1 Introduction

How energy consumption contributes to economic growth and hence forecasts GDP has been a classic research topic in macroeconomic studies. The researches, however, have been focus on probability statistical models including vector autoregression model (VAR), vector error correction model (VEC), or simply panel data linear regression. This dissertation introduces the grey system, brought by Professor Deng Julong in 1892, into the study of this topic. It first studies the contribution power of energy consumption to European countries then forecasts their GDP. Due to the feature of grey system, the forecasting will be done first, followed up by the energy consumption study.

This topic is brought into study for the reason that energy has been a severe problem in recent years. What is the energy consumption pattern? How much are they contributing to economic growth? These questions will be discussed in the dissertation. Also the writer hopes the study may arouse interests in further studying in this topic such as: how long is fossil energy going to supply the social demands? Or is there any further policy needed for the energy consumption revolution from fossil one to clean ones?

Based on the interests in above topic, the dissertation is developed as follows. In Chapter2, some literatures on this filed are reviewed. This chapter summarizes the conclusions drawn by previous researchers and these conclusions may vary from the one drawn in this dissertation. Chapter3 introduces the features of this dissertation and outlines its contribution to the existing studies. In Chapter4, the writer outlines the reasons for the choice of models in grey system and the choice of data used for estimation. The grey model (1.1) and grey relation model are built in Chapter5 and the data is fitted in Chpter6 where further analysis is also provided. Chapter7 provides some further discussion on two key problems in the two models used in this dissertation. Chapter8 summarizes the dissertation and provides a general conclusion.

2 Literature Review

2.1 On GDP Forecasting

GDP forecasting has long been a topic that arouses widely attention. Various researches have been done on this particular field with different statistical methodology. In 2001, Gonzalo et al. forecasted GDP growth in European countries with VAR and ALI models. They found ALI model outperforms the VAR model due to its nature of arbitrary. Baffigi et al. (2004) forecasted euro zone GDP with bridge models and compared the results with traditional benchmark model. They concluded that bridge model is always better than benchmark model as long as required variables are available for forecasting. In 2008, Schumacher and Breitung forecasted German GDP with large factor model using both monthly and quarterly data. They also compared the results with benchmark model and found the former model outperforms the latter. In 2014, Barnett, Mumtazb and Theodoridis forecasted UK GDP using quarterly data from 1955 to 2010. They compared the forecasting of various models and found that ‘rolling VAR, TVP-VAR and ST-VAR models all provide forecasts of GDP growth with lower average RMSEs than AR(p) model’. Also, time varying variables in the model improve the forecasting.

Forecasting has never been easy because of the nature of unpredictability in variables, especially in the field of macroeconomics. GDP is highly depended on government policy and market behavior. Yet researches spared no effort trying to develop new models in forecasting GDP. In 2004, Grenouilleau forecasted GDP in France, Spain, Italy and Germany with Sorted Leading Indicators Dynamic (SLID) Factor Model. His forecasts, according to himself, ‘are based solely on the common factors and cross-sectional information provided by the database and not on traditional few-variable time series systems’. In 2008, Golinelli and Parigi forecasted Italian real-time GDP with automatic general-to-specific adaptive model. There are three main findings of their research: the quarterly data improves the forecasting accuracy, the usage of fully updated data does not make much difference in forecasting, and the forecasting can be improved by combining two variables used in their model. In the same year, Cao et al. (2008) forecasted GDP in Henan Province in China with grey linear regression combined model. They used data from 1990 to 2005 and found the combined model achieves better forecasting compared to either of the models alone.

This dissertation will attempt to use Grey Model (1.1) in GDP forecasting.

2.2 On Energy Consumption & GDP Correlation

It has long been debated whether energy consumption is contributing to economic growth, represented by GDP. Researches on both theoretical and empirical side of this topic have been developed throughout the past few decades. The empirical side is more related to this dissertation and hence well be focused on at this stage. In 1980s, the researchers have found ‘no causal relationship between GNP and energy consumption’ (Eden and Hwang, 1984) using US data from 1947 to 1979. However, early research using the same data conducted by Kraft and Kraft (1978) has drawn exactly the opposite result where there is causal order from GNP to energy. A broadened research conducted by Yu and Choi (1985) indicates the neutrality of energy consumption. They concluded that causal relationship only exists in Germany, Japan and Italy while remained neutrality in Canada, France and UK.

