metadata: authors: 0: author: Aga,Gemechu A.
1: author: Francis,David C.
2: author: Jolevski,Filip
3: author: Rodriguez Meza,Jorge Luis
4: author: Wimpey,Joshua Seth
count: World
docna: 0: docna: Surveying Informal Businesses : Methodology
            and Applications
docty: Policy Research Working Paper
subtopic: Labor Markets,De Facto Governments,Economics and Finance of Public
            Institution Development,Public Sector Administrative & Civil
            Service Reform,State Owned Enterprise Reform,Public Sector Administrative and Civil
            Service Reform,Democratic Government,Green Issues,Climate Change and Agriculture
teratopic: Social Protections and Labor,Public Sector Development,Governance,Environment,Agriculture
abstracts: cdata!: Informal business activity is ubiquitous
            around the world, but it is nearly always uncaptured by
            administrative data, registries, or commercial sources. For
            this reason, there are rarely adequate sampling frames
            available for survey implementers wishing to measure the
            activity and characteristics of the sector. This paper
            presents a methodology to generate a representative sample
            of informal businesses using an adaptive, geographically
            based method called Adaptive Cluster Sampling. Developed for
            populations that are clustered and/or rare, this method
            helps with efficiently sampling Primary Sampling
            Units&#x2014;blocks&#x2014;that are fully
            enumerated, and from which Secondary Sampling
            Units&#x2014;businesses&#x2014;can be randomly
            sampled to conduct interviews. The paper shows how this
            methodology can be applied to surveying informal businesses,
            often reducing both the average variance of population
            estimates and fieldwork effort. Practical considerations and
            guidance for implementation and analysis are also provided.
repnme: repnme: Surveying Informal Businesses : Methodology
            and Applications
display_title: Surveying Informal Businesses :
            Methodology and Applications
listing_relative_url: /research/2022/01/33708379/surveying-informal-businesses-methodology-applications
topicv3: Aquaculture m1325968 1050,State Owned Enterprises m1326323 721,Green Growth m1326430 476,Environment, Natural Resources and Blue
            Economy m1327391 566
publishtoextweb_dt: 2022-01-19T00:00:00Z
dois: 10.1596/1813-9450-9905
historic_topic: Social Protections and Labor,Public Sector Development,Governance,Environment,Agriculture
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 41
author_keys: 0: author_key: 1131266
1: author_key: 1099768
2: author_key: 1429199
3: author_key: 144470
4: author_key: 784583
model_extractions: Policy Research Working Paper 9905

# Surveying Informal Businesses Methodology and Applications

_Gemechu Aga David Francis Filip Jolevski Jorge Rodriguez Meza Joshua Seth Wimpey_ Development Economics Global Indicators Group January 2022
Policy Research Working Paper 9905

# **Abstract**

Informal business activity is ubiquitous around the world, but it is nearly always uncaptured by administrative data, registries, or commercial sources. For this reason, there are rarely adequate sampling frames available for survey implementers wishing to measure the activity and characteristics of the sector. This paper presents a methodology to generate a representative sample of informal businesses using an adaptive, geographically based method called Adaptive Cluster Sampling. Developed for populations that are clustered and/or rare, this method helps with efficiently sampling Primary Sampling Units—blocks—that are fully enumerated, and from which Secondary Sampling Units—businesses—can be randomly sampled to conduct interviews. The paper shows how this methodology can be applied to surveying informal businesses, often reducing both the average variance of population estimates and fieldwork effort. Practical considerations and guidance for implementation and analysis are also provided.

This paper is a product of the Global Indicators Group, Development Economics. It is part of a larger effort by the World Bank 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 dfrancis@worldbank.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
# Surveying Informal Businesses: Methodology and Applications<sup>1</sup>

Gemechu Aga, David Francis, Filip Jolevski, Jorge Rodriguez Meza, Joshua Seth Wimpey<sup>2</sup>

**JEL Codes:** C83, O17, L22, R12 **Keywords:** Adaptive Cluster Sampling, Informality, Informal Businesses, Surveys

> 1 The authors would like to thank Norman Loayza for the guidance and constructive comments, and the participants of the seminar held by the World Bank Development Economic Indicator Group, and the participants at the Sixth International Conference on Establishment Statistics (ICES-VI). All remaining errors are those of the authors. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.

> 2 The authors are with the Enterprise Analysis Unit, World Bank, Washington DC., emails: <u>gayanaaga@worldbank.org; dfrancis@worldbank.org (corresponding author); fjolevski@worldbank.org; jrodriguezmeza@worldbank.org; and jwimpey@worldbank.org.</u>
# **1. Introduction**

In much of the world, a great deal of economic activity is informal (Schneider and Hassan, 2016; Loayza, 2016; Elgin et al., 2021). Estimates show that in the typical developing economy about 70 percent of employment is in the informal sector, though this share of labor only makes up about 30 percent of production (Loayza, 2018). This has led economists and policy makers to have broader concerns that such labor is mis-allocated by being informal, dampening overall productivity (Meghir et al., 2015; Ulyssea, 2018). While recent macro estimates point to a decline of the informal sector as a share of GDP, this downward movement is minor, and informality by and large remains persistently high, particularly in developing economies (Ohnsorge and Shu, 2021).

Informality as a whole has received a lot of attention, but recently a rising emphasis has been placed on one portion of the sector: businesses that operate informally. These businesses are the most analogous to their formal counterparts, yet they also are indicative of important distortions in those economies. Businesses that could formalize and be competitive are excluded from an economy’s tax base and may lack opportunities to scale the size of their business; those informal businesses that could not survive after formalizing may employ labor that could be allocated more efficiently elsewhere, and in ways that provide more support (through regular work, income, and benefits) to those workers (Ulyssea, 2018). However, data on most such informal businesses is lacking. The limited data that is available has been used to examine the constraints to business formalization (De Mel et al., 2013; Campos et al., 2015; Benhassine et al., 2018), the characteristics of the informal businesses (Amin and Islam, 2015; Islam, 2019), and the interlinkages of the informal and formal sectors (Benjamin and Mbaye, 2012; Jolevski and Aga, 2019; Amin and Okun, 2020; Amin, 2021).<sup>3</sup> The size and persistence of the informal sector, and the wealth of research studying informal business activity reflects the need for high-quality, representative firm-level data collected in an efficient manner.

Businesses operating informally are frequently small and less productive, but widely abundant (see La Porta and Shleifer, 2014), implying that the typical (modal) business often does not appear in official registrar records, tax rolls, or most often, both. This very nature of informality

> 3 Several of these analyses rely on data reported by formal firms on informal firms’ activity.

2
implies that estimates of the population of informal businesses and their activity will be missing or incomplete; and sampling frames for developing high-quality, representative survey data will be unavailable. In turn, descriptions of the characteristics of many economies will be lacking information on a sector that is a ubiquitous source of jobs and business activity.

This paper lays out a methodology for conducting an enumeration exercise that generates a representative sample of informal businesses for a subsequent survey; it does so by utilizing an established geographic sampling method, Adaptive Cluster Sampling (ACS). ACS assumes that informal business activity is relatively clustered in certain areas and, in turn, it takes advantage of the information from the discovery of some informal businesses to alter the probability of selection of primary sampling units (PSUs) to capture concentrations of additional informal businesses more efficiently. ACS accounts for this altered probability of PSU selection and is able to provide estimates of the population totals of informal businesses, allowing any subsequent survey of those businesses to be considered representative. In the process, ACS frequently allows for reductions in fieldwork effort without an increase (and often a decrease) in the variance of these population estimates, if they were done repeatedly—a point which is later illustrated in this paper through simulation. The methodology is designed to be implemented in diverse situations, across different countries, while maintaining comparability.

Informal businesses may operate completely outside all or some legal channels (without a tax or business registration or license), or they may include businesses that operate informally by non-compliant behavior, such as employing workers ‘off-the-books’ (Ulyssea, 2018). Operationalizing data collection first requires a clear and functional definition of the underlying population of interest. A useful and basic typology of informality is the following: informality includes partial or full non-compliance with registration and licensing (legal informality), on employment (labor informality), or tax non- or under-payment (fiscal informality) (World Bank, 2020). This paper focuses on businesses’ activities that are _legally_ informal: that is, lacking one or all of the registration or licensing requirements to operate. This definition must be anchored to the local context of implementation but generally consists of those businesses that lack a business license, do not exist on a business registry, and/or are not registered with the relevant tax authority.

