THE MEASUREM ENT OF INTERREGIONAL REDISTRIBUTION
G. C. RUGGERI AND WEIQIU YU*
Department of Economics
University of New Brunswick
Abstract
This paper develops two indices, both local and global, to measure interregional redistribution. The
local indices proposed involve a comparison between federal revenues and expenditures assigned
to various regions and the pattern of income disparities among regions. They are developed by
relating these comparisons under a given regional distribution of federal fiscal activity to three
special cases under known degrees of redistribution, namely, (a) no redistribution, and (b) the
degree of redistribution that would be delivered solely through equal per capita federal spending
in each region, and (c) the maximum degree of redistribution that would equalize per capita income
in all regions . Global indices are then developed as weighted averages of the local indices. A major
benefit of the proposed indices is the direct measurement of how much interregional redistribution
is generated by the federal fisc compared to these known degrees of redistribution. We calculate the
proposed indices using Canadian data for 1996. Our results show that the federal fiscal system in
1996 delivered a degree of interregional redistribution 1.8 times what would have been generated
under equal per capita federal expenditures in each region and nearly half of the maximum
redistribution that could have been delivered by the federal fisc.
J.E.L Classification: H00, H77, H5, H6
______________________
*Department of Economics, University of New Brunswick, P.O. Box 4400/Fredericton, N.B.
E3B 5A3. Tel: (506) 447-3211, Fax: (506) 453-4514, E-mail: <ruggeri@unb.ca>, and
<wyu@unb.ca>. We thank an anonymous referee and Vaughan Dickson for helpful comments.
1. INTRODUCTION
The fiscal activity of government generates a variety of redistributional effects. It may alter the
relative economic position of individuals with different income levels and it may also influence the
relative position of individuals with equal income, but different non-economic characteristics. The first
effect may be called vertical redistribution as it involves vertical equity, while the second effect may
be called horizontal redistribution. In a federal state, the central government may also affect the
relative economic situation of regions with different levels of average income. We call this effect
interregional redistribution, where “region” refers to a state or a province.
Economists have developed a variety of indices to measure the degree of vertical redistribution and
horizontal redistribution. Example of measuring the degree of vertical redistribution are Musgrave
and Thin (1948), Kakwani’s (1976), Reynolds and Smolensky (1977), Baum (1987), and Cassady,
Ruggeri and Van Wart (1996). Examples of measuring the degree of horizontal redistribution are
Plotnick (1982) and Musgrave (1991).
Less attention in the literature on fiscal redistribution has been paid to redistribution among regions
generated by the fiscal activity of the federal government in a federation. When the redistributional
effect of federal fiscal activity is evaluated, the analysis is usually confined to the calculation of what
are commonly called federal fiscal balances. Calculated by assigning to each region a portion of both
federal revenues and expenditures on the basis of a selected methodology, these balances can be
transformed into indices for interregional redistribution. For example, if we represent the economic
position of a province by its per capita income and list the provinces in ascending order of per capita
income, we can treat the resulting series in the same manner as a distribution of average income by
2
income class and apply the indices of vertical redistribution. We can use such series to calculate the
selected Gini values and derive any of the global progressivity measures identified above.
In our view, this approach to the measurement of interregional redistribution fails to capture the
defining fiscal characteristics of a federation. A major policy issue in fiscal federalism is the extent to
which federal fiscal activity affects the degree of regional disparities. In order to capture not only this
effect, but also the channels through which it is delivered, we need indices specifically designed for
interregional redistribution which take into account directly the information incorporated in the
federal fiscal balances.
This paper develops a set of new indices, both local and global, designed explicitly to measure
interregional redistribution by incorporating elements of federal fiscal activity and the relative income
position of regions. The local indices proposed involve a comparison between federal revenues and
expenditures assigned to various regions and the pattern of income disparities among regions. They
are developed by relating these comparisons under a given regional distribution of federal fiscal
activity to three special cases under known degrees of redistribution. Global indices are then
developed as weighted averages of the local indices. A major benefit of the proposed indices is the
direct measurement of how much interregional redistribution is generated by the federal fisc compared
to the cases with no redistribution, the degree of redistribution that would be delivered solely through
equal per capita federal spending in each region and the maximum degree of redistribution which
would equalize average incomes among regions. We calculate the proposed indices using Canadian
data for 1996. Our results show that the federal fiscal system in 1996 delivered a degree of
interregional redistribution 1.8 times what would have been generated under equal per capita federal
expenditures in each region and nearly half of the maximum redistribution that could have been
3
delivered by the federal fisc.
