Evaluating the carbon-macroeconomy relationship: Evidence from threshold vector error-correction and Markov-switching VAR models

Economic Modelling 28 (2011) 2634–2656

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Economic Modelling j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c m o d

Evaluating the carbon-macroeconomy relationship: Evidence from threshold vector error-correction and Markov-switching VAR models Julien Chevallier ⁎ Université Paris Dauphine (CGEMP-LEDa), France

a r t i c l e

i n f o

Article history: Accepted 1 August 2011 JEL classification: C01 C32 C52 E23 E32 G12 G15 Q43 Q47 Q54

a b s t r a c t This paper studies the nonlinear adjustment between industrial production and carbon prices – coined as ‘the carbon-macroeconomy relationship’ – in the EU 27. We model carbon price returns and industrial production as nonlinear and state-dependent, with dynamics depending on the sign and magnitude of past realization of returns and the growth of industrial production. Our findings show that (i) macroeconomic activity is likely to affect carbon prices with a lag, due to the specific institutional constraints of this environmental market; (ii) the joint dynamics of industrial production and carbon prices seem adequately captured by two-regime threshold vector error-correction and two-regime Markov-switching VAR models compared to linear models as main competitors. The regime-switching models proposed are profoundly checked for their economic content and statistical congruency, and are found to provide a sound statistical framework for a comprehensive analysis of the carbon-macroeconomy relationship. © 2011 Elsevier B.V. All rights reserved.

Keywords: Carbon price Industrial production Cointegration Threshold cointegration test Threshold vector error-correction VAR Markov-switching VAR

1. Introduction Absent energy efficiency improvements, the link between growth and carbon pricing unfolds as follows. First, economic activity fosters high demand for industrial production goods. In turn, companies falling under the regulation of the European Union Emissions Trading Scheme (EU ETS) need to produce more, and emit more CO2 emissions in order to meet consumers' demand. This yields to a greater demand for CO2 allowances to cover industrial emissions, and ultimately to carbon price increases.1 In its

⁎ Corresponding author at: Center for Geopolitics and Raw Materials (CGEMP), Dauphine Economics Lab (LEDa), Université Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75016 Paris, France. E-mail address: [email protected]. 1 A disclaimer is necessary here: only the European carbon market can be analyzed and is analyzed in this paper, since it provides an adequate geographical scope in order to measure economic activity, and it offers enough historical data since January 2005. As for the ‘world’ price of carbon, which may be inferred from Certified Emissions Reductions (CERs) for instance, our study would suffer from a lack of historical data (with the first quotes recorded in March 2007) and benchmark against which to gauge the evolution of economic activity (as there is no such thing as a world GDP indicator). 0264-9993/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2011.08.003

Energy Bill 2010/2011, the UK Department of Energy and Climate Change explicitly recognizes that macroeconomic activity has to be one of the main drivers of carbon prices, and that the macroeconomic effects should be taken into account when choosing between various paths towards a low carbon economy (with simulations on the relative impacts of funding alternative energy sources such as renewables in the wake of the recession).2 Analysts also explicitly recognize the influence of macroeconomic fundamentals. 3 In the meantime, given the current state of the art, these arguments suffer from a shortage of empirical evidence and economists are still struggling to understand the intricacies between carbon prices and the macroeconomy. While the assessment of the link between economic activity and energy markets has been the theater of many academic battles (see for instance the ongoing controversy between Hamilton (1996a, 2003, 2009, 2010) and Kilian (2008a,b,c; 2009) concerning the effects of oil price shocks on

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Available at http://www.decc.gov.uk/. See for instance the Point Carbon headlines on April 18, 2011: ‘EU carbon hit by macroeconomic worries’ and on May 17, 2011: ‘Canada's emissions drop 6% during recession’, available at http://www.pointcarbon.com/. 3

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output growth), there exists a scarce literature on this topic applied to the carbon market. The price of carbon is classically driven by the balance between supply and demand, and by other factors related to market structure and institutional policies. 4 On the supply side, the number of allowances distributed is determined by each Member-State through National Allocation Plans (NAPs), which are then harmonized at the EU-level by the European Commission. On the demand side, the use of CO2 allowances is a function of expected CO2 emissions. In turn, the level of emissions depends on a large number of factors, such as unexpected fluctuations in energy demand, energy prices (e.g., oil, gas, coal) and weather conditions (temperatures, rainfall and wind speed). The demand for allowances can be affected by economic growth and financial markets as well, but that latter impact has received little attention in previous literature. This paper precisely aims at placing this topic under greater academic scrutiny. Indeed, if considerable effort has gone so far into modelling the price dynamics of CO2 emission allowances (see among others Paolella and Taschini, 2008; Benz and Trück, 2009; Daskalakis et al., 2009), there lacks empirical grounding to document the impact of economic activity on carbon prices. This research question is nonetheless of general interest for market participants, brokers, academics and governments alike, since with a better grasp of the relationship between economic activity and the carbon market, better hedging strategies, forecasting models and policy recommendations can be formulated. To our best knowledge, only Alberola et al. (2008a, 2009) have opened this ‘black box’ by developing econometric analyses at the sector and country levels. They note that economic activity is perhaps the most obvious and least understood driver of CO2 price changes. As economic growth leads to increased energy demand and higher industrial production in general, Alberola et al. (2008a, 2009) show that carbon price changes react non only to energy prices forecast errors and extreme temperatures events, but also to industrial production in three sectors (combustion, paper, iron) and in four countries (Germany, Spain, Poland, UK) covered by the EU ETS. This early work has assessed the impact of the industrial production on carbon prices with respect to the variation between sectors, but it did not provide the complete ‘big picture’ behind this relationship (based for instance on aggregated industrial production data). Some researchers have indirectly attempted to tackle this research question. Oberndorfer (2009) demonstrates that CO2 price changes and stock returns of the most important European electricity corporations are positively related. This effect is particularly strong for the period of carbon market shocks in early 2006, and differs with respect to the countries where the electricity corporations analysed are headquartered. Chevallier (2009) examines the empirical relationship between the returns on carbon futures and changes in macroeconomic conditions. By estimating various volatility models for the carbon price with standard macroeconomic risk factors, the author documents that carbon futures may be weakly forecast on the basis of two variables from the stock and bond markets, i.e. equity dividend yields and the ‘junk bond’ premium. Moreover, Chevallier (2011a) assesses the transmission of international shocks to the carbon market in a Factor-Augmented Vector Autoregression model with factors extracted from a broad dataset including macroeconomic, financial and commodities indicators. Coherent with the underlying economic theory, the results show that carbon prices tend to respond negatively to an exogenous recessionary shock on global economic indicators. Other studies are remotely connected to our research question by focusing on competitiveness issues (see Demailly and Quirion (2008) for a study focused on the iron and steel industry), or 4 Blyth et al. (2009) and Blyth and Bunn (2011) underline that price formation in carbon markets involves a complex interplay between policy targets, dynamic technology costs, and market rules. Besides, they note that policy uncertainty is a major source of carbon price risk. See Chevallier (2011c) for a literature review.

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on the macroeconomic costs of the EU climate policy (see Böhringer et al. (2009) based on the policy analysis computable equilibrium model). Declercq et al. (2011) analyze the impact of the economic recession on CO2 emissions in the European power sector, based on a counterfactual scenario for the demand for electricity, the CO2 and fuel prices during 2008–2009. By drawing insights from the MERGE model, Durand-Lasserve et al. (2011) also attempt to evaluate the impact of the uncertainty surrounding global economic recovery on energy transition and CO2 prices. In recent contributions, Bredin and Muckley (2011) examine the extent to which several theoretically founded factors including economic growth, energy prices and weather conditions determine the expected prices of the EU CO2 allowances during 2005–2009. Through both static and recursive versions of the Johansen multivariate cointegration likelihood ratio test (including time varying volatility effects), they show that the EU ETS is a maturing market driven by these fundamentals. Creti et al. (2011) further confirm this result, in a cointegrating framework by using the Dow Jones Euro Stoxx 50 as their equity variable and by accounting for the 2006 structural break. However, if previous studies have employed cointegration analysis, none of them has adequately addressed the issue of regime change. Hence, threshold effects in any long-run relationship may have been neglected by the existing studies. As industrial production peaks (with associated increases in carbon prices) may occur only above certain levels of economic activity, the use of threshold cointegration could be potentially more meaningful in characterizing the underlying dynamics of the data. In this paper, we seek to evaluate the carbon-macroeconomy relationship by considering a variety of econometric models for the joint distribution of the EU industrial production and carbon price returns in the presence of regime switching dynamics. Because we are investigating the possibility that both time series are described by two different regimes, it is natural to consider a switching-regime or threshold model. In a threshold model, one set of dynamics often describes the ‘usual’ state of affairs, while another set describes the behavior in less usual periods. One class of switching models is the threshold autoregressive (TAR) models. Other classes of switching models include Markov-switching models. The main justification behind the use of such models is that, for the statistical measurement of macroeconomic fluctuations, the Markov-switching autoregressive time series model becomes increasingly popular as soon as the economy witnesses an alternance of expansion and recession, similar to the recent period. We capture the multivariate dynamics in both time series with two-state models where the regimes are characterized as ‘high-’ and ‘low-growth’. 5 Hence, a novelty is that we explicitly assess the dynamic behaviour of industrial production (taken here as a proxy of economic activity) and carbon prices by examining alternative specifications of models that differ in the parameters that switch across regimes. 6 In sharp contrast to previous work, we consider the possibility that there exist threshold effects 7 and regime

5 The estimation and investigation of higher order regimes are left for further research. See for instance the multivariate Markov Switching Intercept Autoregressive Heteroskedasticity (MSIAH) model with four-state modelling regimes characterized as ‘crash’, ‘slow growth’, ‘bull’ and ‘recovery’ states, with applications in Guidolin and Timmermann (2006), Sarno and Valente (2006), Chan et al. (2011). 6 An alternative approach would consist in evaluating the dynamic correlations between industrial production and carbon prices in a multivariate GARCH framework with mixed data sampling, and to study the transmission of shocks from one market to another as in the DCC-MIDAS model (Baele et al., 2010; Colacito et al., 2011). This model is not studied here, since we aim at evaluating the transition from one economic regime to another between the two variables, but it could be developed by future research in this area. 7 There are numerous explanations that might justify the presence of threshold effects. For instance, it is possible that a given period of economic expansion may have a different impact on carbon futures depending on the initial size of the economic shock ceteris paribus.

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change behind any long-run relationship and short-run dynamics involving the EU industrial production and carbon futures. Let us develop some preliminary remarks concerning our choice of the industrial production index as the variable of interest in this paper to represent economic activity. 8 First, while the EU 27 GDP certainly constitutes the first proxy of economic activity which comes to mind (along with GDI), it is only available with a quarterly frequency (at best) from Eurostat, which would yield to an insufficient number of data points to carry out our econometric analysis during the sample period (January 2005–July 2010). 9 Second, we do not need an exact replication of the industrial production specific to EU ETS sectors, since the motivation of the paper is to work with a proxy of the general state of the economy (i.e. trends of economic growth). Besides, with a proxy covering only EU ETS sectors, the problem of re-aggregation of the individual data to the perimeter of the scheme arises. Since there is no unified methodology to date, arbitrary choices have to be made and they hamper the comparison of the findings between researchers. In our view, the industrial production index from Eurostat appears as the most natural choice, since it benefits from an already established methodology to work with EU 27 aggregated data. Let us detail further the general econometric framework. We mainly use two kinds of models: threshold vector error-correction and Markov-switching VAR models. We study first a two-regime threshold vector error-correction model. Implicit in the definition of cointegration is the idea that every small deviations from the long-run equilibrium will lead to error correction mechanisms. From the seminal paper of Balke and Fomby (1997), threshold cointegration extends the linear cointegration case by allowing the adjustment to occur only after the deviation exceeds some critical threshold. Furthermore, it allows capturing asymmetries in the adjustment, whereby positive and negative deviations are not corrected in the same way. The threshold cointegration technique has been applied recently to investigate various questions: by Lo and Zivot (2001) for the law of one price; by Abdulai (2002) for the asymmetric price transmission in the Swiss pork market; by Peel and Taylor (2002) for the covered interest rate arbitrage in the interwar period; by Sephton (2003) for corn and soybean prices in spatially separated markets in North Carolina; by Bec et al. (2004) for the purchasing power parity; by Enders and Chumrusphonlert (2004) for the properties of long-run purchasing power parity in the Pacific nations; by Million (2004) for the Central Bank's intervention and the Fisher hypothesis; by Oscar et al. (2004) for the evolution of Spanish budget deficits; by Aslanidis and Kouretas (2005) for the parallel and official markets for foreign currency in Greece; by Chen et al. (2005) for the asymmetric price transmission from crude oil to gasoline prices; by Chung et al. (2005) for the prices of American Depositary Receipts and their underlying stocks; by Esteve et al. (2006) for the nonlinear adjustment between goods and services in the USA; by Enders and Granger (1998), Enders and Siklos (2001) and Bec et al. (2008) for the term structure of interest rates; by Hu and Lin (2008) for the relationship between energy consumption and GDP in Taiwan; by Kim et al. (2010) for the nonlinear dynamics in arbitrage of the S&P 500 index and futures; or by Holmes (2011) for the short-run dynamics of the US twin deficit behaviour. Another distinctive feature of the analysis conducted here is the Markov-switching environment. The motivation for examining the influence of macroeconomic variables in this framework comes from the empirical evidence suggesting that switching regimes are better 8

Insofar as emissions are monitored on real-time at the installation level, industrial production also provides a good proxy of the demand for CO2 allowances. 9 Note that we do not work with emissions data in this paper, since accessing such data is difficult (at least at the firm level), and it supposes to resort to panel-data econometric techniques (as in Anderson and Di Maria (2011) who analyze CO2 emissions at the country level). In addition, this approach suffers from the drawback that emissions data is available with a yearly frequency only in the Community Independent Transaction Log (CITL) which oversees national registries in the EU.

descriptions of these variables than single regime models. Indeed, the general Markov-switching VAR proposes a formal statistical representation of the economic ‘boom–bust’ cycle. 10 Hamilton (1989) showed that economic activity may follow one or two different autoregressions, depending on whether the economy is expanding or contracting, with the shift between the regimes governed by the outcome of an unobserved Markov chain. As explained by Engle and Hamilton (1990), the basic idea is to decompose time series into a sequence of stochastic, segmented time trends. Specifically, we model any given change in the industrial production and carbon price returns as deriving from one of two regimes, which could correspond to episodes of rising or falling output, respectively. We hypothesize the existence of a single latent variable (the ‘state’ of the economy), which determines both the mean of industrial production growth and the scale of carbon price changes. The main advantage of this approach consists in offering a fully articulated description of the joint time series properties of economic activity and carbon prices. Since the business cycle goes through different phases, the regimeswitching procedure appears useful to capture such asymmetries in the model. 11 In addition, the Markov-switching approach is in line with theoretical studies predicting that abrupt changes in fundamentals should show up in asset prices (Ang and Bekaert, 2002a,b). Markov-switching models have been applied in various contexts: by Turner et al. (1989) to model risk and learning in the stock market, by Kim and Yoo (1995) to model a new index of coincident economic indicators, by Maheu and McCurdy (2000) to study the behavior of stock and oil returns, by Perez-Quiros and Timmermann (2000) to explore firm size and cyclical variations in stock returns, by Whitelaw (2001) to investigate stock market risk and return, by Fong and See (2001, 2002) to model the conditional volatility of commodity index and crude oil futures, by Harding and Pagan (2002) to compare two business cycle dating methods, by Morana and Beltratti (2002) to test the effects of the introduction of the euro on the volatility of European stock markets, by Psaradakis et al. (2005) to study the causal link between monetary variables and output in the US, by Spagnolo et al. (2005) to test the unbiased forward exchange rate hypothesis, by Assenmacher-Wesche (2006) to estimate Central Banks’ reaction function, by Smith (2006) to model short-term interest rates, by Moore and Wang (2007) to investigate the volatility in stock markets for new EU member states, by Xiao (2007) to analyze the Hong Kong residential property market, by Alizadeh et al. (2008) to hedge energy commodities, by Chen (2010) to investigate whether a higher oil price pushes the stock market into bear territory, by Kumah (2011) to measure exchange market pressure, or by Pinson and Madsen (2011) to model wind power fluctuations at two large offshore wind farms. Besides, Taylor et al. (2005) use this methodology to identify two regimes in Australian GDP growth, with a switch from higher to lower volatility levels. Frömmel et al. (2005) find highly persistent regimes for exchanges rates, with the key fundamental which determines regimes being the interest rate. Moolman (2004) analyzes the South African business cycle, and is able to accurately predict the historical turning points based on a two-state Markovswitching model. Cologni and Manera (2009) investigate how oil price shocks affect the growth rate of output in the G-7 countries by comparing alternative regime-switching models. Through an extensive econometric analysis, the authors are able to document the impact of various oil shocks on output growth. In an interesting 10 When output expands towards a peak, the economy is said to be in ‘boom’ or expansion. When output falls towards a low point or trough, the economy is in ‘bust’ or recession (Hamilton and Raj, 2002). 11 As noted by Morley and Piger (2011), the ‘business cycle’ is a fundamental, yet elusive, concept in macroeconomics which corresponds to transitory deviations in economic activity away from a permanent or ‘trend’ level. Moreover, they define recessions as periods of relatively large and negative transitory fluctuations in output. Recessions are also found to be closely related to other measures of economic slack, such as the unemployment rate and capacity utilization.

