Olivier Massol
email: olivier.massol@ifpen.fr

Albert Banal-Estañol

Derek Bunn

Arash Farnoosh

Steven Gabriel

Frédéric Lantz

Market power across the Channel: Are Continental European gas markets isolated? ☆

Keywords: Law of one price, market integration, spatial equilibrium, interconnectors, natural gas. JEL Classification: D43, F14, F15, L95, Q37

This paper examines the efficiency of the arbitrages performed between two regional markets for wholesale natural gas linked by a capacity-constrained pipeline system. We develop a switching regime specification to (i) detect if the observed spatial arbitrages satisfy the integration notion that all arbitrage opportunities between the two markets are being exploited, and (ii) decompose the observed spatial price differences into factors such as transportation costs, transportation bottlenecks, and the oligopolistic behavior of the arbitrageurs. Our framework incorporates a test for the presence of market power and it is thus able to distinguish between the physical and behavioral constraints to marginal cost pricing. We use the case of the "Interconnector" pipeline as an application, linking Belgium and the UK. Our empirical findings show that all the arbitrage opportunities between the two zones are being exploited but confirm the presence of market power.

Introduction

Over the last two decades, a series of structural and regulatory reforms have been carried out to promote a competitive organization for both the North American and European natural gas industries.

A significant development in this restructuring was the emergence of spatially localized spot markets for wholesale natural gas that are interconnected throughout the pipeline network. By opening access to the pipeline system, these liberalization reforms have allowed gas arbitrageurs to purchase transportation rights and thus compete to exploit spatial price differences between interconnected markets. The efficiency of these spatial arbitrages represents a major regulatory policy issue. For example, the current European policy debates related to the organization of the EU's internal market for natural gas repeatedly underline the importance of spatial arbitrages as a means to prevent balkanization and ensure an efficient supply of natural gas [START_REF] Vazquez | Designing the European Gas Market: More Liquid & Less Natural?[END_REF].

From a theoretical perspective, the definition proposed in [START_REF] Stigler | The Extent of the Market[END_REF] indicates that two geographical markets for a tradable good are integrated if the spatial price difference between these two markets equals the unit transportation cost. However, from an empirical perspective, assessing the geographic expanse of wholesale gas markets represents a challenging task because intermarket price spreads could reflect a variety of other factors, including transportation bottlenecks and oligopolistic pricing by the arbitrageurs. To overcome this problem, we define integration using the equilibrium notion that all spatial arbitrage opportunities between the two markets are being exploited. This notion is derived from the theoretical literature on spatial price determination that was pioneered by [START_REF] Enke | Equilibrium among Spatially Separated Markets: Solution by Electric Analogue[END_REF], [START_REF] Samuelson | Spatial Price Equilibrium and Linear Programming[END_REF], and [START_REF] Takayama | Spatial and Temporal Price and Allocation Models[END_REF]. This paper develops an empirical methodology to assess the arbitrages performed between two regional markets for wholesale natural gas linked by a capacity-constrained pipeline system. This methodology is designed to (i) detect if these markets are "integrated," i.e., if all the spatial arbitrage opportunities are being exploited, and (ii) decompose the observed spatial price differences into factors such as transportation costs, transportation bottlenecks, and the oligopolistic behavior of the arbitrageurs. Our framework incorporates a test for the presence of market power and is thus able to distinguish between physical and behavioral constraints to marginal cost pricing. As an application, we use the spatial arbitrages in the "Interconnector" pipeline which connects Europe's two oldest spot markets for natural gas: the UK's National Balancing Point and the Zeebrugge market in Belgium. 1 A large amount of empirical research has examined the degree of spatial integration between markets for wholesale natural gas with the help of time-series techniques. 2 These studies typically rely 1 The application discussed in the paper examines the possible lack of gas flows in the pipeline infrastructure connecting the UK and mainland Europe. That is why the title of this paper is a veiled reference to the British idiom "Fog in the Channel. Continent isolated," allegedly a newspaper headline in Britain in the 1930s announcing the suspension of ferry services between the UK and mainland Europe because of dangerous weather in the English Channel. 2 A tentative and non-exhaustive methodological clustering of these contributions includes: (i) the early correlation-based analyses [START_REF] Doane | Open Access and the Evolution of the U. S. Spot Market for Natural Gas[END_REF]; (ii) the use of Granger causality tests to examine how natural gas price shocks are transmitted across interconnected wholesale markets [START_REF] Doane | Open Access and the Evolution of the U. S. Spot Market for Natural Gas[END_REF]; (ii) the pure cointegration-based studies on local price data and assess the co-movements of prices at each market location. In these analyses, it is typically argued that high degrees of correlation and/or co-integration between the price series are evidence that the law of one price is being enforced through spatial arbitrages. These price-based empirical models provide useful insights into how local price shocks are transmitted to adjacent markets. However, the methodology used in these studies is of little help in assessing the competitive nature of the observed spatial arbitrages, as they fail to detect the presence of imperfect competition.

Moreover, as suggested by the related agricultural economics literature [START_REF] Barrett | Market Analysis Methods: Are Our Enriched Toolkits Well Suited to Enlivened Markets[END_REF][START_REF] Barrett | Measuring Integration and Efficiency in International Agricultural Markets[END_REF][START_REF] Baulch | Transfer Costs, Spatial Arbitrage, and Testing for Food Market Integration[END_REF][START_REF] Mcnew | Testing Market Equilibrium: Is Cointegration Informative[END_REF], these empirical models are unable to account for the pivotal role played by both intermarket transfer costs and trade flow considerations. 3 In this paper, we consider an alternative approach based on the parity bounds model (PBM) first introduced in [START_REF] Spiller | On the Extent of the Market: Wholesale Gasoline in the Northern United States[END_REF]. 4 In a PBM, arbitrageurs are assumed to be profit-maximizing agents. Using that assumption, intermarket price spreads are examined using a "switching regime" specification, which estimates the probability of observing each of a series of trade regimes. [START_REF] Sexton | Market Integration, Efficiency of Arbitrage and Imperfect Competition: Methodology and Application to U.S. Celery[END_REF], for example, consider three distinct trade regimes: an "arbitrage" regime where the spatial price difference equals the unit intermarket transportation cost, an "autarkic" one where the local prices differ by less than that transportation cost, and a "barriers to trade" regime where the observed spatial price difference is larger than that transportation cost. [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF], our point of departure, make use of trade flow data to further distinguish whether trade occurs or not in each of the three regimes. This direction-specific approach allows them to detect any violation of the theoretical equilibrium conditions that all arbitrage opportunities between the two markets are being exploited.

We propose a series of modifications of existing PBMs to apply them to the case of natural gas markets. Existing models assume the presence of perfect competition in the spatial arbitrages between two markets. So, we first propose an enriched specification to account for the role of market power and show that it can be used to test for the assumption of perfectly competitive arbitrages. Second, the role of transportation bottlenecks has so far been neglected whereas binding pipeline capacity constraints are likely to occur in the gas industry. So, we propose isolating the specific contribution of pipeline capacity constraints in the observed spatial price spreads. Lastly, the existing PBMs are based on a static formulation where shocks are posited to be serially independent and the variance that test for the existence of a long-run equilibrium condition governing the local price series [START_REF] De Vany | Pipeline Access and Market Integration in the Natural Gas Industry: Evidence from Cointegration Tests[END_REF][START_REF] Doane | Open Access and the Evolution of the U. S. Spot Market for Natural Gas[END_REF][START_REF] Serletis | Is There an East-West Split in North American Natural Gas Markets?[END_REF][START_REF] Asche | European Market Integration for Gas? Volume Flexibility and Political Risk[END_REF]; (iv) the analyses examining a time-varying degree of price convergence among natural gas spot markets with the help of the Kalman Filter approach [START_REF] King | Price Convergence in North American Natural Gas Spot Markets[END_REF][START_REF] Neumann | Convergence of European spot market prices for natural gas? A real-time analysis of market integration using the Kalman Filter[END_REF][START_REF] Renou-Maissant | Toward the Integration of European Natural Gas Markets: A timevarying Approach[END_REF][START_REF] Abada | A Generalized Nash-Cournot Model for the Northwestern European Natural Gas Markets with a Fuel Substitution Demand Function: The GaMMES Model[END_REF] the use of an autoregressive model of pairwise price differentials between geographically diverse locations to estimate the speeds of adjustment toward equilibrium [START_REF] Cuddington | Assessing the degree of spot market integration for US natural gas: evidence from daily price data[END_REF](vi) the joint assessments of the degree of market integration and price transmission across natural gas markets using tests of cointegration and the corresponding error-correction models [START_REF] Park | Price interactions and discovery among natural gas spot markets in North America[END_REF][START_REF] Brown | Deliverability and regional pricing in U.S. natural gas markets[END_REF]. 3 These criticisms emphasize a lack of acquaintance with existing economic models of spatial price determination. Two lines of arguments motivate that shortcoming. First, intermarket transfer costs are typically omitted in these early empirical studies whereas, in theory, price equalizing arbitrage activities are triggered only when localized shocks result in spatial price differences which exceed these intermarket transfer costs [START_REF] Barrett | Market Analysis Methods: Are Our Enriched Toolkits Well Suited to Enlivened Markets[END_REF][START_REF] Barrett | Measuring Integration and Efficiency in International Agricultural Markets[END_REF][START_REF] Baulch | Transfer Costs, Spatial Arbitrage, and Testing for Food Market Integration[END_REF][START_REF] Mcnew | Testing Market Equilibrium: Is Cointegration Informative[END_REF]. Second, trade flows information play no role in these early empirical studies whereas theory suggests that either discontinuities in the trade flows or variations in the directions of these flows can have an impact on the degree of comovements among prices at each market location [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF]. 4 This model has been further extended in [START_REF] Spiller | Arbitrage during the Dollar-Sterling Gold Standard, 1899-1908: An Econometric Approach[END_REF], [START_REF] Sexton | Market Integration, Efficiency of Arbitrage and Imperfect Competition: Methodology and Application to U.S. Celery[END_REF], [START_REF] Baulch | Transfer Costs, Spatial Arbitrage, and Testing for Food Market Integration[END_REF], [START_REF] Kleit | Did Open Access integrate Natural Gas Markets? An Arbitrage Cost Approach[END_REF][START_REF] Kleit | Are Regional Oil Markets Growing Closer Together? An Arbitrage Cost Approach[END_REF], [START_REF] Bailey | The Geographic Expanse of the Market for Wholesale Electricity[END_REF], [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF] and [START_REF] Negassa | Estimating Policy Effects on Spatial Market Efficiency: An Extension to the Parity Bounds Model[END_REF].

parameters are held constant throughout the entire observation period. As these assumptions may look too restrictive in applications based on daily data, an enriched dynamic specification is also detailed in the paper.

