GATE Irène Andreou
email: andreou@gate.cnrs.fr

A FOREWARNING INDICATOR SYSTEM FOR FINANCIAL CRISES : THE CASE OF SIX CENTRAL AND EASTERN EUROPEAN COUNTRIES

Keywords: JEL classification : F31; F47 Currency Crisis, Early Warning System, Composite Indicator

We propose a measure of the probability of crises associated with an aggregate indicator, where the percentage of false alarms and the proportion of missed signals can be combined to give an appreciation of the vulnerability of an economy. In this perspective, the important issue is not only to determine whether a system produces true predictions of a crisis, but also whether there are forewarning signs of a forthcoming crisis prior to its actual occurrence. To this end, we adopt the approach initiated by Kaminsky, Lizondo and Reinhart (1998), analyzing each indicator and calculating each threshold separately. We depart from this approach in that each country is also analyzed separately, permitting the creation of a more "custom-made" early warning system for each one.

Introduction

The proliferation of financial crises in the emerging economies during the nineties led economists to spend great efforts in the building of forewarning indicators that could help prevent the detrimental effects of financial turbulence and assist policymakers in taking appropriate actions. In the literature, several modeling approaches have been suggested as frameworks that can help forecast financial crises. Firstly, structural models focus on the factors that generate currency crises : balance of payments crises as described by [START_REF] Krugman | A model of balance of payments crises[END_REF] and [START_REF] Flood | Collapsing Exchange Rates: some linear examples[END_REF]; speculative attack models based on investors' expectations of monetary policy; financial bubble models with moral hazard behaviors (see [START_REF] Krugman | What happened to Asia[END_REF]. A second approach consists of models in which the occurrence of financial crises is a consequence of contagion channels : commercial trade, portfolio re-allocations, political channels (see, among others, [START_REF] Eichengreen | Contagious currency crises[END_REF], [START_REF] Sachs | Financial crises in emerging markets: the lessons from[END_REF], Glick and Rose (1998), [START_REF] Bussière | Towards a new early warning system of financial crises[END_REF], [START_REF] Komulainen | What drives financial crises in emerging markets?[END_REF]). Thirdly, several empirical models have also been proposed. They are based on value at risk analysis, logit/probit regressions, Early Warning Systems, and Markovian models (see, among many others, [START_REF] Burkart | Leading indicators of currency crises for emerging economies[END_REF], [START_REF] Abiad | Early-warning systems: a survey and a regime-switching approach[END_REF], [START_REF] Kumar | Predicting emerging market crashes[END_REF]).

In this paper we propose a measure of the probability of crises associated with an aggregate indicator, where the percentage of false alarms and the proportion of missed signals are combined to give an appreciation of the vulnerability of an economy. In this perspective, the important issue is not only to determine whether a system produces true predictions of a crisis, but also whether there are forewarning signs of a forthcoming crisis prior to its actual occurrence. To this end, we adopt a signal extraction approach, following the methodology suggested in previous papers by [START_REF] Kaminsky | Leading Indicators of Currency Crises[END_REF], [START_REF] Berg | Are currency crises predictable? A test[END_REF], [START_REF] Goldstein | Assessing Financial Vulnerability. An early warning system for emerging markets[END_REF], and [START_REF] Edison | Do indicators of financial crises work? An evaluation of an early warning system[END_REF]. However, our interpretation contrasts with previous studies in the conception of what a good warning system must be for an emerging economy. It is common wisdom that in constructing warning systems, economists usually face a dilemma. On one hand, they attempt to construct a system that yields a high percentage of correctly predicted crises : in this case, the counterpart is a high proportion of false crisis signals. On the other hand, they try to minimize the proportion of false signals, and in this case, they must also accept a low proportion of good crisis predictions. In the case of the countries treated in this study, a monitoring system with a high proportion of false crisis signals is not necessarily something bad, since it may simply mean that the warning system detects situations of increased vulnerability in a context of deteriorating macroeconomic fundamentals. An intertemporal accumulation of false signals can indicate a high probability that a severe crisis will actually occur in the near future. Therefore, false alarms may simply indicate the deterioration of economic fundamentals and potential forthcoming crises. We propose such an indicator in this paper and show that the predicted probabilities of a currency crisis in Russia and, to a lesser extent, Kazakhstan, have remained high during the early and mid nineties. In contrast, a comparison with other Central and Eastern European countries (such as the Czech Republic, Hungary and Poland) reveals that the probabilities of a crisis were high only a few periods prior to the observed crises and low otherwise.

The forewarning model we propose in this paper differs with respect to several aspects when compared to more conventional forewarning system models based on the signal extraction approach. The main differences are threefold. Firstly, banking system collapses often coincide with the onset of a currency crisis. For example, the biggest difference between Russia and other Eastern European countries was the role of the banking system. In the former, credits have continued to be inefficiently directed towards the big state-owned industrialized conglomerates, bad loans increased and the absence of supervisory laws induced high inflation and the development of a barter economy.

In contrast, in Central and Eastern Europe monetary authorities imposed a control of credits that was part of a tightening monetary policy, signaling the authorities' intention to address appropriately their inflation problem. Such a decision was positively interpreted by the markets and helped in assessing the credibility of the monetary policy. In view of these observations, it seems interesting to include among the set of leading indicators a macroeconomic variable that captures the influence of banking crises. Here, we use commercial bank deposits and the ratio of credits to GDP as proxies. The decrease of commercial bank deposits or the rapid expansion of credits are two vectors of banking crises.

Secondly, we use quarterly data, rather than annual or monthly data, as is usually the case. Indeed, in the case of Russia, the 1998 crisis was so severe that any preventive action required some precision about the exact dating of the crisis. An annual periodicity is not informative enough, because in this case the warning system is unable to predict whether a crisis is going to happen at the beginning or at the end of the year.

Thirdly, to assess the potential risk of a financial crisis, we compute the probability that a crisis will occur provided that the composite indicator exceeds certain threshold values. These threshold values vary with specific countries, as we have tried to adapt the forewarning system to each country's special features and crisis history.

The structure of the paper is as follows. Section 2 presents ten macroeconomic leading indicators and shows that their behaviour differs around crisis periods. In Section 3, a composite indicator is proposed to estimate the probability of a crisis. Finally, Section 4 concludes.

Single leading indicators for predicting financial crises

Financial crises can manifest themselves in several ways : currency crises, banking system collapses, rapid increase of short-term debt, pressure on the domestic interest rate markets, high inflationary periods yielding financial bubbles, etc. In all cases, one of the cornerstones of financial turbulence in emerging markets is the observation of severe pressure on the domestic currency with high costs on the external balance. We accordingly adopt a criterion for the definition of a crisis that accounts for both pressures occurring in the exchange rate market and diminishing foreign reserves. The market pressure index is defined as follows:

t t t RESERV REER IND ∆ - ∆ = 2 1 φ φ (1)
where REER is the real exchange rate and RESERV stands for the country's foreign reserves.

Market pressure is thus observed when the real exchange rate depreciates and when a country is confronted with reserve losses.

