Camille Cornand
email: cornand@cournot.u-strasbg.fr.

Céline Gimet
email: gimet@gate.cnrs.fr.

The 2007-2008 financial crisis: Is there evidence of disaster myopia?

Keywords: JEL Classification: G01, G21, C23 disaster myopia, financial crisis, banks, risk taking dynamics, GMM. I

The disaster myopia hypothesis is a theoretical argument that may explain why crises are a recurrent event. Under very optimistic circumstances, investors disregard any relevant information concerning the increasing degree of risk. Agents' propensity to underestimate the probability of adverse outcomes from the distant past increases the longer the period since that event occurred and at some point the subjective probability attached to this event reaches zero. This risky behaviour may contribute to the formation of a bubble that bursts into a crisis. This paper tests whether there is evidence of disaster myopia during the recent episode of financial crisis in the banking sector. Its contribution is twofold. First, it shows that the 2007 financial crisis exhibits disaster myopia in the banking sector. And second, it identifies macro and specific determinant variables in banks' risk taking since the beginning of the years 2000.

Introduction

The disaster myopia hypothesis has been introduced by [START_REF] Guttentag | Disaster Myopia in International Banking[END_REF] to explain why crises are a recurrent event. Under very optimistic circumstances, investors disregard any relevant information concerning the increasing degree of risk. Agents' propensity to underestimate the probability of adverse outcomes from the distant past increases the longer the period since that event occurred and at some point the subjective probability attached to this event reaches zero. This paper tests whether there is evidence of disaster myopia during the recent episode of financial crisis in the banking sector.

The financial crisis of 2007 is generally attributed to a number of factors associated with the housing and credit markets. Macroeconomic factors such as monetary policy, international trade imbalances, and the lack of government regulation are as well considered to have played a role in the crisis. Without denying the effects of the aforementioned factors, this paper suggests that current financial crisis also has its roots in the disaster myopia of market participants and especially banks.

Disaster myopia has been used to explain the LDC debt crisis, the US savings and loans debacle and various commercial property crises. 1 Although [START_REF] Haldane | Why Banks Failed the Stress Test[END_REF] and [START_REF] Herring | Comment on Franke & Krahnen: The Future of Securitization[END_REF] interpret the recent financial crisis as a consequence of disaster myopia and argue that disaster myopia has been one of its predominating factors, there is no empirical test of this hypothesis. In this paper, we precisely empirically test whether the 2007 illiquidity shock can be considered as a myopiainduced disaster by analyzing the (decreasing) risk perception of banks over the period preceding the occurrence of the crisis.

To measure disaster myopia, we focus on risk taking dynamics. Bank risk-taking may be measured by several manners in the literature. First, as in [START_REF] Saunders | Ownership Structure, Deregulation, and Bank Risk Taking[END_REF], [START_REF] Esty | The Impact of Contingent Liability on Commercial Bank Risk Taking[END_REF], and [START_REF] Grossman | Contingent Capital and Bank Risk-Taking: Evidence from British Equity Markets before World War I[END_REF], among others, one can use the volatility of share prices (this corresponds to computing the standard deviation of monthly changes in share prices for a given year for each bank, which is matched up with annual data on bank liability characteristics).2 Three other measures of risk-taking from bank balance sheets are also used: the ratio of loans to total assets, the ratio of cash to total assets, and the rate of growth of assets. The assumption is that loans are riskier and less liquid-and that cash is less risky and more liquid-than other balance sheet assets, primarily securities. Banks with substantial contingent liabilities should have a smaller proportion of their assets in loans and a larger proportion of their assets in cash than limited liability banks if the risk-reducing incentive of contingent liability is strong. Risk-taking can also be measured by the rate at which a bank's assets expand in a given year under the theory that, all other things being equal, banks that engage in riskier activities will grow more rapidly than banks behaving in a more conservative manner [START_REF] Calomiris | Is Deposit Insurance Necessary? A Historical Perspective[END_REF][START_REF] Grossman | Double Liability and Bank Risk Taking[END_REF][START_REF] Grossman | Fear and Greed: The Evolution of Double Liability in American Banking, 1865-1930[END_REF].

In this paper, we consider the maturity mismatch in banks' balance sheets as an indicator of risk taking in the banking sector.3 Indeed, as [START_REF] Diamond | The credit crisis: conjectures about causes and remedies[END_REF][START_REF] Diamond | The credit crisis: conjectures about causes and remedies[END_REF]Fahri andTirole (2009, p. 2) suggest, the current crisis "is one of wide-scale maturity mismatch". More precisely, we look at the distortions in the maturities in banks' balance sheets by considering the share of liquid assets compared to long term liabilities. Maturity mismatches accepted by banks make them vulnerable to acute liquidity risk. We focus on the banking sector as this problem was even more acute because of the interaction between accounting rules and prudential norms (Basel II). During economic 1 For example, [START_REF] Guttentag | Disaster Myopia in International Banking[END_REF] and [START_REF] Herring | Credit risk and financial instability[END_REF]. slowdowns, default rates increase, asset prices decrease, which generates losses for banks that reduce their capital. Simultaneously because of prudential norms, the requirements for capital increase.

Therefore, as capital is reduced and the need for capital is increased, there necessarily is a contraction in credit offer.

In terms of methodology, we use a Generalized Method of Moments (GMM) model as the study of disaster myopia refers to a dynamic process. Indeed, we study to what extent the lagged values of the risk taking variables influence the current value of this variable. The GMM shows first that risk taking in period t is influenced by risk taking in period t-1 at least, and second that there is a set of variables -specific to the banking sector as the size, profitability, vulnerability, but also to the economic and financial environment-that determine risk taking. The main result of the paper is that the disaster myopia hypothesis is relevant to understand the current financial crisis. Regressions reinforces our results as they show that risk taking increases from the mid 2000's and as time goes on until the year 2007. We identify a break in 2007 and a decrease in risk taking in 2008 and 2009.

The article is organized as follows. The next section describes the considered conceptual framework of disaster myopia. Section III presents the data, the methodology used to test the theory and justifies the choice of variables. Section IV establishes test results. Section V discusses the policy implications of evidence of disaster myopia and section VI concludes.

II.

Conceptual framework: the disaster myopia hypothesis Guttentag and Herring 4 analyze the decision making process of investors under uncertainty. Disaster myopia is a situation in which agents tend to underestimate the probability of adverse outcomes. Such a behaviour is especially overriding for small probability events from a distant past. The authors use cognitive psychology5 to build their reasoning. According to this approach, economic agents base their decisions rules on rough heuristic or rules of thumb. The closest conceptual approach is that of [START_REF] Herring | Banking Disasters: Causes and Preventative Measures, Lessons Derived from the U.S. Experience[END_REF]; in this section, we present a simplified and slightly modified version of it. We first describe the context, before presenting the disaster myopia hypothesis and the institutional factors that may give rise to such a behavior. This framework enables us to state our tested hypotheses.

Uncertainty, objective and subjective risk probabilities

In an uncertain environment, individuals use subjective probabilities. A subjective probability is a personal judgment concerning the likelihood of the occurrence of a particular event. Individuals do not use precise computation but base their judgment on a reasonable assessment. A person's subjective probability of an event describes his/her degree of belief in the event. There is no formal calculation, but past experiences are very important to form these probabilities. At the opposite, objective probabilities estimate the occurrence of an event based on a recorded observation, rather than a subjective estimate.

On the one hand, the "availability heuristic" -which refers to the ease with which a decision maker can imagine that an event will occur-rests on the fact that the longer the period since an event occurred, the lower the subjective probability attached to it.

On the other hand, below a certain threshold, this subjective probability sets at zero. This is the "threshold heuristic": it exacerbates the bias toward the underestimation of shock probabilities.

More precisely, threshold heuristic is the rule of thumb by which decision markers devote scarce management time to analyze these probabilities.

Disaster myopia

The ease with which a decision maker can imagine that an event will occur rests on the fact that the longer the period since an event occurred, the lower the subjective probability attached to it (Figure 1). If the period without major shocks is sufficiently long, then subjective probabilities are validated over time and converge toward fully-rational objective probabilities. In such an environment, investors completely disregard information, they have a strong risk appetite since they believe that the probability that a major negative shock6 occur is near zero. We may enter a phase of 'risk indigestion' [START_REF] Allegret | Financial Crisis and Information[END_REF]: a crisis occurs and subjective probabilities start to be very high again, higher than the objective ones. As noted by Haldane (2009, p. 6), 'it is perhaps no coincidence that the last three truly systemic crises -October 1987, August 1998, and the credit crunch which commenced in 2007 -were roughly separated by a decade. Perhaps ten years is the threshold heuristic for risk managers'.

