Tax Expenditures and Evaluations: 2001: 5

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Part 2
Tax Evaluation and Research Report

Present-Value Tax Expenditure Estimates of Tax Assistance for Retirement Savings

1. Introduction

The Department of Finance Canada currently publishes annual estimates of the tax expenditure associated with tax-assisted retirement savings (TARS) programs. However, the Auditor General of Canada has asked the Department to develop an alternative set of estimates that present the net-present-value tax expenditure of contributions made to TARS programs in a given year. This paper first describes the methodology used for measuring the present-value tax expenditure for TARS programs and then provides estimates and projections for the period 1996 to 2003.


Canada provides three tax-assisted programs for retirement savings: registered pension plans (RPPs), registered retirement savings plans (RRSPs) and deferred profit-sharing plans (DPSPs).

These programs benefit individuals in two ways. First, individuals receive a tax deferral on the amount they contribute to a tax-assisted plan. Second, any investment income earned on a contribution accrues tax-free. However, individuals have to pay taxes on both contributions and associated investment income when they withdraw funds from a tax-assisted plan.

For the Government, these programs have costs in terms of forgone revenue. As Figure 1 illustrates, for a given contribution, there is the tax forgone when the contribution is made (since it is deductible from total income). In addition, the Government forgoes the taxes that it would have received in the future on the investment income if the investment had been made in a non-tax-assisted vehicle. However, these costs are offset in part by the taxes the Government will receive in the future when withdrawals are made.

Figure 1
Lifetime Revenue Cost of a Contribution

Figure 1, Lifetime Revenue Cost of a Contribution (2,491 bytes)

Alternative Methods of Measuring the Tax Expenditure

Since there is a tax deferral component in TARS programs, there has been some debate over the appropriate method to measure the tax expenditure.

The Cash-Flow Method

Currently the Government uses a cash-flow method, which answers the following question: If the TARS program were removed today, what would be the estimated revenue impact in the current year? The estimated tax expenditure is arrived at in three steps. First, the Government calculates the value of all the deductions for contributions made in the current year. Second, it imputes the taxes that would have been paid on the investment income earned in TARS plans in the current year and adds that to the cost of the deductions. Third, it deducts from this total the taxes paid on the withdrawals from TARS plans in the current year.

While this method answers the question posed above, it has shortcomings in respect of a number of important issues. In particular, the size of the estimate depends directly on the maturity of the retirement savings system and the relative sizes of the working and retired populations. For example, in the early years of a pension system, contributions tend to be high relative to benefit payouts, whereas under a mature system total payouts will usually exceed total contributions. The estimate is also affected by demographic conditions. Currently, contributions are high relative to benefits because the baby boom generation is in its peak contribution years. Thus, for these two reasons, one could argue that the cash-flow estimates overstate the cost of providing tax assistance. The tax expenditure implied by these estimates may be expected to decline in the future as the pension system matures and members of the baby boom generation begin to draw down their savings.

The Present-Value Method

Another way of measuring the tax expenditure associated with TARS programs is to answer the question: What is the lifetime cost of all contributions made in a given year?1 The present-value method answers a different question than the one answered by the cash-flow method and thus the estimates from the two methods are not directly comparable. The present-value method considers the net revenue forgone in today’s dollars because of contributions made in a year. That is, it adds together the cost of the deduction incurred today for those contributions and the discounted cost of the non-taxation of the accrued investment income earned on those contributions, and then it subtracts the discounted revenue stream received when the contributions and the investment income are withdrawn.

This present-value method does not take into account the revenue forgone on past contributions. However, unlike the cash-flow method, it is not affected by demographic conditions or the maturity of the pension system. The present-value and cash-flow methods will not produce the same result under any demographic conditions.

2. Theoretical Development of the Present-Value Method2

The present-value tax expenditure, P, of a contribution made at age M and withdrawn at age N is estimated using the following formula:

Equation 1 (2,280 bytes) (1)

where C is the contribution, t is the marginal tax rate, u is the average provincial tax rate (expressed as a percentage of federal taxes for convenience), i is the nominal rate of return, r is the discount rate, and j and k are periods during which the contribution earns investment income. Note that P and C represent averages for a cohort of individuals of the same age. The first term in equation (1) is the tax forgone on the contribution, the second term represents the revenue that would have been collected on the investment income, and the last term is the revenue that is collected when the contribution and all investment income are withdrawn.3 We assume that marginal tax rates vary with age. We also assume that any non-sheltered income is taxed as interest income. Later in the paper we relax the latter assumption.

