Trading corn futures: the linear and nonlinear dynamics in light of the upcoming U.S. presidential elections

U

NIVERSITEIT VAN

A

MSTERDAM

M

ASTER

T

HESIS

Trading corn futures: the linear and

nonlinear dynamics in light of the

upcoming U.S. Presidential elections

Author:

M.M. M

IDDELWEERD

stud.nr. 10001301

Supervisor:

Prof. Dr. C.G.H. D

IKS

A thesis submitted in fulfillment of the requirements

for the degree of MSc Financial Econometrics

in the

Faculty of Economics and Business

iii

UNIVERSITEIT VAN AMSTERDAM

Abstract

Faculty of Economics and Business

MSc Financial Econometrics

Trading corn futures: the linear and nonlinear dynamics in light of the

upcoming U.S. Presidential elections

by M.M. M

IDDELWEERD

stud.nr. 10001301

This paper covers the dynamics of the corn industry by exploring the

lin-ear and nonlinlin-ear relationships between the price of corn futures, its main

drivers, and factors determining the U.S. political landscape, such as the

type of political administration in the White House and the presence of a

political gridlock. A thorough causality analysis through both the Linear

Granger Causality test and the nonparametric Diks-Panchenko test reveals

that there is no evidence for the existence of direct, persistent causal

rela-tionships between the price of corn and either the party of the President

or the presence of a political gridlock. With the U.S. Presidential elections

coming up in November, 2016, this study proves that it will instead be more

important to focus on the actions of the Federal Reserve when trading in

corn futures.

Keywords: nonparametric Granger causality nonlinear dynamics

General Additive Model representations corn futures Presidential elections

-Federal Reserve monetary policy

v

Statement of Originality

This document is written by Mees M. Middelweerd who declares to take

full responsibility for the contents of this document. I declare that the text

and the work presented in this document is original and that no sources

other than those mentioned in the text and its references have been used in

creating it. The Faculty of Economics and Business is responsible solely for

the supervision of completion of the work, not for the contents.

vii

Contents

Abstract iii Statement of Originality v 1 Introduction 1 2 Literature Review 3 Corn Price . . . 3

U.S. Political Climate . . . 3

Performance of the Economy . . . 4

U.S. Monetary Policy . . . 5

Weather . . . 5

U.S. Production of Ethanol . . . 6

International Competition . . . 6

3 Theoretical Background 9 Augmented Dickey-Fuller test . . . 9

Information Criteria . . . 10

Johansen Cointegration test . . . 10

Linear Granger causality test . . . 11

Nonparametric Diks-Panchenko test . . . 12

GARCH-BEKK filtering . . . 13

General Additive Models . . . 13

Vector Auto Regression forecasting. . . 14

4 Data and preliminary analysis 17 Corn Price . . . 17

U.S. Political Climate . . . 18

Performance of the Economy . . . 19

U.S. Monetary Policy . . . 19

Weather . . . 20

U.S. Production of Ethanol . . . 20

International Competition . . . 20

5 Empirical Results 23 Linear Granger Causality relations . . . 23

Nonparametric Granger Causality relations. . . 24

GAM Representations of Nonlinear Linkages. . . 28

VAR Forecast on Corn . . . 29

6 Conclusion 33 7 Discussion 35 A Time series 37 References 47 Books . . . 47 Articles . . . 47 Other . . . 48

1

Chapter 1

Introduction

Since 1945 the yearly returns of the Dow Jones Industrial Average have been 8.5% under a Democratic President, whereas under a Republican administration it has been only 6% (Santa-Clara and Valkanov, 2003). However, the best stock market performance in history was during the presidential term of the Republican Ger-ald Ford (Long, 2016). In November, 2016, the U.S. presidential elections will be held and already investing reports are starting to speculate on the relationship be-tween the outcome of the elections and stock market returns. Clearly, being able to predict the next price movement can be valuable to a trader. Just as well, traders in the commodity markets will want to take a preliminary view pending the pos-sible change in the political climate of the United States of America in less than four months. Nevertheless, not much research has been done determining the correlations and causal linkages between the U.S. political climate and the com-modity markets. Rix Hufman (comcom-modity trader Cargill) declares in an interview that recently Cargill has seen fund positions on the Chicago Mercantile Exchange (CME) futures reaching record sizes and that the markets seem to be moving fur-ther away from fundamental supply and demand dynamics. Hufman has noticed that as money got cheaper due to lower interest rates it seems that money has been moving from bonds to other markets, including agricultural commodities. This in turn has brought more volatility to the markets. Hufman concludes that this has made it a more challenging environment for the traditional trading houses, such as Cargill, that rely on solid fundamental analysis.

The agricultural industry attributing to the gross domestic product with 835 billion dollar in 2014 (USDA, 2016) supports the hypothesis that U.S. politics and the agri-cultural market are intertwined. This research will focus on the corn market, as the U.S. is the worlds largest producer, exporter, and consumer of corn. Because the futures markets provide an efficient price discovery mechanism (Bekiros and Diks, 2008), this research will explore the lead-lag causal relationships between the price of a corn futures contract, the key drivers of the corn market, and factors that de-termine the political climate. Moreover, inspired by the research of Beyer, Jensen, and Johnson (2004) the influence of the monetary policy of the Federal Reserve will be taken into account as well. Applying both the Linear Granger Causality test and the Diks-Panchenko test, the lead-lag relationships will be explored. On the basis of those results, one can be able to describe the dynamics within the corn market more accurately. In the end, the objective of this paper is to provide the reader with a better understanding of these dynamics to anticipate changes in the corn market caused by the upcoming Presidential elections in November, 2016. The remainder of this paper is structured as follows. Chapter 2 will discuss the variables included in this research and their relation to the corn market, based on economic theory. Chapter 3 will provide a theoretical background in which all of the econometric tools used for this research are explained. Here, amongst others, the theoretical framework for the Linear Granger Causality test and the Diks-Panchenko test are discussed. In Chapter 4, the data will be described and a preliminary analysis will be done to get an overall better feel of the dynamics of the time series used in this study. Then, in Chapter 5 the results will be presented

2

Chapter 1. Introduction

and conclusions will be drawn in Chapter 6. Finally, some suggestions for further research in order to unravel the dynamics of the corn market even more are listed in Chapter 7.

3

Chapter 2

Literature Review

In this research the influence of the political climate in the U.S. on the price of a corn futures contract will be examined. In order to accurately describe the role of the U.S. political climate, other factors such as the performance of the economy, the U.S. monetary policy, weather, the nation’s production of fuel ethanol, and the international competition within the corn industry are taken into account as well. In the following paragraphs the importance of each of these variables will be explained more thoroughly. Based on economic theory, their relation to the price of a corn futures contract will be clarified.

Corn Price

With 90.6 million acres of planted crop area, corn is the largest crop in the United States of America. Being not only the worlds largest producer of corn, but also its largest exporter and consumer makes the U.S. an influential player in the global corn market (ETF, 2015). Because of the wide scope of products corn is used for, trading in the corn market is appealing. The corn market can be split up into two segments: physical trading and derivatives. A commonly used derivative is a futures contract. In a corn futures contract for example, two parties agree to buy and sell a certain amount of corn for a price agreed upon today. Engaging in a futures contract is an effective way to hedge against future price changes. Although seemingly modern, the agricultural futures contracts have been in use for more than 170 years (Olsen, 1923). Nowadays, the futures markets prove to be an efficient price discovery mechanism. The largest corn futures exchange in the world is the Chicago Board of Trade (CBOT). The futures traded at the CBOT are based on corn produced in the U.S. Therefore, the U.S. plays an important role in determining the fair price of a corn futures contract.

U.S. Political Climate

The U.S. political climate comprises two variables: the political color of the White House and the presence of a political gridlock.