Institutional factors

According to [START_REF] Herring | Comment on Franke & Krahnen: The Future of Securitization[END_REF], institutional factors from the "Golden Decade" -the period referring to the years from 1998 to 2007-encouraged disaster myopia during the 2007-2008 financial crisis.

First, managerial accounting systems favour activities subject to low-frequency losses. Many risk management models developed within the private sector during the Golden Decade could have induced disaster myopia. According to [START_REF] Haldane | Why Banks Failed the Stress Test[END_REF], these models were often data hungry, improvements in data and IT technology feeding them with vast, high-frequency datasets, providing ample degrees of freedom for modellers, enabling them to devise risk frameworks which were very precisely calibrated in-sample. 'The sample in question was, with hindsight, most unusual from a macroeconomic perspective. The distribution of outcomes for both macroeconomic and financial variables during the Golden Decade differed very materially from historical distribution' (Haldane, 2009, p. 7).

Second, underestimation of risk has consequences for the risks facing both individual firms and for the system as a whole. For the system as a whole, one way of illustrating the consequences of underestimating risk is to translate it into "fair value" insurance premia. Haldane (2009, p. 9) illustrates risk under pricing on a dramatic scale: 'The degree of under-pricing of risk is large and is larger for options designed to protect against tail risks (lower strike prices). For at-the-money options on UK equities, the insurance premium would have been under-priced by around 45%; for options well out-of-the-money -say, 50% below equity prices at the time-the mis-pricing would have been nearer 90%'.

Among the other institutional factors mentioned by [START_REF] Herring | Comment on Franke & Krahnen: The Future of Securitization[END_REF], we can find: the recognition of fees upfront as income, the bonuses tied to current revenues, the high job mobility among risk takers, the intense competition in financial markets that drives out participants who are not disaster myopic and the appearance of high profitability attracting new entrants. For more details, see [START_REF] Herring | Bubbles in Real Estate Markets[END_REF] who already identified these institutional factors as a potential source of disaster myopia.

Hypotheses to be tested: disaster myopia in the banking sector

It is particularly relevant to identify bank's myopia not only because the banking sector was at the core of the recent financial disaster but also because exposures in this sector grow so large that they can jeopardize the financial system (for systemic risk analysis during the 2007 financial crisis, see for instance [START_REF] Bullard | Systemic Risk and the Financial Crisis: A Primer[END_REF]). Identifying and limiting the impact of the banking sector's disaster myopia is helpful to limit consequences for the system as a whole. So based on the former conceptual framework, we propose to test the following two hypotheses:

(i) the influence of the macroeconomic and financial context on the one hand and banking sector related financial variables on the other hand on banks' risk taking dynamics;

(ii) the existence of disaster myopia in the banking sector during the recent financial crisis.

III. Testing the disaster myopia hypothesis: the empirical model

This section presents the database constructed owing to Bankscope, IFS and OECD data. Our study is based on a sample of 7,360 banks from 151 countries over the period 2002-2009. After describing the methodology used to test the disaster myopia hypothesis, the choice of macroeconomic and banking variables is justified.

The GMM model

In a first time, a GMM estimator on a large sample and small periods is used in order to underline the dynamic of the bank risk-taking during the 2000's. In a second step, a regression in cross-section and in panel focuses on the 2007 episode. Its purpose is to highlight the presence of disaster myopia phenomenon during the 2007 crisis.

As the study of disaster myopia refers to a dynamic process, we must study to what extent the lagged values of the indicator of risk taking and the initial banking, financial and real conditions influence the current value of risk taking. The starting point for this analysis is a simple regression using the endogenous lagged variable as well as the explanatory variables in t and t-1. When the ordinary least squares estimator is used for this purpose, there is a problem of correlation between the explanatory variables and the error term due to individual effects, which then gives rise to an upward bias. The within estimator enables us to eliminate this problem by integrating fixed effects and allows us to take into account institutions specificities. Nevertheless, in the context of our analysis, there is a limited number of periods, which produces a significant correlation between the dependent lagged variable and the error term. Therefore, the use of this estimator is also biased, but in the opposite direction. Given the problems encountered by these two methods, it is advisable to use a dynamic model allowing for the introduction of instrumental variables. These variables are correlated to the lagged value of the endogenous variable and not with the error term of the model (for t =2, 3, …, T), which solves our problem. The effects of the explanatory exogenous variables on the explained variable can then be interpreted [START_REF] Arellano | Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations[END_REF]. Hence, the GMM seems to be the best adapted method for our estimation. It should be noted that Blundell and Bond's (1998) Monte Carlo simulations showed that the system GMM estimator is more efficient than the first-differenced one.

Indeed when the number of instruments is small and when there is a finite sample, the first-differenced GMM estimator is biased. It should also be noted that in order to validate the use of a GMM model, the estimated coefficient of the dependent lagged variable must be larger than that of the within estimator and smaller than that of the OLS estimator. Our model can be written as follows:

t i i n t n t i t i t i v u X y y , 0 , 1 , , + + + = ∑ = - - β α with i = 1,…,
= + t i i t i v u x E .

Data and justification of the choice of variables

The dependent variable is a measure of risk taking defined by the ratio: Taking the risk variable one and more periods lagged enables us to show the persistence of risk taking over time.

Concerning the explanatory variables, we distinguish between the banking sector and other macro variables, which are described in Table 1. Low volatilities may increase incentives for banks to take on more risk for behavioral, contractual or institutional reasons [START_REF] Brunnermeier | Asset Pricing under Asymmetric Information-Bubbles, Crashes, Technical Analysis and Herding[END_REF][START_REF] Rajan | Has Financial Development Made the World Riskier?[END_REF].

gdp

GDP growth rate (+) Economic growth.

According to the 'paradox of tranquillity' [START_REF] Minsky | The financial instability hypothesis, capitalist processes and the behaviour economy[END_REF] Risk taking dynamics may be more pronounced for industrialized countries which have benefited from emerging markets' current account surpluses [START_REF] Bernanke | The global saving glut and the U.S. current account deficit[END_REF].

Specific banking related variables (by banks) totkt

Total capital ratio (-) Prudential.

Bank of International Settlements roae

Return on average equity (+) Return.

High returns may encourage banks to hold equities [START_REF] Young | Changing Perceptions of Maturity Mismatch in the US Banking System: Evidence from Equity Markets[END_REF]. netincome ii Net income USD (+/-) Size.

+ Too big to fail: big banks' moral hazard induces them to take on more risk as they believe in the implicit guarantee of governments or institutions [START_REF] Kay | arrow Banking: The Reform of Banking Regulation, Centre for the Study of Financial Innovation[END_REF], [START_REF] Barrell | Is there a link from bank size to risk taking?[END_REF]).

-Smaller banks have more risky balance sheets [START_REF] Kashyap | What Do a Million Observations on Banks Say About the Transmission of Monetary Policy?[END_REF]. Small banks are pushed towards higher risktaking due to fiercer competition [START_REF] Hakenes | Bank Size and Risk-Taking under Basel II[END_REF] i. The annual realized volatility is measured by the standard error of the daily returns for each month and thus for each year. The realized volatility is well adapted in the case of high-frequency data. It is an ex-post nonparametric and unbiased volatility estimator (Andersen et al., 2006[START_REF] Andersen | Parametric and Nonparametric Volatility Measurement[END_REF] and represents an unbiased indicator that makes it possible to get close to the true volatility and is largely accepted in the asset price volatility modeling and forecasting literature [START_REF] Chan | The Economic Value of Using Realized Volatility in Forecasting Future Implied Volatility[END_REF].

ii. The Netincome variable is taken in logarithm.

IV. Results

For the period 2002-2009, the dependent variable perfectly fits with the previous model as testified by the following graphs presented on Figure 2: risk taking decreases in the years following a crisis and increases over time, until reaching the next crisis. The panel is unbalanced in the sense that we have more observations on some banks than on others. The OLS and the Within-group estimators are biased in opposite direction but the use of the GMM estimation is validated because the coefficient of the estimated lagged dependent variable is higher than that of the Within-group estimator and lower than that of the OLS estimator. In all cases, the Hansen tests of over-identifying restrictions validate the instruments used in the model.

