Olfa Kaabia
email: olfa.kaabia@u-paris10.fr

Ilyes Abid
email: ilyes.abid@u-paris10.fr

Theoretical Channels of International Transmission During the Subprime Crisis to OCDE Countries : A FAVAR Model Under Bayesian Framework

Keywords: Transmission channels, Contagion, Bayesian estimation and FAVAR models. JEL classi…cation: E44, F20, G15, G01, C11, C32

This paper studies whether and how U.S. shocks are transmitted to other OECD economies in the case of the subprime crisis. Using a large data set of …nancial and macroeconomic variables in 17 OECD countries from 1980:Q1 to 2006:Q2, we characterize the transmission channels by the interpretable factors and make a structural analysis using FAVAR models under a Bayesian approach.

Our main …ndings suggest that di¤erences exist in the contagion e¤ects. This implies that no generalizations can be made for OECD countries even of equal economic size and in the same geographic region. Our results show that a large portion of the variance of domestic economic variables is explained by global factors and that the interest rate shock appears to play an important role in the spillover mechanism from the U.S to the OECD countries.

Introduction

Housing markets are generally viewed as "local" markets, plagued with idiosyncrasies. Nevertheless, there is a large consensus to claim that shock originating from a particular market can easily spread out to other markets in the same segment, or even to other market segments. The housing price boom during the early 2000s raised questions of possible international transmission of shocks across countries [START_REF] Otrok | The Global Housing Price Boom[END_REF]. Moreover, the last housing crisis in USA emerged in the Summer of 2006 was followed by a sharp fall in housing prices in Ireland, New Zealand, Spain and the United Kingdom. These almost parallel developments provide evidence in favor of signi…cant increase in the correlation across national housing markets during the subprime crisis.

The top left graph in Figure 1 illustrates the development of real housing prices for selected countries during 2003-2008. There appears to be a large degree of comovements between very di¤erent and distant countries. Graphically it seems that the U.S. housing boom and bust spread to other parts of the world.

[Figure 1 about here] However, the top right graph in Figure 1 shows that this is not the case for all countries. Germany, the Netherlands and Switzerland seem to be relatively immune to development in U.S. housing market. In contrast to house price developments, GDP growth is severely a¤ected for all eight countries (see bottom panel of Figure 1). To illustrate, Germany and Japan's GDP shrunk stronger than U.S. GDP during 2008. Hence, the exact transmission channel from the U.S. housing market to other countries' real economy is not obvious.

There are several di¤erent explanations possible of an international transmission of housing price shocks.

First of all, housing prices may be driven by economic or …nancial fundamentals (see e.g. Goodhart and Ho¤man (2008) and De Bandt and al. (2010)). The idea is that housing prices would comove if housing prices are driven by correlated fundamentals. For instance, an increase in U.S. interest rates increases global interest rates, which increases the cost of borrowing across countries. Hence, home buyers are credit constrained, which a¤ects directly house prices.

Second, due to the wealth e¤ect a decrease in house prices will induce households to reduce their consumption (See e.g. Lettau and Ludvigson, 2 2004 and [START_REF] Case | Comparing wealth e¤ects: the stock market versus the housing market[END_REF]. Since households consume both domestic and foreign goods and services, these e¤ects reduce demand for other countries' export sectors.

Third, news on housing prices in some countries may lead investors and (potential) house buyers to revise their expectations on housing prices in other countries. For instance, these revised expectations can be unrelated to changes in fundamentals akin to contagion e¤ects in exchange rates and stock markets during the Asian crisis (Kaminsky and Reinhart, 2000). Hence, there are complex international links between housing markets and the real economy.

In this paper we aim at going further beyond questions of international transmission of housing prices in normal period to examine "contagion effects" during the turmoil event of the subprime crisis.

The scope of this study is to contribute to the literature on international transmission of U.S. shocks by exploring the transmission channels process and contagion e¤ects during the subprime crisis. We detect contagion when a sudden local change in one country a¤ects global variables. The contagion is detected in the case that an unanticipated shock appears suddenly in a country and thereof creates a signi…cant increase (or decrease) in the comovements between variables. This paper investigates the two principal questions: Is there evidence of contagion e¤ects on the OECD countries during the subprime crisis? And what are the important channels through which U.S. shocks are transmitted to the OECD economies considered?

To answer these questions, we will measure the international comovements employing a dynamic Bayesian FAVAR approach. The motivation is to identify a few common factors that capture common ‡uctuations in large multi-dimensional datasets. We follow [START_REF] Stock | Understanding Changes in International Business Cycle Dynamics[END_REF], [START_REF] Bai | Inferential Theory for Factor Models of Large Dimensions[END_REF], [START_REF] Bernanke | Measuring the E¤ects of Monetary Policy: a Factor Augmented Vector Autoregressive (FAVAR) Approach[END_REF] and [START_REF] Bai | Extremum Estimation when the Predictors are Estimated from Large Panels[END_REF] dealing with large systems. But as VARs su¤er from dimensionality problems when the number of variables increases, it is not possible to include a large set of variables. The common idea of FAVAR models is that the extracted factors summarize common information in variables to reduce the size of the VAR to allow a more e¢cient estimation, while still incorporating as much information from variables as possible. However, in all the existing studies in the literature 1 , those extracted factors are not interpretable. So, one of the originality of our work is to deal with constrained factors by introducing a Bayesian approach so as to identify and interpret the transmission channels. It is worth emphasizing that there are many methods to extract factors; here we choose to estimate constrained factors from a large database so as to interpret them as global, country-speci…c and variable-type factors. This way, we want to give a precise characterization of the transmission channels in the contagion processes during the housing crisis in USA in 2006. So, the novelty of our FAVAR approach comparing to the one of Bernanke, Boivin and Eliasz (2005) and even that of De Bandt and al. ( 2010) is in the way of extracting the factors.

Our approach di¤ers from the one of [START_REF] Iacoviello | Housing Market Spillovers: Evidence from an Estimated DSGE Model[END_REF], where they aimed to structurally model the di¤erent sources of shocks, including crisis, technology shocks, monetary policy shocks, etc. In this paper we rather focus on short run links across markets, in order to investigate what happened in the recent subprime crisis, which spread out to the world economy.

Our sample consists of 17 OECD countries with quarterly data from 1980:Q1 until 2006:Q2 so as to stop before the outbreak of the subprime crisis. It is worth emphasizing that this sample is larger than related studies by e.g. [START_REF] Otrok | The Global Housing Price Boom[END_REF] and [START_REF] Beltratti | International House Prices, and Macroeconomic Fluctuations[END_REF]. For instance, the latter authors consider only the G-7 and treat the European Monetary Union as one country. Two speci…c American shocks are studied. First, a shock in housing prices and second a shock in short-term interest rates. We consider the subprime crisis and study how these shocks a¤ect the considered OECD economies.

Our results show that a large portion of the variance of domestic OECD economic and …nancial variables is explained by the common factors. However, there are important di¤erences between the OECD countries. This suggests that American shocks, which are able to impact the global factors, will be transmitted to some, but not all OECD countries. More precisely, Australia, the United Kingdom and Scandinavian countries appear to be most sensitive to global shocks. However, even though global developments play an important role in most OECD economies, a large part of the variance is still idiosyncratic.

The plan of the paper is the following. Section 2 recalls the main principles of the econometric methodology. Section 3 presents the data, summarizes the …ndings and section 4 concludes.

Methodology

We recall the main points in the econometric modeling adopted to estimate FAVAR models under a Bayesian approach. Although the VAR approach has been extensively employed in studying contagion e¤ects, di¤erent criticisms have been directed at the sparse information content of VAR models. A typical VAR model for an international contagion study does not usually include more than eight variables because of the degrees of freedom restriction which could not accurately re ‡ect the necessary information. Moreover, a VAR model may exclude variables that may be relevant in that transmission process.

To overcome the shortcomings of VAR models, a new methodology has been proposed by [START_REF] Bernanke | Measuring the E¤ects of Monetary Policy: a Factor Augmented Vector Autoregressive (FAVAR) Approach[END_REF], a FAVAR model. This methodology consists of two basic equations in a two-step procedure similar to that of Stock andWatson (2003, 2005). Here, we follow [START_REF] Bernanke | Measuring the E¤ects of Monetary Policy: a Factor Augmented Vector Autoregressive (FAVAR) Approach[END_REF]. However, our novelty comparing to the previous authors is the inclusion of constrained factors. We assume that dealing with interpretable factors allows a clearer identi…cation of international transmission mechanisms compared to alternatives using principal components2 . This will bene…t the economic interpretation of our results.

