Macroeconomic factors that correlate with the performance of Industrial Transportation Companies

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IN

DEGREE PROJECT TECHNOLOGY, FIRST CYCLE, 15 CREDITS

,

STOCKHOLM SWEDEN 2017

Macroeconomic factors that

correlate with the performance of

Industrial Transportation

Companies

A study using multiple linear regression

OSCAR WIJKSTRÖM

SOFIA ÖHMAN

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Macroeconomic factors that

correlate with the performance of

Industrial Transportation

Companies

A study using multiple linear regression

OSCAR WIJKSTRÖM

SOFIA ÖHMAN

Degree Projects in Applied Mathematics and Industrial Economics Degree Programme in Industrial Engineering and Management KTH Royal Institute of Technology year 2017

Supervisor at SEB: Mathias Sjöberg

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TRITA-MAT-K 2017:18 ISRN-KTH/MAT/K--17/18--SE

Royal Institute of Technology School of Engineering Sciences

KTH SCI

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Abstract

This thesis in Applied Mathematics and Industrial Economics examines which macroeconomic factors, related to the business cycle, that correlate with the performance of Industrial Transportation Companies. The data for the thesis is collected with the help of Nordea and from reports of each variable. The observations stretch from January 2007 to December 2016, a ten-year period. The data is monthly, hence there are 120 observed data points for each variable. A linear regression analysis was performed with the result that there is a linear relationship between the performance of the Industrial Transportation Companies and the variables Price per MWh, Fuel Price, Exchange rate USD-SEK, Exchange rate EUR-SEK, Manpower Em-ployment Outlook Survey, Repo Rate, OECD Index Sweden, and Purchasing Manager’s Index. Further analysis of the Swedish and international eco-nomic history in the last decade was conducted which concluded why said variables were significant.

Sammanfattning

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Acknowledgements

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1 Introduction

1.1 Background

This study is done as a collaboration between two KTH students and Nordea Bank AB, more specifically Nordea Global Stars. The project is performed with guiding from the fund manager of Nordea Global Stars, Johan Swahn.

The idea of Nordea Global Stars is to find and administer companies that are assumed to be positioned well regarding meeting different future challenges and goals. Nordea Global Stars places their securities globally in corporations that are both good at creating financial results and that are at the cutting edge of envi-ronmental and social responsibility as well as of business ethics. The fund holds 50-70 corporations, out of which none are producers of fossil fuel.

There is a general idea that there is a correlation between the business cycle and the performance of cyclical companies. This is the reason to why some corpora-tions are in fact called “cyclical”, as they seem to perform better in one or several parts of the business cycle.

(Krugman, Wells 2015 )

Questions that arise, following these general ideas, concern if there is actually any data that supports a correlation between the performance of cyclical compa-nies and the business cycle? To immerse the study, both variables that are directly, and variables that are indirectly, correlated to the business cycle are considered. Can historical data be used to prove or disprove a pattern?

There are eleven different sectors in which companies can be divided into, as specified by Nordea. These are:

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• Financials • Health Care • Industrials • Information Technology • Materials • Real Estate • Telecommunication Services • Utilities

This thesis will investigate the macroeconomic factors correlation for the Indus-trial Sector, or more specifically the IndusIndus-trial Transportations companies. The common belief in the financial market is that industrial companies in general corre-late with the business cycle, and industrial transportation companies in particular. The ideas and beliefs surrounding the other sectors are not as strongly practiced in investing as of today.

1.1.1 A Priori Research A priori research are extensive:

• Mukherjee (1995) used data for inflation and money supply to analyze the connection between macroeconomic variables and the stock market.

• Akbar, Ali (2012) analyzed the relationship of macroeconomic variables and stock prices with use of evidence from the Karachi Stock Exchange. The study showed a positive relationship between the stock prices and the money supply and interest terms as well as a negative relationship between the stock prices and the foreign exchange reserves and inflation.

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• Gjerde and Saettem (1999 studied the relationship between macroeconomic variables and stock returns in Norway. They found that there was a positive relationship between the fuel price and stock returns.

• Mahedi (2012) examined the relationship between macroeconomic variables and the stock returns of Germany and the United Kingdom. For both coun-tries, the study concluded that the inflation affected the stock returns.

1.2 Aim

The aim of the project is to establish how different variables, that are indirectly or directly related to the business cycle, correlate with the performance of indus-trial transportation companies. The project will also interpret why the different variables do or do not have an effect on the performance of the companies. Looking at what studies and analyses have been done previously, the choice of using linear regression analysis is clear, as the analysis will choose what variables are significant for the response variable and which are insignificant. This study will focus on the same questions as many previous studies, but will concern Sweden and more specifically the Industrial Transportation Sector.

The aim of the results is to provide a foundation for optimizing portfolios. The project was designed to help Nordea Global with their investment decisions and of course the result will aim to do this.

If there is a correlation between at least one variable and the performance of indus-trial transportation companies, the results will provide a greater knowledge about what stocks will earn a better revenue subject to the trend of the variables studied. If there is not a correlation between the variables and the performance, it will imply that these variables are not to be observed when choosing when to invest in the Industrial transportation sector.

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significant no matter if there is a correlation or not.

1.3 Research Questions

This study will analyze different models for the performance using multiple linear regression. The performance variable is set to the OMX Stockholm Industrial Transportation Index. The project will attempt to answer the following research questions:

• Is there a correlation between the performance of industrial transportation companies and the variables that are directly or indirectly influenced by the business cycle?

• Can the performance of industrial transportation companies be modelled using these variables?

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2 Mathematical Theory

2.1 The Multiple Linear Regression Model

In order to fit a linear model, one uses the Multiple Linear Regression Model which is constructed as follows, yi = k X j=1 xijβj+ ei, i = 1, 2..n (1)

where the variable y is called the response variable and depends on the explana-tory variables xij. The βj variables are the regression coefficients which are to be

estimated using the observed data. n represents the number of observations made, which means that yi is the observation of a random dependent variable y.

The variable y is called the response variable and depends on the explanatory variables xij. The βj variables are the regression coefficients which are to be

esti-mated using the observed data.

The model can also be written in matrix form, as follows,

y = Xβ + (2) where, y =       y1 y2 .. . yn       , x =       1 x11 x12 . . . x1k 1 x21 x22 . . . x2k .. . ... ... . .. ... 1 xn1 xn2 . . . xnk       , β =       β0 β1 .. . βn       , e =       e1 e1 .. . en       . (Lang 2016)

2.2 Assumptions

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1. The presence of a linear relationship between the response variable and the explanatory variables. That is, the variable y is a linear combination of the vari-ables plus the residual e.

