metadata: authors: 0: author: Bachas,Pierre Jean
1: author: Gadenne,Lucie
2: author: Jensen,Anders
count: World
docna: 0: docna: Informality, Consumption Taxes and Redistribution
docty: Policy Research Working Paper
subtopic: Labor Markets,Tax Administration,Tax Law,Economic Adjustment and Lending,Macro-Fiscal Policy,Taxation & Subsidies,Public Finance Decentralization and
            Poverty Reduction,Public Sector Economics,Tax Policy,Rural Labor Markets,Gender and Development
teratopic: Social Protections and Labor,Law and Development,Gender,Macroeconomics and Economic Growth,Public Sector Development,Rural Development
abstracts: cdata!: Can consumption taxes reduce inequality
            in developing countries? This paper combines household
            expenditure data from 31 countries with theory to shed new
            light on the redistributive potential and optimal design of
            consumption taxes. It uses the place of purchase of each
            expenditure to proxy for informal (untaxed) consumption
            which enables characterizing the informality Engel curve.
            The analysis finds that the budget share spent in the
            informal sector steeply declines with income, in all
            countries. The informal sector thus makes consumption taxes
            progressive: households in the richest quintile face an
            effective tax rate that is twice that of the poorest
            quintile. The paper extends the standard optimal commodity
            tax model to allow for informal consumption and calibrates
            it to the data to study the effects of different tax
            policies on inequality. Contrary to consensus, the findings
            show that consumption taxes are redistributive, lowering
            inequality by as much as personal income taxes. These
            effects are primarily driven by the shape of the informality
            Engel curve. Taking informality into account, commonly used
            redistributive policies, such as reduced tax rates on
            necessities, have a limited impact on inequality. In
            particular, subsidizing food cannot be justified on equity
            or efficiency grounds in several poor countries.
repnme: repnme: Informality, Consumption Taxes and Redistribution
display_title: Informality, Consumption Taxes and Redistribution
listing_relative_url: /research/2020/06/32084138/informality-consumption-taxes-redistribution
topicv3: Labor Markets m1326488 855,Taxation m1327615 1121,Tax Policy m1327616 983,Gender m1327621 615
publishtoextweb_dt: 2020-06-01T00:00:00Z
historic_topic: Social Protections and Labor,Law and Development,Gender,Macroeconomics and Economic Growth,Public Sector Development,Rural Development
origu: DECRG: Macroeconomics & Growth (DECMG)
no_of_pages: 93
author_keys: 0: author_key: 1245385
model_extractions: Policy Research Working Paper 9267

# Informality, Consumption Taxes and Redistribution

_Pierre Bachas Lucie Gadenne Anders Jensen_ Development Economics Development Research Group June 2020
Policy Research Working Paper 9267

# **Abstract**

Can consumption taxes reduce inequality in developing countries? This paper combines household expenditure data from 31 countries with theory to shed new light on the redistributive potential and optimal design of consumption taxes. It uses the place of purchase of each expenditure to proxy for informal (untaxed) consumption which enables characterizing the informality Engel curve. The analysis finds that the budget share spent in the informal sector steeply declines with income, in all countries. The informal sector thus makes consumption taxes progressive: households in the richest quintile face an effective tax rate that is twice that of the poorest quintile. The paper extends the standard optimal commodity tax model to allow for informal consumption and calibrates it to the data to study the effects of different tax policies on inequality. Contrary to consensus, the findings show that consumption taxes are redistributive, lowering inequality by as much as personal income taxes. These effects are primarily driven by the shape of the informality Engel curve. Taking informality into account, commonly used redistributive policies, such as reduced tax rates on necessities, have a limited impact on inequality. In particular, subsidizing food cannot be justified on equity or efficiency grounds in several poor countries.

This paper is a product of the Development Research 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 pbachas@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
# Informality, Consumption Taxes and Redistribution

Pierre Bachas, Lucie Gadenne & Anders Jensen<sup>_∗_</sup>

## JEL: E26, H21, H23, 023

Keywords: Household Budget Surveys, Inequality, Informality, Redistribution, Taxes.

> _∗_ Pierre Bachas: World Bank DECRG Macro & Growth, pbachas@worldbank.org. Lucie Gadenne: University of Warwick, Institute for Fiscal Studies and CEPR, l.gadenne@warwick.ac.uk. Anders Jensen: Harvard Kennedy School and NBER, Anders ~~J~~ ensen@hks.harvard.edu. The findings and conclusions are those of the authors and do not represent the views of the World Bank. We would like to thank Michael Best, Anne Brockmeyer, Roberto Fatal, Xavier Jaravel, Michael Keen, Joana Naritomi, Henrik Kleven, Wojciech Kopczuk, Joel Slemrod, Mazhar Waseem and numerous seminar participants for helpful comments. We thank Eva Davoine, Elie Gerschel, Mariana Racimo, Roxanne Rahnama and Alvaro Zuniga for excellent research assistance. We gratefully acknowledge financial support from Weatherhead Center for International Affairs at Harvard University, the World Bank Development Economics’ Research Support Budget, and the IFS’s TaxDev center. Replication codes for the paper are available here.
# **1 Introduction**

in countries is than in most rich countries and has re- Inequality developing higher mained high over the past 30 years (Alvaredo and Gasparini, 2015). To what extent can tax systems redistribute income in these countries? In this paper, we combine microdata and theory to shed new light on the redistributive potential and optimal design of consumption taxes, the main source of government revenue in developing countries. We find that consumption taxes are redistributive, lowering inequality by as much as income taxes. These effects are primarily due to different informal (untaxed) consumption patterns along the household income distribution. In addition, we show that, once informal consumption is accounted for, commonly used redistributive policies such as reduced rates on necessity goods have a limited impact on inequality. Our results stand in contrast to the existing literature, which does not take into account the existence of informal consumption, and concludes that consumption taxes have a limited or negative redistributive effect in developing countries (see for example Lustig, 2018).

A major constraint in studying informality is that, by definition, informal sector purchases are hard to observe and to link to consumers’ incomes. We innovate by using the places of purchase reported by households in expenditure surveys to proxy for the share of consumption purchased from the informal sector. Thus, our starting point is the creation of a new micro database that combines expenditure surveys from 31 lowand middle-income countries and contains information on the place of purchase for each transaction (such as street stall or supermarket). To assign each place of purchase to the formal or informal sector, we build on micro evidence from retail censuses and on the literature showing that large modern retailers are much more likely to remit taxes than smaller traditional retailers (Kleven et al., 2016; Lagakos, 2016).

Our makes three contributions. The is to new facts paper first produce stylized on consumption patterns across the income distribution and over development. We document the existence of a downward-sloping Informality Engel Curve (IEC): within each country, the informal budget share declines steeply with household income. The IECs have a stable, log-linear functional form in all countries and their slopes remain negative even after controlling for household location and narrow categories of goods. We provide suggestive evidence that the residual IEC slope may be explained by richer households valuing quality more and formal firms selling higher-quality products, in line with evidence in Faber and Fally (2017) and Atkin et al. (2018b). The shape of the IECs implies that the de facto exemption of the informal sector from taxes makes consumption taxes progressive (the taxed budget shares increase with income). Indeed, 1
we find that with a simple uniform rate on all goods, the richest quintile pays twice as much in taxes as the poorest quintile in the average country. This ’progressivity dividend’ from exempting the informal sector is largest in the poorest countries and decreases with development.

We provide a similar characterization of the food Engel curves within countries. Consistent with an extensive literature (see for example Deaton and Paxson, 1998), we find that food are Engel curves downward sloping in all countries. This shape motivates the commonly observed use of the de jure exemption of food purchases from consumption taxes (or taxation at a reduced rate). We indeed find that applying such an exemption makes consumption taxes progressive, but less so than the de facto exemption of the informal sector, particularly in poor countries. Once informal consumption is accounted for, exempting food increases progressivity only marginally. This is because most poor households’ food consumption takes place in the informal sector.

Our second contribution is to build a simple model to derive the implications of these consumption patterns for tax policy. We extend the multi-person model of optimal commodity taxation of Diamond (1975) in two directions: we introduce formal and informal (untaxed) varieties of each good and we allow for changes in consumption patterns over the development path. We consider a scenario in which the government sets a uniform rate on all goods, and one with different rates on food and non-food goods. Allowing for informal varieties affects both the and characteristics of efficiency equity consumption taxes. It increases the efficiency cost because households can substitute to informal varieties when taxes increase; it makes consumption taxes progressive as long as IECs are downward sloping. Calibrating the model to the data, we find that the optimal level of rate differentiation between food and non-food products increases with development.<sup>1</sup> This is due to the shape of the formal food Engel curve, which is effectively flat in low-income countries but becomes negative in middle-income countries. In some least-developed countries, we find that subsidizing food relative to non-food can neither be justified on equity nor on efficiency grounds.

Our third contribution is to investigate the impact of consumption tax policies on inequality by combining the calibrated optimal rates with the household data. The impact of a tax policy on inequality depends not only on its progressivity, but also on the level of tax rates and size of tax bases which determine the share of taxes in households’ budgets. We find that setting a uniform tax rate on all goods while taking into account

> 1This is true for our baseline value of the elasticity of substitution in consumption between formal and informal varieties, the parameter which determines the size of the efficiency cost of taxation due to the existence of an informal sector. We use a baseline value taken from Faber and Fally (2017) and Atkin et al. (2018b) and discuss the robustness of our results to alternative values.

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the de facto exemption of the informal sector achieves on average as much inequality reduction as the actual direct tax policies (income taxes and social security) in developing countries. Equally remarkable is that this policy achieves 75% of the inequality reduction obtained in a counterfactual world with enforcement in which can perfect governments tax both formal and informal varieties (thereby taxing a much larger base) and optimally differentiates rates between food and non-food goods. In the realistic world in which informal varieties cannot be taxed, the inequality reduction obtained by the de jure optimal rate differentiation is half that obtained by the de facto exemption of the informal sector.

We investigate the robustness of our results to changing our main assumptions. First, we obtain similar results when changing how we assign places of purchases to the formal (informal) sector. This is because the association between budget shares and household income is strongest for places of purchase which are clearly informal (non-market consumption) or clearly formal (large supermarkets). Second, we assume at baseline a zero pass-through of taxes to prices in informal stores. This assumption may not hold if, for example, informal retailers buy inputs from formal suppliers. We relax this assumption by combining our model with microdata from Mexico on formal input purchases of informal retailers. We find a slightly smaller redistributive effect of the de facto exemption of the informal sector, but our main results remain unchanged. Third, due to data limitations, we use total household expenditure to proxy for household income.<sup>2</sup> We relax this assumption by using estimates of saving rates across the income distribution and similar results. we discuss the of our find Finally, implications modeling assumption that no direct tax instrument is available to the government. An important theoretical result in public finance is that redistribution is better achieved through direct rather than indirect taxes (Atkinson and Stiglitz 1976). This result, however, is derived under the assumption of perfect enforcement of direct taxes, which is unrealistic in lower income countries (Jensen 2019). In the more realistic setting where income taxes can be partially evaded, theory suggests a substantial redistributive role for indirect taxes (Burgess and Stern 1993; Boadway et al. 1994; Huang and Rios 2016).

Our results have several main implications. First, our result that consumption taxes can reduce inequality in developing countries runs counter to the consensus view in the policy and academic literatures (Sah 1983; Shah and Whalley 1991; Gemmell and Morrissey 2005; Coady 2006). This negative prior may explain why studies of redistribution in these countries often focus on the design of government transfers (Tanzi 1998;

> 2Expenditure surveys in developing countries often do not attempt to directly measure income because of serious measurement issues - see Deaton (1997) for a discussion.

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Clements et al. 2015). Our findings suggest that more attention should be paid to the redistributive potential of tax design in developing countries. Second, we obtain our results by measuring informality from consumers’ side, while most empirical work measures informality at the firm or worker level (see review in La Porta and Shleifer, 2014). This leads to a more nuanced perspective on the welfare effects of informality. In particular, our findings caution that enforcement policies to reduce informality, which are often found to yield efficiency gains (Ulyssea, 2020), may also have distributional costs by increasing the burden of taxation on poorer households. Third, our classification of retailers as formal or informal overlaps with the ’traditional’ versus ’modern’ retail categories studied in the macro-development literature (Lagakos, 2016). By combining micro survey data from countries spanning a wide income range (from Burundi to Chile), we document stylized facts on consumption patterns across retailers and goods as households get richer, both within and across countries. Our database could be used in future research to test competing theories of development and global retail (Bronnenberg and Ellickson, 2015).

The rest of the paper is structured as follows. In the following sub-section, we summarize our contributions relative to existing literatures. Section 2 describes our data sources and Section 3 new facts on methodology. provides stylized consumption patterns across places of purchase and types of goods as households get richer within and between countries. Section 4 investigates the implications of these consumption patterns for tax progressivity. Section 5 develops a model to characterize optimal commodity tax policy with informal consumption. Section 6 calibrates the model using our data and investigates the impacts of consumption taxes on inequality. Section 7 concludes.

# **1.1 Related Literature**

Our paper makes two main contributions to the literature on tax policy in developing countries. First, we introduce differences in informal consumption along the income distribution as a novel channel through which consumption taxes are redistributive. This contrasts with the existing literature, which omits informal consumption and concludes that consumption taxes have, at best, limited redistributive impacts in developing countries (for recent studies, see Harris et al., 2018 and Lustig, 2018).<sup>3</sup> Our approach is thus related to recent the redistributive of differences in papers investigating implications consumption patterns across the income distribution, though these studies are in rich

> 3Two exceptions are Mu ̃noz and Cho (2003) and Jenkins et al. (2006) who use retailer information to classify expenditures as formal or informal in respectively the Dominican Republic and Ethiopia.

4
countries (Faber and Fally, 2017; Jaravel, 2018; Allcott et al., 2019). Our focus on the equity implications of the informal sector contributes to the literature on optimal tax design under imperfect enforcement (Allingham and Sandmo, 1972; Cremer and Gahvari, 1993; Boadway and Sato, 2009), which has mostly focused on efficiency costs of taxation (see Kopczuk, 2001, for an exception).

Second, we shed new light on the redistributive potential of differentiating consumption tax rates across goods. While such policies are commonly implemented (Ebrill et al., 2001), few papers have studied the redistribution achieved by optimal rate differentiation, and only on a country-by-country basis.<sup>4</sup> We combine theory and novel data to undertake the of rate differentiation and its on first systematic analysis optimal impact inequality across a large sample of low and middle-income countries.<sup>5</sup> More generally, our paper speaks to the growing literature on public finance in developing countries that considers these countries’ limited tax enforcement capacity (Almunia et al., 2019; Basri et al., 2019; Weigel, 2019; Londo ̃no-Velez, 2020), implications for optimal tax design (Brockmeyer and Hernandez, 2019; Gadenne, 2020), and in particular the literature focusing on consumption taxes (Pomeranz, 2015; Naritomi, 2019; Waseem, 2020) This paper is also related to the literature on consumption patterns and development. A large body of work documents how budget shares on specific goods vary with income, including the well-established food Engel curve (Deaton and Paxson, 1998; Anker et al., 2011; Pritchett and Spivack, 2013; Alm ̊as, 2012). We document in addition the association between household income and place of purchase both within and across countries. In doing so, our analysis complements recent studies which document aggregate changes in the retail sector over development (Bronnenberg and Ellickson, 2015; Lagakos, 2016; Atkin et al., 2018b). Our approach relates more broadly to the literature which compiles multi-country microdata to study macro changes over the development path (Bick et al., 2018; Donovan et al., 2018).

Finally, our paper contributes to the literature on the informal sector. Existing pafocus on the side’ of incentives to become for- pers ‘supply informality, by evaluating mal either at the firm-level (DeSoto, 1989; De Paula and Scheinkman, 2010; La Porta and Shleifer, 2014), the worker-level (Gerard and Gonzaga, 2016; Jensen, 2019), or both (Ulyssea, 2018). Our approach complements these studies by considering the ‘demand side’ of informality: consumers’ use of formal or informal retailers. This allows us to construct a new measure of the informal sector, building on a literature in public finance

> 4Including: In United Kingdom, Sah (1983); in India, Ahmad and Stern (1984), Ray (1986), Srinivasan (1989); in Australia, Creedy (2001).

> 5Our main results focus on food versus non-food rate differentiation, but we also show results for optimal differentiation between 12 large goods categories.

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which uses consumption data to infer evasion behavior (see Pissarides and Weber, 1989; Feldman and Slemrod, 2007; Morrow et al., 2019).

# **2 Data and Measurement of Informal Consumption**

We use two data sets to present new evidence on consumption patterns in developing countries and on the redistributive of taxes. Our core potential consumption sample consists of 31 countries for which the data enable us to proxy for informal consumption at the household level. Our extended sample consists of 80 countries for which the data allow us to document food consumption patterns.

## **2.1 Core Sample**

We assemble our core dataset by combining household expenditure surveys from 31 countries that satisfy three selection criteria. First, the survey is nationally representative. Second, the survey records consumption from open diaries rather than pre-filled diaries, which only contain information on selected products. This helps to ensure that the survey covers all expenditures. Third, the diary asks households to report the place where each expenditure is purchased from - the _place of purchase_ - and that this information is in the diaries. This last criterion ensures that we can systematically reported apply our method to robustly measure informal sector consumption, as described below.

Our core sample from 31 countries contains information on over 400,000 households. Table 1 lists the countries in the core with their name alphabetically sample, survey and year, the number of households, and the average number of purchases reported per household. Countries in the sample are principally located in Latin America and Sub-Saharan Africa. Unfortunately, most household expenditure surveys in Asia do not contain information on the place of purchase. for places of purchase.<sup>6</sup> Nonetheless, the core sample covers a wide range of development levels, from Burundi (GDP pc of 250 USD) to Chile (15,000 USD). In Section 3.3, we show that this core sample is very comparable to the large set of developing countries in the extended sample, along detailed expenditure dimensions that can be observed in samples.

Appendix B provides further details on the data sources used. Table B1 shows the geographical coverage of the core sample, table B2 lists the surveys considered for inclusion but ultimately discarded due to selection criteria, and table B3 provides further

> 6Survey design appears correlated across countries within regions, showing the influence of regional development partners and historical ties. Our data contain one Asian country - Papua New Guinea

6
details on the structure of the surveys for each country in the core sample.<sup>7</sup>

# **2.2 Method: Proxy for Informal Consumption Using Places of Purchase**

Our main methodological innovation is to use the place of purchase reported for each expenditure to assign a probability that it was obtained from a formal (tax remitting) source. Most recorded can be of into seven expenditures classified by place purchase categories. The first five pertain to purchases of goods. Ranked by ascending order of retailer size, these are: (1) non-market consumption (e.g. home production); (2) non brick-and-mortar stores (e.g. street stalls, public markets); (3) corner and convenience stores; (4) specialized stores (e.g. clothing stores); and, (5) large stores (e.g. supermarkets, department stores). Purchases of services can be allocated to two main categories: (6) services provided by an institution (e.g. banks, hospitals); and, (7) services provided by an individual (e.g. domestic services).<sup>8</sup> Combined, these categories account for 86% of total household expenditure. The remaining 14% are items for which no place of purchase is specified, primarily utilities, fuel and telecommunication (see Figure A3).<sup>9</sup> We assign each category to either the formal or informal sector. We define a category as belonging to the formal sector if it is likely that consumption taxes are remitted on most from that to this retailers are purchases category. According definition, many informal because they evade taxes due on their sales. Alternatively, small retailers may be informal because they are not required to register for consumption taxes due to their size. We do not distinguish between these channels, as both imply that these retailers do not remit consumption taxes. In addition, these concepts are closely related: in countries with low enforcement capacity, the scope for evasion among small firms is such that the net revenue from bringing them into the tax net is small and outweighed by administrative and compliance costs (Ebrill et al., 2001; Keen and Mintz, 2004).

The key assumption behind our assignment method is that larger retailers are more likely to be formal. This is in part mechanically true, as a frequently used criteria for compulsory tax registration is firm size. In addition, a large literature argues that larger firms are less likely to evade taxes. Theoretically, Kleven et al. (2016) develop a model of tax evasion in which informality must be sustained by collusion between firm managers

> 7 Replication codes for the paper can be accessed here. This includes the cleaning files of each expenditure survey and the files generating the tables and figures of the paper. The data are not provided as we had to require access to the World Bank or Stat Agency for each country. Yet, these data are often accessible, allowing for a replication of the paper on a subset of countries of interest.

> 8We also use two smaller categories to classify entertainment services into (8) entertainment (e.g. restaurants) and (9) informal entertainment (e.g. food trucks).

> 9We exclude housing expenditure due to limited data on owner-occupied imputed rents.

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and their employees, and show that larger firms are more compliant since collusion costs increase with firm size. Hsieh and Olken (2014) similarly argue that the effective burden of taxation in developing countries falls more heavily on larger firms. Empirically, Kumler et al. (2015) find that compliance indeed increases with firm size in Mexico. Naritomi (2019) provides evidence suggesting that larger retail stores have more customers and are therefore less able to sustain evasion. Both Bronnenberg and Ellickson (2015) and Lagakos (2016) categorize retailers as either ‘traditional’ (small, labor intensive retailers - our categories 1 to 3) or modern (large, capital intensive retailers - our categories 4 and 5), and argue that traditional retailers are mostly informal.<sup>10</sup> We provide direct evidence that formality and firm size are positively correlated. We use data on formality status and firm size available in the retail firm censuses of four countries in our core sample (Cameroon, Mexico, Peru and Rwanda). Panel A in Figure 1 shows the share of formal firms as a function of log employment in each country.<sup>11</sup> In all countries, retailers with a few employees are overwhelmingly informal, but more than 80% of retailers with 20 or more employees are formal. In Mexico, the census classifies retailers in categories which are similar to our broad place of purchase categories. This enables us to go one step further and directly observe retailer size and formality status. Figure 1 shows for our categories (1) to (5) the log median number of employees (Panel A) and the share of firms paying value-added taxes on their sales (Panel C). We observe that non-brick-and-mortar stores and convenience stores are small and rarely formal, whereas nearly all large stores are formal.

Given this evidence, our baseline formality assignment assigns categories (1) to (3) to the informal sector, and categories (4) and (5) to the formal sector. Goods in category (1) - non-market consumption - are by definition not purchased in markets and are therefore untaxed. Categories (2) and (3) (non brick and mortar stores and corner stores) are likely very small and mostly informal, whereas category (5) (large stores) consists mostly of supermarkets which are unlikely to be non-compliant. Our approach assigns retailer-types to informality which are all classified as ’traditional’ tax-evading retailers in Lagakos (2016).

For services, we assume that institutions pay taxes while individual providers do not. This leads us to assign category (6) to the formal sector and category (7) to the informal sector. We follow the same logic in assigning expenditures in the unspecified category to

> 10Relatedly, Gordon and Li (2009) explain the high shares of taxes on capital (such as corporate income taxes) in developing countries relative to rich countries by the fact that capital is more observable than labor in these countries. This also implies higher compliance rates among larger retailers.

> 11Formality is defined as ’being registered with tax authority’ in Cameroon and Rwanda, and ’paying value-added-taxes on sales’ in Mexico and Peru.

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the formal sector: the bulk of these expenditures are utilities typically provided by large institutions which cannot evade taxes (Figure A3). Appendix B provides more details on the methodology. Table B4 shows for each country the original names of the places of purchase, their expenditure shares and our formality assignment.

We will investigate the robustness of our results to two alternative formality assignment rules. The first alternative is to assign a non-binary probability to each category that it pays VAT on its sales. We use the share of retailers that pay VAT in each category in the Mexican census to obtain a for each These are probability category. probabilities depicted in Panel C of Figure 1.<sup>12</sup> This enables us to take into account the fact that some small retailers pay taxes – either because a subset of small retailers are fully formal or because all small retailers pay VAT on a subset of their transactions. The second alternative changes specialized stores (category 4) to be fully informal (leaving all other categories unchanged). This is the category for which there is arguably the most uncertainty about its true formality status.

Our formality assignment rule enables us to measure the informal budget share of each household, defined as the share of its total expenditure purchased from informal retailers. In what follows we also consider within-product informal budget shares. We use the UN’s detailed COICOP classification of products, which is available at the 2-digit level (12 products), 3-digit level (47 products) and 4-digit level (117 products).<sup>13</sup>

# **2.3 Extended Sample for Food Expenditures**

We complement our core dataset with microdata from the World Bank’s Global Consumption Database (GCD). The GCD compiles household expenditure surveys across countries and harmonizes product categories across all surveys at the 2-digit COICOP product level. 14 Merging this dataset with our core sample, we obtain consumption data for 89 low and middle income countries which account for over 50% of the world population. While this extended sample does not contain place of purchase information, we can use it to characterize food consumption levels and food Engel curves. Food products are defined as all items pertaining to the COICOP 2-digit category ‘food and non-alcoholic beverages’. This category is a good proxy for the set of products which

> 12We assign the following probabilities that the place of purchase is formal to each category: 10% in category 2; 20% in category 3; 50% in category 4; and 90% in category 5. Other categories are unchanged from the baseline assignment rule.

> 13We use crosswalks to convert survey-specific product categories to COICOP categories when necessary. This could not be done for three countries: Brazil, Chad and Peru. For these countries, we use survey-specific product categories at the 3 and 4 digit levels.

> 14 Aggregate statistics are available at http://datatopics.worldbank.org/consumption. Appendix B.3 provides further information on the dataset and our merge.

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most governments throughout the world tax at a reduced rate in an attempt to make consumption taxes more progressive. We also compare food consumption trends in the core and extended samples and find very similar patterns. This helps us argue that the documented informal consumption facts, while only observed in the core sample, may be relevant for the broader sample of developing countries.

