Gender gaps in entrepreneurship and their macroeconomic effects in Latin America: Prepared for the Institutions for Development Sector

Cuberes, David; Teignier, Marc Working Paper Gender gaps in entrepreneurship and their macroeconomic effects in Latin America: Prepared for the Institutions for Development Sector IDB Working Paper Series, No. IDB-WP-848 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: Cuberes, David; Teignier, Marc (2017) : Gender gaps in entrepreneurship and their macroeconomic effects in Latin America: Prepared for the Institutions for Development Sector, IDB Working Paper Series, No. IDB-WP-848, Inter-American Development Bank (IDB), Washington, DC, https://doi.org/10.18235/0000931 This Version is available at: https://hdl.handle.net/10419/173897 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc-nd/3.0/igo/legalcode IDB WORKING PAPER SERIES Nº IDB-WP-848 Gender Gaps in Entrepreneurship and their Macroeconomic Effects in Latin America Prepared for the Institutions for Development Sector by: David Cuberes Marc Teignier Inter-American Development Bank Institutions for Development Sector November 2017 November 2017 Gender Gaps in Entrepreneurship and their Macroeconomic Effects in Latin America Prepared for the Institutions for Development Sector by: David Cuberes* Marc Teignier** *Clark University ** Universitat de Barcelona Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library Cuberes, David. Gender gaps in entrepreneurship and their macroeconomic effects in Latin America / David Cuberes and Marc Teignier. p. cm. — (IDB Working Paper Series ; 848) Includes bibliographic references. 1. Businesswomen-Latin America. 2. Businesswomen-Caribbean Area. 3. Womenowned business enterprises-Latin America. 4. Women-owned business enterprisesCaribbean Area. 5. Women in economic development-Latin America. 6. Women in economic development-Caribbean Area. I. Teignier, Marc. II. Inter-American Development Bank. Competitiveness, Technology and Innovation Division. III. Title. IV. Series. IDB-WP-848 Copyright © Inter-American Development Bank. This work is licensed under a Creative Commons IGO 3.0 AttributionNonCommercial-NoDerivatives (CC-IGO BY-NC-ND 3.0 IGO) license (http://creativecommons.org/licenses/by-nc-nd/3.0/igo/ legalcode) and may be reproduced with attribution to the IDB and for any non-commercial purpose, as provided below. No derivative work is allowed. Any dispute related to the use of the works of the IDB that cannot be settled amicably shall be submitted to arbitration pursuant to the UNCITRAL rules. The use of the IDB's name for any purpose other than for attribution, and the use of IDB's logo shall be subject to a separate written license agreement between the IDB and the user and is not authorized as part of this CC-IGO license. Following a peer review process, and with previous written consent by the Inter-American Development Bank (IDB), a revised version of this work may also be reproduced in any academic journal, including those indexed by the American Economic Association's EconLit, provided that the IDB is credited and that the author(s) receive no income from the publication. Therefore, the restriction to receive income from such publication shall only extend to the publication's author(s). With regard to such restriction, in case of any inconsistency between the Creative Commons IGO 3.0 Attribution-NonCommercial-NoDerivatives license and these statements, the latter shall prevail. Note that link provided above includes additional terms and conditions of the license. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent. http://www.iadb.org 2017 Gender Gaps in Entrepreneurship and their Macroeconomic Effects in Latin America∗ David Cuberes Clark University Marc Teignier Universitat de Barcelona November 23, 2017 Abstract This paper studies the aggregate effects of the existing differences between male and female-run firms in Latin America and the Caribbean (LAC). Using data from the World Bank Enterprise Survey and the International Labor Organization (ILO), we show that only about one-fourth of the total firms are run by women and that female-run firms are about three times smaller than male-run firms in LAC. We then extend the theoretical framework in Cuberes and Teignier (2016) to account for these facts and quantify their aggregate effects on productivity and income per capita. In our model, men and women are identical in all aspects except for the fact that some women face barriers to becoming entrepreneurs, which may be a function of their talent. The calibration of our model implies that the barriers that some women face to becoming firm managers depend positively on their managerial talent, which results in female-run firms being smaller than those managed by men in equilibrium. In our baseline simulation, we obtain