Silvia Concettini

Anna Creti

Liberalization of electricity retailing in Europe: coming back or going forth?

The aim of this article is to provide a mid-term evaluation of liberalization of electricity retailing in Europe taking into account some relevant analytic constraints: different and often conflicting theoretical points of view, shortage of routinely collected data, problems in isolating the impact of single reforms in power sector and pervasive regulatory interventions. Theoretical approaches and empirical studies are discussed with the goal of testing the consistency of theory and practice. Our analysis suggests that direct benefits of retail competition have been often overstated, particularly for small and residential customers. Final market has proven to be less dynamic than forecast and new entry in supply more difficult to sustain in the medium-long run. Regulatory requirements are demonstrated to be more significant than suggested in previous papers, due to non-negligible market imperfections. Our main conclusion is that it seems unlikely that "light-handed regulation" may fully substitute for "hard regulation" in this sector, especially for small and residential customers. Moreover, direct regulatory interventions remain essential for arranging and managing Default and Last Resort services and avoiding the risk of excluding "vulnerable customers" from trade. In the light of this limitations, further actions appear to be required to give a thorough organization to this business able to let expected outcomes of other related reforms (e.g. liberalization of generation) a stronger impact on final customers' welfare.

Introduction

In any industry the role of retailers is to provide final customers with added-value services. The types and magnitudes of the costs and benefits of retailing adding-value activities vary widely across sectors, final customer dimensions and characteristics, periods, geographical locations and market structures. [START_REF] Anton | Entry auctions and strategic behavior under cross-market price constraints[END_REF] In the electricity industry, retailers perform two main activities: on the one hand, they provide final customers a complex service by aggregating inputs from all upstream actors (generation, transport and distribution); on the other hand, they facilitate upstream firms' sales by finding, arranging and managing relationships with potential and actual buyers.

In the liberalization process of power sector, retailing and generation have been opened to competition, whereas grid operation, maintenance and investments have remained under regulatory oversight. In Europe the opening of retail electricity markets has progressively entitled eligible customers to freely purchase retail services from a supplier of their choice: this right was first awarded to industrial consumers with annual consumption above a certain threshold [START_REF] Borenstein | On the efficiency of competitive electricity markets with time-invariant retail prices[END_REF] and then to all non-household consumers from the 1st of July, 2004, followed by all consumers since the 1st of July, 2007. At present, almost all European countries have formally achieved the objective of a fully open retail market. [START_REF] Brennan | Consumer preference not to choose: methodological and policy implications[END_REF] Before and during the process of liberalization several arguments have been put forth on the costs and benefits of retail electricity competition. Despite the non negligible academic and political interest on this topic, there has never been a consensus on the theoretical framework that should be used to examine retail activities in this type of market. The lack of a shared vision has challenged the definition of a common set of indicators for assessing the success or the failure of the reform. Two additional limitations have discouraged empirical impact analyses: on the one hand, the scarcity of data on European retail markets which de facto impedes a systematic market oversight; on the other hand, the difficulty of disentangling the effects of retail liberalization from those of other related reform (e.g. liberalization of generation) when using available data, such as final prices. On top of that, the powerful regulatory interventions in this business compound the evaluation of retail competition. Indeed, liberalization goals of improving efficiency and effectiveness in electricity retailing have been frequently counterbalanced, both at European and at national level, by the political requirement of ensuring that no consumers were excluded from trade. This objective has often been translated in the co-existence of market prices and regulated tariffs, the latter being kept artificially low with a clear impact on competition's dynamics.

The aim of this article is to provide a mid-term evaluation of liberalization of electricity retailing in Europe taking into account the mentioned analytic constraints: different and often conflicting theoretical points of view, shortage of routinely collected data, problems in isolating the impact of each reform, pervasive regulatory interventions. The objective is twofold: drawing the attention to a relevant topic which has been overlooked in recent debates on power markets and suggesting a set of actions that should be undertaken by policy makers in order to give electricity retail business a definitive and transparent status. In doing so we essentially answer to the dilemma: coming back or going forth with liberalization of electricity retailing? Our analysis suggest that direct benefits of retail competition have been often overstated, particularly for small and residential customers. Final market has proven to be less dynamic than forecast and new entry in supply more difficult to sustain in the medium-long run, notably for small, non integrated companies. The disappearance of captive market seems to have benefited more integrated generators willing to sell their power to newly attracted customers than pure retailers competing on a retail margin. At the same time European regulators seem to have proceeded without truly questioning liberalization paradigm, even when some shortcomings have revealed. They lacked both the courage to let the market freely work and the strength to take a step back when it did not [espandere con elementi fattuali delle ultime sezioni]. Our main conclusion is that it seems unlikely that "light-handed regulation" may fully substitute for "hard regulation"4 in this sector, especially for small and residential customers. In the light of this limitation, further actions appear to be required to give a thorough organization to this business able to let expected outcomes of other related reforms (e.g. liberalization of generation) a stronger impact on final customers' welfare.

The discussion is organized as follows. In the next section we summarize the theory on competition in electricity retailing. In the third section we provide an overview of European retail electricity markets, using the few available data to test some of the theoretical predictions. The fourth section is dedicated to the analysis of market characteristics which may undermine the development of a sound retail competition. In the fifth section we analyse Default and Last Resort services and the implementation of protection mechanisms for "vulnerable customers". The final section contains the discussion of results and suggests the next steps that may be taken to improve reform's outcomes.

Retail electricity competition

The expected impacts of competition on electricity retailing are summarized in Table 1. Some of the benefits concern efficiency gains, while others are more related to the aspect of differentiation; the remaining benefits are associated with equipment innovation.

Dimension

Expected impact The academic debate on retail competition has generally been of a qualitative nature [START_REF] Choné | Universal Service Obligations and Competition[END_REF] although there have been some econometric attempts aimed at examining consumer behaviour and at measuring the impact of retail competition on final prices.

Efficiency

Efficiency

Increasing competitive pressure on electricity retailers is likely to improve the efficiency of retailing. Direct efficiency gains have two main sources: increased use of cost-based pricing [START_REF] Choné | Allocating and funding universal service obligations in a competitive market[END_REF] and a more efficient organization of retailing activities. Using 1996 data, Joskow (2000) estimates the potential savings for the average customer in United States from switching to a competitive retailer that is responsible for all retailing services [START_REF] Creti | The law NOME: some implications for the French electricity markets[END_REF] and is able to provide them at a 25% discount compared to distributors. He finds that the average customer's bill might be reduced by less than 1% or approximately 2 dollars per month if the competitive retailer were to pass all of its cost savings through to the customer.

In the same vein Ofgem, the British energy regulator, roughly calculates for different payment methods8 the retail margin on which the entrants are supposed to undercut incumbents (2004). Littlechild (2005) provides a downward revision of Ofgem's estimates, mainly reflecting larger than forecast costs for credit cover and initial IT and billing system settlement. The author concludes that the retail margin may be positive only for direct debit contract, regardless the size of the entrant, while is negative (small firms) or zero (large and medium sized firms) for standard credit contracts. Finally, prepayment contracts may entail negative margins for all types of new entrants. These estimates support Joskow's opinion on the limited room for gains coming from more efficient retail activities to be passed-through to final customers.

However, according to Littlechild (2000) efficiency gains may be more significant because they may not only originate from direct retail operations but also from upstream procurement, [START_REF]Inquiry pursuant to Article 17 of Regulation (EC) No 1/2003 into the European gas and electricity sectors[END_REF] which is estimated to account for approximately 50% of the final retail price. Fierce competition for end customers may also place downward pressure on transmission and distribution costs. Finally, from Littlechild's perspective, over time, market forces are able to reintroduce the proper incentives for dynamic efficiency: with competition, only the best offers from the efficient suppliers can survive and expand at the expense of unwanted contracts or/and inefficient sellers.

A last source of efficiency, which we may call systemic, has been envisioned in the elimination of the double marginalization effect (Goulding et al., 1999). This effect arises as a consequence of the vertical unbundling of supply activities along the value chain when firms in different segments retain some degree of market power. Economic theory states that when vertical relations do not exist, firms can exercise their market power at all successive stages of the value chain, generating a negative impact on aggregate firm profits and on consumer welfare. [START_REF]2009-2010 Report on progress in creating the internal gas and electricity market[END_REF] From this perspective, retail competition per se is perceived to be a positive element of liberalization reforms: with retail competition, the double (retail) margin is eliminated or at least reduced. [START_REF]End-user energy price regulation: an ERGEG position paper[END_REF] For the supporters of full retail competition, in principle efficiency gains may be passed through to customers in the form of lower final prices. Some authors have attempted to estimate the impact of reforms such as privatization and liberalization on final prices and efficiency. See for instance Newbery and Pollitt (1997) on British data, Steiner (2001) and Hattori and Tsutsui (2004) on OECD Coutries [START_REF]Status review of the definitions of vulnerable customer, default supplier and supplier of last resort[END_REF] and Joskow (2006) on US data. Joskow's paper is the only one that properly accounts for retail competition. The author compares changes in real electricity prices between 1996 and 2004 for US states that introduced retail competition and for those that have not. He finds evidence that households in the states where the reform was adopted benefited from larger reductions in prices (with the exception of Texas), while this trend is not apparent for industrial customers. However, this result cannot be attributed tout court to retail competition, as in the same period, several other reforms were implemented in the electricity sector (increased competition in generation, improvements in the regulation of distribution and transmission services, etc.).

On the downside, several authors agree that opening the market is likely to produce larger advertising, promotional, transactional, and system duplication (e.g. billing or customer assistance) costs, while there is no consensus on the final balance between these costs and the benefits of competition. [START_REF] Giulietti | Pricing behaviour under competition in the UK electricity supply industry[END_REF] For instance, Littlechild (2000) finds that in the long term, efficiency gains may offset increased advertising and promotional costs, whereas Joskow (2000) and Defeuilley (2009) are more skeptical of this prediction.

