QEDQueen’s Economics Department Working Paper No. 1121

The Reform of Equalization Payments

Dan UsherQueen’s University

Department of EconomicsQueen’s University

94 University AvenueKingston, Ontario, Canada

K7L 3N6

2-2007

With thanks for helpful comments to my colleagues Steve Kaliski and James Thompson,1

to Frank Vermaeten and Duane Hayes of the Department of Finance and to Claude Vaillancourtof Statistics Canada.

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The Reform of Equalization Payments1

Dan UsherFebruary, 2007,

Abstract A reasonable and fair interpretation of the mandate for equalization payments inSection 36(2) of the Canadian Constitution differs from the present equalization formula in theserespects: Transfers to the poorer provinces would be financed by transfers from the richerprovinces rather than from the Federal government. Entitlement to equalization payments woulddepend on provincial income rather than upon a tax-by-tax comparison of the provinces’ manytax bases. For this comparison, provincial income would include revenue accruing directly to theprovincial governments as well as private income of the residents of the province. Compensationwould be made for the exemption of provincial resource revenue from Federal income tax. Themost pronounced effect of these proposals would be to transfer the greater burden of equalizationpayments from Ontario to Alberta which is now, by far, the richest province.

Much of the confusion and controversy over the Canadian program of equalizationpayments stems from a mismatch between its constitutionally-sanctioned mandate and two otherprovisions of the Canadian Constitution.

The constitutionally-sanctioned mandate for equalization payments is Section 36(2)requiring the Federal government to provide equalization payments

“to ensure that provincial governments have sufficient revenues to provide reasonablycomparable levels of public services at reasonably comparable levels of taxation”.

Without equalization payments, tax rates would have to be higher in poor provinces thanin rich provinces for any given level of provincially-provided public services: health care,education, policing and so on. Equalization payments are designed not to equalize incomes perhead, but to enable all provinces to afford the same dollar value public services when the sameproportion of taxpayers’ incomes is taxed away by their provincial governments.

The two other provisions of the Canadian Constitution - blocking what is claimed here tobe reasonable interpretation of section 36(2) - supply the provinces with sole jurisdiction overresource revenues and stipulate that “the crown cannot tax the crown”. Specifically, theseprovisions are

Sections 92A(4) and 125 are downright pernicious. Together, they imply that, though 2

people’s earned income may be taxed to finance expenditure by the Federal government,people’s income acquired passively and effortlessly (in the form of provincial public services atlower than otherwise tax rates) by virtue of the province where they happen to reside is exempt.

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Section 92A(4): In each province, the legislature may make laws in relation to theraising of money by.....taxation....of non-renewable natural resources in the province.

and Section 125: No Lands or Property belonging to Canada or any Province shall be Liable to Taxation2

I claim here that a) by itself, Section 36(2) warrants a simpler, fairer and more generally-acceptable system of equalization than what we have today, b) equalization “up-but-not-down”should be replaced by equalization “down-as-well-as-up” ( terms in quotes to be defined below),c) the “representative tax system” in the present Canadian equalization program should bereplaced by a “macro formula”, d) an implicit Federal tax of provincial resource revenues shouldbe incorporated into the equalization formula and e) the constraints in Sections 92A(4) and 125can be circumvented by a fusing of equalization, broadly defined, into a more comprehensiveFederal-provincial transfer. I justify these claims as best I can, and present rough estimates ofwhat equalization payments would be if these proposals were adopted. Four features of theproposed revision of the Canadian equalization program are these:

First, comparable levels of public services at comparable levels of taxation is moreappropriately accounted for by equalization down-as-well-as-up rather than by equalization up-but-not-down” as in the Canadian program of equalization payments today. The presentsystem of equalization payments up-but-not-down is a transfer of revenue from the Federalgovernment to the poorer provinces, lowering provincial tax rates required in the poorerprovinces to supply a given dollar value of public services per head, but without eliminating thegap between required provincial tax rates in rich and poor provinces. Part of the gap remainsbecause provincial tax rates in the richer provinces are left unchanged and because the requiredtax rates in the poorer provinces are reduced only to the national average as it would be in theabsence of equalization payments rather than to the national average as it becomes withequalization payments in place. Equalization down-as-well-as-up is would be a Federally-mandated transfer of revenue from rich provinces to poor provinces, automatically lowering taxrates required in the poorer provinces and raising tax rates required in the richer provinces toallow all provinces to supply the same dollar value of public services at the same tax rates withno net contribution from the Federal government.

Imagine a country of two provinces with equal populations, different incomes perresident, but the same public expenditure. One province is rich with an income per resident of$100,000, the other province is poor with an income per resident of $50,000, but their publicexpenditures are both equal to $15,000 per resident. To finance that expenditure in the absence ofequalization payments, the rich province would need to impose a tax rate of 15%, the poor

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province would need to impose a tax rate a revenue of 30%, and the average provincial tax ratewould be 20% [(15 + 15)/(100 + 50)]. To enable both provinces to finance their commonexpenditure of $15,000 per resident by a common tax rate of 20%, as section 36(2) would seemto require, there would need to a transfer of $5,000 per resident from the rich province to thepoor province. Such a transfer would be down-as-well-as-up, for one province must lose what theother gains.

A system of equalization payments could be designed to create such a transfer, but that isnot how the Canadian system works now. Instead, our system of equalization payments up-but-not-down would transfer $5,000 per head to the poor province from the Federal governmentrather than from the province, lowering the required provincial tax rate in the poor province from30% to 20%, raising Federal tax rates in both provinces to finance the transfer, but leaving theprovincial tax rate of the rich province at 15% as before. This equalization up-but-not-down”violates Section 36(2) because it fails to eliminate the discrepancy between required provincialtax rates. By contrast, equalization down-as-well-as-up would conform to Section 36(2), butwould violate Section 125 instead, for the Federal government would need to tax the governmentof the wealthier province or, equivalently, to impose a special surtax on the residents, rich orpoor, of the wealthier province. The reason, so far as I can tell, why Canada has not adoptedequalization down-as-well-as-up is that Section 125 is seen - wrongly in my opinion, for reasonsto be discussed below - as an insurmountable barrier

Second, levels of taxation is more appropriately represented by a “macro formula” than bythe “representative tax system” in the Canadian program of equalization payments as it is today.Under the representative tax system, a province becomes entitled to equalization payments whenthe rate-weighted sum of its tax bases per head is lower than the average in all provinces nation-wide. Under a macro formula, a province is entitled to equalization payments when its incomeper head is below the national average, or, equivalently, when it would acquire less than theaverage revenue per head form a provincial income tax at a uniform nation-wide rate. There arepros and cons of both systems, but it is argued here that the macro formula is much simpler, lessquirky in response to taxes other than progressive income taxes, more likely to directequalization payments to poor provinces and, all things considered, more in accordance with thespirit and purpose of 36(2).

Once a target rate of provincial taxation - typically the ratio of total provincial revenue tototal income of all provinces together - has been established, a province’s entitlement to receiveor obligation to provide equalization payments should depend entirely upon whether its incomeper head is large or small. Details of provincial taxation should be irrelevant. Here again, that isnot how the Canadian system of equalization payments works now. A complicated formula withpages and pages of detail and oodles of exceptions assigns equalization payments in accordancewith the provinces’ choices of tax bases and tax rates.

Third, it should make no difference to a province’s entitlement whether income is privateor collective. Only the total should matter. My private income is what I earn from work or as the

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return to assets I possess. My collective income is my share of income accruing directly to theprovince where I reside (rather than through taxation of the residents of the province). The maincomponent of collective income is resource revenue. If my province has one million people andtakes in one billion dollars of resource royalties, my collective income on that account is onethousand dollars. A province should be deemed rich or poor for the purpose of assigningequalization payments according to whether the sum of private income and collective income islarge or small.

Fourth, the principle that collective income should be treated on a par with privateincome can be extended to the obligation to pay a share of the cost of the Federal government. Asystem of equalization payments could incorporate a deduction to compensate for the Federalincome tax that would have been collected if resource revenue and other collective income hadaccrued in the first instance to people in a province rather than directly to the provincialgovernment. If the average Federal income tax rate is 25%, a province with a billion dollars ofresource revenue would be debited for a quarter of a billion dollars on the equalization account.

Two degrees of interprovincial sharing of collective income need be recognized. Thelesser degree of interprovincial sharing of collective is to treat such income as though it wereprivate. If my province acquires an extra resource revenue of $1000 per resident, it seems onlyreasonable that, on my behalf, it should contribute the same proportion to the rest of Canada as Iwould be obliged to contribute if the income accrued to me directly. The greater degree ofsharing is when income that does not automatically belong to anybody in particular isautomatically assigned to the nation as a whole. It is the sharing implicit in a unitary state, a statewithout provinces, or in a country where jurisdiction over natural resources and the right to taxtheir extraction lies exclusively with the central government. Sections 125 and 92(a)4 of theCanadian constitution may be read as blocking both degrees of sharing. It is argued here that thelesser degree of sharing should be allowed even if the greater degree remains blocked.

Provincially-owned resource revenue is to the residents of the province like manna fromheaven, either as the source of extra public services at no extra tax or as a lower than otherwisetax to finance a given level of public services. In either case, it is income acquired by virtue ofone’s place of residence rather than from one’s labour or property. It is, moreover, an especiallyprivileged income because, unlike income from work, it appears at the door of the recipient freeof all Federal tax. Together, rigid provincial jurisdiction over natural resources and the rule thatthe crown cannot tax the crown creates the peculiarity that earned income bears a share of thecost of the Federal government but income acquired effortless by virtue of one’s place ofresidence does not. What was referred to above as the lower degree of sharing is a corrective,ensuring that both forms of income are taxed alike. Both are made to contribute equally to thecost of the Federal government, including the cost of augmenting the revenue of the poorerprovinces.

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Since Alberta is now by far the richest province in Canada, the combined effect of theseproposed modifications of the Canadian equalization program would transfer the greater part ofthe cost of equalization payments from the residents of Ontario onto the residents of Alberta. Onthe other hand, this redesign of the Canadian equalization program has to be a gross violation ofSections 94(4) and 125 of the Canadian constitution.