A financial crisis is then defined as follows:

   ≥ = otherwise c IND if crisis t t , 0 , 1 (2)
A crisis occurs when pressures in the exchange rate market and foreign reserve losses are very high. By 'high', one means that exchange rate depreciation and foreign reserve losses have reached a threshold value above which their continued decline is not sustainable. The identification of a crisis is thus conditioned by three important parameters, c , , 2 1 φ φ . The latter must be parameterized (or sometimes estimated) by the modeler. It is common wisdom to interpret the weights when the indicator is δ standard deviations above its mean. C must be determined optimally, in such a way that the crises identified correspond, as much as possible, to the observed episodes of currency crises in the exchange rate markets. After trying different values, we finally choose 75 . 0 = δ . This allows us to capture most of the pressures that the six countries examined in this paper have experienced.

Our study covers the period starting from the first quarter of 1996 and ending at the last quarter of 2003. We use quarterly data for the following countries : Russia, Hungary, Poland, the Slovak Republic, the Czech Republic and Kazakhstan. Our series are taken from the IMF database (IFS statistics). A detailed description of the variables used is given in the appendix.

Evidence of crises provided by the Market Pressure Index

Figure 1 shows signs of tensions in 1996. Furthermore, the market pressure index crosses its threshold value from the third quarter of 1997 until mid-1998. The index as defined above has the following advantage. Not only does it detect the year 1998 as a crisis period, but it also corroborates the observation that in Russia the 1998 crisis did not appear suddenly, but was the height of an economic crisis that lasted many years (cumulative decline in GDP by more than 40% between 1989 and 1996, near-hyperinflation) in a context of failure of the reform strategies undertaken during the transition period. Indeed, macroeconomic fundamentals began to seriously deteriorate in 1996 and 1997 and this was the consequence of a combination of factors: deterioration of the terms of trade, fall in oil prices, sharp depreciation of the Ruble, increases in interest rates and internal problems (fiscal and debt crises). In addition, the index provides evidence of tensions in mid to late 1999, as well as at the end of the year 2003.

Figures 23456depict the case of the other five countries. The Russian crisis and the slowdown of the Western European countries' economies had a negative impact on the Central and Eastern European countries' exports, as well as Foreign Direct Investment, thereby inducing an important slowdown of their activity from 1998 onwards. Moreover, internal issues such as faster growth and higher inflation, as well as fiscal problems, put pressures on these countries' exchange rates. Contagion channels have also been important in explaining financial market turmoil. Figure 6 gives a good illustration of contagion in Kazakhstan. As one sees, the market pressure index has crossed its threshold several times between the first quarter of 1998 and the end of 1999, in the aftermath of the Russian crisis.

This can be expected, given the relations and closeness of the two economies. A similar observation could apply to Hungary, Poland and the Slovak and Czech Republics, though the contagion effects have been delayed over time. The graphs corroborate the historical observation that these countries have continued to suffer from contagion effects in the 2000's.

It is also important to note that for all of these countries the index gives evidence of the influence of the 1997 Czech crisis (triggered by speculative attacks due to weakening fundamentals and the Asian crisis), which encouraged the CEECs to move towards greater exchange rate flexibility.

Economic indicators

A central question in the signaling approach is the choice of the crises' potential determinants. For the countries examined in this paper, we consider different categories of explanatory variables:

• a monetary variable : the ratio of M2 to nominal GDP. The upper bound is considered for this variable, because expansionary monetary policy and/or a decline in GDP are associated with the onset of a crisis.

• a capital account variable: the ratio of M2 to foreign exchange reserves. We take into account the upper bound for this variable, because expansionary monetary policy and/or sharp declines in reserves usually precede financial crises.

• current account variables :

-the real exchange rate : lower bound, for real exchange rate overvaluations (-) are linked to currency crises.

-the value of exports and imports : lower bound for exports and upper bound for imports, because a weak external sector is part of a currency crisis.

-current account balance measured as the ratio of the difference of exports and imports to GDP : lower bound, for the aforementioned reasons.

• banking variables :

-commercial bank deposits : lower bound, for a loss of deposits occurs as a crisis unfolds.

-the ratio of domestic credit to GDP : upper bound, since credit expands prior to a crisis and contracts afterwards.

• real sector indicators : GDP and GDP growth. The lower bound is considered for both these variables, due to the fact that recessions often precede financial crises.

The important issue here is the stability of the financial sector, as is highlighted in third generation currency crisis models. The motivation behind such a choice is rather intuitive.

The Russian crisis was part of a huge financial crisis characterized by a weak banking sector and several bankruptcies of financial intermediaries. For the other countries, the reasons for choosing variables that reflect the stability of the financial sector are similar to those evoked when considering the currency crises in the South-East Asian countries : the degree of the severity and spread of a currency crisis occurring in a neighboring country depends upon the fragility of their own financial markets, or in other words, the strength of the banking sector.

The above variables can be considered as warning indicators of a forthcoming financial crisis for several reasons. First, prior to a crisis, domestic credit tends to increase and the rapid growth of credit is transformed into a sharp contraction when the crisis appears. Furthermore, credit expansion is usually observed in the context of an expansionary monetary policy inducing an increase in the ratio of M2 to GDP. Second, a currency crisis generally follows a sharp deterioration of the external balance : loss of competitiveness, current account deficits and foreign reserve losses. Third, an unstable economic situation is a vector of financial crises. Finally, in a context of immature banking sectors, crisis episodes are accompanied by losses of commercial bank deposits.

Computing noise-to-signal ratios for single indicators

We consider an on/off signal and a variable, S t , that takes the value 1 if a crisis is signaled and 0 otherwise. The prediction of a crisis or a calm period depends upon the behavior of a macroeconomic variable. A crisis signal is detected when this variable deviates from its usual values beyond a certain threshold level:

     < ≥ = X X X X if S signal t t t , 0 , 1 : (4)
where X is a macroeconomic variable. Note that we need a signaling horizon, that is the time horizon at which a variable is expected to predict a crisis. In this paper, we consider a signaling period of four quarters. To define the optimal value of the threshold X , we proceed as follows. Consider the following events:

A: the variable predicts a crisis and the crisis occurs within four quarters (good 'on' signal)

B: the variable predicts a crisis, but no crisis occurs during the signaling period (false crisis signal)

C: the variable does not predict a crisis, but a crisis occurs (missed crisis signal or false calm signal)

D:

The variable does not predict a crisis and no crisis occurs (good 'off' signal)

These four situations are summarized in the following matrix:

) / ( ) / ( ) / ( 1 ) / ( C A A P D B B P C A C P D B B P ∪ ∪ = ∪ - ∪ = α (5)
The noise-to-signal ratio is thus the ratio of false signals to good signals. A macroeconomic variable is considered as a good warning indicator of a currency crisis if this ratio has values near 0. Accordingly, the threshold X , to be selected, must minimize the above ratio. To do this, we use the quantiles of the variable X and retain those yielding the lowest value of α . We also compute the probability of correctly predicting a crisis :

) ( ) ( B A P A P ∪ = β (6)

Performance of economic indicators

Tables 2-7 display the results for the six countries. Column 1 reports the quantiles corresponding to the minimum noise-to-signal ratio for each indicator. In all cases, the quantiles chosen vary with the macroeconomic indicator under consideration. Generally, we could say that for the countries where the quantiles chosen are, in majority, situated below Q5, the proportion of observations corresponding to crises is higher in comparison to those of the periods considered as tranquil. As a consequence, the risk of emitting false signals of future calm periods (or missed signals) is low. When the majority of quantiles chosen is situated above Q5, the conclusion is the opposite. As a high value for the threshold increases the proportion of tranquil periods, the risk of emitting false signals of calm periods is increased.

