metadata: authors: 0: author: Wiedemann,Verena Christina
1: author: Kirui,Benard K.
2: author: Khandelwal,Vatsal
3: author: Chacha,Peter W.
count: Kenya
docna: 0: docna: Spatial Inequality and Informality in
            Kenya’s Firm Network
docty: Policy Research Working Paper
abstracts: cdata!: The spatial configuration of domestic
            supply chains plays a crucial role in the transmission of
            shocks. This paper investigates the representativeness of
            formal firm-to-firm trade data in capturing overall domestic
            trade patterns in Kenya &#x2014; a context with a high
            prevalence of informal economic activity. It first documents
            a series of stylized facts and shows that informal economic
            activity is not randomly distributed across space and
            sectors, with a higher incidence of informality in
            downstream sectors and smaller regional markets. The paper
            then links granular transaction-level data on formal firms
            with data on informal economic activity to estimate a
            structural model and predict a counterfactual network that
            accounts for informal firms. The findings show that formal
            sector data overstates the spatial concentration of
            aggregate trade flows and under accounts for trade within
            regions and across regions with stronger social ties.
            Additionally, the higher the informality in a sector and
            region is, the more formal sector data underestimates its
            vulnerability to domestic output shocks and overestimate its
            vulnerability to import shocks.
display_title: Spatial Inequality and Informality
            in Kenya’s Firm Network
listing_relative_url: /research/2024/09/34396866/spatial-inequality-informality-kenya’s-firm-network
topicv3: Spatial Inequality m1327181 1166,Supply and Distribution Chains m1504201 2870,Trade Linkages, Spillovers and
            Connectivity m1504235 2601,Analysis of Trade Networks m1504236 2602
publishtoextweb_dt: 2024-09-30T00:00:00Z
dois: 10.1596/1813-9450-10932
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 66
author_keys: 0: author_key: 1613235
1: author_key: NA
2: author_key: NA
3: author_key: NA
model_extractions: Policy Research Working Paper 10932

# Spatial Inequality and Informality in Kenya’s Firm Network

_Verena Wiedemann_ _Benard K. Kirui Vatsal Khandelwal Peter W. Chacha_ International Finance Corporation September 2024
Policy Research Working Paper 10932

# **Abstract**

The spatial configuration of domestic supply chains plays a crucial role in the transmission of shocks. This paper investigates the representativeness of formal sector firm-to-firm trade data in capturing domestic trade patterns in Kenya, a context with high informality. It documents stylized facts showing that formal sector trade exhibits a distinct spatial concentration relative to overall economic activity. Linking transaction-level data with data on informal economic activity, the paper estimates a structural model and predict a revised network incorporating informal firms. Findings show that formal sector trade flows underaccount for trade within regions and across regions with stronger social ties. The higher the incidence of informality, the more one underestimates vulnerability to domestic shocks and overestimates exposure to import shocks.

This paper is a product of the International Finance Corporation. It is part of a larger effort by the World Bank Group to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at vwiedemann@ifc.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Spatial Inequality and Informality in Firm Networks<sup>∗</sup> Verena Wiedemann<sup>†</sup> Benard Kipyegon Kirui<sup>‡</sup> Vatsal Khandelwal<sup>§</sup> Peter Wankuru Chacha<sup>¶</sup> Originally published in the Policy Research Working Paper Series on September 2024. This version is updated on August 2025. To obtain the originally published version, please email prwp@worldbank.org.

_Keywords:_ firm networks, informality, spatial inequality, economic development. _JEL classification:_ O11, O17, R12, D22, D85, E26.

> ∗We thank the Kenya Revenue Authority (KRA) for the outstanding collaboration. Romeo Ekirapa, Simon Mwangi, and Benard Sang provided excellent technical support and advice. We thank Elizabeth Gatwiri and Daniela Villacreces Villacis for excellent research assistance. We thank Andrea Bacilieri, Raphael Bradenbrink, Banu Demir Pakel, Kevin Donovan, Douglas Gollin, Justice Tei Mensah, Luke Heath Milsom, Sanghamitra Warrier Mukherjee, Solomon Owusu, Piyush Panigrahi, Nina Pavcnik, Simon Quinn, Alexander Teytelboym, Christopher Woodruff, Hannah Zillessen and participants of seminars and conferences at Oxford, CSAE, STEG, the World Bank’s DaTax group, IFC, KIPPRA, Montreal, the Bank of Italy/OECD, and Jeune Street for comments and feedback. We gratefully acknowledge financial support from the Private Enterprise Development in Low Income Countries (PEDL) and the Structural Transformation and Economic Growth (STEG) programmes, both of which are joint initiatives by the Centre for Economic Policy Research (CEPR) and the UK Foreign, Commonwealth & Development Office (FCDO). Verena Wiedemann further acknowledges funding from the Oxford Economic Papers Research Fund (OEP) and the German National Academic Scholarship Foundation. This study has been approved by the Department of Economics Research Ethics Committee at Oxford (protocol no.ECONCIA20-21-23), and the Kenyan National Commission for Science, Technology and Innovation (protocol no.NACOSTI/P/20/5923). The views in this paper are those of the authors, and do not necessarily represent those of the KRA or any other institution the authors are affiliated with.

> †Economic Research Unit, International Finance Corporation (World Bank Group)

> ‡Privatization Commission Kenya

> §Department of Economics, University of Exeter

> ¶International Monetary Fund
# **1 Introduction**

Limited opportunities for export-led growth and concerns over the unequal allocation of gains from trade have led policymakers and researchers to shift attention towards domestic supply chains and market integration to enhance economic development (Topalova, 2010; Atkin and Donaldson, 2015; Bustos et al., 2020; Grant and Startz, 2022; Goldberg and Reed, 2023). Progress in understanding the structure of domestic supply chains has been facilitated by the increasing availability of granular transaction-level firm network data, which are often sourced from tax records (see e.g. Panigrahi, 2022; Ad ̃ao et al., 2022; Alfaro-Ure ̃na et al., 2022; Boken et al., 2023).<sup>1</sup> These developments reflect a broader trend in the literature on development and structural transformation, where non-traditional novel micro-data such as credit registries, smartphone data, and matched employer-employee data enable new insights into classic questions (Bustos et al., 2020; Blanchard et al., 2021; Dix-Carneiro et al., 2024; Kreindler and Miyauchi, 2023). However, a potential drawback is that the data-generating process underlying such administrative records is often skewed toward particular segments of the economy, e.g. taxpayers in the case of firm-to-firm transaction data. This can leave us with a potentially incomplete view of economic activity due to the size and significance of the informal sector in many low and middle-income economies.

In this paper, we ask how observing only a selected segment of the economy, in our case, formal firms, might bias the inferences drawn from data on firm-to-firm trade networks constructed using tax records. Accounting for this bias is important because the structure of these networks can shape the aggregate and distributional impacts of infrastructure investments, industrial policies, and financial shocks (see e.g. Acemoglu et al., 2012; Liu, 2019; Demir et al., 2022; Balboni et al., 2023; Castro-Vincenzi et al., 2024; Demir et al., 2024; Huremovic et al., 2024; Donaldson, 2025) and inform tax policy and the design of social protection programs.<sup>2</sup> Formalsector data may not be representative of the overall spatial distribution of trade, especially if formal firms are concentrated in specific sectors and regions and exhibit distinct linking patterns. Given the scarcity of granular data on the informal sector, we lack empirical evidence on the nature and degree of the bias caused by neglecting informality.

We address this question by combining transaction-level administrative tax records of over 76,000 formal firms and 5.8 million firm-to-firm relationships in Kenya, with micro and aggregate data on informal sector activity obtained from labor force surveys and national accounts.<sup>3</sup> We first

> 1Transaction-level survey data (see e.g. Startz, 2021) or administrative industry-specific data (see e.g. Hansman et al., 2020), which often cover a wider range of firm and buyer-supplier characteristics, are a popular, albeit costly, complement to data relying on tax records.

> 2An advantage of transaction-level firm-to-firm trade data over traditional sources like input-output tables is the possibility to track spatial heterogeneity in economic activity, rather than being limited to national aggregates.