White House

In November 2016 the U.S. Presidential elections will be held, determining which political party will be seated in the White House for the next four years. In one of their client notes (2012), Goldman Sachs stress to take political elections seri-ously. They argue that the political stakes in Presidential elections often translate into changes in policies that might reshape the economic environment. Moreover, these changes increase political and social uncertainty, which in turn will affect the economy. Extensive research has been done to determine to what extent the

4

Chapter 2. Literature Review

elections influence the economy, and more specifically the stock market. Santa-Clara and Valkanov wrote in 2003 a paper on this subject, which has been cited fre-quently ever since. In their work they found that, when a Democrat has been in the White House, the average return for the Dow Jones Industrial Average (DJIA) has been around 8.5%, whereas for Republicans the average lies around 6%; implying 9% higher stock market gains for large stocks in times of Democratic administra-tions. However, according to Blackrock’s CFA Russ Koesterich (2012), Santa-Clara and Valkanov failed to adjust for the market volatility. Adjusting the average re-turns for the market volatility, the stock market performance during a Democratic administration has been the same as when a Republican took seat in the White House. Koesterich’s position on this subject is in line with the findings of Nieder-hoffer, Gibbs, and Bullock (1970). In their paper, they documented the changes of the DJIA, adjusting for market volatility, before and after election for eighteen Presidents from 1900 through 1968, reaching to the conclusion that the stock mar-ket performance during Democratic and Republican administrations do not differ systematically. However, Udland (2015) states that besides the DJIA returns, the market volatility is subject to political influences as well. Therefore, in his consid-ered opinion, adjusting for market volatility may polish away the political party affiliated differences in returns.

Political Gridlock

The second element that the U.S. political climate comprises is the possible pres-ence of a political gridlock. A political gridlock refers to the situation where two legislative houses are controlled by different political parties. In particular, for the U.S., a political gridlock is lifted when both in the House of Senate and in the House of Representatives the political party of the President has a majority. Under a state of political gridlock there is difficulty passing bills, seriously limiting the power of the sitting President. According to Beyer, Jensen, and Johnson (2004), the rationale that links the presence of a gridlock to the financial market is that fiscal policy interventions are more likely to occur under political harmony than when a gridlock is present.

It will be interesting to explore the interrelations between the corn market and the political climate in the U.S. as not a lot of research has been done on this subject.

Performance of the Economy

In this paper, the state of the economy is measured through two variables: the rate of unemployment and the gold price.

The rate of unemployment

The primary source of personal income in the U.S. is employment. Employment is said to be a major influence on consumer spending and overall economic growth of a country. Adding the unemployment rate as a dependent variable to the model will provide insightful information about the health of the U.S. economy. Although a corn futures contract and the rate of unemployment seem unrelated at first sight, David Kohl (2009) refers to the United States Department of Agriculture (USDA) statistics which indicate that over 70% of American crop producers are reporting non-farm income on their tax return. Kohl (2009) proclaims that the livelihood of mid-sized farms and smaller producers can be negatively affected through loss of off-farm employment, which may in turn decrease the production of corn. A decrease in supply, will be reflected in an increase of the price of a corn futures contract. Moreover, the rate of unemployment can be treated as a variable heavily influenced by politics, as it is one of the key economical indicators a President can be judged on. Therefore, the possible impact of the rate of unemployment can be seen as a indirect effect of the political climate on the price of a corn futures contract.

Chapter 2. Literature Review

5

Gold price

Historically, the gold price reacts to political and financial uncertainty. Gold is said to be a safe haven in times of turmoil, moving as a counter cyclical asset. Thus, increasing gold prices are an indicator of a downturn in the economy. And, whenever the economy is prospering, traders will tend to sell their gold in order to invest in more profitable assets.

However, gold’s role as a haven investment in uncertain times has dwindled lately (MacDonald and Shumsky, 2015). In their article, MacDonald and Shumsky (2015) present that the gold price has been fluctuating, because of shifting expectations about when the Federal Reserve will alter the interest rates. Expectations for an increase in interest rates have slumped the gold price, because gold is treated as an investment paying zero interest. Whereas the announcement that the Federal Reserve will postpone an increase in interest rates, did drive the gold price up. All in all, for this research, the gold price can historically still be seen as measure of the overall performance of the economy. Yet, one needs to keep in mind that statistics have shown that recently gold behaves more and more as any other asset, diminishing its role as a safe haven.

U.S. Monetary Policy

According to The Federal Reserve System: Purposes and Functions (2005) the Federal Reserve has two main goals: stabilizing prices and promoting output and employ-ment. With respect to economic conditions, the chairman of the Federal Reserve has been identified as the second most powerful person on earth (Beyer, Jensen and Johnson, 2004). Besides, in the interview with Hufman (commodity trader at Cargill), it became clear that the actions of the Federal Reserve can cause the money to move away from bonds to other markets, such as the agricultural markets. To incorporate the effects of such an influential body, the discount rate, which is one of the main tools of the Federal Reserve, is therefore included in this research. Kevin Grier (2008) even goes a step further by claiming that the actions of the Fed-eral Reserve are influenced by political pressure. Grier states that “the idea that the Federal Reserve is divorced from politics and real world affairs and conducts matters from an ivory tower setting is more of a myth than a reality”. The indirect effect of the political climate through the Federal Reserve attributes to the fact that the discount rate has to be taken into account for this study.

Weather

In general, the prices of agricultural products are heavily depended on the weather, as the amount of production of crop is directly related to its price. Specifically for corn, severe drought will deliver stress to the crop resulting in a lower yield. Reuters (2012) reported that Goldman Sachs raises its prices for corn in case of worsening drought forecasts. These drought forecasts are quantified with use of one of the Palmer Drought Indices. According to Palmer (1965), a drought period is defined as “an interval of time, generally of the order of months or years in dura-tion, during which the actual moisture supply at a given place rather consistently falls short of the climatically expected or climatically appropriate moisture sup-ply”. Thus, the Palmer Drought Indices measure the balance between moisture demand and moisture supply. In this research the Palmer Drought Severity Index (PDSI) is used, as the National Oceanic and Atmospheric Administration (NOAA) express their findings in this particular index. The NOAA defines the PDSI as a measure of the current month’s cumulative moisture integrated over the last sev-eral months. Furthermore, most of the corn is being produced in the Midwestern states of the U.S.: Iowa, Illinois, Indiana, Southern Michigan, Western Ohio, East-ern Nebraska, EastEast-ern Kansas, SouthEast-ern Minnesota, and Missouri. Together they

6

Chapter 2. Literature Review

comprise the Corn Belt. Therefore, this research includes the historical data on the PDSI for the Corn Belt, gathered by the NOAA.

Moreover, Lobell (2014) states that corn yields have become more sensitive to drought conditions over the past two decades and are likely to grow even more sensitive, despite cultivar improvements. It is therefore interesting to examine the presence of causal relations between the price of a corn futures contract and the PDSI, as in the near future these influences might even become more important.

U.S. Production of Ethanol

As mentioned earlier, corn is the base for a variety of products and has a number of different uses in seed, food and industry. Table 2.1 indicates that in the U.S. corn is used the most for the production of ethanol.

Corn: Seed, Food, and Industrial uses

2012/2013

2013/2014

2014/2015

Ethanol

4641.13

5133.72

5250.00

HFCS*

491.49

477.56

490.00

Glucose & Dextrose

291.92

306.97

290.00

Starch

249.39

218.73

250.00

Alcohol

140.00

140.43

141.71

Cereals & others

199.42

200.51

200.07

Seed

24.58

23.00

23.22

Source: With corn swimming in supply, a difficult market gets no relief (ETF, 2015)

The amount of corn used is measured in million bushels. * HFCS: High Fructose Corn Syrup

TABLE2.1: Usage of Corn

In turn, the ethanol industry contributes significantly to the well-being of the U.S. economy through several ways, amongst others: accounting for 52.7 billion dollars of the GDP, responsible for 10.3 billion dollars in taxes, and creating around 400,000 direct and indirect jobs (RFA, 2016). Therefore, when examining the effect of the political climate on the price of a futures contract for corn, it is insightful to take into account the indirect effect of corn on the economy through the production of ethanol.

