Tax Expenditures and Evaluations: 2001: 6

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Tax Expenditures and Evaluations: 2001: 6
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4. Estimates and Projections of the Federal Tax Expenditure

Table 6 presents the estimates of the present-value tax expenditure for 1998 using various portfolio alternatives. These results are calculated using the long-term government bond rate as the discount rate. This table highlights the effect of the different tax treatments for different types of returns. If the non-tax-assisted portfolio consisted entirely of interest-bearing assets, then the tax expenditure would be $8 billion, or $0.19 per dollar of contributions.¹⁹ If the portfolio consisted of only dividend-bearing assets, the tax expenditure would be $4.7 billion, or $0.11 per dollar of contributions. If the portfolio were the base case defined in Section 3, then the tax expenditure would be $7.1 billion, or $0.17 per dollar of contributions. The results shown in Table 6 also indicate that the tax expenditure estimate is not very sensitive to the capital gains holding period.²⁰ This is because of the low weight given to equity in the portfolio.

Table 6
1998 Present-Value Tax Expenditure Estimates for Various Portfolios
(Using Government Bond Rate as the Discount Rate)


	Gross tax expenditure	Tax expenditure per dollar of contributions

	($ billions)	($)
100% interest	8.0	0.19
100% capital gains (6.3-year rollover)	6.1	0.15
100% capital gains (10-year rollover)	5.8	0.14
100% dividends	4.7	0.11
Base case portfolio	7.2	0.17

If the market rate of return (6.4 per cent) were used as the discount rate rather than the long-term government bond rate (5.5 per cent), the estimate for the portfolio would rise from $7.1 billion to $8.2 billion. Thus, the tax expenditure estimate would rise from $0.17 per dollar of contributions to $0.20 per dollar of contributions.

Table 7 provides both present-value and cash-flow estimates for the years 1996 to 1998 and projections for the years 1999 to 2003.²¹ The two approaches use different definitions of the TARS tax expenditure and therefore differ in both level and trend. The present-value tax expenditure per dollar of contributions falls from $0.17 in 1998 to $0.14 in 2001. This reflects the fall in marginal tax rates projected for this period because of the measures contained in the 2000 budget and the October 2000 Economic Statement and Budget Update. The cash-flow estimates peak at $0.38 per dollar of contributions in 1999, largely due to an interest rate spike in that year. They fall sharply to $0.30 per dollar in 2001, reflecting both the fall in tax rates and a rise in withdrawals relative to contributions.

Table 7
Tax Expenditure Estimates and Projections, 1996-2003


			Present-value estimates		Cash-flow estimates
	Year	Total contributions	Gross tax expenditure	Tax expenditure per dollar	Gross tax expenditure	Tax expenditure per dollar

		($ billions)	($ billions)	($)	($ billions)	($)
Estimates	1996	43.4	7.4	0.17	14.8	0.34
	1997	44.9	7.6	0.17	15.2	0.34
	1998	41.6	7.1	0.17	13.6	0.33

Projections	1999	43.4	7.2	0.17	16.4	0.38
	2000	45.4	7.3	0.16	14.2	0.31
	2001	47.6	6.9	0.14	14.1	0.30
	2002	49.9	7.2	0.14	14.3	0.29
	2003	52.3	7.5	0.14	14.4	0.28

If parameters such as tax rates and interest rates are constant in the future, the present-value estimate per dollar of contributions will remain relatively stable, while the cash-flow estimate will decline over time as the pension and RRSP system matures and members of the baby boom generation begin to draw down their savings. The results in Table 7 point towards this trend since the cash-flow estimate per dollar of contributions falls between 2001 and 2003 while the present-value estimate remains constant.

5. Conclusion

This paper describes the various issues involved in developing a present-value tax expenditure estimate for TARS programs. The key issues in this process are the choice of the discount rate and the development of a withdrawal distribution and investment portfolio. We have used an empirical approach in the development of both the withdrawal distribution and investment portfolio. Based on the analysis in Section 3, we have chosen the long-term government bond rate to be the discount rate used to calculate the estimates.