There is a way around these prohibitions. The Canadian Supreme Court has inventedwhat has come to be called “the spending power”. Just as people may give gifts to whomsoeverthey please and may attach whatever conditions they please upon these gifts, so too according toour Supreme Court may governments, despite the fact that a government’s gift is ultimately apublicly-mandated transfer from one group of people to another.“The simple withholding ofFederal money which had previously been granted to fund a matter within provincial jurisdictiondoes not amount to a regulation of that matter.” [Sopinka J. In Re: The Canada Assistance Plan,1991]

To invoke the spending power, the Federal government would need to combineequalization payments and per capita transfers - such as the Canada Health and Social Transfer -into a single program with a large enough per capita transfer to outweigh the largest of thenegative equalization payments, so that the Federal government could be seen as givingsomething to each and every province. Whether the Canadian Supreme Court would tolerate thisGilbert and Sullivan ploy is another matter. If not, the constraints of Sections 125 and 92A(4)would remain binding and Canadians would continue to suffer the constitutional curse that whatis mandated by one clause of the constitution is rendered imperfect, controversy-laden anddivisive by another.

From here on, the paper examines the four proposed reforms in greater detail. We beginby a comparison of formulas. The equalization formula as it is today is contrasted with theformula as it would become if the four proposed reforms were adopted. There follows adiscussion of the purpose of an equalization program of equalization, of precisely what such aprogram might be designed to achieve. After that, comes a detailed discussion of the contrastbetween down-as-well-as-up and up-but-not-down, with emphasis on the derivation of therevised equalization formula and of the incorporation of resource revenues accruing directly toprovincial governments rather than as deductions from the gross incomes of the residents of theprovince. There follows a discussion of the macro formula with emphasis upon when it can beexpected to conform well to the requirements of Section 36(2) and when it might fail to do so.The paper concludes with calculations of the provinces’ gains or loses from the transformation ofthe system of equalization payments from the present arrangements to the proposed alternative,and of the consequences for the different provinces of an increase in the world price of oil.

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A Comparison of Equalization Formula

The Canadian system of equalization payments from the Federal government to thedeficit provinces is up-but-not-down and tax-by-tax. The proposed alternative would assignequalization payments down-as-well-as-up and in proportion to the income of the recipientprovince. Equalization tax-by-tax is commonly referred to as the “representative tax system”,while equalization in proportion to the income of the recipient province is commonly referred toas the macro formula.

i Broadly speaking, the present Canadian system prescribes an equalization payment of Eper person from the Federal government to province i where

i jc jc ji jc jc jiE = Óô (B - B ) as long as Óô (B - B ) > 0 (1a)

iand E = 0 otherwise. (1b)

where the subscript i refers to a province,

the subscript j refers to a provincial tax base,

Ó refers to the sum over all tax bases,

c (mnemonic for Canada) refers to the country as a whole

jiB is the j tax base per person in province i,th

jcB is the nation-wide average tax base per person for the j tax,th

jcand ô is the nation-wide average provincial tax rate per person on the j tax base. th

A tax base may be a dollar value or a physical quantity. When a tax base is a dollar value,the tax rate must be a percentage. When a tax base is a physical quantity the tax rate must be indollars per unit. A tax bracket for a graduated income tax is an example of the former. A tax perautomobile is an example of the latter.

Two variants of the of the proposed alternative differ depending on whether or not theycompensate for the absence of Federal taxation of collective income in the province. Paymentswith and without such compensation are

i c c c i i iE = ô [(y + r ) - (y + r )] - ô r (2a)F

i c c c i iE = ô [(y + r ) - (y + r )] (2b)

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iwhere, once again, E is the equalization payment to province i,

iy is pre-tax personal income per head in province i

ir is provincially-owned resource revenue per head in province i (or other provincialincome not originating as a gap between pre-tax and post-tax income of the residents ofprovince i)

cy is private income per head in Canada as a whole

cr is provincially-owned resource revenue per head in Canada as a whole

cô is the average provincial tax rate in Canada as a whole, measured as the ratio of thesum over all provinces of total provincial revenue to the sum over all provinces of privateincome augmented to include resource revenues accruing directly to provincialgovernments,

and ô is the Federal income tax rate.F

iThe difference between the two variants of the formula is ô r , the increase in FederalF

income tax that would be levied upon residents of province i if resource royalties and otherpublic revenue accruing directly to the government of the province accrued to the residents of theprovince instead. Equalization payments may or may not be designed to take this into account. Itis argued in this paper that they should be, as indicated in equation (2a). Equation (2b) replacesequation (2a) when, as in Canada today, no share of provincial resource revenue can beappropriated by the Federal government.

An essential difference between present Canadian equalization formula the proposedalternative is that the former can only give while the latter may either give or take and, by taking,would seem to constitute a violation of Section 125 of the Canadian constitution. A way aroundthis constitutional prohibition is to combine equalization payments in conformity with equations(2a) or (2b) above with a subsidy of S dollars per person from the Federal government to all

i provinces, where S is made large enough to create a positive combined transfer, S + E , to everyprovince.

What 36(2) is Intended to Achieve

The translation of 36(2) into a precise equalization formula can be undertakensemantically or politically, that is, with reference to the meaning of the words of the Constitutionor with reference to the objectives for which 36(2) seems to have been designed. Both tests areemployed in this paper to compare the Canadian system of equalization payments as it is and as itwould be if modified in accordance with equation (2b) above: with equalization down-as-well-

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as-up, with a macro formula and with resource revenues treated as though they accrued in thefirst instance to people in the province rather than to the provincial government.

Consider first the language of 36(2). The clause refers to provincial governments havingsufficient revenues to provide reasonably comparable levels of services at reasonably comparablelevels of taxation. Though exceptions are discussed briefly below, it is assumed throughout mostof this paper - and it is implicit in the Canadian equalization formula as it is today - that levels ofservices is appropriately measured as dollars worth of public expenditure per head. Morecontentious is the meaning of the phrase comparable levels of taxation, but this much seemsclear. Comparable levels of taxation mandates equalization down-as-well-as-up because theCanadian equalization formula as it is today - with poor provinces brought up to the average as itwould be in the absence of equalization while rich provinces remain well above that average -corresponds to no reasonable interpretation of comparable.

Implications of the phrase comparable levels of taxation about the choice between therepresentative tax system and the macro formula are not so clear. A case might be made for therepresentative tax system when all provincial revenue is acquired by one and the same scheduleof progressive income taxation On the other hand, a macro formula would seem to be moreappropriate when comparable levels of taxation is interpreted to refer to the total burden ofprovincial taxation upon the average taxpayer in the province, regardless of differences amongthe provinces in their choice of tax bases (one province relying relatively more upon aprogressive income tax, another on property taxes, another on sales taxes and so on) andregardless of how provincial tax rates may differ from a uniform schedule of progressivetaxation. Implicitly, the macro formula interprets the level of taxation as the percentage ofincome that the provincial government appropriates, regardless of the route by which taxpayers’incomes are appropriated. The choice between the representative tax system and the macroformula will be discussed in detail below. A simple case presents a stark contrast between thetwo.

Imagine a triumph of the neocons in all ten provinces, leading to the replacement of thepresent tax system - with income taxes, sales taxes, property taxes and so on - by a head tax, afixed dollar payment per person. To interpret levels of taxation in Section 36(2) as pertaining totax rates on actual provincial tax bases, whatever the bases may be, is to accept “people” as theappropriate provincial tax base, forcing all provincial tax bases per person to be the same, andenabling all provinces to supply not just comparable, but identical, levels of services at identicaltax rates. On that interpretation of levels of taxation, no equalization payments would ever bewarranted no matter how great the disparities among the provinces in their incomes per head.Some provinces may be filthy rich, and others desperately poor. The discrepancy in incomes perhead warrants a substantial equalization payment under the macro formula in equation (1), butthe equality in the tax bases - people - means that no equalization payment whatever is warrantedunder the representative tax system in equation (2).

My sense of the purpose of Section 36(2) is that equalization payments would still be

On alternative measures of the efficiency of equalization payments, see L.S. Wilson,3

“Equalization, Efficiency and Migration: Watson Revisited”, Canadian Public Policy, vol XXIX,No. 4, 2003, 385-96.

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warranted, but to justify that interpretation it seems appropriate to consider what the political andsocial objectives of Section 36(2) might be. Several partially distinct and partially overlappingobjectives might be identified.

One such objective is efficiency. A system of equalization payments is said to be efficient if and in so far as it promotes the maximization of the national income in the country as a whole.Efficiency has many dimensions of which two are especially pertinent for the evaluation of asystem of equalization payments. On the one hand, a system of equalization payments mayinfluence the distribution among provinces of labour and other mobile factors of production. Theinter-provincial distribution of labour is optimal when the marginal product of labour is the samein every province. The value of the marginal products of any two equally-skilled carpenters orany two equally-skilled doctors should ideally be the same everywhere. A system of equalizationpayments promotes this aspect of efficiency if it causes net incomes of equally-skilled carpentersor equally-skilled doctors to be more nearly equal among provinces than they would otherwisebe. For the choice between the representative tax system and the macro formula, the questionbecomes which of the two systems generates the smaller discrepancies among like people indifferent provinces between benefits of public services and taxation to pay for them. The answerdepends very much on provincial tax structures. A representative tax system might be moreefficient if all provincial revenue were acquired by a head tax and if the tax per person were thesame in all provinces. A macro formula might be more efficient when different provinces havevery different tax structures, especially as the prospect of receiving equalization payments mayinduce a province to set taxes in ways that are beneficial to that province but detrimental to thecountry as a whole. Replacement of one tax by another may cost a province $10 in lost revenuebut provide it with $15 of extra equalization payments at the expense of the rest of the nation. Inchoosing among alternative systems of equalization payments, efficiency in the interprovincialallocation of labour and in the provinces’ choice of tax rates need both be taken into account.3

Another objective is equality. A system of equalization payments promotes equality whenit diminishes the variance of the distribution of post-tax income in the national as a whole.Though this consideration should not be ignored, it is hard to believe that equality per se wouldnot be better promoted by an outright grant to poor people wherever they happen to reside thanby the equalization program as it is today or as it might be altered. Redirected to the worst off20% of Canadians, the $11 billion dollars Canada spends on its equalization program wouldsupply almost $2,000 per head, or $8,000 per year for a family of four. There is, of course, aserious difficulty in targeting money to poorest 20% of the population, but the personal incometax could be revised to channel a good deal of the money now devoted to equalization in thatdirection. If efficiency or equality were the principal object of a system of equalization payments,it is something of a mystery why Section 36(2) was included in the Constitution when so manyother efficiency or equality-promoting measures were not.