We illustrate the calculation with the simple example shown in Table 1. Suppose that an individual makes a $100 contribution to a tax-assisted plan at age 50 and withdraws the $100 and any interest at age 55. To simplify matters, assume that the federal marginal tax rate is constant through time (that is, tM=tj=tN)and equal to 25 per cent, that provincial taxes are 50 per cent of federal taxes, and that both the rate of return and the discount rate are equal to 6.4 per cent (we develop this rate later in the paper).

The top section of the table indicates what happens in a tax-assisted environment. The after-tax cost of the $100 contribution is $62.50, because the federal government provides a deduction worth $25 on the contribution while the provincial government forgoes an additional $12.50 in tax revenue. The $100 grows until the end of year five, when the entire amount is withdrawn, resulting in federal taxes of $34.09 and provincial taxes of $17.05.

The next section indicates what happens in a non-tax-assisted environment. The individual first has to pay $25 dollars in federal taxes and $12.50 in provincial taxes on the $100 of income available to be saved, meaning that only $62.50 is invested.4 At the end of each year, the individual pays tax on the interest, but nothing on the withdrawal itself.

Table 1
Calculation of Present-Value Tax Expenditure

Amounts ($)
Contribution Year Withdrawal
(Year 1) 1 2 3 4 5 (Year 5)

TARS investment

Gross balance

62.50 106.40 113.21 120.46 128.16 136.37 136.37

Fed. tax paid (A)

-25.00 34.09

Prov. tax paid (C)

-12.50 17.05

Net balance

100.00 106.40 113.21 120.46 128.16 136.37 85.23

Non-TARS investment

Gross balance

62.50 66.50 69.16 71.93 74.80 77.80

Fed. tax paid (B)

1.00 1.04 1.08 1.12 1.17

Prov. tax paid (D)

0.50 0.52 0.54 0.56 0.58

Net balance

62.50 65.00 67.60 70.30 73.12 76.04

Federal tax loss
(Tax paid B - Tax paid A)

25.00 1.00 1.04 1.08 1.12 1.17 -34.09 Total
value cost

Federal present-value
tax cost

25.00 0.94 0.92 0.90 0.88 0.86 -25.00 4.49

Provincial tax loss
(Tax paid D - Tax paid C)

12.50 0.50 0.52 0.54 0.56 0.58 -17.05

Provincial present-value
tax cost

12.50 0.47 0.46 0.45 0.44 0.43 -12.50 2.25

Total federal and provincial present-value cost: 6.74

The third and fourth sections of Table 1 show the tax cost to the federal government on a current- and present-value basis. In this example, the federal tax expenditure on a $100 contribution is $4.49 or $0.04 per dollar. The remainder of the table shows the tax expenditure for the province and the total for both levels of government. Notice that because the rate of return on the investment and the discount rate are equal, the revenue received from the future withdrawal exactly compensates for the tax lost on the contribution today. If the discount rate were less than the rate of return, the tax on the withdrawal would have a higher present value, leading to a lower tax expenditure.

These observations can also be seen by comparing the first and last terms in equation (1). When tM = tN and i=r , that is, when the tax rates applicable to contributions and withdrawals are the same and when the interest rate and the discount rate are also equal, the terms cancel each other. As r decreases, the last term in equation (1) increases, but because this term is subtracted, the present value of the tax expenditure falls.

Table 2 illustrates how the tax expenditure varies with the length of time the contribution remains in the tax-assisted plan, N–M, using our simple example. The longer the period, the larger the tax expenditure.