an output per capita loss due to these gender gaps of 9.4%, all of which is due to misallocation of resources and the resulting fall in aggregate productivity. This loss is 1.3 times larger than the one obtained in a framework where barriers to entrepreneurship were assumed to be independent of talent. JEL classification numbers: E2, J21, J24, O40. Keywords: firm-size distribution, entrepreneurship talent, gender inequality, aggregate productivity, span of control technology. ∗We wish to thank Matteo Grazzi, Jocelyn Olivari, Janet Stotsky, Phil Keefer, and one anonymous referee. We also thank the participants in the Inter-American Development Bank (IDB) workshop “RESEARCH ON SCIENCE, TECHNOLOGY AND INNOVATION GENDER GAPS AND THEIR ECONOMIC COSTS IN LATIN AMERICA AND THE CARIBBEAN” for their comments and support. This paper is part of the research project "Science, Technology and Innovation Gender Gaps and their Economic Costs in Latin America and the Caribbean," led by the Competitiveness, Technology, and Innovation Division of the IDB and financed by the IDB Gender and Diversity Fund. The information and opinions presented here are entirely those of the authors and do not necessarily reflect the views of the IDB, its Board of Executive Directors, or the countries they represent. 1 1 Introduction Gender inequality is present in many socioeconomic indicators around the world in both developed and developing countries. These gaps can be observed in education, earnings, occupation, access to productive inputs, political representation, or bargaining power inside the household, among others.1One important aspect of gender inequality in the labor market that has been largely overlooked in the literature is the low presence of women in entrepreneurial activities. In this paper we study this issue for LAC using data from the World Bank Enterprise Survey. In LAC, on average, female-run firms represent only about 25% of the total number of firms and the average firm managed by a woman is about 3 times smaller than firms managed by a man. We develop a general equilibrium model, based on Cuberes and Teignier (2016), to quantify the aggregate effects of these gender gaps in entrepreneurship. In our theoretical framework, agents are endowed with a random entrepreneurship skill. Based on this skill, they decide to become employers, self-employed, or workers. An employer in this model produces a homogeneous good using a span-of-control technology that combines his or her entrepreneurship skills with capital and workers. In our model, men and women are identical in terms of their managerial skills in the sense that both groups draw their managerial talent from identical distribution functions. However, women are subject to exogenous barriers in their occupational choices, which results in a a fraction of them being excluded from employership. This generates a loss in income per worker because less able managers run firms of sub-optimal size and productivity. Our framework takes these restrictions as given, that is, we focus on explaining their effects instead of their origins. It may be possible, for instance, that some women choose not to participate in the market and, although this hurts the economy’s productivity, it enhances their welfare. To properly determine the magnitude of this aggregate loss, in our framework, it is extremely important to know which type of women are excluded from employership. If the less talented women were the only ones who did not participate, for instance, the aggregate effects would be quantitatively small because they would be running small firms. If it was the most talented ones, on the other hand, the aggregate effects would be larger because they would run the main firms. We address this question comparing the size distribution of male and female managed firms. Since the data indicates that females run smaller firms than males, this implies, through the lens of our model, that the probability that a woman is excluded from employership increases with her talent. In other words, our framework suggests that there is a negative selection of women into entrepreneurship, meaning that the most talented women are the ones that do not participate into this occupation. Admittedly, 1See the World Development Report 2012 (World Bank, 2012) for a comprehensive review of these and other gender gaps discussed in the literature. 