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Tax Expenditures and Evaluations: 2001: 5 Part 2 |
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Amounts ($) | |||||||||
Contribution | Year | Withdrawal | |||||||
(Year 1) | 1 | 2 | 3 | 4 | 5 | (Year 5) | |||
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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 | ||
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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 | |||
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Federal tax loss |
25.00 | 1.00 | 1.04 | 1.08 | 1.12 | 1.17 | -34.09 |
Total present- value cost |
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Federal present-value |
25.00 | 0.94 | 0.92 | 0.90 | 0.88 | 0.86 | -25.00 | 4.49 | |
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Provincial tax loss |
12.50 | 0.50 | 0.52 | 0.54 | 0.56 | 0.58 | -17.05 | ||
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Provincial present-value |
12.50 | 0.47 | 0.46 | 0.45 | 0.44 | 0.43 | -12.50 | 2.25 | |
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Total federal and provincial present-value cost: | 6.74 | ||||||||
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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 $0.04 per dollar. The remainder of the table shows the tax expenditure for the province and the total for both levels of government. Notice that because the rate of return on the investment and the discount rate are equal, the revenue received from the future withdrawal exactly compensates for the tax lost on the contribution today. If the discount rate were less than the rate of return, the tax on the withdrawal would have a higher present value, leading to a lower tax expenditure.
These observations can also be seen by comparing the first and last terms in equation (1). When tM = tN and i=r , that is, when the tax rates applicable to contributions and withdrawals are the same and when the interest rate and the discount rate are also equal, the terms cancel each other. As r decreases, the last term in equation (1) increases, but because this term is subtracted, the present value of the tax expenditure falls.
Table 2 illustrates how the tax expenditure varies with the length of time the contribution remains in the tax-assisted plan, N–M, using our simple example. The longer the period, the larger the tax expenditure.
Table 2
Change in Present-Value Tax Expenditure Over Time
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|
N – M |
Federal present-value tax expenditure (per dollar of contribution) |
---|---|
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(years) | ($) |
5 | 0.04 |
10 | 0.08 |
20 | 0.15 |
30 | 0.21 |
40 | 0.25 |
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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:
(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:
(3)where M0 and M* are the lowest and highest ages at which contributions can be made.
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
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Contributions | Withdrawals | |||
---|---|---|---|---|
Age |
Males | Females | Males | Females |
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(%) | ||||
19 |
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 | ||
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Weighted average |
27.5 | 25.0 | 21.9 | 18.9 |
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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
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
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:
(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
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
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 6Figure 7
Age Distribution of Withdrawals by Year
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
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Percentage of gross assets | |||||
---|---|---|---|---|---|
1992 | 1993 | 1994 | 1996 | Average | |
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Pooled, mutual and investment funds |
7.3 | 7.9 | 12.4 | 19.6 | 11.8 |
Equities |
44.2 | 32.9 | 32.9 | 34 | 36.0 |
Bonds |
32.6 | 42.2 | 39.6 | 33.1 | 36.9 |
Mortgages |
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 |
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Note: Percentages may not add to 100 due to rounding. |
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Source: Statistics Canada, Trusteed Pension Plans, Cat. No. 74-201. |
Table 5
Accumulated Assets Held in RRSPs
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Percentage of total assets | |||||||
---|---|---|---|---|---|---|---|
Money held by: |
1992 | 1993 | 1994 | 1995 | 1996 | 1997 | Average |
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11.7 | 11.8 | 9 | 7.9 | 6.9 | 4.5 | 8.6 | |
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 |
19.9 | 20 | 19.2 | 17.2 | 16.9 | 16.7 | 18.3 | |
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Note: Percentages may not add to 100 due to rounding. |
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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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Last Updated: 2004-10-28 |