Furthermore, the [START_REF] Arellano | Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations[END_REF] tests do not reject the assumption of the absence of second order autocorrelation on the residuals. This study therefore enables us to interpret the estimation's results correctly. Time dummies are included in order to support the assumption that there is no correlation across individuals in the idiosyncratic disturbances. For the dependent endogenous variables lag 2 and deeper are used. The other variables are considered as endogenous and instrumented with lag 2 and deeper except for the time and region dummies that are taken as exogenous. The table shows different signs for different lags, we take the sum of coefficients to determine the overall sign.

After checking the validity of our estimations, we can now state our results. First, we observe that risk taking in period t is influenced by risk taking in period t-1, t-2, but not always in t-3. Risk taking in period t is affected by overall risk taking in the three previous years (in table 2 the sum of the coefficients L.risk, L2.risk, L3.risk is positive and significant). The closer we get to period t, the higher the influence of the former period risk taking.

Second, as explained above, we control the analysis for the following variables: volatility, housing prices, economic growth, industrialized vs. developing countries, non-performing loans, net income of banks, return on average equity, return on average asset, and prudential ratio.

On the one hand, our results underline the influence of the economic and financial context on banks' risk taking. We observe that the lower the volatility in period t, the higher is risk taking in period t (and t, t-1) (vol). The rationale for such result is that when volatility is low, banks are incited to take on more risks which increases the share of short term assets (dependent variable denominator).

Hence our results are in line with the theoretical analysis of [START_REF] Brunnermeier | Asset Pricing under Asymmetric Information-Bubbles, Crashes, Technical Analysis and Herding[END_REF] and [START_REF] Rajan | Has Financial Development Made the World Riskier?[END_REF].

The procyclical behavior of volatilities is a concrete manifestation of the influence on risk perceptions.

By contrast, the stronger growth, the higher is risk taking (gdp): as output grows there are more yield opportunities and economic agents search for new investment opportunities. Controlling for housing prices, we also observe a positive relationship: as housing prices rise, risk taking increases (prices).

This demonstrates that economic agents and financial institutions try to benefit from a bubble, as suggested by the rational bubbles phenomenon of [START_REF] Blanchard | Bubbles, Rational Expectations and Financial Markets[END_REF]. According to them, rational bubbles may yield multiple equilibria that can explain deviations from the fundamentals and the existence of self-sustaining dynamics. Comparing industrialized to developing countries, we observe that risk taking is higher in the former (region). One interpretation might be that emerging countries have drawn the lessons from previous crises, especially owing to prudential policies implemented in these countries, such as controlling entrance of short term capital inflows and managing the illiquidity risk in the banking sector. Another prominent view [START_REF] Bernanke | The global saving glut and the U.S. current account deficit[END_REF]) is that an excess of saving over investment in emerging market countries, eased financial conditions and exerted significant downward pressure on world interest rates. In so doing, this flow of saving helped to fuel a credit boom and risk-taking in major advanced economies, particularly in the United States.

Over the long run (t, t-1), low interest rates generate high risk taking. The idea is to consider that monetary policy could have contributed to the crisis. Low interest rates affect valuations, incomes and cash flows, which in turn can influence how banks measure risk (Adrian and Shin, 2009a, b, Borio and[START_REF] Borio | Capital regulation, risk-taking and monetary policy: a missing link in the transmission mechanism?[END_REF]. Lower interest rates, for instance, boost asset and collateral values as well as incomes and profits, which in turn can reduce risk perceptions and/or increase risk tolerance. In this respect our results converge toward those of [START_REF] Altunbas | Does monetary policy affect bank risktaking?[END_REF] who empirically analyze the relationship between monetary policy and risk-taking by banks using a sample of 1,100 European and US banks.

They find evidence that relative changes in banks' risk-attitude (i.e. comparing risky versus less risky banks as perceived by the market) are linked to monetary policy even in a period of subdued risk perception. More precisely, unusually low interest rates over an extended period of time contributed to an increase in bank' risk.

On the other hand, the specific bank variables play a role in the risk taking dynamics. At the banks' scale, the higher net income, the lower is risk taking (netincome). This result underlines the fact that smaller banks are induced to take more risk. This phenomenon can be explained by the fact that those banks hold less liabilities compared to bigger ones, and so the share of short term assets relatively to long term liabilities is smaller. Indeed, smaller banks generally have less liquid balance sheets (lower ratios of securities to assets) [START_REF] Kashyap | What Do a Million Observations on Banks Say About the Transmission of Monetary Policy?[END_REF]). The lower the return (roae for return on average equity and), the higher is risk taking, indicating that banks search for yield. Low returns on investments, such as government (risk-free) securities, may increase incentives for banks to take on more risk to meet a nominal return target [START_REF] Young | Changing Perceptions of Maturity Mismatch in the US Banking System: Evidence from Equity Markets[END_REF]. The higher market capitalization (marketkp), the higher is risk taking. The more banks' capitalization is concentrated, the more banks take risks. Indeed, the less a bank has shareholders, the more risks it takes; such a behavior can be associated with a specific management mode of slightly capitalized banks. According to [START_REF] Laeven | Bank governance, regulation and risk taking[END_REF], bank risk taking varies positively with the comparative power of shareholders within the corporate governance structure of banks. Finally, the higher prudential ratio, the lower is risk taking (totcap), which suggests that macro-policy tends to reduce risk on a global basis. Finally, the lower the amount of non-performing loans, the higher should be risk taking, indicating that banks' vulnerability tends to reduce maturity mismatch (npl). The mortgage expansion is accompanied by an increase in NPLs masked by the house prices growth [START_REF] Claessens | The global financial crisis: How similar? How different? How costly?[END_REF]).

This variable is only significant for the GMM system. We cannot therefore make a definitive conclusion.

Testing the disaster myopia hypothesis: the particular case of 2007 and previous years

To test the disaster myopia hypothesis, we resort to two types of estimations: cross-section and crosssection with country dummies. We consider two periods of time: starting from 2009 backward and starting from 2007 backward. We observe that results converge for any of the two methods (Tables 3 and4). We can thus conclude that the episode of the 2007 crisis shows evidence of banks' myopia disaster. This result is in accordance with the aforementioned GMM results.

V. Discussion about policy implications

As regulators and institutions are more immune to disaster myopia 7 , they must design stress scenarios integrating extreme events and impose them to financial institutions. Regulators must also consider more deeply models used by financial institutions, in particular the historical statistics series used to estimate risks. All this can be done via prudential supervision accompanied by measures of transparency.

Prudential supervision

Preventing the development of financial conditions that are vulnerable to crisis is the role of prudential supervision. More precisely, prudential supervision should help identify vulnerable banks before they become weak banks and especially banks that are becoming heavily exposed to a major shock. The recommendations of the Basel Committee on Banking Supervision go in this direction.

According to the Basel Committee on Banking Supervision (hereafter BCBS) (2009a), stress tests should be performed for different risk types including market, credit, operational and liquidity risk. According to [START_REF] Haldane | Why Banks Failed the Stress Test[END_REF], the evaluation of the degree of risk -the value at risk for the private sector and the stress-tests for the public one-was based on data and assumptions relative to the Golden Era. This period is characterized by a strikingly low volatility from an historical perspective inducing a low degree of risk that conduced to disaster myopia. Using British historical data -back in some cases to the 17 th century-Haldane shows that the low macroeconomic and financial volatility level during this Golden Era has been without historical equivalent. As a result, this lack of historical perspective to assess the risk level has led to disaster myopia. According to [START_REF] Haldane | Why Banks Failed the Stress Test[END_REF], 'the stress-tests required by the authorities over the past few years were too heavily influenced by behaviour during the Golden Decade'.Therefore, as required by the BCBS, a bank should enhance its stress testing practices by considering important interrelations between various factors, including: (i)

price shocks for specific asset categories; (ii) the drying-up of corresponding asset liquidity; (iii) the 7 Identifying whether there is or not a difference between the private sector and the official sector in terms of disaster myopia is another issue that is not dealt with in this paper. [START_REF] Haldane | Why Banks Failed the Stress Test[END_REF] stresses that both the private and the public sectors suffer from a disaster myopia behavior.

possibility of significant losses damaging the bank's financial strength; (iv) growth of liquidity needs as a consequence of liquidity commitments; (v) taking on board affected assets; and (vi) diminished access to secured or unsecured funding markets.