We believe that this framework can provide useful guidance to a large audience interested in the functioning of the restructured natural gas industries (e.g., competition authorities, regulators, market analysts), and to researchers engaged in the detailed modeling of these industries. 5 As an application, we examine the spatial arbitrages performed between the two oldest European markets for wholesale natural gas in Belgium and the UK. This allows us to present a series of original empirical findings that: (i) show that all the arbitrage opportunities between the two zones are being exploited, but (ii) confirm the presence of market power in the spatial arbitrages. As the detailed institutional arrangements created for these two markets have largely shaped the designs of the other Continental markets, we believe that these findings provide a valuable contribution to the policy debate related to the restructuring of the European market for natural gas.

Despite the importance of market power concerns in the energy policy debates, the market power potentially exerted by natural gas arbitragers has hitherto been little studied. A notable exception is Rupérez [START_REF] Rupérez Micola | Two Markets and a Weak Link[END_REF] who apply standard regression techniques to examine the relationship between the pipeline capacity utilization (i.e., the ratio of utilized to maximum capacity) and the absolute price difference between Belgium and the UK. Their results document the presence of market splitting at moderate levels of capacity utilization which, according to the authors, suggests the presence of market power inefficiencies. However, neither the direction of the trade flows nor the intermarket transfer costs play any role in their analysis. By taking these features into account, our paper confirms the presence of market power, even if all the arbitrage opportunities are being exploited, and connects the empirical results to the theoretical literature on spatial price determination.

The remaining sections of this paper are organized as follows. Section 2 details the theoretical conditions for spatial equilibrium between two markets linked by a capacity-constrained transportation infrastructure. Section 3 presents an adapted empirical methodology to investigate whether these conditions hold or not. Then, Section 4 details an application of this methodology to the case of the Interconnector UK, a natural gas pipeline connecting the UK to Continental Europe. Finally, the last section offers a summary and some concluding remarks.

Theoretical background

The empirical method described in the next section explicitly refers to the theoretical conditions for spatial equilibrium between two markets connected by a capacity-constrained transportation 5 In recent years, there has been an upsurge of interest in the application of operations research techniques to simulate the functioning of a restructured natural gas industry with the help of large scale equilibrium models (cf. the special issue of the Energy Journal [START_REF] Huntington | World Natural Gas Markets And Trade: A Multi-Modeling Perspective[END_REF]. However, the selection of the behavioral assumptions used to represent spatial arbitrages in these numerical models remains controversial as some models posit the existence of competitive spatial arbitrages (e.g. [START_REF] Golombek | Effects of liberalizing the natural gas markets in Western Europe[END_REF], whereas imperfect competition assumptions are used in others (e.g., [START_REF] Abada | A Generalized Nash-Cournot Model for the Northwestern European Natural Gas Markets with a Fuel Substitution Demand Function: The GaMMES Model[END_REF].

infrastructure. This section presents these conditions, and introduces the notation used in the rest of the paper. We make two polar assumptions regarding the traders' aggregate behavior: perfect competition and monopolistic behavior. We present the short-run spatial equilibrium conditions in these two cases.

We consider two markets i and j located in different regions that trade a homogeneous commodity. We aim to analyze the direction-specific arbitrages that can be performed from market j to market i at time t . These arbitrages are based on a single transportation infrastructure that has a direction-specific, finite capacity jit K that can change over time. 6 The local supply of that commodity is assumed to be competitive in both markets. We assume that, in each market, the aggregate total production cost is a convex, twice-continuously differentiable function. For each region i at time t , we assume that there is a linear inverse demand function:

( )

it it i p q a b q = -
where it a is the intercept and i b is a strictly positive slope coefficient. 7 We ignore price uncertainty and respectively denote it P and jt P the local market clearing prices in each location.

The transportation infrastructure is owned by a regulated infrastructure company that sells transportation rights to a set of identical trading firms. The trading firms' unique activity is to perform spatial arbitrages. A transportation right provides its owner with the right to transfer up to one unit of good from market j to market i at each time period t during the infrastructure's lifetime. At any time t , the operating cost incurred by the infrastructure company is assumed to be recovered from the transportation rights owners in proportion to their use of the infrastructure at that time. Thus, the infrastructure company charges a non-discriminatory price per unit of good transported. The capital cost of this infrastructure is assumed to be recovered in lump sum charges paid by the transportation rights owners and we do not consider this cost further in the analysis. The total arbitrage cost, including all the transportation costs and the transaction costs incurred by a rights owner when performing an arbitrage from market j to market i at time t is assumed to be a linear function of the trade flow at that time. The associated marginal arbitrage cost is denoted jit τ . We assume that there are no transport lags so that spatial arbitrage can take place within each observation period. The nonnegative aggregate trade flow from j to i measured at time t is denoted jit Q .

a -Case A: Perfectly competitive spatial arbitrages

In this case, we assume that traders adopt a price-taking behavior at each location. At time t , their aggregate behavior can be modeled using the following profit-maximization problem:

6 These variations are caused by exogenously determined fluctuations in a series of factors including: the operating pressures of the adjacent national pipeline systems, the flow temperature, the chemical composition of the natural gas. See [START_REF] Chenery | Engineering Production Functions[END_REF] and [START_REF] Massol | A Cost Function for the Natural Gas Transmission Industry: Further Considerations[END_REF] for an engineering-based introduction to gas pipeline economics. 7 We can remark that these slope coefficients are not subscripted with the time index and are thus assumed to be constant. In contrast, the intercepts of these inverse demand functions are assumed to be time-varying parameters (because of the seasonal variations observed in natural gas demand). These assumptions are frequently used in the context of restructured electricity markets (e.g., [START_REF] Day | Divestiture of Generation Assets in the Electricity Pool of England and Wales: A Computational Approach to Analyzing Market Power[END_REF].

jit Q Max ( ) ( ) C jit jit it jt jit jit Q P P Q τ Π = -- (1)
s.t.

jit jit Q K ≤ (2) 0 jit Q ≥ (3)
where: the objective function (1) represents the total profits obtained by these trading firms, condition

(2) describes the transportation capacity constraint, and condition (3) indicates that the trade flow from market j to market i must be non-negative.

Denoting jit

ξ the dual variable associated with the transportation capacity constraint (2), the Karush-Kuhn-Tucker conditions of this constrained optimization problem are:

0 jit Q ≤ , 0 it jt jit jit P P τ ξ --- ≤ and
( ) (  )

0 it jt jit jit jit P P Q τ ξ -- - = , (4)
0 jit ξ ≤ , jit jit Q K ≤ and
0 jit jit jit Q K ξ - = .
(5)

These two complementarity conditions together define the equilibrium conditions for competitive spatial arbitrages at time t .

The marginal profit to spatial arbitrages is equal to the difference between the market-clearing price at location i and the sum of the price at location j and jit τ the marginal arbitrage cost related to trade. The dual variable jit ξ can be interpreted as a marginal congestion cost. The complementarity condition (5) ensures that the marginal congestion cost jit ξ is equal to zero whenever the transportation capacity constraint (2) is slack, and that jit ξ is positive when this constraint is binding.

In case of a zero marginal congestion cost (i.e., 0 jit ξ = ), the complementarity condition ( 4) is fully consistent with the logic of the Enke-Samuelson-Takayama-Judge spatial equilibrium models because it ensures: (i) that there is no trade from market j to market i (i.e., 0 jit Q = ) when the marginal profit to spatial arbitrage is negative, and (ii) that the marginal profit to spatial arbitrage is zero when trade occurs and it is not constrained by the infrastructure's capacity (i.e., 0

jit jit Q K < <
). In our setup, we allow for a binding capacity constraint (i.e.,

jit jit Q K =
) which, according to the complementary condition (4), ensures that the marginal profit to spatial arbitrage is positive (i.e., We now assume, at the other extreme, that traders collectively behave as a monopoly, i.e., that they know how the prices in each region react to the quantities supplied. At time t , their aggregate behavior can be modeled using the following profit-maximization problem:

jit Q Max ( ) ( ) ( ) ( ) M jit jit it it jit jt jt jit jit jit Q p S Q p S Q Q τ Π = + - - - (6) s.t. jit jit Q K ≤ (7) 0 jit Q ≥ (8)
where:

( )

. We denote again jit ξ the Lagrange multiplier associated with the transportation capacity constraint ( 7), and it P and jt P the local market clearing prices. The Karush-Kuhn-Tucker conditions of this constrained optimization problem are:

0 jit Q ≤ , ( )
0 it jt jit i j jit jit P P b b Q τ ξ -- - + - ≤ and ( ) ( ) 0 it jt jit i j jit jit jit P P b b Q Q τ ξ --- + - = (9) 0 jit ξ ≤ , jit jit Q K ≤
and ( )

0 jit jit jit Q K ξ - = (10)
These two complementarity conditions together define the equilibrium conditions for monopolistic spatial arbitrages at time t .

The economic interpretation of the complementarity conditions ( 9) and ( 10) is similar to those detailed for the case of competitive arbitrages except the marginal profit to spatial arbitrage is now equal to ( )

it jt jit i j jit P P b b Q τ -- - +
. Thus, in the event of monopolistic arbitrages, the spatial price differential is always larger than the marginal arbitrage cost when trade is observed (even when the congestion constraint is slack). This reflects the traders' ability to exert market power by restricting intermarket trade to generate some monopoly rents.

Methodology

This section presents the methodology used in this manuscript. We first adapt the existing static PBM framework to take into account the role of both pipeline capacity constraints and market power.

Subsequently, we detail the empirical specification and a dynamic extension to the static model.