Differentiation and equipment innovation

Theoretically speaking, retail competition is expected to bring new offers and contractual arrangements to the market and broaden the range of available services, such as risk-hedging or energy management. Furthermore, competitive pressures on retailers may indirectly force other actors, such as distributors or equipment providers, to develop and install new measuring and reading devices and the equipment necessary to improve service quality.

According to Joskow (2000) and Defeuilley (2009), the potential for product differentiation and developments in the range of value-added services for which small and residential customers are willing to pay an additional fee appears constrained in the electricity industry. Empirical evidence in Europe partly contradicts this pes-simistic view on limited scope for product differentiation. [START_REF] Goulding | The role of vibrant retail electricity markets in assuring that wholesale power markets operate effectively[END_REF] Even though additional services such as energy management were primarily demanded by larger customers, competition in electricity retailing also stimulate the demand for new types of products (mainly with green and dual fuel options) and innovative contractual arrangements for pricing (wholesale price plus mark-up contracts, fixed-price contracts, standard variable contracts, time-of-use contracts, and flat contracts) among small and residential customers. The diffusion of these products remains nonetheless heterogeneous. [START_REF] Hattori | Economic impact of regulatory reforms in the electricity supply industry: a panel data analysis for OECD countries[END_REF] The installation of smart metering and reading devices seems to represent an essential condition for extending the range of products and services offered by electricity retailers as well as for enabling an active demand side participation. Intelligent equipments may foster the development of contracts with dynamic pricing options and the adoption of more efficient consumption behaviours; moreover they may simplify the process of billing and information exchange between retailers and distributors, with a positive impact on competition dynamics. [START_REF] Jamasb | Electricity market reform in the European Union: review of progress toward liberalization and integration[END_REF] Even so the adoption of this new technology seems to have been prompted more by binding legal framework than by competitive forces.

Indeed it is the European Directive 2009/72/EC which has established that 80% of total consumers should have been equipped with an intelligent metering system by 2020. The decision to roll-out smart metering systems has been subject to a preliminary economic assessment at national level, which has resulted in a variety of coverage choices, technical designs and implementation schedules (ERGEG, 2013). At present only Italy and Sweden have completed their roll-out with a 95% and 100% coverage respectively [START_REF] Joskow | Why do we need electricity retailers? or can you get it cheaper wholesale?[END_REF] while Belgium, Czech Republic, Portugal and Lithuania have decided not to invest at all in smart meter deployment. This situation highlights the lack of agreement on the final balance between costs and benefits of smart meter adoption especially in the case of small and residential customers (on this debate see for instance Léautier, 2013).

Retail markets in Europe

A set of economic indicators may be used to test some of the theoretical predictions regarding the outcomes of liberalized electricity retailing. We focus on the European Union because all Member States have adopted a common legal framework to open both the wholesale and retail markets to competition. Therefore, if there are country-specific aspects of retail competition, they reflect different realities in terms of the generation mix, political and strategic objectives, and consumers' attitudes and awareness vis-à-vis the market.

The supply side

On the supply side, liberalization reforms have allowed new firms to enter the market. After a substantial amount of market entry in the first phase of liberalization, over the whole 2003-2011 period, the total number of electricity retailers decreased from about 3379 to about 3242 (see Figure 3 in the Appendix). However, nearly half of European countries have benefited from the opposite trend. The number of retailers has slightly increased from 2010 to 2011.

In 2010, the figures for the main retailers, i.e. those accounting for at least 5% of total national electricity consumption, reveal that only one country, Romania, has eight big players, while the most numerous group of countries is characterized by the presence of three main retailers. [START_REF] Joskow | Markets for power in the United States: an interim assessment[END_REF] Detailed data are reported in Figure 4 in the Appendix. These figures seem to indicate that the retail market has an oligopolistic structure rather than a competitive one. [START_REF] Joskow | Retail electricity competition[END_REF] From 2003 to 2010 the total number of main retailers remained relatively constant, from about 102 companies in 2003 to 101 companies in 2010 (see Figures 5 and6 in the Appendix).

Another relevant indicator of market structure is provided by the cumulative market share of the main retailing companies. The difference between the total market and the cumulative market share of the main retailers indicates the size of the residual market, or the market available to minor competitors. The cumulative market share of the main retailers in 2010 is reported in Figure 1. Source: Authors' elaboration on Eurostat data.

According to the size of the residual market, European countries can be classified into three groups:

• Countries where the market covered by minor retail companies is large, i.e., between 45% and 65% of the total market: Germany (62.4%), Norway (52.2%), Sweden (52.1%) and Italy (45%);

• Countries where smaller retailers cover between 35% and 20% of the total market: Romania (33.2 %), Poland (29.7 %), Estonia (27%), Spain (27.4%), Netherlands (25%) and Hungary (22%);

• Countries characterized by a very narrow residual market: the more striking cases are Ireland and Portugal (3%), Slovenia (1%) and Latvia (0.1%). [START_REF] Joskow | Markets for power in the United States: an interim assessment[END_REF] The relevant market for retailers is the national market. [START_REF] Joskow | Retail electricity competition[END_REF] Recall that in an oligopoly where firms compete à la Bertrand, the presence of two firms is sufficient to restore the market outcome of perfect competition. [START_REF] Klemperer | Competition When Consumers Have Switching Costs: An Overview with Applications to Industrial Organization, Macroeconomics, and International Trade[END_REF] Denmark is excluded because of missing data; Finland does not report the information on the cumulative market share of main retailers; in Netherlands only main retailers selling electricity to small consumers are considered.

Because the market for "minor competitors" is below 20% in 15 out of 26 of the countries considered, the retailing industry in European countries can still be assessed as highly concentrated. It is not possible to discern a clear trend in the cumulative market share of main retailers between 2008 and 2010: the value of this indicator has grown in 8 of the 26 countries, while it has remained unchanged in 4 countries. The data are reported in Figure 7 in the Appendix.

The reduction in the total number of retailers has been justified in some cases by unsuccessful entry attempts and in others by horizontal consolidations or acquisitions of small retailers by larger and often vertically integrated firms. [START_REF] Laffont | Competition in Telecommunications[END_REF]

The demand side

On the demand side, the switching rate of final customers is a commonly used indicator for the level of buyer commitment in a market: it calculates the number of end users who decide to change suppliers when retail services are liberalized. The main idea conveyed by this indicator is that if consumers can easily change service providers when they wish to, producers are less prone to engage in exploitative behaviors, such as imposing high final prices or low quality, and hence the market may be considered more competitive. [START_REF] Laffont | Competition in Telecommunications[END_REF] This trend suggests the presence of economies between retail and generation activities that would favor the integration of upstream and dowstream businesses (Pollitt, 2008). If owning a retail firm has the potential to increase generators' investments by constraining overall business risk, the reduction in the number of actors would lead to a higher level of concentration that may increase the retail margin (Jamasb and Pollitt, 2005). [START_REF] Léautier | Is mandating "smart meters" smart?[END_REF] Belgium, Estonia, Great Britain, Hungary, Poland and Spain are excluded because of missing data; Cyprus, Lithuania and Malta registered zero switchings.

from Austria, all countries exhibit a positive trend in the indicator over the considered period.

The figures change if end users are classified into three categories according to their consumption volume: large consumers, medium-sized industries, small industries and households. [START_REF] Littlechild | Why we need electricity retailers: a reply to Joskow on wholesale spot price pass-through[END_REF] Large consumers have generally exhibited proactive behavior, with 2009 switching rates ranging from 3,3% in Luxembourg to 73% in the Czech Republic. Moreover, the percentage of meter points switching suppliers increased between 2008 and 2009 in all European countries except Austria, Germany, Italy and Luxembourg. Similar figures are reported for medium-sized industries, with relatively small magnitude. In this case, the 2009 indicator ranges from 0,008% in Bulgaria to 39% in Ireland. From 2008 to 2009, a positive overall trend is observable, with the only exception being Austria. The participation of small industries and households in the market has been substantially lower in almost all countries considered, with the switching rate only exceeding the 10% threshold in Ireland (2009) and Italy (in 2008 and 2009). The trend in the indicator for this group of consumers is positive overall, with the exception of a few countries.

Four considerations are noteworthy. First, there is no consensus on the level of the switching rate at which the market can be considered "sufficiently competitive". Littlechild (2009) considers a residential customer switching rate of 10% a sufficient threshold to justify the liberalization of retailing. To the best of our knowledge, this is the only author providing a basis for comparison with real data. Second, the switching rate registers the number of customers who have changed retailers, but does not account for the number of customers who have chosen another contract offered by their current supplier. This number also represents an indicator for customer awareness that is not accounted for in official figures. Third, the difference in switching rates between residential and large customers seems to indicate the presence of market imperfections, and we address this issue in detail in the next section.

The most recent publicly available public figures, from 2009, reveal that 10 of the 28 countries have opted for the complete removal of end-user price regulation, while a few countries have only done so for non-residential consumers. Where tariffs are available, a large share of final customers, both households and firms, continue to purchase electricity under regulated conditions (EC, 2011). While it is true that regulation and competition are two sides of the same coin, there is still no general consensus regarding the necessity of eliminating end-user price regulations to allow the retail market to operate effectively.

Competition with market imperfections

Some authors claim that the presence of market imperfections, such as switching costs, informational complexity and a "consumer preference not to choose", may affect the outcomes of competition in the electricity sector, at least regarding small and residential customers (Joskow, 2000; Brennan, 2006; Defeuilley, 2009). In addition, the specific characteristics of electricity retail seem to undermine the expected benefits of competition by generating negative externalities, such as customer's segmentation and innovation's slowdown (Defeuilley, 2009).