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A third objective is horizontal equity. There is some variation in the usage of theexpression “horizontal equity”. A common usage identifies horizontal equity with the absence ofdiscrimination in taxation. People with high incomes may be taxed at higher rates than peoplewith low incomes, but two people with the equal incomes should be taxed equally. A carpenterand a doctor who earn same income should be confronted with the same tax bill. On thisinterpretation, horizontal equity is a political virtue. The carpenter and the doctor are taxed thesame to avoid the conflict and dissension that would arise if the government chose to set eachtrade’s - or worse still each person’s - tax rate separately. As with efficiency and equality, there issome question about the relevance of horizontal equity for the assessment of differentinterpretations of Section 36(2). As a political virtue, horizontal equity has little bearing oncomparisons of tax rates among countries. It does not matter if people with the same incomes aretaxed more heavily in England than in France because there is no common government to whichthe Englishmen can complain. Similarly, there may be no common government to which thepeople of Saskatchewan can complain if they are taxed more heavily by the government ofSaskatchewan than people with the same income in British Columbia are taxed by thegovernment of British Columbia. They can migrate to British Columbia, but whether or not thatis desirable comes under the heading of efficiency, not horizontal equity.

A literal interpretation of Section 36(2) suggests a closely related objective: thestandardization of the cost of public services nation-wide. Any two residents of Ontario areexpected to receive the same medical services and to be confronted with the same tax schedule,regardless of the dollar value of tax they actually pay. The same is true of any two residents ofManitoba. The corresponding objective of equalization payments is to create a comparableequality between a resident of Ontario and a resident of Manitoba, or, more generally, to create acomparable equality for all Canadians wherever they may reside. People everywhere wouldreceive the same medical services as long as they are both confronted with the same taxschedules in the provinces where they reside. The same would be true for all provincially-supplied public services The application of this principle must take account of the possibilitythat identically-situated people in different provinces might pay different rates of tax to financedifferent levels of public services. This objective is distinct from equality as it is normallyunderstood. It does not warrant a reduction of the variance of the income distribution in thecountry as a whole. It merely warrants that equal public services at equal rates of tax. Rightly orwrongly, it places publicly-provided goods into the domain of equality, while at the same time asleaving privately-provided goods in the domain of markets where inequality of income is to beexpected. I would put considerable weight upon this objective because it approaches the wordingof 36(2) and because it is rightly constitutional in the sense that the objective is unlikely to beobtained unless it is constitutionalized.

The question remains, however, why a country might seek to equalize public servicesamong provinces (for any given tax rates) while at the same time leaving substantial disparities inprivate income among people throughout the land and between average incomes of people indifferent provinces. This is in part an efficiency consideration, but not entirely so. People are freeto relocate from one province to another, but it would be inefficient for them to do so for no other

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reason than to participate in a province’s collective income. If that were the only consideration,natural resources would never have been placed under provincial jurisdiction. Equally importantare the likely spillovers in the provision of public services. A road in Western Ontario mayconvey a greater benefit to a person from Winnipeg than to a person from Toronto. With healthcare in the public sector and financed by the provinces, a person from Prince Edward Island mayreceive medical care in British Columbia and vice versa. Equalization payments equalize thefinancial burden of services we all enjoy, at least to the extent that a province cannot reduce thecost of its spillovers to residents in other provinces without at the same time reducing publicservices to its own residents as well.

In effect, Section 36(2) imports into the Canadian federation some of the financialattributes of a unitary state. Every provinces is empowered to replicate nation-wide tax rates andpublic expenditure per head as they would be if there were no provinces and all public financewere under the authority of the federal government. Provinces still can choose how to spend theirrevenue, and their revenue per head may differ from the national average as long as taxes differaccordingly, but, in this choice, revenue itself is not to reflect private wealth as it would doautomatically in the absence of equalization payments.

There is another consideration. In discussing financial relations among governments, weare accustomed to speak of governments as though they were people. The practice is notespecially misleading when confined to dealings among provincial governments becausestatements about provinces are easily translated into statements about the people who live there.The practice becomes pernicious for relations between a province and the Federal governmentbecause a transfer to a province from the Federal government is really a Federally-mandatedtransfer to the residents of that province from the residents of other provinces. Gifts from theFederal government to a province are really imposed transfers through the intermediary ofFederal income taxation to the people that province from people in other provinces. Gifts fromthe Federal government to all provinces simply cancel out. There are good reasons why it may beadvantageous for Canada as a whole to raise money through the Federal government and to spendit through the provinces, but such reasons are only obscured by talk of gifts from the Federalgovernment. A program of equalization payments can only be assessed by reference to the netgains to people in some provinces and the corresponding net loses to people in others.

Up-but-not-down vs. Down-as-well-up

As explained above, equalization up-but-not-down is one of the two leading features ofthe present Canadian equalization formula while down-as-well-as-up is the corresponding featureof the proposed alternative. The question at hand is which of the two conforms best to themandate in Section 36(2). To focus upon this aspect of equalization, it is helpful to begin with asimple economy in which the tax base for the representative tax system and the macro formulawould be one and the same. Imagine a country, c, where all provincial revenue is acquired byproportional income taxation and where people’s incomes differ between provinces but not

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áwithin them. Everybody in any province á has the same income, y , everybody in any province â

â á âhas the same income, y , but y and y are not the same. With all provincial tax revenueacquired by proportional income taxation, there can be only one provincial tax rate. The tax rate

i in any province i is designated as ô . It turns out that, for such an economy, the requirement inSection 36(2) is best satisfied by the equalization formula in equation (2a) above. Only this formula “provides reasonably comparable levels of public services at reasonably comparablelevels of taxation”.

The line from Section 36(2) to the equalization formula in equation (2a) will be explainedin two stages, first for a nation with no provincially-owned resource revenue and then onceprovincially-owned resource revenues are introduced.

With No Provincially-owned Resource Revenue

In the absence of equalization payments, the budget constraint of the government ofprovince i must be

i i ip = ô y + S (3)

where S is a fixed transfer per head from the Federal government to every province. The

i igovernment of province I must choose some combination of p and ô in accordance with equation

á á á â(3) where, as between any two provinces á and â, it must be the case that either p > p or ô < ô

á áwhenever y > y . Either public expenditure is higher or the tax rate is lower in the wealthier

iprovince. A set of equalization E can be said to conform to Section 36(2) if it supplies the same

c c ccombination of expenditure and taxation, p and ô , to all provinces, where p is is the average

cprovincial expenditure per head in all provinces together and ô is the average provincial tax rate.Some provinces may choose larger public expenditure per head, but only at the cost of imposinga higher tax rate.

A set of equalization payments converts the budget constraint of province i to

i i i ip = ô y + S + E (4)

iWithout affecting anything of substance, values of the S and all E can always be chosen so that positive payments to rich provinces cancel out with negative equalization payments to poorprovinces, in which case

i i ÓE n = 0 (5)

iwhere n is the population of province i. The average provincial budget constraint in the nation asa whole becomes

c c cp = ô y + S (6)

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c c cwhere p is average expenditure per head, ô is the average provincial tax rate and y is incomeper head in the nation as a whole.

c cIt follows at once from equations (4), (5) and (6) that the combination of p and ô canonly be available to all provinces at once when equalization payments are chosen so that

i c c iE = ô (y - y ) (7)

which is the proposed formula in equation (2a) for the special case where there are noprovincially-owned resource revenues.

Though some equalization payments are negative, the letter if not the spirit of Section 125

ican be preserved by setting S large enough that E + S is positive for all provinces. The higher S,

cthe lower ô need be for any given value of p .

Introducing Resource Revenue

The appropriate treatment of resource revenue in the equalization formula depends onhow one defines the tax base for the assessment of “comparable levels of taxation” in Section36(2). The tax base might be interpreted either as private income alone or as private incomeaugmented by the collective income implicit in the presence of provincially owned resourcerevenue. On the former interpretation, a strict reading of 36(2) would require the completeFederal capture of resource revenue. On the latter interpretation, a strict reading of 36(2) wouldrequire provincially-owned resource revenue to be taxed at the same rate as ordinary private

cincome and to be treated as any other source of income under the equalization formula. ô

If the tax base for the computation of “comparable levels of taxation” were privateincome alone (with no allowance for the provincially-owned tax revenue), the appropriateequalization payment for enabling all provinces to supply the same public services at the sametax rate would have to be

i c i i E = ô(y - y ) - r (8)

i i cwhere r is the province’s resource revenue per head and where y and y are pre-tax personalincomes in province i and in the nation as a whole, for in no other way can all provincial budget

i c i cconstraints conform to equation (4) when ô = ô and p = p . Equalization in accordance with thisformula would, in effect, be a complete nullification of the constitutional assignment resourcerevenues to the provinces. Provincial resource revenue equalized in accordance with equation(8) is no resource revenue at all, or nothing more than the share accruing to the residents of theprovince if entitlement to resource revenue had been Federal rather than provincial.

This implication of the equalization down-as-well-as-up can be avoided by enlarging thescope of income in the equalization formula. Equalization payments could be computed as

That gambit was proposed long ago by W. D. Gainer and T. L. Powrie, “Public Revenue4

from Canadian Crude Petroleum Production”, Canadian Public Policy, winter 1975, 1-12.

This proposal has a family resemblance to a recent proposal by Tom Courchene in5

“Energy Prices, Equalization and Canadian Federalism: Comparing Canada’s Energy PriceShocks, Queen’s Law Journal, 2006, 644-96. Courchene proposed that 20% of each province’sresource revenue be placed in a fund to be administered by the provinces collectively rather thanby the Federal government, and that the income in the fund be passed back to the provinces inproportion to their populations. Contributions to the fund would be voluntary, but Courchenebelieves resource-rich provinces would be induced by pressure from other provinces and by aconcern for the country as a whole to supply their designated shares. The rest of the equalizationprogram would remain more or less as it is now. The article contains an account of how theCanadian equalization program responded over the years to changes in the price of petroleum.

This assignment of entitlement has been called “narrow based horizontal equity” as6

distinct from “broad based horizontal equity” which would in effect reassign all public revenueaccruing directly to the province (rather than through the intermediary of taxation of the residentsof the province) to all citizens equally regardless of where they lived. See Robin Boadway andFrank Flatters, Equalization in a Federal State, Economic Council of Canada, 1982.

