Albert Breton

Pierre Salmon

A COMPARISON OF INTERNAL AND INTERNATIONAL BARRIERS TO TRADE

Keywords: barriers to trade, federalism, free trade, regulation Mots-clefs: barrières aux échanges, fédéralisme, libre-échange, réglementation

In a world in which barriers to trade at all levels -international and internal -are mostty^by-product of the implementation by governments of different regulatory policies to deal with "domestie^^o^local" problems, the mechanisms that are set in motion by the operation of competition among the governments inhabiting the different jurisdictional tiers of federal countries lead to outcomes that are different from those generated by the 'agreed-upon' rules that govern the relations of national governments with each other in matters of international trade. A model is used to compare two ways of dealing with the external damages that are consequent on the pursuit of beneficial domestic regulatory policies. It assumes that at the international level the methods used can be synthesized by what is known as the least-restrictive means principle, while in the context of competitive federalism the methods lead to what can be called a proper balancing of benefits and costs of domestic policies, including the spillover costs inflicted on others. With the help of this model, the paper shows that one or the other of the two sets of methods could be more restrictive, depending on the magnitude of spillovers and the relation between the instrument used and the achievement of the domestic objective. It includes also a discussion of the case of the European Union, which falls between these two polar extremes.

Introduction

Barriers to trade which are the product of government policies exist between countries and between sub-central jurisdictions within countries. In the discussion of international barriers to trade, the emphasis has shifted recently from "border" barriers (namely tariffs and quotas) to "non-border" or "behind-the-border" barriers (namely impediments to trade resulting from differences in domestic policies). Three developments have motivated this shift: first, the increased integration or globalization of the world economy, itself in part a consequence of past and current achievements in the dismantling of border barriers to trade; second, the growing importance of services as opposed to goods, both as a share of GDP and of international transactions; and third, the increased concerns of the public with issues like health and the environment.

That shift is reflected in the introduction in trade theory of a new vocabulary: "deep integration" contrasted with "shallow integration", "level-playing field", "single market", "fair trade", and so on. These terms pertain to two closely related but different kinds of relationships between domestic policies and free trade. In a first set of cases, integration or globalization of the world economy brought about by market mechanisms such as technology transfers and capital mobility erodes or endangers, almost mechanically, the domestic policies that pertain to income redistribution, labor standards, or protection of the environment. In such a context, the question is not how to deal with existing barriers but with the absence of barriers. One proposed solution is the implementation or tolerance of some new border barriers (against goods produced with child labor, for example). Another proposed solution is an enlargement of the object of multilateral negotiations to obtain an "upward" international harmonization of domestic policies and standards (upward meaning that the more demanding or ambitious standards would prevail). In a second set of cases, domestic policies are not eroded or endangered by market forces in the absence of some deliberate action to alter them, but they hamper or distort international exchanges. The barriers to trade resulting from domestic policies exist and the question is how to deal with them. Though the paper has relevance for questions of the first kind, the issues we focus on are mainly those that pertain to the second question. 1 In practice, this means that we concentrate on the effects of the regulatory activity of governments on international trade.

When the problem is put in these terms, the analogy with internal barriers to trade is obvious. In this setting, border barriers between regions, states, provinces or localities are relatively unimportant. 2 Thus, as long as thinking on the matter was derived from international trade considerations and internal barriers to trade consequently conceived as border barriers, it was difficult to take very seriously the concerns that were sometimes expressed about these barriers. The change in emphasis in the international context has made the two settings more comparable than hitherto. 3 The regulatory activity of sub-central governments is significant everywhere and is as great as that of central governments in most federal countries. Thus the non-border barriers to trade, created by public policy, that are "domestic" in the sense that their real or nominal goal is unrelated to interjurisdictional trade constitute the main issue in both cases.

The implications of border barriers which are components of a trade policy are different from those of non-border barriers that are created sometimes as components of a trade policy but more often as by-products of domestic policies. One essential difference is that border barriers of the traditional protectionist variety harm first of all (with a few exceptions) the country which implements them, whereas non-border barriers resulting from useful regulation yield benefits to the country -or sub-central jurisdiction -concerned. With ! The reverse is true of most chapters in Bhagwati and Hudec (1996) and in Ehrenberg (1994); see also Krugman (1997). 2 At least in recent times and in industrial countries. The situation in the past or in the third world is another matter [see, for example, Faure (1961) for the situation which prevailed in 18th century France and which Turgot tried to change in 1774-76, and Govinda Rao (1993) for that which still does in India]. 3 This increased relevance of comparisons is reflected, to a still modest extent, both in the work devoted to barriers to trade and integration in a purely international context [see, for example, the discussion of interstate barriers in Esty (1994, chapter 5), Sykes (1995, pp. 102-108), and Farber and Hudec (1996, passim)] and in the work devoted to barriers to trade internal to a single country [see, for example, the discussion of GATT and of the European Union in Trebilcock and Schwanen (1995)]. regard to border barriers, a country "would serve its own interest by pursuing free trade regardless of what other countries do" (Krugman, 1997, p. 113) -a point familiar to students of economics. As a consequence, the discussion of barriers can be focused on a country's own interest and it can be argued that the adoption of free trade as a general principle is unproblematic. The question of why there apparently exists a need for multilateral bargaining over reciprocal "concessions" is a puzzle whose elucidation provides an interesting subject of thought to many political economists. 4 This puzzle does not exist for barriers that are by products of domestic policies. There can be no presumption that a domestic policy which creates barriers to trade will as a rule harm the jurisdiction which implements it. The main issue is not self-inflicted damage but damage to others (or mutual damage), something that calls for collective solutions. No free trade principle, however, is readily available as a basis for these solutions.

Another set of differences of utmost importance in practice concerns the quantitative dimension of the two kinds of barriers. Measuring the trade effects of a tariff or of a quota is more or less straightforward. Assessing the trade side effects of a domestic policy is more difficult. The situation is further complicated by the fact that in the second case the assessment of the trade side effect is not sufficient; a measure of the non-trade benefits of the policy is also required. This poses problems that international trade economists, negotiators, and other officials are particularly ill equipped to address. Furthermore, the quantity of cases to consider is not of the same order of magnitude. Non-border barriers are created on a continuous basis by almost all the domestic activities of government, at all levels of jurisdiction. Each regulatory act of a national government adds, at least potentially, to the fragmentation of the international economy; the same is true, with regard to the domestic economy, of the regulatory acts of sub-central governments.

As a consequence of these characteristics of non-border barriers, the traditional approach to trade liberalization, based on reciprocal concessions in a context of negotiations, meets with serious obstacles. At the international level, it seems, a more rule-based and legal approach is required (see, for example, Pelkmans, 1995, p. 155). This has important implications on what can be achieved. However, and this is the main focus of this paper, within countries the existence of an additional actor, central governments, makes things quite different. In other words, although in respect of the interjurisdictional trade consequences of their domestic activities, sub-central and national governments are more or less in the same position, the existence of a central government introduces a big difference in the way these consequences are dealt with. We discuss the nature of this difference in Section 3. The argument of that section is based on the assumption that relations of central and sub-central governments are competitive. We devote Section 2 to the implications of that assumption.

The European Union (EU) has a large role to play in the way we look at the relationship between domestic policies and free trade, especially since the EU's way of dealing with that relationship has changed profoundly under the so-called "new approach".

Whether trade between member countries of the EU is more like international trade between sovereign countries or more akin to interjurisdictional trade within a federation is a question whose practical relevance is related to the question of whether what has been achieved in the EU can also be achieved in the international context. We turn our attention to the European Union in Section 4.

Intergovernmental competition in governmental systems

The governmental system of a country always includes many governments situated at different levels. 5 The relations between these various governments are horizontal and vertical. The first term refers to the interactions of governments inhabiting the same jurisdictional tier in the hierarchical structure of governmental systems, whereas the second pertains to the interactions between governments located at different tiers. It is now generally accepted that horizontal relations are competitive -there is, indeed, a small empirical literature (see, for example, Kenyon, 1991, Besley and Case, 1995 and Breton, 1996) that documents that reality. Whether vertical relations are also competitive is a question that has retained little of the attention of economists. As a consequence, discussions of intergovernmental competition are discussions of horizontal competition. Furthermore, why horizontal relations are competitive is not well understood. Most analyses of horizontal competition are based exclusively on interjurisdictional mobility, along the line that Charles Tiebout (1956) put at the center of his analysis, but often extended to incorporate the mobility of capital and of firms. This implies that intergovernmental competition as a whole is reduced to what is entailed by interjurisdictional mobility. Whatever views one may have regarding the potential and strength of horizontal mobility, it must be recognized that vertical mobility does not and cannot exist. Thus, because we consider vertical competition as essential to an understanding of the issues that concern us, rather than relying on mobility, we focus in what follows on a completely different approach to intergovernmental competition.