In the following paragraphs, we present a summary of the main findings regarding these issues. Some of these imperfections, such as informational complexities, seem to require the implementation of some forms of "hard regulation". From this perspective, the "light-handed regulation" common in other liberalized industries does not seem to be sufficient to ensure the proper operation of retail electricity markets.

Switching costs

Theoretically speaking, in markets characterized by repeated interactions between buyers and sellers, a consumer who has previously purchased a product from a supplier may incur costs when switching to a competitor, despite the firms' products being identical (Klemperer, 1995). Switching costs arise for the following reasons:

• searching costs to identify offers and the suppliers;

• learning costs to become familiar with the supplier;

• transactional costs to sign and resolve a contract.

Switching costs may be real or perceived and lead to a situation in which "products that are ex ante homogenous become, after the purchase of one of them, ex post heterogeneous" (Klemperer, 1995). These costs prevent customers from changing suppliers even if they are offered a better priced deal and thus have the same effects on market dynamics as a barrier to entry. In the electricity industry, where consumers have long-lasting supply relationships with the incumbent, switching costs may deter complete consumer mobility, leading to under-switching despite the presence of substantial savings (Defeuilley, 2009). Moreover, the situation may be exacerbated if the switching process is delayed or blocked by suppliers without specific reasons [START_REF] Littlechild | Competition in retail electricity supply[END_REF] .

Giulietti et al. ( 2010) analyze the influence of searching and switching costs in the UK retail electricity market by studying the trend in price convergence between new entrants and the incumbent. The authors find that, in line with the general predictions of competition models with switching costs, even after the entry of new competitors, incumbents are able to enjoy a consistent price advantage. Moreover, new entrants, as soon as they are established in the market, tend to exploit the presence of consumer searching and switching costs: over time, new firms' incentives to offer lower prices to gain additional customers are more than offset by the benefits of keeping prices high to increase margins on previously served customers.

Informational complexities

In some sectors, consumers may also be unwilling to change suppliers because they face relevant difficulties in evaluating and comparing suppliers' offers. This might be the case in the electricity industry, where consumers are generally offered twoor multi-part tariffs, which reduce their ability to estimate the per-unit price of the product. This situation might be further complicated if supply contracts contain other advantages that cannot be straightforwardly translated into electricity price savings (e.g., discounts on other purchases). This limitation may imply the following:

• consumers switch to a more expensive supplier (over-switching);

• consumers switch to a cheaper but not the cheapest available supplier (inaccurate switching).

Errors in consumers' switching decisions damage their welfare both directly, as they cannot obtain the maximum surplus provided by existing retailers, and indirectly, by increasing retailers' market power due to a weakened relationship between firms' sales and surplus provision.

Empirical evidence on electricity sector is provided in Wilson and Waddam-Price (2005). The authors employ a sample of more than three thousand face-to-face surveys of UK households, 13% of which has switched suppliers. [START_REF] Littlechild | Smaller suppliers in the UK domestic electricity market: experience, concerns and policy recommandations[END_REF] They find that nearly 30% of households switched to a more expensive supplier, while inaccurate switching led customers to only obtain one forth of the gains available on the market. The paper suggests that information overload and complexity may cause switching decisions to be less efficient when the numbers of retailers and options in the market are large. As a consequence, while increasing the number of competitors may have a positive effect on the total gains available on the market, informational complexity may limit the ability of consumers to exploit such gains, with a net negative impact of competition on equilibrium final prices.

Recently, OFGEM (2012a), the British Regulator, published a package of proposals designed to eliminate, or at least reduce, informational complexities that constrain households' participation in electricity markets. The proposals include a limitation on the number of tariffs that suppliers can offer and the types of tariffs (only two parttariffs are allowed), and impose specific layouts and contents for communications from suppliers to consumers.

Consumer preference not to choose

In open opposition to the assumptions of the standard economic model, Brennan (2006) attributes the likely scarce success of competition in retail electricity market to the consumer preference for not making a choice, which can be considered a type of market failure. While liberalized markets have forced consumers to make informed choices that in turn presuppose increasing efforts at understanding and comparing contract conditions and terms of trade, the experience in electricity, and previously in telecommunication markets, seems to suggest that consumers in these sectors do not always consider having additional options from which to choose an advantage. Brennan's opinion stems from an accurate analysis of the marketing literature which indicates that consumers generally exhibit a limited propensity to revise their choices or change the goods and services in their consumption bundles.

Customers' segmentation

Some authors note that a possible side-effect of introducing competition in the retail electricity market is the segmentation of active and passive customers (Defeuilley, 2009; von der Fehr and Hansen, 2010). Consumers are active in a market when they exercise their freedom of choice by switching suppliers or by renegotiating their contractual conditions without changing retailer. Differences in customers' willingness to switch suppliers or renegotiate contractual arrangements may create the potential for a two-tiered retail market. In this case, active consumers who are consistently involved in market dynamics may benefit from the introduction of competition in retailing because they can obtain access to deals with prices that tend to be more cost-reflective. The inactive customers, conversely, may end up paying prices that are above their pre-liberalization levels, as firms may exploit consumers' reluctance or inability to switch to cross-subsidize their entry to the competitive sub-markets. Empirical evidence from the Norwegian and United Kingdom markets seems to confirm this prediction (OFGEM, 2007; OFGEM 2012b; Von der Fehr and Hansen, 2010).

Innovative processes

According to Defeuilley (2009), some structural characteristics of the electricity industry may limit the opportunities for new entrants, which are supposed to offer price reductions or quality improvements. The author suggests that a more careful analysis of electricity provision reveals that scientific and technological opportunities for new entrants in this retail sector are limited. Actually, investments in innovation seem to be characterized by high levels of appropriability and cumulativeness at the firm level. This implies that the innovative processes in this sector are likely driven by large established firms, rather than by new entrants. Moreover, possibilities for innovation in electricity retailing seems to be triggered more by equipment innovations (installation of more sophisticated devices) or upstream choices (investments in renewable energy sources) that are generally independent of competition in retailing, rather than by radical innovations in business management (new information technologies, improved customer management, etc.).

Regulation in competitive retail markets

In the previous section, we asserted that some direct regulatory interventions are necessary to overcome the market imperfections in electricity retailing. Here, we argue that the need for regulation does not disappear, even after achieving full competition. Three situations are relevant here.

First, when competition is introduced in a market, customers can decide to switch to a new supplier or can be passive and do nothing. In the latter case, the continuity of supply can be ensured by assigning passive customers to a so called Default Supplier (DS). [START_REF] Littlechild | Retail competition in electricity markets -expectations, outcomes and economics[END_REF] As competition expands and more consumers participate in the market, demand for the Default service should fall and nearly disappear in the long run. Second, customers served by a competitive retailer may face the risk of being interrupted if the supplier becomes unable to provide the service, for instance because it is insolvent or bankrupt. In this case, regulators must arrange for the transition of customers to a temporary supplier, the so called Last Resort Supplier (LRS), which ensures service continuity. There may be a third group of customers, often called "vulnerable", that struggles to obtain a counterparty in the market, notably because these customers are not profitable. The lack of profitability may depend on customers' social and economic backgrounds or on the costliness of supply. In the transition to competitive retail markets, these customers face a serious risk of exclusion.

Each situation calls for a specific intervention. In the first two cases, the need to provide an uninterrupted service may be counterbalanced by the objective of ensuring a certain level of customer protection, especially in terms of price. A wide array of implementation patterns are feasible, according to the relative weight placed on these objectives and considering several possible providers (Table 2). In addition, three procedures are available to assign these services to a retailer:

1. a direct "ex ante" entitlement, typically granted to the incumbent firm; 2. a random entitlement among the competitive suppliers; 3. a bidding process based on the competitive selection of the provider [START_REF] Mansur | Upstream competition and vertical integration in electricity markets[END_REF] . these papers question the economic rationale behind keeping USOs in liberalized markets. In particular, while the "ubiquity" constraint may continue to be imposed on regulated network operators, "non-discrimination" constraint is at odds with the concept of competitive markets with efficient cost-reflective prices. Panzar (2000) stresses that there is an unavoidable trade-off between competition and universal service provision in liberalized markets. If there is a need for a universal service policy, this means that the competitive market cannot deliver socially acceptable allocations without direct public intervention. We argue that the need for USOs exists if the transition to competitive retail markets may exclude "vulnerable" or unprofitable customers from the trade of an essential good such as electricity. However, in line with ERGEG (2007), we suggest that to avoid the risk of exclusion more targeted and less distortionary interventions are preferable, such as social tariffs [START_REF] Newbery | The restructuring and privatisation of Britain's CEGB: was it worth it?[END_REF] or direct transfers to customers. It is very common that the two terms are employed synonymously and that a unique supplier is designated to ensure the continuity of supply in each of the three cases examined above. When national regulations do not employ these labels, other forms of interventions are designed to overcome the three possible situations where a retailer is absent. DS and LRS are generally selected by the regulator: the incumbent is generally the DS, while in the half of the countries it also performs the role of LRS. The length of Default service provision is not temporarily limited in most countries, and this fact may partly reduce customer awareness. Universal Service provision is explicitly recognized in European Directives 30 and its implementation frequently coincides with end-user price regulation for small and residential customers. [START_REF]Domestic Competitive Market Review[END_REF] In principle, the justification for end-price regulation seems to rely on the need to reduce the exploitation of final customers resulting from retailers' market power after the introduction of competition (Littlechild, 2000; OFGEM, 2002; ERGEG, 2007). This interpretation requires the withdrawal of pricing restrictions after the passage of the amount of time required to increase customer awareness and [START_REF] Newbery | The restructuring and privatisation of Britain's CEGB: was it worth it?[END_REF] For instance, the duty of serving customers through social tariffs may be allocated to the local distributor, to all retailers or to the incumbent. [START_REF]Review of domestic gas and electricity competition and supply price regulation: conclusion and final proposals[END_REF] The Directive 2009/72/EC states, "Member States shall ensure that all household customers, and, where Member States deem it appropriate, small enterprises, enjoy universal service, that is the right to be supplied with electricity of a specified quality within their territory at reasonable, easily and clearly comparable, transparent and non-discriminatory prices. To ensure the provision of universal service, Member States may appoint a supplier of last resort". [START_REF]Domestic Competitive Market Review[END_REF] The French government, for instance, in 2010 passed the NOME law, which prescribes the complete removal of tariffs for industrial customers beginning in June 2011 and allows residential customers to choose between signing contracts at market prices or being supplied by the incumbent firm, EDF, at regulated tariffs through to 2015, when all end-user regulated tariffs will disappear. The law also entitles competitive retailers to withdraw a share of EDF nuclear generation at a regulated price to supply final consumers. For further details see Creti et al. (2013).

to stimulate the entry of retailers.