An adapted parity bounds model

We now define seven mutually exclusive trade regimes and relate them to the theoretical conditions for spatial equilibrium detailed in the previous section. In addition to the six trade regimes considered in the PBM proposed in [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF], we introduce a new one that takes into account the case of pipeline congestion. Moreover, for each of these trade regimes, we distinguish between the two polar cases of perfectly competitive and monopolistic spatial arbitrages.

As shown in Table 1, marginal profits to spatial arbitrage and trade flow considerations can be combined to define a taxonomy of trade regimes governing the arbitrages from market j to market i .

Regarding marginal profits to spatial arbitrage, three basic states can be defined depending on the value of these marginal profits: zero, strictly positive, and strictly negative. Regarding trade flows, two basic states can be identified depending on whether a positive trade flow is observed or not. Following [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF], each of these six regimes is labeled I to VI, where odd numbers are used for regimes with strictly positive trade flows and even numbers for those without trade.

Table 1. The trade regimes in each direction

Trade is observed: No trade is observed: ( )

0 jit jit Q K < ≤ 0 jit Q = zero marginal
0 it jt jit i j jit P P b b Q τ -- - + = (12)
In case of price-taking behavior (Case A), the spatial price differential is equal to the marginal transfer cost. In case of monopolistic arbitrages (Case B), the possibility to exert market power results in a spatial price differential that exceeds the marginal transfer cost and the difference between the two is proportional to the observed trade flow. In Case A (respectively B), each of the two regimes verifies the complementarity slackness condition (4) (respectively ( 9)) when there is no congestion cost (i.e., 0 jit ξ = ). Therefore, both regimes are consistent with the conditions for a spatial equilibrium.

In regimes III and IV, the marginal profit to arbitrage from j to i is strictly positive:

( )

0 it jt jit i j jit P P b b Q τ -- - + > (14)
In both of these regimes, markets are separated and there are unseized opportunities for profitable spatial arbitrage. Still, in case of positive trade (regime III), the observed insufficient arbitrages might result from the capacity-constrained nature of the transportation infrastructure. Indeed, the complementarity conditions detailed in the preceding section indicate that, in case of a binding capacity constraint (i.e., jit jit Q K =

), observing a strictly positive value for the marginal profit to arbitrage is consistent with the conditions for a short-run spatial equilibrium. In contrast, the joint observation of strictly positive marginal profit to arbitrages and a slackening in the infrastructure's capacity constraint violate the conditions for a spatial equilibrium. Thus, we propose a modification to the original model and further decompose regime III into two mutually exclusive regimes labeled III a and III b . In regime III a , the observed trade flows verify 0

jit jit Q K < <
whereas a binding capacity

constraint (i.e., jit jit Q K =
) is observed in regime III b . Therefore, the latter regime, but not the former, is consistent with the conditions for a spatial equilibrium.

In regimes V and VI, the marginal profit to arbitrage from j to i is strictly negative:

( )

0 it jt jit i j jit P P b b Q τ --- + < (16)
In both regimes, there are no profitable arbitrage opportunities. In regime VI, trade is not occurring and the observed local prices correspond to autarky prices. This regime is consistent with the conditions for a spatial equilibrium. In contrast, regime V indicates that trade is occurring despite negative marginal profits which are not consistent with equilibrium conditions.

In sum, having introduced a further distinction between regimes III a and III b , a total of seven regimes are thus considered in our analysis. The estimated probability to observe regime r is denoted and the estimated probability to observe disequilibrium is ( )

a III IV V λ λ λ + +
.

Empirical specification

We now detail the empirical specification aimed at estimating the probabilities of being in each regime using a data set of N observations for the local market-clearing prices, the observable marginal arbitrage cost, the trade flow, and the available transportation capacity.

From an empirical perspective, the marginal arbitrage cost jit τ can be decomposed into two components: an observable portion named jit T (i.e., a series that comprises all the transportation and transaction costs available to the modeler), and an unobservable one which is assumed to be explained , where ji α and ji β are direction-specific parameters to be estimated. 9

In case of monopolistic arbitrages, the sum of the slope coefficients for the local inverse demand functions is unlikely to be readily available to the modeler. So, we introduce γ an unknown parameter to be estimated that will be interpreted as ( )

i j b b +
the sum of the slope coefficients. So, we expect the estimated value for γ to be non-negative.

Denoting jit it jt jit R P P T ≡ -the series that represents the observable portion of the marginal rent to spatial arbitrage, the marginal profits to arbitrage in each of the three distinct cases (zero, positive and negative) are modeled using the following switching regression model [START_REF] Sexton | Market Integration, Efficiency of Arbitrage and Imperfect Competition: Methodology and Application to U.S. Celery[END_REF][START_REF] Baulch | Transfer Costs, Spatial Arbitrage, and Testing for Food Market Integration[END_REF][START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF]: ( )

jit ji jit ji jit R Z α β ε - + = (17)
Regimes III a , III b & IV:

( )

jit ji jit ji jit jit R Z α β ε µ - + = + (18)
Regimes V & VI:

( )

jit ji jit ji jit jit R Z α β ε υ - + = - (19)
Regimes I & II:

( )

jit ji jit ji jit jit R Z Q α β γ ε - + - = (20)
Regimes III a , III b & IV:

( )

jit ji jit ji jit jit jit R Z Q α β γ ε µ - + - = + (21)
Regimes V & VI:

( )

jit ji jit ji jit jit jit R Z Q α β γ ε υ - + - = - (22)
where: ji α , ji β and γ are unbounded real-valued parameters; jit ε is a random error that is assumed to be i.i.d. normally distributed with a zero mean and variance 2 ε σ ; and jit µ and jit υ are i.i.d. random samples from zero-centered normal distributions truncated above at 0 with respective variance parameters 2 µ σ and 2 υ σ .

The specifications used to model the cases of competitive and monopolistic spatial arbitrages differ only in the markup term jit Q γ . Thus, a statistical test of the null hypothesis 0 γ = (e.g., a likelihood ratio test) can be conducted to test the null hypothesis of perfectly competitive spatial arbitrages. For the sake of brevity, only the unrestricted model based on equations ( 20), (21), and ( 22) is detailed hereafter.

9 From an empirical perspective, this interpretation fails to acknowledge data quality issues in the time series used in the estimation procedure. As argued in [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF], the constant ji α can also reflect any measurement bias in either the price or the observable transaction cost series. We proceed with this caveat in mind, assuming the validity of this interpretation.

Denoting ( )

, , , , , ji ji ε µ υ θ α β γ σ σ σ ≡ the parameter vector to be estimated and ( )

jit jit ji jit ji jit R Z Q π α β γ ≡ - + -
the random variable that gives the marginal profit from spatial arbitrage at time t , the joint density function for the observation at time t is the mixture distribution:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , 1 1 a b I III V jit jit jit I jit jit jit III jit III jit jit V jit jit II IV VI jit II jit jit IV jit jit VI jit jit f A f B B f f A f f f π λ θ λ π θ λ λ π θ λ π θ λ π θ λ π θ λ π θ   ≡ + - + +     + - + +   (23)
where: jit A is an indicator variable that takes a value of 1 if trade is observed and zero otherwise; jit B is an indicator variable that takes a value of 1 if the transportation infrastructure is congested and zero otherwise;

( ) f π θ ) are the density functions derived in [START_REF] Weinstein | The Sum of Values from a Normal and a Truncated Normal Distribution[END_REF] for the sum of a normal random variable and a centered-normal random variable truncated above (respectively below) at 0.

I
Denoting λ the vector of the estimated probabilities to observe the seven regimes, the likelihood function for a sample of observations { }

, , ,

jit jit jit jit R Z Q K is: ( ) ( ) ( ) 1 , , N jit jit t L f λ θ π λ θ = ≡ ∏ (24)
The model can be estimated by maximizing the logarithm of the likelihood function with respect to regime probabilities and model parameters subject to the constraints that the regime probabilities sum to one and that each of these probabilities lies in the unit interval.

This specification differs from that of [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF]

Dynamic extension

The specification above has a static nature. So, we now detail an extended version aimed at capturing the inter-period linkages that may be observed in commodity markets.

a -Correcting for autocorrelation

To the authors' knowledge, most previous parity bound models do not account for autocorrelation. [START_REF] Kleit | Are Regional Oil Markets Growing Closer Together? An Arbitrage Cost Approach[END_REF] is one of the few exceptions. Surprisingly, this omission is seldom discussed. Yet, serial correlation due to both supply shocks and speculative storage activity is commonly observed in the empirical studies dedicated to commodity prices [START_REF] Deaton | Competitive Storage and Commodity Price Dynamics[END_REF]. 11 As the presence of unmodeled autocorrelation can result in inefficient estimates, the presence of serial correlation has to be appropriately corrected for. 12 In this paper, we apply a Bayesian approach that is similar to the one in [START_REF] Kleit | Are Regional Oil Markets Growing Closer Together? An Arbitrage Cost Approach[END_REF]. We aim to extend the Barrett and Li framework to adjust for the presence of serial correlation in the error term jit ε . Yet, a difficulty emerges: the exact value ( )

1 ji t
εcannot be directly observed. However, we can consider the expected value of ( )

1 ji t
ε -, given the evidence provided by the previous observation, which results in the modified specification:

Regimes I & II: ( ) ( ) ( ) ( ) 1 1 E jit ji jit ji jit ji jit ji t ji t R Z Q α β γ ρ ε η ε - - - + - - = (25)
Regimes III a , III b & IV:

( ) ( ) ( ) ( ) 1 1 E jit ji jit ji jit ji jit jit ji t ji t R Z Q α β γ ρ ε η ε µ - - - + - - = + (26) Regimes V & VI: ( ) ( ) ( ) ( ) 1 1 E jit ji jit ji jit ji jit jit ji t ji t R Z Q α β γ ρ ε η ε υ - - - + - - = - (27)
where: ji ρ is an autocorrelation coefficient such that 1

1 ji ρ -< < ;
( )

1 ji t η -is the observed lagged residual, that is ( ) ( ) ( ) ( ) ( ) 1 1 2 2 E ji ji t ji t ji t ji t η π ρ ε η - - - - ≡ - ; and
( ) ( ) ( ) 1 1 E ji t ji t ε η - -
represents the expected value of ( )

1 ji t
εgiven evidence provided by the observed lagged residual.

