Sentiment Augmented Supply and Demand Equations for the Dry Bulk Shipping Market

We present, for the first time in the literature, empirical estimates of the supply and demand curves for the ocean-going dry bulk sector, using a three-stage least squares methodology. Furthermore, we augment these functions with sentiment, which appears to have a positive and significant impact on supply. This supports the view that the outlook shipowners have about the market will undoubtedly influence their decisions regarding purchasing vessels or bringing them out of lay ups. Thus, our results highlight the fact that future expectations have an impact on the current pricing, albeit indirectly through their impact on the supply side. Our results further enhance the behavioral economics literature and provide important insights for both academics and professionals.


Sentiment augmented supply and demand equations for the dry bulk shipping market 1. Introduction
Seaborne trade accounts for more than the 80% of goods transported globally (UNCTAD, 2019), thus its importance it is not solely entrenched in the maritime economics field. Various studies have already shown that the shipping industry has an indicative leading role both in world economy (see Kilian, 2009;Kilian and Zhou, 2018;Hamilton, 2019;Funashima, 2020) as well as the international stock markets (Kilian and Park, 2009). Thus, the forces that are affecting the industry are of interest not only for shipping investors per se, but to the wider economy circle.
An in-depth explanation on how demand and supply are acting in the shipping industry has been given by Stopford (2013). The author describes the demand of seagoing transportation as a derived demand system, i.e. that it is the demand for the transported goods that affects demand for shipping and not for shipping per se. As per Stopford (2013), the demand is affected by the economy, at large.
More precisely, demand is affected by the world economy, the commodity trades that are taking place globally, the demand for transportation given the complex matrix of cargo that will be transported and the distance covered, exogenous economic shocks and finally transportation costs. Recent studies by Michail (2020) and Strandenes and Thanopoulou (2020) have presented empirical evidence on the relationship between shipping demand and the world economy. On the supply side of the equation, the main variables appear to be world fleet, the fleet productivity, the shipbuilding production, the scrapping and losses and finally the freight revenues.
Nevertheless, as Stopford notes, other than price, in this case is the freight rate, which is commonly accepted to impact both demand and supply, there is an additional variable that acts as a catalyst for both the supply and demand functions and eventually for their equilibrium price. That variable is market sentiment. Positive sentiment during the freight auctions will lead shipowners to either ask for higher prices or try to negotiate their services for the spot market, given that they expect that freight rates will increase in the future. On the contrary, negative sentiment will lead shipowners to be more prudent and try to hire their vessels for longer periods of time. However, while the impact of sentiment has been thoroughly studied in the realms of economics (Kahneman et al., 1986) and finance (see Thaler, 1985;Lee et al., 1991;Chiang and Zheng, 2010), research in transportation economics remains thin. Papapostolou et al., (2014) were the first that quantified shipping market sentiment by employing a dataset from the dry bulk sector. In their research, they additionally find that sentiment is a statistically significant and contrarian indicator of future vessel price returns. In addition to the latter research, Papapostolou et al., (2016) show that sentiment is also apparent in the tanker and the containerhsip segments, in addition to the dry bulk segment. Furthermore, they provide evidence of the significance of tanker sentiment as a contrarian global predictor of financial assets in an in-and out-of-sample framework.
Nevertheless, while the shipping finance literature has studied how sentiment can act as an investment indicator for the industry, a literature gap exist when it comes to the actual effect that sentiment can have in an equilibrium setting, with regards to prices in the shipping markets. Going back to the Keynesian theory that the equilibrium aggregate supply is determined by aggregate demand and thus influenced by sentiment (Keynes, 1936;Angeletos and La'O, 2013;Benhabib et al., 2017), research in other industries has shown the latter relationship stands in empirical testing (see Jin et al., Electronic copy available at: https://ssrn.com/abstract=3690190 2014 for the real estate market, Gao andSüss, 2015 for commodities andDeeney et al., 2015 for the oil market).
Thus, in the current research, other than presenting the first empirical estimates of supply and demand curves for the sea transport sector, we also augment them, again for the first time in the literature, with market sentiment to study the impact it can have on the supply and demand functions of the dry bulk market, and subsequently to freight rates. Our research comes to strengthen our knowledge on the market dynamics that exist in the shipping industry by putting the various determinants of the equilibrium price (i.e. freight rates) in the context of supply and demand functions.
The current research benefits literature in various ways. Firstly, as already suggested, this is the first time an empirical estimate of the supply and demand functions in shipping is conducted. Secondly, the introduction of sentiment allows us to quantify its impact on freight rates and further expands our knowledge about the maritime industry. Thirdly, based on the above, we can, for the first time, empirically assess and analyze the conceptual model of supply and demand as described by Stopford. Finally, the current research introduces the three-stage least squares model that provides the best setting for an exploration of demand and supply equations (Amemiya, 1977;Zellner and Theil, 1962) a methodology that has not been previously used in the maritime industry.
Following this introduction, the remainder of this paper is organized as follows: section 2 provides a review of the literature on the issue, section 3 describes the methodology and the data used, section 4 discusses the empirical results obtained, and section 5 concludes on the findings.

