Nowcasting US GDP with Baltic Dry Index

Transcription

1 Nowcasting US GDP with Baltic Dry Index A study investigating the use of the MIDAS Model By: Martin Servin Almkvist Supervisor: Xiang Lin Södertörns University Department of Economics Master Thesis 30 hp Economics Spring 2016

2 Acknowledgement I would like to express my greatest gratitude for the assistance during this work from my master thesis supervisor Xiang Lin, Senior Lecture In Economics at Södertörn University. II

3 Abstract One of the conclusions made in the aftermath of the last financial crisis was that forecasting was failing in the context of predicting the current economic activity, which meant there were few efficient instruments to monitor the economy and thereby no early stage intervention which could have mitigated the severity of the crises. Due to these facts presented nowcasting, forecasting in short horizon, and the use of models that could combine different data frequencies like the Mixed Data Sampling (MIDAS) model gained a lot of attention. This study investigates if the MIDAS model improves nowcasting and if the Baltic Dry Index (BDI) is a good indicator for the US GDP. Before making any conclusions from the result, the characteristic of the BDI is covered and explained as to why it could reflect general growth. The intention of using BDI as an indicator for US GDP was to find an indicator that may explain economic activity in a more accurate way due to the characteristics of the BDI. The result was in line with previous empirical work and proved that the MIDAS model is superior in nowcasting in comparison to the least square model with flat aggregation defined as a benchmark model. The rejection of the cointegration test for BDI may question the use of it as an indicator for US GDP at present time, this due to the extreme circumstances that currently affect the bulk dry market. III

4 Table of Contents List of Figures... V List of Tables... V 1. Introduction General Background Forecasting in general Study Objective Economic Theory Forecasting with Mixed Data Sampling (MIDAS) Literature Review Baltic Dry Index (BDI) Dry Bulk Cargo Commodity Supply and Demand Theoretical Discussions Movements in the BDI Technical Aspect of MIDAS - The General MIDAS Model DATA ESTIMATION Methodology Properties and Necessary Modification Nowcast US GDP with MIDAS-model Cointegration test and ECM MIDAS Least Square with Flat Aggregation Result Findings Conclusion References Appendix IV

5 List of Figures 5.1 Log values of different commodities and BDI Log BDI Log US GDP First Difference Log BDI First Difference Log US GDP Sum of Squared Model Sum of Squared Model RMSE of Updated MIDAS Model Forecasting Result MIDAS Model Forecasting Result MIDAS Model Forecasting Result Least Square Model Nowcasting Comparison Actual vs. Fitted MIDAS Model Actual vs. Fitted MIDAS Model Actual vs. Fitted Least Square Model Q-Q Plot MIDAS Model Q-Q Plot MIDAS Model Q-Q Plot Least Square Model 3.39 List of Tables 8.1 Cointegration of BDI.40 V

6 1. Introduction What does it mean when forecasting fails, generating a false interpretation of the economy that infects all the stages of the economy, from those who manufactures small parts of the fuselage of an airplane to those taking a flight overseas for a business meeting? Producing models that are prone to be inefficient could trigger a disillusion that further on generates faulty conclusions. The error of these conclusions may not be detected before it s too late. In the wake of the financial crisis 2007 reports judged forecasting as not performing well and that high frequent data like financial data was neglected when predicting current growth. Not only did this give a less accurate forecasting result but it also lead to a missed opportunity to intervene at an earlier stage, which may have caused the crisis to erupt to a much more severe one. Forecasting in general have had problems combining data with different frequency structure like stock prices published daily and industrial production published monthly. This is why the potential of being able to use all accessible information has never been fully achieved and analyses in that sense has been limited. Traditional forecasting in general has relied on economic indicators of the same time frequency, which means that some information of high frequency variables involved in the forecasting process have been omitted or treated poorly when forecasting. The last decade several central banks, such as St. Louis FED, Deutsche Bundesbank and Bank of England, have discussed the use of high frequent data for predicting growth. This generates a great interest among macroeconomists to use different sources of data often published daily and monthly, which could be seen as a general conclusion that one needs to observe and track economic activity at present time and not wait for the next quarter. This rather newly embraced use of high frequent data to explain economic activity is due to a couple of econometric models that could archive forecasting efficiency 1

7 without particular loss of information and that are less prone to misspecification error, due to the amount of parameters one need to estimate. This introduction of better and more efficient forecasting models like the Mixed Data Sampling (MIDAS) model and the State and Space model have provided an instrument that could give deeper understanding of the current and future economic activity since it allows one to monitor the economy with use of different high frequency variables. Central banks and other institutions like the IMF and the World Bank could also implement these new methods making more precise analyses, tracking and monitoring up to date activities, known as nowcasting. This strategy makes predictions at a shorter horizon than the frequency of target variable. A great advantage is that tracking economic activity at high frequency could solve, or mitigate, some uncertainties that may arise due to the fact that GDP and other economic indicators are published with several lags. It is even more needed in periods when the economy is considered to move away from equilibrium, which makes forecasting even more difficult. In order to estimate growth one need to pick a set of relevant indicators that could explain it. Since many of the available indicators are influenced and affected by speculation and policy actions, one could instead look for an index that is less influenced by speculations. One daily economic indicator that has a relevant connection to economic activity is the Baltic Dry index (BDI). It is published daily to represent a benchmark rate for shipping bulk cargo on sea. This link between BDI and economic activity is not new information for the financial market 1 but has not yet been studied at a greater scale. However, since the price of shipping is reflecting the demand for trade and further on the demand for intermediate goods, like different type of commodities, BDI could logically explain GDP. 1 Apergis, N and Payne, E, A. (2013) New Evidence on the Information and Predictive Content of the Baltic Dry Index. International journal of financial studies, Vol 1, pp