International Competition

Lastly, as corn futures are traded globally, the international competition is taken into account as well in this study. Therefore, the influence of Brazil, being the world’s second largest exporter of corn, cannot be neglected (Newman and Bunge, 2016). They state that changes in currencies, shipping fees and railroad rates have combined to produce an unexpected result: importing corn from other countries like Brazil can be cheaper than buying it from the Corn Belt.

However, according to the United States Department of Agriculture (USDA) ex-ports account for a relatively small share of demand for U.S. corn - less than 15 percent – and imports still remain a very small part of the U.S. corn market. There-fore, the influence of the Brazilian corn export on a corn futures contract, if any, may be small.

All in all, each of these variables influence the corn market in one way or another. This research will try to capture these influences in terms of Granger Causality

Chapter 2. Literature Review

7

relations. By taking into account these relations, one will be able to extract and describe the specific effect of the U.S. political climate on the price of a corn futures contract more accurately.

9

Chapter 3

Theoretical Background

In pursuance of testing the existence of linear and nonlinear causal lead-lag rela-tionships between the price of corn and the U.S. political climate, the performance of the economy, monetary policy, weather, the production of ethanol and the in-ternational competition, a theoretical framework is needed. First of all, the data is tested for the presence of unit roots with the augmented Dickey-Fuller (ADF) test. Secondly, the Johansen Integration test is applied to detect and correct for pos-sible cointegration between variables. The existence of cointegration determines whether a Vector Auto Regression (VAR) or a Vector Error Correction (VEC) model will be used. After estimating a VAR or a VEC model, the linear Granger Causality test is applied. Filtering the return series, the residuals are examined by the non-parametric Diks-Panchenko test to determine the nonlinear relationships among the time series. Furthermore, a Generalized Additive model (GAM) is estimated to visualize the structure of these causal relationships. Lastly, VAR forecasting will be used to predict what will happen with the price of corn one year from now, based on the historical data and conditional on the linear and nonlinear Granger causality relations this study tries to capture.

Augmented Dickey-Fuller test

The augmented Dickey-Fuller test is a formal test for stationarity. It sets off its null hypothesis of an Autoregressive Integrated Moving Average (ARIMA) against stationarity. The ADF test is based on the following model

φ(L)yt= α + ηt, (3.1)

where the AR-polynomial φ(z)=1 - φ1z -. . . - φlzl has degree l. yt can be either stationary or integrated of order 1. The null hypothesis of a stochastic trend corre-sponds to the case when ytis integrated of order 1. Then the AR polynomial φ(z) should have a unit root so that φ(1)=0. Financial time series are often best specified by an ARIMA model; factorizing the AR polynomial as φ(z) = (1-z)ψ(z), will turn ytinto an ARIMA process. In case all the roots of φ(z) = 0 lie outside the unit circle (i.e. φ(z) = 0 has no solutions for z<1), φ(1) has to be greater than 0. This implies that ytdoes not have a unit root. Thus, the Dickey-Fuller testing problem can be formulated as follows:

H0: φ(1) = 0 H1: φ(1) > 0, with φ(1) = 1 -Pl

k=1φk. According to Heij et. al (2004), the formulated hypotheses can be rewritten using the polynomial ψ(z) = φ(z) - ψ(1)z so that ψ(1)=0 and ψ(z) can be factorized as ψ(z) = (1-z)ρ(z), with ρ(z) = 1 - ρ1z - . . . - ρ(l-1)z(l-1) being a polynomial of degree (l − 1). Then, defining ρ = −ψ(1), the polynomial φ(z) can be written as φ(z) = −ρ z + (1-z) - (1-z)Pl−1

10

Chapter 3. Theoretical Background

rewritten as follows

∆yt= α + ρyt−1+ ρ1∆yt−1+ . . . + ρp-1∆yt−(p−1)+ ηt. (3.2) Now, with ρ = -φ(1), the testing problem can be formulated in terms of the ADF-test:

H0: ρ = 0 H1: ρ < 0.

This can be tested with use of a one-sided t-test. The null hypothesis is rejected if the t-statistic falls below the relevant negative critical value. The one-sided critical values are stated in Exhibit 7.16 (b) in the work of Heij et. al (2004).

Information Criteria

When implementing the ADF test or estimating a VAR or VEC model, an impor-tant practical issue is the specification of the lag length l, because the dynamic properties of a model depend critically on the lag order. If l is chosen too small, the remaining serial correlation in the errors will bias the estimate. However, in-cluding a large number of lags adversely affects the power of a test. There are two commonly used pre-specified criteria to select the lag order: the Schwarz Infor-mation Criterion (SIC) and the Akaike InforInfor-mation Criterion (AIC). According to Ivanov and Kilian (2005), the AIC tends to produce the most accurate estimates when dealing with monthly data, whereas the SIC is more accurate for sample sizes smaller than 120. Therefore, in this research the order of lags is determined using AIC.

Johansen Cointegration test

Already in 1982, Nelson and Plosser pointed out that the presence of unit roots give rise to stochastic trends, opposed to pure deterministic trends. Granger (1981) found out that a vector of variables, all which are stationary after differencing, could have linear combinations which are stationary in levels. This property is denoted as cointegration. Thus, the presence of non-stationarity may lead to coin-tegration which in turn may result in spurious regressions that suggest long-term relationships even when there are none. It is therefore important to test for coin-tegration when dealing with non-stationary time series. Johansen’s methodology to test for cointegration starts off with a VAR model of order l (determined by the AIC):

yt= α + A1yt−1+ . . . + Alyt−l+ ηt, (3.3) where ytis a m x 1 vector of variables that are integrated of order one and ηta mx 1 vector of error terms. Taking first differences, this can be rewritten as

∆yt= α + Πyt−1+ l−1 X i=1 Γ∆yt−i+ ηt, (3.4) with Π = Pl i=1Ai− I and Γi = − Pl

j=i+1Aj. When the variables in ytare all stationary, implying all eigenvalues lie within the unit circle, the determinant of Π is unequal to zero so that Π has full rank. If the matrix Π has reduced rank r < m then there exist (m x r) matrices υ and ζ such that Π = υ(ζ)T _{and (ζ)}T_y

tis station-ary (Hjalmarsson and Osterholm, 2007). r denotes the number of cointegrating relationships, υ represents the adjustment parameters in the VEC model and ζ is

Chapter 3. Theoretical Background

11

the cointegration vector. In case of a 2 x 2 matrix with ¯yt= (yt, xt), this will look like

υ1 −θυ1 υ2 −θυ2 

= υζ0.

Then the VAR(1) model becomes

∆xt= υ1(ζ1yt−1− ζ2xt−1) + ηx,t

∆yt= υ2(ζ1yt−1− ζ2xt−1) + ηy,t. (3.5) Hjalmarsson and Osterholm (2007) state that, for a given r, the maximum likeli-hood estimator of ζ defines the combination of yt−1that yields the r largest cor-relations of ∆yt with yt−1 after correcting for lagged differences. The Johansen integration test proposes two different likelihood ratio test to examine these corre-lations: the trace test and a test based on the maximum eigenvalue. In this research the Johansen trace test is used:

LR(r) = −(n − l) m X

i=r+1

log(1 − ˆλi), (3.6)

with n denoting the sample size, l the lag length, and ˆλithe ithlargest correlation. The test tests the null hypothesis: rank(Π) = r against rank(Π) ≥ r + 1, starting with r = 0. When the null hypothesis is not rejected, the new hypotheses of interest become H0: rank(Π)=1 against H1: rank(Π) ≥ 2.

Linear Granger causality test

When determining dependency relationships between time series, Granger causal-ity has turned out to be a useful notion (Bekiros and Diks, 2008). Granger (1969) defines Granger causality as follows:

(yt+1, . . . , yt+k)|(Fx,t, Fy,t)  (yt+1, . . . , yt+k)|(Fy,t), (3.7) with Fx,tdenoting the information set consisting of past observations of xtup to t and Fy,tcontaining the past observations of ytup to t. Here xtis a strict Granger cause of yt, because past and current values of x contain more information on future values of y than the current and historical values of y alone. Alternatively, Granger (1969) defines this sort of causality as: xtis causing ytif one is better able to predict ytusing all available information than if the information apart from xt had been used.