# **3 Engel Curves of Informality and Food across Development**

## **3.1 Informality Engel Curves**

The informality Engel curve (IEC) traces the relationship between the informal budget share and total household expenditure within a given country. As is commonly done in developing countries, we use household expenditure to proxy for household income because of issues with measuring income ( Deaton and Paxson, 1998; Atkin et al., 2018a). We use the of total in line with the literature on logarithm expenditure, large productspecific Engel curves (starting with Working, 1943; see review in Deaton, 1997).

For illustrative purposes, Figure 2 plots the IEC for one low-income country (Rwanda) and one middle-income country (Mexico). These graphs show a local polynomial fit of household budget share spent in the informal sector on log of household expenditure in 2010 constant USD. The solid and dashed lines the median and per capita represent top/bottom 5 percentiles of the expenditure distribution, respectively. To investigate the functional form flexibly, we plot the non-parametric IEC constructed from kernelweighted polynomial local regressions. In both countries, the IEC is downward sloping and approximately linear. In Rwanda, the informal budget share falls from 90% for the poorest decile of households to 70% for the richest decile. In Mexico, the IEC is steeper, falling from 55% to 25%. Figure A1 plots the IEC for all 31 countries. We find two empirical regularities. First, IECs are downward sloping everywhere. Second, IECs are approximately linear in log expenditure. This suggests there exists a stable functional form relationship between informal budget share and household expenditure in developing countries.<sup>15</sup> To summarize the information contained in the country-level IECs, we focus on two empirical moments: i) the aggregate informal budget share; ii) the level-log slope of the IEC. In Section 4, we explain how these two moments are sufficient to characterize how consumption patterns affect tax progressivity. We obtain the country-specific slopes

> 15 Alm ̊as (2012) similarly finds a stable Engel relationship between food budget share and household income around the world. For more dis-aggregated expenditure categories, however, Engel curves have been found to be non-linear and vary across settings (Banks et al., 1997; Atkin et al., 2018a).

10
from the following regression: where _Share In f ormali_ is the informal budget share of household _i_ , _expenditurei_ is its total expenditure per person. We use household weights from each survey.

In Figure 3, we plot the aggregate informal budget share (Panel A) and the estimated IEC slope (Panel B) against countries’ per capita GDP. Panel A reveals a large drop in the aggregate informal budget share, from over 90% in the poorest countries to 20% in income countries. This decrease in the size of the informal sector over upper-middle development, obtained using our novel approach based on consumer shopping behavior, is consistent with patterns observed using alternative informality measures, based on labor markets (La Porta and Shleifer, 2014; Morrow et al., 2019) or money demand (Enste and Schneider, 2000). In Panel B, we see that the negative IEC slope first increases in magnitude, between low-income and lower-middle income countries, and then decreases, between lower-middle and upper-middle income countries. The average IEC slope is 9.8, implying a nearly 1 percentage point reduction in informal budget share when household expenditure increases by 10%.

**Robustness** Our results are robust to using the alternative formality assignment rules outlined in section 2.2. We re-estimate the informal shares and IEC us- budget slopes ing these two alternative rules and present results in Figure A2. Our key findings are unchanged: over development, the aggregate informal budget share decreases steeply and the IEC slope first increases then decreases in magnitude. In Figures A4 and A5, we show that this robustness is driven by the fact that those expenditure categories with least uncertainty surrounding formality status are also those with the steepest Engel slopes (including non-market purchases, large stores, and institutional services).

# **3.2 Understanding Differences in Informal Consumption across Households**

do households consume a share of their from the informal Why poorer higher budget sector? This question is important, for at least two reasons. First, by attempting to answer it we investigate the mechanisms behind the shape of IECs. Second, if differences in informal consumption across households can be explained by characteristics that governments can easily observe and target tax reductions or exemptions on, then de jure redistributive policies and de facto informality exemption may in practice have very similar redistributive impacts.

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# **3.2.1 Observable Characteristics**

To measure how much of the association between household income and informal consumption shares can be explained by observable characteristics, we estimate the following regression separately for each country: where _i_ indexes a household, _Xi_ are household characteristics and each observation is weighted by the relevant household survey weight. Table 2 shows the average of the slope coefficients _β_ across countries, the average upper and lower bounds of the 95% confidence intervals, and the number of countries for which the coefficient is statistically significant at the 5% level. Column 1 displays results from the specification without controls. Column 2 controls for household demographics: household size and age, education and gender of the household head.<sup>16</sup> We find that these characteristics do not explain the correlation between informal expenditure and income and, if anything, the IEC slopes become slightly steeper.

Columns 3 and 4 add controls for households’ location, either with an indicator for whether the household lives in a rural area (column 3) or with survey block fixed effects (column 4).<sup>17</sup> These controls allow us to test whether the association between informal budget shares and household expenditure is due to poorer households living in areas with worse access to formal retailers. Despite large differences in average informal budget shares between rural and urban households, controlling for rural locations only explains 13% of the slopes.<sup>18</sup> Controlling for survey blocks explains just over 20% of the differences in informal budget shares between poor and rich households.

In columns 5 to 8 we test whether non-homothetic across preferences goods play a role – when richer households spend more on goods predominantly sold in formal stores. We run a product-level version of specification (2) with goods fixed effects and compute an average goods-level estimate of _β_ for each country.<sup>19</sup> We gradually consider variations within narrower goods categories: we first consider food vs non-food (column

> 16Household size controls for economies of scale across households of different size which could affect where households choose to shop - see Deaton and Paxson (1998).

> 17The survey block is the most granular location information and contains on average 74 households in our surveys. The median survey block is representative on average of 52,900 households.

> 18The informal budget share is on average 67% in rural areas versus 52% in urban areas and IEC slopes are steeper in urban locations. Figure A7 shows the IECs separately for rural and urban areas.

> 19Formally we run the regression: _Share In f ormalig_ = _β ∗ ln_ ( _expenditureg_ ) + _αg_ + Γ _Xi_ + _εig_ where _Share In f ormalig_ is the share of household _i_ ’s informal expenditure on good _g_ and _αg_ are goods fixed effects. Each observation is weighted by household survey weights and goods expenditure shares.

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5), then the 12 good categories of the COICOP 2-digit level classification (column 6), then the 47 categories of the COICOP 3-digit level (column 7) and finally the 117 categories at the COICOP 4-digit level (column 8). Preferences across goods explain part of the association: controlling for food goods alone explains 35% of the slopes, while controlling for the 12 broad 41% of the variation. for narrow goods categories explains Controlling goods categories only slightly reduces the slope further.<sup>20</sup> Finally, column 9 shows the average IEC slope with all controls included. The average IEC slope is 4.3 and remains statistically significant in all but three countries. Overall, observable characteristics explain 54% of the association between informal expenditure shares and household income. We these results for our two alternative as- reproduce signment rules and find similar results (see Tables A2 and A3).

# **3.2.2 Quality-Price Trade-off between the Formal and Informal Sectors**

The previous analysis shows that observable location and preferences across goods explain half of the IEC slopes on average, but they remain significantly different from zero in most countries after these controls. In six countries in our the ex- including sample penditure module asks households their main reason for choosing a place of purchase for each item; the possible reasons are access, price, quality, store attributes and other.<sup>21</sup> Table 3 reports the average frequencies for each reason. Column 1 shows that across all store access is chosen for 41% of that even at types, purchases, suggesting controlling the survey block might not capture fully the local nature of shopping preferences.<sup>22</sup> Columns 2 and 3 show the same frequencies separately for informal and formal stores. The key difference that emerges is that households visit informal stores for their prices and formal stores for their quality.<sup>23</sup> This result is robust to a set of controls and to the inclusion of household fixed effects.<sup>24</sup> Figure A9 shows that in each of the six countries, this taste for quality is more prevalent for richer households, as they are up to four times more likely to report quality as the reason for choosing any type of store.

> 20Figure A8 displays visually these results for each country by showing the residual IEC slopes when controlling for increasingly narrow goods categories.

> 21In all surveys, seven reasons are listed which we classify into five categories: access is defined as ”The retailer is closer or more convenient” and ”The good or service cannot be found elsewhere”; price as ”The good or services are cheaper”; quality as ”The goods or services are of better quality”; store attributes as ”The retailer offers credit” and ”The retailer is welcoming or is a friend”; and, other as ”Others reasons”. 22This could reflect the fact that many households in our sample cannot invest in costly durables, such as cars, which may give them access to a wider variety of stores (Lagakos, 2016).

> 23Access is slightly more frequently reported as a reason to visit an informal store, which could reflect a lack of store choices in poorer rural locations.

> 24Within a given household, formal store purchases appear motivated by higher quality while informal store purchases appear driven by lower prices.

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These results suggest that part of the remaining association between informal budget shares and household expenditure in the last column of Table 2 could be due to richer households valuing high-quality goods more and such goods being sold mainly in formal stores. This is in line with results in Faber and Fally (2017) who show that richer households spend more on larger brands in the United States, and Atkin et al. (2018b) who find that richer Mexican households spend more on high-quality products sold by foreign retailers. This explanation could imply that formal varieties of a given good should be more expensive than informal varieties, reflecting quality differences. We test this hypothesis in the 20 core sample countries which report unit values for each purchase. We use unit values to proxy for non-quality adjusted prices. We study price differences between formal and informal stores within the most narrow good classification available, location and measurement units, leading us to interpret price differences as reflecting quality differences (similar to Atkin et al. (2018b)). We limit our analysis to food since this measurement issues and because food items are products mitigates typically exempt from consumption taxes, so that any price difference between formal and informal varieties cannot be due to taxes. Formally, we estimate the price premium in the formal sector in each country separately as follows: where _ln_ ( _unit value_ ) _igmu_ is the unit value reported by household _i_ , for good _g_ , in location _m_ , in units _u_ , and _Formaligmu_ equals one if the good is purchased in a formal store. We add fixed effects at the good * location * unit of measurement level.

Table A5 shows that on food unit values are 6.7% in formal than average, higher informal stores. This formal store premium result is robust to outliers, excluding selfproduction, and controlling for household characteristics. These results are consistent with the hypothesis that formal stores offer high quality varieties at a higher price.<sup>25</sup> Formal stores might of course differ in other ways reflected in prices, such as a higher productivity, which would make it less likely to find positive price differences.

# **3.3 Food Engel Curves**

In this sub-section, we document the shape of the food Engel curve in developing countries. The shape of the IEC determines how much redistribution can be achieved by de facto exemption of informal consumption; the shape of the food Engel curve similarly

> 25Consistent with a quality-gradient in size, we also find that within formal retailers, the larger stores (category 5) charge higher prices than smaller specialized stores formal category (category 4).

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determines how much de jure exemption of food can redistributive. Because food Engel curves are downward set reduced rates or typically sloping, many governments fully exempt food products for redistributive purposes.<sup>26</sup> Previous research has studied the magnitude and approximate log-level linearity of the food Engel curves.<sup>27</sup> We combine our core data with microdata from the Global Consumption Database (discussed in section 2.3) to estimate food Engel curves in a uniquely large sample of 89 low and middle income countries.

In the top panels of Figure 4, we present the aggregate food budget share (Panel A) and food Engel slope (Panel B) against countries’ GDP per capita. The aggregate budget share spent on food decreases with development, but the percentage-point drop over development is less pronounced for food than for informal consumption. Food Engel curves are typically downward sloping and there is no relationship between the magnitude of the slope and development. In Panels C and D of4 we show the _formal_ food aggregate budget share and Engel curve slopes, respectively. The aggregate formal food budget share is small on average (11%) but increases with development. The slope of the formal food Engel curve is small in magnitude but positive on average in low-income countries; it becomes negative in upper-middle income countries.

Panels A and B show that the levels and of food curves are Finally, slopes Engel similar between our core and extended for countries at the same very sample sample, level of development. This could suggest that while we can only characterize informal consumption patterns in our core sample, our results may be relevant for developing countries more broadly.

# **4 Progressivity of Consumption Taxes**

The consumption patterns described in Section 3 determine the progressivity of consumption taxes both in the average developing country and across development, which we turn to in this section. We say a tax policy is progressive if the effective tax rate (ratio of taxes paid to household income) increases with household income.

> 26Some countries apply reduced rates or exempt all food goods, while other countries target ‘basic’ food items. We follow the former approach; targeting narrow items may improve redistribution, but also increases the scope for cross-goods misreporting and distortions.

> 27Recent studies include 10 countries in Alm ̊as (2012), 22 in Anker et al. (2011) and 38 in Pritchett and Spivack (2013).

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# **4.1 Progressivity in the Average Developing Country**

**Set-up** We study the progressivity of three tax policy scenarios. Scenario #1 imposes a uniform rate on all goods, but assumes informal varieties are not taxed (de facto exemption). Scenario #2 sets a zero rate on food goods (de jure exemption), but assumes formal and informal varieties are taxed. Scenario #3 both de facto and de ex- implements jure emptions by setting a zero rate on food and assuming informal varieties are not taxed. Scenario #1 illustrates the progressivity of our new informality channel. Scenario #2 corresponds to a counterfactual setting with perfect enforcement capacity; while practically implausible, it provides an unconstrained benchmark against which to compare the informality-constrained scenarios (#1 and #3). Scenario #3 captures the combined progressivity impacts of the government exemption policy and of informality. Importantly, the difference between scenarios #3 and #1 shows the actual impact of governments implementing a de jure exemption, conditional on the de facto informality exemption. We assume for each scenario that the government sets rates such that it collects 10% of total consumption in taxes, thus maintaining total revenue collected constant across scenarios.<sup>28</sup> Finally, we assume full pass-through of taxes to final consumers at baseline, but relax this assumption below.

To build intuition for our results, we rely on the empirical evidence that the Engel curves of both tax bases (formal goods, non-food goods) are upward sloping and approximately linear with respect to log household income, as shown in Section 3. With a log-linear Engel curve, the progressivity of a tax scenario is decreasing in the aggregate budget share of the tax base, and increasing in the magnitude of the slope of its Engel curve. Consider two countries with the same positive slopes for a good, but different aggregate budget shares. When Engel curves are log-linear, the difference in budget shares spent on the taxed good between rich and poor households is more pronounced in the country with the lower aggregate share. In other words, for the same Engel curve slope the lower the average budget share of a taxed good, the more likely is it that any of that is made a rich household. This means that a given purchase good by purchase of that good becomes a better tag for household income, leading to a more progressive tax system. In addition, when two countries have the same budget share of that good and Engel curves are upward sloping, a steeper slope increases the difference in budget shares between rich and poor households, making the tax system more progressive.

> 28Distributional analyses are based on the first order impacts of small changes in tax rates, which are captured by the mechanical effects. Households’ behavioral responses to tax changes are second order.

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**Results** Figure 5 shows the progressivity of each scenario for the average developing country in our sample. We obtain three main results. First, the existence of the informal sector makes consumption taxes progressive. Under scenario #1 (red circle line), the effective tax rate increases sharply with household income and the richest quintile pays twice as much taxes (as a share of income) as the poorest quintile. This large progressivity is explained by the steep increase of formal expenditure with household income (Figure 3.) Second, the de facto exemption of the informal sector is more progressive than the de jure exemption of food goods in the counterfactual setting with perfect enforcement. This can be observed by comparing scenario #1 to #2 (green cross line): the ratio of effective tax rate paid by the richest quintile to that of the poorest quintile is almost 50% larger under #1 versus #2. This difference is primarily driven by the fact that formal expenditure constitutes on average a smaller budget share of households’ incomes than non-food expenditure among countries in our sample (Panel A, Figure 4 versus Figure 3). Third, the progressivity achieved by the de jure exemption conditional on the de facto exemption is small. We can see this by comparing scenario #3 (orange square line) to scenario #1: exempting food from taxation barely increases progressivity once the exemption of the informal sector is taken into account.

# **4.2 Progressivity across Development**

The evidence presented in Figure 5 for the average country masks considerable heterogeneity across countries. We now turn to characterizing how the progressivity of our policy scenarios changes over the development path. To summarize the progressivity of a scenario we use the ratio of the effective tax rate paid by the richest quintile to that paid by the poorest quintile. The higher this metric, the more progressive the tax policy (a value _>_ 1 implies a progressive tax policy). This metric does not depend on the tax rate used, and is frequently used in the literature (Sah, 1983; Srinivasan, 1989).

Figure 6 plots the country-level progressivity for each scenario as a function of countries’ economic development. Panel A shows that the de facto exemption of informal consumption leads to the most progressivity in the poorest countries, where the top 20% pay on average 3 times as much in taxes as the bottom 20%. In these countries formal consumption is rare and therefore a strong tag for household income. Over development, progressivity decreases. This is primarily driven by the steep increase in aggregate formal budget shares (Figure 3, Panel A), which makes formal consumption a worse tag for income as countries become richer. Between low and lower-middle income countries, this negative budget share effect dominates the positive effect on progressivity from a rise in the slope of the formal Engel curve (Figure 3, Panel B). Between lower17
middle and upper-middle income countries, the formal Engel slope falls, contributing to the decrease in progressivity.

In Panel B of Figure 6, we study progressivity of the de jure food exemption in the unrealistic setting with perfect enforcement and no informal consumption (scenario #2). The de jure food exemption is substantially less progressive than the de facto informal sector exemption (scenario #1) in the poorest countries, while both scenarios achieve similar levels of progressivity in upper-middle income countries. This is because the non-food budget share is much larger than the formal budget share in the poorest countries (making formal consumption a much better tag for household income than nonfood and much less than formal shares over consumption), grows budget development (Figure 4). Finally, by comparing Panel C (scenario #3) to Panel A (scenario #1), we find that de jure exemptions have no effect on progressivity in the poorest countries once the de facto exemption of the informal sector is taken into account. It has a positive impact however in upper-income-countries. This is because the formal food Engel curve is roughly flat in poor countries, and downward sloping among the richest countries in our sample (Figure 4).

# **4.3 Extensions and Robustness**

**Pass-through of taxes in the informal sector** Our analysis thus far assumes zero passthrough of taxes to prices of informal varieties. This assumption may not hold, for several reasons. First, if the consumption tax is a VAT, informal retailers may pay taxes on their inputs from formal suppliers. Second, competition between formal and informal retailers could lead informal retailers to tax increases to We relax pass through prices. this assumption by allowing some pass-through of taxes to informal prices. In Appendix C.6, we show that under a VAT system the pass-through of taxes to informal prices is equal to the share of formal input costs in informal retailers’ total input costs. Using the Mexican census data described above we find that this share is on average 10% among all informal retailers.<sup>29</sup>

Table A6 summarizes our progressivity results under the assumption of a 10% pass-

> 29In the 2013 Census, 85% of retailers are informal by not reporting any payment on VAT. Among informal retailers, only 8% report paying VAT on inputs, which applies on average to 40% of their intermediate input purchases. The informal retailers that report positive VAT on inputs account for 25% of all informal sales. Combined, this leads to our estimate of 10%.

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through of taxes to informal prices.<sup>30</sup> The results are partially affected but our key findings remain. First, we find that scenario #1 (exemption of informal varieties) remains very progressive, with the richest quintile paying over 70% more in taxes than the poorest quintile on average. Second, the de facto exemption of the informal sector continues to be more progressive than de jure exemption of food (scenario #2), although the difference in progressivity has decreased. Third, the progressivity impact of the de jure exemption, conditional on allowing for informal consumption, remains smaller than that of the de facto exemption.

**Distributional savings rates** Our baseline results use total expenditures to proxy for household income, assuming households do not save. Intuitively, allowing for savings both decreases effective tax rates (as savings are not taxed) and decreases the progressivity of all tax scenarios if saving rates increase with income.<sup>31</sup> The distribution of savings across income levels is hard to obtain from expenditure surveys, especially in developing countries where income is hard to measure. To assess how savings could affect our results, we use data from the US Consumer Finance Survey, in which savings rates range from 0% for the poorest households to 15% for the richest quintile.<sup>32</sup> Results are presented in Table A6: allowing for distributional savings decreases the progressivity of all scenarios, as expected, but our main findings are unchanged.

**Alternative formality assignment** Finally Table A6 presents our progressivity results under the two alternative rules for of as formal or in- categorizing places purchases formal, as described in Section 2.2 (the probabilistic formality assignment based on the 2013 Mexican Census of retailers and the assignment of specialized stores to the informal sector). Our three main take-aways are unchanged.

> 30 The share of formal inputs used by informal firms is likely to be an upper bound. First, the 10% number is applied to both fixed and non-fixed establishments, while the latter category (which includes street stalls) is likely to source fewer inputs from formal firms. For this reason, we maintain a 0% passthrough for home production. Second, in Mexico, it is the large informal stores which use formal inputs: The use of formal inputs for smaller stores is closer to 5% on average. Third, segmentation between formal and informal firms is likely to be even larger in poorer countries, leading to lower average pass-through in those countries than in Mexico.

> 31Calculations based on annual income may overstate the regressive nature of consumption taxes since consumption depends on lifetime income, which is less volatile than annual income (Poterba, 1989; Caspersen and Metcalf, 1994).

> 32Source: 1985 US Consumer Finance Survey. Savings rates are in the same range in the few developing countries (China and Chile) for which similar consumer finance surveys are available.

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# **5 Optimal Consumption Tax Policy with an Informal Sector**

## **5.1 Set-up**

This section studies the implications of the novel consumption facts for optimal tax policy. We extend the multi-person Ramsey model of commodity taxation (Diamond, 1975) to a context in which informal varieties of each good cannot be taxed. We then derive optimal tax rates for three policy scenarios and study the changes in optimal rates as consumption patterns change over development. The scenarios are closely related to those in Section 4, but studying optimal tax policy enables us to relax the assumption that differentiating tax rates between food and non-food goods must take the form of full tax exemption of food. We study instead the optimal level of rate differentiation between these two goods categories.<sup>33</sup> Proofs of results are in Appendix C.

**Household preferences** There is a continuum of mass 1 of households _i_ with hetero. geneous exogenous incomes _y_<sup>_i_</sup> Households have preferences over _j_ goods, and for each good over two varieties _v_ , which we assume are imperfect substitutes. The subscript _v_ = 0 indicates a variety produced in the informal sector, _v_ = 1 a variety produced in the formal sector. In most of what follows we assume informal varieties cannot be taxed. Producer prices _qjv_ are exogenous, consumer prices are given by _pj_ 1 = _qj_ 1(1 + _tj_ ), where _tj_ is the tax on good _j_ , and _pj_ 0 = _qj_ 0. These consumer prices reflect the commonly made assumption that there is full (no) pass-through of taxes to formal (informal) consumer prices.<sup>34</sup> We write _v_ ( _p_ , _y_<sup>_i_</sup> ) the indirect utility of household _i_ , _s_<sup>_i_</sup> _jv_<sup>thebudgetsharethat</sup> household _i_ spends on variety _v_ of good _j_ , _s_<sup>_i_</sup> _j_<sup>=</sup><sup>_si_</sup> _j_ 0<sup>+</sup><sup>_si_</sup> _j_ 1<sup>thebudgetshareitspendson</sup> good _j_ , and _εj_ the price elasticity of demand for good _j_ .

We impose additional structure on household preferences to characterize how the cost of taxation the We assume that com- efficiency changes along development path. pensated price elasticities of demand for all goods are equal across households, across products and with development. We set elasticities of substitution across goods equal to zero but allow a positive cross-price elasticity of demand across varieties. This enables us to focus on households’ responses that arise in the presence of an informal sector due to substitution across varieties within each good. This substitution is governed by the

> 33We focus in this section on optimal rate differentiation between these two categories only for simplicity, and because of the policy relevance of this scenario. Our expressions can however be used to consider a government that optimally differentiates rates across a large number of categories; we show results from this full rate differentiation in Section 6.2 below.

> 34Appendix C shows that a simple model in which formal and informal firms compete under monopolistic competition yields these patterns of pass-through.

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cross-variety price elasticities of demand, which are assumed equal across all goods and invariant along the development path. We allow for differences in income elasticities across goods and varieties but assume income effects are fixed across development.

this structure on allows us to determine how uncom- Imposing preferences clearly pensated price elasticities, which drive the efficiency costs of taxation, vary across products and along the development path. In Appendix C, we show that the uncompensated price elasticity of demand for a formal variety of a good, denoted _εj_ 1, can be expressed as a function of compensated price elasticities, income elasticities, and budget shares: This elasticity captures the efficiency cost of taxing only the formal variety of good _j_ and is composed of three components. The first is the compensated price elasticity of demand for a good, _ε_<sup>_C_</sup> . The second is an income effect driven by the income elasticity of demand for the formal variety _ηj_ 1 and its budget share _sj_ 1. The third is a function of the compensated cross-price elasticity of demand, denoted _ε_ ̃<sup>_C_</sup> , and the share of informal consumption in total consumption of good _j_ , denoted _αj_ .<sup>35</sup> Intuitively, as the price of formal varieties increases, households can substitute to informal varieties: this increases the price elasticity of the formal variety, the more so the more households are willing to substitute across varieties (higher _ε_ ̃<sup>_C_</sup> ).