8 2 General Background 2.1 Forecasting in general Forecasting methods have lately achieved great success in using high frequent data such as financial data to predict low frequent economic variables, such as GDP growth at present stage and near future, i.e. nowcasting. This however has not always been the case. In general, forecasting time series have limited the use of data to be in the same frequency structure. This means predicting quarterly GDP one needs to find a quarterly indicator that is able to explain movement in GDP. Or the alternative would be to use the not so reliable method of flat aggregation to match high frequency in to low frequency data, or use the less convenient step-weighting function which will require a lot of work especially since it require the estimate of each lagged weight value, unbearable with large data sets. The much common GARCH model that is widely used in time series analysis is a good method for analyzing data experiencing high volatility. This model however is not capable of directly mixing different frequencies and therefor puts certain limitations in the use of data. The same applies to other models such as ARIMA, VAR or the AR model. From an economical point of view one could see how the MIDAS model contributes to wider use of data that in the past was not regarded as practical. There have been solutions in the past that have been able to explain the dynamics of past high frequent observation. One way of doing so is to use the State and Space model with Kalman filter to estimate missing observations in order to match high frequency to low frequency. Basically it is extract a state of an unobserved independent variable driven by a latent stochastic process to predict the output of the dependent variable. That however is not always easy to conduct and therefore require certain econometric skills. Without this knowledge, models are prone to face misspecification error, this due to a large set of parameters that should be estimated. By including different frequency of macroeconomic data, analysis could clearly improve time intra analysis of GDP. There is a bunch of economic indicators that are 3

9 relevant for predicting economic growth but that is not presented in the same lag structure as GDP. To dismiss such rich information data due to technical difficulties of incorporating mixed frequency would likely affects analyses negatively. Not only does it prevent one from making better forecasting, it also tends to make economists less prone to investigate correlation between untested factors and economic growth. By introducing the MIDAS model one will likely achieve greater knowledge of the contribution of different factors to explain GDP and understand how past observation could have different effect on present state. 2.2 Study Objective Lately there have been several studies about the contribution of nowcasting. This does not only present a great interest of exploring current up-to-date data to explain the current GDP but also legitimates the much-discussed MIDAS model. I will in this paper investigate whether such a model will contribute to better forecasting result than an ordinary benchmark model with flat aggregation. To extract as much as possible information from the MIDAS model I also intend to focus on the contribution of feeding additional data of BDI in to the model and detect if such a process will give further improvement into the analyze of US GDP. The choice of BDI as an explainable variable to predict US GDP is based on the ground that commodity demand is proven to be a good indicator for GDP in general. Marcillino and Schumacher (2007) 2 used a mixture of commodity index to nowcast German GDP. Commodity demand will affect the price of shipping and in that sense BDI should be a proper indicator for predicting economic growth. However it has lately been questioned as to whether it may reflect growth. Due to nonstationarity of BDI and GDP, I try to carry out MIDAS cointegration test on GDP and BDI. If they are cointegrated, nowcasting of GDP growth needs to add residuals from the cointegration relation. Namely, MIDAS-ECM model is required for nowcasting of GDP growth. 2 Marcellino,M and Schumacher, C.(2007) Factor-MIDAS for now- and forecasting with ragged-edge data: a model comparison for German GDP, Deutsche Bundesbank Discussion Paper, Vol. 34 Series1 4

10 3. Economic Theory 3.1 Forecasting with Mixed Data Sampling (MIDAS) MIDAS model is based on a distributed lag model develop 2004 by Ghysel, Santa- Clara and Valkanov 3. The general idea behind the model was to use a fewer parameters to explain a large set of data and that the polynomial lag feature gives the user an option to combine different frequencies of data. This means matching high frequency to low frequency data, doing so by a polynomial lag, which gives a unique weight scheme to explain the dynamic change of past observations. The improvement of analyzing different frequency data should make forecasting more precise instead of the common flat aggregation that treat past observations as a unit, neglecting the dynamic change of the past. The structure of the MIDAS by generating a parsimonious model discussed above does not only appeal in the context of workload but also provides a more convenient way of learning the basic behind the model. A great advantage and a great alternative to the state and space model which require more technical skills. Ghysel, Santa Clara and Valkanov 5 also showed that the MIDAS is an ideal setting to overcome discretization errors. Such problems are common for time series analysis when sampling of a continuous variable like financial data are treated as finite sampling. These problems will be cancelled out as m approaches zero, in other words errors of this type will diminish when there are a lot of observations of high frequent variables in comparison to the low frequent variable. Since the introduction of the general MIDAS model, several studies have been collaborating with different types of parameter polynomials to achieve better forecasting result. Clements and Galvao 4 investigated the US growth with an 3 Ghysels, E. Santa-Clara, P and Valkanov, E (2004) The MIDAS Touch: Mixed Data Sampling Regression Models, Working Paper CIRANO 2004s-20, CIRANO 4 Clements, M and Galvao, A-B. (2008) Macroeconomic Forecasting with Mixed Frequency Data: Forecasting US output growth, Journal of Business and Economics Statistics, Vol. 26, pp

