Are spot freight rates stationary?

Transcription

1 Forthcoming in Journal of Transport Economics and Policy Are spot freight rates stationary? Steen Koekebakker * Agder University College, School of Management Roar Adland Norwegian School of Economics and Business Administration Sigbjørn Sødal Agder University College, School of Management March 2006 Abstract: In the recent literature, empirical tests of stationarity of freight rates often conclude that spot freight rates are non-stationary processes. However, many maritime economists would argue that the freight rate cannot exhibit asymptotically explosive behaviour, as implied by non-stationarity, in a perfectly competitive freight market. This paper restates the theoretical arguments behind mean reversion and boundedness of the spot freight rate process and suggests that the failure to reject non-stationarity may be due to the weak power of tests most frequently used. We employ a non-linear version of the Augmented Dickey-Fuller (ADF) test, based on an exponentially smooth-transition autoregressive model (ESTAR). This test enhances the power against mean-reverting nonlinear alternative hypotheses compared to the linear alternative for traditional ADF tests. Our empirical results show, in line with maritime economic theory, that freight rates in both dry-bulk and tanker markets are non-linear stationary. Keywords: spot freight rate, bulk shipping, non-stationarity, mean reversion. Acknowledgements: Financial support from Agder Maritime Research Foundation is greatly appreciated. Thanks to Ulrich K. Müller and participants at the Annual IAME Conference 2004 in Izmir, Turkey, for helpful comments. Suggestions from the editor, Steve Morrison and an anonymous referee substantially improved and sharpened the focus of the article. Any remaining errors are our own. * Corresponding author. Address: Agder University, School of Management, Serviceboks 422, 4604 Kristiansand, Norway. steen.koekebakker@hia.no. 1

2 1.0 Introduction The freight markets in bulk shipping are usually held as textbook examples of perfectly competitive markets (see Norman (1979) and Stopford (1997)). The potential for supply adjustment in a perfectly competitive market ensures that extremely high or extremely low freight rates are not sustainable. When the freight rate is high, the demolition of vessels will slow down or cease temporarily, while the number of new vessels delivered continues unabated and new orders are placed. The increase in the supply of transportation, gradually shifting the supply curve to the right, will inevitably bring freight rates down to (and often below) a level that yields a normal economic profit. The opposite argument holds during poor freight markets, when the supply of vessels decreases due to the demolition of tonnage. In the very long run, one should expect freight rates to be highly correlated with long term total costs. Consequently, in an economic equilibrium setting with free entry and exit, the freight rate is expectedly a mean-reverting variable in one sense or another. It follows that the freight rate cannot exhibit the asymptotically explosive behaviour implied by a non-stationary process. While the notion of mean reversion in the freight rate has been prevalent in the maritime economic literature (see Zannetos, (1966), Strandenes (1984), Tvedt (1997) and Adland and Cullinane (2006)), most empirical studies have concluded that the spot freight rate, or its timecharter 2

3 equivalent 1 (TCE), contains a unit root; it is non-stationary (see Berg-Andreassen (1996), Glen and Rogers (1997) and Kavussanos and Alizadeh (2002) among others). However, it is perhaps not surprising that empirical tests for stationarity of the freight rates suggest the presence of a unit root. There seem to be at least three main reasons for this. First, most time series of spot freight rates, or their timecharter equivalent, are found to be highly persistent (see Adland and Cullinane (2006)). As pointed out by Dixit and Pindyck (1994), the hypothesis of a unit root is difficult to reject for a very persistent process without access to very long time series. The reasons for such persistency will be discussed in more detail in the next section. For now, it suffices to point out that the supply side of the market will not respond immediately to large unexpected demand shocks. This is usually explained by the time lag between the ordering and delivery of vessels, which is indeed a main reason. However, it should also be mentioned that that the impact of delivery lags on investment is theoretically more complicated, since any rational investor will take into account the effect of the delivery lag at the time of his investment. Therefore a delivery lag could under certain circumstances trigger early investment and contribute to reduce the likelihood of price 1 In this paper, the term spot freight rate refers to the freight rate of a voyage charter in $/tonne (or Worldscale for tankers), while the timecharter equivalent takes into account the voyage costs and duration ($/day). Unless otherwise noted, the empirical analysis concerns the TCE. 3