In this research, both bivariate and multivariate causality are tested. Specifically, in case of bivariate causality, a VAR model is estimated as Hiemstra and Jones (1993) suggested:

xt= A(L)xt+ B(L)yt+ ηx,t

yt= C(L)xt+ D(L)yt+ ηy,t, t = 1, 2, . . . , (3.8) where A(L), B(L), C(L), and D(L) are lag polynomials of respectively orders a, b, c, and d in the lag operator L, determined with the Akaike Information criterion, with roots outside the unit circle so that they are integrated of order one. Taking

12

Chapter 3. Theoretical Background

first differences will lead to a stationary estimation: ∆xt= A(L)∆xt+ B(L)∆yt+ ηx,t

∆yt= C(L)∆xt+ D(L)∆yt+ ηy,t, t = 1, 2, . . . , (3.9) With use of an F-test, the Granger causality test tests the null hypothesis that ∆xt does not Granger cause ∆yt. The null hypothesis is rejected when the coefficients on the elements in C(L) are jointly significantly different from zero, i.e. when C1 6= C2 6= . . . 6= Cc 6= 0 . Then xtis said to Granger cause yt. When both B(L) and C(L) jointly differ significantly from zero Granger causality runs in both direc-tions, suggesting bidirectional Granger causality. For the multivariate VAR model, the same principle holds only then more variables are added to the equation.

Nonparametric Diks-Panchenko test

Although linear Granger causality tests have high power in uncovering linear causal relations, their power against nonlinear causal relationships can be low (Hiemstra and Jones, 1994). For this reason, traditional Granger causality tests might overlook significant nonlinear relationships. Therefore, Hiemstra and Jones (1994) came up with a nonparametric test for Granger causality to be able to cap-ture the nonlinear dynamics. However, in 2006, Diks and Panchenko claimed to have found a new nonparametric Granger causality test, which avoids over-rejection observed in the Hiemstra-Jones test. Accounting for variations in the conditional distributions of the variables that might be present under the null hy-pothesis, Diks and Panchenko (2006) were able to constrain the over-rejection of the Hiemstra-Jones test and thus came up with a refined nonparametric Granger causality test.

Instead of assuming a parametric and linear model, Diks and Panchenko (2006) let xlx

t be equal to (xt+1−lx, . . . , xt)and y

ly

t equal (yt+1−ly, . . . , yt), with (lx,ly ≥ 1). Under the null hypothesis, assuming no Granger causality, this can be mathemati-cally stated as yt+1|(xltx, y ly t ) ∼ yt+1|(y ly t ). (3.10)

In other words, xtcontains no extra information about yt+1. The null hypothesis can be seen as a statement about the distribution of wt= (xltX, y

ly

t, zt)with zt= yt+1 and not allowing for variations. One can show that x and z are independent, by rewriting Eq. 3.10 in terms of joint distributions:

fx,y,z(y, y, z) fy(y) = fx,y(x, y) fy(y) · fy,z(y, z) fy(y) (3.11) Diks and Panchenko (2006) then showed that this equation implies

q ≡ E[fx,y,z(x, y, z)fy(y) − fx,y(x, y)fy,z(y, z)] = 0,

under the null hypothesis. When the alternative hypothesis is true, they recently proved that q > 0 in most systems. Bekiros and Diks (2008) denote a local density estimator of a dw-variate random vector w at wi defined by ˆfw(wi)=(2χn)dw(n − 1)−1P

j,j6=iI w

ij where Iijw = I(||wi− wj|| < χn), χn representing the bandwidth, ndenoting the sample size, and I(·) an indicator function. The test statistic is as follows Tn(χn) = n − 1 n(n − 2) · X i

Chapter 3. Theoretical Background

13

Now, if χn = Cn−κ, C > 0 and 1 4 < κ <

1

3, and lx=ly = 1, Diks and Panchenko (2006) proved in their work that the test statistic satisfies, under strong mixing and strict stationarity: √ nTn(χn) − q Sn d −→ N (0, 1), (3.13)

with Snresembling an estimator of the asymptotic variance of Tn(·). Consequently, whenever Tn in Eq. 3.12 is significantly larger than zero, the null hypothesis of non-causality will be rejected.

GARCH-BEKK filtering

To account for the possible effects of heteroskedasticity, GARCH models can be used. Treating heteroskedasticity as a variance to be modeled, the statistical ev-idence of Granger causality lying in the conditional variances and covariances is filtered out. Parallel to the study of Bekiros and Diks (2008), for this research the GARCH-BEKK model of Engle and Kroner (1995) is used. Engle and Kroner define the BEKK(p,q) model as

Ht= C0C + q X j=1 A0_jkt−j0t−jAjk+ p X j=1 G0_jkHt−jGjk, t= H 1/2 t µt, (3.14)

where C, Ajk, and Gjkare (m x m) matrices. Htdenotes the conditional variance matrix of twith t|Φt−1 (0, Ht)and Φt−1 the information set at time t-1. In the work of Gourieroux (1997) sufficient conditions for At and Gtare stated so that Htis positive definite. Lastly, the residuals of this model are obtained by matrix transformation H1/2_

t.

General Additive Models

A generalized additive model is a generalized linear model with a linear predictor involving a sum of smooth functions of covariates (S.N. Wood, 2006). With the use of a general additive model one can visualize the Granger causal relationships. A simple additive model structure looks like

yi= f1(yt−1) + f2(xt−1) + ηt, (3.15) where the ηi are independent identically distributed N (0, σ2)random variables and fjthe smooth functions. For example in Eq. 3.15, when xiGranger causes yi, the smooth function f2will visualize that relationship.

In order to estimate the general additive model one has to determine the basis of the smooth function fj. With bjidenoting the ithbasis of fj, the smooth function can be represented as fj( ¯zj) = gj X i=1 bji( ¯zj)βji, j = 1, 2,

with (¯z1, ¯z2) = (yt−1, xt−1), and gjdenoting the dimension of the space. One way of determining this basis is by using the thin-plate regression spline technique, as suggested by Wood (2006). The thin-plate regression spline method provides

14

Chapter 3. Theoretical Background

an optimal low rank approximation to the generalized smoothing spline mod-els, being both stable and efficient. Dealing with pure regressions, the thin-plate spline method also provides a way of avoiding the problems of knot placement (S.N. Wood, 2006). Both a design matrix Xj and a matrix Sj, which denotes the wiggliness penalty, need to be produced for each smooth function j. The de-sign matrix for yi in Eq. 3.15 above will look like X = [1, X1, . . . , Xgj]. Here an

identifiability constraint comes into play as the sum of fi over all observed co-variate values should be zero. This condition can be written as 10Xiν = 0, with ν0= [ν₀0, ν₁0, . . . , ν_g0

j]so that the model

L(ν) −1 2

X

i

λiνi0Siνi, (3.16)

with the identifiability constraint on ν in place, is solved by penalized iteratively re-weighted least squares (Wood, 2006). In this model, the log-likelihood is dis-played by L and the second term includes λ, which controls the weight to be given to the objective of making fj smooth, relative to the objective of closely fitting the data. This can be seen as a trade-off between model fit and smoothness: the smoother the model, the wigglier the function gets. On the other hand, choosing λto high will result in a poorly fitting function fj. One method for choosing the optimal λ is by generalized cross validation. Woods (2006) suggests choosing λ which minimizes the generalized cross validation score.

After finding the right λ, the parameter vector ν needs to be estimated in order to estimate a general additive model. Given the jth_{estimate of the parameter vector} beta, minimizing the following weighted least squares problem

||W[k]_(z[k]_{− Xν)||}2₊X i

λiνi0Siνi (3.17)

will give νj+1. Here z[k] ≡ Xν[k]+ Γ[k](y − µ[k]), W[k] is a diagonal matrix with W_ii[k]≡ [g0_(µ[k]

i ) 2_V[k]

i ]

−1/2_{, V}[k]

i the variance of ytaccording to the estimate µ [k] i and implied by ν[k]_{, and Γ}[k]_{representing a diagonal matrix with entry Γ}[k]

ii ≡ g0(µ [k] i ).