> 3The labor force survey module was integrated in the 2019 population census. The public micro data covers

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to other indicators, including population, GDP, employment in micro and small enterprises, the distribution of registered firms, and patterns of internal migration. This spatial concentration is driven by inequality along the extensive margins of the firm network, i.e. the location of firms and trading relationships, rather than transaction volumes. Notably, formal firms maintain twice as many links to buyers and suppliers in urban hubs as they do to formal firms within their own counties, indicating that within-county trade is less common than inter-county trade with firms in Nairobi. Following this, we show that informality is not evenly distributed across space but its incidence varies systematically across sectors, regions, and firm position in the supply chain. Informal firms are more likely to be located downstream of large formal firms, and informality negatively correlates with regional economic size and income. As a result, we expect that accounting for the informal sector can systematically alter the structure of the observed firm network rather than introducing random measurement error. As we do not directly observe trade flows between informal firms, we rely on a structural model to recover a network that accounts for informal activity.

We introduce and estimate a network formation model with heterogeneous firm types following Bramoull ́e et al. (2012) to predict a revised network. In our adaptation of the model, we classify firms based on their sector, location, and size, due to the substantial heterogeneity along these three dimensions documented in the empirical section. The key advantage of the model is that it allows for a flexible network formation process that accounts for heterogeneous linking preferences along the above dimensions. Moreover, it allows firms to form links both independently (undirected search) and through the existing connections of their suppliers (directed search). The model then provides a unique steady-state predictions for the number of links between firms of different sector-location-size types. We first estimate the model to predict the Kenyan firm network as observed. We find that new firms choose 45% of their suppliers through undirected search, conditional on their bias, and the remaining 55% of suppliers are found via existing suppliers.<sup>5</sup> The model-predicted network not only fits the empirical distribution of outlinks (i.e. the number of buyers) well, but also performs well with respect to untargeted moments, such as the share of links accounted for by Nairobi- and Mombasa-based firms.

Using the estimated model, we then predict a revised network that accounts for informal firms by combining the model with granular real-world data on the sectoral and regional composition of the informal sector. Updating the entry probabilities of firms by sector, location, and size requires data on the spatial and sectoral dispersion of economic activity, for which we draw on microdata from the labour force module of the 2019 population census. We initially assume that

> 5In comparison, Chaney (2014) finds that only 40% of all relationships of French exporters with international trade partners are formed via directed search. Our estimate of 55% of links being formed as a result of directed search could suggest that linking frictions are potentially even more binding for firms in Kenya’s domestic firm network.

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informal firms, conditional on sector and geography, exhibit linking patterns similar to those of the smallest quartile of formal firms in the administrative data. This assumption addresses concerns that informal firms might have different linking patterns compared to larger formal firms operating in the same sector and location (e.g. due to internal economies of scale (Grant and Startz, 2022)).<sup>6</sup> Nevertheless, informal firms might encounter additional obstacles specific to informality.<sup>7</sup> To account for this, we implement additional sensitivity checks that account for alternative scenarios with lower linking probabilities between the formal and informal sector.

We use the revised network to answer the question of interest: How do spatial patterns of trade change when informal firms are accounted for? First, we find that sectors and regions with the highest levels of informality have more outlinks in the revised network relative to the baseline network. The spatial inequality in outlinks declines by 7% and the prominence of urban hubs like Nairobi and Mombasa decreases by 5 percentage points. We show that while this decrease in inequality of outlinks is driven by an increase in both inter-county and intra-county trade, intracounty trade rises by a larger margin. Moreover, we find that once informal firms are accounted for, the number of trade relationships between counties is more sensitive to the strength of social ties between them, measured using both online friendship networks and migration inflows.

Next, we simulate the pass-through of domestic and import shocks using both the baseline network estimated from the structural model and the revised network that incorporates informal firms. We find that ignoring informality leads us to underestimate the average impact of domestic shocks and overestimate the average impact of import shocks. In particular, when using the revised network, we find that domestic output shocks have a more pronounced negative effect on sector-regions with higher levels of informality, compared to results based on formal sector data alone. Our results suggest that a 1 percentage point decrease in the formal sector share corresponds with an underestimation of the reduction in output by 5 percentage points. By contrast, for import shocks, the bias goes in the opposite direction. The economy appears less exposed to import shocks once the informal sector is taken into account. This discrepancy arises because import shocks primarily affect larger formal firms, which carry less weight in the overall firm network once informality is incorporated.

Finally, we consider the sensitivity of our results with respect to alternative assumptions about the linking patterns of informal firms. We conduct bounding exercises where we further restrict the degree of integration of informal firms with the formal sector relative to small formal firms. Drawing on survey evidence and the existing literature (B ̈ohme and Thiele, 2014; Gadenne

> 6We provide evidence showing that the linking patterns of small formal firms are similar to what we would expect from informal firms – they link more locally and buy more from intermediaries relative to their larger peers.

> 7This can include wedges introduced by the VAT system itself (De Paula and Scheinkman, 2010; Gadenne et al., 2022).

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et al., 2022), we assume informal firms sell no output to the formal sector and source a smaller proportion of their inputs from formal firms compared to small formal firms. We find that this further reduces spatial inequality in outlinks and the prominence of urban hubs relative to the formal network. Moreover, we continue to underestimate the impact of domestic shocks while overestimating the effects of trade shocks.

Our paper contributes to the literature on macroeconomic development, informality, firm networks, and spatial inequality.

First, we contribute to a growing body of research at the intersection of trade and macroeconomic development that integrates granular administrative data such as employer-employee records and data from credit registries, with broader data sources like population censuses to achieve a more accurate assessment of aggregate economic outcomes. To date, this literature has primarily focused on employment outcomes, sector shares (see e.g. Albert et al., 2021), and consumption (see e.g. Fan et al., 2023), where informal activity is somewhat more observable. However, informal activity along supply chains remains particularly elusive (B ̈ohme and Thiele, 2014; Atkin and Khandelwal, 2020).<sup>8</sup> Our results highlight the implications of the non-random selection of firms into administrative records. This is particularly important, given the growing reliance on such data in the literature (Donaldson, 2025).

Our approach to employ a structural model to bridge gaps in our understanding of informal firm dynamics also aligns with the recent literature in this field (see e.g. Ulyssea, 2018; DixCarneiro et al., 2024). Unlike related studies that focus on firm and worker-level dynamics, we do not model the endogenous response of firms and workers to simulated shocks. Crucially, however, our research design allows us to examine the role of informality for Kenya’s regionlevel input-output matrix. This is particularly relevant for research that seeks to complement predictions about aggregate national welfare with welfare estimates at the regional level to study geographic heterogeneity in the impact of international trade (Topalova, 2010; Arkolakis et al., 2023), infrastructure investments (Demir et al., 2024) or climate and weather shocks (Albert et al., 2021; Castro-Vincenzi et al., 2024).

Second, we contribute to the literature on spatial production networks (Bernard et al., 2019; Panigrahi, 2022; Miyauchi, 2024), shock propagation in firm networks (see e.g. Baqaee and Farhi, 2019; Carvalho et al., 2021; Arkolakis et al., 2023; Chacha et al., 2024), and urban primacy (as published in Jefferson (1989), Jefferson, 1939; Memon, 1976; Ades and Glaeser, 1995; Soo, 2005). We analyze the spatial distribution of formal firms in an economy with a large informal

> 8A related literature in public finance studies why informality arises along supply chains, and how tax policy can alter its incidence (De Paula and Scheinkman, 2010; Zhou, 2022; Gadenne et al., 2022; Almunia et al., 2023). Relative to this literature, we focus on reconstructing a more complete network that includes informal firms rather than studying the marginal firm’s decision to formalize.

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sector and demonstrate that ignoring informality can lead to overestimating spatial inequality in firm-to-firm trade and the extent of urban primacy. This oversight may cause researchers to underestimate the economic connectedness and vulnerability of smaller regions. Our finding that formal sector activity is disproportionately concentrated in urban hubs is also consistent with spatial patterns in other contexts that exhibit a similar formal-core, informal-periphery structure (Z ́arate, 2022). In complementary work, Bacilieri et al. (2023) examine how varying reporting thresholds for firm-to-firm transactions affect the comparability of aggregate network statistics. While they demonstrate that missing data can bias network statistics, our focus differs in two key ways. First, transaction reporting thresholds are not a concern in our setting; we instead address other sources of network incompleteness in tax data. Second, while they analyze aggregate statistics, we examine distributional implications at the regional level – a margin where we find informality plays a substantial role.