The paper is organized as follows. Section 2 presents the proposed indices and explores their
properties through simple examples. Section 3 applies those indices to the Canadian situation in two
steps: first, it discusses the methodology in calculating the main components of federal fiscal balances
and regional income disparities; and then, it estimates the values of the proposed indices. Finally,
Section 4 concludes.
2. INDICES OF INTERREGIONAL REDISTRIBUTION IN A FEDERAL SYSTEM
The proposed indices of interregional redistribution are based on the relationship between the main
components of federal fiscal balances and regional income disparities. They are developed in two
steps. The first step develops measures of the relative contribution that each region makes to the
financing of the federal expenditures assigned to it compared to its relative economic position, called
Relative Share (RS), under the actual pattern of federal revenues and expenditures by region and
under selected assumptions. The second step develops indices of interregional redistribution, called
Relative Share Indices (RSI), from a comparison of the above relative shares.
A. Relative Shares Under Alternative Scenarios
Following Mansell and Schlenker (1995), the basic formula for calculating the relative share for
region i (RSi) is
4
RSi = [(ri/r)/(ei/e)] / (yi/y)
(1)
where ri, ei and yi are per capita federal revenues, per capita federal expenditures, and per capita
income for region i, respectively, and r,e,y are the corresponding averages for all regions. A value
of one indicates that a region’s contribution to the financing of the federal expenditures it receives
is commensurate with its share of income. A value greater (less) than one indicates that a region
contributes more (less) than in proportion to its income share.
Since the population used to derive per capita values is the same for each variable within a region,
and for each variable related to the country as a whole, equation (1) can be expressed in terms of
total federal revenues received from region i (Ri) and total federal expenditures assigned to the same
region (Ei) as follows
RSi = [(Ri/Ei) (E/R)] /yi/y
(2)
where R and E are, respectively, total federal revenues and expenditures. In the case of a balanced
federal budget, E = R and the local relative share value is reduced to the ratio of (Ri/Ei) to (yi/y).
To develop the indices of interregional redistribution, we consider three special cases: (1) the
situation where the federal fiscal system does not generate interregional redistribution, (2) the
situation where redistribution is delivered only via the spending side and through equal per capita
federal spending in each region, and (3) the situation where the federal fiscal system delivers
maximum redistribution by eliminating entirely the existing regional income disparities.
5
Case (a). Distributionally-Neutral Fiscal System (No Redistribution)
Let us consider the case where neither federal revenues nor expenditures affect the interregional
distribution of income by assuming that their per capita values are a fixed proportion of per capita
income in each region. That is, ei = ayi, where a = e/y = E/Y, and ri = byi, where b = r/y = R/Y.
Expanding the terms ri and ei, recognizing that ri/ei = Ri/Ei, we can express the ri/ei ratio as
Ri/Ei = byi/ayi = b/a = R/E
(3)
Substituting (3) for Ri/Ei into (2) yields
RSi(N) = y/yi
(4)
where N stands for distributionally-neutral and RSi(N) distributionally-neutral shares since it is not
affected by the allocation of federal revenues and expenditures. Expression (4) indicates that, when
the federal fiscal system is distributionally-neutral across regions, the relative share values are the
reciprocal of the relative income values. Therefore, RSi(N) turns out to be a measure of regional
disparity.
For the purpose of clarifying this measure, an illustrative calculation of RSi(N) is shown in panel
(a) of Table 1. It is assumed in this example that there are only two regions, each region has only one
agent and the federal government has a balanced budget (as shown by expression (4), the RSi(N)
values are not affect by unbalanced budgets). In this case, the residents of each region pay the full
6
price of the benefits they receive from federal expenditures, in the sense that they collectively
contribute to the federal government exactly as much as the federal government has provided them
in public spending. The net positions of each region remain unchanged and so does the pattern of
regional income disparities. However, since the resident of region 1 pays 100% of the value of federal
expenditures when they have only 80% of the average per capita income, they end up paying 25%
more than if the price had been set at 80% of the value of federal expenditures. Therefore, the
estimated value of RSi(N) is 1.25 (1/.8). In contrast, the resident of region 2 also pays 100% of the
value of federal expenditures but its per capita income is 20% higher than the national average. As
a result, the estimated value of RSi(N) is .83 (1/1.2). Therefore, the higher the per capital income in
region i, the lower is its RSi(N). Graphically, it is represented by a downward sloping curve in a
diagram which has per capita income ranked in ascending order on the horizontal axis and the RSi(N)
values on the vertical axis.