14

though resource revenue had accrued not to the provincial governments, but to the residents ofthe province, or, equivalently as though resource revenue in the hands of provincial governmentswere passed back to residents of the province and then treated as ordinary income by bothFederal and provincial governments. Residents’ net gain from a province’s resource revenue4

would then be twice diminished, but not eliminated altogether. It would be diminished first bythe extra Federal tax that residents of the province would be obliged to pay and diminished onceagain through the equalization program. There would, nevertheless, remain a substantial netadvantage to the residents of the province from the collective ownership of resource revenueaccruing in the first instance to the government of a province rather than to its residents. 5

A new question arises: If resources are appropriately to be treated as though they accruedto the residents of the province directly rather than to the provincial governments, what exactlydoes section 36(2) require a system of equalization payments to equalize? The clause speaks oftax rates but does not say exactly how, or on what base, provincial taxes are to be assigned. Isuggest that the proper criterion in conformity with the spirit of 36(2) is to equalize not tax rates

i i iper se, but the ratio of post tax income, z , to pre-tax income, y + r , as it would be if augmentedby provincial resource revenue. Equalization payments would be designed to equalize the ratiosamong provinces of post-tax to pre-tax income as it would be if a) all resource revenue accruingdirectly to provincial governments were immediately passed to the residents of the provinces, b)people in all provinces enjoyed the same provincial public services per head and c) provincial taxrates - levied on augmented income inclusive of resource revenues passed back from theprovincial government - were the same in all provinces.6

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This conceptual privatization of provincial resource revenue would affect the budgetconstraints of provincial governments and the residents of the different provinces. Without suchprivatization the budget constraint of the residents of province i would be

i i iz = y (1 - ô - ô ) (9)F

i iwhere z and y are the post-tax and pre-tax incomes of the residents of the province i.Privatization of provincial resource revenue converts that budget constraint to

i i i i z = (y + r )(1 - ô * - ô ) (10)F

iwhere ô * is the provincial tax rate as it would become after the expansion of the tax base.

Similarly, without privatization of provincially-owned resource revenue, the budgetconstraint of province i would be

i i i i ip = ô y + r + S + E (11)

and with privatization of provincially-owned resource revenue the budget constraint of province Ibecomes

i i i i ip = ô *(y + r ) + S + E (12)

The purpose of equalization in this context is almost the same as before: to balance all

iprovincial budgets when public expenditures and tax rates are the same, that is when all ô * are

c iequal to a common provincial tax rate, ô *, and all p are equal to a common provincial

c c cexpenditure per head, p , and where, following Canadian practice, the common ô * and p are theaverage provincial tax rate and provincial expenditure per head. The average provincial tax rate ,

cô *, equals the ratio of the average provincial own-source revenue to the average provincial tax

c c cbase, except that now the average provincial tax base is expanded from y to y + r .

c c c c ô * = (p - S)/(y + r ) (13)

as long as equalization payments to some provinces cancel out with negative equalizationpayments to others in accordance with equation (5) above. The revised equalization formula inequation (2a) above will follow automatically from the preceding equations.

Together, the two personal budget constraints in equations (9) and (10) imply that

i i i iy (1 - ô - ô ) = (y + r )(1 - ô* - ô ) (14)F F

i cso that , when all ô * are set equal to ô * ,

16

i i iô = ô* - r (1 -ô* - ô )/y (15)F

iActual provincial tax rates, ô , must be lower in resource-rich provinces than in resource poorprovinces when public expenditure, P, is the same, for in no other way can residents of resource-rich provinces capture the residual benefit of their resource revenue over and above theircontribution to equalization payments and their share of the cost of the Federal government.

iTo say that actual provincial tax rates, ô , are lower in resource-rich provinces thanelsewhere is not to say that actual provincial tax rates are lower too. Actual tax rates would belower if - as shown in equation (15) - provincial expenditure were really the same in allprovinces. But people in resource-rich provinces might prefer to use some of their resourcerevenue to raise provincial public expenditure above the national average, or they might prefer tosave resource revenue for a time when resources run out. In either case, provincial tax rateswould be higher than is suggested by equation (15). The meaning of equation (17) is that section36(2) need not be interpreted to require the taxing away of all resource revenue accruing to theprovinces.

i cFinally, setting all p equal to p , equations (11) and (12) imply that

i i i i c c c ô y + r + E = ô *(y + r ) (16)

i c i i i i i so that E = ô *(y + r ) - ô y - r

c c c i c i c i = ô *(y + r ) - y ô * + r (1 - ô * - ô ) - r F

c c c i c i c i = ô *(y + r ) - y ô * + r (1 - ô * - ô ) - r F

c c c i i i = ô *[(y + r ) - (y + r )] - ô r (17)F

which is precisely the revised equalization formula in equation (2a) above. Each province’sequalization payment becomes the difference between the nation-wide average provincial taxbase and its own tax base (both augmented by provincially-owned resource revenues) weightedby the national average provincial tax rate on that augmented base, less the Federal tax “owing”on provincially-owned resource revenue.

By contrast, equalization up-but-not-down has the perverse effect that any increase in theresource revenue of a donor province (a province prosperous enough not to be entitled toequalization payments) increases entitlements of recipient provinces not primarily at the expenseof the province where resource revenues have increased, but at the expense residents of otherdonor provinces who must help finance the increase in equalization payments through anincrease in their Federal income tax bill. A rise in the price of oil harms Ontario twice over. Oncebecause people in Ontario must pay more for the oil they consume. Again because of the increasein the equalization-induced transfer, through the Federal government, from the people of Ontario

For a more sympathetic treatment of the representative tax system, see Robin Boadway,7

Revisiting Equalization Again: RTS vs. Macro Approaches, Working Paper 2002 (2), IIGR,Queen’s University.

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to the people in provinces receiving equalization payments. More will be said about this matter inthe comparison between the representative tax system and the macro formula.

The Macro Formula vs. the Representative Tax System

Regardless of whether equalization is to be up-but-not-down or down-as-well-as-up, achoice must be made about the specification of the tax system. Equalization may be tax by tax orincome-based; it may be in accordance with the representative tax system in equation (1) aboveor with a macro formula in equation (2). To focus exclusively on the contrast between therepresentative tax system and the macro formula, it will be supposed within this section thatequalization is down-as-well-as-up.

Relative merits of the two procedures depend very much on how provincial revenue isacquired. A case can be made for the greater conformity of the representative tax system to theletter and to the spirit of Section 36(2) in the event that all provincial revenue is raised byprogressive income taxation, but, the greater the departure from progressive income taxation andthe greater the provinces’ reliance on other sources of revenue, the more complex and arbitrarythe representative tax system becomes and the greater the advantages of the macro formula.. 7

Progressive Taxation

To focus on the comparison between formulas when all provincial revenue is acquired byprogressive income taxation, consider a variation on the two-province example in the precedingsection where people’s incomes differ within provinces rather than between them. Country c has just two provinces, á and â, each with a population of 100. Within each province are two classes

Rof people, rich and poor, such that all rich people have the same income, y and all poor people

Rhave the same income, y , regardless of where they reside. Province á is the poor provincebecause it has a small proportion of rich people, and province â is the rich province because ithas a large proportion of rich people. Also both provinces have the same progressive income tax

R Pschedule, which means, in this context, that there are common provincial tax rates, t and t , onthe incomes of rich people and poor people respectively. Progressivity means nothing more in

R Pthis context than that t > t .

Assume that there are 100 people in each province, that every rich person has an income,

R Ry , of $600, that every poor person has an income, y , of $300 and that both provinces impose

R Ptax rates, t and t , on rich and poor people of 30% and 10%. The ingredients of both equalizationformulas - the representative tax system and the macro formula - are derived from these numbersand are contained in table 1. In the table, n refers to population, B refers to a tax base per person

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for use in the representative tax system in equation (1) above, and y refers to income per personfor use in the macro formula in equation (2a) and (2b).

Table 1: Tax Bases for the Representative Tax System and the Macro Formula

Ri Pi Ri Pi in n B B y

province i = á 10 90 (600)(10)/(100) = 60 (300)(90)/(100) = 270 330

province i = â 50 50 (600)(50)/(100) = 300 (300)(50)/(100) = 150 450

the country i = c 60 140 (600)(60)/(200) = 180 (300)(140)/(200) = 210 390

The first two columns in the table show the postulated numbers of rich and poor people in

province á, in province â and in the country as a whole, c. Province â is rich because, and onlybecause, its proportion of rich people (50/100) is higher than that in province á (10/100). The rest

Ráof the table is derived from the postulated numbers. For instance, the tax base, B , is the incomeof rich people per person in the province; it is the combined income of all rich people in theprovince (600 x 10) divided by the total population of the province (100). The three other taxbases are defined accordingly. So defined, the two tax bases in each province add up to the

iincome per head in the province, y as shown in the final column of the table. For this simplifiedeconomy, the the computation of equalization payments according to the representative taxsystem and according to the macro formula is entirely mechanical. Following equation (1) above,the required payment to province á under the representative tax system is

á, RTS R Rc Rá P P PáE = t (B - B ) + t (B c - B ) = (.3)(180 - 60) + (.10)(210 - 270) = 18 - 3 = $12

cApplication of the macro formula requires a national provincial tax rate, t , for rich andpoor people together. The required rate is the combined tax revenue in the two provinces togetheras a proportion of the total national income. The combined tax revenue is $15,000 [(.3)(60)(600)+ (.1)(140)(300)]. The combined income is $78,000. The average tax rate, ô, is therefore 19% [15/78] and the required equalization payment to province á under the macro formula is

á, macro c c á E = t (y - y ) = (.19)(390 - 330) = $11.4

The mandated equalization payment is considerably larger under the representative tax system tocompensate the considerably larger tax revenue acquired in province â on account of its largernumber of rich people paying a larger share of their incomes as provincial tax.

A good case can be made within the context of this example that the representative taxsystem conforms more closely than the macro formula to the letter and the spirit of Section 36(2).A natural interpretation of “comparable levels of taxation” conforms to the mix of tax ratesactually imposed rather than to the average tax rate on all residents. It seems reasonable forequalization payments to make up the shortfall in the revenue of the poor province when all rich

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people everywhere are taxed at one rate and all poor people are taxed at another. Thefundamental principle in the representative tax system is that the choice of types of taxes, ratesand bases should reflect the practice of the provinces themselves, in contrast to the macroformula where the one and only notional provincial tax rate is just the ratio of total tax revenue tototal income in the province.

There are, however, three large problems that have been deliberately swept away in theconstruction of this example. First, the presumption that the Federal government should respectprovincial tax rates in the determination of equalization payments, while plausible enough in thecontext of the example, may not be acceptable in other cases. Second, the representative taxsystem provides every province with a perverse incentive to levy high taxes on its deficit taxbase. Third, nice properties of the representative tax system disintegrate when the different taxbases in the formula cease to be connected, as we have supposed, with the components of totalincome in the province. Fourth, the designation of tax rates and tax bases for inclusion in therepresentative tax system is to a large extent at the mercy of the statisticians and open to politicalmanipulation than our example would lead one to believe. These problems will be examined inturn.