Column 3 reports the noise-to-signal ratio. The indicators have a good explanatory power if the ratio is lower than 1. As seen, this is the case for a majority of variables for the six countries.

For Russia, a bad score is reported by the indicator M2/GDP. This is understandable in a context where the degree of intermediation of the economy is very weak. A better score is obtained by the real exchange rate, a conclusion that is in line with the usual findings in the empirical literature, and the best scores are obtained by GDP, the ratio of the current account to GDP and commercial bank deposits. Though the ratio is lower than 1 for a majority of variables, it seems quite difficult to find indicators with a high degree of reliability in the prediction of financial crises in Russia. This is seen in the fourth column of Table 2, where the ratio of crises accurately predicted has a rather limited explanatory power for many variables, even some of those displaying the lowest noise-to-signal ratios. These findings for Russia corroborate what was observed historically, namely, the difficulty for multilateral international organizations to anticipate the 1998 crisis and to construct reliable forewarning systems.

For Hungary, the best indicators in terms of noise-to-signal ratios are imports and M2/Reserves, which also give satisfactory scores in terms of percentage of correctly called crises and probability of a crisis when a warning signal is emitted by these indicators. As far as Poland is concerned, the best indicator is indisputably the ratio of the current account to GDP. This is not the case for the Slovak Republic, where the best results are given by the real effective exchange rate and the commercial bank deposits variable, a situation mirrored closely by Kazakhstan, as well as the Czech Republic, where the real effective exchange rate also scores high.

In general, good scores are often obtained by the real effective exchange rate (REER), as in most of the recent literature, and the commercial bank deposits variables (supporting the view that banking, financial and currency crises are closely related). However, unsatisfactory scores are usually obtained by M2-based variables and the growth rate variable. According to historical observations, one can explain these results as follows. On one hand, Hungary, Poland, Slovakia and the Czech Republic have experienced successful transitions through a liberalization of the foreign trade sector and a restructuring of their economy, which has increased their credibility vis à vis the financial markets. These reforms have contributed to attenuate the severity of speculative attacks on the local currencies. On the other hand, the economic growth that resulted from successful transition policies has been predominantly concentrated in services and the impact on the manufacturing sector has been limited. The bad performance of GDP growth might be due to the fact that an aggregate index of growth has an imperfect explanatory power. Further, the fact that ratios and growth rates have a lower explanatory power than variables expressed in nominal terms, may partly reflect the fact that the inflation rate has a high signaling role for the financial markets. It is the successful policy of inflation moderation that renders exports more competitive in the foreign trade markets. It is the liberalization of prices that reduces the difference between domestic and world prices, thereby limiting the negative pass-trough effects on imports and economic activity. These effects contribute to increase the level of foreign reserves, thereby preventing the risk of a financial crisis.

Composite indicator and the probability of a crisis

The next step is to combine the different macroeconomic indicators. This avoids placing too strong an emphasis on one variable in particular. Single indicators contain only partial information on forthcoming crises. In order to evaluate the forecasting performance of our indicators in tracking currency crises, we compute the following noise-to-signal ratio weighted indicator:

∑ = j j t j t S I * ) / 1 ( α (7)
where the index j denotes a macroeconomic indicator, j α is the noise-to-signal ratio obtained for the indicator j and s is the signal variable defined above. The signal variable is weighted by the inverse of the noise to signal ratio, thereby giving more weight to indicators that reported low scores. The performance of this composite indicator can be tested using several criteria. Here, it is used to compute the conditional probability of a currency crisis :

∑ ∑ < < < < = < < + U t L U t L U t
We evaluate the probability that a crisis will occur within h quarters (h=4 in this case), provided that the composite indicator is included within certain threshold values, L I (lower bound) and U I (upper bound). These bounds are determined exogenously and do not vary with time, but they do vary from country to country (according to specific characteristics and the values of the composite indicator), permitting the establishment of more custom-made intervals for each country considered.

Once the upper and lower bounds have been determined, we then proceed to the calculation of the empirical conditional probability that a crisis will occur within four quarters given that the composite indicator is included within a certain interval. The results for these calculations are given in Tables 8 to [START_REF] Kaminsky | Leading Indicators of Currency Crises[END_REF]. For example, the conditional probability that a crisis will occur in Russia within t+3, quarters given that the composite indicator at t=1 takes the value 12, is 0.6. Overall, these calculations give reasonable and coherent results, in that in most cases the conditional probability of a crisis tends to increase monotonically with the value of the composite indicator, and tends towards 1 (certainty of a crisis) at very high indicator values.

Table 14 displays simultaneously the value of the composite indicator for each period, the conditional probability associated with it, and the incidence of crises, for each country studied. Analyzing the behavior of the composite indicator, we clearly distinguish two situations. In the cases of Hungary (columns 4-6) and Poland (columns 7-9), the highest probabilities of crises are obtained when a crisis is imminent, or when a crisis actually occurs.

During the periods of non-crisis, the probability values remain relatively small. For the remaining countries, the conclusion is slightly different. The probabilities are high for a longer period before a crisis (especially at the beginning of the nineties), and in the case of the Czech Republic are relatively high for the majority of the period under study. The warning system thus seems to perform rather well for these countries.

Conclusion

The warning system presented here could be refined by adopting approaches recently suggested in the empirical literature, for instance regime switching Markovian early warning systems (Arias and Erlandsson ( 2004)). However, defining an agenda whereby more sophisticated models have to be constructed, seems a difficult task in the case of Russia, given the degree of the spread and detrimental economic repercussions of the 1998 crisis. The current state of the macroeconomic fundamentals does not exclude a repetition of such a crisis in the future. A more promising approach would be to complete our early warning system with other standard approaches : value at risk analysis, logit/probit analysis, and event analysis. The greatest difficulty is to obtain reliable data over the period of the nineties, which reduces the number of potential indicators that can be used in the analysis.

A general conclusion that emerges from this paper is the following. We have proposed a measure of the probability of crises associated with an aggregate indicator, where the percentage of false alarms and the proportion of missed signals can be combined to give an appreciation of the vulnerability of an economy. In this perspective, the important problem is not only whether a system produces true predictions of a crisis, but also whether there are forewarning signs of a forthcoming crisis prior its actual occurrence. For purposes of prevention, policymakers need to have advance warnings in the medium/long-term rather than just a few periods prior to a crisis. Our system seems to perform rather well in this respect for most of the countries studied, but a future venue of research might seek to integrate an indicator for contagion effects to further improve the performance of an early warning system.