The Basel Committee on Banking Supervision (2009b and 2009c) also made a few propositions aiming at limiting banks' risk by establishing some ratios. Both the Liquidity Coverage Ratio and the et Stable Funding Ratio proposed by the Basel Committee on Banking Supervision intend to limit risk. The liquidity coverage ratio is also useful in this respect, as it identifies the amount of unencumbered, high quality liquid assets an institution holds that can be used to offset the net cash outflows it would encounter under an acute short-term stress scenario specified by supervisors. The net stable funding ratio measures the amount of longer-term, stable sources of funding employed by an institution relative to the liquidity profiles of the assets funded and the potential for contingent calls on funding liquidity arising from off-balance sheet commitments and obligations. The standard requires a minimum amount of funding that is expected to be stable over a one year time horizon based on liquidity risk factors assigned to assets and off-balance sheet liquidity exposures. This ratio is intended to promote longer-term structural funding of banks' balance sheets, off-balance sheet exposures and capital markets activities. To deal with banks' liquidity risk, the Committee also proposes that banks should frequently conduct a contractual maturity mismatch assessment.

Announcements and transparency

In parallel, policy-makers may attempt to avert a financial crisis by announcing policies that will reduce the likelihood of a disaster or mitigate its impact. For example, the development of indicators of increasing vulnerability to financial crises could provide a useful counter to disaster myopia.

Macroprudential indicators may help deter disaster myopia.

Factors that encourage disaster myopia should also be dealt with. Opaque accounting practices, which obscure the magnitude of the exposure of the consolidated financial institution or mask deterioration in the market value of exposures, are a fundamental source of vulnerability. Exante public disclosure of exposures to credit risk may exercise some constraining influence.

VI. Conclusion

The contribution of this paper is twofold. First, it shows that the 2007 financial crisis exhibits disaster myopia in the banking sector. Disaster myopia suggests that competitive, incentive-based and psychological mechanisms in the presence of uncertainty lead financial institutions to underestimate the risk of financial instability. Second, this paper identifies macro and specific determinant variables in banks' risk taking since the beginning of the years 2000. The recognition of conditions that promote disaster myopia is the starting point. In terms of economic policy, there is a need for advances in modelling credit risk and greater discipline of the pricing of credit risk. Identifying and limiting the impact of the banking sector's disaster myopia is helpful as it may limit the consequences for the system as a whole. Indeed, because of the particular and systemic role of banks in the financing of the economy, the impact of banking sector myopia on the economy may grow so large that they can jeopardize the financial system.

An open question for future research is whether disaster myopia is more prominent during the recent financial crisis than during previous financial distresses. More precisely, is the current financial crisis special in this respect? We expect the disaster myopia problem to be more acute today because of the complexity and opacity of new financial products.

VII.

Figure 1 .

 1 Figure 1. The disaster myopia hypothesis

Figure 2 .

 2 Figure2. Risk taking over time(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)

  7,360 , and t = 2002, …, 2009, where

							y	i	1 , -t	represents the dependent lagged variable for
	each institution in the period t-1,	t X -i ,	n	the set of explanatory lagged variables, i u the specific
	individual effect for each institution, t i v , the specific shock at each period and on each institution and
	where	[	,	(	,	) ] 0

Table 1 .

 1 Synthesis and definition of the model's explanatory variables.

	Explanatory	Definition		Expected	Role of the variable
	variable			Sign
		Global financial and macroeconomic variables (by countries)
	prices	Collateral	-	(+)	Housing prices growth.
		Housing price		Rational bubbles may explain deviations from the
		growth rate			fundamentals and the existence of risk dynamics (Blanchard
					and Watson, 1983).
	vol	Realized		(-)	Volatility.
		volatility of
		the Stock
		exchange
		index i

  , the fragilities were masked by the success of the economy and the economic agents benefit from new growth opportunities.

	intrate	Monetary	(-)	Monetary policy.
		market rate		Low interest rates may influence bank risk-taking (Adrian and
				Shin, 2009a, b, Borio and Zhu, 2008).
	region	Dummy	(+)	=1 for industrialized countries.
		variable

  .

	npl	Non-	(+/-)	Vulnerability, credit risk
		performing		The mortgage expansion is accompanied by an increase in
		loans		NPLs masked by the house prices growth (Claessens et al.,
		(Impaired		2010).
		Loans (NPLs)/
		Gross Loans
		%)
	marketkp	Market	(+/-)	Market concentration.
		capitalisation /		Bank risk-taking increases as bank shareholders' power rises
		shareholders		in corporate governance (Laeven and Levine, 2009).
		funds

Table 2

 2

presents the GMM system estimation. Different estimations of the same model (OLS, Withingroup and GMM difference) are reported in Appendix B.

Table 2 .

 2 GMM system results

		GMM	GMM	GMM	GMM	GMM	GMM	GMM
		Syst	Syst	Syst	Syst	Syst	Syst	Syst
	L.risk	0.769***	0.822***	0.698***	0.658***	0.823***	0.61***	0.582***
		[0.102]	[0.057]	[0.061]	[0.054]	[0.062]	[0.062]	[0.074]
	L2.risk				0.169***	0.040	0.15***	-0.0063
					[0.052]	[0.075]	[0.054]	[0.069]
	L3.risk						-0.0194	0.0958**
							[0.037]	[0.043]
	Totkt			-0.00144*	-0.0002		-0.0008
				[0.0008]	[0.0006]		[0.002]
	Roae						-0.03***
							[0.011]
	Npl	0.012	-0.001					0.00355**
		[0.021]	[0.003]					[0.002]
	Prices	0.012*
		[0.006]
	Gdp		0.028***	-0.00119	0.026	0.039***	-0.0172
			[0.009]	[0.025]	[0.025]	[0.008]	[0.0132]
	L.gdp					0.001
						[0.010]
	log.netincome	-0.050	-0.037*	-0.115*	-0.129**	-0.053		0.0226
		[0.030]	[0.019]	[0.062]	[0.055]	[0.039]		[0.017]
	L.log.netincome					-0.007
						[0.025]
	Vol	-0.876	-1.608*		5.299	-4.724***
		[1.821]	[0.828]		[3.271]	[1.211]
	L.vol					4.103***
						[0.632]
	Marketcapitalisation							0.0867**
								[0.040]
	Intrate		0.002	0.00513	0.034	0.024**	-0.0103	-0.00531
			[0.006]	[0.017]	[0.020]	[0.011]	[0.0169]	[0.008]
	L.intrate					-0.029**
						[0.012]
	Region			0.0308	0.436*
				[0.177]	[0.240]
	Constant	0.735*	0.315	0.754**	0.032	0.633***	0.78***	-0.262
		[0.418]	[0.192]	[0.309]	[0.405]	[0.241]	[0.230]	[0.194]
	Observations	3361	3907	7777	6142	8540	5834	931
	Number of t	651	661	1749	1566	1532	1726	219
	Hansen statistic	41.32	79.40	18.49	6.316	123.1	23.82	91.80
	p-value of Hansen statistic	0.288	0.215	0.238	0.851	0,123	0.161	0.238
	Arellano-Bond test for
	AR(2)	0.00314	-0.502	1.407	-0.280	0.634	-0.123	0.776
	p-value AR2	0.997	0.616	0.160	0.780	0.526	0.902	0.438

Standard errors in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

Table 3 .

 3 Dynamics of risk taking during the recent crisis (OLS)

	Variables	risk2009	risk2009	risk2009	risk2009	risk2009	risk2007	risk2007	risk2007	risk2007
	risk2008	0.757***	0.757***	0.770***	0.766***	0.766***
	R-squared	0.761	0.761	0.764	0.764	0.764	0.741	0.748	0.749	0.749
	t-statistics in brackets
	* significant at 10%; ** significant at 5%; *** significant at 1%

Table 4 .

 4 Dynamics of risk taking during the recent crisis (Country dummies) For the period from 2002 to 2009, we observe that banks' risk taking in 2009 is positively influenced by their risk taking in 2008 and negatively by their risk taking in 2006 (coefficients are stable from regression to the next). There is therefore a break in risk taking due to the negative shock that occurred in 2007. The lower risk taking in 2008 induced also a lower risk taking in 2009. By comparison, for the period from 2002 to 2007, we observe that the influence of risk taking is increasing over time starting from 2004.