In addition to the operational aspect of this definition, there are important policy implications for surveying unregistered businesses. First, such businesses are prevalent and may 3
draw resources from and compete with the formalized business sector (this has been categorized as the ‘parasitic view’)<sup>4</sup> ; by contrast, a competing view is that widespread informality represents a ‘segmentation’ between a formal labor market, the business environment they experience, and their informal analogs (Perry et al 2007; Maloney 2007; Kanbur, 2017; Ulyssea, 2020). Understanding the estimates and nature of informal sector businesses informs policy, particularly considering the absence of consistently effective policies to address informality, e.g., the limited success of formalization efforts (see Bruhn and McKenzie, 2014; Floridi et al 2020).

Existing methodologies, such as household-based sampling, are not designed to measure informal sector businesses directly. Such methods often do not capture informal sector businesses at their point of business or operation; when they do, businesses are reached via the places of employment of household members and, consequently, they are unable to estimate business density in a geographical area. Likewise, informal sector businesses are, in all but a few cases, excluded from economic censuses, which tend to be infrequent and expensive. Informal sector businesses, virtually by definition, are also not reached by official surveys proceeding from administrative sampling frames. By contrast, the proposed ACS method reaches units at their point of operation and is designed to measure informal sector businesses _per se_ ; this paper builds upon existing ACS literature and shows that this method not only provides a precise, unbiased population estimate but can also provide practitioners with large fieldwork efficiency gains when compared to other methods.

However, the ACS method does bring trade-offs and challenges. As noted above, to operationalize such a survey, a clearly delimited population of inference is needed. In this case, this consists of un-registered business activity, within a delineated geographic area (e.g., a set urban area). This implies that informality in non-covered locations, rural or excluded cities, will not fall within the purview of these surveys. The approach also implies that portions of labor and fiscal informality do not fall within the coverage of the survey, an argument to include potentially sensitive topics on the informal activities of formally registered firms in traditional firm-level surveys.<sup>5</sup> Practitioners should note that such a methodology, unlike household- or labor-surveylinked methods, is not designed to measure household activity; as such, additional care must be

> 4 See La Porta and Shleifer (2014) for a discussion.

> 5 The authors, for example, are also experimenting on different ways to ask for these sensitive topics in the Enterprise Surveys of the World Bank.

4
taken to avoid undercounting household-based informal sector businesses. Attention must also be paid to fluctuations of informal sector movement over different areas or times of the day or week.<sup>6</sup>

# **2. Collecting Data on Informal Businesses: Existing Methods and Trade-offs**

Two main data collection methods are typically used for surveying informal businesses: i) household surveys, the prototypical examples being labor force surveys (LFS) or living standards surveys<sup>7</sup> ; and ii) establishment surveys or censuses (ILO, 2013). For surveys it is useful to consider each method as a multi-stage sampling procedure, where with some probability of selection, units are selected in a first stage, with the selected units denoted as PSUs, followed by secondary sampling units (SSUs), and so on.<sup>8</sup> Define all individual PSUs , where is the universe of PSUs. Likewise, SSUs are defined . Sampling units at each stage are well-defined, so and ii∈NN NN may exclude certain elements.<sup>9</sup> Each allows for the possibility of stratification. jj∈UU NN The household survey approach is implemented through standard household surveys, such UU The household survey approach is implemented through standard household surveys, such as Labor Force Surveys, and can capture informal (i.e., “off-the-books”) employment as well as employment in the informal sector (i.e., employment in legally informal activities). PSUs are enumeration areas defined to capture households. As a result, often excludes explicitly nonresidential areas, such as markets, industrial centers, or commercial zones. Call this set of PSUs NN L .<sup>10</sup> By design, these surveys are representative of L —that is the geographical areas delimited to capture households. Measures of informal businesses only require a few additional LL LL NN NN questions in these surveys, exploiting economies of scale in a cost-effective way.

However, such approaches are not necessarily well suited for representative estimates of informal businesses. The number of businesses and counts of individuals are not always mapped one-to-one; an informal business can be jointly operated across individuals, and one individual may operate several businesses. More fundamentally, L rarely accounts for the concentration LL NN

> 6 Mobility and timing issues are not unique to ACS but plague any attempt to sample informal businesses.

> 7 The most widely known of these is the World Bank’s Living Standards Measurement Survey (LSMS), which is run globally, in partnership with National Statistics Offices. 8 Note that this embeds a single-stage sampling approach, where only PSUs are selected.

> 9 An example of this is where excludes certain inaccessible areas (like a government or military installations). 10 Note the use of subscripts ‘LFS’ and ‘ES’ to denote, by shorthand, the Labor Force Survey and Establishment Survey methods. This notation is dropped from later discussions of the proposed method (Adaptive Cluster Sampling) NN for simplicity.

5
of informal businesses in certain areas. It is not designed to capture these informal businesses in their place of operation. As such, policy-relevant information such as the characteristics of these businesses, information on sales, expenditures, investment, competition, and the interaction with the business environment is de-linked from where these activities take place (with exceptions in household-based businesses). So-called 1-2 methods, where a second module following the household module is administered to an informal business/activity, implement a business-level survey module at the place of business, avoiding this last problem. However, such surveys are still limited to the representativeness of L .<sup>11</sup> A second approach is the establishment survey or census, which may include informal LL NN businesses. In the case of an establishment (or economic) census, all units are selected with certainty, removing a multi-stage framework. By contrast, an establishment survey requires a suitable sampling frame, where each unit in that frame exists within the universe of applicable businesses; call this . In certain cases, they may come from an economic census, but they are infrequent and tend to exclude legally informal businesses.EELL<sup>12</sup> Accurate projections of informal UU business activity also require credible estimates of i i i missing from censuses and administrative counts. In the absence of such adequate frames, EELL,i<sup>, which, virtually by definition, are</sup> UU implementers usually construct a frame through a two-stage process, where an area (PSU, ) is first enumerated to generate a frame, and then a selection of informal businesses are selected in EELL ii∈NN a second stage.<sup>13</sup> However, constructing such a frame is often intensely costly in terms of time and effort, particularly if implementers lack _a priori_ information on the location of informal businesses.

This paper proposes a specific solution to address the implied time, effort, and cost developing such geographically based estimates and sampling frames: namely, we propose that survey implementers use a sampling method designed to adapt and more intensively sample areas where informal businesses are discovered. To do this, we use a sampling method known as Adaptive Cluster Sampling (ACS) (see Thompson, 1990).<sup>14</sup> ACS is a method of essentially guided sampling, where the discovery of informal businesses ( ) in a PSU ( ) triggers more 11 Note that in these cases informal businesses are a tertiary sampling unit (TSU), where even if those businesses are jj ∈ UU ii ∈NN

> 11 Note that in these cases informal businesses are a tertiary sampling unit (TSU), where even if those businesses are selected with certainty, unit non-response will result in three-stage weighting.

> 12 India’s Economic Census and Rwanda’s Establishment Census are two notable exceptions that include informal businesses.

> 13 An example of this approach is the survey of informal businesses in townships in South Africa conducted by Sustainable Livelihood Foundation (http://livelihoods.org.za/).

> 14 The use of ACS to measure informal business activity has been piloted by the World Bank’s Enterprise Analysis Unit (DECEA) for several years, following an initial pilot of the method in Harare, Zimbabwe (2016/17).

6
intensive sampling in adjacent PSUs (Salehi and Seber, 1997). PSUs are selected randomly first, with or without stratification, and—based on a trigger threshold—adjacent PSUs are then enumerated. As such, the process is no less naïve in the initial selection of PSUs than other sampling approaches, but ACS exploits the information revealed in the process to efficiently target the population of interest when that population is clustered and/or rare (Thompson and Seber, 1996). The sampling process to survey informal businesses follows a two-stage method. In the first stage, ACS provides a probabilistic sample of PSUs which are fully enumerated to list all informal businesses. In the second stage, businesses are randomly selected from the list for an indepth interview, discussed more in detail in Section 5.