As explained in Salmon (1987), the theory of labor market tournaments, first suggested by Edward Lazear and Sherwin Rosen (1981), can be used, with some amendments, to analyze intergovernmental competition. The underlying mechanism is a simple one. Suppose that many citizens in a jurisdiction assess their own government's performance in respect of the provision of goods and services at given tax prices by comparing that performance to that of governments in other jurisdictions. 6 These assessments have an influence on the distribution of votes between incumbents and the opposition: dissatisfaction with the relative performance of the government increases the probability that a voter will vote for the opposition rather than for the incumbent. Governing politicians are uncertain about the details of these comparisons but know that their probability of winning the next election and remaining in power will increase if the government they are members of does better than governments in other jurisdictions in as many policy areas as possible.

Two conditions must be satisfied for vertical competition to emerge. First, the powers which are set down in constitutions and/or statutes and interpreted by the courts or are given meaning by accepted conventions, must not be so completely defined and precisely 6 Although, in our opinion, they do not give it the importance that it deserves, Inman and Rubinfeld (1997, p. 1232) are aware of the mechanism on which we focus when they write: "...the important difficulty of monitoring politicians' and regulators' activities is reduced for state and local governments because citizens can look across local and state boundaries to reveal -in ways not possible with centralized regulation -the more obvious effects of regulations harmful to domestic interests"..."For example, Pennsylvanians can discover the disadvantages they face in the purchase of wines and spirits because of regulated "state stores" by simply comparing Pennsylvania liquor prices and wine selection to those available in Delaware and New Jersey". delineated as to altogether impede inroads and forays by governments at a jurisdictional tier into the supply domain of governments located at different tiers. Second, it must be that the utility that citizens derive from the goods and services (including regulation and redistribution) that a government provides is not dominated by other considerations concerning that government and its relations with other governments. These two conditions are generally satisfied in the real world. Enough at least to have provoked Frank Easterbrook (1983, p. 41, note 40) to remark, regarding the United States, that "the time in which state and federal powers of regulation were mutually exclusive is long since over."

Together the two conditions imply that senior and junior governments will provide similar or comparable services, and that office-holders in the government which is judged by citizens to be the more efficient supplier will increase their probability of getting the vote of these citizens. In other words, the tournament mechanism extends to vertical competition.

The expectation of that effect on votes leads governing politicians at each jurisdictional level to observe the performance of governments inhabiting other tiers. If they come to the conclusion that they can do better than these governments, they will act on that conviction and invade the supply domains of these governments. In turn, the expectation that its domain may be invaded in this way is an inducement for a government to do as well as possible as a supplier of goods and services. 7 Under the assumption that there are no interjurisdictional spillovers, we can say that horizontal competition is efficiency-enhancing in the sense that it induces each junior 7 We note that whereas vertical competition is usually accompanied by what, looking at it from the outside, appears to be duplication and overlap of responsibilities, in reality, as in the marketplace, the competition is over near substitutes, so that the duplication and the overlap is more apparent than real. What looks like duplication and overlap are manifestations of actual vertical competition. But duplication and overlap are also heralds of potential vertical competition. In other words, they signal the ability and willingness of senior governments to become suppliers of goods and services that are currently in the supply domain of junior governments should such inroads and forays increase the senior governments' expected vote.

Conversely, duplication and overlap signal the capacity and willingness of junior governments to become providers of goods and services whose supply has hitherto been restricted to senior governments should that be to their advantage. government to move closer to its policy production frontier and to respond as well as possible to the demands of its citizens. We can also say that horizontal competition is complemented in this role by vertical competition. The two forms of competition provide a basis for a presumption that junior governments are efficient, a presumption that plays an important role in what follows. In addition, vertical competition induces the central government itself to move to its production frontier and to respond to the demands of voters. 8 It is not possible, however, to disregard interjurisdictional spillovers. Thus the presumption that as a consequence of horizontal and vertical competition junior governments are efficient means no more, at this juncture, than that they are efficient from a purely "domestic" point of view. To deal with interjurisdictional spillovers, vertical competition must be examined in a second more specific and perhaps more essential role.

To introduce this second role, we must start from the obvious observation that office holders in a lower-level jurisdiction are not directly concerned with the opinions or feelings of voters in other jurisdictions situated at the same level. This is a strong inducement for these office-holders to neglect the effects of their policies on other jurisdictions. Politicians in office in the senior government are in a different position. Their chances of winning the next election depend on assessments made by voters in all lower-level jurisdictions. 9 When considering whether it is worthwhile to invade the policy domain of a junior government, the politicians of the senior government will balance the electoral support that they might gain (or lose) in this government's jurisdiction against the support that they could lose (or gain) in the other jurisdictions at the same level. We now assume that politicians in lower-level jurisdictions understand this and act on the basis of the expectations they form about the response of the senior government to the way they shape their government's policies.

Because, typically, these politicians do not wish the senior government to invade what they efficiency incentives are also provided by horizontal performance competition among central governments at the international level (see Salmon, 1987). 9 We assume that the perceptions and behavior of candidates are governed by probabilistic voting. In other words, we assume that, as perceived by the candidates themselves, the probability that any voter will vote for a given candidate is a continuous function of this voter's expectations about the candidate's policies. What is important for our purpose is that, under that assumption, all voters count -not only the median voter. see as their own territory, they are led, under the threat of entry, to take spillovers into account. At the limit, all spillovers are internalized. The presumption must be that all governments at each tier and the governmental system as a whole are efficient.

In the foregoing discussion, the process that yields an internalization of spillovers is based on a cost and benefit calculation made by each junior government acting in isolation under what it considers to be the threat of entry into its policy arena by the central government. The model of barriers to trade we present in the next section follows that line of reasoning. However, two other types of response to the prospect of spillovers are relevant.

One is negotiation between the junior government whose policy is the source of these spillovers and other junior governments. Another is effective entry by the central government. In both cases, the whole setting in which the junior government operates is modified. In the new equilibrium, the policies of the other junior governments have changed -for instance they have been "harmonized" -or the central government is now pursuing for the whole country the policy that the junior government was originally planning to pursue in its own jurisdiction (the latter's policy has been "preempted"). In fact, the fundamentally competitive nature of the relationship between levels of government does not preclude that, in some circumstances or on some points, junior governments do wish their endeavors to be preempted by centralized policies. The model of the next section cannot deal with systemic responses of that kind. However, in the case of a central government preempting a junior government's policies, the spirit of our analysis remains. How? If the governmental system is really competitive and if it can be assumed that it eventually settles down at a new equilibrium (i.e., at a state at which the actions of each actor are set and compatible), then, at this new equilibrium, spillovers must have been internalized, otherwise the vertical competition mechanism described above tells us that the central government would act to seize the ensuing opportunity, which would contradict the assumption that an equilibrium had been reached. 10 10 There is no problem of revelation of the magnitude of spillovers arising in the setting assumed here because the ultimate criterion of the existence of equilibrium is the central government being satisfied that it cannot increase electoral support by acting. As usual in the theoretical context of probabilistic voting, government is assumed to know the ideal points of voters in the issue space (Coughlin, 1992).

Though the perspective is different, our argument is similar to one repeatedly made by the Supreme Court of the United States in the context of its anti-trust "state-action" doctrine.

That doctrine, enunciated by the Court in 1943 (Parker v. Brown) and elaborated later on, exempts the anti-competitive actions of the states from anti-trust laws (the Sherman Act in particular) in spite of the so-called "supremacy clause" of the U.S. Constitution (which says that in case of conflict the federal law should prevail) on the sole condition that these actions follow from clearly articulated decisions of state governments. In their very thorough study of the doctrine, Robert Inman and Daniel Rubinfeld (1997) argue that the doctrine's only weakness is its neglect of the interstate spillover effects of the anti-competitive policies of states. 11 If it were not for these effects, they agree with the Court that state governments should be trusted to know what they are doing.

