In extensions, we also use four other independent variables at the same “ �� ” level as our main city size variable. First, we obtain the total urban population of each metro area / district from the 2014 Indonesian household survey ( _Survei Sosial Ekonomi_ , SUSENAS). Our main city size variable is essentially a weighted density measure. Using total urban population instead we can assess how sensitive our results are to the use of a simple overall population size measure. Second, we constructed two other agglomeration variables from the information in SAKERNAS that measure: (i) the sectoral specialization of the metro area/district, i.e. the share of a metro’s total employment in the same sector as the worker him/herself; and (ii) the share of skilled workers in a metro/district’s total employment, where we define skilled workers as those that have completed general senior high school or higher. Note that, similar to our main size variable, these two variables, as well as the earlier discussed “ _total urban population measure_ ” are defined at the district level for all districts that are not part of a metro area. Finally, we have calculated each district’s market access that captures a district’s accessibility to the markets of all other districts within Indonesia taking estimated travel times into account.<sup>31</sup> Taking a metro/district’s sectoral specialization, share of skilled workers and access to other districts’ markets into account, we can assess to what extent our findings are sensitive to taking explicit account of alternative explanations for agglomeration economies.

In all our regressions, _β_ is our main coefficient of interest. It measures the size of Indonesia’s agglomeration wage premium. This coefficient is of interest in and of itself, but for the purposes of this paper, we are particularly interested in seeing how the estimated size (and significance) of _β_ depends on the approach used to define metro areas. In establishing its significance, it is important to note that we always cluster our standard errors at the metro or district level (depending on whether a district belongs to a metro area or not), i.e. at the same level at which our main independent variable of interest varies.

We estimate equation (1) using ordinary least squares (OLS) regression, so that we can interpret the estimated _β_ as a consistent estimate of Indonesia’s agglomeration wage premium under the assumption that ε���� is uncorrelated with the included independent variables in the regression. But, in an attempt to deal with the possible endogeneity of the metro/urban size measure (which, if present, would clearly violate this assumption), we also employ a Two-stage Least Squares (2SLS) regression strategy inspired by De la Roca and Puga (2017), Combes _et al._ (2010), and Saiz (2010), where in the first stage, we instrument our size measure with several geographic and climate variables that, historically, (may) have constrained urban development, but that, today, are unlikely to have an important influence on workers’ wages. Hence, we use a district’s elevation, ruggedness, temperature (both its monthly average as well as its standard deviation over the year) and rainfall (both total monthly rainfall as well as its standard deviation over the year) as

> 31 Following, for example, Jedwab and Storeygard (2015), Blankespoor _et al_ . (2017) and Berg _et al._ (2018), we measure market access as MA� �∑��� P�τ���� where MA� is a district _i_ ’s level of market access, P� is the population of district _j_ , and τ�,� is the estimated road travel time between districts _i_ and _j_ . Population data are from the 2014 round of SUSENAS. To estimate road travel time, we construct a road data set by transferring the 2014 road categories on a paper map published by NELLES to a geo-referenced network-enabled road data set (DeLorme) and assume uniform travel time speeds by road category identical to those assumed by Jedwab and Storeygard (2015) and Berg _et al._ (2018): expressway 105km/h, principal highway 100km/h, highway 90km/h, secondary road 75km/h, track 50km/h, 6 km/h for the unknown category and 5 km/h in the absence of a road. For the elasticity of trade, _θ_ , we assume 3.8 following Donaldson (2018).

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