	Variables	risk2009	risk2009	risk2009	risk2009	risk2009	risk2007	risk2007	risk2007	risk2007
	risk2008	0.759***	0.759***	0.771***	0.767***	0.767***
	R-squared	0.770	0.770	0.773	0.773	0.773	0.758	0.762	0.764	0.764
	t-statistics in brackets
	* significant at 10%; ** significant at 5%; *** significant at 1%

This measure has several limitations. First, some banks are privately owned, and thus their shares are not traded. Second, even when banks are publicly traded, shares are not transacted every month, presumably because these shares are not especially liquid.

Note here that maturity mismatch is not used in its traditional sense.Chang and Velasco (1998),Goldfajn and Valdes (1999) and others have argued that foreign asset-liability mismatches in the East Asian economies was an "inevitable" consequence of international financial intermediation. See also[START_REF] Bird | Banks, Maturity Mismatches and Liquidity Crises: A Simple Model[END_REF]. Here, we simply consider that if banks perceived a low risk, they had a tendency to have a wide maturity mismatch, while when they perceived high risk on the market, they tended to reduce the mismatch.

See Guttentag and Herring (1984, 1986),[START_REF] Herring | Banking Disasters: Causes and Preventative Measures, Lessons Derived from the U.S. Experience[END_REF][START_REF] Herring | Credit risk and financial instability[END_REF] and[START_REF] Herring | Bubbles in Real Estate Markets[END_REF].

It is well-established in cognitive psychology that economic agents have a tendency to base decision rules around rough heuristics or rules of thumb. For experimental evidence, see[START_REF] Kahneman | Judgment under uncertainty: Heuristics and biases[END_REF].

This negative shock may even be endogenous, attributed to their own risky behaviour that increases the fragility of the system.

Appendix

A -Summary


Alexandre Lebouvier

François Fresnet

Frédéric Fabry

Valérie Boch

Vandad-Julien Rohani

François Cauneau

Laurent Fulcheri
email: laurent.fulcheri@mines-paristech.fr

Exhaust gas fuel reforming of Diesel fuel by nonthermal arc discharge for NOx trap regeneration application

Keywords: Diesel fuel reforming, syngas production, non-thermal arc discharge, 1D model, plasma reformer, NOx trap regeneration application, Diesel engine after-treatment

come

Exhaust gas fuel reforming of Diesel fuel by non-thermal arc discharge for NOx trap regeneration application

Introduction

Today in Europe, Diesel powered vehicles account for almost 50% of the passenger car market and up to 78% in France. Diesel engines offer several advantages over other internal combustion spark ignition engines due to their high energy efficiency and low level of CO 2 emissions. On the other hand, Diesel engines are generally characterized by higher nitrogen oxides (NOx) and Particulate Matter (PM) emissions than gasoline engines.

In Europe, Euro stage VI regulation for Diesel engines, coming into force in September 2014, set a 56 % reduction of NOx emissions compared to Euro stage V (80 mg.km -1 vs. 180 mg.km -1 ).

This regulation forces car manufacturers to develop new efficient solutions. While current Three-3 Way Catalysts (TWC) can efficiently lower NOx from spark ignition engines which operate under close to stoichiometric conditions, these technologies cannot be applied to Diesel vehicles since they are ineffective under oxidizing environment such as exhaust gas emitted from Diesel engines.

In Diesel engines, technologies based on NOx trap catalysts are one of the technological solutions under development to meet the further emission regulations. NOx trap technology, also called NOx Storage and Reduction (NSR), was first developed by Toyota in 1994 1 . This system operates with cycles composed of successive storage and regeneration modes. In storage mode, the NOx trap stores NOx emitted from the engine on a catalyst material generally based on Ba.

Once full, the classical way to regenerate NOx trap catalysts consists in operating the engine under rich combustion conditions for a short while in order to produce reducing species in the exhaust gas 2 , that will convert NOx into N 2 . This method is not totally satisfying since it suffers from a significant drawback known as oil dilution problem. Oil dilution is the phenomenon characterized by Diesel fuel mixing together with engine oil. This phenomenon requires increasing change oil frequency.

To pass through oil dilution problem, it is possible to produce reducing species such as H 2 and CO by Diesel fuel reforming whose species will be used for NOx trap regeneration. When the NOx trap is full, a part of the Diesel engine exhaust gas is by-passed to the reformer and is mixed with a small amount of Diesel fuel, which provides the necessary species to regenerate the NOx trap catalyst. This method has the distinct advantage of not modifying engine conditions (i.e. avoiding short/rich combustion cycles) and avoiding oil dilution problem.

The catalytic exhaust gas fuel reforming of Diesel fuel is studied for several years by Megaritis et al. mainly for reformed exhaust gas recirculation (REGR) application [3][4][5][6][7] . The authors have demonstrated that REGR can reduce the exhaust emissions. They have investigated different hydrocarbons : natural gas 8 , Diesel fuel 9,10 , ultra low sulphur Diesel fuel (ULSD) and ultra-clean synthetic gas to liquid (GTL) 4,11 , Biodiesel 6,10 , Rapeseed methyl ester (RME) 12 , bioethanol 8,13,14 and mixture 10,13 for Diesel engine [3][4][5]15 or HCCI engine 8,13,16,17 . The authors have focused their analysis on NOx and particulate matter (PM) reduction, the improvement of engine performances and the fuel economy 5,7,18 . The reformer was a nickel-free prototype catalyst, containing a low loading of precious metal promoted by metal oxides designed to promote all of the desired reactions: oxidation, steam reforming, dry reforming, and water gas shift reaction (WGSR) while at the same time inhibiting coke formation 4 . Some experiments have been realized for an aftertreatment unit, containing a HC-SCR catalyst 5,15,19 . The investigations have concerned essentially the EGR rate, the reactor inlet temperatures, the reformer configuration, the O/C ratio and λ. The aftertreatment unit performances was promoted by the presence of H 2 but inhibited by CO. Ref. 15 contains an exhaust gas composition very similar to our condition 2. 18 % of wet fraction of syngas has been achieved. The authors have tried to promote the H 2 production by WGSR and steam reforming for this application. High content of CO 2 has been also produced (+ 8 %) and almost no CH 4 .

NOx can also be treated directly by plasma with DBD 20,21 or by Pulsed or DC Corona discharge 22,23 but the high content of oxygen in exhaust gas leads mainly to oxidize NO to NO 2 24,25 . Hence non-thermal plasmas alone achieve low NOx abatement. Recent researches on NOx removal have focused on hybrid process of non-thermal plasma (NTP) coupled with an absorption process or a catalyst [26][27][28] . In plasma catalysis technology, the NTP is used as a pretreatment, to oxidize NO to NO 2 , and facilitate the catalysis action.

For several years, intensive researches have been dedicated at CEP on reforming processes for fuel cell powering [29][30][31][32] using a non-thermal plasma torch. An alternative to the catalytic exhaust gas reforming of Diesel fuel method is presented in this paper and consists in using a NTP torch.

Using a plasma torch as a reformer has been previously explored by several research teams 33 .

Contrary to catalysts, plasma processes are non-sensitive to sulfur, low weight and low space device, and have short-transient time. The amount of oxygen in the plasma gas is a key point of this application, which directly affects the performance and the electric power needed. At engine high load, the oxygen becomes low in the exhaust gas.

Plasma reforming processes have been widely studied using different hydrocarbons with air (partial oxidation) [33][34][35][START_REF] Bromberg | Proceedings of the 1999 U.S DOE Hydrogen Program Review[END_REF][START_REF] Bromberg | [END_REF][START_REF] Bromberg | [END_REF][START_REF] Bromberg | [END_REF][START_REF] Crane | SAE paper[END_REF] , air and water mixture (autothermal reforming) 29,32,33 or CO 2 (dry reforming) [START_REF] Li | [END_REF][42][43][44]

The high content of H 2 O and CO 2 in the plasma gas (up to 9 % for each) lead to highly endothermic reactions, energetically unfavorable compared to partial oxidation of Diesel fuel, commonly studied.