1 9 9 8 Q 3 1 9 9 9 Q 1 1 9 9 9 Q 3 2 0 0 0 Q 1 2 0 0 0 Q 3 2 0 0 1 Q 1 2 0 0 1 Q 3 2 0 0 2 Q 1 2 0 0 2 Q 3 2 0 0 3 Q 1 2 0 0 3 Q 3 c IND
2 0 0 0 Q 1 2 0 0 0 Q 3 2 0 0 1 Q 1 2 0 0 1 Q 3 2 0 0 2 Q 1 2 0 0 2 Q 3 2 0 0 3 Q 1 2 0 0 3 Q 3 c IND
2 0 0 0 Q 1 2 0 0 0 Q 3 2 0 0 1 Q 1 2 0 0 1 Q 3 2 0 0 2 Q 1 2 0 0 2 Q 3 2 0 0 3 Q 1 2 0 0 3 Q 3 c IND
2 0 0 0 Q 1 2 0 0 0 Q 3 2 0 0 1 Q 1 2 0 0 1 Q 3 2 0 0 2 Q 1 2 0 0 2 Q 3 2 0 0 3 Q 1 2 0 0 3 Q 3 c IND

2 1 ,

 1 φ φ as measures of the volatility of the changes occurring in the real exchange rate and foreign reserves. We normalize 1 φ to 1 and define 2 φ as the ratio of the standard deviation of the rate of change of the real exchange rate and the standard deviation of foreign reserve variation : empirical mean of IND and IND σ is the standard deviation. A crisis occurs

Figure 1 :

 1 Figure 1 : Identification of Crises : Russia

Figure 2 :

 2 Figure 2 : Identification of Crises : Hungary

Figure 3 :

 3 Figure 3 : Identification of Crises : Poland

Figure 4 :

 4 Figure 4 : Identification of Crises : Slovak Republic

Figure 5 :

 5 Figure 5 : Identification of Crises : Czech Republic

Figure 9 :

 9 Figure 9 : Composite Indicator and Conditional Probability : Poland

Table 1 : Indicator Performance

 1

	Crisis within four quarters No crisis within four quarters
	Signal issued by indicator						A	B
	No signal issued by indicator						C	D
	We define the following test:
	    	H H	1 0	: :	a a	not occurs does against crisis crisis	occur
	or
						    	H H	1 0	∪ against D B : ∪ C A :

Table 2 : Performance of Single Indicators : Russia

 2

	Advance	Threshold	Number	Noise to	% of Crises	P(Crisis/Signal) 6
	Indicator	Quantile	of Crises	Signal	Correctly
			Called	Ratio	Called 5
	REER	Q1	4	0,31	21,43%	0,75
	M2 / GDP	Q8	7	0,93	14,29%	0,50
	M2 / Reserves	Q9	4	0,31	21,43%	0,75
	Domestic Credit / GDP	Q9	7	0,31	21,43%	0,75
	Exports of Goods and Services	Q3	10	0,23	57,14%	0,80
	Imports of Goods and Services	Q8	7	0,93	14,29%	0,50
	GDP	Q2	7	0,16	42,86%	0,86
	Growth	Q4	13	0,67	50,00%	0,58
	(EXP-IMP)*100 / GDP	Q2	7	0,16	42,86%	0,86
	Commercial Bank Deposits	Q4	13	0,28	71,43%	0,77

Source : Authors' Calculations

Table 3 : Performance of Single Indicators : Hungary

 3

	Advance	Threshold	Number	Noise to	% of Crises	P(Crisis/Signal)
	Indicator	Quantile	of Crises	Signal	Correctly
			Called	Ratio	Called
	REER	Q3	10	0,48	42,11%	0,80
	M2 / GDP	Q8	7	0,63	15,79%	0,75
	M2 / Reserves	Q6	13	0,21	47,37%	0,90
	Domestic Credit / GDP	Q8	7	0,32	31,58%	0,86
	Exports of Goods and Services	Q2	7	0,76	26,32%	0,71
	Imports of Goods and Services	Q6	13	0,21	47,37%	0,90
	GDP	Q2	7	0,76	26,32%	0,71
	Growth	Q8	27	0,71	84,21%	0,73
	(EXP-IMP)*100 / GDP	Q1	4	0,63	15,79%	0,75
	Commercial Bank Deposits	Q2	7	0,76	26,32%	0,71
	Source : Authors' Calculations

Table 4 : Performance of Single Indicators : Poland

 4

	Advance	Threshold	Number	Noise to	% of Crises	P(Crisis/Signal)
	Indicator	Quantile	of Crises	Signal	Correctly
			Called	Ratio	Called
	REER	Q1	4	0,55	16,67%	0,75
	M2 / GDP	Q5	16	0,73	50,00%	0,69
	M2 / Reserves	Q4	19	0,74	61,11%	0,69
	Domestic Credit / GDP	Q5	16	0,73	50,00%	0,69
	Exports of Goods and Services	Q7	22	0,76	83,33%	0,68
	Imports of Goods and Services	Q3	22	0,58	77,78%	0,74
	GDP	Q1	4	0,55	16,67%	0,75
	Growth	Q1	4	0,55	16,67%	0,75
	(EXP-IMP)*100 / GDP	Q3	10	0,18	50,00%	0,90
	Commercial Bank Deposits	Q1	4	0,55	16,67%	0,75

Source : Authors' Calculations

Table 5 : Performance of Single Indicators : Slovak Republic

 5

	Advance	Threshold	Number	Noise to	% of Crises	P(Crisis/Signal)
	Indicator	Quantile	of Crises	Signal	Correctly
			Called	Ratio	Called
	REER	Q2	7	0,16	42,86%	0,86
	M2 / GDP	Q7	10	0,93	35,71%	0,50
	M2 / Reserves	Q9	4	0,31	21,43%	0,75
	Domestic Credit / GDP	Q5	16	0,73	64,29%	0,56
	Exports of Goods and Services	Q5	16	0,42	78,57%	0,69
	Imports of Goods and Services	Q2	25	0,93	78,57%	0,50
	GDP	Q5	16	0,42	78,57%	0,69
	Growth	Q1	4	0,31	21,43%	0,75
	(EXP-IMP)*100 / GDP	Q3	10	0,62	42,86%	0,60
	Commercial Bank Deposits	Q3	10	0,23	57,14%	0,80
	Source : Authors' Calculations

Table 6 : Performance of Single Indicators : Czech Republic

 6

	Advance	Threshold	Number	Noise to	% of Crises	P(Crisis/Signal)
	Indicator	Quantile	of Crises	Signal	Correctly
			Called	Ratio	Called
	REER	Q3	10	0,29	42,86%	0,90
	M2 / GDP	Q2	25	0,77	80,95%	0,77
	M2 / Reserves	Q7	10	0,29	42,86%	0,90
	Domestic Credit / GDP	Q8	7	0,45	28,57%	0,86
	Exports of Goods and Services	Q2	7	0,45	28,57%	0,86
	Imports of Goods and Services	Q8	7	0,88	14,29%	0,95
	GDP	Q2	7	0,44	28,57%	0,86
	Growth	Q3	10	0,66	38,10%	0,80
	(EXP-IMP)*100 / GDP	Q7	23	0,46	80,95%	0,85
	Commercial Bank Deposits	Q8	25	0,50	100,00%	0,84

Source : Authors' Calculations

Table 7 : Performance of Single Indicators : Kazakhstan

 7

	Advance	Threshold	Number	Noise to	% of Crises	P(Crisis/Signal)
	Indicator	Quantile	of Crises	Signal	Correctly
			Called	Ratio	Called
	REER	Q2	7	0,14	46,15%	0,86
	M2 / GDP	Q1	28	1,03	84,62%	0,44
	M2 / Reserves	Q1	28	1,03	84,62%	0,44
	Domestic Credit / GDP	Q2	25	0,98	76,92%	0,45
	Exports of Goods and Services	Q4	13	0,51	61,54%	0,62
	Imports of Goods and Services	Q2	25	0,81	84,62%	0,50
	GDP	Q4	13	0,51	61,54%	0,62
	Growth	Q8	25	0,74	92,31%	0,52
	(EXP-IMP)*100 / GDP	Q2	7	0,14	46,15%	0,86
	Commercial Bank Deposits	Q2	7	0,14	46,15%	0,86
	Source : Authors' Calculations

