Master’s Thesis
The Impact of the US shale gas boom on coal trade:
Coal market integration between the US and the EU
András Johancsik
S2567458
January 2015
University of Groningen
Corvinus University of Budapest
International Economy and Business, Double Degree
Supervisor: Prof.dr.mr. Catrinus J. Jepma
Co-‐Assessor: Miklós Rosta
Table of Contents
Abstract ... 3
1. Introduction: ... 4
2. Literature review: ... 5
2.1. The international coal market today, and the changing role of the US ... 5
2.2. The US’ power generation and the impact of shale gas ... 6
2.3. Driving forces behind US’ coal exports to the EU ... 10
2.4. Literature review on coal market integration ... 11
3. Framework ... 15
4. Data and Methodology ... 18
4.1. Data ... 18
4.2. Stationarity, Integration, and Spurious regression ... 19
4.3. Testing for stationarity ... 21
4.4. Cointegration testing and error correction ... 22
4.4.1. The Engle-‐Granger cointegration test ... 23
4.4.2. The Error Correction Model ... 24
4.4.3. Johansen Cointegration test ... 25
5. Empirical results ... 27
5.1. Strength of integration between 2006 and 2013, bivariate case ... 27
5.1.1. Stationarity ... 27
5.1.2. Cointegration tests ... 28
5.1.3. Error Correction Models ... 30
5.2. Route wise integration, trivariate case ... 30
5.2.1. Stationarity ... 31
5.2.2. Cointegrating rank test ... 32
5.2.3. Vector Error Correction Model ... 32
Abstract
In my thesis, I will investigate the integration between the US and EU coal markets. Recent studies either neglected the role of the US in the international coal trade, or found weak integration. Because of the increased coal exports, induced by the shale gas boom, I hypothesized that the integration got stronger between the US and the EU. To test my hypothesis, I followed the methodology of von Lossau and Zaklan et al., using Engle-Granger and Johansen cointegration analyses on price and freight rate datasets between 2006 and 2013. I found evidence for stronger cointegration in the recent period between coal prices in the US and the EU. However, this is not supported by the findings of trade route analysis that includes freight rates.
1. Introduction:
Coal production before the 1960s were mostly used in domestic markets, instead of being traded on a global scale. Since then, coal trade has increased significantly due to growing global energy demand, and a number of authors have even argued for the existence of an integrated global coal market. In my thesis, I want to focus on the relation between two participants of the international coal trade, the US and the EU. The US was mostly known in the previous decade for taking a small part in trade, while the EU has been and is the largest importer of coal in the Atlantic Basin. The role of the US changed, after experiencing a rapid drop in natural gas prices, due to the increased shale gas production that continued throughout the recent financial crisis and peaked during March 2012. The price drop made it attractive for utilities to switch away from coal towards natural gas in power generation, leading to a fall in domestic coal demand. At the same time high energy prices and low carbon price in the EU made using imported US coal an economical choice for domestic power producers. The ensuing trade flows made the US join the group of major coal exporters for the EU. My intention is to prove that due to the increased trade, the prices of the two markets have become more integrated. To quantify this relationship in the prices, and make them comparable to the recent literature, I will use the Engle-Granger and Johansen cointegration techniques.
2. Literature review
2.1. The international coal market today, and the changing role of the US
Coal is a fossil fuel that is used in heating, steel production, but mostly for generating electricity in power plants. Even though it is proven to be causing serious environmental problems, it is still the most used fuel in power generation. Mostly because of its abundance, and cheap price relative to other fuel sources, like oil or natural gas. Since the 2000s, global coal consumption has been steadily increasing largely driven by Chinese growth (IEA, 2014). In the past, most of the production was consumed locally, and the shares of traded coal among countries were insignificant. With the escalation in the demand for steam coal, global trade has increased from 500 million tons in 2000, to more than 1,200 million tons in 2012 (Cornot-Gandolphe, 2013). Geographically, we can distinguish two large markets for coal, the Pacific basin and the Atlantic basin. The Pacific basin is home to two of the largest exporters, Indonesia and Australia, which supply Korea, Japan and China. The Atlantic basin has lower amounts of trade, and its main exporters are Colombia, South Africa, Russia and the US. The main importer of the region is the EU (Burger et al, 2014). In this thesis, the focus will be on the Atlantic market, mainly looking at the relationship between the US and the EU.
The US was a swing-supplier before the 1990s, meaning it was driving the international prices through shifting its production. However, this changed in 1997, with the entry of low-cost Indonesian and Colombian coal exporters. The US became a price taker, and started losing its market power. In addition to this, the strong dollar made coal exports from the US less attractive. As coal prices are denominated in dollars, the value of the currency affects trade. For the same amount of coal, an importing country had to pay more from their own currency. On the other hand, the strong dollar was able to buy more from the cheaply produced Colombian coal, for the same amount of dollar from the exporters. Therefore it made more sense to import coal, rather than to export it. In the late 1990s, the US became a net importer of coal, from being a net exporter, and was driven out from the export market (EPRI, 2007).
Most of the recent literature on the international coal trade is silent about the role of the US in the global market. Indeed, after losing its market power as an exporter, the US had a decreasing level of net exports. This figure has remained constant from the early 2000s on, at an insignificant amount compared to domestic coal production. With the exploitation of shale gas reserves, domestic demand for coal was decreasing heavily. In turn net exports started to rise, notably from 2009 (IEA Statistics, 2014). Quite a few articles surfaced between 2013 and 2014, on the shale gas induced coal exports from the US to the EU, and the possible consequences regarding
emissions.1234
2.2. The US’ power generation and the impact of shale gas
The US’ power sector is one of the largest in the world. It produced 4,260 TWh of electricity in
2013, which is roughly 17% of the total world electricity output, second only to that of China5.
The electricity sector relies on a number of resources, which are used for generating power: conventional (coal, gas, oil, nuclear) and renewable sources (solar, wind, hydro, etc.) (Droege,
1 The Economist, 2013, The unwelcome renaissance
2012). By taking a look at the so-called energy mix of the US, it is clear to see that the ratio of the used fuel types is not constant over time.