The present study is dedicated to the reforming of Diesel fuel with Diesel engine exhaust gas by using a non-thermal plasma torch. After a presentation of the experimental set up, experimental results are presented and compared to thermodynamic and 1D multistage kinetic models. The effects of input current, O/C ratio, exhaust gas flow rate and cathode length versus energy efficiency and conversion rate are presented and discussed.

Experimental section

The experimental set-up developed in previous researches for fuel cell powering by gasoline, E85

and ethanol reforming 29,32 has been adapted to NOx trap regeneration application. Henceforth, it enables the injection and evaporation of Diesel fuel which has a higher boiling point than gasoline and ethanol. The experimental device also allows the synthetic reconstitution of Diesel engine exhaust gas composition corresponding to different operating regimes.

The experimental set-up is presented on figures 1 and 2. The plasma reactor is composed of two consecutive zones: a plasma zone and a post-discharge zone. The plasma zone is the part where the arc plasma really takes place. The post-discharge zone is a passive zone, located downstream the plasma zone where most of the reforming reactions ignited in the plasma zone continue to take place depending on their kinetic speed. The power supply is a resonant converter 46 controlled in current. The current can be precisely tuned in the range 0. Detector (TCD). This analyzer enables to continuously measure the dry molar fraction of H 2 , CO, CO 2 and CH 4 . The measurement is based on the assumption that the outlet dry gas only contains nitrogen and the four species above-mentioned. This assumption is verified with the second analyzer.

The second analyzer is a gas phase chromatograph Perichrom PR 2100. It is equipped of two independent analysis channels. The first channel is used to measure hydrogen with a molecular sieve 5Å column and a TCD. The carrier gas is nitrogen. The second channel is used to measure CO, CO 2 , CH 4 and C 2 hydrocarbons with a Poraplot U and a molecular sieve 5Å columns, a methanizer, a TCD, and a Flame Ionization detector (FID). The carrier gas is helium.

The electrical signals are analyzed by a HP 54615B oscilloscope (bandwidth of 500 MHz) with a high voltage probe Elditest GE3830 1:1000 (up to 30 kV) and hall effect current probe Chauvin Arnoux E3N (bandwidth of 100 kHz). The NDIR-TCD analyzer and thermocouples data are collected every second by a computer.

The fuel used is a commercial Diesel fuel. The table 1 reports the main characteristics of the fuel used for data analysis and of its surrogate molecule used for calculations.

Two operating conditions corresponding to different engine loads have been defined for this study: the exhaust gas composition of a Diesel engine for two fuel/air equivalence ratios (Φ) of 0.66 and 0.32 based on combustion equation for a Renault 2.0L 16v dCi turbocharged engine (M9R 842 1995cc). The equivalence ratio is defined by:

stoich air air Q Q Q Q fuel fuel , (4)
where Q fuel and Q air refer to the molar flow rates of fuel and air respectively at engine intake. The first equivalence ratio corresponds to a high engine load and the second one to a low engine load.

The gas composition for these both operating conditions is given in table 2.

The reactant mixture is represented in terms of O/C ratio. The O/C ratio stands for the molar ratio between oxygen atoms from air and carbon atoms from Diesel fuel and is defined in eq. 5. Note that oxygen coming from H 2 O and CO 2 are not taken into account in this ratio. Plasma reformer performances are analyzed in terms of energy efficiency η and conversion rate χ, which are expressed as:

H C air H C O Q Q nQ Q C O m n , ( 5
)
Q i stands
W LHV Q LHV Q LHV Q fuel fuel CO CO H H 2 2 , ( 6
) fuel CH CO CO nQ Q Q Q 4 2 , ( 7
)
where LHV i is the lower heating value of chemical species i and W is the electrical deposited power applied to the discharge. The conversion rate (eq. 4) accounts for the fuel transformation and is an indicator of the mass balance on carbon atoms. ΔQ CO2 corresponds to the difference between the output and input CO 2 molar flow rate. Only the main species (H 2 , CO, CO 2 , CH 4 ) was considered in these energy and mass balances. The other species C n H m O k formed were analyzed and quantified by GC. They were present in minor concentration when the conversion rate is high. In the results presented in this paper, the inlet temperature and working pressure have been set to 573 K and 0.1 MPa, respectively. For each measurement reported, the system is considered to be at the thermal steady state. A waiting time of 5 min is generally observed in order to allow the system to reach this equilibrium.

Modeling approaches

In both models presented below, n-heptane (C 7 H 16 ) molecule has been chosen for calculations because it is a commonly used surrogate molecule for Diesel fuel. n-heptane has a cetane number of approximately 54 47 which is very similar to conventional Diesel fuel.

The thermodynamic equilibrium calculations are performed with EQUIL module from the CHEMKIN II package [START_REF] Kee | Sandia National Laboratories Report[END_REF] . The algorithm is based on Gibbs free energy minimization. The modeling approach is detailed in ref. 6. This model assumes an infinite reactor, a perfect mix of species and a uniform application of the plasma power. Given the initial composition, the initial temperature and the reactor pressure, the initial enthalpy is evaluated. The initial temperature is 573 K and the pressure reactor is 0.1 MPa. The final mixture enthalpy is the sum of the initial enthalpy and the enthalpy coming from the plasma. The equilibrium composition and temperature are calculated from the final enthalpy.

The exhaust gas Diesel fuel reforming has also been simulated with a 1D kinetic model previously developed for gasoline reforming 31 . The model has been adapted for NOx trap regeneration application. Several n-heptane detailed mechanisms have been developed over the past two decades [START_REF] Simmie | [END_REF][50][51][52][53][54][55][56] , widely for engine and propulsion devices. The calculations have been carried out using the n-heptane oxidation mechanism developed by Curran et al. 52,53 (mainly for combustion issues) generally do not include all the ionized and excited species due to a lack of basic knowledge. Some chemical mechanisms including ionized species have been proposed for methane (CH 4 ) 58 , propane (C 3 H 8 ) 59 and n-butane (C 4 H 10 ) 60 with air. Because of the complexity of the involved mechanisms, no kinetic mechanism including charged species is available in the literature for higher hydrocarbons under reforming conditions. The plasmaassisted reforming process is far from these combustion processes due to low amount of present oxygen, and even further from the exhaust gas fuel reforming. However, the relevance of a combustion kinetic mechanism has been proven by Benilov and Naidis for low current arc discharge 61 . The mechanism has been first tested numerically in exhaust gas fuel reforming conditions in a plug flow reactor (PFR) for a very long time (~10 8 s) and then have been passes through the arc discharge, the remaining fraction passes near the arc and there is no mass transfer between the arc and the cold zone around the arc inside the reactor, (iii) these two fractions; i.e. cold and hot streams respectively, are perfectly and instantaneously mixed at the reactor exit. The arc is modeled by a Perfectly Stirred Reactor (PSR) where a homogenous input oxygen rate in the gas mixture which is twice higher at low engine load and CO 2 and H 2 O which are twice lower. Oxygen has the role to bring energy to the system and allows reaching higher temperatures for low engine load as shown on figure 5. In addition, at high load, an important part of calories are absorbed by CO 2 and H 2 O present in high concentrations as in an EGR system. At low load, the higher the temperatures, the better the decomposition of Diesel fuel, the faster the kinetic reactions and therefore the better the energy efficiency. In both conditions, the decreasing temperatures between T3, T4 and T5 are due to thermal losses of the system. fractions vary inversely proportionally with the temperature.

Deposited power is represented on figure 8. The lower the oxygen rate, the higher the deposited power. In condition 2 at O/C = 1.3, 15% and 8% of dry molar fraction of CO and H 2 respectively for a deposited power of 720 W have been reached. In these conditions, the dry molar fraction of CH 4 is only 1.6%. For condition 2, the energy consumption is comprised between 4.6 and 7.7

MJ.kg -1 of outlet syngas (H 2 + CO). Using a pulse discharge could help to decrease the energy cost of the process. The deposited are then taken as an input for models.

In this study, another important parameter to consider is the reducer molar flow rate, which determines the NOx trap regeneration duration. The figure 9 Influence of input current. The monitoring of the input current directly affects the input power injected in the system. The electrical power onboard a vehicle is an expensive resource and its consumption shall be limited for post-treatment purposes. Figure 10 shows the performances of the reformer in function of input current. In the input current range [0.25; 0.6 A], the deposited power varies quasi-linearly with the current (cf. figure 11) as long as we stay in the glidarc zone.

