Forecasting the German forest products trade: A vector error correction model

Journal of Forest Economics 26 (2017) 30–45

Contents lists available at ScienceDirect

Journal of Forest Economics journal homepage: www.elsevier.com/locate/jfe

Forecasting the German forest products trade: A vector error correction model Horst Kolo a, Polia Tzanova b,∗ a b

TUM, Institute of Forest Management, Germany TUM, Chair of Forest Economics, Germany

a r t i c l e

i n f o

Article history: Received 21 December 2015 Accepted 3 November 2016 JEL classification: C32 C53 E370 L73 Q230 Keywords: Forecasts for German forest sector Forest sector models VECM Raw timber German timber market

a b s t r a c t In the forest sector often very complex models are used that take into account a variety of factors. In addition to variables that describe the natural production of wood, into these models flow among others also such variables that depict nature conservation legislation, market contexts, etc. The limited availability of large amounts of data and more particularly of precise data to all these subject areas considerably weakens the validity of the models. Our study therefore takes up the challenge to develop a model, as simple as possible, that can help to estimate export and import volumes as well as export and import prices of raw timber in Germany. To this end, we apply the technique of time series analysis and develop a simple model that allows for short-term and mediumterm forecasting in the German forest sector. We show that using a vector error correction model (VECM) can succeed in a relatively simple modelling of future quantities and prices of raw timber for Germany. © 2016 Department of Forest Economics, Swedish University of ˚ Published by Elsevier GmbH. All Agricultural Sciences, Umea. rights reserved.

Introduction To exploit economic potentials while successfully balancing social and environmental objectives of the ecosystem forest, a wise management of the natural resource timber is necessary. Especially due to the intensifying and at the same time competing diverging claims on timber utilization in recent ∗ Corresponding author. E-mail address: [email protected] (P. Tzanova). http://dx.doi.org/10.1016/j.jfe.2016.11.001 ˚ Published by Elsevier 1104-6899/© 2016 Department of Forest Economics, Swedish University of Agricultural Sciences, Umea. GmbH. All rights reserved.

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

31

years the commercial use of timber has become increasingly important. In this context, knowledge about future developments in the timber market plays a decisive role for forestry and timber industry so that harvesting, storage and production planning can be adjusted to constantly changing market conditions. Future developments of timber products quantities and prices are crucial for production planning and for keeping the working capital at an optimal level. Short-term and medium-term forecasts can help to adjust commodity stocks, to prevent whip effects and to align sales as profitably as possible, which appears to be essential for decision-makers in timber industry. Even traditional forest management such as timber production depends on such forecasts. Forecasts allow to optimize control of the supply chain and based on this to minimize risks in the supply chain management. Although the natural production in the medium term is little influenced, timber harvesting will certainly adapt to changing market conditions in order to increase yield. Hänninen (2004) points out the growing interest in short-term forecasts in forest sector markets and prices. Changes in economic growth rates reflect in fluctuations in the demand for forest products. This results in an increasing need for the use of short-term forecasting models in forestry and forest industry. Hetemäki et al. (2004) also emphasize the importance of short-term analysis and forecasting of forest product markets since these react ever more quickly to changes in macroeconomic conditions due to liberalization of capital and currency markets, globalization of the forest industry, and developments in information technology and logistics. In the forest sector often very complex models are used that take into account a variety of factors. In addition to variables that describe the natural production of wood, into these models flow among others also such variables that depict nature conservation legislation, market contexts, etc. (Buongiorno, 1996). The high complexity of such models has proven to be disadvantageous because it requires an extensive knowledge of economic data, forest growth data as well as data relevant to environmental protection. The limited availability of large amounts of data and more particularly of precise data to all these subject areas considerably weakens the validity of the models. The data is often collected not in a uniform manner or not time-consistently. Therefore, our study takes up the challenge to develop a model, as simple as possible, that can help to estimate export and import volumes as well as export and import prices of raw timber in Germany. To this end, we apply the technique of time series analysis, which is based on investigation of the structure and the regularity of a time series as a basis for those subsequent updating in the future (forecast). Economic time series may be of non-stationary nature. The well-known problem of spurious regression, which is a characteristic of such non-stationary time series, is encountered by the test of cointegration and the estimation of an error correction model. In our investigation we use the property of vector models having to make no distinction between exogenous and endogenous variables. We show that using vector models can succeed in relatively simple modelling of predictions of quantities and prices of timber products for Germany. We encounter the problem of complex data collection by using already available and easily accessible data, namely Gross Domestic Product (GDP) and exchange rate, two in the research literature often occurring economic indicators, which are often brought in connection with exports, imports and prices. As stated by Toppinen and Kuuluvainen (2010), the use of monthly data can introduce more complexity to the model. We therefore work with quarterly data and look at the period from 1995 to 2012 to estimate our model. The forecast period stretches over fourteen quarters, from Q1:2013 to Q2:2016. The aim of our work is to find a simple but useful model, with which based on past values it can be examined whether it is possible to make meaningful predictions of export and import volumes and prices of raw timber in Germany. Similar investigations have been conducted for North America and the Scandinavian countries. To our knowledge, such a model of forest sector from a German perspective has not yet been tested. After a brief overview of the existing scientific literature in forest sector modelling, the statistical framework is described in part two and the model as well as the data used in part three. In part four the model calculations are presented. Finally the results are shown and discussed in part five.

32

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

Overview of econometric literature in forest sector modelling Since the late 1980s forecasting models have been developed for all areas of the forest sector. An early summary can be found in the work of Buongiorno (1996). Part of the newer models, the partial equilibrium models, is summarized in the work of Latta et al. (2013). An overview of the models used in Europe can be found in Toppinen and Kuuluvainen (2010). Common feature of all these models is their complexity since they include parameters describing not only wood trading and the natural production of wood but also the geographical position and many other parameters. Firstly, they are designed to reveal mechanisms of impact and interaction and to predict the effects of different strategies such as e.g. regulatory measures. Secondly, they also serve to examine long-term effects of policy decisions (see e.g. Toppinen and Kuuluvainen, 2010). Buongiorno (1996) describes some of the older forest sector models. He comes to the conclusion, that simple models dealing with particular problem have the advantage that they can be developed relatively easily and quickly. In addition, they are transparent to all users and can be easily applied. Therefore, compared with complex models simple models are much easier to develop. They are either based on econometric theories examined on the basis of simple correlation or regression, or they are vector models that consider variables as exogenous. The advantage of these two model types is that they can be used to deal with a specific field of research, in our case with the field of forestry, which is the focus of our study here. Two additional advantages are offered. On the one hand, theoretical knowledge needed to develop such a model is available. On the other hand, necessary input parameters are less numerous. These models can be created with readily accessible data. In the course of the remaining work, such a model is created and compared with results of other similar models. Below, we present a brief overview of existing research literature on modelling price and volume in the forest sector. Table 1 presents a structured overview based on price and two in the research literature often used economic indicators, GDP and exchange rate, which are also considered in our analysis. The GDP as independent variable The relationship between GDP and exports has been examined for a long time (since the 1950ies). There are two different outcomes typically found in those studies. One is the growth driven export.

