where _osc_ is the number of self-employed people, and _esc_ the number of (wage) employed people.

The denominator sums total private sector employment (both wage and self-employed, formal and informal) across all 13 sectors and 47 counties. The updated sector-region-size probabilities _p_ ( _θa_ ) will again sum to one and hence capture a relative change in the number of firms rather than an absolute change.

Using simple employment shares to compute _p_ ( _θa_ ) relies on the assumption that the mapping of employees to firms is the same across all sectors and regions. However, empirically, manufacturing firms, for example, tend to be larger than businesses in the hospitality sector. Nairobi hosts larger firms than Mandera County in Kenya’s north. We therefore re-scale the number of employees by the average firm size in each sector-county-size cell _<u>x</u>_<sup>_~~f~~_</sup> _sc_<sup>_ormal,informal_</sup> . For small formal and informal firms, we rely on the KNBS (2016) survey to compute the average number of employees, while we use the administrative data for large formal sector firms.<sup>24</sup> For agriculture and non-market services, we estimate their _p_ ( _θa_ ) drawing only on formal private sector employment. Formal VAT-paying firms occupy a very specific niche in both cases (e.g. formal firms in these sectors are disproportionately export-oriented or the sector is dominated by non-profit entities, see discussion in Section 2.2) and informal employment takes vastly different forms (e.g. mainly reflects subsistence farming).

How does the probability _p_ ( _θ_ ) that a formal firm enters in a given sector-county-size cell shift to _p_ ( _θa_ ) once we account for informal firms? Figure C1 suggest that a 10 percentage point increase in formality corresponds with a 0.5 percentage point increase in _p_ ( _θ_ )- _p_ ( _θa_ ) (0.35 standard deviations). As expected, _p_ ( _θa_ ) is lower than _p_ ( _θ_ ) for sectors and counties with a high degree of formality, indicating that their importance for the overall economy is overstated in the administrative data. To recap, our proposed revised network accounts for informal firms being born into the network based on their sector-region profile. Rather than thinking of the exercise as adding new firms, we adjust the weights of each sector-region-size type.

# **5.2 Assumptions about Linking Probabilities of Informal Firms**

Another challenge for integrating informal firms into the network of formal firms arises due to the lack of granular data on the sectoral and geographic composition of how informal firms link

> 24If big formal firms employ informal casual workers not captured in the administrative data, we understate their size and hence overestimate the probability of big formal firms in the network. As a result, our revised network becomes biased towards the baseline network that only covers the formal sector. This is also illustrated in Figure 8 where we compare the spatial inequality in county-level outdegrees in the baseline network to several scenarios that account for informal firms. Comparing the two scenarios where in one case we use the simple employment shares to compute _p_ ( _θa_ ) and in the other case further adjust for differences in firm size across sectors and counties, we find that in line with the intuition on the implications of informal workers in formal firms, the former scenario is closer to the original network with only formal firms.

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