Finally, we contribute to the growing literature on estimating network statistics and reconstructing networks with missing data (e.g., Chandrasekhar (2016); Mungo et al. (2023)).<sup>9</sup> We contribute to this literature by proposing the use of a structural approach. The structural route seeks to tackle two challenges: first, nodes are missing in a non-random manner. Second, we do not observe network characteristics for missing nodes, but linking preferences of missing firms can systematically differ from those of observed firms. To address these challenges, we combine multiple data sources and estimate a network formation model that recovers both the prevalence of missing firms and their linking behavior, accounting for sectoral and geographic preferences. In comparison, Mungo et al. (2023), for example, use a link prediction algorithm to predict the existence of links among missing nodes using data on the characteristics and linking behavior of non-missing nodes. This approach is challenging to apply in the context of informality, as informal firms are missing in a non-random manner and information on their linkages are not available at a sufficient granularity to recover a network with sectoral and spatial heterogeneity.<sup>10</sup> The paper is organized as follows: Section 2 describes our data. Section 3 examines how representative the trade patterns captured in the administrative data are of overall economic activity and discusses the role of the informal sector. We present and estimate a network formation model in Section 4. Section 5 describes the patterns we observe in our revised network that now incorporates informal firms, while Section 6 analyzes the sensitivity of these results to alternative assumptions.

> 9See L ̈u and Zhou (2011) for a survey of algorithms used for link prediction, a technique commonly applied in network reconstruction.

> 10Rare instances where researchers have used survey data to collect information on firm-to-firm links of informal firms focus on specific sub-sectors. Moreover, explicitly prompting for the tax status of trade partners adds an additional challenge due to the sensitive nature of this information.

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Figure A1 plots the sector composition and the respective sales and purchase channels of firms covered in these administrative records. Manufacturing and wholesale and retail firms together account for almost half of the sales in the tax records. The graph on the left in Figure 2 shows the geographical dispersion of formal firm headquarters, which shows that many firms concentrate in Nairobi and Mombasa.

Figure A2 plots the share of total observed firm-to-firm links attributed to different groups of firms, distinguishing by size, sector, and location. Panel A shows that aside from retail, wholesale, and manufacturing, business services account for a substantive proportion of supplier linkages. Mining firms account for the least number of both supplier and buyer links. Panel B shows that firms in Nairobi and Mombasa account for more than three quarters of all buyer and supplier links. Panel C shows that firms in the top sales quartile account for a disproportionately large share of total links, especially as suppliers. Aside from the statistics plotted in Figure A2, 61% of total links are formed among firms located in the same county, 17% of links with firms within the same sector, and 45% among firms in the same sales quartile.

# **2.2 Data on Informal Activity**

Informality in firm-to-firm transaction data can either arise because firms themselves are not registered (extensive margin) or because transactions of registered firms are not recorded (intensive margin). Not being registered as a firm or not recording a transaction in turn can either be the result of non-compliance or because of exemptions (e.g. for small firms).<sup>12</sup> To obtain an updated distribution of overall (formal and informal) economic activity that we can compare to the administrative data, we draw on a series of data sources listed in Table 1. Importantly, we not only measure informality as the gap between overall economic activity and what is captured in the administrative data, but additionally rely on measures generated independently of the administrative records. This helps us to rule out the possibility that our measures of informality capture idiosyncratic patterns that are specific to the VAT system.

Throughout this paper, we draw on three types of measures for economic activity: employment figures, the number of firms, and value added (i.e. the difference between sales and purchases). Our preferred measure of informality uses formal sector employment as a share of total employment, drawing on a comprehensive labor force module in the 2019 population census (KNBS, 2019). Alternative measures of informality based on the number of firms rely on estimates of the universe of businesses in KNBS (2016),<sup>13</sup> while a value-added based measure utilizes estimates

> 12See Appendix A.2 for a detailed discussion of these margins and why administrative data may not fully capture economic activity.

> 13KNBS (2016) obtains information on the number of licensed businesses from county governments and estimates the number of unlicensed businesses based on household survey data.

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Table 1: Overview of data sources

|**Source**|**Year**|**Aggregation**|**Key indicators**|
|---|---|---|---|
|Population & housing census (census)|2019|Sector and county|Formal & informal employment|
|Gross County Product (GCP)|2019|Sector and county|Gross County Product|
|Census of establishments (CoE)|2017|Sector or county|Number of formal sector establishments|
|Micro, small & medium sized<br>enterprises survey (MSMEs)|2016|Firm-level|Main input source and buyer|
|Census of industrial production|2010|Sector and county|Sales of multi-establishment frms|

All data are collected and published by the Kenya National Bureau of Statistics. **Sources:** 2019 Kenya Population & Housing Census KNBS (2019); Gross County Product KNBS (2022); Census of Establishments KNBS (2017); Small & Medium-Sized Enterprises Survey KNBS (2016); Census of Industrial Production 2010 (KNBS, 2010).

of the regional economic size captured by the Gross County Product (KNBS, 2022).<sup>14</sup> The employment-based measure, which later serves as a key input for predicting the revised network with informal firms, offers two distinct advantages. First, it enables joint disaggregation of informal activity by sector and region. Second, it allows us to distinguish between private and public sector employment, a distinction unavailable in alternative measures, but based on which we can rule out that this measure of informality captures a proportion of public sector activity. The graph on the right in Figure 2 shows the geographical dispersion of informal activity as per the employment-based measure derived from the labor force module of the 2019 census. The measure correlates strongly ( _ρ_ = 0.83, Table A3) with a measure of regional formal sector shares that relies on the administrative data to capture the size of the formal sector (see Figure A9).

Finally, we exclude agricultural and non-market service sectors from our informality measures where possible, as their tax records only cover a small and very specific sub-population of firms and employees. In the case of agricultural firms, the administrative data only capture large-scale commercial agriculture, which is often primarily export-oriented (see Figure A1 and Chacha et al. (2024)). Non-market services are dominated by non-profit organizations and the government with only a few for-profit VAT firms.

**Data on linking patterns of informal firms:** In addition to the above, we use data from a survey with small and medium size enterprises (KNBS, 2016) to derive some insights into the sales and purchase patterns of the informal sector. The survey data only record the main type of buyer and supplier of a firm and hence cannot be directly used to reconstruct a network with informal firms. However, we will use these data to inform the assumptions of our model.

# **2.3 Size of the Informal Sector**

To assess how much of economic activity is generated by VAT-reporting firms, we first compare their value added with Kenya’s national accounts. We find that VAT-reporting firms account

> 14To estimate the Gross County Product, KNBS (2022) relies on a series of data sets including the 2016 MSME survey and the 2019 population census. Most data sets covering informal activity are only collected intermittently.

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for 36% of Kenya’s GDP on average between 2015 and 2019 (Appendix Table A4). Excluding VAT-exempt sectors such as agriculture, non-market services and finance, the share increases to 67% of residual economic activity, implying an informal sector share of 33%. The share of informal firms and people employed in the informal sector is even higher. Of the 7.4 million businesses identified in the 2016 MSME report, only one fifth were licensed, and only 2.5% appeared in VAT data (KNBS, 2016). Similarly, VAT-registered private sector firms employed 5% of Kenya’s workforce in 2019.

With data on the formal sector only capturing a proportion of overall economic activity, we now turn to the question on whether the inability to observe informal firms in the VAT data might result in distinct trade patterns that deviate from overall firm-to-firm trade.

# **3 Representativeness of the Formal Firm Network**

In this section, we establish two key stylized facts about the extent to which trade among formal firms might be representative of overall economic activity. First, we show that trade among formal firms is highly concentrated around urban centers and places greater emphasis on inter-county rather than within-county trade. This contrasts with other measures of economic activity that include less formalised activities and which we find to be more geographically dispersed. Second, we document that the incidence of informality varies systematically across geography, sectors, and positions in the supply chain, suggesting that informality is indeed not evenly distributed across the economy. As a result, we expect overall trade patterns to diverge from the ones we document for the formal sector.