We now show how the expected value

( ) ( ) ( ) 1 1 E ji t ji t ε η - -
can be computed. Given the observed value of the lagged residual ( )

1 ji t
ηand the parameter vector

( ) 1 , ji θ θ ρ ≡
, Bayes theorem can be 11 In the application discussed below (an analysis of market integration between two markets connected by a pipeline system), at least two engineering-based arguments can motivate the presence of autocorrelation. First, from a dynamic perspective, a pipeline system can be described as a slow-moving transportation infrastructure as a couple of hours are typically needed to move a given molecule of methane from one market to the other. Second, the operation of a natural gas pipeline system can create temporary energy storage (the so-called line-pack buffer). As a result, daily observations are likely to jointly represent the outcome of decisions taken both today and yesterday. 12 [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF] footnote 3) mentioned the serial correlation issue and claimed that the Cochrane-Orcutt method could be used to correct for serial correlation. However, the distribution of the observed residuals is dramatically modified from one observation to the next in case of a regime switch. Therefore, one may question the validity of a Cochrane-Orcutt approach.

invoked to evaluate ( ) ( )

1 1 1 1 P P , r t t ji t r η θ - - - ≡
the posterior probability that the residual observed at time 1 twas generated by regime r [START_REF] Kiefer | A Note on Switching Regressions and Logistic Discrimination[END_REF][START_REF] Spiller | Arbitrage during the Dollar-Sterling Gold Standard, 1899-1908: An Econometric Approach[END_REF]:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 1 1 1 1 P a b r r ji t ji t r t VI III k III III k ji t ji t ji t ji t k I k III f f f λ η θ λ λ η θ λ η θ - - - - - - - = ≠ = + + ∑ . ( 28
)
The expected value

( ) ( ) ( ) 1 1 E ji t ji t ε η - -
can be constructed from the observed residual ( )

1 ji t
ηby: (i) subtracting ( ) E µ the expected value of the one-sided random variable jit µ weighted by the posterior probability to observe the regimes III a , III b or IV; and, (ii) adding ( ) E υ the expected value of the nonnegative half-normal random variable jit υ weighted by the posterior probability to observe the regimes V or VI, 13 that is:

( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 1 1 E P +P +P E P P E a b III III IV V VI t t t t t ji t ji t ji t ε η η µ υ - - - - - - - -     = - + +     . ( 29
)
The construction of

( ) ( ) ( ) 1 1 E ji t ji t ε η - -
can be nested within the likelihood specification above. So, the estimation proceeds again from a maximization of the log-likelihood function with respect to the regime probabilities λ and the parameters 1 θ subject to the preceding constraints and to 1

1 ji ρ -< < . 14
b -An adapted GARCH specification

Regimes I and II model the cases of zero marginal profit to spatial arbitrage. In these regimes, the random variable representing the marginal profit to spatial arbitrage is assumed to be equal to the stochastic error term jit ε which has the same finite variance 2 ε σ for all observations. Yet, one may question the relevance of this homoscedastic assumption. A large empirical literature has documented the tendency of commodity prices to exhibit time-varying volatilities. Accordingly, the spatial price differential (and thus the marginal profit to spatial arbitrage) is likely to show signs of heteroscedasticity. Therefore, we now detail a modified specification whereby the variance of the marginal profit to spatial arbitrage observed in regimes I and II is allowed to vary over time.

For the purpose of capturing the dynamics of uncertainty, a Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model [START_REF] Bollerslev | Generalized Autoregressive Conditional Heteroskedasticity[END_REF] represents an attractive approach 13 Denoting φ the density function of the standard normal distribution and Φ its cumulative distribution function, these expected values are: ( ) ( ) ( )

( )

E 0 1 0 µ µ σ φ ≡ -Φ and ( ) ( ) ( ) ( ) E 0 1 0 υ υ σ φ ≡ -Φ
. 14 Regarding the particular case of the first observation, an arbitrary value has to be taken for ( )

0 0 E ji ji ε η because 0 ji
η cannot be observed. In this paper, the initial value ( )

0 0 E ji ji ε η
is taken as equal to zero (that is, the conditional mean of jit ε given ( )

1 ji t ε -).
that has been widely applied to model commodity markets. Given the time series jit R , jit Z and jit Q defined above, a GARCH(1,1) specification can be written as follows: 34) where: ( 30), ( 31) and ( 32) are the mean equations; (34) is the conditional variance equation; (33) relates the random error jit ε to the standardized residual jit e which is assumed to be an i.i.d. standard normal random variable; and ji , ji δ and ji ϕ are the usual, non-negative, GARCH(1,1) parameters.

Regimes I & II: ( ) ( ) ( ) ( ) 1 1 E jit ji jit ji jit ji jit ji t ji t R Z Q α β γ ρ ε η ε - - - + - - = (30) Regimes III a , III b & IV: ( ) ( ) ( ) ( ) 1 1 E jit ji jit ji jit ji jit jit ji t ji t R Z Q α β γ ρ ε η ε µ - - - + - - = + (31) Regimes V & VI: ( ) ( ) ( ) ( ) 1 1 E jit ji jit ji jit ji jit jit ji t ji t R Z Q α β γ ρ ε η ε υ - - - + - - = - (32) jit jit jit h e ε = ( 33
) ( ) ( ) ( ) ( ) 2 2 2 1 1 1 E jit ji ji ji ji t ji t ji t h h ϖ δ ε η ϕ - - -   = + +     (
Compared to the usual GARCH specification, equation ( 34) involves the use of the squared expected value

( ) ( ) ( ) 2 1 1 E ji t ji t ε η - -      
in spite of the true value ( )

2 1 ji t
εwhich cannot be observed in this regime switching model. Again, the construction of the expected value

( ) ( ) ( ) 1 1 E ji t ji t ε η - -
is based on a Bayesian approach. Given the observed value ( )

1 ji t η -,

Application

Background

This application focuses on the so-called Interconnector (hereafter abbreviated to IUK), a bidirectional natural gas pipeline system connecting the UK National Transportation System (using the Bacton Terminal) to Zeebrugge (Belgium). This infrastructure allows spatial arbitrages between Europe's two oldest spot markets for natural gas: (i) the UK's NBP, which allows counterparties to trade a standardized lot of natural gas piped via the UK National Transmission System with a delivery point at the so-called National Balancing Point (NBP); and (ii) the Zeebrugge local market in Belgium, which is labeled ZEE.

We consider the period covering October 1, 2003, to October 5, 2006. 15 During that period, the IUK pipeline was the unique infrastructure linking the UK and Continental natural gas markets. In addition, that period corresponds to a steady institutional environment with unchanged access rules for both the IUK and the adjacent national pipeline systems. These features make the IUK case an attractive experiment to investigate the efficiency of the spatial price arbitrages that can be performed in a deregulated natural gas industry.

Data

We use daily transaction price data for day-ahead wholesale natural gas traded during working days as published by Platt's, a price-reporting service. For each working day (i.e., Monday to Friday), they reflect the price range of a standardized quantity of natural gas to be delivered at a constant flow rate throughout the next working day after assessment (e.g., Friday's assessment reflects Monday's delivery). 16 All prices are denominated in €/MWh. Given the extremely limited liquidity of within-day markets, we follow the usual convention and refer to these day-ahead prices as "spot" since they provide traders with a final opportunity to trade gas out of a forward position before physical delivery.

The fuel used by the IUK operator to power its compressor equipment represents the observable portion of the marginal arbitrage costs incurred by the traders. This is a direction-specific cost since, according to the pipeline operator, fuel gas consumption amounts to 0.8% of the quantity of gas transported when natural gas is piped from the UK to Belgium, and to 0.26% of the quantity of gas transported in the other direction. This fuel cost is evaluated using the price of natural gas in the exporting market.

The unobservable portion of the marginal arbitrage costs includes two kinds of costs: (i) the entry (respectively, exit) charges incurred by the traders who import gas to (respectively export gas from)

the UK, and (ii) all the unobserved transaction costs (e.g., unmeasured transactions costs, information gaps...). Hereafter, these costs will be estimated using a constant, a time trend, and two dummy Regarding trade flow data, the wish may be to use an aggregate variable gathering all the transportation nominations communicated at the end of any working day for delivery during the next working day. Unfortunately, these data are confidential. So, this study uses a proxy: a historical flow series representing the physical daily flow of natural gas, measured in GWh/day, that transited through 15 This starting date has been chosen to omit the number of partial closures that happened during the summer of 2003. Moreover, the transited flows of natural gas were almost unidirectional (from the UK to the Continent) before that date [START_REF] Futyan | The Interconnector Pipeline: a Key Link in Europe's Gas Network[END_REF]. This terminal date corresponds to the opening of the Langeled infrastructure, a pipeline system that together with already existing offshore pipelines, allowed Norwegian gas producers to perform spatial arbitrages between the UK and the Continent, thereby offering an alternative to the IUK. 16 Further information on the methodology used to construct these market-on-close price assessments is available in [START_REF] Platt's | European Natural Gas Assessments and Indices[END_REF].

the IUK as reported on the pipeline operator's website. 17 Thus, we proceed under the assumption that the physical gas flow measured during a given working day represents an unbiased estimator of the aggregate transportation nominations decided during the previous working day (at the time when trade occurs in the corresponding day-ahead market). 18 According to the Interconnector operator, the nominal transportation capacity from the UK to Belgium remained unchanged during the entire sample period. In the other direction, the installation of some compressor equipment in Zeebrugge on November 8, 2005, increased the transportation capacity. Unfortunately, information related to the available daily transportation capacities remains unavailable. So, we follow Rupérez Micola and Bunn ( 2007) and consider the historical maximum values of the trade flows. The historical maxima were: 624.63 GWh/day from the UK to Belgium, and 310.24 GWh/d prior to November 8, 2005, (respectively 511.80 GWh/d after that date) in the other direction.

The daily flow capacity of a point-to-point natural gas pipeline is a time-varying parameter that depends on a series of exogenous factors (e.g., the operating pressures of the adjacent national pipeline systems, the flow temperature, the chemical composition of the natural gas). Hence, the historical maximum daily flow cannot necessarily be attained. We proceed by assuming that congestion is likely to be a source of concern when the observed capacity utilization ratio (measured against the historically maximum) exceeds 80%. Hereafter, this threshold is used to distinguish regimes III a and III b .