# **3. Technical Foundations of Adaptive Cluster Sampling**<sup>15</sup>

ACS begins with the definition of PSUs, . For the sake of generalization, let be a well-defined geographic area, divided into a grid of equal-sized squares. For this reason, PSUs will ii∈NN NN also be described in this application of ACS as block areas, (henceforth BAs).<sup>16</sup> The first step draws an initial sample of BAs of size ; all informal businesses are fully enumerated in these BAs. Implementers set some condition , which is an expansion threshold: if a BA contains nn sufficient units of the target population ( ), additional BAs adjacent to all squares where CC the count of units that meets or exceeds that threshold are sampled. Implementers can set specific ii∈ii ∑jj ≥CC rules for this expansion, with the most straightforward being all eight adjacent neighbors. If these newly sampled BAs meet condition , they trigger additional sampling of adjacent squares, and so on. CC Define a **_neighborhood_** as a collection of BAs that includes both an initially selected BA, and in the case that it satisfies , an expansion into additional, adjacent BAs. In this case, we use the pre-set rule of expanding into all eight, adjacent BAs; additional neighborhood expansions are CC shown in Appendix Figure A.1. A **_cluster_** is the collection of all connected neighborhoods that are enumerated because of the initial selection of BA . Figure 1 below shows clusters highlighted in ii

> 15 Note that the emphasis in this section is in the first stage of sampling informal businesses where BAs are selected using ACS and then fully enumerated. The second stage is just a simple random selection from the resulting enumeration list, which can be implemented via any number of random selection algorithms.

> 16 This term is also to differentiate from city blocks or public squares, with a ready comparison of ‘enumeration area.’

7
|Example 1:<br>|Cl<br>|uste<br>|r for C=1<br>|Example 2: Cl<br><br>|us<br>|ter<br>forC=1<br>|
|---|---|---|---|---|---|---|
|folofo<br>|loj<br>|of<br>|ojolol<br>|olo|<br>folololol<br><br>|olo<br>|jololjoloa|<br>|
|jo{olo<br>|lo<br>|lo<br>|ololo<br>|lojo<br>}o/ololo<br><br>|fo<br>|olololalo<br>|
|}oojol<br>|ol<br>|fo<br>|jololo<br>|]:z|<br>folololo<br><br>|lo<br>|olojolofa<br>|
|<br>folofol<br>|o|<br>|iz<br>|}ojolol<br>|olo|<br>folololo|<br><br>|al<br>|ojo/jolola|<br>|
|fololol<br>|{i<br><br>||3<br><br>|]3|olol<br><br>|olo|<br>fololol{i<br><br><br>||3<br>|{3|o/ololo|<br>|
|}1|o[<br>|o[<br><br>|3<br>sol<br>|<sup>3{ajolo</sup><br>|<sup>l|o|</sup><br>}2{<br><br> <br>|o<br><br>|}o[3<br><br>|
|||20}|3/0[/|lofo<br>}o|o[1|3{|20]|{o/o]olo|
|folo[2z<br>|<br>{1|<br>|3]<br>|<br>{1jolol<br>|<br><br>ol]o|<br>folo{iz{1}<br><br>|<br><br>32{<br>|<br> <br>i]ofolol|o|<br>|
|fololo<br>|lo<br>|la<br>|olojo<br>|jojo<br>folofojo<br><br>|af<br>|ololojoljo<br>|
|fololo|lo|ol|ojolol|ola|<br>folololo|lol|ojololola||

|Exa<br>|mple 3: Cl<br>|uster for C=1<br>|
|---|---|---|
|fo<br>|lololo<br>|jolojolololo|<br>|
|fo<br>|lololo<br>|jolojolololo|<br>|
|fo<br>||o[oloj<br>|ojo|ololo|:z|<br>|
|}o<br>||ololj<br>|lajojojojojo<br>|
||o<br> <br>|o[o{a<br> <br>|3]3|o/o]ol|o|<br> <br>|
||1 <br> <br>|<br>|o{o|3 <br> <br>|50}3/a/o]o/o<br> <br>|
|<br> <br><br>|<br> <br>|<br> <br>|
|<br><br>|<br><br>|<br><br>|
|<br> <br><br>|<br><br>folo<br>|<br><br>i}o}<br>|
|<br><br>fo|<br>lololo|<br>}ajo}olololo||

|Example 4: Cl<br>|us<br>|ter<br>forC=3<br>|
|---|---|---|
|folololol<br>|ol<br>|ojololjola|<br>|
|folololol<br>|olo<br>|joljoljofo|<br>|
|folololol<br>|ol<br>|ojofojo|z|<br>|
|folololo<br>|la<br>|jojolojolo<br>|
|fo|o|o{i<br><br>|3]<br><br>|3]o]ololo|<br><br>|
||1|<br><br>|0<br><br>|[o|3<br> <br>|
|<br>||<br> <br>|
|<br><br>||<br> <br><br>|
|<br><br>|lolo}<br>|<br><br>af<br>|<br><br>o|ofoljo<br>|
|<br>folololo|ol|ojolololo||

|Example 5:<br>|Cl<br>|uste<br>|r for C=5<br>|
|---|---|---|---|
|jololo<br>|lo<br>|lo<br>|olofolojo<br>|
|folofo<br>|lo<br>|ol<br>|ololololo|<br>|
|jo{olo<br>|lo<br>|lo<br>|olofojo}i<br>|
|folofo<br>|lo<br>||ij<br>|ojolololo|<br>|
|folo[o<br><br><br>|[a<br><br><br>|}3]<br><br><br>|3}o/olola|<br><br>|
||io<br><br>|[3<br>|o<br>{so}<br>||
||o[<br>|<br>/<br>|3<br>|\@op3||lolol|o|<br>|
|<br>jo{oli<br>|la<br>|l3<br>|<br>ajofolojo<br>|
|folofol<br>|o|<br>|iz<br>|fojolololo|<br>|
|fololo|o|lo|folojololo|