Table 1 Literature overview. Author

GDP Regression

Arize (1998) Baek (2012) Bolkesjo and Buongiorno (2006) Buongiorno et al. (1988) Buongiorno et al. (1979) Dutt and Ghosh (1996) Hetemäki et al. (2004) Hietala et al. (2013) Jennings et al. (1991) Kim et al. (2003) Limaei et al. (2011) Marin (1992) Nagubadi and Zhang (2013) Nanang (2010) Pindyck and Rotemberg (1990) Sharma et al. (1991) Song et al. (2011) Wisdom and Granskog (2003)

Exchange rate VAR

VECM

Regression

VAR

Price VECM

Regression

VAR

VECM

X X X X

X

X X

X X X

X

X X

X X X X X X X

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

33

Here, rising GDP is thought to cause rising exports (e.g. Afxentiou and Serletis, 1991; Awokuse, 2003). The other relationship is the opposite. Here, growing export is made accountable for increasing GDP (e.g. Ahmad, 2001; Awokuse, 2005; Balassa, 1978; Giles and Williams, 2000). Some studies also found a mixture of both theories (e.g. Awokuse and Bessler, 2003; Marin, 1992). There are some studies using the same methodology as we and examining Germany as part of their analysis. Sharma et al. (1991) used a VAR model to examine the relationship between total export, GDP, labour force and capital for five industrialized countries. They came to the conclusion that there is no overall causal relationship. Instead, the causal relationship is country-specific. For Germany, they found export quantity to be causal for GDP. Dutt and Ghosh (1996) used a cointegration framework to study the relation between exports and economic growth. In their paper, they examined industrialized, newly industrializing and developing countries. They did not find an overall relationship for all countries or at least for the same subset of countries. For a part of the included industrialized countries (Germany, Japan and England) they did not find any long-term relationship at all, although Japan and Germany are highly export-oriented countries. Arize (1998) examined GDP and import quantity for eight European countries. He used an error correction framework and proved GDP to have significantly positive influence on import quantity. There are also several studies examining the relationship between the GDP and export or import of timber products. A very basic analysis has been done by Limaei et al. (2011). He investigated the effect of GDP, population size and domestic wood production on Iranian export and import quantity of wood. This is done using a simple linear regression and the result suggests that GDP has the most influence on export quantity, but not a significant influence on import. A paper which partly agrees with these findings is the one of Hetemäki et al. (2004). In their paper they addressed a problem fairly similar to ours. They examined lumber import demand of Germany as well as Finnish export to Germany and Finnish sawlog demand. For the import demand they have chosen import price, domestic price, GDP and sum of construction permits as independent variables. The authors aim to compare different models to choose the model which best represents the data. For lumber import demand, the best model is a vector autoregressive model VAR(5) in-sample and a partial model out-of-sample. In the VAR model only the lagged variables of the import quantity, the GDP and the construction permits are significant. The independent variables of the Finish lumber export to Germany are total lumber imports to Germany, price for Finnish lumber in Germany and price for Swedish Lumber in Germany. Here, the vector error correction model (VECM) suits the data best. This holds true both in-sample and out-of-sample. Only some of the coefficients of the error correction term, total import quantity and Finish price are significantly different from zero. Concerning the influence of GDP on export quantities, Jennings et al. (1991) used a vector autoregressive model (VAR) to examine the relationship between five variables describing the economy and five variables describing the Canadian wood sector. Among other findings, they cannot find evidence that any variable describing the Canadian wood market influenced the GDP. The exception is the variable of inventory of lumber held by lumber manufacturers. Neither price of lumber nor export quantity got any influence on GDP. Also, housing starts in the United States seem to be the only variable having a significant influence on export quantity. Neither exchange rate nor GDP seem to influence export quantity. The exchange rate as independent variable A second variable we used as possible predictor for export and import quantities and prices was the exchange rate between Euro and US Dollar. Papers studying export or import quantities and exchange rate have come to mixed results. Wisdom and Granskog (2003) used a simple linear regression to determine the influence of exchange rate on total export value of southern pine. They found a negative significant influence of exchange rate on exports. For export quantity of Finnish and Swedish sawn wood, Hietala et al. (2013) came to a similar result. They used cointegration framework and found significantly positive impact of exchange rate on export quantity for both countries. They also discovered that there is a difference on the magnitude of impact which seemed to be country specific.