11 autoregressive MIDAS model. The two main findings of their study were that the MIDAS concept provides better forecasting than the benchmark ARDL model and, second, that MIDAS model seems to be much more suitable for forecasting on short horizon, hence nowcasting. Another study by Ferrara, Marsilli and Ortega 5 investigated if a combination of stock prices and commodity indexes could improve forecasting by a MIDAS model. Their primary motivation was to detect if such a model and source of explainable variables would be accurate in forecasting growth in a period of recession. Their study used data that was collected from 2007 to 2009 when the financial crises took place. The conclusion from the study showed in accordance with previous work that MIDAS model and the use of daily stock prices and commodity indexes is relevant and contributes to better forecasting results. Marcillino and Schumacher 6 investigated German GDP with different setups of the MIDAS model and other alternative model using macroeconomic data. They found that the general MIDAS with just one lag outperformed the other in nowcasting. When nonstationary series are involved, forecasting on growth relying on short-run developments, namely first-order differences might subject to misspecification errors due to ignoring possible cointeragtion relation. One needs to construct an error correction model (ECM) to take into consideration of both short run and long run dynamics between the two variables. This gives a quite interesting aspect since it may reveal both equilibrium and disequilibrium between two variables. Götz, Hecq and Urbain 7 compared an MIDAS-ECM model to the models without long-term relation. They found statistical evidence that MIDAS-ECM model is much 5 Ferrara, L. Marsilli, C and Ortega, J-P (2013) Forecasting growth during the great recession: is financial volatility the missing ingredient? Banque de France Document de Travail, No Marcellino,M and Schumacher, C.(2007) Factor-MIDAS for now- and forecasting with ragged-edge data: a model comparison for German GDP, Deutsche Bundesbank Discussion Paper, Vol. 34 Series1 7 Götz T. B, Hecq, A. and Urbain, J.P (2014) Real-Time Forecast Density Combinations: Forecasting US GDP Growth Using Mixed-Frequency Data, Journal of Forecasting, Vol. 33, Issue 3, pp

12 more accurate in forecasting Note that MIDAS-ECM model requires cointegration between two variables. According to the previous studies on MIDAS, in general it performs quite well compared to most of the other models. This is especially true for nowcasting. The MIDAS model provides a platform to deal the problem of data with various frequencies. As the previous discussion pointed out, there is a need for monitoring the current economic activity. Updating the model with additional high frequent data as time approaches the end of the current period will provide a good hint of the current economic activity. The attention drawn to nowcasting is likely long lasting. It has a potential to be applied in a greater scale since many of the most important indicators as GDP and Industrial Production are published with lags of several weeks. This delay of publishing important indicators is likely to increase the anxiety of the economic state. That s why nowcasting is important as it could give an early signal of the predicted economic state. Central banks could in that manner achieve a great tool for observing if the GDP is in line with expectation. Several central banks around the world have discussed the importance of applying nowcasting, which further gives credit to the application of it 8,9,10. This generally positive approach towards the application of nowcasting in the context of economic analyzing comes with statistical facts that financial data are providing rich information about the real economic activity Stratford, K (2013) Nowcasting world GDP and trade using global indicators, Bank of England Quarterly Bulletin, Vol. 53, No. 3 pp Kliesen, L, K and McCracken, M, W (2016) Tracking the U.S. Economy with Nowcasts, St. Louis FED [Accessed 05/24/2016] 10 Banbura, M. Giannone, D. Modugno, M and Reichlin, L (2013) Now-casting and the real-time data flow, European Central Bank Working Paper Series, No Andreou, E. Ghysels, E and Kourtellos, A (2013) Should macroeconomic forecasters use daily financial data and how? Journal of Business and Economic Statistics, Vol. 31, Issue 2,pp

13 4. Literature Review In order to predict US GDP with BDI we need to understand how BDI is constructed and how the price of shipping bulk cargo is determined. In the following section I will provide a greater background of the shipping market and how it makes decisions to avoid low shipping price. In that way the reader will be given a chance to get familiar with both demand for commodities, fleet operation and other important aspects that will explain movements in the BDI. I will also discuss the essential basic behind BDI. 4.1 Baltic Dry Index (BDI) BDI is more than an index reflecting cargo rates; it s an extension of market activity, generated by the interaction between relative fixed supply and a competitive demand. For many participants on the global market, BDI has been considered as an indicator for economic activity. The index represents the weighted average of four different dry bulk cargo rates transported at several major routes at sea, namely, Capesize, Panamax, Supramax and Handysize. These four categories are based on ship size, transporting different types of dry bulk cargo like metals, oil, wood and other types of commodities, in contrast to container cargo. Dry bulk stands for a major proportion of all cargo transported, namely 40 % in First published in 1985 to indicate a benchmark for the price of shipping, published and tracked daily by those who sell and buy and modified during the years to produce a solid indicator of bulk cargo rates. BDI is indirectly reflecting global economic activity and it has been used as a measurement for commodity demand, which in turn signals a general picture of investment, hence economic activity. Several studies have shown that movements in 12 Hlyette, G and Smith, W, O. (2012) Shipping markets and freight rates: an analysis of the Baltic Dry Index, Journal of Alternative Investments, Vol 15, Issue 1, pp

