metadata: authors: 0: author: Sarıkaya,Furkan
1: author: Tamkoc,Mehmet Nazim
2: author: Torres Coronado,Jesica
count: World
docna: 0: docna: Informality and the Life Cycle of Plants
docty: Policy Research Working Paper
abstracts: cdata!: This paper documents the life cycle of
            formal and informal plants using five waves of the Mexican
            establishment census. Formal plants begin operations with
            three times more workers than informal plants and exhibit
            faster growth rates. Throughout their life cycle, formal
            establishments more than double their size, while informal
            plants increase their size by only 77%. A general
            equilibrium model is developed to quantify the aggregate
            economic losses stemming from these growth rate disparities.
            In the model, plants grow through productivity investments,
            and informality emerges from incomplete enforcement. In
            equilibrium, informal plants exhibit flatter life cycle
            profiles to avoid detection and taxation. Model parameters
            are calibrated to match key properties of plant size
            distribution and the life cycle of plants in Mexico.
            Quantitative results indicate that a revenue-neutral full
            enforcement increases aggregate output and the overall
            growth rate by sixteen and twenty-five percent relative to
            the benchmark, respectively.
display_title: Informality and the Life Cycle of Plants
listing_relative_url: /research/2025/01/34443901/informality-life-cycle-plants
topicv3: Macroeconomic Analysis of Economic
            Development m1327386 1066,Informal Sector Productivity m1504064 2882,Firm Dynamics and Productivity Growth
            m1504195 2864
publishtoextweb_dt: 2025-01-08T00:00:00Z
dois: 10.1596/1813-9450-11022
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 44
author_keys: 0: author_key: NA
1: author_key: 1914753
2: author_key: 1840056
model_extractions: Policy Research Working Paper 11022 Informality and the Life Cycle of Plants _Furkan Sarıkaya M. Nazım Tamkoç Jesica Torres_ Development Economics Global Indicators Group January 2025
Policy Research Working Paper 11022

# **Abstract**

This paper documents the life cycle of formal and informal plants using five waves of the Mexican establishment census. Formal plants begin operations with three times more workers than informal plants and exhibit faster growth rates. Throughout their life cycle, formal establishments more than double their size, while informal plants increase their size by only 77%. A general equilibrium model is developed to quantify the aggregate economic losses stemming from these growth rate disparities. In the model, plants grow through productivity investments, and informality emerges from incomplete enforcement. In equilibrium, informal plants exhibit flatter life cycle profiles to avoid detection and taxation. Model parameters are calibrated to match key properties of plant size distribution and the life cycle of plants in Mexico. Quantitative results indicate that a revenue-neutral full enforcement increases aggregate output and the overall growth rate by sixteen and twenty-five percent relative to the benchmark, respectively.

This paper is a product of the Global Indicators Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at fsarikay@asu.edu, mtamkoc@worldbank.org, and jtorrescoronado@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 and the Life Cycle of Plants**<sup>*</sup>

Furkan Sarıkaya<sup>†</sup> M. Nazım Tamkoç<sup>‡</sup> Jesica Torres<sup>§</sup> December 2024

**JEL classification:** E23, J24, L25, O41, O33 **Keywords:** Informality, Life-cycle, Development, Productivity, Distortions

> *We would like to thank Edgar Avalos for his superb research assistance. We thank participants at LACEA/LAMES 2024 for comments. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Tamkoç and Torres thank DECRG for providing Research Support Budget. INEGI has reviewed our results to ensure that no confidential plant-level information is disclosed.

> †Arizona State University

> ‡The World Bank. Corresponding author, mtamkoc@worldbank.org.

- §The World Bank
# **1. Introduction**

Hsieh and Klenow (2014) have documented that plants in the U.S. grow more over their life cycle compared to plants in Mexico and India.<sup>1</sup><sup>_,_2</sup> Less developed countries also face widespread informality.<sup>3</sup> This paper argues that informality, arising from incomplete enforcement, distorts incentives for growth over the life cycle.<sup>4</sup> Since tax compliance increases with plant size, informal plants may optimally choose to keep operating at smaller scales to escape detection. Hence, we study the role of informality in explaining the life cycle of plants. We ask how aggregate economic outcomes such as output and plant-size distribution, as well as the life cycle of plants, would change if informality were reduced by improving enforcement or reducing the burden of formality.

One of the key challenges in studying how informality distorts plant life cycles is the limited availability of plant-level panel data containing information on registration status. This study overcomes this challenge by analyzing Mexico’s census plant-level data from Instituto Nacional de Estadística, Geografía e Informática (INEGI). The data tracks plants over 20 years, from 1998 to 2018, and includes information about establishments’ registration with different tax authorities. Therefore, unlike Hsieh and Klenow (2014), this allows for analysis of a balanced panel of registered and unregistered plants.

In our analysis, an informal establishment is a plant which is not registered with either the central tax authority or the social security administration. In contrast, we refer to plants as formal if they are registered with either the central tax authority or the social security administration. We first show that young formal plants are bigger in terms of employment than young informal plants. Formal establishments in Mexico start operations with 6.1 workers on average whereas their informal counterparts report only 1.9 workers on on average. Second, formal plants grow faster over their life cycle compared to informal plants. While formal plants grow by a 136% during their life cycle, informal plants are only 1.77 times bigger when old compared to young informal plants.

In order to quantify the losses of informality from distortions to the life cycle growth

> 1We use the terms establishment and plant interchangeably throughout the paper.

> 2Eslava et al. (2022) shows that Colombian plants grow less than plants in the U.S.

> 3ILO estimates 57.4% and 89.1% of the employment as informal employment in Mexico and India, respectively whereas 77% of plants operate informally in Mexico according to INEGI census data.

> 4Compliance with taxes varies with plant size: the effective tax rate is higher among large establishments compared to smaller plants (See López and Torres (2020) for Mexico).

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of plants, we develop a one-sector growth model where both formal and informal plants grow by investing in their productivity. Our model is based on Guner et al. (2018) (GPV in what follows) which in turn builds on the Lucas (1978). In the model, agents choose to be workers and entrepreneurs. Our main innovation to their setup is introducing a proportional tax on output that entrepreneurs can escape by operating informally due to incomplete enforcement, in the spirit of Leal (2014). There are two enforcement mechanisms in the model. First, tax officials are not able to enforce taxes to all plants. at the of their face a tax with some Agents, beginning life-cycle, official probability. Second, regardless of whether agents are assigned to an official at the beginning of their life-cycle, informal entrepreneurs are caught if they use capital more than a certain amount. Entrepreneurs must therefore choose whether to operate informally or formally as well as when to transition into formality if they start operating informally at the beginning of their life-cycle.

In equilibrium, smaller and relatively unproductive plants operate informally, while larger plants and those assigned to tax officials early in their life cycle operate formally. Informal plants with higher productivity eventually transition to formal operation as they invest and grow. Consequently, less productive informal plants grow more slowly than formal plants to avoid tax enforcement.