Regressive Taxation

The letter and the spirit of Section 36(2) would seem to diverge when provincial tax ratesare regressive. To see why, it is sufficient to reverse the tax rates on rich and poor people.

R P Suppose that ô = 10% and ô = 30% rather than the other way round. Several things wouldhappen. When equalization payments are determined by the macro formula, province á wouldkeep its place as the recipient province because its income per head is less than that of provinceâ. The equalization payment itself would increase because the effect of the larger number of poorpeople in province á outweighs their smaller income per head in the determination of total taxrevenue, while the total national income remains the same. Specifically, with the tax ratesreversed, the combined tax revenue is increased from 15,000 to 16,200 [(.1)(60)(600) +(.3)(140)(300)], while the total income in the two provinces remains unchanged at 7,800,increasing the average provincial tax rate from 19% to 21%, and increasing the equalizationpayment per head to province á from 11.5 to 12.6.

The effect upon the representative tax system is much more dramatic. Though province áremains the poorer province, it is no longer the recipient of equalization payments. Regressivityimposes a high tax rate upon its relatively large base of poor people. Specifically, the requiredequalization under the representative tax system would have been

á, RTS R Rc Rá P P PáE =ô (B - B ) + ô (B c - B ) = (.1)(180 - 60) + (.3)(210 - 270) = 6 - 18 = - 12

implying that province â rather than province á must be the recipient of equalization payments. Itis proved in an appendix, that payment to a poor province under a macro formula is less than,

There is some question about the implications of this result. There is no doubt that the8

Canadian income tax schedule is progressive, but it is at least arguable that the appropriateindicator of progressivity in this context is the progressivity of the tax structure as a whole, notjust the income tax. A somewhat out of date study showed Canadian taxation to be on balancemildly regressive. Were that still so and if the progressivity or regressivity of the entire taxstructure were the relevant consideration, equalization to poor provinces would be slightly largerunder the macro formula than under the representative tax system. See W. Irwin Gillespie, TheRedistribution of Income in Canada, Carleton Library #124, 1980.

The locus classicus of this argument is Thomas Courchene and David Beavis, “Federal-9

Provincial Tax Equalization: An Evaluation”, Canadian Journal of Economics, 1973, pp.483-502. See also Dan Usher, The Uneasy Case for Equalization Payments, Fraser Institute, 1995.

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equal to or greater than payment under the representative tax system depending upon the incometax is progressive, proportional or regressive.8

Now the best choice for the Federal government is not so clear. Should the Federal

government respect provincial tax rates even when that means supplying equalization paymentsto the richer province, or should the reference to “comparable rates of taxation” in Section 36(2)be interpreted as an injunction to equalize average tax burdens regardless of the tax structuresthat the provinces choose to impose?

Earlier on in this paper, we considered the impacts of the two formulas when allprovincial revenue is levied by a head tax; the macro formula still supplied equalizationpayments to the poorer province, but no equalization payments whatsoever were supplied underthe representative tax system because the tax base per head (people per person) was necessarilyequal to 1 in all provinces. That example can now be seen as postulating a provincial taxstructure just regressive enough to wipe out all equalization payments. The example lay upon theboundary between positive and negative payments to the poorer provinces as provincial taxstructures become more and more regressive.

The second difficulty with the representative tax system is the incentive that it creates forprovinces to levy high tax rates on its relatively small tax bases. This comes out strongly in the9

example we have employed. Knowing that its equalization payment - ultimately a payment frompeople in province â to people in province á - is an increasing function of the averageprogressivity of taxation in the two province together, the government in province á has everyincentive to make its tax system more progressive than it would be in the absence of equalizationpayments. Knowing that the equalization payment to province á is a decreasing function of theaverage progressivity of taxation in the two province together, the government in province â hasevery incentive to make its tax system less progressive than it would be in the absence ofequalization payments. The representative tax system breeds progressivity in poor provinces andregressivity in rich provinces. Like the representative tax system, the macro formula allows theequalization payment to be influenced by the average tax rate in the two provinces together

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(Double all tax rates, and you double all equalization payments), but the macro formula isimpervious to progressivity or regressivity. The representative tax system’s accommodation ofprogressivity must be set against its susceptibility to tax gambits by the provinces to increasetheir entitlements to or decrease their net contributions to equalization payments.

Consider another example. Two provinces have identical populations and identical totalincomes. In both provinces total income consists of income from the production of apples andincome from the production of oranges, but province á generates $1,000,000 from the productionof apples and $9,000,000 from the production of oranges, while province â generates $9,000,000from the production of apples and $1,000,000 from the production of oranges. If equalizationpayments are determined by a macro formula or if both provinces impose the same rate of tax onapples and on oranges, then no equalization payments are warranted. By contrast, therepresentative tax system allows á to generate equalization payments at the expense of provinceâ by taxing oranges but not apples, and allows province â to generate equalization payments atthe expense of province á by taxing apples but not oranges.

Alternatively, if the population of province á is one million Catholic and nine millionProtestant while the population of province â is nine million Catholic and one million Protestant,if everybody’s income is the same, and if equalization payments are in accordance with a representative tax system where the Federal government respects existing provincial tax rates andtax bases, then province á can generate equalization payments for itself by taxing only Catholics,while province â can generate equalization payments for itself by taxing only Protestants.

Fictitious Tax Bases and Tax Rates

jiWhen the tax bases, B , are amounts of income in the different tax brackets, as in therepresentative tax system, there is an immediate connection between the revenue acquired by thegovernment at any given tax rate and to the burden of the tax to the taxpayer. The larger the base,the larger the revenue and the larger the burden. This connection may be wholly or partiallysevered when the tax base becomes, as it must for some taxes, a value or volume of productionrather than a portion of people’s incomes. A base may be said to be fictitious when it representssomething other than the income of people paying the tax. Among the fictitious bases in theCanadian equalization formula are the number of cigarettes for the tax on tobacco, the number oflitres of diesel fuel, the volume of spirits sold in the province and the volume of production ofpetroleum.

To see how differences among provinces in tax base can fail to reflect differences inprovincial revenue acquired, consider a two-province country where a natural resource isextracted in both provinces and where royalties to the provincial governments constitute one ofthe components of the equalization formula under the representative tax system. Suppose the“facts” are these: Production is 100 tons per head in province á and 300 tons per head in provinceâ. The selling price of the extracted resource is $50 per ton everywhere. The cost of extraction is

22

$10 in province á and $40 per ton in province â. Provincial governments acquire the differencebetween price and cost of extraction in royalties. Royalties are $4,000 per head in province á [(50- 10) x 100] and $3,000 per head in province â[(50 - 40) x 300]. Suppose, finally, that thevolume of production is the chosen tax base for the assignment of equalization payments underthe representative tax system.

Designate the tax on this resource as j. With volume of production as the assigned taxbase, the j component of the equalization payment to country i in accordance with theth

equalization formula in equation (1) becomes

ji jc jc jiE = t (B - B ) (18)

já jâ jcwhere, in this example, B = 100 tons, B = 300 tons, B = 200 tons (the average base in the two

jcprovinces together), and t = $17.50 per ton, which is the total royalties per ton in the twoprovinces together, equal to [(40 x 100) + (10 x 300)]/[100 + 300]. The mandated transfers to orfrom each province for this category of taxation are

já jâE = $1,750 per head and E = - $1,750 per head

These components of the total equalization payment are added in accordance with equation (1) toother components associated with different tax bases to determine whether the total payment ispositive or nothing.

In this example, province á is the recipient of equalization payments in this category andprovince â is the contributor despite the fact that royalties are significantly higher in province áthan in province â, demonstrating how fictitious tax bases can generate perverse payments underthe representative tax system. By contrast, the macro formula would simply include royalties aspart of the combined income of provincial governments in the computation of the implicit taxrate on the sum of collective and private income in all provinces together, so that, other thingsequal, the larger a province’s royalties, the smaller its equalization payment would be.

Or consider the extreme case of a province that is like a stylized Gulf State whereresource revenue is the one and only source of income and where such income accrues in the firstinstance to the government and is then transferred back to residents. Since the income accrues inthe first instance to the government, the implicit tax rate on such income must be 100% so that anequalization program would in effect be a complete sharing of that income nation-wide, leavingnothing for its residents of the province over and above their share of the total resource revenuein all provinces together. If a provincial income tax of 20% is imposed on incomes between$40,000 and $60,000, then only 20% of people’s incomes between these limits is shared throughequalization under the representative tax system, while the remaining 80% is retained unshared.By contrast, when a province’s resource revenue is shared through equalization on a strictinterpretation of the representative tax system, there is nothing left unshared for the residents of

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the province. Hence the enormous contradiction between the representative tax system on the onehand and Sections 92(a) and 125 on the other. Strictly speaking, the one mandates a 100%sharing among the provinces of all provincial resource revenue, while the other prohibits anysharing at all. Much of the ad hockery in the Canadian equalization formula is attributable to theattempt to wiggle out of this contradiction without appearing to do so.

Administrative Discretion in the Application of the Representative Tax System

The final problem is the large requirement under the representative tax system fordiscretion by public officials in deciding what the different tax bases and tax rates are to be.Ideally, the representative tax system should be as straightforward and mechanical as the macroformula. Rates and bases in the formula should be the rates and bases that the provinces actuallyemploys. In practice, they are no such thing. The base for the property tax might be the dollarvalue of the stock of housing in the province or the dollar value of the imputed rents (in whichcase tax would be graduated as a percent), or the number of square feet of housing or some morecomplex measure of the quality-weighted amount of housing (in which case the tax rate must begraduated as dollars per unit, whatever the chosen unit happens to be).Many taxes are “macroed”;for example, the implicit tax rate on provincial lotteries is taken to be the ratio provincial revenuefrom lotteries to total income in the province. As mentioned above in connection with resourcerevenue, the choice of tax bases can misrepresent a province’s “comparable levels of taxation”when the ratio of revenue to postulated base varies from province to province not because oneprovince it taxing something more heavily, but because some activity yields less surplus to betaxed in one province than in another.

Many ad hoc adjustments have been introduced into the Canadian equalization formula todeal with the perverse effects of the representative tax system when equalization is up-but-not-down. Resource revenue has been removed from the equalization formula. Quite arbitrarily andto avoid designating Ontario as a have-not province, the so-called national average provincial taxbase includes only five of the ten provinces. The five provinces are Quebec, Ontario, Manitoba,Saskatchewan and British Columbia. Subsidiary rules have been introduced to avoid situationswhere a recipient province with a near-monopoly on some particular tax base would stand to losealmost all of its revenue from the taxation of that base because its entitlement to equalizationpayments would be reduced accordingly. As mentioned above, items, such as gambling revenue,with no well- defined tax base have been “macroed”, treated as though they were a tax onordinary personal income, Some province’s resource revenue have been ignored altogether.