Figure 2: Energy mix of the US, from 2000, billion kWh, seasonally adjusted Source: IEA Statistics, 2014
Renewable sources of energy are becoming more popular. However, strong critiques have been made regarding the competitiveness of renewables. Those opposing the deployment of renewables emphasize that without the support of the government, theses sources of power cannot be considered more feasible on a dollar per kilowatt-hour basis, when compared to conventional energy sources. Proponents of renewables argue, that huge subsidies are given for fossil-fuel producers, rendering renewables uncompetitive. Furthermore, they claim that carbon prices are not reflecting the true social costs of greenhouse gasses (IEA, 2011).
the largest emission rate per kWh, it is the most widely used generation source throughout the US, and in the world as well. Another fossil fuel that is frequently used for power generation is natural gas. On average, CO2 emissions from natural gas based electricity production are about 45% less for the same amount of kWh produced, compared to emissions from a coal-fired power generator. Therefore, when only accounting for emissions, natural gas based generators are preferred over coal fired ones. However, power generators have to keep an eye on fuel prices, as it greatly impacts operation costs (Schernikau, 2010). In case the relative price of fuel source drops below a certain threshold in absolute terms, it becomes feasible to shift a part of production towards the more competitive fuel source. In the short run, this leads to changes in operation, but within the installed capacity. If the price imbalance persists in the long run, part of the installed capacity from one source could be retired, while new plants are built for the other fuel source. In the case of coal and natural gas, this can even mean conversion of the power stations, given the similar technical characteristics of the two plants (Yanagisawa, 2013).
The phenomenon of fuel switching is not unprecedented; a good example is the recent shale gas boom in the US. Due to the development in hydraulic fracturing and drilling technologies, large amounts of previously inaccessible natural gas reserves were exploited (Wakamatsu, 2013). The scale of the production increase is so large that the US is expected to become a net exporter of
natural gas by 2016, after decades of importing6. For the domestic natural gas market, this meant
a hike in supply, which in turn driven down natural gas prices. The price of natural gas was so low, that the two fuels reached parity in April 2012. Lower emissions from natural gas, tough government regulations requiring the installment of costly scrubbers for coal fired plants, and record low relative price facilitated a shift of generation from coal towards natural gas (Macmillan et al., 2013). Indeed, the effects of the shale gas boom are evident from the energy mix. Another evidence can be derived from the reduction of greenhouse gas emissions, which also shows how polluting coal-based generation is compared to natural gas (Figure 3).
Figure 3: CO2 Emissions and fuel prices in the US, from 2006
Source: IEA Statistics, 2014
2.3. Driving forces behind US’ coal exports to the EU
In the previews section, I have reviewed the supply side of the exports. Now I will look at the demand side of the equation. One of the reasons why export coal from the US was sought after in the EU is the price difference. Even when taking into account the transport costs, the US export prices were lower than that of the European markets. The price difference could be partly explained by the Chinese government’s policy to restrict coal exports. Until 2008, China was a net exporter of coal, but became one of the largest net importer in 2009 (Chi-Jen Yan, 2012). Therefore part of the coal supplies to the EU was retained, and in addition to this, international demand for coal - and prices as well - increased.
As coal is mostly used for power generation in both the US, and the EU, the price of substitute fuel sources is also important to mention. While in the US, the shale gas boom drove prices downwards, the EU was facing high costs for natural gas based power generation. When comparing the two natural gas prices, the US has a clear cost advantage, due to the large domestic production levels. Natural gas prices in the EU increased so much recently that Statoil stopped
the common practice of oil-indexation for prices7.
The low European carbon price also played a part in the increased demand for coal imports from overseas. Because of the imperfectly assigned emission permits, and lower industrial production after the crisis, carbon price was low. Thus emission penalties that threatened power generators in
the US were not as severe as in the EU8. Naturally, more and more coal was used for producing
electricity in the EU. It has been noted by observers that the US is “exporting emissions” by exporting coal.
Clearly, through these additional factors accompanying the shale gas boom, the role of the US has changed in the international coal market. It has become a major coal exporter for the EU, affecting the underlying dynamics of the Atlantic market. In the following section, I will review
7 http://www.ft.com/intl/cms/s/0/aad942d6-‐4e25-‐11e3-‐b15d-‐00144feabdc0.html#axzz3Mu6SeIhQ
the literature on the integration of the international coal market to provide a base of reference for the subsequent analysis of the two regions’ coal prices.
2.4. Literature review on coal market integration
Prior to the 1960s, most of the global steam coal production ended up being used within the home market, and trade was mostly restricted to between neighboring countries. In the following decades, level of seaborne coal trade had increased. Warell (2006) emphasizes three key drivers that facilitated the emergence of global coal trade: Decrease of transportation costs, the switching from oil to gas in the 1970s due to security of supply concerns, and the increase in demand for energy around the world. Ellerman’s 1994 paper was one of the first to claim the existence of a unified global coal market. Since then, a handful of authors have analyzed the state of integration between coal markets. They have taken the price-based definition of a market to investigate the existence and the degree of integration (Li, 2007).
One common theme that exists in these studies is the Law of One Price. This theory states that given perfectly competitive markets (homogeneous product, no transaction costs, perfect information, large number of sellers/buyers, etc.), prices of a good – in this case coal – should be
similar across a market.9 In case there is a price difference, the information becomes common
knowledge, and the market corrects itself.10 If we consider the global coal market as a single
market, proving that the Law of One Price holds would confirm the previous assumption. This in turn would imply that the individual markets for coal are integrated with each other (Yang et al, 2000).
However, claiming that perfect competition exists in the international coal market has a number of shortcomings. The transparency of the markets is not high enough, limiting the flow of information, while the supplier side is highly concentrated (Zaklan et al., 2011). Indeed, Haftendorn (2012) finds evidence for the oligopolistic behavior in the Atlantic market between 2003 and 2006. Regarding the homogeneity of the product, steam coal characteristics can differ
9 http://ec.europa.eu/economy_finance/publications/publication10179_en.pdf
in energy content, moisture content, or sulfur and ash content, and in a few other aspects
(Schernikau, 2010). Therefore the similarity of products around the world is questionable. In relation to this, Li (2007) argues that more efficient power plants are able to accommodate steam coal of various types, thus differentiation should not affect the Law of One Price. All in all, the global coal market does not bear the textbook-characteristics of a perfectly competitive market. Still, through technological advancements in power generation, and with the increasing level of trade and the entry of more suppliers, it converges to one. With the relaxation of the previous assumptions, most papers proceed by testing the relations between the specific coal markets. A preferred method of analysis is the cointegration technique and the Error Correction Model. I will describe those in the next section, after the discussion of the relevant papers.