The glidarc frequency is determined by hydrodynamic parameters and cannot be varied. In NOx trap regeneration conditions, the quasi-continuous regime which gave the best results with ethanol, E85 and gasoline 4,5 cannot be reached anymore. A typical oscillogram is shown on figure 12. The instabilities of the discharge are mainly due to reactive conditions. The stability increases with the current.

The performances at high load are quite low and even a current of 0.6 A (P = 940 W) cannot reach an adequate temperature to quicken the POx reaction. At low load, the energy efficiency grows quasi-linearly with the input current and hence with the deposited power until 0.4 A. The energy efficiency and the conversion rate reached 31% and 58% respectively for I = 0.4 A and 35% and 60% respectively for I = 0.6 A while the deposited power raises from 730 to 1180 W.

Afterwards, an input current of 0.4 A is therefore considered because of onboard application which has limited usable power.

Influence of exhaust gas flow rate. One can observe in figure 13 that the higher the exhaust gas flow rate, the lower the volume power injected and the lower the performances. Figure 14 shows that the syngas molar flow rate is quasi-constant at 1.9.10 -3 mol.s -1 for the first engine condition.

For the second condition, a better syngas molar flow rate is attained (4.8.10 -3 mol.s -1 ) between 30.10 -3 and 40.10 -3 mol.s -1 exhaust gas flow rate. This exhaust gas molar flow rate corresponds to a 3.5 -4.5% range of total exhaust gas emitted by the engine. Figure 15 shows that post-discharge temperatures reach a maximum for both engine conditions around an exhaust gas molar flow rate of 42.10 -3 mol.s -1 . For lower exhaust gas flow rate, the partial oxidation reaction is aided by a higher plasma power density but the low quantities of fuel and oxygen release less energy, for a similar enthalpy of reaction. For higher exhaust gas flow rate, the resident time becomes lower, the POx reaction cannot set completely and temperatures drop. A scale up of the exhaust gas flow rate was not further considered because it did not decrease the NOx trap regeneration duration.

Influence of cathode length. In order to optimize the energy cost, the arc length can be tuned by means of cathode length. The plasma reactor allows using different lengths of cylinder electrode.

If the arc can reach the cathode extremity, the higher the cathode length, the higher the plasma length and the higher the voltage drop. Thus the deposited power can be increased with an input current held constant. Figure 16 shows that, even if the input power increases slightly (on average 7%), the energy efficiency and conversion rate decrease for a longer cathode. We suppose that, for a 100 mm long cathode, the arc does not reach the extremity and therefore the arc treats less gas. Previous results in POx conditions showed that a shorter cathode (50 mm long) leads also to decrease performances. For shorter cathode, the deposited power is insufficient and the reaction volume too small. The 75 mm cathode is the most adapted one regarding the energy cost and the performances.

Comparison between the 2 models and the experimental results. for O/C close to 1 is due to the consideration of real input power because it does not appear for a constant input power (not shown in this paper). In the first case, for O/C = 3.2, the experimental point is higher than thermodynamics results. This can be due either to measurement uncertainties or to a shift in O/C we have observed and seen by the efficiency peaks.

Conclusions and Perspectives

The exhaust gas Diesel fuel reforming has been investigated using a non-thermal high voltage and low current arc plasma torch. The low O 2 availability in the plasma gas made the plasma assisted Diesel fuel reforming harder. First, it has been demonstrated that the oxygen from CO 2 and H 2 O hardly ever intervene in the exhaust gas Diesel fuel reforming. At contrary, they absorb a part of calories and lower the temperature. This implies lower temperatures, lower kinetic reaction speed and lower energy efficiency compared to POx reaction. To higher the temperature, more oxygen is needed but local combustion can happen and promote H 2 O and CO 2 production.

A compromise has to be done between the Diesel fuel consumption, electric consumption and methane production. At high engine load, O/C = 1 is the most suitable condition. At low engine load, an energy efficiency of 40% and a conversion rate of 95% have been reached which corresponds to a syngas dry molar fraction of 25%. For these operating conditions, a 75 mm long cathode has demonstrated the best results.

The 1D model has shown good consistency with experimental and thermodynamics trends but a shift deriving above all from the strong model hypotheses (adiabaticity and perfectly and instantaneously gas mix). In a further step, to obtain better correlations between modeling and experimental results, thermal losses and non-perfect mix will have to be taken into account together with a 2D fluid model.

The plasma torch technology for creating reducing species is a promising technology for NOx trap regeneration application which needs to be improved. Indeed, for the highest oxygen rate case, the results obtained have led to a regeneration duration of 12 s of a typical NOx trap designed to respect the Euro VI regulation. The first case, even less oxidative environment, does not seem to be competitive compared to catalytic reformer due to high regeneration duration. For this particular case, one solution could be the use of a hybrid plasma-catalysis system where the plasma will allow to decrease the catalyst volume and consequently to decrease the amount of precious metal and catalyst price. The plasma can also heat very quickly the catalyst and so get it active quicker. Plasma catalysis technology can compensate the energy cost of heat it up by another way and it allows to pre-activate the reforming reactions.

  22 -0.66 A. The maximum voltage provided by the source is 15kV. A high voltage is applied to the tip electrode (anode as we work in inverse polarity) and the cylinder electrode (cathode) is grounded. The anode is 2.5 mm diameter composed mainly of Nickel. The cathode is a stainless steel cylinder with 8 mm inner diameter, 25 mm outer diameter and 75 mm or 100 mm long. Three mass flow controllers supply a mixture of air, N 2 and CO 2 in the range 0-100 slpm (Brooks 5831 ES), 0-200 slpm (Air Liquide EL-FLOW) and 0-10 slpm (Bronkhorst F-201-CV) respectively. Two diaphragm metering pumps (KNF Stepdos FEM03 TT.18/RC) provide liquid water and Diesel fuel in the range 0-0.03 slpm. Water and Diesel fuel are then evaporated separately by two glow-plug systems to avoid steam cracking. The electrical consumption of the plug flow systems is not considered in the energy efficiency calculations. The swirl injection of the reactants in the plasma torch is realized 10 mm before the tip electrode. The reactant temperature can be adjusted between ambient temperature and 600 K.The post-discharge zone is 510 mm long. It is composed of a ceramic tube (Mullite C530) of 4 mm thickness and 22 mm inner diameter for thermal and electrical insulation. The ceramic is covered with a stainless steel tube of 1.6 mm thickness for mechanical purpose. The postdischarge zone is instrumented with 5 type K thermocouples, numbered from T1 to T5, located axially at 120, 180, 250, 330 and 460 mm from the cylindrical cathode output respectively. The thermocouples are located along the reactor axis except T1 and T2 thermocouples which have been off-centered to avoid thermal damage. T1 is located at the surface of the ceramic while T2 is located at 5.5 mm from the axis. After the post discharge output, a fraction of the reformate gas is deflected from the main flow and is rapidly cooled down before entering two analyzers placed in series. The reformate gas composition is first analyzed by a Rosemount NGA 2000 composed of two detectors: a Non-Dispersive InfraRed (NDIR) detector and a Thermal Conductivity

  for the molar flow rate of species i and n the number of C atoms in the empirical formula of the fuel (C n H m ). The stoichiometry of the partial oxidation reaction of Diesel fuel is O/C =1.

  compared to a thermodynamic model based on T&TWinner 62 database. The results with the nheptane kinetic mechanism from Curran et al. were consistent with the thermodynamic model. It has been demonstrated that low current arc discharges are highly non-homogenous. This 1D multistage model, presented on figure 3, has been detailed in ref. 31. This model is based on the following assumptions: (i) the medium is adiabatic, (ii) only a fraction of reactants' inlet flow

  shows that the highest syngas production rate is for O/C = 0.8 for the first operating condition and O/C = 1.3 for the second one. A production of 2.10 -3 mol.s -1 has been reached in the first operating condition and 7.10 -3 mol.s -1 for the second one. The best compromise between energy efficiency, syngas molar flow rate and pollutant emissions are at O/C = 1 and O/C = 1.4 for the operating conditions 1 and 2 respectively. The Euro V passenger car engines have to emit less than 180 mg.km -1 of NOx, and typically their real NOx emission are close to 150 mg.km -1 of NOx. The Euro VI regulation imposes a NOx emission lower than 80 mg.kg -1 . Consequently, 70 mg.kg -1 of NOx have to be treated by the NOx trap. The homologation of European vehicles is based on NEDC (New European Driving Cycle) which is 11 km long. Assuming one regeneration during the cycle and that the NOx emitted are essentially NO 2 , the NOx trap has to store 16.7.10 -3 mol of NOx. Internal experiments in Renault showed that 5 moles of syngas are needed to reduce 1 mole of NOx. Without scaling up the mass flow rate, 7.10 -3 mol.s -1 of syngas leads to a NOx trap regeneration duration of 12 seconds which is a very promising. At the contrary, the first condition leads to a NOx trap regeneration duration of 45 s and is not competitive compared to catalytic processes. The catalytic reformers achieve results close to thermodynamics i.e. close to an energy efficiency of 70 % and a conversion rate of 100 %. In the second case, the plasma reformer achieved an energy efficiency of 40 % and a conversion rate greater than 90 %. These results are hopeful for a NTP working in a weakly oxidative environment.