The data set has been modified in two ways. First, both the Belgium and UK markets are closed on national bank holidays. To account for differences in the national calendars, all the observations related to a bank holiday in either Belgium or the UK have been disregarded in the subsequent analyses. Second, we excluded observations made on dates during which the Interconnector service was unavailable due to planned maintenance (these dates are documented on the IUK's website). As a result, we assembled time series data containing 723 daily observations on prices, compressor fuel costs, and trade flows in each direction.

Descriptive statistics

An examination of trade data indicates that out of these 723 observations, 369 correspond to net positive exports to Belgium (of which 26 correspond to a congested infrastructure), 341 to net imports to the UK (of which 46 correspond to a congested infrastructure) and 13 to zero trade.

17 Cf. www.interconnector.com 18 On a given working day, pipeline users are offered the possibility to revise the transportation service requested at the end of the previous working day. This is the so-called within-day re-nominations. Yet, for the pipeline operator, these within-day re-nominations generate a significant extra operation costs. As a result, the detailed pricing rules adopted by the pipeline operator have been explicitly designed to render these within-day re-nominations extremely costly. So, users have a strong incentive to contract their real transportation needs for day d+1 at the end of day d (i.e., before the close of the day ahead market). Therefore, we proceed assuming that these within-day re-nominations can be neglected.

Table 2 details the correlation coefficients between the two local price series in both levels and first differences. Following [START_REF] Stigler | The Extent of the Market[END_REF], these high values could be interpreted as positive signs of market integration, though the "degree" of that integration seems to be weaker when the natural gas is exported from the UK. So, a direction-specific approach seems to be needed to further investigate the degree of spatial integration between these two markets. ). This finding is in favor of a dynamic specification able to correct for serial correlation.

Estimation and empirical results

a -Estimation procedure

The estimation procedure involves the constrained maximization of a non-trivial log-likelihood function. This is a non-linear, non-convex, constrained optimization problem that has to be solved numerically using hill-climbing procedures. 19 To obtain a feasible starting point, we first consider the simplest possible static specification (i.e., omitting the exogenous explanatory variables jit Z and assuming zero values for both the autocorrelation and the GARCH parameters). The converged solution for this restricted specification is then used as a feasible starting point for the unrestricted model. The optimization problem at hand has the potential for local maxima, which is a source of concern because the outcome of a non-linear programming solver may depend on the location of the starting point. To address this problem, the 19 All the estimates reported in this paper have been obtained using an iterative procedure that performs 20 iterations using the Davidon-Fletcher-Powell (DFP) algorithm followed by 20 iterations using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) one, and then a switch back to DFP for 20 iterations, and so forth.

first solution is systematically compared to the ones obtained with a sample of 1,000 starting points uniformly drawn over a range of possible starting values. The converged solution that provides the highest likelihood value is systematically stored.

b -Empirical results

Estimation results are reported in

D

β -), the market power coefficient ( γ ), the autocorrelation parameter ( ρ ), the regime probabilities ( λ 's), the GARCH parameters used to model the heteroscedasticity related to regimes I and II (ϖ , δ , ϕ ), the standard deviation parameters for the truncated normal distributions ( µ σ , υ σ ), and a series of likelihood ratio tests.

From these estimation results, several facts stand out. First, the estimated values for the coefficient γ are positive, as expected. These estimates are highly significant in both directions, which reveals the presence of imperfectly competitive arbitrages across the Channel. A further confirmation is provided by the likelihood ratio tests: the null hypothesis of competitive arbitrages is firmly rejected in both directions. So, we cannot reject the assumption of imperfectly competitive arbitrages during that period. This finding is consistent with the results in Rupérez-Micola and Bunn (2007).

Second, the high estimates obtained for I λ and II λ in both directions reveal that the observed spatial price difference is predominantly explained by the sum of the unobserved marginal transaction costs and the markup term. These very high values result in a very high probability of observing an imperfectly competitive spatial market equilibrium. Following [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF] λ are larger and highly significant. Infrastructure congestion issues that are directly related to the Interconnector pipeline cannot be invoked to explain the presence of these strictly positive marginal profits to spatial arbitrage. These observed trade barriers could, for example, be due to pipeline congestion in the adjacent systems. Still, in relative terms, the probability of observing this regime is small.

Fourth, the marginal cost parameters included in the mean equation are significant in both directions, which confirms the presence of unobserved marginal transaction costs. The estimated unobserved marginal costs are strictly negative for all the observations, which suggests the presence of unobserved marginal benefits to trade. Fifth, the estimated autocorrelation coefficients ρ are significant at the 0.01 level. These estimated values are positive and their order of magnitude is comparable to those of the series jit R .

Sixth, the estimated ARCH coefficients δ are highly significant in both directions, which indicates that the variance of the errors term jit ε has a time-varying nature. Moreover, the estimated values for δ are high, which suggests that in both directions the variance of the marginal profit to spatial arbitrage obtained in regimes I & II is directly affected by the preceding shocks. Consistent with the large empirical literature dedicated to the dynamics of natural gas markets, these high values suggest the presence of a "volatility clustering" phenomenon.

Seventh, the null hypothesis of a static model (H 0 : ) is firmly rejected by the data.

0 ρ δ ϕ = = =
This finding clearly justifies the need to use a dynamic specification to correct for the presence of both autocorrelation and time-varying heteroscedasticity.

Lastly, note that the use of a unique variance parameter for the half-normal distributions of the two non-negative error terms ijt µ related to regimes III a , III b , and IV and ijt υ related to regimes V and VI is firmly rejected by the data.

Model validation

The specification above is based upon arbitrary distributional assumptions of normal and halfnormal errors and these distributional choices are, of course, questionable. According to the Monte Carlo experiments reported by [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF], deviations from the half-normal distribution for the positive errors jit µ and jit υ are not problematic. In contrast, the use of normal assumption for both regimes I and II deserves some investigations to verify the validity of the PBM approach.

So far, little attention has been paid to these verifications in the PBM literature. To explore this question, we propose using the obtained estimates to generate, for each trade direction, two time series Table 5 reports the descriptive statistics for the standardized residual series. These figures indicate the presence of both mild asymmetry and leptokurtosis. To gain further insights on the magnitude of these departures from normality, Figure 2 illustrates the quantile-quantile (Q-Q) plots of the standardized residual (i.e., the empirical quantiles versus the quantiles of a standard normal distribution). Each of these two Q-Q plots indicates a relatively good fit between the empirical quantiles and the theoretical one, except for several outliers. According to the Monte Carlo experiments reported in [START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF], moderate departures from normality caused by both mild asymmetry and leptokurtosis are not really problematic. Thus we proceed, assuming the relevance of the normal distributional assumption.

Concluding remarks

The question of how to detect market power in the spatial arbitrages observed in a restructured natural gas industry is one of the key challenges that regulators and competition authorities across the world have to address. The objective of this paper is to offer an empirical methodology which is able to test for the presence of perfect competition in these spatial arbitrages. Our approach explicitly builds upon the literature dedicated to natural gas markets integration and extends it by focusing on the relationship between the observed spatial price difference and the intermarket trade flows.

A case study focusing on the IUK pipeline during the period 2003-2006 provided us with an opportunity to obtain a series of original findings. The estimated probability of spatial market equilibrium conditions holding is very high, suggesting high degrees of wholesale natural gas market integration, consistent with previous research on IUK price co-movements [START_REF] Neumann | Convergence of European spot market prices for natural gas? A real-time analysis of market integration using the Kalman Filter[END_REF].

But, the empirical evidence also suggests the presence of imperfect competition in the observed spatial arbitrages, consistent with the price-data results in [START_REF] Rupérez Micola | Two Markets and a Weak Link[END_REF]. Although our discussion is centered on this specific infrastructure, it should be clear these results imply that some care is needed when interpreting the high degree of co-movements which is typically documented in the empirical studies conducted on European spatial market price data. Though these co-movements can be interpreted as objective signs of market integration, they do not necessarily reveal the existence of a perfectly competitive internal market.

Experience indicates that the institutional arrangements implemented in the UK have played a large part in shaping the EU's restructuration process. Future research will thus examine whether or not market equilibrium conditions hold in less mature continental markets. Such research could be useful for informing the current EU regulatory debates related to the functioning of the internal market for natural gas.

  inverse demand functions, and it S and jt S are the aggregate supplies decided by all the local producers at each location.

λ

  In regimes I and II, the marginal profit to spatial arbitrage is equal to 0. As shown in the previous section, depending on the assumption posited for the behavior of the trading sector, one of the following conditions is binding:

  by a constant and by a vector of observable exogenous factors jit Z . 8 So, in what follows, the marginal arbitrage cost is assumed to be jit jit

  in four ways. First, we show how a parity bound model can be used to test the null hypothesis of competitive spatial arbitrages. Second, contrary to Barrett and Li, the two markets under scrutiny are connected by a capacity-constrained transportation infrastructure. So, a seventh regime labeled III b is introduced to account for the explanatory role played by infrastructure congestion issues in the observation of positive marginal profits to spatial arbitrage. Third, we introduce a vector of observable exogenous factors jit Z to capture the effects of omitted arbitrage costs. This specification provides fuller information to analyze market relationships. Lastly, we follow[START_REF] Baulch | Transfer Costs, Spatial Arbitrage, and Testing for Food Market Integration[END_REF] and[START_REF] Negassa | Estimating Policy Effects on Spatial Market Efficiency: An Extension to the Parity Bounds Model[END_REF] and relax the restriction to use a unique variance parameter for the half-normal distributions of the two non-negative error terms ijt µ and ijt υ in the likelihood functions. 1010 One might argue that, in certain applications, sample size considerations could motivate the use of the restriction µ υ σ σ = to reduce the number of parameters to be estimated. Yet, this restriction can hardly be justified a priori.

  value 1 during the period coveringOctober 1, 2004, to September 30, 2005, and 2005[START_REF] Futyan | The Interconnector Pipeline: a Key Link in Europe's Gas Network[END_REF] D - that takes the value 1 after October 1, 2005. Each period corresponds to a "standard gas year" during which the regulated Entry-Exit tariff system used by the UK National Transportation System is kept unchanged.