The matter is particularly interesting when one moves down one tier and considers the anti-competitive policies of local government. The Supreme Court extends its doctrine to this tier only when the regulatory autonomy of a local government in the area concerned can be presumed to be the result of an avowed policy of the state government. When this is the case, the Court's benevolence also applies, explicitly this time, to the spillover effects of the local government's policies. The Court's reasoning, approved by Inman and Rubinfeld, is -in our words -that the democratic governmental system of the state as a whole can be trusted to take care of spillovers associated with municipal policies. Obviously, the same reasoning could be moved up one tier and justify the observed neglect of interstate spillovers by the Supreme Court. Inman and Rubinfeld, however, explicitly deny the U.S. Congress the capacity or willingness to act in regard of the states as the states act in regard of local u Palmer v. Brown was about a regulation of raisin prices in California that had caused a rise in the price of raisin in the whole country. To this day this case remains the most clear-cut illustration of an anti-competitive act on the part of a state government that also has important effects on non-residents. Other judicial cases concern for instance regulation of cable television, regulation of attorneys, or even rent-control (see Inman and Rubinfeld, 1997, notes 85 and 92 on pages 1234 and 1239, respectively). 12 Inman and Rubinfeld (1997, p.1275) observe that the Court "did make clear that if the state authorizes a regulatory activity by a local government, that regulation is immune from the anti-trust laws even if it generates substantial spillovers across the jurisdiction's boundaries". government. According to them, "although Congress might provide protection to affected out-of-state residents without judicial prodding, current analyses of congressional policymaking suggest this is unlikely. The incentives of Congress are to favor local constituents. One effective way to favor them is to grant a regulation with monopoly spillovers to particular industries that are economically important to a state or congressional district" (p. 1276). In other words, the authors see a fundamental difference between the way democratic politics operates at the level of the states and the way it does at the level of the federal government. We find that pulling and difficult to accept. As a consequence we do not concur with their -and admittedly other commentators' -critical assessment of the way the Court's anti-trust state-action doctrine deals with interstate spillovers.

Why then is the Court's solution different (much less favorable to the autonomy of the states) when spillovers concern interstate trade and fall under the so-called "dormant" or "negative" Commerce Clause of the U.S. Constitution? This question is a very difficult one.

Many legal scholars consider the doctrine based on the dormant commerce clause as being quite confused (cf. Sykes, 1995, pp. 104-106; Farber and Hudec, 1996, pp. 65-67; Revesz, 1996, p. 2398). Let us note, however, that the clause played an essential role in the creation of a U.S. internal market at a time when barriers to trade were mostly of the "border" variety and were typically openly protectionist. It should also be stressed that the dormant commerce clause becomes inapplicable as soon as federal regulation is present and that Congress can wave it for the purpose of authorizing specific state regulations. Thus, although it might be argued, as some authors do, that the clause duplicates a capacity that should be exercised only by a political branch of government, it is probably a speedy or cost-efficient way of solving the most clear-cut cases. However, as we shall see with a reference to international adjudication which also applies to judicial possibilities within countries, in the more delicate cases in which the government under scrutiny pursues a defensible domestic objective, no judicial means can replace what competitive politics can achieve.

A Model

As noted in Section 1, in international settings, the trade effects of domestic policies are, as a general practice, addressed by means of agreed upon rules rather than by means of case-by-case negotiations. Depending on the exact institutional setting, these rules may vary.

In general, however, they include things such as national treatment of, or non-discrimination against, foreign suppliers; 'sham' principles (i.e. no disguised barriers to trade); notice, comment and publication requirements; generality requirements; presumptions in favor of international standards; mutual acceptance or recognition; etc. Alan Sykes (1995, p. 118) shows, convincingly in our opinion, that more or less all rules can be derived from a single principle which is the "least-restrictive means principle -the requirement that policy objectives be achieved in the manner that is least restrictive of free trade and open markets."

This principle seems benign. It leaves to governments the freedom to pursue the domestic objectives they wish and interferes only with the instruments that they employ for meeting these objectives* It dodges, however, the issue of a proper balancing of domestic benefits against trade-distortion costs. Only in cases in which domestic benefits are clearly negligible and trade distortions substantial, that is in cases of "gross disproportion" between the two, is the least-restrictive means principle complemented by balancing -with a third party, usually a panel, allowed to formulate a negative judgment on the domestic policy.

The matter is different in federal contexts. Like the central governments of countries, sub-central governments implement policies in the pursuit of "domestic" (intrajurisdictional) objectives which at the same time have consequences on interjurisdictional trade that are costly for their own as well as for other jurisdictions. However, in the case of subcentral governments, a balancing of the domestic benefits of these policies against their costly effects on trade is the rule rather than the exception. This essential fact is not always perceived because the balancing is a tacit and automatic effect of competition between governments in general and of vertical intergovernmental competition in particular, as analyzed in Section 2. If on balance, costs exceed benefits (from the perspective of the whole country), the central government can always intervene, namely 'preempt' the subcentral government's regulations, at the limit without having to justify itself. For example, in the United States, the federal government, using the Food, Drug and Cosmetic Act, preempts state drug regulation and using the Ports and Waterways Safety Act preempts more stringent state standards (see Sykes, 1995, p. 103). However, preemption does not need to take place for it to have an effect, and in fact the model that follows assumes it to remain potential.

What counts is that the threat of preemption provides a powerful incentive for a junior government to seek the right balance, from the perspective of the whole country, between benefits and costs. 13 If we compare a system in which domestic policies are submitted to a least restrictive means principle and a system in which these policies are submitted to a proper balancing of benefits and costs ('proper' here means that spillover effects on the welfare of other jurisdictions are taken into account), it seems obvious that the latter (which authorizes the assessment of both objectives and instruments) will always be more constraining, less tolerant of impediments to trade, than the former (in which objectives may not be questioned). In the remainder of this section, we take objection to this view. We argue that it is often the case that a domestically oriented policy would be found acceptable under proper balancing, whereas it would not under a less-restrictive means regime. As a consequence, we can expect to find within countries, and especially within federal countries, impediments to interregional trade that are currently disallowed in the context of international trade.

For the purpose of our demonstration, we will compare three polar cases: as the benchmark, unconstrained policy-making by the government of a jurisdiction; policy-making by the same government under a least-restrictive means rule; and policy-making by the same government or by a higher authority under a mechanism that performs a proper balancing of benefits and costs. We interpret the least-restrictive means rule as one which compels governments to choose policy instruments that, for any level of fulfillment of a domestic objective, minimize the associated negative effects on international trade. The very fact that governments have to be compelled to abide by the principle is prima facie evidence that following the rules is costly. The neglect of these costs often appears to be a consequence of an unwitting disregard of the definition of the least-restrictive means principle itself which is in terms of a constant level of policy achievement. For example, to achieve the same level of consumer protection by labeling that can be obtained through a partial ban of a product would require a volume of labeling that would be very costly indeed. Usually a reduction in the level of consumer protection is implicitly accepted. In what follows, we assume that As we noted at the end of Section 2 when we considered the case of the dormant clause of the US constitution, many internal barriers to trade are handled by the courts. These typically apply a least-restrictive means principle and only occasionally some balancing test.

complying with the least-restrictive means principle always entails the consumption of some domestic resource.

The benchmark: unconstrained policy-making

Assume that the level of fulfillment of a domestic policy objective (say, the safety of the consumption of a particular product) can be expressed by a continuous variable Q. To achieve any level of Q two "inputs" are needed. A first one is the consumption of a domestic resource. We call it R. The second input, which we call T (for trade), is the benefit of international -more generally, interjurisdictional -trade foregone. In turn, this second input has two components. One concerns the country itself (in federal context, the junior jurisdiction itself). We call it N (for national). It is the self-inflicted damage to the jurisdiction caused by trade impediments or distortions associated with the pursuit of Q. The second component concerns the 'rest of the world' (to be understood literally if the context is international and as the rest of the country if the context is federal). We call it S (for spillover). To simplify, we assume that S/N is equal to a constant A, and thus that T= N + S = (1 + X) N. We assume that R, 7 1 , JV, and S are continuous variables and are measured in dollars.

We therefore have a function Q = Q (R, T) in which R and T are, up to a point, substitutes. 14 As should become clear as we proceed, 'up to a point' means two things: first, for any level of Q, there is a limit to the possibility of substitution between R and T (or AO; second, at higher levels of Q, substitution possibilities may vanish altogether.

[Figure 1

goes about here]

In Figure 1, we portray cost minimization by a government pursuing a given level of achievement / of the particular policy objective Q. In the absence of any constraint, that government will neglect spillovers S and base its decision on R and N alone as necessary Given that T and N are linearly related, we could and will, in what follows, sometimes replace rby N in the Q -relationship. inputs. For that government, the relevant iso-achievement curve is, in Figure 1, shown as Q d } s When spillovers are taken into account -what is known in the literature as the "cosmopolitan perspective" -the appropriate iso-achievement curve is instead the curve labeled . The vertical distance between the two curves is therefore equal to S and hence proportional to N. In Figure 1, iso-cost curves are straight lines of slope -1. Cost minimization, absent the cosmopolitan perspective, is at A so that costs are equal to C^n c

("unc" standing for "unconstrained") on the vertical axis. 16

[Figure 2 goes about here]

When Q is allowed to vary, the minimum cost function is C unc (Q) as shown in Figure 2. In that figure it is assumed that the function is convex, but it could be linear. Assuming that the marginal value the government attaches to the policy objective Q is decreasing, V(Q), the curve representing the value attached to Q, is concave. The optimum for the government is at Q unc where marginal cost and marginal value are equal. Obviously, Q will not be pursued whenever the cost curve lies completely above the value curve.