The idea underlying the FAVAR models estimated by [START_REF] Bernanke | Measuring the E¤ects of Monetary Policy: a Factor Augmented Vector Autoregressive (FAVAR) Approach[END_REF] is the following: if a small number of estimated factors e¤ectively summarize large amounts of information about the economy, then a natural solution to the degrees-of-freedom problem in VAR analyses -which have to be of limited dimensions -is to augment standard VARs with estimated factors.

Accordingly, one considers a (M 1) vector Y i;t of observable economic variables of interest. One assumes that additional economic information, not fully captured by the series, may also be relevant to modeling the dynamics of these series. More precisely, this additional information can be summarized by an (K 1) vector of unobserved factors, F , where K << M . The joint dynamics of (Y t ; F t ) are given by:

F t Y t L) F t 1 Y t 1 + t (1)
with F t and Y t denote respectively the unobserved factors and the shocked key variable at date t. Also, t is denoting a white noise process.

The FAVAR model cannot be estimated directly because the factors F t are unobservable. However, as the factors represent forces that potentially a¤ect many economic variables, [START_REF] Bernanke | Measuring the E¤ects of Monetary Policy: a Factor Augmented Vector Autoregressive (FAVAR) Approach[END_REF] suppose that it is possible to infer something about the factors from observations on a variety of economic "informational" time series, denoted by a (N 1) vector X t . The number of informational time series N is assumed to be greater than the number of factors. The series X t is related to the unobservable factors F t and the observable factors Y t as follows:

X t = f F t + y Y t + t ( 2
)
where f is an (N K) matrix of factor loadings, y is (N M ) matrix, and t , is the (N 1) vector of the error terms, which are mean zero and assumed as either weakly correlated, or uncorrelated, depending on whether estimation is obtained by principal components, or likelihood methods because, according to Bernanke and al., the model can be estimated in two ways.

In our case, we adopt the two-step procedure, but, at the …rst stage, we estimate the constrained factors by using a Bayesian estimation method. First, to identify unobservable forces (factors), we use a dynamic factor model originally introduced by Otrok and Whiteman (1998) and further developed by Kose and al. (2005) and Del [START_REF] Negro | 99 Luftballons: Monetary Policy and the Housing Price Boom across US States[END_REF]. The factor structure itself is directly motivated by general equilibrium models as shown in [START_REF] Altug | Time-to-Build and Aggregate Fluctuations: Some New Evidence[END_REF] and [START_REF] Sargent | Two Models of Measurements and the Investment Accelerator[END_REF].

For each country i, we consider a set of economic and …nancial variables (X i;j;t ) 1 j J. We assume that these variables obey a factor model as follows:

X i;j;t = (G) i;j F (G) t + # X v=1 (v) i;j F (v) t + C X c=1 (c) i;j F (c) t + " i;j;t (3)
where F (G) denotes a global factor, F (c) a factor speci…c for country c and F (v) a factor representative of a type of variable v.

For clearness, the dynamic factor model used in this paper assumes that housing prices and the other macroeconomic and …nancial variables, can be explained by the following three types of factors: the global factor or world one, the country-speci…c factors and the variable-type factors. The idiosyncratic errors " i;j;t are serially correlated, and are modeled as p -order autoregressions. Also, we suppose that: E(" i;j;t ; " i 0 ;j 0 ;s ) = 0 for (i; j) 6 = (i 0 ; j 0 ) and t 6 = s E(" i;j;t ; " i 0 ;j 0 ;s ) = 2 i;j otherwise .

Each factor F t is dynamic and obeying an autoregressive model of order q (F ) as follows:

F (F ) t = ' (F ) 0;1 F (F ) t 1 + ' (F ) 0;2 F (F ) t 1 + : : : + ' (F ) 0;q F (F ) t q + (F ) 0;t ; F = G; v or c (4)
If the dynamic factors were observable, the estimation of the equations ( 3)-( 4) would be straightforward. Since it is not, special methods must be employed as is done in the literature. Stock andWatson (2003, 2005) treat the model as an observer system and employ Kalman …lter to estimate the model parameters and extract an estimate of the unobserved factors. In our analysis, we choose an alternative procedure based on a recent development in the Bayesian literature on, that of "data augmentation" 3 .

Also, as to give an interpretation to the di¤erent factors (world, country-speci…c, and variable-type factors), we identify them by making two sign restrictions because neither the signs nor the scales of the factors and the factor loadings are separately identi…ed.

Signs are identi…ed by requiring one of the factor loadings, i;j , to be positive for each of the factors. In practice, the factor loading for the world factor is imposed to be positive for the U.S. GDP. In this sense, country factors are identi…ed by positive factor loadings for GDP for each country. The speci…c-type factors are identi…ed by positive loadings for the U.S variables listed for each speci…c factor. Then the scales are identi…ed, following Sargent and Sims (1977) and Stock andWatson (2003, 2005), by assuming that each factor variance, 2 F (F ) , is equal to a constant. If we denote by the set of unknown parameters ( i;j , 2 i;j , i;j;t p , ' (F ) 0;q , 2 F (F ) ) the idea is given a prior of the factors, one determine posterior distributions for all unknown parameters conditional on the latent factors, noted p( j F (F ) ). And then determine the conditional distribution of the latent factors given the observables and the other parameters, noted p(F (F ) j ). So the joint posterior distribution for the unknown parameters and the unobserved factors can be sampled by using a Markov Chain Monte Carlo procedure on the full set of conditional distributions. In other words, we will generate a Markov chain whose stationary distribution is the distribution of interest4 using a Gibbs sampling procedure.

Then once the factors extracted and at the second stage, a FAVAR model is estimated. It is worth noticing that the Bayesian method provides a tightly estimation of the factors at the …rst step and so, the uncertainty in the estimated factors is negligible [START_REF] Kose | International Business Cycles: World, Region, and Country-Speci…c Factors[END_REF] allowing to estimate the FAVAR model like a standard VAR model as [START_REF] Bernanke | Measuring the E¤ects of Monetary Policy: a Factor Augmented Vector Autoregressive (FAVAR) Approach[END_REF] do. Moreover, to account for the uncertainty in the factor estimation, we implement a bootstrap procedure, in order to obtain accurate con…dence intervals on the impulse response functions deduced from the FAVARs.

Our interest is to investigate contagion e¤ects on X t by assuming an initial positive shock on Y t which spreads through the extracted factors F t . According to that, we put in the FAVAR models two factors in addition to a key observable variable, Y t , on which we simulate an initial shock. Then, we study the e¤ects on the informational time series X t . This captures the idea that both Y t and F t represent pervasive forces that drive the common dynamics of X t . Let us note that in our analysis, the innovations of the FAVAR models are orthogonalized according to a Cholesky ordering as it is the common practice in previous studies 5 . If one can get empirical evidence of a signi…cant dynamic transmission of a local shock (originating from a local market or country) to a particular common factor, one can derive the dynamic responses of the other markets as transmitted by a factor. Such responses are pandemic as much as they simultaneously a¤ect all markets whose dynamics are signi…cantly explained by the factor. Once the di¤erent constrained factors are extracted, they are included in a FAVAR model, alongside an observable indicator Y associated with the local shock under study. For example, we include the American housing price growth rate in the FAVAR model if we aim at investigating the impact of a shock originating from the American housing market. Next, by inverting the chosen FAVAR model (F 1 ; F 2 ; : : : ; Y j ) we can obtain the impulse responses IR(F 1 ; " Y j ; h) , IR(F 2 ; " Y j ; h),. . . of the di¤erent factors (F 1 ; F 2 ; : : :) to a shock to Y j .

If one gets empirical evidence in favor of signi…cant responses for a sig-ni…cant number of countries, one can conclude that there may be contagion e¤ects, as the local shock spreads out through factors to a large number of countries at the same time.

3 Empirical Framework

Data

Our dataset is primarily drawn from Banque de France and Global Financial Data. This dataset includes quarterly data from 1980:Q1 to 2006:Q2 for 17 OECD countries :United States (US), Canada (CAN), Finland (FIN), France (FRA), Germany (DEU), Ireland (IRL), Italy (ITA), Netherlands (NLD), Spain (ESP), Denmark (DNK), Norway (NOR), Sweden (CHE), Switzerland (SWI), United Kingdom (UK), Australia (AUS), Japan (JPN) and New-Zealand (NZL).

For each considered country, seven economic variables are included as : GDP, Consumption, Investment, Housing Price Index, Short Run Interest Rate (3-month), Long Run Interest Rate (10-year) and Stock Market Index. Except for the interest rates (IRS and IRL), all variables are taken in real terms (taken as nominal and divided by the Consumer Price Index) so as to take into account the in ‡ation.