Figure

  Figure 1. Data plots

λ

  the probability of spatial market equilibrium conditions holding is in the range defined by the minimum and the maximum values of the direction-specific sums ( ) to jointly observe infrastructure congestion and strictly positive marginal profits to spatial arbitrage regime are either zero or extremely low. These estimated values are consistent with the analysts' consensus summarized in Futyan (2006) on: (i) the oversized nature of the IUK's transportation capacity when natural gas is flowing to the Continent and (ii) the likely capacity-constrained nature of the IUK in the opposite direction (before the November 2005 capacity increase). In contrast, the estimated probabilities a III

  of binary indicator variables ɵ I jit d and ɵ II jit d indicating whether or not regime I, respectively II, is the regime with the highest probability at time t . The construction of these semiparametric estimates of time-varying regime probabilities follows those detailed in[START_REF] Barrett | Distinguishing between Equilibrium and Integration in Spatial Price Analysis[END_REF]Assuming that the regime with the highest probability is the one that generated each observation, we can gather all the observations in the sample period that verify ɵ

Figure

  Figure 2. Q-Q plots of the standardized residual series (sample: ɵ

  the values of the parameters

						θ	2	≡	( θ ϖ δ ϕ 1 , , , ji ji	ji	)
	and ( ) 2 2 ji t h -, we can evaluate the posterior probabilities 1 P r t -and thus	( ) 1 E ji t ( ε -	η	( ) 1 ji t -	)	using (29).

Table 2 . Correlation coefficients for the two price series

 2

				Subsample defined by	Subsample defined by
	Entire sample	net positive exports	net positive exports
				to Belgium	to the UK
	correlation in levels	0.989	***	0.985 ***	0.988 ***
	correlation in first differences	0.900	***	0.760 ***	0.905 ***
	Note: *** indicate significance at the 0.01 level.

Table 3

 3 summarizes the descriptive statistics for the two series jit R (i.e., the observable portion of the marginal rent to spatial arbitrage). The distributional properties of these series show some signs of non-normality as a very large leptokurtosis is observed in both cases. Figure1provides plots of these two series and the measured pipeline flow from Bacton (UK) to Zeebrugge (Belgium). A visual inspection of these plots suggests the presence of volatility clustering which motivates the use of a specification that incorporates some GARCH features. The estimated first-order autocorrelation coefficients reveal clear evidence of serial correlation (0.311 *** for the series

	, NBP ZEE t R →	and 0.301 ***

Table 3 . Descriptive statistics for the marginal rent to spatial arbitrage

 3

		Entire sample
		NBP ZEE R →	ZEE NBP R →
	Mean	-0.232	0.044
	Median	-0.100	-0.051
	Maximum	7.484	25.189
	Minimum	-25.543	-8.096
	Std. Dev.	1.581	1.557
	Skewness	-7.394	7.396
	Kurtosis	108.946	112.664
	Jarque-Bera	344730.200	368877.600
	(p-value)	(0.000)	(0.000)
	Observations	723	723

Table 4 .

 4 That table details the estimates obtained for: the unobserved marginal transaction costs (α , time

	β ,	2004 2005 D β -,	2005 2006

Table 4 . Estimation results for natural gas trade across the Channel

 4

						From UK to Belgium	From Belgium to UK
	Mean parameters
		α	-0.3164 ***	-0.0990 ***
		β	time	0.2019	-0.7017 ***
		2004 2005 D β -	-0.0401	0.2442 ***
		2005 2006 D β -	-0.2391 **	0.5304 ***
		γ		0.0012 ***	0.0026 ***
		ρ	0.3396 ***	0.4860 ***
	GARCH parameters
		ϖ	0.0151 ***	0.0315 ***
		δ		0.9413 ***	0.8691 ***
		ϕ	0.0254	0.0257
	Standard deviations
		σ		µ	2.2147 ***	8.4446 ***
		σ	υ	6.3419 ***	2.0899 ***
	Probabilities (in %)
		λ	I	48.5613 ***	41.5957 ***
		II λ	41.1580 ***	50.4989 ***
		III λ	a	2.4462 ***	1.6899 ***
		III λ	b	0.0000	0.9188 **
		IV λ	2.8750 ***	0.4921
		V λ	0.0028	3.0477 ***
		VI λ	4.9568 ***	1.7569
	Log likelihood	-982.6623	-991.7400
	LR tests
	H 0 :	γ =	0	128.868 (0.000)	115.345 (0.000)
	H 0 : µ σ σ =	υ	44.278 (0.000)	41.018 (0.000)
	H 0 :	ρ δ ϕ = = =	0	206.992 (0.000)	228.932 (0.000)
	Observations	723	723
	Note: Asterisks indicate significance at 0.10 * , 0.05 ** and 0.01 *** levels, respectively. Numbers in parentheses are the p-
	values of the χ 2 statistics.

Table 5 . Descriptive statistics for the standardized residual series (sample: ɵ

 5

	d	I jit	+	ɵ d	II jit	1 = )

Consistent with our assumption of total arbitrage costs that vary linearly with the trade flows, this vector does not include the trade flow variable.

We also gratefully acknowledge helpful discussions with participants at the EURO (Roma, This research has been supported by the French Energy Council (Conseil Français de l'Énergie) under grant CFE-73. The views expressed herein are strictly those of the authors and are not to be construed as representing those of IFP Énergies Nouvelles or those of the French Energy Council.

The "Cahiers de l'Économie" Series

The "Cahiers de l'économie" Series of occasional papers was launched in 1990 with the aim to enable scholars, researchers and practitioners to share important ideas with a broad audience of stakeholders including, academics, government departments, regulators, policy organisations and energy companies.

All these papers are available upon request at IFP School. All the papers issued after 2004 can be downloaded at: www.ifpen.fr

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MD, MScPH Sabine Oertelt-Prigione

PhD Lucie Dalibert

PhD Petra Verdonk

MD, MPH Elisabeth Zemp Stutz

PhD Ineke Klinge

Implementation Strategies for Gender-Sensitive Public Health Practice: A European Workshop

Keywords: gender, public health, implementation

Objectives: Providing a robust scientific background for the focus on gender-sensitive public health and a systematic approach to its implementation. Methods: Within the FP7-EUGenMed project (http://eugenmed.eu) a workshop on sex and gender in public health was convened on February 2-3, 2015. The experts participated in moderated discussion rounds to (1) assemble available knowledge and (2) identify structural influences on practice implementation. The findings were summarized and analyzed in iterative rounds to define overarching strategies and principles. Results: The participants discussed the rationale for implementing gender-sensitive public health and identified priorities and key stakeholders to engage in the process. Communication strategies and specific promotion strategies with distinct stakeholders were defined. A comprehensive list of gender-sensitive practices was established using the recently published taxonomy of the Expert Recommendations for Implementing Change (ERIC) project as a blueprint. Conclusions: A clearly defined implementation strategy should be mandated for all new projects in the field of gender-sensitive public health. Our tool can support researchers and practitioners with the analysis of current and past research as well as with the planning of new projects.

Introduction

S ex and gender represent fundamental dimensions of human biology, psychology, and anthropology that influence self-perception, self-expression, and social interaction. Healthcare institutions and healthcare practice have neglected these determinants for many decades, with detrimental consequences for healthcare access and healthcare provision, for both women and men, resulting in health inequity and avoidable morbidity and mortality. [START_REF] Worldbank | Gender Equality and Development[END_REF] Due to the 2015 landmark decisions by the NIH [START_REF] Clayton | Policy: NIH to balance sex in cell and animal studies[END_REF] and the European Commission [START_REF] Commission | Promoting Gender Equality Research and Innovation[END_REF] to mandate the inclusion of sex and gender-related factors into research funding applications, the consideration of sex and gender as research variables has experienced much attention. In the health sciences field both ''sex,'' the biological components, as well as ''gender,'' the sociocultural aspects that define identity are considered. [START_REF] Krieger | Genders, sexes, and health: What are the connections-and why does it matter?[END_REF] While this is seen as a major leap forward toward the inclusion of sex-specific analysis into biomedical research it still does not ensure gender sensitivity in all areas of healthcare. Furthermore, while these important steps will significantly increase the ongoing knowledge production in the field, they will not guarantee that these results will find their way into practice. The inclusion of gender in public health analysis and practice has been advocated for decades [START_REF] Lawrence | Methodologic and ethical ramifications of sex and gender differences in public health research[END_REF] and related information is more frequently available in public health than in other medical and healthcare-related disciplines. Although epidemiological data are supposed to be analyzed systematically by age and sex, [START_REF] Aulakh | Sex and gender subgroup analyses of randomized trials[END_REF][START_REF] Runnels | The challenges of including sex/gender analysis in systematic reviews: A qualitative survey[END_REF] this does not always occur in practice and, hence, much valuable information may be lost. Furthermore, this potentially gendersegregated analysis is rarely translated into gender-specific practice. Fundamental limitations in the transfer of research findings into healthcare practice have been identified in the last decade [START_REF] Peters | Implementation research: What it is and how to do it[END_REF] and the NIH in the United States enacted significant corrective efforts. [START_REF] Westfall | Practice-based research-''Blue Highways'' on the NIH roadmap[END_REF] Knowledge transfer or implementation research is rapidly developing its own methodologies, classifications, and practices. [START_REF] Powell | A compilation of strategies for implementing clinical innovations in health and mental health[END_REF][START_REF] Powell | A refined compilation of implementation strategies: Results from the Expert Recommendations for Implementing Change (ERIC) project[END_REF][START_REF] Proctor | Outcomes for implementation research: Conceptual distinctions, measurement challenges, and research agenda[END_REF][START_REF] Proctor | Implementation strategies: Recommendations for specifying and reporting[END_REF] As the field of gender-sensitive interventions is growing, [START_REF] Alexander | Gender-based health interventions in the United States: An overview of the coalition for healthier community initiative[END_REF] we aim at bypassing lag times between discoveries, trial, and practice and decided to focus on implementation strategy early in the process. While the focus of gender medicine has been primarily on (bio) medical aspects of healthcare, gender-sensitive public health addresses broader issues employing a systemic approach involving a wide array of stakeholders. These conditions imply the need for adequate design, targeted practices for implementation, and formal evaluation strategies.