Table 2
Change in Present-Value Tax Expenditure Over Time

N – M Federal present-value tax expenditure
(per dollar of contribution)

(years) ($)
5 0.04
10 0.08
20 0.15
30 0.21
40 0.25

Now we add a further dimension to the analysis. Because payouts from retirement savings plans are normally received in a stream of payments over the retirement period, it is necessary to allow for more than a single payout at age N. Therefore, the present-value tax expenditure of a given contribution will be the sum of several calculations of the type made in equation (1). For example, a $1 contribution is made at age 50, but 10 cents (plus the associated interest) is withdrawn every year for 10 years. More generally, there will be a distribution of withdrawals over time. In our model, we assume that the maximum age that a person can withdraw funds from a tax-assisted plan is 99. Algebraically, the calculation of the tax expenditure is as follows:

Equation 2 (1,282 bytes) (2)

where Q is the tax expenditure for a contribution that is withdrawn over several periods, aN is the proportion of the contribution made at age M that is paid out at age N, and PN is the present-value cost of contributions made at age M and withdrawn at age N, as calculated in equation (1). We discuss how we calculate the factor aN in the next section.

The last step is to aggregate the individual results. This is accomplished by weighting the results from equation (2) (Ql) by the proportion of total contributions made in the year by individuals of different ages, cl:

Equation 3 (1,299 bytes) (3)

where M0 and M* are the lowest and highest ages at which contributions can be made.

3. Applying the Present-Value Method

In calculating the present-value tax expenditure estimate, this paper follows the assumptions made in recent Tax Expenditures and Evaluations reports. First, the estimates are based on a broadly defined benchmark tax system, which uses nominal income as the tax base rather than real income. Second, the estimates are made assuming that there would be no change in savings or in the timing of withdrawals if the tax expenditure were removed. In other words, it is assumed that there is no behavioural change.

Although estimates are presented separately for RPP and RRSP programs5 under the cash-flow method, we calculate only one estimate for these two programs under the present-value method. This is because the longitudinal tax return data we use in the development of the estimates does not separate RPP income from RRSP income.

We require several pieces of information to calculate the present-value tax expenditure.

First, we need information on the marginal tax rates on contributions and withdrawals.

Second, since there is a tax deferral on contributions made to a tax-assisted plan, we need to know how long a given contribution remains in such a plan (recall the factor aN from equation (2) in the previous section). Therefore, a distribution by age of how the contribution is withdrawn from the plan over an individual’s remaining lifetime is required.

Third, since the tax treatment of various forms of investment income varies, we need to know the investment portfolio of individuals in the absence of a TARS program. For example, capital gains and dividends are taxed at a lower rate than interest income.

Finally, we must make assumptions about the rate of return on contributions and the discount rate. The model assumes that both the rate of return and the discount rate are constant.

We provide further details below about how these pieces of information were obtained and what assumptions were made.

Calculating Federal Marginal Tax Rates

The T1 model has been used to generate average federal marginal tax rates by age and sex for both contributions and withdrawals at five-year age intervals. The tax rates used for 1998 are shown in Table 3, which indicates that the marginal tax rates on withdrawals are less than the rates on contributions.6 These rates are consistent with those used to calculate the cash-flow estimate. Based on estimates of provincial tax revenues as a percentage of federal tax revenues, we assume that the provincial marginal tax rates are just over half of the federal tax rate.

Table 3
Average Federal Marginal Tax Rates, 1998

  Contributions Withdrawals


Males Females Males Females



17.4 16.9 7.3 10.8

20 - 24

21.5 19.3 17.8 14.6

25 - 29

25.4 23.8 22.8 20.9

30 - 34

27.4 25.2 25.5 21.6

35 - 39

28.2 25.9 24.9 22.1

40 - 44

28.3 25.8 25.3 22.2

45 - 49

27.8 25.2 24.3 20.5

50 - 54

27.6 24.7 23.3 19.6

55 - 59

27.1 24.2 22.3 19.0

60 - 64

26.7 23.5 21.8 18.4

65 - 69

29.3 27.3 21.8 18.6

70 - 74

22.6 19.4 21.6 19.0

75 - 79

29.3 19.4 21.4 19.2

80 - 84

    19.4 18.3

85 - 89

    16.7 15.8

90 - 99

    15.2 11.7

Weighted average

27.5 25.0 21.9 18.9

The rates presented in Table 3 reflect the benefit reduction rates on federal income-tested programs that are part of the tax system, such as the Canada Child Tax Benefit, the goods and services tax credit, and Old Age Security repayments. A case could be made that the benefit reduction rates for the Guaranteed Income Supplement (GIS) should also be taken into account in the marginal tax rates, even though the GIS is not linked directly to the tax system. If the GIS benefit reduction rates were reflected in the marginal tax rates shown in Table 3, then the tax expenditure estimates under the present-value and cash-flow methods would be reduced. We are reviewing whether GIS effects should be taken into account when calculating TARS tax expenditures.