4 spikes. More generally, delivery lags could have quite spurious effects on investment (see Bar-Ilan and Strange (1996) for a seminal model and Sødal (2006) for an extension with a shipping application). One other reason that many studies conclude that freight rates are non-stationary appears to lie in the choice of test method. The commonly used Augmented Dickey-Fuller (ADF) unit root test (Dickey and Fuller (1979) and Said and Dickey (1984)) is based on a linear additive model displaying symmetric adjustment. In a recent paper, Adland and Cullinane (2006) apply non-parametric estimation techniques to show that the drift term of the spot freight rate process in the tanker markets is mean-reverting only in the extremes of the spot freight rate distribution, while the process exhibits unit root behaviour over most of its empirical range. They argue that this apparent non-linear behaviour can explain why non-stationarity can be difficult to reject over short samples yet the spot freight rate process is globally mean reverting as implied by maritime economic theory and overall stationary. In a non-linear environment, the traditional unit root tests, such as the ADF test, are inherently unsuitable tests for non-stationarity. Finally, even if the assumption of non-stationary freight rates does not hold in a strict sense, it may be a convenient one from a technical point-of-view. Stationary processes are typically more complicated to deal with as far as investments and other 4

5 decisions in the shipping industry are concerned. This fact should not stop the maritime research environment from questioning the standard assumption that freight rates are non-stationary, and using all available technical tools to shed light on this topic. With the above in mind, the main objective of this paper is to assess whether the non-stationarity property put forth in the empirical literature is robust. In addition to this important empirical contribution, we argue with a basis in fundamental maritime economic theory, for the first time, that spot freight rates are not only stationary but also must have non-linear mean dynamics. As all extant research consider spot freight rate dynamics in a linear framework, the paper therefore belongs to a new and potentially important strand of the maritime economic literature and backs up the empirical results in the most recent empirical research (see Adland and Cullinane (2006)). The remainder of the paper is structured as follows. Section 2 reviews the relevant classical maritime economic theory. Section 3 reviews the statistical methodology applied to test stationarity of the spot freight rate series. We consider unit root tests against both linear and non-linear stationary alternatives. Section 4 describes the data and outlines the empirical results. Section 5 contains concluding remarks and suggestions for future research. 5

6 2.0 Maritime Economic Theory and Mean Reversion In a perfectly competitive spot freight market, the freight rate is normally determined by the marginal cost of the marginal vessel required to satisfy the demand for transportation. The short-term supply curve indicates the amount of transportation willingly supplied by the fleet at a given freight rate. In the classic maritime economic literature, starting with Koopmans (1939), the short-term supply curve in bulk shipping is characterized by two distinct regimes, distinguished by whether or not the fleet is fully employed. When all vessels in the fleet are employed, the only possibility to increase the supply of sea transportation in the short term is through higher utilization of the existing ships. This can be achieved through higher vessel speed, reduced port time, shorter ballast legs or by delaying regular maintenance. However, this increase is limited by technical constraints and implies a higher marginal cost of operation due to higher fuel consumption and increased wear and tear. When the fleet sails at close to the maximum capacity, the aggregate supply function becomes almost perfectly inelastic with the result that demand rationing takes place through very high freight rates. Conversely, when the available supply exceeds demand, leading to lower freight rates and vessel unemployment, the least cost-efficient vessels will withdraw from the market, resulting in a series of perfectly 6

7 elastic steps in the short-term supply function. Accordingly, Koopmans (1939) proposed a short-term supply curve that is very elastic when tonnage is unemployed (low freight rates) and very inelastic during periods with full employment (high freight rates). This characteristic shape has later been confirmed in several empirical works (Zannetos (1966), Devanney (1973), and Norman and Wergeland (1981)). In the classic literature, the refusal rate below which the vessel no longer supplies transportation is assumed to be its lay-up point, i.e. the TCE spot freight rate at which the shipowner is indifferent between lay-up and operation. As there are switching costs related to laying up the vessel, this threshold rate must be lower than the daily operating cost less the daily lay-up cost (see Mossin (1968) and Dixit (1989)). 2 Under certain conditions the threshold rate for exit (lay-up or scrapping) may even be negative, but it will be bounded from below because steadily more vessels will leave the market as demand turns lower. The demand for sea transportation is governed by changes in world consumption of bulk commodities, as well as changes in the geographical demand and supply patterns. Following Koopmans (1939), the short-term demand for sea transportation is usually assumed to be inelastic with respect to the freight rate. The price elasticity 2 The question of whether lay-up is viable depends on the total cost of switching, which includes irreversible switching costs as well as daily costs of keeping the vessel laid up. For many such cost combinations it could be optimal to scrap a ship directly instead of laying it up even if the daily lay-up cost is significantly lower than the daily operating cost see Dixit and Pindyck (1994). 7

