THE ROBUSTNESS OF THE CAUSAL AND ECONOMIC RELATIONSHIP BETWEEN CONSTRUCTION FLOWS AND ECONOMIC GROWTH: EVIDENCE FROM WESTERN EUROPE

Keywords: Construction, Economic Growth Construction, Economic Growth, Granger causality, Business cycles, Housing Policy

Our main objective is to analyze whether we have a problem of parameter heterogeneity across countries and over time in the estimation of the relationship between infrastructure investments and economic growth. The research approach concerning causality and the estimating of the long run equilibrium is based on the error correction model. The problem of parameter heterogeneity is handled by the use of interaction terms. The result indicates that residential construction Granger causes GDP in the short and long run and it seems likely that the interaction term indicating high unemployment do add some explanation power to the model. This is not true when it comes to infrastructural and other building construction and its impact on economic growth. A high housing stock per capita seems to reduce the short run effect. That implies that residential construction seems to have a larger effect if the accumulated residential stock is on a low level. The speed of adjustment to long run equilibrium differs considerably between a country with a low residential capital stock and a country with a high capital stock. Moreover, high owner occupation rates seem to be associated with a stronger relationship between residential construction and economic growth.

Introduction

There is a belief among politicians and policy makers that public infrastructure investments and other construction enhance the economy of a country (see e.g. [START_REF] Turnovsky | Fiscal Policy in a Growing Economy with Public Capital[END_REF][START_REF] Delgado | Network infrastructure spillover in private productive sectors: evidence from Spanish high capacity roads[END_REF][START_REF] Delgado | Network infrastructure spillover in private productive sectors: evidence from Spanish high capacity roads[END_REF]. This belief is also supported by a number of investigations and research done by such as e.g. Aschauer (1989), [START_REF] Green | Follow the Leader: How Changes in Residential and Non-residential Investment Predict Changes in GDP[END_REF], [START_REF] Coulson | Residential Investment, Non-residential Investment and GDP[END_REF] and Esafahani and Ramirez (2003). On the other hand, there have also been some indications that the causality between public investments and economic growth is not that straightforward as first expected, see e.g. [START_REF] Holtz-Eakin | Infrastructure in a Structural model of economic growth[END_REF] and Wigren and Wilhelmsson (2007a).

In the present paper, we analyze structural breaks over time, as causality and economic effects are not expected to be constant in boom and bust. The objective is also to examine whether the effects are a function of the accumulated capital stock, i.e. if the marginal effect is different depending on the level of the stock. We are also investigating if the housing policy in the country has any impact on the relationship between residential construction and economic growth. That is, our main objective is to analyze whether we have a problem of parameter heterogeneity across countries and over time. Our hypotheses are that construction investments have a stronger effect on economic growth in an economic bust; residential construction will have a larger impact on GDP growth if residential capital stock is low; and less state intervention is associated with a stronger impact on GDP from residential construction.

The rest of the paper is organized as follows. Section 2 presents a brief literature review. The methodology is presented in section 3. In section 4, we discuss the data and the empirical model.

Section 5 and 6 presents the results concerning the level of the residential capital stock and choice of housing policy, respectively. Section 7 concludes and summarizes the paper.

A Brief Literature Review

A huge literature analyzing economic growth and its determinants exist 1 . Lately, many of them are based on endogenous growth model theory (see e.g. [START_REF] Romer | Increasing returns and long-run growth[END_REF][START_REF] Temple | The New Growth Evidence[END_REF]. At the end of 1980 and early 1990, a number of studies presented a strong and positive relationship between public infrastructure and economic productivity in the private sector (see e.g. Aschauer, 1989, and[START_REF] Munnell | Why has productivity growth declined? Productivity and public investment[END_REF]. Furthermore, results indicate that the construction industry generates one of the highest multiplier effects with other sectors of the economy, [START_REF] Park | Linkages between industry and services and their implications for urban employment generation in developing countries[END_REF]. Recently, [START_REF] Shioji | Public Capital and Economic Growth: A Convergence Approach[END_REF] find that infrastructure capital has a significant positive, but modest effect on economic growth using a panel data set of United States and Japanese regions.

The result by Aschauer and Munnell were e.g. criticized by [START_REF] Holtz-Eakin | Public-Sector Capital and the Productivity Puzzle[END_REF]. The main objection he raises is that earlier studies did not correctly account for fixed effects. To be able to correctly estimate the short and long run effect of construction on economic growth one need to remove country 1 A complete literature review can be found in [START_REF] Gramlich | Infrastructure Investment: A Review Essay[END_REF], [START_REF] Temple | The New Growth Evidence[END_REF] and [START_REF] Jiang | A Review of Studies on the Relationship between Transport Infrastructure Investments and Economic Growth[END_REF]. -3 -fixed effects, see e.g. [START_REF] Temple | The New Growth Evidence[END_REF] and [START_REF] Shioji | Public Capital and Economic Growth: A Convergence Approach[END_REF]. With a neoclassical growth model with fixed or random effects Holtz-Eakin and Schwartz (1995) repeated the above analysis by Aschauer (1989) and found no or only marginal impact of infrastructure investments on growth. [START_REF] Nijkamp | Meta-analysis of the effect of fiscal policies on long-run growth[END_REF] found "evidence for a positive effect of conventional fiscal policy on growth is rather weak".

Causality

Using U.S. data for the period 1959 to 1992, [START_REF] Green | Follow the Leader: How Changes in Residential and Non-residential Investment Predict Changes in GDP[END_REF] found that residential investment Granger causes GDP, while non-residential investment is Granger caused by GDP. However, the opposite is not true. Green also tested for the existence of structural breaks in the causality relationship and found such ones. Later, [START_REF] Coulson | Residential Investment, Non-residential Investment and GDP[END_REF] confirm the result by [START_REF] Green | Follow the Leader: How Changes in Residential and Non-residential Investment Predict Changes in GDP[END_REF]. Wigren and Wilhelmsson (2007a) examined the statistical relationship between gross domestic product and a broad group of construction in Western Europe from 1980 to 2004. The overall conclusion was that public infrastructure policies have an effect on short-run economic growth but only a weak effect on the long run. [START_REF] Lean | Empirical tests to discern linkages between construction and other economics sectors in Singapore[END_REF] empirically tests the linkage between construction and other economic sectors in Singapore. In the paper, an econometric procedure is proposed that can be used for determining the construction linkage to economic growth and involves unit-root testing and Granger causality. The study shows the causal relationships between construction and GDP is two-way.