Case (b) Redistribution Only Through Federal Spending (Standard Redistribution)
In the previous case, the government acts as a private firm with no power of price discrimination: it
provides bundles of publicly-supplied goods and services to the residents of all regions and then
collects from each region an amount of revenue equal to its expenditures assigned to that region. One
of the functions of governments in a federation, however, is to reduce regional disparities. In Canada,
this commitment is enshrined in the Constitution. What is the degree of interregional redistribution
that fulfills this commitment, one may ask? The answer to this question requires a normative answer.
For analytical purposes, we propose as a standard degree of redistribution the situation where each
7
province contributes to the financing of the federal expenditures assigned to it in a manner
commensurate to its relative income position. Specifically, standard redistribution occurs when the
ri/ei ratio equals the yi/y ratio under a balanced budget (i.e., E=R). This happens when, given
redistributional neutrality on the revenue side, federal expenditures are distributed on an equal per
capita basis among regions. That is, federal revenues per capita are a fixed percentage of per capita
income in each region, i.e., ri = byi, as in case (a); and federal expenditures per capita are equal in
each region, i.e., ei=e. Accordingly,
ri/ei = byi/e = (R/Y)(yi/E/P) = (R/E)yi(Y/P) = (R/E)(yi/y)
(5)
where P represents the national population. Recognizing that ri/ei = Ri/Ei and substituting this into
equation (2) yields the relative share values under the above-defined degree of standard redistribution
as follows:
RSi(S) = 1 , where S symbolizes standard redistribution.
(6)
Graphically, it is represented by a horizontal line in a diagram which has per capita income on the
horizontal axis and the RSi(S) values on the vertical axis. By comparison, below-standard
redistribution is represented by a downward-sloping line such as in case (a) while above-standard
redistribution is represented by an upward-sloping line.
This particular version of the standard level of redistribution is particularly useful in the context
of the Canadian federation. As shown by Ruggeri and Yu (2000) interregional redistribution in
8
Canada is delivered through both federal revenues and expenditures. On the revenue side, the most
powerful instrument of redistribution is the personal income taxes with its progressive rate structure.
As the federal government reduces personal income taxes, partly in response to international tax
competition, the degree of interregional redistribution is likely to fall as the contribution of
consumption taxes and payroll taxes to the federal tax mix increases. On the spending side,
interregional equity is increasingly being identified with equal per capita federal expenditures in all
regions. As an example, the largest federal transfer to provinces, the cash transfer for health case,
social services and post-secondary education, has recently been transformed into an equal per capita
payment.
An illustration of this special case is given in panel (b) of Table 1. We notice that, since each region
receives equal amount of federal spending but pays taxes only in proportion to income, the Ri/Ei ratio
is equal to the yi/y ratio and the estimated relative share values are one in both regions. In this case,
the residents of region 1 pay to the federal government $750 less than they receive in federal spending
while the residents of region 2 pay $750 in excess of what they receive. As a result, income is
redistributed from region 2 , whose share of post-fisc income falls from 1.2 to 1.16, to region 1,
whose share of post-fisc income rises from .8 to .84.
Case (c). Maximum Redistribution
For analytical purposes, we introduce another special case where the allocation of federal revenues
and expenditures produces maximum redistribution by equalizating the post-fisc income of all regions.