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application of Markov-switching models to default spreads, Dionne et al. (2011) show that macroeconomic factors are linked with various spreads increases during the recent period, indicating that the spread variations may be related to macroeconomic undiversifiable risk. Earlier on this topic, based on Markov-switching models, Alexander and Kaeck (2008) sent a warning signal by demonstrating that credit default swap (CDS) spreads are extremely sensitive to stock volatility during periods of CDS market turbulence. Based on threshold vector error-correction and Markov-switching VAR models, the central research question tackled in this paper may be stated as follows: what is the impact of economic activity on the growth rate of carbon prices from an empirical point of view? To summarize our findings at the outset, this paper makes two important contributions. First, we examine the possibility that threshold cointegration provides an accurate empirical description of the carbon-macroeconomy relationship within a vector errorcorrection model (VECM). For this purpose, we employ Hansen and Seo (2002)'s model to develop a multivariate threshold cointegration analysis, where the short-run dynamics comprise two regimes based on a threshold in the size of the lagged error correction term. We confirm the presence of threshold cointegration in the data based on Davies (1987)'s adapted Lagrange Multiplier (LM) test statistic. This result suggests that the effectiveness of the threshold cointegration model surpasses that of the linear cointegration model. Thus, the estimated two-regime VECM provides highly satisfactory results, as the error-correction coefficients describe quite different dynamics of adjustment towards the long-run equilibrium. We identify a standard regime spanning most of the sample, along with an extreme regime (containing about 6% of the data). Most of the dynamic adjustment towards the long-run equilibrium between the two variables occurs during the latter regime, with the EU industrial production index having a predominant role (i.e. a significant and lagged impact on EUA futures, but not vice-versa). The empirical evidence from this paper therefore points out that there exist significantly asymmetric dynamic adjusting processes between macroeconomic and carbon price variables in the EU, implying important policy features. Second, we use a two-regime Markov-switching VAR to capture the inter-relationships between the EU industrial production and carbon prices. We confirm the existence of two distinct regimes: a ‘high-growth’ regime with periods of economic expansion, and a ‘low-growth’ regime with periods of economic decline. As one would expect from theoretical groundings, this model confirms that economic activity has a statistically significant impact (with a delay) on carbon prices, but there are no ‘rebound effects’. 12 The main switches between high-growth and low-growth regimes are found in January–April 2005, April–June 2006, October 2008, and April 2009 until the end of the sample period. We cautiously suggest some interpretations based on changes in macroeconomic fundamentals and actual market developments in the EU ETS. The statistical soundness of the Markov-switching model is demonstrated by showing that the estimates match well both time series in the dimension of the mean, variance, skewness and kurtosis, along with other diagnostic tests. More generally, our results suggest that threshold vector errorcorrection and Markov-switching VAR models constitute promising tools to understand carbon price dynamics with macroeconomic activity effects. The paper is structured as follows. Section 2 details the data used. Section 3 deals with threshold cointegration. Section 4 introduces the Markov-switching VAR. Section 5 briefly concludes.

12 It is hardly conceivable nowadays that carbon prices may have a global impact on the economy, through for instance cost pass-through in the energy sector, or greater anticipated inflation coming from the rise in carbon prices and the price of manufactured goods ceteris paribus. Nevertheless, this hypothesis may be explicitly tested in our econometric framework.

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2. Data 2.1. Industrial production and carbon prices Let us explore first the data at hand. For industrial production, the EU 27 seasonally adjusted industrial production index is gathered in monthly frequency from Eurostat. 13 The current base year is 2005 (Index 2005 = 100). Its perimeter covers total industry excluding construction, i.e. it also covers non-ETS economic activity (and thereby reflects global economic activity within the geographical zone). For carbon prices, the European Union Allowance (EUA) Futures price is gathered in daily frequency from the European Climate Exchange (ECX). 14 The choice of the frequency of analysis is a natural consequence of the availability of financial data on a daily basis, 15 while macroeconomic aggregates are published on a monthly basis (at best). Therefore, we have a combination of two sampling frequencies: one monthly and one daily time series. The daily time series is denoted Xj,D t for the j th day in month t (with j = 1 the first day of the month and j = ND the last, with ND the number of days in a month). The conventional approach, in its simplest form, consists of aggregating the daily data to a monthly frequency by computing averages to obtain D XtM = (XND, t D + XND − 1, t D + … + X1, t)/ND. In what follows, we will check thoroughly whether this procedure introduces some bias by testing that the residuals of our various models are not autocorrelated. Hence, the monthly EUA Futures prices are computed as the average value of daily observations during a given month. 16 Note that carbon spot prices are not used in this paper since they were contamined by the ban on banking between Phases I and II of the EU ETS (therefore plummeting towards zero near the end of 2007, see Paolella and Taschini (2008), Alberola and Chevallier (2009), Daskalakis et al. (2009) and Hintermann (2010) on this topic). The study period goes from January 2005 (i.e., the creation of the EU ETS) until July 2010. The data sample consists of 67 monthly observations. The left panel of Fig. 1 shows the raw time series of the EU industrial production and EUA Futures prices. Concerning the EU industrial production, we may distinguish three distinct phases during our study period. First, the period going from January 2005 to May 2008 may be viewed as a phase of economic growth. Second, 13 The EU ETS included 25 Member States during the first two years, Bulgaria and Romania having integrated the trading scheme in 2007 (see Alberola et al., 2009). Therefore, we consider the industrial production for the EU 27 (instead of the Euro area) as the best proxy during our study period. Besides, to obtain the EU 27 aggregated industrial production index, we rely on the methodology developed by Eurostat (2010, see Methodology of the industrial production index). 14 From January to March 2005, EUA Futures prices were recovered from Spectron, one of the major brokers in the energy trading industry, and stem from OTC transactions (see Benz and Trück, 2009 for more details), as ECX was not yet created. The time series of EUA Futures prices were obtained by rolling over futures contracts after their expiration date. Carchano and Pardo (2009) analyse the relevance of the choice of the rolling over date using several methodologies with stock index futures contracts. They conclude that regardless of the criterion applied, there are not significant differences between the series obtained. Therefore, it is unlikely that we introduce any bias by constructing our time series of carbon futures prices. 15 Note that carbon futures prices are also available at the intra-day frequency but, due to a lack of availability of the data before 2008, the liquidity would be too low to construct a reliable dataset over the period 2005–2010. See Chevallier and Sévi (2010, 2011) and Conrad et al. (in press) for more details. 16 Alternative methodologies are left for future research. On the one hand, the Kalman filter (Harvey, 1991) that emerges from a state space model approach requires a full system of measurement and state equations, which in turn results in computational complexities that often limit the scope of its application (see Bernanke et al. (1997) for an application to monetary policy and the effects of oil price shocks). On the other hand, we could perform MIxed DAta Sampling (MIDAS), in the spirit of Ghysels et al. (2002, 2006, 2007) and Andreou et al. (2010). However, this methodology is more often used for forecasting purposes (for instance using parsimonious regressions with a data-driven weighting scheme to improve quarterly macro forecasts with monthly data, see Clements and Galvão, 2009). Thus, the latter approach does not appear appropriate to the research question tackled in this paper.

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EU 27 Seasonally Adjusted Industrial Production Index (Eurostat) 115

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Fig. 1. EU 27 Industrial Production Index (top) and EUA Futures Price (bottom) in raw (left panel) and logreturn (right panel) forms from January 2005 to July 2010. Note: The source of the data is Eurostat and ECX. NBER business cycles reference dates are represented by shaded areas.

we notice after May 2008 an abrupt decline in the industrial production, characterizing the entry of EU economies into the recession. These events follow with some delay the developments of the US economy, following the first interest rate cut by the Federal Reserve in July 2007. This event is mostly viewed as the start of the economic downturn, as the first signs of financial distress in the housing sector met the headlines. 17 Third, from April 2009 until July 2010, we may observe a timid uptake in the industrial production. Therefore, our study period contains an interesting mix of economic growth, recession and recovery that we aim at analyzing jointly with the behavior of EUA Futures prices. The latter time series seems to follow the same pattern, with the presence of shocks during 2005–2007 originating from institutional features of the EU ETS (see Ellerman et al. (2010) for an exhaustive coverage of this topic). 18

17 While analysts detected anomalies in Credit Default Swaps as soon as January 2007, early concerns by the US Board of Governors of the Federal Reserve System concerning the effects of the credit crunch may be related to August 2007. On August 17, 2007 the Board approved an initial 50 basis point reduction in the primary credit rate. See further press releases at the following address: http://www. federalreserve.gov/newsevents/press/monetary/2007monetary.htm. 18 Irregularities in the carbon market data during the first months of trading could be justified by the fact that market participants had no prior knowledge on how to price futures for carbon during that ‘warm-up’ period. As information has been gradually flowing on the market, this time series has gained a more stable price signal around €20/ton of CO2. We choose to keep these observations in our data sample in order to obtain the largest possible dataset.

Fig. 1 also displays in shaded areas the NBER business cycle reference dates, as published by the NBER's Business Cycle Dating Committee. 19 Recessions start at the peak of a business cycle, and end at the trough. During our sample period, the ‘peak’ date is December 2007, and the ‘trough’ date is June 2009. We may remark that the EU industrial production data corresponds fairly closely to the NBER classification of business-cycle turning points. These dates also correspond to a period of high price variability for carbon futures prices (among other episodes, as explained later on). Kim et al. (2005) have shown that Markov-switching regimes applied to US real GDP are closely related to NBER-dated recessions and expansions. Based on visual inspection, it appears that none of the time series under consideration is stationary in raw form. In the right panel of Fig. 1, however, the time series look somewhat stationary when transformed to logreturns. This first diagnostic is confirmed by usual unit root tests (ADF, PP, KPSS) in Appendix A. Both variables are integrated of order 1 (I(1)). However, linear unit root tests may not be adequate if the underlying process is nonlinear, or even piecewise nonlinear (Dufrenot and Mignon, 2002; Pippenger and Goering, 1993, 2000). That is why we also test explicitly for the presence of thresholds and unit root tests (as in Caner and Hansen (2001), Basci and Caner (2005)) in the next subsection. 19 See more on the NBER Business Cycle Expansions and Contractions at http://www. nber.org/cycles.html.

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In the right panel of Fig. 1, there seems to remain some instability in the transformed time series, 20 more especially for the EU 27 Industrial Production Index in logreturn form (between May 2008 and March 2009). Structural changes have also been detected in the carbon market data during April–June 2006, which corresponds to the first compliance event (Alberola et al., 2008b; Chevallier, 2011b). To investigate further this question, we run Ordinary Least SquaresCumulative Sum of Squares tests (OLS-CUSUM, Kramer and Ploberger, 1992), which are based on cumulated sums of OLS residuals against a single-shift alternative. These results, reported in Appendix A, do not allow us to identify any kind of structural instability. For both variables, the empirical fluctuation processes stay safely within their bounds, and do not seem to indicate the presence of structural breaks in the data. 21 As emphasized by Carrasco (2002), structural changes may also be captured by nonlinear stationary models such that threshold and Markov-switching models, which constitute a robust way to detect parameter instability in economic and financial time series. We thoroughly follow this approach in this paper. Since there is no proof of structural instability based on the OLSCUSUM test, 22 the subsequent cointegration and Markov-regime switching analyses are developed over the full sample going from January 2005 to July 2010. Descriptive statistics are shown in Table 1. We may observe that carbon futures prices have a mean value of €18.93 during the period. For both assets, the Jarque–Bera test indicates that returns are not normally distributed (unconditionally), as the time series appear to be slightly skewed compared to the normal distribution, and consistent with the existence of excess kurtosis. In Appendix A, we present the sample autocorrelation (ACF) and partial-autocorrelation (PACF) functions, as well as the ACF of the squared returns, for both series in raw and logreturn forms. By looking at these figures, we may clearly observe an autocorrelation structure for the raw returns of the EU industrial production index, while the logreturns would need to be configured at least with an AR(2) process. Concerning EUA Futures Prices, there is also evidence of autocorrelation in the raw returns, while the logreturns seem to follow and AR(1) or AR(2) process. In Table 1, the Ljung–Box test statistics confirm the existence of significant autocorrelation, except in the logreturns of carbon futures prices. For both variables, the Engle ARCH test does not show significant evidence in support of GARCH effects (heteroskedasticity), except in the raw data of the EU industrial production index. 3. Testing for threshold nonlinearity and unit root Next, we consider tests that allow for the joint consideration of nonlinearity (threshold) and nonstationarity (unit roots). As pointed out by Pippenger and Goering (1993, 2000) and Dufrenot and Mignon (2002), there is a need to develop methods to detect stationarity (or cointegration) when the underlying process follows a threshold model. Caner and Hansen (2001) have derived

Table 1 Descriptive statistics.