Vector Auto Regression forecasting

When estimating a vector auto regression model forecasting can be one of the ob-jectives. Forecasting for a horizon with length h is obtained by exploiting the chain-rule of forecasting (Zivot and Wang, 2006):

YT +h|T = c + Π1YT +h−1|T + . . . + +ΠlYT +h−l|T, (3.18) where YT +j|T = Yt+jfor j ≤ 0. The h-step forecast errors are expressed as

YT +h− YT +h|T = h−1 X

s=0

ΨsηT +h−s,

and through recursive substitution the matrix Ψsis obtained by

Ψs= l−1 X

j=1

Ψs−jΠj,

with Ψ0= Inand Πj= 0for j > l. Since the forecast errors have expectation equal to zero, the forecast with length h is unbiased and the mean squared error matrix

Chapter 3. Theoretical Background

15

is as follows: Σ(h) = M SE(YT +h− YT +h|T) = E( d X j=1 (ˆθj− θj)2) = d X j=1 E((ˆθj− θj)2) = h−1 X s=0 ΨsΣΨ0s, (3.19)

with Σ denoting the time invariant covariance matrix. Concluding, a VAR model is estimated based on the whole sample. Then h observations are added and esti-mated with use of the VAR forecasting technique above. However, the VAR fore-casting in this research is done conditional on future paths of other variables. Con-ditional forecasting is in contrast to unconCon-ditional forecasting, where no knowl-edge of future paths of any variable is assumed. Using conditional VAR forecasting one can compare paths based on different future scenarios.

17

Chapter 4

Data and preliminary analysis

The data consist of nine time series covering a period from February, 1981, through December, 2015. The time series used for this research are monthly, totaling 419 ob-servations. In Appendix A the monthly data are visualized. The rest of this chapter is organized as follows. First of all, Table 4.1 represents both the basic descriptive statistics and the correlation matrix, reporting the measure of correlation between the raw data. Then, in the following paragraphs each of the time series will be explained in more detail. Moreover, a preliminary analysis will be done to deter-mine the contemporaneous correlation between the time series and to investigate the possible existence of non-stationarity and cointegration.

As previously stated, Table 4.1 displays the descriptive statistics of the variables used in this paper in order to develop a better understanding of both the size and variation of the time series. The correlation matrix provides the reader with a first impression of the interdependence of the multiple variables. According to the correlation matrix, the sample cross-correlation between the price of a corn futures contract and a gold futures contract, the existence of a political gridlock, the unemployment rate and the U.S. fuel ethanol production appear to be significant. However, since linear correlations may not fully capture the long-term dynamic linkages in a reliable way, a proper long-term causality analysis is needed.

Descriptive Statistics

Log[Corn] Log[Gold] Log[Fed.Rate] White House Gridlock Unemployment Log[PDSI] Log[U.S. Ethanol] Log[Brazilian Export]

Mean 0.265761 0.496045 0.515952 0.572792 0.766110 0.063983 0.778280 2.109846 2.406294 Std. Deviation 0.142190 0.183319 0.397977 0.485859 0.404309 0.016397 0.239711 0.558707 1.623010 Correlation Matrix Log[Corn] 1 Log[Gold] 0.666819 1 Log[Fed.Rate] 0.083525 -0.404313 1 White House -0.001138 -0.142781 0.472204 1 Gridlock 0.294767 0.040058 0.201415 0.063826 1 Unemployment 0.593362 0.644460 -0.251782 0.024487 -0.065288 1 Log[PDSI] -0.045205 -0.025845 -0.071681 -0.116028 -0.154816 0.224303 1 Log[U.S. Ethanol] -0.182064 0.358999 -0.858644 -0.423467 -0.271640 -0.022003 0.023308 1 Log[Brazilian Export] -0.031742 0.307694 -0.622472 -0.321057 -0.259453 0.108849 0.069393 0.63019 1

TABLE4.1: Descriptive Statistics & Correlation Matrix

Corn Price

For the corn price, the monthly continuous corn futures contract traded at the Chicago Board of Trade (CBOT) is used. The corn futures traded at the CBOT

18

Chapter 4. Data and preliminary analysis

contain 5000 bushels (∼ 127 metric tons) per contract and the pricing unit is mea-sured in U.S. dollars per bushel. For this research, the settlement price of a corn futures contract is taken into account. The settlement price, denoting the average price at which a contract has been traded in a particular month, reflects the market the most realistically and is crucial for investors as it is an indication of whether money has been made or lost during a given period. Moreover, the natural loga-rithm of the settlement price of a corn futures contract is taken in order to be able to compare it with other time series of different magnitude and the prices are cor-rected for inflation.

According to Table 4.2, the p-value of the Augmented Dickey-Fuller test implies that the logarithmic levels of a monthly corn futures contract in the given period are stationary (I(0)).

U.S. Political Climate

In this research, two variables are used to describe the political climate of the United States of America, namely: the political party in the White House and the presence of a gridlock between the White House, the House of Senate and the House of Representatives.

First of all, in the given period, there have been five different Presidents, represent-ing either the Democratic or the Republican party: Ronald Reagan (February, 1981 – January, 1989; Republican), George H.W. Bush (February, 1989 – January, 1993; Republican), Bill Clinton (February, 1993 – January, 2001; Democrat), George W. Bush (February, 2001 – January, 2009; Republican), and Barack Obama (February, 2009 – December, 2015; Democrat). Secondly, in order to determine the presence of a gridlock, the political color of both the House of Senate and the House of Rep-resentatives are determined by the formation of the two Houses. A Republican or Democratic House is the result of a majority of Republican or Democratic mem-bers, respectively. For this period, the House of Senate can be divided into seven sub periods, categorized being either Republican or Democratic. In the same way, the House of Representatives can be divided into four sub periods. Thus, during the terms of these five Presidents, there have been four periods of political grid-lock: February, 1981 – January, 1993; February, 1995 – January, 2003; February, 2007 – January, 2009; and February, 2011 – December, 2015.

These two time series are incorporated in this research as dummy variables. How-ever, the effect of a new political party (and thus the beginning of a new term) in either the White House, the House of Senate, or the House of Representatives is not directly noticeable, especially when looking at (macro)economic consider-ations (Stovall, 1992). A newly elected President cannot change tack in terms of economic policy within a month. In some of the states of the U.S. it takes at least ninety days for a bill to become effective. In other states a bill will only become ef-fective on one or two specific dates per year. Therefore, in this research the average term for a bill to become effective has been set to six months. To correct for this lag, the weighted-moving average principle is applied to the two time series dummies by assigning weights to the last six months, where the nth _{date has the highest} weight and the (n-6)th_{date the lowest. More specific, the value of the n}th _date is multiplied by seven, the (n-1)th_{value by six and so on until the (n-6)}th_value is multiplied by 1. Then, by dividing by the sum of the weights, which equals P7

k=1k = 28, the weighted-moving average procedure is completed.

Furthermore, the Augmented Dickey-Fuller test is not applied, because time series of dummy variables are stationary by definition.

Chapter 4. Data and preliminary analysis

19

Performance of the Economy

As mentioned earlier, the state of the economy is measured using two variables: the rate of unemployment and the gold price. Firstly, concerning the rate of un-employment, the data is obtained from the Federal Reserve Bank of St. Louis. The p-value in Table 4.2 points out that the U.S. unemployment rate is integrated of order zero (I(0)) and thus stationary.

For the gold price, the second indicator of the economy, the monthly continuous futures contract traded at the Chicago Board of Trade (CBOT) is used. The size of a single gold futures contract traded at the CBOT is hundred troy ounces and the pricing unit is measured in U.S. dollars per troy ounce. For the same reason as with corn, the settlement price of the futures contract is used, the natural logarithmic is taken, and prices are corrected for inflation.

The p-value of the ADF test in Table 4.2 for the logarithmic levels of gold indicate that the H0of stationarity can be rejected. However, taking first differences of the logarithmic levels result in a stationary time series. Therefore, the time series for gold are said to be integrated of order one (I(1)).