Least-restrictive means principle

We assume that after a point the iso-achievement curves become horizontal because we take it as evident that trade distortions cannot be eliminated completely by incurring higher domestic costs. In Figure 1, it is at B and B' that Q d and , respectively, become 15 Recall that the curve refers to the achievement by the government of a particular policy objective Q. 16 From the "cosmopolitan" perspective, the cost entailed by the equilibrium solution at A At would be C-. However, because cost minimization is not bound by international or federal concerns governing spillovers, is irrelevant to decision-making by the government. It only gives an idea of the problem to be resolved.

horizontal. B and B 1 correspond to the same achievement level / of Q and the same mix of inputs. This mix is the ieast-restrictive means' required to produce Qf. It minimizes the effects on trade of the achievement of Qf. 17 However, the total cost to the government, shown on the vertical axis, is now cj rm (Irm standing for least restrictive means). It is necessarily higher than C^n c , 18

When Q is allowed to vary and when the government adopts the least-restrictive means principle to achieve 0, the cost function is C^r m (Q). Since for any value of Q, the cost will be higher than when the government minimizes costs without constraint, in Figure 2 curve C lrm (Q) lies above curve CM^iQ). This moves the optimum from Q unc to 0 /rw . 19 In other words, a government compelled to follow a least-restrictive means principle is induced to reduce Q. Indeed, it may well happen that curve C^r m (Q) lies above curve V(Q) whereas curve C unc (Q) does not. This means that when compelled to follow a least restrictive means principle, a government may well decide to give up the pursuit of Q altogether.

Balancing benefits against total costs

If decision-makers take spillovers into account, the relevant curve for a given level of Q is no longer QfbwX and the relevant cost is the sum of R and T. In Figure 1, minimum cost is at point C, corresponding on the vertical axis to C. (for balancing).

is necessarily higher than C^n c . The consequence, as portrayed in Figure 2, is that the 17 It minimizes all the effects on trade, whether viewed as N 9 as T, or as 5; for instance, S is reduced from AA'XoBB \ From a cosmopolitan perspective, the relevant total cost is C-. Depending on the curvature of the iso-achievement curves, that cost may be higher or lower than cf . When Cj > Cj , as in Figure 1, world welfare, as defined by the cosmopolitan perspective, would be reduced by the imposition of the least-restrictive means principle if Qi were forced to remain constant. That will, however, not be the case as explained in the text.

cost curve C^(Q) 9 derived from the minimization of O 47 for all values of Q, necessarily lies above the cost curve C unc (Q)^ The optimum now moves from Q unc to Q bal . 20 When submitted to a proper balancing of the benefits and costs of the policy, governments reduce the magnitude of implementation compared to what they would do when unconstrained. They may even decide not to pursue Q\ this will happen if curve C ba ^(Q) lies completely above curve V(Q).

The least-restrictive means principle and the balancing of total costs and benefits compared

As Figures 1 and2 are drawn, total cost is higher when the government follows a leastrestrictive means principle than when it balances total costs and benefits and internalizes S:

in Figure 1, where the level of Q is held constant, C^m is higher than C* a ' and, in Figure 2, where Q is allowed to vary, curve C lrm (Q) lies above curve As a consequence glrm j s sm aller than $ a h there is a larger sacrifice of the domestic policy objective Q under the least-restrictive means principle than under the balancing of benefits against costs principle. It may even happen that curve C^r m (Q) lies completely above curve V(Q) while curve C ba ^(Q) does not. If that is the case, Q will not be pursued at all under a leastrestrictive means rule whereas it will be pursued under a proper balancing of costs (including spillovers) and benefits. This proves what was asserted earlier that the least-restrictive means regime is not always more tolerant of trade-distorting policies than is the proper balancing one.

Of course, the reverse can also be true. To see this, it is sufficient to imagine an increase in spillovers, everything else remaining constant. In Figure 1, such an increase would be reflected by an outward shift of curve . This would not change the levels of Q pursued under the benchmark and the least-restrictive means regimes. 21 However, the 20 We make the same assumption as we did in the previous footnote.

As can be seen in Figure 1, an increase in S will not affect Q" and neither, consequently, points A and B which are attached to Qf; it will not either affect costs C^n c and cj rm increase in spillovers will shift point Cf upwards and if S is sufficiently large, shift it beyond C l f m . As a consequence, in Figure 2 C bal (Q) would lie above C Irm (Q), and Q bal be smaller than Q^r m . It might be the case once more that curve C ba ^(Q) will lie above curve V(Q), and that Q will not be pursued. Thus, ceteris paribus, the larger the spillovers the greater the likelihood that proper balancing will be more restrictive than least restrictive means.

As can be seen from Figure 1 though, without changing S, changing the shape of Q d and in such a way that B is now below line Ccf al also makes cf aI > C l [ m . This can reflect two different phenomena, depending on whether B is close to A or far from it. In the first case, especially if S is small, the least restrictive means solution is not very different from the benchmark solution and its adoption entails no large increase in R, that is, in the non-trade cost of the domestic policy. In the second case, the effect onR, that is, the entailed increase in the non-trade cost of the domestic policy is larger but, in terms of total cost, it is more than compensated by a large diminution of N (those ill-effects on trade the government is concerned with). A formulation which covers the two cases goes as follows: ceteris paribus, the least restrictive means principle is more likely to be more restrictive than proper balancing when it entails a large increase in the non-trade cost of the policy unmatched by a large decrease in its ill-effects on trade. 22 If we assume, as is not unreasonable, that international trade organizations are concerned with the total effects on trade T or with the trade effects on other countries S and not with the benefits of domestic policies 0, it is then imperative to compare the effects of the two regimes on T or S alone. As was the case earlier, these effects are ambiguous. It is true that for a given level of Q, as is clear from Figure 1, Twill always be smaller under least which are derived from A and B. This implies that in Figure 2, cost curves C^^iQ) and C lrm (Q) will not be affected either and, therefore, neither will points Q unc and Q lrm .

22

In other words, the least-restrictive means principle bites more, that is, has the larger restrictive effect on Q, when it is particularly cost-inefficient (for instance a large non-trade cost for a small diminution of spillover). On reflection, this is perfectly obvious.

restrictive means than under proper balancing (the ordinate of B' is smaller than that of Q and so will be S (BB' will always be smaller than CC). If a government left the level of Q unchanged, the least-restrictive means principle would be more efficient in reducing the distortive trade effects of Q than would trade balancing. However, Q is endogenous which means that the government will necessarily reduce Q under both regimes. We have seen earlier that it is possible for Qbal to be smaller than Q^r m . This means that there can be a larger reduction in Q under proper balancing than under least-restrictive means. The difference in the reduction in Q may compensate for the fact that, given any level of Q, the least-restrictive means principle reduces T and S more than proper balancing does. It may even be the case that T and S would be completely eliminated under proper balancing whereas they would not be under a least-restrictive means rule.23

The European experience

As noted at the end of Section 2, the foregoing model does not purport to be a complete description of the way the effects of domestic policies on interjurisdictional trade are dealt with. It corresponds to what some authors (Nicolaidis, 1995, p. 142) call a setting of "unilateral assessments". In its "proper balancing" part, it most directly applies to situations in which a new regulatory action is contemplated in one jurisdiction and the threat of a reaction by the "rest of the world" constrains the scope and modalities of the action, the regulatory set-up in the rest of the world in fact remaining constant. The reason for this condition is that if the regulatory set-up in the rest of the world was to change as a response to the junior government's action this would upset the parameters and pre-suppositions underlying the model. In particular, if what we called the "domestic objective" were now met by uniform provisions at the level of the whole federal or international system, preempting or replacing the one adopted or contemplated in the particular jurisdiction under discussion, this would eliminate the interjurisdictional spillover effects on trade considered in the model.