**Government preferences** The government chooses the tax rates _tj_ levied on each good _j_ to maximize:

where _xj_ 1 =<sup>�</sup> _i_<sup>_xi_</sup> _j_ 1<sup>(</sup><sup>_p_,</sup><sup>_yi_) is total consumption of the formal variety of good</sup><sup>_j_.Govern-</sup> ment preferences are characterized by _μ_ , the marginal value of public funds, and _G_ (), an increasing and concave social welfare function. We write _g_<sup>_i_</sup> household _i_ ’s social marginal welfare weight, which represents how much the government values giving an extra unit of income to household _i_ , and _g_ ̄ is the average social marginal welfare weight (see Saez and Santcheva, 2016).<sup>36</sup> We assume that _g_<sup>_i_</sup> is decreasing with household income and _μ_ = _g_ ̄. The latter simplifies expressions and corresponds to a government that has no

> 35This expression also assumes variety-level own-price elasticities of demand are equal across varieties for each good, and differences in prices across varieties are negligible, such that _pj_ 0 _≈ pj_ 1. Section 3 presents evidence regarding the value of _p_<sup>_<u>p</u>_</sup> 0<sup><u>1</u>.Inallcountriesthedifferencebetweenpricesofformaland</sup> informal varieties is small, around 5%.

> 36Formally _gi_ =<sup>_∂G_</sup> _∂_<sup><u>(</u></sup> _v_<sup>_v_</sup> (<sup><u>(</u></sup> _p_<sup>_<u>p</u>_</sup> , _y_<sup><u>,</u></sup><sup>_<u>yi</u>_</sup> )<sup>_i_</sup><sup><u>))</u></sup> _∂v_ <u>(</u> _∂py_ <u>,</u><sup>_i_</sup> _<u>y</u>_<sup>_i_</sup> <u>)</u> .

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preference assumption for taxation unless it enables redistribution.

# **5.2 Optimal Tax Policy over the Development Path**

In this sub-section, we consider how optimal tax policies vary with development. We model as an increase in all households’ income the same development by proportional amount, so that the distribution of income across households does not change, and assume it leads to the changes in budget shares and Engel curve slopes documented in Section 3. To build intuition, and consistent with our empirical evidence, we assume that the Engel curves of all taxed goods are approximately linear with respect to log household income. We relax this assumption when we calibrate the model to our data. We first consider optimal uniform taxation in a world in which only formal varieties can be taxed. We then consider optimal rate differentiation between food and non-food in a counterfactual with enforcement where all varieties can goods: first setting perfect be taxed; then, in the realistic setting in which only formal varieties can be taxed.

# **5.2.1 Optimal Uniform Commodity Taxation**

We start that the levies a uniform tax rate on all by assuming government products, _tj_ = _t_ , _∀j_ , but cannot tax informal varieties. Writing _τ_ = 1+ _<u>t</u> t_<sup>,welfaremaximization</sup> yields the following expression for the optimal uniform rate: where _s_ 1 = ∑ _j_ � _i_<sup>_si_</sup> _j_ 1<sup>_di_istheaggregatebudgetsharespentonallformalvarieties,</sup><sup>_φi_=</sup> _<u>yy</u>_ ̄<sup>_i_istheratioofhousehold</sup><sup>_i_’sincomerelativetotheaverageincome</sup><sup>_y_ ̄and</sup><sup>_ε_1isthe</sup> uncompensated price elasticity of demand for all formal varieties. Equation (6) shows that the optimal uniform rate is increasing in the co-variance between household income and formal budget shares: the more richer households spend on formal varieties relative to the poor, the more redistribution is obtained from taxing only formal varieties and the higher the optimal rate on those varieties. The optimal rate is also decreasing in the absolute value of the uncompensated price elasticity of demand for formal varieties: the more households respond to changes in formal prices by consuming fewer formal varieties, the higher the efficiency cost of taxing only those formal varieties.

The change in the optimal uniform rate over the development path is given by: 22
The first and second terms capture, respectively, the change in the redistributive effect and efficiency cost of taxing only formal varieties. The direction of these changes is summarized in the following proposition.

# **Proposition 1.** **_Optimal uniform commodity taxation when only formal varieties can be taxed_**

- _The redistribution gain from taxing all products uniformly is decreasing over the development path as long as: i) the formal Engel curve is upward sloping, ii) the aggregate formal budget share increases more than the slope of the formal Engel curve._

- _The efficiency cost of taxing all products uniformly is decreasing over the development path as long as, in addition, ε_  ̃<sup>_C_</sup> _>_<sup>_<u>η</u>_</sup> 2<sup><u>1</u></sup><sup>_, whereη_1</sup><sup>_is the income elasticity of demand for all formal_</sup> _varieties ε_  ̃<sup>_C_</sup> _is the cross-variety price elasticity of demand._

_Proof: see Appendix C._ The first part of Proposition 1 formalizes the intuition (outlined in Section 4) for how in the formal shares and of the formal curve af- changes aggregate budget slope Engel fect the redistributive effect of taxing formal varieties. As shown above, formal Engel curves are upward sloping in all countries. Among poorest countries, the likelihood that a formal variety purchase is made by rich households is high because the aggregate formal budget share is small. As this budget share increases with development, formal purchases become a worse tag for higher household income. This decreases the redistribution gain from taxing all formal varieties, and therefore pushes the optimal rate on these varieties downwards, as long as the slope of the formal Engel curve does not increase substantially with development.

The second part of Proposition 1 states the conditions under which efficiency considerations will on the contrary push the optimal uniform rate upwards over development. The increase in aggregate formal consumption share over development lowers the opportunities for substitution towards informal varieties; this decreases the efficiency cost of taxing all formal varieties (see equation 4). At the same time, the growth in formal consumption share increases the responses to changes in prices due to income effects, which leads to higher efficiency costs. The first effect dominates as long as _ε_ ̃<sup>_C_</sup> _>_<sup>_<u>η</u>_</sup> 2<sup><u>1</u>.</sup> Overall, the presence of large informal sectors in poorer countries tends to increase both 23
the redistributive gain and the efficiency cost of taxing consumption relative to richer countries with smaller informal sectors.

# **5.2.2 Optimal Rate Differentiation When All Varieties Can Be Taxed**

We now turn to a government which sets a different rate on food and non-food goods. We start by considering rate differentiation under the assumption that the government has perfect enforcement capacity and can therefore tax both formal and informal varieties.<sup>37</sup> This unrealistic assumption enables us to consider how optimal rate differentiation would change over the development path in the absence of an informal sector and a ’no enforcement constraint’ benchmark which to more provides against compare realistic scenarios in the following section. The optimal rate on product _j_ is given by: This expression shows that the optimal rate is increasing in the co-variance between household income and budget share spent on good _j_ . We know from Section 3 that the slopes of all non-food (food) Engel curves are positive (negative). Holding efficiency considerations constant, this implies that the optimal policy taxes food less than nonfood goods.

The following proposition characterizes the change in the optimal tax on food relative to non-food over the development path.

# **Proposition 2.** **_Optimal rate differentiation when all varieties can be taxed_**

- _The redistribution gain from taxing food less than non-food goods is increasing over the development path as long as: i) food Engel curves are downward sloping, ii) aggregate food budget shares decrease, iii) the aggregate food budget share is lower than the aggregate non-food budget share, iv) food Engel curves do not flatten too much._

- _In addition, the efficiency cost of taxing food less than non-food products increases with development as long as non-food budget shares increase._

# _Proof: see Appendix C._

The first part of proposition 2 states the conditions under which the redistribution gain from rate differentiation increases over development. Intuitively, for a given Engel

> 37Formally we assume that _tj_ is levied on both _xj_ 1 and _xj_ 0, so that _pj_ 0 = _qj_ 0(1 + _tj_ ).

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curve slope, this redistribution gain is minimized when food and non-food aggregate budget shares are equal: in this case, observing a food or non-food purchase yields little information about a household’s income, such that differentiating rates across these categories has little redistributive effect. This is the situation in the poorest countries in our sample where food and non-food goods are consumed in roughly equal proportions. As countries grow the food budget shares fall, so food purchases become a better tag for household income. This increases the optimal level of rate differentiation (decreasing the optimal rate on food relative to non-food) over the development path, as long as food Engel curves do not flatten too much.<sup>38</sup> The second part of Proposition 2 states that efficiency considerations will on the conincrease the rate on food relative to non-food over trary optimal development (decrease rate differentiation). The intuition for this stems from the fact that the average budget share spent on food falls while that spent on non-food products increases as countries grow. This decreases the efficiency cost of taxing food relative to non-food products due to income effects.

# **5.2.3 Optimal Rate Differentiation When Only Formal Varieties Can Be Taxed**

Finally, we consider optimal rate differentiation under the more realistic assumption that informal varieties cannot be taxed. The optimal rate on product _j_ when only variety _j_ 1 can be taxed is now given by: The following proposition characterizes the change in the optimal tax on food relative to non-food products over the course of development when only formal varieties can be taxed.

# **Proposition 3.** **_Optimal rate differentiation when only formal varieties can be taxed_**

- _The redistribution gain from taxing food less than non-food products is increasing over the development path as long as: i) the slope of the Engel curve for formal food varieties decreases relative to that for formal non-food varieties, ii) the aggregate budget share of_

> 38Condition iii) is not strictly necessary, but constitutes the relevant empirical setting we observe in Section 3: food budget shares are typically smaller than non-food budget shares in our sample. In Appendix Section C, we show that proposition 2 holds even when the food budget share is higher that the non-food budget share, as long as the slope of the food Engel curve increase sufficiently in magnitude as countries develop.

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_formal non-food varieties does not increase much faster than the aggregate budget share of formal food varieties._

- _The efficiency cost of taxing food less than non-food products increases with development as long as, in addition, the informal share of food consumption falls faster than that of non-food consumption._

_Proof: see Appendix C._ The first part of Proposition 3 states under what conditions equity considerations push the optimal rate of food down relative to that on non-food goods over the development path. As discussed above, the Engel curve slopes for formal food varieties are very close to zero in the poorest countries in our sample. In these countries subsidizing food relative to non-food products will therefore not necessarily be equity-improving. As countries grow however the Engel curve slopes of formal non-food varieties grow, whilst those of formal food varieties fall (see Figure 4). This change in slopes increases the redistributive gain from subsidizing food relative to non-food over the development path, as long as the aggregate budget share of formal non-food products does not increase too much with development relative to that of formal food products.

The second part of Proposition 3 states that, in contrast, efficiency considerations tend to push the optimal relative rate on food down over development. Recall from expression (4) that the efficiency cost of taxing only the formal variety of a good is increasing in the share of informal consumption in total consumption of that good. Over the development path these informal shares fall, lowering the efficiency cost of taxing both food and nonfood products. They fall faster for food products than for non-food products, however (see Figure A12). This implies that the efficiency cost of taxing formal food varieties drops faster than that of taxing non-food formal varieties as countries grow.<sup>39</sup>

# **6 Implications for Redistribution and Inequality**

This section presents the implications of our results for the impact of consumption tax policy on disposable income inequality in developing countries. The extent to which a tax policy redistributes across households depends on both its progressivity (studied in Section 4) and the average effective tax rate levied. The latter is itself a function of the level of the statutory tax rates, which we obtain from our model, and the size of the tax

> 39In addition, it must be that the aggregate budget share of formal non-food products does not increase much faster than that of formal food products over development. This ensures that behavioral responses to taxation through income effects do not increase much faster for food products.

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base, which varies across tax scenarios. We calibrate the optimal tax rates in section 6.1, and then calculate the effect of different tax policy scenarios on inequality in section 6.2.

# **6.1 Calibrated Optimal Tax Rates**

This sub-section calibrates the optimal tax rates defined in expressions (6), (8) and (9). Table 4 summarizes our choice of calibration parameters. We calibrate several parameters directly from our data: we use the observed budget shares described in section 3, total household expenditure to proxy for household income, the slopes of the Engel curves to obtain income elasticities, and the observed informal budget shares for each good and country.<sup>40</sup> We relax our theoretical assumptions that Engel curves are loglinear and that inequality is fixed, using instead the observed budget shares and income distributions in each country. We consider a range [1,2] for the cross-variety compensated price elasticity. This is in line with estimates in Faber and Fally (2017) and Atkin et al. (2018b), and we use 1.5 as our baseline value, while setting a value of -0.7 for the own-price compensated elasticity of goods. Together, these parameters yield values for the own-price uncompensated elasticity of goods that are in the [ _−_ 2.2, _−_ 0.7] range, in line with estimates from the literature (Deaton et al., 1994). Finally, we specify government preferences by setting a social welfare weight for households in each decile of the household expenditure distribution in each country. Our specification implies that governments place 10 times more weight on income received by households in the poorest decile than in the richest decile. Our calibration choices yield optimal uniform rates in the 10% to 25% range, in line with the range of statutory consumption tax rates set by developing countries. Appendix D details our calibration choices further.

Figure 7 plots the country-level ratio of optimal food to non-food rate (the relative food subsidy) as a function of economic development. The left two panels refer to the counterfactual scenario where all varieties are taxed; the right panels refer to the more realistic scenario where only formal varieties are taxed. The top panels show calibrated rates holding uncompensated price elasticities constant over development: in these figures all the variation across countries is due to varying redistribution gains from differentiating rates. The bottom panels allow price elasticities to vary with development:

> 40Our model calls for using budget shares observed under a counterfactual ’no tax or transfers’ scenario. We do not attempt to adjust observed budget shares to take into account the fact that they are affected by current tax systems as this would require an in-depth understanding of the tax and transfer system in each country in our sample which is beyond the scope of this paper.

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here, the variation is due to both redistribution gains and efficiency costs.<sup>41</sup> There are two main take-aways from Figure 7. First, consistent with our model predictions, we find that over development, equity considerations tend to decrease the rate on food relative to non-food goods (thus increasing rate differentiation) but efficiency considerations tend to increase it. Equity effects dominate, so that optimal relative rates on food fall with development when both effects are taken into account. Second, comparing panels B and D, we see that once we take into account the fact that only formal varieties can be taxed, the optimal policy no longer subsidizes food relative to non-food in some poor countries (the ratio of food to non-food rates is higher than 1). Once the impossibility of taxing informal varieties is accounted for, taxing food less than nonfood goods cannot by justified on equity or on efficiency grounds in these countries. Appendix Figure A14 shows that both of these findings are robust to changing values of the cross-variety price elasticity.<sup>42</sup>

# **6.2 Effect of Consumption Tax Policy on Inequality**

Figure 8 presents the effects of different consumption tax scenarios on income inequality in the average country in our sample. In Panel A we use the calibrated optimal tax rates for each scenario (allowing efficiency costs to vary with development) and use these rates to calculate the net of tax income of each household in our data. Our redistribution metric is the percent change in Gini from the pre-tax income distribution to the netof-tax distribution. To benchmark our results against estimates in the literature, Panel B reports the inequality impacts of actual tax policies in place in a comparable sample of developing countries obtained by Lustig (2018). To calculate these effects, we use their Commitment to Equity (CEQ) database which contains information on income and estimates of taxes paid (consumption taxes, direct taxes and social security) for each income decile in 25 developing countries.<sup>43</sup> Importantly, their methodology does not systematically consider the possibility that some places of purchase may be informal,

> 41Formally, in the top panels we set the uncompensated price elasticities in expressions equal to -1 for all countries when calibrating expressions (6), (8) and (9). In the bottom panels we calibrate these elasticities using expression (4) and the parameter values detailed in Table 4.

> 42In Appendix Figure A13 we also show the calibrated optimal uniform rates on all formal varieties. Consistent with our theory, the optimal uniform rate falls over development for redistributive purposes. As predicted, allowing efficiency costs to vary with development lowers the optimal rates, especially in the poorest countries and more so the higher the cross-variety elasticity of substitution.

> 43In the first row of Panel B, we calculate the change in Gini from applying general consumption and excise taxes to disposable income plus indirect subsidies. In the second row of Panel B, we calculate the change in Gini from applying the direct tax and social security contributions to market income plus direct cash transfers. These exercises allow us to calculate the marginal Gini impacts of the indirect and direct tax systems, respectively.

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and therefore cannot take into account the redistributive effect of de facto exemption of informal consumption.

Several key results emerge from Figure 8. First, our different optimal consumption tax scenarios achieve substantial reduction. The effects are policy inequality inequality large compared to estimates of the effect of current consumption tax policies, which suggest consumption taxes in developing countries achieve very little inequality reduction (0.3% reduction in Gini, row 1 of Panel B), despite taking into account reduced rates and exemptions. On the contrary, we find that when we take into account the de facto exemption of informal varieties, simply setting a uniform rate on all goods achieves a non-trivial inequality reduction (a 2.3% decrease in the Gini, row 1 of Panel A). Second, the amount of redistribution achieved by this scenario is still large when we compare it to a scenario with perfect enforcement in which governments optimally differentiate rates on food and non-food products (row 2 of Panel A). Comparing rows 1 and 2 of Panel A, we see that taxing only formal varieties achieves 75% of the inequality reduction obtained under the perfect enforcement and de jure rate differentiation scenario.<sup>44</sup> Third, introducing rate differentiation on top of de facto exemption of the informal sector further reduces inequality (row 3 of Panel A). Comparing rows 1 and 3, however, we see that simply setting a uniform rate on all goods achieves two-third of the redistribution obtained by optimally differentiating rates once we assume that only formal varieties can be taxed.

Finally, by comparing panel A to row 2 of Panel B, we find that our estimated effects of consumption tax policy on inequality have the same magnitude as the effect of the direct tax system (income taxes and social security) in developing countries.<sup>45</sup> We note however that the redistributive potential of direct tax systems in these countries is constrained because they only cover the small share of the workforce which is not selfemployed (Jensen, 2019). Direct tax systems that do not face this constraint have a much larger effect on inequality.<sup>46</sup>

> 44Optimally differentiating rates when all varieties are taxed reduces inequality substantially, despite the relatively small progressivity achieved by differentiating rates on food and non-food described in section 4.3. It occurs because this (unrealistic) scenario assumes the government can tax the entire consumption base, which yields much higher effective tax rates.

> 45Since direct taxes are generally considered most strongly suited for redistribution, our results are large in magnitude among tax policy impacts. They are, however, smaller in magnitude than the inequality reduction achieved in CEQ-countries by in-cash and in-kind transfers (Lustig, 2018).

> 46Using data from the OECD Income Distribution Database, we calculate that direct taxes in developed countries achieve a 11.2% Gini-reduction in inequality.

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# **6.3 Extensions and Discussion**

**Full rate differentiation** We have thus far only considered scenarios in which governments set at most two tax rates, on food and non-food goods. How much more inequality reduction can be achieved if we allow for different rates on each of the 12 large COICOP 2-digit good categories? To answer this, we calibrate optimal tax rates at the level of each good and for each country and recompute the changes in Gini.<sup>47</sup> The last two rows of Table A7 display the results. In the realistic case with an informal sector (last row), the inequality reduction achieved by full rate differentiation is 30% higher than that achieved by simply differentiating rates between food and non-food goods. Given that administrative costs from managing multiple rates may be high (Ebrill et al., 2001), this result further suggests a limited role for rate differentiation across goods in developing countries.

**Robustness** Table A7 reports a large range of robustness checks on our inequality results. First, we show that results are broadly robust to the checks implemented in Section 4 for the progressivity results. In particular, allowing for some pass-through of taxes to prices in the informal sector has two opposite effects on inequality which tend to cancel each other out. On the one hand, it decreases the progressivity of consumption tax scenarios in which the informal sector is exempt, as seen in Section 4. On the other hand, it increases the tax base (and therefore the aggregate effective tax rates), which reduces The effect dominates to lower effects on inequality. first slightly, leading marginally inequality. Allowing for distributional saving rates reduces the inequality effects, especially in the counterfactual scenario in which all varieties are assumed to be taxed, but our main results are unchanged. Changing the rule used to assign a place of purchase to the formal or informal sector similarly leaves our key results qualitatively unchanged. Second, in the final two rows of Table A7 we present results using alternative values of the cross-variety price elasticity of demand. This is the parameter which governs the strength of the efficiency cost of taxation. Our results are largely unchanged.

**Absence of direct tax instruments** Our result that indirect taxes are optimal robustly redistributive is derived in a model where no direct tax instrument is available. A central result in public finance is that redistribution is better achieved through direct rather than indirect taxes (Atkinson and Stiglitz, 1976; Jacobs and Boadway, 2014). However, this theoretical result relies on the assumption that income taxes cannot be evaded, which is at odds with reality in developing countries (Jensen, 2019). When income taxes can be

> 47Formally, we re-calibrate expressions (8) and (9) for each good and country.

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evaded, a greater redistributive role is found for indirect tax instruments (Boadway et al., 1994; Huang and Rios, 2016).<sup>48</sup> This discussion suggests that an extended model with direct tax instruments, even constrained, would lead to less optimal redistribution through consumption taxes. Jointly studying the optimal direct and indirect tax instruments over development would, however, require additional empirical moments, including how opportunities to evade income taxes vary along a country’s income distribution and as the country develops. Such an undertaking is beyond the scope of this paper.

# **7 Conclusion**

In this we how with household income both paper study consumption patterns vary within and across countries and derive implications for the optimal design and redistributive potential of consumption taxes. We consider two channels for redistribution: the de facto tax exemption of informal expenditure and the de jure tax exemption of necessities, in particular food. To measure informal expenditure, we harmonize expenditure surveys across 31 developing countries which contain information on the place of for each transaction. We each of to the informal or purchase assign place purchase formal sector using a robust assignment rule, and calculate the informal budget share at the household level. This enables us to characterize Curves: we Informality Engel find that informal budget shares decrease with household income in every country. This implies that the de facto exemption of the informal sector is progressive. We then extend the standard optimal commodity tax model to allow for informal consumption and calibrate it to our data to the effects of different tax on study policies inequality. Contrary to the existing consensus, we find that consumption taxes are redistributive, lowering inequality by as much as personal income taxes in developing countries. This effect is mainly driven by the existence of the informal sector. Once informal consumption is accounted for, reduced rates on necessities only have a limited impact on inequality.

Our findings have sharp implications for the use of reduced rates on necessities and on food items in particular. We find that differentiating rates across goods has limited redistributive potential once informal consumption is accounted for. In particular, these have no redistributive in some of the countries in our policies impact poorest sample. As practice shows, removing reduced rates on food and other necessities is often met with fierce resistance. An equity-improving policy would most likely have to combine

> 48For example, Huang and Rios (2016) find that incorporating income tax evasion and the existence of a consumption tax reduces the optimal income tax by 28%. Note that Boadway et al. (1994) and Huang and Rios (2016) both assume consumption taxes are perfectly enforceable. Given our findings, incorporating consumption tax evasion in their models would further reinforce the redistributive role of indirect taxes.

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the removal of reduced rates with further investments in transfer and social programs protection (Hanna and Olken, 2018). Finally, our results do not mean that efforts to reduce the size of the informal sector should be abandoned; rather, they caution that any benefits from reducing the informal sector’s size should be weighed against the distributional costs. Currently, firms below a size threshold are often exempt from taxation. This policy is typically motivated by the large compliance costs of monitoring smaller firms incurred by tax administrations. The growing availability of digital technologies could lower these monitoring costs and make it possible to bring increasingly smaller firms into the tax net, removing the administrative rationale for exempting small firms from taxation. Our results suggest that this policy could however still be justified on equity grounds.

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Figure 1: Employment Size, Store Types & Formality

- (a) # Employees on Formality in Retail Censuses

<!-- Start of picture text --> Rwanda<br>Cameroon<br>Peru<br>Mexico<br>0 1 2 3 4<br>Log Employment<br>1<br>.8<br>.6<br>Share Formal .4<br>.2<br>0<br><!-- End of picture text -->

- (b) # Employees by Store in Mexico

- (c) % Paying VAT by Store in Mexico

<!-- Start of picture text --> (1) Non-Market N.A. (1) Non-Market N.A.<br>(2) Non-Brick & Mortar (2) Non-Brick & Mortar<br>(3) Convenience Stores (3) Convenience Stores<br>(4) Specialized Stores (4) Specialized Stores<br>(5) Large Stores (5) Large Stores<br>0 1 2 3 4 5 0 .2 .4 .6 .8 1<br>Log of Median Number of Employees Share of Firms Reporting VAT Payments<br><!-- End of picture text --> These panels shows the association between formality status, employment and firm type. Panel A shows the share of formal firms as a function of log employment, using retail censuses of four core sample countries (Cameroon, Mexico, Peru and Rwanda). Formality is defined as ’being registered with the tax authority’ in Cameroon and Rwanda, and ’paying Value-Added-Taxes on sales’ in Mexico and Peru. Panels B and C use the 2013 Mexican retail census, which classifies retailers in similar categories as our broad place of purchase taxonomy. The figures show the log median number of employees by place of purchase (Panel C) and the share of firms paying Value-Added-Taxes on sales (Panel C). The data comes from the following firm censuses, keeping only firms which operate in the retail sector: Recensement G ́en ́eral des entreprises 2016 (Cameroun), Censo Econ ́omico 2014 (Mexico), Censo Nacional Econ ́omico 2008 (Peru), Establishment Census 2011 (Rwanda).

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Figure 2: Selected Informality Engel Curves <!-- Start of picture text --> (a) Rwanda (b) Mexico<br>6 7 8 7 8 9<br>Log Expenditure per Person, Constant 2010 USD Log Expenditure per Person, Constant 2010 USD<br>100 100<br>80 80<br>60 60<br>40 40<br>Informal Budget Share Informal Budget Share<br>20 20<br>0 0<br><!-- End of picture text --> These panels show the local polynomial fit of the Informality Engel Curves in Rwanda (Panel A) and Mexico (Panel B). Per person total expenditure on the horizontal axis is measured in log. Informal budget share is on the vertical axis. The shaded area around the polynomial fit corresponds to the 95% confidence interval. The solid grey line corresponds to the median of each country’s expenditure distribution, while the dotted lines correspond to the 5th and 95th percentiles. See Appendix Figure A1 for each core sample country’s informality Engel curve.

