This paper examines three key issues encountered when estimating the relationship between agglomeration and multi factor productivity ('agglomeration elasticities'): the sorting of heterogeneous firms, the convexity of agglomeration effects, and the challenges of identifying the impact of persistent spatial differences in effective density. We use a firm-level panel containing production data together with detailed information on the geographic location of employment, covering a high proportion of the New Zealand economy. We are able to control for heterogeneity along firm, region, and industry dimensions, and to estimate separate agglomeration elasticities across industries and regions. Sorting leads to upward biased elasticity estimates but using firm fixed effects can lead to downward bias due to the highly persistent nature of agglomeration variables. Our preferred estimates control for sorting across regions and industries. Overall, we find a positive agglomeration elasticity of 0.066. Within industries and, to a lesser extent within regions, there is pronounced variation in the strength of agglomeration effects, and evidence of decreasing returns to agglomeration. High density areas attract firms that benefit most from agglomeration.