Literature Review
Shipping has served as a frutiful setting for behavioral studies given its volatile nature (see Scarsi, 2007;Alexandridis et al., 2018). The overall literature of the field lies primarily in three different pillars of the behavioral research agenda, namely, overextrapolation, herding behaviour and sentiment.
The first researcher that pointed out a standard practise that is used by the shipwoners was Zannetos (1959), who implied that an extrapolation of the existing fundamentals takes place when investment decisions are taken. Interestingly, the first conceptual justification of such an extrapolation was made much later, by Tversky and Kahneman (1974). In the following years, both Metaxas (1971) and Beenstock and Vergottis (1989) looked into the matter, however, the limited availability of data was not helpful to reach concrete conclusions on the results of the extrapolating behavioral bias of the shipowners. Also, Bulut et al. (2013) likewise suggest that shipping companies are more prone to invest during the boom of the cycle and consequently have a drop in their return on equity.
More recently, Alizadeh and Nomikos (2007), have employed a dataset of monthly data for 28 years and they have shown that co-integrating techniques can be more useful for shipping investors, again showcasing that fundamentals play an important role. These results are complemented by Michail and Melas (2019) who show that a co-integrating technique based on fundamentals is also useful for stock trading purposes.
Finally, in the same spirit as the previous researches is the study by Greenwood and Hanson (2015). In their research, they provide theoretical evidence of the extrapolation of fundamentals by the shipowners. More precisely, they show that Electronic copy available at: https://ssrn.com/abstract=3690190 shipping investors extrapolate the exogenous demand shocks and thus more vessels are ordered creating an endogenous shock. However, given the time lag between ordering and receiving a vessel, that exists intrinsically in the shipping industry, investors become disappointed and thus create a shorter than average business cycle.
More recently, Moutzouris and Nomikos (2020) have developed a conceptual behavioral model for the market of the handysize dry bulk vessels. Following, the findings of Greenwood and Hanson as far as extrapolation is concerned, they hypothetize on a system of shipping investors who are either conservatives or extrapolators. Their results suggest that a market where a small fraction of the agents overextrapolates can explain the positive relationship between earnings, vessel prices and trading activity. Still, empirical studies on the topic remain scarce.
In a similar stream of literature, research has focused on the hearding behavior of investors, where herding is defined as the imitation of actions between investors/economic agents (Spyrou, 2013). The latter can take place either intenionally, due to asymmetry of information, or unitntentionally, due to the same information that investors share (Krokida et al., 2020).
Herding behavior is at large what casues the boom-bubble-bust cycle in the shipping industry according to Duru (2013), while herding behaviour also exists in in newbuilding contracts and scrapping in the industry (Papapostolou et al., 2017). More precisely, the latter study looks into the dry bulk segment, and identify that unintenional herding is apparent. Moreover, in the lower parts of the business cycle, unintentional herding is more statistically significant with regards to scrapping. This means that given the same information for the market, shipowners will tend to act similarly, and thus decide to scrap in order to minimise the excess vessel capacity in the market. Intentional Electronic copy available at: https://ssrn.com/abstract=3690190 herding, while apparent in their research, is in scarcity and it seems that there are very few established shipowners of the older generation that the rest of the investors seem to mimic.
In a similar context, Lee and Yip (2018) also conclude that herding behavior exists in the shipping industry when studying the building of new vessels in Korea.
They document that unintenional hearding is apparent in the country for the period between April 2003 and September 2009. Finally, Syriopoulos and Bakos (2019) provide evidence that the herding behavior that it is apparent in shipping businesses is also reflected in their stocks.
As already disscussed in the intorduction of this paper, Papapostolou et al. (2014;2016) were the first to introduce the idea of market sentiment in the shipping industry and by quantifying it they have shown its implications both as a trading strategy for vessels as well as a leading indicator for the shipping stocks. The current research builds on these findings and extends the previous literature by establishing the economic realtionship between sentiment, and demand and supply for sea going transportation services.