The application of statistical methodology into further depth in later times has introduced the research process to a new level. A relatively long dimension studying is made possible when cointegration test and Granger causality test are put into usage of time series data. These tests provide a way to research into the correlation of non-stationary independent variables and contribution of regressors in explaining dependent variables. As a result, the compatibility of VAR and VEC models is to be formally tested. In 2007, Mahadevan and John used panel VEC model in studying the causality between energy and GDP in both developing and developed countries. They found two ways in which the increment of GDP affects energy consumption: households increasing their energy-intensive activities and energy usage increasing as an input. Tsani (2010) looked into the same topic using VAR model with Greece data from 1960 to 2006. He improved the data by dividing energy consumption into aggregate and disaggregate levels and found the presence of bi-directional relationship of GDP and energy consumption at disaggregate level.

Recent researches have revealed the insufficiency of traditional unit root test in VAR and VEC models. Yet new correlation estimation models thrived. The Grey system brought by Deng (1982) provides a completely new way of modeling time series. Yang et al. (2010) applied the model in estimating the economic development and energy consumption using Chinese data from 1985 to 2007. They concluded that Chinese economy benefited most from coal consumptions, by which follows the crude oil and natural gas. Hydro-power, wind power and nuclear power, however, have just started their way in contributing to the economy.

This dissertation will try to apply the grey relation model to the EU data and further adjustments will be made.

3 Research Feature and Contribution

3.1 Research features

3.1.1 Introduction to grey system theory

Constructed based on the grey systems, Grey system theory is brought by Professor Deng Julong in 1982. It is a theory specially developed to describe the behavior of systems that fall in the ‘grey’ category.

Various systems have been constructed in the development of humanity history; examples include technical system, social system, economic system and so forth. Some systems contains massive amount of information and hence can be described by the characterized facts revealed in those informations. Traditional statistical models performed well in modeling objective behavior of those systems and give relatively precise results. However, most systems either contain less information or are highly influenced by variables that cannot be quantified. These systems falls into the ‘grey’ category, in which traditional models fail to give precise results. Grey system theory, as a result, is developed to describe these systems and attempt to produce accurate results.

Grey system theory is constructed on the concept of systems. It believes that certain characters or orders always exist in a system, but those orders are unrevealed sufficiently so as to be modeled. The grey system theory, however, tries to model these features by treading those ‘appeared to be stochastic’ variables as grey variables. It then processes the raw data in certain means so as to quantify the system. According to Si (2007, p.415-416), this process breaks the limitations of traditional probability statistical models where results are drawn from empirical rules based on massive data analysis. The process that grey variables are clarified is called ‘whiten’

3.1.2 Economic system as a grey system

Economic system describes macroeconomic phenomenon in the modern world. It appears to be a well-structured system with massive historical data available; however, the fact may not prove so. In terms of the system structure, difference in categorization may results in the statistical inconsistence in data collection. A very common example is double counting. When one variable belongs to two categories simultaneously, fail to consider this fact when summing the two categories would results in problem. In terms of data availability, historical data may not be available in each sector of each country, yet it could be the case that it is the field without sufficient data that are to be studied in. Therefore economic system is grey, at least to some extent.

This dissertation will look into the GDP forecasting and the relative contribution power of energy consumption to GDP. GDP forecasting, as discussed before, depends on different variables. Some of these variables may be well recorded. However, other variables like climate, geographical location, extent of country development, and resourcefulness in energy storage can also influence GDP, while it is hard to measure and quantify these variables. Accurate forecasts may not be produced under such circumstances. The relative contribution power of energy consumption is even harder to measure. This is due to the correlation within the energy consumption itself. The lack of clearance in sets limitations on related researches and makes the field ‘grey’.

3.2 Research contribution

To begin with, the grey system theory is not widely used in economic researches. The application of it in this dissertation results in complete abolishing of traditional regression models. This actually broadens the way of further economic researches. What’s more, the combination of grey model and grey relation analysis has never appeared in previous researches of macroeconomic field. This approach may be applied on other macroeconomic researches rather than being limited to energy researching only. It is a creative way of splitting one estimation into two separate ones. While some efficiency may be lost in estimation two models, accuracy is improved by a significant level. Last but not least, the insufficiency in model accuracy due to insufficient mathematical background of the writer may motivate on further researches in the energy field or in improving the model. A wider application of grey system theory in improvement of scientific studying is to be looking forward to.