Warell (2006) looks at the integration of steam and coking coal market in global terms. She analyzes the European and Japanese market between 1980 and 2000, relying on quarterly data. She uses Engel-Granger cointegration test for long term, and an Error Correction model for the short-term dynamics. Her findings state that the coking and the steam coal markets are integrated in the long run. In the short run, the coking coal markets price adjustments were stronger than that of the steam coal market. In the coking coal market, the Japanese prices are driving the European prices, while in the steam coal market the European prices are affecting the Japanese prices. Warell explains this by the timing of the contract settlement. A policy implication regarding mergers is drawn from the findings. Policies should not be too severe concerning mergers and acquisitions, as the global nature of the market will counter the increased local market power.
test allows for these kinds of divergences, and does support the hypothesis of integration. In general, he concludes integration for the international steam coal market.
In his thesis, von Lossau (2010) uses quarterly import prices of steam coal, for three regions (US, EU, Japan) between 1980-2009. As the three regions accounts for half of all coal imports, he hypothesizes global market integration, in case of proven cointegration between the regions. He uses the Two-Step Engle-Granger and Johansen Test for cointegration, followed by three different Error Correction models. The results indicated a long-term equilibrium between the prices of the three regions. Nonetheless, a stronger relationship was found between Japan and the EU, where EU acts as a price leader. The US import market was found to be less integrated with the other two markets. He finds deviations from the equilibrium in the short term, explained by high transport costs, which prevents exploitation of price differences. The role of the US has changed since the covered timeframe of the analysis. Therefore it will be interesting to investigate whether the relation between the EU, and the US has changed or not.
3. Framework
In the literature review, I have shown that cointegration analysis is a method that is frequently used when describing price relationships between and within markets, namely the integration of markets. As I will rely heavily on cointegration, I will briefly summarize the main concepts involved, through a theoretical case. The cointegration technique is used to check whether a long-run relationship exists between a number of variables. Let’s take for example the prices of a
uniform good 11 in two countries A and B. We want to describe the relationship between the two
figures. They seem to be trending over time, which causes a problem in estimation, meaning the
relationship of the prices cannot be quantified with the regular OLS method12. If we take a closer
look it seems like the processes never drift too far from each other.
Figure 4: Prices of a uniform good in country A and country B Source: Hill et al, 2011
It is like if some kind of force was keeping the two price figures together. Speaking really coarsely, we could say that the difference between the prices is constant in the long run. A more technical and statistically correct way of saying it is that a linear combination of the two prices is stationary. If that is the case, the variables are said to be cointegrated, and thus have a long-term equilibrium (Engle and Granger, 1987). The short-run dynamics can also be estimated by building on the cointegration method. I will describe the technicalities more in detail in the following chapter. It should also be mentioned that cointegration can arise between more than two variables. Now about the economics, relating to the idea of cointegration.
As noted earlier, a number of papers investigated whether the Law of One Price holds in certain markets for certain goods. This theory states that if two identical goods are sold in two different markets, given a perfectly competitive market, the prices should be the same. In case there is a price difference, part of the supply will “move” to the location where the prices are higher, a practice known as arbitrage. The increased supply in turn, will depress prices, until equilibrium is restored. In perfectly competitive markets, this correction should happen right away. In less competitive markets, the correction could take a longer time, allowing for periodical disequilibrium of the prices. In case of markets in real life, like the global coal market, a number of other conditions exist that weaken the assumption of perfectly competitive markets. Still, the LOP should hold to a certain degree. The prices of coal can drift apart for some time, but as soon as the price difference covers costs of transportation and transaction, trade will balance the price gap. The LOP is analogous to the force that does not let the prices drift too far away from each other in the example above. Furthermore, when a market is defined as the area having similar prices (Li, 2007), proving that the LOP holds between countries can be considered a proof for market integration. Based on these facts, cointegration analysis is a useful methodology that connects well with economic theory. Thus I will also rely on it in my own research.
prices of the two regions. In my first calculation, I will rely on the methodology used in the thesis of von Lossau, who’s data does not cover the period containing the recent peak in US coal exports. I expect to find stronger market integration using data that covers this period. Thus my first hypothesis is:
1.The coal market integration was stronger in the time period between 2006 and 2013, than during the previous two decades.
In my second calculation, I will build on the methodology of Zaklan et al., who did not cover the role of the US in the global coal market. I am going to test whether the trading route between the US and the EU is integrated when freight costs are included alongside the respective price series. Which brings me to my second hypothesis:
2. The coal prices of the US, the fright rates and the European import prices are cointegrated.
4. Data and Methodology
4.1. Data
I will be using three variables in my calculations: the price of coal from the US, the import price of coal in the EU, and the freight cost of transportation from the Hampton Roads region in Virginia, US to the port of Rotterdam in The Netherlands. The prices of US coal are relatively difficult to obtain, compared to prices of electricity, for example. The main providers of coal data
are Platts, Argus Media, and IHS Mccloskey13. After receiving a price estimate for the desired
dataset, I resorted to using data that is available online free of charge. The most comprehensive and freely available data on US coal prices were obtained from the website of the US Energy
Information Agency14. The daily data covers the Central Appalachian coal daily prices, and is in
the form of $/short ton. According to the EIA’s site, the CAPP prices are the most widely used
benchmark for the East Coast coal.15 For the European coal, I use the daily API2 C.I.F. ARA
price benchmark for North-Western Europe, obtained from the Thomson Reuters Datastream16
database, provided by the University of Groningen. The API2 price index17 was also used by
Zaklan et al. (2011), as the reference price for the European imports. The ports of Amsterdam, Rotterdam, and Antwerp form a trading hub, receiving coal from the major exporters around the
world (Australia, Colombia, Poland, Russia, South Africa or US)18. The data is in denominated in
$/metric tons, thus the US price data will be converted from $/short tons to $/metric tons, using
the rates from the EIA19. The daily fright rates between the two regions are also obtained from
the Datastream computers, and are denominated in the same units as the API2 coal price. All three variables will be converted into their natural logarithms.
