The impact of potential Brexit scenarios on German car exports to the UK: an application of the gravity model

The gravity model

The gravity model is commonly applied in economics and has been deemed to be a successful tool for estimating international trade (Anderson 1979), a general framework to examine trade patterns (Eichengreen and Irwin 1995) and one of the most “empirically successful” trade analytical tools in economics (Anderson and van Wincoop 2003, p.170). The theoretical foundation of the model has been established through the work of several scholars, such as Linnemann (1966); Bergstrand (1985); Evenett and Keller (2002) and Anderson and van Wincoop (2003).

The gravity model estimates bilateral trade flows where trade is positively related to the level of GDP of the trading partners and negatively related to the distance between them. In the model, bilateral trade flows are based on the mutual gravitational force between the nations, with the gravity variable GDP reflecting mass. In addition to the conventional standard version of the model, several modifications can be made and dummy variables added (Chi and Kilduff 2010).

The gravity model has been widely used to estimate product and factor movements within the context of bilateral trade flows across international borders (Anderson 1979; Bergstrand 1985; McCallum 1995; Baier and Bergstrand 2001; Hummels 2001; Feenstra 2002; Anderson and van Wincoop 2003; Anderson and van Wincoop 2004; Anderson 2011) and trade agreements (McCallum 1995; Lavergne 2004; Rose 2004; Carrere 2006; Baier and Bergstrand 2007; Caporale et al. 2009; Cipollina and Salvatici 2010; Kepaptsoglou et al. 2010). Nobel laureate, Jan Tinbergen, was the first to apply the gravity model to the effect of Free Trade Agreements (FTAs) on bilateral trade flows, by including them in the model as a dummy variable (Tinbergen 1962). Since then, the gravity model has become the foundation for estimating the effects of FTAs and customs unions on bilateral trade flows (Bayoumi and Eichengreen 1995), particularly in relation to bilateral trade flows between fellow members of the EU (Balassa 1967; Aitken 1973; Abrams 1980; Brada and Mendez 1985; Frankel et al. 1995).

There is minimal agreement as to which variables should be included in the gravity equation, and which ones that should be omitted (Yamarik and Ghosh 2005). Anderson and van Wincoop (2003) point out that bias can appear in both the estimation and the analysis through the omission of the wrong variables. However, trade data appears to perform empirically well in the gravity model (Feenstra 2002) and, as a result, the gravity model has gained in popularity in the empirical trade literature (Yamarik and Ghosh 2005).

The gravity equation is derived as a reduced form from a general equilibrium model of international trade in final goods. According to Chi and Kilduff (2010) the original gravity model in international trade is defined as:

…where the variables are defined as follows:

T_ij trade flow from country i to country j;

Y_i GDP of country i;

Y_j GDP of country j;

D_ij physical distance between country i and country j and;

A is a constant.

…where the parameters to be estimated are denoted by β and the variables are defined as follows:

T_ij trade flow from country i to country j;

Y_i GDP of country i;

Y_j GDP of country j;

D_ij physical distance between country i and country j;

A_ij other factor(s) either aiding or resisting trade between country i and country j and;

μ_ij a logarithmic-normally distributed error term with E(ln μ_ij) = 0.

The gravity equation is normally specified in a double-logarithmic form and estimated using Ordinary Least Squares (OLS) regression analysis (Eichengreen and Irwin 1995), although there are some exceptions to this general practice. Variations which have been applied to resolve a number of different issues include the use of non-linear OLS (Anderson and van Wincoop 2003), maximum likelihood estimation (Baier and Bergstrand 2007), a tobit model form (Chen 2004; Martin and Pham 2015), poisson pseudo maximum-likelihood estimation (Santos Silva and Tenreyro 2006) and a semi-logarithmic form (Eichengreen and Irwin 1995).