14 commodity return, industrial production and financial data could be forecasted by BDI 13. Demand and supply of commodities is having a great impact on the operating decisions in the shipping market. An increasing fleet is a reflection of a brighter outlook, the opposite being scraping, operating at low steam or delaying investments of new ships. In 2015, according to United Nation Conference on Trade and Development (UNCTAD), the fleet age reached it s peak mainly due to the uncertainty of the future, making shippers hold on to old ships instead of investing in new ones 14. The world supply of cargo ships is mainly influenced by the factors described above, however there are other dynamics that may shift the supply curve in both directions. New technology that provides more advanced ships and also produce alternative energy sources, implementation of regulations and embargos, which may create imbalances in the market for demand and supply. In 2014 Indonesia set up an embargo for certain unproceeded metals that created a downturn in the demand for shipping in certain parts of Asia. This is evidence on how the market could react to a certain policy change. The inflexibility that characterizes the shipping industry put certain limits that prevent shippers from a strategic reduction of supply. The intention of restricting supply is to influence the price of shipping and hence avoid over supply and much too low price setting. These tactical decisions could in some sense soften the low demand that the market may experience. But it would not likely stop a strong force of decreasing demand for shipping. Even if the supply is rather fixed in short term as discussed, a common scenario among shippers is to use the operational speed as an instrument to scale up or down the supply. Ships steaming at lower speed would decrease supply and may reduce the cost to a certain level. Evidence also shows that the operational speed that the ships are 13 Bakshi, G. Panayotov, G and Skoulakis, G (2011) The Baltic Dry Index as a Predictor of Global Stock Returns, Commodity Returns, and Global Economic Activity, Pocedia Social and Behavioral Sciences, Vol. 210, Issue 2, pp UNCTAD, (2015) Review of Maritime Transport 2015, [accessed 05/19/2016] 9

15 constructed for is well above the average speed used, a clear signal that shippers could expand their productivity if needed. Meaning if the market is facing relatively high demand, they would increase the average speed by a couple of knots 15. One could describe the relation between market price for cargo transported at sea and speed as a rather positive curve with an increasing rate, almost like a j-curve. Transportation cost is also likely to affect the shipping cost, how much the BDI deviate from its initial path due to higher or lower oil price is hard to tell. Cheaper goods are more prone to react to a high oil prices than expensive goods. There are two sides of the same coin regarding the oil price, a high oil price may be generated by high demand for industrial production that would boost export, and the other aspect of a high oil price is that cost of transporting would likely dampen demand of trade. One has to analyze the underlying forces that affect the oil price, we all know that the supply side is highly coordinated sometimes and inventories may vary due to some political change. There are several papers investigating the correlation between BDI and the financial market, commodity demand and growth rate, and several studies have shown evidence of statistical correlation 16,17,18. Although the global economy may experience variations in activities that may lead to unbalanced market equilibriums and deviation of the BDI to other global indicators. In fact one study that could motivate those who criticize BDI as only predicting economies that may demand huge capital and investment as the Chinese economy does is a work by Shen and Lo 18. Their study showed only long termed causality between Chinese growth rate and BDI when testing this on the rest of the BRIC countries growth, Brazil, Russia and India Stopford, M. (2009) Maritime Economics 3rd ed., New York, Routledge 16 Papailias, F and Thomakos, D (2013) The Baltic Dry Index: Cyclicalities, Forecasting and Hedging Strategies, Rimini Centre for Economic Analysis Working Paper 65_13 17 Bildirici, M. Kayikci, F and Sahin Onat, I. (2015) Baltic Dry Index as a Major Economic Policy Indicator: The relationship with Economic Growth, Procedia - Social and Behavioral Sciences Vol 210, pp Shen, C-W and Lo, C-H (2010) Causality Analysis of Dry Bulk Cargo Freight and BRIC Economic Growth, The Global Studies Journal, Vol. 3, pp