Example 6: Cluster for C=15

|jolololjolo<br>|fololojolo<br>|
|---|---|
|fololololol<br>|ojoljolojo|<br>|
|folojojolo|fololojoji|
|fololololal<br>|ojofololjo|<br>|
|folololi|3{|3]ololola||
|**f**1{**o**}o[**3**|sol<br>o||2{\ao<br>|3|1/ol]**o**|o|<br>}3|ofol|o|<br>|
|<br>folojiji{3<br>|<br>}ilolojolo<br>|
|fololololalo<br>|lolololjoa|<br>|
|fololololo|lololojolo|
Within a cluster there is a subcollection of BAs, termed a **_network_** , with the property that selection of any square within the network would lead to inclusion in the sample of every other square in the network. By definition, then, a network consists of adjacent BAs that each meet the condition . The examples in Figure 2 below highlight the networks in orange with the equal-sized or broader cluster highlighted in green. Note that in examples 1 and 6, the cluster and network are CC identical. An **_edge unit_** is one not satisfying , but in an enumerated neighborhood with at least one BA meeting . Green squares in Figure 1.b are all edge units. Note that in the case of example CC 1, where no expansion is triggered, the initial BA is a network size=1 with no edge units. CC 9
<!-- Start of picture text --> Example 1: Networkfor C=1 Example 2: Networkfor C=1<br>folololololololololoa| folololololololololo|<br>fololololololololola| fololololololo|olalal<br>fo fej ololololololo|:z| fololololololo|ola}a<br>folololo|z{ololololo| fololololilolo|olelol<br>folololi}s{s{olololo| folololi|s{s{olololo|<br>[1 |o}o[s|sof3]ilololo| fi {o}o|3|sol3|{1|olol]o|<br>folo}i{3|1o{ s{o]ololo| folo|i{3io] s{o|olol]o|<br>fololiz{a}s{ilolololoa| fofolzli|s]{ilolololo|<br>folofolo|z{ololololo| fololololalololololo|<br>folojolojolofololola| folojolojolfolololol|o|<br>Example3: Netwofo r C=1k Example4: Netwofo r C=3k<br>fololololololololola| folololololololololo|<br>folololololfololololoa| folololololololololo|<br>folololo}alolololol:z| fololololololololo|:z|<br>|o|o |o|o | o}o]olo/o| folo|olo}a}o}o]ololo|<br>Lo] o [al polo} olo folojala} folololol<br>[1 |o|o| polo |o| [1 [0 |o| fijololo|<br>|o|o|o |||| [oo] olGols Glo]folololooO} ol|o/o| 0} oo |o|folo|a|afolol|ololalololo | a |Site]NGO oO] o|0 ololo| | o|<br>folololo}olalolololoa| folojololofolololojo|<br>Example 5: Networkfor C=5 Example 6: Networkfor C=15<br>folololololololololo| folololololololololo|<br>folololololfololololoa| folololololololololo|<br>folololololfolololo|z| fololololololololo|:|<br>folololo|z{olololola| fololololalololololo|<br>folojol{a}3{3]olololo| fofojoli|3]s3{olololo|<br>[1folo|1/3folo|i{a}s{a}olololo||o|o[3 \aeps|olololo56]5]1/o]olo | f folo|i{i|s]{ili { o }o|3|sols|{1[olol|o|lo|i|sae} s[ olololo|<br>folololo}z{ololololoa| fololololalololololo|<br>folofolojofofolololoa| folojololofolololojo|<br><!-- End of picture text -->
In ACS a BA can be selected either initially or as part of an adaptive expansion, where selection through expansion is a function of units ( ) in all adjacent BAs.<sup>19</sup> This presents a challenge: we have information on all BAs in a neighborhood, but we do not have information on the count of jj units ( ) in adjacent, unenumerated BAs (i.e., the white squares in Figure 1). As a result, one cannot know if a BA could have been selected through an alternative expansion pattern, via unenumerated jj BAs. This is an important difference with simple random sampling (SRS), where selection probabilities are known. With ACS, it is not possible to compute the probability of inclusion in the sample for all sampled BAs as not enough information is discovered for all sampled BAs to produce these calculations. However, the subset of BAs that make up the networks within a sample can have their inclusion probabilities computed. In other words, inclusion probabilities can be computed for the discovered cluster, minus any edge units _._ A specific selection probability is required for the ACS HT estimator. Define the probability that a given BA, , is included in the sample as i, where initial BAs are selected using SRS without replacement. Formally i is expressed as: ii ππ ππ <u>�</u><sup>NN−ii</sup> 1<sup>ii−iiii</sup> <u>�</u> i = 1 − (E . 1) ii �<sup>NN</sup> 1<sup>�</sup> ππ where is the total number of BAs in the study area; ii 1 is the number of initially selected BAs before any expansion takes place; is the number of squares in the network to which belongs; NN nn and denotes the total number of squares found in networks to which square ii _i_ is an edge unit. mm ii This probability can be used to write an HT estimator of the number of BAs for ACS as: ii aa = 1 <u>yk∗</u> μ�H ∑ (E . 2) KK IIkk Where ∗ is an aggregated indicator of NN values in network kk=1 ππkk , where . For example, for ∗ a population estimate, kk is the sum of all informal businesses (ii ) in BA , that form part of yy yy kk ii∈kk∈KK network ( ), that is: ∗kk= ∑ ∑ .<sup>20</sup> = 1 with probability ii i if the sample intersects yy jj ii IIkk kk ii=1 jj=1 ii kk kk yy jj II ππ

> HT estimator for ACS is more efficient than the HH estimators even when Rao-Blackwell adjustments are made (Tout 2009, Christman 1996, 1997, Thompson 1990, Salehi 2003). For that reason, the HT estimator is presented here.

> 19 Technically of course, it is all adjacent squares that conform to the chosen expansion pattern defined for the neighborhood. See Appendix A.1 for some examples.

> 20 Note for completeness is the total number of BAs in network . kk

> II 11 kk
network and = 0 otherwise. Following Thompson (1990), the population and unbiased, estimated variance of kk μ�H are shown in Appendix A.2. kk II

# **4. ACS and Simple Random Sampling**

ACS generally provides gains reducing what will be called here ‘fieldwork effort’, the number of blocks to be enumerated, particularly, when the underlying population of interest is rare and/or clustered (Borkowski and Turk, 2013).<sup>21</sup> ACS exploits data where concentrations of units of interest are in adjacent BAs (clustering) and where networks of these concentrations occur rarely: as such ACS can identify areas of notably high concentrations of these populations (Thompson and Seber, 1994). The definitions of relative clustering and rarity are specific to particular populations of interest; ACS has been shown to reduce fieldwork effort across a variety of fields, including rare populations of interest for the natural sciences.<sup>22</sup> The application of ACS to informal businesses presented in this paper is novel, however, and so the following sections discuss practical details for implementers interested in this application.

ACS implementers face a variety of design decisions that include the choice of expansion threshold , the delineation of the total geographic area , the size of BAs, the pre-set rule defining neighborhoods, and if stratification will be utilized. What follows is a simulation of different CC NN design choices and parameters to see how these choices perform against baselines based on SRS of BAs. The simulations use a unique data set from Eswatini (at the time in 2014, Swaziland) that provides a full census of all businesses operating in the country, including informal businesses. Uniquely, the data set includes GPS coordinates, and so allows for a real-life estimate of the

> 21 Fieldwork effort has also been referred to as ‘sampling effort’.

> 22 ACS has been used in a variety of fields, including ecology, ethology, and environmental studies. More specifically, ACS techniques have been used to estimate the density of freshwater mussels (Smith et al., 2003) sea urchins (Skibo et al., 2008) black sea bass (Cullen et al. 2017), yellow perch (Yu et al., 2011) and thresher sharks landings along the California coast (Hariharan et al., 2013); to monitor the populations of endangered species (Davis et al, 2011, Salehi et al., 2015); to determine infestation extent and spread rates of forest insect pest (Coggins et al., 2010); to identify disease levels in plants (Gattone et al., 2013) as well as their restoration levels (Bried, 2013), or simply the abundance levels of specific plant species (Philippi, 2005, Bowering et al., 2017). The conclusions of most of the studies above suggest that ACS tends to overperform other sampling techniques when populations are rare and clustered.

12
clustering of informal-sector businesses.<sup>23</sup> As noted, these comparisons are drawn relative to SRS (which readers will note is equivalent to ACS with ). All simulations set BA size to 150 by 150 meters<sup>24</sup> and use a neighborhood definition of eight adjacent BAs; they vary by changing CC= ∞ expansion thresholds ( ) and the initial selection number of BAs, . Later simulations build on these by also varying geographic scope, density, and by adding stratification. ii CC nn The simulations focus on the largest metropolitan area in Eswatini—Manzini and the periurban neighboring city of Matsapha. Together, the area covers approximately 120 square kilometers and has a daytime population of over 150,000. An overlay of BAs yields 5,616 BAs of 150 meters by 150 meters, as shown in Figure 3. These squares contain 4,471 establishments, the true value of the population total. The population appears clustered and rare, with only about 13% of squares containing any establishment at all. Simulations were run using Stata, and every simulation contains 10,000 initial draws of BAs. For comparison, two sets of simulations were run: one set for SRS and one for ACS. SRS simulations include samples ( 1) of 2%, 3%, 5%, 10%, 20% and 30% of the 5,616 BAs. ACS simulations include samples where the initial sample of nn BAs, before any expansions, cover 2%, 3%, 5%, 10%, and 20% of the 5,616 squares and examine the following possible values for . CC= {1, 2, 5, 10}

> 23 The simulation results presented here incorporate all 4,471 businesses, 1,901 formal and 2,570 informal businesses. Simulations run using only the informal businesses show similar clustering and yield similar results and efficiency gains.

> 24 The choice of a 150-meter-squared BA is as much practical as one driven by data: in an urban environment that can include large clusters of informality, interviewers must be able to enumerate a given BA in a reasonable amount of time. As described in later sections, the 150-meter-squared BA is an experience-based size that makes this fieldwork feasible.