Parameter heterogeneity

Gauger and Snyder ( 2003) investigate if the financial deregulation has changed the relationship between residential construction and key macroeconomic variables. The overall results indicate that residential construction shocks have increased the prediction power concerning changes in GDP under a more deregulated regime. Hence, less state intervention on the housing market may increase the impact of construction on growth. This is in accordance with e.g. [START_REF] Smith | What Determines Housing Investment? Housing and Urban Policy Studies 12[END_REF] arguments that housing policies have an effect on residential constructions. The argument for that is that countries differing widely in housing policy are unlikely to fulfill the statistically modeling assumption about parameter constancy [START_REF] Temple | Robustness tests of the augmented Solow model[END_REF][START_REF] Temple | The New Growth Evidence[END_REF] even if non-linearity may explain some of the parameter heterogeneity [START_REF] Masanjala | The Solow Model with CES Technology: Nonlinearities and Parameter Heterogeneity[END_REF]. In this paper, parameter heterogeneity is analyzed by introducing a set of interaction variables concerning the degree of state intervention on the housing market suggested by [START_REF] Temple | The New Growth Evidence[END_REF]. [START_REF] Odedokun | Alternative Econometric Approaches Analysing the Role of the Financial sector in Economic Growth: Time-Series evidence from LDCs[END_REF] investigated the relationship between the financial sector and economic growth in 71 countries. The conclusion drawn in the paper is that the financial sector promotes economic growth, but this impact is stronger in low income than in high-income countries. Hence, it indicates that changes in construction may have a larger impact on economic growth if the public capital stock is low compared to high one. Furthermore, [START_REF] Smith | What Determines Housing Investment? Housing and Urban Policy Studies 12[END_REF] argues that the size of the housing stock influence the residential construction. Here, the problem with parameter heterogeneity between -4 -countries with high capital stock compared to low areas will be handled in the same manner as housing policy, i.e., with a set of interaction variables.

It is not only parameter heterogeneity across countries that could be a problem. It is not likely that the parameters are constant over time. The argument for that is that when there are idle resources in the economy, construction would have a larger impact on GDP compared to a situation when all resources are used. That is, in a business cycle boom there is a risk that construction will crowd-out other types of investments with higher productivity and thereby decreasing the economic growth. In an attempt to control for parameter heterogeneity over time and eliminate business cycle effects, we introduce a set of interaction terms relating construction with unemployment rates.

Methodology

We investigate the relationship between construction and economic activity using a simple stylized model. That is, we merely relate change in production to exogenous changes in the construction, measured by investments in residential building, other construction, and investments in infrastructure.

The basic model is derived from a production function model where we have added public capital stock (buildings and infrastructure) to labor and stock of private capital. There are some potential econometric problems in the estimating of the production function such as non-stationarity, causality, and omitted variables, see e.g. discussion in Gramlish (1994) and [START_REF] Holtz-Eakin | Public-Sector Capital and the Productivity Puzzle[END_REF], as well as [START_REF] Temple | The New Growth Evidence[END_REF] and [START_REF] Gobbin | Different ways of looking at old issues: a time-series approach to inequality and growth[END_REF]. We have addressed these problems by using a pooled cross-sectional and time series data, allowing us to use fixed effects, and estimated the model in an error-correction framework. The problem of parameter heterogeneity is handled by the use of interaction terms (see [START_REF] Temple | The New Growth Evidence[END_REF].

The research approach concerning causality and estimating the long run equilibrium is based on Engle and Grangers (1987) error correction model (see e.g. [START_REF] Ramajo | Time-varying parameter error correction models: the demand for money in Venezuela, 1983.I-1994.IV[END_REF]. If two variables y and x are both integrated of order 1, I(1), and if a linear combination between them exists that yields a stationary variable, y and x are said to be co-integrated. If we assume y to be a function of x in a simple linear regression framework, we can write the following equation:

t i it t i e bx y , , , + = (1)
where both y and x are I(1), and e is I(0), subscript i indicate country and t years. Following [START_REF] Banerjee | Co-Integration, Errorcorrection, and the Econometric Analysis of Non-Stationary Data[END_REF], a general dynamic regression model in the form of error correction model (ECM) is equal to:

t i j t i j j t i j t i i t i x j y j e y , , 0 2 , 1 1 1 , 1 , ) ( ) ( + + + + = = = (2)
where y is equal to the dependent variable and x the independent. is equal to fixed country effects.

Subscript i is equal to country and t is equal to year. Index j is equal to number of lag. e i,t-1 is equal to -5 -(y i,t-1 -x i,t-1 ) in equation 1 above, that is, the ECT. By using the error-correction framework, it is possible to capture the adjustment in economic growth, by not only the changes in construction and fixed effects but also by how much GDP deviates from the long run equilibrium.

If 2 are jointly significantly different from zero, x Granger causes y in the short run. The long-run Granger causality can be found by testing the significance of the ECT. As we are using panel data, a fixed effect model will be used to account for idiosyncratic country effects. Among other things, the fixed effects controls for initial endowment that is constant over time. To control for business cycles, capital accumulation and housing policy, 2 and will be estimated separately in boom and bust and with high or low capital accumulation or depending on the housing policy in the country (Equation 3).

t i j t i t i j t i t i j t i t i j t i j j t i j t i t i t i t i t i t i t i i t i x j F x j C x j D x j y j e F e C e D e y , 0 2 , 5 , 0 2 , 4 , 0 1 , 3 , , 0 2 , 1 1 1 , , 4 1 , , 3 1 , , 2 1 , 1 1 , ) ( ) ( ) ( ) ( ) ( + + + + + + + + + + = = = = = = (3)
where D is a binary variable indicating if unemployment is high in the country, C is a binary variable indicating whether the country has low housing capital accumulation in the beginning of the period and F depending on the housing policy (less state intervention) in the country. If 2 are jointly significantly different from zero, x Granger causes y in the short run. If 3 are jointly negatively significantly different from zero, x Granger causes y in the short run to a higher degree if unemployment is high. Furthermore, if 4 are jointly significantly different from zero, x Granger causes y in the short run to a higher degree if the country has a low residential capital stock in the beginning of the period. Finally, if 5 are jointly significantly different from zero, x Granger causes y in the short run to a higher degree if the country has a less state intervention as a housing policy.