All the data is seasonally adjusted and the variables are measured at constant national prices. As is usually done in the literature, interest rates are di¤erenced and activity variables are logarithmized. We compute the growth rates and remove the mean from each series. Growth rates are used because we aim to investigate the short run e¤ects and not long run e¤ects of shocks in the FAVAR. The subprime crisis may represent a break in the dynamic relationships between variables and factors so for that we stop before it and it is not accounted in our sample.

Results

In our analysis and according to the equation (3), we consider for each of the seventeen OECD country, a set of seven economic and …nancial variables, 1 j 7, namely, GDP, consumption, investment, interest rates (long and short), stock index returns and housing price index returns. Also, we took # = 4; C = 17 and p = q (F ) = 4.

We assume that housing prices and the other macroeconomic and …nancial variables, can be explained by the following three types of factors:

The Global factor or World factor captures the common shocks a¤ecting all the variables. A Country-speci…c factor, which captures common shocks to variables in a country.

A Variable-type factor, which captures common shocks a¤ecting a type of variable in all the countries but not for other variables. We distinguish four types of variable speci…c factors. First, the real factor (or real activity factor) captures comovements among GDP, consumption and investment. Second, the interest factor captures comovements for short run and long run interest rates. Third, the stock factor captures comovements among stock markets and fourth, the housing factor is the common factor for all domestic housing series. So using this set-up the total number of factors extracted from the 119 series is K = 22 (1+17+4).

The Transmission Channels Analysis

So as to better characterize the transmission channels in the case of studying contagion e¤ects during the subprime crisis, we propose to start by analyzing the dynamic extracted factors.

We examine the evolution of the di¤erent factors and analyze their ability to track important events or business cycle episodes since 1980 by analyzing the factors' graphs reported in the appendix.

Unlike Figure 2 displays the posterior median of the global factor along with the 10% and 90% quantiles. The tight con…dence bounds indicate the precision with which the factor is extracted. This precision is important when including the factor as observable in the FAVAR.

[Figure 2 about here] The global factor summarizes the common behavior of all 119 series in the database. This factor is clearly time-varying and provides a general indication of the state of the world economy. The recessions of the early 1980s and early 1990s are clearly visible.

However, for a better understanding on the speci…c development of economic variables we need to consider the variable-type factors too.

[Figure 3 about here] The variable-speci…c factors are presented in Figure 3. The top graphs represent the real factor and the interest rate factor, and the bottom graphs represent the stock market factor and house price factor, respectively. Note again the tight con…dence bounds around the factors, with the only exception being the house price factor, which has wider con…dence bounds.

Let us …rst consider the housing factor which re ‡ects the main developments in global housing markets. It is worth noting that it accounts for the housing price bust of the early 1980s and the housing price boom of the late 1980s. In the beginning of the 1990s the economic recessions resulted in a slump in house prices, which started to stabilize in the mid 1990s. The house price boom of the late 1990s and early 2000s is clearly captured. However, it is important to keep in mind that the con…dence bounds are relatively large, indicating that there is not one single global house price factor, but that there important di¤erences between countries' housing markets : i.e, [START_REF] Giuliodori | The Role Of House Prices In The Monetary Transmission Mechanism Across European Countries[END_REF] shows the importance of institutional di¤erence for monetary policy transmission across European countries.

Second, the real factor summarizes the information contained in all countries' GDP, consumption and investment series. This factor captures the recessions of the early 1980s and early 1990s quite well. Moreover, common variations in the two interest rate series are captured by the interest rate factor. This factor also captures several important events. The ERM crisis of 1992-1994 is clearly captured, with …rst increasing interest rates, followed by decreasing ones. During 1999-2000 interest rates were very low and increased after the burst of the Dot-com bubble. We remark clearly the increase in the interest rates. This maybe a consequence of the increase in the Fed funds rate in 2005. Also as expected, the stock factor captures the past declines in the stock markets, such as the 1987 crash and also the long boom of the 1990s. Comparing to the other type-variable factors, this factor appears to be more volatile. However, note that the con…dence bounds are very tight, indicating a large degree of synchronization across national stock market indexes.

Next, we will use variance decompositions to measure the relative contributions of the global factor, the variable-type and country-speci…c factors to business cycle ‡uctuations in each country. The variance decomposition analysis is crucial in such contagion studies. If we found in the subprime crisis that the variance part is signi…cantly more pronounced, we found evidence of contagion e¤ects.

The Variance Decompositions

The graphical investigation of the factors is complemented by the variance decompositions of the explained factors to assess how important each factor is for each variable. Such decompositions provide indications about how country's ‡uctuations are associated with global ‡uctuations and variable type. The variance decompositions reported in Table 1 show the percentage of the variation in each series explained by the global factor, the type factors (real, interest, stock, housing) and country factors.

We are interested on what is explained by the fundamental so the part of the variance not explained by these factors is idiosyncratic. For each variable we will discuss in turn the importance of common factors. However, in order to avoid spurious correlation, the common factor that we used in the variance decompositions for a given variable is computed from a database that excludes that variable. For instance, in the case of getting the variance decomposition of the world factor in the Americain consumption, we exclude that last variable.

[Table 1 about here] First, the country factor is an important determinant of GDP in many countries. For about half of the countries more than 25% percent is explained by the country factor. However, global developments captured by the global and real factors are important as well. For most countries over 20% of the variation in GDP is explained by global factors. However, in some countries, such as Norway, GDP growth behaves rather idiosyncratially and global developments do not seem to matter as much as for other countries, e.g. France, Italy and Spain. Consumption and investment show a rather similar picture as GDP, where investment seems to be even more independent from international events. For example, in Denmark and Sweden over 90% of the explained variance in investment is idiosyncratic.

Second, turning to the four interest rate related variables, there is quite some variety in the variance explained by the common factors.

The interest rate factor explains much cross-country variation in short run and long run interest rates. For example, the interest rate factor explains over 70% of the movements in long term interest rates in Germany and the Netherlands. Only in New Zealand this factor has low explanatory power.

The global interest rate and country factors do not explain more than 25% in any country. In addition, country factors also matter for the long-run interest rate, especially in Scandinavia.

Third, the equity market shows, perhaps unsurprisingly, much comovement across markets. In most countries the equity factor explains over 50% of the variance. Both the global and country factors only play a marginal role here. The high degree of stock market synchronization is well documented in the literature (See e.g. [START_REF] Longin | Is the Correlation in International Equity Returns Constant: 1960-1990?[END_REF] or [START_REF] Chinn | A Decomposition of Global Linkages in Financial Markets Over Time[END_REF]). With easy cross border access and highly liquid markets, prices can adjust quickly across all markets.

Fourth, for housing prices the story is di¤erent and there are large di¤erences on the importance of each factor across countries. The global factor plays a meaningful role in the United States, Canada, Finland, Spain, United Kingdom and New Zealand. When considering the global housing factor a large portion of the variance is explained in the United States, Finland, Spain, Sweden and United Kingdom. Consequently, housing prices in the United States, Finland, Spain, Sweden and United Kingdom are explained by global factors. Not surprisingly, Spain, U.K. and the U.S. show a large degree of housing price comovements since the burst of the housing market bubble in the United States. The country factor also plays an important role in some countries like Finland, Ireland, the Netherlands, Japan and New Zealand. However, some housing markets seem to behave idiosyncratically, where the factors do not explain much. This is the case in e.g. France, Italy and Norway.

The Forecast Analysis

The idea underlying extracting the constrained factors using Bayesian techniques is to represent large datasets using a small number of transmission channels allowing the transmission process. A little attention has been devoted to the forecasting power of these factors.

When forming our idea about detecting contagion e¤ects, we extract the best signals (factors) as to be the paths of the transmission process of a local U.S shock to other economies.

We evaluate the forecast performance of the di¤erent common factors over the period going from 2006:Q3 until 2008:Q4.

[Figure 4 about here] Brie ‡y, we can say that it seems that all the factors are impacted by the subprime and the …nancial crises of the U.S.

According to the world factor, two clear declines happened respectively in mid-2007 and mi-2008. Those are more probably re ‡ecting the subprime and …nancial crises.

For the global real activity factor, it seems that a decline happened in the …rst quarter of 2007. It maybe a delay between the beginning of the subprime crisis and its impact on the real activity of the OECD countries. Moreover, the most increase happened in the third quarter of 2008, the period of the Lehmans Brothers bankruptcy. The lowest point was noticed in the last quarter of 2008. Also, the interest rate factor seems to be very volatile. It appears that the rates were declining since mid-2006 until mid-2007, then increasing from that last date until the …rst quarter of 2008 to fall and achieve the lowest point in mid-2008 before increasing again. The global stock channel seems to be impacted in mid-2007 by the subprime crisis. For the housing price factor, it seems to be a continuous little decline since mid-2006 until the end of 2008.