We calibrate the model parameters to match key properties of the plant-size distribution and the growth rates of both formal and informal plants in Mexico. The model is able to successfully match the mean sizes of formal and informal plants as well as the concentration of employment in large plants. In addition, the model is able to capture the markedly different growth rates of formal and informal plants over their life cycle. We first document the effects of changes in the burden of formality, i.e. the tax rate. As the tax rate declines, the formal managers increase their demand for inputs and marginal informal plants decide to operate formally to enjoy higher output and growth potential. This reduces the fraction of informal plant numbers and increases productivity investment, resulting in larger plants and higher aggregate output and growth. Lower taxes also increase the fraction of informal plants transitioning into formality along their life-cycle. Quantitatively, when the tax rate halves, the fraction of transitioning plants rises from 1.9% to 5.8%. This is another factor that contributes to higher growth rate of plants along their life-cycle on average because of the level effect. In other words, the transitioning plants start their life-cycle small and informal; and they don’t have any limit to grow when they become formal. So their growth rates are higher compared to other plants at similar productivity levels.

2
Another formalization policy studied in the literature is through stricter enforcement. We experiment with the effects of improving enforcement policies in revenue neutral set-up on the aggregate variables and the life-cycle of plants on average. The mean size and aggregate output increases by 63.5% and 16.4% under the revenue-neutral full enforcement scenarios, respectively. When taxes are fully enforced such that there is no option of operating informally, plants have no incentive to stay small. Therefore, the overall plant growth rate increases by 25.2% and the entrepreneurial quality increases by 68.1%.

**Background** Our paper contributes to the informality and misallocation literature. The informality literature, as explored by De Soto (1989), La Porta and Shleifer (2008), Maloney (2004) and Loayza (2016) provides a comprehensive understanding of the economic implications of informal sectors.<sup>5</sup> Our research is closely related to the works of Leal (2014), Meghir et al. (2015), Ulyssea (2018), and Tamkoç (2024b). We contribute to this body of work by demonstrating that informal establishments do not growth as much as formal establishments do throughout their life-cycle and by developing a model to quantify the impact of informality on aggregate output.

In addition, our paper engages with the misallocation literature, including seminal works by Hsieh and Klenow (2009), Restuccia and Rogerson (2008) and Bartelsman et al. (2013).<sup>6</sup> We specifically draw on literature examining the growth of plants over their life cycle, such as Hsieh and Klenow (2014), Guner et al. (2018), Garcia-Macia et al. (2019) and Eslava et al. (2022). Our unique contribution lies in constructing a model where formal and informal plants coexist and grow over their life cycle, thereby providing new insights into the dynamics of plant growth and the role of informality in economic development.

# **2. Establishment-Level Data**

Our quantitative exercises exploit data from the Mexican establishment census.<sup>7</sup> The census is administered by Mexico’s statistics agency INEGI and targets the universe

> 5For a detailed survey of this literature, see La Porta and Shleifer (2014) and Ulyssea (2020)

> 6Please see Restuccia and Rogerson (2017) and Hopenhayn (2014) for an overview of the misallocation literature.

> 7Access to the census data is restricted and requires clearance from INEGI. Data for this paper were processed at INEGI’s data lab in Mexico City.

3
of establishments in non-rural areas.<sup>8</sup> Enumerators conduct door-to-door visits and data collection is not restricted to registered (or formal) businesses. Establishments are included regardless of their size (even establishments without employees), as long as the economic activity takes place within delimited fixed building structures.<sup>9</sup> The census is administered every five years. We exploit the five waves between 1998 and 2018. We consider only establishments in manufacturing, wholesale and retail, and non-financial services.<sup>10</sup> In these three broad sectors, the number of establishments in the census increased from 2.5 million in 1998 to 4.3 million in 2018. In 2018, 14% of establishments were in manufacturing, 52% were in wholesale and retail, and the remaining 34% were in (other) non-financial services. Average establishment size in the census has hovered at about 4.5 employees (about 7.5 excluding establishments with no employees).<sup>11</sup> 96% of establishments employ 10 or fewer employees (a fraction that has not changed since 1998) and accounted for 44% of employment in 2018; less than 0.5% of establishments employ more than 100 workers but in 2018 accounted for 36% of employment (Table 2 below and Table B.3 in the appendix).

# **2.1 Formal and Informal Plants**

The 2018 questionnaire introduced two new questions where the respondent is asked whether the establishment is registered with the central tax authority SAT ( _Servicio de Administración Tributaria_ ) and with the social security administration IMSS ( _Instituto Mexicano del Seguro Social_ ). SAT collects corporate and personal income taxes (similar to the IRS in the US), value added taxes, and federal excise taxes. IMSS, on the other hand, collects social security contributions, which employers are required both to contribute to and to withhold on behalf of their employees.<sup>12</sup> The two questions on registration

> 8Rural areas have fewer than 2,500 residents but INEGI does include rural areas in the census when they are the capital of the municipality.

> 9For example, businesses located inside residential properties are included, but street vendors are

not.

10To be precise, our analysis excludes agriculture (11 in the NAICS classification system); mining (21); utilities (22); construction (23); finance (52); real estate (53); management services and administrative support (55-56); education (61); healthcare and social assistance (62); postal services (491); religious and civic organizations (813); private households (814); and employment services (5613).

> 11We measure employment by adding white collar and blue collar employees, unpaid workers, third-party employees (who don’t have an official employment relationship to the establishment), and contractors.

12IMSS also delivers some social services. The share of employers’ social security contributions amount to a tax of about 24% of profits (World Bank Group Doing Business 2020).

4
with SAT and IMSS had yes-or-no answers, with the possibility of a refusal to respond.<sup>13</sup> A third of establishments in the 2018 cross-section report registration with SAT and only 0.23% have missing values in this question. In contrast, only 6.6% of plants report registration with IMSS, but the rate of non-response is 11.5% (see Table 1 below). As we show below, rates of non-response are correlated with the size of the plant—smaller establishments are less likely to report registration with tax authorities.

Table 1: Sorting of establishments into formal and informal and share of plants and employment in each category. 2018.

|**SAT**|**IMSS**|**Formal / informal**|**Share of**<br>**plants**|**Share of**<br>**workers**|
|---|---|---|---|---|
|Yes|Yes|Formal|6_._48|40_._14|
|No|Yes|Formal|0_._11|0_._33|
|Yes|No|Formal|26_._24|30_._24|
|Yes|Non-response|Formal|0_._76|0_._33|
|Non-response|Yes|Formal|0_._00|0_._00|
|No|No|Informal|55_._71|25_._03|
|Non-response|Non-response|Informal|0_._23|0_._54|
|No|Non-response|Informal|10_._48|3_._39|
|Non-response|No|Informal|0_._01|0_._00|

**Notes:** Total in each column may not add up to 100 due to rounding error.

In our analysis, establishments registered with SAT and/or IMSS (as reported by the respondent) are formal; establishments that are not formal are informal (unregistered) as we list in Table 1.<sup>14</sup> Non-responses are thus included in the informal category. Figure 1 shows, for each size bin, the fraction of registered or formal establishments in the 2018 cross-section. The share of formal establishments according to our definition markedly increases with size. The figure also shows that the share of plants not registered with either SAT or IMSS and the rate of non-response to the two questions is higher among small plants. Under our definition, 34% of establishments are formal, accounting for

> 13In Spanish, the questions read _¿Este establecimiento cuenta con registro ante el Servicio de Administración Tributaria (SAT)?_ and _¿Cuenta con registro patronal ante el Instituto Mexicano del Seguro Social (IMSS)?_ Two follow-up questions asked the respondent to provide the identification numbers of the establishment with each tax authority. These four questions were not included in 1998-2013 waves.