The Data

The data 2 consist of information about total construction. As it is potentially important to be able to disaggregate construction as different types of constructions have different effects on GDP, see e. we are using a panel data set, it is possible to avoid the endogeneity problem by using lags as instruments [START_REF] Temple | The New Growth Evidence[END_REF]. Another advantages using panel data set is that it allows us to control for

Pre-test of the data

Our central interest is to test the data concerning stationarity as this indicates that there is a long run relationship between construction and economic growth. Stationarity is defined as a variable where the mean, variance, and autocovariance are constant over time. A stationary variable is integrated of order zero and a variable that must be differentiated once to become stationary is said to be integrated of order one (see [START_REF] Granger | Spurious regressions with stationary series[END_REF]).

An augmented Dickey-Fuller test for a unit root has been utilized, but we have used the Levin and Lin-test (LL) version of the test (see [START_REF] Levin | Unit Root Tests in Panel Data: Asymptotic and Finite Sample Properties[END_REF]. The tested model is given by: i=1-14; t=1980-2004 (4)

t i t t i t i i t i Y Y Y , 1 , 1 , , µ + + + + =
The test implicitly assumes that all countries series have a common autoregressive coefficient. The data are said to follow a unit root if is not significantly different from zero. As Levin and Lin have showed, the parametric test statistics converges to a standard normal distribution under certain condition. We have used the critical values provided by Levin and Lin in their first version of the paper (1992). The critical value concerning the t-statistics (LL-test) without time trends is -2.00. We do relax the strong assumption about homogeneity in Levin and Lin's test by also utilizing the Im,

Pesaran and Shin's ( 2003) test (IPS) 3 . The test is parametric and critical values are presented in their paper. The 5% critical value is equal to -1.83 with the use of 25 periods and 14 cross-sections with no time trends. See Harter-Dreiman ( 2004) and [START_REF] Alba | Purchasing Power Parity and Country Characteristics: Evidence from panel data tests[END_REF] for an empirical use of the IPStest and LL-test.

Table 1 in here

3 See also [START_REF] Jönsson | Time-specific disturbances and cross-sectional dependency in a small-sample heterogeneous panel data unit root test[END_REF]. The unit root tests (without a time trend) for the panel indicate that a unit root is rejected for all the variables except GDP. However, when the individual countries are analyzed, most of the series are integrated of order 1.

Causality and Economic Effects

To proceed with the test concerning Granger causality, we test the error correction term (ECT) considering unit root. In the next stage, we estimate equation 3 with all the variables as dependent variables, respectively. The estimations will be carried out on the panel data with fix country effects.

Due to lack of data, we are only testing when j=2. The Granger causality test implies that the errorcorrection term is integrated of order zero, that is, the error term is stationary. The ADF-tests concerning the ECT in the panel set are all stationary, except the ECT concerning GDP regressed on investments (residential, buildings and infrastructure).

In table 2-5 below, the parameters in equation 3 are presented. In the first results is the dependent variable is equal to the change in GDP and the independent variables are lagged changes in GDP (Dgdp), lagged changes in residential construction (Dresi) and the error correction term (e). Some models also include dummy variables indicating high and low unemployment (HUE and LUE). The result suggests that residential construction Granger causes GDP in the short and long run (high Fvalues). It seems likely that the interaction variable adds some explanation power to the model, i.e., if unemployment is high, residential construction has a higher impact on economic growth. However, none of the individual parameters is significantly different from zero. Surprisingly, the results also indicate that construction in low unemployment periods have a higher positive effect on economic growth. If residential construction increases by 1 percent, GDP will increase by 0.02 percent the following years. In periods with high unemployment, the effect is about 0.07 percent and in periods with low unemployment, the effect is as high as 0.15 percent. The speed of adjustment to long run equilibrium is about 10-11 years, that is, if expected GDP is higher compared to actual GDP, the change in GDP is expected to be positive and the adjustment will be a tenth of the gap per year. The Granger causality is not conclusive. Residential construction Granger causes GDP both in short and long term. If expected residential construction is lower than the actual residential construction, the speed of adjustment to long run equilibrium is about 5 years.

Table 2 in here

The relationship between other building construction and economic growth is presented in Construction Granger causes GDP but GDP also Granger causes construction of other buildings.

Residential Stock

Additional residential construction in a country where the housing stock is already high compared to the population could affect the short and long run relationship between economic growth and residential construction. Our hypothesis is that high accumulation of residential stock should have a negative effect on residential construction effects on the change in GDP.

As a measure of the accumulation of residential stock in a country, we are using housing stock per capita. If the housing stock per capita is equal or above the median housing stock per capita in the investigated countries, we interpret it as high accumulation of residential capital. To be able to investigate its impact on the short and long run effect, we interacts the dummy variable with the change in residential construction (lagged 0 to 2 years) and the error correction term. The results are presented in the table 6 below (Model A6). The main results indicate that the models explanation power increases. As before, residential construction has a short run and long run effect on GDP. If residential construction increases by 1 percent, we expect that GDP will change with around 0.05 percent. However, we expect also that the effect will be higher if the unemployment is high (around 0.1 percent). Unexpectedly, the effect in short run seems to be even higher if the unemployment is very low (up to 0.17 percent). The latter is probably a demand driven effect and the former a supply driven effect. A high housing stock per capita seems to reduce the short run effect. That is, residential construction seems to have a large effect if the accumulated residential stock is on a low level. The speed to adjustment to long run equilibrium differs considerably between a country with a low residential capital stock and a country with a high. The results indicate that the speed to adjustment is approximately 5 years if the capital stock is low. On the other hand, if the capital stock is already high, it will take some considerably time to adjust long to run equilibrium (50 years). This effect is highly significant.