The present-value estimates complement the cash-flow estimates currently published by the Department. The cash-flow method gives estimates of the net revenue cost of providing a deduction on current-year contributions, not taxing the current-year investment income earned by past contributions, and taxing current-year withdrawals. The present-value method estimates the present value of taxes forgone today and in the future as a result of contributions made in a given year. Each measure has its advantages, and together, the cash-flow and present-value estimates provide more information on the revenue cost of tax-assisted retirement savings programs than was available previously.

Appendix: Alternative Approach to Estimating the Present-Value Tax Expenditure

In the main text we use a method that focuses on the tax cost to the Government over time (the "tax-cost" method). This section describes another approach that has been used in the literature to obtain a present-value tax expenditure estimate of TARS: the "benefit" method. This approach views the problem from the perspective of the individual. It assumes that the present value of the net proceeds to the individual is equal to the present value of the costs to the Government. But this is only true when the rate of return and the discount rate are equal. Therefore, this method can be used only if the discount rate is the same as the rate of return.²² We illustrate this method with an example similar to that used to describe the method in the main text (that is, we assume that marginal tax rates vary with age, the rate of return is constant and any non-sheltered income is taxed as interest income).

The net proceeds in a future year of saving a dollar in a tax-assisted plan from age M to age N are given by:

(A1)

where NP_TA is the net (or after-tax) proceeds of tax-assisted saving, C is the amount saved in pre-tax dollars, i is the nominal rate of return, M and N are the ages when the contribution is made and withdrawn (with interest) respectively, and t_N is the marginal tax rate at the time of withdrawal. The factor (1+ i)N–M indicates that no tax is paid on investment income as it accrues in the plan. The factor (1–t_N) indicates that the gross proceeds are subject to tax when withdrawn from the plan in year N.

In contrast, the net proceeds in a future year of saving the after-tax amount from one dollar of pre-tax income in a non-tax-assisted investment are given by:

(A2)

where NP_NTAis the net proceeds of non-tax-assisted saving. Here, the factor C(1–t_M) indicates that only after-tax dollars are being saved. The product term indicates that investment income is subject to tax each year.

The future net benefit to the contributor of saving in a tax-assisted plan is given by the difference between the tax-assisted proceeds and the non-tax-assisted proceeds. This net benefit is equal to the loss in tax revenue for the Government (in future dollars).

(A3)

To arrive at the tax expenditure in current dollars (that is, when the contribution is made), the future loss in tax revenue must be discounted by the factor 1/(1–r ), where r is the discount rate.

Therefore, substituting equations (A1) and (A2) into (A3) and discounting yields:

Equation A4 (1,724 bytes) (A4)

where P¢ is the present-value tax expenditure using this approach.

Let us illustrate the calculation with a simple example. Suppose that an individual makes a $1 contribution to a tax-assisted plan at age 50 and withdraws the dollar and any interest at age 55. To simplify matters, we assume that the federal marginal tax rate is constant through time (that is, t_M=t_j=t_N) and equal to 25 per cent.²³ We use a 6.4 per cent yield on plan funds. Therefore, the net proceeds from the tax-assisted plan will be:

(A5)

If the identical investment were made in a non-tax-assisted investment, the net proceeds would be:

(A6)

If we use the rate of return on plan funds as the discount rate, then the present-value tax expenditure is:

(A7)

In other words, under these assumptions, $1 invested today in a retirement savings plan will be worth $0.07 ($1.02-$0.95) more after five years than if it had been invested in a non-tax-assisted instrument. This difference is equal to the lost tax revenue for the

Government. Therefore, the discounted present value of the tax expenditure associated with this benefit to the individual is $0.05 of each dollar contributed to a retirement savings plan. This is the same result as that in the example in Section 2 of the main text.