The net effect of such ad hoc adjustments is the emergence of a serious risk of severingthe connection between 36(2) and actual equalization payments, and of converting the design ofthe equalization formula into a justification for some pre-ordained allocation of benefits andcosts among the different provinces, or, worse still, for allowing provinces’ entitlements toequalization payments to become the playthings of political pressure or public opinion. Thebigger the chip on your shoulder, the larger your entitlement to equalization payments, or the

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smaller your share of the cost of financing other provinces’ equalization payments, will turn outto be. If God appointed a unique base for every provincial tax in the application of equation (1),the representative tax system would still be a long way from the ideal in Section 36(2). Withoutsuch divine intervention, the representative tax system can be politically divisive as well. Themacro formula is much superior in this respect. It is more horizontally equitable in the sense ofconforming to well-formulated rules not easily modified under political pressure. It has less needfor special arrangements to correct for this or that defect, notably the five-province average tosuppress the influence of resource revenue, the rule for compensating provinces with a nearmonopoly on some tax base, and the difficulties in specifying a tax base for each and everysource of public revenue. It deals collective income naturally by treating all income, private orcollective, alike. It is a reasonably accurate corrective differences among provinces in the burdenof provincial taxation at any common level of public expenditure per head as is warranted bySection 36(2)

Some Measurement Problems

Tax Exporting: Imagine a country where total income per head is the same in allprovinces, where all provincial revenue is raised by a sales tax, where all of the sales in one ofthe provinces are to residents of the province, but where only half of the sales in the remainingprovinces are to the residents of the province and the other half are to non-residents. In theseconditions, the sales tax rate in the province without sales to non-residents would have to betwice the rates in the remaining provinces if public revenue per head is to be the same. For such acountry, the representative tax system may have the edge over the macro formula. With arepresentative tax system and with sales as the only tax base in the equalization formula, theprovince with no sales to non-residents would be the deficit province and the recipient ofequalization payments. With a macro formula, there would be no equalization payments at all.Bearing in mind that the purpose of equalization payments is to equalize not income per head,but public services per head at a given tax rate, the outcome under the representative tax systemwould seem to be more in accordance with the purpose of 36(2) in this example.

There is, in principle, a simple way around this problem. Revenue raised by a provincefrom non-residents could be looked upon as collective income analogous to resource revenue. Inthe computation of equalization payments, sales tax revenue acquired from non-residents couldbe treated as though it were passed back to residents of the province and taxed accordingly. Sales

itax acquired from non-residents could be included as part of R in equation (17). More generally,

i ithe provincial tax base corresponding to the expression Y + R in equation (17) could berepresented statistically in each province as the sum of “personal disposable income” and “ownsource revenue” of the provincial government. Personal disposable income is defined net of alltaxation, but tax paid by residents is automatically included in own source, together with taxrevenue from resource royalties and tax paid by non-residents. A province’s entitlement toequalization payments (or its obligation to contribute to the equalization program as the case maybe) would then be the difference between its tax base per head and the national average tax base

25

per head, multiplied by the population of the province and by the national average provincial taxrate in accordance with equation (18). This procedure is employed below in a comparison amongprovinces of the net consequences of equalization payments in accordance with the macroformula and the Canadian representative tax system.

On the other hand, tax exporting might be ignored because it is thought to be empiricallyinsignificant or because it is not too different as a proportion of total income from one provinceto the next. Measured and accounted for correctly, tax exporting is actually less of a problem forthe macro formula than for the representative tax system because of the sensitivity of therepresentative tax system to the mix of taxes a province chooses to impose.

Differences among Provinces in Expenditure Needs: Decrepit old folks go to BritishColumbia to retire, imposing a considerable cost on the health system of the province. A case canbe made that levels of public services should be interpreted as the cost per head of meetingcertain needs rather than as actual spending per head. There are differences among provinces inthe cost per person of maintaining uniform standards of health care, road construction andmaintenance, crime prevention and so on, differences that would automatically be reflected inexpenditures for the residents of the different provinces but not in provincial tax rates if theseservices were provided by the Federal government rather than by the provinces. I believe that thewe do not have a needs-based standard because differences in needs among provinces aredifficult to measure and because the attempt to incorporate need into the equalization formulawould generate controversy among provinces, each claiming its needs to be greater than theFederal government is prepared to recognize. The choice of whether or not to account fordifferences in needs has little bearing on the questions discussed in this paper. The case fordown-as-well-as-up and for a macro formula is largely independent of how levels of publicservices are measured.

Differences among Provinces in Price Levels: When 36(2) speaks of “levels of publicservices”, there is some question as to whether levels should be interpreted as dollar values or asreal values. The practice in the Canadian equalization program is to ignore differences amongprovinces in price levels. As with differences in needs, the pros and cons of correcting for pricelevel differences among provinces are probably much the same under a macro formula withequalization down-as-well-as-up as under the representative tax system as it is today.

Special Characteristics of Natural Resources: It is sometimes argued that provincialroyalties from natural resource should be less than fully incorporated into the equalizationformula to account for i) the cost of extraction including expenditure on exploration and capitalgoods and ii) the depletion of natural resources over time. The “cost of extraction” argument isthat a province’s resource revenue might be looked upon as gross income in circumstances whereonly net income (revenue minus cost) is properly subject to taxation. The strength of the gross vs.net argument depends on who bears the cost of extraction. In so far as that cost is borne by theprivate sector, depreciation would already be accounted for in the assessment of provincial andFederal tax. Provincial resource royalties must be over and above the cost of extraction, inclusive

26

of the normal return to investment, for why else would a company be in the resource extractionbusiness? Only in so far as the cost is borne by the provincial government in the development ofinfrastructure might some analogue of depreciation be warranted. Even here, the argument isquestionable. The premise is that resource extraction creates special needs for public expenditurewhich should then be taken into account in the taxation of resource revenue. The counter-argument is that expenditure “needs” of any kind have never been taken into account in thecomputation of equalization payments, and that provinces may differ in their needs for a varietyof reasons. One province needs more miles of roads because its population is widely dispersed.Another province needs greater than average expenditure on education because its residents arerelatively young. What has to be shown is that resource revenue creates special needs for publicexpenditure outweighing the special needs of other provinces for other reasons.

The depletion argument is that any sharing of resource revenue today should recognizethat resources will run out tomorrow. If a province invests some of its resource revenue in, forexample, US government bonds, then that part of resource revenue should be exempt fromFederal tax because the interest on the bonds will be taxed when it finally accrues. This is, ineffect, an argument against the double taxation of saving under the income tax, an argument forthe taxation of consumption rather than income. Though there is much to be said for theargument in general, it is a little strange to invoke it in the context of provincial resource revenuewhen the rest of public revenue is acquired on very different principles. It is hard to see whyinvestment of resource revenue should be exempted from Federal tax and ignored in thecomputation of a province’s entitlement to equalization payments when no comparableexemptions are allowed for other types of investment. That resources are expected to run outeventually would seem to have no bearing on current taxation and equalization. A provincewould pay tax on resource revenue when it is there and would stop payment when it is gone,exactly as a person is assessed on ordinary income under proportional taxation.

There is, on the other hand, an argument for the imposition of an especially high Federaltax on provincially-owned resource revenue and for an especially large dip into resource royaltiesto finance equalization payments. It is that resource revenue appears to the typical resident ofresource-rich provinces like manna from heaven rather than as a reward for work or a return toproperty. If God dropped manna selectively, with plenty in some places and nothing in others,there would be a good case for compulsory sharing, to escape the inefficiency that wouldinevitably arise as people located themselves where manna is likely to fall rather than where theycan produce the most valuable goods and services. That is the rationale for the macro formula inequation (2a) rather than for the formula in equation (2b).

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Equalization Payments to (+) or from (-) Each Province

a) in the Present Canadian System,

b)with a Macro Formula, with Equalization Down-as-well-as-up, but WithoutCorrection for the Exemption of Provincial Resource Revenue from Federal IncomeTaxation, and

c) with a Macro Formula, with Equalization Down-as-well-as-up, and WithCorrection for the Exemption of Provincial Resource Revenue from Federal IncomeTaxation.

The comparison is shown in tables 2, 3 and 4. Table 2 shows the equalization paymentsthemselves. Table 3 converts dollar values of payments from the Federal government into nettransfers to or from each province. Table 4 converts total net transfers into net transfers percapita which can be compared for each province with income pre capita to show peopels’ gainsor losses from the program. Data for the construction of these tables are presented and discussedin Appendix table A.

Table 2 shows payments under each of the three systems considered. Column (a) showsactual Canadian payments for the year 2005. Column (b) shows equalization payments as theywould have been with macro formula down-as-well-up in accordance with equation (2b). The

iterm y in the formula - representing income per person in the province - is measured for eachprovince i as the sum of “personal disposable income” and “provincial and local governmentown-source revenue” divided by the population of the province. The rationale for thismeasurement is to avoid double-counting of taxes paid to provincial governments. They areincluded in “provincial and local government own-source revenue”, but excluded from “personal

c idisposable income”. The term y is the population weighted average of y for all provinces. The

cremaining term in the formula is the average provincial tax rate, ô . It is estimated as the ratio ofthe sum over all provinces of “provincial and local government own-source revenue” to the sumover all provinces of “personal disposable income” and “provincial and local government own-source revenue”.

The principal effects of the switch from the present equalization formula (a) to theproposed alternative in (b) is that over half of what would otherwise be paid by the Federalgovernment to the deficit provinces would instead be borne by the province of Alberta which isfar and away the richest province today. The cost to the Federal government falls from $10.9billion to nothing. Instead, Alberta would contribute $6.4 billion, and Ontario would contribute $2.7 billion. All the other provinces would be recipients. As pointed out above, the required“payments” by Alberta and Ontario can be masked as reductions in one combined transferincluding equalization payments together with other Federal-provincial transfers to preserve theform if not the substance of Section 125 of the Canadian Constitution.