Housing Policy

In general, housing policy reflects the political ideology of the government in power (see [START_REF] Balchin | Housing Policy in Europe[END_REF]. Here we will categorize the countries in Europe into three broad groups based on only a few aspects of housing policy, namely (1) support to social-rented sector, (2) promote owner-occupation and (3) promote private landlordism. Countries in the first group are the Netherlands, Austria, Sweden, Denmark and France. The second group consists of Switzerland, Germany and Belgium. Finally, in the third group we find countries such as Spain, Finland, Italy, UK, Portugal and Norway. Our hypothesis is that the short run effect will be lower in countries with more state intervention and that the speed of adjustment in countries with a high social-rented sector will be lower compared to in countries where the housing policy are focused to less state intervention. The results are shown in the table below (Model A7).

Table 5 in here

The conclusions are that by introducing variables indicating choice of housing policy, we explain more that 50 percent of the variation in GDP. However, the results are more or less the same, but accumulated residential stock seems to be of less importance if we add variables indicating choice of housing policy. However, housing policy and housing stock is not correlated so there is not a problem of multicollinearity. On the other hand, housing policy seems to have a major effect on the relationship between residential construction and GDP. For example, residential construction in countries with housing policy characterized by a private rented sector above EU average or owner-occupation above the EU average have a larger effect on GDP compared to countries with a social-rented sector above or broadly at the EU average. However, the housing policy does not have any impact on the speed of adjustment to long run equilibrium. Even if there is little statistical evidence to support the view that owner occupation is associated with high income per capita (see e.g. [START_REF] Balchin | Housing Policy in Europe[END_REF], high owner occupation rates seem to be associated with a stronger relationship between residential construction and economic growth. If residential construction increases by 1 percent, the expected effect on GDP growth is 0.04 percent if the owner occupation rate is low and 0.08 percent if the owner occupation rate is high. This result is highly statistically significant.

Conclusion and Policy Implications

The research task in the present study is to analyze the statistical causality relationship and parameter heterogeneity between gross domestic product and a broad group of construction in Western Europe.

The long run Granger causality tests are in most cases inconclusive, that is, the Granger causality goes in both directions. Our results are in accordance with e.g. [START_REF] Wang | Public infrastructure and economic growth: a new approach applied to East Asian economies[END_REF] and [START_REF] Lean | Empirical tests to discern linkages between construction and other economics sectors in Singapore[END_REF] whose result

shows that both public infrastructure and economic growth have significant effects on each other. On the other hand, [START_REF] Tse | Causal relationship between construction flows and GDP: evidence from Hong Kong[END_REF] results suggest that construction Granger Cause GDP but not wise versa in Hong Kong.

Furthermore, if we examine the individual parameters concerning the error correction term, it could be concluded that they are of small magnitude, indicating slow adjustment to long run equilibrium. Our results are in accordance with e.g. [START_REF] Green | Follow the Leader: How Changes in Residential and Non-residential Investment Predict Changes in GDP[END_REF] and recently [START_REF] Coulson | Residential Investment, Non-residential Investment and GDP[END_REF], whose result

shows that the impact of residential investments on GDP is more evident than non-residential investments.

The long run Granger causality between the different types of construction goes in both directions. For example, residential constructions Granger cause public infrastructure investments in the long run, and vice versa. The model concerning residential construction and economic growth indicate that residential constructions short run effect are higher if we have a high unemployment, but it is also true that its effect is higher when we have a low unemployment. Supply-side variables probably drive the former relationship and the latter by demand-side variables. Furthermore, high residential capital stock seems to reduce the impact of residential construction on GDP growth.

  g. the results by[START_REF] Shioji | Public Capital and Economic Growth: A Convergence Approach[END_REF], we are using disaggregated data concerning of residential construction (variable name: Resi); other construction (Build) and infrastructure construction (Infra). All the variables are measured in million USD in 1999 years prices and come from Euroconstruct. The data are supplemented with data on GDP in billion USD and in 2000 years prices from OECD and Euroconstruct. The cross section is 14 European countries. The period under studied is1980[START_REF] Harter-Dreiman | Drawing Inferences about housing supply elasticity from house price responses to income shocks[END_REF]

  F-tests are used to find out whether there is any improvement going from model A3 to A4 or from Model A4 to A5. A high F-value indicates that the parameters of the change in residential construction multiplied by the dummy representing high unemployment (Dresi*HUE(t) etc) are jointly significantly different from zero.

  are constant over time (the fixed effects) and that we have more degrees of freedom (see[START_REF] Baltagi | Econometric Analysis of Panel Data[END_REF][START_REF] Temple | The New Growth Evidence[END_REF].Data concerning business cycles is measured by using unemployment rates to define periods where unemployment is very high or low (variable names HUE and LUE). Accumulated residential stock is measured by using housing stock per capita (HS). It is a dummy variable where one represents if the country has a housing stock per capita above or equal to median housing stock per capita among the investigated countries. Housing policy is measured by looking at private rented sector, social-rented sector and owner occupation. The definition is based on[START_REF] Balchin | Housing Policy in Europe[END_REF]. Two dummy variables are included in the residential model. The first measure represents if the country has a private rented sector above the EU average (PR) and the second measure if the country has an owner-occupation above the EU average (OW). That is, the default indicates if the country has a social-rented sector above or broadly at the EU average.

	omitted variables that
	F o r
	P
	e
	e r
	R e v
	i e
	w
	-6 -

2

The data comes from reports from Euroconstruct conferences 1990-2004 (two each year, different places of publication) and a compilation from Euroconstruct conferences 1980-1995 made by Hans Georg Graf, SGZZ, St Galler Zentrum für Zukunftsforschung.

  , such as office building, Granger causes GDP in both short and long run. The model is not improved by including the interaction variables. That is, the results indicate that the parameters are constant over the business cycle.

	construction of other building
	F o r
	P
	e
	e r
	R e v
	i e
	w
	-8 -

table 3 below. The model can explain almost 44 percent of the variation in changes of GDP. Concerning

Table 3

 3

	in here
	If construction of other building increases by 1 percent, GDP is expected to increase by 0.03 percent
	the following years. The speed of adjustment to long run equilibrium is about 10 years. However, the
	Granger causality is not conclusive. Construction Granger causes GDP but GDP also Granger causes
	construction of other buildings. If expected level of other building construction is higher than the
	actual building activity, the speed of adjustment to long run equilibrium will be around 7 years. The
	relationship between infrastructure construction and economic growth is presented in table 4 below.

