As a result of these mergers and exclusions, the number of administrative units we retained as the universe of places for the analysis fell to 564,052.

Two concerns can be raised on the use of such administrative units as the unit of analysis. The first one, known as the modifiable areal unit problem (MAUP), is the potential sensitivity of results to their considerable diversity in shape and size. It has been shown that shape does not make much of a difference for three important topics in the economic geography literature (namely, spatial concentration, agglomeration economies, and inter-regional trade). As for size, administrative boundaries do not suffer significantly from the MAUP, except in the case of large-scale spatial units, such as states or provinces (Briant, Combes and Lafourcade 2010). However, none of the administrative units considered here reaches such large scale.

A second concern is whether administrative units, self-standing or merged in the case of bigger cities, provide an accurate representation of integrated labor markets. An alternative is to delineate the urban extent by aggregating contiguous cells. Depending on the studies, the aggregation of cells is based on criteria such as the density of their built-up or the intensity of their nighttime light (Baragwanath et al. 2019; Ch et al. 2018; Rozenfeld et al. 2011). However, the nature of the links between cells in a broader spatial context may vary across localities. The aggregation process can introduce other biases (Bosker et al. 2018).

For selecting a representative sample, we further restricted the set of administrative units to those of the 21 largest states and union territories (hereafter states). These large states are covered by the high-quality household surveys whose data are needed for a proper stratification. Focusing exclusively on them resulted in 561,624 places being considered for sampling.

The total population of these 561,624 polygons in 2011 was 1,174 million, or 3.0 percent less than reported by the 2011 Census of India for the country as a whole (ORGI 2011a). Almost a third of this population gapabout 11.3 million peopleis accounted for by the small states excluded from the analysis. Some of these small states are richer than the Indian average and some are poorer, which suggests that their exclusion from the analysis may not bias results much. The rest of the gap is associated with the villages excluded because their boundaries or population figures were unavailable in the official  sources. These villages are most likely rural in practice, and their population is small about 200 people at the medianwhich implies that they too are unlikely to be an important source of bias.

# _A two-stage stratification sampling_

We used a two-stage disproportionate stratification strategy to select the sample of administrative units for human judgment (figure 1). In the first stage, we divided the universe into seven strata by administrative categories, following the definitions of the 2011 Census of India. Four of these categories state capitals and municipal corporations, municipalities, industrial towns, and other townsare   statutorily designated as urban. Two of the categories census towns and outgrowths are statutorily rural but recognized by the 2011 Census as urban. The seventh category is villages, or areas that are rural according to both the Constitution and the 2011 Census of India (ORGI 2011a).

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