13
<!-- Start of picture text --> SSSCCSCH-SUROT“SEP<_ALLL‘SGRCIUCERESCSTEOSDLea SOTERASECAESCERESSSSee eetaeTTS che£4668SSSESSTESHSTS eY8607eeSSEREESEEE:AeCieLK 2STSEASEEEIS) HEGRESKEPPACeSSO KKEKeeeeeeTfA * kTeSPEATE\ sooPPPSaESETS SSEeee ESEESA TAL eeeFAALESa OEFeee POETFSETPeeOTEEESSPFSETPFeTseeasPERE e rde EOC TTTeeoePeeCREEPERSieee.eetee<br>~_O@re-,T)/4S588td."6) €e~S868e.orn) SOP“S60= o=PEERED860888088==**889084.OOkae Leeeee822,eeeeeSENSES2°eeLe"ESEEeee) Fibs PRESSE| RROLise)Sete REEEEe ESEESBeeeeee,eeestVE.ASHbee 4.FeyFUG"eeeHRS¢@ 88TET.. £0088, SSSTSS-o,te EEEOb.“3 O_OEE189SEPSESSOPSEOE*8 BF Edeee!ESOFOR".OF AEE4°.eee CESSES¢ ERLESOTLeeVERE TESTSBOREeeeCCRR SEBSCHR eeeeSeeeeeeEEe<br>—Seekeeeerae.-—SbobTHO.B18O08Ge?te t6b,£08866?tee.O.0008-89OPPCSS~2sSe.PPPCSCS600888608.&_BGBGe.-*eeeceeSG eeeegeSi./eee-«@.@seoB66.*8R +deueesiCER28786see.--522 eRAethaeyf+ +2bit,Fise1h‘efHk''SESi f@f82=e. OeVES\ieoeeeeeée-8855S%@e;TeeSee EE4EEFres ee},Cea? eReGbefet, “beeFTE=F‘onveafe4EEee"see.,Vee8enO°?)ieif”S050<p-efpeeve. eee+yetorss4i08.)8-—_—SFGT Ioe-.f8@08**TEESE,eeeoe “de,CEEE..-260082cee) teers>* i.«—-|se28e8t5F= 280888. 4028LOREPSS SSEESEESee CHOE-“FE8EDOFeeeeee240858reeeee. =<br>=" s8ee8ieen. eertr ou ee eee= 2 PhSesses ee,: Selesaea8 * 8 “Seen,@60 Or’Be (steam2298 +500)4h07 SOP~e(1 5587ee"* ‘ = ¥ 4.“_6| £eeeeeo)""8R=LOEESh SEROeRe._fateCEEREC8<br>-aenbe-a- +885 Pho ie! eda Yr 2488. \ 58 hee sPS45e+ . 88S | Lee Pe fe p> S88 ot . sSEOSE Os<br>oe.)s.r"aoers.7“stots«wees?eeefe".6,8 6 5!, \)&9°a*veOFOF=A,ow 28 4 + ieee\'eer# "teretot ye |SGR#2« iaeeGG.VEeeeseedod_ Deie!*?beeA1,.*“Se-_.eéeGeeeeee *Teer2SSSEESL.* Pe ee.howTh-—-,reOw... oea vy.—_*7=.&._,.of eed eee!ésae., JOPtLESsdSAPLe£8888el58808eee8C8Rek etRSGOL BBO*EPo KKDeeborCeeeeeOEEees|<br>aenaea”2007.85" _ can. & Seeie; &*L*4? 4,£2SSSRL620SE886.uheTe, |Bee1° fe£2° SSeSWSS SSenseebenbeeee,eed FXbe or 2 ISSVERSEDSeee) "886" PROCESSESRRERSER Eee”CCEEEETSERREsh2SHS),LEBOSSEEE BSeS<br>= .hhe = 4 £aPs, ye 4 -# SSE)€6@1)FESSORBOSSP HRSAEOH EPLOSEROS PeesES) TSSPOHL PeePERT eeeLES, 2)it”BS.o.Ls TERRORSeenRESOG0008ROETTHEYfa Reecot POPESOE HeEee HeeeeEeH eee<br>2088se‘ol we,a OeOL TCT 490'TTS888 TTTCSS ITIPSSSRB40 TTISSPETESTAEES)ierPTEVERSESS SSE.S TERCES,litiiitieliniiililissTERSRRERERCHSCs|eeeeer- ve. es*, tt 88Oeee “TTT S SSPSTSTTSF TTTSTEFSEST”StierrisctigiiiiiiiSTEPS9RTE ATTCSREESeee.ESL WORSEteesso<br>Ea-.4426“5,fhif«SOOOeaeoOeeR. thee- 7 SSOsiBESESSSSOESEEES POSERPHSESSSSEHSAEEE.PESO PSSSTSSS EEEHT 8) SHSSSSELRCHSSEEEEEREE SSEEL1sTR,eeENS,PPCPERSR CESSESCRESSERE RE ERRCEHRORES|eeHT SFBELEeeeLk LEERFPOBHSHEHESSES HSTES SESEERREPSRCEECSECSESEESCHER HEEEeeeeeeESE eee EEE<br>ae #, USL -SCR_ ESOESOSS!SSS SSSAE- CSGSSSRSPSSP CSTE ASSESS, S ECTSSES THs CHER CSREES TES 8 Fr. Ok SSCS SCRE. PCRS ESS ETERS<br>Ti471(SGOSS6bk08TeriVOcP“*,-sPSSST"SSSPSCCe 2%ESSEREESSE'-oo0 TIItiiitlilit FOSSSRRSSSSF 80888808888"RSREESSEEFSRRRESOGRESSSOOT FESEFECSETRSSEEHH)REESER ESSASSSREG)ogREEtiltlistlisililiit1FSEEOESESSSESESSRETAERSRE$OSOE S EK!CeeHE)E?SESSSEHRcowPeeFPSSSSReFHSSPRSHS eSE ERRReeeESTESSSTSOREEPSEERSPSSHOG)eeHS ee E EREESEs4)SSSHRSE”CHEESESPRESPRSLEE(SSHSSSRil ESHESS EEESUTREEAEH.,SSLeEEN, E SHEETEL eeLeeSEE,EE SOTEeCeOhTHAVeLOSSSORELSHSSEEeFOEEBoyee * °FTeheon ESE1RKSSEELESelade,reerPOoeFoFOF[AF6,.7F498.Owepis1fso.OR88@§OPER|) TERESOCCERBOSSsOSASROTRPEREPOSSESt E ESCOOTlitle EOEEEEEIEESSOSLSEES!PETES OEERE FSSBES.CSFFIOPESes iiIPERSAEETEPBOOS?ORE| EeeEEROE EL.RRReeeCOTTERLPOSORESPTESEES ESOyEP) ESASeeeTTTies”TeePeePeeDeeeTOES “TeeeeeeeiiiAeSeeeeeEeeRee eeeeeeeesOe<br>FSRbb CRESS TE RRR ESSEKSE . SHEE RRR EERE RHEE ES PERK RESEREEE.) PETES) SERRE CERREEE!DORE IGEE ES, SHRED RRREEE<br>es POSSESS SSS SSS SSE LACTATE SPS SCHR SST EERIE SRT SSS ee ST Pe. OSS VEEL ed eee chee<br>2996SSSSSKSSCRSTSREESSSSSSHFPHHSHELOFFS=o OFESSOPILEOO SSSRVET. SSEEAFASSHCESSAEERRSETCFSESSAHTSSHTSEHEFOSTER EEE HESSSE EEESSRRSPASEE EST TESTESHEEA S EESSSR S ES NESTOR1 COSTESSHSSSFSSTS SE ESE EERE,RTEESSHS SOS E ELESBeeSF),11BcFECHESTPCRS|JOHORE ROECERTSSSES,Fe 1A- SOOTOESLESS)DAESee HOREPSTPECOR EE e RESH LOePHFLESSEEaeeeSRPRoe SREP E CHRREeeeReeREE eeSEES eeES<br>SSS SSS STS TH SSS § SSNS HSS SS SSS SS TSA S SS | SSSSTT EST SH Se, APPT H TT ASSES TLS) PRET A SSS Ree<br>SSSCSASSSSEAESSESsee08 PSSTOC OP E E ESSESSSSSERSPT TTPO TET ESSEHTS TOTPSESS SSE EEE:T TS) SECEESERSSCKSSAeee eee ‘Trip THERtiiiaanly EREESSCESS©. £88)198 S89CEEEE0° 48CHEESE8D ECEC[REEESLTIGL ESR ESR eeS<br><!-- End of picture text -->
below 100% indicates a fieldwork effort reduction of ACS relative to SRS; above 100% indicates an increase in fieldwork effort.