4 Choice of the model and data

As mentioned in earlier chapters, there are to parts of the dissertation: forecasting GDP and testing the relative contribution power of energy consumption to GDP growth.

4.1 Choice of the grey model

In terms of forecasting, traditional statistical model forecast variables by fitting the historical data with regression. Firstly, such regression requires massive amount of observations for the fitted equation to be precise. Secondly, the choosing of explanatory variables requires precise consideration, fail to consider some important variables will cause omitted variable problems, the unconsidered information contained in residuals may change the result considerably; on the contrary, including non-necessary variables will cause misspecification problems, what’s more, similar variables used as explanatory variables may cause colinearity or endogeneity problems. Thirdly, traditional models tend to forecast energy consumption as an aggregate variable, the forecasting in individual type has been hard. This is because the colinearity problem existing in energy consumption itself. A simple example would be the correlation between coal consumption contributes and electricity consumption, due to involvement of coal in electricity production. By applying the grey model, the main idea of forecasting is to dig into historical connection of the time series data itself. Each variable is forecasted individually without the interference by any problems existing in the explanatory variables. This is because the model tries to explain the variable by itself instead of any other variables.

As for the contribution power testing part, traditional models try to regress each type of energy consumption on the economic output. The contribution power is outlined by comparing the magnitude of the parameter of each variable. The key problem is energy consumptions tend to be correlated and hence there is endogeneity problem. This is address above in the third point. Also, the first two problems do exist. Energy consumption is not the only reason that economic output growths, failure to consider other variable causes omitted variable problems. Meanwhile, the data availability sets limitation on the accuracy on the model as well. The grey relation model, however, estimates the relation of each variable to the reference variable separately, whilst it still produces the coefficients that are comparable for each variable. This separation in estimation uses the information provided by the variable only and hence eliminates all the noise outside the variable. None of the problems addressed above exits.

In summary, grey model reveal the relationship within the variable historical observation. This process overcomes the limitation of traditional models which forecast and estimate the relative significance in one fitted equation. The information in data is efficiently used and interruption of out-data noise is minimized.

4.2 Choice of data

In GDP forecasting part, we choose the GDP yearly data (in national currency) of UK, Germany, France and Norway from year 1983 to 2013, with the break due to 2008 financial crisis being considered. The consideration in choosing the stated data is as follows: 1. Year 1970s saw the 3rd industrial revolution when computers were put into widely use. The application of advanced technology in productions has boosted the efficiency in economic growth. It is the belief of forecasting being more consistent under similar technology basis that leads to the choice of the data starting point in 1980s. This choice removes the initial shock from the invention of computers and provides the data under constant improvement of technology. 2. GDP tends to be influenced by seasons. It is reasonable that it is more productive during spring and autumn. The inappropriate temperature in winter and summer make it less productive in these seasons. The choice of yearly data removes the seasonal effect and does not influence the forecasting overall. 3. The choice of these four countries is under the sense that this dissertation studies European OECD countries and UK, Germany and France are the leading countries in terms of economic growth. These countries are the motivations that drives European economy forwards. The choice of Norway is for comparison. This country is geographically far away from the above three countries and also small in terms of GDP growth. 4. GDP is expressed in national currency with constant price. The consideration here is that: constant price and national currency remove the influence of inflation and exchange rate variation respectively. This choice generates economic growth data purely from the value created domestically. The dependence of energy on GDP will then be more reliable.

In the contribution power testing part, data from same time period will be chosen. The reasons are addressed before. The difference in data choosing of this part is the European OECD counties as a whole will be included. In terms of the energy consumption, the data will include final consumption of electricity, fuel oil, hard coal, motor gasoline, natural gas. The choice is because that these energy consists of the main energy consumption in daily production and households living. The reason for not including crude oil, which many researches do, is crude oil cannot be used directly. What’s used is the end product of crude oil, namely fuel oil, motor gasoline and so forth. Including these two types of energy is a substitution for crude oil and is more realistic.

To sum up, the choice of data follows the main idea that more information can be reflected without interference of noise. The amount of data is proper for estimation and reliable conclusion can be drawn from the results. All the data comes from International Energy Association statistic on UK data service website (2014).

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