# Meta-analysis data

The primary focus of our paper is a meta-analysis of agglomeration productivity elasticities differentiating between developing and developed countries, where our paper follows the approach outlined in Stanley et al (2013) to construct the sample of studies (further details are given in the Appendix).

We build on the meta-analysis data of Melo et al. (2009) and Ahlfeldt and Pietrostefani (2019) by extending their sample on elasticity estimates for developing countries. We use a combination of keywords, such as “agglomeration” or “density” or “urban”, and “elasticity” or “productivity” or “wages”, applied to the academic databases EconLit, Web of Science, and Google Scholar. We supplement the keyword search by conducting an analysis of citation trees of key published and working papers by eminent researchers in the field and papers that inspired the study.<sup>4</sup> We also consulted with experts in academia (including the University of Pennsylvania, Johns Hopkins University, and Oxford) and practice (including the World Bank) to identify ongoing work in the field. The initial sample included peer-reviewed papers, working papers of universities, research institutes and international organizations (World Bank, NBER, CEPR, CESIfo, and IZA), chapters in books and conference proceedings.

We restrict the initial sample to papers with one of four outcome variables --- labor productivity, wages or earnings, TFP and output using a production function -- and four agglomeration measures: population size, population density, economic density and market potential. To ensure comparability, we only retain studies that either estimate unit-free agglomeration elasticities, or those that could be converted to an elasticity (e.g. semi-elasticities). Estimates reporting analysis pooled across several countries are excluded; country specific estimates are retained.

To test and correct for publication bias, we also collect standard errors of estimates either from the papers or by requesting the authors. Studies without the standard errors needed for precisionweighting are excluded from the meta-analysis. Most studies are empirical; however, studies estimating structural models are also included provided they report agglomeration elasticities and standard errors. To avoid double counting several versions of the same study, in particular for working papers, we include only the latest version.

Our resulting sample comprises of 1,242 elasticity estimates sourced from 70 studies across 33 countries covering 1973 to 2020. Of the 70 studies, 29 are reported in Melo et al. (2009), 16 are drawn from Ahlfeldt and Pietrostefani (2019), with 25 additional studies included here. Table A5 in the Appendix reports the full list of 70 studies. Among the estimates, 388 are for developing countries.

Even within a single study or a single country in our data there are often a wide range of estimates, highlighting substantial heterogeneity in data and estimation methods. Figure 3 reports a forest plot of the estimated 1,242 agglomeration elasticities across the 33 countries. The figure suggests that countries show a broad range of elasticities, with some reporting both large positive and negative estimates. While some of the variation is likely a result of differences in time period, spatial scale, estimation methods and so on across papers, Appendix Figure A1 shows a similar spread in estimates within individual studies. The wide range of estimates strongly suggests key differences in underlying factors within and across studies, highlighting the importance of controlling for such distinctions

> 4 Melo et al. (2009), Chauvin et al., (2017) and Ahlfeldt and Pietrostefani (2019).

9