Both ACS and SRS produce unbiased population estimates; only SRS, _n_ =2% has a mean bias with an absolute value greater than 1%. What is more, ACS estimates are consistently less variant compared to SRS. It is useful to compare rows with similar values for ‘Total BAs’. The last two rows of the table show that SRS samples of 20% and 30%, with a range of mean enumerated BAs from 1,123 to 1,685, mean S.E. of 1,189 and 1,021, respectively. Illustrative of the gains from ACS, all ACS rows with a mean “Total BA” count in that range, indicated by bold italics, have demonstrably lower mean standard errors. Likewise, the relative effort gains of ACS are apparent in the last three columns. As expansion thresholds increase, the measures of relative effort decrease. The intuition being that with higher thresholds of , a triggered expansion is more likely to efficiently discover clusters of informal business activity (i.e., there are fewer empty CC squares enumerated).

15
||Table 1<br>Initial B<br>|: Simul<br>As (n~~1~~)<br>|ated Res<br>Mean<br>|ults of ACS<br>of 10,000 Simu<br>|Paramet<br>lations<br>|ers comp<br>|ared to<br>Relativ<br>|SRS<br>e Effort<br>SRS<br>|ACS to<br>|
|---|---|---|---|---|---|---|---|---|---|
|**(1)**|**(2)**|**(3)**|(4)|(5)<br> <br>|(6)|(7)|(8)|(9)|(10)|
|**C**|%|#|Total<br>BAs|Mean Pop.<br>Estimate<br><sup>�</sup>|Mean<br>SE|Bias|SRS|SRS|SRS|
|||||(Uia.)|..||10%|20%|30%|
||2|112|1,047|4,477|593|0.14%|186%|**93%**|**62%**|
||3|168|1,209|4,474|580|0.07%|215%|108%|**72%**|
||5|281|1,404|4,468|573|-0.07%|250%|125%|**83%**|
|1|10|<br>562|<br>1,758|<br>4,472|572|0.02%|313%|156%|104%|
||20|1,123|2,314|4,473|574|0.04%|412%|206%|137%|
||30|1,685|2,804|4,475|576|0.09%|499%|250%|166%|
||2|112|580|4,471|648|-0.01%|103%|**52%**|**34%**|
||3|168|721|4,469|612|-0.05%|128%|**64%**|**43%**|
||5|281|917|4,471|586|0.01%|163%|**82%**|**54%**|
|2|10|562|1,300|4,466|577|-0.11%|232%|116%|**77%**|
||20|1,123|1,911|4,457|576|-0.31%|340%|170%|113%|
||30|1,685|2,443|4,458|577|-0.30%|435%|218%|145%|
|**ACS**|2|112|233|4,508|831|0.83%|**42%**|**21%**|**14%**|
||3|168|328|4,447|742|-0.54%|**58%**|**29%**|**19%**|
||5|281|490|4,472|661|0.03%|**87%**|**44%**|**29%**|
|5|10|562|844|4,461|611|-0.23%|150%|**75%**|**50%**|
||20|1,123|1,470|4,459|591|-0.26%|262%|131%|**87%**|
||30|1,685|2,045|4,454|586|-0.39%|364%|182%|121%|
||2|112|166|4,494|1,009|0.52%|**30%**|**15%**|**10%**|
||3|168|240|4,460|884|-0.24%|**43%**|**21%**|**14%**|
||5|281|375|<br>4,491|753|0.44%|**67%**|**33%**|**22%**|
|10|10|562|683|4,475|654|0.08%|122%|**61%**|**41%**|
||20|1,123|1,265|4,473|611|0.04%|225%|113%|**75%**|
||30|1,685|1,832|4,472|597|0.01%|326%|163%|109%|
||2|11|2|4,420|2,486|-1.14%||||
||3|16|8|4,455|2,238|-0.37%||||
||5|28|1|4,432|1,901|-0.87%||||
|SRS|10|56|2|4,475|1,530|0.09%||||
||20|1,12|3|4,488|1,188|0.37%||||
||30|16|5|4492|1004|046%||||
|_Note: Authors’_<br>|_calculations_<br><br><br>|,<br>_based on 1_<br>|_0,000 simul_<br>|, <br>_ation runs for eac_<br>|, <br>_h row’s par_<br>|.<br>_ameters. The_<br>|_true popul_<br>|_ation value_<br>|_is U=4,471._<br>|
|_Bias (Col. 7) is_<br><br>_over 10,000 sim_<br>_20%, and 30% r_<br>_SRS._|U<sup>�</sup>aa.−U<br>U<br>_~~,~~ wher_<br>_ulations. Th_<br>_espectively._|_e_U<sup>�</sup>ia._is th_<br>_e relative ef_<br>_In the last t_|_e average (_<br>_fort column_<br>_hree colum_|_mean) population e_<br>_s are based on the_<br>_ns, figures in bold_|_stimate of t_<br>_total enume_<br>_and blue ind_|_he total numb_<br>_rated BAs co_<br>_icate a lower_|_er of inform_<br>_mpared to t_<br>_relative fie_|_al businesse_<br>_he SRS sam_<br>_ldwork effor_|_s, averaged_<br>_ples of 10%,_<br>_t of ACS vs._|

Since the fieldwork effort of ACS cannot be known ahead of time, it is helpful to compare different sampling methods with approximately the same values of (mean) effort. Consider Figure 4. The figure shows the mean standard deviation of population estimates from 10,000 16
simulations on the y-axis; the x-axis shows the mean amount of the fieldwork effort, that is the percentage of BAs that are enumerated. The sampling methods that are shown include SRS, and ACS with expansion thresholds, . We leave the bias of these estimates aside, as Table 1 confirms that both ACS and SRS are unbiased. What is first clear is that, at a given level CC= {1, 2, 5, 10} of mean standard deviation (that is, holding the value of the y-axis constant), ACS results in lower fieldwork effort by reducing the share of BAs that are enumerated. Intuitively, at lower expansion thresholds, fieldwork effort shifts rightward: as more expansions are triggered, naturally fieldwork effort increases. As increases, fieldwork effort reduces, at generally no cost in terms of the variability of these estimates (recall that SRS is equivalent to an expansion threshold ). An CC illustration of how increasing affects the rareness and clustering of a population is provided in CC= ∞ Appendix A.3. Similarly, at roughly equivalent fieldwork efforts (on average)—that is, holding a CC value of the x-axis constant—ACS generally provides lower mean standard deviations. There is a noteworthy exception: at lower fieldwork efforts, the mean standard deviation for ACS can exceed that of SRS. This is because at lower fieldwork efforts, not enough expansions are triggered, resulting in more variable estimates of the total populations (this is further illustrated in the leftward mode in the distribution shown in Appendix A.5.) Under these conditions, then, ACS generally provides less variant population estimates on average, but does not strictly improve over simple random sampling under all conditions.