34

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

This result is also supported by Bolkesjo and Buongiorno (2006). They examined the effect of exchange rate on export and import quantity of several forest product groups. One of these was sawn wood (CN 4407). They found a negative impact of exchange rate on export quantity in the short run as well as in the long run. This effect is only significant for coniferous sawn wood. In the long run only the appreciation is significant. The effect for import quantity is positive but insignificant in the short run. In the long run only the appreciation is significant. Along with coefficients they examined causality and found that exchange rate is significant only for export quantity of coniferous sawn wood. Regarding import quantity, Song et al. (2011) came to a similar result. Among other equations they examined import demand of Canadian sawn wood, which equals the import quantity. Along with other explanatory variables describing Canadian economy, they used exchange rate as independent variable in their equation. They came to the conclusion that exchange rate had significantly positive effect on import quantity of sawn wood. That is, import quantity rises as exchange rate rises and the dollar grows stronger. Kim et al. (2003) calculated a VAR model and came to a different result. They examined import quantity of various wood products to Korea in dependence of exchange rate and import price. Although their model explains data only moderately, they found a significantly negative effect of exchange rate on import quantity. Additionally they found a Granger causal impact of exchange rate on import quantity only for hardwood round wood and no causal link for sawn wood. Another paper examined the relationship of exchange rate on lumber price. In the first part of their paper, Pindyck and Rotemberg (1990) established a model of lumber price in dependence of macroeconomic variables. One of these variables is an index of exchange rates. They only found a significantly positive relationship of the one period lagged index to the price. Additional to the mentioned differences there are also papers, which did not find any effect of exchange rate on quantities or prices. Buongiorno et al. (1988) used a bivariate system of equation to determine the relationship between exchange rate and import quantity and domestic price of lumber in the U.S. respectively. In the short run they found no evidence that exchange rate influenced import quantity. They found statistical evidence that imports of Canadian lumber influenced exchange rate. None of those two relations hold on long-term observation. A similar result is reported in the previously mentioned paper of Jennings et al. (1991) who also examined exchange rate in their VAR model. Here too, exchange rate had no significant influence on export quantity of lumber from Canada to the United States. Baek (2012) also studied import quantity of Canadian lumber to the United States. He came to the same conclusion that exchange rate had no significant role in explaining import quantity. Nanang (2010) came to an analogue result as well. He discovered a significantly positive long-term effect of exchange rate on export quantity. The price as independent variable The last parameters frequently associated with import and export volumes are prices of exports respectively imports. In their study concerning import quantity of Canadian wood to the United States, Buongiorno et al. (1979) developed a model which explains import quantity in dependence of import price, domestic wood price, overall price level, housing starts in the United States and one-period-lagged import quantity. The factor having the largest effect on import quantity was domestic wood price followed by housing starts and import price. In all five alternative models considered here import price influenced import quantity negatively. Similar results are reported in Nagubadi and Zhang (2013). Along with other explanatory variables they examined the impact of import price on import quantity of Canadian softwood lumber to the United States. A part of the paper examined the Granger causality. They found that import price Granger-caused import quantity and vice versa. They also found a significantly negative influence of import price on import quantity in the long-term relationship deviated from the cointegration vector. The short-run relationship deduced from the VECM, is not significant. The already mentioned paper of Buongiorno et al. (1988) also revealed the relation between import quantity of Canadian lumber to the U.S. and the domestic softwood lumber price. They found evidence

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

35

that prices influenced quantities and that import quantities influenced prices. This effect holds in the short run as well as in long run. The sign of price coefficient is positive for all considered models. The model Examinations of time series have a long history in many fields of science. Shumway and Stoffer (2006) list an example of Schuster (1906) who studied sunspots. Since then, many applications have been derived. Beginning in the 1970s more sophisticated methods have been used. Box and Jenkins (1970) developed a first univariate autoregressive moving average (ARMA) time series approach accounting for the statistical character of time series. Hannan (1970) considered multivariate models. With the use of more than one time series there came additional difficulties (Tsay, 2000). Granger and Newbold (1974) came to the conclusion that one cannot ignore the possible time series properties without the results being spurious. Therefore, Granger (1981) introduced the concept of cointegration in a later article. This method accounts for possible statistical interrelations between the examined time series. Based on this work, Johansen (1988) and Johansen and Jusélius (1990) developed an approach to use this method for more than two time series. Determine the lag length For the specification of a VAR or VECM, one must balance between the additional explanatory power of an additional variable and the loss of degrees of freedom. Therefore, our work used three different information criteria to determine the number of lags for each variable and thus the number of used variables. Those are Akaike’s information criterion (AIC), Bayesian information criterion (BIC) and Hannah-Quinn (HQ) information criterion. Unit root tests and cointegration Before testing for existence of cointegration, we tested for the existence of unit roots in the time series. In this study, we did this by employing the well-known augmented Dickey–Fuller test (ADF) and the Philipps–Perron test. Additionally, we included seasonal dummies in the ADF test to account for seasonality. According to the test results, both tests were determined with a time trend and a constant, only a trend, only a constant or none of them. To test whether some time series are cointegrated or not and to determine the number of cointegrating relationships we used the methodology of Johansen and  Jusélius (1990). For this purpose, Johansen’s framework uses the magnitude of the eigenvalues of (see below). This framework starts off with a normal VAR model, which can be solved with the ordinary least square method (OLS): X t = 1 X t−1 + · · · + k X t−p +  + Dt + ␧t

(t = 1, . . ., T )

where Dt is a matrix of seasonal dummy variables,  is a vector of constants and εt is a vector of independent, identical, normally distributed errors. Xt is a vector containing all used variables. From this equation we deviate the error correction model. Here  = 1 − L is the lag operator: X t = 1 X t−1 + . . . + p−1 X t−p+1 + X t−1 +  + Dt + ␧t

(t = 1, . . ., T )

Except for the error correction term Xt−1 the upper equation is a normal one-time-differentiated VAR(p) model. To achieve equivalence on both sides, Xt−1 has to be stationary. The further exam  ination depends on the rank r of . If has the full rank, the term is stationary. If the rank is zero, the term is no longer part of the equation. But if the rank is reduced   (i.e. if the number of non-zero eigenvalues of is r < k, where r is the rank of the k × k-matrix and 0 ≤ r ≤ k), than there is cointegration. If so, there exist  = ␣␤ for which Xt−1 is stationary. Each column r of ␤ corresponds to one long-run equilibrium. ␣ describes the speed of adjustment, with which the system returns to the equilibrium after a disturbance. Before ␣ and ␤ can be estimated, we must determine the number r of the cointegration relationships. Johansen and Jusélius (1990) proposed two maximum likelihood test to do this, the trace test and the maximum eigenvalue test. Although both statistics test functions

