1. Included are all current EU members with the exception of Malta for data reasons.

2. These overall effects are captured to an extent by country and regional NUTS-1 dummies in the econometric specification below.

3. Note that we assume the rental price of capital to be country and sector specific. This might be justified in the way that the capital stock differs across industries in its intensity with respect to asset types. If the rental prices of these asset types differ (but are equalized across the country) these are sector specific. If we assume r _ic =r _c , i.e. rental prices are equalized across sectors within a country, we would reach the same conclusions in that Γ _ic would still be sector and country specific.

4. Ciccone (2002) discusses in detail the conditions under which θ _i >0.

5. From our data we can distinguish only three types of educational attainment levels.

6. In the specifications reported below we set d _ii =0. We also experimented, however, by including internal distances (measured by replacing zero with an internal distance measure given by ). These results are not reported, for brevity, but are available upon request.

7. LFS data are collected according to the ‘principle of living condition’, that is, people are counted in the region where they are living. This introduces a slight inconsistency in our data set which cannot be resolved. Using employment levels from the LFS data (instead of employment levels from Regional National Accounts data), however, yields similar results.

8. Agriculture and fishing (AtB), however, is left out in the analysis for reasons outlined below (see Note 13).

9. The countries considered in our analysis are: Austria, Belgium, Bulgaria, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Spain, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, the Netherlands, Poland, Portugal, Romania, the Slovak Republic, Slovenia, Sweden, and the UK.

10. In particular, the modifiable areal unit problem suggests that the choice of spatial scale is likely to affect the results. Moreover, we may expect larger spillovers at the NUTS-2 level owing to the average distance between regions at the NUTS-2 level being much larger. As discussed above, the existing literature suggests that spillovers decline rapidly with distance.

11. As mentioned above, in some specifications we also include internal distances in the spillover variable to account for the fact that internal distances at the NUTS-2 level can be quite large. When doing this the results for density tend to be consistent with those reported above, while the coefficients on the spillover variables tend to increase, reinforcing the short-distance nature of spillovers. Results are available on request.

12. The full set of results are available upon request.

13. We also estimate agglomeration effects for agriculture, finding a significantly negative coefficient on density of about −0.03. This could point towards a congestion effect, which may reflect the smaller average land holdings of farmers in denser regions that may limit the ability to exploit economies of scale. As a referee pointed out, however, there are some severe problems with the omission of land as a factor of production in the agricultural sector. Apart from the problem of measuring labour productivity properly in the agricultural sector there is the additional problem that the density measure is defined as the employment to land ratio, implying that one would expect a negative density effect as land area is supposed to correlate positively with labour productivity. We considered a number of possible solutions, including the addition of the ‘utilized agricultural area’ (taken from the Eurostata Regio database) as an additional regressor to take this effect into account. Surprisingly, however, it turned out that the density effect remained significantly negative. Moreover, the coefficient on agricultural area also turned out to be negative and significant in most specifications. This latter result could be explained if regions with a lower share in agriculture use only the most productive land or if they use agricultural land more intensively. Similarly, the kinds of crops might play a decisive role. In large regions crops consist mainly of low-value-added products (like wood). Unfortunately, we are not able to control for such effects properly. For these reasons we do not include results on agriculture in the remainder of the paper, though we continue to report aggregate results in which agriculture is combined with the other five sectors.

14. Regressing employment density on area, country and time dummies at both the aggregate and sectoral level results in a significant negative association between density and area. These results are available upon request.

15. For reasons of brevity we choose not to report the results when including internal distances in the spillover specification. These results are, however, available upon request.

16. The group of new Member States (i.e. countries that became EU members in 2004 or after) consists of Bulgaria, Cyprus, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, the Slovak Republic, and Slovenia.

17. It should be noted that we still allow for spillovers across regions from the total sample.

18. In this respect most countries in the new Member States are rather small and in some cases the country as a whole (i.e. including the capital city) is counted as the NUTS 2 region.

19. The OLS results are available upon request. The coefficients from the OLS regressions are generally larger in size and more often significant for both groups of countries.

20. These results also suggest that it may be interesting to distinguish the regions according to various typologies to test for differences in density effects by types of regions. We leave this possibility for future research.