Table 4

 4

	in here

The model can explain approximately 37 percent of the variation in GDP. Construction in infrastructure Granger causes GDP both in short and long term. The model is not improved if the interaction variables are included in the model. The results indicate that investments in infrastructure do not have a larger impact on GDP growth if the unemployment is high and low. If infrastructure construction increases by 1 percent, GDP is expected to grow by 0.02 percent. The speed of adjustment to long run equilibrium is about 12 years. The Granger causality is not conclusive.

  Construction of other building and infrastructure investments has a positive effect on economic growth both in short and long term. The policy implication from our results indicates that residential construction can have a substantial effect on economic growth in countries with e.g. high unemployment, less state intervention on the housing market and a low stock of housing per capita. An increase in construction by 1 % can effect GDP growth by as much as 0.15 %. On the other hand, residential construction will have very small or no effect on economic growth if the housing stock per capita is already high or if the housing market is state intervened (e.g. large social housing sector). -value within parenthesis. Parameters concerning fixed effects are not shown in the table, but available upon request. All short run effects are compared to model A1 and all long run effects are compared to model A2. -value within parenthesis. Parameters concerning fixed effects are not shown in the table, but available upon request. All short run effects are compared to model B1 and all long run effects are compared to model B2. -value within parenthesis. Parameters concerning fixed effects are not shown in the table, but available upon request. All short run effects are compared to model C1 and all long run effects are compared to model C2.

	Table 1. Table 2. Table 3. Table 4.	Unit Root Test (t-statistics) Economic Growth and Residential Construction. Economic Growth and Other Construction. Economic Growth and Infrastructural Construction.
		(Dependent variable=Dgdp) (Dependent variable=Dgdp) (Dependent variable=Dgdp)
	GDP	Total			Residential	Buildings	Infrastructure
	Level Diff. Level Diff. Model A1 Model A2 Model A3 Model A4 Model A5 Level Diff. Level Diff. Level Diff. Model B1 Model B2 Model B3 Model B4 Model B5 Model C1 Model C2 Model C3 Model C4 Model C5
	LL-test Dgdp(t-1) Dgdp(t-1) Dgdp(t-1) IPS-test Dgdp(t-2) Dgdp(t-2) Dgdp(t-2)		-2.5 0.6220 0.6268 0.6150 -0.4 -3.1 (11.16) (11.23) (11.18) -0.2025 -0.2048 -0.1824	-3.8 0.5938 0.4218 0.6030 -2.0 -2.8 0.5970 -3.7 0.4309 0.6034 -2.2 -2.7 0.5359 0.4007 -3.7 0.5343 0.4041 0.6039 0.6021 -3.8 -2.0 -2.9 -1.3 (10.63) (10.93) (9.60) (9.54) (6.88) (7.16) (6.43) (6.45) (10.58) (10.77) (10.57) (10.50) -0.2608 -0.1968 -0.1757 -0.1788 -0.1984 -0.1495 -0.1173 -0.1127 -0.2259 -0.1741 -0.1674 -0.1728	-3.2
	Austria		0.0 -3.7 (-3.56) (-3.64) (-3.23)	-0.7 (-4.60) (-3.19) -4.1 (-3.40) -2.2 -2.5 (-3.02) (-2.39) (-1.81) -0.8 -3.9 (-3.06) (-1.71) 0.9 (-3.94) (-2.98) (-2.82) (-2.89)	-4.8
	Belgium Dresi(t) Dbuild(t) Dinfra(t)		0.3 -2.6 ---		-1.5 0.0589 0.0692 -2.3 0.0644 -1.4 -2.8 0.0534 0.0737 0.0677 -1.8 -2.9 0.0526 0.0673 -1.3 0.0413 0.0416 0.0381 0.0381	-2.3
	Denmark		-0.5 -2.6		-2.0 (7.31) (6.54) -3.4 (8.04) -1.6 -3.3 (5.80) (7.05) (5.54) -2.2 -3.2 (5.66) (5.48) -1.7 (3.63) (3.72) (2.88) (2.87)	-5.1
	Finland Dresi(t-1) Dbuild(t-1) Dinfra(t-1) France Germany Dresi(t-2) Dbuild(t-2) Dinfra(t-2)		-0.3 -2.8 ---0.0 -2.6 -0.8 -3.3 ---		-3.1 -0.0307 -0.0081 -3.1 -0.030 -2.5 3.1 -0.0371 -0.0106 -0.0193 -2.9 -2.6 -0.0373 -0.0202 -2.6 -0.0277 -0.0272 -0.0314 -0.0311 -4.0 -3.1 -3.2 -3.3 -4.1 -3.4 -1.9 (-3.20) (-3.23) (-3.60) (-3.59) (-0.73) (-0.97) (-1.53) (-1.59) (-2.57) (-2.57) (-2.50) (-2.47) -1.5 -2.1 -1.9 -2.5 -0.5 -1.6 -1.6 0.021 0.0082 0.0046 0.0044 -0.0156 -0.0172 -0.0205 -0.0214 -0.0048 -0.0054 0.0047 0.0049 (1.45) (0.99) (0.50) (0.48) (-1.57) (-1.76) (-1.83) (-1.90) (-0.45) (-0.52) (0.39) (0.41)	-4.1 -2.3 -2.6
	Italy Dresi*HUE(t) Dbuild*HUE(t) Dinfra*HUE(t)		-0.9 -2.9 ---		-1.8 -	--	-2.9	-	-2.6 -2.5 0.0218 -0.0094 -2.1 -2.8 0.0238 0.0111 0.0 -0.0321 0.0327	-2.4
	Netherlands		-0.7 -3.9		-2.0		-3.2		-1.4 -4.2 (1.43) (0.46) -3.2 -1.9 (1.54) (0.53) -1.5 (1.24) (1.26)	-3.2
	Norway Dresi*HUE(t-1) Dbuild*HUE(t-1) Dinfra*HUE(t-1)	-0.2 -3.3 ---		-2.3 -	--	-2.6	-	-1.8 -2.6 0.0281 -0.0292 -2.7 -2.8 0.0297 0.0298 -1.9 -0.0048 0.0048	-4.0
	The results also indicate that countries with a housing policy with less state intervention have a stronger effect from residential construction on economic growth. F o r P e e r R e v i e w F o r P e e r R e v i e w F o r P e e r R e v i e w Portugal -0.9 -2.8 -1.6 -2.1 -2.6 -2.3 -0.9 -4.8 -0.7 -2.0 Switzerland 0.1 -2.6 -0.6 -2.9 -0.3 -2.5 -1.0 -2.7 -1.2 -3.5 Spain 0.1 -3.3 -3.1 -2.8 -3.2 -2.6 -2.8 -3.3 -1.0 -4.1 Sweden -0.8 -3.0 -1.2 -2.2 -3.7 -4.8 -1.7 -1.8 -1.5 -2.5 UK -0.3 -3.4 -3.2 -2.2 -3.0 -4.8 -1.5 -2.7 -1.5 -2.4 F o r P e e r R e v i e w (1.82) (1.91) Dresi*HUE(t-2) ---0.0139 0.0150 (0.91) (0.98) Dresi*LUE(t) ---0.1043 0.1042 (3.52) (3.51) Dresi*LUE(t-1) ---0.0278 0.0291 (0.89) (0.92) Dresi*LUE(t-2) ---0.0124 0.0122 (0.37) (0.35) e(t-1) -0.0599 --0.1013 -0.0993 -0.0824 (-2.10) (-3.80) (-3.81) (-2.58) e*HUE (t-1) --0.0613 (-0.91) e*LUE (t-1) --0.0253 (-0.30) Constant 0.0129 0.0145 0.0130 0.0136 0.0137 (8.70) (10.07) (8.91) (9.04) (9.04) R 2 0.3069 0.4063 0.4346 0.4745 0.4762 n 308 308 308 308 308 k 3 5 6 12 14 F-value: A4 vs A3 ---3.73 -A5 vs A4 ----0.48 F-value: Short run effect --22.66 10.45 8.61 Long run effect --15.07 5.47 4.34 Note: tF o r P e e r R e v i e w (1.44) (1.47) Dbuild*HUE(t-2) ---0.0110 0.0127 (0.57) (1.47) Dbuild*LUE(t) 0.0539 0.0537 (1.63) (1.62) Dbuild*LUE(t-1) 0.0125 0.0177 (0.37) (0.51) Dbuild*LUE(t-2) -0.0167 -0.0180 (-0.44) (0.47) e(t-1) -0.0697 --0.099 -0.0974 -0.0833 (-2.29) (-3.50) (-3.44) (-2.42) e*HUE(t-1) -----0.0368 (-0.48) e*LUE(t-1) -0.0655 (-0.71) Constant 0.0128 0.0166 0.0153 0.0150 0.01474 (8.69) (10.15) (9.34) (8.52) (8.21) R 2 0.3088 0.3965 0.4211 0.4349 0.4363 N 308 308 308 308 308 K 3 5 6 12 14 F-value: B4 vs B3 ---1.20 -B5 vs B4 ----0.36 F-value: Short run effect --19.46 7.31 6.02 Long run effect --12.79 2.86 2.30 Note: tF o r P e e r R e v i e w (0.19) (0.19) Dinfra*HUE(t-2) ----0.0348 -0.0346 (-1.38) (-1.37) Dinfra*LUE(t) -0.0306 -0.0312 (-0.65) (-0.66) Dinfra*LUE(t-1) 0.0161 0.0127 (0.49) (0.34) Dinfra*LUE(t-2) -0.0334 -0.0346 (-1.00) (-1.03) e(t-1) -0.0823 --0.0826 -0.0810 -0.0701 (-3.28) (-3.38) (-3.27) (-2.32) e*HUE(t-1) -----0.0456 (-0.74) e*LUE(t-1) -0.0166 (0.15) Constant 0.0126 0.0136 0.0125 0.0123 0.0125 (8.69) (9.56) (8.70) (8.40) (8.35) R 2 0.3214 0.3380 0.3632 0.3740 0.3754 n 308 308 308 308 308 k 3 5 6 12 14 F-value: C4 vs C3 ---0.85 -C5 vs C4 ----0.33 F-value: Short run effect --6.59 2.75 2.30 Long run effect --11.91 2.42 1.95 o r P e e r R e v i e Note: tF w
									-1 --2 --3 --4 -