This harmonization solution to the problem created by trade spillovers is widespread both in international and in federal settings. As noted earlier, there is a difference between the forms the solution takes in the two settings. In international settings, harmonization is sought by multilateral negotiations which run into various social dilemmas and cannot be presumed to lead to an equilibrium which is also an optimum. Such a presumption, however, is not illegitimate in an individual country when the preemption by a central government takes place in a context of vertical competition. As to interstate or interprovincial negotiations within federations, they can also be presumed to lead to an optimum when these negotiations take place in the shadow, or under the threat, of preemption by the federal government. 24 The European Community /Union is an interesting case from this perspective. Within an evolution which is not completely deprived of continuity, it will be nonetheless convenient to distinguish three successive states of affairs. The first corresponds to the legitimization of a number of principles whose importance was to be felt only later. In other words, these principles would not have been accepted as easily if their exact consequences had been foreseen. The first of these principle is central to the treaty of Rome itself: the obligation for member states to dismantle all barriers to trade or more generally all obstacles to mobility between themselves. What is interesting is that the courts, both at the European level and in the member countries gave the principle a legal force that had not been anticipated at the outset and that is uncommon in international treaties (whose national impact varies according to the constitutional set-up of each country party to the treaty). As noted by several authors (e.g., Majone, 1996), the principle of freedom of trade and movement in the Treaty has a constitutional status which is comparable to that of the Commerce Clause in the United States Constitution. The judicial interpretation of this status as implying the supremacy of European law over national law in the domains in which the Treaty applies, and the "direct effect" of a large component of European law in national proceedings created at the systemic level a hierarchy of laws of the kind that can be observed Which is not the case of the recent Agreement on Internal Trade in Canada (see Trebilcock, and Schwanen, 1995) only in federal systems (Weatherill, 1995, chapter 6). However, this was acceptable to the member states because of two factors: they could rely on their veto power to block any new legislation or extension of Community competence they disagreed with -lawmaking remained intergovernmental -and the courts' interpretation of existing laws showed much restraint. 25 The second state of affairs was alike the first with one single, albeit far-reaching, difference. The courts, and especially the European Court of Justice, adopted, without encountering any serious opposition, an increasingly aggressive or "activist" interpretation not only of the supremacy but also of the scope of European rules. The "mutual recognition" principle, spelled out most notoriously in the Cassis de Dijon ruling (1979), was a major step in the establishment of the new state of affairs, labeled "dualistic" by Joseph Weiler (1981).

As a consequence of the unanimity voting rule, the capacity to make new laws was very limited at the European level, and thus mainly localized at the level of the individual member states; but, as a consequence of the increasingly creative interpretation of the Treaty's liberalizing requirements by the European Court of Justice, a rapidly increasing proportion of the regulations enacted by the member states was censured or curtailed by the Court, which imposed one variant or another of the least-restrictive means principle.

From a perspective of global distrust of government's interventions in the economy, this state of affairs could be deemed quite satisfactory. It resembles a system of governance analyzed with great favor by Barry Weingast (1993) under the name of "market-preserving federalism". Weingast, who attributes the success of the US economy in the nineteenth century to the adoption of this system, constructs its two specific characteristics as being "first, that the authority to regulate markets is not vested with the highest political government in the hierarchy; and, second, that the lower governments are prevented from 25

As observed by Stephen Weatherill (1995, p. 210), "the far-reaching principles of supremacy and direct effect were developed by the European Court in a climate that was propitious to their absorption at national level, because the areas in which those principles applied were determined by all the Members States possessing a veto".

using their regulatory authority to erect trade barriers against the goods and services from other political units". As noted before, to eliminate "border barriers" impeding interstate trade, the courts, under the negative Commerce Clause of the US constitution, were particularly well suited. However, when trade barriers are mostly of the non-border variety, namely the kind of barriers that have retained our attention and which are the most relevant in the current context, Weingast's two requirements are incompatible except under drastically down-sized government. 26 In the European case, member countries (Thatcherite Britain included) could not durably accept a deregulation process of the order of magnitude that a dualistic system of the kind described, from different perspectives, by Weiler and by

Weingast, could well have entailed if it had been allowed to last. 27

The third state of affairs, brought about by the Single Act of 1986, has little to do with the dualistic system described by Weiler and others. The crucial difference is the replacement of unanimity by qualified majority as the normal voting procedure in the Council of Ministers. As a consequence, the dominant regulatory or norm-making capacity is no more to be found in the member states but rather in the Commission and the Council of Ministers in For a generalized criticism of Weingast's market-preserving federalism, see Rodden and Rose-Ackerman (1997).

That such system is hardly a realistic alternative in the modern world also finds an illustration in the Reagan administration, whose "response to the growth of state regulatory activity was to propose preemptive regulations in such areas as nuclear power, trucking, state workfare, drug labeling, products liability, coastal zone management, taxicab licensing, affirmative action, the minimum drinking age, and the transport of hazardous waste.

According to one study, ninety-one explicit federal preemption statutes were enacted during the two Reagan administrations. These statutes represented 25 percent of all federal preemption laws enacted since the founding of the republic. This seems an odd outcome to emerge from an administration supposedly committed to the "new federalism" of increased state authority" (Rose-Ackerman, 1991, p. 163).

Brussels. This has led to preemption by the center becoming perhaps the main way to deal with interjurisdictional barriers to trade in Europe. 29 As stressed in particular by David Vogel (1995), this feature also contributes to make the experience of the European Union very different from what can be expected from any international agreement. 30 28 As Majone (1996, p. 57) observes: "in 1991, the European authorities in Brussels issued 1,564 directives and regulations as against 1,417 pieces of legislation (laws, ordinances, decrees) issued by Paris, so that by now the Community introduces into the corpus of French Law more rules than the national authorities themselves". Also: "Today, European environmental regulation includes more than two hundred pieces of legislation, and in many member states the corpus of environmental law of Community origin outweighs that of purely domestic origin." Another observation, contradicting a basic premise of the pessimistic interpretations proposed by Scharpf (1996), is that " while the first directives were for the most part concerned with product regulation, and hence could be justified by the need to prevent that national standards would create non-tariff barriers to the free movement of goods, later directives increasingly stressed process regulation (emission and ambient quality standards, regulation of waste disposal and of land use, protection of fauna and flora, environmental impact assessments), and thus aimed explicitly at environmental rather than free-trade objectives". However, as explained by Vogel (1995), environmental objectives at the collective level typically become relevant as a condition for pursuing free-trade objectives (i.e., for the most environment-minded member countries to support free trade). 29 In spite of the increasing decision-making capacity provided the Council by the new voting rules, the European Court, however, remains important (Weatherill, 1995; Cooter and Ginsburg, 1998).

30 Thus, Vogel (1995, p. 53) writes: "The European Union not only has the authority to strike down national regulations that interfere with trade; all international trade agreements, by definition, subject some national laws to international review. What distinguishes the EU from other international institutions is that it also has the power to impose regulations on its member states. Thus, unlike the GATT, which only has the authority to engage in negative harmonization (that is, to instruct governments not to enforce laws which conflict with their obligations under the General Agreement), the EU also has the legal and political capacity to engage in positive harmonization -to enact regulations that governments must enforce". As At the same time, it must be observed that neither actual preemption nor the threat of it are subject, at the present stage of European integration, to political calculations of the kind that underlies governmental competition in an individual country, as analyzed in Section 2.

Thus there is no mechanism in the European Union case that justifies a presumption of efficient internalization of spillovers along the lines developed in that section.

Harmonization or preemption, in the European case, might even be interpreted as being often a means for the member-state governments, or for the most inefficient among them, to reduce horizontal governmental competition -another means to the same end being, albeit only potentially, what would be an unbalanced attention to interjurisdictional trade spillovers on the part of the judiciary. In both cases, the trade-off between competition in markets and competition in government or politics would be modified in favor of the first, which is not necessarily advisable (see also Trebilcock and Howse, 1998). 31

Conclusion

We have argued that in a world in which barriers to trade at all levels -international and internal -are mostly a by-product of the implementation by governments of different regulatory policies to deal with "domestic" or "local" problems such as environmental degradation, health, and labor standards, the mechanisms that are set in motion by the operation of competition among the governments inhabiting the different jurisdictional tiers we noted earlier, however, the supremacy and direct effect principles that guide European jurisprudence make the enforcement of the obligations contracted by the member states in the European Treaties quite different already from what obtains in all the other "international trade agreements".

The political objectives of the European "construction" should be kept in mind, though.