The current work is the first attempt to assemble this knowledge in a systematic fashion. An expert workshop on sex and gender in public health was organized as part of the 2014-2015 European FP7-project ''EUGenMed'' (www .eugenmed.eu) dedicated to designing a roadmap for the implementation of sex and gender in biomedicine and health research. We report on this meeting, which aimed to (1) assemble available knowledge about methods and practices of incorporation of gender aspects into public health practice and (2) identify structural influences on practice implementation at all levels of the public health process.

Materials and Methods

A group of expert stakeholders (n = 23), representing a broad array of professional approaches and positions, were invited to a workshop taking place within the European FP7project ''EUGenMed'' (www.eugenmed.eu) in Brussels in February 2015. Specifically, we included practitioners, researchers, advocacy groups, politicians, policymakers, educators, international organizations, and funding bodies. We divided the participants into three heterogeneous groups and invited them to engage in moderated discussions in topicoriented round tables.

The discussion rounds were designed to match the three levels of evidence for public health interventions. [START_REF] Brownson | Evidence-based public health: A fundamental concept for public health practice[END_REF] Level one was entitled ''priorities'' and focused on urgency for action, motivation for action, and targets to lobby for action. Level two, ''principles,'' identified the main messages for gender-sensitive action and assembled ideal conditions and structures for implementation. Level three, ''practices,'' further detailed implementation in defining target groups, identifying communication nodes, and strategies for promotion and practical uptake. All participants rotated through the three tables. One moderator joined each table and conversations were audiorecorded and transcribed.

The three moderators summarized the discussion results. The workshop outputs were then analyzed in recursive rounds of synthesis to define emerging themes. The results were assembled in topic tables with focus on single steps of a structural implementation process. Furthermore, the identified strategies were compared with the recently published catalogue of implementation measures identified in the Expert recommendations for implementing change (ERIC) project. [START_REF] Powell | A compilation of strategies for implementing clinical innovations in health and mental health[END_REF][START_REF] Powell | A refined compilation of implementation strategies: Results from the Expert Recommendations for Implementing Change (ERIC) project[END_REF] Since this project focused on taxonomy through extensive literature searches and expert consensus rounds, we decided to use the agreed-upon taxonomy as reference for our results. [START_REF] Powell | A refined compilation of implementation strategies: Results from the Expert Recommendations for Implementing Change (ERIC) project[END_REF] Proposed or employed strategies were aligned with the overarching strategies from the ERIC project to develop a general compendium of strategies for gender-sensitive prevention implementation.

Results

The following results are presented according to the flow of policy implementation, such as starting with framing an issue, identifying its urgency, and defining process steps for implementation. The latter process is split into substeps, such as identification of target groups and supporters, development of general communication strategies and of specific issue-based promotion strategies.

Framing the issue: why do we need gender-sensitive public health practice?

The participants identified several objectives to achieve through the application of a gender-sensitive perspective to public health practice (Table 1). Individual values and goals were thematically grouped into broader dimensions. The first and most frequently cited motivation for the inclusion of a gendered perspective into practice was for ideological and ethical reasons. Participants described gender sensitivity as a matter of social justice and health equity, as a fundamental human right, and as a measure against discrimination. Individual empowerment was also identified as a major potential achievement of gender-sensitive public health practice, in allowing for tailored choices and preventative offers. While most of the identified goals involved a proactive approach, the obligation to respect people's choices-even if Set actionable goals for health based on differentiated analysis Do not take status quo for granted unhealthy-and the need to accept the status quo in some instances were also mentioned several times as part of a participatory and person-centered strategy. Last, the increase of efficiency and potential cost savings through a gendersensitive approach was mentioned. While potentially more costly during the set-up phase, attention to sex and gender could save significant follow-up cost stemming from, for example, pharmacological side effects, as well as insufficient adherence and uptake of prevention programs.

Overall, the participants described a holistic, multidimensional, and participation-oriented approach as the eventual goal for gender-sensitive public health.

Most urgent needs: where should we focus our efforts?

Clear strategies for implementation at different levels of the research and healthcare system as well as within the general society are the most urgent needs identified by the participants (Table 2). The need to increase awareness for the relevance of sex and gender for public health with a range of stakeholders, including the public, healthcare, and service providers, is still present. Furthermore, the fact that gendersensitive public health is neither women's health nor an issue of feminism in science, but a discipline that gains new insights and fosters innovation through the analysis of differences, still needs emphasizing. The potential gains for a gender-sensitive public health approach should be pointed out, and information about gender differences in risk inci-dence and perception provided. Awareness raising needs to be combined with lobbying for increased political pressure to obtain specific funding and support gender-sensitive practice. Attention to sex and gender in data production and analysis as well as for the development of common taxonomies is also fundamental. Intersectional aspects need to be considered at this stage to allow for their incorporation into analysis once data are available. While all of these strategies concern implementation, workshop participants emphasized the need to define modes, practice standards, and specific strategies, so highlighting the relevance of methodological development.

Process: what are the practical steps toward implementation?

Identification of target groups. Workshop participants identified a vast array of potential stakeholders in the process of implementing gender-sensitive public health (Table 3). As well as the strictly professional community (e.g., public health practitioners, physicians, researchers, and pharmacists), we identified stakeholders from the civil society (e.g., schools and universities, NGOs, community initiatives, and unions) as particularly important to foster a participatory agenda. Many institutions or professional bodies have defined constituents, for example, professional societies represent physicians or researchers, politicians represent their electorate etc. This needs to be taken into account when promoting gender-sensitive approaches to these organizations.

Participants identified several examples of target groups with predefined access modes. The example of the World Health Organization (WHO) was discussed, where priorities are set by evidence, health impact, health burden, and inequalities. In such a framework, gender needs to be mainstreamed across all policy lines to achieve successful implementation. To gain access to such an organization, based on state and nonstate actors, representatives at the national level will have to be targeted to achieve inclusion of the topic. At the EU level, the process is similar, yet with a limited number of involved countries. Here, the influence of single countries or alliances of several countries can have a more direct impact on policymaking and could thus be addressed. All of these strategies call for direct connections between academia, the practice community, and politicians. Some groups might function as both a target group and a facilitator; for example, the general public can be a target population for receipt of information about the advantages of gendersensitive public health, but also a potent lobby that influences policy and organizations.

General communication strategies. The aims of gendersensitive public health and its potential advantages for the target populations/stakeholder groups need to be communicated more clearly, requiring the use of different modes and sources of communication (Table 4). While traditional media process information from their sources, digital media can serve as an unfiltered information supply and can be used by researchers and practitioners.

Scientists could identify trending topics in their area of expertise and add a gender-sensitive point of view to their analyses. Gender-sensitive analysis can be potentially applied to every human-centered research topic as it represents a uniquely crosscutting issue. When analyzing, for example, the uptake of a prevention program, risk factor distribution, or health literacy, incorporation of the gender dimension will most likely produce more nuanced results, which will improve the following implementation steps. Furthermore, they should ensure public engagement, and presentation of meaningful results and practices in lay terms, to broaden the target audience. Broadening of target audiences also fosters a more participatory approach, which guarantees increased usercenteredness in addition to continuous audience/participant feedback to the researchers about the project they are developing. Direct community contact can be achieved by targeting high-transit and target group-specific settings, for example, malls, pharmacies, or community centers. The choice of these contact areas will also harbor an intrinsic gender dimension, which should be taken into account. There should be a focus on identification of communication nodes within organizations, as these people are valuable assets in networking and rapid spreading of information.

The gendered nature of communication patterns and spread needs to be taken into account. In the case of policymakers and politicians, the main hurdle is often the set-up of an initial contact and the need to pitch short and concise information that the policymaker can further use with her or his audience. Specific promotion strategies. The participants then identified specific strategies for the promotion and implementation of gender-sensitive public health with different target audiences such as research institutions, journals, and funding agencies (Table 5). All of these stakeholders will have to be addressed and informed about the need to include gender-sensitive practice. Ideally, mandatory trainings should be provided and guidelines developed for the inclusion of sex and gender into research and project design, reporting, and evaluation practices. Gender sensitivity in implementation should be considered early in project design. Several instruments are available in the area of policymaking. Gender impact assessment instruments, gender audits, and comparative effectiveness research for gender-sensitive policies should be used extensively. In addition, gender Give your project an attractive name and develop a recognizable logo Include women and men both as targets and promotors of initiatives to emphasize the mutual support and interconnection between sex-specific issues Use infographics Include ''gender'' into the working group, institute's name if possible mainstreaming at the institutional level needs to be scaled up, especially in large organizations. A combination of careful planning and adequate monitoring should allow for more effectiveness and more rapid adoption.

At the community level, tailored population targeting of gender-sensitive public health-related communications should be implemented. Gender-sensitive approaches could be promoted through existing health consultation offers, both online and offline, and connected to issues the public relates to.

Structured process steps

We summarized the inputs from the discussion sessions about ideal practice and implementation experiences and assembled them as compilation (Supplementary Table S1; Supplementary Data are available online at www.liebertpub .com/jwh) of possible practice approaches. Results were compared with the strategies from the ERIC project [START_REF] Powell | A refined compilation of implementation strategies: Results from the Expert Recommendations for Implementing Change (ERIC) project[END_REF] and gender-sensitive elements for implementation were specified wherever these could be identified. Fifty-eight items found a definite match and for an additional five relevance for gendersensitive practice appears very likely, but the audience identified no specific example. No definite match could be identified for only 9 of the 72 items.

Different stakeholders will apply different types of strategies based on their competences, needs, and settings; this has been incorporated into the table to facilitate the selection for specific endeavors.

Discussion

To our knowledge, the presented work is the first systematic assembly of gender-sensitive implementation strategies in public health. Following the implementation continuum, the workshop participants first defined the goals and needs for a gender-sensitive approach and then detailed the communication and implementation strategies needed for translation into practice. We provide a list of implementation practices that users at all levels of the healthcare system can draw upon for information and transfer.

Implementation practice and analysis requires a systemic approach that addresses both the practical steps within a project and the structural needs to translate the project idea into practice. [START_REF] Brownson | Dissemination and implementation research in health: Translating science to practice[END_REF] Much of the work toward gender-sensitive practice has to be performed before the project starts and implies raising awareness, expertise, lobbying for political attention, for funding, and for adequate representation in the media. Hence, much of the discussion during our expert meeting focused on these activities identifying strategies, contacts, and steps to improve their outcome.