Table 8 : Conditional Probabilities of Financial Crises : Russia

 8

	Value Of Composite Index	Probability of Crisis
	0 -2	0,0000
	2 -5	0,4286
	5 -10	0,5000
	10 -15	0,6000
	Over 15	1,0000
	Source : Authors' Calculations

Table 9 : Conditional Probabilities of Financial Crises : Hungary

 9

	Value Of Composite Index	Probability of Crisis
	0 -2	0,1667
	2 -5	0,6000
	5 -10	0,6667
	10 -12	1,0000
	Over 12	0,8333
	Source : Authors' Calculations

Table 10 : Conditional Probabilities of Financial Crises : Poland Value Of Composite Index Probability of Crisis

 10

	0 -2	0,0000
	2 -6	0,6250
	6 -10	0,6364
	10 -13	1,0000
	Over 13	1,0000
	Source : Authors' Calculations

Table 11 : Conditional Probabilities of Financial Crises : Slovak Republic

 11

	Value Of Composite Index	Probability of Crisis
	0 -3	0,0000
	3 -5	0,2000
	5 -10	0,3333
	10 -13	0,7500
	Over 13	0,8333
	Source : Authors' Calculations

Table 12 : Conditional Probabilities of Financial Crises : Czech Republic

 12

	Value Of Composite Index	Probability of Crisis
	0 -2	0,0000
	2 -5	0,1667
	5 -10	0,9000
	10 -15	0,8571
	Over 15	1,0000
	Source : Authors' Calculations

Table 13 : Conditional Probabilities of Financial Crises : Kazakhstan Value Of Composite Index Probability of Crisis

 13

	0 -5	0,0000
	5 -10	0,3571
	10 -20	0,6667
	20 -30	0,8000
	Over 30	1,0000
	Source : Authors' Calculations

Table 14 : Summary Table : Composite Indicator, Conditional Probability and Incidence of Crises

 14

			RUSSIA			HUNGARY			POLAND		SLOVAK REPUBLIC		CZECH REPUBLIC		KAZAKHSTAN
		Composite Conditional Incidence Composite Conditional Incidence Composite Conditional Incidence Composite Conditional Incidence Composite Conditional Incidence Composite Conditional Incidence
		Indicator	Probability of Crises	Indicator	Probability of Crises	Indicator Probability of Crises	Indicator	Probability of Crises	Indicator Probability of Crises	Indicator	Probability of Crises
	1996Q1	22,2143	1,0000	0	10,6140	1,0000	1	6,8095	0,6364	0	10,6071	0,7500	0	15,7397	1,0000	1	7,2738	0,3571	0
	1996Q2	20,7143	1,0000	1	10,6140	1,0000	1	6,8095	0,6364	0	11,1429	0,7500	0	15,7397	1,0000	1	6,2482	0,3571	0
	1996Q3	14,2857	0,6000	0	12,1930	0,8333	0	6,8095	0,6364	0	11,1429	0,7500	0	15,7397	1,0000	1	4,9055	0,0000	0
	1996Q4	15,7857	1,0000	0	9,2105	0,6667	0	3,1429	0,6250	0	12,7500	0,7500	0	15,7397	1,0000	0	7,2152	0,3571	0
	1997Q1	15,7857	1,0000	0	10,6140	1,0000	1	4,9762	0,6250	1	18,4133	0,8333	0	17,2635	1,0000	1	21,9844	0,8000	0
	1997Q2	20,7143	1,0000	0	6,0526	0,6667	0	1,3095	0,0000	0	8,7704	0,3333	1	14,4444	0,8571	0	29,6328	0,8000	0
	1997Q3	14,2857	0,6000	1	7,4561	0,6667	0	1,3095	0,0000	0	6,0918	0,3333	0	9,8730	0,9000	0	17,9692	0,6667	0
	1997Q4	15,7857	1,0000	1	0,0000	0,1667	0	6,8095	0,6364	0	6,0918	0,3333	0	14,5968	0,8571	0	23,2152	0,8000	0
	1998Q1	25,4286	1,0000	1	4,5614	0,6000	0	1,3095	0,0000	0	13,0561	0,8333	0	10,5333	0,8571	0	15,6254	0,6667	1
	1998Q2	14,2857	0,6000	0	1,4035	0,1667	0	1,3095	0,0000	0	13,0561	0,8333	0	5,4286	0,9000	1	31,6254	1,0000	0
	1998Q3	6,7857	0,5000	0	3,5088	0,6000	0	3,0206	0,6250	0	11,4490	0,7500	0	2,0000	0,1667	1	30,6584	1,0000	1
	1998Q4	10,0000	0,6000	0	3,5088	0,6000	0	8,5206	0,6364	0	22,6990	0,8333	0	6,9778	0,9000	1	24,2408	0,8000	0
	1999Q1	13,2143	0,6000	0	8,2456	0,6667	1	13,1040	1,0000	0	22,1633	0,8333	1	4,8190	0,1667	0	23,0101	0,8000	1
	1999Q2	6,4286	0,5000	0	0,0000	0,1667	0	12,6151	1,0000	1	21,0918	0,8333	0	5,4286	0,9000	0	7,5024	0,3571	1
	1999Q3	3,2143	0,4286	1	1,4035	0,1667	0	11,2401	1,0000	0	10,9286	0,7500	1	2,0000	0,1667	0	3,2234	0,0000	0
	1999Q4	4,7143	0,4286	0	0,0000	0,1667	0	9,8651	0,6364	0	11,4490	0,7500	0	5,6825	0,9000	0	5,5331	0,3571	0
	2000Q1	3,2143	0,4286	0	2,9825	0,6000	0	14,4484	1,0000	1	10,1633	0,7500	1	6,9778	0,9000	0	5,5331	0,3571	0
	2000Q2	0,0000	0,0000	0	1,4035	0,1667	0	12,6151	1,0000	0	5,3571	0,3333	0	8,8825	0,9000	0	4,1905	0,0000	0
	2000Q3	0,0000	0,0000	0	6,1404	0,6667	0	12,6151	1,0000	1	1,0714	0,0000	0	8,8825	0,9000	1	5,5331	0,3571	0
	2000Q4	1,5000	0,0000	0	12,4561	0,8333	0	8,5556	0,6364	0	3,7500	0,2000	0	11,5492	0,8571	0	5,5331	0,3571	0
	2001Q1	1,5000	0,0000	0	12,4561	0,8333	0	8,9484	0,6364	1	3,5204	0,2000	0	10,4063	0,8571	1	5,5331	0,3571	0
	2001Q2	0,0000	0,0000	0	4,7368	0,6000	1	7,1151	0,6364	1	4,2857	0,2000	0	10,0254	0,8571	0	5,5331	0,3571	1
	2001Q3	0,0000	0,0000	0	10,8772	1,0000	1	5,8056	0,6250	0	2,4490	0,0000	0	8,8825	0,9000	0	4,1905	0,0000	0
	2001Q4	1,5000	0,0000	0	10,8772	1,0000	0	4,4306	0,6250	1	5,1276	0,3333	0	10,0254	0,8571	0	12,9177	0,6667	0
	2002Q1	2,5714	0,4286	0	12,4561	0,8333	1	7,1151	0,6364	0	3,5204	0,2000	0	8,2476	0,9000	1	5,5331	0,3571	0
	2002Q2	2,1429	0,4286	0	9,4737	0,6667	0	5,8056	0,6250	0	1,0714	0,0000	0	1,2952	0,0000	0	4,1905	0,0000	0
	2002Q3	1,0714	0,0000	0	10,8772	1,0000	0	5,8056	0,6250	0	1,0714	0,0000	0	3,4540	0,1667	0	5,5331	0,3571	0
	2002Q4	3,6429	0,4286	0	12,4561	0,8333	1	3,0556	0,6250	0	3,7500	0,2000	0	4,5968	0,1667	0	5,5331	0,3571	0
	2003Q1	3,6429	0,4286	0	12,4561	0,8333	0	7,6389	0,6364	0	5,3571	0,3333	0	2,8190	0,1667	0	5,5331	0,3571	0
	2003Q2	2,1429	X	0	12,4561	X	0	5,8056	X	0	1,0714	X	0	2,4381	X	0	4,1905	X	0
	2003Q3	2,1429	X	1	12,4561	X	0	5,8056	X	0	1,0714	X	1	4,5968	X	0	5,5331	X	0
	2003Q4	3,6429	X	0	12,4561	X	0	5,8056	X	0	1,0714	X	0	4,5968	X	0	5,5331	X	0
	Source : Authors' Calculations