Liberalization of the internal market is one of the few means available to the European Union, still so weak in many respects, financial in particular, to exert an immediate and substantial influence on the economy and to build-up a strong power (both political and judicial) at the center. Here, there is something of an analogy with the build-up of the federal level in the United-States in the nineteenth century (see also Majone, 1996).

  of federal countries lead to outcomes that are different from those generated by the 'agreedupon' rules that govern the relations of national governments with each other in matters of international trade.In a formal model, we have compared two ways of dealing with the external damages that are consequent on the pursuit of beneficial domestic regulatory policies by assuming that at the international level the methods used can be synthesized by what is known as the leastrestrictive means principle, while in the context of competitive federalism the methods lead to what we have called a proper balancing of benefits and costs of domestic policies, including the spillover costs inflicted on others. With the help of this model, we have shown that one or the other of the two sets of methods could be more restrictive, depending on the magnitude of spillovers and the relation between the instrument used and the achievement of the domestic objective. We have also discussed the case of the European Union, which falls between these two polar extremes.

  Figure 1

Although we pay no attention to them, it also includes many special authorities supplying specific services.

We assume, of course, that for all values of Q the slope of curve C^r m (Q) is higher than the slope of curve C unc (Q).

This follows from the fact that curve C ba ^(Q) could lie above curve V(Q) and thus Q ba ^ be equal to zero, while curve C^r m (Q) would lie below curve V(Q) and thus Q^r m be positive.


Prof Louis De Mesnard

Analyzing structural change: the biproportional mean filter and the biproportional bimarkovian filter

Keywords: JEL classification C63, C67, D57. KEYWORDS. Input-Output, Change, Biproportion, RAS

The biproportional filter was created to analyze structural change between two input-output matrices by removing the effect of differential growth of sectors without predetermining if the model is demand or supply-driven, but with the disadvantage that projecting a first matrix on a second is not the same thing than projecting the second matrix on the first. Here two alternative methods are proposed which has not this last drawback, with the additional advantage for the biproportional bimarkovian filter that effects of sector size are also removed. Methods are compared with an application for France for 1980 and 1996.

Introduction

The basic idea inside biproportional methods of structural analysis is to become free from the hypothesis about orientation of the economy, demand driven or supply driven, by generalizing the comparison of two technical coefficient matrices, A and A*, as Leontief and followers did.

The choice made in (Mesnard, 1990a(Mesnard, , 1990b[START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF][START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF] consist into indirectly generalize the simple comparison of two technical coefficient matrices 1 by working on two flow matrices Z and Z*, then giving to Z the same margins than Z* by the mean of a biproportion, i.e. K(Z, Z*), and then comparing K(Z, Z*) to Z*. The justification of this method is the following: comparing two technical coefficient simply is the same thing than comparing two x absolute values z,, -and zj:

where the symbol "<->" signifies: "compared to". So technical coefficient are not compared directly, but only indirectly. So, in (Mesnard, 1990a, 1990b, 1996, 1977), a biproportional filter is proposed to analyze structural change. The principle consists into projecting the first flow table Z that one wants to compare to the margins of the second flow table Z* to obtain K(Z, Z*) and then to compare the result to the second table by calculating the difference matrix Z*-K(Z, Z*). Here, this method is called the ordinary biproportional filter. See in annex some elements about biproportion.

The next step of the ordinary biproportional filtering method consists into computing the Frobenius norm of this difference matrix is calculated, or the Frobenius norm of vectors of this matrix, which is the absolute variation I between Z and Z*for demanding sectors (column vectors, X,) or supplying sectors (row vectors, I,):

Then, the relative variation is calculating by dividing the absolute variation by the total of the row or the column of flow matrix Z*.

o, • =

and Gj = J Remember that with simple coefficient matrices, there are two possibilities, either compare technical coefficient, either compare allocation coefficient matrices.

This remove the effect of change of both margins of the table from Z to Z*, i.e. the effect of differential growth of demanding and supplying sectors, without predetermining if the model is supply or demand driven.

Instead of projecting Z on the margins of Z*, what is called the direct calculation, different results can be also obtained when Z* is projected to the margins of Z what is called the reverse calculation. Are calculated, £(Z\ Z), then Z-K(Z*, Z) and,

I, = [z,j-K{Z\ Z) y ] 2 ,1, = [z,j-K{Z\ Z)"] 2
and,

Oj = - ^r- , Oi = y ' J
As these reverse results are not the same than direct results, it is necessary to conduct both computations (see Annex). This is a disadvantage, not only because it force to have two computations, but because results can diverge strongly and the ordering of sectors from the most changing to the less changing could be difficult as the application above will prove or as it can be seen in Mesnard (1990aMesnard ( , 1990b[START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF][START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF].

Fortunately, another choice could have been made to perform the analysis of structural change as a direct generalization of the simple coefficient comparison by generalizing the comparison of two technical coefficient matrices A and A*, i.e. two Markovian matrices. As before, this will not predetermine the orientation of the economy but without the disadvantage of two different results. I call this method the biproportional bimarkovian filter because it will based on the transformation of both matrices Z and Z* into bimarkovian matrices by the mean of biproportion. The present article will develop this idea.

II. The problem

A. Basic idea

The basic idea of biproportional filtering consists into giving to the flow matrices Z and Z* the same margins. The matrix Z B which will provide these margins can be, for example, a third matrix of an intermediary year, 1988 if Z is 1980 and Z* is 1996, but in fact only the margins of this matrix are important.

If Z B has the same margins than Z, or is equal to Z, then K(Z,Z B )=Z and A^(Z*, Z B )=£(Z*, Z), so one have the reverse projection of the ordinary biproportional projector; if Z B has the same margins than Z*, then K(Z*,Z B ) = Z* and K(Z, Z B )=K(Z, Z*), so one have the direct projection of the ordinary biproportional projector. For all positions between these two "polar" matrices, one can obtain a wide range of results: I call this the biproportional fixed-base filter.

An good idea could consists into choosing Z B such a manner that the variance would be maximized, either by measuring the variance in absolute terms as the square of the Frobenius norm of the difference matrix:

\\K(Z, Z B )-K{Z\ z%
either by measuring it in relative terms:

\\K(Z, Z B )-K{Z\ z% ]L ]L Z IJ 1 J
Unfortunately, these expressions are nonlinear regarding to the terms of Z, Z* and to the margins of Z B and moreover they have no analytical solution because biproportion is a transcendent operator. So, such a problem can be solved only by a succession of computations of biproportion, what is too much heavy even for small matrices.

However, there are two particular matrices that are good candidates to play the role of Z B :

• a matrix, function of Z and Z*, for example the mean of Z and Z*, denoted Z with Z = -(Z + Z*). I call this the biproportional wean filter.

• the bimarkovian matrix 1 M : this is the biproportional bimarkovian filter.

However, there is clear difference between these two methods: all column vectors have the same margin and all row vectors have the same margins in the biproportional bimarkovian filter, where it is not the case with the biproportional mean filter.

S.

A representation by an Edgeworth box

A figure based on an Edgeworth box will illustrate it.

III. The methods

A. The biproportional single-base filter and the biproportional mean filter

1.

First step

Each matrix Z and Z* is projected to the margins of another intermediary matrix Z B which provide a fixed base, for example the mean Z of Z and Z*, to give AT(Z, Z B ) and AT(Z*, Z B ) 2 Also, note that for these school-case (2, 2) matrices, the corresponding bimarkovised matrices are always symmetrical, what removes much interest in this example for the biproportional bimarkovian filter. At least, matrices must be (3, 3). with the biproportional mean filter. This operation allows to remove the effects of differential growth of sector.

There are many tools to perform this operation of projection of a matrix and the problem is to choose one of these tools, or, in other words, there are an infinite number of matrices that can have the same margins and the problem is to choose one of these matrices. The resulting matrix may vary depending on the tool chosen to perform the projection, and consequently the results of the methods may vary (see annex). Here, we choose biproportion. In particular, with some methods like the minimization of the least squares between a matrix, Z or Z*, and the matrix Z B , this may create negative terms in K(Z, Z B ) because the form becomes additive: K(Z, Z B ) = U + Z +V, where U and V are diagonal matrices. This is why the tool that we choose to perform binormalization is biproportion. With biproportion, one have tf(Z, Z B ) = U Z V, and,

u, =

-, for all /, and v 7 = ^ ----, for all j y=i 1=1 so, if all terms uf* are positive, all terms vf ] will be also positive, as soon as all terms of Z are positive [START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF][START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF]. The same reasoning holds for Z*. One have the guarantee that there will be no negative terms inside the projected matrix if there are no inside Z or Z*. So, the operation of projection by means of a biproportional method signifies that the projected matrix is the nearest to the initial matrix, in the sense of information theory among other theories, see (Mesnard, 1990a), but with the guarantee that there will be no negative terms inside the projected matrix if there are no inside Z or Z*.