8 depends on the magnitude of the freight rate relative to the value of the bulk commodity, and will be larger for certain dry-bulk cargoes (for instance, coal and iron ore) than for crude oil and oil products. Zannetos (1966) adds that oil transportation is itself an input to a production factor for which the demand is rather inelastic. Moreover, technical substitution (using air or land transportation) is not feasible in most cases. However, the demand for sea transportation gradually becomes more elastic as freight rates increase to very high levels due to increasing demand efficiency. Koopmans (1939) argues that the quality of oil, the location of refineries, and the strategic importance of oil affect the trade pattern and that such constraints would be relaxed in times of high freight rates. Strandenes and Wergeland (1982) point out that charterers will tend to look for sources of raw materials closer to the consumer market when freight rates increase. From a theoretical point of view, a maximum freight rate will exist that no charterer (shipper) is willing to exceed. The demand for bulk shipping is derived from the demand for seaborne bulk commodities, the prices of which are generally set in perfectly competitive world markets. Hence, for a given CIF price of the commodity, the maximum freight rate is the rate that absorbs all profit from international trade and results in a net loss equal to the loss of goodwill and/or the penalty of contractual default. Moreover, although higher freight costs can sometimes be transferred to the 8

9 consumer through higher commodity prices, other vessel types or modes of transportation (for instance, containers or pipelines) can economically substitute bulk vessels at some extremely high freight rate level. As argued by Tvedt (1996), it follows that there must also exist a theoretical ceiling to the freight rate. The stylized shape of the theoretical short-run demand and supply curves in bulk shipping is illustrated in the figure below. The existence of a lower and upper bound to the spot freight rate implies that it cannot exhibit the asymptotically explosive behaviour implied by non-stationarity. < Insert Figure 1 about here > The persistency of the spot freight rate process is caused by the fact that the supply side cannot generally react to changes in demand with sufficient speed and magnitude to eliminate all demand shocks that bring the freight rate away from levels that yield a normal return to investment, for at least two main reasons. First, the ability to increase supply is limited, in the short run 3, by the delivery schedule of new ships from shipyards and, in the longer run, by the time lag between the ordering and delivery of vessels. For instance, given that the current level of deliveries is a result of 3 We here interpret short run as the shortest possible delivery lead time for the relevant ship type under the prevailing market conditions, generally in the order of 1 4 years. 9

10 freight market conditions and ordering activity in the past, there need not be any new vessels coming into the market in the space of a few months, despite record freight rates. The lead times for delivery tend to increase in times when demand for new vessels is high due to capacity constraints in the shipbuilding industry. The lead time is also influenced by technology and productivity developments in shipyards. Conversely, the availability of scrapping candidates will limit deletions from the fleet. Consequently, the speed of self correction in the market is limited, creating a highly persistent price process. Second, from theory of investment under uncertainty, it follows that it is not always optimal for an investor to respond to a positive demand shock even if the current price level indicates expected gains from investment. Investors typically require an option premium in terms of freight rates exceeding long term average costs in order to compensate for possible costs of regret in case the market goes down after an irreversible investment (Dixit and Pindyck (1994)). Thus, even without investment lags there is a possibility that freight rates for long periods of time will stay above a level for which investment would be profitable based on a standard NPV investment rule. Similar arguments apply with respect to scrapping decisions. More generally, this line of reasoning is particularly relevant in capital-intensive industries with limited alternative uses of existing capital, which is clearly the case in many shipping 10

11 market segments. The hypothesis that the spot freight rate must be mean reverting in the long run, however, is based on the dynamic interaction of the demand and supply curves over time. We can illustrate this by the following simple example: If we ignore the potential for shipyards to increase productivity, the marginal addition to the fleet (new deliveries) is given by the orderbook and known in the short run. It follows that the only way to change the total capacity of the fleet in the short run is through the level of scrapping. Empirical data confirm that scrapping levels increase (decrease) during periods of low (high) freight rates. This is illustrated in the scatter plot in Figure 2, which graphs the monthly net supply change (new deliveries in DWT less scrapping in DWT) versus the average monthly TCE spot earnings in the VLCC market for the period January 1994 through October The slope of the estimated relationship is statistically significant and positive, confirming that supply, on average, tends to adjust to changes in demand so as to bring the freight rate towards some long-run average (i.e. mean reversion). In particular, all observations are non-negative for very high freight rates (> $40,000/day), implying increasing supply. < Insert Figure 2 about here > 11