This percentage can be computed as (A/A+C).

This probability corresponds to β, and is calculated as (A/A+B).

APPENDIX Data Description

Indicators

Definition and units


Emilie Dargaud Mars

Emilie † Dargaud
email: dargaud@gate.cnrs.fr

Gate
email: gate@gate.cnrs.fr

Mergers and collusion with asymmetric capacities

Keywords: Mergers, Collusion, Leniency programmes JEL classification: L11, L41, K42

When it examines the risk of coordinated effects, an antitrust authority will usually compare the situation where the merger is accepted with an attendant risk of collusion with the benchmark case in which competition is present ex-post. The main objective of this paper is to show that the antitrust authority must take into account the possibility for firms to collude if a merger is rejected. In fact, firms can have incitations to make collusion ex-post (after a rejection of a merger) whereas they would not make collusion ex-ante. All the papers on mergers and collusion tend to look at a minimal discount factor threshold for collusion to be sustained. This article does not only suggest necessary and sufficient conditions for collusion to be enforced but it also analyses the choice which firms have as to whether to collude. We consider an industry with cost-asymmetric firms and we study the analysis of collusion under leniency programmes.

Introduction

Collusion enables firms to exert market power they would not otherwise have, restricts competition and increases prices. Combatting collusion is a major area of activity for any antitrust authority. In particular, this point is addressed in merger cases. Ex ante, competition authorities can prevent the emergence of an industry structure that is prone to collusion, by taking into account this concern when examining proposed mergers. They can also ban facilitating practices. Ex post, competition authorities can take steps to fight collusion per se, e.g., by uncovering evidence of explicit coordination or by attacking specific agreements that again facilitate collusion.

Economic theory suggests that a merger might engender the creation of collusive outcomes because the merger reduces the number of firms and also gives rise to a more symmetric distribution of assets. [START_REF] Compte | Capacity constraints, mergers and collusion[END_REF], inspired by the Nestlé-Perrier merger case1 , showed that the introduction of asymmetric capacities makes collusion more difficult to sustain when aggregate capacity is limited. Giving larger shares of the collusive profits to the bigger firms alleviates somewhat the tension generated by asymmetric capacities, but it does not eliminate it entirely, and the scope for collusion is nonetheless reduced. [START_REF] Rothschild | Cartel stability when costs are heterogeneous[END_REF] and [START_REF] Vasconcelos | Tacit collusion, cost asymmetries, and mergers[END_REF] both dealt with collusion under cost asymmetry when firms compete à la Cournot. Rothschild used standard grim trigger strategies. Vasconcelos looked for more general punishments with a stick-and-carrot structure as proposed by [START_REF] Abreu | Extremal equilibria of oligopolistic supergames[END_REF][START_REF] Abreu | Towards a theory of discounted repeated games[END_REF] and analysed tacit collusion in quantity-supergames involving costasymmetric firms and showed that if a merger brings about an increase in the inequality of asset holdings then collusion will be inhibited.

All proposed mergers notified to the antitrust authority are examined to see if they would significantly impede effective competition. The antitrust authority analyses if the proposed merger can make more likely or more effective for firms to coordinate their actions (coordinated effects) and if it can make profitable for the merging firms to reduce output and raise price unilaterally (unilateral effects)2 .

When it examines the risk of coordinated effects, an antitrust authority will usually compare the situation where the merger is accepted with an attendant risk of collusion with the benchmark case in which competition is present ex-post. But the latter is a strong assumption since it considers that firms automatically act competitively after a rejection of a project of merger. The antitrust authority does not take into account the possible collusion after a rejection of a merger.

The main objective of this paper is to show that the antitrust authority must take into account the possibility for firms to collude if a merger is rejected. In fact, firms can have incitations to make collusion ex-post (after a rejection of a merger) whereas they would not make collusion ex-ante (before a project of merger).

We analyse how asymmetry in cost function across firms, as was suggested by [START_REF] Perry | Oligopoly and the incentive for horizontal merger[END_REF], can affect the scope of collusion after a merger. [START_REF] Perry | Oligopoly and the incentive for horizontal merger[END_REF] but also [START_REF] Farrell | Horizontal mergers: an equilibrium analysis[END_REF] challenged the view that a merged firm is no larger than any of the constituent firms (as in the model of [START_REF] Salant | Losses due to merger: the effects of an exogenous change in industry structure on Cournot-Nash equilibrium[END_REF]. These studies introduce the existence of some crucial assets that are in limited supply in order to capture the notion that some firms are larger than others in a homogeneous product industry. This assumption implies rising marginal cost of output production and, consequently, internal cost savings from mergers could make a merger profitable.

In this setting we show that a merger, under certain conditions, can create a market structure which decreases the possibility of collusion. In particular, when two firms with high production capacities merge, then the space of parameters for which firms collude decreases after this merger.

All the papers on mergers and collusion tend to look at a minimal discount factor threshold for collusion to be sustained. There is one main difference between these papers and ours : this article does not only suggest necessary and sufficient conditions for collusion to be enforced but we do analyse the choice which firms have as to whether to collude. We look at the equilibrium path of firms. The analysis indicates whether collusion is taking place or not in reality.

Another strand of literature related to this paper deals with leniency programmes (as [START_REF] Motta | Leniency programs and cartel prosecution[END_REF](henceforth LP). These programmes reduce fines for cartel members who report themselves to and assist the antitrust authority, and the impact of LP can be seen in the recent increase in successful cartel investigations. For example, in the period from 14 February 2002 to the end of 2005, the European Commission received 167 applications under the 2002 Leniency Notice. Of these applications, 87 were requests for immunity and 80 were requests for reduction in fines. The Commission has granted 51 decisions for conditional immunity. Over the same period, the Commission rejected or decided not to deal any further with 23 applications and had under scrutiny 13 more recent applications. 3The presence of LP introduces a coordination game between the cartel members (apply for leniency or not?). As in [START_REF] Motta | Leniency programs and cartel prosecution[END_REF], LP have two possible effects. The first is the deviation from the cartel agreement by firms which report to the antitrust authority. The second (being a negative effect) is the attenuation of the expected cost of anticompetitive behaviour because of reduced fines. The key mechanism of LP is the rule that allows firms to receive fine reductions even after an investigation is opened. [START_REF] Motta | Leniency programs and cartel prosecution[END_REF] showed that if the antitrust authority has limited resources, then the scope of collusion can be decreased by using LP. The main difference between the paper of Motta and Polo and ours is that here there is a possibility for some firms to merge. Moreover, we consider asymmetric firms.

