Appendix III: Sensitivity analysis

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Variation in the interest rate

The baseline specification used in the paper assumes a 3% constant return. This appendix replicates the analysis using 1.5% as the lower bound and 5% as the upper bound of the interest rate in order to test the sensitivity of the results to changes in the assumption. The tables below show that the main conclusions are robust, regardless of the choice of interest rate.

Alternative account of house value

This section provides an alternate method of deriving the potential income arising from housing equity. Here, it is assumed that households sell their dwelling (rather than taking out a reverse mortgage) and convert the proceeds into a lifetime annuity. Because these households would then need to rent, the income they receive is obtained by estimating the difference between the value of the income stream derived from this annuity and the implicit rental service from their property. Imputed rents, by housing value, are taken from Brown et al. (2010).

Text tables 5 and 6 show that the results are not very sensitive to this assumption. Taking housing into account still significantly increases the relative financial position of retirement-age households, although the effect is slightly smaller.

After-Tax Income

The after-tax values of the income measures are obtained as follows:

1. Income taxes, which should be deducted from total income, are derived by calculating the median tax rate for each of the four household types at different income ranges. ¹  These tax rates are applied to the taxable portion of the wealth-adjusted income.
2. The housing services obtained from Brown et al. (2010) are considered as non-taxable income.
3. The annuity derived from the home equity (via reverse mortgage) is only partially taxed. The taxable portion is determined by an "exclusion ratio" obtained by dividing the value of the home equity by the present value of the total amount of annuities that will be paid to the households over their lifetime. ² 
4. The annuity payments obtained from liquidating non-housing assets are assumed to be taxable in their entirety. This is because the assets when liquidated will face some capital gains taxes, but the amount is difficult to calculate. To compensate for the overestimation of the amount available for purchasing an annuity, the tax rate is not reduced as it is for housing (where capital gains taxes are less important or non-existent in most cases).

For seniors, additional calculation steps are required. Old Age Security (OAS) and Guaranteed Income Supplement (GIS) benefits are subtracted from gross total income. The taxable portion of the income stream obtained from annuitizing net worth is then added. Given the resulting gross income levels, the OAS/GIS payments to which each household is entitled are then adjusted. ³  The tax rates are applied to the totals obtained (excluding GIS).

Text tables 7 and 8, which replicate Tables 4 and 5 using after-tax income, show that the changes across the distributions from income to wealth-adjusted income are more favourable to senior households. Taking taxation into account reinforces the main results obtained on a before-tax basis.

Calculations using number of family members to derive adult-equivalent scale

This section reproduces Tables 2, 4 and Text table 7 using the number of household members rather than the square root of the number of household members for comparisons across age groups. This technique implicitly assumes no economies of scale in consumption.

Median income levels

Text table 12 reproduces Table 4 using medians rather than means. Based on medians, the income of households headed by 65- to 74-year-olds increases 31% overall when the annuitized value of the principal residence is taken into account, which is almost identical to the results obtained using mean income levels.

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