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Table 2: Equalization Payments to (+) or from (-) Each Province ($ million for the Year 2005)

Province

(a)ActualEqualizationPayments inCanadaToday

(b)Proposed AlternativeWithout Implicit FederalTax on ResourceRevenue Accruing to theProvince (equation 2b)

(c)Proposed Alternative WithImplicit Federal Tax onResource Revenue Accruingto the Province (equation 2a)

Newfoundland 861 915 904

P E I 227 245 245

Nova Scotia 1,344 1,060 1,057

New Brunswick 1.348 1,108 1,084

Quebec 4,798 3,092 3,027

Ontario 0 - 2,953 - 3,040

Manitoba 1,601 1,101 1,052

Saskatchewan 82 362 - 32

Alberta 0 - 6,377 - 10,103

British Columbia 590 1,447 338

Total 10,851 0 - 5,466

Column (c) incorporates a substitute for Federal taxation of resource revenue accruing tothe provincial governments. All positive equalization payments are necessarily lower in column (c) than in column (b), the more so the greater the resource revenue of the province, and allnegative payments are larger in absolute value. There would be a net acquisition of about $5.5billion by the Federal government.

But there is an important sense in which the Federal government can neither give to nortake from the provinces. All transfers are ultimately from people to people, in this case frompeople in one province to people in another. Net transfers are shown in table 3. For column (b),there is no difference between total and net transfers because there is no net contribution by theFederal government. The numbers in column (a) of table 3 are all lower than the correspondingnumbers in table 2 because the Federal government is a net contributor. The numbers in column(c) of table 3 are all higher than the corresponding numbers in table 2 because the Federalgovernment is a net recipient of funds under that version of the equalization program.

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Table 3: Net Transfers to (+) or from (-) Each Province ($ million for the Year 2005)

Province

(a)ActualEqualizationPayments inCanadaToday

(b)Proposed AlternativeWithout Implicit FederalTax on ResourceRevenue Accruing to theProvince (equation 2b)

(c)Proposed Alternative WithImplicit Federal Tax onResource Revenue Accruingto the Province (equation 2a)

Newfoundland 731 828 970

P E I 184 222 267

Nova Scotia 1,084 961 1,188

New Brunswick 1,153 1,004 1,182

Quebec 1,564 2,801 4,656

Ontario - 4,677 - 2,664 - 684

Manitoba 1,286 989 1,210

Saskatchewan - 200 328 110

Alberta - 1,346 - 5,779 - 9,425

British Columbia - 701 1,306 989

The story in column (a) of table 3 is that benefits to the poorer provinces are somewhatsmaller than they appear in table 2 because residents of recipient provinces must pay a share ofthe cost of the program through Federal income taxation, that residents of the province of Ontariobear more than half of the cost of the program but that residents of the province of Alberta bearthe highest cost per head because Alberta is by far the richest province. The story in column (c) isof the virtually complete displacement of Ontario by Alberta as the contributor to theequalization program. Alberta contributes $8.8 billion. Ontario contributes a little. All otherprovinces are recipients.

The gains and losses per capita in columns (a), (b) and (c) of table 4 are derived fromcorresponding numbers in table 3 by dividing through by the population of each province. Thefinal column in income per person in each province, where income is defined as the sum of“personal disposable income” and “provincial and local own source revenue”. So defined,income per person varies from a low of about $26, 529 in Prince Edward Island to a high of$40,473 in Alberta.

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Table 4: Net Transfers Per Capita to (+) or from (-) Each Province as Compared With Income Per Capita

($ per capita for the Year 2005)

Province

(a)ActualEqualizationPayments inCanadaToday

(b)ProposedAlternativeWithout ImplicitFederal Tax onResource RevenueAccruing to theProvincialGovernment(equation 2b)

(c)ProposedAlternative WithImplicit FederalTax on ResourceRevenueAccruing to theProvincialGovernment(equation 2a)

(d)PersonalDisposableIncome PlusGovernmentOwn-sourceRevenue

Newfoundland 1,415 1,768 1,876 26,557

P E I 1,333 1,775 1,932 26,529

Nova Scotia 1,156 1,129 1,267 28,928

New Brunswick 1,535 1,476 1,574 27,643

Quebec 207 409 615 31,607

Ontario - 376 - 237 - 55 34,005

Manitoba 1,094 937 1,030 29,643

Saskatchewan - 201 364 111 31,772

Alberta - 418 - 1,979 - 2,925 40,473

British Columbia - 166 343 234 31,850

Table 4 shows that the most extensive equalization - that in column (c) - lowers theincome per person of Alberta by $2,925 bringing it about half way down to the income perperson of Ontario. Income per person in Alberta would be reduced to $37,548 as compared withthe income of Ontario of $34,005.

The largest source of the gap between the income per person of Alberta and incomes perperson in the rest of Canada is Alberta’s disproportionate share of provincial resource revenue,about $15 billion out of a Canadian total of $22 billion, or about $5 thousand per person inAlberta as compared with about $240 per person in the rest of Canada. Equalization down-as-well-as-up with a macro formula and with compensation for the non-taxability of provincial

The required increase in equalization payments per person in the recipient province can10

be read off the Canadian equalization formula in equation (1) above. As no tax base in the

ijrecipient province is affected by the increase in resource revenue in Alberta, all B where i refersto the recipient province and j refers to a tax base must remain unchanged. Nor, with theexception of the tax base on resource revenue, can there be any change in any national average

jc kcprovincial tax base per head. All ÄB = 0 with the exception of ÄB where k refers to provincialresource revenue. As the increase of $30 million of resource revenue is an increase of $1 per

31

resource revenue by the Federal government, transfers about half of the gap to the rest of Canada,26.9 % due to pure equalization in accordance with equation (2b) and another 25% ascompensation for the exemption from Federal income taxation.

The Impact in Ontario of an Increase in Resource Revenue in Alberta

The story in the preceding section is reinforced a rough and ready estimate of the netgains and loses to the different provinces when a rise in the world price of petroleum leads to anincrease in the resource revenue of the province of Alberta.

Consider a stylized Canada with a total population of 30 million and with three provinces,Alberta, Ontario and a third province which is less prosperous than the other two and is therecipient of equalization payments from the Federal government. Alberta has 10% of thepopulation and pays 12% of Federal tax. Ontario has 40% of the population and pays 43% ofFederal tax. The third province has 50% of the population and pays 45% of Federal tax. WhenFederal expenditure is increased or decreased, the increases or decreases in tax payment byresidents of the different provinces are proportion to their shares of Federal tax revenue today.The Federal income tax rate and the Canadian average provincial tax rate are both 25%, Albertaalone acquires provincial revenue from natural resources. [These assumptions simplify thecalculation, but they can be relaxed considerably without changing the essence of the example.]Equalization payments are assigned in accordance with the Canadian equalization formula inequation (1) above.

Suppose an increase in the world price of petroleum causes an increase of $30 million inthe resource revenue of the province of Alberta: about $10 per person in Alberta, or about $1 perperson in Canada as a whole.

Under our stylized version of the Canadian system of equalization payments - withequalization up-but-not-down, with a 10-province average and with 100% inclusion of resourcerevenues - the increase in the resource revenue in Alberta must give rise to an increase inequalization payments of $1 per resident in the recipient province that can only be financed -since the recipient province is half the population of Canada - by an increase in Federal taxrevenue of 50¢ per person in the country as a whole. Of that 50¢ increase, 6¢ [50 x .12] is10

kc kperson in the nation as a whole, it must be the case that ÄB = 1. The corresponding tax rate, ô ,must equal 1 as well, because collective income accruing in the first instance to the governmentof a province is logically equivalent to a provincial tax rate on that income of 100%. With these

isubstantial restrictions on the variables in equation (1), the required change, ÄE , in theequalization payment to the recipient province becomes

i k kc iÄE = ô ÄB N

The increase in the required equalization per person in the recipient province becomes

i i k kcÄE /N = ô ÄB = 1

k kcbecause both ô and ÄB are equal to 1.

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borne by the residents of Alberta, 21.5¢ [50 x 0.43] is borne by the residents of Ontario, and theremaining 22.5¢ [50 x .45] is borne by the residents of the recipient provinces themselves. Sincethe population of Alberta is 10% of the population of Canada, a payment by Alberta of 6¢ perresident of Canada becomes a payment of 60¢ per resident of Alberta, leaving Alberta with a netgain of $9.40 [10 - .6] per resident of the province. Almost all of the increase in resource revenueremains as a net increase in the incomes of the people of Alberta.

Since the population of Ontario is 40% of the population of Canada, their tax burden of 21.5¢ per resident of Canada requires a tax payment of 54¢ [21.5 / .4] per resident of Ontario,with no compensating benefit. Since the population of the recipient province is 50% of thepopulation of Canada, their tax burden of 22.5¢ per resident of Canada requires a tax payment of45¢ per resident of the recipient province, leaving them with a net benefit of 55¢ [1 - .45] perperson, the difference between their gain from the increase in equalization payments and theirloss from the extra Federal tax to finance it.

All but 6% of the increase in the resource revenue of Alberta remains as an increase in thecollective income of the people of Alberta, but it is a peculiarity of the Canadian system ofequalization payments that the increase in resource revenue in Alberta triggers a substantialtransfer from Ontario to the equalization-receiving provinces. A gain of $9.40 per resident ofAlberta triggers a gain of 55¢ per person in the recipient provinces and a loss of 55¢ per personin Ontario. T he total increase in equalization payments amounts to $15 million or half theincrease in resource revenue that gave rise to it.

A very different pattern emerges under a macro formula with equalization down-as-well-as-up and with the inclusion of a Federal tax equivalent in the equalization formula in equation(2). The increase of $10 per person in the resource revenue of the province of Alberta, raises itsFederal tax bill by $2.25, leaving residents of Alberta with a net gain of $7.75 per person. Allother provinces gain 25¢ per person from the increase in the gap between their incomes per head

There has recently been some debate in Canada as to whether all resource revenue, 50%11

of resource revenue or no resource revenue at all should be included in the equalization formula.Suffice to say here that it is one thing to include resource revenue in the formula when therecipient of additional resource revenue is the payer of additional equalization payments aswould be the case with equalization down-as-well-as-up, but quite another thing to includeresource revenue in the equalization formula when additional resource revenue in one provincegives rise to additional equalization payments that must in the end be financed by people in adifferent province as is the case with the system of equalization in Canada today.

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and the income per head in the nation as a whole. The proposed reforms avoids the anomaloussituation in which Alberta’s good fortune triggers a transfer from Ontario to the poorer provincesof Canada, redirecting the additional cost of the program of equalization payments to theprovince from which the extra revenue that gave rise to the extra equalization paymentsoriginated.. The degree of sharing would be larger still if a system of equalization payments11

iwere designed to include a corrective - represented by the expression ô R in equation (2a) for theF

share of the cost of the Federal government evaded by the beneficiaries of collective incomeaccruing in the first instance to provincial government.