We notice from the forecast exercise that the factors or transmission channels were impacted in a good sense by the subprime and then by the …nancial crisis.

In the next section, we will investigate the internationally transmission mechanisms, where shocks originating from the United States are transmitted across the world through the transmission channels in the subprime crisis.

Impulse Responses Analysis

In this section, we augment a standard VAR model by including unobserved factors akin to [START_REF] Bernanke | Measuring the E¤ects of Monetary Policy: a Factor Augmented Vector Autoregressive (FAVAR) Approach[END_REF]. These unobserved factors are chosen from the ones estimated in the previous section as previously explained. We will restrict our attention to the U.S. economy, which is a large economy and whose domestic shocks are likely to in ‡uence the common factors. Hence, the common factors are treated as endogenous in this model 6 . The vector of endogenous variables of the FAVAR is given by:

Y t = h HP I USA;t F C USA;t F W t F REAL t F INT t F EQ t F HP I t i 0 (5) which HP I USA;t , F C USA;t , F W t , F REAL t , F INT t
, F EQ t and F HP I t represent respectively, the growth rates of U.S. housing prices, the U.S. country factor, the real activity factor, the global interest rate factor, the stock market factor and the global housing factor.

Using this set-up the Akaike Information Criterion indicates that four lags of the endogenous variables need to be included in the model. The Hannan-Quinn Criterion and the Schwarz criterion indicate only two or one lag, respectively. Choosing four lags seems to be a natural choice since we are dealing with quarterly data. Moreover, further analysis shows that four lags are necessary to eliminate all residual serial correlation. One alternative is to allow an unrestricted estimation involving 6 endogenous variables. However, for e¢ciency reasons we choose to use a top-down approach with the Hannan-Quinn criterion to …nd possible coe¢cients which we can set to zero. The Lütkepohl and Doornik-Hansen tests for joint non-normality show signs of excess kurtosis in the innovations. There appear to be no problems concerning skewness. However, the joint non-normality tests reject normality. On the individual series level the Jarque-Bera test shows that normality at the individual series level is rejected only for the residuals of domestic US housing prices. There are no signs of residual serial correlation, which appears to be eliminated with the inclusion of four lags. In sum, the assumptions of normality and no autocorrelation appear to be satis…ed for most individual series. However, we will estimate this restricted model using Feasible GLS. Moreover, we will use bootstrapped con…dence bounds to conduct conservative conclusions in the impulse response analysis.

A positive shock to U.S housing prices

In the following section, we will investigate the emergence of a positive housing price shock originating in the United States mid-2006. This shock is a simulation of the subprime crisis. Such a crisis is likely to boost housing prices. Note that the analysis is symmetric and can be used to analyze housing price decreases as well. Figure 5 shows the cumulative impulse response functions of a positive shock to United States real housing prices. The …rst graph shows the response of the U.S. country factor, the second of the housing price factor, the third of the real factor and the fourth of the global factor. The 90% con…dence bounds are constructed using bootstrapped Hall studentized standard errors. This will make the con…dence bounds more robust against possible non-normalities.

[Figure 5 about here] The positive U.S. housing price shock has an unclear e¤ect on the U.S. country factor. However, the other graphs show strong spillover e¤ects to the global factors.

First, the increase in U.S. house prices results in a signi…cant increase in the global house price factor. This implies that countries whose housing market has a positive loading on the housing factor will experience an increase in housing prices, ceteris paribus.

Second, the e¤ects of the U.S. housing price shock are not restricted to only the housing market. Instead, the world factor and real factor show a signi…cant increase as well. This e¤ect sheds light on the transmission channel of global GDP decreases. Since the real factor explains a large portion of global GDP developments, an increase in this real factor will result in increases in domestic GDP.

[Table 2 about here] Table 2 displays the loadings on each factor for all variables. A bold number indicates that the loading is signi…cantly di¤erent from zero at the 90% con…dence level. The following countries will experience a signi…cant increase in domestic housing prices as a result of the increase in the global housing factor: Finland, Denmark, Norway, Sweden, Switzerland, United Kingdom and Australia. However, note that Canada, Ireland and Denmark have a relatively large loading on the housing price factor, but due to larger con…dence bounds, these loadings are not signi…cantly di¤erent from zero. Fewer countries are signi…cantly a¤ected by the increase in the world factor.

One limitation of this FAVAR model is that is not able to capture the effect of the U.S. housing price shock on the respective country factor. We can infer spillover e¤ects from the world factor to other sectors of the economy. For example, since the real factor increases signi…cantly the real economy of all countries is a¤ected by the shock to U.S. housing prices. Basically and from the results, only the Japanese economy would be rather isolated from the global real activity factor. In order to obtain more insight in the determinants of the housing factor, we perform a forecast error variance decomposition (FEVD). Table 3 reports the FEVDs of : 1) The global housing price factor and 2) U.S. domestic housing prices. The forecast horizon ranges from 1-20 quarters.

[Table 3 about here]

The variance decompositions in Table 3 show that U.S. housing price shocks appear to behave rather idiosyncratically. Even after 20 quarters, the variable itself explains over 80% of the shock. In contrast, the included variables explain more of the shocks on the global housing factor. For example, the real factor explains about 22% of the variance after 20 quarters and U.S. housing prices explain about 8%.

A positive shock to U.S short run interest rates

According to the literature and to most economists, the subprime crisis was, at least, partly the U.S. Fed's fault. We simulate the subprime crisis in mid-2006 taking into account the policy of the Fed during 2005-2006 with large increases.

So in a second speci…cation, we replace U.S. housing prices with the U.S. short run interest rate and study the e¤ect of a positive shock to U.S. short run interest rates. The FAVAR model estimated is as follows:

Y t = h IR USA;t F C USA;t F W t F REAL t F INT t F EQ t F HP I t i 0 (6)
where

IR USA;t , F C USA;t , F W t , F REAL t , F INT t
, F EQ t and F HP I t represent respectively, the growth short-term 3-month American interest rate, the U.S. country factor, the world factor, the real activity factor, the interest rates factor, the stock market factor and the global housing factor. Again four lags are chosen and the speci…cation tests do not reject the assumptions of normality and no residual serial correlations where found. The impulse responses along with 90% con…dence bounds are reported in Figure 6.

[Figure 6 about here] First, the short interest rate shock signi…cantly decreases the U.S. country factor. This indicates that general economic activity will decrease.

Second, the short interest rate shock has a large e¤ect on common factors: for instance, the housing factor and the real activity one both decrease, after some delay. It is well-known that it takes several quarters before interest rate changes a¤ect the real economy. In addition, the world factor is also signi…cantly a¤ected by shocks to interest rates.

In sum, both changes in U.S. interest rates and housing prices are sig-ni…cantly transmitted to international common factors.

Using the loadings from Table 2 we can infer again the consequences on domestic housing markets across the world. As the results are qualitatively similar to those from the housing price shock we will not discuss these in detail again. However, what is interesting to observe is that the interest rate policy of the Fed during 2005-2006 with large increases has likely played an important role in housing price changes across the world.

In the above analysis we studied the e¤ect of a shock to U.S. housing prices and a shock to U.S. short interest rates on the unobserved international factors. Hence, we need to infer what the e¤ect of the U.S. is on those country speci…c factors.

So our analysis is interesting and can be made for several countries. The same analysis can be made for other countries even also can be extended with two-country FAVAR models. Specially, for most countries, their country factor plays an important role in domestic house price developments. For example, to study the e¤ects of the U.S. housing price shock on Spanish housing markets, it will be possible to estimate the following model:

Y t = h HP I USA;t F C USA;t HP I ESP;t F C ESP;t F INT t F EQ t F HP I t F REAL t F W t i 0 (7
) By using these types of FAVAR models we will have a clearer picture when analyzing the contagion e¤ects of a housing price shock or interest rate shock originating in the United States on any other country. These models will be included in a new version of the paper.

Moreover, our analysis can be done in the case of a national country study. For instance, it might be important to allow for dynamic interaction between U.S. …nancial variables and other types of U.S. variables in the FAVARs.

Conclusion

In this paper we have focused on international transmission of shocks across housing markets around the world, in order to detect and measure contagion e¤ects during the subprime crisis.

We have characterized contagion as a pandemic process: it happens once a local shock originating from a national market spread out to other OECD markets.

We follow [START_REF] Bernanke | Measuring the E¤ects of Monetary Policy: a Factor Augmented Vector Autoregressive (FAVAR) Approach[END_REF] and use a two-step FAVAR approach by introducing a Bayesian framework.