> 14In comparison to the definition developed by Busso et al. (2012) and Levy (2018), which focuses on the intensive margin of informality (defined by Ulyssea (2018)), our analysis looks at informality on the extensive margin.

5
71% of employment in the census.

Figure 1: Share of formal and informal establishments in each size category. 2018.

<!-- Start of picture text --> 100<br>80<br>60<br>Formal<br>Not registered<br>40 Not registered and non-response<br>20<br>0<br>Number of workers<br>Share of formal establishments<br>1-5 6-10 11-50 51-100 101+<br><!-- End of picture text -->

**Notes:** Formal establishments are registered with SAT, IMSS, or both, as self-reported by the respondent. Establishments that are not formal are informal.

Table 2 shows the size distribution and the employment size distribution of formal and informal establishments in the 2018 cross-section. Micro-establishments (with 1-10 workers) amount to 90% of establishments and account for 26% of employment among formal plants. Among informal plants, micro-establishments amount to 99% of plants and account for 90% of employment. Large establishments (with 101 or more workers) account for almost 50% of employment among formal plants but only 4% of employment among informal establishments. Informal establishment size averages 2.03, while average formal establishment size is 10.1 workers.

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Table 2: The size distribution of formal and informal plants in the Mexican census. 2018.

||**To**|**tal**|**Formal**|**plants**|**Informa**|**l plants**|
|---|---|---|---|---|---|---|
|Size|Share of<br>plants|Share of<br>workers|Share of<br>plants|Share of<br>workers|Share of<br>plants|Share of<br>workers|
|1-10|95.89%|43.70%|89.10%|26.00%|99.32%|89.22%|
|11-20|2.06%|6.22%|5.28%|7.57%|0.44%|2.98%|
|21-50|1.19%|7.84%|3.21%|9.99%|0.18%|2.65%|
|51-100|0.39%|5.81%|1.10%|7.75%|0.03%|1.09%|
|101+|0.46%|36.42%|1.31%|48.69%|0.03%|4.06%|
|**Total**|**100%**|**100%**|**100%**|**100%**|**100%**|**100%**|

**Notes:** Formal establishments are registered with SAT, IMSS, or both, as self-reported by the respondent. Establishments that are not formal are informal.

# **2.2 The Life Cycle of Formal and Informal Plants**

We estimate size at birth as the average size of formal and informal plants ages 0-4 in the 2018 cross-section: 6.1 workers among formal establishments and 1.9 among informal plants (2.9 for the total average). To estimate growth rates, we exploit the panel dimension of the data. INEGI has developed identifiers that track establishments across the 2008, 2013, and 2018 waves of the census. Busso et al. (2018) developed synthetic identifiers to follow establishments from 1998 through 2008, which we leverage in our analysis.<sup>15</sup> Busso et al. (2019) first exploited the synthetic identifiers to try to compute the life cycle of formal and informal plants in Mexico, but they focused on informality on the intensive margin while our definition looks at the extensive margin. Moreover, while they restrict their analysis only to the balanced panel (the panel of surviving plants between 1998 and 2018), our estimates of the average growth rates leverage micro data from entering and exiting establishments as well as in Eslava et al. (2022). Our analysis also corrects for differences across sectors.

We first sort establishments in the 2018 cross-section into formal and informal using the self-reported registration with SAT and IMSS as described above. We then treat establishments that were informal (formal) in 2018 as informal (formal) every period back through 1998. That is, we do not estimate separate profiles for plants that transition in and out of informality during their life cycle and for plants that never changed their

> 15Busso et al. (2018) use the location, the name, and the 6-digit sector to find establishments in two consecutive waves of the census.

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status since we are not able to observe in the data transitions across informality status using our definition (the questions on registration with SAT and IMSS were not available in previous waves of the census).<sup>16</sup> Still, in our quantitative exercises, we do allow for establishments to change their informality status during their life cycle to assess the potential effect on their growth rates.

We sort formal and informal establishments in every period into age bins (0-4, 5-9, 10-14, 15-19, 20-24, 25-29, 30-34, and 35-39). Next, we restrict the data to those establishments that were ages 0-4 in any cross-section between 1998 and 2013. That is, we restrict the analysis to establishments in the 2018 cross-section (when we observe their formality status) that started operations between 1998 and 2013 (3,006,254 unique establishments). For each establishment, we follow Eslava et al. (2022) and divide their size in every period by their size at age 0-4. We then regress these cumulative growth rates on the (double) interaction between age (in bins) and a binary indicator for whether the plant is formal or informal, 2-digit sector and cohort fixed effects, and another indicator for whether the year is before or after 2008, to control for whether the identifier that links establishments across waves is synthetic (as generated by Busso et al. (2018)) or developed by INEGI.

The exercise just described only allows us to obtain average growth rates through ages 20-24 since we only observe an establishment for 5 periods at most. We therefore repeat these steps for different starting ages. For example, to obtain the average growth rate through ages 30-34, we restrict the data to establishments in the 2018 cross-section that were 10-14 at any point between 1998 and 2013. Our life cycles, which we show in Figure 2, are the average of the different estimates for the cumulative growth rates from the separate regressions using different starting ages. More details on our methodology, together with the full set of results from least squares, are offered in the appendix.

Our estimates show that formal establishments more than double their size during their life cycle. In Figure 2, the size of formal establishments at ages 35-39 is on average 2.4 times their size at birth. In contrast, informal plants increase their size only by 77%. These estimated growth rates do not differ significantly when we focus only on

> 16One potential proxy is the transitions across status of informality on the intensive margin. Busso et al. (2019) estimate that almost 90% of informal establishments in 1998 were still informal in 2013. Formality on the extensive margin, however, is more likely than informality on the intensive margin. While 34% of establishments is registered with SAT and/or IMSS, less than 10% of the 2018 cross-section employ salaried employees and fully contribute to their social security (the definition of formality on the intensive margin first coined by Busso et al. (2012)). Moreover, only 27% of formal establishments according to our definition are also formal on the intensive margin (Table B.4 in the appendix).

8
manufacturing or services (see B.2 in the appendix). Formal plants then not only start their life cycle with more workers relative to informal plants (three times more), but also grow at a markedly faster rate.