Augmented Dickey-F uller statistic

t-Statistic

significance

Log[Corn]

-3.3608

∗

Log[Gold]

-1.3965

∆

Log[Gold]

-22.9623

∗∗

Log[Fed.Rate]

-1.6485

∆

Log[Fed.Rate]

-5.2905

∗∗

Unemployment

-3.0478

∗

Log[PDSI]

-4.8218

∗∗

Log[U.S. Ethanol]

-0.4046

∆

Log[U.S. Ethanol]

-5.2318

∗∗

Log[Brazilian Export]

-0.5405

∆

Log[Brazilian Export]

-20.3797

∗∗

The number of lags for the Augmented Dickey-Fuller test is determined by the Akaike Information Criterium. The test statistic critical values for 5% and 1% are -2.86827 and -3.44585, respectively. (*) denotes 5% significance level, (**) denotes 1% significance level. Dummy variables: White House and Gridlock are not included.

TABLE4.2: Augmented Dickey-Fuller Unit Root tests

U.S. Monetary Policy

To depict the policy of the Federal Reserve, the logarithmic monthly discount rates for the United States of America in the given period have been taken into account as well. The data is provided by the Research Division of the Federal Reserve Bank of St. Louis. Again, according to Table 4.2, the logarithmic levels of the Federal

20

Chapter 4. Data and preliminary analysis

Reserve interest rates appear to be non-stationary. Resolving the non-stationarity issue by taking first differences proves to be effective once more.

Weather

The weather variable is expressed in terms of the Palmer Drought Severity Index (PDSI). For this paper, the monthly logarithmic levels of the PDSI for the entire Corn Belt are being used, released by the National Oceanic and Atmospheric Ad-ministration (NOAA).

The p-value of the ADF test in Table 4.2 indicates that the weather time series in the given period is stationary.

U.S. Production of Ethanol

Data of the U.S. production of ethanol is provided by the United States Energy Information Administration (USEIA) and measured in thousands of barrels on av-erage per day (Mbbl/d). The USEIA have listed annually production statistics only and thus the data needs to be converted to monthly observations. One way of doing this is by cubic spline interpolation. However, this technique imposes an artificial internal structure of the data, which might influence the results when testing for Granger causality. Therefore, in this research a more conservative tech-nique is applied: the production measured in thousands of barrels on average per day is set to be equal for every month in the same year. At least in this way there are no relationships imposed, using future values, that are otherwise nonexistent. Testing for stationarity, Table 4.2 indicates that taking first differences of the log-arithmic levels of fuel ethanol production will result in a stationary time series. Consequently, the time series are said to be integrated of order one (I(1)).

International Competition

The Brazilian corn export statistics are provided by the United States Department of Agriculture (USDA) and are measured in thousands of metric tons of corn per year. The USDA has listed only the annual data on Brazilian corn export. Convert-ing this into a monthly time series is done the same way as with the U.S. ethanol production time series. Table 4.2 suggests that the null hypothesis of stationary logarithmic levels can be rejected and that the first differences of the logarithmic levels are indeed stationary.

Chapter 4. Data and preliminary analysis

21

J ohansen Cointegration trace statistic

p-value

significance

Log[Gold]

Log[Fed.Rate]

0.2626

Log[Gold]

Log[U.S. Ethanol]

0.0260

∗∗

Log[Gold]

Log[Brazilian Export]

0.5765

Log[Fed.Rate]

Log[U.S.Ethanol]

0.0742

Log[Fed.Rate]

Log[Brazilian Export]

0.5659

Log[U.S. Ethanol]

Log[Brazilian Export]

0.0152

∗

The number of lags for the Johansen Cointegration trace test is determined by the Akaike Information Criterium. (*) denotes 5% significance level, (**) denotes 1% significance level. Only variables of higher order are included.

TABLE4.3: Johansen Cointegration Rank test - bivariate

Now that the order of integration has been determined for all the time series, the preliminary analysis finishes up with the Johansen test. The possible presence of cointegration among the variables, which are integrated of higher order, has to be examined. Ignoring cointegration when formulating a VAR model will result in wrongful estimations and misleading results. In this study, both a pairwise and a multivariate model is implemented. Whereas the pairwise model provides a gen-eral understanding of the individual effects among the time series, the multivariate model is more complete as the pairwise dynamics can be distorted by indirect ef-fects of omitted variables. With use of the Johansen cointegration test, the presence of cointegration is examined in both the pairwise and multivariate model.

Table 4.3 reports the presence of a cointegration vector for two pairs of variables: Log[Gold]-Log[U.S. Ethanol] and Log[U.S. Ethanol]-Log[Brazilian Export], at the 1% and 5% significance level respectively. Thus, when estimating a bivariate model including at least one of these time series, one has to account for the presence of a cointegration relation by implementing a VECM instead of a VAR model.

J ohansen Cointegration trace statistic

Hypothesized number of cointegration relations

p-value

significance

None

0.0001

∗∗

At most 1

0.0000

∗∗

At most 2

0.0000

∗∗

At most 3

0.0000

∗∗

At most 4

0.0005

∗∗

At most 5

0.0058

∗∗

At most 6

0.0735

The number of lags for the Johansen Cointegration trace test is determined by the Akaike Information Criterium. (*) denotes 5% significance level, (**) denotes 1% significance level.

TABLE4.4: Johansen Cointegration Rank test - multivariate

These bivariate dynamics may alter when all of the time series are implemented in a multivariate model. Thus, the Johansen cointegration test is again applied to the multivariate model and the results are displayed in Table 4.4. The test re-sults show that the hypothesis of at most five cointegration relations is rejected and that the null hypothesis of the existence of six cointegration relations cannot

22

Chapter 4. Data and preliminary analysis

be rejected at the 5% significance level, implying that there are six cointegration relations present. Again, one has to take these cointegration relations into account and use a VECM instead of a VAR model. Now, for the multivariate model, one has to include six cointegration relations.

23

Chapter 5

Empirical Results

After completing the preliminary analysis, the time series are properly adjusted for stationarity and cointegration. Further research is structured into five steps to investigate and display the causal relations between the price of a corn futures contract and the other time series. First of all, the linear causality linkages are examined by applying the Granger Causality test. Secondly, with use of the Diks-Panchenko test the nonparametric Granger causality relations are explored. Then, using the theory of the Generalized Additive Models, the nonlinear nonparametric causal linkages are visualized. Lastly, after determining the significant relations between the time series, the development of the price of a corn futures contract one year ahead is forecast applying the VAR forecast method.

Linear Granger Causality relations

The linear linkages are examined through directly applying a Granger Causality test on the raw data, both pairwise and multivariate. The findings in Table 5.1 pro-vide an overall better understanding of the interrelatedness among the time series, although only allowing for linear linkages.

The results reveal that overall the influence of White House plays a modest role. Only in the pairwise implementation, White House Granger causes Unemployment. In the multivariate implementation, this effect disappears. Table 5.1 does demon-strate that White House is persistently influenced by ∆Log[Fed. Rate] in both the pairwise and multivariate implementation. Then, for corn, the results imply uni-directional linear effects of Log[Corn] on ∆Log[Gold], Unemployment, ∆Log[U.S. Ethanol], and ∆Log[Brazilian Export], noticeable only in the pairwise implemen-tation. Moreover, both ∆Log[Fed. Rate] and Log[PDSI] appear to affect Log[Corn] persistently. The pairwise results for ∆Log[Gold] indicate that the price of a futures contract for gold is linearly Granger caused by ∆Log[Fed. Rate], Unemployment, and Gridlock. However, only the effect of ∆Log[Fed. Rate] remains in the multivariate implementation. ∆Log[U.S. Ethanol] Granger causes ∆Log[Gold] in the multivariate implementation as well. Consistently, in the two implementations, the gold price appears to have an effect on the presence of a political gridlock, as ∆Log[Gold] Granger causes Gridlock. Furthermore, Table 5.1 shows significant evidence for the unidirectional Granger relation from ∆Log[Fed. Rate] to Gridlock. And, in the mul-tivariate implementation, the Federal Reserve discount rate is affected by the rate of unemployment as Unemployment Granger causes ∆Log[Fed. Rate] significantly. Moreover, the results show that Unemployment Granger causes ∆Log[U.S. Ethanol] in both implementations, indicating that the amount of ethanol produced in the U.S. is causally related to the historic rates of unemployment. Also, in the mul-tivariate model, Unemployment Granger causes Gridlock and is Granger caused by ∆Log[Brazilian Export]. Lastly, ∆Log[Brazilian Export] Granger causes Gridlock.