We calculate the RSi for maximum redistribution by keeping federal revenues distributionally-neutral
9
(i.e., ri = byi as in the previous cases) and assigning federal expenditures to each region in a manner
that results in equal post-fisc income per capita for all regions. This is done by choosing ei values that
equalize this post-fisc income so that yi + (ei-ri) = y. Accordingly, we need to derive the relative
share values on the assumption that
ei = y - yi + ri
(7)
Expression (7) incorporates a balanced budget situation. When the federal budget is not balanced,
we must solve yi + (E/R)ei - ri = y for ei. The value of ei for maximum redistribution in this case is
ei = (R/E)(y - yi + ri)
(8)
Substituting expression (8) for ei in expression (1), we can derive the relative share values under
maximum redistribution as1
RSi (M) = b/[1 - (1-b)(yi/y)]
(9)
where M symbolizes maximum redistribution. Since the value of b is common to all regions, the
interregional differences in RSi(M) values depend entirely on the degree of regional income
disparities.
An illustrative example of the calculation of RSi(M) is found in panel (c) of Table 1. Federal
revenues per capita are still proportional to per capita income in each region, but in this case almost
all federal expenditures are assigned to region 1. As a result, per capita net income is equalized in
10
each region. Since region 1 now pays less than half of the federal expenditures it receives although
its per capita income is 80% of the national average, its RSi(M) is substantially less than one. The
opposite pattern is found in the case of region 2.
The final illustrative example, found in panel (d) of Table 1, shows an intermediate case where the
degree of interregional redistribution is higher than the standard but less than the maximum. In our
illustrative example, we treat this case as the “actual” situation and call the relative share values
RSi(A).
In this section, we presented the definition of RS and its calculation under three special cases,
namely no redistribution (RSi(N)), maximum redistribution (RSi(M)) and standard redistribution
(RSi(S)), namely, redistribution that would be delivered solely through equal per capita federal
expenditures in each region, The next section introduces two indices based on the RS defined above.
B. Two Indices of Interregional Redistribution
To develop the indices, we ask the following two questions: (1) does the existing allocation of federal
revenues and expenditures generate more or less than the standard degree of redistribution and by
how much? (2) what proportion of maximum redistribution is generated by the existing allocation of
federal revenues and expenditures?
To address the first question, we propose an index of regional redistribution based on a comparison
of the difference between the actual and distributionally-neutral relative shares and the difference
between the standard and distributionally-neutral relative shares. Called Relative Share Index
(RSIi(S)) with respect to standard redistribution, where S indicates that the comparison is made with
11
the standard degree of redistribution, it is calculated by
RSIi(S) = [RSi(A) - RSi(N)]/[RSi(S) - RSi(N)]
(10)
Substitution equations (2), (4), and (6) into expression (10) yields,
RSIi(S) = [(Ri - Ei)/Ei]/[(yi - y)/y]
(11)
A comparison between (10) and (11) shows that the proportional difference in actual from standard
redistribution is equal to the proportional difference between the percentage deviation in federal
revenues from expenditures and the percentage deviation in per capita income.
By replacing RSi(A) in (10) with RSi(N) and RSi(M) respectively, the lower and upper limits of
this index are 0 and [RSi(M) - RSi(N)]/[RSi(S) - RSi(N)]. When RSI(S)=0, there is no interregional
redistribution generated by federal fisc activities; when RSI(S)=1, the federal fiscal system generates
a degree of interregional redistribution equal to that under standard distribution; a value greater
(smaller) than one indicates that the federal fiscal system generates a degree of interregional
redistribution greater (smaller) than that under standard redistribution.
To address the second question, we propose a second index called relative share index with respect
maximum redistribution, RSIi(M), where M indicates that the comparison is made with respect to
maximum redistribution. In this case,
RSIi(M) = [RSi(A) - RSi(N)]/[RSi(M) - Rsi(N)]
12
(12)
By replacing RSi(A) in (12) with RSi(N) and RSi(M), the lower and upper limits of the index relative
to maximum redistribution are simply zero and one. Thus, the value of RSIi(M) represents the
proportion of maximum redistribution generated by the existing allocation of federal revenues and
expenditures.
The two local indices of interregional redistribution can be transformed into the corresponding
global indices in the form as weighted averages where the weights are the relative shares of total
income in each region (Yi/Y). The global lower and upper limits can also be derived as the weighted
average of the local limits using the total income shares as weights.