12 Finally, it is worth pointing out that there is empirical evidence of non-linearity in the drift function (see Adland and Cullinane (2006) and Tvedt (1997)). This further reduces the value of applying standard unit root tests for detecting mean reversion in the spot freight market, as these are based on a linear model with symmetric adjustment. There is also theoretical support for such non-linearity, as the convex supply function in Figure 1 combined with a non-linear 4 supply response function will produce a non-linear drift function that exhibits a low (high) speed of mean reversion for low (high) freight rates with a speed of mean reversion that is increasing in the spot freight rate level (see Adland and Strandenes (2004)). To summarize, in this section we have applied basic maritime theory to show why the spot freight rate process must be mean reverting and non-linear. This suggests that the appropriate null hypothesis is non-linear stationarity. We have also illustrated empirically why, although such mean reversion will exist in the long run, the spot freight rate process will be highly persistent in the short run. We suggest that this persistency, combined with non-linearity of the first-order conditional moment of the freight rate changes, limits the power of traditional tests for non-stationarity (in particular the ADF) in this market. 4 The theoretical supply response function must also be non-linear. Above the freight rate level where all demolition activity ceases, the function (i.e. the net additions to the fleet) is a constant and equal to the tonnage scheduled for delivery. Below this level, the function is a decreasing function of the freight rate level (see Adland and Strandenes (2004)). 12

13 3.0 Testing for Non-stationarity We have argued that non-linear stationarity is the natural null hypothesis for testing the stochastic property of shipping freight rates. Unfortunately, to our knowledge no such test exists. The most popular tests take non-stationarity as their null, and test against a stationary linear alternative (linear unit root tests). Linear unit root tests are common in the empirical shipping literature. In this article we also consider unit root tests against a non-linear stationary alternative. In the following we provide a brief review of linear and non-linear unit root tests, some of which we will apply in the empirical part in this paper. We only present the main ideas behind the tests. (See the original articles for technical details.) 3.1 Unit root tests against a linear alternative Consider the following version of the Augmented Dickey Fuller (ADF) test: y t d t k 0 yt 1 j yt j t j 1 (1) where the term d t picks up deterministic components and is the lag operator so that y t y t y t 1. In the empirical part of this article we will restrict our attention to dt d and d d t. The unit root test is a one-tailed t-test on the parameter 0 t d0 1 0 =0 against the stationary alternative 0 <0. Dickey and Fuller (1979) considered tests 13

14 with k=0 (DF-test), whereas Said and Dickey (1984) augmented the Dickey and Fuller (1979) regression to allow for serial correlated errors in the process under investigation (the ADF test). The ADF test in (1) is thus appropriate for alternatives in the linear ARMA-class of processes. The researcher must pick a sensible value of k to adjust for additional serial dependence. Usually an information criterion is used to select k. The ADF test is given by the t-statistics ˆ ˆ ADF 0 ŝ AR, where 0 ˆ is estimated by OLS and ŝ AR is the estimated standard deviation of ˆ 0. The distribution of ˆ is non-standard and depends on the specification of d t. Asymptotic critical values can be found in Fuller (1976). The asymptotic distribution in Dickey and Fuller (1976) is valid only for i.i.d. innovations. Phillips (1987) and Phillips and Perron (1988) demonstrate that the ADF test is not asymptotically justified when innovations follow general forms of serial correlation and heteroscedasticity. They proposed modified versions of the statistics ˆ 0 and ˆ that allow for fairly general forms of serial correlation and heteroscedasticity (the PP test). In an influential paper Schwert (1989) shows the low power of both ADF and PP tests, especially for stationary processes with a large negative root in the moving average term. Perron and Ng (1996) analyzed a class of modified tests that can be interpreted as modified PP tests. They showed that tests are robust to size distortions when the residuals have negative serial correlation and, moreover, that the size distortion reported in Schwert (1989) 14

15 does not apply to these modified PP tests provided a suitable way of choosing the number of lags (k) in (1) is used. Elliot et al. (1996) proposed a point-optimal test for unit roots. Point-optimal tests follow a two-step procedure by first de-trending the data and then testing for unit roots. They showed that a substantial increase in power is possible by de-trending the data using generalized least squares (GLS) and then running the traditional DF-test on GLS-detrended data. Ng and Perron (2001) proposed a new class of modified information criteria (MIC) for selecting the appropriate number of lags in the auto-regression, and within this class they suggested a modified version of the Akaike information criterion (MAIC). They argued that MAIC has better theoretical and empirical properties than other criteria. We will apply this criterion in the empirical analysis in section 4. All the abovementioned (unit-root) tests are tests for non-stationary, as the null hypothesis for the variable under investigation is non-stationarity. Kwiatkowski et al. (1992) designed a test (the KPSS test) that starts from the null hypothesis of stationarity. A standard way to proceed in empirical work is to first apply the ADF and/or PP tests. The KPSS test is then used for a final confirmation of either the unit root or stationary property. However, the KPSS test has been shown to have undesirable properties. Caner and Kilian (2001) demonstrate in a Monte Carlo study that the tests massively over-reject the null hypothesis of stationarity in the presence 15