13 http://www.platts.com http://www.argusmedia.com https://www.ihs.com 14 http://www.eia.gov/coal/nymex/html/nymex_archive.cfm
15 http://www.eia.gov/todayinenergy/detail.cfm?id=8030 16 http://thomsonreuters.com
17 http://www.argusmedia.com/Methodology-‐and-‐Reference/Key-‐Prices/API-‐2
In my calculations, I am going to use two different samples for the two hypotheses, to make my findings comparable to the respective literature. For the first hypothesis, I will compare my findings to that of the ones in the thesis of von Lossau. He uses quarterly data, which I cannot replicate as my dataset runs from 2006 to 2013, and the small sample would cause problems in estimation. Therefore I am going to use US and EU coal prices of monthly frequency. The data includes 90 observations, between July 2006 and December 2013, derived from averaging daily data. As my second hypothesis follows the methodology of Zaklan et al., I have to use weekly data for the three variables: US coal price, EU coal price and the freight rate. This frequency
allows for a much richer sample consisting of 387 observations, ranging from the 30th week of
2006 till the last week of 2013. The weekly dataset is obtained by averaging daily figures.
4.2. Stationarity, Integration, and Spurious regression
In the previous chapter I introduced some very basics concepts relating to cointegration. To fully explain cointegration, these concepts have to be understood in depth. The starting point here is an attribute of time series, called stationarity. Stationarity means that the tested time series’ mean and variance are constant in time, and covariance of two elements of the series does not depend on the actual time of the observation, but on the length of time between them (Hill et al, 2011, p:476). Hill et al use an autoregressive process of order one to further explain stationarity:
y
t= ρy
t-1+ v
t (1)Here, the present value of y is explained by its value in the previous period multiplied by ρ, and an error v, which is random and independent. In case the value of ρ is |ρ|< 1, the process is stationary. Using graphical inspection, it can be observed that a stationary process will return to its mean periodically. The smaller the value of ρ, more often the process will cross its mean value. It is apparent from the graphical inspection that the process is frequently returning to its constant mean, which in this case is zero (Figure 4., Stationary process). There are processes that can be stationary around a non-zero mean, or even around a deterministic trend. Non-stationary processes can be random walks with our without drift terms, or possess deterministic trend
terms.20 These processes possess a unit root, meaning the value of ρ equals 1, thus are not
considered to be stationary. While it gives a general idea about the processes in question, it is not enough to solely rely on graphical inspection, and actual tests have to be done to assure stationarity.
Stationary process, ρ = 0.7 Unit root process, ρ = 1
Figure 5: Stationary and Unit root process Source: Simulation with Stata
In case a process is non-stationary, it could be transformed into a stationary process by differencing it. The order of integration gives the number of differentiations needed to achieve a stationary process. A process that is integrated of order zero, I(0), is stationary. While a process that is integrated of order one, I(1), is non-stationary, and it takes one differentiation to make it stationary (Brooks, 2014). The reason why this attribute is of major importance is that our estimates given by the OLS technique can be invalid, if it is used on non-stationary processes, as opposed to using stationary variables. Granger and Newbold have shown that two non-stationary
and unrelated variables can produce a seemingly meaningful (high t statistics, high R2 value)
While the levels of the variables might not be non-stationary, a linear combination of them can be stationary in theory, assuring that the variables are related in some way. Let’s hypothesize that y and x are I(1) variables, and are suspected of being cointegrated, thus having a long run equilibrium relationship. Then the regular OLS model would be:
y
t= β
0+ β
1(x
t) + v
t (2)Alternatively:
y
t- β
0- β
1(x
t) = v
t (3)Here, the error term vt is a linear combination of the two variables yt and xt. If the error term is
stationary, then the OLS estimates for the coefficients produce a long-run equilibrium relationship between the two variables (Engle and Granger, 1987). Equation (3) will be referred to as the cointegrating equation, and will have a major role in the coming sections. But first, after having discussed how important it is, I will show how to test for stationarity.
4.3. Testing for stationarity
A number of tests exist for stationarity, but the most widely used one is the Dicky-Fuller test. As
the test is based upon whether the value of ρ is equal to 1, it is also called a unit root test. The
formulation of the test depends on our assumption regarding the structure of the process. For the original AR(1) example, the model for testing takes the following form:
Δy
t= (ρ-1)y
t-1+ v
t= γ(y
t-1) + v
t (4)As indicated above, time series can also be stationary around a non-zero mean, or a deterministic trend. The formulations respectively:
Δy
t= α + γ y
t-1+ v
t (5)Δy
t= α + γ y
t-1+
λt + v
t (6)Where α is a constant for both equations, and λt stands for the deterministic trend part. If the null hypothesis is accepted, the series possess a unit root. If the alternative hypothesis is selected, the series are stationary. The hypothesis is identical for each test variant:
H
0: ρ = 1
⇔ H
0: γ = 0
The selection of the right model formulation can be done by graphical inspection of the series. However, the standard Dicky Fuller test does not allow for serial correlation in the errors (autocorrelation), which is a very likely phenomenon in the case of time series. (Hill et al, 2011) Therefore we should opt for the augmented version of the Dicky-Fuller test (ADF). The ADF test allows for the inclusion of lagged first differences that can eliminate the serial correlation in the errors. Thus the original equation to test for the AR(1) process becomes:
Δy
t= γ y
t-1+
𝒎𝒔!𝟏
𝒂
sΔy
t-s+ v
t (7)The determination of the lags to be included can be done manually by looking at the autocorrelation function of the errors, or by conducting a Breusch-Godfrey LM test for autocorrelation. After specifying the expected nature of stationarity (zero, non-zero mean, deterministic trend), and the selection of sufficient amount of lags, the test will provide the critical values and the test statistic. If the test statistic is larger in absolute terms than the critical value, the process is stationary (Becketti, 2013).
To be sure about the stationarity of the series, I will also use the Phillips-Perron unit-root test as a crosscheck. This method does not require the manual selection of additional lags like the ADF test. Instead, it uses Newey–West standard errors to account for the autocorrelation (Phillips and Perron,1988).