3.1.Estimating Sentiment
Measuring sentiment, whether it is for whole markets or specific sectors like shipping, is not an easily conducted task given that there is no universal consensus on the proxies that one should be using (Schmeling, 2009). Nevertheless, specifically for the shipping market, Papapostolou et al. (2014;2016) have provided five proxies that are an indication of the level of pessimism or optimism that may prevail at a given point in time, either in the tanker, the dry bulk or the containership sectors.
Electronic copy available at: https://ssrn.com/abstract=3690190 The five proxy variables fall under three categories: 1) market expectations; 2) valuation and 3) liquidity. Market expectations are measured by the net contracting, and the money committed proxies which take into consideration the change in the orderbook and amount of funds committed to these new vessels. Valuation is measured by the price-to-earnings and the second-hand-to-newbuilding price ratio, which offers a view of the valuations that are present in the industry. Finally, liquidity is measured by the Turnover proxy, i.e. how fast sales transactions are taking place compared to the overall fleet. The proxy variables are calculated as follows: where , is the order book, that is, the number of vessels awaiting construction or being constructed, for sector i and month t, , is the number of vessel deliveries, and , the number of vessels being scrapped.
where , is the price of newbuilding vessels for sector i and month t and , is as above.
where ℎ , is the price of 5-year-old, second-hand vessels, and , are the annualized earnings (1-year time charter rates) in sector i for month t.
Electronic copy available at: https://ssrn.com/abstract=3690190 where , is the total number of available vessels in sector i and month s, and , the number of vessels sold.
After calculating the proxies, using data from March 1995, we follow the procedure suggested by Papapostolou et al. (2014;2016) and orthogonalise them, one by one, in order to exclude the impact of any macroeconomic factors from the nonsentiment part (i.e. the world economy part). To do so, we regress each proxy with three variables: (i) 7 monthly industrial production growth, (ii) a dummy variable for the recession periods of G7 (monthly), and (iii) a dummy variable for the recession periods of the five major Asian countries. To get results that are qualitatively similar, we are using year fixed effects in the orthogonalising process.
After the latter regressions are estimated, we employ their residuals given that this is the part of the proxy that is not explained by macroeconomic, fundamental factors and can thus be viewed as a proxy for sentiment. To avoid any potential one-off events, the final stage of the estimation process uses the Hodrick-Prescott filter on the residuals in order to smooth them out.
After this process, in accordance with Papapostolou et al. (2014;2016), we proceed with a principal component analysis, using the contemporaneous value of the proxy, as well as its one-month and two-month lags. For example, we include , , , −1 , and , −2 in the matrix. Thus, given the five proxies enters the final estimation for the sentiment index. As such, the sentiment index includes one value from each of the five previously described proxies, which are then weighted using the first principal component of the selected proxies.

3.2.Estimating Supply and Demand
Once the sentiment index has been constructed, we move to estimate the supply and demand functions, using a three-stage least squares (3SLS) methodology as proposed by (Zellner and Theil, 1962). 1 In particular, the 3SLS methodology such that: where a consistent estimator for can be obtained via the residuals of the 2SLS estimates of each equation in the system. Hence, replacing with ̂ we get the 3SLS estimate of the system parameters, while the asymptotic variance-covariance matrix is just the Generalized Least Squares estimator, ̂= [̂′( −1 ⨂ )̂] −1 . 3SLS estimates are usually iterated to reach convergence.
To consider something a true supply-demand equation, a clear measure of both the supply and the demand needs to be available. For the case of shipping, supply is straightforward, and it relates to the number of available vessels, regardless of whether these are hired or not. In general, the idea is that a larger number of vessels would result in more ship-owners competing for the same routes and products, something that would push prices lower.
Concerning demand, however, one needs to proxy for the willingness of charterers to employ a vessel. While no such data will ever be available, one could proxy this using the quantity of goods transported. The idea behind this is that the charterers' willingness to transport changes every year, as the factors that affect this willingness (which may be unobservable such as cultural characteristics, marketing, or preferences) also change. Thus, while we, by definition, cannot observe the unobservable, we can instead rely on the end-product, which in this case is the quantity of transported goods.
Furthermore, to account for the fact that shipping is a derived demand system, and hence demand for shipping is driven by demand for other goods, we also employ industrial production for the main industrial regions (US, China, Europe) to account for this. Given that shipping is related to the goods and not the services trade, industrial production better captures shipping-related goods trade than employing the overall GDP figure. Furthermore, to capture any potential income-related effects from demand (i.e. as income rises, demand also increases), we also employ the US real Personal Consumption Expenditure (PCE).
In both supply and demand, the researcher would require a common price proxy, which is expected to have a positive relationship with the former and a negative one with the latter. In both cases, the price proxy would be the price of the contract, i.e. the freight rate. This can be easily proxied by the Baltic Dry Index (BDI), which serves as the equilibrium between supply and demand 2 . Furthermore, given that the index is freely traded on a global basis, any arbitrage opportunities are quickly eliminated, allowing us to capture the point at which demand and supply cross.
In both cases, demand and supply equations need, other than the BDI as the price proxy, and the various demand drivers given that the derived demand nature of shipping, a variable to capture the market's attitude at each point in time. As mentioned before, sentiment is a variable that acts as a catalyst for both the supply and demand functions and eventually for their equilibrium price. A positive sentiment will lead shipowners to either ask for higher prices or try and negotiate their services for the spot market, given that they would expect that freight rates will increase in the future. On the contrary, a negative sentiment will lead shipowners to be more prudent and try to hire their vessels for longer periods. To this end, a sentiment proxy is used, with details on its construction offered in the next section.