## **Fact 1: Formal sector trade is more spatially concentrated than overall economic activity and distinctly centered around urban hubs.**

### **Formal sector data reveal a high degree of spatial concentration compared to overall economic activity.**

Our first observation is that formal sector trade flows are strongly concentrated around Kenya’s largest metropolitan areas Nairobi and Mombasa. In 2019, as much as 68% of the total sales within the network of formal firms was generated by Nairobi-headquartered firms (see Table 2). However, in the same year, as little as 9% of Kenya’s population lived in Nairobi County and the city contributed only 33% of Kenya’s GDP outside the agricultural sector (also reported in Table 2).<sup>15</sup> These comparisons suggest that the role of urban centers in the Kenyan firm network is disproportionate relative to their population and their contribution to aggregate GDP.

> 15While Nairobi’s metropolitan area extends into neighboring counties, for simplicity, references to Nairobi in this paper exclude these areas.

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As a proxy for the spatial dispersion of economic activity beyond simple shares attributed to major cities, we compute Pareto exponents ( _α_ ) (Gabaix, 2009; Soo, 2005). The third column in Table 2 shows that while county-level GDP and population show relatively even distributions ( _α_ close to one), measures of economic activity derived from the VAT data exhibit much higher inequality. The Pareto exponents for employment, value added, and trade flows are 57-76% lower than for overall economic activity, indicating higher spatial concentration.

Is this spatial concentration driven by firm locations and number of firm-to-firm relationships (i.e. the extensive margin of trade) or trade volumes (i.e. the intensive margin of trade)? In Appendix A.5, we show that the spatial concentration of both trade out- and inflows is primarily driven by firm locations and the number of firm-to-firm relationships. The number of transactions and average trade volumes per transaction only play a minor role in explaining spatial variation in trade patterns. This insight later informs our choice to focus on a model that allows us to predict the structure of the production network along the extensive margins.

To assess whether the observed spatial concentration and urban bias are idiosyncratic features of VAT data or reflect patterns innate to formal activity, we also compute the spatial concentration for a range of other indicators for economic activity. These range from the least formal to increasingly formalized economic activities and are included in Table 2. We observe a clear pattern: activities that capture very little formal activity such as the number of micro-, small-, and medium-size enterprises (MSMEs) and employment in MSMEs exhibit relatively little spatial concentration ( _α_ = 0.86 and 0.78, respectively). As we focus on more and more formalized activity, e.g. licensed businesses from micro to medium sized, all the way to firms in the census of industrial production, the degree of concentration increases. This suggests that the spatial concentration observed in the VAT data represents a feature of the formal sector more broadly.

Unlike formal sector trade, we find that other observable types of domestic flows, like migration flows also do not exhibit a similar spatial concentration (see Table 2).<sup>16</sup> For instance, while Nairobi is the destination for 29% of all long-term inter-county migration, it accounts for 69% of total outlinks and 65% of total inlinks in the formal sector firm network.

A potential concern is that the observed spatial concentration in urban centres is mainly driven by firm headquarter locations being more likely to be based in Nairobi or Mombasa. While this concern is mitigated by the fact that we observe a similar spatial concentration in other measures of formal economic activity, we also use micro-data from the 2010 Census of Industrial Production to address the question about the role of multi-establishment firms more explicitly. In Appendix A.6, we compare the spatial concentration of sales and firm locations with and

> 16We compute long-term migration flows using data on birthplace and current residence from the 2019 population census.

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Table 2: Geographic concentration of economic activity by degree of formalisation

||**Nairobi**<br>**Mombasa**|**Rank r**|**egression**|
|---|---|---|---|
||in %|_α_|SE|
|Population overall|9<br>3|1.29|0.18|
|Population of cities & towns|31<br>9|0.85|0.01|
|Migration infows|29<br>6|0.59|0.04|
|Migration outfows|5<br>2|0.77|0.07|
|GDP|25<br>5|1.00|0.07|
|GDP w/o agriculture|33<br>7|0.97|0.05|
|GDP w/o non-market services|25<br>5|0.91|0.08|
|No. MSMEs|14<br>3|0.86|0.17|
|Employment in MSMEs|19<br>3|0.78|0.13|
|No. licensed MSMEs|18<br>3|0.73|0.09|
|Employment in licensed MSMEs|28<br>3|0.67|0.07|
|No. SMEs|37<br>3|0.58|0.06|
|Employment in SMEs|36<br>3|0.60|0.05|
|No. census establishments|36<br>4|1.10|0.12|
|No. frms census of industrial production|48<br>6|0.54|0.02|
|Sales census of industrial production|61<br>7|0.32|0.03|
|No. VAT frms|64<br>9|0.63|0.03|
|Employment in VAT frms|62<br>9|0.36|0.03|
|Value added of VAT frms|72<br>10|0.38|0.03|
|VAT network sales|68<br>13|0.35|0.02|
|VAT network outlinks|69<br>11|0.35|0.02|
|VAT network purchases|60<br>9|0.43|0.02|
|VAT network inlinks|65<br>10|0.48|0.02|

The columns for Nairobi and Mombasa report their share of the respective national aggregate figures (e.g., Nairobi’s contribution to Kenya’s GDP). The Pareto exponent _α_ is the estimated coefficient from a county-level regression of each county’s rank (log) on the respective measure _x_ (log): log rank = log _A − α_ log _x_ . All measures reported in the final section of the table are derived from the VAT data. All other measures are based on data sources summarised in Table 1.

without multi-establishments. We find that the excess spatial concentration introduced by multi-establishments does not explain the aggregate concentration patterns of formal private sector activity.

# **Formal firms predominately source from and sell to firms in urban hubs.**

Consistent with the previous section, a plot of county-by-county trade flows in Figure 3 highlights the primacy of Nairobi and Mombasa. The width of each segment on the left reflects the county’s total sales within the network, while segments on the right are proportional to total purchases. The color of the trade flows aligns with the county of origin.

Importantly, visualizing trade flows also reveals that Nairobi not only has more outlinks to other counties but also is the most important buyer of goods and services by firms from other counties. Given the high concentration of manufacturing firms and their upstream position in the network, 12
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randomly distributed, we expect that accounting for the informal sector will systematically alter the structure of the observed network. A first piece of suggestive evidence is that regions with higher levels of informality have fewer observed firm-to-firm links in the VAT data, even after controlling for population and travel time to metropolitan areas (Table A1).

# **Informal-sector shares correlate negatively with regional economic size and income.**

First, we explore the spatial distribution of informal firms, which we find predominantly reside in smaller markets. Figure A4 plots the distribution of formal sector shares across counties, measured using both value-added and employment metrics. The graph shows that in most counties, the formal sector accounts for less than 20% of economic activity.

We find a strong correlation between a county’s formal sector share and both its economic size (measured by Gross County Product) and income level (measured by Gross County Product per capita). As shown in Figure A5, economic size alone explains between 35% and 52% of the variation in formal sector shares across counties. This pattern is consistent across all three measures of economic activity: employment, value added and the number of firms.

To validate that this positive correlation between market size and formal sector share is not merely an artifact of the administrative data, Figure 5 presents correlations between Gross County Product and three additional employment-based formality measures that do not rely on the administrative data. Notably, while more stringent definitions of informality yield flatter slopes, the _R_<sup>2</sup> remains stable. This consistency suggests that economic size explains similar proportions of county-level informality variation regardless of the measurement approach.

# **The incidence of informality systematically varies across sectors.**

Beyond geographic patterns, informality also varies systematically across sectors. Figure 6 compares a sector’s value added (from administrative data) with its contribution to Kenya’s GDP (from national accounts). Manufacturing and business services show the closest alignment between these measures, which suggests that the bulk of economic activity in those two sectors takes place in the formal economy. This pattern is consistent with the fact that both sectors rely predominantly on inputs from other firms and tend to sell to other businesses (Figure A1).