2. The expected value of the residual is zero. This means that the distribution, from which the error e is calculated, is zero,

E[ei] = 0. (3)

3. All error terms have the same variance so that the variance of the residuals is constant. The model is therefore homoscedastic,

E[(ei)2] = σ2. (4)

4. The independent variables are deterministic, which means that they remain the same in repeated samples.

5. The number of observations is larger than the number of variables and there are not any linear relationships between the variables.

(Williams, Gómez Grajales, Kurkiewicz 2013) (Hayes, Cai 2007)

2.3 Ordinary Least Square Estimation

The Ordinary Least Squares method is used to estimate the β- coefficients. The goal of the method is to minimize the sum of the squares of the residuals,

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In order to find the vector ˆβ that minimizes the sum of the squared residuals, the normal equation (6) is solved for ˆβ,

Xte = 0.ˆ (7)

This yields the expression,

Xt(Y − X ˆβ) = 0 (8) which is solved for ˆβ to get,

ˆ

β = (XtX)−1XtY. (9)

(Lang 2016)

(Belsley, Kuh and Welsch 2004)

2.4 Possible Errors

2.4.1 Multicollinearity

Multicollinearity occurs when two or more variables are strongly linearly depen-dent. The consequence of multicollinearity is that the standard error of at least one of the coefficients becomes large which causes imprecise estimates of the co-efficients. As the number of observations grow larger, the standard errors tend to decrease which implies that the problem of multicollinearity often is caused from lack of data. A solution in this case may therefore be to add more observations into the analysis. If the problem of multicollinearity still remains, the next step to solve it would be to remove one of the variables which are correlating or to merge them together.

If two or more of the variables are perfectly linearly dependent, the Ordinary Least Squares estimate has no unique solution which means that the Xt_{X -matrix}

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Variance Inflation Factor

One way of detecting multicollinearity is to look at the variance inflation factor (VIF). VIF is defined as,

V IF = (1 − R2)−1 (10) where R2 _{is derived for every variable by using the investigated variable as a}

de-pendent variable against the other variables and is a scale of how precise the model is. R2 _{is further explained in section 2.6.1 in Mathematical Theory.}

A VIF-value >10 indicates that there is multicollinearity present in the model. (Lang 2016)

2.4.2 Micronumerosity

If the number of observations is small, there could occur a problem with micronu-merosity, meaning that the asymptotics do not occur. Hence, the assumptions of homoskedasticity must be relied on.

(Lang 2016) (Hansen 2015)

2.4.3 Heteroscedasticity

In a heteroscedastic linear regression model the variances are, as implied by the name, unequal. This defies one of the assumptions of the multiple linear regression model stated in section 2.2. Heteroscedasticity can be defined as,

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Figure 1: Display of residual plots of homoscedastic and some heteroscedastic models.

If the density plot appears symmetric, the model is homoscedastic, while a non-symmetric plot implies that the model is heteroscedastic.

Figure 2: Density plots of homoscedastic (the blue line) over heteroscedastic mod-els.

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Figure 3: QQ-plot of a model with tails that do not agree with a normal distribu-tion.

If the problem of heteroscedasticity remains after reformation, the covariance ma-trix can be estimated using White’s Consistent Variance Estimator,

Cov( ˆβ) = (XtX)−1XtD( ˆe2 i)X(X t_X)−1 (12) where D( ˆe2 i) is a diagonal matrix.

The problem of heteroscedasticity may also be approached by transforming the linear regression model. For example, it can be transformed into a log-linear re-gression model, meaning that the logarithm of the response variable is used which will impact the spread.

(Lang 2016)

2.4.4 Endogenity

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and if it is negative, the coefficient will be under estimated. One can define the problem of endogenity as,

E[e2_i] 6= 0. (13)

Endogenity is apparent when at least one of the following situations occur: 1. Sample Selection Bias

The data selection is biased leading to one or more groups being over represented subject to other groups. This may cause misleading assumptions.

2. Simultaneity

Occurs when the dependent variable influences at least one of the variables in the regression model, which means that the residual influences the variable.

3. Missing Relevant Variables

If the regression model does not contain all the explanatory variables which are necessary, these variables will be part of the residual which may lead to incorrect estimates.

4. Measurement Errors

A measurement error on at least one of the variables will lead to a correlation between the variable and the residual, under the assumption that β is non-zero. The problem of endogenity may be approached with a process known as "Two Stage Least Squares" which replaces the variables affected by endogenity with strongly correlated variables known as instruments.

(Lang 2016) (Hansen 2016)

2.5 Model Evaluation

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2.5.1 R2

R2 is a measurement of comparison. One can say that it is a measure of the goodness of fit. By comparing the different reduced models to the empty model, y = β0+e, one can see which model has the most variance. The measure is however

not a measure of adequacy, so a large value of R2 may not necessarily mean that the model is adequate. The R2 -measure is defined as,

R2 = 1 − P(y − ˆy)

2

P(y − y)2 (14)

where y is the estimed y and ˆy is the fitted value of y.

One can define the statistic as the proportion of variance for the response variable y which is achieved by fitting the response variable y to a particular model, com-pared to the isolated y.

There is one big issue with the R2-measure and that is that it increases with the number of variables in the model.

(Hansen 2016)

2.5.2 Adjusted R2

The Adjusted R2 is used more often than R2, since it adjusts the value for degrees of freedom. This means that the value will not necessarily increase with the number of variables. The Adjusted R2-measure is defined as,

R2_adj = 1 − (n − 1)P(y − ˆy)

2

(n − k)P(y − y)2 (15)

where k is the number of variables and n is the number of observations. (Hansen 2016)

2.5.3 F-test

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The test includes a F-statistic and an alpha quantile of the distribution, hence if the alpha quantile is larger than the F-statistic, the null hypothesis shall be rejected. The F-statistic for the hypothesis βi = β0 is defined as,

F = ( ˆβi 0 − β0 i)2 V ar( ˆβi) (16) and the alpha quantile is defined as,

Fα(1, n − k − 1). (17)

One can test if a number r of the β-estimates should be excluded from the model, hence if they are equal to zero. The F-test is defined as,

R2

1 − R2

n − k − 1

r (18)

where k is the number of variables and n is the number of observations. (Lang 2016)

2.5.4 P-value

The P-value is a measure of the probability that the obtained results occur under the null hypothesis. A low value indicates that the null hypothesis shall be rejected. The P-value is on the form p = P r(X ≥ (F ) and is defined as,

Pvalue = P (F (r, n − k − 1) > F ) (19)

where r is the number of variables which are null hypothesis tested, k is the total number of variables, n is the number of observations and F is the F-statistic, and n − k − 1 is the degrees of freedom.

