has an asymptotic N(0,1) distribution.