First, constrained factors are extracted from a large database including housing prices and other economic indicators (GDP, consumption, investment, interest rates and stock index returns) for a panel of 17 countries observed over the period 1980:Q1-2006:Q2. The extracted factors are iden-ti…ed as world, country-speci…c and variable-type speci…c factors. They are orthogonal and estimated using Bayesian estimation methods.

Second, we have estimated FAVAR models for two speci…c shocks: 1) A U.S. housing price shock and 2) A U.S. short interest rate shock. These FAVAR models include both observed economic variables as well as unobserved factors chosen among the factors extracted in the …rst step.

We have shown that contagion can be observed: 1/ as local housing price shock originating from America is proved to a¤ect the international common factors, which in turn impact signi…cantly other local or international variables, according to a pandemic mechanism.

In addition, there are spillovers to the rest of the economy as the world factor and the real activity one are a¤ected as well.

2/ due to the FED's monetary policy. More particularly, we have examined whether the sharp increase in the interest rates decided by the FED after the low interest rates that were o¤ered during 2003 and 2004 may have been the local shock starting the so-called subprime mortgage crisis, which has involved the generalized troubles observed in many housing markets, notably, USA, U.K and Spain and also stock markets and have more recently a¤ected the activity of so many countries.

Our results show that the interest rate shock appears to play an important role in the spillover mechanism from the United States to the rest of the world.

Our main …ndings suggest that di¤erences exist in the contagion e¤ects. This implies that no generalizations can be made for OECD countries even for one of equal economic size and in the same geographic region.

We …nd that a large portion of the variance of OECD variables is explained by the common factors. This suggests that American shocks, which are able to impact the common factors, will be transmitted to some, but not all OECD countries. More precisely, Australia, the United Kingdom and Scandinavian countries appear to be most sensitive to global shocks. However, even though global developments play an important role in most OECD economies, a large part of the variance is still idiosyncratic. Besides, the con…dence bands for the housing factor are not tight enough. It may indicate that it may be necessary to consider several house price factors, because the dynamics of countries housing markets are not highly synchronized.

In our future work, we will formally compare models containing more than one housing factor with models without housing factor and then redecide. We will follow Ng and Moench (2011) by using a hierarchical factor analysis of the OECD housing markets dynamics. Also, as a furthur research, we propose to compare and distinguish our results using a plain vanilla FAVAR approach .

2 0 0 0 Q 3 2 0 0 1 Q 2 2 0 0 2 Q 1 2 0 0 2 Q 4 2 0 0 3 Q 3 2 0 0 4 Q 2 2 0 0 5 Q 1 2 0 0 5 Q 4

  previous authors like Stock and Watson (2005) and Bernanke and al. (2005), we trace the factors and study the precision with which the factors where extracted.

See for example,[START_REF] Bai | Inferential Theory for Factor Models of Large Dimensions[END_REF],[START_REF] Stock | Understanding Changes in International Business Cycle Dynamics[END_REF]

2005) and Bernanke and al. (2005).

See Eickmeier (2007) for instance.

See Tanner and Wong (1987) for more details on missing data problems.

For more details concerning the implemented algorithm, see Otrok and Whiteman (1998).

Cf. Stock and Watson (2005) and Bernanke and al. (2005).

Treating these global variables as endogenous will be less realistic when a small economy, e.g. Ireland, is considered.


Marc Joëts
email: marc.joets@u-paris10.fr

Energy price transmissions during extreme movements

Keywords: JEL Classi…cation: C32, Q40 Forward energy prices, Value-at-Risk (VaR), CAViaR approach, risk spillover, Granger causality

This paper investigates price transmissions across European energy forward markets at distinct maturities during both normal times and extreme ‡uctuation periods. To this end, we rely on the traditional Granger causality test (in mean) and its multivariate extension in tail distribution developped by Candelon, Joëts, and Tokpavi (2012). Considering forward energy prices at 1, 10, 20, and 30 months, it turns out that no signi…cant causality exists between markets at regular times whereas comovements are at play during extreme periods especially in bear markets. More precisely, energy prices comovements appear to be stronger at short horizons than at long horizons, testifying an eventual Samuelson mechanism in the maturity prices curve. Diversi…cation strategies tend to be more e¢ cient as maturity increases.

Introduction

Energy price dynamics are known to be frequently volatile with extensive amplitude a¤ecting the whole economy [START_REF] Sadorsky | Oil Price Shocks and Stock Market Activity[END_REF], [START_REF] Hamilton | What Is an Oil Shock?[END_REF], [START_REF] Kilian | A Comparison of the E¤ects of Exogenous Oil Supply Shocks on Output and In ‡ation in the G7 Countries[END_REF], among others). In the literature, these ‡uctuations are attributed to both real and …nancial factors, such as international energy demand/supply conditions and market manipulation [START_REF] Hamilton | Causes and Consequences of the Oil Shock of 2007-08[END_REF], [START_REF] Kaufmann | Oil prices, speculation, and fundamentals: Interpreting causal relations among spot and futures prices[END_REF], [START_REF] Kilian | Comment causes and consequences of the oil shock of 2007-2008[END_REF], [START_REF] Cifarelli | Oil price dynamics and speculation: A multivariate …nancial approach[END_REF], [START_REF] Zwinkels | Oil price dynamics: A behavioral …nance approach with heterogeneous agents[END_REF], [START_REF] Lombardi | Do …nancial investors destabilize the oil price?[END_REF], among others), leading to extreme market risks for energy participants and governments. Moreover, energy markets have recently experienced signi…cant developments likely to in ‡uence price dynamics. European gas and electicity markets, initially monopolistic, have become competitive due to the freshly deregulation process, allowing emergence of new contracts making prices more in ‡uenced by participants than regulators [START_REF] Mjelde | Market integration among electricity markets and their major fuel source markets[END_REF]). In this light, market volatility may increase and the quanti…cation of the maximum prices appears to be primordial in risk management for one's ability to make proper investment, operational, and contractual decisions. Due to the globalization process, economies are related each other notably through trade and investment, so any news about economic fundamentals in one country most likely have implications in other countries [START_REF] Lin | Do Bulls and Bears Move Across Borders? International Transmission of Stock Returns and Volatility[END_REF], [START_REF] Ding | Asymmetric correlations in equity returns: a fundamental-based explanation[END_REF], among others). From a general viewpoint, this perspective may obviously be extended to energy market behaviors which are known to be interrelated through production, substitution and competitive processes. Indeed, several studies have validated the fact that oil, gas, coal and electricity prices may be interconnected on the long run [START_REF] Bachmeier | Testing for Market Integration: Crude Oil, Coal, and Natural Gas[END_REF], [START_REF] Mjelde | Market integration among electricity markets and their major fuel source markets[END_REF], [START_REF] Mohammadi | Electricity prices and fuel costs: Long-run relations and short-run dynamics[END_REF], [START_REF] Ma | The integration of major fuel sources markets in China: Evidence from panel cointegration tests[END_REF], and [START_REF] Joëts | On the link between forward energy prices: A nonlinear panel cointegration approach[END_REF], among others). However, previous analyses mainly focus on "regular" time ‡uctuations without considering periods of extreme price movements (upward and downard) whereas energy prices are often characterized by intense dynamics. The general feeling along this way is that correlations between assets tend to be stronger during excessive ‡uctuations periods. This phenomenon, which has been largely studied in the …nancial literature1 suggests that comovements are larger when we focus on large absolute-value returns, and seem more important in bear markets. Under this market-comovement scenario, price movements are driven by fads and a herd behavior may be transmittable across markets (in the sense of [START_REF] Black | Noise[END_REF] and [START_REF] Delong | Noise traders Risk in Financial Markets[END_REF]). High volatility is therefore coupled with highly interrelated markets making diversi…cation almost im-possible under uncertain movements. These comovements in absolute price changes are often associated with belief dispersion [START_REF] Shalen | volatility, and the dispersion of beliefs[END_REF]) resulting in a lack of con…dence in market fundamentals. When new information occurs, distinct prior beliefs give incitation to trade leading to price changes. When traders revise their prior beliefs according to new information, it takes time for the market to "resolve" these heterogeneous behaviors which contribute to volatility clustering [START_REF] Shalen | volatility, and the dispersion of beliefs[END_REF] and [START_REF] Lin | Do Bulls and Bears Move Across Borders? International Transmission of Stock Returns and Volatility[END_REF] among others). Thus, the diversi…cation strategy aiming at limiting the impact of excessive movements would be almost impossible because of the markets integration, whereas it has more sense in "regular" times. As periods of extreme high energy prices have been proved to be economically detrimental [START_REF] Sadorsky | Oil Price Shocks and Stock Market Activity[END_REF], [START_REF] Oberndorfer | Energy prices, volatility, and the stock market: Evidence from the Eurozone[END_REF], among others), this paper proposes to extend this issue by analysing energy price comovements during periods of erratic ‡uctuations. This phenomenon would have important macroeconomic and microeconomic implications since absence of diversi…cation can lead to heavy potential losses for market participants and governements. For instance, from a macroeconomic viewpoint, a perfect perception of price movements and market risk are of primary importance for policy targeting of energy-importing or exporting countries. At a microeconomic level, the price behavior, market risk and their potential transmission mechanisms are relevant to evaluating real investment decisions using the well-known asset pricing model.