Sample

The sample used to estimate the model consisted of all countries to which Germany exported more than 1000 passenger cars in the designated year and for which data were available. Country i in the model denotes Germany and country j the import country. The total sample consists of more than 80 observations per year, representing approximately 98% of the total quantity of passenger cars exported by Germany over the 4-year period 2012 to 2015 inclusive.⁵

In specifying the sample, the work was delimited by focussing solely on the export of complete cars. Thus, interactions between countries or industries which take place either before or after a complete car is exported are not accounted for. This means that the following are not addressed in the sample specification, data collection, model estimation or forecasts: the movement of components; whether Brexit scenarios bring about a change in the export quantities of passenger cars from Germany to other countries or; from where the UK would import cars in the future in the case that export quantities from Germany are predicted to decline. Model forecasts assume ceteris paribus applies to external factors. Thus, for example, they do not take into account the expected growth in demand for electric cars which, inevitably, will disrupt the current market structure. Finally, the work does not distinguish between new and used passenger cars.

Selection of variables and data collection

The core of the gravity model is based on GDP and distance, but a variety of variables were considered for initial inclusion (Yamarik and Ghosh 2005). Selecting the appropriate variables for inclusion is important since including irrelevant variables can lower the precision of the model, while omitting variables that are important could introduce bias into the model estimates (Greene 2003).

The independent variables included within the initial specification of the gravity model to be tested are as follows: the GDP of countries i and j; the GDP per capita of countries i and j; the population of countries i and j; the geographical distance between the trade partners; the quality of logistics in country j and; the import tariff on passenger cars moving from country i to country j. In addition to these, the gravity model is initially specified to include a number of dummy variables controlling for: membership of the EEA; if country j has direct access to the sea; country adjacency and; if countries i and j share a common language. The choice of these variables was made by reviewing work by, for example, Aitken (1973), Rose (2004) and Chi and Kilduff (2010), who have all performed similar studies.

Model specification

..where the parameters to be estimated are denoted by β and the variables defined as follows:

EX_ij export of passenger cars from country i to country j, in units;

GDP_i GDP of country i, in current USD;

GDP_j GDP of country j, in current USD;

D_ij physical distance between the trade centre in country i and country j, in kilometres;

POP_i total population of country i;

POP_j total population of country j;

GDPCAP_i GDP per capita of country i, in current USD;

GDPCAP_j GDP per capita of country j, in current USD;

TARIFF_ij tariff rate that country j imposes on passenger cars from country i;

LOGIS_j quality of logistics of country j;

CA_ij country adjacency, a dummy variable with a value of 1 if country j shares a common border with country i, 0 otherwise;

LC_ij common language, a dummy variable with a value of 1 if country j shares an official language with country i, 0 otherwise;

EEA_j European Community, a dummy variable with a value of 1 if country j is a member of the European Community, 0 otherwise;

SEA_j direct access to the sea, a dummy variable with a value of 1 if country j has direct access to the sea, 0 otherwise; and.

e_ij the error term.

This model is estimated using OLS regression analysis. A higher GDP and population in country j were expected to lead to greater demand and, consequently. to higher passenger car exports from country i to country j. A higher GDP and population in country i were expected to increase the production capacity. Similarly, a higher quality of logistics in the importing country can also be expected to be positively related to trade volumes. With respect to the dummy variables, the adjacency of trading nations, a common language, membership of the EEA and direct access to the sea would all also be expected to facilitate trade. Hence, the variables GDP_j; POP_j; GDPCAP_j; LOGIS_j; CA_ij; LC_ij; EEA_j and SEA_j were all expected to be positively correlated to export quantities. On the other hand, increasing physical distance between trade partners, as well as higher tariffs, were both expected to have a depressing effect on trade quantities. Hence, the variables D_ij and Tariff_ij were expected to be negatively correlated to trade volumes.

Systematic elimination of variables

As shown in Table 1, the dummy variables representing direct access to the sea and EEA membership were excluded from the model, due to their low impact on the overall explanatory power of the regression; almost all countries in the dataset had access to the sea. Moreover, the dummy variable EEA was also removed, since it was strongly correlated with distance and tariffs, suggesting that the trade-creating benefits of EEA membership are captured by other regressors. The two remaining dummy variables - common language and country adjacency - were also excluded, since they were statistically insignificant. Lastly, the population of country j was removed due its low overall impact on the model.