2 there could be other important reasons to explain the difference in firms size. For example, it is possible that women face more constraints in accessing capital than men. We do not claim that these types of barriers, which are likely to affect both entry to entrepreneurship and firm size conditional on being an entrepreneur, are less important than the barrier based on skills that we exploit here. We focus on this specific barrier of entry because our data allows us only to identify barriers of entry and not barriers to size and because the model has a very clear testable implication regarding the relationship between the barrier, female’s skill, and firm size. We find that the effects of these employership gender gaps on aggregate and productivity are large. In our baseline simulation, we estimate an 8.9% fall in aggregate output in the short run, when we keep the stock of capital fixed, and 9.4% in the long run, when this stock is also negatively affected. These losses are 1.3 times larger than the ones we would obtain using a model where the exclusion probability was independent of talent. The intuition behind the output loss is as follows: When a woman with very good management skills cannot become an employer, a less skilled man takes her position and becomes the manager of a firm and, as a consequence, the average firm size and output per worker in the economy fall. If more talented women face a higher exclusion probability, the average talent of employers falls even more, which results in a larger loss. We check the sensitivity of the results to some of our assumptions, and we find that the short-run losses are between 5.6% and 11.8%, while the long-run ones are between 6.3% and 12.5%. To our knowledge, there are very few articles that quantify the macroeconomic effects of gender gaps in the labor market.2The ILO provides some estimates of the output costs associated with labor gender gaps in the Middle East and Northern Africa but without proposing any specific theoretical model (ILO, 2014). One shortcoming of that exercise is that it does not allow one to shed light on the mechanisms through which gender gaps in the labor market may affect aggregate efficiency. Cavalcanti and Tavares (2016) construct a growth model based on Galor and Weil (1996) in which there is exogenous wage discrimination against women. Calibrating their model using U.S. data, they find very large effects associated with these wage gaps: a 50% increase in the gender wage gap in their model leads to a decrease in income per capita of a quarter of the original output. Their results also suggest that a large fraction of the actual difference in output per capita between the U.S. and other countries is indeed generated by the presence of gender inequality in wages. Hsieh et al. (2013) use a Roy model to estimate the effect of the changing occupational allocation of white women, black men, and black women between 1960 and 2008 on U.S. economic growth and find that the improved allocation of talent accounts for 17% to 20% of growth 2See Cuberes and Teignier (2014) for a critical literature review of the two-directional link between gender inequality and economic growth. 3 over this period. Finally, in the model summarized in Section 3.1 of this paper, Cuberes and Teignier (2016) calculate the macroeconomic effects of gender inequality in the labor market using data from the ILO for a large sample of countries, including several countries from the LAC region, among them, Chile, Colombia, and Peru. An important difference is that in the present paper we use firm-level data rather than labor aggregates to carry out our analysis. These data allows us to make implications in terms of firm size and selection that were not possible to derive in Cuberes and Teignier (2016). In terms of analyzing firm size by gender in Latin America, Arellano and Peralta (2015) report significant differences in firms size and productivity in Chile but they do not use any theoretical model in their analysis. The rest of the paper is organized as follows. Section 2 presents the empirical facts, while Section 3 sketches the general equilibrium occupational choice model based on Cuberes and Teignier (2016). The numerical results of the paper are presented and discussed in Sections 4 and 5. Finally, Section 6 concludes. 2 Empirical facts We start the analysis documenting the existing differences in employership between men and women in the LAC region. First, using data for the latest available year on all the countries in this region from the ILO (KILM, 8th edition) on employers by gender, we find that women are clearly underrepresented in employership.3As we can see in Table 1, the share of female employers in the population is less than one-third the male share, which is significantly lower than the fraction of women who are self-employed or workers. Table 1: Female-to-male ratios by occupation (Data source: ILO KILM, 8th edition) Employers Self-Employed Workers LAC 0.31 0.60 0.76 We then compute the size distribution of firms with male and female top managers in LAC using from the World Bank Enterprise Survey for 2010.4The World Bank Enterprise Survey is a firm-level survey of a representative sample of an economy’s private sector conducted for a large set