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis JB Prob. JB LB test (p-value) ARCH test (p-value) Observations

EU27INDPROD

EU27INDPRODRET

EUAFUT

EUAFUTRET

101.3036 102.1396 110.4501 89.1814 6.2696 − 0.3872 1.9608 4.6891 0.0958 0.0001 0.0024 67

− 0.0002 0.0003 0.0213 − 0.0414 0.0122 − 1.0601 4.5063 18.6019 0.0001 0.0001 0.0826 66

18.9262 19.0600 29.3315 6.2253 5.2402 − 0.0914 2.3710 1.1977 0.5494 0.0001 0.0705 67

0.0135 − 0.0047 0.4976 − 0.2992 0.1313 0.6373 4.8131 13.5091 0.0012 0.4137 0.5886 66

Note: EU27INDPROD stands for the EU 27 Seasonally Adjusted Industrial Production Index, EU27INDPRODRET for the EU 27 Seasonally Adjusted Industrial Production Index in Logreturn form, EUAFUTfor the EUA Futures Price, and EUAFUTRET for the EUA Futures Price in Logreturn form. Std. Dev. is the standard deviation. JB stands for the Jarque Bera test. LB stands for the Ljung–Box test, whose p-values have been computed with a number of 20 lags (the values found are qualitatively similar with 10 or 15 lags). The same comments apply for the Engle ARCH test.

such a test, which has been applied recently by Basci and Caner (2005) 23: Δyt = θ1′ xt−1 + et

if jyt−1 −yt−m−1 j < λ

Δyt = θ2′ xt−1 + et

if jyt−1 −yt−m−1 j≥ λ

ð1Þ

where yt is the selected time series, xt − 1 = (yt − 1, 1, Δyt − 1, …, Δyt − k)′ for t = 1, 2, …, T. et is the i.i.d error term, m represents the delay parameter, and 1 ≤ m ≤ k. The threshold variable is the absolute value of yt − 1 − yt − m − 1. The threshold value λ is unknown and takes the value in the compact interval λ ∈ Λ = [λ1, λ2] where these values are picked according to P(|yt − 1 − yt − m − 1| ≤ λ1) = 0.15, P(|yt − 1 − yt − m − 1| ≤ λ2) = 0.85. Next, we decompose the coefficients: 0

1 ρ1 @ θ1 = β1 A; α1

0

1 ρ2 @ θ2 = β2 A α2

where ρ1 and ρ2 are scalar, β1 and β2 have the same dimension as yt, α1 and α2 are k × 1 vectors. (ρ1, ρ2) represent the slope coefficients on yt − 1, (β1, β2) are the slopes on the deterministic components, and (α1, α2) are the slope coefficients on (Δyt − 1, …, Δyt − k) in the two regimes (see the underlying assumptions for this model in Caner and Hansen (2001)). Eq. (1) may be rewritten as: Δyt = θ1′ xt−1 1f j yt−1 −yt−m−1 j < λg + θ2′ xt−1 1f j yt−1 −yt−m−1 j ≥λg + et

ð2Þ

with 1{.} the indicator function. Under the null of unit root, we have H0: ρ1 = ρ2 = 0. As emphasized by Basci and Caner (2005), there are two interesting alternatives at hand. First, if the time series follows a stationary threshold autoregressive pattern, the alternative of interest is H1: ρ1 b 0, ρ2 b 0. Second, there is the case of partial unit root:  H2 :

20 Stock and Watson (1996) first highlighted the importance of this problem for macroeconomic time series. They suggested that nonlinearity and structural instability (defined as permanent large shifts in the long-run mean growth rate of the economies) shall not be analyzed in isolation, which leads to consider time-varying models (see Granger and Teräsvirta (1999), Timmermann (2000) and Krolzig (2001) for examples). However, this class of models falls beyond the scope of this article and is left for future research. 21 Recall that the dataset for this paper has been gathered in monthly frequency. 22 The same comment applies for alternative estimation techniques that would require the introduction of a dummy variable for the recession period (such as in October 2008), or to regress in sub-samples. Note that the latter strategy would suffer from the drawback of insufficient number of observations in the respective sub-samples.

2639

ρ1 < 0 and ρ2 = 0 ρ1 = 0 and ρ2 < 0

If H2 holds, then the time series is nonstationary, but we do not deal with a classic unit root. The test statistics for testing H0 vs. H1 and H0 vs. H2 are given by Caner and Hansen (2001). Since H1 is one-sided, we test H0: ρ1 = ρ2 = 0 with a simple one-sided Wald as test statistic: 2

2

R1T = t1 1f ρˆ 1 < 0g + t2 1f ρˆ 2 < 0g

ð3Þ

23 The implementation of other unit root tests in nonlinear models, such as Kapetanios and Shin (2006), Bec et al. (2004, 2008), goes beyond the scope of this paper and is left for future research.

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J. Chevallier / Economic Modelling 28 (2011) 2634–2656

^2 . In order to test H0 vs. with t1, t2 the t-ratios for respectively ρˆ 1 and ρ H2, we use the negative of the t statistics − t1,− t2. For both unit root tests, Caner and Hansen (2001) have obtained the limit distributions, and the critical values are tabulated in Table 3 of their article. Even though the unit root tests have the asymptotic bound distribution, we may benefit from a bootstrap in finite samples. In Appendix A, the ADF, PP and KPSS tests for unit roots against linear stationary alternatives have shown that both time series have a unit root (when taken in raw form). This result is not surprising, since standard unit root tests have almost no power when the alternative is nonlinear (Basci and Caner, 2005). Now, let us use the one-sided Wald test (R1T) and t1, t2 tests for unit roots to determine whether the regimes identified above are nonstationary or not. We use the bootstrap procedure described in the Section 5.3 of Caner and Hansen (2001), since this seems to work better in finite samples. Hence, the bootstrap p-values are reported for the one-sided Wald and the t-ratio tests in Table 2. Both R1T statistics are significant at the 10% level, with bootstrap p-values of 0.002. Therefore, the one-sided Wald test (unit root vs. two-regime stationary nonlinear model) is rejected for both time series. For EU27INDPROD, the individual t ratios t1 and t2 have bootstrap p-values of 0.274, and 0.011, respectively. The rejection is due to the second regime, where the p-value for the t test is statistically significant. Turning to EUAFUT, the t1 and t2 tests have bootstrap p-values of 0.014, and 0.322, respectively. The rejection is due to the first regime, where the p-value for the t test is statistically significant. Together, these test statistics indicate that ρ1 = 0 and ρ2 b 0 for EU27INDPROD and ρ1 b 0 and ρ2 = 0 for EUAFUT. Thus, we may conclude that both time series are partially stationary threshold processes. Let us now extend our analysis to the bivariate threshold cointegration model. 4. Two-regime threshold cointegration As in Hansen and Seo (2002), we propose here to examine more closely the carbon-macroeconomy relationship in a two-regime vector error-correction model with a single cointegrating vector and a threshold effect in the error-correction term (see Lo and Zivot, 2001 for an overview). Indeed, multivariate thresholds models seem adequate to tackle the research question highlighted in this paper, i.e. how can we characterize the joint evolution of economic activity (proxied by industrial production) and carbon futures prices? In addition, the topic of asymmetric properties of the adjustment process between these two variables has been paid scant attention in previous literature. Threshold cointegration appears as an appropriate tool to combine nonlinearity and cointegration between the variables of interest in this paper. Specifically, this class of model allows for the nonlinear adjustment to the long-run equilibrium. Neglecting the asymmetric adjustment with macroeconomic variables in particular may lead to biased inferences, and hence to misleading results. Besides, this methodology allows us to investigate the presence of asymmetry in Table 2 Bootstrap p-values of threshold unit root tests (Caner and Hansen, 2001). Variable

R1T

t1

t2

EU27INDPROD EUAFUT

0.002* 0.002*

0.274 0.014*

0.011* 0.322

Note: EU27INDPROD stands for the EU 27 Seasonally Adjusted Industrial Production Index, and EUAFUT for the EUA Futures Price. R1T, t1, t2 are unit root tests described in Caner and Hansen (2001). R1T is for testing H0 vs. H1. t1, t2 are tests for H0 vs. H2. Under their respective columns, we report the bootstrap p-values. m is estimated by minimizing the Sum of Squared Errors (SSE). Bootstrap p-values are calculated from 10,000 replications. * represents significance at the 10% level.

Table 3 Johansen cointegration rank tests. Series: lags interval

LOG(EU27INDPROD)

Trace test Hypothesized No. of CE(s) None * At most 1*

Eigenvalue 0.3167 0.0712

Maximum Eigenvalue Hypothesized No. of CE(s) None * At most 1*

LOG(EUAFUT) 1 to 2 Trace Statistic 29.1060 4.7299

0.05 Critical value 18.3977 3.8414

Prob.** 0.0011 0.0296

Max-Eigen Statistic 24.3769 4.7299

0.05 Critical value 17.1476 3.8414

Prob.** 0.0037 0.0296

test Eigenvalue 0.3167 0.0712

Note: LOG(EU27INDPROD) and LOG(EUAFUT) stand for the logarithmic transformation of the EU 27 Industrial Production Index and the EUA Futures Price, respectively. CE refers to Cointegrating Equation. Included observations: 64 after adjustments. Trend assumption: Quadratic deterministic trend. * denotes rejection of the hypothesis at the 0.05 level. **MacKinnon et al. (1999) p-values. Trace test indicates 2 cointegrating equations at the 0.05 level. Max-eigenvalue test indicates 2 cointegrating equations at the 0.05 level.

the cointegrating relationship between the two variables, whereby increases or decreases of the deviations are not corrected in the same way (Granger and Lee, 1989). The traditional linear approach to error correction modelling assumes that the speed of adjustment towards the long-run equilibrium is the same in every time period. The alternative view is that the presence (or nature) of error correction is dependent on some threshold. Therefore, if asymmetric cointegration is evident, then the conventional vector error-correction models will yield to wrong specifications. The existing approaches to test for threshold cointegration include Balke and Fomby (1997), Lo and Zivot (2001) and Hansen (1996a). These authors have proposed univariate and multivariate tests, where the cointegrating vector is known. More recently, Hansen and Seo (2002) have extended the methodology to the case of an unknown cointegration vector based on a VECM, and a threshold effect based on the error-correction term. They have also developed a Lagrange multiplier test for the presence of threshold effects. This is the approach followed in this section.

4.1. Linear cointegration with a dummy variable We start classically our empirical analysis by showing that there exist two cointegrating relationships among the nonstationary variables of interest. Note that, as a preliminary condition for cointegration, we have checked in Section 2 that the two time series are integrated of the same order (I(1)). Next, we implement the linear Johansen cointegration rank tests. As shown in Table 3, these preliminary tests easily reject the null hypothesis of no-cointegration, indicating the presence of bivariate cointegration. Therefore, we estimate a linear VECM with one dummy variable accounting for the recession of 2008. 24 The linear VECM estimates with one dummy variable are shown in Table 4. They show, by and large, that there exists a statistically significant error-correction term coming from the industrial production equation, which ensures the adjustment towards the long-run equilibrium for the two variables in the system. Other statistically significant coefficient estimates concern the intercept and lagged values of the industrial production index in the industrial production equation. However, the coefficient estimates for the 2008 dummy variable are not significant, which suggests that this approach is not fully satisfactory to model the underlying non-linearities in the data. 24 This technique allows to include a structural (dummy) break in the cointegration exercise. We wish to thank a referee for this suggestion.

J. Chevallier / Economic Modelling 28 (2011) 2634–2656 Table 4 Linear VECM estimates.

Cointegrating vector μ wt − 1 ΔEU27INDPRODt − 1 ΔEUAFUTt − 1 DUMMY2008

ΔEU27INDPRODt

ΔEUAFUTt

0.1114 − 0.1483*** (0.0326) 1.1961*** (0.2753) 0.1601*** (0.0545) − 0.0049 (0.0135) − 0.0050 (0.0074)

0.0110 0.0525 (0.0326) − 0.6181 (0.2753) 0.0434 (0.0545) − 0.0029 (0.0135) − 0.0008 (0.0090)

Note: EU27INDPROD stands for the EU 27 Seasonally Adjusted Industrial Production Index. EUAFUT stands for the EUA Futures Price. DUMMY2008 stands for the 2008 dummy variable. Standard errors are in parentheses. ***,**,* denote respectively statistical significance at the 1%, 5% and 10% levels.

Besides, the estimation of a standard linear VECM could yield to a mis-specification problem owing to the threshold-type nonlinearities present in the data. That is why we apply the threshold cointegration technique in what follows. 4.2. Threshold cointegration 4.2.1. Threshold cointegration model Let xt be a p-dimensional I(1) time series which is cointegrated with one p × 1 cointegrating vector β, with n observations and l as the maximum lag length. Let wt(β) = β′xt denote the I(0) error-correction term. The two-regime threshold cointegration model, or nonlinear VECM of order l + 1, takes the form (Hansen and Seo, 2002):  Δxt =

A1′ Xt−1 ðβÞ + ut ; if wt−1 ðβÞ ≤ γ A2′ Xt−1 ðβÞ + ut ; if wt−1 ðβÞ > γ

ð4Þ

with A1 and A2 the coefficient matrices governing the dynamics of the regimes, Δ the first-order difference operator, Xt − 1(β) = [1 wt − 1(β) Δxt − 1 Δxt − 2, …, Δxt − l]′. The nonlinear mechanism depends on deviations from the equilibrium, above or below the threshold parameter γ. The error ut is assumed to be a vector martingale difference sequence with finite covariance matrix ∑ = E(utu′t). The notation wt − 1(β) and Xt − 1(β) indicates that the variables are evaluated at generic values of β. In our setting, p = 2 since we have a bivariate system for the industrial production and carbon futures, where Δxt corresponds to [ΔEU27INDPRODt ΔEUAFUTt] and one cointegrating vector. Therefore, we may set one element of β equal to unity to achieve identification. Eq. (4) allows all coefficients (except β) to switch between the two regimes. The threshold effect only has content if 0 b P(wt − 1(β) ≤ γ) b 1, otherwise the model simplifies to linear cointegration. Therefore, we assume that: π0 ≤ Pðwt−1 ðβÞ ≤ γ Þ ≤ 1−π0

ð5Þ

with 0 b π0 b 1 a trimming parameter set to π0 = 0.05 (see Andrews, 1993; Andrews and Ploberger, 1994). The model is estimated by maximum likelihood under the assumption that the errors ut are  ˜ , with ũ the ˜ A˜ i ;∑ i.i.d Gaussian. Let the estimates be denoted by β; t residual vectors. The threshold model in Eq. (4) has two regimes, defined by the value of the error-correction term in relation to some threshold γ. It is conceivable that the error-correction may occur in one regime only, or that the error-correction occurs in both regimes but at different speeds of adjustment on the side of EU27INDPROD or EUAFUT. Thus,

2641

this approach provides richer insights than the standard linear errorcorrection modelling, which assumes the same error-correction mechanism throughout the whole sample period. 4.2.2. Threshold Cointegration Test Let us test explicitly for the presence of linear vs. threshold cointegration. 25 Hansen and Seo (2002) suggest to use the LM test statistic proposed by Davies (1987): SupLM =

sup

γL ≤ γ ≤ γU

  ˜ γ LM β;

ð6Þ

˜ t−1 with [γL, γU] the search region, so that γL is the π0 percentile of w and γU is the (1 − π0) percentile. β˜ is the null hypothesis estimate of β (linear cointegration) against the alternative of threshold cointegration. This means that there is no threshold under the  null,  so that ˜ γ is nonthe model reduces to a linear VECM. As the function LM β; differentiable in γ, to implement the maximization defined in Eq. (6), it is indeed necessary to perform a grid evaluation over [γL, γU]. The LM statistics are computed with heteroskedasticity-consistent covariance matrix estimates. To assess the evidence of threshold cointegration, we use the SupLM test (estimated β) with 300 gridpoints, and the p-values calculated by the parametric bootstrap (see Hansen and Seo, 2002) where the true cointegrating vector is unknown for the complete bivariate specification. Fig. 2 shows the resulting LM statistics computed as a function of γ. In Table 5, all p-values have been computed with 5000 simulation replications. The multivariate LM test points to the presence of threshold cointegration, with a test statistic equal to 58.684. This result provides a strong rejection of the null of linear cointegration at the 1% significance level. 26 This empirical finding of threshold cointegration paves the way for the estimation of the asymmetric VECM (instead of the misspecified conventional vector error-correction model). 4.2.3. Threshold cointegration estimates Next, we estimate and test the two-regime model of threshold cointegration between the EU industrial production and carbon futures prices. To select the lag length, we find that the AIC and BIC applied to the threshold vector error-correction model (VECM) pick the value of l = 1. Moreover, we report our results by letting β˜ be estimated. From the grid search procedure, the model with  the lowest ˜ γ ˜ , with the value of log|∑(β, γ)| is used to provide the MLE β; limitation of β in Eq. (5). Then, we use the grid-search algorithm developed by Hansen and Seo (2002) to obtain the parameter    ˜ γ˜ . ˜ γ˜ and A˜2 = A˜2 β; estimates, with MLE(Ã1, Ã2) being A˜ 1 = A˜ 1 β; Table 6 reports the parameter estimates, which were obtained by minimizing the likelihood function over a 300 × 300 grid on the parameters γ, β (see Appendix A for the results of the concentrated negative log-likelihood with respect to each parameter). The estimated threshold is γ˜ = 13:292, with the threshold itself being determined by the relative level of the two time series. The error-correction term is defined as: wt = EU27INDPRODt − 0.118EUAFUTt. Thus, the first regime occurs when EU27INDPRODt ≤ 0.118EUAFUTt + 13.292, i.e. when EU27INDPRODt is less than 13.3 percentage points above 0.118EUAFUTt. 94% of the observations are

25 Note that we leave for further research the implementation of other tests developed by Bec et al. (2004, 2008), Kapetanios and Shin (2006), and Seo (2006). 26 As noted by Esteve et al. (2006), the tests for threshold effects are sensitive to structural breaks. We leave for further research the use of other techniques to detect structural breaks in the data (Bai and Perron, 1998, 2003a,b; Gregory and Hansen, 1996; Perron, 1997). Of course, the limit of the structural break tests is that the shifts are smooth, hence it is difficult to model them unless there are multiple numbers of breaks considered.