24

Chapter 5. Empirical Results

Then, after applying the Linear Granger Causality test on the raw data, both the VAR and VECM residuals and the GARCH-BEKK residuals are subject to the Lin-ear Granger Causality test. Table 5.1 shows that all the linLin-ear effects of the raw data have now disappeared, indicating that the VAR and VEC models accurately captured all the linear effects.

As stated earlier in Chapter 4, although the pairwise implementation provides a general understanding of the individual effects among the time series, the dynam-ics can be distorted by indirect effects of variables that are left out. Therefore, from now on this research will focus on the results of the multivariate model.

Nonparametric Granger Causality relations

Table 5.2 shows the significant nonparametric Granger causality linkages, which have been obtained by applying the Diks-Panchenko test to the data. This section is split up in three parts, describing the output of each of the three columns of Ta-ble 5.2 respectively.

Raw Data

Interestingly, the Diks-Panchenko test reports other Granger causality relations when examining the raw data than when applying the Linear Granger Causality test. Now, only Gridlock Granger causes White House; the linear effect of ∆Log[Fed. Rate] on White House in Table 5.1 is not significant according to the results of the Diks-Panchenko test. However, the nonparametric test still shows significant ev-idence for both ∆Log[Fed. Rate] and Log[PDSI] Granger causing Log[Corn]. Also, Table 5.2 indicates a significant bi-directional relationship between Log[Corn] and Unemployment. Intriguingly, the effects of ∆Log[Fed. Rate] and ∆Log[U.S. ethanol] on ∆Log[Gold] and ∆Log[Gold] on Gridlock are not statistically significant according to the Diks-Panchenko test. Moreover, the nonparametric test results show that the causality relationship between ∆Log[Fed. Rate] and Unemployment has switched direction. Now, the historical values of the discount rate of the Federal Reserve Granger causes the unemployment rate. Also, according to Table 5.2, ∆Log[Fed. Rate] is said to Granger cause ∆Log[U.S. Ethanol]. Finally, Table 5.2 reports that ∆Log[Brazilian Export] Granger causes Gridlock.

The differences between the results in Table 5.1 and Table 5.2 when testing on raw data can be explained by the possible impact of unidirectional nonlinear linkages that are not detected in the Linear Granger Causality test.

Chapter 5. Empirical Results

25

Linear Granger Causality Raw Data V AR/VECM Residuals GARCH-BEKK Residuals Pairwise Multivariate Pairwise Multivariate Pairwise Multivariate X Y Lags (AIC) V AR/VECM X->Y Y ->X X->Y Y ->X X->Y Y ->X X->Y Y ->X X->Y Y ->X X->Y Y ->X WH Log[Corn] 3 V AR WH ∆ Log[Gold] 2 V AR WH ∆ Log[Fed.Rate] 4 V AR ** ** WH Unemployment 7 V AR * WH Log[PDSI] 10 V AR WH ∆ Log[U.S. Ethanol] 8 V AR WH ∆ Log[Brazilian Export] 2 V AR WH Gridlock 2 V AR Log[Corn] ∆ Log[Gold] 1 V AR ** Log[Corn] ∆ Log[Fed.Rate] 7 V AR * * Log[Corn] Unemployment 7 V AR ** Log[Corn] Log[PDSI] 9 V AR * * Log[Corn] ∆ Log[U.S. Ethanol] 8 V AR * Log[Corn] ∆ Log[Brazilian Export] 2 V AR * Log[Corn] Gridlock 2 V AR ∆ Log[Gold] ∆ Log[Fed.Rate] 2 V AR ** ** ∆ Log[Gold] Unemployment 7 V AR * ∆ Log[Gold] Log[PDSI] 5 V AR ∆ Log[Gold] ∆ Log[U.S. Ethanol] 2 VECM ** ∆ Log[Gold] ∆ Log[Brazilian Export] 1 V AR ∆ Log[Gold] Gridlock 2 V AR * ** * ∆ Log[Fed.Rate] Unemployment 7 V AR * ∆ Log[Fed.Rate] Log[PDSI] 9 V AR ∆ Log[Fed.Rate] ∆ Log[U.S. Ethanol] 8 V AR ∆ Log[Fed.Rate] ∆ Log[Brazilian Export] 1 V AR ∆ Log[Fed.Rate] Gridlock 1 V AR ** ** Unemployment Log[PDSI] 7 V AR Unemployment ∆ Log[U.S. Ethanol] 8 V AR ** * Unemployment ∆ Log[Brazilian Export] 7 V AR * Unemployment Gridlock 7 V AR * Log[PDSI] ∆ Log[U.S. Ethanol] 8 V AR Log[PDSI] ∆ Log[Brazilian Export] 5 V AR Log[PDSI] Gridlock 5 V AR ∆ Log[U.S. Ethanol] ∆ Log[Brazilian Export] 1 VECM ∆ Log[U.S. Ethanol] Gridlock 8 V AR ∆ Log[Brazilian Export] Gridlock 1 V AR * (*) and (**) denote the 1 % and 5 % significance level respectively . ’X->Y’ translates to: X Granger causes Y . One cointegration relation is included when estimating both bivariate VEC models and six cointegration relations ar e accounted for in the multivariate model, based on the results of the Johansen Cointegration tests. The number of lags for the VEC models ar e estimated using the W ald exclusion criterion. The second moment-filtering was performed with a GARCH-BEKK (1,1) model. T A B L E 5 .1 : Linear Granger Causality Results

26

Chapter 5. Empirical Results

VAR/VECM Residuals

The results of the Linear Granger Causality test in Table 5.1 and the nonparametric Diks-Panchenko test in Table 5.2 on the raw data imply that there are significant linear and nonlinear causal linkages between the time series. To ensure that the causal relations are nonlinear, a VEC model is estimated in the multivariate imple-mentation and its residuals are again subject to the Diks-Panchenko test.

Both ∆Log[Fed. Rate] and Gridlock now Granger cause White House and a bi-directional Granger causality relationship is present between White House and Unemployment. Moreover, ∆Log[Gold] Granger causes ∆Log[Fed. Rate], which in turn is Granger caused by Gridlock. Besides, the results show also that Gridlock has an unidirec-tional effect on Unemployment. Also, both ∆Log[U.S. Ethanol] and ∆Log[Brazilian Export] Granger cause Gridlock. Interestingly, according to Table 5.2, no statisti-cally significant nonlinear linkages between Log[Corn] and other time series exist. GARCH-BEKK Residuals

In the last column of Table 5.2 the results of the GARCH-BEKK filtered residu-als are shown. Through GARCH-BEKK filtering, one controls for conditional het-eroskedasticity, which can be one of the sources of the detected nonlinearities. As the results show, it turns out that the nonlinear relationships found in the sec-ond column of Table 5.2 remain almost unchanged, even their statistical signifi-cance have not been reduced. This implies that the causality relations are not im-posed by volatility effects. In total there are ten nonparametric nonlinear Granger causality relations.