Figure 2: Cumulative growth rates in the life cycle of formal and informal plants in the Mexican census.

<!-- Start of picture text --> 2.50<br>2.36<br>2.27<br>2.21<br>2.01 2.00<br>2.00 1.92<br>1.88 1.86<br>1.74<br>1.71<br>1.77<br>1.62<br>1.70<br>1.48 1.49 1.64<br>1.50 1.54<br>1.48<br>1.30<br>1.36<br>1.22<br>1.00<br>1.00<br>Age<br>Informal plants Total Formal plants<br>Average cumulative growth rate<br>[0-4] [5-9] [10-14] [15-19] [20-24] [25-29] [30-34] [35-39]<br><!-- End of picture text -->

**Notes:** Formal establishments are registered with SAT, IMSS, or both, as self-reported by the respondent. Establishments that are not formal are informal. These cumulative growth rates are (rescaled) marginal effects from least squares regressions that also control for fixed effects for 2-digit sector and cohort, and a dummy for whether the panel identifier is synthetic (before or after 2008).

In Figure B.3 in the appendix, we compute growth rates for formal and informal plants according to our definition but exploiting the 2018 cross-section only, as in Hsieh and Klenow (2014). Interestingly, the cross-sectional estimates seem to bias downward the growth of informal establishments (40% in the cross-section vs. 77% exploiting the panel) but overestimate growth among formal plants (170% in the cross-section vs. 140% in our estimations). We show in Figures B.4 and B.5 the life cycles for formal and informal plants using different definitions of informality. Figure B.4 looks at a strict definition that does not sort non-responses into the informal category: plants registered with both SAT and IMSS are formal, while plants not registered with SAT nor IMSS are informal. Figure B.5 follows the formality definition on the intensive margin of 9
Busso et al. (2012) and Levy (2018). The estimated growth rates for informal plants do not vary significantly across definitions (from 77% in our extensive margin definition, to 75% under a stricter classification, and 81% in the intensive margin definition), but estimated growth rates among formal establishments are significantly higher under these alternative definitions, from 136% in our extensive margin definition, to 265% under a stricter classification, and 240% in the intensive margin definition of Busso et al. (2012) and Levy (2018).

# **3. Model**

We build on the model developed by GPV where entrepreneurs run bigger plants by investing in their entrepreneurial ability over their life cycle. Our main innovation is introducing in this framework a tax on output that some plants can escape from by operating informally due to incomplete enforcement.

## **3.1 Environment**

In every period, a group of agents (cohort) endowed with entrepreneurial ability _z_ is born. This initial endowment of entrepreneurial ability is drawn from the (exogenous) probability density function _f_ ( _z_ ) with cumulative distribution function _F_ ( _z_ ) and support <u>[</u> _<u>z, z</u>_ <u>].</u> Agents live for _J_ periods. Each agent maximizes the expected present value of lifetime utility derived from consumption: where _β ∈_ (0 _,_ 1) is the discount factor, _cj_ denotes the consumption of an agent at age _j_ , and _u_ ( _c_ ) = log( _c_ ).

Agents have one unit of time which they supply inelastically until they reach their retirement age _JR < J_ . Along their life-cycle, agents choose to be workers (working for a wage for someone else) or entrepreneurs, and following GPV, this decision is not reversible. Furthermore, each period, entrepreneurs choose whether to operate formal plants, i.e., complying with all taxes, or informal plants, i.e., escaping from taxation.

Production of the single final good of the economy takes place in plants that combine entrepreneurial ability, _z_ , capital, _k_ , and labor, _n_ , as follows: 10
where _γ_ is the span-of-control parameter, with _γ ∈_ (0 _,_ 1), indicating decreasing returns to scale. The parameter _A_ denotes the aggregate productivity term common across all entrepreneurs.

Entrepreneurs can improve their skills by investing their income according to the following skill accumulation technology: where _g_ ( _zj, xj_ ) = _zj_<sup>_θ_1</sup><sup>_xθ_</sup> _j_<sup>2and</sup><sup>_xj_denotestheincomeinvestedinentrepreneurialskill</sup> by an entrepreneur at age _j_ . The parameters _θ_ 1 and _θ_ 2 control the importance of existing entrepreneurial skills and investment in entrepreneurial skill, respectively, where 0 _< θi <_ 1 for _i ∈{_ 1 _,_ 2 _}_ . Hence, the skill accumulation technology exhibits complementarity between the existent entrepreneurial skill and investments in skill ( _gzx >_ 0); and diminishing returns to skill investments ( _gxx <_ 0). Moreover, investment in entrepreneurial skill is an essential input for the skill accumulation technology ( _g_ ( _z,_ 0) = 0). In this law of motion, there is no depreciation of managerial skills.

# **3.2 Taxation with Incomplete Enforcement**

Entrepreneurs face a proportional output tax, _τ ∈_ (0 _,_ 1). Enforcement of this output tax, however, is incomplete for two reasons. First, at the beginning of their life cycle (before choosing their occupation), agents are assigned to a tax official only with some exogenous probability _φ_<sup> ̄</sup> _∈_ [0 _,_ 1]. If an agent faces a tax official, the output tax will be fully enforced if she becomes an entrepreneur. In other words, agents who meet a tax official can only operate formally when they choose to become entrepreneurs.<sup>17</sup> These agents therefore have to decide only between becoming workers or formal entrepreneurs. This component of the enforcement technology does not directly affect the choice of capital or labor for entrepreneurs but does affect occupational choices.

If an does not face a tax at the of the life she can agent official beginning cycle, escape from taxation by operating informally (fully avoiding the output tax). Operating informally, though, carries the risk of detection and subsequent punishment (even if

> 17As we discuss in the calibration section, this probability of meeting with an official, inspired from Tamkoç (2024a), results in a fraction of small formal plants operating in equilibrium.

11
the individual does not face a tax official when they were born). The enforcement of taxation, in turn, follows a size-dependent technology: Informal entrepreneurs then can completely avoid paying taxes as long as they keep their capital equal to or less than the threshold _b_ . Note that no informal entrepreneur will then optimally choose to exceed this threshold as long as the fine if caught evading is strictly larger than zero. If the entrepreneur is informal, she will be caught by the tax authorities when producing with more than _b_ capital. In that case, the informal entrepreneur will be required to pay a fine in addition to the output tax, which would lead to lower profits compared to producing at _k_ = _b_ or operating in the formal sector.<sup>18</sup>

# **3.3 Optimization Problem of Entrepreneurs and Workers**

We focus on a stationary environment where factor prices _W_ and _R_ are constant. We assume that both entrepreneurs and workers can lend and borrow assets, _a_ , at the risk-free rate _r_ = _R − δ_ .

**Workers** The problem of a worker is choosing consumption and savings at each age to maximize the present value of life-time utility:

Workers supply their time inelastically and receive a market wage, irrespective of their initial entrepreneurial skills and of whether they work for a formal or an informal entrepreneur. Hence, workers’ income includes wages and asset returns until retirement.