In contrast, downstream sectors closer to final consumers exhibit larger disparities between value added and GDP contributions (Figure A8). This pattern aligns with weaker self-enforcement in consumer-facing sectors inherent to most VAT systems (Pomeranz, 2015; Naritomi, 2019). We observe similar patterns in both the extensive margin of informality (comparing firm counts across data sources, Figure A6) and the intensive margin (comparing formal and informal em15
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relationship between firm sales and firm-to-firm connections (Bernard et al., 2022; Bacilieri et al., 2023) as well as potential differences in how small firms organize their supply chains across space and sectors.<sup>21</sup> Table B1 shows that small firms within the same sector and county are less likely to directly source from manufacturing firms (upstream), but instead are more likely to source from retailers or wholesalers (downstream). Further, they are less likely to source from Nairobibased suppliers and more likely to source locally.

Third, the model incorporates a flexible network formation process such that the emergent degree distribution can follow a power law. The underlying dynamic network formation process gives rise to the substantial inequality in outdegrees across firms that has been widely documented in the literature (Bernard and Moxnes, 2018; Panigrahi, 2022; Bernard et al., 2022; Bacilieri et al., 2023). Figure B1 plots the outdegree and indegree distribution of the formal firms in our VAT data, revealing a very unequal degree distribution that resembles a power law. Our framework is flexible and allows us to estimate the share of firm-to-firm links formed via directed search (searching among the trade partners of existing suppliers) versus undirected search (often referred to as _random search_ in the networks literature (Jackson and Rogers, 2007)).

# **4.2 Model Setup**

Consider an economy with a set of firms denoted by _N_ . Each firm _i ∈ N_ is of a given type _θi ∈_ Θ where Θ is the set of all possible types. In our application, we specify firm types as unique sector-county-size combinations, i.e. all firms in the same sector, county, and size group are classified as the same type. Our aim is to predict a matrix _π_ that captures the number of links that exist between every possible pair of firm types.

The network formation process is as follows. In every period _t_ , a new buyer firm of type _θ_ enters with probability _p_ ( _θ_ ). Hence, the number of firms in the network in any given time period is equal to the number of time periods that have passed since _t_ = 0. In order for its operations to be viable, the new firm needs to source inputs from a fixed number of suppliers _m_ . To do this, it first chooses a sector-county-size pair (i.e. a type) with probability _p_ ( _θ, θ_<sup>_′_</sup> ) for all _θ_<sup>_′_</sup> in Θ. The probabilities _p_ ( _θ, θ_<sup>_′_</sup> ) represent the firm’s bias in terms of sectors, regions, and firm size types it wants to link with. In other words, the probability that a buyer of type _θ_ finds a supplier of type _θ_<sup>_′_</sup> may not necessarily be equal to the probability of _θ_<sup>_′_</sup> in the firm population. These biases can reflect production technologies or homophilous preferences arising out of search costs and information frictions. Firms in a location _θ_ might find it easier to link to firms in location _θ_<sup>_′_</sup> that is close to them as opposed to firms in location _θ_<sup>_′′_</sup> that is far. Likewise, firms in sectors that

> 21Economies of scale in trade cost at the firm level give rise to supply chain structures with several intermediaries (Grant and Startz, 2022). Hence, we expect the linking patterns of small firms to diverge from large firms. Relevant for our case, economies of scale can result in firms of different sizes, but operating within the same geography and sector exhibiting different sourcing patterns.

19
supply services like electricity or telecommunication, which almost every firm requires as inputs, might find themselves with linking probabilities _p_ ( _θ, θ_<sup>_′_</sup> ) that exceed their entry probability _p_ ( _θ_ ).

Having chosen the sector-region-size type it wants to link with, the firm now relies on two different search technologies to form its _m_ links: first, undirected search (a.k.a. random search). Here, the new firm ‘randomly’ links to other firms of the chosen type. It forms a fraction _r_ of its total _m_ links in this manner. Second, preferential attachment. The new firm forms the remaining fraction 1 _− r_ of its _m_ links to suppliers by searching among the existing suppliers it acquired via undirected search. In other words, once the buyer firm forms links to the first set of suppliers, it then ‘randomly’ links with the suppliers of its suppliers. The second step of this process is preferential in that suppliers that are more connected are more likely to be chosen. This process continues for several time periods and the network evolves accordingly.<sup>22</sup> Ultimately, we are interested in the number of links between each sector-county-size type and their outdegrees. To this end, consider a matrix _B_ where each row and column represents a type _θ ∈_ Θ. Its _θθ_<sup>_′_</sup> ’th entry is then equal to _p_ ( _θ_ )<sup>_<u>p</u>_</sup> _p_<sup><u>(</u></sup> (<sup>_θ_</sup> _θ_<sup>_<u>,θ′</u>_</sup> )<sup>_′_</sup><sup><u>)</u>.Bramoull ́eetal.(2012)relyon</sup><sup>**B**toderive</sup> the matrix _π_ whose _ij_ ’th entry shows the number of directed links at time _t_ between buyers of type _i_ and suppliers of type _j_ which are born in _t_ 0: Here, _t_ refers to the time period, **I** is the identity matrix, and _f_ is a scaled geometric series of the matrix **B** defined as follows: Newly entered buyers form _m_ inlinks in every period. As a result the outdegree of existing firms, i.e. the suppliers of the newly entered firms, evolves over time. Thus, the matrix _π_ **t**<sup>**t**</sup> **0**<sup>gives</sup> the expected outdegree (i.e. number of buyers) of each column node born in time _t_ 0 to a row, computed at time _t_ . The purpose of the dynamic network formation process is to rationalise the heterogeneity in outdegree. Our focus on predicting outdegrees while keeping indegrees fixed is further discussed in Appendix B.3. We motivate this assumption using stylized facts observed in the data. While this assumption helps us characterize the steady state of the model, we also discuss how relaxing it would likely reinforce our results.

> 22The model takes the distribution of firm types as given, abstracting from firms’ endogenous entry decisions across sectors, regions, and size categories (and subsequently, formality status). Instead, we capture these entry patterns through exogenous probabilities _p_ ( _θ_ ) for each firm type, which correspond to the observed spatial, sectoral, and size distributions in our data. While one could extend the model to microfound these entry choices — for instance, to explain the concentration of economic activity in Nairobi —we prioritise matching the observed proportions of different firm types rather than explaining their underlying determinants.

20
# **4.3 Estimation Strategy**

Given the granular data on the empirical formal sector firm-to-firm network, we are able to obtain the majority of the model parameters directly from the data (see Table 3 for an overview). These include all entry probabilities _p_ ( _θ_ ) _∀ θ ∈_ Θ that a firm enters in a given sector, county, and size group as well as all interaction probabilities _p_ ( _θ, θ_<sup>_′_</sup> ) between all possible sector-county-size types. We use the cross-section from 2019, the last pre-COVID year of our panel, to obtain the _p_ ( _θ_ )s and _p_ ( _θ, θ_<sup>_′_</sup> )s.<sup>23</sup> The parameter we need to estimate is _r_ , the fraction of input links a firm obtains via undirected search independent of the network environment.

Table 3: Model parameters

|**Parameters**|**Description**|**Source**|**Proxy**|**Value**|
|---|---|---|---|---|
|_r_|Share of suppliers via random search|Estimated|-|0.45|
|_p_(_θ_)|Entry probability of type _θ_|Data|Share of frms observed as _θ_|(0,0.12]|
|_p_(_θ, θ_<sup>_′_</sup>)|Linking probability of _θ_ and _θ_<sup>_′_</sup>|Data|Share of links between _θ_ and _θ_<sup>_′_</sup>|(0,1]|
|_m_|Indegree|Data|Avg. number of suppliers|30|
|_t_|Number of entry periods|Data|Number of frms in admin data|56822|

First, we classify firms into types defined by unique sector-location-size combinations. Sectors refer to 13 aggregate sectors, namely, agriculture, mining, manufacturing, utilities, construction, transportation and logistics, wholesale, hospitality, retail, business services, non-market services, other services, and miscellaneous (incl. international organisations and non-classified firms). Locations are given by the county in which the firm is located. Within each sector and county we further group firms into large and small firms. We define small firms as firms in the bottom sales quartile within a sector-county group. By restricting ourselves to two size bins only, we avoid having too few observations in each firm-type bin and the matrix of linking probabilities becoming too sparse. For example, all firms in the top three sales quartiles of Nairobi’s manufacturing sector are classified as the same type.