Dr Peter M Schulze

Alexander Prinz

Dipl.-Kfm Alexander Prinz

Quantitative Methods, C53 -Forecasting and Other Model Applications < C5 -Econometric Modeling < C -Mathematical and Quantitative Methods, L99 -Other < L9 -Industry Studies: Transportation and Utilities < L -Industrial Organization

Keywords: Globalization, Container transshipment, Time Series Analyses, Forecasting

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Seaborne trade laid the foundations for the rapid and mostly steady growth of world trade during the past decades. Especially the rapidly increasing container transport, measured in TEU (Twenty Foot Equivalent Unit), is an important indicator to represent the dynamics of world trade. Despite the fact that, in 2005, container ships only accounted for 14% (as share of the world gross tonnage) of world seaborne trade (Heymann, 2006: 4) the value of goods transported in containers is much higher -oil and gas tankers as well as bulkers are more significant according to weight.

World wide container transshipment grew with an annual rate of about 11% between 1995 and 2005. Forecasts predict annual growth rates of about 10% until 2010 (Heymann, 2006: 6).

In 2005, Germany held about 9% of the worlds' real exports (in prices and exchange rates of the year 2000) (Deutsche Bundesbank, 2006: 33) and more than 3% of the rapidly growing market of container transshipment. Furthermore, Germany controls one third of the worlds' container fleet. Put into figures, German shipping companies controlled 1,157 of the 3,499 container ships in 2006. (ISL, 2006a: 23) Quantitatively analytical literature on international container throughput, as well as on container transport, is rather scant: On the one hand, there is no freely accessible broad supranational database for international maritime shipping. On the other hand, the theoretical side of this theme is mostly integrated into general logistics, at least in scientific publications. Some institutions like Drewry Shipping Consultants Ltd., London (Drewry), Institut für Seeverkehrswirtschaft und Logistik, Bremen (ISL) and Ocean Shipping Consultants Ltd., Surrey (OSC) regularly publish analyses for certain market segments on a descriptive-empirical base, and sometimes medium term forecasts without giving the methodology.