18The profits of an informal entrepreneur are: For _k > b_ , the profits for an informal entrepreneur will be strictly less than the profits if the plant were to operate formally as long as the fine _F_ is above 0.

12
After retirement, their only income comes from asset holdings (which is also the case of retired entrepreneurs).

**Entrepreneurs** A formal entrepreneur with ability _z_ is subject to the output tax and chooses capital and labor each period to maximize her profit Π<sup>_F_</sup> ( _z_ ):

_z_ Similarly, an informal entrepreneur with ability chooses capital and labor each period to maximize her profit, Π<sup>_I_</sup> ( _z_ ). Unlike formal entrepreneurs, informal entrepreneurs don’t pay taxes but they are subject to a probability of getting caught that constrains their size: In a stationary equilibrium, if an agent chooses to become a worker at the beginning of her life-cycle, she will remain a worker until retirement, as she will not be accumulating entrepreneurial ability that would incentivize her to transition into entrepreneurship later in life. Similarly, if an agent chooses to become a formal entrepreneur at the beginning of her life-cycle, she will remain a formal entrepreneur until retirement since entrepreneurial abilities don’t depreciate in our framework and the skill-investment technology doesn’t feature stochastic returns. In contrast, agents who choose to become informal entrepreneurs at the beginning of their life-cycle could transition into the formal sector as they keep accumulating entrepreneurial abilities (which would make paying the output tax more profitable). We assume that this potential transition from informal to formal entrepreneurship is costless.

The income of an entrepreneur is the profit from running her plant plus the asset income until she retires. After retirement, her income consists of only asset income. An entrepreneur with initial ability _z_ who runs a formal plant for the last<sup>ˆ</sup> _j_ periods of her working time chooses consumption, savings, and investment in her entrepreneurial ability to maximize the present value of life-time utility: 13
When<sup>ˆ</sup> _j_ = 0, the entrepreneur operates informally every period of her working time. _V_<sup>0</sup><sup>_,F_</sup> ( _z_ ) denotes the corresponding value. When<sup>ˆ</sup> _j_ = _JR −_ 1, the entrepreneur starts her working time in the formal sector. The value of being a formal entrepreneur until retirement is _V_<sup>_JR−_1</sup><sup>_,F_</sup> ( _z_ ). When 1 _≤_<sup>ˆ</sup> _j ≤ JR −_ 2, the entrepreneur operates in the informal sector through age _JR −_ 1 _−_<sup>ˆ</sup> _j_ to then transition into the formal sector until retirement. _z_ An entrepreneur with ability selects the age of transition into the formal sector that yields the highest life-time value. The value of lifetime discounted utility of being an entrepreneur is then:

# **3.4 Occupational Choices**

Agents select the occupation that results in the maximum life-time utility. Agent with ability _z_ chooses to become an entrepreneur if _V_<sup>_E_</sup> ( _z_ ) _≥ W_ ; otherwise, she becomes a worker. Furthermore, since an agent with ability _z_ who is not assigned to the tax official has an option to operate informally, she further chooses whether to operate formally or informally at each age.

# **3.5 Discussion of Equilibrium Properties**

Appendix C provides the first-order condition of entrepreneurs’ factor input choices and the definition of the equilibrium. In this section, we discuss properties of the stationary 14
equilibrium.

First, the profits of a formal entrepreneur with ability _z_ can be expressed as the function of parameters and factor prices by using optimal factor demands, Equations (C.1) and (C.2), as follows: As in GPV, the profits of formal entrepreneurs are linear in entrepreneurial skill. In equilibrium, some informal entrepreneurs will choose a level of _k_ strictly below _b_ , but others will opt to adjust their capital level precisely to _b_ , maintaining just enough capital to remain undetected. We refer to informal entrepreneurs operating with capital levels less than _b_ as unconstrained informal entrepreneurs, an informal entrepreneurs operating exactly at _b_ as constrained informal entrepreneurs. Unconstrained informal entrepreneurs choose labor and capital (which is less than _b_ ) while the constrained informal entrepreneurs choose labor given that their capital is _b_ . Using equations C.3, C.4, and C.5 in the Appendix, the profit of informal entrepreneurs can be expressed as follows: Notice that the profit function of unconstrained informal entrepreneurs (i.e., when _k_<sup>_I_</sup> _< b_ ) is linear in _z_ , while the profit function of constrained informal entrepreneurs is 1 _−γ_ concave in _z_ as 1 _−γ_ (1 _−α_ )<sup>_<_1.</sup> The inter-temporal decision between today’s consumption and the next period’s asset can be characterized by the Euler equation: which indicates that agents are indifferent between consuming at age _j_ and saving to consume at age _j_ + 1 in equilibrium.

Entrepreneurs also decide how much to invest on their entrepreneurial skills. This decision can be found from the no-arbitrage condition for asset and investment in entrepreneurial ability as follows: 15
and The left-hand side of Equation (13) represents the opportunity cost of investing in entrepreneurial skills. In other words, an entrepreneur could earn (1 + _r_ ) units of the consumption good by investing one unit in assets rather than investing one unit in entrepreneurial skills. The right-hand side of the equation is the net marginal benefit of skill investment. The first term represents the benefit deduced from the next period profit generated by additional entrepreneurial ability. An extra unit of skill investment in the current period is transformed into next period entrepreneurial skill with _gx_ ( _zj, xj_ ) and Π<sup>_i_</sup> _z_<sup>(</sup><sup>_zj_+1) transforms the additional entrepreneurial ability to profit.Also, an extra</sup> unit of investment in entrepreneurial ability in a given age affects skill accumulation decisions in all subsequent periods. The second term in the right-hand side of Equation (13) represents this effect. This term disappears in the last working age period of entrepreneurs as shown in Equation (14).

Occupational choices can be determined by a set of threshold abilities. First, for agents assigned to a tax official, the occupational choice is characterized by a single _z_ . threshold ability, _w,e_ Agents with abilities below this threshold become workers, while those above the threshold become formal entrepreneurs. For agents not assigned to a tax official, there are at most _JR_ threshold ability levels that sort agents into occupations and into sectors due to the additional option of operating informally and the possibility of transitioning to formal entrepreneurship over their life cycle.<sup>19</sup> In equilibrium, agents not (randomly) matched with a tax official and in the left-tail of the entrepreneurial skill distribution become workers. The least skilled entrepreneurs will start and remain in the informal sector until retirement while the most skilled entrepreneurs will start and remain in the formal sector until retirement. Entrepreneurs in segments in the middle of the entrepreneurial skill distribution will start operating informally and transition into the formal sector for the remaining periods of their working time, with relatively skilled entrepreneurs operating in the formal sector for longer (for more periods).

> 19Without loss of generality, we refer to formal and informal entrepreneurship, including the transition out of informal entrepreneurship, as different occupations.