36

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45



of the estimated eigenvalues of , they use different null and alternative hypotheses. Both tests are calculated recursively, beginning with r = 0. The trace-tests H0: number of cointegrating relationships is at most r. The maximum eigenvalue test compares H0: exactly r cointegrating relationships against H1: more than r relationships. Both tests follow the critical values calculated by Johansen and Jusélius (1990). The corresponding values of the two tests together with the critical values are tabulated in Table 4. In order to examine the robustness of our model, we examined the Granger causality. Granger causality does not identify real causality between variables. Instead, it identifies variables helping to predict another variable. For the detection of Granger causality we used the test of Toda and Yamamoto (1995). It can be applied independently of the properties of the time series. Empirical data When selecting the time horizon for our study we tried to consider as many data points as possible. Additionally, we have accounted for the restriction that reliable data for Germany in the present borders exists only for the time after the reunification of Germany. Therefore, our first data are from January 1995. According to Hietala et al. (2013) the time before the introduction of the Euro is relatively short. Additionally, Germany was part of the European exchange mechanism after 1996. Because of that, there should be no structural break in time series. We examine export and import quantities and export and import prices in our study. The variables GDP and exchange rate are also included as indicators of the German economy. Both, quantities as well as prices are exported from the Statistical Office of the European Communities (Eurostat). The data is selected according to the Combined Nomenclature. That is, it is not directly exported from the database Eurostat, but from the foreign trade database COMEXT, which is maintained by Eurostat. This is available at http://epp.eurostat.ec.europa.eu/newxtweb/. The Combined Nomenclature of the data is as follows: 4403: Wood in the rough, whether or not stripped of bark or sapwood, or roughly squared. The prices per unit are determined through the quotient of aggregated value of export or import per year and aggregated quantity of export or import per year. This method is in accordance with the one used by Hietala et al. (2013). Also, the data are aggregated because in CN 4403 all species are combined. According to Chambers and Just (1981) this is justified because the study examines the impact on the whole market. This data is available on a monthly basis. Because the data of GDP is only available quarterly, we aggregated the rest to quarterly data, too. To do this, we used the sum of three months for the quantities and the mean of three month for the prices and the exchange rate. The GDP is extracted from the database of the German Federal Statistics Office (https://destatis.de/DE/Startseite.html). The exchange rate data is extracted from the European database Eurostat, too. The data of the exchange rate between Euro and US Dollar and the ECU (European Currency Unit) respectively is extracted from the table “Euro/Ecu-Wechselkurse–Monatliche Daten (ert bil eur m)”. The monthly mean of exchange rate was chosen. The unit of the exchange rate is ECU from 1995:1 to 1998:4. We did not convert the ECU to German Mark to get a uniform time series. Model calculations For Germany as a highly export oriented country it is of utmost interest to estimate the export quantity in advance. For that reason, the long-term equilibrium is normalized to the export quantity. With the aid of a vector model, it is possible to estimate the effects of the examined variables on each other. There is no need to distinguish between exogenous and endogenous variables. In the long-term equilibrium import quantity is expected to influence export quantity negatively because import is used to satisfy domestic demand and this implicates that there is already insufficient wood supply. Therefore, nothing is left to be exported. Export price should influence export quantity positively because high export price stimulates exports. Because of the fact that Germany should act as a price taker on the world market, import price should be equivalent to export price and therefore, should influence export quantity positively, too. GDP should have negative impact on export quantity because a high GDP reflects a high demand

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

37

Table 2 Lag length determination. Optimal lag-length

AIC

BIC

HQ

All

Export quantity Import quantity Export price Import price GDP Exchange rate All time series together

4 1 5 5 5 2 8

1 1 5 1 3 2 1

1 1 5 5 5 2 8

2 1 5 3 4 2 4

for wood inside the country and for that reason, there should be less wood left to export. Exchange rate should influence export quantity negatively because a high exchange rate implies a high price abroad and that should decrease the export demand. For the calculation of the model we employed the log-transforms on the variables of interest. Further, we use information criteria to determine the lag length k to be used in the model. A maximum lag length of 8 was imposed because of the limited amount of data points. The results of the tests are reported in Table 2. The results are mixed. Because of the mixed results, we used a lag length of 4. This is a reasonable compromise, because the seasonal cycle of 5 of the 6 variables was 4. To select suitable criteria for the unit root tests, meaning the use of constant and time trend, time series were examined visually (see Baak et al., 2007). Additionally, the coefficients of the trend or the constant respectively were tested for significance. Unit root tests were conducted separately for each time series. Because the existence of a unit root in a time series is important to determine whether one must test for cointegration or not, unit root tests were conducted beforehand. In the first run, all unit root tests were conducted with the assumption that there is a trend and a constant. Corresponding coefficients were tested for significance and were dropped if they were not significant. The results are reported in Table 3. The exact values of the information criteria and the unit root tests are not reported here to save space, but are available on request. Each time series with unit roots was differentiated and tested for unit roots once again. We did not find unit roots in any of the differentiated time series. Therefore, the conclusion is, that they are at most I(1) processes. Because we detected unit roots in some of the time series, we tested the time series for cointegration. Due to the fact that we found significant coefficients for a trend and a constant in some of the time series, we conducted the cointegration test with the assumption that there is a trend and a constant. We also estimated dummy variable to account for seasonality. The results of the cointegration tests are reported in Table 4. The trace test clearly rejects zero and one cointegration relations as r = 0 and r = 1 on every level of significance, but it failed to reject the H0 of two cointegration relations. The Maximum Eigenvalue test came to the same result when a significance level of 5% was applied. Thus we concluded that there are two cointegration relationships. Before estimating the error correction model we estimated ␤ and ␣. As mentioned before, both are normalize to the export quantity. Through the normalization, the results are shown in Table 5. After determining ␣ and ␤, we estimated the error correction model. The results are summarized in Table 5. The error correction term (ECT) corresponds to Xt−1 . L1, L2, L3 stand for variables with lags Table 3 Unit root tests. ADF-test

Export quantity Import quantity Export price Import price GDP Exchange rate

PP-test

ADF-test with seasonal dummies

Unit root

Trend

Drift

Unit root

Trend

Drift

Unit root

Trend

Drift

x x – – – x

– – – x x –

– – – x x –

x x – – – x

– – – x x –

– – x x x –

x x – – – x

– x – x x –

– x x x x –

38

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

Table 4 Trace test and maximum eigenvalue test. Rank

Trace-test

Threshold values 10%/5%/1%

Max.-eigen value-test

Threshold values 10%/5%/1%

r=5 r=4 r=3 r=2 r=1 r=0

4.29 13.61 28.43 55.42 97.19 158.27

10.49/12.25/16.26 22.76/25.32/30.45 39.06/42.44/48.45 59.14/62.99/70.05 83.20/87.31/96.58 110.42/114.90/124.75

4.92 8.70 14.82 26.99 41.77 61.08

10.49/12.25/16.26 16.85/18.96/23.65 23.11/25.54/30.34 29.12/31.46/36.65 34.75/37.52/42.36 40.91/43.97/49.51

Table 5 Long-run equilibrium and speed of adjustment (both normalized to export quantity). Long-run equilibrium ␤ coefficients for log-transformed variables r