of countries.5For the LAC region, it contains information for 13,855 3http://kilm.ilo.org 4http://www.enterprise surveys.org/ 5The Enterprise Survey is answered, in most cases, by business owners and top managers. Typically 12001800 interviews are conducted in larger economies, 360 interviews are conducted in medium-sized economies and for smaller economies 150 interviews take place. The manufacturing and services sectors are the primary business sectors of interest. This corresponds to firms classified with ISIC codes 15-37, 45, 50-52, 55, 60-64, and 4 firms, with sizes between 1 and 21,955 employees, and from 26 different countries.6In order to count the number of firms with female managers we use the question b7a: “Is the top manager a female?”. Another possibility would be to use the question b4a: “What percentage of the firm is owned by females?”. The first problem with this second proxy is that, in many cases, this percentage is greater than zero but less than 100, which implies that both men and women own the firm. While it may be interesting to study the performance of firms jointly owned by both men and women, our model is not well-suited to do so. Second, for large firms that sell their shares in the stock market, it is unclear what is the role of small owners in making relevant decisions for the firm. For these two reasons, we prefer to use the first question in the main results of the paper. As we can see in Table 2, female-run firms are significantly smaller in terms of employees. The median size of firms with a female manager, for example, is 16 workers, while it is 30 workers for firms with a male manager. It is important to point out here that we do not make any attempt to control for other determinants of firm size by gender. Arguably, these differences may change if we control for sector, manager age and education, and many other covariates. However, lack of accurate data prevents us from carrying out this analysis here.7 Table 2: Percentiles of the firm-size distribution by gender (Data source: WB Enterprise Survey) Min 10 pct 25 pct 50 pct 75 pct 90 pct Max Females 1 5 8 16 45 119 2137 Males 1 6 12 30 100 279 11718 Figure 1shows graphically that the firm-size distribution of female-run firms (i.e. firms with a female manager) is shifted to the left relative to the distribution of firms managed by men or, in other words, the distribution of female-run firms has a thicker density at low numbers of employees.8 72. Formal (registered) companies with 5 or more employees are targeted for interview. Firms with 100% government/state ownership are not eligible to participate in an Enterprise Survey. In each country, businesses in the cities/regions of major economic activity are interviewed. The sampling methodology for Enterprise Surveys is stratified random sampling, that is, all population units are grouped within homogeneous groups and simple random samples are selected within each group. 6The countries are Argentina (1054 firms), The Bahamas (150 firms), Barbados (150 firms), Bolivia (362 firms), Brazil (1802 firms), Chile (1033 firms), Colombia (942 firms), Costa Rica (538 firms), Dominican Republic (360 firms), Ecuador (360 firms), El Salvador (360 firms), Grenada (153 firms), Guatemala (590 firms), Guyana (165 firms), Honduras (360 firms), Jamaica (376 firms), Mexico (1480 firms), Nicaragua (336 firms), Panama (365 firms), Paraguay (361 firms), Peru (1000 firms), St. Kitts and Nevis (150 firms), St. Vincent and the Grenadines (154 firms), Trinidad and Tobago (370 firms), Uruguay (607 firms), and Venezuela (320 firms). 7See IDB (2016) for a survey of papers that carry out this micro analysis in different countries in LAC. 8We plot the natural logarithm of the number of employees to help visualize the plots. Without taking logs, the large number of small firms in the data make it hard to appreciate the shape of the entire distribution. 5 Figure 3: Slope of cumulative density functions by gender (females: orange dashed line; males: blue solid line) y = -1.2153x + 4.943 y = -1.6139x + 5.5787 -12 -10 -8 -6 -4 -2 0 2 4 2.3 3.3 4.3 5.3 6.3 7.3 8.3 9.3 1-Cumulative density function, in logs Number of employees, in logs 4.2 Economic losses due to the entrepreneurship gender gaps The introduction of the employership gender gap leads to an important fall of aggregate output, both in the short run, when the capital stock is kept fixed, and in the long run, when the capital stock is adjusted to its new steady-state level.15 Specifically, as Table 4shows, we estimate a fall of aggregate output of 9.4% both in the short run and in the long run. These losses are almost one-third larger than the ones we would obtain using a model where the exclusion probability was independent of talent (i.e. where γ= 0) since the fact that γ < 0 implies that there is a negative selection