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Figure 3: Informal Expenditure Across Countries

# (a) Informal Budget Share (b) Informality Engel Curve Slope

<!-- Start of picture text --> BI CD<br>NE<br>BFTD TZBJ ST SN CG BI CD CL<br>MZ RW KMCM PG NE BJ ST CG<br>TD<br>BO TZ CM PG ZA CRBR<br>MA MZ BF RW KM BO CO<br>EC RSPE SZ UYMX<br>TN TN<br>DO<br>SZ DOCOME MXBR SN MA<br>PEME<br>CR CL EC<br>UY RS<br>ZA<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>5<br>100<br>0<br>80<br>−5<br>60<br>−10<br>40<br>−15<br>Informal Consumption Share 20 Informal Consumption Slope<br>−20<br>0<br>−25<br><!-- End of picture text --> Panel A plots country-level informal budget shares on log per capita GDP. The average informal budget share is 52%. Panel B shows the slope of the informality Engel curves on log per capita GDP. The average slope is 9.8. The bars correspond to the 95% confidence interval of the slope coefficient. GDP per capita is in constant 2010 USD (Source: World Bank WDI).

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# Figure 4: Food Expenditure Across Countries

## (a) Food Budget Share

## (b) Food Engel Curve Slope

<!-- Start of picture text --> Core Sample β Core Sample<br>Extended Sample β Extended Sample<br>CG<br>CD TD PG M Z<br>MZ CD RW<br>ST<br>BI N E TZ SNKM M AC G SZ RS TD ST PG SZ CRBR<br>BF R BJW BO PM E E MX NE BF BJ KMCM MA TN ZA UY CL<br>CM TN EC BI BO DOCOME MX<br>CO ECPE<br>DO ZA CRUYBR SN<br>CL<br>TZ<br>RS<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>(c) Formal Food Budget Share (d) Formal Food Engel Curve Slope<br>Core Sample PG<br>MA SZ<br>BI CDNE MZ BF TD RWTZ BJ ST SNKM CMBO CG TN DOECCORSPEME CRUYMXBR<br>ZA<br>CL<br>SZ<br>ME<br>PG TN RS ZA CRUYMX<br>MZ ST MA CO BR CL<br>BI CD NE BF TD RWTZ BJ SNKMCMBO CG DOEC PE β Core Sample<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>5<br>100<br>0<br>80<br>-5<br>60<br>-10<br>40 -15<br>Food Budget Share<br>Food Engel Curve Slope -20<br>20<br>-25<br>0<br>5<br>100<br>0<br>80<br>-5<br>60<br>-10<br>40<br>-15<br>Formal Food Budget Share 20<br>Formal Food Engel Curve Slope -20<br>0<br>-25<br><!-- End of picture text --> This figure combine two sources: data from the core-sample of 31 countries and data from the Global Consumption Database (GCD) which adds 58 developing countries not included in the core-sample. Panel A shows each country’s food budget share, plotted against log per capita GDP. The average food budget share in the core sample is 49%, while the average in the GCD sample is 48%. Panel B shows the countryspecific slope of the food Engel curve, plotted against log per capita GDP. The average slope in the core sample is 12.5, while the average in the GCD sample is 13. The lines correspond to local polynomial fits. GDP per capita is in constant 2010 USD (Source: World Bank WDI). Panels C and D are constructed similarly to Panel A and B, but for formal food expenditure which can only be measured in the core sample.

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Figure 5: Progressivity of Tax Policy Scenarios <!-- Start of picture text --> Uniform rate, only formal taxed<br>Food exempt, formal & informal taxed<br>Food exempt, on l y formal taxed<br>1 2 3 4 5 6 7 8 9 10<br>Decile of Expenditure Distribution<br>.16<br>.14<br>.12<br>.1<br>.08<br>Taxed Budget Share<br>.06<br>.04<br><!-- End of picture text --> This figure plots the share of expenditures that is paid in taxes (effective tax rates), by decile, for each tax scenario. The three scenarios are simulated in all 31 countries, each point corresponds to the average effective tax rates of each decile across all countries in our sample. The red-circle line corresponds to a tax scenario where a uniform tax is levied on all goods, but where purchases in informal stores are de facto not taxed (scenario #1 defined in Section 4). The green-cross line corresponds to a scenario where food purchases are de jure exempt, but where formal and informal stores are taxed (scenario #2 in Section 4). The green-square line corresponds to a tax scenario where both de facto informality exemption and de jure food exemption are present (scenario #3 in Section 4).

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# <u>Figure 6: Progressivity over Development</u>

<!-- Start of picture text --> (a) Formal Taxed (b) Non-Food Taxed (c) Formal Non-Food Taxed<br>SN<br>MZ<br>PG<br>SN<br>CD BF RW BF RW<br>MZ<br>KM PG CD NE KM RS<br>TZ SN TD TZ MA<br>BI TD TZ MA BI ST<br>NE BJ ST CMBO CG TNSZ DOECCORSPEMEZA CRUYMXBR BI CDNE MZ BFTD RWBJ ST KMCMBO PG MA CG TNSZ DOECCORSPEMEZA CRUYMXBR CL BJ CMBO CG TNSZ DOEC CO PEMEZA CRUYMXBR CL<br>CL<br>5 6 7 8 9 10 5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>5 5 5<br>4 4 4<br>3 3 3<br>2 2 2<br>1 1 1<br>0 0 0<br>Budget Share Ratio Top 20-Bottom 20<br><!-- End of picture text --> These panels plot the ratio of effective tax rate paid by the richest quintile relative to the poorest quintile in each country as a function of the country’s level of economic development. The left panel corresponds to a scenario where a uniform tax is levied on all goods, but purchases in informal stores are de facto not taxed (scenario #1 in Section 4). The middle panel corresponds to a scenario where food goods are de jure exempt, but purchases in both formal and informal stores are taxed (scenario #2 in Section 4). The right panel combines de facto informality exemption and de jure food exemption (scenario #3 in Section 4). In each panel, the ratio is plotted for all 31 countries of our sample against log GDP per capita.

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# Figure 7: Optimal Rate Differentiation over Development

- (a) All Varieties Taxed, No Efficiency Change

<!-- Start of picture text --> (b) Only Formal Varieties Taxed, No Efficiency Change<br><!-- End of picture text --> <!-- Start of picture text --> CD<br>BJ CG<br>BI<br>KM<br>BF RW EC<br>CM<br>TD PGMA TN<br>CD RW PG CG MZ TZ STSN BO SZ DO ME CRUYBR<br>PE<br>MZ TD BJ ST KM MA TNSZ CRBR CORS ZA MX<br>BI NE BF CMBO EC CORSPEMEZA UYMX CL NE<br>TZ<br>SN DO<br>CL<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>(c) All Varieties Taxed, With Efficiency Change (d) Only Formal Varieties Taxed, With Efficiency Change<br>BR CD<br>RW TN CR BI BJ<br>CG CG BR<br>ZA UY CL CR<br>CD BF BJ KM BOPGMA SZ CO BFTD RWTZ KMCM PG TN ZA UY<br>BI MZ TD ST CM ME MX STSN BO MA SZ EC ME<br>NE EC PE MZ DO CO MX<br>RS NE RSPE<br>TZ DO<br>SN<br>CL<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>1.4 1.4<br>1.2 1.2<br>1 1<br>.8 .8<br>.6 .6<br>.4 .4<br>Ratio Food Rate / Non Food Rate .2 Ratio Food Rate / Non Food Rate .2<br>0 0<br>1.4 1.4<br>1.2 1.2<br>1 1<br>.8 .8<br>.6 .6<br>.4 .4<br>Ratio Food Rate / Non Food Rate .2 Ratio Food Rate / Non Food Rate .2<br>0 0<br><!-- End of picture text --> All panels plot for each country the ratio of the calibrated optimal rate on food products relative to the optimal rate on non-food products, as a function of that country’s log GDP per capita. Optimal rates are calibrated using expressions (8) (panels A and C) and (9) (panels B and D). A value equal to 1 indicates that both optimal rates are set at the same level, a lower value indicates that it is optimal to subsidize food products relative to non-food products. In panels A and C we assume that all varieties can be taxed; in panels B and D, we assume that only formal varieties can be taxed. In panels A and B we hold efficiency considerations constant by assuming that uncompensated price elasticities of demand are equal across goods and countries, while in panels C and D we allow price elasticities to vary across goods and countries by calibrating values using expression (4).

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# Tax Policy

Effect Size

|Panel A: Simulated Optimal Consumption Taxes (This paper N=31)||||
|---|---|---|---|
|Uniform rate, only formal taxed|@|||
|Food rate differentiation, formal and informal taxed|cra|||
|Food rate differentiation, only formal taxed|&|||
|Panel B: Studies Using CurrentTax Policies (CEQ N=25)||||
|Indirecttaxes: General consumption & excise|||r|
|Direct taxes: PIT & Social Security|e|||
|—_<br>-4.0|><br>r<br>-3.0<br>-2.0|r<br>-1.0|es<br>><br>0.0<br>0.5|
||PercentchangeinGini|frompolicy||
Table 1: Household Expenditure Surveys for Core Sample

|**Country**|**Code**|**Survey**|**Year**|**GDPper capita**|**Sample size**|**Nb items/HH**|
|---|---|---|---|---|---|---|
|**Benin**|BJ|EMICOV|2015|828|19871|32|
|**Bolivia**|BO|ECH|2004|1658|9149|49|
|**Brazil**|BR|POF|2009|10595|56025|41|
|**Burkina Faso**|BF|EICVM|2009|563|8404|152|
|**Burundi**|BI|ECVM|2014|245|6681|90|
|**Cameroon**|CM|ECAM|2014|1400|10303|81|
|**Chad**|TD|ECOSIT|2003|572|6697|94|
|**Chile**|CL|EPF|2017|14749|15239|129|
|**Colombia**|CO|ENIG|2007|5999|42373|60|
|**Comoros**|KM|EDMC|2013|1373|3131|82|
|**Congo DRC**|CD|E123|2005|301|12098|107|
|<br>**Congo Rep**|CG|ECOM|2005|2569|5002|85|
|<br>**Costa Rica**|CR|ENIGH|2014|8994|5705|68|
|**Dominican Rep**|DO|ENIGH|2007|5121|8363|88|
|**Ecuador**|EC|ENIGHUR|2012|5122|39617|89|
|**Eswatini**|SZ|HIES|2010|4169|3167|44|
|**Mexico**|MX|ENIGH|2014|9839|19479|61|
|**Montenegro**|ME|HBS|2009|6516|1223|149|
|**Morocco**|MA|ENCDM|2001|2095|14243|90|
|**Mozambique**|MZ|IOF|2009|416|10832|221|
|**Niger**|NE|ENCBM|2007|330|4000|192|
|**Papua NG**|PG|HIES|2010|1949|3810|111|
|**Peru**|PE|ENAHO|2017|6315|43545|78|
|**Rwanda**|RW|EICV|2014|690|14416|54|
|**Sao Tome**|ST|IOF|2010|1095|3545|100|
|**Senegal**|SN|EDMC|2008|1278|2503|299|
|**Serbia**|RS|HBS|2015|6155|6531|105|
|**South Africa**|ZA|IES|2011|7455|25328|44|
|**Tanzania**|TZ|HBS|2012|788|10186|318|
|**Tunisia**|TN|ENBCNV|2010|4142|11281|139|
|**Uruguay**|UY|ENIGH|2005|9079|7043|77|

This table lists alphabetically the 31 countries in the core sample, the survey names and years. GDP per capita is in PPP USD in the year of the survey, obtained from the World Bank Development Indicators. Code refers to the country acronym which we use in the figures. The sample size refers to the number of households in the survey, and the number of items reported is the number of expenditure items reported on average across all households in the survey.

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Table 2: Average Slopes of the Informality Engel Curves

|**Specifcation:**|**Ma**|**in**|**Geog**|**raphy**||**Product**|**Codes**||**All**|
|---|---|---|---|---|---|---|---|---|---|
|Avg. of 31 Countries|(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)|(9)|
|(Negative of) Slope|9.8|10.6|9.2|8.5|6.9|6.3|6.1|5.4|4.3|
|Confdence Interval|[9.2,10.4]|[9.9,11.2]|[8.5,9.9]|[7.7,9.2]|[6.2,7.4]|[5.7,6.7]|[5.5,6.5]|[4.8,5.7]|[3.7,4.7]|
|# of p-values_<_0.05<br>|31|31|31|30|30|29|30|29|28|
|_R_<sup>2 </sup>adjusted|0.19|0.21|0.25|0.41|0.43|0.51|0.51|0.50|0.54|
|Household Characteristics||X|X|X|X|X|X|X|X|
|Urban/Rural|||X|||||||
|Survey Blocks||||X|||||X|
|Food Products|||||X|||||
|COICOP 2-dig||||||X||||
|COICOP 3-dig|||||||X|||
|COICOP 4-dig||||||||X|X|

This table shows the (negative) average slope of the Informality Engel Curves across countries for different specifications. In column 1, we report the slopes that are estimated from the following regression: _Share In f ormalip_ = _β_ 0 + _β_ 1 _ln_ ( _expenditurei_ ) + _εip_ where _Share In f ormalip_ is the share of household _i_ ’s informal expenditure on product _p_ . We weigh each observation using household survey weights and the expenditure share of the product. Average of lower and upper bound of 95% confidence intervals in brackets, from robust standard errors. In column 2, we augment this regression with controls for household characteristics (household size, age, gender, education of head). In column 3 (4), we instead add fixed effects for urban/rural (survey enumeration blocks). In column 5, we instead add fixed effects for food versus non-food products. In column 6/7/8, we instead add fixed effects for product codes at 2nd/3rd/4th level of the COICOP classification. In column 9, we add household characteristics, as well as fixed effects for survey blocks and COICOP-4.

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Table 3: Main Reason for Choosing Place of Purchase

|**Reason**|**Outco**<br>**All Stores**|**me: Share of purcha**<br>**Informal Stores**|**ses (in %)**<br>**Formal Stores**|
|---|---|---|---|
|Access|41.5|42.1|31.3|
|Price|28.6|29.4|17.7|
|Quality|13.4|11.8|40.6|
|Store Attributes|6.9|6.9|5.0|
|Other|9.6|9.8|5.5|

The table reports for each potential reason households report for using a particular place of purchase, the share of purchases associated with this reason. Each number is an average across the six countries in our core sample in which the household survey asks this questions. These countries are Benin, Burundi, Comoros, Congo Rep., Morocco and RD Congo. In all surveys seven reasons are listed which we classify into five categories as follows: access is defined as ”The retailer is closer or more convenient” and ”The good or service cannot be found elsewhere”, price as ”The good or services are cheaper”, quality as ”The goods or services are of better quality”, store attributes as ”The retailer offers credit” and ”The retailer is welcoming or is a friend” and other as ”Others reasons”. Note that Morocco has a few additional small categories, which pertain to attributes of retailer. The table lists the frequency for all purchases of goods and excludes services, which are less comparable along these dimensions, although their inclusion does not impact the results.

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Table 4: Baseline Calibration Parameters

|Parameter|Value|Justifcation|
|---|---|---|
|Budget shares _s_<sup>_i_</sup><br>_j_ <sup>and</sup> <sup>_si_</sup><br>_j_1|Varying|Observed in our data|
|Household income (scaled) _φ_<sup>_i_</sup>|Varying|Observed in our data|
|Income elasticities of goods _ηj_|Food: 0.65,<br>Non-food: 1.2|From our data, using _ηj_ =1+<br>_βj_<br>_sj_<br>1|
|Income elasticities of formal varieties _ηj_1|Food: 1.14,<br>Non-food: 1.31,<br>All goods: 1.25|From our data, using _ηj_1 =1+<br>_βj_1<br>_sj_1<br>1|
|Informal share of consumption _αj_|Varying|From our data|
|Cross-variety compensated elasticity ̃_ε_<sup>_C_</sup>|1.5|Faber and Fally(2017);Atkin et al.(2018b)<sup>2</sup>|
|Own-price compensated elasticity _ε_<sup>_C_</sup>|-0.7|Deaton et al.(1994)<sup>3</sup>|
|Government preferences _g_<sup>_i_</sup>|1-10|Uniform tax rates in the[0.10, 0.25] range<sup>4</sup>|

1 The parameter _βj_ ( _βj_ 1) refers to the estimated slope of the Engel curve for good _j_ (variety _j_ 1). 2 For the cross-variety price elasticity we use estimates of the elasticity of substitution _σ_ across store types in consumption obtained by Faber and Fally (2017); Atkin et al. (2018b) which are in the [2, 4] range. With a CES utility function _ε_ ̃<sup>_C_</sup> = _σs_ 0 where _s_ 0 is the aggregate budget share spent in the informal sector, equal to 0.5 on average in our sample.

3 _C_ Our choice of value for _ε_ together with our estimated income elasticities and observed budget shares yield uncompensated own-price elasticities for goods in the [ _−_ 2, _−_ 0.5] range, in line with estimates obtained by Deaton et al. (1994) in the developing country context.

> 4 We set _gi_ = 10 for the first decile, _gi_ = 9 for the second decile, _gi_ = 8 for the third decile, ..., _gi_ = 1 for the tenth decile. This, together with our other calibration choices, yields optimal uniform rates when we assume only formal varieties can be taxed in the 10-25% range, in line with observed consumption tax rates in developing countries.

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# Online Appendix for ’Informality, Consumption Taxes and Redistribution’

Pierre Bachas, Lucie Gadenne & Anders Jensen May 2020
# **A Additional Figures and Tables**

Figure A1: Informality Engel Curves <!-- Start of picture text --> 5 6 7 6 7 8 7 8 9<br>(a) Benin (b) Bolivia (c) Brazil<br>6 7 8 6 7 6 7 8 9<br>(d) Burkina Faso (e) Burundi (f) Cameroon<br>6 7 8 8 9 10 7 8 9<br>(g) Chad (h) Chile (i) Colombia<br>7 8 9 7 8 9 5 6 7<br>(j) Comoros (k) Costa Rica (l) Dem. Rep. of Congo<br>100 100 100<br>80 80 80<br>60 60 60<br>40 40 40<br>20 20 20<br>0 0 0<br>100 100 100<br>80 80 80<br>60 60 60<br>40 40 40<br>20 20 20<br>0 0 0<br>100 100 100<br>80 80 80<br>60 60 60<br>40 40 40<br>20 20 20<br>0 0 0<br>100 100 100<br>80 80 80<br>60 60 60<br>40 40 40<br>20 20 20<br>0 0 0<br><!-- End of picture text --> 51
<!-- Start of picture text --> 7 8 9 7 8 9 6 7 8<br>(m) Dominican Rep. (n) Ecuador (o) Eswatini<br>7 8 9 8 9 7 8<br>(p) Mexico (q) Montenegro (r) Morocco<br>100 100 100<br>80 80 80<br>60 60 60<br>40 40 40<br>20 20 20<br>0 0 0<br>100 100 100<br>80 80 80<br>60 60 60<br>40 40 40<br>20 20 20<br>0 0 0<br><!-- End of picture text --> <!-- Start of picture text --> 5 6 7 6 7 6 7 8<br>(s) Mozambique (t) Niger (u) Papua New Guinea<br>100 100 100<br>80 80 80<br>60 60 60<br>40 40 40<br>20 20 20<br>0 0 0<br><!-- End of picture text --> <!-- Start of picture text --> 8 9 6 7 8 6 7 8<br>(v) Peru (w) Rep. of Congo (x) Rwanda<br>100 100 100<br>80 80 80<br>60 60 60<br>40 40 40<br>20 20 20<br>0 0 0<br><!-- End of picture text --> 52
<!-- Start of picture text --> 6 7 8 7 8 8 9<br>(y) Sao Tome (z) Senegal (aa) Serbia<br>100 100 100<br>80 80 80<br>60 60 60<br>40 40 40<br>20 20 20<br>0 0 0<br><!-- End of picture text --> <!-- Start of picture text --> 7 8 9 6 7 8 8 9<br>(ab) South Africa (ac) Tanzania (ad) Tunisia<br>100 100 100<br>80 80 80<br>60 60 60<br>40 40 40<br>20 20 20<br>0 0 0<br><!-- End of picture text --> <!-- Start of picture text --> 7 8 9<br>100<br>80<br>60<br>40<br>20<br>0<br><!-- End of picture text --> (ae) Uruguay Local polynomial fit of the Informality Engel Curves in all 31 core sample countries. Per person total expenditure on the horizontal axis is measured in log. Informal budget share is on the vertical axis. The shaded area around the polynomial fit corresponds to the 95% confidence interval. The solid grey line corresponds to the median of each country’s expenditure distribution, while the dotted lines correspond to the 5th and 95th percentiles. The construction of informality Engel curves is presented in section 3.1.

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# Figure A2: Alternative Assignment Scenarios for Informal Expenditure

## (a) Budget Shares (Probability Scenario)

## (b) Slopes (Probability Scenario)

<!-- Start of picture text --> CD<br>BI<br>TZ<br>NE BF TD BJ SN CG BI CD CL<br>MZ RW ST KMCM PG NE TD BJ ST CG CRBR<br>BO MA MZ BF TZ KMCMBOPG TN CO ZA<br>EC RS RW SZ<br>TN CO PEME MXBR SN MA DO ME UYMX<br>SZ DO EC<br>CR RSPE<br>CL<br>UY<br>ZA<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>(c) Budget Shares (Robustness Scenario) (d) Slopes (Robustness Scenario)<br>CD<br>BI TZ<br>NE BFTD BJ SN CG CL<br>MZ RW ST KMCMBOPGMA TN EC RS BR BI CDNE MZ BFTD TZBJ ST KM BO CG TN CRBR<br>CM<br>RW PG SZ COMEZA<br>PE MX MA<br>ME<br>CO SN DO<br>SZ DO CR EC RS UYMX<br>PE<br>UY CL<br>ZA<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>5<br>100<br>80 0<br>−5<br>60<br>−10<br>40<br>−15<br>Informal Consumption Share 20 Informal Consumption Slope<br>−20<br>0<br>−25<br>5<br>100<br>80 0<br>−5<br>60<br>−10<br>40<br>−15<br>Informal Consumption Share 20 Informal Consumption Slope<br>−20<br>0<br>−25<br><!-- End of picture text --> This figure is the equivalent of figure 3 for the two alternative assignments of store types to formality. The Probability scenario uses the observed probability of VAT payment by store type in the Mexican census as the formality probability of each store type across countries (see Figure 1). The robustness scenario differs from the central scenario by assigning specialized stores to the informal sector, in addition to maintaining corner stores, non brick and mortar and self-production in the informal sector. Panel (a) and (c) show informal budget shares, on log per capita GDP. Panel (b) and (d) show the the slope of informality Engel curves on log per capita GDP. The bars correspond to the 95% confidence interval of the slope coefficient. GDP per capita is in constant 2010 USD (Source: World Bank WDI).

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Figure A3: Unspecified Places of Purchase by Good <!-- Start of picture text --> (a) Percentage of Total Expenditure (b) Percentage of Goods’ Expenditure<br>FoodAlcoholClothesUtilities & FuelsFurnishing & Equipment HealthTransportCommunicationCultureEducationRestaurantsMisc. Goods FoodAlcoholClothesUtilities & FuelsFurnishing & Equipment HealthTransportCommunicationCultureEducationRestaurantsMisc. Goods<br>5<br>60<br>4<br>3 40<br>2<br>20<br>1<br>0 0<br><!-- End of picture text --> This figure shows the share of expenditures with an unspecified place of purchase by goods categories (COICOP-2 digit level) on average, across the 31 countries of the core sample, discussed in section 2.2. Panel (a) shows this share as a percentage of total expenditures and Panel (b) as a percentage of each goods’ total expenditure.

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Figure A4: Average Expenditure of Each Decile by Place of Purchase <!-- Start of picture text --> (a) Non Market (b) Non Brick&Mortar (c) Corner Stores (d) Indiv. Providers<br>1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10<br>(e) Specialized Stores (f) Large Stores (g) Instit. Services (h) Unspecified<br>1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10<br>30 30 30 30<br>25 25 25 25<br>20 20 20 20<br>15 15 15 15<br>10 10 10 10<br>5 5 5 5<br>0 0 0 0<br>30 30 30 30<br>25 25 25 25<br>20 20 20 20<br>15 15 15 15<br>10 10 10 10<br>5 5 5 5<br>0 0 0 0<br><!-- End of picture text --> This figure shows the average expenditure of each decile across countries by type of retailer, following the retailer taxonomy described in section 2.2. Panel (a), (b), (c), (d) show the places of purchase classified as informal and Panel (e), (f), (g) and (h) show the places of purchase classified as formal in the central scenario of the paper.

Figure A5: Average Expenditure of Each Decile By Formality Assignment

# (a) Informal Places of Purchase (b) Formal Places of Purchase

<!-- Start of picture text --> Informal Services<br>Corner Stores<br>Unspec i fied<br>No Store Front<br>Formal Services<br>Large Stores<br>Non−market<br>Specialized Stores<br>1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10<br>Decile of Expenditure Distribution Decile of Expenditure Distribution<br>70<br>70<br>60<br>60<br>50 50<br>40 40<br>30 30<br>20 20<br>Mean Share of Expenditures Mean Share of Expenditures<br>10 10<br>0 0<br><!-- End of picture text --> This figure shows the average expenditure of each decile across countries by type of retailer, following the retailer taxonomy described in section 2.2. Panel (a) shows the places of purchase classified as informal and Panel (b) shows the places of purchase classified as formal in the central scenario of the paper.