Export quantity

Import quantity

Export price

Import price

GDP

Exchange rate

Trend

1 2

1.00 1.00

−3.86 2.31

17.65 −6.55

11.81 9.79

−60.72 −30.73

14.6 1.41

0.52 0.05

4.85 −0.03

−1.28 0.3

−3.78 −0.02

−1.03 0

9.91 0

Speed of adjustment ␣ 6.99 1 −0.07 2

one to three. SD abbreviates the seasonal dummies. For each time series the residuals were examined visually on the one hand, and through calculations on the other hand, to check on whether they were normally distributed around the mean zero. All residuals are normally distributed around the mean zero. We also checked for any autocorrelation and found none except for export quantity and GDP, where the third lag is autocorrelated. Because the value was very close to the threshold value, we did not correct it. Additionally, we checked for the existence of heteroscedasticity with a residual2 -modelvalue plot. When no heteroscedasticity is present, residuals should be distributed in the same part of the plot over the whole range of calculated values. We did not find any evidence for heteroscedasticity. We checked the multivariate normality, autocorrelation and heteroscedasticity. The multivariate normality was checked with the Jarque–Bera-test (Jarque and Bera, 1987). It did not reject the H0 of normality (test value: 19.22; p = 0.08). The serial autocorrelation was tested with the Breusch–Godfrey LM statistic (Breusch, 1978; Godfrey, 1978) together with the correction for small sample size proposed by Edgerton and Shukur (1999). This test fail to reject the H0 of no serial correlation with test value of 1.24 (p = 0.25). We used an ARCH model to test for multivariate heteroscedasticity (Lütkepohl (2006)). It did not rejected the H0 of homoscedasticity with a test value of 1323 (p = 0.99). The calculated models show medium to good in-sample fits depending on dependent variable of the particular time series. The adjusted R2 are reported in Table 5 and range from 0.36 to 0.80. The number of the coefficients which are significantly different from zero are between 2 and 13. As can be seen in Fig. 1, the fact is that both models showed there follow the general pattern of the original data. Although they both do not always hit the exact value of the original data, they are capable of reproducing the development of the original time series. All calculations were performed using the statistical software R (R Core Team, 2016) and the packages “vars” and “urca” (Pfaff, 2006, 2008) (Tables 6 and 7). Results and discussion Results Our study shows several results. The forecasts were made with a confidence interval of 0.99. Forecasts are generated for 14 quarters implying a 14-steps ahead forecast. The last known value for the forecast was 2012:Q4. The time series of export volume, export price and GDP provide qualitatively good forecasts. Considering only the first four quarters of time series export volume, the values are also quantitatively well forecasted.

Table 6 VECM raw timber. VECM(4) raw timber Export quantity

Import quantity

Export price

Coefficient

p

Coefficient

p

Coefficient

p

Coefficient

p

Coefficient

p

Coefficient

p

ECT 1 ECT2 Constant SD1 SD2 SD3

−0.004 −0.44 16.140 −0.316 0.0592 −0.358

0.954 0.03* 0.076# 0.456 0.219 0.299

0.016 −0.262 11.351 0.406 0.573 −0.893

0.855 0.312 0.332 0.463 0.36 0.051#

0.016 0.116 −3.013 −0.019 −0.062 −0.114

0.151 0.001*** 0.041* 0.72 0.422 0.044*

−0.053 0.11 −8.621 0.049 0.055 0.04

<0.001*** 0.01** <0.001*** 0.484 0.489 0.476

0.003 0.013 −0.24 0.007 0.036 0.024

0.223 0.053# 0.405 0.622 0.024* 0.033*

0.005 0.01 0.009 0.004 0.004 −0.051

0.553 0.647 0.993 0.936 0.939 0.196

Export quantity L1 Import quantity L1 Export price L1 Import price L1 GDP L1 Exchange rate L1

−0.21 0.133 0.181 1.860 3.617 −0.448

0.144 0.39 0.826 0.048* 0.528 0.724

0.052 −0.37 2.351 0.395 1.598 −1.070

0.778 0.071 0.033 0.742 0.83 0.518

0.05 0.042 −0.473 −0.05 0.128 0.314

0.51 0.098# 0.001*** 0.737 0.89 0.129

0.054 0.002 −0.33 −0.83 10.135 0.354

0.025* 0.932 0.018 <0.001*** 0.232 0.095#

0.002 0.009 −0.056 0.054 −0.318 0.043

0.616 0.080# 0.038* 0.070# 0.089# 0.293

0.012 0.001 0.032 0.148 −0.525 0.318

0.448 0.942 0.733 0.16 0.419 0.031*

Export quantity L2 Import quantity L2 Export price L2 Import price L2 GDP L2 Exchange rate L2

−0.263 0.027 0.135 0.8 7.578 −1.441

0.066# 0.872 0.894 0.358 0.2 0.314

0.07 −0.116 2.330 0.387 −9.680 −0.35

0.703 0.592 0.082# 0.732 0.209 0.85

−0.01 0.077 −0.617 −0.056 0.066 0.017

0.646 0.006** <0.001*** 0.69 0.944 0.941

0.046 −0.009 −0.644 −1.053 2.893 0.441

0.054# 0.736 >0.001*** <0.001*** 0.004** 0.065#

−0.002 0.016 −0.029 0.075 −0.095 0.033

0.678 0.005** 0.368 0.010** 0.625 0.474

−0.007 −0.001 −0.067 0.073 −1.203 −0.131

0.655 0.977 0.557 0.455 0.075# 0.418

Export quantity L3 Import quantity L3 Export price L3 Import price L3 GDP L3 Exchange rate L3

0.002 −0.015 0.441 2.334 3.605 −1.129

0.99 0.934 0.706 0.028* 0.536 0.407

0.136 0.003 0.585 0.092 −23.013 −1.790

0.447 0.991 0.702 0.946 0.004** 0.314

−0.002 0.124 −0.906 0.027 −1.275 0.232

0.927 <0.001*** <0.001*** 0.871 0.178 0.291

0.025 0.05 −0.605 −0.918 3.780 0.66

0.269 0.102 0.003** <0.001*** <0.001*** 0.005**

0.001 0.017 −0.029 0.039 −0.596 −0.02

0.749 0.005** 0.442 0.248 0.002** 0.649

0.017 0.011 0.054 0.19 −1.142 0.1

0.275 0.601 0.682 0.111 0.088# 0.516

** ***

GDP

Exchange rate

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

* #

Import price

Represents the significance level of 0.05. Represents the significance level of 0.1. Represents the significance level of 0.01. Represents the significance level of 0.001.

39

40

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

Fig. 1. Raw wood export quantity and price.