17
Figure 4: Comparison of Select ACS and SRS Parameters over 10,000 Simulations <!-- Start of picture text --> 4200<br>SD of Population Estimates' Distributions by Method<br>3600<br>3000<br>2400<br>ACS, C=10 1800<br>ACS, C=5<br>1200<br>ACS, C=2 SRS<br>ACS, C=1 600<br>0<br>4% 5% 9% 11% 16% 21% 27% 33% 51%<br>Total Squares Enumerated (Fieldwork Effort)<br><!-- End of picture text --> _Note: Authors’ calculations based on 10,000 simulation runs. Fieldwork effort (x-axis) represents the mean share of block areas enumerated over all runs; the standard deviation (SD, y-axis) is the standard deviation of all 10,000 of the population estimates for each case._

# **ACS and Stratified Random Sampling**

In many cases additional information may be available that allows for stratifying a geographic area before sampling. With business activity (including informality), stratification variables that may be useful include land-use categorization, population density, road density, vegetative cover, nighttime lights, or any geographically mapped variable where one category is significantly more likely to intersect with business activity. In what follows, we use a nighttime lights satellite imagery to generate a stratification variable. Nighttime lights are readily available to the public and have been used widely as predictors of concentrated economic activity (Donaldson and Storeygard, 2016). Figure 5 shows the result of a binary stratification using nighttime lights overlaying the establishment locations, with higher concentrations shaded. Despite the relatively low resolution of the lights data at 500m resolution the strata are very 18
<!-- Start of picture text --> SGS25420008084GRRsee Rierateeee2eeea S023BeeSERS 486CDBRREERS_REESPORACR SEERSURReRe eeeEEE SEENseeeeeeeeeee eee.ee eeeAes CONCHESEEMSRVDREESRRRA RAPRSERREeeeABS Aeeeeaeeee eeeee eeeeee<br>(SESSSSRSSSER8aNeS eeeeeNeee SCORERSERS EERE REESEEERE EERE4ES RSP SeesSSeS See eeUPLAE SEERSESE.USERSS40 Sh FERRESERREREESE 62Ae4eeeeee eee eee eee,<br>SaaS TSS eeeee See eee eee eee eee GEES" [SSR SERRA eee eee eee<br>Saeaun " Sana? a8 HERBS OSRAaEe<br>ae 208 SEESLANES DESEESaRReRe<br>B2Srae : - SEeeeeac / r NRERE BEARS<br>obama gh pe TE ‘2g kB<br>LiLi tigiTo 4 SESESRe8EEGEMREE 5 BERERESRaeeeHEBREHERZHRaS<br>crit Ri SERSe8E5 SERRSSRESZae<br>BOBEERSaeera ‘ 4 i pitSSeeeepenees tietiaril<br>Lite SEEES2 480088<br>Listy ‘ | : i biaey TIN GT<br>ci tii sa 3 r 5 CASBEREEENEP<br>Litt aA. SRBBEERe loan<br>eee.aarvan9% L Seoamait Pl . A BSSVas2raneeee(SSS2erPUEEs<br>Lit iy OA Go Be Od Ca<br>auGboBgaeaae CieSU NSeeeetr : B2sRteeeeeeeGEE RN\SEEeeee<br>BeGERs ’ Liev itt DESH RUE Ooo<br>aaeza. Wieoe tea he : eaeSSSEE 12 eS See eeeNaeens<br>. "|bISRGS SERRRESERRE ESRY SRECSREES TERRCEN SESSESESS SSRRSCSRS eeeERR eeeeeeeee eeeeae<br>< BW BRE P SSSR RSPR Rees<br>SESE ES ER EERE ERRORS eee SES 400 SSS SSR eeeee eee<br>SERRE RE RESRERUEE REE Se ER ERNE eee SE 40 0S SRS See eee eee<br>‘ POUPENN ES] OS) 0) YO WE Bd RYE TY NC Yd 6 ST OGGER 0 PMYGSR EES REESSRREBSDRESRERREGeee<br>( ES)PECLSERS CED) 0SERRERY SD EECCAAERE YYR EENCC ELCCCOEEEEELELLE!eee ‘CQPEE LEEPEC E09)CEEDD EECEEE ED SN CEEDD)CEE CEEEEC EEEELECELEREELLCE LELEEEEEL,<br>SR SSREREEE ES SRR ESSER I SERS ERE RP SNES OAR eee eee eee<br>aua "48 pitt lar eee AN SERREREESE<br>PATGianeeERUBEo TT BERSeeENSSE OL GRRE EES ERE EER AN ENEeerEeeeeeEa SSSSSREPitSERRE RERbBONESERSEEGeeeSSURERRR eeeE> ANEee<br>seaSae88see EESESS REESEEERE EEERE SR EEESSeS EEeeeCELEeeeCECE eeeEEE eeeEEE SERSSS SSSSSSP RSEESRSSSRSNESeNSSE ER SeeReeseeee<br>aanieee HARB RRR PRE SAS URS Pee HERR HEE dR eRe eRe ae<br>ae Ne EEE EE EEA EE EEE EEE ZEEE<br>AteBEESESSacSESERESERRENSEeeeerSSS eee ee Seaeeeee aAONBREeaRRSEEREESNEREREREERESEeesaeela_1Be SeNERSBURBSaSSEUNSEREERUE SERENESCean eeeereeee eee eeeeee<br>CEE EE EEE ECE EEE CECE SRR SSSR SES eee eee eee EP SEER SERRE eee eee<br>he BERR ESR RE RES BERR eee SLE REP BERR ee eee eee eee eee eee<br>EEE EERE EERE BE eh EE EEB SERS RSS ES EES ERR R EERE ER VERE ERE R EEN AS Bee eee eee<br>LITITTI TT rit rr titi tii ry LITT TTT TTT TTTT<br><!-- End of picture text -->
<!-- Start of picture text --> Figure 6: Comparison of Select DS-ACS and DS-SRS Parameters over 10,000 Simulations<br>2000<br>SD of Population Estimates' Distributions by Method<br>1500<br>DS-ACS, C=10 1000<br>DS-ACS, C=5<br>DS-ACS, C=2 8:1 DS-SRS 500<br>DS-ACS, C=1<br>0<br>4% 5% 9% 11% 16% 21% 27% 33% 51%<br>Total Squares Enumerated (Fieldwork Effort)<br><!-- End of picture text --> _Note: Authors’ calculations based on 10,000 simulation runs. Fieldwork effort (x-axis) represents the mean share of block areas enumerated over all runs; the standard deviation (SD, y-axis) is the standard deviation of all 10,000 of the population estimates. DS: disproportionate, stratified indicates a comparatively high initial starting share in high-density nightlight areas (Figure 4). For Simple Random Sampling (SRS) this ratio is 8:1. For ACS, this ratio is 5:3 for initial starting squares, as the expansions in the high-density areas are expected to make the ratio more disproportionate._ Figure 6 replicates Figure 4 but with all simulated samples using the two-category stratification. As without stratification, the ACS methods (now denoted with the prefix DS for disproportionate, stratified) require far less fieldwork effort for a given standard deviation (that is, holding the y-axis value constant). Very importantly, for a given level of sufficiently high fieldwork effort, ACS methods all provide less variable population estimates. This is partially due to the fact that, with well-defined strata, the underestimations that resulted before are minimized; compare Appendix A.5 to A.6. Note that since expansions will necessarily require that more BAs are enumerated, fieldwork effort (especially at lower expansion thresholds) will trend upward. Lastly, readers should note that even ACS without stratification generally reduces the standard deviation of population estimates and reduces fieldwork burden even over SRS with stratification. We provide an illustration of this in Appendix A.7; Appendix A.8 also replicates these exercises 20
with synthetic data that increases population density (given that Eswatini is a generally sparsely populated country) and shows that ACS’s benefits largely hold throughout.

# **5. Implementing ACS in practice**

Practically, implementers must first clearly define delineated geographical areas—that is . While ACS can be applied in rural areas, this paper focuses on urban settings. When defining this geographical area, three broad sources of information are considered, often in combination: NN (1) administrative and natural boundaries; (2) supplementary information likely to be correlated with informal business activity; and (3) local knowledge. Implementers should balance the tradeoffs of relying on any single one or particular combination of these information sources. Administrative boundaries (or delineated statistical areas like a census tract) can correspond to official statistics, important for policy-relevant comparisons. However, administrative boundaries may be insufficient. This will be the case when political boundaries are outdated, or when informality occurs in the outskirts of administrative areas. Implementers will likely need to consult alternative sources of information—such as land-use or, even, night light intensity—as well as local knowledge.