16 of autocorrelation. Also, somewhat counterintuitive, the performance of the test worsens as the sample size increases. Kuo and Tsong (2004) show that, in the presence of a stationary but highly persistent process, the KPSS-statistics diverge to infinity with probability one as samples increase to infinity. Other stationarity tests (for instance Saikkonen and Luukkonen (1993) and Leybourne and McCabe (1994)) have been shown to suffer from similar size distortions as the KPSS test (see discussion in Kuo and Tsong (2004) and Müller (2005)). Müller (2005) studies the KPSS test analytically in the asymptotic local-to-unity framework. He finds that the point-optimal unit root test statistics pioneered by Elliott et al. (1996) (see also Elliott (1999) and Müller and Elliott (2001)) have much more discriminating power than tests for stationarity. The strong persistence of freight rates (high degree of autocorrelation) suggests that the KPSS test is undesirable and we will not apply it here. 3.2 Unit root tests against a non-linear alternative Both the traditional ADF test and the point-optimal ADF test (with GLS-detrending) are set up against a linear stationary alternative. Kapetanios et al. (2003a) suggested a unit root test against a non-linear globally stationary exponentially smooth transition autoregressive (ESTAR) process (the KSS test). They find that this test has good size and power properties compared to the traditional ADF test when the process is 16

17 stationary and highly persistent. The non-linear regression investigated by Kapetanios et al. (2003a) is y t 2 1 exp( y t 1 t k j yt j y t 1 ) j 1 (2) where y t is the de-meaned freight rate defined by y t y t d. The term d t may be a t constant or a constant plus trend as in the previous section. Note that the k serial correlated errors enter linearly in equation (2). The null hypothesis of a linear unit root is H 0 : =0 against the non-linear alternative H 1 : >0. It is not feasible to test the null directly in (2), since is not identified under the null hypothesis. Instead, computing a first order Taylor series approximation, Kapetanios et al. (2003a) base their test on the auxiliary regression y t k 3 t 1 j j 1 y y error (3) t j Parallel to the ADF test, the KSS test is given by the t-statistics ˆ ˆ ŝ, where KSS AR ˆ is estimated by OLS and ŝ AR is the estimated standard deviation of ˆ. The test does not have an asymptotic standard normal distribution. Simulated critical values are given in Kapetanios et al. (2003a). The authors suggest using standard model selection criteria for determining k in the equations above. Kapetanios and Shin (2003a) investigate efficiency improvements using GLS-detrending inspired by the point-optimal procedures of Elliot et al. (1996). In a Monte Carlo study they find that GLS-detrending can improve the power performance of the KSS test. We employ both 17

18 the KSS test and the point-optimal version in the empirical part of this paper. For both linear and non-linear unit root tests we follow the recommendation of Ng and Perron (2001) when selecting k. The same criteria can be used since both tests share the same null hypothesis. 3.3 Other non-linear alternatives The ADF test is by far the most popular test in the empirical maritime economic literature. The KSS test is also computationally inexpensive and, moreover, it has the same null hypothesis as the ADF test. It is therefore a natural contestant to the ADF test in empirical work. But other non-linear alternatives may also be considered. ESTAR is a particular alternative in the class of smooth transition autoregressive models. Kapetanios and Shin (2003a) develop a Wald-type unit root test when the alternative process is of the so called self-exciting threshold autoregressive (SETAR) type. Kapetanios and Shin (2002) develop unit root tests against a three regime threshold model. The null hypothesis is a linear unit root process against the alternative of a globally stationary three regime SETAR model with a unit root process in the corridor regime. They develop a Wald test for joint significance of the autoregressive parameters in the upper and lower regime. The transition variable in the SETAR/ESTAR models is the lagged dependent variable. A different approach to 18

19 unit root testing in threshold models is suggested by Caner and Hansen (2001) who develop unit root tests for threshold nonlinearity when the underlying univariate process follows a unit root. In their approach the transition variables must be stationary, typically a constant. Their framework does not allow a SETAR/ESTAR specification, since lagged dependent variables become non-stationary under the null hypothesis. The other broad class of regime models is the so called Markov regime-switching models (Hamilton (1989)) where the regime changes are driven by an unobservable Markov chain. In a Monte Carlo study, Nelson et al. (2001) investigate the power of linear unit root tests when the data generating process is Markov switching. They conclude that linear unit root tests are ill-equipped to distinguish a stationary Markov switching process from unit root processes. Carrasco et al. (2004) propose various non-stationarity tests in Markov switching models. It is also possible to model freight rates as processes with long memory. In the general econometric literature, long memory and non-linearity have rarely been jointly analysed. There is, however, a small strand of literature that addresses the relationship between long memory and non-linearity. Kapetanios (2004) shows in a simulation study that stationary threshold and Markov switching models can exhibit long memory properties (slowly decaying autocovariance). This means that non-linear models may 19