We present quantitative short-run forecasts by using quarterly data for the German container throughput, separated by the world´s main economic areas Asia, Europe and North America, the socalled triad of globalization. These three regions cumulate around 80 percent of global container shipment. As well, we provide forecasts for the German container throughput in total. These forecasts are important for logistics companies, e.g. shipping companies, port authorities and shipyards. Using quarterly data and therefore catching seasonal effects, it is possible to give a detailed outlook for a manageable time period. Given attention to the seasonal structure of the data, forecasts can account for this level of detail. This can be a great advantage for companies when allocating capacities. The methodologies we use are two univariate time series approaches: the traditional exponential smoothing analysis of Holt-Winters and the ARIMA framework adapted to seasonal data (SARIMA). Certain model specifications of these two approaches are formal equivalents, so another question here is to see whether, when applied, they lead to similar results.

Next, we outline the main estimation and forecast equations. This theoretical part is followed by some remarks on the database. The principle part contains estimation, diagnosis and interpretation of the main results. Finally, using forecast error measures, we compare the results of the two approaches, and present our forecast results.

II. Estimation and Forecast Techniques

High frequency data often exhibit seasonal behavior, that is there are returning characteristics within certain periods of a year. For data with higher than annual frequency it is therefore often appropriate to make seasonal adjustments. Traditionally, seasonality is seen as some kind of pollution of the data. In modern time series analysis, trend and seasonality is seen as a chance to lead to more exact forecasts. Especially in business matters, knowledge of seasonal changes can help to improve outcomes or reduce costs. From the theoretical point of view, taking account of seasonality may reduce forecasting errors.

In the SARIMA methodology (Newbold/Bos, 1994: 319-325)

=

The forecasting equation for the onestep-ahead out-of-sample forecast of the often used so-called airline model (Box/Jenkins, 1970: 300-322) SARIMA(0,1,1)(0,1,1) applied to quarterly data, is

5 h T 4 h T 1 h T h T y ŷ ŷ ŷ ˆ + + + + + + =
which indicates that after h = 5, the estimated MA-parts have disappeared.

We then use the Holt-Winters algorithm for seasonal time series based on the exponential smoothing approach (Newbold/Bos, 1994: 199-210). This technique is capable of producing shortterm forecasts for a large collection of time series with a trend and additive or multiplicative seasonal variation. The model of the time series

t y ( T ..., , 2 , 1 t =
) with linear trend and multiplicative seasonality consists of the following three equations:

(4)

(

)( )

1 t 1 t 1 L t t 1 t b a 1 s y a + + = (5) ( ) ( ) 1 t 2 1 t t 2 t b 1 a a b + = (6) ( ) L t 3 t t 3 t s 1 a y s + =
In these equations, 1 , 2 and 3 ( 1 0

) are smoothing coefficients, t a in (4) yields the current level estimate, t b in (5) shows the estimate of current slope, and t s in (6) determines the current seasonal factor. L denotes the number of periods per year in the data, e.g. for quarterly data 4 L = . Forecasts in the case of a linear trend and multiplicative seasonal factor can be made by

F o r P e e r R e v i e w (7) ( ) h L t t t h t s h b a y ˆ+ + + = with ... , 2 , 1 h =
. The additive and multiplicative algorithm may yield quite different forecasting values. So the concrete data set leads to considerations about the combination of the model parts as well as the choice of values for the smoothing terms. This decision has been taken by using the model with the smallest forecasting error.

It can be shown that under certain conditions the additive Holt-Winters model is theoretically equivalent to the seasonal ARIMA model (SARIMA) (Mills, 1990: 180-183) and the interesting question to answer is whether the two approaches lead to equivalent forecasting results in applications. The estimations are compared by using the forecast error measures (Greene, 2003: 113) Root Mean Square Error (RMSE), and Theil´s U which is defined as

III. Database

The worldwide container transshipment has increased with impressing two digit growth rates during the past years. Figure 1

IV. Model Analysis

The analysis will concentrate on the container transshipment at German ports with destination to one of the three main regions of container shipping Asia, Europe, North America. We will give forecasts for each of these destinations separately and for the container throughput at German ports in total. The development of the latter for the time The graph in figure 3 exhibits a nonlinear trend with seasonal variations. The seasonal variations show a strong downward movement at the beginning of each year. Graphs for the three regions look similar and are not presented here.

Using the double differencing filter according to equation (1) on German container handling leads to estimated ACF and PACF values visualized in figure 4.

The PACF shows two significant values at lags 4 and 8. The significant ACF value at lag 4 ( = ˆ0.454) is a typical feature of many doubly differenced seasonal time series. It takes values near -0.5 which may suggest overdifferenced seasonal data. Therefore we additionally apply a unit root test for quarterly series to identify the most appropriate differencing filter for t y .

To confirm the use of the correct differencing filter we carry out the HEGY unit root test for quarterly data with different auxiliary regressions [START_REF] Hylleberg | Seasonal Integration and Cointegration[END_REF]. Table 1 gives the results for the double differenced container handling in Germany (SDTEU).

The series are tested with different specifications: without a deterministic term (0), with a constant (C), constant and seasonal dummies (C, SD), constant and linear trend (C, Tr), and constant, seasonal dummies and linear trend (C, SD, Tr). If 0 1 = , the null hypothesis "presence of a non-seasonal unit root" cannot be rejected; if 0 2 = , a halfyearly unit root is present, and the corresponding tests are designed as and the conventional significance level of 5% are smaller than the corresponding critical values (Hylleberg et al., 1990: 226-227). The value for 4 is greater than the critical values, but that does not restrict the results in general. So the nulls are rejected and stationarity by double differencing is achieved. The last column of table 1 indicates the p-values of the LM-test on autocorrelation in the error term which indicates no autocorrelation. These considerations lead to the identification of a SARIMA(0,1,0)(2,1,0) model. Furthermore, we identified several other possible SARIMA models, but the model mentioned above proved to be the best one. Analogously, for the three destinations Asia, Europe and North America we identified similar models. Table 2 shows the details of the estimation results of the respectively best model for each destination and total German container handling (world), concerning significance and autocorrelations of the error term. Estimations were done with WinRATS 6.3 using the Gauss-Newtonalgorithm.