Chapter 5. Empirical Results

27

Nonparametric Granger Causality Raw Data V AR/VECM Residuals GARCH-BEKK Residuals Pairwise Multivariate Pairwise Multivariate Pairwise Multivariate X Y Lags (AIC) V AR/VECM X->Y Y ->X X->Y Y ->X X->Y Y ->X X->Y Y ->X X->Y Y ->X X->Y Y ->X WH Log[Corn] 3 V AR WH ∆ Log[Gold] 2 V AR WH ∆ Log[Fed.Rate] 4 V AR ** ** * ** WH Unemployment 7 V AR * * * * * WH Log[PDSI] 10 V AR WH ∆ Log[U.S. Ethanol] 8 V AR * WH ∆ Log[Brazilian Export] 2 V AR * * WH Gridlock 2 V AR * * Log[Corn] ∆ Log[Gold] 1 V AR Log[Corn] ∆ Log[Fed.Rate] 7 V AR * * * Log[Corn] Unemployment 7 V AR * * * * Log[Corn] Log[PDSI] 9 V AR * * * * Log[Corn] ∆ Log[U.S. Ethanol] 8 V AR Log[Corn] ∆ Log[Brazilian Export] 2 V AR Log[Corn] Gridlock 2 V AR ∆ Log[Gold] ∆ Log[Fed.Rate] 2 V AR * * ∆ Log[Gold] Unemployment 7 V AR ∆ Log[Gold] Log[PDSI] 5 V AR ∆ Log[Gold] ∆ Log[U.S. Ethanol] 2 VECM ∆ Log[Gold] ∆ Log[Brazilian Export] 1 V AR ∆ Log[Gold] Gridlock 2 V AR ∆ Log[Fed.Rate] Unemployment 7 V AR * * * ∆ Log[Fed.Rate] Log[PDSI] 9 V AR ∆ Log[Fed.Rate] ∆ Log[U.S. Ethanol] 8 V AR * * ∆ Log[Fed.Rate] ∆ Log[Brazilian Export] 1 V AR ∆ Log[Fed.Rate] Gridlock 3 V AR * ** * ** Unemployment Log[PDSI] 7 V AR Unemployment ∆ Log[U.S. Ethanol] 8 V AR Unemployment ∆ Log[Brazilian Export] 7 V AR Unemployment Gridlock 7 V AR * * * Log[PDSI] ∆ Log[U.S. Ethanol] 8 V AR Log[PDSI] ∆ Log[Brazilian Export] 5 V AR * Log[PDSI] Gridlock 5 V AR ∆ Log[U.S. Ethanol] ∆ Log[Brazilian Export] 1 VECM ∆ Log[U.S. Ethanol] Gridlock 8 V AR * * * ** * ** ∆ Log[Brazilian Export] Gridlock 2 V AR ** ** * ** (*) and (**) denote the 1 % and 5 % significance level respectively . ’X->Y’ translates to: X Granger causes Y . One cointegration relation is included when estimating both bivariate VEC models and six cointegration relations ar e accounted for in the multivariate model, based on the results of the Johansen Cointegration tests. The number of lags for the VEC models ar e estimated using the W ald exclusion criterion. The second moment-filtering was performed with a GARCH-BEKK (1,1) model. The number of lags used for the nonlinear causality tests ar e lX = lY = 1 and the bandwidth χn in Eq. 3.12 set to 1. T A B L E 5 .2 : Nonparametric Granger Causality Results

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GAM Representations of Nonlinear Linkages

As stated earlier, the results in Table 5.2 indicate the presence of ten nonparametric nonlinear non second moment Granger causalities. With use of a General Additive Model, it is possible to visualize these relations by plotting Eq. 3.14 incorporating the different time series. Therefore, Eq. 3.14 is estimated with the use of thin-spline regression and the statistical significance of ˆf2(xt−1)of every pair of time series is examined and displayed in Table 5.3. According to Wood (2006), the results in Ta-ble 5.3 have to be interpreted with care as the p-values are on average fairly low due to the fact that the smoothing parameters βji have to be estimated. The es-timation of βjiprovides more uncertainty and this uncertainty in turn translates to rejecting the null hypothesis too easily (Wood, 2006). One way to counter this problem is to set the benchmark of the significance level to 1%. Therefore, only the GAM representations with smoothing parameters, which have a p-value of 1% or lower, will be considered.

GAM Representations - significance of parameters p-values

yt xt fˆ1(yt−1) significance fˆ2(xt−1) significance

White House Gridlock 3.99E-09 ∗∗ 2.40E-15 ∗∗

White House ∆Log[Fed. Rate] 0.4455 0.0169

White House Unemployment 0.892 0.948

Unemployment White House 0.1626 0.0509

Unemployment Gridlock 0.204 0.132

Gridlock ∆Log[U.S. Ethanol] 1.29E-08 ∗∗ 3.84E-09 ∗∗

Gridlock ∆Log[Fed. Rate] 0.00801 ∗∗ 0.00107 ∗∗

Gridlock ∆Log[Brazilian Export] 2.77E-07 ∗∗ 2E-16 ∗∗

∆Log[Fed. Rate] ∆Log[Gold] 0.882 0.993

∆Log[Brazilian Export] Log[PDSI] 0.952 0.812

The time series are the GARCH-BEKK filtered residuals of the five-variate VEC model that show significant evidence of Granger causality. (**) denotes 1% significance level.

TABLE5.3: Significance of parameters in the GAM representations

In general, when plotting the GAM representations, along the x-axis the values of the covariates of the smooth parameter are shown and the y-axis captures the effective degrees of freedom of the time series being plotted. Figure 5.1 (A) dis-plays the smoothing function ˆf2(Gridlockt−1)in the GAM representation on White House.

Chapter 5. Empirical Results

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(A) ˆf2(Gridlock)on White House with 95% confidence limits

(B) ˆf2(∆Log[U.S.ethanol]) on Grid-lock with 95% confidence limits

(C) ˆf2(∆Log[F ed.Rate]) on Gridlock with 95% confidence limits

(D) ˆf2(∆Log[BrazilianExport]) on Gridlock with 95% confidence limits

FIGURE5.1: GAM Representations visualized

Figure 5.2 (B), (C) and (D) correspond to the smooth parameters of ∆Log[U.S. Ethanol], ∆Log[Fed. Rate], and ∆Log[Brazilian Export] respectively, in the GAM rep-resentation on Gridlock. Clearly, all four graphs display a nonlinear structure, reaf-firming that the dynamics shown in the last column of Table 5.2. are indeed of nonlinear nature.

VAR Forecast on Corn

The results of Table 5.1 and Table 5.2 indicate that Log[Corn] is only influenced by ∆Log[Fed. Rate] and that a linear model accurately captures this linkage. Based on this information, the course of a corn futures contract in the next year can be forecast, using the historical data of the nine time series. After applying the VAR forecasting technique to the multivariate VEC model, three scenarios of the loga-rithmic time series of the price of a corn futures contract are plotted. The green line

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denotes the forecast values with no restrictions imposed. The other two forecast scenarios are conditional on the discount rate; in these scenarios, the discount rate is treated as exogenous in order to examine the influence of the Federal Reserve on the price of corn. The blue line represents the forecast in which the Federal Reserve discount rate remains unchanged. The red line denotes a single raise of the discount rate in January, 2016, with a usual increment (historically seen) of 0.25 percentage point to 1.25%. The results are displayed in Figure 5.2 (A) and (B).

(A) overview

(B) zoomed-in

FIGURE5.2: Forecast Log[Corn] conditional on Fed. Rate

Whereas Figure 5.2 (A) provides a better understanding of the overall course of the price of corn, Figure 5.2 (B) displays a more zoomed-in version to accurately capture the differences between the three scenarios. The green line represents a forecast from January, 2015, up to the December, 2016, treating all the available data of the year 2015 as unknown. This scenario will be used later on to explore the permanent shock effects. For now, in order to evaluate the accuracy of the VAR forecast methodology, the second scenario denoted by the blue line is used as a forecast base. The blue line displays the forecast conditional on the actual dis-count rates in 2015, leaving the rate unchanged in 2016. Comparing the historical values (denoted by the black line) with this forecast base, the forecast values of Log[Corn] prove to be fairly accurate, apart from some historical spikes. In Decem-ber, 2015, the Federal Reserve increased the discount rate to 1% and a dip in the blue line shortly after is noticeable. Thenceforth, the price of a corn futures con-tract decreases but flattens out towards the end of 2016, conditional on the Federal Reserve keeping the discount rate at 1%.