Challenges in the review processes, biased funding allocations, troubleshooting, and the publication process have all been addressed. Next to the intrinsic difficulties that these processes harbor for any researcher, the field of gender-sensitive research, practice, and training is complicated by the enmeshment of the issue and its political perception. Although specialists in the gender medicine and public health community point out that a gender-sensitive approach does not mean a focus on female careers or women's reproductive health, [START_REF] Legato | Beyond women's health the new discipline of gender-specific medicine[END_REF] it is difficult for many audiences to separate the two and this still represents a hurdle in many ways. The reality that empowerment is indeed a part of gender-sensitive public health does not simplify this distinction. [START_REF]WHO: Women's empowerment and gender equality: Essential goals for saving women's lives[END_REF] Gender-sensitive approaches frequently need to include female empowerment strategies to be effective; especially in regions of the world where healthcare access is not Use different types of social media to reach different audiences, tailor audio-visual materials to the user Use formal online health outlets to inform the public about the issue Target specific communities with messages that are locally meaningful and they can relate to Leverage corporate responsibility efforts to leverage a meaningful inclusion of gender aspects guaranteed to either women or men and in societies, organizations, or families with inequities in decision-making power. Addressing these issues goes beyond the spectrum of medicine and involves dimensions such as ethics, politics, economics, and education. [START_REF] Ostlin | Gender and health promotion: A multisectoral policy approach[END_REF] Hence, the implementation of gender-sensitive approaches in public health requires more significant communication efforts than in many other domains.

Examples of gender-sensitive public health practice are quite limited, yet some very successful examples can be pointed out. The WISEWOMEN and Strong Women-Healthy Hearts project in the United States [START_REF] Folta | National dissemination of StrongWomen-Healthy Hearts: A community-based program to reduce risk of cardiovascular disease among midlife and older women[END_REF][START_REF] Wisewoman Workgroup | Cardiovascular disease prevention for women attending breast and cervical cancer screening programs: The WISEWOMAN projects. The WISEWOMAN Workgroup[END_REF] as well as the Prime Time Sister Circles 22 both represent specific approaches to potentially high-risk women in the community. Both combine advantages of group dynamics with preventative counseling for traditional risk factors; in the case of the Prime Time Sister Circles empowerment and multiplication effects within the community are also addressed. A similar approach was chosen in the United Kingdom Football Fans in Training weight loss and healthy living program, which targets overweight/obese male football fans and uses gender-sensitized content and style, delivered in professional football clubs. [START_REF] Hunt | A gender-sensitised weight loss and healthy living programme for overweight and obese men delivered by Scottish Premier League football clubs (FFIT): A pragmatic randomised controlled trial[END_REF] Another successful project was a mass media intervention to prevent smoking among girls, which had a long-term effect on the behavior of the girls receiving the intervention compared with the ones obtaining standard prevention in school. [START_REF] Worden | Using mass media to prevent cigarette smoking among adolescent girls[END_REF] These programs have all been extraordinarily successful; all have also required careful analysis, project development, and lengthy planning. The need for extensive knowledge of structural implementation hurdles is particularly evident.

The list that is being provided might not be universally appropriate, and it should not be perceived as a checklist. As the authors of the ERIC project point out in their publication [START_REF] Powell | A refined compilation of implementation strategies: Results from the Expert Recommendations for Implementing Change (ERIC) project[END_REF] such a collection should be seen as a list of potential strategies that can be applied in specific cases-in sequence and in various combinations. No project should aim at including all 72 listed options, yet a multitude of them will apply at different times during project design, execution, and evaluation. Different stakeholders will most likely apply different strategies based on their needs and expertise, as we have tried to exemplify in our table.

The strategies presented here were suggested by a group of experts and do not represent the entire gender-sensitive public health community. Furthermore, although a representative of the WHO and one from Canada were part of the expert group, the main focus on the discussions was on experiences in a European context and, hence, might not be fully applicable to other regions. However, this risk should be minimized as attention was placed on formulating statements that could be intended as precisely, yet as broadly as possible.

This article represents the first systematic list of implementation strategies for gender-sensitive public health to aid knowledge transfer from science into practice. This collection can both aid the systematic analysis of completed projects to generate implementation and reproducibility blueprints and serve as inspiration during the development of new projects. Future implementation may profit from a wide distribution and application of the list by the practice community.

Table 1 .

 1 Overarching Goals of Gender-Sensitive Public Health

	Dimensions	Values/goals
	Ideology	(Health) Equity
		Remove health inequalities
		Social justice
		Fight discrimination
		Support fundamental rights
	Outcomes	Health promotion for women and men
		Better quality of life
	Practice	Transdisciplinary teams working
		on intersectional issues
	Empowerment	Support informed choice
		Offer tools for behavioral change
		Acceptance of people's lifestyle choices
	Economy	Achieve effectiveness
		Reduce costs through improvement
		of measures
	Policy

Table 2 .

 2 Most Urgent Needs of Gender-Sensitive Public Health

	Strategies	Examples
	Raise awareness	For sex and gender differences
		(with the general public, with
		health services providers, with
		politicians/policymakers)
		About gender-specific risk factors
		Focus on health gains
	Intervention targets	Risk factors (e.g., smoking)
	and priority issues	Demographic change
		(e.g., aging population,
		migration, urbanization)
		Chronic diseases and
		metabolic diseases
	Data production	Produce more sex-segregated
	and integration	and gender-sensitive data
		Define a shared taxonomy
		of classification
		Define professional, economic,
		and legislative resources needed
	Develop translational/	How-strategies
	implementation	What-evidence-based
	strategies	public health
		Where-cross-country,
		context-specific work
	Political lobbying/	Harness political will,
	support	find champions
		Increase public funding
		Promote regulation
		(potentially against
		industrial interests)

Table 3 .

 3 Stakeholders for Gender-Sensitive Public Health

	Stakeholders
	Policymakers	NGOs
	Politicians	Funding agencies
	Governments	Researchers
	Local governments	Institutions for women's
	and municipalities	and men's studies
	Transnational regulators	Charities
	(e.g., food, transport,
	built environment)
	International Organizations	Religious organizations
	(e.g., UN, ECDC,
	OECD, World Bank)
	Regulatory agencies	Trade unions
	(e.g., EMA, FDA)
	Physicians	General population
	Nurses	Parents
	Pharmacists	Relatives and families
		of patients
	Health makers	Schools, kindergartens
	Health insurers	Media (traditional and new)
	Journal editors	Social media
	Teachers in healthcare	Industry
	Patients
	Patient organizations
	Professional societies

Table 4 .

 4 General Communication Strategies

	Sources

Table 5 .

 5 Formal Promotion Strategies Targets Examples Science/medicine Continuous incorporation of the gender dimension (into the literature, at conferences, in reports etc.) Hold cross-sectoral transdisciplinary conferences with different stakeholders Include gender dimension in proposals for nonspecific calls Lobby journal editors, request formal guidelines for submission and review Combine epidemiological data, behavioral information, and practice examples to exemplify the impact of gender Include gender into trainings for professionals Include it into training, mentoring, and supervision-mandate if possible Include it into national reports, even if not explicitly requested Consider gender-sensitive implementation aspects during early planning of projects Policy/politics Establish a group of charismatic people to lobby politicians, funding agencies, and policymakers Offer structured mentoring Request a gender impact assessment for every policy Request gender audits Employ a selected group of experts to vet all documents, projects, publications of the organization for inclusion of the gender dimension Mainstream gender into agency's/organization's priorities Request comparative effectiveness research (CER) for policy making Take PR value into account when presenting the topic to politicians Link gender to issues your target cares about (e.g., costs, benchmarking, specific health topics etc.) Work with the policy cycle, try to influence annual programs Community

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Acknowledgments

The current work was supported by EU grant EU/FP7 602050 (EuGenMed project).

The following experts have participated in the workshop and contributed substantially to the present article:

Olga Barna (Department of General Practice, Bogomolets National Medical University, Kiew, Ukraine), Marrie Bekker (Department of Clinical Psychology, Tilburg University, Tilbug, The Netherlands), Carole Clair (Faculty of Biology and Medicine, University of Lausanne, Lausanne, Switzerland), Lucie Dalibert (Department of Health, Ethics and Society, Maastricht University, the Netherlands), Miriam de Kleijn (general practitioner, Utrecht region), Isabel de la Mata (Principal Advisor for Health and Crisis Management, European Commission), Dirk Gansefort (Leibnitz Institute for Prevention Research and Epidemiology, Bremen, Germany), Olena Hankivsky (School of Public Policy, Simon Fraser University, Vancouver, Canada), Radu Iliescu (University of Medicine and Pharmacy ''Gr. T. Popa.'' Iasi, Romania), Ineke Klinge (Department of Health, Ethics, and Society, Maastricht University, the Netherlands), Peggy Maguire (European Institute of Women's Health, Dublin, Ireland), Shanti Mendis (Chronic Disease Prevention and Management, World Health Organization, Geneva, Switzerland), Jo ¨rg Mu ¨ller (Universitat Oberta de Catalunya, Barcelona, Spain), Sabine Oertelt-Prigione (Charite ´-Universita ¨tsmedizin, Berlin, Germany and Department of Primary Care, Radboud University Medical Center, Nijmegen, the Netherlands), Dorota Sienkiewicz (The European Public Health Alliance, Brussels, Belgium), Astrid Stuckelberger (Institute of Global Health, University of Geneva, Geneva, Switzerland), Helen Sweeting (Institute of Health and Wellbeing, University of Glasgow, Glasgow, UK), Margo van den Berg (ZonMW, Program Diversity, Den Haag, the Netherlands), Petra Verdonk (Department of Medical Humanities, VU University Medical Center, Amsterdam, the Netherlands), Barbro Westerholm (Swedish Liberal People's Party, Sweden), Alan White (Center for Men's Health, Leeds Beckett University, Leeds, UK), and Elisabeth Zemp-Stutz (Swiss Tropical and Public Health Institute, Basel, Switzerland and University of Basel).

Author Disclosure Statement

No competing financial interests exist.