16 4.2 Dry Bulk Cargo Reaching higher levels of prosperity does not just mean better living standard, demand for goods and services are likely to increase as well and trade could flourish in a greater scale. The modernization in the 20 th century replaced passenger lines with cargo lines. Vessels main purpose to transport passenger were reconfigured to handle cargo as labor costs increased. New technology as fax, telex and enhanced opportunities for trade and the process of independency among countries meant increased trading flows 19. The shipping companies were not late to react to the increasing demand for international goods as many changed the domestic coal for imported oil, which lead to bigger ships and economies of scale. Sizes increased from the biggest crude cargo ship, 122,867 DWT in 1966 to Seawise Giant 555,843 DWT operating in the early The demand for transportation of bulk cargo increased during the beginning of 1960 s and larger bulk ships grew in larger proportion, mainly due to the purpose of achieving economies of scale. The implementation of the flag of convenience, gave the possibility to register ships in countries that only required a small fee instead of the much more expensive national tax. More private firms entered the sea shipping market and the national shipping firm faced harder competition 21. All this contributed to the possibility to import and export commodities at a much lower cost. 4.3 Commodity Supply and Demand Developing countries have in general higher relative demand for commodities than countries defined as developed. This general belief was supported when the high price level of commodities mainly driven by the increased demand from emerging economies was observed during the beginning of Several of these countries experienced double-digit growth, which did not only increase demand but also added 19 Stopford, M. (2009) Maritime Economics 3rd ed., New York, Routledge 11

17 large number of orders of new ships 20 and a surprisingly fast recovery of commodity prices after a decline in the world economy 21. Chinese growth contributed in large proportion to the increase of the worlds demand for commodities, importing around 40% of all base metals and 23% of the agriculture corps in These numbers reveals some how why critics may argue that BDI only indicates the activity for certain major economies and not reflecting the general state of the world economy. Prices of commodities react to different shocks and economic cycles that have a major effect on global economy, historically, high volatility in prices have been explained by extreme events that made prices to be abnormally high or low. Debt crises in the 1980 s and the fall of the Soviet Union made prices to fall. Evidence states that the price variation during the 80 s mainly was driven by different states of supply. However the fall of the Eastern block also had an impact on prices but not in the supply 23. The increase in export of commodities during the early 90 s was driven by a couple of different factors, which today is still accurate when analyzing the price volatility. Price differences and liberalization created geographical arbitrages, techniques in production made metals cheaper and certain parts of the world considered to be in higher stability from a war perspective, those factors had all an impact on commodity trade and price levels of different commodities 24. Another interesting finding is that short time real interest rates will have a large effect on commodity prices. By increasing interest rates, storage of oil or other commodities are less desirable, creating higher value of consuming that commodity today than tomorrow. It will likely shift the speculative trends from certain spot contracts for commodities to more 20 Geman, H.; Smith, W.O. (2012) Shipping markets and freight rates: an analysis of the Baltic Dry Index, Journal of Alternative Investments Vol.15 Issue 2, pp Erten, B and Ocampo, J.A (2012) Super-cycles of commodity prices since the mid-nineteenth century, DESA Economic & and Social Affair Working Paper, No Roache, S. K (2012) China's Impact on World Commodity Markets, IMF Working Paper, No. 12/ Borenzstein, E and Reinhart, C. M (1994) The Macroeconomic Determinants of Commodity Prices, IMF Working Paper, No. 94/9 12

18 favorable treasury bills. That proved to be the case during the 1980 s when interest rate in the US was abnormally high. Shifting money speculation from commodities to treasury bills. One would also observe the same mechanism but the other way around when interest rates are considered to be low. If that proved to be true, would we observe a high price on commodities at present time since most of the driving economies have relative low interest rates? Going back to the beginning of the 2000, there were significant low interest rates and relative expensive commodities. However there other speculative securities that money could flow in to like, currency and emerging market 24. The impression from the historical aspects discussed above gives a clear picture that movements in commodity rates are likely not only driven by natural forces but also generated by artificial forces, which in turn may give volatile movements in BDI, however these forces may not be sustainable in long term. It takes more than a quick fix to restore the economy that will create a more stable demand for commodities and in other words BDI. 24 Frankel, J. A (2006) The Effect of Monetary Policy on Real Commodity Prices, Asset Price and Monetary Policy NBER Working Paper, pp

19 5. Theoretical Discussions 5.1 Movements in the BDI Disturbances in the economy will trigger more extreme volatile movements in the BDI relative to other economic indicators 25. This could be explained by characteristics of the shipping industry, which is rather fixed in supply. To be able to understand how this index reacts, one also needs to look at the capacity utilization of ships. A rather flat movement in the BDI reflects a normal use of the capacity of the global fleet. Once demand of shipping exceeds the supply, steep peaks in the BDI are assumed to be observed 6. The combination between demand and supply could be visually describes as a j- shaped curve reflecting the price of cargo, once there is a unit of service available nothing drastic will happen with the price but as the last unit of cargo ship is used, a steep price increase is likely to be observed. This extreme scenario is due to the fixed supply in short term. Other markets in general could bring new products in to the market more quickly as an effect of increasing demand but in the shipping markets, ships are not built overnight, at least it will take two years before putting in to service. As other indexes, BDI also experience seasonal pattern. These however are not always easy to detect. Other types of cargo rates like container cargo have seasonal occurrences that are affected by big holidays and growth in general. The BDI though is likely besides be affected by different kinds of chocks, be affected by fast prosperity that may cause expansion in the supply of bulk cargo ships. This will influence the price of shipping. The outlook of such procedure is not always clear, historical evidence show that shipping companies may overreact to fast economic growth which may lead to oversupply and a drastic drop in the BDI Batrinca, G and Cojanu, S, G. (2014) The determining factors of dry bulk market freight rates, International Conference on Economics, Management and Development 26 Stopford, M. (2009) Maritime Economics 3rd ed., New York, Routledge 14