As an illustration, we calculate these indices in Table 2 which is based on the information contained
in Table 1. The first three columns of this table show for each region the differences in relative shares
between the RS values under actual redistribution, standard redistribution and maximum
redistribution and the RS values under no redistribution. The local indices are shown in the last two
columns while the last row contains the values of the global indices. The results show that, given the
pattern of regional income disparities assumed in Table 1, the regional allocation of federal revenues
and expenditures assumed in panel (d) results in a degree of interregional redistribution that is more
than three times the standard degree of redistribution and 38% of the degree of redistribution that
would have equalized regional levels of per capita income.
13
3. INTERREGIONAL REDISTRIBUTION IN CANADA, 1996
As an application, we use the above indices to derive, in two stages, estimates of interregional
redistribution in Canada for 1996. The first stage discusses the methodology used in the calculations
of federal expenditures and revenues (Ei and Ri) allocated to each province and the measurement of
regional income (Yi). The second stage presents the estimates of the redistributional indices as
defined in the previous section.
A. Federal Fiscal Balances and Regional Income Disparities
In calculating federal expenditures and revenues allocated to each province, we confine our analysis
to Canadian residents only because federal revenues collected from non-residents do not impose a
burden on the residents of the various regions; similarly, those residents do not benefit from federal
spending directed at non-residents. We also focus our analysis on jurisdictions rather than individuals
by calculating the contribution that a province makes to the federal coffers through the tax burden
borne by its residents and the contribution that federal expenditures make to the economic position
of that province. In allocating federal revenues we use the assumptions generally applied in tax
incidence studies2. Specifically, personal income taxes were allocated to individual taxpayers based
on their residence. Social insurance (payroll) taxes were allocated on the basis of the location of
employment. The broad-based consumption tax such as the Goods and Services Tax (GST) was
allocated according to the provincial distribution of personal consumption expenditures. Excise taxes
such as levies on fuels tobacco and alcoholic beverages were allocated on the basis of the provincial
14
distribution of the consumption of the taxed products. On the expenditure side, transfer payments to
persons and businesses were allocated on the basis of the residence of the recipients. Interest on the
public debt was allocated according to the provincial distribution of interest income. The wage
component of federal purchases was allocated on the basis of the location of employment. The nonwage component was assigned on the basis of the provincial distribution of private income from
current production, approximated by net national income at factor cost net of the total government
component.3
The federal expenditures and revenues by province derived through the above allocation are shown
in Table 3 which also contains the federal fiscal balances by province. We notice that, in 1996, the
federal fiscal system in Canada generated some redistribution among provinces. The three richest
provinces - Alberta, Ontario and British Columbia - paid in federal taxes more than received in federal
expenditures while the remaining seven provinces received more in federal spending than they paid
in federal taxes. The net loss to the richest provinces ($5.2 billion), however, was much less that the
net gain by the other provinces ($23.1 billion) because the federal government run a deficit of $18
billion.
To measure regional income disparities, we need an income concept that represents the economic
status of each province under the assumption that federal fiscal activity does not redistribute income
among provinces. The derivation of this income measure is shown in Table 4. The first component
includes the sources of income from current production that are usually found in the National Income
and Expenditure Accounts. We then add a number of income sources which are received by persons,
but are not generated from current production, and the amount of taxes assigned to labour income.
We call the sum of these two components private income. Finally, we include the actual fiscal
15
balances of provincial and local governments and the federal fiscal balances assigned to the various
provinces under the assumption that federal revenues and expenditures are allocated in proportion
to private income in each province. We call this income measure neutral-fisc income.
We notice from Table 4 that neutral-fisc income is not distributed equally among provinces. Three
provinces - Alberta, Ontario and British Columbia - have above-average per capita incomes; Quebec,
Saskatchewan and Manitoba have per capita incomes about 10% below the national average, while
the four Atlantic provinces have per capita incomes substantially lower than the national average.
B. Calculation of Interregional Redistribution Indices
Given the federal expenditures (Ei) and revenues (Ri) calculated in Table 3 and neutral-fisc per capita
income (yi)calculated in Table 4, we first calculate the relative shares (RSi) under the actual and the
three special cases (i.e., RSi(A), RSi(N), RSi(S), RSi(M)) using equations (2), (4), (6) and (9)
respectively. The results are shown in columns (A) to (D) of Table 5. The actual relative shares in
column (A), also graphed in Figure 1 against per capital income ranked in ascending order, show that,
with the exception of Nova Scotia, there is a clear demarcation between richer and poorer provinces.