Developing the Withdrawal Distribution

The empirical approach to develop the withdrawal distribution has four stages. First, an average RPP/RRSP income profile for a typical individual as he or she ages from 19 to 99 is derived using longitudinal tax return data.7 Second, this profile is then modified to take into account the lifespan of the population as a whole. The third stage discounts the modified income distribution in order to obtain the withdrawal profile of contributions rather than a withdrawal profile of both contributions and investment income. The fourth stage adjusts this profile for individuals who are older than 19.

The first stage begins with longitudinal tax return data for the years 1985 to 1997.8 Individuals are grouped by their age in 1985. Therefore, for each age level, there are 13 observations representing the total RPP/RRSP withdrawal made in each year from 1985 to 1997. For each observation, an age is assigned based on the 1985 age for that group of individuals. For instance, someone who was 20 in 1985 would be 21 in 1986 and 32 in 1997. This process is repeated for each age level in 1985. Therefore, for most age levels, there are multiple observations of income withdrawn from RPPs and RRSPs. The dollar values of RPP/RRSP income are converted into constant 1992 dollars. These observations are plotted on an X-Y graph with age on the X-axis and income on the Y-axis (Figure 2). An average of the income amounts for each age level is used to generate a lifetime RPP/RRSP income distribution for a typical individual (also shown in Figure 2). The average value for each age is then divided by the sum of all average values to obtain a percentage distribution. This distribution represents the withdrawal distribution for a 19-year-old individual who will live until 99 years of age.

Figure 2
Average RPP/RRSP Income (in Constant 1992 Dollars)
Based on Longitudinal Tax Return Data, 1985-1997

Figure 2, Average RPP/RRSP Income (in Constant 1992 Dollars) Based on Longitudinal Tax Return Data, 1985-1997 (4,189 bytes)

This distribution should be adjusted to take into account the probability that the individual will die before reaching the age of 99. Therefore, in the second stage, survival rates are calculated using mortality rates from Statistics Canada’s Vital Statistics Compendium.9 These survival rates are then modified to account for survivor benefits.10

The percentage distribution is then multiplied by the survival rates and adjusted so that the final withdrawal distribution adds to 100 per cent. We compare these adjusted distributions in Figure 3. These adjusted distributions indicate that 15 per cent of withdrawals are made before age 60, 65 per cent are made between ages 60 and 79, and 20 per cent are made at ages 80 and up.

Figure 3
Distribution of RPP/RRSP Income
Before and After Adjustment for Survival Rates

Figure 3, Distribution of RPP/RRSP Income Before and After Adjustment for Survival Rates (12,961 bytes)

Since we need to know the length of time a contribution remains in an RPP or RRSP, the withdrawal distribution should indicate the proportion of contributions withdrawn, not the sum of both contributions and interest. However, we cannot observe the ratio of contributions to interest being withdrawn. Therefore, in the third stage the total income distribution is discounted assuming that the contribution was made when the individual was 19.11 This distribution is shown by the solid line in Figure 4.

Up to this point, we have discussed a withdrawal distribution for a 19-year-old making a contribution. For contributions made by those over age 19, the distribution needs to be adjusted so that the entire contribution will be withdrawn. The concept is illustrated in Figure 4 for a 40-year-old making a contribution. The dashed line represents the distribution for a 40-year-old which is almost identical to the distribution for a 19-year-old up to age 62. The area under each of the lines is equal to 1. The new distribution is obtained as follows:

Equation 4 (1,376 bytes) (4)

where W40(N) is the probability of withdrawal at age N for a contribution made at age 40, and W19(N) is the probability of withdrawal at age N for a contribution made at age 19. Graphically, each point on the 19-year-old distribution is divided by the area under the distribution to the right of age 40, as shown in Figure 4.

Figure 4
Discounted Withdrawal Distributions

Figure 4, Discounted Withdrawal Distributions (10,578 bytes)

Note: The discount rate used is the real market rate of return (4.4 %).
This rate is derived later in the text.