(Lang 2016)

2.5.5 Akaike Information Criteria

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reduced model compared to using the original model. It indicates what variables to include in the final model. Compared to the Bayesian Information criteria, it does not assume that any of the models tested are actually the true model, as it looks upon all models as approximations of the reality. The Akaike Information Criteria is defined as,

AIC = n ln(|ˆe|2) + 2k (20) where n is the number of observations and k is the number of variables.

Since it measures the information loss, a low value of AIC is preferable. Hence, when comparing the original model to a reduced model, the model with the lowest value of AIC is the preferable.

(Lang 2016) 2.5.6 η2

The η2-statistic measures the variance reduction in the residual term by comparing the original model to a reduced model. The reduced model includes all variables except the one which is currently being studied. The statistic therefore presents how much of the variance in the residual term was affected by the removed variable. The η2 -statistic is defined as,

η2 = | ˆe∗|

2_{− |ˆ}_e|2

| ˆe∗2|

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the reduced model.

A high value of η2 _{indicates that the removed variable has a significant effect}

on the response variable. Hence, if the value is close to zero, the reduced variable have little or no impact on the residual term. This implies that the variable in matter may be reduced.

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3 Economic Theory

3.1 The macroeconomic perspective

Macroeconomics is the study of the behaviour of the economy as a whole. A large portion of the macroeconomics is the business cycle. The business cycle is the period of alternation between expansions and recession. Expansions are periods where employment rises and the industries boom. Recessions are periods where employment decreases and industries struggle. Where the business cycle shifts from expansion to recession is called the peak of the business cycle.

Other commonly discussed areas of macroeconomics are the inflation and the de-flation, both closely related to the business cycle in the short run. Inflation occurs when the overall prising increases and the opposite yields for the deflation. The Swedish central bank has a goal to achieve an inflation of two percent. In order to obtain that level of inflation, instruments for adjusting the repo rate are commonly used. The repo rate is the rate that banks have to pay when they lend money from the central bank.

3.1.1 Financial Policy

Expansionary and contractionary monetary policies are two types of monetary policies that increase and decrease demand.

(Krugman P, Wells R. 2015)

The central banks can adjust the money supply in order to change the interest rate. When central banks increase the quantity of money, the interest rate de-creases. Similarly, a reduction in the money supply drives the interest rate up. By adjusting the money supply, the central bank can adjust the interest rate.

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A too high inflation is harmful for the economy since the inflation tends to vary substantially when it is high. This makes the long-time planning, that investors and companies rely on, unfeasible. On the other hand, too low inflation is not good either. If the inflation is too low, the risk of deflation becomes significantly higher. Deflation is not desirable because it reduces the consumption, on which the economy is based on.

(Riksbanken 2011)

To achieve low inflation, in order to reach the inflation target, the central bank has an active monetary policy. This means that it stimulates the economy when the inflation is under the target and moderates the economy when the inflation is above the target level. To stimulate the economy, the central bank can lower the interest rate and start buying bonds to increase the money supply. Similarly, to moderate the economy, the central bank can reduce the money supply.

(Krugman P, Wells R. 2015)

To conclude; a low inflation is favorable and fundamental for households and firms to rely on when making economic decisions. To maintain a low inflation, the cen-tral bank can use different methods for adjusting the money supply.

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4 Methodology

4.1 Previous Knowledge and Software

Literature studied before beginning the project are:

• Introduction to Linear Regression Analysis by D. C. Montgomery, G. Geof-frey Vining, and Elizabeth A. Peck, 2015

• Economics by P. Krugman and R. Wells, 2015 • Elements of Regression Analysis by H. Lang, 2016 • Corporate Finance, J. Berk and P. DeMarzo, 2013

Previous knowledge is collected from courses SF2930, Regression Analysis, ME1310, Economics for I, and ME1311, Corporate Finance.

Software used for the thesis are Microsoft Excel, LaTex (overleaf) and RStudio.

4.2 The trend of data points

Instead of using the gathered data points in a straight forward approach, the trends are taken into consideration. Using the two models, the delta- and the rolling twelve month- methods, more significant values are constructed.

4.2.1 Unit Root

Unit root refers to the problem of variables which correlate simply because they are both growing. This is why the delta approach to economic data is preferred over just analyzing the data points. The data is therefore collected as,

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4.2.2 Rolling twelve month

Rolling twelve month is used for data that varies a lot from month to month with-out any visible linear trend. The rolling twelve month trend means that for each observed month, that month’s data is added to the sum of the last eleven months’ data. This means that the gathered data will change from month to month, but will give a more fair representation of the situation and often a better linear trend. The downside to this method is the same as its upside, since correlation between observations is obvious as they have eleven months in common.

4.3 Variable selection

4.3.1 Response Variable

In regression analyses, the first initial step is to determine which variables should be included in the model, starting with the response variable. With the aid of the response variable, one can choose the explanatory variables.

The response variable is set to the be the index OMX Stockholm Industrial Trans-portation GI. The index is designed to track the total return on NASDAQ OMX Stockholm for the Industrial Transportation sector. The data points are calculated as,

∆(OM X) = OM X(M onthn+1) − OM X(M onthn), n = 1, 2, ..., 119. (23)

4.3.2 Explanatory Variables

In this section, the definition of each explanatory variable will be explained. Each variable was selected on the basis that they may have an impact on the response variable, which in its turn is based on a priori research.

Consumer Price Index

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The data points are calculated as,

∆(ConsumerP riceIndex) = CP I(M onthn+1) − CP I(M onthn), n = 1, 2, ..., 119.