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Figure A6: Informality Engel Curve Slopes Controlling for Geography

# (a) Control: Rural Location (b) Control: Survey Block

<!-- Start of picture text --> CL<br>BI CD CL BI<br>NE TD BJ ST CG CDNE TD TZ BJ ST<br>MZ BF RWTZ CMBOPG ZA CRBR MZ BF RW KMCMBOPG CG TN CO ZA CR MX BR<br>SNKM TNSZ CO UYMX SN MA SZ DO PE UY<br>MA DO<br>PEME EC ME<br>EC<br>RS RS<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>5 5<br>0 0<br>−5 −5<br>−10 −10<br>−15 −15<br>Informal Consumption Slope Informal Consumption Slope<br>−20 −20<br>−25 −25<br><!-- End of picture text --> This figure shows each countries Informality Engel curves’ on their GDP per capita, when controlling for geographical variables. Panel (a) controls for a rural/urban dummy variable and panel (b) controls for survey enumeration blocks.

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Figure A7: Rural vs Urban Informal Consumption

# (a) Rural: Budget Share (b) Urban: Budget Share

<!-- Start of picture text --> BI CD<br>NE MZ BFTD RWTZBJ CG BI CDNE BJ<br>ST KM CM BOPGMA TZ ST KM CG<br>BF<br>EC RSPE MZ TD RW CM<br>BO<br>TN MA<br>MX<br>SZ DOCOME BR PG EC RSPE<br>TN<br>CO<br>DO MX<br>CR SZ ME BR<br>ZA UY CR<br>UY<br>ZA<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>(c) Rural: IEC slope (d) Urban: IEC slope<br>BI CD<br>BJ<br>NE BFTD ST CG BJ CG<br>MZ RWTZ CMBOPG TN CO CR BI CDNE TZ ST CM PG ZA CRBR<br>KM MA SZ DO PE ZA UYMXBR BFTD RW KM BO TN SZ CO UYMX<br>EC MZ<br>MA DO ME<br>PE<br>ME<br>EC<br>RS<br>RS<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>100 100<br>80 80<br>60 60<br>40 40<br>Informal Budget Share Informal Budget Share<br>20 20<br>0 0<br>5 5<br>0 0<br>-5 -5<br>-10 -10<br>-15 -15<br>Informality Engel Curve Slope Informality Engel Curve Slope<br>-20 -20<br>-25 -25<br><!-- End of picture text --> This figure plots informality levels and the slopes of the informality Engel curves for households located in rural regions (graphs a and c) and urban regions (graphs b and d). It only contains 29 countries instead of 31, since the expenditure surveys in Chile and Senegal concern urban population only.

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# Figure A8: Informality Engel Curve Slopes Controlling for Goods Composition

<!-- Start of picture text --> (a) Control: Food Products (b) Control: COICOP2<br><!-- End of picture text --> <!-- Start of picture text --> CL CL<br>NE<br>BI BJ BI TZBJ<br>CDNE TD TZ ST CMBO CG DOCO CD BFTD RW ST CM BO CG DO<br>BF SNKM PG ZA CRUYBR MZ SNKM PG CO ZA CRUYBR<br>MZ RW PE MX PE MX<br>TNSZ MA SZ RS<br>MA EC<br>EC TN<br>RS<br>ME<br>ME<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>(c) Control: COICOP3 (d) Control: COICOP4<br>CL<br>CL<br>BI CDNE MZ BF TD RWTZBJ STSNKMCM BO PGMA CG DOCO BI CDNE MZ BFTD RWTZBJ ST SN KMCMBOPGMA CG DOCO<br>ZA BR PE ZA BR<br>SZ RSPE CRUY MX SZ RS CRUYMX<br>EC EC<br>TN ME<br>ME<br>TN<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>5 5<br>0 0<br>−5 −5<br>−10 −10<br>−15 −15<br>Informal Consumption Slope Informal Consumption Slope<br>−20 −20<br>−25 −25<br>5 5<br>0 0<br>−5 −5<br>−10 −10<br>−15 −15<br>Informal Consumption Slope Informal Consumption Slope<br>−20 −20<br>−25 −25<br><!-- End of picture text --> This figure shows the informality Engel curves’ slopes across countries when controlling for increasingly narrow products (and household controls). Panel (a) only controls for food products, panel (b) controls for the 12 COICOP2 good categories, panel (c) controls for the 47 COICOP3 categories and panel (d) controls for the 117 COICOP4 categories.

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Figure A9: Share of Purchases where Store is Chosen for its Quality by Income <!-- Start of picture text --> 5 6 7 6 7 7 8 9<br>Log Expenditure PP, Constant 2010 USD Log Expenditure PP, Constant 2010 USD Log Expenditure PP, Constant 2010 USD<br>(a) Benin (b) Burundi (c) Comoros<br>5 6 7 7 8 9 6 7 8<br>Log Expenditure PP, Constant 2010 USD Log Expenditure PP, Constant 2010 USD Log Expenditure PP, Constant 2010 USD<br>(d) Dem. Rep. of Congo (e) Morocco (f) Rep. of Congo<br>.3 .3 .3<br>.2 .2 .2<br>.1 .1 .1<br>Purchased for Quality (%) 0 Purchased for Quality (%) 0 Purchased for Quality (%) 0<br>.3 .3 .3<br>.2 .2 .2<br>.1 .1 .1<br>Purchased for Quality (%) 0 Purchased for Quality (%) 0 Purchased for Quality (%) 0<br><!-- End of picture text --> Local polynomial fit of the share of households buying any product for its quality on household’s total expenditure per person (log). Each panel corresponds to one of the six countries, for which the expenditure survey asks respondents why they chose this place of purchase for each expenditure. The solid vertical line corresponds to the median household total expenditure, while the dotted lines correspond to the 5th and 95th percentile.

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Figure A10: Budget Shares <!-- Start of picture text --> (a) Informal Food (b) Formal Food<br>CD<br>SN<br>TD<br>BI NE MZ TZ ST PG CG<br>KM<br>BJ<br>MA<br>BF RW<br>BO RSPE<br>CM EC SZ<br>TN SZ DOCOME MX PG TN RS ME ZA CRUYMXBR<br>ZA CRUYBR CL BI CD NE MZ BF TD RWTZ BJ STSNKMCMBO MA CG DOECCOPE CL<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>(c) Informal Non-Food (d) Formal Non-Food<br>ZA<br>UY CL<br>DO CR<br>CO<br>BR<br>EC PEME MX<br>BI TNSZ<br>BF BJ CM BO RS<br>RW MA<br>NE TZ<br>CM<br>CD MZ TD ST SN KM BOPGMA CG TN DOECCORSPEME CRMX BR CL NE MZ BFTD RWTZBJ STSNKM PG CG<br>SZ ZA UY BI CD<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>100 100<br>80 80<br>60 60<br>40 40<br>Informal Food Budget Share 20 Formal Food Budget Share 20<br>0 0<br>100 100<br>80 80<br>60 60<br>40 40<br>20 20<br>Informal Non−Food Budget Share Formal Non−Food Budget Share<br>0 0<br><!-- End of picture text --> Panel (a) shows country informal food consumption as a share of total consumption, plotted against log per capita GDP. Panel (b), (c) and (d) are constructed similarly to Panel (a), respectively showing formal food consumption, informal non-food consumption and formal non-food consumption.

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Figure A11: Engel Curve Slopes <!-- Start of picture text --> (a) Informal Food (b) Formal Food<br>PG<br>CD MZ TD RW ST CG ZA CRBR CL BI CDNE MZ BF TD RWTZ BJ ST SNKM CMBO MA CG TNSZ DOECCORSPEMEZA CRUYMXBR<br>NE BF BJ KMCMBO PG MA TNSZ CO UYMX CL<br>BI DO EC PE ME<br>RS<br>TZ SN<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>(c) Informal Non-Food (d) Formal Non-Food<br>RS<br>PE<br>EC<br>TZ ME<br>BI SN MA TN DO CO ZA UYMX<br>NE BJ SN MZ BF RWTZ KMCMBO SZ CRBR CL<br>CM PG<br>CD MZ BFTD RW ST KM BOPGMA CG TNSZ DO EC CO RSPEMEZA CRUYMXBR CL BI CDNE TD BJ ST CG<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>20 20<br>15 15<br>10<br>10<br>5<br>5<br>0<br>0<br>−5<br>−5<br>−10<br>−10<br>−15<br>Formal Food Engel Curve Slope<br>Informal Food Engel Curve Slope<br>−15<br>−20<br>−20<br>20<br>20<br>15<br>15<br>10<br>10<br>5<br>5<br>0<br>0<br>−5<br>−5<br>−10 −10<br>−15 Formal Non−Food Engel Curve Slope −15<br>Informal Non−Food Engel Curve Slope<br>−20 −20<br><!-- End of picture text --> Panel (a) shows the country-specific slope of informal food consumption with respect to log household expenditure, plotted against log per capita GDP. The slope measures the drop in informal food consumption for a doubling of households’ income. Panel (b), (c) and (d) are constructed similarly to Panel (a), respectively showing formal food consumption, informal non-food consumption and formal non-food consumption.

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Figure A12: Share of Informal Consumption for Food and Non Food Goods <!-- Start of picture text --> (a) Informal Food (b) Informal Non-Food<br>BI CD BF BJ<br>NE TD RWTZ SNKMCMBO CG PE<br>MZ ST EC BI CD<br>MA DO<br>PG NE BJ<br>BF<br>RS TD TZ<br>CL RW ST SN<br>TN MX<br>CO KMCM PG<br>ME CG<br>SZ<br>MZ BO TN<br>UY<br>CRBR<br>MA<br>ZA SZ DOECCORSPE ME CR MX BR<br>CL<br>ZA UY<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>100 100<br>80 80<br>60 60<br>40 40<br>20 20<br>Share of Food Consumption in Inf. Sector<br>0 0<br>Share of Non Food Consumption in Inf. Sector<br><!-- End of picture text --> Panel (a) shows the share of food consumption which occurs in the informal sector. Panel (b) shows the share of non food consumption which occurs in the informal sector. For each good, this is constructed by taking total informal consumption of the good and dividing it by the total consumption of that good.

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# Figure A13: Optimal Uniform Tax on Formal Varieties

<!-- Start of picture text --> (a) No efficiency consideration (b) Cross price elasticity = 1.5<br><!-- End of picture text --> <!-- Start of picture text --> MZ ZA<br>BI BF PG<br>CD<br>RW ZA<br>NE TD BJ KMCMBO MA CG SZ DO EC CO CRMXBR MZ BF RW BOPGMA SZ DOECCO CRUYMXBR CL<br>ST SN TN PE UY CL BI CD TD BJ KM TN PE<br>TZ CM RS<br>RS NE STSN CG<br>TZ<br>ME<br>ME<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>(c) Cross price elasticity = 1 (d) Cross price elasticity = 2<br>ZA<br>RW<br>ZA<br>MZ PG<br>BF BR<br>BI CO<br>CD TD BJ KM BO MA SZ DOEC CR UYMX<br>CL BR<br>TN PE CRUY<br>NE SNCM CG CO<br>TZ ST RS MZ RW PG SZ DO MX CL<br>BF BO MA EC<br>ME BI KM TN PE<br>CD TD BJ<br>RS<br>CM<br>NE STSN CG ME<br>TZ<br>5 6 7 8 9 10 5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD Log GDP per capita, Constant 2010 USD<br>.6 .3<br>.55<br>.25<br>.5<br>.45 .2<br>.4<br>.15<br>.35<br>Optimal Uniform Rate Optimal Uniform Rate<br>.3<br>.1<br>.25<br>.2 .05<br>.3 .3<br>.25 .25<br>.2 .2<br>.15 .15<br>Optimal Uniform Rate Optimal Uniform Rate<br>.1 .1<br>.05 .05<br><!-- End of picture text --> The panels plot the optimal uniform rate for each country calibrated using expression (6) as a function of each country’s log GDP per capita. In panel (a) we hold efficiency considerations constant by assuming that uncompensated elasticities of demand are equal across all countries, in panels (b), (c) and (d) we allow price elasticities to vary across goods and countries by calibrating values using expression (4) above. We vary the value of the cross-variety compensated elasticity _ε_ ̃<sup>_C_</sup> across the three panels: it is 1.5 (our baseline value) in panel (b), 1 in panel (c) and 2 in panel (d).

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# Figure A14: Optimal Rate Differentiation: Robustness

- (a) Only Formal Varieties Taxed, Cross price elasticity = 1.5

<!-- Start of picture text --> CD<br>BI<br>BJ<br>CG<br>BR<br>CR<br>BF RW KMCM TN ZA<br>TD TZ PG UY<br>EC ME<br>STSN BO MA SZ<br>MZ DO MX<br>CO<br>PE<br>NE RS<br>CL<br>5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD<br>(c) Only Formal Varieties Taxed, Cross price elasticity = 2<br>CD<br>BI BJ<br>CG CRBR<br>BF RW KMCM TN ZA UY<br>TD TZ PG EC ME<br>MZ STSN BO MA SZ DOCO MX<br>PE<br>RS<br>NE<br>CL<br>5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD<br>1.4<br>1.2<br>1<br>.8<br>.6<br>.4<br>Ratio Food Rate / Non Food Rate .2<br>0<br>1.6<br>1.4<br>1.2<br>1<br>.8<br>.6<br>.4<br>Ratio Food Rate / Non Food Rate .2<br>0<br><!-- End of picture text -->

- (b) Only Formal Varieties Taxed, Cross price elasticity = 1

<!-- Start of picture text --> CD<br>BI<br>BJ<br>CG<br>BR<br>CR<br>BF TD RWTZ KMCM PG TN ZA<br>ST EC ME UY<br>MZ SN BO MA SZ DOCO MX<br>NE RSPE<br>CL<br>5 6 7 8 9 10<br>Log GDP per capita, Constant 2010 USD<br>1.6<br>1.4<br>1.2<br>1<br>.8<br>.6<br>.4<br>Ratio Food Rate / Non Food Rate .2<br>0<br><!-- End of picture text --> The panels plot for each country the ratio of the calibrated optimal rate on food products relative to the optimal rate on non-food products, as a function of that country’s log GDP per capita. Optimal rates are calibrated using expression (9). A value equal to 1 indicates that both optimal rates are set at the same level, a lower value indicates that it is optimal to subsidize food products relative to non-food products. In all panels we assume only formal varieties can be taxed and allow price elasticities to vary across goods and countries by calibrating values using expression (4) above. We vary the value of the cross-variety compensated elasticity _ε_ ̃<sup>_C_</sup> across the three panels: it is 1.5 (our baseline value) in panel (a), 1 in panel (b) and 2 in panel (c).

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|Tax Policy||Effect Size|||
|---|---|---|---|---|
|Panel A: LowerIncomeCountries (Source: This paper N=16)|||||
|Uniform rate, only formal taxed||@|||
|Food rate differentiation, formal and informal taxed<br>*|||||
|Food rate differentiation, only formal taxed||Be|||
|Panel B: Middle IncomeCountries (Source: This paper N=15)|||||
|Uniform rate, only formal taxed||3)|||
|Food rate differentiation, formal and informal taxed||a|||
|Food rate differentiation, only formal taxed<br>@|||||
|Panel C: Middle IncomeCountries (Source: CEQ N=25)|||||
|Indirect taxes: Generalconsumption & excise|||e||
|Direct taxes: PIT& Social Security||@|||
|rr<br>-4.0|-3.0|i<br>-2.0<br>-1.0<br>PercentchangeinGinifrompolicy||a<br>|<br>0.0<br>0.5|
Table A1: IEC Slopes by Country

|**Country**|**Ma**<br>(1)|**in**<br>(2)|**Geog**<br>(3)|**raphy**<br>(4)|(5)|**Produc**<br>(6)|**t Codes**<br>(7)|(8)|**All**<br>(9)|
|---|---|---|---|---|---|---|---|---|---|
|Benin|3.31|3.61|3.18|4.54|0.92|1.49|1.36|1.03|1.26|
|Bolivia|(0.15)<br>977|(0.16)<br>1143|(0.16)<br>899|(0.22)<br>722|(0.16)<br>571|(0.11)<br>487|(0.10)<br>513|(0.10)<br>293|(0.15)<br>274|
||.<br>(0.29)|.<br>(0.33)|.<br>(0.38)|.<br>(0.44)|.<br>(0.29)|.<br>(0.19)|.<br>(0.18)|.<br>(0.16)|.<br>(0.25)|
|Brazil|7.60|7.98|7.07|6.41|7.50|7.15|7.79|8.11|6.64|
||(0.15)<br>|(0.17)<br>|(0.17)<br>|(0.18)<br>|(0.16)<br>|(0.16)<br>|(0.15)<br>|(0.13)<br>|(0.14)<br>|
|Burkina Faso|9.71|10.56|7.58|6.89|7.97|5.20|4.92|3.73|2.39|
||(0.30)<br>|(0.32)<br>|(0.30)<br>|(0.32)<br>|(0.28)<br>|(0.19)<br>|(0.18)<br>|(0.17)<br>|(0.19)<br>|
|Burundi|1.89<br>(0.16)|2.35<br>(0.17)|1.44<br>(0.17)|0.80<br>(0.18)|0.83<br>(0.17)|1.54<br>(0.12)|1.20<br>(0.10)|0.84<br>(0.10)|0.33<br>(0.12)|
|Cameroon|821|935|713|581|572|430|461|455|288|
||.<br>(0.13)|.<br>(0.14)|.<br>(0.16)|.<br>(0.22)|.<br>(0.13)|.<br>(0.12)|.<br>(0.10)|.<br>(0.09)|.<br>(0.13)|
|Chad|5.72|6.21|4.54|3.10|3.35|2.37|2.29|2.23|0.90|
||(0.29)<br>|(0.30)<br>|(0.30)<br>|(0.37)<br>|(0.25)<br>|(0.19)<br>|(0.16)<br>|(0.15)<br>|(0.22)<br>|
|Chile|0.97|0.91|0.91|0.03|0.00|0.00|0.00|0.00|0.00|
||(0.21)|(0.23)|(0.23)|(0.25)|(0.21)|(0.18)|(0.17)|(0.16)|(0.18)|
|Colombia|9.76<br>|10.52<br>|10.56<br>|8.32<br>|5.31<br>|6.51<br>|4.28<br>|3.22<br>|3.37<br>|
|Comoros|(0.23)<br>9.54<br>058|(0.25)<br>11.65<br>071|(0.26)<br>11.08<br>074|(0.28)<br>8.84<br>082|(0.22)<br>7.28<br>058|(0.21)<br>6.95<br>047|(0.20)<br>6.16<br>042|(0.17)<br>5.93<br>037|(0.19)<br>4.42<br>056|
||(.)<br>|(.)<br>|(.)<br>|(.)<br>|(.)<br>|(.)<br>|(.)<br>|(.)<br>|(.)<br>|
|CongoDRC|2.04|2.76|1.62|2.66|2.34|2.36|2.17|1.99|1.51|
||(015)|(017)|(014)|(020)|(015)|(014)|(013)|(010)|(016)|
|Congo Rep|.<br>4.21<br>|.<br>5.62<br>|.<br>4.13<br>|.<br>7.06<br>|.<br>4.22<br>|.<br>4.01<br>|.<br>3.96<br>|.<br>2.97<br>|.<br>2.78<br>|
||(0.32)|(0.33)|(0.33)|(0.43)|(0.27)|(0.22)|(0.18)|(0.16)|(0.25)|
|Costa Rica|722|860|772|595|725|844|1060|1069|884|
|<br>Dominican Rep|.<br>(0.35)<br>14.39|.<br>(0.37)<br>14.89|.<br>(0.38)<br>14.48|.<br>(0.45)<br>11.78|.<br>(0.35)<br>5.70|.<br>(0.33)<br>4.76|.<br>(0.30)<br>4.57|.<br>(0.25)<br>3.52|.<br>(0.30)<br>2.36|
||(031)|(035)|(035)|(042)|(028)|(027)|(026)|(023)|(025)|
|Ecuador|.<br>19.11|.<br>20.90|.<br>19.11|.<br>16.57|.<br>13.02|.<br>12.22|.<br>11.92|.<br>12.34|.<br>9.46|
||(0.18)|(0.19)|(0.21)|(0.21)|(0.16)|(0.15)|(0.14)|(0.12)|(0.13)|
|Etii|1164|1238|1155|1256|1017|1047|1089|1005|988|
|swan|.<br>(0.51)|.<br>(0.62)|.<br>(0.67)|.<br>(0.65)|.<br>(0.55)|.<br>(0.51)|.<br>(0.54)|.<br>(0.50)|.<br>(0.51)|
|Mexico|12.01|13.57|11.51|9.83|9.14|9.33|9.70|10.39|7.09|
||(0.20)<br>|(0.23)<br>|(0.24)<br>|(0.25)<br>|(0.22)<br>|(0.20)<br>|(0.20)<br>|(0.16)<br>|(0.19)<br>|
|Montenegro|18.16|18.88|16.04|16.60|14.61|15.83|15.91|14.23|12.52|
||(0.84)<br>|(0.94)<br>|(0.97)<br>|(1.11)<br>|(0.79)<br>|(0.68)<br>|(0.67)<br>|(0.53)<br>|(0.59)<br>|
|Morocco|16.85<br>|18.11<br>|14.05<br>|12.09<br>|12.35<br>|10.57<br>|4.34<br>|2.14<br>|0.00<br>|
||(0.21)|(0.22)|(0.23)|(0.27)|(0.19)|(0.18)|(0.21)|(0.25)|(0.28)|
|Mozambiue|967|1128|883|930|943|659|523|366|274|
|q|.<br>(0.37)|.<br>(0.39)|.<br>(0.40)|.<br>(0.44)|.<br>(0.33)|.<br>(0.29)|.<br>(0.27)|.<br>(0.23)|.<br>(0.29)|
|Niger|3.90|4.66|3.68|4.29|2.62|0.25|0.34|0.20|0.61|
||(0.34)<br>|(0.37)<br>|(0.41)<br>|(0.40)<br>|(0.31)<br>|(0.25)<br>|(0.24)<br>|(0.23)<br>|(0.26)<br>|
|Papua New Guinea|8.59|9.35|7.14|7.36|8.10|6.88|6.40|4.24|3.06|
|P|(0.49)<br>1804|(0.49)<br>1892|(0.50)<br>1604|(0.52)<br>1259|(0.43)<br>931|(0.40)<br>926|(0.38)<br>941|(0.30)<br>789|(0.32)<br>415|
|eru|.<br>(0.20)|.<br>(0.22)|.<br>(0.23)|.<br>(0.27)|.<br>(0.16)|.<br>(0.16)|.<br>(0.16)|.<br>(0.12)|.<br>(0.16)|
|Rwanda|9.90|10.61|8.68|9.75|9.04|5.23|2.14|0.97|0.09|
||(0.19)<br>|(0.20)<br>|(0.20)<br>|(0.25)<br>|(0.18)<br>|(0.12)<br>|(0.08)<br>|(0.08)<br>|(0.09)<br>|
|Sao Tome|4.66|5.23|5.26|5.06|3.50|2.64|2.46|1.84|1.84|
||(0.48)<br>|(0.56)<br>|(0.57)<br>|(0.58)<br>|(0.48)<br>|(0.44)<br>|(0.43)<br>|(0.37)<br>|(0.38)<br>|
|Senegal|15.20<br>(0.67)|12.19<br>(0.74)|12.19<br>(0.74)|11.56<br>(0.84)|6.57<br>(0.63)|7.39<br>(0.59)|5.53<br>(0.57)|4.83<br>(0.56)|4.47<br>(0.65)|
|Serbia|2091|2424|2274|2303|1367|1048|950|948|847|
||.<br>(0.58)|.<br>(0.58)|.<br>(0.56)|.<br>(0.56)|.<br>(0.51)|.<br>(0.49)|.<br>(0.47)|.<br>(0.29)|.<br>(0.29)|
|South Africa|7.50|8.69|7.78|7.29|6.78|6.49|7.69|7.59|6.92|
||(012)|(014)|(015)|(018)|(013)|(012)|(010)|(008)|(011)|
|Tanzania|.<br>8.47|.<br>7.52|.<br>7.26|.<br>4.88|.<br>3.18|.<br>1.03|.<br>1.11|.<br>2.11|.<br>0.80|
||(0.20)|(0.20)|(0.20)|(0.27)|(0.19)|(0.15)|(0.14)|(0.11)|(0.15)|
|Tunisia|13.68<br>|12.98<br>|10.72<br>|9.05<br>|10.18<br>|12.97<br>|17.60<br>|14.57<br>|13.03<br>|
||(0.15)|(0.17)|(0.18)|(0.21)|(0.16)|(0.12)|(0.15)|(0.26)|(0.29)|
|Uruguay|11.57<br>|11.73<br>|11.65<br>|10.87<br>|8.18<br>|8.48<br>|8.96<br>|9.31<br>|8.36<br>|
||(0.25)|(0.27)|(0.28)|(0.32)|(0.24)|(0.22)|(0.22)|(0.19)|(0.21)|
|All Countries(Mean)|9.8|10.6|9.2|8.5|6.9|6.3|6.1|5.4|4.3|
|<br>Household Characteristics<br>Urban/Rural||X|X<br>X|X|X|X|X|X|X|
|Survey Blocks<br>||||X|||||X|
|Food Products|||||X|||X||
|COICOP 2-dig<br>COICOP 3di||||||X|X|||
|-g<br>COICOP 4-dig||||||||X|X|

This table shows the average slope of the Informal Engel curve across countries for different specifications. The slopes are estimated from: _Share In f ormali_ = _β_ . _ln_ ( _expenditure pc_ ) _i_ + Γ _Xi_ + _εi_ , where the dependent variable is the informal expenditure share and the explanatory variable is the log expenditure pp. Controls include household characteristics (household size, age, gender, and education of head), geographic indicators (urban/rural and survey enumeration blocks), and product codes for food compared to the rest and at the 2nd, 3rd and 4th level of the United Nation’s COICOP classification.