By weighting the truncated distributions by the contribution profile, one can obtain a projected withdrawal distribution for the contribution profile made in a given year. This is shown in Figure 5 for 1997 contributions. This chart indicates the average length of time a contribution is held before it is withdrawn, which in this case is about 19 years.

Figure 5
Contributions and Projected Withdrawals

Figure 5, Contributjion and Projected Withdrawals (10,806 bytes)

The empirical approach we use in this paper could be criticized because the withdrawals made today do not fully take into account the increase in both the use and generosity of TARS programs (in short, the pension system is not fully mature). One could argue that because the increased generosity and use of the program will lead to higher withdrawal amounts (in real terms) for those retiring in the future, the share of the total withdrawals occurring in retirement will increase in the future. However, while the amounts withdrawn will increase for those in retirement, it is also possible that the amounts withdrawn before retirement will increase proportionately, meaning that there will be no change in the shares of retirement income withdrawn at a given age. The arguments are illustrated in Figure 6. Distribution A represents the level of withdrawals currently observed. Distribution C presents the first argument, where only withdrawals in retirement increase, thereby changing the shares for each age. Distribution B is simply an upward shift of distribution A, meaning that the shares of retirement income withdrawn at a given age remain the same.

We checked our distribution by comparing the distribution of 1985 with that of 1997 (Figure 7). We found that there was little change in the withdrawal distribution between these two years, leading us to believe that despite the changes in the TARS programs and their use, the age distribution of withdrawals will remain relatively constant in the future.

As a final point, it should be noted that in a non-tax-assisted environment, the discounted withdrawal profile may be different as individuals respond to the differences in tax treatment of various investments. However, since we are assuming no behavioural change between tax-sheltered and non-sheltered investments, it is assumed that the withdrawal distribution is the same for non-tax-assisted investments as it is for tax-assisted investments.

Figure 6
Level of Withdrawals From RPPs and RRSPs

Figure 6, Level of Withdrawls From RPPs and RRSPs (3,461 bytes)

Figure 7
Age Distribution of Withdrawals by Year

Figure 7, Age Distribution of Withdrawals by Year (15,081 bytes)

Developing the Investment Portfolio

As mentioned earlier, different investments receive different tax treatment. Interest income from bonds, Treasury bills, and guaranteed investment certificates is taxed the same as employment income. Meanwhile, capital gains are treated favourably in two ways. First, they are taxed only upon realization, creating a tax deferral. Second, capital gains are not fully taxed.12 In addition, the effective tax rate on dividend income is reduced at the personal level by the dividend gross-up and tax credit.

In accordance with the standard approach for estimating tax expenditures, the alternative portfolio should not take into account any behavioural changes. Therefore, we assume that individuals invest in exactly the same instruments that they currently invest in through their RPPs or RRSPs. A more realistic approach would allow for investment in owner-occupied housing (such as paying down a mortgage). However, this would imply a behavioural change. If investment in housing were included in the model, the tax expenditure would be lower because owner-occupied housing benefits from the non-taxation of capital gains and the non-taxation of imputed rents.

Data to develop the portfolio are taken from Statistics Canada’s Trusteed Pension Funds and Pension Plans in Canada.13 Stock data are used to determine the proportion of the portfolio in different types of investments. To be useful for estimating the present-value tax expenditure of TARS programs, these investments need to be classified between interest-bearing and equity-type assets (capital-gain-bearing or dividend-bearing). For trusteed RPPs (Table 4), mutual and investment funds, equities and real estate are assumed to produce capital gains or dividends, while the remaining items are interest-bearing. For RRSPs (Table 5), only investment funds are assumed to produce capital gains or dividends, while investments held by the financial institutions are assumed to be interest-bearing. In addition, the assets in non-trusteed public employee pension plans and insurance plans are assumed to be interest-bearing. Taken together, the average portfolio of all of the above plans is 67.9 per cent interest-bearing and 32.1 per cent equity.

To determine the proportion of dividend and capital gain income for equity investments, we can use the ratio of the Toronto Stock Exchange (TSE) 300 return to the "total return" on the TSE 300, which represents the combined return from dividends and the index. The ratio for the 1956-1999 period was 41 per cent capital gains and 59 per cent dividends.