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More precisely, there will be at most _JR_ thresholds _z_ 0 _,F ≤ z_ 1 _,F ≤ ... ≤ zJR−_ 2 _,F ≤ zJR−_ 1 _,F_ such that agents with skills in the segment <u>[</u> _<u>z, z</u>_ 0 _,F_ ] will become workers (employed for a wage); the set of agents with ability in [ _z_ 0 _,F , z_ 1 _,F_ ] always operate informally (never transition into formal entrepreneurship); agents with abilities in [ _z_ 1 _,F , z_ 2 _,F_ ] operate informally until the last period of their working life; agents with abilities in [ _z_ 2 _,F , z_ 3 _,F_ ] operate informally until the last two periods of their working life; and so on. Entrepreneurs with abilities in [ _zJR−_ 1 _,F ,_ ̄ _z_ ] operate in the formal sector their entire working life. Notice that there may not be any agent who would like to transition into formality for the last periods of their working life as they don’t have much time to invest on their entrepreneurial ability and grow. In these cases, the occupation choices of agents who are not assigned to a tax official are characterized by fewer threshold ability levels.

In sum, there are at most _JR_ + 1 threshold ability levels that determine the occupational choices in equilibrium (one for agents who are assigned to a tax official and _JR_ for those who are not assigned to a tax official).

# **4. Calibration**

We set the model to 5 to the intervals used in our data period years, corresponding analysis. In this framework, agents work for 40 years (8 model periods) and then spend 15 years in retirement (3 model periods). We set the following parameter values from Leal (2014): depreciation rate _δ_ = 0 _._ 055, discount factor _β_ = 0 _._ 945, and tax rate _τ_ = 0 _._ 25. After calibrating the span-of-control parameter _γ_ , we set _α_ such that the importance of capital in the production ( _αγ_ ) equals 0.33, the standard value in the development literature. We assume that entrepreneurial ability follows a log-normal distribution with parameters _μz_ and _σz_ . We normalize the mean parameter _μz_ = 0 and the productivity _A_ = 1. parameter These parametric assumptions leave six parameters to be determined: _γ, σz, θ_ 1 _, θ_ 2 _, b,_ and _φ_ . We jointly calibrate these parameters to match key features of the establishment size distribution in the Mexican census data, with particular attention to the low growth rate of informal plants. Our calibration targets the following moments: (i) the overall mean establishment size; (ii) the mean size of informal establishments; (iii) the fraction of establishments with fewer than 10 workers; (iv) the employment share of establishments with more than 50 workers; (v) the life-cycle growth rate of formal establishments (from ages 0-4 to 35-39); and (vi) the life-cycle growth rate of informal establishments (from 17
ages 0-4 to 35-39).

To align our model moments with data moments, we make several adjustments. Our definition of informality is based on establishments’ registration status with SAT and IMSS in the last year of the census. Therefore, when calculating moments related to the plant-size distribution in the model, we classify retiring entrepreneurs according to their operational status: those retiring as informal entrepreneurs are counted as informal plants, and similarly for formal plants. The mean size of informal plants is defined as follows: where _n_<sup>0</sup><sup>_,F_</sup> ( _z, j_ ) represents the labor demand of an informal entrepreneur with initial ability _z_ at age _j_ . In Equation (15), the numerator represents the total labor demand by informal entrepreneurs across all eight generations, while the denominator represents the fraction of informal entrepreneurs in equilibrium.

To maintain consistency with the data, we focus on entrepreneurs who remain in their initial sector (formal or informal) when calculating growth rates. The growth rate of informal plants from age 0-4 to 35-39 is defined as: Hence, _g_<sup>_I_</sup> represents the average growth rate of informal establishments, analogous to our empirical measure.<sup>20</sup> The growth rate for formal entrepreneurs follows a similar definition.

Table 3 shows the calibrated parameters whereas the targeted moments and their calibrated counterparts are shown in Table 4. The model matches the overall mean size and smaller informal mean size very successfully. It also matches the growth rates of informal and formal plants closely. Moreover, the model doesn’t have any problem capturing the large concentration of employment in bigger plants and the large fraction of plants with fewer than 10 workers.

> 20The growth rate measured in the cross-sectional data differs from the average growth rate of individual establishments, both in the data and the model. The growth rate in the cross-section would be <u>�</u> _zz_ 01 _,F,F_<sup>_n_0</sup><sup>_,F_(</sup><sup>_z,_8)</sup><sup>_f_(</sup><sup>_z_)</sup><sup>_dz_</sup> defined as <u>�</u> _zz_ 01 _,F,F_<sup>_n_0</sup><sup>_,F_(</sup><sup>_z,_1)</sup><sup>_f_(</sup><sup>_z_)</sup><sup>_dz−_1.</sup>

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Table 3: Parameters Values

|Parameter|Value|
|---|---|
|Technology level (_A_)|1|
|Depreciation rate (_δ_)|0.055|
|Discount factor (_β_)|0.945|
|Output tax (_τ_)|0.25|
|Importance of capital (_α_)|0.56|
|Mean of logentrepreneurial ability (_μz_)|0|
|Span-of-control (_γ_)|0.59|
|Dispersion in entrepreneurial ability (_σz_)|1.97|
|Return on previous productivity (_θ_1)|0.58|
|Return on productivity investment (_θ_2)|0.56|
|Enforcement threshold (b)|1.91|
|Probabilityof meetingoffcial at birth(<br>_φ_)|0.31|

Note: This table summarizes all model parameters. First six parameters are set exogenously and the last six parameters are calibrated jointly.

Table 4: Model Performance

|Moment|Data|Model|
|---|---|---|
|Overall mean size|4.77|4.77|
|Informal mean size|2.03|2.03|
|Formal growth (0-4 to 35-39) (%)|136.03|136.03|
|Informal growth (0-4 to 35-39) (%)|77.28|77.28|
|Fraction of plants <10 workers (%)|95.89|95.51|
|Emp. share ofplants with +50 workers(%)|42.23|42.08|

Source: INEGI Note: This table compares moments of the data with that of the benchmark calibration given the parameters values in Table 3.

Next, we evaluate the benchmark economy’s performance by examining nontargeted moments and its detailed features. We begin by comparing the plant size distributions in the model and the data. Figures 3a and 3b contrast the size distribution in the Mexican census with that in the calibrated The benchmark economy. model successfully replicates two key features of the Mexican census data: the large share of micro-plants (those with fewer than 10 workers) and the high concentration of employment in both micro-plants and large plants (those with more than 100 workers).

The model also approximates the formal plant size distribution. Figures 4a and 4b show that the model closely matches the fraction of formal plants among smaller plants 19
(those with fewer than 10 workers). While the model accurately reflects the majority of plants operating in the informal sector, as observed in the data, it slightly overestimates the number of informal plants. In the model, the fraction of informal plants is around 77%, compared to 66% in the data. Similarly, the mean size of formal plants in the model is 14.1 workers, while in the data, it is 10.1. To sum up, only a small fraction of plants are formal and they are bigger in terms of employment compared to informal plants. Formal plants account for 67.1% of all employment and 72.5% of aggregate output in the benchmark economy.