In order to apprehend extreme movements, the Value-at-Risk (VaR) approach is an important tool and is widely used in …nancial markets. 2 VaR is often used to measure market risk with a single numeric value by means of the probability distribution of a random variable. It is de…ned as the expected maximum loss over a target horizon for a given con…dence interval (see Jorion (2007)). Due to the strong volatility of commodity markets, this methodology has been recently extended to oil markets-see, [START_REF] Cadebo | Estimating oil price 'Value at Risk'using the historical simulation approach[END_REF], [START_REF] Giot | Market risk in commodity markets: a VaR approach[END_REF], [START_REF] Feng | To compute the oil market value at risk by applying semi-parametric approach[END_REF], [START_REF] Sadeghi | Energy risk management and value at risk modeling[END_REF][START_REF] Sadeghi | Energy risk management and value at risk modeling[END_REF][START_REF] Fan | Estimating 'Value at Risk' of crude oil price and its spillover e¤ect using the GED-GARCH approach[END_REF]-and to the oil and gas markets-see, Aloui and Mabrouk (2006)-which evaluate the risk losses in WTI, Brent crude oil and gas markets using di¤erent techniques (Historical simulation standard approach, RiskMetrics (RM), variance-covariance method based on various GARCH models, among others). However, these methodologies are quite restrictive because they are based on several strong assumptions. For instance, the nonparametric Historical simulation approach is based on a time-constant returns unconditional distribution and fractile. The parametric RM approach is based on the linear risk and the normality of price changes, which is not consistent with the market reality. Finally, GARCH methodologies su¤er from the positivity and/or symmetry constraints of-ten imposed on the coe¢ cient parameters. We improve this literature by considering extreme movements (upward and downward) of European oil, gas, coal and electricity markets using the semiparametric Conditional Autoregressive VaR (CAViaR) approach developed by [START_REF] Engle | CAViaR: Conditional autoregressive Value at Risk by regression quantile[END_REF], which is considered to be less restrictive than other methodologies. 3Despite the apparent market globalization, transmission e¤ects among energy markets during extensive periods have been scarcely studied. [START_REF] Lin | Spillover e¤ects in energy futures markets[END_REF] …rst studied spillover e¤ects among NYMEX and IPE crude oil contracts in both non-overlapping and simultaneous trading hours, and found signi…cant transmission mechanism. However, they do not use the crucial information about the quantile of the distribution, which is of primary importance to apprehend tremendous variations. 4 More recently, [START_REF] Fan | Estimating 'Value at Risk' of crude oil price and its spillover e¤ect using the GED-GARCH approach[END_REF] evaluate the market risk of daily Brent and WTI crude oil returns from May 20th, 1987 to August 1st, 2006 using a GED-GARCH model. They examine the downside and upside extreme risk spillover between both markets using the Granger causality test developed by [START_REF] Hong | Granger Causality in Risk and Detection of Extreme Risk Spillover between Financial Markets[END_REF]. Results show that the VaR model based on GED method perform relatively well, and that the WTI and Brent returns have signi…cant two-way causality e¤ect in both downside and upside risks at 95% or 99% con…dence levels. Further analysis reveals that at the con…dence level of 99%, the WTI market risk information can help to forecast extreme Brent market risk when negative news occur, but the reverse e¤ect does not exist. However, their results are based on a restrictive parametric GARCH approach which is again not consistent with market reality, and authors investigate risk spillover at speci…c con…dence level (95% and 99%) while the information in tails distribution is of primary importance. 5 To overcome this problem, Candelon, Joëts and Tokpavi (2012) (hereafter CJT) develop a multivariate extension of the Granger causality test in distribution tails and use this speci…cation to investigate international market globalization during periods of extreme price movements of 32 crude oil weekly prices on the period from April 21, 2000to October 20, 2011. In this paper, our aim is to investigate energy price return transmissions during both "normal" and extreme ‡uctuations periods by using the traditional Granger causality test (in mean) and its multivariate CJT extension the later focusing on causality in distribution tails rather than quantile at speci…c level. Relying on European forward energy prices rather than spot data, we purge short-run demand and supply from noise that a¤ects market ‡uctuations and account for both fundamental and speculative pres-sures [START_REF] Joëts | On the link between forward energy prices: A nonlinear panel cointegration approach[END_REF]). 6 Because comovements between markets can vary considerably over time and in order to see if diversi…cation can be more pro…table as maturity increases, we propose to investigate forward price transmission mechanims at 1, 10, 20, and 30 months.

We …nd that energy price return relationships increase during periods of extreme movements, especially in bear markets circumstances. Indeed, while almost no causality exists during "normal" times, price comovements are higher during market downturns as compared to upturns. This phenomenon leads to asymmetric interactions in energy price returns, showing that energy markets behave as stock markets making diversi…cation almost impossible during high volatility periods. However, this phenomenon tends to disappear as maturity increases, indicating that diversi…cation could be more pro…table at longer horizons (such as 20 and 30 months).

The rest of the paper is organized as follows. Section 2 describes the econometric methodology. The empirical part is provided in Section 3, and Section 4 concludes the article.

2 Model speci…cation and extreme risk causality test

CAViaR model

Energy price returns are known to be extremely volatile with clustering phenomenon. These characteristics were well modelled by [START_REF] Engle | Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom In ‡ation[END_REF] and [START_REF] Bollerslev | Generalized autoregressive conditional heteroskedacticity[END_REF] using ARCH and GARCH models. These models have become common tools to measure market risk by VaR approach due to their relative simplicity and various extensions. However, they are also well known for their limitations such as unrealistic parametric assumptions (normality or i.i.d returns). To overcome these issues, we rely on the semiparametric CAViaR approach developed by [START_REF] Engle | CAViaR: Conditional autoregressive Value at Risk by regression quantile[END_REF] to estimate energy VaR models which does not require any of the extreme assumptions invoked by existing methodologies. In short, this approach has the particularity to estimate directly VaRs using an autoregressive speci…cation for the quantiles rather than inverting a conditonal distribution of returns as usual in a purely parametric framework. This autoregressive evolution of the quantile over time and unknown parameters are then determined by the regression quantile framework introduced by [START_REF] Koenker | Regression quantiles[END_REF]. Beside, the autoregressive nature of the CAViaR captures directly in the tails of the distribution some stylized facts in empirical …nance, such as autocorrelation in daily returns arising from market microstructure biases and partial price adjustment [START_REF] Boudoukh | A Tale of Three Schools: Insights on Autocorrelations of Short-Horizon Returns[END_REF], [START_REF] Eom | Partial Price Adjustment and Autocorrelation in Foreign Exchange Markets[END_REF] [START_REF] Ahn | Partial Adjustment or Stale Prices? Implications from Stock Index and Futures Return Autocorrelations[END_REF]), volatility clustering [START_REF] Engle | Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom In ‡ation[END_REF] and [START_REF] Bollerslev | Generalized autoregressive conditional heteroskedacticity[END_REF]), and the time-varying skewness and kurtosis [START_REF] Hansen | Autoregressive Conditional Density Estimation[END_REF], Harvey andSiddique (1999, 2000), [START_REF] Jondeau | Testing for Di¤erences in the Tails of the Stock-Market Returns[END_REF]).

Following [START_REF] Engle | CAViaR: Conditional autoregressive Value at Risk by regression quantile[END_REF], we consider a vector of portfolio returns fy t g T t=1 . Let , x t and be respectively, the probability associated to VaR, a vector of observable variables at time t, and a vector of unknown parameters. Let also f t ( ) f (x t 1 ; ) ; the -quantile of the distribution of the portfolio returns at time t formed at time t 1. In this context, a general CAViaR speci…cation might be as follows:

f t ( ) = 0 + q X i=1 i f t i ( ) + p X i=1 i l (x t i ; ') (1)
where 0 = ( 0 ; 0 ; ' 0 ) and l the function of a …nite number of lagged values of observable variables. To allow a smooth transition quantile, Engle and Manganelli introduce an autoregressive term i f t i ( ), i = 1; :::; q. Moreover, to permit a relationship between the -quantile f t ( ) and the observable variables they introduce the term l (x t i ; '). According to the general CAViaR formulation, [START_REF] Engle | CAViaR: Conditional autoregressive Value at Risk by regression quantile[END_REF] develop the four following alternative speci…cations for the function l.