The three richer provinces have RSi(A) in excess of one, indicating that they make a contribution to
the federal fisc more than commensurate to their level of per capita income relative to the national
average. The poorer provinces, with the exception of Nova Scotia, make a less than commensurate
contribution. Columns (B)-(D) of Table 5 show the RSi values under fiscal neutrality, standard
redistribution and maximum redistribution, respectively. As a comparison, the simple OLS regression
lines of RSi(A), RSi(S), RSi(M) against per capital income ranked in ascending order is shown in
Figure 2. We know from the above discussion that standard redistribution is represented by a
16
horizontal line at RSi = 1 and that maximum redistribution involves an upward sloping line. Figure
2 shows that the line representing actual redistribution is also upward sloping, but with a flatter slope
than the line of maximum redistribution. This indicates that in 1996 the fiscal activity of the federal
government in Canada generated a degree of interregional redistribution higher than standard
redistribution, but less than maximum redistribution. But by how much one may ask?
To address this issue, we proceed to the calculation of the two proposed indices using equations
(10) and (12). The results are shown in the last two columns of Table 5. Starting with the index that
relates actual to standard redistribution (RSI(S)), column (E) shows that with the exception of Nova
Scotia, federal fiscal activity generated interregional redistribution in excess of the standard level. The
excess over standard redistribution, however, varied considerably among the various provinces. For
the country as a whole, by redistributing income from the richer to the poorer provinces through its
revenues and expenditures, the federal government generated a degree of redistribution 80% higher
than the standard degree of redistribution. The last column of Table 5 shows that, with the exception
of Saskatchewan, actual redistribution was a fraction of maximum redistribution and the value of this
fraction varied considerably among provinces. Overall, the estimated degree of interregional
redistribution in Canada in 1996 was 48% of maximum redistribution. This means that in 1996 federal
fiscal system cuts interprovincial income disparities almost in half.
The last column of Table 5 also shows that the geographic distribution of economic activity in
Canada is favorable to interregional redistribution. With the exception of Quebec, the poorer
provinces are also the smaller provinces in terms of population and total value of economic activity.
By contrast, the three richer provinces ( Alberta, Ontario and British Columbia) accounted for more
than half of the Canadian population and nearly two-thirds of neutral-fisc income in 1996. Therefore,
17
it only takes a relatively small proportion of maximum redistribution in the richer provinces in order
to finance a relatively large degree of redistribution in the poorer provinces. For example, although
Alberta made the largest per capita net contribution to the federal fisc in 1996, federal balances
eroded only a small portion of the income differential from the national average ( RSIi(M) = .20).
For the country as a whole, it took on the average 38% of maximum redistribution in the three richest
provinces to deliver 68% of maximum redistribution for the remaining seven provinces.
4. CONCLUSION
This paper has developed a set of local and global indices of interregional redistribution. Called
Relative Share Index (RSI), each index incorporates explicitly the basic components of federal fiscal
balances by region and the degree of regional income disparities. To develop the indices, we first
introduced the concept of relative shares (RS) under the actual and three special known degrees of
redistribution. We showed that, when the federal fiscal system does not generate redistribution among
regions, the RS simply reflects the degree of income disparities measured by the reciprocal of the ratio
of per capita income in a region to the national average. If redistribution was delivered solely on the
expenditure side in the form of equal per capita federal expenditures in each region, the RS has a
value of one. When redistribution was delivered to equalize per capita income in all regions (the case
of maximum redistribution), the RS value depends on the average federal tax rate and the degree of
income disparities. Based on these RS values, we then developed two indices, RSI(S) and RSI(M),
to compare the degree of redistribution generated by the federal fiscal system to the standard and the
maximum degree of redistribution.
18
As an application, we used these indices to measure the degree of interregional redistribution in
Canada for 1996. Our results show that the federal fiscal system in 1996 delivered a degree of
interregional redistribution1.8 times what would have been generated under equal per capita
expenditures by province and nearly half of the maximum degree of redistribution.
19
REFERENCES
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Public Finance Quarterly, 15:166-87.
Cassady, K., G.C. Ruggeri and D. Van Wart. 1996. On the Classification and Interpretation of
Global Progressivity Measures. Public Finance, 51:1-22.