Next, we compute the probability that a type exists for all types in Θ. We do so by dividing the number of formal firms of a sector-county-size type by the total number of formal firms in the economy. The interaction probabilities _p_ ( _θ, θ_<sup>_′_</sup> ) then represent the fraction of a sector-county-size type _θ_ ’s supplier relationships that it forms with type _θ_<sup>_′_</sup> . We compute the above probabilities for all possible combinations of types and use them to construct the matrix **B** . Moreover, we follow Jackson and Rogers (2007) and define _m_ as the average indegree (i.e. average number of suppliers) in the network. The variable _t_ , by definition, is equal to the number of firms observed in the data equal to 56,822.

> 23We exclude a small proportion of firms with zero suppliers in the data, as the model requires all entrants to form _m_ buying links.

21
Using the parameters from the empirical data, we are able to predict the matrix of type-to-type network links _π_ ( _r_ ) for different choices of _r ∈_ [0 _,_ 1]. Appendix B.2 discusses the practical steps needed to construct the matrix during the estimation.

In addition to the predicted version of the matrix _π_ , we also observe the actual _π_ in the data where the _ij_ ’th entry of _π_ is just the number of links between types _i_ and _j_ . We match the model predicted matrix and the matrix in the data using the method of moments procedure to obtain _r_<sup>_∗_</sup> . Each moment is weighted by the probability with which we observe a specific sector-regionsize type in the data. In doing so, we assign greater weight to more common sector-region-size types whose probabilities tend to be more stable over time. _r_<sup>_∗_</sup> is defined as follows: _r_<sup>_∗_</sup> is obtained by minimising the distance between the model predicted matrix of type-by-type interactions and the corresponding matrix obtained from the data (method of moments). We estimate _r_ using simulated annealing. With only one parameter to estimate, we can plot the objective function for various values of _r_ to ensure that our estimated value is indeed the global minimum (see Figure B4).

# **4.4 Estimation Results**

Our estimation strategy yields a result of _r_<sup>_∗_</sup> = 0 _._ 45. It suggests that a newly entered firm chooses 45% of its _m_ suppliers at random, and the remaining 55% among the suppliers of its existing suppliers. A network with 55% of all links being formed via directed search suggests a prominent role for information frictions as firms rely on their suppliers to form new links. It aligns with previous research documenting the importance of relational contracts in Kenya and neighbouring economies (Fafchamps, 2003). In a variant of this model, Chaney (2014) estimates _r_ = 0 _._ 6 for French exporters forming links with trade partners abroad, which also suggests a substantial, but not quite as prominent role of information asymmetries.

# **4.5 Model Fit**

To assess how well our model does in fitting the targeted outdegree distribution (i.e. distribution of the number of buyers), we plot the degree distribution (i.e. total number of outlinks) of each sector-county-size type as observed in the data and as predicted by the model. Figure B5 shows that the key properties of the outdegree distribution are replicated by the model’s predictions. The model and data match particularly well in the right tail of the distribution i.e. the part that is specifically targeted by allowing for directed search in the network formation process.

22
We also estimate the Pareto exponent _α_ , which was not explicitly targeted by the model, for both degree distributions. We obtain an _α_ of 0 _._ 36 from the model and 0 _._ 37 from the data. In addition, since we have previously shown that the formal firm network is spatially concentrated, we also assess how well the model predicts the share of buyer relationships in the economy that originate from firms in Nairobi, Mombasa, to firms in other counties. We find that the model performs well on this dimension too (Table 5). In the administrative data, 69% (11%) of all outlinks in the economy are captured by Nairobi (Mombasa) based firms and the model predicts a share of 70% (11%).

# **5 Predicting a Revised Network**

With the estimated model at hand, we are now able to tackle the question of how including informal firms might affect the spatial patterns of domestic trade. Our proposed thought experiment is the following: suppose we were to observe informal firms. What would happen to the outdegree distribution of various types _θ_ ? To obtain a ‘revised network’ that accounts for informal firms, we rely on updated information on the spatial and sectoral dispersion of economic activity in Kenya – now including the informal sector. In model terms, our exercise shifts the probabilities _p_ ( _θ_ ) with which we observe nodes of certain sector-region-size types _θ_ to be born. Knowing _r_<sup>_∗_</sup> and our updated _p_ ( _θ_ )s, we can then once again predict the type-by-type matrix of firm-to-firm links _π_ , keeping everything else constant. We will also make additional assumptions about the linking probabilities of informal firms.

## **5.1 Predicting the Sector-County Profile of Non-VAT Firms**

To incorporate informal firms into the network, we first update the firm-type probabilities _p_ ( _θ_ ) for each sector-county-size cell, this time accounting for the entire firm size distribution. To update _p_ ( _θ_ ), we ideally would want to observe the number of firms _Ncs_ in each sector _s_ , county _c_ , and size cell – irrespective of their formality status. However, none of the KNBS records available to us feature a breakdown of the firm count along both the sector _s_ and the county _c_ dimension, let alone size dimension. Therefore, instead of the firm count, we rely on granular sector and region level information on formal and informal employment in the 2019 census labor force module to compute our alternative entry probabilities _p_ ( _θa_ ): 23
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.

24
with both each other and with the formal sector. An ideal data set would provide details on sourcing and selling patterns by sector, geography, and formality status. In the absence of such data and given the strong correlation of size and formality status, our default approach will be to assume that informal firms exhibit linking preferences _p_ ( _θ, θ_<sup>_′_</sup> ) similar to those of small formal firms, conditional on sector and geography.

This approach is particularly attractive given its straightforward implications for the sectoral and geographic composition of linking patterns. It further allows for informal and small formal firms to experience different wedges in link formation, provided these wedges generate aggregate linking patterns that are still comparable to those of small formal firms at the sector-countysize level. Consider, for instance, a small formal retailer and an informal retailer both seeking to purchase soap. While neither can source directly from manufacturers in Nairobi, the small formal retailer might purchase from a large formal wholesaler locally, whereas the informal retailer—potentially excluded due to their tax status—might source from an alternative local wholesaler. Despite sourcing from different individual suppliers, both retailers exhibit the same patterns once their sourcing is aggregated at the sectoral and geographic levels. The similarity assumption is also motivated by findings in the administrative data, where we document that small formal firms tend to source more locally and from intermediaries (see Table B1).

Nevertheless, this assumption may not fully capture the implications of challenges specific to informal firms for their linking patterns. Therefore, we subsequently introduce modifications to our approach, drawing on stylized facts from the existing literature, to assess the sensitivity of our results to alternative assumptions about the linking patterns of informal firms.

# **5.3 Characteristics of the Revised Network**

How does the revised network that accounts for informal firms compare to the baseline network? First, we find that firm types in sectors and counties with a high incidence of informality are predicted to have a relatively larger increase in outdegrees (Figure C2). Second, the share of total outlinks attributed to Nairobi- and Mombasa-based firms declines from 80% to 75% (see Table 5). While the two cities maintain their prominent role in the network, this shift is meaningful for the remaining counties in relative terms as it represents a 25% increase in their outdegrees. Third, accounting for informal firms reduces the variation in outdegrees across counties by 7.5% (Table 4). We visualize this reduction in inequality by plotting the Lorenz curve for county-level outlinks in Figure 8.

What drives the reduction of outdegree inequality? First, Nairobi and Mombasa become less important as a destination for products and services from other counties. In Figure 9 we plot the row-normalised adjacency matrices, before and after accounting for informal firms, at the county 25
<!-- Start of picture text --> 1-<br>8-<br>)<br>x<br>&<br>5<br>0 .6-<br>g<br>2<br>J<br>O4-<br>o—_<br>oO<br>B<br> 2- Z]<br>ot<br>— — _<br>o- — oe<br>IIIIII<br>02 4 8 1<br>_ 6<br>Share of counties<br>——- Baseline<br>Informal firms ~ small firms: --—— Default p(8) employ. share only<br>Alternative linking patterns: --— 50% input formal ====: 75% input formal<br>-===' 50% input & 25% sales formal<br><!-- End of picture text -->
informal firms, both inter- and intra-county outdegree increase for the median county as well as on average. However, for 83% of counties, the increase in intra-county outdegrees exceeds the increase in inter-county links.<sup>25</sup> If informal firms source an even higher share of their inputs locally, the predicted shift towards intra-county trade represents a lower bound. We will discuss this in Section 6.1.