20 As discussed above, seasonally adjustments are not easy to predict or observe directly and especially not knowing how long it is between one will come and go. However historical data show that seasonal events occur between 5 to 9 years 27. The correlation between long run equilibrium in the BDI and cost of operation leads one to wonder how the oil price could affect the BDI. We know that the oil price in general could reflect global investment and hence global growth. Though one should be careful to draw any major conclusion based on the oil price at present time due to different types of influencing factors, like internal chocks and circumstances that is hard to predict like wars in different regions. A cheap oil price could in some sense affect the price of shipping and give new incitements to export but also indicate that the market is not demanding any new investment. It stands clear that one need to regard other economic factors as well before making any further judgment. Another interesting finding that somehow reveal that the BDI tends to revert back to its initial state is that the index in short period seems to be nonstationary and experience a drift that back to its natural position. This finding was revealed when investigating different types of shipping rates, which is likely to explain the movements of BDI 30. Some of characteristics of the BDI discussed above could be visually detected in the figure 5.1 below, showing BDI, Oil & Metal, Energy and Agriculture price index 2009 to This graph gives a quite good interpretation of the characteristics of BDI compared to the other commodity indexes. The graph clearly indicates how the BDI have a rather volatile path and reacts with larger swings in comparison to the other commodity indexes presented. This is in accordance to the special feature of the BDI. 27 Stopford, M. (2009) Maritime Economics 3rd ed., New York, Routledge 15

21 Figure 5.1 Log values of different commodities and BDI BDI OILMETALS ENERGY AGRICULTURE Figure 5.1 also expose a slightly drop in each commodity price from 2013, but BDI seems to be more extreme compared to the other except the Energy price which also drop quite drastically. Another interesting aspect that has been discussed earlier is the oversupply of the global fleet and cause of it. Considering the empirical evidence discussed that shippers tend to overact in investment of new ships due to misinterpretation of the economic outlook. The negative trend in the BDI detected in the graph is likely due to an oversupply of the vessel fleet caused by the bright outlook before Such long affected trend is quite problematic and may cause several companies to give up and file for bankruptcy, this also has been noticed in news media during the last year 28. If commodity prices will drop even further it may trigger the BDI to fall even deeper since it tends to react in more drastic manner. Such behavior could only be ceased if demand for certain commodity start to increase or if shipper in greater scale pull out from operating which may reduce the supply for ships for a certain period. We should 28 Saul, J. (2015) Dry Bulk Shipping Record Low a Warning Flag for global Economy, Time Nov 20, [Accessed 05/25/2016] 16

22 remember that not all of the dry bulk companies own their fleet instead has a leasing contract, this will likely lead to less reduction of the world s supply of vessel. 5.2 Technical Aspect of MIDAS - The General MIDAS Model If one start from the distributed lag model which the MIDAS model originates from one could distinctly see some familiar feature. The general distributed lag model is defined as the following: y! = β! + B L X! + ε t And the general MIDAS model without the polynomial weight function is defined as: y! = β! + B L!! X!! + ε! (!) MIDAS model with the weight function is: y! = β! + β! B(L!!; θ)x! (!) + ε! (!) From the first lag distributed model presented above to our MIDAS model one could detect certain differences. x (!)! Is the high frequency variable with subscript m indicating the amount of observations observed to match the dependent variable y!, this variable and it s subscript transform high frequency to match the low frequency of the dependent variable. For instance, if one predict annual data with monthly observation, m = 12. This is kind of straightforward. On the other hand, using daily data explain quarterly would mean that we are observing 66 days (22 days on average per month) per quarter, in contrast to when estimating the same frequency data, m = 1. Hence, the subscript allows one to set the proper amount of high frequent observation to fit the characteristic lag structure of the target variable. 17

23 In order to explain the current or the future state of the target variable we need to specify the proper setting of lags for the explanatory variable, the purpose of this setting is to decide how much of the past high frequent observations that should affect the dependent variable. If we manage a set of high frequent monthly data to predict quarterly data and including monthly observations up to February, hence 2 month in to the first quarter of the year and only have low frequency quarterly data up December the last year, i.e. quarter 4. This will imply that we could use this two-month of additional data to (!) explain the first quarter. To do so we will set the j = 1, in the x!!!/! parameter, which mean we will use 2/3 of high frequent information of the current period to explain the present quarter. This is the definition of nowcasting, using daily, weekly or monthly information of high frequency to predict the low frequent variable of the current period. One of the main attributes of MIDAS model is the parsimonious characteristic, namely how it transform large set of parameters to a set of few ones without any particular loss of information. Including high frequency observations in general would mean estimating many parameters in forecasting time series that however is solved by a function that estimates the dynamic change of past lagged values. Several studies discussed the different weighting techniques 29. The most discussed ones are the Almon polynomial lag, Exponential Almon function and Beta function. Our model uses the Almon polynomial distributed lag model (PDL) to reduce the number of coefficient without loosing to much information, in other words creating a parsimonious model. The decision to choose PDL was mainly determined on the result achieved by several test made on the data set chosen. 29 Galvaom, A.B (2010) The role of high frequency data and regime changes in predicting economic activity with financial variables, Working Paper Queen Mary University of London, [Accessed 05/25/2016] 18