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Gross Domestic Product

The Gross Domestic Product is the monetary value of all goods and services that are produced in a country over a time period. GDP is simply a measurement of the economic activity in a country. The data used here is the Real GDP, the GDP adjusted according to the inflation. This measure is released on a quarterly basis, hence the same data has been used for the three months occurring during said quarter. The data points are calculated as,

∆(GDP ) = GDP (M onthn+1) − GDP (M onthn), n = 1, 2, ..., 119. (25)

Number of bankruptcies within the industry

This is a value published on a monthly basis, which says how many of the corpo-rations within the transportations industry have gone bankrupt in said observed month. The data used is the 12 month rolling trend, with the data points calcu-lated as,

∆(R12) = R12(M onthn+1) − R12(M onthn), n = 1, 2, ..., 119. (26)

Price per Megawatt Hour

The price per megawatt hour is a good indicator of how large a company’s energy costs will be. The data used for is the spot-price for electricity, which is the price set each day on NordPool, Europe’s leading power market. The data points are calculated as,

∆(P rice) = P rice(M onthn+1) − P rice(M onthn), n = 1, 2, ..., 119. (27)

Fuel Price

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will be. The observed data is the average selling price by pump at a staffed station excluding possible discounts. The data points are calculated as:

∆(F uelP rice) = P rice(M onthn+1) − P rice(M onthn), n = 1, 2, ..., 119. (28)

Exchange Rate USD-SEK

The USD-SEK exchange rate variable explains the observed exchange rates in the observed time period. The data is defined as How many SEK does one get for 1 USD? The data points are calculated as,

∆(U SDExchangeRate) = U SD(M onthn+1) − U SD(M onthn), n = 1, 2, ..., 119.

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The EUR-SEK exchange rate variable explains the observed exchange rates in the observed time period. The data is defined as How many SEK does one get for 1 EUR? The data points are calculated as,

∆(EU RExchangeRate) = EU R(M onthn+1) − EU R(M onthn), n = 1, 2, ..., 119.

(30) Manpower Employment Outlook Survey

The Manpower Employment Outlook Survey is a survey which measures the trends of employment on the job-market. The data is defined as the number of employers who believe that the rate of employment will rise, minus the number of those who believe it will sink. The measure is then adjusted for seasonly variations. This measure is released on a quaterly basis, hence the same data has been used for the three months occuring during said quarter.

Repo Rate

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OECD Index Sweden

The OECD Index is a number of measures weighted together. It is a measure of the business cycle. The leading indicators is a times series which is formed by a number of component indicators that show a fairly consistent relationship with a reference series. The data points are calculated as,

∆(OECDIndexSweden) = OECD(M onthn+1) − OECD(M onthn), n = 1, 2, ..., 119.

(31) Purchasing Manager’s Index

The Purchasing Manager Index measures the business cycle for the Swedish econ-omy. The data is achieved through a collaboration between Swedbank and Silf. A value over 50 indicates growth while a value below 50 indicates a decrease. The data points are calculated as,

∆(P M I) = P M I(M onthn+1) − P M I(M onthn), n = 1, 2, ..., 119. (32)

4.4 Data Collection

All data used is collected for Sweden. The data is collected from January 2007 to December 2016, a time period of ten years. The data is collected from companies as described below:

The response variable: Nasdaq.

The Consumer Price Index, the Gross Domestic Product, and the Number of bankruptcies: Statistiska Centralbyrån.

The Repo Rate and the exchange rates: Riksbanken. The price per Megawatt Hour: Bixia.

The Fuel price: SPBI.

The Manpower Employment Outlook Survey: Manpower Group. The OECD Index Sweden: OECD.

The Purchasing Manager Index: Nordea.

4.5 Original Model

The original, full, model is described as follows,

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where the different variables are,

Variable Name

yi OMX Stockholm Industrial Transportation GI

x1 Consumer Price Index

x2 Gross Domestic Product

x3 Number of bankruptcies within the industry

x4 Price per Megawatt Hour

x5 Fuel Price

x6 Exchange Rate USD-SEK

x7 Exchange Rate EUR-SEK

x8 Manpower Employment Outlook Survey

x9 Repo Rate

x10 OECD Index Sweden

x11 Purchasing Manager’s Index

4.5.1 Heteroskedasticity

The first test to the original model will provide information about whether the model is approved under the main assumptions (see section 2.2 in the Mathemat-ical Theory).

A Normal Quantile-Quantile plot and other plots of the standardized residuals and the density are plotted in R. The plots shows whether the data is Normal distributed, meaning if the model is accepted under the homoskedasticity assump-tion.

4.5.2 Variance Inflation Factor

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4.5.3 Reduction of the Original Model

By performing a F-test, the β-estimates are obtained, as well as p-values, η2-values, and confidence intervals for the coefficients. The values obtained indicate which variables shall be included in the model and which variables may be insignificant. P-value

A large P-value indicates that the null hypothesis is true, hence the variables with larger values than 0.05 are removed from the model.

η2 -value

The η2 -values indicate how much variance a specific variable accounts for in the model. Hence, the variables with low values are removed. The data is computed as,

η2(OriginalM odel) − η2(ReducedM odel). (34) (Cohen 1988)

Adjusted R2

This measure is calculated for each new model, that is every model which is new because one variable has been removed. If the reduced model’s value is higher than the original model’s, the reduced model is better than the original.

Akaike Information Critera

An Akaike Information Criteria test is performed on each variable in the original model. Here each reduced model tested consists of the original model with said variable removed from it. A negative ∆AIC-value indicates that the reduced model is preferred over the original model. The measure is defined here as:

∆(AIC) = AIC(ReducedM odel) − AIC(OriginalM odel) (35) These statistics are valued together, hence a variable that produces a high p-value, a low η2_{-value, a negative ∆AIC-value, and a high adjusted R}2_{-value, is removed}

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4.5.4 Lag of significant variables

When the final model has been found, a test of lagging the variables will be per-formed. This means that the relationship between the response variable is tested against each significant variable for month t − 1 and t + 1 to see whether it is the variable that influences the response variable or if the relationship is the opposite, y = xi(t − 1): the explanatory variable influences the response variable.

y = xi(t + 1): the response variable influences the explanatory variable.

The P-values for the variables in each new fitted model corresponding to,

y = xi(t − 1) + xi(t + 1), t = 1, 2, 3, ..., 119 (36)

is calculated and evaluated to see if any of the variables is more significant than the other.

4.5.5 Model over time

To see whether or not the model remains true for a specific time period within the data evaluated, the data is divided into three parts that each corresponds to a new time-specific model,

• February 2007 - May 2010 • June 2010 - September 2013 • October 2013 - December 2016

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5 Results

5.1 The Original Model

5.1.1 Heteroskedasticity

The Residuals, Normal Quantile Quantile Plot, and the density plot for the original model are displayed below,

Figure 4: The Residuals of the Original Model plotted against the fitted values.

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Figure 6: The Density Plot of the original model.

Looking at these plots, and seeing as the value of skewness for the residuals is -0.55, the assumptions of homoskedasticity are verified.