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J. Chevallier / Economic Modelling 28 (2011) 2634–2656

LM Statistic as function of Gamma

Table 6 Threshold VECM estimates.

60

55

Threshold estimate Cointegrating vector Estimate Negative log-likelihood

13.2923 0.1182 895.3653

50

First regime

ΔEU27INDPRODt

ΔEUAFUTt

μ

0.0674 (0.0700) 0.6894 (0.7057) 0.0409 (0.0395) − 0.0004 (0.0183)

Percentage of observations

− 0.1109*** (0.0317) − 0.9083*** (0.2718) 0.3033*** (0.0594) − 0.0219 (0.0116) 0.9415

Second regime

ΔEU27INDPRODt

ΔEUAFUTt

μ

− 1.5883*** (0.2897) − 23.5795*** (4.2598) − 0.5070*** (0.1453) 0.6383 (0.1125) 0.0584 48.6385 26.5437

− 0.1215 (0.2339) − 1.2808 (3.2803) 0.2195*** (0.0806) − 0.5704** (0.2155)

45 wt − 1 ΔEU27INDPRODt − 1

40

ΔEUAFUTt − 1

35

30

25 4

5

6

7

8

9

10

11

12

13

wt − 1

Gamma ΔEU27INDPRODt − 1 Fig. 2. LM statistic for the bivariate threshold cointegration model. ΔEUAFUTt − 1

found in this regime, which we label the ‘typical’ regime. In turn, the second regime occurs when EU27INDPRODt N 0.118EUAFUTt + 13.292. This regime is relevant to about 6% of the observations, and may be viewed as an ‘extreme’ regime. This kind of repartition of the data in usual and unusual regimes is consistent with other studies (see for instance Aslanidis and Kouretas, 2005; Chung et al., 2005; Esteve et al., 2006; Hu and Lin, 2008). Since the two-regime threshold vector error-correction model is well specified (as evident from Table 5), parameter estimates in Table 6 convey highly interesting results in terms of regime-specific adjustment dynamics. Indeed, most of the significant variables concern the EU industrial production index, which even impacts positively the EUA futures price in regime 2 at the 1% significance level. During this ‘extreme’ period, the carbon-macroeconomy relationship goes from the EU industrial production index (lagged one period) to the carbon futures price, with a coefficient equal to 0.22. This result is in line with our previous comments. Finally, note that the EUA futures price has no statistically significant effect on the EU industrial production index in either of the regimes. The estimation of the error-correction term, wt − 1, allows for a straightforward investigation into the behavior of the gap between the industrial production and carbon prices in the EU 27 economy. We can also examine the sign and magnitude of these coefficients in order to analyze the adjustment process through which the long-run equilibrium between the two time series is restored. As expected, the EU industrial production index governs most of the adjustment from the short-run to the long-run equilibrium of the model: its coefficients for wt − 1 are highly significant in both regimes. There is a strong and statistically significant error-correction effect

Table 5 LM tests results for threshold cointegration. LM threshold test statistic (Asymptotic) .05 critical value Bootstrap .05 critical value (Asymptotic) p-value Bootstrap p-value

58.6848 19.5843 19.7316 0.0001 0.0001

Note: The model estimated is the bivariate specification with the EU 27 Seasonally Adjusted Industrial Production Index, and the EUA Futures Price. The number of gridpoints for threshold and cointegrating vector is equal to 300. For p-values, the number of bootstrap replications is set to 5000.

Percentage of observations Wald test equality dynamic Coefs. Wald test equality EC coefs.

0.0001 0.0001

Note: EU27INDPROD stands for the EU 27 Seasonally Adjusted Industrial Production Index. EUAFUT stands for the EUA Futures Price. Eicker-White standard errors are provided in parentheses. In Wald test diagnostics, the null hypothesis is of equality of the dynamic coefficients and of the coefficients on the error correction terms across the two regimes, respectively. ***,**,* denote respectively statistical significance at the 1%, 5% and 10% levels. The model estimated is defined in Eq. (4).

in the EU27INDPROD equation, whether the gap is relatively high or low. The coefficients on the error-correction term also indicate that the magnitude of the response for EU27INDPROD is between 1.33 (regime 1) and 18 (regime 2) times greater than the coefficient of EUAFUT. The fact that only for the EU27INDPROD equation is the parameter accompanying wt − 1 significant, indicates that the error-correction in both regimes is based only on the adjustment of the industrial production index, and not on carbon futures (while EU27INDPROD and EUAFUT move together in the long-run). Therefore, we are able to confirm our earlier finding that the industrial production leads the nonlinear mean-reverting behavior of the carbon price, but not vice versa (since the wt − 1 coefficient for EUAFUT is never statistically significant). A comparison of the estimated error-correction coefficients across both regimes suggests that the adjustment process towards the longrun equilibrium is relatively faster in the ‘extreme’ regime. Indeed, the wt − 1 coefficient for EU27INDPROD is especially important (−23.58) with significance at the 1% level, which implies that a mean-reverting dynamic behavior of the ‘gap’ between the two time series should be expected more especially once the threshold (13.3 percentage points) has been reached. A value of the gap above 13.3 percentage points in one month will produce a downward pressure on the industrial production index in the subsequent month in order to restore the long-run equilibrium relationship (see Holmes (2011), among others, for further clues on the interpretation of threshold ECM). We find that the four error-correction coefficients (for the EU industrial production and carbon futures in both regimes) are either negative or insignificantly different from zero if positive. Given these findings, we test whether the adjustment back to the equilibrium is symmetric when the threshold effect is confirmed in the cointegrating equations, i.e. whether the error-correction term is equal within the two regimes. In the bottom lines of Table 6, the Wald

J. Chevallier / Economic Modelling 28 (2011) 2634–2656

Model Response to Error−Correction 3 EU27INDPROD EUAFUT

2

Model Response

1

0

−1

−2

−3

−4 −10

−5

0

5 10 Error Correction

15

20

Fig. 3. Model response to the error-correction.

test results reject the null hypothesis of the coefficients of the errorcorrection terms in the two regimes having the same value. This provides further evidence that a threshold effect does exist in the underlying dynamics of the data. To allow further visual interpretation of the results, the errorcorrection mechanism, which leads toward the long-term cointegrating relationship between the EU industrial production and carbon futures prices in this two-regime threshold model, is pictured in Fig. 3. This figure plots the error-correction effect, i.e. the estimated regression functions of ΔEU27INDPRODt and ΔEUAFUTt as a function of wt − 1 by holding other variables constant. In the figure, it can be seen the strong error-correction effect for EU27INDPROD (and the minimal error-correction effect for EUAFUT) on the right-hand side of the estimated threshold. In contrast, we may observe the minimal error-correction effect for EU27INDPROD (and the flat near-zero error-correction effect from EUAFUT) on the lefthand side of the estimated threshold. For EU27INDPROD, asymmetry is implied in the sense that there is a stronger error-correction effect in the ‘extreme’ regime compared to the ‘typical’ regime (with almost all dynamic coefficients being statistically significant). This finding comes up when we take account of the nonlinearity in the underlying processes, and mirrors the results obtained in previous studies (see for instance Million, 2004; Aslanidis and Kouretas, 2005; Chung et al., 2005; Esteve et al., 2006; Hu and Lin, 2008). Another interesting implication of the statistically significant error-correction term in EU27INDPROD but not in EUAFUT (in either regime) is that the one-period-lagged value of the industrial production index may be used to help forecast the current value of the carbon price. Therefore, our threshold cointegration analysis allows identifying strong feedback effects from the EU industrial production index to carbon futures prices during the second regime. The dynamics come from the EU industrial production index, which may be seen as the leader in the long-term relationship. 27 Once again, the equation for EUAFUT produces statistical insignificant dynamics and negligible

27 In general, the regimes defined by the simple class of threshold autoregressive models are proxies for some underlying latent process that affects the switching between the linear submodels. With more substantive knowledge of the switching mechanism, the threshold mechanism may, however, be explicitly modeled. STAR modelling applied in a vector error-correction model is left for further research (see Martens et al., 1998).

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error-correction effects. Clearly, this implies that there is no ‘bounceback effect’ running from the carbon price to the industrial production index. Finally, our estimates reveal that the shifts between the ‘standard’ and ‘extreme’ regimes are more prevalent during July–August 2007 and December 2008–January 2009. Starting in January 2005, there is a prolonged experience of the standard regime which corresponds to the increasing phase of economic activity (until July-August 2007). It seems that on the onset of the financial crisis, the industrial production sufficiently worsens in relation to carbon futures so as to facilitate a regime switch. Recall that July 2007 is characterized by the first interest rates cut by the US Federal Reserve. Hence, there seems to be an indirect connection between the start of the financial crisis in the US and the shift to the extreme regime (with an associated decreasing pattern recorded in the EU 27 industrial production index). The second marked shift to the extreme regime occurs during December 2008-January 2009. The most recent times have been characterized by an improving EU27INDPROD (i.e. the EU economy starts to pick up), but worsening EUAFUT (i.e. with a delayed adjustment of the EU carbon market to the global recession). With four months of switches between the two regimes over the 67-month study period, the threshold cointegration approach used here offers more flexibility than alternative methodologies based on a single imposed structural break date. In this section, we have examined the long-run relationship between the industrial production and carbon futures by means of the threshold cointegration approach proposed by Hansen and Seo (2002), using EU data covering January 2005–July 2010. More precisely, our empirical methodology makes use of recent developments on threshold cointegration (Balke and Fomby, 1997) that consider the possibility of a nonlinear relationship between the two time series. While cointegration generally assumes that the adjustment of the deviations towards the long-run equilibrium is made instantaneously at each period, threshold cointegration considers the case where the adjustment towards long-run equilibrium does not occur after each small deviation but more realistically only when the deviations exceed some critical thresholds. According to our results, the null hypothesis of linear cointegration would be rejected in favor of a two-regime threshold cointegration model. Consequently, a system of two regimes would seem to characterize the nonlinear adjustment between industrial production and carbon prices towards the long-run equilibrium, with the threshold parameter being estimated at 13.3 percentage points. The short-run dynamics are investigated through an estimated threshold vector error-correction model. The threshold parameters lead to a classification between the ‘standard’ and ‘extreme’ regimes. Depending on the regime under consideration, the magnitude of the error-correction mechanism varies. Another important finding of the estimated threshold VECM is that the error-correction term for EU27INDPROD is negative. This implies specifically that, from the long-run equilibrium, short-run responses are mainly executed by the adjustment of the industrial production in the ‘extreme’ regime. In both cases of the adjustment process, however, the industrial production is found to exert an influence on carbon futures (at statistically significant levels). This result has important implications for the use of public policy to understand the effects of macroeconomic activity on the carbon market. To gain more insights about the inter-relationships between the EU industrial production index and carbon futures prices, we shift our modeling to the Markov-switching VAR in the next section. 5. Markov-switching VAR The normal behavior of economies is occasionally disrupted by dramatic events that seem to produce quite different dynamics for

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the variables that economists study. Chief among these is the business cycle, in which economies depart from their normal growth behavior and a variety of indicators go into decline (Hamilton and Raj, 2002). Following Hamilton (1989), time series may be alternatively modelled by following different processes at different points in time, with the shifts between processes determined by the outcome of an unobserved Markov chain. In this framework, the presence of multiple regimes can be acknowledged using multivariate models where parameters are made dependent on a hidden state process. Consider an n-dimensional vector yt ≡ (y1t, …, ynt)′ which is assumed to follow a VAR(p) with parameters: p

yt = μ ðst Þ + ∑ Φi ðst Þyt−i + t

ð7Þ

i=1

t ∼N ð0; ∑ðst ÞÞ where the parameters for the conditional expectation μ(st) and Φi(st), i = 1, …, p, as well as the variances and covariances of the error terms εt in the matrix ∑(st) all depend upon the state variable st which can assume a number q of values (corresponding to different regimes). Given the initial values for the regime probabilities, and the conditional mean for each state, the log-likelihood function can be constructed and maximised numerically to obtain the parameters estimates of the model. 28 By inferring the probabilities of the unobserved regimes conditional on an available information set, it is then possible to reconstruct the regimes in a spirit similar to the Kalman filter (Harvey, 1991). Our statistical definition of a turning point is that proposed by Hamilton (1989), who has suggested modeling the trends in nonstationary time series as Markov processes, and has applied this approach to the study of post-World War II real GNP 29. Consequently, we view economic recession as an abrupt shift from a positive to a negative growth rate in the aggregate economic activity. Specifically, when the economy is in expansion, growth is μ1 N 0 per month, whereas when the economy is in recession, average growth is μ2 b 0. The general idea behind the class of Markov-switching models is that the parameters and the variance of an autoregressive process depend upon an unobservable regime variable st ∈ {1, …, M}, which represents the probability of being in a particular state of the world. A complete description of the Markov-switching model requires the formulation of a mechanism that governs the evolution of the stochastic and unobservable regimes on which the parameters of the autoregression depend. Once a law has been specified for the states st, the evolution of regimes can be inferred from the data. Typically, the regime-generating process is an ergodic Markov chain with a finite number of states defined by the transition probabilities:  pij = Prob st

+ 1

 = jjst = i ;

M

∑ pij = 1∀i; j ∈ f1; …; Mg

ð8Þ

j=1

In such a model, the optimal inference about the unobserved state variable st would take the form of a probability. Conditional on observing yt, for example, the observer might conclude that there is a probability of 0.8 that the economy has entered a recession, and a probability of 0.2 that the expansion is continuing. The transition probabilities of the Markov-switching process determine the probability that volatility will switch to another regime, and thus the expected

28

As noted by Fong and See (2002), it is common practice to assume that the maximum likelihood estimators are consistent and asymptotically normal. 29 Other studies have concurred that this is a useful approach to characterizing economic recessions (see among others Boldin (1994), Durland and McCurdy (1994) and Filardo (1994)).

