A gravity equation for commuting - with an application to estimating regional and language border effects in Belgium

This paper derives a gravity equation for commuter flows from a simple spatial labor market model based on the classic model developed by Anderson and Van Wincoop in the context of international trade. The approach shows the importance of taking into account the effect of the economic structure of neighboring regions when explaining the size of the commuter flow between two locations, the omission of which would be a significant source of omitted variable bias. As an application, we use this model to identify the effect of regional borders and language borders on commuting using Belgian data on intermunicipality-level commuting between all pairs of municipalities. To handle observations with zero commuters, we estimate the model by means of a negative binomial regression. We went at length to control for relevant variables such as the driving time between two municipalities, but also the travel time by public transport. The theoretical model is used to calculate the relevant controls for economic size of the municipalities and their surroundings. We find that regional borders exert a sizable residual deterrent effect on commuting. This border-effect differs significantly between regions and depends on the direction in which the border is crossed, with commuting flows going from French-speaking areas to Dutch-speaking areas experiencing a stronger deterrent effect from the border; which probably reflects the fact that knowledge of French is relatively more wide-spread in the Dutch-speaking areas compared to the other way around. We consider two extensions of the model. In a first one, we estimate the elasticity of substation for labour from different locations. With an estimated value of 1.3, it seems workers from different localities are hardly substitutable. In the second extension, we use the regional wage-equilibrium condition from our theoretical framework to estimate how the counter-factual removal of a regional border would change regional wages. As it turns out, the estimated effect is quite large, with an upsurge in wages of about 50 percent in the entire south of the country, and with an effect which dies only slowly with distance. As this prediction seems unrealistic, we re-estimated the effects while imposing a higher elasticity of substitution of 2.3. Using this value still gives a rise of about 50 percent, but only for a selection of municipalities in the South of Belgium, with very high unemployment rates, and located closely to high labour demand in the North (in Flanders and Brussels). The effect on municipalities about 20-30 kms from the language border becomes negligible.