Before comparing the non-targeted life-cycle profiles in the model and the data, we first discuss the mean sizes at the initial period. In the data, informal plants employ an average of 1.9 workers at birth, whereas in the model, the mean size of informal plants at birth is 1.5 workers. The model also closely matches the overall mean size at birth. In Mexico, the overall mean size at birth is 2.1 workers, compared to 2.9 workers in the model.

Figure 3: Plant size distribution in the benchmark economy <!-- Start of picture text --> (a) Fraction of Plants (b) Employment Shares<br>data model data model<br><= 10 11-20 21-50 51-100 101+ <= 10 11-20 21-50 51-100 101+<br>1<br>.4<br>.8<br>.3<br>.6<br>.2<br>.4<br>.1<br>.2<br>0 0<br><!-- End of picture text --> Source: INEGI Notes: This figure compares the overall plant size distribution in the benchmark economy with the data for different size categories.

Next, we compare the life-cycle profiles of formal and informal plants in the benchmark equilibrium with those observed in the data. Figure 5 shows that the model is able to replicate the life cycle of the average plant in Mexico. It also closely matches the life cycle of informal plants observed in the data. However, for formal plants, the model predicts a lower growth profile compared to the data, resulting in an overall growth rate in the model that is slightly lower than in the data. The growth rates in the 20
Figure 4: Formal plant size distribution in the benchmark economy <!-- Start of picture text --> (a) Fraction of Plants (b) Employment Shares<br>data model data model<br><= 10 11-20 21-50 51-100 101+ <= 10 11-20 21-50 51-100 101+<br>1<br>.5<br>.8<br>.4<br>.6<br>.3<br>.4 .2<br>.2 .1<br>0 0<br><!-- End of picture text --> Source: INEGI Notes: This figure compares the formal plant size distribution in the benchmark economy with the data for different size categories.

cross-section of plants shows similarities with the data. In the model, the growth rates of formal plants in the cross-section are higher than their average growth rates, while the growth rates of informal plants in the cross-section are lower than their average growth rates, as in the data. Informal plants in the cross-section grow by 61.3% over their life cycle (from the 0-4 to the 35-39 age group) in the model, compared to a 583.5% growth rate for formal plants in the cross-section Finally, we discuss informal plants transitioning into formality over their life cycle before presenting the quantitative exercises. In the benchmark economy, no informal plants transition into formality during the last or the last two periods of their life cycle. Only 1.9% of plants begin their life as informal and switch to formality during their life cycle. Therefore, the occupation choices of agents are characterized by eight threshold ability levels in the benchmark economy.

# **5. Quantitative Findings**

The development literature mainly focuses on the role of reducing the burden of being formal and increasing enforcement on the prevalence of informality.<sup>21</sup> In this section, we first present the equilibrium effects of changes in the tax rate, _τ_ , and changes in 21Please see Kuehn (2014), Orsi et al. (2014), Leal (2014), Ulyssea (2018), Johnson et al. (1998), Fajnzylber et al. (2011), De Mel et al. (2013), Bruhn and McKenzie (2014), De Andrade et al. (2016) and Rocha et al. (2018) among many others.

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Figure 5: Life-cycle of informal and formal plants in the benchmark <!-- Start of picture text --> (a) Informal Plants (b) Formal Plants<br>1.8 2.50<br>1.6<br>2.00<br>1.4<br>1.50<br>1.2<br>1 1.00<br>Age Age<br>Model Data Model Data<br>(c) Total<br>2<br>1.8<br>1.6<br>1.4<br>1.2<br>1<br>Age<br>Model Data<br>Average cumulative growth rate Average cumulative growth rate<br>[0-4] [5-9] [10-14] [15-19] [20-24] [25-29] [30-34] [35-39] [0-4] [5-9] [10-14] [15-19] [20-24] [25-29] [30-34] [35-39]<br>Average cumulative growth rate<br>[0-4] [5-9] [10-14] [15-19] [20-24] [25-29] [30-34] [35-39]<br><!-- End of picture text --> Source: INEGI the enforcement levels, _b_ and _φ_<sup> ̄</sup> . Then we discuss the implications of revenue-neutral changes in enforcement where the tax rates are adjusted to keep tax revenues constant as enforcement levels change.

In this economy, the only burden of being formal is the output tax, _τ_ . Table 5 shows how the model behaves under different values of the tax rate. As the output tax increases, more plants choose to operate informally to escape from taxation. Doubling the output tax increases the share of informal plants by 13.1 percentage points, and decreases mean size and aggregate output by 36.1% and 37.6%, respectively. The overall plant growth rate in the economy rises as more productive formal plants in the benchmark decide to operate informally. A higher tax rate generates stronger incentives to avoid it, which can happen in this economy by investing less in entrepreneurial skill 22
to remain small. This results in a higher rate of informality, a lower average plant size, and a worse selection into entrepreneurship (lower average entrepreneurial ability).

On the other hand, removing all output taxes more than doubles the mean size and average entrepreneurial quality compared to the benchmark. When there is no output tax in the economy, aggregate output increases by 46.5% and the life-cycle growth rate increases by 85%. As _τ_ decreases, the share of informal plants transitioning into formality over their life-cycle increases. For example, when the output tax is reduced by half (from 25 to 12.5%), the fraction of transitioning informal plants increases to 5.8% compared to 1.9% in the benchmark.

Table 5: Effects of Changes in the Output Tax

||_τ_ = 0|_τ_ = 0_._125|Benchmark<br>_τ_ = 0_._25|_τ_ = 0_._375|_τ_ = 0_._50|
|---|---|---|---|---|---|
|Mean size|9.83|6.85|4.77|3.56|3.05|
|Informal mean size||1.51|2.03|2.56|2.94|
|Frac. Of informal plants (%)|0|62.84|77.32|84.77|90.42|
|Aggregate output|146.49|122.37|100|78.83|62.38|
|Employment share of 50+ (%)|62.85|55.30|42.08|21.94|4.20|
|Growth rate, 0-4 to 35-39 (%)|172.28|109.07|93.12|102.08|119.37|
|Entrepreneurial Quality|269.14|163.17|100|65.16|48.73|
|Tax revenue|0.00|73.39|100|81.81|39.23|

Note: This table presents the effects of different output taxes, _τ_ ’s, on the benchmark economy when holding other parameters constant. The aggregate output, the entrepreneurial quality and the tax revenue at the benchmark case are normalized to 100 for ease of exposition.

Table 6 shows how changes in the enforcement threshold _b_ in this economy would affect plant sizes, aggregate output, selection into entrepreneurship (average entrepreneurial ability), and plant growth. When the output tax is fully enforced ( _b_ = 0), establishments have no incentive to remain small to avoid detection, and average size increases by 46.1% relative to the benchmark. Moreover, while the average growth rate remains almost the same, the average entrepreneurial quality increases by 30.2%. The effect of full enforcement on aggregate output is less than 1 percent.