The grid of block areas, BAs, can be easily generated using GIS<sup>27</sup> software, such as ArcGIS or QGIS. BAs should be small enough that they can be enumerated in a reasonable timeframe, but large enough to capture concentrations of informal businesses. Since 2016, the World Bank’s Enterprise Analysis Unit has been piloting an ACS approach in a survey of informal businesses, known as the Informal Sector Business Survey (ISBS). From several initial rounds of the implementation of the ISBS, a practical suggestion is to begin with BAs sized at 150 by 150 meters. However, implementers will want to consider their own restrictions, such as budget and staffing, the relative density of informal businesses, and the appropriateness of other design decisions, such as the choice of neighborhood definitions. All of these choices will be interlinked. Stratification will require mutually exclusive categories and in the case of the ISBS, six stratification categories have proven quite useful: residential, commercial/industrial, mixed residential and commercial/industrial, market areas, open areas, and inaccessible.

> 27 Geographic Information Systems.

21
Informal businesses or establishments ( ), as defined earlier, are those that are _legally_ informal, that is they lack full or partial formal registration. The definition of legal informality jj ∈ UU must be uniquely tailored to each country based on relevant legislation and regulation for formal registration. In the case of the ISBS, an interview is administered to eligible informal business activities randomly selected from the list of informal businesses discovered as part of the enumeration exercise ( ). Combining ACS and a random selection of businesses within the enumerated blocks is not only an appropriate method of providing unbiased population estimates, jj with comparatively low variance and fieldwork efficiency, but also a means—as in the case of the ISBS—of providing a framework for more detailed information, while preserving representativeness.

Implementers will also want to establish monitoring and quality control procedures for both data and fieldwork effort. Since the latter concern is the main focus of this paper, a few key details merit attention. Specifically, the integration of GPS-linked software is often important to ensure enumerators sufficiently apply the listing exercise to all potential units in selected BAs. Sufficiently doing so requires full coverage of paths without enumeration outside of a delineated BA; path tracking software can be used for this purpose.<sup>28</sup> Implementers may also want to integrate fieldwork quality controls to minimize known potential pitfalls, such as undercounting of household-based activities.

Implementing this methodology also requires close monitoring of fieldwork efforts, since under ACS, the total number of BAs to be enumerated is not known _a priori_ . Practically, it may be recommended to enumerate the initial random sample of BAs to calibrate the value selected for the expansion threshold ( ). Based on simulation exercises such as those presented in Section 4, it is recommended to initially select a somewhat high value of , as a more conservative approach. CC That section showed that along the two dimensions of fieldwork effort and variance of population CC estimates, ACS is widely more efficient on both dimensions, holding the other constant: i.e., if one holds the level of variance constant, ACS is almost always more efficient in terms of fieldwork effort. However, practically, a survey implementer may want to have control over the expansions that occur through ACS, as they trigger additional fieldwork—which can be costly. That is, an implementer can start with a higher expansion threshold and then evaluate if the triggered expansions are within the needs and limits of the survey.

> 28 For example, the ISBS is integrated with the open source OruxMaps.

22
While implementers will be interested in the population counts and characteristics available from the enumeration exercise, they will also want to use the much more extensive information collected through in-depth interviews with the randomly selected subset of informal businesses, which captures more detailed information on informal businesses’ operations. In the case of the ISBS, second-stage selection for an interview happens in real-time, during the enumeration of BAs. This is made possible using readily available CAPI software.<sup>29</sup> As explained above, the first-stage enumeration of BAs ( ) is unbiased even when unequal probabilities of selection are considered. This requires the calculation of first-stage weights ii implied by the inverse of E . 1, that is w 1 i (that is, the first-stage weight). A sub-script for stratification is omitted, but readers should note that BA selection probabilities ( i) are often = 1/ππ within strata, which can be multiple urban areas and/or categories within these urban areas.<sup>30</sup> ππ Specifically, re-write E . 1 by substituting , giving: ii ii GG= NN−mm −aa 1 −<sup>GG! (NN−nn)!</sup> (E . 3) E . 3 can be expressed in exponentiated natural logs (as shown in NN! (GG−nn)! E . 4) which can be computed using programs such as Stata and R.<sup>31</sup> Implementers can also calculate a second-stage weight, as the inverse probability of selection for an interview within an enumerated BA. Analysis of the data of interviewed businesses, at the level of SSUs ( ), can then be done using weighting given by w ∗ w . 1(ii) 2(jj) jj

> 29 The ISBS currently uses the World Bank’s Survey Solutions. For more details, see https://mysurvey.solutions. 30 Note that while stratification can help reduce fieldwork effort due to the grouping of similar BAs, it can present an issue when there is the possibility of networks crossing strata due to expansions (as initial PSU selection probabilities are a function of strata). The ISBS deals with this issue by not allowing expansions that cross strata. Also, note that where stratification is defined as separate urban areas (and not further stratification within an urban area), the issue is fully ignorable.

> 31 For example, the Stata function ln factorial(n) can be applied to E . 4. Code for this calculation is available from the authors upon request. Implementers should also note that it is important to set variable storage to ‘double’ to maximize storage precision. Note that storage precision may be machine and processor dependent.

23
Statistical packages—notably Stata—are equipped to handle such multi-stage sampling and weighting.<sup>32</sup> Since the probability of selection, p L ) , is set before enumeration, implementers will most likely want to apply weight adjustments based on unit refusals and the jj (sseess misclassification of units during fieldwork.<sup>33</sup> Implementers can adjust w based on the total number of encountered informal businesses in a BA. The ISBS specifically applies three such 2(jj) adjustments, based on different assumptions, all of which remove confirmed formal businesses: i) counting all unit refusals as ineligible (strict assumption); ii) counting unit refusals with visible signage or permits as ineligible (median assumption); and iii) counting all unit refusals as eligible (weak assumption).

# **6. Discussion and Conclusions**

While this paper lays out a proposed methodology for surveying informal businesses— along with several practical guidelines and informative results—several challenges remain. The methodology requires intensive enumeration, which must go hand-in-hand with monitoring. Some of these challenges can be minimized by technology, through data and fieldwork quality control, including path monitoring. There also remain risks to under-counting of informal businesses that are not readily visible, including those in households or that intentionally remain less visible, perhaps to avoid detection by authorities. This is borne out by the range of the share of businesses operating in the household. Examples from iterations of the ISBS include 59 percent of informal Somali businesses operate within the owners’ household compared to just 14 percent in Lao PDR. Missing these types of businesses during enumeration is a potential form of design-based bias.

> 32 In Stata, this can be done by correctly specifying the svy: prefix via svyset. For example, the following code snippet will declare survey data, with two-stage sampling, with stratification in the first stage (given by strata).  The first stage weight (wt_1) is at the level of an identified cluster (id_cluster), while the second stage is identified at the level of id_j - - with a second-stage weight. For a discussion, see: <u>https://www.stata.com/support/faqs/statistics/stratified multiple</u> - <u>stage designs/</u>

> svyset id_cluster [pw=wt_1], strata(strata) || id_j [pw=wt_2]

> 33 In the case of ISBS, p L ) is a function of a ’s position in an enumerated roster. Enumerators may encounter either refusals or list an ineligible business (e.g., one that is registered), resulting in the need for a weight jj adjustment. (sseess jj

24
Some of the selected BAs are market centers, often the largest concentrations of informal business activity and those with higher selection probabilities, in turn. However, this raises logistical challenges due to the sheer number of these businesses, making it daunting for a single enumerator to cover the entire BA in one visit. This may require assigning more than one enumerator per square. Secondly, markets may be open some days of the week and at certain times of the day, which requires visiting the area at the right time. In open markets, operators may sit next to each other, which may result in greater refusal. Finally, it is important to note that the survey may require visiting areas with safety issues. In some cases, the area could be outright dangerous for enumerators; such areas may need to be excluded from the survey with implications in the extent of representativeness (via the definition of ). One last, specific challenge is that policy makers and researchers may want to build panels NN of data for informal businesses (or even of BAs/PSUs), as the dynamics in and out of informality are an important area for analysis. Likewise, implementers may want to recontact businesses in the course of implementing an ISBS-type survey. Revisiting businesses and building such panels is notably difficult when informal businesses are mobile or have no fixed premises. Recontacting such businesses may require the collection of contact information, such as mobile numbers, requiring full compliance with any existing privacy protocols.

25