People spend about 8% of their workday commuting to and from work (Duranton and Turner 2012, Redding and Turner 2015). They make this significant daily investment, to live and work in different locations, so as to balance their living costs and residential amenities with their wage.

- The ability of firms in a location to attract workers depends not only on their ability to attract local residents through migration, but also on their ability to attract commuters from other nearby locations.
- Together, the response of migration and commuting to any local shock, including regulatory changes and infrastructure investments, determines the local employment elasticity.

This elasticity is of great policy interest since it determines the effectiveness of local policy. Estimating its magnitude as a response to a variety of shocks (such as aggregate industry shocks, the discovery of natural resources, financial crises and regression discontinuities associated with state policy interventions) has been the main concern of a large empirical literature. In a recent paper (Monte et al. 2015), we demonstrate the importance of commuting ties for the elasticity of local employment with respect to shocks in the local economic environment.

Commuting flows are large and heterogeneous across counties. For the median county in the US, around 27% of its residents work outside the county and around 20% of its workers live outside the county. For the county at the 90th percentile, these two figures rise to 53% and 37%, respectively. Furthermore, commuting zones are quite imperfect in capturing these flows. For the median county, around 33% of the workers who commute outside their county of residence also commute outside their commuting zone of residence. For the commuting zone at the 90th percentile, these two figures rise to 79% and 73%, respectively. Taken together, these results highlight the quantitative relevance of commuting as a source of spatial linkages between counties and commuting zones within the US.

In parallel with goods trade flows, commuting flows exhibit a strong gravity relationship. In fact, we estimate an elasticity of commuting flows with respect to distance of 4.43, more than three times as large as the elasticity of trade flows with respect to distance which is given by 1.29. We use these gravity equation relationships to estimate the key parameters of the model and calibrate the model to exactly rationalise the observed cross-sectional distributions of employment, residents and income across US counties as an equilibrium of the model. We show how the model can be used to undertake counterfactuals for the impact of changes in the local economic environment using only the observed values of these variables in an initial equilibrium and model parameters.

To provide evidence on local employment elasticities, we compute 3,111 counterfactual exercises where we shock each county with a 5% productivity shock (holding productivity in all other counties and all other exogenous variables constant). Figure 1 shows the estimated kernel density for the distribution of the general equilibrium elasticity of employment with respect to the productivity shock across these treated counties (black line). We also show the 95% confidence intervals around this estimated kernel density (grey shading). The mean estimated local employment elasticity of around 1.52 is greater than one because of the home market effects in the model. Around this mean, we find substantial heterogeneity in the predicted effects of the productivity shock, which vary from close to 0.5 to almost 2.5. This variation is surprisingly large. It implies that if we were to use a local employment elasticity estimated for a county at the top of this distribution to evaluate a policy in a county at the bottom of the distribution, we would overstate the actual effect by a factor of five. For a policy that increases productivity by, say, 5% this implies that we would be calculating increases in employment of 12.5% rather than 2.5%. A big mistake, indeed!

**Figure 1**. Kernel density for the distribution of employment and residents elasticities in response to a productivity shock across counties

*Note*: Eliminating bottom and top 0.5%; gray area: 95% boostrapped CI.

To provide a point of comparison, Figure 1 also includes the general equilibrium elasticity of residents in a county with respect to the same 5% productivity shock in that county. Again we show the estimated kernel density across the 3,111 treated counties (black line) and the 95% confidence intervals (grey shading). We find far more heterogeneity across counties in the employment elasticity than in the residents’ elasticity (which ranges from around 0.2 to 1.2). Since employment and residents can only differ through commuting, this implies that the heterogeneity in the local employment elasticity in response to the productivity shock is largely driven by commuting links between counties. We also show that we continue to find substantial heterogeneity in local employment elasticities if we undertake the same analysis using commuting zones rather than counties, or if we shock counties with patterns of spatially correlated shocks reproducing the industrial composition of the US economy.

## Conclusions

The heterogeneity in the local employment elasticities that we estimate cannot be explained by measures of county size, wages, as well as other standard county characteristics. Furthermore, it cannot be explained by measures of the characteristics of surrounding counties. We show that all these variables together can account at most for 51% of the variation in treatment effects. In contrast a simple measure of commuting (the number of agents that work in the county where they live) can account for on its own for 89% of the variation in local employment elasticities across counties. These results suggest, we believe, that adding measures of commuting in all the empirical studies of regional treatment effects is essential to guarantee their external validity. Their inclusion is simple and data is in general easily available.

## References

Duranton, G and M A Turner (2011) “The Fundamental Law of Road Congestion: Evidence from US Cities”, *American Economic Review* 101(6): 2616–2652.

Monte, F, S Redding and E Rossi-Hansberg (2015), “Commuting, Migration and Local Employment Elasticities”, *NBER Working Paper* 21706.

Redding, S J and M Turner (2015), “Transportation Costs and the Spatial Organisation of Economic Activity”, in G Duranton, J Vernon Henderson and W Strange (eds.) *Handbook of Urban and Regional Economics*, Chapter 20, pp. 1339-1398.