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 through productivity investments, and informality emerges plants using five waves of the Mexican establishment census. from incomplete enforcement. In equilibrium, informal Formal plants begin operations with three times more work- plants exhibit flatter life cycle profiles to avoid detection ers than informal plants and exhibit faster growth rates. and taxation. Model parameters are calibrated to match Throughout their life cycle, formal establishments more key properties of plant size distribution and the life cycle of than double their size, while informal plants increase their plants in Mexico. Quantitative results indicate that a reve- size by only 77%. A general equilibrium model is developed nue-neutral full enforcement increases aggregate output and to quantify the aggregate economic losses stemming from the overall growth rate by sixteen and twenty-five percent these growth rate disparities. In the model, plants grow 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* Furkan Sarıkaya† M. Nazım Tamkoç‡ Jesica Torres§ 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.1 , 2 Less developed countries also face widespread informality.3 This paper argues that informality, arising from incomplete enforcement, distorts incentives for growth over the life cycle.4 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 1 We use the terms establishment and plant interchangeably throughout the paper. 2 Eslava et al. (2022) shows that Colombian plants grow less than plants in the U.S. 3 ILO 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. 4 Compliance with taxes varies with plant size: the effective tax rate is higher among large establish- ments compared to smaller plants (See López and Torres (2020) for Mexico). 1 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. Agents, at the beginning of their life-cycle, face a tax official with some 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 distri- bution 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.5 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).6 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.7 The census is administered by Mexico’s statistics agency INEGI and targets the universe 5 For a detailed survey of this literature, see La Porta and Shleifer (2014) and Ulyssea (2020) 6 Please see Restuccia and Rogerson (2017) and Hopenhayn (2014) for an overview of the misallocation literature. 7 Access 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.8 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.9 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.10 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).11 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.12 The two questions on registration 8 Rural areas have fewer than 2,500 residents but INEGI does include rural areas in the census when they are the capital of the municipality. 9 For example, businesses located inside residential properties are included, but street vendors are not. 10 To 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). 11 We 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. 12 IMSS 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.13 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 Share of plants 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 1.14 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 13 In 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. 14 In 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. 100 Share of formal establishments 80 60 Formal Not registered Not registered and non-response 40 20 0 1-5 6-10 11-50 51-100 101+ Number of workers 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. 6 Table 2: The size distribution of formal and informal plants in the Mexican census. 2018. Total Formal plants Informal plants Share of Share of Share of Share of Share of Share of Size plants workers plants workers plants 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 respon- dent. 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.15 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 15 Busso et al. (2018) use the location, the name, and the 6-digit sector to find establishments in two consecutive waves of the census. 7 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).16 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 16 One 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. 2.50 Average cumulative growth rate 2.36 2.27 2.21 2.01 2.00 2.00 1.88 1.92 1.86 1.74 1.71 1.62 1.77 1.70 1.49 1.64 1.48 1.50 1.54 1.48 1.30 1.36 1.22 1.00 1.00 [0-4] [5-9] [10-14] [15-19] [20-24] [25-29] [30-34] [35-39] Age Informal plants Total Formal plants 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 (exoge- nous) probability density function f (z ) with cumulative distribution function F (z ) and support [z, z ]. Agents live for J periods. Each agent maximizes the expected present value of lifetime utility derived from consumption: J β j −1 u(cj ) (1) j =1 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 γ f (z, k, n) = Az 1−γ k α n1−α , (2) 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: zj +1 = zj + g (zj , xj ) (3) θ1 θ2 where g (zj , xj ) = zj xj and xj denotes the income invested in entrepreneurial skill by an entrepreneur at age j . The parameters θ1 and θ2 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¯ ∈ [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.17 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 agent does not face a tax official at the beginning of the life cycle, she can escape from taxation by operating informally (fully avoiding the output tax). Operating informally, though, carries the risk of detection and subsequent punishment (even if 17 As 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:  0 if k ≤ b p(k ) = (4) 1 if otherwise 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.18 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: J W = max β j −1 u(cj ) cj ,aj +1 j =1 (5) s.t. cj + aj +1 = w + (1 + r)aj , ∀ j ≤ JR − 1 cj + aj +1 = (1 + r)aj ∀ j ≥ JR 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. 18 The profits of an informal entrepreneur are: γ Az 1−γ k α n1−α − wn − Rk if k ≤ b Π I (z ) =max γ k,n (1 − τ ) Az 1−γ k α n1−α − wn − Rk − F if k > b 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 ΠF (z ): γ ΠF (z ) = max (1 − τ ) Az 1−γ k α n1−α − wn − Rk (6) k,n Similarly, an informal entrepreneur with ability z chooses capital and labor each period to maximize her profit, ΠI (z ). Unlike formal entrepreneurs, informal entrepreneurs don’t pay taxes but they are subject to a probability of getting caught that constrains their size: γ Π I (z ) = max Az 1−γ k α n1−α − wn − Rk (7) k,n s.t. k ≤ b 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 accumulat- ing 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 be- ginning 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 ˆ 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 J ˆ V j,F (z ) = max β j −1 u(cj ) cj ,xj ,aj +1 j =1 s.t. cj + xj + aj +1 = Π(zj ) + (1 + r)aj ∀ j ≤ JR − 1 cj + aj +1 = (1 + r)aj ∀ j ≥ JR zj +1 = zj + g (zj , xj ) ∀ j < JR − 1 Π(zj ) = ΠI (zj ) if ˆ j=0  ΠI (z ) if j ≤ J − 1 − ˆ j j R Π(zj ) = if ˆ j ∈ {1, 2, ..., JR − 2} ΠF (z ) if J − 1 − ˆ j