instruments.<sup>32</sup> These variables are either related to a location’s agricultural potential and/or the constraints its geography poses on urban expansion (ruggedness, elevation). Especially when focusing on the urban workers in our sample only (see the next sub-section), these instruments should plausibly satisfy the exclusion restriction.

# 4.1.2. Main Sample

In estimating equation (1), we follow De la Roca and Puga (2017) as closely as possible, and restrict attention to working age (15 - 64) males that report a non-zero income in the August 2014 round of SAKERNAS. This initial sample consists of 116,156 workers. Next, we further exclude workers employed in agriculture, forestry, livestock and fishing, mining and quarrying, public administration and defense, education, health and social work. These activities are typically rural or much more controlled / regulated by the national and local governments in Indonesia. Also, we only focus on workers who have worked at least 32 hours (four working days) during the last week. These restrictions reduce the sample to 56,577 workers. In several robustness checks to these choices, we also show results when extending the sample to females; workers who have worked at least 24 hours (3 working days) in the previous week; workers in public administration and defense, education, health and social work; and/or non-production occupations in agriculture, forestry, livestock, fishing and mining and quarrying. We also perform robustness checks based on restricting the sample to employees or prime age (25-54) males only, or measuring the hourly wage using cash income only.

# _4.2. Baseline results_

Table 2 and Figure 4 show our main results using De la Roca and Puga’s (2017) preferred measure of metro/urban size as our main independent variable of interest – i.e. the number of people within 10 km of the average person in the metro area or district. Table 2, as well as Tables A1 – A10 in Appendix A that contain various robustness check to our main specification, show the estimated agglomeration wage premia when relying on seven different ways to define Indonesia’s metro areas – namely, Duranton’s algorithm based on commuting flow thresholds of 10 percent and 7 percent; the AI; the cluster algorithm using both the UC (i.e. T<sup>�</sup> � = 300 people per km<sup>2</sup> ; T<sup>�</sup> � = 5,000) and the HDC (T<sup>�</sup> � = 1,500 people per km<sup>2</sup> ; T<sup>�</sup> � = 50,000) sets of thresholds; and the NTL approach using the 25<sup>th</sup> and 80<sup>th</sup> percentile thresholds.<sup>33</sup> We focus on these seven based on our discussion in 32 We derived our temperature and rainfall measures from 2013 data produced by the University of East Anglia’s Climate Research Unit (https://crudata.uea.ac.uk/cru/data/hrg/). Meanwhile, we derived out elevation and ruggedness variables using data that were originally generated by NASA's Shuttle Radar Topography Mission (SRTM). Terrain ruggedness at the central point of a grid cell is defined as the mean of the absolute differences in elevation of the central point between the central grid cell and its eight adjacent grid cells, i.e., grid cells in the north, northeast, east, southeast, south, southwest, west, and northwest of the central grid cell. That is, TRI� �∑�����E� �E��⁄8, where _TRIi_ denotes the ruggedness in the central grid cell _i_ , _Ei_ and _Ej_ represent the values of elevation in the central grid cell _i_ and neighboring grid cell _j_ , respectively (Wilson _et al._ , 2007). Using our elevation data, we ran the TRI command from a Python library (GDAL: https://docs.qgis.org/2.8/en/docs/user_manual/processing_algs/gdalogr/gdal_analysis.html) and generated a single-band output raster with the index values. The resultant raster was subsequently used as an input value layer for the zonal statistics to obtain the mean terrain ruggedness for Indonesian district.

33 All tables and figures in this section, as well as the tables showing various robustness checks to our main results (see Appendix A), only report the estimated agglomeration wage premium, _β_ in equation (1). All regressions always include the full set of controls discussed in Section 4.1.1. Table A1 in Appendix A shows the estimated effect of the 19