Table 4
Book Value of Assets in Trusteed RPPs

  Percentage of gross assets
  1992 1993 1994 1996 Average

Pooled, mutual and investment funds

7.3 7.9 12.4 19.6 11.8


44.2 32.9 32.9 34 36.0


32.6 42.2 39.6 33.1 36.9


3.2 2.8 2.6 1.9 2.6

Real estate

3.5 3.3 3.5 3.2 3.4

Cash and short-term deposits

7 8.6 6.9 6.3 7.2

Miscellaneous assets

2.3 2.3 2.1 1.8 2.1

Note: Percentages may not add to 100 due to rounding.

Source: Statistics Canada, Trusteed Pension Plans, Cat. No. 74-201. 

Table 5
Accumulated Assets Held in RRSPs

  Percentage of total assets

Money held by:

1992 1993 1994 1995 1996 1997 Average

Trust companies

11.7 11.8 9 7.9 6.9 4.5 8.6

Credit unions

11.2 11.2 11.6 11.7 11.1 10.2 11.2

Chartered banks

33.8 33.2 32.3 34 31 26.3 31.8

Other deposit taking intermediaries

0.5 0.5 0.4 0.4 0.3 0.1 0.4

Investment (mutual) funds

22.9 23.1 27.5 28.9 33.9 42.1 29.7

Insurance companies

19.9 20 19.2 17.2 16.9 16.7 18.3

Note: Percentages may not add to 100 due to rounding.

Sources: Statistics Canada, Trusteed Pension Plans, (Cat. No. 74-201), and Pension Plans in Canada, (Cat. 74-401).

We also have to make an assumption regarding the length of time a capital gain is held before it is realized. Our base case will rely on U.S. data that suggest that the average holding period is about 6.3 years.14 To test the sensitivity of the results, we also use 10 years as the holding period.

Therefore, the base-case portfolio used in the analysis will have the following characteristics:

Choosing the Rate of Return and the Discount Rate

There are two perspectives that we can take regarding the discount rate. The first is to take a "social approach." This approach attempts to take into account the impact on social welfare of TARS programs. Since tax expenditures can be interpreted as a form of government spending, we can turn to the cost-benefit analysis literature on public spending for some insight regarding the appropriate discount rate. Economic theory defines a range of plausible values.15 Essentially, one can regard public sector spending as a reallocation of resources from the private sector to the public sector. That is, the tax expenditure is financed through higher taxes. These private sector resources could have been used for either consumption or investment. If the resources were used only for investment, the appropriate discount rate is the marginal rate of transformation (MRT), which is equal to the rate of return before all corporate and personal income taxes. If the resources were used for consumption, then the discount rate should be the marginal rate of substitution (MRS), which is the after-tax rate of return to individuals.16

In general, the resources are reallocated from both consumption and investment, so the discount rate should be between the MRS and the MRT. One possibility is to use the after-corporate, before-personal-income-tax rate of return. This is more generally referred to as the before-tax rate of return earned on bonds and other forms of investment. This rate is both well known and within the range dictated by economic theory. Using the pre-tax portfolio rate of return also has some intuitive appeal. In Section 2 we point out that when the rate of return and the discount rate are equal, the taxes received on withdrawal have the same present value as the cost of the deduction for the contribution.

The second perspective is the "financial approach." This perspective considers how much it costs the Government, in terms of lost revenue, to provide TARS programs. In this case, the discount rate would be the Government’s cost of borrowing – the pre-tax long-term government bond rate. The financial approach is consistent with the way we measure other tax expenditures. Note that using this rate will lead to a lower tax expenditure. While we present results using both rates in the next section, we will report the estimates using only the financial approach in the future.

We estimated the rate of return on our portfolios based on data for the 1956-1999 period. The estimate is a weighted average of the long-term government bond rate, the long-term corporate bond rate and the total return on the TSE 300.17 We calculated the real return on the portfolio to be 4.4 per cent and the average real government bond rate to be 3.5 per cent.18 Assuming that inflation is 2 per cent, the nominal rates are 6.4 per cent on the portfolio and 5.5 per cent on long-term government bonds.

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