Nevertheless, there is no consensus regarding the necessity to withdraw electricity tariffs to allow the market to operate effectively. For instance, Vásquez et al. (2006) maintain that a permanent, well-calculated tariff including a shopping credit32 achieves the objective of guaranteeing the supply to all customers without deterring consumer switching. Other authors such as Joskow (2000) and Littlechild (2000) are more skeptical of the benefits of including a shopping credit in regulated tariffs. It is likely, however, that consumers may be deterred from switching and new entry may be hampered if tariffs do not reflect the underlying costs (Joskow 2006; EC, 2007).

Discussion and conclusions

We proposed a comprehensive analysis of liberalization in electricity retailing using the European Union as case study. Despite several attempts to analyze retail market dynamics, there is still a lack of consensus on the type of theoretical framework that should be used to study competition in this segment. We fill this gap by highlighting the main economic dimensions on which competition is expected to have a relevant impact.

The estimation of competition effects over small firms and households represents the most controversial point in the academic debate. The presence of market imperfections, such as switching costs or informational complexities, seems to limit the possibilities for end users to fully engage in the market. As a consequence, the segmentation of active and passive customers may occurs, thereby hampering the process of developing effective competition. To overcome these limitations, we argument that some forms of "hard" regulation may still be required.

Furthermore, we show that the introduction of competition in electricity retailing requires ex-ante regulation of Default and Last Resort services. We present a complete array of implementation models and discuss their advantages and drawbacks. Finally, we assess the case for Universal Service in competitive retail markets and suggest less distortionary interventions to avoid the risk of customer exclusion.

The data and the figures on European Union have revealed that the transition to a completely competitive retail market remain an ongoing process. Altough new firms are active in the market, the supply is still highly concentrated in the hands of a few large operators. Relatively low switching rates for small firms and residential customers demonstrate the limited engagement by this group of end users. From a policy perspective, our analysis suggests that further steps should be taken and that we are far from eliminating direct regulation in this sector. Source: Authors' elaboration on European Commission data.

Note: Belgium, Denmark, Estonia, Finland, Great Britain, Greece, Hungary, Norway, Poland, Spain and the Netherlands are excluded because of missing data; Cyprus, Latvia, Lithuania, Malta and Slovenia have registered zero switchings.

21 Source: Authors' elaboration on European Commission data.

Note: Belgium, Finland, Hungary, Poland and Spain are excluded because of missing data; Bulgaria, Cyprus, Estonia, Latvia, Lithuania and Malta have registered zero switchings.

  Direct gains on retail services Indirect gains on wholesale, transport and distribution services Systemic gains (elimination of double marginalization effect) Differentiation New offers and contractual arrangements Wider range of services (risk-hedging services, energy management) Equipment innovation Innovative measuring and reading devices Empowered equipment for quality services

20

 20

Figure 1 :

 1 Figure 1: Cumulative market share of retailers (%), 2010.Source: Authors' elaboration on Eurostat data.

Figure 2 :

 2 Figure 2: Annual switching rate in the total retail market (%), 2008/2009. Source: Authors' elaboration on European Commission data.

Figure 2

 2 Figure 2 22 indicates that Ireland and the Nordic Countries represent the most active European electricity markets. Only Ireland, Sweden and the Netherlands had switching rates above 10% during the period 2008/2009, while Finland, Norway and Denmark reached the 5% threshold. France, Germany and Italy are next, with the remaining European countries reporting switching rates close to zero. However, apart

Figure 5 :

 5 Figure 5: Number of main electricity retailers, 2003-2010.Source: Authors' elaboration on Eurostat data.

Figure 6 :

 6 Figure 6: Number of main electricity retailers, 2003-2010.Source: Authors' elaboration on Eurostat data.Note: Some information about Denmark are missed; in Netherlands only main retailers selling electricity to small consumers are considered.

20

 20

Figure 7 :

 7 Figure 7: Evolution of cumulative market share of main retailers (%), 2008/2010.Source: Authors' elaboration on Eurostat data.Note: Denmark and Finland are excluded because of missing information.

Figure 8 :

 8 Figure 8: Annual switching rate for large industry (by eligible meter points; %), 2008-2009.

Figure 9 :

 9 Figure 9: Annual switching rate for medium sized industry (by eligible meter points; %), 2008-2009.Source: Authors' elaboration on European Commission data.Note: Belgium, Estonia, Finland, France, Great Britain, Hungary, Poland, Spain and the Netherlands are excluded because of missing data; Cyprus, Lithuania and Malta have registered zero switchings.

Figure 10 :

 10 Figure 10: Annual switching rate for small industry and households (by eligible meter points; %), 2008-2009.

Table 1 :

 1 Expected impacts of retail electricity competition

  5.1 Default Supplier, Last Resort Supplier and Universal Service Obligations in Europe In Europe, the application of DS and LRS regulations is highly heterogeneous. The term Default Supplier does not appear in the European Directives, and ERGEG (2009) reports that most European Countries (11 over 27) do not use this term in their national regulations. When this term is employed, it generally refers to the provider serving passive and "vulnerable" customers. Conversely, the Supplier of Last Resort is explicitly mentioned in European Directives as the provider of Universal Service. The majority of European Countries (20 out of 27) use this label to indicate the provider serving customers whose retailer exited the market and "vulnerable" customers.

Retailing activities add-value optimizing consumers' allocations of time; increasing consumer awareness of product features, price and quality; offering customer assistance; reducing searching, switching, transportation, transaction and stock-out costs(Joskow,

2000).[START_REF] Borenstein | On the efficiency of competitive electricity markets with time-invariant retail prices[END_REF] See Directive 96/92/EC.[START_REF] Brennan | Consumer preference not to choose: methodological and policy implications[END_REF] By 2009, Cyprus, Estonia (which was, however, subject to a transitional regime) and Hungary had yet to achieve the goal of completely open retail markets (EC, 2011).

By "light-handed regulation", we mean market monitoring and ex-post enforcement, while by "hard regulation", we mean ex-ante regulatory interventions.

The contributions of[START_REF] Borenstein | On the efficiency of competitive electricity markets with time-invariant retail prices[END_REF] and[START_REF] Joskow | Retail electricity competition[END_REF] are, to the best of our knowledge, the only attempts to formalize models of retail electricity competition. In these papers, the authors estimate the price distortions arising when competitive retailers are active and settlement obligations for wholesale power purchases are determined on the basis of load profiles when final customers do not react to real time prices. For models of retail competition in the gas industry, see for instanceCremer et al. (2006) and[START_REF] Polo | Liberalizing the gas industry: take-or-pay contracts, retail competition and wholesale trade[END_REF].

Real time pricing is one of the possibilities.

It should be noted that, even after full unbundling, distributors will continue to be responsible for, and thus will bear the costs of, some retailing services such as requests to connect, disconnect, or change the level of service, resolve outages and power quality problems, and interface with competitive retailers[START_REF] Joskow | Why do we need electricity retailers? or can you get it cheaper wholesale?[END_REF].

Standard credit, direct debit and prepayment.

[START_REF] Littlechild | Why we need electricity retailers: a reply to Joskow on wholesale spot price pass-through[END_REF] provides some quantitative estimations of this effect in the United Kingdom, while recognizing the inherent difficulty of such an exercise.

The double marginalization problem may also be overcome by reestablishing vertical contractual relationships between actors (with some sided-effects) or by using special types of contracts, e.g., two-part tariffs (Motta, 2004).

An empirical paper by von Der Fehr and Hansen (2010) reveals that when fierce competition has been introduced in Norwegian retail electricity market, firms has begun to behave as in a standard Bertrand setting, which has ensured cost-reflective pricing, even in the presence of a small number of competitors.

The first paper presents a social cost-benefit analysis, while the others perform regressions using panel data. Both approaches present specific limitations: cost-benefit analyses require the assessment of a credible counterfactual; in the regressions, endogeneity issues are likely to arise.

Advertising and marketing are useful tools for spreading information about products, prices and competitors. However, a general mistrust toward electricity retailers, energy brokers and their advertising campaigns endures, undermining the engagement of consumers and the gains from communication (OFGEM, 2012b). Consumer attitude has been sometimes exacerbated by misleading advertising campaigns which have been fined worldwide by competition authorities (see for instance the cases of ENI in Italy and Airtricity in Ireland).

The analysis of the relationship between the numbers and types of available contracts and the ability of consumers to seize the better market opportunities by switching supplier is postponed to section 4.2.

For a survey of newly introduced products, see for instance Von der Fehr and Hansen (2010) on the Norwegian market and[START_REF] Littlechild | Competition in retail electricity supply[END_REF] on British market.