3.3.A Look at the Data
The quantity of transported goods, as offered by UNCTAD, exists only at an annual frequency, thus limiting the amount of available observations. Thus, while an estimation is conducted and the results are presented in the following section, we also provide an additional estimation, using monthly data. As suggested, while the quantity of transported goods is not available on a monthly frequency, we need to result to a "pseudo" supply and demand model, where the supply side is still proxied by the number of vessels but the demand side is proxied by the freight rate. Thus, while this estimation is not a clear illustration of supply and demand, it does help separate demand and supply effects from the BDI and, as such, provides a robustness check on the findings based on the annual data. Furthermore, sentiment is calculated on a monthly basis in accordance with Papapostolou et al. (2014;2016) and the year average of the latter observations is used in our year analysis.
With regards to the data sources for the variables employed in the estimation, we have obtained monthly data for the number of dry bulk vessels, the Baltic Dry Index  Table 1 offers the estimation results based on the annual data, as obtained from the sources mentioned above. The first specification shows the supply and demand functions, without the presence of sentiment, while the second column adds the sentiment proxy to the equation.

Sentiment-Augmented Supply and Demand
In specification (1) in the absence of sentiment, the quantity of vessels is only explained via their own lag. In this case, the price proxy, i.e. the BDI, does not appear to be statistically significant. With regards to the demand equation, price does not appear to be a determinant of the dry load equation, while only US industrial production appears to be a significant determinant of the quantity of goods transported. Even though the results appear to be as expected, there does not appear to any linkage between price and quantity in the equations. While this can be justified for demand, given that it is inelastic to changes in price (Stopford, 2013), there is no justification as to why this would happen for the supply side.
This issue is resolved once the sentiment variable is included in the estimation.
As specification (2) illustrates, the BDI now has the expected positive and significant relationship with the quantity of vessels (at 0.05), while sentiment also has a significant positive impact on the quantity of vessels on the market. While the impact of sentiment appears to be small at first (at 0.001), it should be remembered that the standard deviation of the series is at 1871, suggesting that the impact would be much higher than originally considered. *,**,*** suggest significance at the 10%. 5%, and 1% levels respectively. Variable definitions can be found in the appendix.
Of equal important importance is the fact that sentiment has a positive relationship with the quantity of goods transported. In this case, positive sentiment is expected, as mentioned earlier, to get shipowners to either ask for higher prices or try and negotiate their services for the spot market. As the results show, however, this further builds into the shipowners' mentality, as it appears that expectations over improved market conditions translate into more vessels being put into the market.
Hence, it is only reasonable to reach the conclusion that positive sentiment not also brings ships from lay up into operation but could also mean that shipowners proceed with orders for new vessels. This is also intuitively appealing, given that it is more than justified for shipowners to expect better market conditions in the future before placing an order that could take 2-3 years to complete.
Furthermore, this relationship between sentiment and the supply of vessels also makes sense during a recession or other market distress period. In such times, the price impact would drive the supply of vessels lower, but, as sentiment improves, and despite the fact that prices are low, shipowners will start to bring back their vessels into the market, thus increasing the overall vessel supply. Similarly, in times of booming prices, it could be the case the shipowners are skeptical about the future. In such a scenario, the availability of vessels would decline as sentiment drops. As expected, sentiment has no impact on the demand for seaborne trade.
The findings support and enhance those of Greenwood and Hanson (2015) and others in the extrapolation of fundamentals literature, given that they empirically support the view that sentiment has a strong impact on vessel supply. Furthermore, the results also support the findings of Papapostolou et al., (2014), given that higher than usual sentiment can be a bad sign for future vessel price returns, while lower than usual sentiment may be interpreted as a positive signal.
Moving on to table 2, and the monthly estimates, it appears that, in general, these are broadly in line with the annual results. In particular, price (BDI) appears to have a positive and significant relationship with the supplied quantity, while sentiment also comes out to have a positive impact, for the reasons and with the implications presented above.