20 mistakenly be taken to be long memory non-stationary processes. See Kapetanios (2002) and Kapetanios and Shin (2003b) for tests of non-stationary long memory against the alternative of particular forms of non-linearity. We do not employ such tests in this article, but investigations into long memory models or non-linear models with long memory properties may be a possible path for future research. 4.0 Empirical results In this section we first discuss various freight rate measures and provide an overview of previous research on time series analysis in the freight market. Next we present our data and the results from linear and non-linear unit root tests. 4.1 Freight rate measures and data issues Several measures of freight rates exist and have been used in the empirical literature. In particular, spot freight rates can be quoted either as time-charter equivalent (TCE) spot freight rates (also called tripcharter rates) denoting the daily earnings ($/day) generated by a vessel for a particular roundtrip or simply the (gross) spot freight rate denoting the price agreed per tonne of cargo ($/tonne) for a particular loaded voyage. One crucial difference between the two measures in this context is that the former measure represents the economic profit net of voyage costs such as canal, port and 20

21 fuel costs, while the latter will include this stochastic cost element. Given that the spot freight rate is set in a perfectly competitive market, and in theory represents the marginal cost of the marginal vessel required for transport, the spot freight rate measured in $/tonne will therefore inherit, to an unknown extent, the dynamic properties of the fuel price. Despite the fact that this is an exogeneous process to the shipping market 5, the important implications this will necessarily have for the characteristics of the spot freight rate process (e.g. stationarity) has been overlooked in the maritime economic literature. Moreover, it follows that testing for stationarity of the spot freight rate is effectively a joint test where it is hard to assign the stochastic property of either freight and fuel costs in isolation. Care should therefore be taken when relying on stationarity tests of the spot freight rate in light of the well-known structural shifts in the global oil market during the last 30 years (see Nelson and Plosser (1982) for a general discussion of unit roots and structural shifts). We note that an additional challenge arises in the tanker spot freight rate, where spot freight rates are quoted in Worldscale points (WS) 6. It is well known that the 5 The bunkers price in a given port is set primarily by local refinery output, fuel oil import and storage facilities and the global price of crude oil. 6 Under the Worldscale system, the spot freight rate is expressed in terms of a percentage of the nominal freight rate (flat rate) for a particular route. Thus Worldscale 100 would mean the rate for the 21

22 reference flat rates for the WS schedule change at the start of every year, which means that WS spot freight rates are not comparable across time. Clearly, tests for stationarity can therefore not be based on WS spot rates. The TCE spot freight rate is the true measure of economic profit for shipowners and therefore what matters when evaluating whether, for instance, to put a ship in layup or sell it for demolition (see Dixit and Pindyck (1994)). It follows that the TCE spot freight rate is what matters to the supply/demand equilibrium dynamics in the spot market, the theory of which is discussed in detail in Section 2. Given that stationarity of the TCE spot freight rate has a sound basis in fundamental maritime economics, and is also used in prominent empirical research in the literature such as Kavussanos and Alizadeh (2002), it is the natural choice of spot freight rate measure in this paper. However, the difference in dynamics between gross spot freight rates and their TCE equivalent, induced by the stochastic fuel price process, is an interesting topic and well worth pursuing in future research. While the spot freight rate is the fundamental underlying variable in the bulk shipping markets, there also exist freight rate measures reflecting future delivery of freight services. In particular, period time charter (TC) rates reflects the price for the voyage in question as calculated and issued by the Worldscale Association, while Worldscale 175 would mean 175 per cent of that rate and Worldscale 75 would mean 75 per cent of that rate. 22

23 use of a ship during a given future time period. In a theoretical setting TC rates are very different from spot rates as they are conditional expectations of the future average TCE spot rate, subject to a possible time-varying risk premium (Kavussanos and Alizadeh (2002)). A conditional expectation is always non-stationary by the martingale property, whether the underlying process is stationary or not. It follows that if TC rates are found to be stationary, this is due to the dynamics of the risk premia. The theoretical arguments supporting the stationarity of the spot freight rate therefore do not apply to TC rates, or indeed financial freight contracts (FFAs) 7, and this freight rate measure is therefore not of interest in our context. Moreover, it is not appropriate to assume that the finding of a non-stationarty TC rate 8 of FFA price should have any relation to the stationarity or otherwise of the spot freight rate process. A final choice made by the researcher relates to data frequency and data sample. While it is generally recommended to use as long a time series as possible 7 Price series of second hand values of ships have also been investigated. Theoretically, these prices are also based on future expectations, and therefore more likely to be non-stationary. This is in line with standard no-arbitrage financial theory as ships are tradable assets whereas the spot freight rate is not. 8 There are also severe data quality issues for time series of TC rates as the physical market is extremely illiquid and heterogeneous, leaving researchers to rely on guesses made by brokers. 23