5.1.2 Model Estimation and VIF

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Table 1: The β-estimates, standard errors, and VIF values for the original model. Variable β -estimate Standard Error VIF

Intercept 1.080e+01 9.291e+00 -CPI -5.028e+00 4.055e+00 1.1215 GDP -2.049e-04 1.898e-04 1.0671 Bankruptcies -1.424e+00 2.154e+00 1.8130 Price per MWh 2.043e-01 6.445e-02 1.0856 Fuel Price 3.281e+01 1.417e+01 1.1682 USD-SEK 4.653e+01 2.943e+01 1.4261 EUR-SEK -8.437e+01 4.021e+01 1.4533 Manpower EOS -2.591e+02 1.695e+02 1.9524 Repo Rate -2.005e+00 4.721e+00 1.9214 OECD Index -2.292e+00 1.564e+00 8.6632 PMI 4.098e+00 2.285e+00 8.2975

The F-statistic for the original model is 3.821 on 11 and 107 Degrees of Freedom. As one can see, the VIF values of the variables OECD Index and PMI are highly correlated. But since the cutoff value for the Variance Inflation Factor, for when one should take actions to reduce the multicollinearity, is 10 - no actions are taken. 5.1.3 Model Reduction

P-values larger than 0.05 indicate that the null hypothesis β = 0 on a significance level 0.05 can not be rejected, hence the variables connected to these values should be removed.

η2 -values lower than 0.01 correspond to variables that provide little variance to the model, hence these variables are removed.

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0.2031, imply that said variable should be removed.

AIC(OriginalM odel) = 1300.695, hence all variables which produce a AIC(ReducedM odel), when said variable is removed contributing to there being a reduced model, that

is equal to or less than this value, will contribute to ∆(AIC) being less than zero. The values corresponding to variables which should be removed according to each criteria are marked in bold in table 2. Reduced Model refers to the original model where the variable in question is removed.

Table 2: The P-values, η2_{-values, Adjusted R}2_{-values, and AIC-values for the}

original model.

Variable P-value η2 _-value _AdjustedR2 _{AIC(Reduced Model)}

Intercept 0.2478 - - -CPI 0.4181 0.0056 0.2043 1300.392 GDP 0.3764 0.0067 0.2070 1299.984 Bankruptcies 0.6509 0.0018 0.2123 1299.180 Price per MWh 0.0112 0.0538 0.1418 1309.381 Fuel Price 0.0069 0.0606 0.1762 1304.513 USD-SEK 0.7317 0.0010 0.1972 1301.443 EUR-SEK 0.0061 0.0626 0.1833 1303.493 Manpower EOS 0.0017 0.0809 0.1984 1301.264 Repo Rate 0.0068 0.0610 0.2142 1298.895 OECD Index 0.7823 0.0007 0.1998 1301.058 PMI 0.4057 0.0059 0.1919 1302.220

The variables that are chosen to be removed are, in this case, the ones which match all the above criterias for being removed; a P-value larger than 0.05, a η2

-value smaller than 0.01 and which produces a reduced model once removed, with an adjusted R2_{-value larger than 0.2031, and an AIC-value smaller than 1300.695.}

These are:

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• Gross Domestic Product

• Number of Bankruptcies in the Industry

5.2 The Final Model

The reduced model becomes,

yi = β0+ β1x1+ β2x2+ β3x3+ β4x4 + β5x5+ β6x6+ β7x7+ β8x8+ ei (37)

where the variables are presented in table 3.

Table 3: The variables and their corresponding data.

Variable Name

x1 Price per MWh

x2 Fuel Price

x3 Exchange rate USD-SEK

x4 Exchange rate EUR-SEK

x6 Repo Rate

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Table 4: The β-estimates, standard errors, and P-values for the reduced model. Variable β -estimate Standard Error P-Value

Intercept 9.9115 9.2674 0.0000 Price per MWh 0.1767 0.0624 0.0005 Fuel Price 30.4332 13.9970 0.0001 USD-SEK 49.9852 29.1321 0.0001 EUR-SEK -91.6865 39.7615 0.0002 Manpower EOS -268.9470 169.5139 0.0000 Repo Rate -2.1448 4.6814 0.0000 OECD Index -2.6447 1.5228 0.0001 PMI 4.1700 2.2684 0.0001

The model can therefore be written as,

y = 9.9115 + 0.1767x1+ 30.4332x2+ 49.9852x3− 91.6865x4

−268.9470x5− 2.1448x6− 2.6447x7+ 2.2684x8.

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5.3 Model Validation

5.3.1 Variance Inflation Factor

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Table 5: The VIF-values for the variables in the reduced model. Variable VIF

Price per MWh 1.0144 Fuel Price 1.1373 Exchange rate USD-SEK 1.3943 Exchange rate EUR-SEK 1.4176 Manpower EOS 1.9478 Repo Rate 1.8844 OECD Index 8.1904

PMI 8.1590

Since both variables OECD Index Sweden and the Purchasing Manager’s Index are still included in the reduced model, there is still some level of multicollinearity present in the model. Both Variance Inflation Factors are less than 10, so no action is taken to remove this.

5.3.2 Adjusted R2

The original model had an adjusted R2_{-value of 0.2031. The final model has an}

adjusted R2_{-value of 0.2063. Since this value is higher than the one for the original}

model, one can conclude that the final model better explains the response variable than the original model does.

5.3.3 F-statistics

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5.3.4 Residual Analysis

In the figure below, the residual and density plots are shown. From the residual plot (Figure 7), it can be seen that the residuals are randomly distributed which implies homoskedasticity,

Figure 7: The Residuals of the Final Model plotted against the fitted values. The skewness of the residuals against the theoretical quantiles (as shown in Fugure 8) is -0.58, which is close to zero, implying homoskedasticity.

Figure 8: The QQ plot of the final model.

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Figure 9: The Density plot for the final model. The conclusion is therefore that the final model is homoskedastic.

5.4 Lag of significant variables

In table 6, the P-values for each new fitted model containing only the response variable and two variables; xi(t − 1) and xi(t + 1) are presented. The values

marked in bold are the values that are less than 0.05 which is the significance level. Values below 0.05 indicate that the corresponding lag variable is significant to the model and correlates with the response variables, which in this case are the original explanatory variables.

Table 6: The P-values for 1-month-lag in different directions. Variable P-value(t+1) P-value(t-1)

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Clearly, the index OMX Stockholm Industrial Transportation is affected by: • Price per MWh

• Fuel Price

• Exchange Rate EUR-SEK

• Manpower Employment Outlook Survey • Purchasing Manager’s Index

For the remaining variables; the exchange rate USD-SEK, the Repo Rate, and the OECD Index, neither the relationship between the xi(t + 1) or xi(t − 1) proved to

be significant under the significance level 0.05, implying that the variables most likely affect OMX Stockholm Industrial Transportation as well as OMX Stockholm Industrial affects said variables.