duration of each regime. Transition probabilities may be constant or a time-varying function of exogenous variables (see among others Hamilton and Susmel (1994), Cai (1994), and Gray (1996)). 30 A major advantage of the Markov-switching model is its flexibility in modelling time series subject to regime shifts. Markov-switching models have been used in contemporary empirical macroeconomics to characterize certain features of the business cycle, such as asymmetries between the expansionary and contractionary phases. The Hamilton (1989) model of the US business cycle has fostered a great deal of interest as an empirical vehicle for characterizing macroeconomic fluctuations, and there have been a number of subsequent extensions and refinements (see Hamilton and Raj, 2002; Hamilton, 2008 for an introduction). The Markov-switching model has been tested against a linear autoregressive model by Hansen (1992, 1996b). Its interest has been confirmed by Layton (1996) and Sarlan (2001) as a very reliable advance signalling system for the cyclical aspects of the US business cycle turning points, and by Krolzig (1997) to formalize what it means for the economy to go into recession. It can also be extended to multivariate settings. For instance, Krolzig (2001) has generalized Hamilton's model of the US business cycle to analyse regime shifts in the stochastic process of economic growth in the US, Japan and Europe (see among other contributions Albert and Chib (1993), Diebold et al. (1994), Ghysels (1994), Goodwin (1993), Kähler and Marnet (1994), Lam (1990) and Phillips (1991)). By imposing further interpretable restrictions on Hamilton's Markovswitching model, Bai and Wang (2011) have identified short-run regime switches and long-run structural changes in the US macroeconomic data. Typically, we set the number of states equal to 2. Therefore, state 1 represents the ‘high growth’ phase, whereas state 2 characterizes the ‘low growth’ phase (for more details, see Hamilton, 2008 and references therein). During state 1, the growth of the endogenous variable is given by the population parameter μ1, whereas during state 2 the growth rate is μ2. As the number of regimes rises, it becomes increasingly easy to fit complicated dynamics and deviations from the normal distribution in the returns (Guidolin and Timmermann, 2006). However, this comes at the cost of having to estimate more parameters. As Bradley and Jansen (2004) put it, a well-known problem with any application of nonlinear models is the problem of overfitting. There is a trade-off between the depth of the economic interpretation which one would have available with higher degrees for state variables, and the numerical difficulties which accompany such an effort. In its most popular version, which we use here, the Markovswitching model is estimated by assuming two states, while higherorder processes are much less frequently used. This choice of a two-state process is motivated by the fact that this model is intuitively appealing to track the ‘boom–bust’ economic cycle, since these two states may be associated with periods of ‘high-’ and ‘low-growth’. In this configuration, it will be indeed relatively straightforward to interpret the two regimes. Besides, we need a similar econometric setting to compare the regimes generated by the Markov-switching model with those obtained previously with the threshold vector error-correction model. Finally, in papers dealing with a higher number of regimes (see Chan et al., 2011; Guidolin and Timmermann, 2006; Maheu and McCurdy, 2000), it is often the case that the two-regime model brings the best statistical results.31 The model is estimated based on Gaussian maximum likelihood with st = 1, 2. The calculation of the covariance matrix is performed by using the second partial derivatives of the log likelihood function. P is

30 We rely on a constant specification to keep the model parsimonious, and leave the study of more complicated specifications of the transition probabilities for further research. Each regime is thus the realization of a first-order Markov chain with constant transition probabilities. 31 See Psaradakis and Spagnolo (2002) and Cho and White (2007) for statistical tests to determine the number of regimes in Markov-switching models.

J. Chevallier / Economic Modelling 28 (2011) 2634–2656 Table 7 Linear VAR estimates with a dummy.

ΔEU27INDPRODt − 1 ΔEU27INDPRODt − 2 ΔEUAFUTt − 1 ΔEUAFUTt − 2 C DUMMY2008

ΔEU27INDPRODt

ΔEUAFUTt

0.1093 (0.1119) 0.5181*** (0.1109) 0.0102 (0.0106) 0.0043 (0.0105) − 0.0002 (0.0012) − 0.0049 (0.0058)

0.9539 (1.3519) 0.2434 (1.3392) 0.2041* (0.1291) 0.1223 (0.1270) 0.0025 (0.0155) − 0.0016 (0.0098) 252.4406 − 7.5762 − 7.2389

Log-likelihood AIC SC

Note: EU27INDPROD stands for the EU 27 Seasonally Adjusted Industrial Production Index. EUAFUT stands for the EUA Futures Price. DUMMY2008 stands for the 2008 dummy variable. Standard errors are in parentheses. ***,**,* denote respectively statistical significance at the 1%, 5% and 10% levels.

Table 8 Estimation results of the two-regime Markov-switching VAR for EU27INDPRODRET and EUAFUTRET. EUAFUTRET Log-likelihood μ (Regime 1) μ (Regime 2)

 P=

p11 p12

p21 p22



The sum of each column in P is equal to 1, since they represent the full probabilities of the process for each state. Based on this econometric strategy, we begin our analyses by using as a benchmark a linear VAR model with a dummy. Second, we discuss the results obtained for the effects of the EU economic activity (proxied by the industrial production) and carbon futures prices estimated jointly in a Markov-switching VAR. Third, we evaluate the quality of the regime-switching model in fitting the data through diagnostic checks. Fourth, we compare the regimes obtained with the two different classes of regime-switching models. 5.1. Linear VAR estimates with a dummy In Table 7, it may be seen that linear VAR models fail to detect any significant effect coming from macroeconomic activity (proxied by industrial production) to the carbon market. These results are not surprising, given the fact that linear VAR models neglect the underlying nonlinear dynamics of the data, and that the 2008 dummy variable is not statistically significant. Besides, these results are in line with Smith and Summers (2005), who find that Markov-switching VARs overwhelmingly outperform linear VAR models when actually modelling business cycles. 5.2. Bivariate evidence that carbon futures prices are driven by economic activity Table 8 reports the estimation results for the two-regime Markovswitching VAR for EU27INDPROD RET and EUAFUTRET. 32 The order of the VAR has been set to p = 2 by minimizing the AIC. 33 An examination of the coefficients of the two means (μ(st)), which are all statistically significant, shows the presence of switches in growth between the two regimes. In Regime 1 (expansion), output growth per month is equal to 0.14% on average, while in Regime 2

32 We have also estimated another specification with three states. We did not find convincing statistical evidence that the data are really characterized by three separate regimes. These results may be obtained upon request to the authors. 33 These results are not reported here to conserve space.

270.01 0.0014*** (0.0009) − 0.0048*** (0.0006)

Equation for EU27INDPRODRET

EU27INDPRODRET

EUAFUTRET

/1 (Regime 1)

0.1387* (0.0777) − 0.2079 (0.3383) 0.4343*** (0.1178) 1.3421*** (0.5488)

− 0.0003 (0.0043) 0.0192 (0.0213) 0.0043 (0.0136) 0.0134 (0.0559)

/1 (Regime 2) /2 (Regime 1) /2 (Regime 2)

Equation for EUAFUTRET

EU27INDPRODRET

EUAFUTRET

/1 (Regime 1)

1.3369 (1.1483) − 1.5452 (8.7970) 0.7754*** (0.1893) − 0.9257*** (0.2448) 0.0009 0.0013

0.1253* (0.0760) 0.3455 (0.5497) − 0.0313** (0.0151) 1.7236 (1.4546)

/1 (Regime 2)

the transition matrix which controls the probability of a switch from state 1 to state 2:

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/2 (Regime 1) /2 (Regime 2) Standard error (Regime 1) Standard error (Regime 2) Transition probabilities matrix

Regime 1

Regime 2

Regime 1

0.8873*** (0.1700) 0.1211 (0.0815)

0.5189* (0.3111) 0.4927 (0.4326)

Regime properties

Prob.

Duration

Regime 1 Regime 2

0.8029 0.1971

8.60 1.96

Regime 2

Note: EU27INDPRODRET stands for the EU 27 Seasonally Adjusted Industrial Production Index in Logreturn form, and EUAFUTRET for the EUA Futures Price in Logreturn form. Standard errors are in parentheses. ***,**,* denote respectively statistical significance at the 1%, 5% and 10% levels. The model estimated is defined in Eq. (7).

(recession) the average growth rate amounts to − 0.48%. In line with our comments in Section 5.3, the effects of the recessionary shock are found to be quite strong during our study period. Besides, an AR(2) seems necessary to describe the autocorrelation structure of EU27INDPRODRET. For EUAFUTRET, the process seems be characterized by an AR(1). Interestingly, the coefficient estimates suggest that the EU industrial production (variable EU27INDPRODRET) has two kinds of delayed impacts on carbon futures: positive during Regime 1 (as /2 is equal to 0.78 and highly significant), and negative during Regime 2 (as /2 is equal to −0.93 and highly significant). Therefore, these results confirm our analysis from Section 5.3, as well as the insights by Chevallier (2009, 2011a) concerning the delayed impact of macroeconomic activity on carbon markets. Other coefficient estimates do not suggest that carbon futures have any statistical impact on the EU industrial production. The bottom lines of Table 8 report the matrix of transition probabilities for the latent variable st (standard error in parentheses). During an expansionary phase, the series are most likely to remain in Regime 1 (with an estimated probability equal to 88.73%). On the contrary, the probability that the series switch from Regime 1 to Regime 2 is lower (equal to 12.11%). Once the economy finds itself in a depression, the probability that it will be in a depression the following month is estimated to be 49.27%. Finally, if the economy is in Regime 2 (recessionary phase), the probability that it will change directly to a

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J. Chevallier / Economic Modelling 28 (2011) 2634–2656

1 Regime 1 Regime 2

Smoothed Transition Probabilities

0.9 0.8 0.7 0.6 0.5 0.4

Jan.−Apr.05

Apr.−Jun.06

Oct.08 Apr.09−

0.3 0.2 0.1 0 JAN05

NOV05

SEP06

JUL07

MAY08

MAR09

JAN10

Fig. 4. Smoothed transition probabilities estimated from the two-regime Markovswitching VAR for EU27INDPRODRET and EUAFUTRET. Note: EU27INDPRODRET stands for the EU 27 Seasonally Adjusted Industrial Production Index in Logreturn form, and EUAFUTRET for the EUA Futures Price in Logreturn form. Regime 1 is ‘expansion’. Regime 2 is ‘contraction’. NBER business cycles reference dates are represented by shaded areas.

growth regime is equal to 51.89%. Hence, the recessionary phase has a relatively high probability to be followed by a growth period (which is conform to the fact that the economy is picking up near the end of our study period). Let us now have a look at the average duration for each regime. While Regime 2 is assumed to last 1.96 months on average, the average duration of an expansionary phase is equal to 8.60 months. Therefore, the transition probabilities associated with each regime point out that the first regime is more persistent, and that the economy spends considerably more time in the ‘high-growth’ regime. Indeed, the ergodic probabilities imply that the economy would spend about 80% of the time spanned by our sample of data in the first regime (i.e. expansion). In contrast, regime 2 has an ergodic probability of about 20%. Hence, these transition probabilities reveal the presence of important asymmetries in the business cycle. Finally, another relevant feature of this model lies in the difference in the residual standard errors across different regimes. Regime 2 exhibits a relatively higher standard error (0.0013) than Regime 1 (0.0009), which reflects the view that recessions are less stable than expansions. Next, we examine the regime and smoothed probabilities 34 generated by the bivariate Markov-switching model of the industrial production and carbon price returns to trace how both time series have evolved over the sample period. Fig. 4 shows the associated smoothed transition probabilities (with regime transition probabilities in Appendix A). Switches from one regime to another now have a clearer economic meaning. They are especially perceptible during January-April 2005, April-June 2006, October 2008 and April 2009 (until the end of the study period). Whereas there are common effects associated with broad macroeconomic conditions, we may also distinguish market-specific effects. The first two significant changes of regime may tentatively be

34 The estimation routine generates two by-products in the form of the regime and smoothed probabilities. Recall that the regime probability at time t is the probability that state t will operate at t, conditional on the information available up to t − 1. The other by-product is the smoothed probability, which is the probability of a particular state in operation at time t conditional on all information in the sample. The smooth probability allows the researcher to ‘look back’, and observe how regimes have evolved overtime (Fong and See, 2002). Since both plots are similar, we only reproduce the smooth probability in the paper to conserve space. The plot of the regime probability may be found in Figure 9 of Appendix A.

related to early market developments in the EU ETS. From January to April 2005, market agents had heterogeneous anticipations with regard to the actual level of carbon prices in a context of sustained EU economic growth (Ellerman et al., 2010). From April 2005 to April 2006, our model globally stays in the growth regime (with associated probabilities higher than 80%). In April 2006, carbon prices were characterized by a strong downward adjustment due to a situation of ‘over-allocation’ compared to verified CO2 emissions (Ellerman and Buchner, 2008). This situation of high price volatility lasted until the end of June 2006 (Alberola et al., 2008b). Then, the model is characterized by another period of growth (with associated probabilities higher than 80%). It is interesting to relate these states to the underlying business cycle: the switches between high- and low-growth based on the econometric inference do not match the NBER dating of the economic recession (as detailed in Section 2). There is evidence of the recession in October 2008, which corresponds to the first regime switch in the carbon-macroeconomy relationship. Indeed, the EU industrial production had been falling since July 2007 (see Section 4). However, the carbon market seems to adjust to this situation only in October 2008, when most operators were looking to sell allowances in exchange of cash (Chevallier, 2009; Mansanet-Bataller et al., 2011). This time period also corresponds to the arrival of a lot of information on the carbon market (including VAT fraud) in a context of strong macroeconomic uncertainty (with liquidity crises on the interbank market). Owyang et al. (2005) note that, for the US aggregate business cycle, states differ significantly in the timing of switches between regimes, indicating large differences in the extent to which state business cycle phases are in concord with those of the aggregate economy. This may contribute to explain why the switches in our two-regime system appear later than the NBER business cycle end-of-recession date (June 2009). At the regional level, Hamilton and Owyang (2011) show that differences across US states appear to be a matter of timing of business cycles, with some states entering recession or recovering before others. This may tentatively be advanced here as a justification for the different timings of entry into the recession identified for the industrial production and the carbon market. Finally, other important events are recorded during the end of our study period. They are characterized by a delayed adjustment of most commodity markets (among which the carbon market) to the global recessionary shock (Caballero et al., 2008; Chan et al., 2011; Chevallier, 2011a; Tang and Xiong, 2010) with various switches from high- to low-growth regimes. 35 We also note that the ‘high-growth’ regime (Regime 1) is considerably more persistent and generally less volatile than the other regime. The data generating process is generally more likely to be in Regime 1, with occasional episodes of relatively short-lived crises (Regime 2). As the smoothed transition probabilities become blurred near the end of the study period, one may wonder whether the macroeconomic effects become less prevalent. One likely explanation is that from December 2009 onwards, it is possible that the relationship is weakening due to the failure of the COP/MOP Copenhagen Meeting, when Member States failed to back up the Kyoto Protocol with a broader regime. This might presumably translate into a perception that environmental constraints will be less (legally) binding in the near future. Fig. 4 along with Table 8 suggest that the statistical characterization of the macroeconomic activity/carbon market business cycle afforded by the Markov-switching VAR model is adequate, as our regime-switching model is able to capture the dramatic changes in the evolution of both time series highlighted in Sections 2 to 4.

35 For more studies on the linkages between financial assets and commodities, see Jones and Kaul (1996), Sadorsky (1999) and Driesprong et al. (2008) for the relationships between oil price movements and stock returns, or Baur and McDermott (2010) who identify gold as a safe-haven in extreme market conditions.