Table 5: The importance of Kenya’s primary cities in a revised network

|**Nairobi**|**Momb**|**asa**<br>in %|**Other counties**|
|---|---|---|---|
|Population<br>9|3||88|
|GDP<br>25|5||70|
|GDP w/o agriculture<br>33|7||60|
|**Number of outlin**|**ks**|||
|_Model ft_||||
|Administrative data<br>69|11||20|
|Model predicted network<br>70|11||19|
|_Revised network: informal frms ≈small frms_||||
|Default scenario<br>65|10||25|
|_p_(_θ_) using employ. share only<br>66|10||23|
|_Revised network: alternative linking patterns for _|_informal _|_frms_||
|0% sales, 50% input to/from formal<br>59|9||32|
|0% sales, 75% input to/from formal<br>63|10||28|
|25% sales, 50% input to/from formal<br>59|9||32|

The above table documents the share of overall firm-to-firm links which have a supplier based in Nairobi, Mombasa or the remaining 45 counties. We present the spatial dispersion of outlinks in the data, the predicted (formal sector) network as well as our default scenario for the revised network and four alternative scenarios to assess sensitivity.

If counties are selling less to Nairobi and Mombasa, where do their inter-county trade links shift? We find that the number of bilateral trade links is now more sensitive to social ties between counties. In Table C2, we regress the number of links between two counties on both travel distance and social connectedness (Bailey et al., 2021), and compare the results for the baseline and the revised network.<sup>26</sup> The findings indicate that, in the revised network, inter-county trade links are more strongly associated with the strength of social ties between counties.

The increased importance of within-county trade and trade between socially connected counties gives rise to a network with a more pronounced group structure. We quantify the extent to which the network is partitioned by measuring the network’s modularity (Newman, 2006). The modularity of a network is higher when groups of nodes have more links among each other

> 25While inter-county trade rises for the median county, 18 out of 47 counties actually have fewer links with other counties in the revised network.

> 26Social connectedness is measured using friendship network data provided by a popular social media platform, see Bailey et al. (2021).

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than what we would expect in a random network. We compute the modularity of the weighted adjacency matrix at the sector-county level. We find that modularity in the revised network with informal firms increases by about 46% suggesting that the revised network exhibits a more pronounced group structure.<sup>27</sup> To further characterize this group structure, we apply a community detection algorithm to the trade flows between counties as per the revised network. As illustrated by Figure C3, the group structure now correlates strongly with Kenya’s geography, i.e., geographically proximate counties are now more likely to be clustered in the same group.

Next, we explore for which group of counties we underestimate the overall number of links the most. To do so, we regress the change in county-level outlinks between baseline and revised network on various county characteristics, including the aggregate level of formality, population, Gross County Product, and market access (Table C3). The results reveal that the baseline network, which relies exclusively on formal sector data, most significantly underestimates connectivity in smaller counties and those with high market access. Notably, after controlling for these other characteristics, the relationship between a county’s aggregate formality share and the change in outlinks is no longer statistically significant.

Finally, we find that incorporating informal firms also reshapes inter-sector trade patterns (Figure 9). Sectors with substantial informal activity like other services, retail, and wholesale, now gain prominence as buyers in the network. Manufacturing, wholesale, and mining experience the largest relative gains in new links.

# **5.4 Simulating the Effect of Economic Shocks**

As a next step, we ask how the newly predicted network that accounts for informal firms compares to the previous network in terms of its role in propagating domestic and international shocks. How does the predicted impact of the shock depend on whether we account for informality? Are sectors and regions with more informality more or less vulnerable to shocks than the administrative data would suggest? To answer these questions, we first simulate a series of domestic output shocks that reduce each firm type’s output and then analyse how it affects the output of all other types, both directly and indirectly, by propagating through the network over multiple time periods. Then, we simulate international supply shocks that affect firm types depending on their exposure to international markets. We discuss the results for both domestic and international shocks below.

> 27We compute this by running the Leiden algorithm multiple times and averaging the resulting modularity scores. See Traag et al. (2019) for details on the algorithm.

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<!-- Start of picture text --> 0.7<br>0.6<br>0.5<br>0.4<br>0.3<br>0.2<br>0.1<br><!-- End of picture text --> <!-- Start of picture text --> 0.7<br>0.6<br>0.5<br>0.4<br>0.3<br>0.2<br>0.1<br><!-- End of picture text --> <!-- Start of picture text --> Business services 04<br>Construction 0.35<br>Hospitality<br>0.3<br>Manufacturing<br>0.25<br>Mining<br>Other services. 0.2<br>Retail 0.15<br>Transport o4<br>Utilities 0.05<br>Wholesale<br><!-- End of picture text --> <!-- Start of picture text --> Business services<br>Construction 0.25<br>Hospitality<br>02<br>Manufacturing<br>Mining 0.15<br>Other services.<br>Retail 04<br>Transport<br>Utilities 0.05<br>Wholesale<br><!-- End of picture text -->
the normalized cells of our type-by-type matrix _π_ that captures the total number of links between all types. We normalise the rows of _π_ by dividing each entry in a row by the sum of that row. We abstract from any endogenous network adjustments (see e.g. Panigrahi, 2022; Eaton et al., 2022; Arkolakis et al., 2023). We assume that _υjt_ is an independent draw from a uniform distribution _U_ [ _−_ 10 _,_ 10] for every type _j_ in every time period _t_ . Each type starts with a randomly chosen output drawn from the distribution _U_ [0 _,_ 100] in _t_ = 0.

Using this set-up, we first simulate the output process without any shock. Then, we simulate the output process following a negative output shock to sector-region-size type _j_ ’s value added _υjt_ in the first time period.<sup>29</sup> We repeat this exercise for all types _j_ .

To study the relevance of unobserved informal firms, we conduct our simulation exercise twice. In the first scenario, we use the matrix _π_ derived from administrative records. In the second scenario, we use an alternative version of _π_ using our revised network that accounts for the presence of informal firms.<sup>30</sup> Our primary question is: how do domestic shocks impact each type when informal firms are considered versus when they are not? For each simulated shock, we compute: (i) the absolute reduction in output of each type using the original adjacency matrix (excluding informal firms) and (ii) the absolute reduction in output of each type using the new adjacency matrix (including informal firms), both averaged across all time periods. This yields a matrix of shock impacts where each row corresponds to a supplier who is shocked and each column corresponds to a buyer who faces the impact of the shock. We then aggregate across rows to compute the average impact of the shocks on buyers.

We find that the higher the incidence of informality in a sector and region, the more we underestimate the adverse impact of a domestic output shock. Figure 10 shows that our established employment-based measure of informality negatively correlates with the impact of the shock under the two scenarios. To align with our most granular measure of informality, we aggregate the response to shocks at the sector-region level.<sup>31</sup> As shown in Table C4, a one percentage point decrease in the formal sector share corresponds with a 4.9 percentage point larger output drop following a domestic shock.

Figure C5 presents the distribution of the ratio of the shock impact at the sector-county level (revised network/baseline network). This ratio exceeds one for 48% of the sector-county pairs and 42% of the sector-county-size types, indicating the baseline network on average underestimates the impact of domestic shocks for these types. Among the types for which we underestimate

> 29We compute the impact of the shock on each type’s output over 100 periods of time by comparing the two output processes. All of the outputs reported below are averages across the 100 time periods. 30 We ensure that the random component of output, _υjt_ , is identical across these two scenarios for each type _j_ in every time period _t_ to ensure it does not affect our results.

> 31Put differently, we average the impact across each buyer’s suppliers and then compute a weighted sum for each sector-region cell. The weights are determined by a type’s entry probabilities.