5.5 Model over time

The different parts of the data,

• February 2007 - April 2010 • May 2010 - August 2013

• September 2013 - December 2016 correspond to three new alternative models.

The reductions of these models are presented in sections 5.5.1, 5.5.2, and 5.5.3. 5.5.1 February 2007-April 2010

The Adjusted R2_{-value for the original model is 0.1062 and the AIC for the original}

model is 467.233, and the values marked in bold in table 7 follow the reduction criterias:

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• Adjusted R2_{-value larger than 0.1062}

• AIC-value smaller than 467.233

Table 7: The P-values, η2-values, Adjusted R2-values and AIC-values for the orig-inal model within the time period February 2007-April 2010.

Variable P-value η2 -value AdjustedR2 AIC(Reduced Model) CPI 0.4517 0.0010 0.1191 466.0566 GDP 0.2682 0.0571 0.0977 467.0161 Bankruptcies 0.6929 0.0008 0.1321 465.4598 Price per MWh 0.2322 0.0350 0.0911 467.3088 Fuel Price 0.4138 0.0341 0.1158 466.2041 USD-SEK 0.0757 0.0024 0.0322 469.8202 EUR-SEK 0.0416 0.1094 -0.0035 471.2696 Manpower EOS 0.4366 0.0636 0.1179 466.1133 Repo Rate 0.3144 0.0341 0.1047 466.705 OECD Index 0.1198 0.0005 0.0577 468.7518 PMI 0.0889 0.0032 0.0413 469.4419

Hence, the least significant variables are the Consumer Price Index and the num-ber of bankruptcies in the industry.

The most significant variable is the Exchange Rate EUR-SEK.

The final model for this time period is presented in table 11 in Appendix. 5.5.2 May 2010 - August 2013

model is 425.6918, and the values marked in bold follow the criterias: • P-value larger than the significance level 0.05

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Table 8: The P-values, η2-values, Adjusted R2-values and AIC-values for the orig-inal model within the time period May 2010 - August 2013.

Variable P-value η2 -value AdjustedR2 AIC(Reduced Model) CPI 0.6736 0.0003 0.4697 423.9499 GDP 0.5544 0.0000 0.4664 424.2000 Bankruptcies 0.5234 0.0486 0.4652 424.2839 Price per MWh 0.0439 0.1351 0.3893 429.597 Fuel Price 0.0052 0.1379 0.3001 435.0499 USD-SEK 0.8747 0.0585 0.4726 423.728 EUR-SEK 0.1091 0.1408 0.4216 427.4249 Manpower EOS 0.2260 0.1370 0.4443 425.8231 Repo Rate 0.3942 0.1872 0.4590 424.7474 OECD Index 0.8635 0.1064 0.4725 423.7348 PMI 0.2159 0.0501 0.4429 425.919

Hence, the least significant variables are Consumer Price Index and the Gross Do-mestic Product.

The most significant variables are Price per MWh and the Fuel price. The final model for this time period is presented in table 12 in Appendix. 5.5.3 September 2013-December 2016

model is 404.643, and the values marked in bold follow the criterias: • P-value larger than the significance level 0.05

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Table 9: The P-values, η2-values, Adjusted R2-values and AIC-values for the orig-inal model within the time period September 2013 - December 2016.

Variable P-value η2 -value AdjustedR2 AIC(Reduced Model) CPI 0.0146 0.0666 -0.0082 411.4099 GDP 0.7138 0.0017 0.1907 402.8409 Bankruptcies 0.1687 0.0264 0.1351 405.4297 Price per MWh 0.9441 0.0142 0.1946 402.6502 Fuel Price 0.0207 0.1234 0.0146 410.5195 USD-SEK 0.3417 0.0075 0.1668 403.973 EUR-SEK 0.1451 0.0094 0.1276 405.7661 Manpower EOS 0.5490 0.0001 0.1838 403.1714 Repo Rate 0.2520 0.0014 0.1539 404.5734 OECD Index 0.7474 0.0466 0.1916 402.7956 PMI 0.2550 0.0661 0.1544 404.5495

Hence, the least significant variables are the Gross Domestic Product, the exchange rate USD-SEK, and the Manpower Employment Outlook Survey.

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6 Discussion

6.1 Method

The use of Linear Regression Analysis is a fairly obvious approach when analyzing which variables in a model are more significant than others and which are less significant for said model.

A large demarcation in this project is that the data used stretches from January 2007 to December 2016, which is a ten-year period. The data used is on a monthly basis, meaning that there are 120 observations being tested. The more observa-tions, the more significant the results could have been, but the variables chosen did not have enough data points available for the observation time period to stretch any further back.

6.1.1 Response Variable

The response variable is performance, meaning that there could be several possible choices for the response variable. Since the thesis is concentrated towards the Industrial Transportations sector, an appropriate index to use as the response variable is OMX Stockholm Industrial Transportation.

6.1.2 Explanatory Variables

All variables that are chosen represent Sweden while many industrial transporta-tion companies are internatransporta-tional. Therefore many more variables could have been included and tested for significance, and would maybe have proven to be signifi-cant. Significant and insignificant variables will be further discussed under section 6.2.2-6.2.3.

Consumer Price Index

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Gross Domestic Product

A high value of the Gross Domestic Product means that the GDP is increasing at a fast pace, hence that big change have happened domestically leading to more products being produced and sold - including within the Industrial Transportation sector. One can argue that the Gross Domestic Product for big industrial coun-tries would possibly be interesting variables to analyze as those values of GDP may impact the import and export of produced goods, but since it is very difficult to decide which countries that would be included and which would be excluded - this thesis focuses on what is known, which is that Sweden is affected. This decision is also supported by the fact that the OMX Stockholm Industrial Transportation Index is made up of only Swedish companies.

The data for the Gross Domestic Product is only available on a quarterly basis, hence a monthly based data could have resulted in a difference of the significance of the variable, especially for the time period models.

Number of bankruptcies within the industry

The high number of bankruptcies within the industry indicates that it is hard for companies within the industry to survive. However, since there is no linear rela-tionship between the observations for this variable, one can argue how significant this variable could possibly be.

Price per Megawatt Hour

For big industrial companies, the price for energy is very important since a lot of energy is used. A high price means that the companies’ margins become smaller while a low price means that margins grow bigger. This variable proved to be significant for both the time period 2010-2013 and for the final model.