Final Observations

Equalization payments are not ultimately a transfer from the Federal government to thegovernments of the provinces. They are a transfer through the intermediary of the Federalgovernment from Canadians in some provinces to Canadians in other provinces . Section 36(2) isreasonably clear about who is whom. Beneficiaries are to be people who would otherwise bear alarger than average burden of taxation to finance a given level of provincially-supplied publicservices. With by far the highest income per head and with hugely disproportionate resourcerevenue not subject to Federal income tax, Alberta should be the principal contributor ofequalization payments. It is not so under the present Canadian system of equalization payments.It would become so with the reforms proposed in this paper.

The other advantage of the proposed reform is simplicity. The representative tax systemis infinitely complex, with pages and pages of rules and vast numbers of exception designed todirect the benefits of the program to those whom designers of the rules see as worthybeneficiaries. The system is not merely unfair; it is in danger of converting the system ofequalization payments into Federal rewards for provincial good behaviour or, worse still, intoFederal bribes in response to provincial threats. No system of equalization can avoid thesepitfalls altogether, but the macro formula with equalization down-as-well-as-up is simple enoughthat each province’s entitlement can be estimated on the back of an envelope, and, once adopted,it leaves little room for Federal-provincial negotiation.

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Appendix A: Derivation of Tables 2 and 3

All of the data for the construction of equalization payments and corresponding nettransfers of incomes among the provinces in tables 2 and 3 are presented in the table A below.

Table A: Data for the Derivation of Equalization Payments, 2005.

POP = population (thousands), Cansim 051-0005

PER DIS = personal disposable income ($ million), cansim 384-0012

PRO REV = provincial and local government own-source revenue ($million), cansim 385-0001

RES REV = resource revenue of provincial governments ($ million), Communication from Statistics Canada

FED SH = percentage of Federal revenue collected in each province in 2003, Achieving National Purpose, Department of Finance, 2006, figure 3, page 27

CAN EQU = actual equalization payments in Canada today ($ million), Achieving National Purpose, Department of Finance, 2006, table 1, page 31

PROVINCE POP PER DIS PRO REV RES REV FED SH CAN EQU

Ten Provinces 31,976 773,997 285,182 21,873 - 10,900

Newfoundland 517 10,404 3,326 40 1.2 861

P E I 138 2,805 856 1 0.4 227

Nov Scotia 938 20,582 6,552 10 2.4 1,344

New Brunswick 751 15,708 5,052 96 1.8 1,348

Quebec 7,569 168,092 71,141 257 20.8 4,798

Ontario 12,450 316,327 107,037 346 43.1 0

Manitoba 1,175 25,568 9,263 197 2.9 1,601

Saskatchewan 995 21,821 9,792 1,576 2.6 82

Alberta 3,223 93,384 37,060 14,905 12.4 0

British Columbia 4,220 99,306 35,103 4,435 11.9 590

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The actual Canadian equalization payments to each province, shown in column (a) intable 2, are reproduced directly from the final column of table A. The proposed alternativewithout correction for implicit Federal taxation of resource revenue is in accordance withequation (2b)

i c c c i iE = ô [(y + r ) - (y + r )] (2b)

Since this equation shows equalization payment per person rather than in total, the entry in

icolumn (b) of table 2 must be E multiplied by the population of the province.

cThe estimate of the term ô in this expression is

cô = [PRO REV]/[PER DIS + PRO REV] for all ten provinces combined 1. = [285,182]/[773,977 + 285,182] = 26.9 %

It is the proportional tax rate that would be required to raise existing provincial revenue in theprovince if total income in the province - private and public alike - accrued in the first instance aspre-tax private income.

The estimate of average Canada-wide pre-tax income per person (as it would be if allincome in the province accrued in the first instance privately) is

c cy + r = [PER DIS + PRO REV] / [POP x 1,000] for all ten provinces together

= [773,977 + 285,182] /[31.976] = $33,124

Similarly, the estimate of pre-tax income per head in any province i (as it would be if all incomein the province accrued in the first instance privately) is

i iy + r = [PER DIS + PRO REV] / [POP x 1,000] for that province alone.

iFinally, the appropriate equalization payment in column 3 of table 2 is E as estimated inaccordance with equation (2b) multiplied by the population (POP) of the province.

The final column (c) of table 2 incorporates a correction for the extra Federal income taxthat would be paid if resource revenue accruing in the first instance to the government of theprovince had accrued instead to the residents of the province directly. From each payment to orfrom the province in column (b) is deducted 25% of RES REV, the 25% being the assumed rateof Federal income tax.

Table 3 presents estimates of the implicit transfers among people in the differentprovinces resulting from each of the three variants of equalization payments. Each of the entriesin table 3 is the corresponding entry in table 2 less the provinces share of the Federal revenue

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required to finance the program as a whole. For each column, the amount deducted is

FED SH x the total for all provinces together in that column

By construction, the total of each column in table 3 must be 0. The first three columns of table 4is constructed by dividing all entries in table 3 by the appropriate population of the province. The

i ifinal column (d) is the estimate of y + r as shown above.

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Appendix B: With Tax Bases Stratified by Personal Income, Equalization Payments underthe Representative Tax System are Greater than, Equal to or Less than under the MacroFormula Depending on whether the Tax Structure is Progressive, Neutral or Regressive

This proposition is to be established for the simple case of a country with two distinctclasses of people, rich and poor, allocated between two provinces with equal populations butdifferent proportions of rich and poor, so that one can speak unambiguously of the rich provincewith a high proportion of rich people, and the poor province with a low proportion of poorpeople.

Designate income per person, population and tax rates as y, n and ô respectively, withsubscripts representing the different provinces or income classes. Suppose

R P 1)Everybody in this society has either a high income, y , or a low income , y ,

R Pwhere, of course, y > y .

2) There are two provinces, á and â.

áR áP 3) In province á, there are n rich people and n poor people.

âR âP 4)In province â, there are n rich people and n poor people.

5) Province â is the richer province with the larger proportion od rich people.

6) Public revenue in both provinces is raised by a schedule of provincial income

áR áPtaxes, at rates ô and ô on rich and poor people in province á and at rates

âR âPô and ô on rich and poor people in province â.

Equalization payments per head to provinces á and â under the macro formula and under

á, macro á, RTS â, macro â, RTSthe representative tax system are E , E , E and E where

á, macro c c áE = ô (y - y )

â, macro c c âE = ô (y - y )

á, RTS R R Rá P P PáE =ô (B - B ) + ô (B - B )

â, RTS R R Râ P P Pâand E =ô (B - B ) + ô (B - B )

where all ô are tax rates, all B are tax bases per person, all y are incomes per person and thesubscripts refer to rich, R, poor, P, province á and province â.

á â cPopulations of province á, of province â and of the country as a whole are n , n , and n

38

where

á áR áP â âR âP c á ân = n + n , n = n + n and n = n + n

á â cIncomes per head in province á, in province â and in the country as a whole are y , y , and ywhere

á R áR P áP á â R âR R âP â c R áR âR P áPy = (y n + y n )/n , y = (y n + y n )/n and y = y [n + n ] + y [n +

âP cn ])/n

These income measures are the tax bases in the macro formula. All tax bases in therepresentative tax system - for rich people and for poor people, and in province á, in province âand in the country as a whole, c, - are incomes in the designated group per person in the provinceor country. Specifically,

Rá R áR á Pá P áP á, Râ R âR â Pâ P âP â, B = y n /n , B = y n /n B = y n /n , B = y n /n

R R áR âR á â P P áP âP á âB = y ( n + n ) /(n + n ) and B = y ( n + n ) /(n + n )

It follows at once that

á Rá Pá â Râ âá c R Py = B + B y = B + B and y = B + B

because all tax bases in the representative tax system are “tax bases as components of income”when provincial revenue is raised by income taxation with different rates on different taxbrackets.

Average tax rates - ratios of tax revenues to tax bases - in on rich people, on poor people

R P cand in the country as a whole - are designated as ô , ô , and ô where

R áR áR âR âR áR âRô = (ô n + ô n )/(n + n )

P áP áP âP âP áP âPô = (ô n + ô n )/(n + n )

c R áR áR âR âR P áP áP âP âP R áR âR P áP âPand ô = {y (ô n + ô n ) + y (ô n + ô n )}/ {y (n + n ) + y (n + n )}

c R R áR âR P P áP âP R áR âR P áP âPso that ô = {y ô (n + n ) +y ô (n + n ) }/ {y (n + n ) + y (n + n )}

R R áR âR R áR âR P áP âP = ô [{y (n + n )}/ {y (n + n ) + y (n + n )}]

P P áP âP R áR âR P áP âP+ô [y (n + n ) }/ {y (n + n ) + y (n + n )}]

R P = ô S + ô (1-S)

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where S is rich people’s share of the national income as a whole. The national average provincial

c R Ptax rate, ô , is the share-weighted average of provincial tax rates, ô and ô , on rich and poorpeople. Under the macro formula, the mandated equalization to province á becomes

á, macro c c á c á á â â c á c á á â â c á á â cE = ô (y - y ) = ô [(y n + y n )/n - y ] = ô [(y n + y n )/n - y (n + n )/n ]

c â á â c = ô [(y - y )n /n ]

â, macro c á â á c á â á, macro and, by symmetry, E = ô [(y - y )n /n ] = - (n /n )E

â â, macro á á, macro so that n E + n E = 0 as in equation (7) in the text. The same relation holds for therepresentative tax system.

á, RTS á, macroWhat now needs to be shown is that E > E if and only if the tax system is

R P cprogressive which means in this context that ô > ô for any given average national tax rate ô .

á, RTS á, macroThis follows mechanically from the definitions of E and E .

á, RTS á, macro R R Rá P P Pá c c áE - E = ô (B - B ) + ô (B - B ) - ô (y - y )

R R Rá P P Pá c R P Rá Pá = ô (B - B ) + ô (B - B ) - ô (B + B - B - B )

R c R Rá P c P Pá = (ô - ô )(B - B ) + (ô - ô )(B - B )

R Rá R áR âR c áR áwhere (B - B ) = y [( n + n ) /(n ) - (n /n )] > 0 because province á is a poor province withless than the national average number of rich people,

P pá P áP âP c áP áwhere (B - B ) = y [( n + n ) /(n ) - ( n ) /(n )] < 0 because province á is a poor provincewith more than the national average number of poor people,

R c P cwhere (ô -ô ) > 0 and (ô -ô ) < 0 as long as provincial taxation is on the average progressive,

R c P cbut where (ô -ô ) < 0 and (ô -ô ) > 0 if provincial taxation is regressive. It then follows at oncethat

á, RTS á, macroE > E when provincial taxation is progressive and

á, RTS á, macroE < E when provincial taxation is regressive. QED

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