Second step

K(Z, Z B

) is compared to K(Z*, Z B ) by calculating the Frobenius norm of the difference matrix K(Z\ Z B )-K(Z, Z B ). This is done in absolute values,

• for one single coefficient H,j:

H,, = [K(Z\ Z B ) IR K(Z\ z B ) V J
• for demanding sectors (i.e. for column vectors, Zy):

I, = jl(K(Z*, z B )IR K(Z\ z B ) V J
• for supplying sectors ((i.e. for row vectors, L,):

i,-= (*(z*, z% R K(z\ z\) 2

• or for the whole economy, Z:

z= JSE(*(Z\ z B ) R K{Z\ z B )(; ) 2
This is done also in relative terms, by dividing absolute variabilities by the value of the margin of Z B ,

• for one single coefficient, a,,:

(K<Z\Z B ) V -K<Z\ Z*)J On =
for demanding sectors ((i.e. for column vectors, a,):

jl(*(Z\ Z B ) r K(Z\ Z*)J a > =
for supplying sectors ((i.e. for row vectors, a,):

a, =

• or for the whole economy, a:

I(V(Z*, Z B ) tj -K{Z\ Z*)J 4 o = ' J II(^(Z S , Z B ) tj -K(Z\ Z B ) TJ 2
Remark. Because of their not linear nature, relative variabilities have not the property of aggregation. So, one can compare relative variabilities for sectors between them, or relative variabilities for individual cells between them, or even relative variabilities for the whole economy at different dates, but must not compare the relative variability for the whole economy to the relative variabilities for sectors, or relative variabilities for sectors to relative variabilities for individual cells.

For the biproportional mean filter, matrix Z B is simply replaced by matrix Z.

B. Particular case of the biproportional bimarkovian filter

In the biproportional bimarkovian filter, the matrix Z B becomes the bimarkovian matrix \ M . Not only the effect of the differential growth of sectors will be removed without predetermining if the economy is demand or supply-driven as in the ordinary biproportional filter, not only the problem of the double result will be removed as in the biproportional single-base or the biproportional mean filter, but as an additional advantage of the biproportional bimarkovian filter, the effect of differential size of sectors will be removed: after projection all sectors in column will have the same margin, i.e. the same size, and all sectors in column will have the same margin.

1.

First step

Each matrix Z and Z* is transformed into a bimarkovian matrix, Z M and Z* M . A bimarkovian or binormalized matrix is a matrix of which all margins in a same side, column or row, are equal to 1 \ In fact, this is exactly possible only for square matrices. For rectangular matrices or dimension (//, m), the margins of one side, say the side of dimension a/, are equal to and the margins of the other side are equal to X:

l Af s = \i s and s' 1 A/ = Xs'

For example, one can take:

(i) n_ m m
(2)

I A/ _ m m
This operation of projection with the biproportional bimarkovian filter not only removes the effects of differential growth of sectors, but also it removes the effect of difference of size of sectors.

As said before, there are many tools to project a matrix and the results may vary depending on the tool chosen to perform it: here biproportion is chosen: the name of the filter is not the bimarkovian filter but the biproportional bimarkovian filter.

In particular, with some methods like the minimization of the least squares between a matrix, Z or Z*, and the matrix this may create negative terms in K(Z, l M ) because the form becomes additive: K(Z, l M ) = U + Z + V, where U and V are diagonal matrices. This is why the tool that we choose to perform binormalization is biproportion. With biproportion, one have£(Z, 1 A/ ) = UZ V, and, with matrix 1 A/ defined in (1):

(3)

5>,

, for all /, and v y =m n /•=1 for all j or with the matrix 1 A/ defined in (2):

(4) m 2> y
-, for all /, and v 7 = -, for all / /=i so, if all terms are positive, all terms Vj k) will be also positive, as soon as all terms of Z are positive [START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF][START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF]. The same reasoning holds for Z*. One have the guarantee that there will be no negative terms inside the projected matrix if there are no inside Z or Z*. Effectively, a separable modification of Z (or Z*) is ineffective [START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF][START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF]: if Z is replaced by Z = ¥ Z £2, then K(Z, l M j =#(Z, 1 M ), and the exact form of the bimarkovian matrix has no importance. So, the above expressions (3) and (4) are equivalent.

Second step

Z A/ is compared to Z* A/ , i.e. the Frobenius norm of the difference matrix z* M -Z M is calculated. The rest of the method is similar as for the biproportional single-base filter, except that absolute variations and relative variations are homothetical: with a bimarkovian matrices like l M in (2), one divide by m for columns and by n for rows the absolute variations when calculating relative variations. So it is sufficient to construct only relative variations.

• For one single coefficient:

Remark. In this case, the real value of the term {/, /} in the matrix l M is in fact completely arbitrary and does not plays a role in the calculation (even if matrices are square). But it seems logical to consider that all terms inside are equal:

m m n n
so, the absolute variability of an individual cell is divided by 1.

• For demanding sectors (i.e. for column vectors, a,-):

• For supplying sectors (i.e. for row vectors, a,):

• For the whole economy, a:

Remark. The influence of a multiplicative parameter X is effectively neutral: so, the choice between forms (1) or (2) for matrices 1 A/ is itself neutral. For the direct projection, the results in terms of relative variabilities between AT(Z, Z*) and Z* are respectively:

• overall: 9.63%

• for rows: 11.817%, 23.41%, 11.651%

• for columns: 24.87%, 2.17%, 12.50%.

For the reverse projection, the relative variabilities between K(Z*, Z) and Z are:

• overall: 7.49%

• for rows: 7.54%, 27.39%, 8.39%

• for columns: 16.77%, 3.01%, 12.64%.

For the biproportional fixed-base filter, consider the following base: and the relative variations between K(Z, Z B ) and K(Z*, Z B ) are:

rB _ then, K(Z, Z B ) = K{Z\ Z B ) =
• overall: 8.28%

• for rows: 9.31%, 23.56%, 9.77%

• for columns: 18.23%, 3.39%, 15.54%. and the relative variations between K[Z, Z j and A^Z*, Z j are.

• overall: 8.92%

Here, Z B seems a better base than Z for a projection by a biproportional single-base projector because the overall relative variability is lower.

• for rows: 9.88%, 26.32%, 10.32%

• for columns: 21.29%, 2.55%, 13.17%.

• With the biproportional bimarkovian filter: The results in terms of relative variabilities between Z M and Z are:

• overall: 8.61%

• for rows: 10.54%, 21.02%, 10.67%.

• for columns: 19.37%, 3.08%, 16.80%.

D. Remarks

It is ineffective to project K{Z, Z B ) to K{Z\ Z B ), or Z M to Z* A/ , by a biproportion because both matrices have the same margins [START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF]:

K[K(Z, Z B ), K(Z\ Z B )] = K(Z, Z B ) and K(Z M , Z* M ) = Z M
This is why both matrices can be compared directly.

Unlike for the biproportional filter, where a direct computation, K(Z, Z*), and a reverse computation, K(Z*, Z), can be done with a different result in both case, here the same results are found when K(Z, Z B ) (respectively Z A/ ) is compared to K(Z\ Z B ) (respectively Z* M ) or when K(Z\ Z B ) (respectively Z* A/ ) is compared to K(Z, Z B ) (respectively Z M ).

This is a real advantage: it is no more necessary to have a complicated and more or less empirical procedure to interpret the results by comparing two series of results. For this reason, the new method is more satisfying.

One can also remark that in both methods two biproportional projections are required, so the amount of computations remains similar, excepting that there is only one calculation of relative variabilities (with simpler computations) and no computations of absolute variabilities.

IV. Application

The bimarkovian filter will be compared to the ordinary biproportional filter for the results of an application based on data for France for the period 1980-1996. The two tables are given in the base of 1980, at the prices of 1980.

The biproportional bimarkovian filter is calculated after 30 iterations. They will be compared to similar results based on the same data but with the ordinary biproportional filter. Remember that, if the percentages of variation obtained with this method and with the bimarkovian filter can be compared (both provide relative variations), there are two ways of projection in the biproportional filter and only one in the bimarkovian filter: one will synthesize these results, direct and reverse, in a completely empirical way, by computing the mean of these two; this provide an help for the comparison with the results of the biproportional bimarkovian filter. However, the comparison must be cautious even it is done over data in relative terms. Here, the biproportional bimarkovian filter has the lower overall relative variability.

In the following tables, the results for the biproportional bimarkovian filter will be presented in a first column, a second column will contain the results of the biproportional mean filter, a third and fourth column will present the results for the ordinary biproportional filter for direct and reverse computations are presented and a last column will indicate the average of column two an three. Table 2 presents results for column sectors and table 3 for row sectors. Higher values for relative variations are indicated in bold for the biproportional bimarkovian filter, the biproportional mean filter and for the average of the ordinary biproportional filter.