24 The general PDL Function looks as: B(k; θ) =!!!! θ! k! The underlying technique implemented by the PDL function is that each coefficient will follow the polynomial order, hence the degree of p that will affect the weight scheme of the high frequent variable. To be more precise each lag of the high frequent variable will contribute in different amount to explain the prediction of the low frequent variable. To avoid biased error of the weights of each lagged value, it s necessary to specify the proper set of lag length and the polynomial degree 30. The amount of coefficient to estimate will not be affected by the amount of high frequency lags, it is determined by the number of orders of the polynomial. The PDL differs in the setup compared to Exponential function and Beta function that has a different process of lags determination. Lags will be chosen by data driven process for the Exponential and Beta function, hence as long as the model is specified, the dynamic change of past lagged values will be affected by the amount lags included in the model. In PDL function, one has to specify the lag selection. The appropriate set of lags could be determined by looking at sum squared of residual and look for the lowest value. This will give good indication of the proper set of lags. To integrate the PDL in to the MIDAS concept we allow for some modification. Here is K represented by L!! with a subscript to transform high frequency data. L!! In the B(L! (!)! ; θ) is the lag operator equal to x!!!/!. This is the essential part of the MIDAS setting; B(L!!; θ) is the PDL that smoothies the past K observation of x! (!) on the basis of a few parameters. This setup is essential in the prediction of the target variable since our high frequent variable BDI is not likely to have a constant effect over time predicting US GDP, more likely to have a dynamic effect that constantly vary with past K lags. 30 Dallas, S. B and Thornton, D. L (1983) Polynomial Distributed Lags and the Estimation of the St. Louis Equation, Federal Reserve Bank of St. Louis, Review, April, pp

25 A usual scenario is that lags closer to the end of the contemporary period normally have greater weights, meaning that they will have more effect on the dependent variable, this however does not apply to all time series. The polynomial function described above is constructed in rather clever fashion, extending the model with additional variable only requires estimating one more parameter, our model only requires three parameters θ!, θ! and β!. 20

26 6. DATA The Data set includes US GDP ranging from 2011q1 to 2014q1 downloaded from the Federal Reserve St. Louis and BDI downloaded from the Quandl platform. BDI in model 1 ranges from 2011d1 to 2015d22 (each month on average includes 22 working days). The second model includes US GDP in the same interval as in the model 1 but BDI extends from 2011d1 to 2015d44, hence including two month in to the first quarter of Both US GDP and BDI is in logarithm in order to make more economic sense and more assessable. For the third model, the least square model, I use observations of BDI that will range from 2011d1 to 2015d44, exactly the same as model 2 of the MIDAS model. 21

27 7. ESTIMATION 7.1 Methodology To extract as much as possible from the BDI variable to predict the current quarter of US GDP, I execute a general MIDAS model. This method proposed by Ghysel, Santa-Clara and Valkanov 31 contributed to a simple and efficient way of mixing data of different frequencies. Two MIDAS models and a least square model with flat aggregation will be generated in order to compare the MIDAS concept to a benchmark model. The two MIDAS models differ in the amount of observation of BDI included, this to see if additional data will provide better nowcasting model. I will also present a graph that indicates the result of a constantly updated MIDAS model. This means feeding additional BDI observations to the MIDAS nowcast model as time approaching target quarter. Starting from first observation of January 2015 to the last one in Mars One will be able to follow the Root Mean Square Error (RMSE) result for each updating, displayed in a graph. My intention is also to test for cointegration between US GDP and BDI and also construct an ECM MIDAS-model, this to some extent see if there is a strong argument for using BDI for explaining economic growth in US and also to evaluate if such model will contribute to better nowcasting result. 31 Ghysels, E. Santa-Clara, P and Valkanov, E (2004) The MIDAS Touch: Mixed Data Sampling Regression Models, Working Paper CIRANO 2004s-20, CIRANO 22

28 7.2 Properties and Necessary Modification Before we start modeling and make any conclusions regarding the result, we must consider the characteristics of the BDI and US GDP series. Even if I believe and know that there are statistical evidence of correlation between BDI and economic growth in past I will test for spurious result This problem may occur when regressing nonstationary time series that at first glance seems to be correlating but further analyzes prove that there is no such relation. There are though some clues that could show signs of spurious regression. If R! -value is high and the Durbin Watson D statistics is exposing a rather low value, lower than the R! -value, one could argue that this suffer from spurious regression. The test shows no such result and we can proceed with the estimation. Both US GDP and BDI is in logarithm in order to make more economic sense and more assessable. First plotting these series is done, this reveals if there is a trend and an intercept. Figure 7.1 and 7.2 reveals both trends and an intercept. The Augmented Dickey Fuller test is executed to test for stationary. Both series fail to reject stationary, at any reasonable level. This was in line with expectation, as discussed earlier in the movement of BDI, cargo rates seem to be nonstationary in levels. This will require some modification, in this case, solved by first difference of both series. The test also reveals that both series are stationary at first difference. Figure 7.3 and 7.4 in the Appendix section shows what both series look like when taking the first difference of each series. Figure 7.1 Logarithm BDI Figure 7.2 Logarithm US GDP LBDI LGDP I II III IV I II III IV I II III IV I II III IV I 960 I II III IV I II III IV I II III IV I II III IV I