67
Table A2: IEC Slopes: Probabilistic Formality Assignment

|**Specifcation:**|**Ma**|**in**|**Geogr**|**aphy**||**Product**|**Codes**||**All**|
|---|---|---|---|---|---|---|---|---|---|
|Avg. of 31 Countries|(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)|(9)|
|Slope|7.8|8.3|7.1|6.4|5.0|4.5|4.4|3.8|3.0|
|Confdence Interval|[ 7.3,8.4 ]|[ 7.7,8.9]|[ 6.4,7.7]|[ 5.7,7.1]|[ 4.4,5.5]|[ 4.0,4.9]<br>|[ 3.9,4.7]|[ 3.4,4.1]|[ 2.4,3.3]|
|# of p-values_<_0.05<br>|30|30|30|30|30|29|29|30|26|
|_R_<sup>2 </sup>adjusted|0.15|0.17|0.22|0.39|0.42|0.54|0.54|0.54|0.58|
|Household Characteristics||X|X|X|X|X|X|X|X|
|Urban/Rural|||X|||||||
|Survey Blocks||||X|||||X|
|Food Products|||||X|||||
|COICOP 2-dig||||||X||||
|COICOP 3-dig|||||||X|||
|COICOP 4-dig||||||||X|X|

This table shows the average slope of the Informal Engel curve across countries for different specifications under the probabilsitic assignment of places of purchase to formality. The Probabilistic scenario uses the observed probability of VAT registration by store type in the Mexican census as the formality probability of each store across countries (see Figure 1). The slopes are estimated from: _Share In f ormali_ = _β_ . _ln_ ( _expenditure pc_ ) _i_ + Γ _Xi_ + _εi_ . The dependent variable is informal expenditure share and the main explanatory variable is log expenditure per capita. Controls include household characteristics (household size, age, gender, education of head), location indicators (urban/rural, survey enumeration blocks), and product codes for food vs all other purchases, 2nd, 3rd and 4th level of the COICOP classification.

68
Table A3: IEC Slopes: Robustness Formality Assignment

|**Specifcation:**<br>Avg. of 31 Countries|**Ma**<br>(1)|**in**<br>(2)|**Geog**<br>(3)|**raphy**<br>(4)|(5)|**Produc**<br>(6)|**t Codes**<br>(7)|(8)|**All**<br>(9)|
|---|---|---|---|---|---|---|---|---|---|
|Slope|7.0|7.4|6.3|5.8|4.3|3.8|3.8|3.3|2.7|
|Confdence Interval|[6.4,7.6]|[6.7,8.1]|[5.6,7.0]|[4.8,6.4]|[3.5,4.7]|[3.1,4.1]|[3.1,4.1]|[2.7,3.5]|[2.0,3.0]|
|# of p-values_<_0.05<br>|30|30|29|28|28|28|27|25|25|
|_R_<sup>2 </sup>adjusted|0.12|0.13|0.17|0.34|0.38|0.52|0.53|0.54|0.57|
|Household Characteristics||X|X|X|X|X|X|X|X|
|Urban/Rural|||X|||||||
|Survey Blocks||||X|||||X|
|Food Products|||||X|||||
|COICOP 2-dig||||||X||||
|COICOP 3-dig|||||||X|||
|COICOP 4-dig||||||||X|X|

This table shows the average slope of the Informal Engel curve across countries for different specifications under the robustness scenario assignment of places of purchase to formality. The robustness scenario differs from the central scenario by assigning specialized stores to the informal sector, in addition to maintaining corner stores, non brick and mortar and self-production in the informal sector. The slopes are estimated from: _Share In f ormali_ = _β_ . _ln_ ( _expenditure pc_ ) _i_ + Γ _Xi_ + _εi_ . The dependent variable is informal expenditure share and the main explanatory variable is log expenditure per capita. Controls include household characteristics (household size, age, gender, education of head), location indicators (urban/rural, survey enumeration blocks), and product codes for food vs all other purchases, 2nd, 3rd and 69
Table A4: Main Reason for Choosing Place of Purchase

|Reason|All Stores|**Benin**<br> Informal|**Ou**<br> Formal|**tcome: Sha**<br> All Stores|**re of purc**<br>**Burundi**<br> Informal|**hases (in**<br> Formal|**%)**<br><br> All Stores|**Comoros**<br> Informal|Formal|
|---|---|---|---|---|---|---|---|---|---|
|Access|39.0|39.3|29.9|49.8|49.9|41.5|36.2|38.6|16.4|
|Price|26.4|26.8|11.6|27.6|27.8|14.8|31.1|31.7|26.1|
|Quality|24.3|23.5|51.4|6.4|5.7|41.0|12.4|9.0|39.8|
|Store Attributes|7.4|7.6|3.3|3.7|3.8|0.8|13.4|14.3|6.0|
|Other|2.9|2.9|3.9|12.6|12.8|1.9|7.0|6.4|11.7|
||**Dem. **|**Rep of Co**|**ngo**||**Morocco**||**Rep**|**. of Cong**|**o**|
|Reason|All Stores|Informal|Formal|All Stores|Informal|Formal|All Stores|Informal|Formal|
|Access|28.7|28.9|16.1|58.5|58.7|57.3|36.8|37.5|26.8|
|Price|34.3|34.4|27.2|20.1|22.5|6.4|32.4|33.3|20.0|
|Quality|16.6|16.3|46.5|6.3|3.9|19.7|14.3|12.2|45.0|
|Store Attributes|7.8|7.8|7.6|1.7|0.6|7.7|7.2|7.4|4.3|
|Other|12.6|12.7|2.7|13.5|14.3|8.9|9.3|9.7|3.8|

The table reports the frequencies across all purchases by reason of choosing a place of purchase, and shows the average for the six countries in the core sample which ask this question. These countries are Benin, Burundi, Comoros, Congo Rep., Morocco and RD Congo. In all surveys seven reasons are listed which we classify into five categories as follows: access is defined as ”The retailer is closer or more convenient” and ”The good or service cannot be found elsewhere”, price as ”The good or services are cheaper”, quality as ”The goods or services are of better quality”, store attributes as ”The retailer offers credit” and ”The retailer is welcoming or is a friend” and other as ”Others reasons”. Note that Morocco has a few additional small categories, which pertain to attributes of retailer. The table lists the frequency for all purchases of goods and excludes services, which are less comparable along these dimensions, although their inclusion does not impact the results.

70
Table A5: Unit Values Across Places of Purchase

||**Outcome: **|**% dif. in form**|**al sector unit**|**values**|**# Purchases**|**# FE**|
|---|---|---|---|---|---|---|
|**Country**|(1)|(2)|(3)|(4)|(5)|(6)|
|Benin|5.25|1.10|3.38|-0.39|262,280|5,065|
||(7.10)|(5.66)|(7.53)|(6.19)|||
|Bolivia|4.08<br>|3.53<br>|4.69<br>|3.86<br>|120,971|1,549|
||(1.40)|(1.12)|(1.40)|(1.15)|||
|Brazil|-0.11<br>|-0.20<br>|0.14<br>|0.01<br>|704,639|9,437|
||(0.37)|(0.35)|(0.38)|(0.35)|||
|Burundi|2.53<br>|4.39<br>|4.81<br>|5.23<br>|250,139|2,454|
||(4.65)|(4.73)|(4.39)|(4.23)|||
|Chad|-4.36|-3.21|-4.36|-3.21|380,462|1,968|
||(1.80)|(1.77)|(1.80)|(1.77)|||
|Colombia|-0.33|-0.04|-0.30|-0.06|778,203|7,861|
||(0.55)|(0.30)|(0.55)|(0.30)|||
|Comoros|22.56<br>|14.93<br>|21.81<br>|14.49<br>|113,228|1,142|
||(5.01)|(3.64)|(4.98)|(3.64)|||
|CongoDRC|4.62|0.87|9.77|5.89|865,754|5,556|
||(16.79)|(12.88)|(17.47)|(14.15)|||
|Congo Rep|27.84|23.70|27.12|23.01|208,557|1,182|
||(5.88)|(4.67)|(6.03)|(4.78)|||
|Costa Rica|3.04|2.37|1.93|1.58|122,467|1,593|
||(2.40)|(2.11)|(2.17)|(1.93)|||
|Dominican Rep|18.86|13.64|18.94|13.73|340,303|4,416|
||(1.69)|(1.01)|(1.68)|(1.00)|||
|Ecuador|2.29|1.86|2.23|1.82|1,030,387|12,104|
||(0.63)|(0.63)|(0.63)|(0.62)|||
|Eswatini|3.09|2.38|1.31|1.06|89,209|852|
||(2.10)|(1.79)|(1.89)|(1.46)|||
|Mexico|1.10|1.00|1.10|1.00|446,417|6,195|
||(1.16)|(1.02)|(1.16)|(1.02)|||
|Montenegro|10.36|9.57|7.13|6.45|138,446|867|
||(3.70)|(3.25)|(3.08)|(2.85)|||
|Morocco|7.10|5.43|6.88|5.22|743,979|3,598|
||(0.87)|(0.70)|(0.92)|(0.75)|||
|Peru|14.70|13.29|14.69|13.29|1,300,408|10,721|
||(2.74)|(2.46)|(2.74)|(2.46)|||
|Sao Tome|6.81|4.87|6.69|4.86|215,527|2,946|
||(1.39)|(1.37)|(1.39)|(1.34)|||
|Serbia|2.39|2.03|2.86|2.49|503,344|9,332|
||(0.49)|(0.46)|(0.51)|(0.48)|||
|Tanzania|2.11|1.59|2.80|2.21|1,169,193|13,771|
||(0.73)|(0.68)|(0.59)|(0.55)|||
|**Avg. of 20 Countries**|6.70|5.16|6.68|5.13|||
|Confdence Interval|[0.7,12.7]|[0.2,10.1]|[0.7,12.7]|[0.1,10.1]|||
|# ofp-values_<_0.05|12|12|11|11|||
|Winsorization [5,95]||X||X|||
|Self Consumption|||X|X|||

This table shows the percentage difference in unit values in the formal sector compared to the informal sector. The sample is restricted to food purchases, for which units and unit values are detailed, in the 20 core sample countries with such data. Formally it runs the following specification: _ln_ ( _unit value_ ) _ipmu_ = _β Formalipmu_ + _μpmu_ + _εipmu_ , where _ln_ ( _unit value_ ) _ipmu_ is the unit value reported by household _i_ , for product _p_ , in location _m_ , in units _u_ , and _Formalipmu_ equals one if the product is purchased in a formal store. We add fixed effects at the product * location * unit of measurement. Standard errors are clustered at the location level.

71
Table A6: Ratio Top over Bottom Quintile of Effective Tax Rates

||**Baseline**|**Baseline +**|**Baseline + Distri-**|**Probabilistic**|**Robust**|
|---|---|---|---|---|---|
|**Tax policy**|**Assignment**|**VAT on Input**|**butional Savings**|**Assignment**|**Assignment**|
|Uniform rate, only formal taxed|2.06|1.62|1.89|1.76|1.95|
|Food exempt, formal and informal taxed|1.67|1.67|1.54|1.63|1.67|
|Food exempt, only formal taxed|2.36|2.18|2.17|2.11|2.19|

This table shows the progressivity of consumption tax policies, measured as the effective tax rate of the richest household quintile over that of the poorest quintile. The numbers are averages for the 31 countries in the core sample. The rows correspond to the three tax policies considered: (1) a uniform rate on all goods in a context where only formal goods can be taxed, (2) a tax exemption on food in a context where both formal and informal goods can be taxed, and (3) an exemption on food, in a context where only formal goods can be taxed. The columns correspond to the different assumptions on our data. Column (1) corresponds to the central informality assignment of retailers. Column (2) models a 10% pass-through of taxes onto prices in the informal sector, following the share of formal inputs in informal firms in Mexico’s census. Column (3) allows for savings rate, which increases linearly from 0 for the bottom decile to 15% for the top decile, following evidence form consumer finance surveys. Columns (4) and (5) use the alternative assignment of store types to formality, by using either the probability of formality by store type from Mexico’s census, or by assigning specialized stores to the informal sector instead of the formal sector.

Table A7: Percent Change in Gini from Optimal Tax Policy

||**(1)**<br>**Baseline**<br>**Assignment**|**(2)**<br>**Baseline +**<br>**VAT on Input**|**(3)**<br>**Baseline + Distri-**<br>**butional Savings**|**(4)**<br>**Probabilistic**<br>**Assignment**|**(5)**<br>**Robust**<br>**Assignment**|**(6)**<br>**Cross**<br>**Elas**|**(7)**<br>**-variety**<br>**ticity**|
|---|---|---|---|---|---|---|---|
|**Tax policy**|||||| ̃_ε_<sup>_C_ </sup>= 1| ̃_ε_<sup>_C_ </sup>= 2|
|Uniform rate, only formal taxed|-2.30|-2.02|-1.24|-1.71|-1.54|-2.82|-1.95|
|Food rate differentiation, formal & informal taxed|-3.16|-3.16|-0.96|-3.16|-3.16|-3.16|-3.16|
|Food rate differentiation, only formal taxed|-3.26|-3.11|-1.88|-2.42|-2.03|-3.84|-2.85|
|Full rate differentiation, formal & informal taxed (12 goods)|-4.81|-4.81|-2.40|-4.60|-4.81|-4.81|-4.81|
|Full rate differentiation, only formal taxed (12 goods)|-4.19|-4.01|-3.11|-3.22|-2.83|-4.73|-3.82|

This table shows the redistributive impact of different consumption tax policies under different hypothesis, as presented in section 6. Our metric for redistribution is the percent change in Gini from the pre-tax income distribution to the net-of-tax distribution. We take the average across the 31 countries in the core sample. The rows correspond to the tax policy scenarios considered. (1) a uniform rate on all goods in a context where only formal goods can be taxed, (2) optimal tax rates on food and non food goods in a context where both formal and informal goods can be taxed, (3) optimal tax rates on food and non food goods, in a context where only formal goods can be taxed, (4) optimal tax rates for each of the 12 COICOP-2 digit level goods in a context where both formal and informal goods can be taxed, and (5) optimal tax rates for each of the 12 COICOP-2 digit level goods in a context where only formal goods can be taxed. The columns correspond to the different assumptions on our data. The baseline in column (1) corresponds to the central assignment of retailers to informality status, and to a value of the cross-variety elasticity of 1.5. Column (2) adds to the baseline scenario a 10% pass-through of taxes onto prices in the informal sector, following the share of formal inputs in informal firms in Mexico’s census. Column (3) adds the baseline scenario a distributional savings rate which ranges from 0 for the bottom decile to 15% for the top decile, following evidence form consumer finance surveys. Columns (4) and (5) use the alternative assignment of store types to formality. Finally columns (6) and (7) keep the central store assignment to informality but vary the value of the elasticity of substitution between the formal and informal variety of goods.

72
# **B Data Appendix**

All statistical codes to replicate the paper are available at https://github.com/ pierrebachas/Informality_Taxes_Redistribution. This includes the cleaning files for the micro data of each country’s survey, as well as all files generating the tables and figures of the paper.

## **B.1 Core Sample**

## **Inclusion Criteria**

Our dataset consists of 31 nationally representative household expenditure surveys. We use surveys which satisfy the following four criteria:

1. The household expenditure survey is nationally representative and dates from the 21st century.

2. The expenditure module(s) in the survey is structured as an open consumption diary, rather than a pre-fill diaries for a limited set of products.

3. The expenditure survey includes a variable for the place of purchase (data on where each item was purchased). The place of purchases are detailed enough for us to B.2.

apply our taxonomy of store types, as further outlined in section 4. The place of purchase variable rarely contains missing values, particularly for food, clothing and household goods product categories (see Figure A3).

## **Data Sources and Coverage**

We obtained the data principally from two sources: (i) the World Bank Microdata Library and (ii) National Statistical Agencies. Our first step for accessing data was to search the restricted-access World Bank Microdata Library for household Income and Expenditure, Living Standards, and Budget Surveys to see in which countries criteria (1)-(4) above appeared to be satisfied. The datasets which satisfied these criteria varied in their ease of access: for some countries, the micro data were accessible for download on the World Bank platform, others were licensed and required applications through the World Bank, which would in turn sometimes contact the country’s national statistical agency for approval. If a survey was listed without its micro through the World Bank platform, we reached directly the country’s’ statistical agency. Most countries for which we requested the data sent us the micro data, but in a few cases we could not obtain data 73
which included the place of purchase variables. The countries which ultimately satisfied the criteria for inclusion span four regions of the world, concentrated in Sub-Saharan Africa and Latin America and the Caribbean, as detailed in Table B1. Unfortunately we were not able to include countries in Asia, since the question on the place of purchase was almost always missing from their budget surveys.

Table B1: Regional Survey Representation

|**Region**|**# Countries **|**Pop. of Surveyed Countries **<br>(Millions)|**Total Pop. **<br>(Millions)|**Proportion of pop.**|
|---|---|---|---|---|
|Sub-Saharan Africa|16|379|1078|35%|
|Middle East & North Africa|2|48|449|11%|
|Europe & Central Asia|2|9|918|1%|
|Latin America & Carribean|10|489|641|76%|
|East Asia & Pacifc|1|9|2328|0.4%|

While some surveys appeared from their questionnaire to satisfy our criteria, we ultimately could not include them, either because of issues with data access, or because when we looked more closely at the data one of our criteria was violated. For completeness, Table B2 further details countries that were considered, but could not be included/ Table B2: Discarded Household Expenditure Surveys

|**Country**|**Survey**|**Year **|**Reason not Included**|
|---|---|---|---|
|**Armenia**|Integrated Living Conditions Survey|2016|PoP often missing|
|**Bosnia & Herzegovina**|Household Budget Survey|2007|PoP asked as a purchasing habit|
|**El Salvador**|Encuesta de Hogares de Propositos Multiples|2010|PoP often missing; limited product categories|
|**The Gambia**|Integrated Household Survey|2003|No Data access to PoP|
|**Gerogia**|Integrated Household Survey|2018|Limited product categories|
|**Ghana**|Living Standards Survey|2006|No Data access to PoP|
|**Guatemala**|Encuesta Nacional sobre Condiciones de Vida|2000|PoP often missing; limited product categories|
|**Mauritius**|Household Budget Survey|2012|PoP asked as a purchasing habit|
|**Namibia**|Namibia Household Income and Expenditure Survey|2015|limited product categories|
|**Nicaragua**|Encuesta Nacional de Hogares sobre Medicion de Nivel|2014|PoP asked as a purchasing habit; limited product categories|
|**Tajikistan**|Household Budget Survey|2016|limited product categories|
|**Turkey**|Household Income and Consumption Survey|2009|No Data access to PoP|

Table B3 lists the 31 countries which we could include, with summary statistics and the structure of each survey. Any slight deviation from our inclusion criteria is outlined in the last column.

74
Table B3: Household Expenditure Surveys

|**Country name**|**Survey**|**Year**|**Source**|**# HH**|**# items/HH**|**Exp/HH**<br>Cst. 2010 USD|**Urban**|**HH Size**|**# PoP**|**# Modules**|**Product Code**|**Comments**|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|**Benin**|EMICOV|2015|World Bank|19872|31.9|261|48.2%|4.3|12|22|COICOP||
|**Bolivia**|ECH|2004|Stat. Offce|9149|49.4|585|60.7%|4.2|24|3|COICOP||
|**Brazil**|POF|2009|Stat. Offce|56049|48|3892|84.4%|3.3|33|8|Country-specifc||
|**Burkina Faso**|EICVM|2009|Stat. Offce|8404|161.6|563|29.3%|6.7|45|1|COICOP||
|**Burundi**|ECVM|2014|World Bank|6681|90.2|242|9.0%|4.8|13|23|COICOP||
|**Cameroon**|ECAM|2014|World Bank|10303|95.8|1889|44.5%|4.6|17|1|COICOP||
|**Chad**|ECOSIT|2003|World Bank|6747|92|356|10.9%|5.9|17|18|Country-specifc||
|**Chile**|EPF|2017|Stat. Offce|15237|129.2|6872|100.0%|3.3|22|1|COICOP|No self-production, Only urban|
|**Colombia**|ENIG|2007|Stat. Offce|42733|79.6|1850|82.4%|3.8|24|5|COICOP||
|**Comoros**|EDMC|2013|Stat. Offce|3139|83.5|1809|49.1%|5|12|19|COICOP||
|**Congo DRC**|E123|2005|World Bank|12098|106.9|198|16.0%|5.3|13|1|COICOP||
|**Congo Rep**|ECOM|2005|World Bank|5002|84.8|641|63.8%|5.1|17|1|COICOP||
|**Costa Rica**|ENIGH|2014|Stat. Offce|5705|67.5|5256|73.2%|3.4|41|1|COICOP||
|**Dominican Rep**|ENIGH|2007|Stat. Offce|8363|89.1|2396|67.6%|3.7|88|3|COICOP||
|**Ecuador**|ENIGHUR|2012|World Bank|39617|88.6|1923|68.0%|3.9|75|7|COICOP||
|**Eswatini**|HIES|2010|World Bank|3167|43.9|1283|37.4%|4.5|13|2|COICOP||
|**Mexico**|ENIGH|2014|Stat. Offce|19459|57.4|2272|64.5%|3.8|19|1|COICOP||
|**Montenegro**|HBS|2009|World Bank|1223|148.9|3731|62.7%|3|7|3|COICOP|Cant separate categories 3 & 4|
|**Morocco**|ENCDM|2001|World Bank|14243|87.5|1679|61.6%|5.9|47|17|COICOP||
|**Mozambique**|IOF|2009|World Bank|10809|48.7|363|28.9%|4.7|6|6|COICOP||
|**Niger**|ENCBM|2007|World Bank|4000|221.2|325|17.2%|6.4|15|6|COICOP||
|**Papua NG**|HIES|2010|World Bank|3811|111.2|1002|11.3%|5.1|6|1|COICOP||
|**Peru**|ENAHO|2017|Stat. Offce|43545|78.5|2609|76.8%|3.9|41|8|Country-specifc||
|**Rwanda**|EICV|2014|World Bank|14419|53.6|417|17.1%|4.6|11|8|COICOP|Pre-flled items|
|**SaoTome**|IOF|2010|World Bank|3145|105.9|705|68.1%|3.8|21|3|COICOP||
|**Senegal**|EDMC|2008|World Bank|1443|517.8|640|100.0%|7.7|41|1|COICOP|Only urban|
|**Serbia**|HBS|2015|World Bank|6531|106|1888|61.9%|2.8|9|2|COICOP||
|**South Africa**|IES|2011|U. of Cape Town|25325|44.2|3557|67.3%|3.8|6|1|COICOP|Cant separate categories 3 & 4|
|**Tanzania**|HBS|2012|World Bank|10186|317.8|478|21.9%|5|13|2|COICOP|Cant separate categories 3 & 4|
|**Tunisia**|ENBCNV|2010|Stat. Offce|11281|139.1|1732|67.6%|4.3|9|1|COICOP|Cant separate categories 3 & 4|
|**Uruguay**|ENIGH|2005|Stat. Offce|7042|77.5|2855|84.9%|3|39|1|COICOP||

The column ’# PoP’ refers to the number of different places of purchase in the country classification.
# **Consumption Module Structure**

Expenditure surveys do not have a fully homogeneous structure across countries. Table B3 presents information on their structure and we provide a summary below:

# _•_ **Number and frequency of modules**

- The number of consumption modules ranges from 1 to 17 across countries in the All have a module which is a of over some

- sample. surveys diary consumption short to medium period of time and some countries complement these with recall modules for more infrequent purchases. For example, Costa Rica has a single consumption module, while Morocco has 17, with modules specialized by frequency and products. Surveys with multiple modules typically asked for consumption linked to the frequency of expenditures (e.g. weekly diary, quarterly recall).

- **Durables**

Durable items, which are not purchased frequently are included whenever available, but their inclusion is more probable in surveys which have recall modules.

- **Self-production**

- Self production is included as a “place of purchase” for all countries but Chile where it was not available. In some countries, it was pre-coded as an option for the place of purchase, while in other cases we added it as a place of purchase based on other variables, such as “mode of acquisition,” which had “purchased or “self/home production.” Self-production values are typically asked as value if you had purchased(or sold) this item at a market place.

# _•_ **Product codes**

All surveys have product codes for each consumption item, which typically follow the United Nations Classification of Individual Consumption According to Purpose (COICOP) or which we could matheced to the COICOP with a cross-walk. For a few countries the COICOP classification was not available and we could not find a product crosswalk. We used the nationally-specific product classification scheme for these countries (Brazil, Chad, Peru and Tunisia).

76
# **B.2 Categories of Places of Purchase**

Our core sample of 31 surveys has by construction a place of purchase for each household purchase. Evidently, the names of places of purchases (PoP) available to respondents differ across countries. However, the places of purchases can be classified into broad categories which are approximately equivalent across countries. We detail below the taxonomy used in this paper, which separates the consumption of goods into five broad categories of places of purchase, and services into four broad categories.

# _•_ **Goods**

(1) Non-market consumption (e.g. Self-production) (2) Market consumption, no store front (e.g. markets, street stalls) (3) Market consumption, corner and convenience shops (4) Market consumption, specialized shops (e.g. brand stores, bakeries)

- (5) Market consumption, large stores (e.g. supermarkets, malls)

# _•_ **Services**

(6) Services provided by institutions (e.g. bank, hospital, university) (7) Service provided by individuals (e.g. maid services, gardening) (8) Entertainment (e.g. restaurants, hotels) (9) Informal Entertainment (e.g. food truck)

# _•_ **Unspecified**

(99) N.A/other (e.g. other, not applicable, unspecified) The majority of countries have places of purchase for each of the five good categories. In some countries one of these categories is missing, all such cases are reported in the last column of table B3. Four countries in particular do not distinguish between specialized stores (category 4) and corner/convenience stores (category 3). For these countries we imputed at the decile level the relative shares of categories 3 and 4, based on countries with income up to 50% smaller or larger.