[START_REF] Littlechild | Smaller suppliers in the UK domestic electricity market: experience, concerns and policy recommandations[END_REF] discusses in details the importance of metering and data communication in the process of entry.

In both cases the distributor is in charge for the roll-out and the investment is financed through regulated tariffs.

Switching data by end user category are reported in the Appendix (Figures 8 to 10).

Compare for instance Ofgem (2012a).

While the percentage of switching customers is in line with the national figure, the sample is biased toward low-income customers.

An alternative is the immediate disconnection of passive customers, but we do not consider this hypothesis politically feasible.

An empirical application of this measure can be found in Italy, where non-residential customers

A shopping credit is an extra charge over the regulated tariff that creates a retail margin over which new entrants can compete.

Acknowledgments

A. Creti gratefully acknowledges financial support from the Ecole Polytechnique Chair EDF-Sustainable Development and the Business Sustainability Initiative at Europlace Institute of Finance.

For instance, when ensuring the continuity of supply is the only regulatory goal, network system operator may provide Default and Last Resort services as part of its balancing activity. Price formation occurs in real time: the consumers pay an imbalance payment, which is generally burdensome, to discourage imbalances from the day-ahed production plan. Conversely, if a regulator wishes to guarantee a high level of customer protection, Default and Last Resort services may be offered at a tariff and provided by a retailer or the local distributor. [START_REF] Mirabel | Mechanisms of funding for Universal service obligations: the electricity case[END_REF] Note that each solution presents specific advantages and drawbacks in terms of market distortions, political sustainability, required regulatory oversight and enforcement.

The problem of "vulnerable" customers is slightly different and may be better understood within the Universal Service Obligations (USOs) framework. The primary argument in favor of USOs has been a concern for full market coverage at reasonable prices, including more costly market segments such as rural areas. Accordingly, some obligations have been imposed on network service providers in the form of restrictions on price discrimination ("non-discrimination"constraint) or obligations to provide the service regardless a customer's geographical location ("ubiquity" constraint). Often, the two constraints have been combined, asking the firms to ensure full market coverage at a uniform price. Prior to liberalization, vertically integrated monopolies were able to finance USOs by cross-subsidizing unprofitable and profitable market segments in their customer portfolio.

From a theoretical perspective, when competition is introduced in markets with profitable and unprofitable end users, new entrants only compete with the incumbent for profitable customers, generating the so-called "cream skimming" phenomenon, which challenges the incumbent's ability to finance USOs through cross-subsidies (Laffont and Tirole, 2000). Several authors (see for instance Anton et al., 2002; Choné et al., 2000; Choné et al. 2002; Mirabel and Poudou, 2004) have attempted to assess the welfare effects and distortionary impacts of different regulatory instruments that governments may implement to allocate and finance USOs. However, none of who temporarily lack a retailer can benefit from a "safeguard service", the supply of which is assigned for a period of two years to the winner of a reverse auction, where the participants offer to provide the service at a mark up with respect to the wholesale price of electricity. [START_REF] Mirabel | Mechanisms of funding for Universal service obligations: the electricity case[END_REF] When Default and Last resort services are offered at a tariff, they generate two distortions: the first is to provide customers with inaccurate price signals for their withdrawals; the second is that the tariff becomes the reference price for market contracts, i.e., the so called "price-to-beat".

Appendix


Corinne Chaton

Anna Creti

Benoît Peluchon

Banking and backloading emission permits

Keywords: D4, Q58 -Key words: CO 2 prices, banking, backloading, ETS reform

In this article we focus on carbon price dynamics, more speci…cally the impact of a policy envisaged by the European Commission to increase the CO 2 price. This policy consists of removing a share of the allowances allocated for a period in order to reallocate some or all of them during the following period. To analyze the impact of this backloading we determine the CO 2 market equilibrium with and without the policy, considering not only the market for permits but also the output market of regulated sectors. We propose a two-period model without uncertainty, where the market for permits is perfectly competitive, and the output market can be either competitive or oligopolistic. First, we de…ne the condition for which banking from one period to another is optimal. This condition, that is the absence of arbitrage opportunities (AOA), depends on not only from the per period initial allocation but also on production market fundamentals. When this condition is satis…ed, the market for emission is shown intertemporally e¢cient. Second, we show that the "back-loading" policy may be such that the AOA is no longer veri…ed and thus create ine¢ciencies or being ine¤ective.

Introduction

The EU-ETS has undergone signi…cant changes since its inception in 2005. During the …rst phase (2005)(2006)(2007) the permit price collapsed and reached zero during the last months of 2007, when it became clear that too much allowances were issued (see Figure 4 in Appendix 9.1). In response, the Climate and Energy Package, adopted in December 2008, authorized the banking of permits between di¤erent phases, ie the ability to use permits issued in one year (vintage) for compliance in the years following. Banking was already authorized between di¤erent years inside a phase and borrowing, i.e. the possibility to use permits issued for a speci…c year for compliance in the preceding year, is allowed within a phase. Therefore, even if a phase is "long" (total emissions lower than the sum of allowances), the value of permits is positive because of the possibility to use them in the next phase. That was the situation at the beginning of 2013: due to the European sovereign crisis, the emission permit price on the EU-ETS had fallen to levels considered too low to have an impact on investment decisions. In fact, the price did not re ‡ect the value of using phase 2 allowances during phase 3, since 2012 emissions was estimated below the cap for that year and there was a surplus of permits on the market. This situation shows the importance of EU-ETS temporal ‡exibilities in order to understand how prices are formed, especially when those features are being replicated in other markets currently being introduced around the world (Australian, California, New Zealand but also China and South Korea). However, the 2008 recession and the euro crisis beginning in 2010 have seen much lower emissions than what was expected when emissions reductions targets were de…ned. As a consequence, a permits surplus has grown in importance and is now expected by the European Commission to reach 2000 Mt in 2013 (European Commission, 2012). The carbon price has fallen a lot and is now at levels deemed insu¢cient to induce investments in cleaner production capacities. Along this, repeated e¤orts by the Commission to de…ne targets for 2030 or beyond have back…red under political opposition by coal-dependent countries. The backloading proposal is a mean to prop up the price that allows to get around this opposition. The ETS amendment approved on July 3rd 2013 by the European Parliament states that 900 million of permits will be withdrawn from auctions between 2013 and 2015, and reintroduced in 2019 and 2020. During fall 2013, the amendment has moved to the European Council to discuss several features, including how to connect backloading with long-term objectives of the EU-ETS. As such, a backloading measure still implies a high uncertainty on the …nal quantity of permits e¤ectively supplied during the last years of phase 3, since the possibility exists that withheld permits are not completely re-injected in the market. This means that expected permits supply would be lower than phase 3 cap. How do those features a¤ect the price dynamic in the EU-ETS? In order to answer that question it is necessary to go beyond the analysis found in the literature and build a model in which the rules characterizing its intertemporal ‡exibilities are precisely handled. Moreover such measures, often described as "capacity adjustment mechanisms" can be found in market designs of emissions markets currently being set-up in di¤erent parts of the world (Australia, California, South Korea, China to name the most advanced projects). The goal of the present paper is to investigate how and when such an operation may succeed.

To do so, we consider …rst the speci…cities of banking. This latter is allowed inside a phase and between phases: a permit from a given vintage may be used for all following compliances. This set-up also implies that borrowing is partly allowed whithin a phase: since allowances for vintage t are issued before the compliance for vintage t 1, it is possible to surrender them, in e¤ect allowing to borrow permits in advance (for a presentation of these rules see [START_REF] Carmona | Optimal Stochastic Control and Carbon Price Formation[END_REF] or [START_REF] Peluchon | Banking and borrowing in emissions trading systems[END_REF]). The gradual evolution towards auctioning does not alter this possibility as long as enough future vintages are sold in advance (phase 3 permits have begun to be auctioned). 1Our work is related to papers studying temporal ‡exibilities in permits markets. The …rst articles to tackle this issue are [START_REF] Rubin | A model of intertemporal emission trading, banking, and borrowing[END_REF] and [START_REF] Cronshaw | Regulated Firms in Pollution Permit Markets with Banking[END_REF]. While the latter shows that banking leads to the least-cost solution, provided that no …rm is subject to a rate of return regulation, the former extends the model and provides a rigorous treatment allowing for the inclusion or not of borrowing. Rubin …nds the necessary conditions for a perfectly competitive permits market equilibrium to exist, without uncertainty. The …rms must comply with a cap and each one must decide: (1) the level of their emissions at each time, knowing that the less they emit, the more it costs (the cost function may be di¤erent between …rms); (2) the quantity of permits bought/sold at each time. The equilibrium is found by means of optimal control in continuous time and …nite horizon, with a terminality condition such that if a …rm holds a permit at the terminal period, its value is zero. Banking and borrowing allow …rms to equalize their present value marginal abatement costs, and, as a consequence the permit price grows at the discount rate (Hotelling's rule). If borrowing is not allowed and the constraint is binding, then the permit price will grow at a lower rate, re ‡ecting the fact that a …rm would need to borrow permits from the future in order to equalize its present value marginal abatement costs. Rubin also obtains the growth path of equilibrium emissions, which allows him to conclude that banking allows for less social damages, when the cap decreases with time and the damage function is convex and cumulative damage is the integral of damages in all time periods. This helps to highlight the social bene…ts coming with intertemporal ‡exibility: …rms have an incentive to reduce their emissions sooner than without banking, because they are "saving" their reduction in the form of permits for a future more constrained. [START_REF] Kling | Bankable permits for the control of environmental pollution[END_REF] show that this property does not necessarily imply that banking and borrowing are socially optimal, when taking into account the fact that lower emissions mean higher production costs for price-taking …rms (the price of the good produced is exogenous, no demand is represented in the model). They propose to modify the banking-borrowing provisions in order to lower social costs by introducing a "discount ratio" for borrowed permits (i.e. …rms would have to pay more when they borrow). [START_REF] Schennach | The Economics of Pollution Permit Banking in the Context of Title IV of the 1990 Clean Air Act Amendments[END_REF] treats equilibrium on the emission market in the same way that [START_REF] Rubin | A model of intertemporal emission trading, banking, and borrowing[END_REF] but in in…nite horizon. Schennach shows that, when borrowing is disallowed and when abatement marginal cost does not increase faster than the discount rate the only incentive to bank allowances is the fact that there are di¤erent phases with a decreasing cap. Banking allows …rms to smooth the evolution of those costs between the two phases by "saving" permits during the …rst phase and depleting that stock until a …nite time in the second phase, after which permit price only changes because of changes in costs. She provides explicit solutions for the optimal emissions path and the permit price when borrowing is not allowed by restricting abatement marginal cost to a linear function. Sensitivity analysis can thus be performed when abatement cost decrease exogenously because of the introduction of a new low-emissions fuel or of a new technology. This framework is then extended to uncertainty. This latter case implies that a kind of convenience yield exists: the expected permit price grows at a lower rate than the discount rate, because of the borrowing constraint. [START_REF] Maeda | Impact of Banking and Forward Contracts on Tradable Permit Markets[END_REF] explicitly introduces a futures market with uncertainty and shows that prices depend of the distribution between pure traders and regulated actors, when both are risk-averse and the pure traders use permit futures to hedge an exogenous but correlated risk. The question of market power in emissions permits market when there is banking has been studied by [START_REF] Montero | A note on market-power in emissions permits market with banking[END_REF] and a review of the di¤erent connected questions can be found in the thorough review by [START_REF] Montero | Market power in pollution permits markets[END_REF]. In all preceding articles, the regulated market equilibrium is never introduced 2 . Baseline emissions are always exogenous and the decisions are how much and when to abate emissions. As such, it is di¢cult to analyze when and why Hoteling's rule is not valid, since it is almost always the case, as long as caps are decreasing and baseline emissions at least non-decreasing. Moreover, the sensivity analysis performed by Schennach cannot be thorough since marginal abatement costs variations have to be interpreted either as baseline emissions shocks or technology shocks. Being able to distinguish between causes a¤ecting the output market whose emissions are regulated is important if we want to assess the impact of backloading measures described in the following paragraph.