As suggested in the previous section, the absence of an available series at a monthly frequency constricts us from estimating a proper demand curve. As such, we instead use the system to estimate the determinants of BDI, which also includes supply and demand factors. The results appear to be intuitively appealing and qualitatively similar to the annual estimates. *,**,*** suggest significance at the 10%. 5%, and 1% levels respectively. Variable definitions can be found in the appendix.
In particular, vessels have the expected negative relationship with the BDI, given that the higher the available supply the lower the equilibrium price will be, ceteris paribus. In the short run, as the monthly indicators suggest, China's industrial production can explain more of the BDI's variance, perhaps due to the increased importance of the country in the global landscape over the recent years. Importantly, sentiment appears to be negatively related with the BDI, even though only weakly significant. The result is as expected, given that since higher sentiment would cause an increase in the supply of vessels, thus implicitly increasing supply and thus lowering the price.
Overall, the results suggest that while the standard postulates of economic theory hold, i.e. that prices have a positive relationship with supply and a negative one with demand, sentiment also has a significant effect on the quantity of available vessels, suggesting that a positive view about the market could bring vessels from lay ups and also increase orders. This suggests that a discounting effect also exists in the shipping market, albeit indirectly, with sentiment working its way to an impact on price through its impact on the supply of vessels. The current findings come to build up on a literature conundrum that has to do with whether the Efficient Market Hypothesis (Malkiel and Fama, 1970) holds for the shipping industry and thus whether arbitrage opportunities are non-existing. Unlike Ådland (2000) and Ådland and Koekebakker (2004), we verify that sentiment is an important variable in the formation of the market's equilibrium and thus is affecting market's fundamentals (for similar results on the matter see Kavussanos and Alizadeh, 2002;Hale and Vanags, 1992;Glen, 1997). This behavior is justified in both booming as well as distress periods where shipowners would want to purchase or sell vessels also on the basis of their view about the market's future and not just on how the market behaves at this point in time.

Conclusions
In this paper, we present, for the first time in the literature, empirical estimates of the supply and demand functions in shipping. Furthermore, we augment these functions with sentiment, which appears to have a significant impact on supply. The results suggest that, according to economic theory, a positive relationship between supply and prices (freight rates -BDI) exists, and a negative one between demand and prices.
Sentiment has a positive impact on the supply of vessels, suggesting that a positive view about the market's future affects it today, as expectations build into the shipowners' mentality and translate into more vessels being put into the market. Hence, it appears that discounting is also present in shipping markets, similar to finance ones.
The intuition behind this situation is straightforward: positive sentiment not only brings ships from lay up into operation but could also mean that shipowners proceed with orders for new vessels. This is also intuitively appealing, given that it is more than justified for shipowners to anticipate better market conditions in the future before placing an order that could take 2-3 years to complete. Furthermore, the relationship between sentiment and the supply of vessels is also reasonable during a recession or other market distress period. In such times, the price impact would drive the supply of vessels lower, but, as sentiment improves, and despite the fact that prices are low, shipowners will start to bring back their vessels into the market, thus increasing the overall vessel supply. Similarly, in times of booming prices, it could be the case that shipowners are skeptical about the future. In such a scenario, the availability of vessels would decline as sentiment drops.
The results provide an important insight into the shipping market, as they are the first to confirm that market sentiment plays an important role in supply and demand functions. Certainly, further studies should also address the topic, but we would like to note that one of the most important implications is the possibility of a different type of discounting factor across various sectors, as well as across different vessel classes.

Net Contracting
The net number of vessels that have been order each month when demolitions and scrapping is considered.

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Intelligence Network

Money Committed
Amount of dollars spend each month for newly order vessels.
Clarksons Shipping Intelligence Network

Price-per-Earnings
Ratio between the price of a 5-year-old secondhand vessel and the equivalent time charter rate multiplied by 360 days.

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Ratio

Second-hand-to-Newbuilding
Ratio between the price of a 5-year-old secondhand vessel and a newly built equivalent vessel.

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Intelligence Network

Turnover
The 12-month average ratio between the new deliveries of vessels and the total fleet size.