After conducting the systematic elimination, the remaining independent variables were: GDP of country j; geographical distance between country i and country j; import tariffs and; the quality of logistics of country j. A value of 1 was added to the variable TARIFF_ij so that logarithms could be applied. The variable LOGIS_j was based on the country with the highest index value as defined in Eq. (4).

…where the variables are defined as follows:

EX_ij Export of passenger cars from country i to country j, in units;

GDP_j GDP of country j, in current USD;

D_ij Physical distance between the trade centres in country i and country j, in kilometres;

TARIFF_ij Tariff rate that country j imposes on passenger cars from country i; and.

LOGIS_j Quality of logistics of country j.

A confidence interval of 95% was used to test the model. All variables were statistically significant, the results were consistent over several years and contributed to the overall explanatory power of the model. Hence, the variables were considered robust and efficient in measuring the impact of Brexit on German car exports to the U.K.

Diagnostic testing

The final estimated gravity model, as arrived at through systematic elimination and expressed in Eq. (6), was further analysed with respect to the assumptions which underpin the OLS regression technique utilised (Montgomery et al. 2012).

A Q-Q plot (Liang et al. 2004) suggests that the normality assumption is complied with. Figure 1 presents, however, a scatterplot of the squared residuals relative to the unstandardized predicted values, which suggests that the assumption of homoscedasticity is being violated. Both the Breusch and Pagan (1979) and the White (1980) tests yielded probability values of less than 0,05, indicating heteroscedasticity in the sample. In line with the approach recommended by Huber (1967) and White (1980), robust error terms were introduced to deal with this.

The final diagnostic tests involve the calculation of Cook’s distance, as the basis for identifying outliers and analysing their leverage (Cook 1977; Montgomery et al. 2012). The calculations reveal that there are outliers present and that some of these observations have leverage. To determine the extent to which the leveraged observations impact parameter estimates and whether the sample is robust, a set of diagnostic tests suggested by Rose (2004) is implemented. While the final dataset includes approximately 98% of the total quantity of cars exported from Germany for all 4 years measured, this suggested approach involves estimating a model for a sub-sample of the full dataset such that: sample (1) excludes 3σ outliers; sample (2) excludes 2σ outliers; sample (3) includes only those exports to countries reported as having a high income by the World Bank (2017d); sample (4) includes only those exports to countries reported as having upper middle income by the World Bank (2017e) and; sample (5) includes only those exports to countries reported as having lower middle income by the World Bank (2017f) .

In summary, these diagnostic tests do not yield any categorical evidence of a lack of robustness in the parameter estimates derived from a regression analysis using the full dataset. In any case, since outliers contain important evidence of irregular activities which the data describes, many would argue that they should remain in the dataset analysed (Aggarwal and Yu 2001). Thus, the parameter estimates derived from a regression analysis of the original full dataset remain as the basis for the forecasting model utilised in the ensuing section.

The forecasting model

The estimated coefficients for the 2015 gravity model were utilised in the forecasting model. Based on the gravity equation defined in Eq. (6), both short-term and long-term forecasts were derived (for 2020 and 2030 respectively) to quantify the effect of Brexit on German car exports to the U.K.

Forecast input values for GDP are based on a report by the Organisation for Economic Cooperation and Development which presented a GDP forecast for a base-case ‘No Change’ (No Brexit) scenario and then forecasts of how GDP would change with Brexit under different possible future scenarios, expressed as ‘optimistic’, ‘central’ and ‘pessimistic’ (OECD 2016). Forecast input values for the tariff rate were assumed to be: the current ‘Most Favoured Nation (MFN)’ rate in the absence of a Preferential Trade Agreement (PTA) for the ‘pessimistic’ scenario; the most popular tariff rate in the dataset that was greater than zero for the ‘central’ scenario and; a tariff rate of zero for the ‘optimistic’ scenario.