The remainder of this paper is organised as follows. The model is presented in section 2. In section 3, we show that the no intertemporel arbitrage opportunity condition (equivalent to Hotelling's rule) depends on the fundamentals of the output market. Section 4 focuses on CO 2 prices. When the no-arbitrage opportunity condition is ful…lled, intertemporal e¢ciency is achieved on the emissions market, since it implies that …rms can minimize the sum of environmental discounted costs. Moreover, we show that rules such a cap decreasing in a pre-determined percentage every year can be ine¢cient as this rule might create ine¢ciencies in the market for permits. In section 5, we discuss how backloading impact the permit market. We de…ne a quota threshold such that below this threshold the backloading policy has no e¤ect, and above this threshold e¢ciency is not guaranteed since present value carbon prices are no longer equal. If only a share of permits backloaded is re-injected in the market, then total cap is modi…ed and prices are higher in both cases.

The model

The model focuses on the determination of prices for emissions permits. To enhance the clarity of the analysis, we do not consider uncertainty. We consider two periods, corresponding to two successive phases of a market for permits. The discount rate between the two periods is r: For any variable or parameter y relating to the …rst period, y 0 relates to the second one. In the following, we detail our modelling assumptions.

Demand and production. There are n symmetric3 …rms which compete in quantities in a market for a homogeneous good. The demand for the produced good is elastic. We use a linear inverse demand function p = b dnq for the …rst period (p 0 = b 0 d 0 nq 0 for the second period).

A …rm chooses q in the …rst period and q 0 in the second period at a cost assumed linear, for ease of calculation

C (q; q 0 ) = cq + 1 1 + r c 0 q 0 : (1)
Carbon Emissions and Abatement Technologies. When the …rm produces q in the …rst period (q 0 in the second period) it emits an amount e (q) of pollution in the …rst period (e 0 (q 0 ) in the second period) such that e (q) = e 0 q (e 0 (q 0 ) = e 0 0 q 0 respectively) where e 0 > 0 and e 0 0 > 0 are exogenous factors associated to the production technologies. For each period, each …rm has the option of reducing emissions (from e 0 to in the …rst period and from e 0 0 to 0 in the second period) bearing an cost (e 0

) q in the …rst period ((e 0 0 0 ) q 0 in the second period). This cost is mainly related to the cost of fuel-switching which is a short-term cost because production technologies are already in place. Producer change production technology if this cost is lower than the gain obtained through the use of cleaner technology.

Carbon Quotas and Emissions. Each period, a …rm has to hold a permit in order to pollute one unit. During each period the total volume of emissions is limited by the initial allocation A in the …rst period (A 0 in the second period with A 0 A), whose amount is decided by the regulator. The emissions units can be traded and sold in a market of emission permits in which …rms are price-taker and competition is perfect. A producer can buy at a price per unit, z permits in the …rst period (z 0 permits at a price 0 per unit in the second period). For each period, he must have at least as many permits as units that emits. In the …rst period, he can store permits, z, in order to use it in the second period (banking). Permits are stored at zero costs. We assume that borrowing is impossible, therefore z 0; and that all inventories have to be emptied by the end of the second period. 4Firms' pro…ts. Firms' pro…ts can be decomposed into three terms: net revenues from selling in the output market, (p c

) q + 1 1+r (p 0 c 0 0 0 )q 0 , cost of emissions after abatement, (e 0

) q 1 1+r (e 0 0 0 ) q 0 0 and net revenues from banking (trading) on the CO 2 permits (market), (

)z.

Notice that the sign of the last term depends on the value of the demand and cost parameters and on the CO 2 quota. In particular, quotas from the …rst period may not be enough to allow banking. In this case 0 1+r > . In the following, we determine conditions on A and A 0 such as in equilibrium there is no arbitrage opportunity 0 1+r = :

Banking. Banking is a trading tool allowing to earn pro…ts from the price spread in the two phases of the market for permits. This is similar to physical storage that smooths the seasonal price di¤erential. Banking helps suppliers to meet their obligation 5 (have as many permits as emissions) at a lower cost.

3 Solving the model Equilibrium conditions on the CO2 market. Given the assumptions above, the equilibrium conditions on the CO 2 market are as follows z = q + z;

(2) z 0 = 0 q 0 z;

(3) nz A;

(4) nz 0

A 0 :

(5)

Equations ( 2) and (3) represent the fundamental relationship between banking in the market for permits and the output market.

Equilibrium prices of emission permits and supply. To determine the equilibrium price in the market for CO 2 permits, in a …rst step, we determine the market equilibrium of the good considering permit prices ( and 0 ) exogenous, then in second step, we calculate the equilibrium on the CO 2 market.

Firms maximize their pro…t given by

= (p c ) q + 1 1 + r (p 0 c 0 0 0 ) q 0 (e 0 ) q 1 1 + r (e 0 0 0 ) q 0 + 0 1 + r z: (6)
We solve the model as follow. We …nd the symmetric Nash equilibrium on the …nal market the quantities produced by a …rm and get the total quantities 5 Since traders do not have this obligation, emission permits are more valuable for a supplier than for a trader. As a consequence, traders can be active only if some suppliers are …nancially constrained. Since the environment is certain, if producers are not …nancially constrained so pure traders do not exist (the producers have the highest willingness to pay). If during the …rst period the producers do not have the …nancial capacity to store permits then the traders can act as a portfolio manager of permits if producers have the …nancial capacity to buy them during the second period. In this case, (with a discount rate equal for each type of agent) the equilibrium obtained is identical to that obtained without …nancing constraints. The pure traders act as an intermediary (on a market that is considered competitive). produced in the two periods

q = b c (e 0 ) (1 + n) d ; (7)
q 0 = b 0 c 0 0 0 (e 0 0 0 ) (1 + n) d 0 : (8)
The equilibrium on the CO 2 market implies (4), ( 5) and

@ @z = 0 1 + r = 0 if z > 0: (AOA)
For ease of calculations, in the following Sections, we assume c 0 = c; b 0 = b , d 0 = d and = 0 = e 0 = e 0 0 (see the Appendix 9.3 for the general case).

4 Equilibrium.

If the number of permits A + A 0 is such as

A + A 0 < n n + 1 2(b c) d (9)
then the …rms are constrained. If furthermore

(1 + r) A A 0 > n n + 1 (b c) r d ( 10
)
there is an opportunity to store permits and at equilibrium the abscence of arbitrage opportunities, AOA is characterized by 0 = (1 + r) and equilibrium is de…ned by

q = A + A 0 n (2 + r) + r(b c) (n + 1) (2 + r) d ; (11)
q 0 = (1 + r) (A + A 0 ) n (2 + r) r(b c) (n + 1) (2 + r) d ; (12) z = (1 + r) A A 0 n (2 + r) r(b c) (n + 1) (2 + r) d ; (13) = 2(b c) (2 + r) (n + 1) (A + A 0 ) d n (2 + r) 2 ; ( 14
) 0 = (1 + r) : (AOA)
The condition on A and A 0 such that …rms are constrained by the number of permits on the two periods combined (Equation ( 9)) and the optimality condition of the banking (Equation ( 10)) imply …rms are "quota constrained" in period 1; i.e.

A < n n + 1 (b c) d : (15)
Since by assumption A 0 < A; Equation (15) implies …rms are "quota constrained" in period 2; i.e.