Fuel Price

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Exchange Rate USD-SEK

Since a lot of companies have parts of their operations abroad, the exchange rate USD-SEK is an interesting variable to observe, simply based on that imports be-come more expensive at a higher exchange rate.

Exchange Rate EUR-SEK

The exchange rate EUR-SEK is included in the original model for the same rea-sons as the Exchange Rate USD-SEK. This variable proved to be significant for the time period 2007-2010 and the final model.

Manpower Employment Outlook Survey

The Manpower Employment Outlook Survey is simply a survey. This means that the observed data points are guesses of what the future will look like from the perspective of the observed quarter. This variable therefore needs to be analyzed with great suspicion, especially in the time-restricted models since the number of observations per variable becomes small.

Repo Rate

The Repo Rate is the rate at which banks lend money from the central bank. One can argue that a more interesting rate to analyze would be the lending rates at which companies can lend money from general banks at, since that rate is what affects the companies directly. However, the lending rates are based on the repo rate and therefore, there should not be a difference in the basis of relationship between the two of them and the response variable.

OECD Index Sweden

The OECD Index Sweden is one of the most interesting variables to look at, as it includes a large number of information sources and therefore can be a measure of the business cycle.

Purchasing Manager’s Index

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and the analysis has to be done with consideration to this. The PMI may be looked at as measure of the business cycle. This variable proved to be significant for the final model.

6.1.3 Model Reduction

All variables in the original model which showed a negative ∆(AIC), a large ad-justed R2-value, a large η2-value, and a p-value lower than 0.05 were removed, as presented in table 2.

The Exchange Rate USD-SEK showed a large p-value and a small η2-value. It did not however meet the AIC- and Adjusted R2 criterias for reduction, meaning that the reduced model was not better than the original according to these mea-sures, and was therefore not removed.

For the variable OECD Index, the same reasoning was used as for the variable Exchange Rate USD-SEK.

The Repo Rate showed a large Adjusted R2-value and a small AIC-value (re-sulting in a negative ∆(AIC), but did not show that it had a small p-value nor that it only contributed a small part of the variance of the original model.

Hence, all variables that were removed from the original model were implied by all model reduction methods that they should be removed. The reasoning for the three variables above to not be removed is that they according to at least one statistical measure proved to be important to the model.

6.2 Results

6.2.1 Model Validation Micronumerosity

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regarding the approach of the analysis. Endogenity

There may be an underlying problem of endogenity in the model as an explanatory variables may be correlated with the error term. The problem of endogenity may also be recognized as missing variables, hence that not all variables which would explain the response variable are included in the original model. Since the per-formance of Industrial transportation companies is most likely affected by more factors than the ones in the original model, this may be a problem. The problem may also have arisen due to measurement erros.

6.2.2 Model over time

These results must be regarded with carefulness as the number of observations per model is only 40 and the relationship between the number of observations and the number of variables therefore is only 3.6.

February 2007 - April 2010

The reduction results of this time period are presented in table 7 in section 5.5.1 and the final model is presented in table 11 in appendix.

This period was heavily affected by the financial crisis that was going on all across the world. The global crisis 2007-2008 is considered to be the worst financial crisis since the great depression in the 1930:s. The crisis is assumed to have started in the United States. As the crisis in the United States grew bigger, the Dollar value grew. This was an effect from the United States Central Bank having to adjust the interest rate as described in section 3.1.1 in Economic Theory.

2008-2009 is described as the time period for the Swedish financial crisis, that is, when the financial crisis started to severely affect Sweden.

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Crisis which began in 2009, where several European countries’ financial institu-tions collapsed.

The Euro grew stronger in this time period and in the historic data, one can see that March 2009 showed a EUR-SEK exchange rate of 11.2 compared to to-day’s rate of circa 9.5 and the rate of December 2006 which was circa 9.0.

As a lot of large Swedish industrial companies have at least parts of their pro-duction process outside the Swedish borders, the exchange rate will of course affect the price of their imported components and products and hence greaten the production costs for the company as a whole. Therefore it is not strange that the Exchange Rate EUR-SEK is significant during this time period.

As the Euro grows, SEK shrinks compared to the Euro. This means that the export will grow larger since it will be cheaper for people in Euro-countries to buy products from Sweden. Even though many components may be ordered from abroad, implying that the importing costs rise, the demand for Swedish products grew larger.

During 2007-beginning of 2008, the inflation was fairly high. In 2009 and 2010, the inflation had stagnated. The inflation of course affects how much companies can sell their products for as well as what they will have to pay for their components. One can interpret the result of this varible being insignificant as that the normal 2 percent inflation rate shows no importance in the model, and since the period of high inflation was shorter than the period of a two percent inflation in the time period 2007-2010, the impact of just the high inflation is hard to observe.

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if the number of bankruptcies in Sweden should not be seen as an indication of the number/percentage of bankruptcies that the financial crisis caused globally. Active monetary policy most likely affected both the inflation (represented in the Consumer Price Index) and the number of bankruptcies. To prevent the number of bankruptcies to grow, the state may have offered financial aid to help save com-panies, as well as the inflation is adjusted using the interest rate.

May 2010 - August 2013

The reduction results of this time period are presented in table 8 under section 5.5.2 and the final model is presented in table 12 in appendix.

In 2011, the last American soldiers left Iraq. Violence in Syria and Sudan also caused disturbance in the market. During the period Mid 2010- Mid 2013, many oil countries’ politics changed and several of these countries went into war. This strongly affected the oil market and the oil price rose tremendously. From the pre-vious selling price in Sweden of circa 12 SEK to circa 15 SEK, there is no wonder that the cost of transportation grew.

Especially for the transportation sector, the cost of fuel strongly affects businesses. A high cost for fuel makes the doubtful consumer seek other options than buying new vehicles.

Of course, the fuel price also affects the transportation costs for the companies themselves. If the routes for their components and products from raw material to complete are long, the fuel price will affect the companies even more.

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SEK/MWh, the lowest price in the last decade.

Whether the price is at an extreme high or at an extreme low, the energy price clearly affects the production decisions of many companies. One of Industrial Companies’ biggest costs is their energy cost, since so much energy is needed to produce the products. When the energy prices are low, they can afford to produce more, and when the energy costs are high, they may have to lower their production rate. However, in an uncertain market, the companies which are largely affected by the energy price, most likely decide to produce less in order to make sure that their marginals are met.

As in the time period 2007-2010, monetary policies are in effect to keep the in-flation around its two percent goal, and therefore the inin-flation, and hence the consumer price index, does not affect the model significantly.