29 7.3 Nowcast US GDP with MIDAS-model Since the MIDAS model convert an unbalanced data set to be balanced with no major loss of information, explanation of the more technical part with the selected data is needed. This will provide a more convenient way of interpreting this quite advanced technical part. Nowcasting the current quarter with the past quarter of US GDP available would mean h! = 1, step ahead. Extending the nowcasting or forecasting horizon one step or several steps ahead requires are quite large set of past US GDP observation, this to be able to present accurate predictions 32. First one need to select the proper set of observation of BDI to match US GDP, Second, to reach effectiveness of the model, find an appropriate set of K lags of high frequent observations is required. This is done by looking at the presentation of the sums of squared residual (SSR). Third and last, chose the amount of observations that should be extracted from the high frequent variable BDI, hence decide how updated the nowcasted model should be. This is what our MIDAS model look like. y!" + h = 1!!! = β! + β! B(L!;! (!) θ)x!!!/! + ε! (!) To match daily to quarterly data we need to set the proper amount of high frequent observations to match low frequency. Our high frequency variable containing daily observations, there are 66 of them in each quarter, that s why m=66. Note that the superscript on the high frequency (!!) indicator x!!!/!, is telling that the 66 th daily observed value in time is included to represent the high frequency variable BDI to match our quarterly data. 32 Kuzin, V. Marcellino, M and Schumacher, C (2011) Midas vs. mixed-frequency var: nowcasting GDP in the euro area, Internation Journal of Forecasting, Vol. 27, Issue 2, pp

30 Next thing to do is to specify the proper set of lag length K of the PDL function. B(k; θ) =!!!! θ! k! Remember that the Almon PDL weighting is not data driven, this means that we need to determine the lag length with the lowest SSR value. There will be different set of proper lag length depending on the amount of BDI observation included and the amount of polynomial parameters to be included. One can observe figure 7.5 and figure 7.6 in the Appendix to see the selection of lag length for model 1 and 2. The last thing we should do before finishing the setup of the two MIDAS models is to set the appropriate amount of high frequency data that should be linked to our dependent variable US GDP. The following description will explain the setup. (!) x!!!/! The subscript j in the high frequency parameter will be equal to 44, for model 1 (less updated model), hence extracting 1/3 of the current period or to be more clearly one month of BDI observations of the first quarter And j = 22 for the model 2 (more updated model), hence 2/3 of the current quarter of BDI observation. When J = 0, the model includes data up to the end period, hence in our model that would mean we are including the last observation of BDI of Mars. 7.4 Cointegration test and ECM MIDAS The relationship between BDI and economic activity has lately been questioned in news media. This gives a quite good reason to explore if an ECM can describe if such disequilibrium between BDI and US GDP exists. The purpose using ECM is to explain both short and long-term dynamics. Such method might reveal evidence of equilibrium in long run but not in short run. Which may reflect the questioning of BDI. 25

31 The ECM MIDAS model can both show short dynamics and long dynamic. In order to extract short dynamics one need to take the first difference of the high frequency variable, though it could be modified to include differences of low frequency as well since we work with different time lag data. The long-term effect is extracted from a MIDAS regression in levels. To make this more straight forward, I will extract the long-term effect by regress the BDI and US GDP at the same time period, hence US GDP at time t = BDI at time t with a MIDAS model. This requires though that we find a cointegration between the two series at this certain time lag. If not, the empirical advice is to find a matching pair that is cointegrated 33. Hence, look at several time lags back to find cointegrated pair of BDI and US GDP. This process originates from the two-step Engle-Granger method. Before one is able to draw any conclusions about the ECM model, certain requirement most be fulfilled regarding the attributes of the time series. Confirming that both series are integrated at the same order, we need to check whether there is long-term effect, do so by testing for stationary of the residual given from the regression of BDI on US GDP, in accordance with the empirical advice discussed above. Performing an ADF test for unit root concludes that we can t reject nonstationary at any reasonable level. Hence, the residual is not stationary when testing at levels. This was tested for several lag pair of US GDP and BDI. Since different test for stationary are available and may differ slightly, I proceed with Johansen cointegration test, the result also states that there is no cointegration at any reasonable level. This prevent us from generating a proper ECM MIDAS-model, though the test reveal some interesting aspect regarding the market for commodity demand and supply of service of dry bulk cargo. A further discussion of this will be presented in the Conclusion section. 33 Götz T. B, Hecq, A. and Urbain, J.P (2014) Real-Time Forecast Density Combinations: Forecasting US GDP Growth Using Mixed-Frequency Data, Journal of Forecasting, Vol. 33, Issue 3, pp