The article is organized as follows. In section 2 we describe the basic model. Characterizations of equilibria and implications for merger control are provided in section 3. Concluding remarks follow in section 4. Proofs of results and graphics appear in the appendix.

The model

Consider an industry with n asymmetric firms. By asymmetry it is meant that firms have a different share of a specific asset that affects marginal costs.

More precisely, in the model, two identical firms have the same production capacity, denoted by k 1 = k 2 . The other firms have the same fraction of the industry capital stock k j (∀j ∈ n, j = 1, 2). This asymmetry is introduced in each firm´s cost function. A firm is deemed large for the purposes of the model if it owns a large fraction of the capital stock.

Following [START_REF] Perry | Oligopoly and the incentive for horizontal merger[END_REF], cost is assumed depend on the capital owned by the firms :

C(q i , k i ) = q 2 i 2k i + q i c, ∀i ∈ [1, n]
where q i denotes the quantity chosen by firm i, ∀i ∈ [1, n]. Fixed costs are zero.

Cost asymmetry is conventionnally seen as hindering collusion because low-cost firms are more difficult to discipline, both because they might gain more from undercutting their rivals and because they have less to fear from possible retaliation from high-cost firms.

Firms compete on a Cournot basis with a homogeneous product. We assume that the demand function is linear i.e., p = 1 -Q.

Firms can make collusive agreements after firms 1 and 2 have proposed a merger which has either been accepted or rejected by the competition authority in the first period. The outcome of the execution of a collusive agreement is assumed to be that the colluding firms will thence reduce output below the competitive level. Quantity competition also affects retaliation possibilities as well as the short-run gains of deviations from collusive conduct. Indeed, under quantity competition, one is less tempted to increase production levels in order to deviate from a tacitly collusive level, since prices will adjust to enable the competitors to sell all their output. This would tend to make collusion easier to sustain. However, retaliation is somewhat harder under quantity competition because the firm that is the object of retaliation can always soften the blow (compared to a situation of price competition) by changing its output level accordingly.

We extend the framework of [START_REF] Motta | Leniency programs and cartel prosecution[END_REF] by introducing a first stage in which the antitrust authority decides to accept or reject a notification of merger between two firms. The antitrust authority (henceforth : AA) uses leniency programmes; these programmes provide the incentive of reduced fines to firms which reveal information about collusion to the AA.

Four exogenous parameters summarize the enforcement policy:

• F ∈ [0, F ] : the value of the fine if firms are detected by the AA and have not cooperated with it, F being the maximum possible fine which can be imposed.

• f ∈ [0, F ] : the value of the reduced fine for the firm which denounces the collusive agreement. It is assumed that all firms which cooperate with the AA will be granted reduced fines. It is also assumed that the reduction is high enough in order for the LP be really effective because if f is close to the full fine, F there is no incentive to reveal.

• α ∈ [0, 1] : the probability that firm is reviewed by the AA.

• s ∈ [0, 1] : the probability that the AA successfully concludes the investigation when firms do not cooperate.

Type I errors (firms not colluding are still prosecuted) are assumed not to happen and Type II errors (colluding firms not fined) are assumed to happen.

The collusion strategy is modelled on the basis of a trigger strategy: once a firm deviates from the collusive agreement, all the firms will play non cooperatively until the end of the game. These strategies have been initially suggested by [START_REF] Friedman | A non-cooperative equilibrium for supergames[END_REF].

The timing of the game is as follows:

The game starts (t = 0) with the AA approving or rejecting the notification of the merger between two firms, 1 and 2.

After this first stage, the game is repeated indefinitely. It can be formally described as follows.

At t = 1, firms decide to reach a collusive agreement or to deviate (playing non cooperatively). If no firm deviates until a time t then they collude again and get a profit π M . We study the case in which firms can sustain the joint profit maximisation, so the subscript M indicates a collusive outcome since collusion aims at monopolizing the industry. If at time t the AA decides to open an investigation then there are two assumed outcomes :

• Cooperation: firms denounce the cartel to the AA; they pay the reduced fine f and play non cooperatively during one period and restart collusion after an inquiry is concluded. If however a firm deviates from the collusive agreement, firms play non cooperatively until the end of the game.

• No cooperation: the investigation begins at t + 1. If firms are not condemned, which occurs with probability (1 -s), then they continue to play cooperatively; if they are found guilty, then they pay the total fine F and they have to play non cooperatively during one period.

As in the cooperation case, if one firm deviates from the collusive agreement, firms play non cooperatively until the end of the game.

Consequently, there are two types of deviation in this game: the deviation from the collusive agreement and the reporting to the AA.

The equilibrium of the game can now be analysed.

Equilibria

This section describes the various types of equilibria. We describe the perfect Nash equilibria of the game and we have to resolve this game considering merger or not in the first period. [START_REF] Motta | Leniency programs and cartel prosecution[END_REF] suggested that there are three types of equilibria: no collusion (NC), collusion and revelation (CR) and collusion and no revelation (CNR). The existence of these equilibria depends on the value of the relevant parameters.

CR equilibrium exists if the profit of firm colluding and revealing to the AA is greater than the profit of a firm which deviates. CNR equilibrium exists if firm which colludes and does not reveal information has no incentive to reveal information to the AA and also to deviate from the collusive agreement.

Let δ ∈ (0, 1) be the common discount factor.

The results obtained by [START_REF] Motta | Leniency programs and cartel prosecution[END_REF] are as follows: lemma 1. [START_REF] Motta | Leniency programs and cartel prosecution[END_REF] for low values of f )

• for s ∈ [0, s CN R ) and α ∈ [0, min(1, α N C (s)) : CNR exists. • for s ∈ [s N C , 1] and α ∈ [max(α N C (s), α CR ), 1] : NC exists. • for s ∈ [s CN R , 1] and α ∈ [0, α CR ) : CR exists. with:                s N C = (1+δ)(π M -(1-δ)π D -δπ N ) δ 2 (π M -π N +F ) s CN R = (1+δ)(π M -π N +f ) δ(π M -π N +F ) α CR = π M -(1-δ)π D -δπ N (π M -π N +f ) α N C = (1+δ)(π M -(1-δ)π D -δπ N ) δs(π M -π N +F ) [Insert figure 1]
Figure 1 in the appendix represents graphically the Subgame Perfect Equilibria.

The region labelled 1 in the figure 1 represents the area where parameters lead to CR under leniency programs with no actual leniency. Region 2 represents the area where the parameters are such as to make ex-post desistence more easy by encouraging revelation and by shortening investigation time.

Note that α CR ≥ 0 for δ > δ = π D -π M π D -π N which is the usual critical discount factor when firms collude with no threat of prosecution.

The impact of a merger on collusion

In this subsection, the first stage of the game is examined in more detail.