J. Chevallier / Economic Modelling 28 (2011) 2634–2656

Overall, our results tend to confirm that the carbon market adjusts to the macroeconomic environment only with a delay (see Chevallier, 2009, 2011a). The main reason lies in its dependence on institutional news events (Conrad et al., in press). Indeed, the EU ETS was created by the EU Commission in 2005, and amendments to the scheme profoundly impact its price path (Alberola et al., 2008a). Therefore, if recessionary shocks can be shown to have a negative effect on the carbon market (Chevallier, 2011a), the price of CO2 allowances is only weakly connected to the variables which traditionally impact other equity, bond and commodity markets, such as dividend yields, ‘junk’ bond yields, T-Bill rates and excess returns (Chevallier, 2009). Next, we report various robustness tests for the two-regime Markov-switching VAR. 5.3. Models diagnostics As put forward by Cecchetti et al. (1990), to assess the quality of the Markov-switching model, we need to develop robustness checks. The diagnostic checking of estimated Markov-switching models has been dealt with by Hamilton (1996b). The tests are LM-type tests, which have the attractive property that their computation only requires the estimation of the model under the null hypothesis. 36 The upper panel of Table 9 reports the results of two diagnostic tests. The first is a test of the Markov-switching model against the simple nested null hypothesis that the data follow a geometric random walk with i.i.d innovations. Because the Markov-switching model is not identified under the null of the geometric random walk, the likelihood ratio statistic does not have the standard χ 2 distribution. Therefore, to assess whether the difference in log-likelihood between the null and Markov-switching models is statistically significant, we compute the standard likelihood ratio statistic as twice the difference in the maximized log-likelihood values of the null and alternative models, but adjust the p-value of this statistic upward to reflect the problem of nuisance parameters (see Hamilton, 1989; Garcia, 1998 for extensions). To adjust the p-value, we use the methods developed in Davies (1977, 1987) who applies empirical process theory to derive an upper bound for type I error of a modified LR statistic under the null, assuming nuisance parameters are known under the alternative. Note M the p-value from the LR test:

  VMðd−1Þ = 2 e−M = 2 2−d = 2 2 Prob½LRðqÞ > M = Prob χd > M + Γ ðd = 2Þ

ð9Þ

where Prob(LR(q ∗) N M|H0) is the upper bound critical value, LR is the likelihood ratio statistic, q ∗ is the vector of transition probabilities (q ∗ = argmax LnL(q)|H1) and d is the number of restrictions under the null hypothesis. Based on this framework, Davies (1977, 1987) derived a simple analytical formula assuming that there is a unique global optimum for the likelihood function:

V = 2M

1=2

ð10Þ

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Table 9 Robustness checks of the two-regime Markov-switching VAR for EU27INDPRODRET and EUAFUTRET. Markov-switching VAR LR statistic p-value Symmetry test p-value RCM 2-State

18.226 0.001 1.698 0.047 6.5115

Distributional characteristics

EU27INDPRODRET

EUAFUTRET

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

− 0.0001 0.0002 0.0156 − 0.0237 0.0098 − 0.5717 2.7062

0.0081 − 0.0126 0.3122 − 0.2777 0.1236 0.1229 2.8208

Note: Distributional characteristics are given for the Markov-switching processes implied by the estimates in Table 8. EU27INDPRODRET stands for the EU 27 Seasonally Adjusted Industrial Production Index in Logreturn form, EUAFUTRET for the EUA Futures Price in Logreturn form, and RCM for the Regime Classification Measure.

the carbon-macroeconomy relationship is better described by a tworegime Markov-switching model than by the random walk model. The second test reported in Table 9 is for the symmetry of the Markov transition matrix, which implies symmetry of the unconditional distribution of the growth rates. 37 This test examines the maintained hypothesis that p (the probability of being in a highgrowth state or ‘boom’) equals q (the probability of being in a lowgrowth state or depression) against the alternative that p b q. Table 9 reports statistics that are asymptotically standard normal under the null. We reject the hypothesis of symmetry at the 5% level. Next, Table 9 reports the distributional characteristics for the Markov-switching processes implied by the estimates in Table 8. Among others, we report the population values of the mean, standard deviation, skewness and kurtosis computed from the point estimates of the Markov-switching VAR for EU27INDPRODRET and EUAFUTRET. Compared to Table 1, these values demonstrate that the two-regime model we employ matches quite well the first four central moments of the data. We conclude that the Markov-switching model produces both the degree of skewness and the amount of kurtosis that are present in the original data. Finally, Ang and Bekaert (2002a) set out a formal definition of and a test for regime classification. They argue that a good regime switching model should be able to classify regimes sharply. Weak regime inference implies that the regime-switching model cannot successfully distinguish between regimes from the behavior of the data, and may indicate misspecification. To measure the quality of regime classification, we therefore use Ang and Bekaert's (2002a) Regime Classification Measure (RCM) defined for two states as:

RCM = 400 ×

1 T ∑ p ð1−pt Þ T t =1 t

ð11Þ

In Table 9, this adjustment produces a LR statistic equal to 18.226. We reject the random walk at the 1% level. We conclude that

where the constant serves to normalize the statistic to be between 0 and 100, and pt denotes the ex-post smoothed regime probabilities.

36 See Smith (2008) for a review, which confirms that the LM tests have the best size and power properties among several specification tests for Markov-switching models.

37 As noted by Cecchetti et al. (1990), this is a one-sided test of symmetry against the alternative of negative skewness.

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Good regime classification is associated with low RCM statistic values. A value of 0 indicates that the two-regime model is able to perfectly discriminate between regimes, whereas a value of 100 indicates that the two-regime model simply assigns each regime a 50% chance of occurrence throughout the sample. Consequently, a value of 50 is often used as a benchmark (see Chan et al., 2011 for instance). Adopting this definition to the current context, the RCM 2-State statistic is equal to 6.51 in Table 9. It is substantially below 50, consistent with the existence of two regimes. It is very interesting that our estimated Markov-switching model has classified the two regimes extremely well, which capture potentially the relevant information over the period about the carbon-macroeconomy relationship. In sum, there is substantial evidence of nonlinearity in the dynamics of both the EU industrial production and carbon futures as depicted by the regime-switching model. Therefore, we have been successful in fine-tuning our understanding of the carbonmacroeconomy relationship thanks to the two-regime Markovswitching VAR. To draw this discussion to a conclusion, the purpose of this section has been to demonstrate that the Markov-switching model is well-specified. In addition to its ability to capture certain prominent features of the data that linear models cannot, the added attractiveness of the Markov-switching model for our purposes is its analytical tractability. Thus, a credible case can be made for the Markov-switching VAR model to evaluate the carbonmacroeconomy relationship. 6. Comparing the regimes generated by the threshold vector error-correction and Markov-switching VAR models At this stage, it is useful to compare the regimes generated by the threshold vector error-correction model (Section 4.2) with those of the bivariate Markov-switching VAR (Section 5.2). On the one hand, the threshold vector error-correction model is characterized by two major shifts from the ‘standard’ regime (which concerns 94% of the sample) to the ‘extreme’ regime (during which most of the error-correction adjustment occurs) in July-August 2007 and December 2008-January 2009. On the other hand, the bivariate Markov-switching VAR model identifies switches between expansion (with an ergodic probability of 80%) and recession during January– April 2005, April–June 2006, October 2008, and April 2009 until the end of the sample. Besides, it is well known that there is a difference between the percentage of observations covered by each regime, and the persistence of the given regime (as a high percentage may be compatible with frequent switches from one regime to another). Therefore, in our setting, the Markov-switching model seems to identify more switches between regimes than the threshold vector error-correction model (essentially during four months). Overall, both classes of models are successful in identifying important regime switches in the dataset which, given the recent economic turmoil, further reinforces the need to resort to nonlinear econometric techniques. 7. Conclusions Many economic time series occasionally exhibit dramatic breaks in their behavior, associated with events such as financial crises or abrupt changes in government policy. Of particular interest to economists is the apparent tendency of many economic variables to behave quite differently during economic downturns, when the under-utilization of production factors governs economic dynamics (Hamilton, 1989; Hamilton and Lin, 1996). The study of the inter-relationships between economic activity and energy

markets has been the battlefield of an important academic literature, predominantly concerning the link between oil price shocks and output growth (see Ravazzolo and Rothman (2010) for a review). Despite the importance of understanding the linkages between the macroeconomic environment and the carbon market, relatively little work has been done in this area. The purpose of this paper is to spark the general interest for studying the carbonmacroeconomy relationship. The motivation for examining macroeconomic fundamentals as drivers of the carbon price behavior comes from the link between industrial production and the macroeconomy. This variable, which should influence carbon prices, fluctuates over the business cycle, and it should come as no surprise that macroeconomic fundamentals play a role in explaining the carbon price behavior. Moreover, it is a virtually unquestioned assumption that fluctuations in the level of economic activity are a key determinant of the level of carbon prices: as industrial production increases, associated CO2 emissions increase and therefore more CO2 allowances are needed by operators to cover their emissions (see Hocaoglu and Karanfil (2011) for further arguments linking industrial activity in the whole economy and CO2 emissions). This economic logic results in carbon price increases, due to tighter constraints on the demand side of the market ceteris paribus. Only Alberola et al. (2008a, 2009) have investigated a number of factors that could potentially influence carbon price changes – ranging from production to environmental conditions – and identified the industrial production as a key determinant in the combustion, paper and iron sectors (which account for nearly 80% of allowances allocated), and in four countries (Germany, Spain, Poland, UK). More recently, Bredin and Muckley (2011) and Creti et al. (2011) have confirmed that EUAs respond to economic growth (among other drivers) in a linear cointegrating framework. Therefore, the puzzle that remains to be solved in relation to carbon price drivers is to determine the influence of economic activity, through changes in CO2 emissions levels, initiated by such empirical analyses. Recently, several studies have uncovered some econometric links between the carbon market and several indicators related to macroeconomic and financial markets. For instance, Chevallier (2009) observes similar changes between carbon prices and macroeconomic risk factors. This behavior of carbon prices may be explained by the increased linkages between the financial and macroeconomic spheres (Caballero et al., 2008; Chan et al., 2011; Tang and Xiong, 2010), whereby commodity markets are linked to economic activity with various lags (Chevallier, 2011a). Compared to previous literature, our approach is to model the carbon-macroeconomy relationship based on threshold vector errorcorrection and Markov-switching VARs. Formally, regime-switching models are designed to capture the asymmetry observed in the business cycle, whereby expansions and contractions are quite different from each other, with the former typically long-lived and the latter more violent. Besides, we pursue an empirical approach which lets us test for the existence of nonlinearities in the data. We do this in the hope of contributing to the understanding of how the carbon market responds to macroeconomic fluctuations. In summary, the joint process of industrial production and carbon price returns follows a rich and complex dynamic pattern. We find evidence that two-regime models are required to capture the variation between both time series. The empirical findings from our study advance the literature along several dimensions. First, we study the carbon-macroeconomy relationship with a two-regime threshold vector error-correction model. Its rationale was introduced by Balke and Fomby (1997), who emphasized the possibility that movements towards the long-run equilibrium need not occur in every period, and that there could be a discrete adjustment to the equilibrium only when the deviation

J. Chevallier / Economic Modelling 28 (2011) 2634–2656

from the equilibrium exceeds a critical threshold. The threshold cointegration test with asymmetric dynamic adjusting processes proposed by Hansen and Seo (2002) is applied. We follow thoroughly their approach by employing parametric residual bootstrap procedures to approximate the null distribution of the SupLM test, and calculate asymptotic critical values and p-values. By using the EU industrial production and carbon price data, the results confirm the presence of threshold cointegration. We also show that the estimated two-regime threshold VECM forms statistically an adequate representation of the data with distinct regimes. The regime classification tells us that the ‘typical’ regime concerns 94% of the sample, while the ‘extreme’ regime contains 6% of the observations. The EU industrial production is found to influence (with significant error-correction effects) carbon futures mostly in the latter regime. The threshold vector error-correction model uncovers strong asymmetries in that the speed of adjustment to the long-run equilibrium is higher in the ‘extreme’ regime than in the ‘typical’ one. Through the recent economic and financial events impacting the EU 27 economy, we are able to identify that the industrial production index is the leader in the system to restore the long-term equilibrium between the two time series (as expected on theoretical grounds). The long-run causality between the two time series runs only in one direction (i.e. the industrial production index impacts the carbon price in both regimes but not vice versa), and this effect depends on the size of the equilibrium error. Thus, any assessment of the long-run relationship between the EU industrial production and carbon prices should take into account thresholds, and the possibility of the short-run dynamics being characterised by different regimes. Second, we extend the modeling of the carbon price to incorporate regime-switching with a macroeconomic factor. To the extent that both time series vary nonlinearly across regimes (especially between ‘high-’ and ‘low-growth’ states), regime switching models have the potential to provide a more complete specification of the carbon-macroeconomy relationship. In this paper, we use the approach innovated by Hamilton (1989) in his analysis of the US business cycle. That approach consists in fitting a Markov-switching process to a vector of economic time series in question. In summary, we find highly satisfactory results with the Markov-switching VAR approach, given the alternance of expansion and recession periods in the business cycle during 2005–2010. Our analysis identifies two states: the model classifies the majority of 2005–2007 as a ‘high-growth’ period, and the late 2008–2010 as a crisis period. The significance to be drawn from these models is that the Markovswitching VAR picks up most of the representative shocks identified by carbon market analysts: January–April 2005, April–June 2006, October 2008 and April 2009 until the end of the sample period. Moreover, our results indicate that the carbon-macroeconomy relationship may fade for some periods. One possible cause is changes unique to the carbon market that diminish its ability to react to macroeconomic factors. The results are robust to a wide range of diagnostic tests. The key messages of the paper may be summarized as follows: (i) macroeconomic activity is likely to affect carbon prices with a lag, due to the specific institutional constraints of this environmental market; (ii) the carbon-macroeconomy relationship seems adequately captured by two-regime threshold vector error-correction and two-regime Markov-switching VAR models compared to linear models as main competitors. Of particular interest will be the evolution of such a relationship between macroeconomic fundamentals and carbon prices during Phase III, with the introduction of auctioning rules on the supply side of the market and the 20/20/20 targets of the ‘Energy-Climate’ package. Of course, there needs to be more work on understanding the theoretical and empirical aspects of the carbon-macroeconomy relationship. This paper only stresses the effect of the industrial

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production index on the carbon price, as well as the merits of threshold vector error-correction and Markov-switching models. It does not provide suggestions on how to reduce CO2 emissions as industrial production increases, or how to prevent increases in CO2 emissions in the expansion regime. Besides, the current literature lacks the theoretical concepts to describe the economic rationale behind these two variables' relationship. With a sound modeling framework, future research could choose to focus on trade, investment, or any other proxy of macroeconomic activities rather than on the industrial production index. There are several extensions of this work that would be interesting to consider. In the spirit of Section 4, the carbonmacroeconomy relationship may also be tracked with smooth transition error-correction models (see for instance Martens et al. (1998) and Tsay (1998) for applications to index returns), or with Markov error-correction models (see Krolzig (2001) for an application to the US business cycle, Clements and Krolzig (2002) for an explanation of asymmetries in the US business cycle based on oil shocks, Krolzig et al. (2002) for a model of the UK labour market, or Psaradakis et al. (2004) for an analysis of stock prices and dividends). In the spirit of Section 5, a second extension of our results is to test both nonlinearity and structural instability in the carbon-macroeconomy relationship based on time-varying transition-probability Markov-switching models (see Diebold et al. (1994) for a review, Filardo (1994) for a study of the US business cycle, Peria (2002) for a study of speculative attacks against the European Monetary System, Schaller and van Norden (2002) for an investigation of bubbles in US data, and Kanas (2008) for an application to stock index futures markets). As an alternative nonlinear model, it would also be relevant to apply Beaudry and Koop's (1993) ‘Current Depth of the Recession’ approach, which evaluates the difference between output and the previous peak of output, to the level of industrial production. Finally, it appears worthy of interest to document the volatility properties of carbon futures (instead of returns) through Markov-switching GARCH models (see Marcucci (2005), Henry (2009), Janczura and Weron (2010) for recent applications), in order to understand its evolution following economic activity shocks.