Adaptative :

f t ( 1 ) = f t 1 ( 1 ) + 1 n [1 + exp (G [y t 1 f t 1 ( 1 )])] 1 o Symmetric Absolute V alue : f t ( ) = 1 + 2 f t 1 ( ) + 3 jy t 1 j Asymmetric Slope : f t ( ) = 1 + 2 f t 1 ( ) + 3 (y t 1 ) + + 4 (y t 1 ) Indirect GARCH (1; 1) : f t ( ) = 1 + 2 f 2 t 1 ( ) + 3 y 3 t 1 1=2
In the …rst speci…cation, G is some positive …nite number which as G ! 1, the last term converges to 1 [I (y t 1 f t 1 ( 1 )) ], where I(:) is the indicator function. Following Engle and Manganelli, the Adaptative speci…cation allows that whenever you exceed your VaR you should direclty increase it, but when you don't exceed it, you should decrease it very slightly. The second and fourth respond symmetrically to past portfolio returns and are mean reverting since the coe¢ cient of the lagged VaR is not constrained to equal one. The third model is also mean reverting but less restrictive in the sense that it permits asymmetric response to positive and negative past portfolio returns.7 Therefore, the asymmetric component adresses the asymmetric response of volatility to news (Black (1976), Christie (1982)). Due to the skewness and kurtosis properties of …nancial series, the asymmetric CAViaR speci…cation has become the most popular for practitioners.

CJT risk causality test

In parallel to risk measurement, a new concept of risk causality has recently emerged in line with Granger seminal work. This new approach focuses on tail causality rather than causality in mean and variance, and allows to study extreme risk spillover across markets. [START_REF] Hong | Granger Causality in Risk and Detection of Extreme Risk Spillover between Financial Markets[END_REF] were the …rst to propose a class of kernel-based tests to check whether a large downside risk in one market will Granger cause a large downside risk in another market. In their Granger causality approach, they consider risk transmission of two time series at a given quantile level which is relatively restrictive because they do not consider causality between tails behavior. According to [START_REF] Engle | CAViaR: Conditional autoregressive Value at Risk by regression quantile[END_REF], dynamics of VaRs can vary considerably across risk level. Hence, application of the [START_REF] Hong | Granger Causality in Risk and Detection of Extreme Risk Spillover between Financial Markets[END_REF] test can lead to contradictory results with respect to the risk levels. To overcome these constraints and improve the power properties of the Granger cause approach, we use the multivariate CJT test which extends this setup by testing simultaneous Granger causality in downside risk for multiple risk levels across left tails distribution. More formerly, our testing procedure is an extension in multivariate context of the Granger causality test in mean and contains all tail distribution information. The purpose of the test is to make inference on interactions between groups of variables. Let A = f 1 ; :::; m g be a discrete set of m risk levels which is relevant for downside risk study. Let W i;t ( i;A ) = [Z i;t ( i; 1 ) ; :::; Z i;t ( i; m )] the vector of tail-events variables Z i;t ( i; 1 ) of dimension (m; 1) associated to the risk levels at time t. i;A = 0 i; 1 ; :::; 0 i; m 0 is the vector of dimension (4m; 1)

with parameters of the m CAViaR. Therefore, the multivariate Granger causality test can be stated as follows

H 0 : E [W 1;t ( 1;A ) j t 1 ] = E [W 1;t ( 1;A ) j 1;t 1 ] (2)
where 1;t and t are respectively de…ned by 1;t = fW 1;s ( 1;A ) ; s tg and t = n W 0 1;s ( 1;A ) ; W 0 2;s ( 2;A ) 0 ; s t o . If the null hypothesis holds, downside movements do not Granger cause spillover e¤ect whatever the risk levels k considered (with k = 1; :::; m). This test can be interpreted as the Granger causality in mean approach for two multivariate process W i;t ( i;A ), i = 1; 2. According to [START_REF] Gelper | Multivariate out-of-sample tests for Granger causality[END_REF] and Barret et al. (2010), the CJT test statistic is based on the following multivariate linear regression model W 1;t ( 1;A ) = 0 + 1 W 2;t 1 ( 2;A ) + :::

+ p W 2;t 1 ( 2;A ) + " 1t (3)
where 0 and s are respectively vectors of constant terms and matrices of parameters, " 1t is the residual vector with covariance matrix 1 . Following (3), the null hypothesis can be expressed as follows

H 0 : 1 = 2 = ::: = p (4)
As a result, the multivariate likelihood ratio test statistic is de…ned by ( 5) which followed under the null hypothesis a chi-squared distribution with pm 2 degrees of freedom

LR = [T (mp + 1)] log " 0 2 " 2 log " 0 1 " 1 2 pm 2
(5)

Following [START_REF] Candelon | Testing for crude oil markets globalization during extreme price movements[END_REF], the above approach is not computationally feasible because the multivariate process depends on unknown vector of CAViaR models. However, these vectors can be replaced by consistent estimator ^ i;A . But in turn, the values of the vector are incertain because they are estimated rather than oberved. This parameter uncertainty could a¤ect the distribution of the test statistic. 8 To overcome this constraint, [START_REF] Candelon | Testing for crude oil markets globalization during extreme price movements[END_REF] suggest to perform Monte Carlo tests by generating M independent realizations of the test statistic. As shown by [START_REF] Dufour | Monte Carlo Tests with Nuisance Parameters: a General Approach to Finite Sample Inference and Nonstandard Asymptotics[END_REF], the Monte Carlo critical region corresponds to pM (S 0 )

with 1 the con…dence level.

pM (S 0 ) = M ĜM (S 0 ) + 1 M + 1 ; (6) where ĜM (S 0 ) = 1 M M X i=1 I (S i S 0 ) ; (7)
when Pr (S i = S j ) 6 = 0, or otherwise

ĜM (S 0 ) = 1 1 M M X i=1 I (S i S 0 ) + 1 M M X i=1 I (S i = S 0 ) I (U i U 0 ) (8)
We use the later speci…cation to investigate transmission mechanisms among energy forward prices of oil, gas, coal and electricity at di¤erent maturities during periods of extreme movements.

3 Empirical analysis

Risk measurement

We consider daily data over the January 3, 2005 to December 31, 2010 period. In order to allow for both fundamental and speculative pressures, we rely on European forward price returns at 1, 10, 20, 30 months for oil, gas, coal and electricity markets.9 Energy prices are quoted in US dollars per tonne of oil equivalent ($/toe) and are extracted from the Platt's Information Energy Agency. Figure 1 in Appendix depicts the one month forward returns (de…ned as prices in …rst log di¤erence) in the whole sample and reveals the volatility clustering of energy markets. 10 , 11 Basic descriptive statistics for prices at 1 month are computed and reported in Table 1. They reveal that each return series, compared to the standard normal distribution, are asymmetric (oil, gas and electricity returns are right skewed while coal returns are left skewed) and leptokurtic, revealing fat tail distributions. Due to the speci…c nature of its market (i.e. non-storablility, inelasticity of the supply,...) electricity returns are frequently a¤ected by regime switching causing tail behavior higher than fossil energies (1.7 and 25 for skewness and kurtosis respectively).

The energy returns seem to behave as strongly volatile …nancial assets. The …nancial properties of forward energy markets lead us to use an asymmetric CAViaR speci…cation to model energy VaRs. From Table 2 to Table 5 in Appendix, estimations and backtesting for each return series (at 1 month) are reported at 1%, 5% and 10% quantile levels for both downside and upside risks. Results con…rm the asymmetric behavior of each market for both downside and upside risks ( (2) and (3) are signi…cant for all series). This asymmetric component appears between bullish and bearish markets and between left and right tails, which reveals that energy price behaviors are di¤erent depending on the mood of the market. Generally, for fossil energies, negative returns are predominant in downside risk while positive returns are higher in upside one. Moreover, left tail behavior (downside risk) seems to be higher than right tail dynamic (upside risk). For electricity returns, relying to CAViaR estimation, asymmetric dynamic seems to be less pronounced. It may come from a misspeci…ed risk model. Indeed, the dynamic quantile (DQ) test is applied to check the adequacy of the VaRs estimation, and results show that our models are well speci…ed for energy fossil only. The misspeci…cation of electricity VaR model may be due to the high occurrence of extreme values and potential regime switching. In our analysis, the misspeci…ed problem is not a constraint because risk apprehension is more widely a¤ected by parameter incertainty. Risk estimation is therefore strongly in ‡uenced by model assumptions and parameterizations. In our Granger causality context, CJT approach deals with this issue by using Monte Carlo procedure to compute p-values of test. In this way, p-values are simulated and the misspeci…ed parameters of electricity VaR model are corrected. The statistics are computed over the period 2005-01-04 : 2010-12-30.