With all methods, the main result is the overwhelming role of sector T37 (Services of Financial Institutions), for both column and row vectors. This is caused by the strong development of exchanges between financial institutions, which can appear partially artificial because only balances are really exchanged each month. This is why in the future reform of the French national accounting system, only these balances will be taken into account. But a discussion remain concerning these phenomenons. apart this sector, the results are the following.

For other sectors, the results are the following with the biproportional bimarkovian filter:

• For column vectors, T32 {Telecommunications and Mail) and T06 {Electricity, Gas and Water) are largely changing but less than T37; also T36 (Insurances), T38 (Non Marketable Services), T22 (Press and Publishing), T34 (Marketable Services to Private Individuals), T17 (Shipping, Aeronautics, Weapons) are significantly changing (by more than 10%). This can be summarized in a two series of figures, where two columns are reported. When points are along the first diagonal, both methods provide the same result. When points are to the right of the diagonal, as T37 in figure 4, the variation found with the biproportional bimarkovian filter is higher than with the biproportional mean filter, and conversely when points are above the diagonal as T06 or T32 in the same figure.

As it can be seen in tables 2 and 3, more than half the number of sectors are above the diagonal, often the biproportional bimarkovian filter provide lower estimation for relative variabilities than the ordinary biproportional filter. In figure 3, when the biproportional mean filter is compared to the ordinary biproportional filter for columns, points seem to be correctly aligned along the first diagonal: ordinary biproportional filter and biproportional mean filter provide similar results. In figure 4, when comparing the biproportional bimarkovian filter to the biproportional mean filter for columns, except for point T37 (Services of Financial Institutions) which is to the right of the first diagonal, many points are to the left. Note that, except for T37, the sectors which are far from the diagonal are not generally the sectors with the greater size in Z, so the differences between both methods are not linked to a simple size effect: if only large sectors would have be far from the diagonal, the biproportional bimarkovian filter would have detect only large sectors and it would have be trivial. In figure 6 when the biproportional bimarkovian filter is compared to the biproportional mean filter, almost all points are to the right of the first diagonal for high values as T32 {Telecommunications and Mail), T24 (Building Trade, Civil and Agricultural Engineering), T29 (Car Trade and Repair Services), T35 (Hiring, Leasing for Housing), etc., except for T37 (Services of Financial Institutions). Again, except for T37 and T24, sectors which are far from the diagonal are not the larger.

Mean

V. Conclusion

In the ordinary biproportional filter, one matrix Z (respectively Z*) is projected on the margins of the another matrix Z* (respectively Z) by the mean of biproportion and then the projected matrix is compared to Z* (respectively Z); this method avoids to remove the differential effects of sectors without predetermining if the model is demand driven or supply driven, but there are two different results possibly strongly diverging. A first generalization of this method, the biproportional mean filter, which avoids this difficulty, provides results which are close to the ordinary biproportional filter. However, the differences of sizes of sectors are not removed. In the biproportional bimarkovian filter, both matrices Z and Z* are transformed into bimarkovian matrices by the mean of biproportion and then these two transformed matrices are compared. This method also avoids to predetermine if the model is demand or supply driven by removing the effect of differential growth of sectors and with only a single result but with the advantage that the differences of sizes of sectors are removed: so it is more satisfying. Results are not exactly the same with other biproportional filter, but the heavier tendencies are conserved in the application for years 1980-1996 in France.

VI. Annex

A.

Remind about the computation of a biproportion

The result of a biproportion, K(Z, Z*), is equal to UZV, where U and V are diagonal matrices, of which terms guarantee that K(Z, Z*) have the same row and column margins than Z*; for example, the following algorithm is correct for this purpose [START_REF] Bachem | On the RAS-Algorithm[END_REF]):

(5) // 7 = m mi *-, for all /, and vy = n W * J -, for all / X Vy Zij X Uj Ztj y=l 1=1 As many algorithms are possible to obtain the same result, it is demonstrated in [START_REF] De | A biproportional filter to compare technical and allocation coefficient variations[END_REF]) that all algorithms K lead to the same results 4 5 . Among these algorithms, considering three matrices, Z a known matrix to be projected to the margins of another matrix M (i.e.

under constraints of margins: Z^y^Z'W;; and Z^^Z^y) and Y the searched matrix ' / J j result of the projection, one have:

• the algorithm (1),

• Stone's empirical method RAS, 4 One must understand "the same theoretical result", because there can be differences in terms of speed of computations and in terms of effects of successive rounds. Among these algorithms, there is Stone's RAS method and the concept of biproportion was first formalized by [START_REF] Bacharach | Biproportional Matrices and Input-Output Change[END_REF].

Balinski and Demange (1989) have studied the axioms of biproportion in real numbers and in integers (see also (Ait-Sahalia, Balinski and Demange, 1988)); this is applied to voting problems; see also [START_REF] Michel | Apportionment[END_REF] and Balinski and Gonzalez (1996).

• the maximization of entropy [START_REF] Wilson | Entropy in Urban and Regional Modeling[END_REF]:

min H^y log^y ' j under the constraint X X^/y c o where C is a cost matrix linked to Z, i J

• Kullback's minimization of information 6 [START_REF] Kullback | Information, Theory and Statistics[END_REF]:

min ZZ^iy Jog^ So the computation of a biproportion is a safe operation. However, a confusion must no be done: the unicity of biproportion concerns the choice of an algorithm and not the fact that the solution of one specific algorithm leading to a biproportional form is unique.

B. Other methods to compute a biproportion

Also, there exists other methods to found a matrix Y projection of one matrix Z to the margins of one another matrix M (i.e. under constraints of margins: X^/y^X^/y and

• the minimization of the quadratic deviation (Frobenius norm of the difference matrix):

min IZ(y r : (i ) 2

• or as a generalization of two preceding, the minimization of the Holder norm at the power • the minimization of the absolute differences: For example, Aït-Sahalia, Balinski and Démange (1988) establish that the matrix that minimizes the information criteria is unique (note that in their paper, they make a confusion between the maximization of entropy and Kullback's minimization of information).

Figure 3 .

 3 Figure 3. Comparison of methods: mean Vs average direct + reverse, for columns

Figure 4 .

 4 Figure 4. Comparison of methods: bimarkovian Vs mean, for columns

Figure 5 .Figure 6 .

 56 Figure 5. Comparison of methods: mean Vs average direct + reverse, for rows In figure 5 when comparing the biproportional mean filter to the ordinary biproportional filter for rows, some points are to the right of the first diagonal, for example T24 (Building Trade, Civil and Agricultural Engineering), T29 (Car Trade and Repair Services) and T32 (Telecommunications and Mail), T35 (Hiring, Leasing for Housing), but T37 (Services of Financial Institutions) is far to the left.

Table 1 .

 1 Comparison of methods, overall change, in %

	The overall change is:
		Bimark. Biprop.	Biprop.	Biprop.	Average
			mean	direct	reverse	direct +
						inverse
	Overall	2.20	5.30	6.61	1.23	3.92

Table 3 .

 3 Biproportional mean filter and the average of the ordinary biproportional filter provide very similar results. When the results of the biproportional bimarkovian filter are compared to the biproportional mean filter or to the average of the ordinary biproportional filter, Comparison of methods, row vectors, in %

	• For row vectors, T32 (Telecommunications and Mail), T15B (Domestic Equipment Goods
	for Households), T17 (Shipping, Aeronautics, Weapons), T24 (Building Trade, Civil and
	Agricultural Engineering), T08 (Mining and non Ferrous Metals), T29 (Car Trade and
	Repair Services), T35 (Hiring, Leasing for Housing), T22 (Press and Publishing).

• for the list of column vectors, one must remove T38 (Non Marketable Services) and T22

(Press and Publishing), but one must add T15B (Domestic Equipment Goods for Households), T24 (Building Trade, Civil and Agricultural Engineering), T25 (Trade), T29 (Car Trade and Repair Services) and T35 (Hiring, Leasing for Housing).

• for the list of row vectors, one must add T12 (Parachemestry, Pharmaceuticals), T21 (Paper, Cardboard), T22 (Press and Publishing), T33 (Marketable Services to Firms), T34 (Marketable Services to Private Individuals). A noticeable fact is that sector T24 (Building Trade, Civil and Agricultural Engineering) becomes the most changing sector, a few before T37 (Services of Financial Institutions).

In fact, any other number can be chosen, the important thing is that all margins of the same side would be equal.