Another way of increasing enforcement is through the probability of agents meeting with a tax official at birth, _φ_<sup> ̄</sup> in the model. Since agents who encounter a tax official do not have the option to escape taxation by operating informally, any increase in _φ_<sup> ̄</sup> implies a stricter enforcement level. The case where all agents meet with a tax official, i.e., _φ_<sup> ̄</sup> = 1, corresponds to full enforcement, which is also achieved by _b_ = 0. Table 7 presents the quantitative role of _φ_<sup> ̄</sup> . When no agents encounter a tax official, the fraction 23
Table 6: Role of Enforcement Threshold _b_

||0_∗bbench_|0_._5_∗bbench_|Benchmark<br>_bbench_ = 1_._91|1_._5_∗bbench_|2_∗bbench_|
|---|---|---|---|---|---|
|Mean size|6.97|4.62|4.77|4.90|5.03|
|Informal mean size||1.35|2.03|2.50|2.89|
|Frac. Of informal plants (%)|0|72.94|77.32|78.65|79.36|
|<br>Aggregate output|100.84|99.49|100|100.60|100.77|
|<br>Employment share of 50+ (%)|48.51|45.86|42.08|38.98|36.08|
|<br>Growth rate, 0-4 to 35-39 (%)|92.15|68.97|93.12|113.15|127.57|
|<br>Entrepreneurial Quality|130.20|97.45|100|102.05|103.72|
|<br>Tax revenue|138.97|113.24|100|91.40|84.46|

Note: This table presents the effects of different enforcement levels, _b_ ’s, on the benchmark economy when holding other parameters constant. The aggregate output, the entrepreneurial quality and the tax revenue at the benchmark case are normalized to 100 for ease of exposition.

of informal plants increases, and as a result, the mean size, entrepreneurial quality, and overall growth rate decline.

Table 7: Role of Probability of Meeting Tax Official _φ_<sup> ̄</sup>

||0_∗_<sup> ̄</sup>_φbench_|0_._5_∗_<sup> ̄</sup>_φbench_|Benchmark<br> ̄_φbench_ = 0_._30|1_._5_∗_<sup> ̄</sup>_φbench_|2_∗_<sup> ̄</sup>_φbench_|
|---|---|---|---|---|---|
|Mean size|4.18|4.45|4.77|5.16|5.54|
|Informal mean size|1.94|1.98|2.03|2.08|2.13|
|Frac. Of informal plants (%)|95.41|87.11|77.32|65.65|51.02|
|Aggregate output|99.64|99.87|100|100.42|100.66|
|<br>Employment share of 50+ (%)|39.86|40.98|42.08|43.52|44.81|
|<br>Growth rate, 0-4 to 35-39 (%)|89.68|91.59|93.12|94.12|94.27|
|Entrepreneurial Quality|91.61|95.54|100|105.69|110.89|
|<br>Tax revenue|84.83|92.35|100|108.38|116.81|

Note: This table presents the effects of different probabilities of being assigned to a tax official, _φ_ ’s, on the benchmark economy when holding other parameters constant. The aggregate output, the entrepreneurial quality and the tax revenue at the benchmark case are normalized to 100 for ease of exposition.

# **6. Revenue-Neutral Changes in Enforcement**

Table 8 shows the results of a policy experiment where we reduce the enforcement threshold _b_ while we adjust the tax rate relative to the benchmark to keep the tax revenue constant. When there is full enforcement, mean size increases 63.5% (from 4.77 to 7.8). Average entrepreneurial ability increases by 68.1%, and the average life cycle growth rate increases by 25.2%. As a result, aggregate output increases by 16.4%.

Figure 6 presents the effects of revenue-neutral full enforcement on average cumula24
Table 8: Revenue-Neutral Policy Experiments

||0_∗bbench_|0_._25_∗bbench_|0_._5_∗bbench_|0_._75_∗bbench_|Benchmark<br>_bbench_ = 1_._91|
|---|---|---|---|---|---|
|Mean size|7.80|6.31|5.62|5.29|4.77|
|Informal mean size||0.70|1.14|1.56|2.03|
|Frac. Of informal plants (%)|0.00|42.65|64.22|71.71|77.32|
|Aggregate output|116.35|114.15|110.72|107.04|100.00|
|<br>Employment share of 50+ (%)|54.01|53.75|51.73|48.43|42.08|
|<br>Growth rate, 0-4 to 35-39 (%)|116.60|93.93|81.43|84.62|93.12|
|Entrepreneurial Quality|168.13|141.00|125.45|115.62|100.00|
|<br>_τ_|0.16|0.17|0.19|0.21|0.25|

Note: This table presents the effects of stricter enforcement while keeping the tax revenue constant at the benchmark level by adjusting the output tax rate, _τ_ . The aggregate output, the entrepreneurial quality and the tax revenue at the benchmark case are normalized to 100 for ease of exposition.

tive growth rates and average sizes across the cross-section of plants over their life cycle. When plants are younger (up to age 15-19), they don’t benefit from full enforcement in terms of average cumulative growth rates as much as older plants. This is because the increase in input prices under full enforcement offsets some of the benefits of lower taxes when plants are younger and smaller. However, this doesn’t mean their size remains unaffected by the policies. While the growth rates in the cross-section are overstated, we can use the average size at the cross-section to assess the policy’s impact over the life cycle. Figure 6b shows that as a result of revenue-neutral full enforcement, plants of all ages increase their size, with older plants growing larger compared to younger plants, consistent with the average cumulative growth rate results.

Figure 6: Effect of revenue-neutral full enforcement on the life-cycle <!-- Start of picture text --> (a) Average Growth Rate (b) Average Size at the Cross-Section<br>2.5 15<br>2 10<br>1.5 5<br>1 0<br>Age Age<br>Benchmark Full enforcement Benchmark Full enforcement<br>Average Size<br>Average cumulative growth rate<br>[0-4] [5-9] [10-14] [15-19] [20-24] [25-29] [30-34] [35-39] [0-4] [5-9] [10-14] [15-19] [20-24] [25-29] [30-34] [35-39]<br><!-- End of picture text --> 25
# **7. Concluding Remarks**

In this we data from Mexico’s census data to the paper, exploit plant-level quantify output losses that arise from the marked differences in growth rates between formal and informal plants. Unlike Hsieh and Klenow (2014), we are able to focus on a panel of registered and unregistered plants to estimate their life cycle employment profiles. We build on the model developed by Guner et al. (2018) where plants grow by investing in their productivity. Our innovation is introducing a tax on output that some plants can escape from by operating informally due to incomplete enforcement. Our policy experiments suggest that reducing the tax rate while improving the enforcement technology to keep the tax revenue constant would lead to output gains of 16.4% relative to the benchmark. It also implies an increase in the average growth rate by 25.3%.

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