For services, it is more frequent that some of categories are missing. In particular some countries do not have a detailed list of institutions as potential places of purchases for services. These are typically also countries in which the share of expenditures with 77
Figure B1: Average Share of Unspecified Category by COICOP <!-- Start of picture text --> Utilities, Telecom, Gas<br>Health & Education<br>Diverse G&S, Recreation<br>Other<br>BI CD NE MZ BF TD RW TZ BJ ST SN KM CM BO PG MA CG TN SZ DO EC CO RS PE ME ZA CR UY MX BR CL<br>60<br>50<br>40<br>30<br>20<br>10<br>Share of Unspecified Place of Purchase (in %)<br>0<br><!-- End of picture text --> an ’unspecified’ place of purchase is relatively large. Indeed when looking at what types of products compose the unspecified category, over half are utilities, while the remaining is principally education and health spending.

Finally, we assign the remaining places of purchase that are harder to categorize (as purchases over the internet or from abroad) to category (6) “services provided by institutions”. While this might not be accurate, we note that these PoP typically represent a very small share of total expenditure.

The countries-specific assignment of places of purchase to the broad categories presented above is detailed in Table B4, for each PoP representing more than 0.5% of total purchases. The table also reports the share of expenditures purchased from each category, including the unspecified category.

Finally, we note that, to the best of our knowledge, the only other project which constructs a common taxonomy of places of purchases across countries is the International Price Comparison (ICP) project, which builds purchasing power parity indexes. The ICP provides a store type classifier for marketed consumption which is used by individual countries to obtain price quotes from a variety of retailer types. Our classification mirrors that of the ICP.

78
# **B.3 Global Consumption Database**

A limitation of our core sample of 31 countries is that it tends to be geographically clustered and in does not contain countries in Asia. To obtain an idea on particular whether our results might be relevant for all low and middle income countries, we compare food expenditure with that of the Global Consumption Database (GCD). The GCD is the most data source on consumer in comprehensive spending patterns developing countries to date, by assembling all available representative household expenditure surveys across countries. In particular, it includes most countries in Asia. The dataset is curated by the World Bank: aggregatef consumption statistics and further details on sources and methodology are available at http://datatopics.worldbank.org/ consumption/.

We obtained access to the Global Consumption Database microdata, in order to comfood in our core of 31 countries to the 79 low and middle pare expenditure sample income countries available in the GCD. From our sample of 31 countries, 21 countries with the GCD and have the exact same as an source. overlap usually survey original With this enhanced dataset, which represents 51% of the world population,<sup>49</sup> we measure food consumption as a share of total consumption and the slope of the food Engel curve. First we note that for the 21 countries we curve overlapping find Engel slopes within 5% of the GDC estimate. Second we compare food expenditure patterns in our core sample 31 countries to the 58 countries which only appears in the GCD. We find remarkably similar food expenditure shares and food Engel curve slopes, as a function of development, which supports that our core sample informality measures could be informative to the entire population located in developing countries, with the caveat that informality patterns might still differ geographically.

> 49We exclude rich countries by design, but a few populous countries such as China, Egypt and Iran are not part of the GCD. This explains the lion’s share of the missing population in the GCD sample.

79
Table B4: Country-Specific Places of Purchase

|**Assigned**|**%**|**BENIN**<br>**Original name**|**Classifcation**|**CAMEROON**<br>**Assigned**<br>**%**<br>**Original name**<br><br><br>|**Classifcation**<br>|
|---|---|---|---|---|---|
|**Formal**|1.9<br>07|<br>autre lieu d’achat formel sur le territoir<br>achat dans un suer march ́e|5 large stores<br>5 lare stores|**Formal**<br>1.0<br>Supermarche/Grand magasin<br>3.8<br>Magasin specialistes|5 large stores<br>4 specialized shops|
||.<br>0.6<br>|p<br>achat dans un magasin ou un atelier formel<br>|g<br> 4 specialized shops<br>|2.9<br>Presetation de services publics<br>7.5<br>Secteur transport|6 institutions<br>6 institutions|
|**Informal**|2.8<br>28.3|achat au secteur public ou parapublic<br> achat au domicile du vendeur, dans une pet|6 institutions<br> 3 corner shops|2.1<br>Cliniques<br>7.0<br>Hotels/bars/restaurants|6 institutions<br>8 entertainment|
||22.8<br>26.1|achat sur un march ́e public<br> achat chez un ambulant, ou poste fxe sur|2 no store front<br>2 no store front|**Informal**<br>10.7 Epiceries/Boutiques/Echoppes<br>0.8<br>Vendeurs specialises hors magasins|3 corner shops<br>2 no store front|
||7.0<br>06|<br>autre lieu d’achat informel (ind ́ependant)<br>adau ru|1 non-market<br>1 nn-markt|3.4<br>Kiosque de jeux et Call Box<br>3.4<br>Vente ambulante|2 no store front<br>2 no store front|
||.<br>|ce ec<br>b d|oe<br>k|26.4 Marches|2 no store front|
|**Unspec.**|8.6<br>0.0|ien ou service autoprouit<br>other<br>|1 non-maret<br>99 n.a./other|14.8 Don, cadeau recu<br>1.9<br>Domicile de vendeur|1 non-market<br>1 non-market|
|**Formal**|0.9|**BOLIVIA**<br>supermercado|5 large stores|3.6<br>Auto production<br>0.9<br>Dans la nature/forit/brousse|1 non-market<br>1 non-market|
||11.5<br>1.2<br>05|tienda especializada<br>instituci ́on de salud<br>ii ́|<br>4 specialized shops<br>6 institutions<br>6 ititti|2.5<br>Prestation de services individuels<br>**Unspec.**<br>7.3<br>Other<br>**CHAD**|7 service from individual<br>99 n.a./other|
||.<br>3.5<br>|comuncacon<br>instituto educativo<br>|nsuons<br>6 institutions<br>|**Formal**<br>0.7<br>Supermarche<br>5.7<br>Boutique|5 large stores<br>4 specialized shops|
||1.5|hotel, bar, restaurante|8 entertainment|1.1<br>Magasins|<br>4 specialized shops|
|**Informal**|14.2<br>2.0|tienda de conveniencia<br>vendedor ambulante|3 corner shops<br>2 no store front|0.6<br>Prestataire service sant ́e public<br>4.1<br>Autre prestataire de service priv ́e|<br>6 institutions<br>6 institutions|
||3.5|puesto/kiosco|2 no store front|<br>0.7<br>Enseignement priv ́e|<br>6 institutions|
||39|feria|<br>2 no store front|<br>07<br>Transport priv ́e|<br>6 institutions|
||.<br>192|d|<br>2 f|.<br> <br>06<br>Enseignement public|<br>6 institutions|
||.<br>1.5<br>|mercao<br>auto consumo<br>|no store ront<br>1 non-market<br>|.<br> <br>0.9<br>Autre prestataire de service public<br>06<br>Prestataire service sant ́e riv ́e|<br>6 institutions<br>6 institutions|
||1.9|de un hogar / transferencia|1 non-market|.<br>p<br>16<br>Hˆotel Restaurant|<br>8 entertainment|
|**Unspec.**|5.4<br>28.0|cantina<br> other<br>**BRAZIL**|9 informal entertainment<br>99 n.a./other|.<br>, , ..<br>**Informal**<br>0.5<br>Echoppe<br>2.6<br>Marchand ambulant<br>258Mh ́ d ti ́ili ́|<br>3 corner shops<br>2 no store front<br>2 t ft|
|**Formal**|11.5<br>|supermarket<br>|5 large stores<br>|. arce e quarer ou specase<br>30.1 March ́e centraux<br>12<br>Tbli|no sore ron<br>2 no store front<br>2 t ft|
||0.7<br>22.1<br>6.5|department store<br> specialized shop<br>vehicle|5 large stores<br>4 specialized shops<br>4 specialized shops|.<br>aer<br>17.3 Self-Consumption<br>**Unspec.**<br>4.9<br>Other<br>|no sore ron<br>1 non-market<br>99 n.a./other|
||4.0|pharmacy|4 specialized shops|**CHILE**<br><br>|l|
||0.7|bank|<br>6 institutions|**Formal**<br>26.5 supermercados<br><br>|5 arge stores<br>|
||06|internet|<br>6 institutions|4.3<br>distribuidoras - mayoristas<br><br><sup> ́</sup> <sup> ́</sup>|5 large stores<br>|
||.<br>1.5<br>2.5<br>|health institution<br>education institution<br>|<br>6 institutions<br>6 institutions<br>|1.6<br>ferreterIas y multiferreterIas<br>0.5<br>tienda especializada<br>4.9<br>farmacias<br><br>|4 specialized shops<br>4 specialized shops<br>4 specialized shops<br>|
||0.5<br>2.7|lottery<br>restaurant|6 institutions<br>8 entertainment|2.0<br>internet<br>0.5<br>extranjero<br><br> <sup> ́</sup>|6 institutions<br>6 institutions<br>|
|**Informal**|3.4|grocery store|3 corner shops|2.4<br>hospital pUblico y consultorios<br><sup> ́</sup>|6 institutions|
||08|<br>small shop|<br>2 no store front|5.4<br>clInicas|6 institutions|
||.<br>1.2<br>|<br>fair<br>|<br>2 no store front<br>|1.0<br>restaurantes y bares<br>**Informal**<br>13.3 almac<sup> ́</sup>En tradicional|8 entertainment<br>3 corner shops|
||1.4<br>1.4|small market<br>street seller|2 no store front<br>2 no store front<br>|3.3<br>ferias libres<br>2.9<br>comercio ambulante|2 no store front<br>2 no store front|
||8.3<br>4.8|person<br>private service|1 non-market<br>7 service from individual|0.9<br>vegas - mercados<br>**Unspec.**<br>30.5 other|2 no store front<br>99 n.a./other|
||2.1<br>05|<br>bar-cafe<br>recreation events|9 informal entertainment<br>9 informal entertainment|**COLOMBIA**<br>**Formal**<br>4.7<br>Supermercados de barrio|5 large stores|
|**U**|.<br>208|<br>th|<br>99 /th|<br>10.1 Almacenes o supermercados de cadena y tien|<br> 5 large stores|
|**nspec.**|.|oer<br>|n.a.oer|<br>2.1<br>Plazas de mercado y galer ́ıas|<br>5 large stores|
|**Formal**|0.6|**BURKINA FASO**<br>magasin de gros a petits prix|5 large stores|<br>0.6<br>Hipermercados<br>11.1 Establecimientos especializados en la vent|<br>5 large stores<br>4 specialized shops|
||0.7<br>0.5<br>13|grands magasin<br>quincallerie (petite taille)<br>atelier service reparation|5 large stores<br>4 specialized shops<br>4 specialized shops|<br>1.7<br>Farmacias y droguer ́ıas<br>1.0<br>Televentas y ventas por cat ́alogo<br>5.1<br>Restaurantes|<br>10 pharmacies<br>6 institutions<br>8 entertainment|
||.<br>17|,<br>station service (lubrifants)|<br>4 secialized shos|**Informal**<br>0.9<br>Graneros|3 corner shops|
||.<br>|<br>|p p<br>|13.5 Tiendas de barrio|<br>3 corner shops|
||1.0<br>|pharmacie<br>|4 specialized shops<br>|1.7<br>Vendedores ambulantes o ventas callejeras|<br>2 no store front|
||1.0<br>|clinique, laboratoire medical public<br>|6 institutions<br>|<br>1.1<br>Persona particular|<br>1 non-market|
||0.7<br>1.2|ecole, lycee, universite publics<br>ecole, lycees, universite privas|6 institutions<br>6 institutions|<br>0.9<br>Transfers, from household<br>103Self production|<br>1 non-market<br>1 non-market|
||0.6|<br>cabine telephone privee|6 institutions|. <br>10<br>Cafeter ́ıas establecimientos de comidas|<br>9 informal entertainment|
||20|<br>telehone eau electricite|6 institutions|.<br>y<br>**Unspec**<br>329Other|<br>99 na/other|
||.<br>1.8<br>|p, ,<br>bar, cafe, restaurant, hotel<br>|<br>8 entertainment<br>|**.**<br>. <br>**COMOROS**<br>**Formal**<br>20<br>Achat dans un suer march ́e|..<br>5 lare stores|
|**Informal**|14.3<br>|boutique de quartier<br>|3 corner shops<br>|.<br>p<br>169Autre lieu d’achat formel|g<br>5 lare stores|
||0.9<br>40.5<br>1.0|kiosque ou echoppe quartier<br> marche<br>marchant ambulants|2 no store front<br>2 no store front<br>2 no store front|. <br>4.9<br>Achat dans un magasin ou un atelier formel<br>8.3<br>Achat dans un magasin ou un atelier formel<br>61<br>Aht h li d ́id` l’ ́t|g<br>4 specialized shops<br>4 specialized shops<br>6 ititti|
||10.1<br>124|bien ou service autoproduit<br>menae|1 non-market<br>1 non-market|.<br>ca ors eu e resence ou a er<br>8.6<br>Achat au secteur public ou parapublic<br>**Ifl**<br>191Aht diil d d d t|nsuons<br>6 institutions<br>3 h|
||.<br>|g<br>d|<br>k|**norma**<br>. ca au omce u veneur, ans une pe<br>**CONGO DRC**|corner sops|
||0.5<br>|caeau recu en nature ou en espace<br>|1 non-maret<br>|<br>126Ah h ́ bli|2 f|
||2.1<br>|autres service prives<br>|7 service from individual<br>|. cat sur un marce puc<br><br>Ah h bl f|no store ront<br>f|
|**Unspec.**|1.4<br>0.3|service de transport prive<br>other|7 service from individual<br>99 n.a./other|5.5<br>cat cez un amuant, ou poste xe sur<br>4.2<br>Bien ou service autoproduit<br><br>d|2 no store ront<br>1 non-market<br>k|
|**Formal**|36|**BURUNDI**<br>Autre lieu d’achat formel|5 large stores|2.3<br>Caeau rec ̧u<br>8.3<br>Autre lieu d’achat informel (ind ́ependant)<br><br><br>|1 non-maret<br>1 non-market<br>|
||.<br>08|<br>Mi tli fl (it) t|<br>4 ilid h|**Formal**<br>0.5<br>Achat supermarche<br><br>|5 large stores<br>|
||.<br>|agasn, aeer orme socee enu<br>|specaze sops<br>|3.2<br>Achat magasin indo-pakistanais<br><br>|4 specialized shops<br>|
|**Informal**|2.0<br>26.8<br>32.9|Secteur public ou parapublic<br> Domicile du vendeur, petite boutique<br> Marche public|6 institutions<br>3 corner shops<br>2 no store front|3.1<br>Achat secteur public<br>**Informal**<br>3.8<br>Achat magasin non indo-pakistanais<br>36.5 Achat marche public<br>|6 institutions<br>3 corner shops<br>2 no store front<br>|
||3.9|Vendeur ambulant ou poste fxe sur voie|2 no store front|10.1 Achat Ambulant<br>|2 no store front<br>|
||0.9|<br>Cadeau Recu|1 non-market|17.5 Bien ou service autoproduit<br><br>|1 non-market<br>|
||143|<br>Bien ou service autoroduit|<br>1 non-market|5.8<br>Autre lieu informel<br>|1 non-market<br>|
||.<br>13.9<br>|p<br> Autre lieu d’achat informel<br>|<br>1 non-market<br>|17.9 Achat domicile<br>1.4<br>Cadeau recu<br><br><br>|1 non-market<br>1 non-market<br>|
|**Unspec.**|0.0|Other|99 n.a./other<br>80|**Unspec.**<br>0.1<br>Other|99 n.a./other|
|**Assigned**<br>**%**|**COSTA RICA**<br>**Original name**|**Classifcation**|**ESWATINI**<br>**Assined**<br>**%**<br>**Oriinal name**|**Classifcation**|
|---|---|---|---|---|
|**Formal**<br>1.2<br>171|<br>tienda por departamentos<br>suermercado|5 large stores<br>5 lare stores|**g**<br><br>**g**<br>**Formal**<br>27.5 supermarket<br><br>|5 large stores<br>|
|. <br>113|p<br>ll ilid|g<br>4 ilid h|1.4<br>butchery|4 specialized shops|
|. <br>|oca especazao<br> ́|specaze sops<br>|1.7<br>hardware store|4 specialized shops|
|4.3<br>|gasolinera y estacion de servicio<br> ́ ́|4 specialized shops<br>|56<br>lth/ft/li|<br>4 ilid h|
|1.1<br>1.0|carnicerıa / pescaderıa<br>salones de est ́etica o belleza|4 specialized shops<br>4 specialized shops|.<br>coesoowearnen<br>**Informal**<br>5.8<br>grocery|specaze sops<br>3 corner shops|
|3.4|almac ́en de electrodom ́esticos y de tecnol|4 specialized shops|0.5<br>spaza|3 corner shops|
|3.4|<br>tienda de ropa / zapater ́ıa / perfumer ́ıa|<br>4 specialized shops|40<br>street vendor|<br>2 no store front|
|19|<br>laboratorio / cl ́ınica / centro m ́edico|<br>6 institutions|.<br> <br><br>|<br>|
|.<br>|<br>|<br>|1.9<br>market|2 no store front|
|1.1<br>|en el exterior<br> ́|6 institutions<br>|11.2 gifts/transfers|1 non-market|
|3.9<br>|restaurante / soda / cafeterıa / helader<br>|8 entertainment|69<br>self roduction|1 non-market|
|1.7|comedor en lugar de trabajo|8 entertainment|.<br>p<br><br>|<br>|
|**Informal**<br>6.2|pulper ́ıa o minisuper|3 corner shops|**Unspec.**<br>33.4 other<br>|99 n.a./other|
|2.4<br>05|<br>vendedor ambulante o a domicilio<br>feria del aricultor|<br>2 no store front<br>2 no store front|**MEXICO**<br>**Formal**<br>2.1<br>tiendas departamentales|5 large stores|
|.<br>0.8<br>|g<br>local de art ́ıculos usados<br>|<br>2 no store front<br>|<br>1.0<br>tiendas con membresia<br>|<br>5 large stores<br>|
|9.1<br>|recibido o comprado a otros hogares<br>|1 non-market<br>|11.4 supermercados|5 large stores|
|0.8|retiro del negocio|1 non-market|21.1 tiendas especifcas del ramo|4 specialized shops|
|**Unspec.**<br>25.1|other<br>**DOMINICAN REPUBLI**|99 n.a./other<br>**C**|<br>0.5<br>compras fuera del pais<br><br>|<br>6 institutions<br>|
|**Formal**<br>3.8<br>36|tienda por departamentos<br>suermercados|5 large stores<br>5 lare stores|0.7<br>diconsa<br>2.4<br>restaurantes|6 institutions<br>8 entertainment|
|.<br>|p<br>|g<br>|**Informal**<br>128tiendas de abarrotes|3 corner shos|
|0.7<br>|tienda de respuestos de vehiculos<br>|4 specialized shops<br>|. <br><br>|p<br>|
|1.1<br>0.6|taller de mecanica en general, desabulladu <br>puesto de rifa de aguante y loteria electr|4 specialized shops<br>4 specialized shops|0.6<br>tiendas de conveniencia<br>5.6<br>persona particular|3 corner shops<br>2 no store front|
|1.2|tienda de ropa|4 specialized shops|<br>31<br>vendedores ambulantes|2 no store front|
|1.0<br>08|<br>ferreterias<br>carniceria|<br>4 specialized shops<br>4 secialized shos|.<br> <br>2.0<br>tianguis o mercado sobre ruedas<br><br>|<br>2 no store front<br>|
|.<br>1.2<br>|tienda de electrodomesticos<br>|p p<br>4 specialized shops<br>|3.7<br>mercado<br>1.3<br>auto producci ́on|2 no store front<br>1 non-market|
|0.5<br>1.4|peluqueria<br>salon de belleza|4 specialized shops<br>4 specialized shops|<br>2.6<br>loncherias, fondas, torterias , cocina<br><br>|<br>9 informal entertainment<br>|
|2.3<br>1.2|farmacias<br>compa ̃nia de tel ́efonos|4 specialized shops<br>6 institutions|**Unspec.**<br>28.8 other<br>**MONTENEGRO**|99 n.a./other|
|1.9|<br>envasadora de gas|6 institutions|**Formal**<br>172suermarket|5 lare stores|
|1.8<br>|<br>comedor popular<br>|<br>6 institutions<br>|. p<br>36.2 store|g<br>4 specialized shops|
|2.4<br>1.3|clinica<br>hospitales<br>|6 institutions<br>6 institutions|**Informal**<br>5.3<br>stall<br>53<br>own roduction|2 no store front<br>1 non-market|
|1.7|corporaci ́on de electricidad|6 institutions|.<br>p<br><br>|<br>|
|3.5<br>1.5|estaci ́on de gasolina<br>colegio|6 institutions<br>6 institutions|**Unspec.**<br>35.8 other<br>**MOROCCO**|99 n.a./other<br>|
|0.5<br>**Ifl**<br>203|restaurante<br>ld|8 entertainment<br>3 h|**Formal**<br>0.7<br>Gas stations (benzine)<br>05<br>Sll Bkh kik|4 specialized shops<br>4 ilid h|
|**norma**<br>. <br>|comao<br>|corner sops<br>|.<br>ma oosop, os<br><br>|specaze sops<br>|
|0.7<br>|almacen de provisiones<br>|3 corner shops<br>|0.8<br>Modern clothing shop|4 specialized shops|
|0.6|picapollo|2 no store front|3.1<br>Butcher or retail chicken seller|4 specialized shops|
|0.5<br>3.2<br>1.2|puesto de pollo<br>vendedora ambulante<br>mercados|2 no store front<br>2 no store front<br>2 no store front|1.2<br>Craftsman’s shop (hairdresser, tailor)<br>1.8<br>Pharmacy|<br>4 specialized shops<br>10 pharmacies|
|09|uestos de venta|<br>2 no store front|35.5 Public and semi-public agencies|6 institutions|
|.<br>|p<br>d|<br>k|<br>15<br>Reular transortation means (bus train|6 institutions|
|1.9<br>1.6<br>|autoprouction<br>cafeteria<br>|1 non-maret<br>9 informal entertainment<br>|.<br>g p ,<br>1.7<br>Public administration|, <br>6 institutions|
|**Unspec.**<br>29.5|other|99 n.a./other|0.7<br>Public baths, shower, swimming pool|6 institutions|
|**Formal**<br>4.0<br>12|**ECUADOR**<br>supermercados de cadena<br>hiermercados|5 large stores<br>5 lare stores|<br>4.1<br>Private education institution<br>1.3<br>Medical care in private institution<br><br><br>|6 institutions<br>6 institutions<br>|
|.<br>05|p<br>t d tt|g<br>4 ilid h|**Informal**<br>1.9<br>Grocer’s|3 corner shops|
|.<br>|repuesos e auomoores<br>|specaze sops<br>|9.7<br>Neighborhood or village grocer|3 corner shops|
|0.5<br>|tercena/carnicera<br>|4 specialized shops<br>|<br>26<br>Nihbhd kt|<br>2 t ft|
|1.3|librerias y papelerias|4 specialized shops|.<br>egoroo mare<br><br>|no sore ron<br>|
|1.4|otros sitios de compra especializados|4 specialized shops|1.3<br>Itinerant merchant selling on sidewalks|2 no store front|
|1.0|salas de belleza|4 specialized shops|10.7 Weekly market|2 no store front|
|0.5|computadoras y accesorios|<br>4 specialized shops|<br>05<br>Cit market or central market|2 no store front|
|11|<br>asolineras|<br>4 secialized shos|.<br>y<br><br>|<br>|
|.<br>2.1<br>|g<br>electrodomesticos y accesorios<br>|p p<br>4 specialized shops<br>|3.6<br>Self production/consumption<br>0.7<br>Cafe, non-standing restaurant|1 non-market<br>9 informal entertainment|
|4.1<br>1.9|ropa de todo tipo<br>calzado de todo tipo|4 specialized shops<br>4 specialized shops|<br>**Unspec.**<br>11.2 Other<br>|99 n.a./other|
|1.2|panaderas|4 specialized shops|**MOZAMBIQUE**<br><br><br>||
|1.2|mecanicas automotrices|<br>4 specialized shops|**Formal**<br>8.8<br>loja|4 specialized shops|
|0.8<br>51|muebles y enceres<br>bti fi|<br>4 specialized shops<br>4 ilid h|**Informal**<br>18.6 mercado informal<br>122d|<br>2 no store front<br>2 f|
|.<br>|ocas y armacas<br>|specaze sops<br>|. mercao<br>|no store ront<br>|
|2.2<br>|establecimientos privados de salud<br>|6 institutions<br>|31.5 auto produc ̧ ̃ao|1 non-market|
|4.7<br>0.5|establecimientos educativos<br>instituciones publicas|6 institutions<br>6 institutions|**Unspec.**<br>28.5 Other<br>**NIGER**|99 n.a./other|
|2.2|<br>transporte de pasajeros|6 institutions|||
|1.2<br>06|<br>venta por cat_·_logo o television<br>aseuradoras|6 institutions<br>6 institutions|**Formal**<br>2.6<br>Clinique, laboratoire, ecole<br>6.7<br>Prestation services publiques|6 institutions<br>6 institutions|
|.<br>14|g<br>fl bd|<br>|<br>64<br>Secteur transort|6 institutions|
|.<br>|servicios proesionaes (aogaos, arqu)<br>|6 institutions<br>|.<br>p<br><br>|<br>|
|2.3<br>**Informal**<br>12.8|restaurantes, salones<br> tiendas de barrio|8 entertainment<br>3 corner shops|1.5<br>Hotel, bar restaurant<br>**Informal**<br>27.1 Epicerie, boutique|8 entertainment<br>3 corner shops|
|1.5|bodegas, distribuidores|3 corner shops|<br>130Marche|<br>2 no store front|
|10.4|<br> mercados|<br>2 no store front|. <br><br>l|<br>f|
|11|ferias libres|2 no store front|2.9<br>Vente ambuante<br><br>|2 no store ront<br>|
|.<br>20|<br>dd blt|<br>2 t ft|1.6<br>Cadeau recu|1 non-market|
|.<br>|veneores amuanes<br>|no sore ron<br>|15.2 Auto production|1 non-market|
|11.1 <br>0.9|productos autoconsumo, autosuministro<br>personas particulares|1 non-market<br>7 service from individual|<br>4.7<br>Prestation service individuels<br><br>|<br>7 service from individual<br>|
|**Unspec.**<br>12.9|other|99 n.a./other|**Unspec.**<br>18.1 Other|99 n.a./other|