Two cases must be analysed depending on whether the merger is accepted in the first period or not. If the AA rejects the merger in the first period, then the repeated game is played with n firms. As said before, the two firms which are proposing to merge are identical (k 1 = k 2 ). The others have the same production capacity :

k i = k j , ∀i ∈ n, i = (1, 2); n i=1 k i = 1.
Received wisdom suggests that mergers may tend to create structural conditions which facilitate collusion. Firstly, coordination is easier to sustain when the number of competitors is smaller and secondly, as the number of firms decreases, each firm gets a higher share of the market. This has two implications, the gain from deviating decreases for each firm and the longterm benefit of maintaining collusion is increased because it gets a higher share of the collusive profit.

The impact of a merger on collusion is captured in our framework by the comparative static on α CR , α N C and s CN R .

We are going to detail the proceeding of the comparative static on α CR and it will be the same conduct for the others.

To do this, we compute the value of φ = Therefore, there exists some values of α and p for which firms collude and reveal before merger whereas they do not collude if the merger is accepted by the AA. In other words, a merger would attenuate the scope of collusion.

To simplify calculations, we assume that c = 0.

Individual profit functions of the firms (∀i = 1...n) are given by :

         π M = 1 6 k i π D = k i (-2-k i ) 2 18(1+2k i ) π N = β i (2k i -β i ) 2k i (1+β) 2 with β i = k i k i +1 .
Proof. See Appendix A.

These profit functions correspond to the case where a proposed merger is rejected in the first period (n firms compete in the industry). If the merger is accepted in the first period (n -1 firms), production capacity of the merger entity is calculated as follows :

k 1+2 = k 1 + k 2 = 2k 1 .
Numerical simulations of φ and δ are represented in figure 2 in the appendix.

We see in figure 2 for k 1 high enough (k 1 > 0.3) and where δ is sufficiently high that φ > 1. But for low values of k 1 , φ is always stricly less than unity (which is normalized by a plane with φ = 0). All these lemmas are summarized in Figure 3 in the appendix.

The following proposition gives the impact of a merger on collusion :

proposition 1. The impact of a merger on collusion

• With high (resp. low) production capacity of the merging firms, a merger will reduce (resp. increase) the space of parameters under which firms tend to collude.

• With high (resp. low) production capacity of the merging firms, a merger will increase (resp. reduce) the space of parameters under which firms tend to collude with revelation, in comparison with the space of parameters under which firms tend to collude without revealation.

The inference to be drawn from this result is that the larger the firm, the more able it is to derogate from the collusion agreement because the ability of outsiders to punish deviations is attenuated.

Profitability of the merger

In this section we study the profitability incentives for a merger.

First, comparison must be between the individual profit of a merging firm and the individual profit of this firm without any merger in a Nash environment.

To simplify we denote by π N ind (M ) (resp. π N ind ( M )) the individual profit of a firm prior to merge in a Nash environment with the merger (resp. without the merger).

When we compute the static profits, we obtain :

π N ind (M ) > π N ind ( M ) (1)
So the actualised profits of the firms are greater with a merger than without a merger :

π N ind (M )[1 + δ + δ 2 + ...] > π N ind ( M )[1 + δ + δ 2 + ...] (2)
Therefore, firms have incentives to merge if we do not take into consideration the possibility for firms to collude.

What is interesting is to compare the values of the profits when we take into account collusion. More precisely, we compare the interesting case in which a merger is accepted and no collusion follows with the case in which the merger is rejected with collusion after. There are two possibilities : CR equilibrium and CN R equilibrium.

The static profit of the firm 1 or 2 when all firms collude in the industry and without any merger is :

π coll ind ( M ) = k 1 6 < π N ash ind (M ) (3)
• if the equilibrium strategy is CN R the actualised profit (without merger) in a one-shot game is :

α(π coll ind + δ([(1 -s)(π coll ind ) + s(π N ind ( M ) -F )])) + (1 -α)(1 + δ)π coll ind (4)
• if the equilibrium strategy is CR the actualised profit (without merger) in a one-shot game is :

(

1 -α)π coll ind + α[π N ind ( M ) -f )] (5)
The actualised profit in a Nash environment (with merger) is always greater than the actualised profit in CR or CN R environment because π N ind (M ) > π N ind ( M ) and π coll ind ( M ) = k 1 6 < π N ash ind (M ). So the merger is always profitable.

Conclusion and policy implications

Assessing the scope for collusion is a difficult issue.

All the papers on mergers and collusion tend to look at a minimal discount factor threshold for collusion to be sustained. However, the fact that firms could sustain collusion does not mean that they really succeed in doing it. This paper does not only suggest necessary and sufficient conditions for collusion to be enforced but we do analyse the choice which firms have as to whether to collude. We look at the equilibrium path of firms; here we predict whether collusion is actually taking place.

We consider an industry with n asymmetric firms. By asymmetry it is meant that firms have a different share of a specific asset that affects marginal costs (as suggested by [START_REF] Perry | Oligopoly and the incentive for horizontal merger[END_REF]. Some important policy implications can be derived from our results.

They shed some light on the complex problem of assessing the potential jointdominance effects which some mergers bring about. The impact of a merger depends on the nature of the firms involved. The antitrust authorities have to approve, under certain conditions, a merger between two "big" firms in order to fight collusion (these result reinforce those obtained by [START_REF] Vasconcelos | Tacit collusion, cost asymmetries, and mergers[END_REF]. But when small firms want to merge, the risk of collusion is increased. Therefore, mergers reinforcing market asymmetry should be considered by AA as pro-competitive. Remark that this point is divergent from the analysis of unilateral effects because although the asymmetric distribution of costs has the effect of reducing the likelihood of collusion, the implication is, clearly, that dominance is increased.

  bm and am denote the threshold value α CR before and after the merger. If φ is stricly greater than unity, then the border line α CR in figure 1 moves down.

lemma 2 .

 2 With high (resp. low) production capacity of the merging firms, a merger will cause the border line α CR to move down (resp. up)As noted before, we do the same with the other border lines α N C and s CN R and two lemmas follow : lemma 3. With high (resp. low) production capacity of the merging firms, a merger will cause the border line α N C to move to the southwest (resp. northwest) lemma 4. With high (resp. low) production capacity of the merging firms, a merger will cause the border line s CN R to move to the left (resp. right).

European Commission, Case Number IV/M 190: Nestle and Perrier, 92/553/EEC

Council Regulation (EC) no 139/2004

European Commission, MEMO/06/357.

Appendix A : Expression of profit functions NASH PROFIT M ax q i (a -b( n i=1 q i ))q i -

Then : [START_REF] Mcafee | Horizontal mergers and antitrust policy[END_REF].

COLLUSION PROFIT

As [START_REF] Vasconcelos | Tacit collusion, cost asymmetries, and mergers[END_REF], we suppose that monopoly aggregate output is simply divided in proportion to capital endowments.

2b+1 and then we replace in the profit function to obtain the collusion profit.

DEVIATION PROFIT

As in [START_REF] Rothschild | Cartel stability when costs are heterogeneous[END_REF], we suppose here that deviation takes the form which is conventionally assumed in models of this type : the deviant takes the allocated cartel outputs of all other firms as given and selects the output which maximizes its own profits.

M ax q

i and then we replace in the profit function to obtain the deviation profit.