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<!-- Start of picture text --> e<br>© e °<br>Cc<br>=°<br>@3-<br>n<br>oO<br>a<br>2 e e °<br>= e<br>oO 2-<br>dq<br>°°<br>38e e<br>><br>® 4- Ge<br>=] e<br>£e<br>5e<br>fo}<br>qd<br>o-<br>i] i i 1 i<br>0 2 A 6 8<br>Formal sector share of total private sector employment (buyer)<br>@ Buyer sector-county bins<br><!-- End of picture text -->
analyse how it affects total output in the economy and the heterogeneous effects on various firm types.

The bottom graph of Figure C5 plots the impact of the shock relying on the revised network as a proportion of the impact based on the baseline network. Unlike domestic shocks, our findings for import shocks indicate that extrapolating from data on the formal sector network to the overall economy leads to an overestimation of the reduction in output. The impact is consistently less negative when using the revised network.

This effect is particularly pronounced in sectors and regions with a higher incidence of informal activity (see Figure 11). Specifically, Table C4 shows that a 10 percentage point increase in the informal sector share corresponds to a 1 percentage point overestimation of the reduction in output. This pattern emerges because formal firms in predominantly informal markets have more unobserved connections than captured in administrative data, reducing their effective exposure to import shocks.

Why do the predictions differ for domestic and import shocks? When accounting for informality, sectors and counties with a high share of informal activity become more prominent in the network, making them more susceptible to economic shocks. Conversely, this adjustment reduces the relative importance of formal-dominated sectors, which typically have higher import shares and international exposure. By adjusting their prominence (i.e., modifying their entry probabilities and considering informality), we find that the economy seems more resilient to trade shocks but more vulnerable to domestic shocks. The intuition behind our result aligns with the mechanism discussed in Di Giovanni and Levchenko (2012), who show that smaller economies tend to experience more volatility due to having fewer firms and less diversification. Applied to our setting, focusing only on formal sector firms leads to overstating the importance of internationally-linked formal firms and underestimating the diversification of the regional economy.

# **6 How Sensitive are Results to Alternative Linking Patterns?**

What happens if we relax the assumption that informal firms have similar linking patterns to small formal firms? Given our lack of disaggregated data on how informal firms link with the formal sector, we stress-test our results relying on alternative assumptions motivated by evidence provided in the literature and consistent with the stylized facts presented in Section 3. First, informal firms almost exclusively sell to final consumers. Second, informal firms purchase from formal firms, but not as much as formal firms purchase from each other (B ̈ohme and Thiele, 2014; Gadenne et al., 2022). Finally, informal firms predominately source locally (Amodio et al., 2024). These assumptions allow us to construct extreme bounds for linking patterns that we 32
<!-- Start of picture text --> .35-<br>x<fo} A<br>5 A<br>eaa<br>2 A 4-7<br>= mn ——<br>% 3- A A A<br>ao A az _— —=—<br>~ —_— A<br>S —_—— A<br>c=]a —_— —_— A<br>i] —_——<br>° — A A<br>dq<br>3 A<br>BO” x<br>><br>2<br>=]<br>£<br>3 A<br>qd<br>27<br>1 1 i i} i<br>) 2 A 6 8<br>Formal sector share of total private sector employment (buyer)<br>4 Buyer sector-county bins<br><!-- End of picture text -->
claim input VAT (Pomeranz, 2015). In summary, for all formal and informal types we make the following extreme assumptions regarding the sales patterns of informal firms: We now turn to informal firms and their sourcing patterns. In this case, we assume that informal firms source only 50% of their inputs from formal firms (large or small) in one scenario and 75% in an additional sensitivity check. Conditional on sourcing from the formal sector, the sectoral and geographic preferences of informal firms will again follow those of small formal firms. As documented in our empirical section, MSMEs do source some of their inputs from large firms. B ̈ohme and Thiele (2014) find that informal firms buy about half as much from formal firms than the amount formal firms source from each other. Gadenne et al. (2022) find that the smallest group of firms under the simplified tax scheme in West Bengal source a similar share from VAT firms, while the largest non-VAT firms source as much as three-quarters of their inputs from VAT firms. We rely on these point estimates to make the following assumption: Informal firms will then source the remainder of their inputs from other informal firms. This requires assumptions about their preferences on which sectors and counties to source from. Motivated by evidence from the literature where Amodio et al. (2024) find that the vast majority of small, largely informal firms in Ethiopia obtain their inputs from local sources, we allow inputs obtained from other informal firms to only be sourced locally.

Consider any counties _a_ and _b_ in the set of counties _C_ and let _θf,a_ be the type of small or large firm _f_ in _Fs ∪ Fl_ in county _a_ . The assumption implies the following: Finally, we now compute separate _p_ ( _θ_ )s for informal and small formal firms, splitting the main term of Equation 4. For additional details see Section C.2.

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## **6.2 Implications for the Revised Network**

Figure 8 and Table C1 summarize how alternative assumptions about informal firms affect the distribution of outlinks across counties. If we assume informal firms source half of their inputs from the formal sector but have no formal buyers, inequality in county-level outlinks declines by 16% compared to our model-predicted network. This represents an 8.5 percentage point larger reduction than our default scenario where small formal and informal firms share similar linking patterns. The share of total outlinks accounted for by Nairobi- and Mombasa-based firms now drops down to 69%, down from 80% in the baseline network and 75% in the first scenario with informal firms (see Table 5).

Allowing informal firms to sell 25% of their output to formal firms, instead of none, has little implication for both the overall decline in inequality and Nairobi’s share of outlinks. Allowing for a larger share of informal firms’ inputs to be sourced from the formal sector results in a smaller reduction in inequality (11%) and a higher share of Nairobi- and Mombasa-based links (73%), more closely matching the initial network with informal firms. This pattern is driven by the greater reliance of informal firms on formal suppliers in this scenario, which in turn tend to locate in counties with larger formal economies.

Our simulations of domestic and international trade shocks under these alternative assumptions reinforce our earlier findings, showing even stronger relative effects in sectors and counties with high informality (Figure C6). This more pronounced impact stems from increased intra-county linkages among informal firms. While more prominent local linkages reduce spatial inequality and urban concentration, they amplify the impact of domestic shocks through stronger withincounty multiplier effects.

# **7 Conclusion**

Firm-to-firm transaction-level data sourced from tax records have become a valuable tool for mapping domestic firm networks and trade flows. Aside from studying the micro dynamics of firm-to-firm relationships, they allow researchers to compute often hard-to-observe flows of goods and services across regions within national economies, which can be leveraged to estimate the welfare implications of policy interventions. This paper shows that applying such data in settings with high informality can pose important challenges. We find evidence that formal sector trade patterns provide a skewed representation of overall economic activity: they are more spatially concentrated and underestimate intra-regional trade in favor of trade with urban hubs.

We incorporate informal firms into a structural model of network formation leading to a revised 35
network that is more locally connected and spatially less concentrated. We further provide evidence for the implications of extrapolating from formal sector data about the aggregate impact of economic shocks, i.e. ignoring the presence of the informal sector. Simulations of the pass-through of output shocks using the revised network reveal that formal sector data leads us to underestimate the impact of domestic output shocks in regions and sectors with high informality. Conversely, we may overstate the local output effects of international trade shocks in sectors and regions with a high incidence of informality. This is because formal sector data places more weight on formal firms with stronger links to international markets, when in fact the overall economy has weaker ties to import markets.

Our findings are applicable to a variety of contexts with high informality across the world. Informality matters given its systematic occurrence as it is not randomly distributed across sectors and geographies. Our proposed approach for incorporating informal firms is useful for settings where data on the links of informal firms are not available with sufficient information on heterogeneity across key dimensions (e.g. sector and geography) and researchers therefore have to rely on secondary sources to recover the structure of the broader network. Our findings highlight the value of complementing administrative firm-to-firm data with auxiliary data on informality to draw inferences about the aggregate implications of economic policies.

An important question for future research, beyond the scope of this paper, is whether the observed spatial concentration of formal sector firm networks is a result of market frictions or a feature of structural transformation (Gollin, 2008). Understanding its drivers can inform policy recommendations about the optimal distribution of formal economic activity across space.

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