In summary, the specific scenarios tested for 2020 are specified as follows:

No change: A GDP reduction of 0.00% and a tariff rate of 0.00% are assumed. This scenario reflects a development whereby the U.K. did not exit the EU. It could also reflect the successful negotiation of a transitional agreement. OECD (2016) suggests that either of these two outcomes will serve to strengthen external perceptions of the EU and provide a stimulus to trade and foreign direct investment in every member state. In fact, the assumptions for GDP growth and tariff rates under this scenario could actually be viewed as rather conservative if the UK’s decision to remain aligned to the EU were to facilitate further free trade and investment agreements with non-EU nations.

Central scenario: A GDP reduction of 3.30% and a tariff rate of 5.00% are assumed. The tariff rate is meant to reflect a semi-beneficial scenario whereby, for example, the U.K. successfully negotiated a bilateral agreement with the EU. The logic underpinning these forecast values revolves around the greater economic uncertainty that the U.K. would face after leaving the EU, especially during the early years (OECD 2016). Investor and consumer confidence is likely to fall and spending decisions deferred therefore. The potential also exists for a flight of capital out of the country. While the latter means a reduced availability of capital, the former implies the presence of a risk premium which will raise the cost of capital. In addition, since it will take time to develop new trade agreements, the OECD (2016) suggests that the UK will initially have to trade under WTO rules with both EU and third-party nations. Planned changes to immigration policies within the UK and the deterrent effect of a stuttering economy will also lead to reduced GDP, exacerbated by a depreciation in the value of sterling.

For the forecast year of 2030, two additional scenarios are also tested, specified as follows:

Pessimistic scenario: A GDP reduction of 7.70% and a tariff rate of 9.70% are assumed. The tariff rate is based on the current MFN rate and the scenario could reflect trade under WTO terms. OECD (2016) forecasts that longer-term structural changes to the U.K. economy would result in lower business investment than would otherwise occur and a continuous decline in capital stock. A predicted reduction in innovation, the skills base and managerial quality also contributes to this longer-term pessimistic scenario, all of which undermines future potential returns on what is expected to become a declining asset base in the U.K.

Optimistic scenario: A GDP reduction of 2.72% and a tariff rate of 0.00% are assumed. This reflects a scenario in which the U.K. either remains within the Single Market or where some of the losses outlined in the pessimistic scenario are offset by greater deregulation of the U.K. labour and product markets, as well as by fiscal savings from stopping the net transfer of funds to the EU. Since UK labour and product markets are already highly deregulated and the OECD (2016) predicts UK fiscal savings of only 0.3–0.4% of GDP, the potential for this offset value is rather minimal.

where the variables were defined as follows:

GDP_f forecast GDP for country j under scenario f;

s_t forecast GDP for country j in the absence of Brexit; and.

x_f forecast percentage GDP change for country j under scenario f.

In the forecasting model, country i denotes variables related to Germany and country j variables relate to the UK. Moreover, the distance in kilometres between London and Berlin is used; the value of 1 was added to the tariff rate; and the quality of logistics in 2016 was applied to all scenarios, no matter year and severity.

Model outputs

The results from the forecasts show that if there were to be no Brexit or, alternatively, if a transition deal without changes to the current agreement could be negotiated, Germany is predicted to export 1.3 million passenger cars to the UK in 2020. Nevertheless, if Brexit does occur and a 5% tariff is applied, this quantity would decrease by 7.73%, representing lost sales volume of approximately 102,000 passenger cars.

The forecast for 2030 was based on three different scenarios. The pessimistic scenario projected that Germany would export 15.39% less cars to the UK than if no Brexit would occur; the optimistic scenario would lead to 0.92% less exported cars compared to a scenario in the absence of the Brexit; and the central scenario would lead to a reduction of 9.20% exported passenger cars from Germany to the UK.

In summary, based on a model which includes GDP, distance, tariffs and the quality of logistics – capturing demand factors and logistics-related costs – all Brexit scenarios are estimated to reduce German export quantities compared to a situation where Brexit did not occur.