24 in order to uncover stationarity of a highly persistent process (Dixit and Pindyck (1994)), the changes in the shipping markets over time with regards to assumed standard ship size, technical vessel efficiency and structural shifts in the fuel market may induce a higher probability of wrongly rejecting stationarity. Similarly, the fact that monthly freight rates quoted by standard data sources are averages of weekly sampled freight rates rather than monthly samples from the underlying spot freight rate process will necessarily make the process appear more persistent than it actually is, further increasing the chance of wrongly rejecting stationarity. In light of the above, care should be taken when attempting to draw robust conclusions about the stationarity of spot freight rates based on very long time series of monthly average freight rates. In our empirical research we use nearly 16 years of weekly data in order to balance these two issues, with unanimous results. 4.2 Overview of empirical results in the literature A partial list of recent empirical research is summarized in Table 1. Berg-Andreassen (1996) and Tvedt (2003) concentrate entirely on the issue of (non-)stationarity of freight rates while topics vary widely for the other articles. For instance, Kavussanos and Nomikos (2003) study the causal relationship between spot and freight futures prices. Their empirical investigation proceeds as follows: First various tests for unit 24

25 roots and stationarity are conducted. Then a vector error correction model is estimated to establish the long-run relationship between spot and futures prices. Next tests for Granger causality are performed. Finally the forecasting performance of the error correction model is investigated. Many of the articles in Table 1 share the basic structure of the Kavussanos and Nomikos (2003) study, in that unit root tests are conducted initially, before turning to the actual issue of investigation. Here we report only the results of (non)-stationarity of freight rates, even though this might not be the focal point of the particular article. <Insert table 1 about here> We see from Table 1 that the traditional ADF test is the most widely used test. Several authors report some indications of stationarity for some of the freight rate series investigated (see Haigh et al. (2004), Kavussanos and Nomikos (2003), Veenstra (1999) and Veenstra and Franses (1997)). Interestingly, all these series are spot series that theory suggests should be stationary (see caption of Table 1 for details). However, the overall conclusion in the empirical literature is non-stationarity of all freight rates. An exception is Tvedt (2003) who suggests that the reason non-stationarity is not rejected in the empirical literature, contrary to the economic arguments in the classical 25

26 literature, is that freight rates are denominated in USD. Based on the argument that Japan and the rest of Asia is of greater importance than North America in the drybulk freight market, both in terms of shipbuilding and import demand, he transforms the time series to Japanese Yen denomination. This leads to rejection of the hypothesis of non-stationarity using the standard ADF test. Our theoretical arguments of stationarity are broader in scope and apply to both the tanker and dry bulk markets. In particular, we propose that the empirical findings of non-stationarity are not robust due to the low power of commonly applied statistical tests when faced with the highly persistent nature and non-linear dynamics of the spot freight rate process. We should stress that the issue of stationarity need not affect the general empirical results in many of the papers reported in Table 1. For instance, Veenstra (1997) and Kavussanos and Alizadeh (2002) use Vector Error Correction models (VECM) to investigate the relationship between spot freight rates and forward freight rates or TC rates. While the VECM is a linear framework, it enables the simultaneous modeling of long-term equilibrium and short-term adjustment between variables and does not depend on stationarity. 4.3 Data description On the basis of the discussion above, our empirical analysis in the remainder of the 26

27 paper is based on TCE spot freight rates. Time series of weekly TCE spot freight rates were kindly provided by Clarkson Research (2005) for five tanker markets (VLCC, Suezmax, Aframax, Dirty products, Clean products) and three drybulk markets (Capesize, Panamax, Handymax) for the period January 5, 1990 to May 20, These time series are plotted in Figure 3 below. <Insert Figure 3 about here> Of note in Figure 3 is the close correlation of freight rate changes across market sectors and the significant increase in volatility over time, with the tanker markets historically being the more volatile. Also, the average freight rate levels appear to have drifted upwards after A historically unprecedented peak was reached for tankers in November 2004, when the VLCC rate reached almost 200,000 $/day, and for drybulk carriers in December 2004, when the spot freight rate for Capesize vessels touched $100,000/day. However, freight rates dropped significantly shortly thereafter. 4.4 Unit root tests against a linear alternative In our unit root tests we need to specify the alternative of stationarity around a 27