The time series import volume, import price and exchange rate provide no useful predictions. The error characteristics of MAPE and RMSE rise for all time series except for the time series of the export price. The RMSE and MAPE of the GDP remain the same. In order to assess the forecasting quality of the model Theil’s inequality coefficient was additionally calculated as a measure of accuracy. It compares values predicted by the model with values of the so

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

41

Table 7 Measures of accuracy of the model. In-sample error Kolmogorov–Smirnov test

Export quantity Import quantity Export price Import price GDP Exchange rate

D-value

p-Value

0.11 0.11 0.07 0.07 0.05 0.05

0.38 0.39 0.91 0.91 0.99 0.98

Root mean square error

% Root mean square error

Mean absolute error

Mean absolute percentage error

0.31 0.39 0.05 0.05 0.01 0.03

0.01 0.01 0.01 0.01 0.00 0.55

0.24 0.31 0.04 0.04 0.01 0.03

0.01 0.01 0.01 0.01 0.00 0.00

Out-of-sample error

Export quantity Import quantity Export price Import price GDP Exchange rate

Root mean square error

% Root mean square error

Mean absolute error

Mean absolute percentage error

Theils U (14 quartals)

Theils U (4 quartals)

0.37 0.74 0.03 0.17 0.01 0.10

0.01 0.02 0.01 0.04 0.00 0.90

0.29 0.64 0.03 0.17 0.01 0.08

0.01 0.02 0.01 0.04 0. 00 0.65

0.66 2.51 0.66 4.70 0.41 5.08

0.28 1.00 0.47 3.58 0.29 2.18

called naïve model (where the predicted value is the same as one period before, yt = yt−1 ). Deviations are squared in order to weight large errors more strongly than smaller ones. Theil’s U-statistic is 1 or greater when the naïve model describes the data as good as or better than the forecasting model. The forecasting model should be dropped then. Using the model should be considered only if Theil’s U-statistic is smaller than 1. The smaller it is the more accurate forecasts are obtained using the proposed model. Theil’s U-statistic equal to 0 indicates perfect forecasting accuracy. Theil’s inequality coefficients for export quantity is 0.66 for export quantity and export price. It is 0.41 for the GDP. All three values indicate a moderate to good predictive ability. However, considering only four quarters as forecast timeframe for calculating Theil’s inequality coefficient, it improves to 0.28 for export quantity, to 0.47 for export price and to 0.29 for GDP. This indicates a very good forecast for one year. In the first long-term equilibrium all coefficients got the expected signs. The second long-term relation describes a substitution of German raw wood with cheap foreign raw wood. German lumber can be exported to higher prices. Therefore, import quantity and import price are positively related to export quantity. GDP is negatively connected because a high GDP implies that German raw wood and foreign raw wood are needed to meet German demand. The exchange rate has a positive impact because imports, as substitution for German raw wood demand, can be bought cheap, if the exchange rate is high. To check the robustness of our VECM results we calculated the Granger causality to verify if the relations hold. Table 8 presents the results of Granger causality tests where asterisked figures indicate causality of a variable entitling the column over a variable entitling the row. When calculating the Granger causality for raw wood it should be noted that none of the studied variables is significantly causal for the export quantity. This underlines the VECM with the exception of the import price, which is significant in the lags two and three. However, the two economic indicators considered are Granger-causal for import quantity. This partly confirms the results of the error correction model, where only the GDP is significant, but the result is reasonable. A high economic output increases the demand for timber and thus induces timber imports. The exchange rate determines the relative import price and along with this the attractiveness of imported timber. Kim et al. (2003) came to the same conclusion. They established a causal relationship in the exchange rate to import volume of hardwood in Korea. Import quantity and import price are causal at a significance level of 5% and 10%, respectively for the export price. In the VECM the coefficients of Export price and import quantity are significant. Each of the parameters is causal for

42

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

Table 8 Granger causalities (column heads are the causal X variables and the row heads are the effect variables Y). Causal variables X

X

Y Export quantity Import quantity Export price Import price GDP Exchange rate * # ** ***

Export quantity

Import quantity

Export price

Import price

GDP

Exchange rate

– 5.60 (0.23) 2.50 (0.65) 15.60 (0.004)** 6.50 (0.16) 4.70 (0.32)

1.10 (0.89) – 11.1 (0.03)* 11.10 (0.03)** 6.30 (0.18) 6.40 (0.17)

3.30 (0.51) 7.70 (0.10)# – 12.80 (0.01)** 3.70 (0.45) 5.90 (0.20)

7.11 (0.13) 3.00 (0.55) 8.20 (0.08)# – 2.40 (0.66) 7.30 (0.12)

2.80 (0.59) 13.20 (0.01)* 3.40 (0.49) 22.20 (>0.001)*** – 1.9 (0.76)

3.60 (0.46) 7.80 (0.10)# 0.98 (0.91) 12.20 (0.02)** 4.30 (0.37) –

Represents the significance level of 0.05. Represents the significance level of 0.1. Represents the significance level of 0.01. Represents the significance level of 0.001.

import price. Thus, there is a reciprocal causality between export price and import price. This can be explained by the fact that the world market price can be taken for granted. One can deduce therefrom that Germany has limited market power and occurs as a rate taker. None of the variables are causal for GDP and exchange rate. This is reasonable because the timber sector in Germany is small compared to the whole economy and therefore cannot influence the economy or the value of the Euro. Discussion In the present study, we have developed a simple model based on time series that allows for shortterm or even medium-term forecasting in the German forest sector. We have shown that using a VECM can succeed in modelling future volumes and prices of timber products for Germany. In a further step we have calculated the Granger causality to underline the results of the VECM. In summary, we note that although the results of time series analysis vary and not all variables could be well predicted, the predictive power of GDP performed well. The VECM, which was estimated for the analysis manages to predict trends of export volume and export price quite well considering the relatively long forecasting period of 14 quarters. When the forecast is made for one year, the model performs very well for these two variables. However, the model fails in the prediction of import volume and import price. Although it is not the aim of our model to predict the GDP, the model was able to give good predictions for it as well. Hetemäki and Mikkola (2005) showed that a VECM can sometimes fail to predict time series properly. Considering the performance of our model, we cannot confirm this in general. Our results indicate that a VECM can be a quite valuable tool to predict time series, but it sometimes may also fail to predict time series properly. For the poor forecasting performance of import quantity and import price there could be several reasons. It is possible that the time series be distorted by the strong aggregation of different raw timber products. Especially for raw timber it is conceivable that high quality timber logs show another development than e.g. raw timber for paper production. It is conceivable that these trends cancel each other out and thus the time series lose information value. Different types of wood could behave as own products and react differently to changes in market conditions as Hseu and Buongiorno (1993) confirm. They show that depending on prices the import volumes of various types of wood can vary. Although there are studies that use shorter time periods, it is possible that the relatively short period we consider in our study is partly responsible for the poor forecasting performance of some of the examined variables. Consequently, the model may perform better when longer time periods are taken into account. By aggregating monthly data to quarterly data instead of 216 data points per time series only 72 points remain available for analysis. This was necessary, because the data for GDP was available only as quarterly data. Another very likely reason may be the omission of important variables. In other studies, in addition to GDP and exchange rate, also considered in our study, a variety of other factors are mentioned as