81
|**Assigned**|**%**|**PAPUA NEW GUINEA**<br>**Original name**|<br>**Classifcation**|**Assigned**|**%**|**SENEGAL**<br>**Original name**|**Classifcation**|
|---|---|---|---|---|---|---|---|
|**Formal**<br>|34.<br>|<br>5 Supermarket<br>|5 large stores<br>|**Formal**|2.0|<br>Station service (carburants, lubrifants,e|4 specialized shops|
|**Informal**|9.4<br>10.|Small shop, canteen, tuck shop<br>5 Local market|3 corner shops<br>2 no store front||1.8<br>12|Boulangerie, pˆatisserie<br>Si d tt bli|4 specialized shops<br>6 ititti|
||3.8<br>|Street vendor<br>|2 no store front<br>||.<br>11.6|ervce e ranspor puc<br> Bar, caf ́e, restaurant, hˆotel|nsuons<br>8 entertainment|
||14.<br>|Home production<br>|1 non-market<br>|**Informal**|403|Boutique de quartier|3 corner shops|
|**Unspec.**|10.<br>17.|2 Gift<br>6 Other<br>**PERU**|1 non-market<br>99 n.a./other||. <br>0.6<br>10.8|<br>Marchand Ambulant<br> Kiosque ou ́echoppe au quartier|<br>2 no store front<br>2 no store front|
|**Formal**|3.4|Supermercado|5 large stores||16.3 <br>|<br> March ́es<br>|2 no store front<br>|
||1.1|Bodega (por mayor)|5 large stores||3.5|Cadeau rec ̧u en nature|1 non-market|
||0.8<br>|<br>Panader ́ıa<br> ́|<br>4 specialized shops<br>||1.6<br>12|Bien ou service autoproduit<br>A i i ́|1 non-market<br>7 i f idiidl|
||0.6<br>0.9|Peluquerıa<br>Librer ́ıa|4 specialized shops<br>4 specialized shops||.<br>5.1|utres servces prves<br>Service de transport priv ́e|servce rom nvua<br>7 service from individual|
||0.5<br>5.8<br>|Tienda especializada al por mayor<br>Tienda especializada al por menor<br>|<br>4 specialized shops<br>4 specialized shops<br>|**Unspec.**|1.4|Other<br>**SERBIE**|99 n.a./other|
||3.6|Farmacia|10 pharmacies|**Formal**|8.9|Hypermarket|5 large stores|
||3.4<br>16|Empresas de Transporte formales<br>Cntr d tdi|6 institutions<br>6 intittin||23.8 <br>|Specialized shop<br>|<br>4 specialized shops<br>|
||.<br>|eo e esuos<br>|suos<br>||2.9|Discounted shop|4 specialized shops|
||1.3<br>0.5|Grifos de empresas<br>Talleres formales|6 institutions<br>6 institutions|**Informal**|29.6 <br>48|Minimarket<br>Mk|3 corner shops<br>2 f|
||06|Cl ́ınica particular|6 institutions||.<br>|aret/open<br>|no store ront<br>|
||.<br>|<br> ́ b|<br>||1.8|Gray economy|2 no store front|
||1.0<br>|Restaurantes y/o ares<br>|8 entertainment<br>||53|<br>Own production/Own business|1 non-market|
|**Informal**|14.<br>24.|Bodega (por menor)<br>0 Mercado (por menor)|3 corner shops<br>2 no store front||.<br>2.2|<br>Gifts/received transfers|<br>1 non-market|
||27|<br>Fi|<br>2 t ft|**Unspec.**|20.7|Other|99 n.a./other|
||.<br>|era<br>|no sore ron<br>|||**SOUTH AFRICA**||
||3.3<br>5.0|Mercado (por mayor)<br>Ambulante|2 no store front<br>2 no store front|**Formal**|38.6|<br> Chain store|5 large stores|
||05|Emresas de Transorte informales|7 service from individual||11.2|Other retailer|4 specialized shops|
||.<br>|p p<br>|<br>|**fl**|<br>|<br>d|<br>f|
|**Unspec.**|22.|Other<br>**CONGO REPUBLIC**|99 n.a./other|**Inorma**|0.9<br>2.7|Street traing<br>Other|2 no store ront<br>2 no store front|
|**Formal**|1.0|Grands magasins|5 large stores||06|From a household|1 non-market|
||7.0<br>3.9|<br>Autres commerces modernes<br>Secteur transports|<br>4 specialized shops<br>6 institutions|**Unspec.**|.<br>45.7|<br> Other<br>**TANZANIA**|<br>99 n.a./other|
||2.5|Cliniques, laboratoires m ́edicaux et ́ecol|6 institutions|**Fl**|05|Dk kb(Dtt t)|5 l t|
||5.8<br>3.9<br>|<br>Prestataires de services publics<br>Hotels, restaurants, bars, cafes<br>|6 institutions<br>8 entertainment<br>|**orma**<br>**Informal**|.<br>37.3 <br>2.4|ua uwaeparmen sores<br> Shop<br>Street vendor|arge sores<br>4 specialized shops<br>2 no store front|
|**Informal**|3.4|Epiceries modernes|3 corner shops|||<br>|<br>|
||8.4|<br>Echoppes sur marches et sur bord de route|<br>2 no store front||22.8|Market<br>|2 no store front<br>|
||62|<br>Mhd blt|<br>2 t ft||4.7|Other household|1 non-market|
||.<br>42.|arcans amuans<br>8 Marches|no sore ron<br>2 no store front||0.5<br>|Gift from other household<br>|1 non-market<br>|
||3.9|M ́enages|1 non-market||16.0|Produced by household|1 non-market|
||45|Produit autoconsommes|1 non-market||1.8|Gift or free|1 non-market|
||.<br>0.5|<br>Cadeau recu<br>|<br>1 non-market<br>|**Unspec.**|13.7|Other<br>|99 n.a./other|
|**Unspec.**|5.5<br>0.0|Prestataires de services individuels<br>Other<br>**RWANDA**|7 service from individual<br>99 n.a./other|**Formal**|1.3<br>|**TUNISIA**<br>Hyper, supermarche<br>|5 large stores<br>|
|**Formal**|0.6|Supermarket/big shop|5 large stores|**Informal**|67.8 <br>1.2|Boutique privee<br>Point de vente marche|4 specialized shops<br>2 no store front|
||4.6|Specialized shop|4 specialized shops||45|Ambulant|2 no store front|
||2.4<br>|<br>Bar/restaurant<br>|<br>8 entertainment<br>||.<br>1.6|Cadeau|<br>1 non-market|
|**Informal**|13.|Small shop/boutique<br>|3 corner shops<br>||1.3|Auto production|1 non-market|
||1.7<br>0.8<br>|Individual<br>Mobile seller<br>k|2 no store front<br>2 no store front<br>f|**Unspec.**|22.2|<br> Other<br>**URUGUAY**|99 n.a./other|
||12.<br>|Maret<br>|2 no store ront<br>|**Formal**|117|autoservicio cadena de supermercados|5 large stores|
||11.<br>26.|Self production<br>5 From a household|1 non-market<br>1 non-market||. <br>1.0|,<br>shopping o galeria|<br>5 large stores|
||13|Service rovider|7 service from individual||0.5|barraca, ferreteria, vidrieria|4 specialized shops|
||.<br>|p<br>|<br>||13|<br>casa de electrodomesticos telefonos|<br>4 secialized shos|
|**Unspec.**|12.|Other<br>**SAO TOME**|99 n.a./other||.<br>0.7|,<br>verduleria, puesto, fruteria|p p<br>4 specialized shops|
|**Formal**|5.2<br>|Lojas modernas<br>|5 large stores<br>||0.9<br>23|zapateria, marroquineria, talabarteria<br>i id|4 specialized shops<br>4 ilid h|
||5.4<br>|Grandes Lojas<br>|5 large stores<br>||.<br>|mercera, tena<br>|specaze sops<br>|
||1.3|Outros comercios modernos|4 specialized shops||1.5|panaderia, confteria|4 specialized shops|
||0.5|Clinicas laboratorios medicos Hospitais|6 institutions||26|<br>carniceria olleria escaderia|<br>4 secialized shos|
||08|<br>Str d trnrt|6 intittin||.<br>|, p, p<br>|p p<br>|
||.<br>4.3|eco e aspoes<br>Prestates de servicios publicos|suos<br>6 institutions||0.7<br>0.8|farmacia, perfumeria, panalera<br>fuera del pais|4 specialized shops<br>6 institutions|
|**Informal**|0.9<br>33|Hotels, restaurantes, bares, cafes<br>Quiosue / Quitanda|8 entertainment<br>3 corner shos||0.5<br>|<br>cantina, trabajo, colegio<br>|8 entertainment<br>|
||.<br>|q<br>|p<br>||0.9|restaurante, parrillada|8 entertainment|
||24.<br>|Mercado<br>|2 no store front<br>|**Informal**|7.8|almacen|3 corner shops|
||7.8|Vendedor Ambulante|2 no store front||1|l d l|<br>h|
||0.5|Prendas Recebidas|1 non-market||0.<br>|amacen e ramos generaes<br>|3 corner sops<br>|
||09|<br>C t|<br>1 kt||1.0|vendedor ambulante, puesto callejero, car|r 2 no store front|
||.<br>|ampo, mao<br>|non-mare<br>||07|<br>uiosco salon|<br>2 no store front|
||1.9<br>0.6|Auto Consumo<br>Autoabastecimento|1 non-market<br>1 non-market||.<br>1.5|q,<br>feria vecinal|<br>2 no store front|
||37|Prestates de servicios individuais|7 service from individual||0.5|distribuidor o repartidor a domicilio|1 non-market|
||.<br>1.6|<br>Candongueiro|<br>7 service from individual||0.8<br>|<br>bar, pizzeria<br>|9 informal entertainment<br>|
|**Unspec.**|6.4|Other|99 n.a./other|**Unspec.**|59.6|other|99 n.a./other|

82
# **C Theory Appendix**

## **C.1 Proof of expression** (4)

Under our assumption that _pj_ 1 _≈ pj_ 0, _∀j_ we can write the uncompensated elasticity of product _j_ as a function of the uncompensated elasticities of varieties _j_ 1 and _j_ 0 and the cross-variety price elasticities in the following way: where _αj_ =<sup>_<u>p</u>_</sup> _px_<sup><u>0</u></sup><sup>_x_</sup><sup><u>0</u></sup> is the share of informal consumption in total consumption of the product and _εj_ 0,1 it the elasticity of demand for the informal variety with respect to the price of the formal variety.

Writing _ε_<sup>_C_</sup> _j_<sup>thecompensatedpriceelasticityofproduct</sup><sup>_j_theSlutskyequationis</sup><sup>_εj_=</sup> _ε_<sup>_C_</sup> _j_<sup>_−ηjsj_.Usingthisandtheequalities</sup><sup>_ηj_=</sup><sup>_ηj_1(1</sup><sup>_−αj_) +</sup><sup>_ηj_0</sup><sup>_αj_and</sup><sup>_sj_=</sup><sup>_sj_1 +</sup><sup>_sj_0we</sup> obtain: Slutsky symmetry implies _ε_<sup>_C_</sup> _j_ 1,0<sup>(1</sup><sup>_−αj_)=</sup><sup>_εC_</sup> _j_ 0,1<sup>_αj_.Usingourassumptionsofequal</sup> compensated cross-variety elasticity across products ( _ε_<sup>_C_</sup> _j_ 0,1<sup>=</sup><sup>_ε_ ̃</sup><sup>_C_,</sup><sup>_∀j_) , equal compensated</sup> own-price elasticity across varieties within products ( _ε_<sup>_C_</sup> _j_ 1<sup>=</sup><sup>_εC_</sup> _j_ 0<sup>,</sup><sup>_∀j_)andequalcompen-</sup> sated own-price elasticities across products ( _ε_<sup>_C_</sup> _j_<sup>=</sup><sup>_εC_,</sup><sup>_∀j_), and re-arranging, we obtain:</sup> To obtain an expression for the compensated price elasticity _εj_ 1, the parameter of interest, we use the Slutsky equation again and obtain:

## **C.2 Proof of Proposition 1**

In what follows we assume that all product and variety Engel curves are linear with respect to log household income. Taking a first-order Taylor approximations around _y_<sup>_i_</sup> = _y_ ̄ and assuming _s_<sup>_i_</sup> _j_<sup>( ̄</sup><sup>_y_) =</sup><sup>_sj_we can write</sup><sup>_si_</sup> _j_<sup>=</sup><sup>_sj_+</sup><sup>_βj_(</sup><sup>_φi −_1)where</sup><sup>_βj_is the slope of</sup> the EC for product _j_ . We can then write the tax rate on a product _j_ when all varieties are taxed as: 83
The change in the optimal rate over the development path, holding efficiency considerations constant ( _∂εj_ = 0), can therefore be written as: <u>�</u> _<u>i</u>_<sup><u>( ̄</u></sup><sup>_<u>g−gi</u>_</sup><sup><u>)</u></sup><sup>_<u>φi</u>_</sup><sup><u>(</u></sup><sup>_<u>φi−</u>_1)</sup> where _−gεj >_ 0.

Similarly we can write the tax rate on a product _j_ when only formal varieties are taxed as: and The first part of proposition 1 states that the redistribution gain from taxing all formal varieties uniformly is decreasing over the development path, ie that equity considerations push the optimal uniform rate _τ_ 1<sup>_∗_downwardswithdevelopment.Applyingthe</sup> above to the case of _τ_<sup>_∗_wefindthatthat,holdingefficiencyconsiderationsconstant,</sup> 1<sup>,</sup> _∂τ_ 1<sup>_∗<_0 if the following condition holds:</sup> The negative slope of the Informality Engel Curves implies _β_ 1 _>_ 0. Equity considerations therefore push the optimal uniform rate down over the development path as long as the formal aggregate budget share _s_ 1 increases faster than the slope of the Engel curve for all varieties _β_ 1, which is minus the slope of the Informality Engel Curve depicted in the paper. This proves the first part of the proposition.

To prove the second part of the proposition, which relates to how the efficiency cost of taxing all formal varieties changes over the development path, start from expression (4) in the paper for a ‘product’ consisting of all formal varieties. Writing _η_ 1 this product’s income effect, _s_ 1 it’s budget share, _α_ the share of all formal varieties in total consumption, we obtain: 84
where the last expression is obtained by using _s_ 1 = (1 _− α_ ). The change in _ε_ 1 over the development path, under our assumptions, can therefore be written as: As shown in the paper the size of the informal sector falls with development, so _∂α <_ 0. The term is therefore positive as long as _ε_ ̃<sup>_C_</sup> _>_<sup>_<u>η</u>_</sup> 2<sup><u>1</u>.Whenthisconditionismet</sup> the price elasticity of demand for formal varieties increases over the development path, so the efficiency cost of taxing these varieties falls.

# **C.3 Proof of proposition 2**

We start by proving the first part of the proposition, which states under which conditions the redistribution gain from taxing food less than non-food products increases over the development path when all varieties can be taxed. This implies that, absent efficiency considerations, the optimal rate on food _τF_<sup>_∗_falls over development relative to the optimal</sup> rate on non-food _τ_<sup>_∗_Usingexpression(15)aboveweobtainthefollowingconditionfor</sup> _N_<sup>.</sup> _∂τN_<sup>_∗>∂τ_</sup> _F_<sup>_∗_:</sup> Re-arranging and using the fact that _βN_ = _−βF_ and _sF_ = 1 _− sN_ when all varieties can be taxed, we obtain Where, as shown in the paper, we have _∂sN >_ 0 and _βN >_ 0. There are two cases of interest, depending on which of _sN_ or _sF_ is highest. When households spend on aggregate more on non-food than on food products ( _sN >_ 0.5), as is the case in most countries in our sample, the right-hand-side of the expression is negative, so that the condition holds as long as _βN_ (minus the slope of the food Engel curve) does not fall too much over the development path. This is the case described in the first part of proposition 2 in the text. Note however that if _sN <_ 0.5 the condition can still hold as long as _∂βN_ is positive and _sN_ does not increase too much relative to _βN_ . This case is less empirically relevant, but note that it can be explained using the intuition developed in the paper. All else equal (in particular, holding the slope of Engel curves constant), the redistribution potential of taxing food and non-food at different rates is minimized when 85
food and non-food are consumed in same proportions in the aggregate. An increase in the slope of the non-food Engel curve (or, equivalently, a steepening of the food Engel curve), all else equal, increases this redistribution potential. The redistribution potential will thus fall in a context in which _sN_ starts below 0.5 and increases, unless the slope of the Engel curve increases enough to compensate for the increase in _sN_ .

The in the cost of food less than non-food over change efficiency taxing products the development path, discussed in the second part of proposition 2, is governed by the relative values of _∂εN_ and _∂εF_ . The uncompensated price elasticity of demand for product _j_ is given by: Under our assumptions the change in this elasticity can be written as: As shown in the paper over the development path _∂sN_ = _−∂sF >_ 0, which implies _∂εN < ∂εF_ . The efficiency cost of taxing non-food products therefore increases relative to that of taxing food products: efficiency considerations push the optimal rate on food up relative to that non non-food products over the development path.

# **C.4 Proof of Proposition 3**

To prove the first part of proposition 3, we use expression (17) above to write the change in optimal rates on food and non food when only formal varieties can be taxed, _∂τN_<sup>_∗∗_and</sup> _∂τ_<sup>_∗∗_The condition for</sup><sup>_∂τ∗∗∂τ∗∗_</sup> can be written as: _F_<sup>.</sup> _N_<sup>_>_</sup> _F_ Re-arranging, we obtain: This expression will hold as long as the non-food formal Engel curve slope increases more (or decreases less) than the food formal Engel curve slope (<sup>_∂_</sup> _s_<sup>_<u>β</u>_</sup> 1<sup><u>1</u></sup> _N_<sup>_<u>N</u>_</sup> _>_<sup>_∂_</sup> _s_<sup>_<u>β</u>_</sup> 1<sup><u>1</u></sup> _F_<sup>_<u>F</u>_)andthe</sup> non-food formal budget share doesn’t increase too fast relative to the food formal budget share.

The second part of the proposition states under what conditions the efficiency cost of taxing non-food products increases relative to that of taxing food products in a world 86
in which only formal varieties can be taxed, ie _∂εF_ 1 _> ∂εN_ 1. Under our assumptions the change in the price elasticity of the formal variety of product _j_ over the development path is given by: The condition _∂εF_ 1 _> ∂εN_ 1 is satisfied when: This condition holds as long as, over the development path, the informal share of food consumption falls faster than that of non-food consumption ( _∂αF < ∂αN_ ) and the aggregate budget share of formal food varieties does not increase too fast relative to that of non-food varieties.

# **C.5 Supply-side assumptions**

This subsection shows that our assumptions regarding the pass-through of taxes to prices in the formal and informal sector can be modelled as a equilibrium responses of firms with a simple supply-side model.

Each variety _j_ 1 is produced by a firm that pays taxes (a formal firm), and each variety _j_ 0 by a firm that does not pay taxes (an informal firm). All firms produce using only labor _L_ with the following production function _xjl_ = _φjl Ljl_ , _∀l_ = 0, 1, labor is paid a fixed wage _w_ . Firms maximize their profit _πjl_ = _qjl xjl − wxjl_ / _φjl_ where _qjl_ are the endogenous producer prices, which then determine consumer prices _pj_ 1 = _qj_ 1(1 + _tj_ ) if the firm is = formal, _pj_ 0 _qj_ 0 if the firm is informal.

We assume firms compete under monopolistic competition, which implies that firms maximize profit _πjl_ whilst taking into account the demand function _xjl_ ( _pjl_ ) they face. _ε_ Writing _jl_ the price elasticity of demand for variety _jl_ and taking the first-order-condition with respect to _qjl_ we obtain: This implies the following expression for consumer prices: and 87
This in turn implies a pass-through of one to prices in the formal sector, zero to prices in the informal sector.

# **C.6 Supply-chain considerations**

To consider how our pass-through assumptions are affected by allowing informal retailers to buy from formal suppliers, consider an extension to the above model in which downstream firms produce varieties _jl_ using inputs produced by upstream firms _k_ . Upstream firms produce using only labor _xk_ = _Lk_ . Downstream firms’ production function is given by: where _xjlk_ is the quantity of inputs _k_ used by the downstream firm producing variety _jl_ , and _ρ_ the constant elasticity of substitution in production.

The consumer price of variety _jl_ can now be written as: where _fjl_ = 1 if the firm producing _jl_ is formal, zero otherwise, and _Pjl_ is its input cost index. _Pjl_ is obtained by cost minimization and equal to: Here _pjlk_ is equal to the net of tax price paid for the product _k_ by the firm producing variety _jl_ . We assume the consumption tax is a Value-Added-Tax, so that if both firms _k_ and _jl_ are informal no tax is paid, if firm _k_ is informal no tax is paid, and only if firm _k_ is formal and firm _jl_ informal the tax is paid on the transaction between them. Formally: Combining expressions (33), (34) and (35), we can write the pass-through of taxes to the price of formal and informal downstream firms. The pass-through of taxes to the 88
= price of formal downstream firms ( _fjl_ 1) is still equal to 1: = The pass-through of taxes to the price of informal downstream firms ( _fjl_ 0) can be written as: where _sj_ 0 _F_ is the share of formal inputs in firm _j_ 0’s total production costs:

# **D Calibration Appendix**

This sub-section how we calibrate tax rates under the three sce- explains optimal policy narios defined in expressions (6), (8) and (9). Table 4 summarizes our choice of calibration parameters.

First, we calibrate several parameters directly from our data: we use the observed budget shares described in Section 3, total household expenditure to proxy for household income and the the observed informal shares of consumption for each good and country. We relax our theoretical assumptions that Engel curves are log-linear and that economic development does not affect within-country inequality, using instead the observed budget shares and income distributions in each country. Note that our model calls for using budget shares observed under a counterfactual ’no tax or transfers’ scenario. We do not attempt to adjust observed budget shares to take into account the fact that they are affected by current tax systems as this would require an in-depth understanding of the tax and transfer system in each country in our sample which is beyond the scope of this paper.

We similarly use our data to obtain estimates of income elasticities for all goods and varieties.To obtain an estimate of the income elasticity of demand for the formal variety, _ηj_ 1 we use our estimates of the slope of the formal Engel curve for good _j_ , _βj_ 1, and the expression _ηj_ 1 = 1 + _<u>βsjj</u>_ 11<sup>.We similarly obtain income elasticities</sup><sup>_ηj_using</sup><sup>_ηj_= 1 +</sup> _<u>βsjj</u>_<sup>.</sup> Second, we use existing literature to calibrate the remaining parameters.There are no estimates of the cross-price compensated elasticity of demand between formal and informal varieties _ε_ ̃<sup>_C_</sup> _α_ so we use estimates of the of substitution in _j_ elasticity consumption across stores of different types available in the literature. The cross-price elasticity 89
is related to this elasticity of substitution _σ_ in a CES utility function by the expression _ε_ 0,1<sup>_C_=</sup><sup>_σs_0where</sup><sup>_s_0istheshareofinformalconsumptionoftotalconsumptionofthe</sup> good. Faber and Fally (2017) estimate an elasticity of substitution between large and small stores in the US of 2.2, Atkin et al. (2018b) estimate the elasticity of substitution between foreign and domestic supermarkets and find estimates in the 2-4 range. We therefore use 3 as our baseline of _σ_ . For an average value of _s_ 0 of 0.5 this yields a baseline value of _ε_ ̃<sup>_C_</sup> _αj_ of 1.5, we consider the range 1-2 as a robustness check. We set a value of -0.7 for the own-price compensated elasticity of goods. Together, these parameters yield values for the own-price uncompensated elasticity of goods (calibrated using expression (33) that are in the [ _−_ 2, _−_ 0.5] range, in line with estimates from the literature (see for example Deaton et al., 1994).

Finally, we specify government preferences by setting the same social welfare weight for households in a given decile of the household expenditure distribution in each country. Our specification implies that governments place ten times more weight on income received by households in the poorest decile than in the richest decile. In all countries the richest decile is assigned a weight _gi_ equal to 1, the second richest decile a weight equal to 2, the third a weight equal to 3, and so on, until the poorest decile, which is assigned a weight equal to 10.

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