A 0 < n n + 1 (b c) d : (16)
If there is no banking, …rms are "quota constrained" during the second period if Inequality ( 16) is veri…ed and during the …rst period if Inequality ( 15) is veri…ed.6

Proposition 1.

-No-arbitage condition -If the optimality condition of the banking (Equation ( 10)) does not hold then the equation of AOA is not veri…ed. In this case, banking is not the optimal and since by assumption borrowing is impossible, carbon prices are such that 0 < (1 + r) and the equilibrium is de…ned by

q nb = A n ; (17)
q 0 nb = A 0 n ; (18) nb = b c 1 + n n dA 2 ; (19) 0 nb = b c (1 + n) n dA 0 2 : (20)
No banking. Equations ( 17) -( 20) de…ne also equilibrium in the case where the banking is not allowed and the …rms are "quota constrained" in period 1 (Equation (15) veri…ed). In this case, we have 0 nb > nb . Indeed,

0 nb = nb + (A A 0 ) (1 + n) d n 2 > nb : (21)
The di¤erence between the prices of permits ( 0 nb nb ) is an increasing function of the elasticity of the demand. In competition on the market of the good (n tends to in…nity) the prices of permits are nb = (b c) Ad 2 and 0 nb = (b c) A 0 d 2 : These prices are increasing functions of the number of …rms. Indeed, when this number is higher, the quantity produced becomes more important and consequently the volume of emissions is increasing therefore the need for permits is more important.

If the number of permits is su¢ciently low (

A < n 2(n+1) (b c) d , A 0 < n 2(n+1) (b c) d
), the prices of permits decrease with the polluting factor and when n 2(n+1)

(b c) d < A < n (n+1) (b c) d and n 2(n+1) (b c) d < A 0 < n (n+1) (b c) d
the prices of permits increase with . If the …rms are constrained only on the second period and the banking is not allowed, the quantity produced by each …rm in the …rst period is

q = b c (1 + n) d ; (22)
the CO 2 permit price in the …rst period is = 0; the CO 2 permit price in the second period is de…ned by the Equation ( 20) and the resulting outputs sold by each …rm on the second period by the Equation ( 18).

No constraint. If the …rms are not constrained by the permits allocation, the quantities produced by each …rm are

q = q 0 = b c (1 + n) d (23)
and the CO 2 permit prices are = 0 = 0:

Equilibrium properties. Equation ( 13) shows that banking decreases with a factor that depends from the parameter or demand and costs of the output market ( r(b c) (n+1)(2+r)d > 0). Indeed, production of goods o¤ers ‡exibility and weakens the borrowing constraint. Combining Equations ( 11) and ( 12) yields

q 0 = (1 + r)q r (b c) (1 + n) d : (25)
Consequently q 0 < (1 + r)q : Since banking links the productions of the two periods, if the parameters of demand and costs are the same from one period to another, while the production of the second period will be at best equal to the capitalized production of the …rst period. Moreover, given that we are in the case where …rms are constrained by the number of permits, the total output (n (q 0 + q )) depends only on the number of permits (A + A 0 ) and emission factor . Indeed, the Equations ( 11) and ( 12) provide

q 0 + q = A + A 0 n : (26)
When n tends to in…nity (competitive markets) then q 0 tends to (1 + r)q :

Remark 1. The equilibrium quantities with (Equations ( 11) -( 12)) and without banking (Equations ( 17) -( 18)) and the optimality condition of the banking (Equation (10)) provide (1 + r) q + q 0 < (1 + r) q nb + q 0 nb :

Equation ( 27) does not mean that there is strategic restriction of the output.

Obviously, the pro…t of a …rm obtained when there is banking, is greater than the pro…t without banking, nb : The ability to store permits o¤er ‡exibility to the …rm. This ‡exibility has a value that can be quanti…ed. Indeed,

= nb + P ( 28
)
where

P = ((1 + r) A A 0 ) n 2 (1 + r) (2 + r) 2 [(1 + n) ((1 + r) A A 0 ) d n (b c) r ] : (29)
The terms in brackets are those of the optimality condition of the banking (Equation ( 10)). As a result, if the banking is optimal Equation ( 10) is satis…ed then the expression in brackets in Equation ( 29) is positive and therefore P is positive. P is the value of the ‡exibility obtained with the banking. This value tends to 0 when n tends to in…nity. It is equal to zero when A 0 = (1 + r) A:

In the appendix (see 9.2) the impact of banking on the mark-up is studied.

Lemma 2. The equilibrium quantity q de…ned by the Equation (11) (respectively q 0 de…ned by the Equation ( 12)) is increasing (respectively decreasing) in the discount rate, r:

Proof. @q @r = 2(b c) (n+1)(2+r) 2 d A+A 0
n(2+r) 2 : Since by assumption Equation (9) holds then

A + A 0 < n n+1 2(b c) d
, @q @r > 0: Furthermore @q 0 @r = @q @r :

5 Analysis of CO 2 prices.

Initial allocations and banking

Let us de…ne = A 0 A : In Figure 1, excluding the area where > 1 (since by assumption A 0 < A) three zones are represented.

1. The amount of permits allocated are such that banking is not optimal, ie.

AOA is not veri…ed. This is achieved when A and are located in the shaded region. This case occurs when A is su¢ciently small.

If

A > n n+1 (b c) d
for all the banking is optimal ie. AOA is veri…ed.

3. If A > n n+1 2(b c) d
for all …rms will never be constrained in emission and hence = 0 = 0: Lemma 3. The domain of A and A 0 such as there are AOA is decreasing in r. By contrast, the discount rate has no impact on the …elds of A and A 0 for which …rms are "quota constrained".

Proof.

@[(1+r)A n n+1 (b c)r d ] @r = A n 1+n (b c) d : Then @[(1+r)A n n+1 (b c)r d ] @r < 0 if A < n 1+n (b c) d : Since by assumption A 0 < A; (9) yields A < n 1+n (b c)r d < n 1+n (b c) d : In opposition n n+1 2(b c) d
A 0 is independent of r. So an increase in the discount rate leads to a decrease of areas A and A 0 where the AOA is veri…ed.

Insert …gure1.gif

CO 2 prices.

To each region plotted in Figure 1 above, correspond CO 2 prices we have plotted in Figure 2, more precisely we drew and 0 1+r as a function of A, the number of permits allocated in the …rst period. Let

a = n n + 1 (b c) r d (1 + r ) (30)
and

a = n n + 1 2 (b c) d (1 + ) : (31)
1. When A is less than a the banking is not optimal and the CO 2 prices are de…ned by the Equation ( 19) and Equation ( 20), > 0 1+r : 2. If A is greater than a, then the permit price in the second period is equal to the capitalized permit price of the …rst period, = 0 1+r and, if A is greater than a the …rms are not constrained by emissions and consequently permit prices are zero. Insert …gure2.ppt Figure 2: CO 2 prices as a function of A:

If A 0 increases (ceteris paribus), the price of CO 2 decreases (increases and hence a and a decrease). A decrease in the cost of production increases production thus emissions are increased and consequently permit prices are increased. There is the same e¤ect when the elasticity increases7 . If A 2 [a; a] ; the permit price in a competitive market is

= 2(b c)d (2+r)
(A+A 0 )d (2+r) 2 . Lemma 4. The equilibrium price of permits for the …rst period, (respectively second, 0 ) is decreasing in r (respectively increasing).

Proof. @ @r = 2(b c)

(2+r) 2 1+n n (A+A 0 ) (2+r) 2 2 :
Since by assumption Equation ( 9) holds then

A + A 0 < n n+1 2(b c) d
, @ @r < 0: Furthermore @ 0 @r = @ @r :

6 E¤ect of "set aside" or "backloading" of emission certi…cates.

The backloading policy is meant to be implemented only in EU-ETS second phase. This means that the two periods considered in the model must be thought as two group of years included in the same phase. 8 Two con…gurations must be studied.

1. A "pure backloading" case, where the quantity of permits withheld in the …rst period is equal to the quantity of permits supplied in the second period, and 2. A "partial backloading" case, where the quantity supplied in the second period is lower, re ‡ecting the lower expected supply because of uncertainty on the policy (as explained in the description of backloading measures).

6.1 "Pure backloading" case.

If a portion of the permits allocated in the …rst period are removed to be redistributed to the second period, the condition on A and A such that …rms are constrained by the number of permits on the two periods combined (Equation ( 9)) is not changed, but the optimality condition of the banking (Equation ( 10

)) becomes(1 + r) (A ) (A 0 + ) n n+1 (b c)r d () (1 + r) A A 0 n n + 1 (b c) r d + (2 + r) : (32)
Setting aside permits has no impact on the tightness of the constraint but may increase the area where the banking is not optimal.

A policy that may have no e¤ect. If the quantity of permits withheld in the …rst period is too small then backloading has no impact on CO 2 prices. Indeed, if initially the optimality condition of the banking (Equation ( 10)) is veri…ed, for all set aside where

= max (1 + r) A A 0 2 + r n n + 1 (b c) r (2 + r) d ; 0 ; (33)
…rm still bank permits in the …rst period in order to use them during the second period. The threshold is equal to the amount of permits that would be e¢ciently banked in the absence of any set aside. Figure 3.a presents the impact of a set aside 1 such as 1 < : Thus, when the constraint of the …rst period is tightened (A is reduced by 1 ) and the constraint of second period is released by 1 then there is a translation to the right of a (which becomes a 1 ) as well as a translation towards the left of a (which becomes a 1 ). The equilibrium is unchanged ( 1 = and 0 1 = 0 ): Insert …gure 3.a.ppt A policy that creates ine¢ciencies. If the quantity of permits withheld in the …rst period is higher, AOA can not be veri…ed and thus the policy may create ine¢ciencies. Indeed, if > banking is no longer optimal. For exemple, in Figure 3.b, = 2 > : In this case a and a respectively become a 2 and a 2 and the new equilibrium is 2 > and 0 2 > 0 : Insert …gure 3.b.ppt Figure 3.b: Impact of "backloading" on CO 2 prices where = 2 > Therefore, a policy of "pure backloading" has either no e¤ect on CO 2 prices or increases them such as the AOA does not longer hold. Is a "partial backloading" policy would increase the CO 2 price in the …rst period? 6.2 "Partial backloading" case.