28 constant or a constant with trend. Can theory tell us what specific alternative to pick? Tvedt (2003), referring to Tinbergen (1934), argues for trend stationarity in bulk shipping. Tinbergen argues that the competitive nature of the shipping industry leads to improvement in technology, decreasing costs and a downward trend in freight rates. This argument is valid for both tanker and dry bulk markets. From an empirical point of view, the argument is not a very strong one since most empirical studies use nominal freight rates, in which case inflation will counteract and may even dominate such long-term downward price trends in real terms. Which force is the stronger one may vary across different time periods. Therefore we consider both alternative hypotheses (constant mean and trend) in both our linear and non-linear unit root tests. The results from the ADF tests are given in Table 2. <Insert Table 2 about here> Using the standard ADF test we find that only the Suezmax series shows evidence of stationarity around a constant mean. When adding a trend to the alternative hypothesis the test statistics cannot reject the null of non-stationarity for this market. For all the other series we can conclude that that the ADF test suggests non-stationary. Note that the number of lags given in parentheses are all very high. This is indicative of 28

29 persistent series. Most previous research mentioned in Table 1 uses traditional information criteria for lag selection, resulting in substantially fewer lags. However, the overall conclusion from our standard ADF tests is non-stationary in the majority of cases, in line with previous empirical research. The results from the point-optimal ADF test using GLS-detrending are presented in the second set of columns. This test weakens the evidence of non-stationarity from traditional ADF tests. Two tanker series and two dry bulk series are now found to be stationary around a constant mean, while the Panamax series is trend stationary. 4.5 Unit root tests against a non-linear alternative There is no clear-cut conclusion from the linear unit root tests in the previous section. The tests with GLS-detrending are known to have better empirical properties, but they still suggest non-stationarity for most series on 5% level of significance. In Table 3 we present results from the non-linear KSS tests. <Insert Table 3 about here> The results are very different from the linear unit root tests. The test statistics suggest that both dry bulk and tanker freight rates are non-linear stationary, both for the 29

30 constant and constant with drift stationary alternative. We arrive at this conclusion both with the original KSS test and the point-optimal version. Consequently, when we account for non-linearity, the conclusion from previous research that freight rates are non-stationary seems premature. 4.6 Implications for future research The nature of shipping markets, as argued at the start of this paper, suggests that periods of high freight rates will occur from time to time, due to the inability of the supply side to remove capacity imbalance in the market with sufficient speed and magnitude. Bonanza periods, recently experienced in both the tanker and dry bulk markets, can persist for quite some time since the delivery of new ships is fixed in the short run and the building of new ships does not happen momentarily. We have established that one particular non-linear alternative is in line with theory in that tests indicate stationary behaviour. Tests with different non-linear alternative processes may reach the same conclusion (for instance the non-stationarity test against a Markov switching alternative proposed by Carrasco et al. (2004)). The econometric theory concerning these kinds of models has developed rapidly over the last decade, and even textbook expositions of both model specification and estimation procedures are now available (see Franses and van Dijk (2000)). In future research we would 30

31 ultimately like to see non-linear quantitative models that can be used for empirical testing based on a sound theoretical foundation. One interesting theoretical contribution is Tvedt (2003). He develops a dynamic equilibrium model with a two-regime freight rate process which is, in effect, mean reverting. This is obtained by linking the deterministic component of freight rate changes to capacity changes in the shipbuilding industry: when freight rates are sufficiently high, growth of shipyard capacity will increase, and put a downward pressure on freight rates. The resulting equilibrium price then becomes dependent on both the current level and the historical evolution of freight rates. Tvedt s model is in fact a continuous-time threshold model for the freight rate, where the degree of mean reversion varies in different regimes. It would be interesting to see further theoretical contributions along these lines. Also, an empirical investigation in a reduced form version using such ideas could be a promising starting point. Based on a non-linear model for spot freight rates, the relationship between spot and forward freight rates can also be investigated (see Kapetanios et al. (2003b) for a testing procedure for cointegration in a non-linear threshold model). 5.0 Conclusions In this article we have investigated empirically whether or not freight rates are 31

32 stationary. In order to find a statistical test that does the job, the researcher needs extensive information on the data generating process of the data to be investigated. For this he needs theory, which typically is not specific on particularities such as whether to employ a linear or non-linear model. As argued in this paper, maritime economic theory suggests non-linear stationary dynamics. A substantial body of empirical research suggests that freight rates are non-stationary, but this conclusion is based on traditional linear unit root tests. Standard unit root tests are known to have low power against relevant non-linear alternatives, in particular in the presence of a highly persistent price process as is the case for spot freight rates. The empirical results in our paper is based on 15 years of weekly freight rates in five tanker markets and three dry bulk markets. In line with previous research, the traditional linear unit root tests suggest that freight rates are non-stationary. The results are somewhat more mixed for point-optimal linear unit root tests. When we employ the test proposed by Kapetanios et al. (2003a) against a non-linear stationary alternative (a stationary exponential smooth transition autoregressive model (ESTAR)), the results suggest that freight rates across all bulk shipping sectors are stationary, in line with the classical maritime economic theory. Based on our finding we suggest future paths of research in theoretical and empirical maritime economics. 32

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