Appendix I: Appendix

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Multivariate results

The descriptive results presented above do not take into account differences in the replacement rates of male retirees attributable to socio-economic characteristics, aside from pension coverage. In their original analysis, Ostrovsky and Schellenberg (2009) run an Ordinary Least Squares (OLS) regression model in which the earnings replacement rates achieved by retirees in 2006 is the dependent variable, and pension status, immigration status, marital status, years since retirement, and 1989-1991 earnings are included as explanatory variables. Separate regression models were run for retired men in each of the five 1989-1991 earnings quintiles. Selected results from that model—specifically, the coefficients associated with pension coverage—are presented in Panel 1 of Text Table 1. As noted earlier, RPP coverage is not significantly associated with earnings replacement rates in the original model. 1  This is also the case when earnings replacement rates in 2005-2007 are included as the dependent variable in the model (Panel 2).

However, when a dependent variable is a positive ratio (such as is the case with earnings replacement rates), economists and statisticians often prefer to use the log of the dependent variable (Y) in regression models. There are several reasons for doing so. First, if there are outliers in the distribution of the dependent variable, their influence on coefficient estimates will be considerably smaller when the variable in the regression is log(Y) rather than Y. Second, the distribution of log(Y) is often more likely than the distribution of Y to resemble a normal distribution than the distribution of Y. The normality of log(Y) improves the efficiency of estimates, and many statistical tests rely on the assumption of such normality. Finally, if the variable is log(Y), coefficient estimates can be interpreted as percentage changes in Y associated with marginal changes in the explanatory variables.

The results from the OLS regression, with the log of replacement rates included as the dependent variable, are shown in Panels 3 and 4 of Text Table 2. Considering log replacement rates in 2006, there is a consistent (across quintiles) and significant correlation with pension coverage, in the range of 6% to 10% among retirees in Q2, Q3, and Q4. The correlation is slightly weaker, in the range of 5% to 9% among retirees in Q2, Q3, and Q4, when log replacement rates over 2005-2007 are included as the dependent variable in the model.

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