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

43

relevant economic indicators. One commonly used variable for analysis of quantities and prices for timber imports and exports from Canada to the USA e.g. is housing starts (see Baek, 2012; Jennings et al., 1991; Nagubadi and Zhang, 2013). Certainly, this is less suitable for Germany since US conventional timber construction is not as wide spread in Germany as in the USA. Nevertheless, it is generally true that the omission of certain variables could cause a poor forecasting performance. As an indicator of the local economy interest rate is used in some studies (see e.g. Jennings et al., 1991; Nagubadi et al., 2009; Nagubadi and Zhang, 2013). Other authors use population size (see Limaei et al., 2011), overall domestic price level (see Nagubadi and Zhang, 2013) or income (see Baek, 2007; Nanang, 2010). Also domestic timber production and domestic wood prices are mentioned in research literature when describing timber sector (see Jennings et al., 1991; Limaei et al., 2011; Nagubadi and Zhang, 2013). Alavalapati et al. (1997) include domestic use of pulp wood as an independent variable. Another one is e.g. the economic situation of the rest of the world as a trading partner measured by trade-value-weighted average of real GDP of major importers (see Sun and Zhang, 2003). Jennings et al. (1991) use the price of products in the partner country. For a meaningful causal relationship between exports and GDP, it is necessary that a long-term equilibrium exists, as proved by Ahmad and Harnhirun (1995). For Germany, as an export oriented country, it is expected that this is fulfilled. By cointegration of time series, the results of our study confirm such a connection. Our results also prove the export-led growth theory for Germany that the exports boost growth. Sharma et al. (1991) found also a causal link between exports and economic growth for Germany. Marin (1992) also confirms a causality of exports to economic growth for Germany. In contrast to this, other studies as the study by Dutt and Ghosh (1996) find no causal connection between exports and growth for Germany. As well as Arize (1998) and Zang and Baimbridge (2012) our study also finds a causal connection between GDP and import volume. The results of our study suggest that GDP and exchange rate have impact on import quantity and import price in the sense of Granger causality. The VECM underlines the importance of the GDP for both variables. In the VECM the exchange rate is significant only for the price. Arize (1998) shows for seven European countries a causal link between exchange rate and import quantity which we also find in our study. In Arize (1995), Baak et al. (2007) and Kroner and Lastrapes (1993) a relationship between exchange rate and export amount is also found. In our study, however, no link between export price and exchange rate could be detected. In conclusion, we can only say that given the intended simplicity of the presented model the insamples show good to very good fits, while the out-of-samples of individual variables are often not as successful. Time series for export volume and export price of raw timber show that good predictions with VECM are possible. A glance at Fig. 1 shows that forecast of export quantity is nearly perfect for the first three quarters and that the price can be predicted very well for the whole forecast period. In contrast, there are some shortcomings of the model. Although it fits quite well in-sample with respect to import quantity and import price, it fails when it comes to out-of-sample prediction of those. This is proved by a Theil’s inequality coefficients of 2.51 for import quantity and even 3.58 for import price. A possible improvement would be the attempt after a first regression with all variables included to exclude all insignificant ones. A similar procedure describe Hetemäki et al. (2004). They examine import of sawn timber and come to the conclusion that the partial model is far superior and leads to better results than the VAR and VECM. Hetemäki and Mikkola (2005) see in the combination of different models another possible way to improve the prediction. References Afxentiou, P.C., Serletis, A., 1991. Exports and GNP causality in the industrial countries: 1950–1985. Kyklos 44 (2), 167–179. Ahmad, J., Harnhirun, S., 1995. Unit roots and cointegration in estimating causality between exports and economic growth: Empirical evidence from the ASEAN countries. Bd. DP 9523. Discussion paper series. Dept. of Economics, Concordia University, Montreal. Ahmad, J., 2001. Causality between exports and economic growth: what do the econometric Studies tell us? Pac. Econ. Rev. 6 (1), 147–167.