Kakwani, N. C. 1976. Measurement of Tax Progressivity: An International Comparison. The
Economic Journal. 87: 71-80.
Kjetan, C. P. and S.N. Poddar. 1976. Measurement of Income Tax Progression in a Growing
Economy: The Canadian Experience. The Canadian Journal of Economics. 9:613-29.
Mansell, R. and R. Schlenker. 1995. The Provincial Distribution of Federal Fiscal Balances.
Canadian Business Economics. Winter: 3-19.
Musgrave, R.A. 1991). Horizontal Equity, Once More. National Tax Journal. 43: 113-22.
Musgrave, R.A. and T. Thin. 1948. Income Tax Progression, 1929-48. Journal of Political
Economy. 56:498-514.
Plotnick, R. 1982. The Concept and Measurement of Horizontal Equity. Journal of Public
Economics.17:373-91.
Reynolds, M. and E. Smolensky. 1977. Public Expenditures, Taxes, and the Distribution of
Income: The United States, 1950, 61, 1970, New York, Academic Press.
Ruggeri, G.C., D. Van Wart and R. Howard. 1996. The Government as Robin Hood: Exploring
the Myth. School of Policy Studies, Queen’s University.
Ruggeri, G.C. and Weiqiu Yu. 2000. Federal Fiscal Balances and Redistribution in Canada,
1992-97. Canadian Tax Journal. 48:625-55.
Suits, D.B. 1977. Measurement of Tax Progressivity. American Economic Review. 67:747-52.
Statistics Canada. Provincial Economic Accounts, Cat. No. 13-213.
Statistics Canada, National Income and Expenditure Accounts, Cat. No. 67-202.
20
TABLE 1: Illustrative Examples of Calculating Relative Shares Under the Three Special Cases
yi
yi/y
Ri
Ei
Ri/Ei
Postfisc yi
Postfisc yi/y
RSi
(A)
RSi
(N)
RSi
(S)
RSi
(M)
(a) Redistributionally-Neutral (No Distribution)
Region 1
15,000
.8
3,000
3,000
1.0
15,000
.8
1.25
Region 2
22,500
1.2
4,500
4,500
1.0
22,500
1.2
.83
Total
37,500
7,500
7,500
Average
18,750
37,500
18,750
(b) Redistributionally through Equal per capital Expenditures (Standard)
Region 1
15,000
.8
3,000
3,750
.8
15,750
.84
1.0
Region 2
22,500
1.2
4,500
3,750
1.2
21,750
1.16
1.0
Total
37,500
7,500
7,500
Average
18,750
37,500
18,750
(c) Maximum Redistribution
Region 1
15,000
.8
3,000
6,750
.44
18,750
1.0
.56
Region 2
22,500
1.2
4,500
750
6.00
18,750
1.0
5.00
Total
37,500
7,500
7,500
Average
18,750
37,500
17,750
(d) Intermediate Case (Treated as Actual)
Region 1
15,000
.8
3,000
5,000
.60
17,000
.91
.75
Region 2
22,500
1.2
4,500
2,500
1.80
20,500
1.09
1.50
Total
37,500
7,500
7,500
Average
18,750
37,500
18,750
21
TABLE 2: Illustrative Examples of Calculating the Indices of Interregional Redistribution
Differences among RS Values
Indices
RSi(A)-RSi(N)
(1)
RSi(S)-RSi(N)
(2)
RSi(M)-RSi(N)
(3)
RSIi(S)
(1)/(2)
RSIi(M)
(1)/(3)
Region 1
-.50
-.25
-.69
2.00
.72
Region 2
.67
.17
4.17
4.00
.16
3.20
.38
Weighted Average
Note:
The weights are .4 for region 1 and .6 for region 2 because, under the assumption that each region
has a single agent, i.e., Yi = yi.