Energy price transmission

Using Granger causality approach, we propose to investigate transmission mechanisms between energy price returns during both regular times and extreme volatility periods.

Table 6 in Appendix reports results of Granger causality in mean, to investigate energy price interactions at 1 month during normal times. It re-veals that, except for oil and coal prices, no short-run causalities exist across energy markets con…rming the results in favor of long-run interactions rather than short-term comovements. The same result (not reported here) is also observable for prices at 10, 20, and 30 months. Considering extreme occurrences, Table 7 gathers Granger causality test in tails distribution for prices at 1 month through CJT approach. It shows that comovements are higher between markets during periods of price decrease, while during situations of price increase no signi…cant causalities exist. These relations appear to be relevant mainly across fossil energies. Energy prices at 1 month behave as stock returns which are characterized by asymmetric causalities between downturn and upturn situations making diversi…cation almost impossible during extreme volatility periods.

According to [START_REF] Ding | Asymmetric correlations in equity returns: a fundamental-based explanation[END_REF] for …nancial markets, this asymmetric phenomenon could be attributed to several fundamental and speculative factors. For instance, a popular incidence documented by many studies [START_REF] Kim | Pricing stock market volatility: does it matter whether the volatility is related to the business cycle?[END_REF]Campbell and Diebold, 2009, among others) is that when economy experiences negative shock, the volatility of fundamental variables is usually higher and accompanied by an increase of fundamental risk. Moreover, [START_REF] Campbell | No news is good news: an asymmetric model of changing volatility in stock returns[END_REF] …nd that during extreme price movements, market downturn is more likely associated with high market risk. This …nding is consistent with our results on energy market behaviors.

Furthermore, [START_REF] Demirer | Firm-level return dispersion and correlation asymmetry: challenges for portfolio diversi…cation[END_REF] …nd that during periods of extreme prices decrease, individual …rm returns tend to comove more closely causing stronger transmission mechanism between companies. It is therefore reasonable to think that such behaviors also exist across energy industries.

The energy market causality dynamics could also be explained by various behavioral considerations. Indeed, there is evidence that investors react more sensitively to bad news than good news. According to [START_REF] Barberis | A model of investor sentiment[END_REF], following a string of positive shocks, the investors expect that the trend will continue in the same way (i.e. they expect another positive shock). If good news is announced, the positive shock is largely anticipated and the market response appears to be relatively small. However, negative shocks impact returns signi…canlty since bad news appears more as a surprise. In the same context, the popular prospect theory of [START_REF] Kahneman | Prospect Theory: An analysis of decision under risk[END_REF] shows that investors react di¤erently to market circumstances due to the notion of loss aversion. They are more hesitant to sell in overvaluation than to buy in undervaluation (they are more sensitive to undervaluation) causing asymmetric dynamics between bearish and bullish markets. Another possible explanation could be relative to the emotion component of energy markets. Recent researches have found that feelings can have significant impact on equity returns under uncertain and risky environment even if emotions are unrelated to the decision context. 12 According to Forgas (1995), feelings will become predominant as risk and uncertainty increase. Considering that market risk increases during downturn periods, investors should be more in ‡uenced by their emotions during extreme prices decrease. In this context, Joëts (2012) con…rms that energy market dynamics tend to be more in ‡uenced by emotions when extreme bearish market movements occur. This phenomenon is likely to cause asymmetric causality behaviors making diversi…cation almost impossible.

Maturity e¤ect

While energy forward prices at 1 month appear to be characterized by an asymmetric comovement with a downturn predominence, energy markets dynamic seems to be di¤erent as maturities increase. Considering comovements during extreme ‡uctuations, Table 8 to Table 10 gather CJT Granger causality tests for energy forward prices at 10, 20, 30 months respectively. 13 They show that causality between markets varies strongly over time. Indeed, compared to the 1 month prices maturity, energy market interactions seem to be less pronounced as maturity increases. For instance, asymmetric downturn causality remains signi…cant for energy prices at 10 months, while this dynamic fades strongly at 20 and 30 months making diversi…cation more pro…table at longer maturities. This phenomenon could be attributable to the well known Samuelson e¤ect which reveals an eventual prices maturity segmentation across energy markets. This e¤ect would tend to in ‡uence the volatility of the series across maturity leading to a decrease of comovements between energy markets.

Conclusion

This paper investigates energy transmission mechanisms across forward price returns of oil, gas, coal, and electricity during both normal and extreme volatility periods. Using Granger causality approach in mean as well as in tails distribution, we show that energy price comovements increase during extreme ‡uctuations, while they are almost nonexistent in regular times. More precisely, energy market causalities appear to be stronger during bear markets, indicating a possible relation between volatility and comovements at shorter maturities. The phenomenon could be attributed to several fundamental and speculative factors, showing that energy markets behave as et al. (2000), [START_REF] Kamstra | Winter blues: a SAD stock market cycle[END_REF], and Dowling andLucey (2005, 2008), among others.

1 3 Granger causality tests in mean (normal times) are also computed showing no significant energy price relationship (results available upon request to the author). …nancial assets. Regarding portfolio diversi…cation, unstable asset relationships might lead energy risk managers to exaggerate the bene…ts of diver-si…cation during extreme downturn variations making suboptimal portfolio allocations. However, probably due to a Samuelson e¤ect, energy markets comovements vary from shorter to longer maturity and seem to be fading as maturity increases. This maturity e¤ect shows that, contrary to short maturity, diversi…cation could be more pro…table at longer ones.

One month forward daily returns of gas

  -values for corresponding null hypotheses are reported in parentheses.

Figure 1 :

 1 Figure 1: One month forward energy returns (prices in …rst log di¤erence)

Table 1 :

 1 Summary statistics for the daily forward energy returns at 1 month

		Brent	Gas	Coal	Electricity
	Mean	0:00053 0:00017	0:00038	0:00062
	Variance	0:00053 0:00035	0:00033	0:00088
	Skewness	0:13679 0:00327	0:57407	1:76840
	Kurtosis	8:97939 6:47279	9:93896	25:31240
	Jarque-Bera test 2333:29

See[START_REF] King | Transmission of volatility between Stock Markets[END_REF],[START_REF] Lin | Do Bulls and Bears Move Across Borders? International Transmission of Stock Returns and Volatility[END_REF],[START_REF] Longin | Is the correlation in international equity returns constant: 1960-1990?[END_REF],Karolyi and Stulz (1996),[START_REF] Longin | Extreme correlation of international equity markets[END_REF],[START_REF] Ramchand | Volatility and Cross Correlation in Global Equity Markets[END_REF],[START_REF] Ang | International asset allocation with regime shifts[END_REF],[START_REF] Hong | Asymmetries in stock returns: statistical tests and economic evaluations[END_REF],Amira et al. (2009), and[START_REF] Ding | Asymmetric correlations in equity returns: a fundamental-based explanation[END_REF] to name few.

One of the main advantage of VaR cited in literature is its user friendly way to concisely presents risk supported by the regulatory authorities.

See Section 3.

According to[START_REF] Gouriéroux | Local Likelihood Density Estimation and Value at Risk[END_REF], volatility cannot be considered as a statisfactory measure of risk when extreme market movements occur.

 5 According to[START_REF] Engle | CAViaR: Conditional autoregressive Value at Risk by regression quantile[END_REF], dynamics of VaRs can vary considerably across risk levels.

Indeed, the forward energy markets can result in both physical delivery and speculative purposes.

(y) + = max(y; 0); (y) = min(y; 0):

For more details, see[START_REF] Candelon | Testing for crude oil markets globalization during extreme price movements[END_REF].

Due to space constraints, we only report results corresponding to 1 month. The results for the other maturities are similar and are available upon request to the author.1 0 The volatility clustering is e¤ective when strong ‡uctuations (resp. low) are followed by strong (resp. low) perturbations.1 1 Energy forward prices at

10, 20, and 30 month (not reported here) are characterized by the same clustering property.

2 See[START_REF] Saunders | Stock prices and wall street weather[END_REF],[START_REF] Hirshleifer | Good day sunshine: Stock returns and the weather[END_REF],[START_REF] Cao | Stock market returns: A temperature anomaly[END_REF], Kamstra

Appendix