The first row gives information about the chosen model. The values in parenthesis in the coefficient rows give the p-values of the t-tests for the coefficient estimators. "Q-sign" indicates the pvalues of the Box-Pierce statistic on no autocorrelation in the error term. Constants have been generally omitted, because of non-significance.

As an alternative to the SARIMA analysis, the Holt-Winters method provides an easy way to analyze and predict seasonal time series. For the smoothing coefficients in equations ( 4) to ( 6) we apply, as commonly made in . Other values were tested, though they did not change the results substantially, but rather led to unstable outcomes. Investigating the diagrams of the original series for the different regions, we chose the following specifications: an exponential trend with a multiplicative seasonal factor for the destination Asia and the whole German container throughput, while for the destinations Europe and North America we assume a linear trend combined with a multiplicative season.

To compare the two methods -SARIMA and Holt-Winters exponential smoothing -concerning their predictability we computed two measures for ex-post forecast errors, the RMSE and Theil's U. Table 3 gives details on the results. The RMSE show a mean deviation between 22 and 30 thousand TEU for the three destinations, but 57 thousand TEU for the total German container transshipment. These differences arise from the overall strongly different and heterogeneous development of the worlds´ economic regions. Due to RMSE there are remarkable differences between the two types of models: the RMSE values of the SARIMA approach are about 10% smaller for the destinations Asia and Europe, and more than 30% for the whole container handling. For the destination North America the exponential smoothing approach obviously led to better results. For Theil's U we use the observed value with a lag of four quarters as 'naive forecasts'. Experience shows that values smaller than 0.5 for Theil's U lead to useful forecasting results (in the past). Again, only the value for North America leads to a value greater than 0.5, which means that the two approaches produce better results than the 'naive model', but it should not be used for ex ante forecasts. For all datasets except North America the SARIMA U-values are smaller than those of the Holt-Winters model.

Therefore, the SARIMA approach should be used for ex ante forecasting rather than the Holt-Winters approach. The identified SARIMA models will lead to better and more stable forecasts, given stationarity. Visualizing these findings, figure 5 compares the forecasting results of the SARIMA and the Holt-Winters model for the whole German transshipment from 3/2006 until the end of 2008. It can be seen that the Holt-Winters approach overestimates the development of the container throughput in the future.

In figure 6, the forecasts of the SARIMA-models are shown for the three regions Asia, Europe and North America. Table 4 contains the numerical forecasting values. Taking a look at the graphical illustration, the seasonal variation which is inherent in the quarterly data can be found in the forecast values as well.

Our forecasts give a continuingly positive outlook for the container industry in Germany. Especially the destinations Asia and Europe are the driving forces for development. We forecast that within the forecasting period the German container throughput will rise by 22.8 percent in total, for the destination Asia we predict a gain of 25.3 percent and for Europe 21.5 percent. A moderate increase of 9.5 percent is given for destination North America. Given such detailed forecast information as in table 4, port authorities can do their planning more efficiently. Furthermore, capacity planning of shipping companies can be positively influenced.

V. Conclusions

This analysis discusses SARIMA and exponential smoothing models for estimating and forecasting quarterly data of the German container transshipment

(0,1,0)(1,1,0) (0,1,0)(0,1,1) (1,1,0)(1,1,0) (0,1,0)(2,

  our model, for Theil´s U we use the value of the prevailing last period 4 t y as forecasting values of the naive model.

Figure 5 :Figure 6 :

 56 Figure 5: SARIMA and Holt-Winters forecasts for the whole container throughput in Germany (in 1,000 TEU)

Page 12 of 18 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  Figure 4: Estimated ACF and PACFvalues of the double differenced German container throughput

		Submitted Manuscript
	(measured in TEU). Different models are identified and tested for the whole HEGY unit root test: testing for seasonal integration in the series SDTEU 400
	German container throughput and for the Effective sample: 1992:03 to 2006:02 throughput with the destinations Asia, 350 Auxiliary Europe and North America. The regressions ) ( t 1 ) ( t 2 ) ( t 3 SARIMA models are examined by the 300 0 -5,816 -5,565 -8,543 ACF and PACF, the HEGY test on C -5,949 -5,562 -8,537 stationarity for quarterly data, the Box-250 C, SD -5,839 -5,535 -8,482 Pierce statistic and t-tests. Although there is, C, Tr -5,946 -5,527 -8,519 theoretically, equivalence between the two types of 200 C, SD, Tr -4,375 -3,495 -4,789	) 0,752 ( t 4 0,780 0,722 0,741 1,185	, 37,733 ( F 4 3 37,732 37,193 37,540 12,931	)	LM-sign 0,259 0,160 0,118 0,101 0,108
	150	models, the SARIMA models perform slightly better than the Holt-Winters
	F o r P e e r R approach -expressed by the forecasting measures MSE and Theil's U. The quarterly forecasts up to the end of the year 2008 show a permanent dynamic growth of German container throughput, especially with the destinations Asia and Europe. A moderate increase can be anticipated for the container handling concerning North America. The methodologies we use can be easily applied to many kinds of time series data. Given more detailed data, for F o r P e e r F o r P e e r 1985 1987 1989 1991 1993 1995 1997 1999 F o r F o r F o r Figure 1: Container transshipment 1985 -2005 (in Mln. TEU) worldwide 100 0 50 2001 2003 2005 P e P P Figure 3: Container transshipment in Germany 1/1989-2/2006 (in 1,000 TEU) Source: Statistisches Bundesamt e e Source: ISL (2006b) e r e r e r example on smaller aggregates such as a small group of countries, valuable information on the further development R R R R R
		e v i e in a special sector can be produced. For e e e e e Germany, container handling with the destination of Baltic Sea abutters could be of particular interest. v i e v i e v i e v i e v i e
				w w w w w w

Table 1 :

 1 Results of the HEGY test for German container throughput

	Asia	Europe	North America	World
	SARIMA
	F o r
		P
		e
		e r
			R
			e
			v i e
			w

Table 2 :

 2 Estimation results for the different SARIMA models

	1,0)

Table 3 :

 3 Model types and forecast errors

Page 16 of 18 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	F o r
	P
	e
	e r
	R
	e
	v i e
	w

Table 4 :

 4 Forecasting values for container throughput (in 1,000 TEU)

	TEU)

19 of 18 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript