Modelling productionconsumption flows of goods in Europe: the trade model within Transtools3
 Gerard de Jong^{1, 2}Email author,
 Reto Tanner^{1, 3},
 Jeppe Rich^{4},
 Mikkel Thorhauge^{4},
 Otto Anker Nielsen^{4} and
 John Bates^{5}
Received: 14 April 2017
Accepted: 10 October 2017
Published: 25 October 2017
Abstract
The paper presents a new model for trade flows in Europe that is integrated with a logistics model for transport chain choice through Logsum variables. Logsums measures accessibility across an entire multimodal logistical chain, and are calculated from a logistics model that has been estimated on disaggregated micro data and then used as an input variable in the trade model. Using Logsums in a trade model is new in applied largescale freight models, where previous models have simply relied on the distance (e.g. crowfly) between zones. This linkage of accessibility to the trade model makes it possible to evaluate how changes in policies on transport costs and changes in multimodal networks will influence trade patterns. As an example the paper presents outcomes for a Europeanwide truck tolling scenario, which showcases to which extent trade is influenced by such a policy. The paper discusses how such a complex model can be estimated and considers the choice of mathematical formulation and the link between the trade model and logistics model. In the outcomes for the tolling scenario we decompose the total effects into effects from the trade model and effects from the logistics model.
Introduction
Trade models can be used to forecast future trade patterns conditional on scenarios about the economic development of various regions. If they would contain transport time and cost as explanatory factors of the trade volumes, trade models could also be used to simulate the impact of changes in transport costs (e.g. introduction of road toll) or transport time (e.g. constructing new links or expanding existing links) on trade flows. However, most existing largescale trade models use a simple (e.g. crowfly) distance variable as the measure of resistance between zones on trade, not transport times and costs. Very little empirical material is available on the impact of changes in transport costs and times (by mode) on the trade flows, but the few studies that have been done show that these effects are potentially large (see de Jong et al. 2010). This paper presents a new European trade model that is integrated with a logistics model (and a network assignment model), where Logsums are consistently used at largescale. Accessibility is measured in this model across an entire multimodal logistical chain, on the basis of a logistics model which has been estimated on micro data. This makes it possible to evaluate how changes in policies and changes in multimodal networks will influence trade patterns.
In the literature, there are basically three different approaches (Ivanova 2014) for modelling the regional transport distribution of trade, e.g. PC flows. These are: i) Gravity models, ii) Inputoutput (IO) models and iii) Spatial Computable General Equilibrium (SCGE) Models.
The most commonly used method is the gravity model (e.g. used for the Netherlands in Significance et al. 2010; or for Sweden in Edwards et al. 2008). In such models the flow between zone i and zone j is a function of production and attraction measures of zone i and zone j and some measure of distance or (generalised) transport cost in order to account for the fact that the transport distribution is sensitive to changes in transport costs. Gravity models, as a mean of explaining trade or transport in money or weight units, have long been regarded as models without a clear theoretical justification. However, in more recent economic literature, a theoretical basis for the gravity model has been derived from the factor proportions model (Deardorff 1998), Ricardo’s trade model (Eaton and Kortum 2001, 2002) or monopolistic competition with differentiated products (Anderson and van Wincoop 2003; Bergstrand et al. 2013).

Fixed technical and trade coefficients: the present production and trade patterns are extrapolated into the future.

Elastic technical and trade coefficients: functions are estimated (e.g. multinomial logit) in which the fraction that is consumed in region i of the production of sector s in region j depends on the total production of region j in sector s and the (generalised) transport cost, in relation to other regions.
The third option for productions and attractions is the computable general equilibrium (CGE) model that establishes equilibrium in several related markets (not only transport, but also goods markets, labour markets and possibly land markets). CGE models in economics (not focussing on transport) often include economic issues that are not handled in transport models, such as type of competition and economies of scale. Spatial computable general equilibrium (SCGE) models can be seen as a spatial extension of the CGE framework with at least the same data requirements as IO models (e.g. multiregional IO tables or make and use tables). Examples of operational SCGE models that are used for transport distribution are Bröcker et al. (2010), Ivanova et al. (2006) and Ivanova et al. (2007).
For this application we have applied the gravity model instead of the IO and the SCGE models. The first reason for this choice is that in Transtools3, we had no ambitions to model markets other than transport. The second reason is that uptodate information on regional inputoutput relations for our study area was missing for many regions. By contrast, as part of a previous data project (ETISplus 2014) a base PC matrix was made available. As this matrix was already expressed in tonnes, we avoided the conversion from money to tonnes, which would otherwise have been necessary prior to an IO and SCGE model application to transport.
The trade model in Transtools3 explains the transport flows by commodity type (NST/R 1) either between NUTS3 zones or between countries. It was estimated partly on data at the country level and partly at the NUTS3 level, and it is applied at the NUTS3 level. The reason for partly estimating on country level is discussed in chapter 3. The model is based on the (unconstrained) gravity formulation, using characteristics of zones and the transport costs between zones. The dependent variables are PC flows between zones (measured in tonnes). The independent variables are GDP, GDP per capita (both obtained from the World Bank) and dummies for common trade zone (EU, EFTA), common currency zone (EURO), common language, zones being neighbours and zones being in the same country. The effect of transport cost is integrated in a Logsum variable (see BenAkiva and Lerman 1985 for an exposition of the Logsum as an accessibility measure) which is calculated from the Transtools3 logistics model (see Jensen et al. A model for freight transport chain choice in Europe, submitted). It includes a range of different transport time components and transport costs components (for all modes considered).
The use of a Logsum variable as a measure of accessibility in a trade model and as a link between trade and logistics has been suggested in theoretical papers (e.g. de Jong and BenAkiva 2007). However, to our knowledge it has not yet been applied in largescale practical freight transport models. To investigate how accessibility affects trade, we provide a Europeanwide model application of a truck toll scenario.
In the estimation of the trade model we also take into account the influence of relative trade resistance between countries instead of absolute resistance (in line with trade theory) by estimating a random effects model (see “Accounting for relative trade cost” subsection).
The trade model is applied using a pivot point approach (Daly et al. 2011). This means that in the current model implementation we only use the trade model to predict relative changes over time that result from (scenariobased) changes in GDP by zone and in the population. These relative changes are then used to compute changes in the transport flows by commodity type and zone pair by applying these relative changes to the base PC matrix. All other variables are assumed to remain constant.
The key objective of this paper is to present the trade model component of the Transtools3 freight transport model and show how it was developed and which choices were made in the development process (and why). As a second objective, we want to show the sensitivity of this model to changes in policyrelated variables.
In “The gravity model for trade” section of this paper, we present the gravity model for trade between zones. The data are described in “The data used” section. The logistics model section discusses key features of the logistics model. The estimation results for the trade model are presented in “Estimation results” section. The model implementation is described in “Model implementation” and “Conclusions” section offers the conclusions of the paper.
The gravity model for trade
Accounting for relative trade cost
We start with a trade model with distance as measure of resistance, at the country level.
The modern theoretical literature on gravitybased trade models (Anderson and van Wincoop 2003; Kepaptsoglou et al. 2010; Plummer et al. 2010) has emphasised that trade between two countries is not simply determined by the absolute trade costs between the two countries, but by the relative trade cost (the trade cost of country i from importer j relative to its overall trade cost for all the countries from which it imports). In an empirical gravity model, this can be taken into account by adding multilateral resistance terms. However a simpler method is to use importer or exporter fixed effects (dummy variables), which are meant to absorb effects that are specific to a country including its overall level of imports or exports.

x _{ ij }: flow of goods between country i and j, in tonnes;

d _{ ijk }: distance splines, for distance bands k, with distance measured as crowfly kilometres;

gdp _{ i }: gross domestic product in euro of 2010;

pop _{ i }: population;

euefta _{ ij }: dummy that equals 1 if both countries are member of EU or EFTA; 0 otherwise;

euro _{ ij }: dummy that equals 1 if both countries have the EURO as a currency; 0 otherwise;

neig_ij: dummy that equals 1 if both countries are neighbours; 0 otherwise;

lang_ij: dummy that equals 1 if both countries have the same language; 0 otherwise;

In general Greek symbols indicate parameters to be estimated.
The model is double logarithmic in its continuous variables, which is in line with the multiplicative gravity model formulation and also usually works better (here as well) than linear models and yields coefficients which can be directly interpreted as elasticities.
Note that in this model we cannot estimate parameters for the destination zone variables gdp _{ j } and \( \frac{gdp_j}{po{p}_j} \) because these are specific to the destination countries j and would be perfectly correlated with the destination country dummy. But using one constant per destination country may more accurately explain the effects specific to the destination country that influence the imports and thus reduce the variance of the error terms ε. Nonetheless, it follows that in this model we cannot calculate the total impact of a rise of GDP in the total economy. This is a big disadvantage in application.
Replacing distance by the Logsum variable

LS_{ijk}: Logsum variable for the accessibility of zone pair ij for commodity type k. This variable is computed from the transport chain choice model that is also part of the Transtools3 freight transport model.
Please note that in the estimation of the Logsum coefficients we use NUTS3 zones instead of countries, as the logistics model (which generates the Logsums) is estimated and applied at a zonal level.
The data used
Transtools3 uses a zoning system which is similar to the NUTS3 level, but sometimes, where NUTS3 zones are relatively large, contains subdivisions of NUTS3. Hence, the application of the trade model takes place at this rather detailed zoning level. This does however not require that all the estimation also uses this zoning level.
We received from the ETISplus project transport flows in tonnes, by NST/R 2 at the NUTS3 level (‘zonal’ level) for 2010. However, we prefer to use the country data for estimation, since at this level the flows are observed data, obtained from international organisations, and harmonised by ETISplus. To produce matrices at the zonal level, ETISplus made a synthetic split using GDP and population data, so that to some degree estimating a trade model at this level is remodelling the model used for imputing the trade flow data. This is not the case when estimating at the country level, where we also have GDP and other explanatory data directly from international organisations. At the country level, there are also good reasons to believe that zero observations really indicate the absence of trade. At the zonal level, zero (or missing observations) might indicate other things.
The basis of our data is the productionconsumption matrix (PC matrix) from ETISplus at the NUTS3 level (ETISplus 2014). Each observation covers the flow of a specific type of goods following the NST/R level 2 (NST/R 2) classification (which we aggregated to NST/R 1) from an origin zone to a destination zone. They used a PC matrix of observed data at country level and then, as noted, imputed trade flows for each individual pair of zones. We estimated models explaining this PC matrix (de Jong et al. 2016), as well as models explaining the matrix of flows aggregated to the country to country level (using 214 countries in total). As a check, we compared the results of estimation at the country level with those at the zonal level. Both gave elasticities of comparable magnitude.
Our main explanatory variables are GDP, GDP per capita and a measure of resistance to trade (in the model according to Eq. (2) we used countrycountry distance for this and in the model described in Eq. (3) we used the zonezone Logsum from the transport chain choice model that is also part of the Transtools3 freight transport model). As data source for the GDP (and population) we use the World Bank database “World development indicators (WDI)”, GDP at current prices in USD, which we converted to EURO of 2010 using a factor of 1.32414. For distance, we use crowfly distance between the points defined by the longitude and the latitude of each pair of countries. We also defined a number of dummy explanatory variables (largely prepared manually, meaning that we coded these variables ourselves for all the zones), see list of variables following Eq. (1) in “The gravity model for trade” section.
Many trade models explain trade measured in money units. This is then followed by a conversion step to go from money units to tonnes (needed because subsequent submodels, such as modal spit, are in tonnes). Since we are using data on goods flows in tonnes, we do not require this additional conversion step (one could say that we are explaining transport rather than trade). The downside of this is that we cannot easily link the model to economic statistics of trade in money units.
The logistics model
 1.
Dry bulk
 2.
Liquid bulk
 3.
Containers and general cargo.

Road direct (includes roadferry combinations) – container

Road direct (includes roadferry combinations) – noncontainer

Road with roll on/roll off (RORO) – container

Road with RORO – noncontainer

Rail – container

Rail – noncontainer

Inland waterways (IWW)

Rail and IWW

Sea

Rail and sea

IWW and sea

Rail and IWW and sea.
Road can be included in all these alternatives (e.g. as access/egress mode). It is assumed that nonbulk goods transport by sea or IWW will be in containers. For road and rail there is the choice in the model between transporting this as general cargo or in containers.

Transport cost

Transport time

Commodity type

Value density of the goods

Direct access to rail or IWW.
The Logsum from the logistics model provides a measure of accessibility over all available transport chains between any two zones: it is the expected maximum utility from transport chain choice. Since the logistics model is a logit model, the Logsum is the denominator of the choice probability, which includes a summation over all transport chain alternatives. The Logsum will respond to changes in the above influencing factors of the logistics model.
Estimation results
During the estimation of the trademodel it has been considered whether we should estimate the model at the level of the NUTS3 zones or at the level of the countries. We decided to use a twostage estimation approach instead. In a first stage, we estimate a reference model at the aggregation level of the countries. At this stage we estimate the impact of GDP effects but also the impact of EFTA and EURO dummies on the overall trade pattern. As previously discussed, this is preferable, since the country level reflects the level at which the trade data has been collected. In the first stage we absorb effects related to all countries. More specifically, we used the parameters for the random effects model at country level and then fixed these in a subsequent estimation at the zone level (the second stage). The resistance variables in this first stage are distance splines, which is a much more flexible specification than its competitors (e.g. linear, logarithmic, quadratic) and explains the data clearly better than using continuous distance. In the secondstage estimation, we apply the parameters from the first stage as regards GDP and EFTA/EURO dummies in a NUTS3 version of the model where we estimate Logsum parameters. It is not possible to estimate Logsum parameters at the level of the countries as this would virtually “destroy” the variation in the Logsum variables from the logistics model (they vary a lot within countries).
Estimation stage 1
All models are estimated per NST/R 1 commodity type (10 models). We found that the GDP elasticities of trade flows in tonnes were rather similar for models estimated on zonal and country data. We started the estimation of the trade models on the country data (nonzero flows only) by estimating a gravity model without fixed or random effects, using ordinary least squares estimation, and then moved on to estimate fixed effects models (both models not reported here for the sake of space) with fixed effects referring to the destination countries. The results showed that the origin GDP elasticities do not change much compared to the models without fixed effects. Replacing GDP by (sectoral) gross value added did not improve the fit of the models or the significance of the estimates.
Estimation results for a model at the country level with countryspecific random effects at the destination and distance as splines
NST/R  (0) ln_tonnes_0  (1) ln_tonnes_1  (2) ln_tonnes_2  (3) ln_tonnes_3  (4) ln_tonnes_4  (5) ln_tonnes_5  (6) ln_tonnes_6  (7) ln_tonnes_7  (8) ln_tonnes_8  (9) ln_tonnes_9 

Distance 0–20 km  0  0  −0.701*  −0.533*  −0.398  −0.986*  −0.890*  −0.524*  0  0 
(.)  (.)  (−2.38)  (−2.14)  (−1.45)  (−4.86)  (−4.73)  (−2.17)  (.)  (.)  
Distance 20–50 km  0  0  0  0  0  0  0  0  0  0 
(.)  (.)  (.)  (.)  (.)  (.)  (.)  (.)  (.)  (.)  
Distance 50–100 km  0  0  0  0  0  0  0  0  0  0 
(.)  (.)  (.)  (.)  (.)  (.)  (.)  (.)  (.)  (.)  
Distance 100–300 km  1.327  0.657  2.068  1.827  −1.257  −0.975  −1.779  1.429  −0.991  0.321 
(0.76)  (0.41)  (0.81)  (0.80)  (−0.55)  (−0.50)  (−1.00)  (0.64)  (−0.69)  (0.22)  
Distance 300–500 km  −2.881*  −3.236*  −3.169+  −2.125  −3.409*  −1.358  −2.667*  0.834  −3.191*  −3.548* 
(−2.59)  (−3.21)  (−1.81)  (−1.45)  (−2.29)  (−1.15)  (−2.34)  (0.59)  (−3.51)  (−3.82)  
Distance 500–1000 km  −2.025*  −1.985*  −0.481  −2.048*  −2.150*  −2.041*  −3.325*  −1.450*  −2.141*  −1.965* 
(−4.62)  (−4.99)  (−0.60)  (−3.43)  (−3.48)  (−4.39)  (−7.17)  (−2.34)  (−5.95)  (−5.41)  
Distance 1000–2000 km  −2.200*  −2.182*  −0.314  −0.655+  −0.558  −2.903*  −2.449*  −0.520  −2.639*  −2.902* 
(−8.90)  (−10.01)  (−0.57)  (−1.80)  (−1.38)  (−10.77)  (−8.90)  (−1.30)  (−13.15)  (−14.83)  
Distance 2000 + km  −0.339*  −0.0479  0.399+  −2.141*  −0.0960  −1.005*  −1.177*  −0.547*  −1.075*  −0.696* 
(−4.64)  (−0.80)  (1.89)  (−15.00)  (−0.65)  (−11.17)  (−12.41)  (−3.78)  (−17.63)  (−12.64)  
Ln(origin gdp)  0.824*  0.899*  0.474*  0.735*  0.587*  0.921*  1.054*  −0.00223  1.123*  1.175* 
(39.12)  (56.08)  (8.42)  (20.92)  (14.93)  (35.88)  (39.03)  (−0.05)  (66.81)  (80.25)  
Ln(destination gdp)  0.598*  0.618*  0.430*  0.499*  0.532*  0.781*  0.625*  0.619*  0.931*  0.814* 
(12.43)  (20.14)  (5.46)  (7.80)  (5.73)  (19.70)  (14.80)  (11.65)  (30.71)  (28.93)  
Ln(origingdp/cap)  −0.274*  −0.211*  −1.051*  −0.425*  −0.352*  −0.393*  −0.556*  −0.627*  0.119*  −0.0177 
(−8.37)  (−8.39)  (−9.78)  (−7.00)  (−5.22)  (−9.95)  (−13.22)  (−8.89)  (4.32)  (−0.78)  
Ln(dest. Gdp/cap)  −0.111  −0.0938*  0.422*  0.316*  −0.0390  −0.0936+  −0.163*  −0.390*  −0.137*  −0.104* 
(−1.64)  (−2.10)  (3.06)  (3.41)  (−0.30)  (−1.70)  (−2.73)  (−5.30)  (−3.30)  (−2.59)  
Both member of EU or EFTA  0.743*  1.103*  0.264  −1.204*  0.357  0.435*  0.357*  −0.0620  0.215+  1.183* 
(5.07)  (8.65)  (0.77)  (−5.44)  (1.45)  (2.72)  (2.15)  (−0.26)  (1.83)  (10.31)  
Both Euro as currency  0.596*  −0.0153  0.245  −0.298  0.562*  0.124  0.423*  1.191*  0.324*  0.181 
(3.36)  (−0.10)  (0.76)  (−1.20)  (2.13)  (0.65)  (2.22)  (4.63)  (2.25)  (1.24)  
Neighbour countries  1.734*  1.287*  0.949*  1.933*  1.570*  1.184*  1.720*  1.730*  1.037*  0.659* 
(7.03)  (5.77)  (2.36)  (5.85)  (4.60)  (4.54)  (6.76)  (5.38)  (5.12)  (3.21)  
Both same language  0.742*  1.020*  0.899*  0.968*  0.903*  0.671*  0.777*  0.106  0.945*  0.963* 
(5.64)  (9.06)  (2.81)  (4.76)  (4.01)  (4.30)  (5.06)  (0.49)  (8.56)  (9.37)  
constant  −9.103*  −8.608*  0  0  0  0  0  0  −10.86*  −11.49* 
(−4.88)  (−5.35)  (.)  (.)  (.)  (.)  (.)  (.)  (−7.40)  (−7.73)  
N  6388  7905  1379  4039  2619  5063  4442  2380  6465  8686 
Elasticity of trade flow in tonnes in random effects model if the GDP increases (by 1%) and population remains constant
Product type  Elasticity 

0 Agricultural prod. & live animals  0.79 
1 Foodstuffs and animal fodder  0.86 
2 Solid mineral fuels  0.27 
3 Petroleum products  1.10 
4 Ores and metal waste  0.46 
5 Metal products  1.09 
6 Crude and manufactured minerals  0.78 
7 Fertilisers  −0.24 
8 Chemicals  1.69 
9 Machinery  1.45 
Besides the random effects model, we also estimated a Heckman model (Heckman 1979), that explicitly takes account of the fact that many relations have no trade in a product. This model contains two related choices, one discrete choice to participate in trade (“selection”) and one continuous choice on the amount of trade (when positive; “demand”). In the Heckman model some of the GDP elasticities of the demand equation (see Appendix 1) are higher now than in the random effect model, but many are also rather similar to the model in Table 1 that was estimated on the positive observations only. The impact of GDP on the selection equation (trading or not) is on the other hand usually smaller. It is not possible to have random effects and the Heckman specification at the same time (in the software used: Stata). Linders and de Groot (2006) concluded that the Heckman model gave the best treatment of the zero flows, but that simply deleting the zero flows and estimating a model on the positive observations only (as we did in all models except the Heckman model) was acceptable. Given this finding, and the finding that most elasticities were rather similar, we decided to implement the random effects model in Transtools3.
Estimation stage 2
Trade model with random effects with estimation results for Logsums at the NUTS3 level (results of step 2 of the 2step procedure)
(1) ln_tonnes_0  (2) ln_tonnes_1  (3) ln_tonnes_2  (4) ln_tonnes_3  (5) ln_tonnes_4  (6) ln_tonnes_5  (7) ln_tonnes_6  (8) ln_tonnes_7  (9) ln_tonnes_8  (10) ln_tonnes_9  

ln_o_gdp  0.824  0.899  0.474  0.735  0.587  0.921  1.054  −0.002  1.123  1.175 
ln_d_gdp  0.598  0.618  0.43  0.499  0.532  0.781  0.625  0.619  0.931  0.814 
ln_o_gdp_cap  −0.274  −0.211  −1.051  −0.425  −0.352  −0.393  −0.556  −0.627  0.119  −0.018 
ln_d_gdp_cap  −0.111  −0.094  0.422  0.316  −0.039  −0.094  −0.163  −0.39  −0.137  −0.104 
both EU or EFTA  0.743  1.103  0.264  −1.204  0.357  0.435  0.357  −0.062  0.215  1.183 
both EURO  0.596  −0.015  0.245  −0.298  0.562  0.124  0.423  1.191  0.324  0.181 
neighbour countries  1.734  1.287  0.949  1.933  1.57  1.184  1.72  1.73  1.037  0.659 
same language  0.742  1.02  0.899  0.968  0.903  0.671  0.777  0.106  0.945  0.963 
same country  2.202  2.428  3.059  2.097  3.486  1.597  2.833  3.432  1.017  1.409 
(278.871)  (341.09)  (236.361)  (390.437)  (375.926)  (224.792)  (416.866)  (322.995)  (159.475)  (224.089)  
LogSum_NSTR_0  0.219  
(168.795)  
LogSum_NSTR_1  0.223  
(223.05)  
LogSum_NSTR_2  0  
–  
LogSum_NSTR_3  0.04  
(91.606)  
LogSum_NSTR_4  0.056  
(41.201)  
LogSum_NSTR_5  0.301  
(305.503)  
LogSum_NSTR_6  0.382  
(373.995)  
LogSum_NSTR_7  0.397  
(261.085)  
LogSum_NSTR_8  0.41  
(470.569)  
LogSum_NSTR_9  0.29  
(327.156)  
Intercept  −9.538  −9.504  −14.393  −12.59  −11.417  −12.199  −10.299  −0.816  −8.78  −12.604 
(−105.409)  (−118.787)  (−126.565)  (−185.125)  (−64.125)  (−135.462)  (−94.105)  (−8.148)  (−83.572)  (−161.173)  
Observations  1,144,042  1,281,877  356,789  1,249,786  636,420  1,005,574  1,150,606  491,506  1,197,438  1,472,537 
Adjusted R ^{2}  0.2047  0.3655  0.3094  0.4088  0.3061  0.3155  0.3341  0.3293  0.2556  0.3505 
Model implementation
Implementation method and elasticities
In the application of the trade model, apart from the Logsums, we only use the GDP and GDP per capita elasticities from Table 3, assuming that the dummies do not change (although in principle the model can also be used to calculate the trade effects of changes in the composition of the European Union, such as Brexit, or the EURO zone).
Data structure of trade matrices
Variable  Description  Transformations 

OriginEZ2006  Production zone using the NUTS3 system of 2006  Transfer to TT3 zones 
DestinationEZ2006  Consumption zone using the NUTS3 system of 2006  Transfer to TT3 zones 
NSTR2  Commodity type using the NST/R classification at 2 digits  Aggregation to NST/R 1 digit 
Tonnes  Goods transport flow in tonnes 
From these, we can also calculate the percentage growth in GDP per capita. In addition, a change in the Logsum between a production and consumption zone influences the trade level between the zones. In order to account for such an effect, the percentage change in Logsums between a production and consumption zone is calculated.
Where E _{ g }(y _{ z }) above denotes the estimated elasticity for changes in y (e.g. GDP per capita) for zones at the z end (either P or C) for commodity group g (see Table 1). The elasticities for GDP and GDPCAP for the production and consumption zones can be taken directly from the random effects model (presented in Table 1) as it is a loglog representation where elasticities are essentially identical to parameters. They have been estimated as independent GDP effects of P and C zones, and can therefore be added to give the total effect (as in Eq. (5)), even though in reality the underlying GDP trends of regions can be correlated.
Elasticities for the trade model
NSTR 0  NSTR 1  NSTR 2  NSTR 3  NSTR 4  NSTR 5  NSTR 6  NSTR 7  NSTR 8  NSTR 9  

\( E\left({gdp}_{P_g}\right) \)  0.824  0.899  0.474  0.735  0.587  0.921  1.054  −0.002  1.123  1.175 
\( E\left({gdp}_{C_g}\right) \)  0.598  0.618  0.430  0.499  0.532  0.781  0.625  0.619  0.931  0.814 
\( E\left({gdpcap}_{P_g}\right) \)  −0.274  −0.211  −1.051  −0.425  −0.352  −0.393  −0.556  −0.627  0.119  −0.018 
\( E\left({gdpcap}_{C_g}\right) \)  −0.111  −0.094  0.422  0.316  −0.039  −0.094  −0.163  −0.390  −0.137  −0.104 
\( E\left( Logsu{m}_{C{P}_g}\right) \)  0.533  0.141  0.000  0.079  0.110  0.740  0.209  0.322  0.174  0.164 
Obviously, the Logsum elasticities are artificial in the sense that we cannot directly link these with underlying LoS variables. Hence, it is necessary to link the sensitivity of the Logsum to the sensitivity of the underlying LoS variables, which can be interpreted.
Where \( \%\varDelta {F}_{PC_g} \) represent the percentage change in flow for commodity g and F _{ PCg }(base) is the base flow.
The output of the trade model consists of a new PC matrix (for a scenario in a future year).
The trade model is then followed by the logistics model (see Fig. 1 and “The logistics model” section). We considered doing the application of the transport chain model by means of a prototypical sample of shipments. However, given the limited dependency on shipment characteristics, it is computationally much more efficient to apply the model at the level of the number of tonnes per aggregate PC flow.
For this reason we chose to apply the transport chain models to the aggregate number of tonnes per NST/R 1 category from the trade model. Having programmed the transport chain choice model, the alternativespecific constants were recalibrated to reflect the observed aggregate mode shares in Europe for the base year (as in the EU Energy and Transport in Figures Statistical Pocketbook for 2010).
The legs of the chain by mode and commodity are summed over the PC relations to produce aggregate OD matrices by mode and commodity type (in tonnes), which are then (after pivoting) used as input to the network assignment.
A Europeanwide kilometrebased charging experiment for road transport
To further test the trade model we have carried out a Europeanwide kilometrebased truck toll experiment within the Transtools3 freight model. A simulation of the impact of a toll on trade would not be possible in a trade model with distance as the only resistance term. Of course it is possible to increase the distances (for the zone pairs with a toll) as a proxy, but not all transport costs are distancedependent and it would be unclear by how much the distances should be increased to mimic the toll. The Logsum on the other hand makes it possible to simulate both changes in time and in costs (or more generally; any attribute that is includes in the utility function of the logistics model), since the transport chain choice model includes both of these factors separately.
Reference scenario for kilometrebased truck tolls, source: Hylen et al. (2013)
Country  Type of tolling  Baseline (Euro/KM) 

Austria  KM based  0.35 
Czech Republic  KM based  0.26 
France  KM based  0.2 
Germany  KM based  0.18 
Greece  KM based  0.16 
Italy  KM based  0.13 
Poland  KM based  0.09 
Portugal  KM based  0.09 
Russia  KM based  0.09 
Slovakia  KM based  0.19 
Slovenia  KM based  0.22 
Spain  KM based  0.17 
Switzerland  KM based  0.61 
Belgium  Hourly based  0.006 
Denmark  Hourly based  0.006 
Hungary  Hourly based  0.00375 
Lithuania  Hourly based  0.00375 
Luxembourg  Hourly based  0.006 
Netherlands  Hourly based  0.006 
Sweden  Hourly based  0.006 
Results for kilometrebased truck tolls by transport modes and model
Comparison  GtkmRoad  GtkmRail  GtkmIww  GtkmSea  Total 

A / Ref: full model  −5.46%  5.72%  5.26%  0.22%  −0.25% 
B / ref.: full model  −2.55%  1.85%  2.25%  0.14%  −0.10% 
A / Ref: Logistic only  −3.93%  5.42%  4.94%  0.05%  −0.12% 
B / ref.: Logistic only  −2.13%  2.05%  1.68%  −0.01%  −0.05% 
A / Ref: Trade only  −1.52%  0.30%  0.33%  0.17%  −0.12% 
B / ref.: Trade only  −0.42%  −0.20%  0.57%  0.15%  −0.05% 
For countries not listed in the reference scenario in Table 6 we assume a toll cost of 0. The two additional scenarios are then as follows. In the first, scenario A, we assume that the Austrian toll level applies to all of Europe, whereas, in the second, scenario B, we assume that the German toll level applies to all of Europe. These tolling levels also apply to countries which in the reference case had a charge of 0.
Hence, according to these scenarios, scenario A represents a relative aggressive tolling scenario where all other countries except Switzerland experience a cost increase. Scenario B also represents a cost increase on average although slightly less aggressive. However, the scenario is interesting as Germany is by far the biggest country in Europe when it comes to road transport. Other countries often act as pricefollowers when defining their respective tolling schemes.
Clearly, the “tradeonly” model is somewhat artificial in that we disentangle trade effects at the level of modes (whereas Logsums aggregate over the modes to provide a summary measure over all modes). This is achieved by simply running the model with all Logsum parameters at zero, thus bypassing levelofservice effects in the trade model to give the logistics model only effects at the mode level. We can then compare this with a model where Logsum variables are active to yield the trade model only effects. This makes it possible to present the results by activity.
Conclusions
This paper has presented a new European trade model that is integrated with a logistics model, where Logsums are consistently used at largescale. Accessibility is measured in this model across an entire multimodal logistical chain, on the basis of a logistics model which has been estimated on micro data. This makes it possible to evaluate how changes in policies and changes in multimodal networks will influence trade patterns. Most existing largescale trade models use a simple (e.g. crowfly) distance variable as the measure of resistance between zones. This makes it hard to simulate the impact of changes in transport costs and transport networks on the trade flows.
The paper has discussed the existing literature on gravitybased trade models. It described the data and model structures used and presented the estimation results for random effects specifications with a either distance splines or Logsums as the measure of resistance to trade. Overall elasticities for changes in GDP were provided. The paper also discussed the structure of the overall Transtools3 freight and logistics model and how PC matrices from the trade model are combined with the transport chain choice model in model application.
Trade models that include countryspecific fixed or random effects are more in line with modern economic theory, in particular with the relative costs hypothesis. Fixed effects models have the practical problem that they cannot give the full effect of an increase in GDP on trade. Due to this the Transtools3 model has applied a random effects model.
The estimation of the trade model involved a number of considerations in terms of the level of estimation. It was decided to apply a twostage approach, where in the first stage we estimated a generic randomeffects model at the level of the countries. As the trade data originates at the countrytocountry level it is natural to estimate GDP and country specific border effects at this level. These parameters were then transferred to a second stage estimation where we estimated regional variables and accessibility effects through a Logsum variable.
In Transtools3 the random effects model is used in the implementation of the freight and logistics model. Through the Logsum variable from the logistics model, there is an influence of transport cost and time on the pattern of PC flows, and not only on the choice of transport chain for each given PC flow.
As a final assessment of model sensitivity, we analysed two truck toll scenarios against a reference tolling scenario. For these three scenarios we compared a complete model run involving both logistics and trade effects with a model run where only the trade model was allowed to change. This allowed us to disentangle the isolated effects from the trade model in the final model framework. Results indicate that logistic effects are dominating although trade effects are substantial.
Notes
Declarations
Funding
The Transtools3 project was funded by the European Commission DGMOVE, as part of the 7th Framework Programme (contract MOVE/FP7/266182/TRANSTOOLS3).
Authors’ contributions
GdJ supervised the research project and took the lead in writing the paper. RT estimated all models except the one with the logsums. JR and MT estimated the model with logsums and performed the policy simulation on tolling. OAN is the Transools3 overall project leader and JB provide advice on the model specification. All authors read and approved the final manuscript.
Ethics approval and consent to participate
Not required.
Consent for publication
Consent for publication is granted and all data and materials used can be made available.
Competing interests
The authors declare that they have no competing interests.
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