4.4. Cointegration testing and error correction
4.4.1. The Engle-‐Granger cointegration test
The first step of the Engle Granger test is determining whether the variables in question are stationary or not. The order of integration can be assessed with a unit root test, like the ADF test. If the variables are found to be stationary in their levels, a simple OLS procedure is sufficient for further testing, and the cointegration analysis is not necessary. In case the variables are not stationary in levels, their differences should be checked. In case both of the processes are found to be stationary in their first differences, then they are potentially cointegrated (Engle and Granger, 1987).
The second step of the test is the formulation of the cointegrating equation. The equation relies on the assumption of cointegration, that a linear combination of the series is stationary.
y
t= β
0+ β
1x
t+ e
t (8)Which becomes:
e
t= y
t- β
1x
t-
β
0 (9)Where ytand xt are the potentially cointegrated variables, et is the error term, and the coefficients
β0and β1are the slope and the intercept terms of the equation. As noted before, equation (9) is the
cointegration equation. Here, et is referred to as the error correction term, that will be used in
further estimations.
This leads to the final part of the test of cointegration, where the linear combination – the residuals – of the two processes are tested for stationarity. The procedure is the same as in the case of individual variables. The residuals are examined using the ADF unit-root test, to decide whether they are stationary or not.
Δe
t= γ y
t-1+
𝒎𝒔!𝟏
𝒂
sΔe
t-s+ v
t (10)regular critical values used for the individual variables’ stationarity test. As the residuals are estimated and not observed, stricter critical values apply, which makes it more difficult to reject the null hypothesis of non-stationarity. The hypotheses are the same as for the regular unit root testing:
H
0: ρ = 1
⇔ H
0: γ = 0
H
1: ρ < 1
⇔ H
1: γ < 0
Just as before, if the test statistic is larger in absolute terms than the critical value, the process is stationary. In that case, we can conclude that the two original series are cointegrated, meaning there is a long-run equilibrium relationship between them. Thus equation (8) will describe the long-run relationship between the two variables. In the long-run equilibrium, the value of variable
yt should equal xt multiplied by β1 when not accounting for the constant term. The cointegrating
relationship will ensure adjustments in case of disequilibrium. But this adjustment may not happen instantaneously, thus it is important to make estimations for the short-term as well (Hill et al, 2011).
4.4.2. The Error Correction Model
The Granger Representation Theorem states, if cointegration is present, a valid error correction representation of the data should be in place (Engle and Granger, 1987). In plain language if the variables have an equilibrium relationship in the long run, there has to be a force that “pulls” the variables back in the short-run, when they drift too far from this equilibrium. This force can be quantified by formulating the so-called Error Correction Model.
Δy
t= β
0+ β
1(Δx
t-1) + α
1(e
t-1) + v
t (11)long-run equilibrium at time t-1. The coefficient α1 is a number between the value of 0 and 1, and is
measuring the speed of the adjustment in the short-run. The larger the value of α1, the faster the
equilibrium relationship would be restored (Greene, 2007 and Hill et al, 2011).
The estimated error correction model can differ depending on how many lags are included in the model (see equation (12)). Additional lags are necessitated by the possible autocorrelation, as in the case of the ADF unit-root test.
Δy
t= α
1+ α
2e
t-1+
𝒎𝒔!𝟏
𝒂
sΔy
t-s+ v
t+
𝒏𝒌!𝟎
𝒂
kΔx
t-s+ v
t (12)In the examples, for the sake of simplicity, I hypothesized that only one of the variables are correcting for the errors. In practice, both “channels” of correction should be, and will examined.
4.4.3. Johansen Cointegration test
The Johansen approach is capable of analyzing more than two variables for cointegration. The idea is the same as in the case of the Engle-Granger test. We would like to quantify the long and short run relationship between variables. In the case of the Engle-Granger test, the investigation resorted to the connection between two variables. Therefore only one long run equilibrium existed, and the identification of the cointegrating equation was relatively easy. When the Engle-Granger test indicates that the variables are integrated, we readily quantify our only long-run relationship based on the OLS estimation. However, when multiple variables are involved, there can be multiple cointegrating equations. Also, the regular OLS estimation is no longer valid under these conditions. Therefore the Johansen analysis relies on maximum likelihood estimation (Johansen, 1988). I will follow the explanation of Becketti (2013), and the methodology of Zaklan et al (2011).
The core of the test is the Vector Error Correction Model. It is derived from VAR with p lags,
and vector yt of k variables. It contains all the parts that the Engle-Granger’s Error Correction
Model possessed, although in a slightly different form.
Δy
t= Π(y
t-1)+
𝒑!𝟏𝒕!𝟏𝚪
i(Δy
t-i) + v
t (13)Where:
Γ accounts for the short-run dynamics of the equation. Π is the matrix holding both the long-run
equilibrium representation(s) in matrix β, and the speed of adjustment coefficients in matrix α. To formalize the VECM form, the number of cointegrating relationships in the system has to be determined first. This is done by analyzing the rank of matrix Π, which is equal to the number of linearly independent cointegrating vectors in the system. The actual process of estimation is highly involved in linear algebra, which is not the subject of this thesis. Therefore I will resort to briefly describe the steps to be taken (Zaklan et al, 2011).
The very first step, just as in case of the Engle-Granger test, is determining whether the variables are stationary. This is done with the usual unit-root tests. Then, the lag selection for both testing the rank of matrix Π, and for the VECM is conducted. The decision in choosing the lags is based on the information criterions. Having selected the number of lags, the rank of the matrix Π should be determined. I will rely on the trace statistic that is calculated by the statistical software. The test has multiple null hypotheses relating to a specific number of cointegrating relationships, represented by the letter r. The respective alterative hypotheses are implying a larger number of equations than r. In case r equals 0, none of the variables are cointegrated according to the respective null hypothesis. If 0 < r < k-1, where k is the number of variables in the system, the matrix will have a reduced rank r, meaning r number of cointegrating relationships. If r equals k, matrix Π is said to have a full rank. In that case, all variables are stationary at their levels, implying flawed unit-root tests. All the hypotheses are tested against the respective alternative hypotheses by comparing the trace statistics to the critical values of the test.
When both the lags to be added, and the number of cointegrating equations are determined, the VECM can be estimated. The output from the estimation will include the long run equilibrium in the form of the cointegrating equation(s), the speed of adjustment coefficients, and the short run dynamics as well. A few follow up tests regarding stability and autocorrelation will also be conducted, before drawing conclusions (Becketti, 2013).
5. Empirical results
In this chapter, I will analyze the two datasets, according to the steps outlined in the methodology. Furthermore, I will compare my results to that of the respective literature. For reasons of convenience, not all of the outputs will be displayed here. The less important, and lengthily calculations will be stored in the Appendix. The datasets were created and modified using Microsoft Excel, while the statistical tests are all conducted with Stata 13.
5.1. Strength of integration between 2006 and 2013, bivariate case
My first hypothesis that the integration in coal prices between the US and the EU has got stronger in the recent period. To test whether this is true, I will test monthly data running from 2006 until 2013. After testing for stationarity, the long run relationship of the price series is going to be tested. To conclude my findings, the results of the Error Correction Models will be compared to that of von Lossau.
5.1.1. Stationarity
Figure 6: Monthly prices of coal in the EU and the US, in natural logarithms
Therefore I can conclude that both variables are indeed I(1), thus potentially cointegrated. To make sure their relationship is not purely spurious, I will test the stationarity of their linear combination with the ADF test.
5.1.2. Cointegration tests
By following the steps of the Engle-Grager analysis, the two variables are regressed on each other, to obtain their linear combination by estimating the residuals later on. The results from the
OLS estimation are comparable to that of von Lossau. The R2 value is clearly higher by
Variables Yt Xt β γ R2
von Lossau EU US EU US 1.226 0.499 -0.566 1.716 0.610 0.610 Johancsik EU US EU US 0.968 0.813 0.491 0.154 0.7862 0.7862
Table 1: OLS estimation results
The ADF test statistics for the estimated residuals are also higher in absolute value, and indicates cointegration between the two variables at 10% significance level.
Variables Yt Xt DF test on residual von Lossau
EU US US EU -‐2.948 -‐2.864
Johancsik
EU US US EU -‐3.042 * -‐2.847
Table 2: ADF test on residuals
As von Lossau pointed out, the ADF test has its shortcomings in case of small samples, thus the more powerful Johansen cointegration test is used as a crosscheck. The Johansen approach is used with 2 lags, which is recommended by the Schwarz Bayesian information criterion.
Rank Test Statistic 5% critical value
von Lossau
r<= 0 21.4030 12.53 r<= 1 0.3436** 3.84 Johancsik
r<= 0 16.9408 12.53 r<= 1 0.0067** 3.84
The null hypothesis of no cointegration is rejected, while hypothesis for the existence of one cointegrating equation is accepted at 5% level of significance. Thus I conclude that the two price series are indeed cointegrated, and share a long-run equilibrium relationship.
5.1.3. Error Correction Models
While the existence of a long-run equilibrium was proven between the two price series with the aid of cointegration analyses, the short run dynamics will be investigated using ECMs. Again, I will compare my findings to that of von Lossau, for all three models. In general, the models for
the more recent period have higher R2 values, an improvement in the goodness-of-fit. Also, the
speed of adjustment parameters are significant, and show an increase compared to the older dataset. While it seems that, the response of the US to disturbances in the equilibrium has changed, the finding for the EU are more ambiguous. In the first two models, the speed of adjustment is in line with the findings of von Lossau, and is low. However, in the third model, the speed of adjustment is unreasonably high compared to the other two models, and becomes significant. To be on the safe side, I turn to the more reliable Johansen-based VECM. As noted earlier, the Johansen cointegration test indicated the presence of 1 cointegrating equation, while using 2 lags for the estimation. Based on the VECM, it is apparent that the equilibrium relationship is mainly maintained by the US, as the EU’s price changes are not affected by the disturbances in the relative prices. Therefore I conclude that while a long-run equilibrium relationship exists between the two prices, the adjustment is solely done by the US, which is in line with the conclusion of von Lossau. However, a larger estimate for the speed of adjustment coefficient applies in the more recent data. Based on this, I accept my first hypothesis of stronger integration.
5.2. Route wise integration, trivariate case
Figure 7: Weekly freight rates and weekly prices of coal in the EU and the US, in natural logarithms
After the usual tests for stationarity, cointegration will be inspected using the Johansen multivariate framework. The results are comparable to the estimations of Zaklan et al., where the major trading routes were investigated.
5.2.1. Stationarity
tests uniformly reject the null hypothesis of non-stationary at all levels. All three variables are
stationary in their first differences, and thus I(1).
5.2.2. Cointegrating rank test
The next step in testing is determining whether the I(1) variables are cointegrated or not, and the number of cointegrating relationships. This is done by the Johansen trace test. Given that I am testing three variables, at most two cointegrating relationships are possible. Prior to testing, the lag selection has to be done. Using conventional information criterion, 2 lags were selected, and a constant is included in the model. The estimation for the three variables does not indicate any significant cointegrating relationship, thus none of the null hypotheses can be accepted. Following Zaklan et al, I will estimate the VECM regardless, hypothesizing the existence of 1 cointegrating equation. The cointegrating equation describes the long run relationship between
the variables, to which they should adjust in case cointegration holds.
5.2.3. Vector Error Correction Model
The VECM is specified with 2 lags selected in the previous calculations by the information criterion, 1 hypothesized cointegrating equation, and a constant. As expected, the individual testing for the three variables (US coal, EU coal, freight rates) does not yield any significant results. Aggregating the freight rates and the export prices leads to the same finding, thus rejecting the existence of cointegration in the system as a whole. Therefore, the freight costs cannot be considered to be related to the two price series. However, it is apparent from the output that the relationship between the two price series is strong under higher frequency data, which supports the first hypothesis. Still, the hypothesis of route wise integration between the US and
6. Conclusion
In my thesis I have investigated the integration between the US and EU coal markets, by relying on their respective price series, using data spanning from 2006 to 2013. During this time period, the abundant shale gas displaced coal in the US power generation sector, lowering domestic demand for coal. At the same time, economic growth in developing countries was driving global demand for coal, leading to a hike in import coal prices. The largest import market in the Atlantic Basin, the EU, faced high energy prices. Thus a number of European countries started buying coal from the US, displacing their gas-based power generation with coal, within their installed capacity.
Most recent studies on coal market integration disregarded the role of the US, because of its low share in international trade. With the increase in coal exports, induced by the shale gas boom, the US became a major exporter in the Atlantic Basin. Building on recent literature, I hypothesized the increased integration between the US and EU coal markets, and the integration of the trading route between the two regions. I tested each hypothesis by conducting both Engle-Granger and Johansen cointegration analyses, which are widely used methods for investigating market integration.
For the first hypothesis, I compared my findings to that of von Lossau, who used data not covering the period of increased exports. As expected, the calculations for the more recent timeframe indicated a stronger long and short run relationship between the price series. Therefore I accepted the hypothesis of stronger integration for the recent time period.
7. Limitations
8. References
Becketti, S. (2013) “Introduction to Time Series Using Stata”, Stata Press
Brooks, C. (2014) “Introductory Econometrics for Finance”, Third Edition, Cambridge
University Press
Burger, M., Graeber, B., Schindlmayr, G. (2014) “Managing Energy Risk: A Practical Guide
for Risk Management in Power, Gas and Other Energy Markets”, Second Edition, Wiley Finance
Series
Chi-Jen, Y., Xiaowei, X., Jackson, R. (2012) "China's coal price disturbances: observations,
explanations, and potential implications for global energy economies." Energy Policy
Cornot-Gandolphe, S. (2013) “Global Coal Trade: From Tightness to Oversupply”, Institut
Français des Relations Internationales
Droege, P. (2008) “Urban Energy Transition: From Fossil Fuels to Renewable Power”, First
Edition, Elsevier Science
Electric Power Research Institute (2007) “International Coal Market Analysis” Available at:
http://www.epri.com/abstracts/Pages/ProductAbstract.aspx?ProductId=000000000001014922
Ellermann, D. (1994) “The World Price of Coal”, Energy Policy
Enerdata (2014) “Global Energy Statistical Yearbook 2014”, Electricity production, Available
at: https://yearbook.enerdata.net/world-electricity-production-map-graph-and-data.html
Engle, R.F., Granger, W.J. (1987) “Cointegration and Error Correction: Representation,
Estimation, and Testing”, The Econometric Society
Granger, C. W. J., Newbold, P. (1974) “Spurious regressions in econometrics”, Journal of
Econometrics
Greene, W. H., (2007) “Econometric Analysis”, Sixth Edition, Prentice Hall
Haftendorn, C. (2012) “Evidence of Market Power in the Atlantic Steam Coal Market Using
Oligopoly Models with a Competitive Fringe”, DIW Discussion Paper
Hill, R. C., Griffiths, W. E., Lim, G. C. (2011) “Principles of Econometrics”, Fourth Edition,
John Wiley & Sons Inc.
International Energy Agency (2014) “Medium-Term Coal Market Report 2014 - Market
Analysis and Forecasts to 2019”, Executive Summary, Available at:
http://www.iea.org/Textbase/npsum/MTCMR2014SUM.pdf
Johansen S. (1988) “Statistical Analysis of Cointegration Vectors”, Journal of Economic
Dynamics and Control
Li R. (2007) “International Steam Coal Market Integration”, Mimeo, Macquarie University Macmillan, S., Antonyuk, A., Schwind, H. (2013), “Gas to Coal Competition in the U.S. Power
Sector”, OECD/IEA, Available at:
http://www.iea.org/publications/insights/CoalvsGas_FINAL_WEB.pdf
Phillips, P. C. B., Perron, P. (1988) "Testing for a Unit Root in Time Series Regression",
Biometrika
Schernikau, L. (2010) “Economics of the International Coal Trade: The Renaissance of Steam
Coal”, Springer
U.S. Energy Information Administration (2014) “Monthly Energy Review” Available at: http://www.eia.gov/totalenergy/data/monthly/
von Lossau, P. (2010) “The Coal Market: Structure and Price Dynamics - A Cointegration
Approach”, University of St. Gallen
Wakamatsu, H., Aruga, K. (2013) “The impact of the shale gas revolution on the U.S. and
Japanese natural gas markets”, Energy Policy
Warell L. (2006) “Market Integration in the International Coal Industry: A Cointegration
Approach”, Energy Journal
Yanagisawa, A. (2013) “Impacts of shale gas revolution on natural gas and coal demand: Power
generation mixes in both sides of Atlantic swung with natural gas price in the U.S.”, The Institute
of Energy Economics
Yang, D., Bessler, A., Leatham, D.J. (2000), “The Law of One Price: Developed and
Developing Country Market Integration”, Journal of Agricultural and Applied Economics
Zaklan, A., Cullmann, A., Neumann, A., von Hirschhausen, C. (2009) "The Globalization of
Steam Coal Markets and the Role of Logistics: An Empirical Analysis", Discussion Papers of DIW Berlin 956, DIW Berlin, German Institute for Economic Research
9. Appendix
Hypothesis 1 1.StationarityADF test for levels . dfuller leu, lags(2)
Augmented Dickey-Fuller test for unit root Number of obs = 87 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(t) -2.814 -3.528 -2.900 -2.585 --- MacKinnon approximate p-value for Z(t) = 0.0563
. dfuller lus, lags(2)
Augmented Dickey-Fuller test for unit root Number of obs = 87 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(t) -2.591 -3.528 -2.900 -2.585 --- MacKinnon approximate p-value for Z(t) = 0.0949
ADF test for first differences
. dfuller d.leu, lags(2)
Augmented Dickey-Fuller test for unit root Number of obs = 86 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(t) -4.207 -3.530 -2.901 -2.586 --- MacKinnon approximate p-value for Z(t) = 0.0006
dfuller d.lus, lags(2)
PP test for levels
. pperron leu
Phillips-Perron test for unit root Number of obs = 89 Newey-West lags = 3 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(rho) -8.728 -19.602 -13.612 -10.934 Z(t) -2.215 -3.525 -2.899 -2.584 --- MacKinnon approximate p-value for Z(t) = 0.2009
. pperron lus
Phillips-Perron test for unit root Number of obs = 89 Newey-West lags = 3 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(rho) -7.949 -19.602 -13.612 -10.934 Z(t) -2.051 -3.525 -2.899 -2.584 --- MacKinnon approximate p-value for Z(t) = 0.2647
PP test for first differences
. pperron d.leu
Phillips-Perron test for unit root Number of obs = 88 Newey-West lags = 3 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(rho) -54.399 -19.584 -13.604 -10.928 Z(t) -6.161 -3.527 -2.900 -2.585 --- MacKinnon approximate p-value for Z(t) = 0.0000
. pperron d.lus
2.Cointegration
reg leu lus
Source | SS df MS Number of obs = 90 ---+--- F( 1, 88) = 323.67 Model | 5.35573125 1 5.35573125 Prob > F = 0.0000 Residual | 1.45613028 88 .016546935 R-squared = 0.7862 ---+--- Adj R-squared = 0.7838 Total | 6.81186153 89 .07653777 Root MSE = .12863 --- leu | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---+--- lus | .9675895 .0537824 17.99 0.000 .8607082 1.074471 _cons | .490992 .2250186 2.18 0.032 .0438149 .9381691 ---
predict ehateu, resid dfuller, lags(2) ehateu
Augmented Dickey-Fuller test for unit root Number of obs = 87 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(t) -3.042 -3.528 -2.900 -2.585 --- MacKinnon approximate p-value for Z(t) = 0.0312
. reg lus leu
Source | SS df MS Number of obs = 90 ---+--- F( 1, 88) = 323.67 Model | 4.49768898 1 4.49768898 Prob > F = 0.0000 Residual | 1.2228435 88 .013895949 R-squared = 0.7862 ---+--- Adj R-squared = 0.7838 Total | 5.72053247 89 .064275646 Root MSE = .11788 --- lus | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---+--- leu | .8125719 .045166 17.99 0.000 .7228141 .9023298 _cons | .4937682 .2050644 2.41 0.018 .0862457 .9012906 --- predict ehatus, resid
dfuller ehatus, lags(2)
vecrank leu lus, trend(none)
Johansen tests for cointegration Trend: none Number of obs = 88 Sample: 2006m9 - 2013m12 Lags = 2 --- 5%
maximum trace critical rank parms LL eigenvalue statistic value 0 4 229.75966 . 16.9408 12.53 1 7 238.22669 0.17505 0.0067* 3.84 2 8 238.23004 0.00008
---
3.Error Correction Models
Model 1: Δy
t= β
0(Δx
t) + Φ(e
t-1)
Variables Yt Xt β0 Φ R2 von Lossau EU US 0.154 0.017 0.029 US EU 0.105 -0.198*** 0.140 Johancsik EU US 0.77*** -0.103* 0.411 US EU 0.493*** -0.197*** 0.480
Model 2: Δy
t= β
1(Δy
t-1) + β
2(Δx
t-1) + Φ(e
t-1)
Model 3: Δy
t= β
0(Δx
t) + β
1(Δy
t-1) + β
2(Δx
t-1) + Φ(e
t-1)
Variables Yt Xt β0 β1 β2 Φ R2 von Lossau EU US 0.150 0.336*** -0.060 -0.034 0.118 US EU 0.100 -0.064 0.019 -0.189*** 0.142 Johancsik EU US 0.668*** 0.210 * 0.180 -0.157** 0.50 US EU 0.483*** 0.112 -0.089 -0.213*** 0.489 Hypothesis 2 1.StationarityADF test for levels dfuller leu, lags(2)
Augmented Dickey-Fuller test for unit root Number of obs = 384 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(t) -1.858 -3.449 -2.875 -2.570 ---
MacKinnon approximate p-value for Z(t) = 0.3519 .
dfuller lus, lags(2)
Augmented Dickey-Fuller test for unit root Number of obs = 384 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(t) -1.679 -3.449 -2.875 -2.570 --- MacKinnon approximate p-value for Z(t) = 0.4420
dfuller lf, lags(2)
ADF test for first differences
dfuller d.leu, lags(2)
Augmented Dickey-Fuller test for unit root Number of obs = 383 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(t) -8.823 -3.449 -2.875 -2.570 --- MacKinnon approximate p-value for Z(t) = 0.0000
dfuller d.lus, lags(2)
Augmented Dickey-Fuller test for unit root Number of obs = 383 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(t) -12.766 -3.449 -2.875 -2.570 --- MacKinnon approximate p-value for Z(t) = 0.0000
dfuller d.lf, lags(2)
Augmented Dickey-Fuller test for unit root Number of obs = 383 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(t) -8.849 -3.449 -2.875 -2.570 --- MacKinnon approximate p-value for Z(t) = 0.0000
PP test for levels pperron leu
Phillips-Perron test for unit root Number of obs = 386 Newey-West lags = 5 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(rho) -6.230 -20.409 -14.000 -11.200 Z(t) -1.921 -3.449 -2.875 -2.570 --- MacKinnon approximate p-value for Z(t) = 0.3223
pperron lus
Z(rho) -5.922 -20.409 -14.000 -11.200 Z(t) -1.794 -3.449 -2.875 -2.570 --- MacKinnon approximate p-value for Z(t) = 0.3835
pperron lf
Phillips-Perron test for unit root Number of obs = 386 Newey-West lags = 5 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(rho) -8.324 -20.409 -14.000 -11.200 Z(t) -2.032 -3.449 -2.875 -2.570 --- MacKinnon approximate p-value for Z(t) = 0.2727
PP test for first differences .
pperron d.leu
Phillips-Perron test for unit root Number of obs = 385 Newey-West lags = 5 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(rho) -322.902 -20.408 -14.000 -11.200 Z(t) -15.543 -3.449 -2.875 -2.570 --- MacKinnon approximate p-value for Z(t) = 0.0000
pperron d.lus
Phillips-Perron test for unit root Number of obs = 385 Newey-West lags = 5 --- Interpolated Dickey-Fuller --- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value --- Z(rho) -248.122 -20.408 -14.000 -11.200 Z(t) -14.724 -3.449 -2.875 -2.570 --- MacKinnon approximate p-value for Z(t) = 0.0000
pperron d.lf