Acknowledgements I wish to thank warmly the Editor, Prof. Stephen G. Hall, as well as anonymous referees for their detailed comments which led to an improved version of the paper. For insightful comments on earlier drafts, I wish to thank David Newbery, Michael Grubb, Michael Pollitt, David Reiner, Pierre Noël, Ajay Gambhir, Andreas Löschel, Tim Mennel, Waldemar Rotfuß, Jean-Pierre Ponssard, Anna Creti, Pierre-André Jouvet, Michel Boutillier, Alain Bernard, Guy Meunier, Vanina Forget, Neil Ericsson, Richard Baillie, Barkley Rosser, Bruce Mizrach, and Daniel Rittler. Helpful comments were also received from audiences at the EPRG Energy & Environment Seminar (Electricity Policy Research Group, University of Cambridge, UK), the CEP Seminar Series (Centre for Environmental Policy, Imperial College London, UK), the ZEW Research Seminar (Centre for European Economic Research, Mannheim, Germany), the Envecon 2011 Conference (UK Network of Environmental Economists, London, UK), the Environment & CSR Seminar (Ecole Polytechnique, Paris, France), the 19th SNDE Annual Symposium (Society for Nonlinear Dynamics & Econometrics, Washington DC, USA), the EconomiX Lunch Seminar, the 65 th ESEM European Meeting (Econometric Society, Oslo, Norway), and the 60th AFSE Annual Congress (French Economics Association, Paris, France). Last but not least, I thank Eurostat and ECX for providing the data. All errors and omissions remain that of the author.

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Appendix A A.1. ACF, PACF

Sample Autocorrelation Function (ACF) 1

0.8

0.8 Sample Autocorrelation

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Fig. 5. ACF (top), PACF (middle) and ACF of the Squared Returns (bottom) for the EU 27 Industrial Production Index in Raw (left) and Logreturn (right) Forms.

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Sample Autocorrelation Function (ACF)

1

1

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A.2. Unit Root Tests (ADF, PP, KPSS) Table 10 Unit root tests for EU27PRODINDRET.

Augmented Dickey–Fuller test statistic Phillips–Perron test statistic Kwiatkowski–Phillips–Schmidt–Shin test statistic

t-Statistic

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− 2.5281 − 6.3820 LM-stat. 0.1660

− 1.9459 − 1.9459 Asymptotic critical values 0.4630

Note: For the ADF and PP tests, the null hypothesis is EU27PRODINDRET has a unit root (where EU27PRODINDRET stands for the EU27 Seasonally Adjusted Industrial Production Index in Logreturn form). For the ADF test, a lag length of 1 is specified based on the Schwarz Information Criterion. For the PP test, a Bartlett kernel of band with 5 is specified using the Newey–West procedure. For both tests, Model 1 (without trend nor intercept) is chosen. Test critical values at the 5% level are based on MacKinnon (1996). For the KPSS, the null hypothesis is EU27PRODINDRET is stationary. A Bartlett kernel of bandwidth 5 is specified using the Newey-West procedure. Asymptotic critical values at the 5% level are based on Kwiatkowski et al. (1992). Model 2 (with intercept) is chosen.

Table 11 Unit root tests for EUAFUTRET. t-Statistic

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Augmented Dickey–Fuller test statistic Phillips–Perron test statistic

− 5.9533 − 5.8921

− 1.9459 − 1.9459

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LM-Stat. 0.1087

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Note: For the ADF and PP tests, the null hypothesis is EUAFUTRET has a unit root (where EUAFUTRET stands for the EUA Futures Price in Logreturn form). For the ADF test, a lag length of 0 is specified based on the Schwarz Information Criterion. For the PP test, a Bartlett kernel of bandwidth 1 is specified using the Newey–West procedure. For both tests, Model 1 (without trend nor intercept) is chosen. Test critical values at the5% level are based on MacKinnon (1996). For the KPSS, the null hypothesis is EUAFUTRET is stationary. A Bartlett kernel of band with 3 is specified using the Newey-West procedure. Asymptotic critical values at the 5% level are based on Kwiatkowski et al. (1992). Model 3 (with intercept and deterministic trend) is chosen.

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A.4. Concentrated Negative Log-Likelihood of the Two-Regime Threshold Cointegrated Model

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A.5. Regime transition probabilities for the Markov-switching VAR with EU27INDPRODRET and EUAFUTRET

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Fig. 9. Regime transition probabilities estimated from the two-regime Markov-switching VAR for EU27INDPRODRET and EUAFUTRET.

References Abdulai, A., 2002. Using threshold cointegration to estimate asymmetric price transmission in the Swiss pork market. Applied Economics 34, 679–687. Alberola, E., Chevallier, J., 2009. European carbon prices and banking restrictions: evidence from Phase I (2005–2007). The Energy Journal 30 (3), 51–80. Alberola, E., Chevallier, J., Chèze, B., 2008a. The EU emissions trading scheme: the effects of industrial production and CO2 emissions on carbon prices. International Economics 116 (4), 93–125.

Alberola, E., Chevallier, J., Chèze, B., 2008b. Price drivers and structural breaks in European carbon prices 2005–07. Energy Policy 36 (2), 787–797. Alberola, E., Chevallier, J., Chèze, B., 2009. Emissions compliances and carbon prices under the EU ETS: a country specific analysis of industrial sectors. Journal of Policy Modeling 31 (3), 446–462. Albert, J., Chib, S., 1993. Bayes inference via Gibbs sampling and autoregressive time series subject to Markov mean and variance shifts. Journal of Business and Economic Statistics 11, 1–16. Alexander, C., Kaeck, A., 2008. Regime dependent determinants of credit default swap spreads. Journal of Banking and Finance 32 (6), 1008–1021.

2654

J. Chevallier / Economic Modelling 28 (2011) 2634–2656

Alizadeh, A., Nomikos, N., Pouliasis, P., 2008. A Markov regime switching approach for hedging energy commodities. Journal of Banking and Finance 32, 1970–1983. Anderson, B., Di Maria, C., 2011. Abatement and allocation in the pilot phase of the EU ETS. Environmental and Resource Economics 48, 83–103. Andreou, E., Ghysels, E., Kourtellos, A., 2010. Regression Models With Mixed Sampling Frequencies. Journal of Econometrics 158 (2), 246–261. Andrews, D.W.K., 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821–856. Andrews, D.W.K., Ploberger, W., 1994. Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383–1414. Ang, A., Bekaert, G., 2002a. Regime Switches in Interest Rates. Journal of Business and Economic Statistics 20 (2), 163–182. Ang, A., Bekaert, G., 2002b. International asset allocation with regime shifts. Review of Financial Studies 15 (4), 1137–1187. Aslanidis, N., Kouretas, G.P., 2005. Testing for two-regime threshold cointegration in the parallel and official markets for foreign currency in Greece. Economic Modelling 22, 665–682. Assenmacher-Wesche, K., 2006. Estimating Central Banks' preferences from a timevarying empirical reaction function. European Economic Review 50, 1951–1974. Baele, L., Bekaert, G., Inghelbrecht, K., 2010. The determinants of stock and bond return comovements. The Review of Financial Studies 23 (6), 2374–2428. Bai, J., Perron, P., 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66, 47–78. Bai, J., Perron, P., 2003a. Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18, 1–22. Bai, J., Perron, P., 2003b. Critical values for multiple structural change tests. The Econometrics Journal 6, 72–78. Bai, J., Wang, P., 2011). Conditional Markov chain and its application in economic time series analysis. Journal of Applied Econometrics 26 (5), 715–734. Balke, N.S., Fomby, T.B., 1997. Threshold cointegration. International Economic Review 38 (3), 627–645. Basci, E., Caner, M., 2005. Are real exchange rates nonlinear or nonstationary? Evidence from a new threshold unit root test. Studies in Nonlinear Dynamics and Econometrics 9 (4), 1–19. Baur, D., McDermott, T., 2010. Is gold a safe haven? International evidence. Journal of Banking and Finance 34, 1886–1898. Beaudry, P., Koop, G., 1993. Do recessions permanently change output? Journal of Monetary Economics 31, 149–163. Bec, F., Salem, M.B., Carrasco, M., 2004. Tests for unit-root versus threshold specification with an application to the purchasing power parity relationship. Journal of Business and Economic Statistics 22, 382–395. Bec, F., Guay, A., Guerre, E., 2008. Adaptive consistent unit-root tests based on autoregressive threshold model. Journal of Econometrics 142 (1), 94–133. Benz, E., Trück, S., 2009. Modeling the price dynamics of CO2 emission allowances. Energy Economics 31 (1), 4–15. Bernanke, B.S., Gertler, M., Watson, M., 1997. Systematic monetary policy and the effects of oil price shocks. Brookings Papers on Economic Activity 1, 91–157. Blyth, W., Bunn, D., 2011. Coevolution of policy, market and technical price risks in the EU ETS. Energy Policy 39, 4578–4593. Blyth, W., Bunn, D., Kettunen, J., Wilson, T., 2009. Policy interactions, risk and price formation in carbon markets. Energy Policy 37, 5192–5207. Böhringer, C., Löschel, A., Moslener, U., Rutherford, T.F., 2009. EU climate policy up to 2020: an economic impact assessment. Energy Economics 31 (S2), 295–305. Boldin, M.D., 1994. Dating turning points in the business cycle. Journal of Business 67, 97–131. Bradley, M.D., Jansen, D.W., 2004. Forecasting with a nonlinear dynamic model of stock returns and industrial production. International Journal of Forecasting 20 (2), 321–342. Bredin, D., Muckley, C., 2011. An emerging equilibrium in the EU emissions trading scheme. Energy Economics 33 (2), 353–362. Caballero, R., Farhi, E., Gourinchas, P., 2008. Financial crash, commodity prices and global imbalances. Brookings Papers on Economic Activity 2, 1–55. Cai, J., 1994. A Markov model of unconditional variance in ARCH. Journal of Business and Economic Statistics 12, 309–316. Caner, M., Hansen, B.E., 2001. Threshold autoregression with a unit root. Econometrica 69 (6), 1555–1596. Carchano, O., Pardo, A., 2009. Rolling over stock index futures contracts. Journal of Futures Markets 29, 684–694. Carrasco, M., 2002. Misspecified structural change, threshold, and Markov-switching models. Journal of Econometrics 109, 239–273. Cecchetti, S.G., Lam, P.S., Mark, N.C., 1990. Mean reversion in equilibrium asset prices. The American Economic Review 80 (3), 398–418. Chan, K.F., Treepongkaruna, S., Brooks, R., Gray, S., 2011. Asset market linkages: evidence from financial, commodity and real estate assets. Journal of Banking and Finance 35 (6), 1415–1426. Chen, S.S., 2010. Do higher oil prices push the stock market into bear territory? Energy Economics 32, 490–495. Chen, L.H., Finney, M., Lai, K.S., 2005. A threshold cointegration analysis of asymmetric price transmission from crude oil to gasoline prices. Economics Letters 89, 233–239. Chevallier, J., 2009. Carbon futures and macroeconomic risk factors: a view from the EU ETS. Energy Economics 31 (4), 614–625. Chevallier, J., 2011a. Macroeconomics, finance, commodities: interactions with carbon markets in a data-rich model. Economic Modelling 28 (1–2), 557–567. Chevallier, J., 2011b. Detecting instability in the volatility of carbon prices. Energy Economics 33 (1), 99–110.

Chevallier, J., 2011c. Carbon price drivers: an updated literature review. Working Paper SSRN #1811963. Social Science Research Network, Cambridge, MA, USA. Chevallier, J., Sévi, B., 2010. Jump-robust estimation of realized volatility in the EU Emission Trading Scheme. Journal of Energy Markets 3 (2), 49–67. Chevallier, J., Sévi, B., 2011. On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics, and forecasting. Annals of Finance 7, 1–29. Cho, J.S., White, H., 2007. Testing for regime switching. Econometrica 75 (6), 1671–1720. Chung, H., Ho, T.W., Wei, L.J., 2005. The dynamic relationship between the prices of ADRs and their underlying stocks: evidence from the threshold vector error correction model. Applied Economics 37, 2387–2394. Clements, M.P., Galvão, A.B., 2009. Forecasting US output growth using leading indicators: an appraisal using MIDAS models. Journal of Applied Econometrics 24 (7), 1187–1206. Clements, M.P., Krolzig, H.M., 2002. Can oil shocks explain asymmetries in the US business cycle? Empirical Economics 27, 185–204. Colacito, R., Engle, R., Ghysels, E., 2011. A component model for dynamic correlations. Journal of Econometrics 164 (1), 45–59. Cologni, A., Manera, M., 2009. The asymmetric effects of oil shocks on output growth: a Markov-Switching analysis for the G-7 countries. Economic Modelling 26, 1–29. Conrad, C., Rittler, D., Rotfuß, W., in press. Modeling and explaining the dynamics of the European Union allowance prices at high-frequency. Energy Economics. doi: 10.1016/j.eneco.2011.02.011. Creti, A., Jouvet, P.A., Mignon, V., 2011. Carbon price drivers: Phase I versus Phase II equilibrium. Working Paper n°2011-06, Climate Economics Chair, Paris. Daskalakis, G., Psychoyios, D., Markellos, R.N., 2009. Modeling CO2 emission allowances prices and derivatives: evidence from the European trading scheme. Journal of Banking and Finance 33, 1230–1241. Davies, R.B., 1977. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64, 247–524. Davies, R.B., 1987. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74, 33–43. Declercq, B., Delarue, E., D'haeseleer, W., 2011. Impact of the economic recession on the European power sector's CO2 emissions. Energy Policy 39, 1677–1686. Demailly, D., Quirion, P., 2008. European Emission Trading Scheme and competitiveness: a case study on the iron and steel industry. Energy Economics 30, 2009–2027. Diebold, F.X., Lee, J.H., Weinbach, G.C., 1994. Regime switching with time-varying transition probabilities. In: Hargreaves, C. (Ed.), Non-stationary Time-series Analysis and Cointegration. Oxford University Press, pp. 283–302. Dionne, G., Gauthier, G., Hammami, K., Maurice, M., Simonato, J.G., 2011. A reduced form model of default spreads with Markov-switching macroeconomic factors. Journal of Banking and Finance 35 (8), 1984–2000. Driesprong, G., Jacobsen, B., Maat, B., 2008. Striking oil: another puzzle? Journal of Financial Economics 89, 307–327. Dufrenot, G., Mignon, V., 2002. Recent developments in nonlinear cointegration with applications to macroeconomics and finance. Springer Verlag, New York. Durand-Lasserve, O., Pierru, A., Smeers, Y., 2011. Effects of the uncertainty about global economic recovery on energy transition and CO2 price. MIT-CEEPR Working Paper #11-003. MIT, USA. Durland, J.M., McCurdy, T., 1994. Duration-dependent transitions in a Markov model of U.S. GNP growth. Journal of Business and Economic Statistics 12, 279–288. Ellerman, A.D., Buchner, B.K., 2008. Over-allocation or abatement? A preliminary analysis of the EU ETS based on the 2005–06 emissions data. Environmental and Resource Economics 41, 267–287. Ellerman, A.D., Convery, F.J., De Perthuis, C., 2010. Pricing carbon: the European Union emissions trading scheme. Cambridge University Press, Cambridge. Enders, W., Chumrusphonlert, K., 2004. Threshold cointegration and purchasing power parity in the Pacific nations. Applied Economics 36, 889–896. Enders, W., Granger, C.W.J., 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business and Economic Statistics 16 (3), 304–311. Enders, W., Siklos, P.L., 2001. Cointegration and threshold adjustment. Journal of Business and Economic Statistics 19 (2), 166–176. Engle, C., Hamilton, J.D., 1990. Long swings in the dollar: are they in the data and do markets know it? The American Economic Review 80 (4), 689–713. Esteve, V., Gil-Pareja, S., Martinez-Serrano, J.A., Llorca-Vivero, R., 2006. Threshold cointegration and nonlinear adjustment between goods and services inflation in the United States. Economic Modelling 23, 1033–1039. Eurostat, 2010. Industrial production up by 0.9% in euro area. Up by 0.7% in EU27. Eurostat News Release Euro Indicators #50/2010available at http://ec.europa.eu/ eurostat/euroindicators2010. Filardo, A.J., 1994. Business cycle phases and their transitional dynamics. Journal of Business and Economic Statistics 12 (3), 299–308. Fong, W.M., See, K.H., 2001. Modelling the conditional volatility of commodity index futures as a regime switching process. Journal of Applied Econometrics 16, 133–163. Fong, W.M., See, K.H., 2002. A Markov switching model of the conditional volatility of crude oil futures prices. Energy Economics 24, 71–95. Frömmel, M., MacDonald, R., Menkhoff, L., 2005. Markov switching regimes in a monetary exchange rate model. Economic Modelling 22, 485–502. Garcia, R., 1998. Asymptotic null distribution of the likelihood ratio test in Markov switching models. International Economic Review 39 (3), 763–788. Ghysels, E., 1994. On the periodic structure of the business cycle. Journal of Business and Economic Statistics 12, 289–299. Ghysels, E., Santa-Clara, P., Valkanov, R., 2002. The MIDAS touch: mixed data sampling regression models. Working paper, UNC and UCLA. Ghysels, E., Santa-Clara, P., Valkanov, R., 2006. Predicting volatility: getting the most out of return data sampled at different frequencies. Journal of Econometrics 131, 59–95.