There can be many reasons to the Gross Domestic Product not being a signifi-cant variable in 2010-2013. Most likely, the uncertainty and unevenness of the fuel price and energy price caused many companies to take a step back and not make large expansion decisions. Another aspect of the Gross Domestic Product variable is that it is collected quarterly, hence only 13 data points are observed in this time period. If more data points had been collected there might have been a different result showing that the variable was more significant, hence the data may be too unspecific.

The Adjusted R2_{-value for this time period proved to be a lot higher than the}

ones for the two other time periods. This can be explained by which factors are significant. Most likely this time period reflects the final model better than the other two time periods.

September 2013 - December 2016

The reduction results of this time period are presented in table 9 under section 5.5.3 and the final model is presented in table 13 in appendix.

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fuel price was still affected under the same reasoning as in the previous time pe-riod. Transportation costs are therefore still expensive, as well as the consumers may seek other choices than buying new means of transportation.

In 2014 and 2015, the inflation rate was extremely low. In 2016 it started ris-ing again but it was still low. The price increase for services which for the last 15 years have been around two percent, have since 2013 sunk. The explanation for this is that the weak demand-situation has caused the companies to not be able to raise their prices according to their cost increases.

The low inflation therefore has caused companies to have to lower their cost sup-plement charge, which of course affects their marginals and therefore their produc-tions.

Since the fuel price is one of the most significant variables, it is fairly odd that the exchange rate USD-SEK is not. The insignificance may on some level be explained by the fact that the United States is not one of the countries from which Sweden imports most from (it ranks outside the top 10).

Regarding the Gross Domestic Product being insignificant, the same reasoning is used as for 2010-2013; the market uncertainties make the companies not explore new production opportunities nor may the data be significant enough for this to be a correct result of the analysis.

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6.2.3 The Final Model

Looking at the analyses of the three different time periods ranging from 2007-2016, the final model is already quite self-explanatory.

The significances of the three variables Fuel Price, Price Per MWh, and the Ex-change Rate EUR-SEK are results of the big economic happenings during the decade. The insignificance of the Gross Domestic Product may be explained by the lack of observations or market uncertainties. The insignificance may be ex-plained by the inflation rate target.

The final model showed a fourth variable as significant; the Purchasing Man-ager’s Index. None of the analyzed time period models picked it up as neither significant nor insignificant, meaning that some model reduction methods wanted to delete it for all time periods, while other model reduction methods wanted to keep the variable for all time periods. The fact that it showed up as significant for the final model means that the results of the survey very much correlate with the performance of Industrial Transportation companies within this decade, that is; the survey has proved to be correct looking at the decade as a whole while it for specific time periods may have been incorrect and therefore does not show up in the time limited models. The case may also be that the number of observations in each time limited model was too small, and that the larger number of observations in the final model gave the variable its rightful place.

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exports as the United States is Sweden’s third largest countries to export to. The cheaper the SEK, the more the demand for Swedish products increase.

The non-conclusive result of the time lagging may also mean that the variables are in case non significant for the model at all. Non-proved significance for nei-ther the +1-month lag nor the -1-month lag may mean that the variable in fact is not significant at all. This problem then has to do with the methodology of the thesis, that only the variables which are called out by all reduction methods to be reduced, are actually reduced. A better approach of this study could have been to include lagged version of the explanatory variables in the original model to see if they showed significance for the model to begin with.

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7 Conclusion

All final models, for the complete decade and the partial models, are presented in appendix (section 7.1.1-7.1.4) for a better overlook for the reader.

In conclusion, the final model provides a better approximation of the development in the Industrial Transportation index than the original model does. Neverthe-less, it is shown that which variables, that the final model consist of, change when the time-period is divided into smaller parts. In the defined three-year intervals, different variables constitute the model. This can be explained to some extent by macroeconomic factors but also by the complexity of the model as a whole. Creating a model to approximate the trend in the Industrial Transportation index is complex. To improve the model, the scope of the project needs to be enlarged so that a larger number of variables and data is processed.

For Nordea Global, this study is relevant for managing their portfolios. Observing what is happening in the world, one can see which variables should be important in the model and base their assumptions on this.

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Mukherjee. T and Naka. A. Dynamic relations between macroeconomic vari-ables and the japanese stock market: An application of a vector error correction model. Journal of Financial Research, 18(2):223–37, 1995. URL http://EconPapers.repec.org/RePEc:bla:jfnres:v:18:y:1995:i:2:p:223-37. Kurkiewicz D Williams M.N, Gómez Grajales C.A. Assumptions of Multiple

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7.1 Appendix

7.1.1 Table 10: Final Model 2007-2016

Table 10: The variables and their corresponding data.

Variable Name

x1 Price per MWh

x2 Fuel Price

x3 Exchange rate USD-SEK

x4 Exchange rate EUR-SEK

x6 Repo Rate

Table 11: The variables and their corresponding data in 2007-2010.

Variable Name

x1 Gross Domestic Product

x2 Price per MWh

x3 Fuel Price

x7 Repo Rate

x8 OECD Index

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Variable Name

x1 Number of Bankruptcies

x2 Price per MWh

x3 Fuel Price

x7 Repo Rate

x8 OECD Index

Variable Name

x1 Consumer Price Index

x2 Numer of Bankruptcies

x3 Price per MWh

x4 Fuel Price

x6 Repo Rate

x7 OECD Index

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Macroeconomic factors that correlate with the performance of Industrial Transportation Companies

Macroeconomic factors that

correlate with the performance of

Industrial Transportation

Companies

A study using multiple linear regression

OSCAR WIJKSTRÖM

SOFIA ÖHMAN

Macroeconomic factors that

correlate with the performance of

Industrial Transportation

Companies

A study using multiple linear regression

OSCAR WIJKSTRÖM

SOFIA ÖHMAN

Contents

1

Introduction

1.1

Background

1.2

Aim

1.3

Research Questions

2

Mathematical Theory

2.1

The Multiple Linear Regression Model

2.2

Assumptions

2.3

Ordinary Least Square Estimation

2.4

Possible Errors

2.5

Model Evaluation

3

Economic Theory

3.1

The macroeconomic perspective

4

Methodology

4.1

Previous Knowledge and Software

4.2

The trend of data points

4.3

Variable selection

4.4

Data Collection

4.5

Original Model

5

Results

5.1

The Original Model

5.2

The Final Model

5.3

Model Validation

5.4

Lag of significant variables

5.5

Model over time

6

Discussion

6.1

Method

6.2

Results

7

Conclusion

References

7.1

Appendix