If backloading is such that the number of additional permit redistributed in the second period is equal to then the optimality condition of the banking (Equation (32)) can be rewritten

(1 + r) A A 0 n n + 1 (b c) r d + (1 + + r) (34)
which gives the threshold:

= max (1 + r) A A 0 1 + + r n n + 1 (b c) r (1 + + r) d ; 0 : (35)
If the number of permits withdrawn the …rst period is less than the "partial backloading" policy has no e¤ect. In contrast, if this number is greater than it creates ine¢ciencies.

If a portion of the permits allocated in the …rst period is removed to be reinjected in whole or in part in the second period, the area (A; A 0 ) such that it is optimal to store permits between the two periods is widened. It is possible that the decrease of permits allocated in the …rst period is so high that banking permits between the two periods is no longer optimal. In the "pure backloading" case, the permit prices are not modi…ed, provided that the quantity withheld is lower than a given threshold. Otherwise, the borrowing constraint becomes active and Hotelling's rule does not apply anymore. Present value permit price in the second phase is lower than the price in …rst phase. This situation is unlikely when the number of permits injected the second period is less than the number of permits withdrawn the …rst period (that is to say < 1). In the "partial backloading" case, prices rise, provided that the quantity withheld is lower than another threshold, given that the total of allowances supplied is modi…ed in comparison with the "pure backloading" case. This means that "backloading" may succeed in propping-up prices, due to expectations. 9

Conclusion

This paper has analyzed the joint equilibrium of an emissions permits market and the output market whose emissions are capped. Banking allows …rms to minimize their compliance costs as long as it is optimal to bank. We provide the conditions for which this is true, implying that the permit price follows Hotelling's rule. Those conditions depend on the values of demand, cost, emission and allocations parameters. When the conditions are not ful…lled, the present value of second period permit price is lower than …rst period price and no permits are banked. Our model thus allows to understand how backloading proposals are supposed to work on the EU-ETS, and under which conditions they may distort the intertemporal e¢ciency 9 When the parameters of the output market take di¤erent values at each period (see Appendix 9.3) and banking is not optimal, the …rst period permit price may be higher than the present value of the second period price, even though the cap is decreasing. Such a case is possible if, for example, on the product market, demand in the second period is lower than the one in the …rst, or if expected second period emission rate is lower than in the …rst period. This last example may happen if for instance a strong development of renewables is expected between the two periods. of the market. Our model provides elements on how to make those adjustments taking into account structural of the fundamentals in the output market of …rms under environmental constraints. 9 Appendix 9.1 Evolution of CO2 price Insert Figure4.gif (1 + n) dA 0 : (37)

These rates are increasing functions of the number of permits and decreasing functions of n and of the emission factor : With banking, the mark-up rate of the …rst period is given by

m = nr (b c) + (1 + n) d (A + A 0 ) (1 + n) [n (2b + cr) (1 + n) d (A + A 0 )] (38)
and the mark-up rate of the second period is equal to

m 0 = nr (b c) (1 + n) d (A + A 0 ) (1 + n) [n (cr 2 (1 + r) b) + (1 + n) (1 + r) d (A + A 0 )] : (39)
These rates are decreasing functions of the number of permits and tend obviously to 0 as n tends to in…nity. Combining Equations ( 36) and ( 38) yield m > m if Equation ( 10) is veri…ed. As a result, store permits in the …rst period reduces the mark-up of the …rst period. What is the e¤ect of storage on the mark-up of the second period? Combining Equations ( 37) and ( 39) yields m 0 < m 0 if A > S where 15)) then (10) implies A > S: Therefore, store permits in the …rst period increases the mark-up of the second period. [(1 + r) (b c e 0 ) 0 (b 0 c 0 e 0 0 ) + r 0 ] 0 (41) there is an opportunity to store permits and at equilibrium the abscence of arbitrage opportunities, AOA is characterized by (AOA) and equilibrium is de…ned by

General case

Figure 1 :

 1 Figure 1: AOA vs no AOA zones.

Figure 3

 3 Figure 3.a: Impact of backloading on CO 2 prices where

Figure 4 :

 4 Figure 4: Prix spot EUA in e/t (Source -Point Carbon )

  We consider the case in which c 0 6 = c; b 0 6 = b , d 0 6 = d and e 0 6 = e 0 0 : If the number of permits A + A 0 is such as

Figure 1 :

 1 Figure 1: AOA vs no AOA zones.

Figure 2 :

 2 Figure 2: CO 2 prices as a function of A:

  Figure 4: Prix spot EUA in e/t (Source -Point Carbon )

	2005 emissions	Beginning of phase 2
	made public : lower
	than expected
						Certainty that
		Quasi-certainty that phase 1 will				phase 2will be long
		be long
	2006/09/15	2007/09/15	2008/09/15	2009/09/15	2010/09/15	2011/09/15	2012/09/15

For a survey on banking literature, see[START_REF] Chevalier | Carbon Price Drivers: An Updated Literature Review[END_REF], whereas a more general review of the literature about cap and trade systems can be found in[START_REF] Taschini | Environmental economics and modeling marketable permits: A survey[END_REF].

Papers which focuses on both the permit market and the output market (see for exemple[START_REF] Hintermann | Market Power and Windfall Pro…ts in Emission Permit Markets[END_REF]) do not take banking into account.

The …rms use the same polluting technology as well as the same abatement technology in order to reduce their pollution.

For similar setting where …rms in the output market can be competitive (if n tends to in…nity and the demand is inelastic) or oligopolisitc and no market power exists in the allowance market, see[START_REF] Requate | Environmental Policy under Imperfect Competition: A Survey[END_REF].

Inegality (15) implies > 1; or e 0 q > q + (e 0 ) q that is a …rm will adopt the new technology including adoption costs. Said di¤erently, allocations A and A 0 give incentives to adopt the technology with the abatment factor .

That is to say, when 1 d increases.

The fact that borrowing is partially allowed does not modify the conclusions from the model, since the quantities supplied in advance are completely equivalent to a higher cap in the given period.

Acknowledgments A. Creti gratefully acknowledges nancial support from the Ecole Polytechnique ChairEDF-Sustainable Development, and the Business Sustainability Initiative at Europlace Institute of Finance.

We thank Khalil Helioui for its comments and suggestions. The views, assumptions and opinions expressed in this paper are those of the author and do not necessarily re ‡ect the o¢cial policy or position of EDF.

y EDF R&D, FiME (Finance for Energy Market Research Centre) and CABREE (Centre for Applied Business Research in Energy and the Environment).

If the condition (41) does not hold then the equation of AOA is not veri…ed and the equilibrium is de…ned by

Notice that the mark-up rates are the same as in the case without abatement cost.The area of AOA is larger when there are abatement costs. The possibility to switch technology bearing abatement costs in order to emit less emission provides ‡exibility to the …rm. As a result, permit prices after switching technologies are weaker than before and the area where prices of CO 2 permits are zero is wider.


Annie-Claude Bayeul-Lainé
email: annie-claude.bayeul-laine@ensam.eu

Patrick Dupont

Giovanna Cavazzini

Antoine Dazin

Patrick Cherdieu

Gérard Bois

Olivier Roussette

INVESTIGATIONS IN A VANED DIFFUSER OF SHF IMPELLER

ABSTRACT: The paper presents the numerical and experimental analysis of performance and internal flow behaviour in the vaned diffuser of a radial flow pump (Fig. 1) using PIV technique (Fig. 2), pressure probe traverses and numerical simulations. PIV measurements have been performed at different heights inside one diffuser channel passage for a given speed of rotation and various mass flow rates. For each operating condition, PIV measurements have been made for different angular positions of the impeller. For each angular position, instantaneous velocities charts have been obtained on two simultaneous views, which allows, firstly, to cover the space between the leading edge of the impeller and the diffuser throat and secondly, to get a rather good evaluation of phase averaged velocity charts and "fluctuating rates ". Hub to shroud directional probe traverses (Fig. 3) have also been performed using a 3 holes pressure probe along the diffuser width at different radial locations between the two diffuser geometrical throats. The numerical simulations were realized with the two commercial codes: i-Star CCM+ 7.02.011 (at LML), ii-CFX 10.0 (at University of Padova). Fully unsteady calculations of the whole pump were performed. Comparisons between numerical and experimental results are presented and discussed for different mass flow rates. In this respect, the effects of fluid leakage due to the gap between the rotating and fixed part of the pump model are analysed and discussed. Experimental results strongly depend on impeller position during its rotation. Pressure probe results are also depending on unsteady effects and this has to be taken into account for further data reduction analysis. The contours of radial and tangential velocity at mid high (Fig. 4) as well as the time-averaged values of radial and tangential velocity distributions allow leakage to be an important parameter that has to be taken into account in order to make comparisons between numerical and experiments. Henceforth, simulations with fluid leakages will be realized and unsteady probes will be used in order to confirm these previous results. PIV G. Cavazzini [START_REF] Cavazzini | Analysis of unsteady flow velocity fields inside the impeller of a radial flow pump : PIV measurements and numerical calculation comparisons[END_REF]

Figure 1 Figure 4 -

 14 Figure 1 : SHF impeller Figure 2 : Test Apparatus Figure 3: Probestraverses locations