Equivalence to the Method Used in the Main Text

If we assume that the rate of return is equal to the discount rate and that the marginal tax rate is constant, then the present-value tax expenditure formulas for the two methods are as follows:

(A8)

(A9)

If we multiply equation (A9) by (1+r)^N–M/(1+r)^N–M, we obtain:

(A10)

Comparing equations (A8) and (A10) we can cancel the C(1–t) /(1+r)^N–M term. Therefore we need to show that:

(A11)

By noting that the right-hand side of equation (A11) resembles a geometric series of the form å apa qb where a is increasing and b is decreasing we can show that the right-hand side simplifies to:

Equation A12 (2,716 bytes) (A12)

^{1. The present-value approach was first put forward by Samuel Rae. However, unlike the estimates in this paper, which are for the lifetime cost of one year’s contributions, Rae was proposing a means to estimate an annual tax expenditure of all past and present contributions to RRSPs. See Samuel A. Rae, Jr., "Registered Retirement Savings Plans as a Tax Expenditure," Canadian Tax Journal, 28(4) (1980), pp. 459-464.  [Return]
^{2. An alternative approach to estimating the present-value tax expenditure is described in the Appendix.  [Return]
^3. Note that in the first year after the investment is made (M+1), the product operator will be equal to 1 since k> j–l.  [Return]
^4. Note that the after-tax cost to the individual is the same under both the tax-assisted and non-tax-assisted environments.  [Return]
^{5. Data on DPSPs are not available.  [Return]
^{6. The overall weighted average shown in Table 3 is based on the distributions of contributions and withdrawals.  [Return]
^{7. As noted earlier, we assume that all contributions are taxed by age 99.  [Return]
^8. The longitudinal data file has information on RPP/RRSP withdrawals only for the 1985-1997 period.  [Return]
^{9. Statistics Canada, Cat. No. 84-214, 1996. The survival rate is equal to 1 minus the mortality rate (expressed as a per cent). The probability of survival to a given age is the product of all previous survival rates. Survival rates are calculated separately for males and females. We also investigated the effect of higher-income individuals living longer. Based on 1991 data from Statistics Canada, we found that even though high-income people lived longer, the net effect on our preferred tax expenditure estimate was only 0.2 per cent.  [Return]
^10.The survivor benefit is assumed to be 50 per cent of the contributor’s benefit. Female spouses are assumed to be three years younger than male spouses. Therefore, the modified survival rate for a male would be calculated as z´ p(m) + (1-z)´ [p(m)+(1-p(m))´ p(f) ´ 0.5], where p(m) is the male survival rate, p(f) is the female survival rate and z is the proportion of individuals who are not married, in this case 0.1. No adjustment needs to be made for spousal RRSPs since these are implicitly taken into account through the data.  [Return]
^{11. The discount factor is adjusted for inflation (i.e. the real market rate of return is used).  [Return]
^{12. The inclusion rate was reduced from three-quarters to two-thirds as of February 28, 2000, and was further reduced to one-half as of October 18, 2000. For simplicity, the inclusion rate for 2000 is assumed to be two-thirds when calculating the tax expenditure estimate.  [Return]
^13. Statistics Canada, Catalogues No. 74-201 and 74-401 respectively.  [Return]
^14. This value is for corporate stocks. Unfortunately, only U.S. data were available. See Leonard E. Burman and Peter D. Ricoy, "Capital Gains and the People Who Realize Them," National Tax Journal, L(3) (1997), pp. 427-451.  [Return]
^{15. An excellent discussion on the choice of a discount rate is contained in Richard W. Tresch, Public Finance: A Normative Theory (Plano, Texas: Business Publications, 1981).  [Return]
^16. In a world with no taxes, the MRT would be equal to the MRS.  [Return]
^{17. The weights used are based on the RPP/RRSP portfolio. The interest-bearing component was assumed to be 80 per cent government bonds and 20 per cent corporate bonds, which corresponds to the relative shares of total bonds in the National Accounts (personal sector). The TSE 300 total return, which represents the combined return on the index and dividends, was used for the equity portion of the portfolio.  [Return]
^18. The real rate on corporate bonds averaged 4.4 per cent while the total real return on the TSE averaged 5.8 per cent.  [Return]
^19.Based on total RPP/RRSP contributions of $41.6 billion in 1998.  [Return]
^20.In the weighted RPP/RRSP portfolio, the difference in the estimate is 0.6 per cent. If the capital gain is held for the entire period that a contribution remains in an RPP or RRSP, we estimate that the tax expenditure will fall by 3.1 per cent.  [Return]
^{21. In this table we use the long-term government bond rate as the discount rate for the present-value estimates.  [Return]
^{22. At the end of this appendix we show that the two methods are equivalent when the rate of return is equal to the discount rate.  [Return]
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