22
TABLE 3: Federal Fiscal Balances by Province in 1996, $ Million
Province
Federal Expenditures
(Ei)
Federal Revenues
(Ri)
Balances
(Ei-Ri)
Newfoundland
4762
2237
2525
Prince Edward Island
1179
680
499
Nova Scotia
7822
5173
2649
New Brunswick
5819
3712
2107
Quebec
38678
29566
9112
Ontario
67658
69852
-2194
Manitoba
8839
5831
3008
Saskatchewan
8149
4914
3234
Alberta
15884
17619
-1735
British Columbia
22942
24189
-1247
181733
163774
17959
All Provinces
23
TABLE 4: Calculation of Neutral-fisc Income by Province in 1996 $ million
NF
PEI
NS
Wages and Salaries and Supplementary Labour 5602 1419
Income
Government Components 1778
432
Private Wages and Salaries 3824
987
Accrued Income of Farm Operators
5
18
Net Income of Non-Farm Unincorporated Business
693
213
Interest and Miscellaneous Investment Income
701
144
Profits Retained in Canada
308
122
Current Transfers from Corporations
15
4
Subtotal 5546 1488
Superannuation
376
111
RRSP Withdrawals
81
24
Realized Capital Gains
70
41
CIT Assigned to Capital Income
31
19
Employer Portion of Payroll Taxes
420
97
Private Income 6524 1780
Net Provincial Balances
110
29
Net Local Balances
51
10
Federal Balances Allocated to Private Income
206
56
Neutral-fisc Income 6891 1875
Neutral-fisc Income Per Capita ($) 12283 13786
10539
NB
QC
ON
SK
AB
BC
Total
8859 96885 175317 14336 11443 43952 58450 426802
3147 2327 22530 34104
7392 6532 74355 141213
43
28
774
298
1491
981 10096 19586
1137 1170 11920 18576
623
645 7422 17431
25
20
194
297
10711 9376 104761 197401
1089
669 6016 12210
197
146 1475 3034
224
128 2048 4613
122
73 1084 2264
736
546 8706 12038
13079 10938 124091 231560
-60
177 5499 5748
38
73 2066 1656
412
345 3910 7296
13469 11532 135566 246261
14468 15315 18637 22184
24
MB
3726
10610
557
1830
2627
775
30
16429
1044
269
373
171
976
19262
43
183
607
20095
17721
2894
8549
1399
1579
2744
1679
27
15977
839
221
521
219
697
18474
-554
176
582
18678
18330
7832
36120
844
4708
9146
7229
74
58121
2066
769
1992
940
2289
66176
-2303
508
2085
66467
23900
11679
46771
81
7065
8600
3545
104
66166
3781
1073
2388
1105
3566
78079
1381
1300
2460
83221
21438
90449
336353
4047
48242
56765
39779
790
485976
28201
7289
12398
6029
30071
569964
10070
6061
17959
604054
20427
TABLE 5: Calculated Values of RSi for Canada, 1996, Actual and under Selected Cases
RSI(S)
RSI(M)
RSi(A)
RSi(N)
RSi(S)
RSi(M)
(A-B)/(C-B) (A-B)/(D-B)
(A)
(B)
(C)
(D)
(E)
(F)
Newfoundland
0.86
1.66
1
0.48
1.21
0.68
Prince Edward Island
0.94
1.48
1
0.53
1.13
0.59
Nova Scotia
1.02
1.41
1
0.56
0.95
0.46
New Brusnwick
0.94
1.33
1
0.60
1.18
0.53
Quebec
0.92
1.10
1
0.82
1.80
0.64
Ontario
1.04
0.92
1
1.28
1.50
0.33
Manitoba
0.83
1.15
1
0.73
2.13
0.76
Saskatchewan
0.73
1.11
1
0.79
3.45
1.19
Alberta
1.04
0.85
1
1.80
1.27
0.20
British Columbia
1.10
0.95
1
1.17
3.00
0.68
1.80
0.48
Weighted Average
25
FIGURE 1: The Actual RSi(A) and Neutral-fisc Income Per Capita
26
FIGURE 2:
The Regression Lines of Actual Relative Shares and Relative Shares Under Standard
and Maximum Redistribution Against Per Capita Income
27
Notes
1. In order to obtain positive values of RSIi(M) it is necessary that, for any region, yi/y > (1-b).
A situation of low average tax rates and high regional disparities would yield negative values of
RSIi under maximum redistribution.
2. See, for example, Ruggeri, Van Wart and Howard (1996).
3. A more detailed explanation of the allocation procedure is found in Ruggeri and Yu (2000).
28