Figure 19 represents

 19 Figure19represents the main species along the reactor. N 2 is not represented for convenience

Figure 1 .

 1 Figure 1. Schematic of the experimental set-up.

Figure 2 .

 2 Figure 2. Photograph of the experimental bench.

Figure 3 .

 3 Figure 3. Diagram of the 1D multistage kinetic model describing the low current plasma

Figure 4 .

 4 Figure 4. Experimental results of energy efficiencies and conversion rates as a function of O/C

Figure 5 .

 5 Figure 5. Temperature along the axis of the reactor.

Figure 6 .

 6 Figure 6. Dry molar fraction as a function of O/C. (left: condition 1; right: condition 2). I = 0.4

Figure 7 .

 7 Figure 7. H 2 yield for both engine conditions.

Figure 8 .

 8 Figure 8. Deposited power into the arc discharge in function of O/C.

Figure 9 .

 9 Figure 9. Experimental H 2 + CO molar flow rate as a function of O/C.

Figure 10 .

 10 Figure 10. Performances of the plasma reformer as a function of input current for both conditions (left: condition 1, O/C = 0.6; right: condition 2, O/C = 1). Q fuel = 0.13 g.s -1 .

Figure 11 .

 11 Figure 11. Deposited power as a function of input current.

Figure 12 .

 12 Figure 12. Typical oscillogram. Operating condition 2. I = 0.6 A.

Figure 13 .

 13 Figure 13. Performances of the plasma torch in function of exhaust gas molar flow rate. (left: high load; right: low load). I = 0.4 A. Q fuel = 0.13 g.s -1 .

Figure 14 .

 14 Figure 14. Syngas molar flow rate as a function of exhaust gas molar flow rate. I = 0.4 A. Q fuel = 0.13 g.s -1 .

Figure 15 .

 15 Figure 15. Temperature along the axis for both conditions. I = 0.4 A. Q fuel = 0.13 g.s -1 .

Figure 16 .

 16 Figure 16. Experimental investigation on the influence of cathode length. Energy efficiency and

Figure 17 .

 17 Figure 17. Exhaust gas Diesel fuel reforming: 1D model, thermodynamics model and

Figure 18 .

 18 Figure 18. Equilibrium temperature from the thermodynamics model.

Figure 19 .

 19 Figure 19. Main species molar fraction along the reactor. Engine condition 2. O/C = 1.54.

  . It has been extensively validated in a wide range of temperature and pressure in different reactors, shock tubes and rapid compression machine experiments. This kinetic mechanism is composed of 160 species and 1540 reactions and can be applied to a wide range of conditions. This large mechanism makes it applicable to a wide range of conditions. Recent researches have focused on reduced n-heptane mechanisms56 based on the Curran et al. mechanism to integrate them in CFD models for example. This mechanism includes radicals, atoms and vibrationaly excited species but does not include ionized species. Most of kinetic mechanisms that have been developed

  To investigate the highest energy efficiency which can be obtained, thermodynamics calculations have been realized. The results are shown on figure17. The input power is not kept constant and is based on experimental results (cf. figure8) because the deposited power varies with the operating conditions and O/C. For both conditions, the highest energy efficiency is attained for O/C = 0.8 and the energy efficiency reaches 86 % for the first condition and 92 % for the second one. For the second condition, the highest energy efficiency is at stoichiometry of n-heptane with oxygen from O 2 , CO 2 and H 2 O. For the first condition, the maximal energy efficiency does not correspond to the stoichiometry of n-heptane with oxygen from O 2 , CO 2 and H 2 O. Figure18shows that, at stoichiometry, the equilibrium temperature is too low (900 K). n-heptane is not completely oxidized and a high CH 4 fraction is produced.The exhaust gas Diesel fuel reforming has also been simulated by means of a 1D model and the results have been compared to the experimental results and thermodynamics results. It can be observed, also on figure17, an important shift in energy efficiency between experiments and 1D model. Firstly, the energy efficiency discrepancy mainly comes from thermal losses. The model assumes the adiabaticity of the medium. Secondly, the perfect and instantaneous mix at the torch exit is far removed from experimental torch exit which is highly non-homogeneous. Local nonhomogeneities could also appear in the plasma reactor leading to H 2 O and CO 2 production instead of H 2 and CO. However, the model trends are similar to the experimental trends. For O/C higher than 1.5, the experiments and the 1D model are very close to thermodynamics results and consequently close to the maximum achievable results. The small bump in figure17(right side)

  high fraction of H 2 O is produced (+ 6%) due to reactions wherein hydroxyl radicals (OH·) are involved. Hydroxyl radicals are highly reactive and promote H 2 O production. This slight CO 2 production and this high H 2 O production lead to decrease the syngas production and especially H 2 . Nevertheless, after the reaction peak, H 2 O and CO 2 rates slightly decrease to form H 2 and CO. As a consequence, water gas shift, steam and dry reforming play a minor role in the process after the reaction peak. To achieve the kinetic equilibrium, a 6 times longer adiabatic reactor is needed.These results corroborate the experimental results which show a high conversion rate but a low H 2 yield, up to 40 % on figure7. However, with the current state of development of our

experimental test bench and associated diagnostics, it is not possible to compare the experimental reaction rates with the model. Such a comparison requires advanced diagnostic methods (intrusive and non-intrusive) such as mass spectrometry or emission optical spectroscopy.

Table 1 . Main physical characteristics of Diesel fuel and n-heptane.

 1

		Diesel fuel	n-heptane
	Empirical formula	C 12.31 H 22.49	C 7 H 16
	Density (g.cm -3 )	0.833	0.684
	Low heating value (MJ.kg -1 ) 43.7	44.6
	Molecular weight (g.mol -1 )	170.21	100

Table 2 . Definition of both operating conditions used for calculations and experimentations.

 2

		1	2
	Conditions
		High load	Low load
	Φ	0.66	0.32
	O 2 (% mol )	6.8	13.9
	N 2 (% mol )	75.8	77.4
	CO 2 (% mol )	9.1	4.5
	H 2 O (% mol )	8.3	4.1

Acknowledgments

The authors gratefully acknowledge the financial and technical support of RENAULT SAS.

power is applied. Experimentally, we can observe that the plasma radius is around 1 mm, the cathode radius being 4 mm. The assumption made is that the fraction of the gas that passes through the arc is equal to the ratio between the arc volume and the inner cathode volume. As a consequence, the fraction ratio, which can be expressed with the section ratio of the arc and the cathode, is equal to 1/16 (6.25%). The mixing temperature is calculated from the global enthalpy balance. Finally, the post-discharge is modeled by means of PFR. The model has been implemented in FORTRAN code using the PSR and SENKIN modules of the CHEMKIN II package [START_REF] Kee | Sandia National Laboratories Report[END_REF] .

Results and discussion

Various parameters have been studied to assess their influence on the reformer performances: O/C, input current, mass flow rate and cathode length. Unless otherwise specified, O/C is equal to 0.6 for the first operating condition and equal to 1 for the second operating condition, the input current is 0.4 A, the exhaust gas molar flow rates are 39.10 -3 and 32.10 -3 mol.s -1 respectively and the cathode length is 75 mm. For condition 2, the Diesel fuel decomposition is higher than 80% for O/C greater than 1.3. The second operating condition (Φ = 0.32) reaches an energy efficiency of 40% against only 15% for the first one (Φ = 0.66). The strong difference in energy efficiencies is essentially due to the

Influence of O/C ratio.