reflected in the constant term. For developing countries, agglomeration elasticities appear to be significantly higher than developed countries – of the range 1.1 to 2.3 percentage points.

The pervasive evidence of publication bias suggests that the raw meta-estimates cannot be taken at their face value. The state of the art methodology, PET-PEESE, that outperforms other estimations under publication bias is presented in columns 4 and 5 of Table 5. We start with PET-PEESE estimation in column 4. Given that the publication bias is stronger for studies post-1990, we augment our estimating equation (2) to allows for publication bias that differs across studies based on these variables (column 5).<sup>11</sup> We find that controlling for publication bias in PET-PEESE does not substantially change the results relative to estimates that do not control for the bias. Agglomeration elasticities appear to be significantly higher than developed countries by around 2.1 to 2.2 percentage points (column 4 and 5).<sup>12</sup>

**_Table 5: Homogeneous meta-estimates – agglomeration elasticities across developed and developing countries_**

||**(1)**|**(2)**|**(3)**|**(4)**|**(5)**|
|---|---|---|---|---|---|
|Estimation Method:|Meta RE|Meta FE|WLS|PET-|PEESE|
|Publication Bias Correction:||N|||Y|
|Developing Country|0.011***|0.023***|0.023**|0.022**|0.021**|
||(0.004)|(0.001)|(0.009)|(0.009)|(0.010)|
|Post-1990s|||||-0.025*<br>(0.013)|
|Constant|0.051***|0.014***|0.014***|0.014***|0.037***|
||(0.002)|(0.000)|(0.004)|(0.004)|(0.013)|
|Observations|1,242|1,242|1,242|1,242|1,242|

Notes: Outcome is the reported agglomeration elasticity. Meta RE reflects meta-analysis random effects estimation, Meta FE reflects meta-analysis fixed effects estimation, WLS are precision weighted least squares estimates, using the inverse of the reported estimate’s variance as the weight. PET-PEESE are “precision-effect estimates with standard errors” following Stanley and Doucouliagos (2019), which to correct for publication bias includes a squared standard error term in column 6, and its interaction with a developing country dummy, and with a post-1990s dummy in column 7. The standard error terms are omitted for parsimony. PET-PEESE and WLS are precision-weighted, using the inverse of the reported estimate’s variance as the weight. Robust standard errors are presented in parentheses, these are clustered at the study level for all except Meta RE and FE estimation. ***, ** and * reflect significance at the 1, 5 and 10 percent levels respectively.

11 Our results are robust, although somewhat less precisely estimated, when not allowing for heterogeneous publication bias.

> 12 A robustness check using Andrews and Kasy (2019) estimator finds similarly meta estimates are around 2 percentage points higher in non-high income countries.  Depending on the choice of cutoff for probability of publication, the estimator finds a mean high-income true elasticity of 1.6 percent to 2.0 percent, compared to 3.8 percent to 4.8 percent for non-high income.  The estimator is available at

<u>https://maxkasy.github.io/home/metastudy/</u> . We employ PET-PEESE as our preferred estimator it is readily adaptable to heterogeneity by study characteristics.

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