J. Chevallier / Economic Modelling 28 (2011) 2634–2656 Ghysels, E., Sinko, A., Valkanov, R., 2007. MIDAS regressions: further results and new directions. Econometric Reviews 26, 53–90. Goodwin, T.H., 1993. Business-cycle analysis with a Markov-switching model. Journal of Business and Economic Statistics 11, 331–339. Granger, C.W.J., Lee, T.H., 1989. Investigation of production, sales and inventory relationships using multicointegration and non-symmetric error correction models. Journal of Applied Econometrics 4, 145–159. Granger, C.W.J., Teräsvirta, T., 1999. A simple nonlinear time series model with misleading linear properties. Economics Letters 62, 161–165. Gray, S.F., 1996. Modelling the conditional distribution of interest rates as a regime switching process. Journal of Financial Economics 42, 27–62. Gregory, A.W., Hansen, B.E., 1996. Residual-based tests for cointegration in models with regime shifts. Applied Economics Letters 16, 1155–1164. Guidolin, M., Timmermann, A., 2006. An econometric model of nonlinear dynamics in the joint distribution of stock and bond returns. Journal of Applied Econometrics 21 (1), 1–22. Hamilton, J.D., 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357–384. Hamilton, J.D., 1996a. This is what happened to the oil-price macroeconomy relationship. Journal of Monetary Economics 38 (2), 215–220. Hamilton, J.D., 1996b. Specification testing in Markov-switching time series models. Journal of Econometrics 70, 127–157. Hamilton, J.D., 2003. What is an oil shock? Journal of Econometrics 113 (2), 363–398. Hamilton, J.D., 2008. Regime-Switching Models, In: Durlauf, S.N., Blume, L.E. (Eds.), The New Palgrave Dictionary of Economics, Second Edition. Palgrave Macmillan, pp. 1–15. Hamilton, J.D., 2009. Causes and consequences of the oil shock of 2007–2008. Brookings Papers on Economic Activity 1, 215–261. Hamilton, J.D., 2010. Nonlinearities and the macroeconomic effects of oil prices. NBER Working Paper, 16186. National Bureau of Economic Research, USA. Hamilton, J.D., Lin, G., 1996. Stock market volatility and the business cycle. Journal of Applied Econometrics 11, 573–593. Hamilton, J.D., Owyang, M.T. 2011. The Propagation of Regional Recessions. The Review of Economics and Statistics, forthcoming, doi: 10.1162/RESTa.00197. Hamilton, J.D., Raj, B., 2002. New directions in business cycle research and financial analysis. Empirical Economics 27 (2), 149–162. Hamilton, J.D., Susmel, R., 1994. Autoregressive conditional heteroskedasticity and changes in regime. Journal of Econometrics 64, 307–333. Hansen, B.E., 1992. The likelihood ratio test under nonstandard conditions: testing the Markov-switching model of GNP. Journal of Applied Econometrics 7, S61–S82. Hansen, B.E., 1996a. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64, 413–430. Hansen, B.E., 1996b. Erratum: the likelihood ratio test under nonstandard conditions: testing the Markov-switching model of GNP. Journal of Applied Econometrics 11, 195–198. Hansen, B.E., Seo, B., 2002. Testing for two-regime threshold cointegration in vector error-correction models. Journal of Econometrics 110, 293–318. Harding, D., Pagan, A., 2002. A comparison of two business cycle dating methods. Journal of Economic Dynamics and Control 27, 1681–1690. Harvey, A.C., 1991. Forecasting, structural time series models and the Kalman Filter. Cambridge University Press, Cambridge. Henry, O.T., 2009. Regime switching in the relationship between equity returns and short-term interest rates in the UK. Journal of Banking and Finance 33, 405–414. Hintermann, B., 2010. Allowance price drivers in the first phase of the EU ETS. Journal of Environmental Economics and Management 59 (1), 43–56. Hocaoglu, F.O., Karanfil, F., 2011. Examining the link between carbon dioxide emissions and the share of industry in GDP: Modeling and testing for the G-7 countries. Energy Policy 39 (6), 3612–3620. Holmes, M.J., 2011. Threshold cointegration and the short-run dynamics of twin credit behaviour. Research in Economics 65 (3), 271–277. Hu, J.L., Lin, C.H., 2008. Disaggregated energy consumption and GDP in Taiwan: a threshold co-integration analysis. Energy Economics 30, 2342–2358. Janczura, J., Weron, R., 2010. An empirical comparison of alternate regime-switching models for electricity spot prices. Energy Economics 32, 1059–1073. Jones, C., Kaul, G., 1996. Oil and stock markets. The Journal of Finance 51, 463–491. Kähler, J., Marnet, V., 1994. Markov-switching models for exchange rate dynamics and the pricing of foreign-currency options. In: Kähler, J., Kugler, P. (Eds.), Econometric Analysis of Financial Markets. Physica Verlag. Kanas, A., 2008. Modeling regime transition in stock index futures markets and forecasting implications. Journal of Forecasting 27 (8), 649–669. Kapetanios, G., Shin, Y., 2006. Unit root tests in three-regime SETAR models. The Econometrics Journal 9 (2), 252–278. Kilian, L., 2008a. A comparison of the effects of exogenous oil supply shocks on output and inflation in the G7 countries. Journal of the European Economic Association 6 (1), 78–121. Kilian, L., 2008b. Exogenous oil supply shocks: how big are they and how much do they matter for the US economy? The Review of Economics and Statistics 90 (2), 216–240. Kilian, L., 2008c. The economic effects of energy price shocks. Journal of Economic Literature 46 (4), 871–909. Kilian, L., 2009. Not all oil price shocks are alike: disentangling demand and supply shocks in the crude oil market. The American Economic Review 99 (3), 1053–1069. Kim, M.J., Yoo, J.S., 1995. New index of coincident indicators: a multivariate Markov switching factor model approach. Journal of Monetary Economics 36, 607–630. Kim, C.J., Morley, J., Piger, J., 2005. Nonlinearity and the permanent effects of recessions. Journal of Applied Econometrics 20 (2), 291–309.

2655

Kim, B.H., Chun, S.E., Min, H.G., 2010. Nonlinear dynamics in arbitrage of the S&P 500 index and futures: a threshold error-correction model. Economic Modelling 27, 566–573. Kramer, W., Ploberger, W., 1992. The CUSUM test with OLS residuals. Econometrica 60, 271–285. Krolzig, H.M., 1997. Markov-switching vector autoregressions. Modelling, statistical inference and application to business cycle analysis. Lecture Notes in Economics and Mathematical Systems, 454. Springer. Krolzig, H.M., 2001. Business cycle measurement in the presence of structural change: international evidence. International Journal of Forecasting 17 (3), 349–368. Krolzig, H.M., Marcellino, M., Mizon, G.E., 2002. A Markov-switching vector equilibrium correction model of the UK labour market. Empirical Economics 27, 233–254. Kumah, F.Y., 2011. A Markov-Switching approach to measuring exchange market pressure. International Journal of Finance and Economics 16 (2), 114–130. Kwiatkowski, D.P., Phillips, P.C.B., Schmidt, P., Shin, Y., 1992. Testing the null hypothesis of stationarity against the alternative of the unit root: how sure are we that economic time series are non stationary? Journal of Econometrics 54, 159–178. Lam, P.S., 1990. The Hamilton model with a general autoregressive component: estimation and comparison with other models of economic time series. Journal of Monetary Economics 26, 409–432. Layton, A.P., 1996. Dating and predicting phase changes in the U.S. business cycle. International Journal of Forecasting 12 (3), 417–428. Lo, M., Zivot, E., 2001. Threshold cointegration and nonlinear adjustment to the law of one price. Macroeconomic Dynamics 5, 533–576. MacKinnon, J.G., 1996. Numerical distribution functions for unit root and cointegration tests. Journal of Applied Econometrics 11, 601–618. MacKinnon, J.G., Haug, A., Michelis, L., 1999. Numerical distribution functions of likelihood ratio tests for cointegration. Journal of Applied Econometrics 14 (5), 563–577. Maheu, J., McCurdy, T., 2000. Identifying bull and bear markets in stock returns. Journal of Business and Economic Statistics 18, 100–112. Mansanet-Bataller, M., Chevallier, J., Herve-Mignucci, M., Alberola, E., 2011. EUA and sCER phase II price drivers: unveiling the reasons for the existence of the EUA-sCER spread. Energy Policy 39 (3), 1056–1069. Marcucci, J., 2005. Forecasting stock market volatility with regime-switching GARCH models. Studies in Nonlinear Dynamics and Econometrics 9 (4), 1–53. Martens, M., Kofman, P., Vorst, A.C.F., 1998. A threshold error correction for intraday futures and index returns. Journal of Applied Econometrics 13, 245–263. Million, N., 2004. Central Bank's intervention and the Fisher hypothesis: a threshold cointegration investigation. Economic Modelling 21 (6), 1051–1064. Moolman, E., 2004. A Markov switching regime model of the South African business cycle. Economic Modelling 21, 631–646. Moore, T., Wang, P., 2007. Volatility in stock returns for new EU member states: Markov regime switching model. International Review of Financial Analysis 16, 282–292. Morana, C., Beltratti, A., 2002. The effects of the introduction of the euro on the volatility of European stock markets. Journal of Banking and Finance 26 (10), 2047–2064. Morley, J., Piger, J. 2011. The Asymmetric Business Cycle. The Review of Economics and Statistics, forthcoming, doi: 10.1162/RESTa.00169. Oberndorfer, U., 2009. EU emission allowances and the stock market: evidence from the electricity industry. Ecological Economics 68, 1116–1126. Oscar, B.R., Carmen, D.R., Vicente, E., 2004. Searching for threshold effects in the evolution of budget deficits: an application to the Spanish case. Economics Letters 82, 239–243. Owyang, M.T., Piger, J., Wall, H.J., 2005. Business cycle phases in U.S. states. The Review of Economics and Statistics 87 (4), 604–616. Paolella, M., Taschini, L., 2008. An econometric analysis of emission allowances prices. Journal of Banking and Finance 32 (10), 2022–2032. Peel, D., Taylor, M.P., 2002. Covered interest rate arbitrage in the interwar period and the Keynes–Einzig conjecture. Journal of Money, Credit and Banking 31, 51–75. Perez-Quiros, G., Timmermann, A., 2000. Firm size and cyclical variations in stock returns. Journal of Finance 55, 1229–1262. Peria, M.S.M., 2002. A regime-switching approach to the study of speculative attacks: a focus on EMS crises. Empirical Economics 27, 299–334. Perron, P., 1997. Further evidence on breaking. Trend functions in macroeconomic variables. Journal of Econometrics 80, 355–385. Phillips, K., 1991. A two-country model of stochastic output with changes in regime. Journal of International Economics 31, 121–142. Pinson, P., Madsen, H. 2011. Adapative modelling and forecasting of offshore wind power fluctuations with Markov-switching autoregressive models. Journal of Forecasting, forthcoming, doi: 10.1002/for.1194. Pippenger, M.K., Goering, G.E., 1993. A note on the empirical power of unit root tests under threshold processes. Oxford Bulletin of Economics and Statistics 55, 473–481. Pippenger, M.K., Goering, G.E., 2000. Additional results on the power of unit root and cointegration tests under threshold processes. Applied Economics Letters 7, 641–644. Psaradakis, Z., Spagnolo, F., 2002. On the determination of the number of regimes in Markov-switching autoregressive models. Journal of Time Series Analysis 24 (2), 237–252. Psaradakis, Z., Sola, M., Spagnolo, F., 2004. On Markov error-correction models, with an application to stock prices and dividends. Journal of Applied Econometrics 19 (1), 69–88. Psaradakis, Z., Ravn, M.O., Sola, M., 2005. Markov switching causality and the moneyoutput relationship. Journal of Applied Econometrics 20 (5), 665–683. Ravazzolo, F., Rothman, P., 2010. Oil and US GDP: a real-time out-of-sample examination. Working Paper. East Carolina University, USA. Sadorsky, P., 1999. Oil price shocks and stock market activity. Energy Economics 21, 449–469.

2656

J. Chevallier / Economic Modelling 28 (2011) 2634–2656

Sarlan, H., 2001. Cyclical aspects of business cycle turning points. International Journal of Forecasting 17 (3), 369–382. Sarno, L., Valente, G., 2006. Deviations from purchasing power parity under different exchange rate regimes: do they revert and, if so, how? Journal of Banking and Finance 30, 3147–3169. Schaller, H., van Norden, S., 2002. Fads or bubbles? Empirical Economics 27, 335–362. Seo, M., 2006. Bootstrap testing for the null of no cointegration in a threshold vector error correction model. Journal of Econometrics 127 (1), 129–150. Sephton, P.S., 2003. Spatial market arbitrage and threshold cointegration. American Journal of Agricultural Economics 85, 1041–1046. Smith, D.R., 2006. Markov-switching and stochastic volatility diffusion models of short-term interest rates. Journal of Business and Economic Statistics 20 (2), 183–197. Smith, D.R., 2008. Evaluating specification tests for Markov-switching time-series models. Journal of Time Series Analysis 29 (4), 629–652. Smith, P.A., Summers, P.M., 2005. How well do Markov switching models describe actual business cycles? The case of synchronization. Journal of Applied Econometrics 20 (2), 253–274.

Spagnolo, F., Psaradakis, Z., Sofa, M., 2005. Testing the unbiased forward exchange rate hypothesis using a Markov switching model and instrumental variables. Journal of Applied Econometrics 20 (3), 423–437. Stock, J.H., Watson, M.W., 1996. Evidence of structural instability in macroeconomic time series relations. Journal of Business and Economic Statistics 14, 11–30. Tang, K., Xiong, W., 2010. Index investing and the financialization of commodities. NBER Working Paper n°16385, National Bureau of Economic Research, MA, USA. Taylor, A., Shepherd, D., Duncan, S., 2005. The structure of the Australian growth process: a Bayesian model of selection view of Markov switching. Economic Modelling 22, 628–645. Timmermann, A., 2000. Moments of Markov switching models. Journal of Econometrics 96, 75–111. Tsay, R.S., 1998. Testing and modeling multivariate threshold models. Journal of the American Statistical Association 93, 1188–1202. Turner, C., Startz, R., Nelson, C., 1989. A Markov model of heteroskedasticity, risk, and learning in the stock market. Journal of Financial Economics 25, 3–22. Whitelaw, R., 2001. Stock market risk and return: an equilibrium approach. Review of Financial Studies 13, 521–548. Xiao, Q., 2007. What drives Hong Kong's residential property Market – A Markov switching present value model. Physica A 383, 108–114.