44

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

Alavalapati, Janaki, R.R., Adamowicz, W.L., und Luckert, M.K., 1997. A cointegration analysis of Canadian wood pulp prices. Am. J. Agric. Econ. 73 (3), 975–986. Arize, A.C., 1995. The effects of exchange-rate volatility on US exports: an empirical investigation. South. Econ. J. Arize, A.C., 1998. The long-run relationship between import flows and real exchange rate volatility: the experience of eight European economies. Int. Rev. Econ. Financ.: IREF 7 (4), 417–435. Awokuse, T.O., 2003. Is the export-led growth hypothesis valid for Canada? Can. J. Econ. 36 (1), 126–136. Awokuse, T.O., Bessler, D.A., 2003. Vector autoregressions, policy analysis, and directed acyclic graphs: an application to the US economy. J. Appl. Econ. 6 (1), 1–24. Awokuse, T.O., 2005. Export-led growth and the Japanese economy: evidence from VAR and directed acyclic graphs. Appl. Econ. Lett. 12 (14), 849–858. Baak, S.J., Al-Mahmood, M.A., Vixathep, S., 2007. Exchange rate volatility and exports from East Asian countries to Japan and the USA. Appl. Econ. 39 (7–9), 947–959. Baek, J., 2007. The J-curve effect and the US-Canada forest products trade. J. Forest Econ. 13 (4), 245–258. Baek, J., 2012. The long-run determinants of US lumber imported from Canada revisited. Forest Policy Econ. 14 (1), 69–73. Balassa, B., 1978. Exports and economic growth: further evidence. J. Dev. Econ. 5 (2), 181–189. Bolkesjo, T.F., Buongiorno, J., 2006. Short- and long-run exchange rate effects on forest product trade: evidence from panel data. J. Forest Econ. 11 (4), 205–221. Box, G.E., Jenkins, G.M., 1970. Time Series Analysis. Forecasting and Control. [Reprint]. Holden-Day (Holden-Day series in time series analysis), San Francisco. Breusch, T.S., 1978. Testing for autocorrelation in dynamic linear models. Aust. Econ. Pap. 17 (31), 334–355. Buongiorno, J., Chou, J.J., Stone, R.N., 1979. Monthly model of the United-States demand for softwood lumber imports. Forest Sci. 25 (4), 641–655. Buongiorno, J., Chavas, J.P., Uusvuori, J., 1988. Exchange-rates, Canadian lumber imports, and United-States prices – a time-series analysis. Can. J. Forest Res. 18 (12), 1587–1594. Buongiorno, J., 1996. Forest sector modeling: a synthesis of econometrics, mathematical programming, and system dynamics methods. Int. J. Forecast. 12 (3), 329–343. Chambers, R.G., Just, R.E., 1981. Effects of exchange rate changes on U. S. agriculture: a dynamic analysis. Am. J. Agric. Econ. 63 (1), 32–46. Dutt, S.D., Ghosh, D., 1996. The export growth-economic growth nexus: a causality analysis. J. Dev. Areas 30 (2), 167–182. Edgerton, D., Shukur, G., 1999. Testing autocorrelation in a system perspective testing autocorrelation. Econ. Rev. 18 (4), 343–386. Giles, J.A., Williams, C.L., 2000. Export-led growth: a survey of the empirical literature and some non-causality results. Part 1. J. Int. Trade Econ. Dev. 9 (3), 261–337. Godfrey, L.G., 1978. Testing for higher order serial correlation in regression equations when the regressors include lagged dependent variables. Econometrica 46 (6), 1303–1310. Granger, C.W.J., Newbold, P., 1974. Spurious regressions in econometrics. J. Econ. 2, 111–120. Granger, C.W.J., 1981. Some properties of time series data and their use in econometric model specification. J. Econ. 16 (2), 121–130. Hannan, E.J., 1970. Multiple Time Series. Willey, New York. Hänninen, R., 2004. Econometric models in forest sector forecasting. J. Forest Econ. 10, 57–59. Hetemäki, L., Hänninen, R., Toppinen, A., 2004. Short-term forecasting models for the Finnish forest sector: lumber exports and sawlog demand. Forest Sci. 50 (4), 467–472. Hetemäki, L., Mikkola, J., 2005. Forecasting Germany’s printing and writing paper imports. Forest Sci. 51 (5), 483–497. Hietala, J., Hanninen, R.H., Toppinen, A., 2013. Finnish and Swedish sawnwood exports to the UK market in the European monetary union regime. Forest Sci. 59 (4), 379–389. Hseu, J.-S., Buongiorno, J., 1993. Price elasticities of substitution between species in the demand of U.S. softwood lumber imports from Canada. Can. J. Forest Res. 23 (4), 591–597. Jarque, C.M., Bera, A.K., 1987. A test for normality of observations and regression residuals. Int. Stat. Rev. 55 (2), 163–172. Jennings, S., Adamowicz, W., Constantino, L., 1991. The Canadian lumber industry and the macroeconomy: a vector autoregressive analysis. Can. J. Forest Res. 21, 288–299. Johansen, S., 1988. Statistical analysis of cointegration vectors. J. Econ. Dyn. Control 12 (2–3), 231–254. Johansen, S., Jusélius, K., 1990. Maximum likelihood estimation and inference on cointegration: with applications to the demand for money. Oxf. Bull. Econ. Stat. 52 (2), 169–210. Kim, D.-J., Schreuder, G.F., Youn, Y.-C., 2003. Impacts of the currency value change on the forest products import quantities in Korea. Forest Policy Econ. 5 (3), 317–324. Kroner, K.F., Lastrapes, W.D., 1993. The impact of exchange-rate volatility in international trade-reduced form estimates using the GARCH-in-mean model. J. Int. Money Financ. 12 (3), 298–318. Latta, G.S., Sjolie, H.K., Solberg, B., 2013. A review of recent developments and applications of partial equilibrium models of the forest sector. J. Forest Econ.: JFE 19 (4), 350–360. Limaei, S.M., Heybatian, R., Vaezin, S.M.H., Torkman, J., 2011. Wood import and export and its relation to major macroeconomics variables in Iran. Forest Policy Econ. 13 (4), 303–307. Lütkepohl, H., 2006. New Introduction to Multiple Time Series Analysis. Springer, Berlin. Marin, D., 1992. Is the export-led growth hypothesis valid for industrialized countries? Rev. Econ. Stat. 74 (4), 678–688. Nagubadi, R.V., Thompson, H., Zhang, D., 2009. Productivity and trade during the softwood lumber dispute. Int. Trade J. 23 (3), 301–324. Nagubadi, R.V., Zhang, D., 2013. US Imports for Canadian softwood lumber in the context of trade dispute: a cointegration approach. Forest Sci. 59 (5), 517–523. Nanang, D.M., 2010. Analysis of export demand for Ghana’s timber products: a multivariate co-integration approach. J. Forest Econ. 16 (1), 47–61. Pfaff, B., 2006. Analysis of Integrated and Cointegrated Time Series with R. Springer, New York (Use R!). Pfaff, B., 2008. VAR, SVAR and SVEC models: implementation within R package vars. J. Stat. Softw. 27 (4), 1–32.

H. Kolo, P. Tzanova / Journal of Forest Economics 26 (2017) 30–45

45

Pindyck, R.S., Rotemberg, J.J., 1990. The excess co-movement of commodity prices. Econ. J. 100 (403), 1173–1189. R Core Team, 2016. R: A Language and Environment for Statistical Computing. Version 3.2.3. R Foundation for Statistical Computing, Vienna, Austria, Available at: https://www.R-project.org/. Schuster, P., 1906. Auflösungen zu den Aufgaben aus der Erd-u. Himmelskunde etc. von Dr. Paul Schuster, Oberl. zu Breslau. Preuß & Jünger, Breslau. Sharma, S., Norris, M.E., Cheung, D.W.-W., 1991. Exports and economic growth in industrialized countries. Appl. Econ. 23 (4A), 697–707. Shumway, R.H., Stoffer, D.S., 2006. Time Series Analysis and Its Applications. With R Examples, 2nd [updated] ed. Springer, New York (Springer texts in statistics). Song, N., Chang, S.J., Aguilar, F.X., 2011. U.S. softwood lumber demand and supply estimation using cointegration in dynamic equations. J. Forest Econ. 17 (1), 19–33. Sun, C., Zhang, D., 2003. The effects of exchange rate volatility on U.S. forest commodities exports. Forest Sci. 49 (5), 807–814. Toda, H.Y., Yamamoto, T., 1995. Statistical inference in vector autoregressions with possibly integrated processes. J. Econ. 66 (1/2), 225–250. Toppinen, A., Kuuluvainen, J., 2010. Forest sector modelling in Europe – the state of the art and future research directions. Forest Policy Econ. 12 (1), 2–8. Tsay, R.S., 2000. Time series and forecasting: brief history and future research. J. Am. Stat. Assoc. 95 (450), 638–643. Wisdom, H.W., Granskog, J.E., 2003. The effect of exchange rates on southern pine exports. Forest Prod. J. 53 (10), 19–23. Zang, W., Baimbridge, M., 2012. Exports, imports and economic growth in South Korea and Japan: a tale of two economies. Appl. Econ. 44 (3), 361–372.