of women into employership. Table 4: Output losses due to employership gender gaps in LAC Short run Long run Baseline sim. (%) Ratio to γ= 0 Baseline sim. (%) Ratio to γ= 0 8.9 1.3 9.4 1.3 When a woman with good management skills happens to be barred from employership, the demand for labor and capital decreases. As a result, the equilibrium wage and interest rate decreases, which makes it more profitable for less skilled agents to become entrepreneurs. In other words, both occupational thresholds z1and z2fall, implying that the average talent of both employers and self-employed drops. On top of that, if more talented women face a higher exclusion probability, the average talent of employers falls even more, 15To compute the steady-state capital stock, we assume a gross interest rate of 0.125, which is consistent with a depreciation rate of 0.075 and an intertemporal discount factor of 0.05 in a continuous-time model. 12 which results in a larger fall of total output. Table 5illustrates this intuition: the introduction of the gender gaps reduces the equilibrium wage rate as well as the talent thresholds z1 and z2. If γis negative, the fall is even larger and, moreover, the gender gap in the average earnings of employers becomes positive because now the average talent of female managers is lower than that of males. Specifically, the talent thresholds and the wage rate fall by almost 10%, while the fall would be 7.5% if we did not take into account the difference in the size distribution (i.e. if we assumed that γ= 0). Table 5: Short-run results under different scenarios No gender gaps (normalized at 100) Gender gaps with γ < 0 Gender gaps with γ= 0 Workers’ wage 100 90.8 92.5 Interest rate 100 91.1 93.1 Talent threshold z1100 90.8 92.5 Talent threshold z2100 90.8 92.5 Employers earnings gender gap (%) 0 44.0 0 5 Sensitivity analysis In this section we present our main results for other parameter values in order to see the sensitivity of the results to some of the assumptions made. The first row of Table 6shows the results under the benchmark simulation, as in Table 4, while the rest of rows show the short and long-run losses under different scenarios. The first alternative scenario, presented in the second row, shows the loss in per-capita output due to the introduction of the employership gender gaps in a context where the selfemployment gender gap is also present. To be precise, we infer from the data that about 16% of women barred from employership can become self-employed while the rest become workers. Taking this into account, we find that introducing the gender gaps in employers generates significantly larger losses, both in the short run and the long run. Intuitively, the output loss is now larger because there is a larger fall in the share of entrepreneurs and because there is larger fall in equilibrium wage and, consequently, on the average talent of entrepreneurs. The third row displays the losses under the parameter values used in Cuberes and Teignier (2016), namely [η, ρ,τ]=[0.79,6.5,0.7], which were estimated using data for the OECD countries. In this case, the model predicts significantly smaller losses (about one 13 third smaller) as well as a lower difference with respect to the γ= 0 framework. The main difference with respect to the benchmark parametrization is a somewhat larger value for η, which reduces the contribution of managerial talent to firm productivity, and especially a larger value for ρ, which increases the slope of the probability density function and reduces the thickness of the talent distribution tail. As a result, the fall in the talent threshold due to the introduction of the employership gaps is smaller, which implies a lower fall of aggregate income. The fourth row, on the other hand, shows the income losses if firm profits (or compensation to managerial talent ) were considered labor income instead of capital income (i.e. if αη = 1/3and α= 0.41). The long-run results are not affected because the capital stock adjusts to its steady-state value, which makes the value of αirrelevant to determine the income fall. In the short-run, however, the income fall is lower than in the baseline simulation because the importance of the fixed factor, namely, capital, is larger. Intuitively, in this case, there is a larger difference between the short and long run results because the long-run capital adjustment increases with α. Finally, the last row shows the results under an alternative setup where self-employment is never an optimal occupational choice but only a necessity occupation for those unable to find a job as a worker. In this setup, the loss in income would be somewhat lower than in the benchmark simulation, especially in the short run, although the ratio to the γ= 0 case is the same. The explanation is that the parametrization of this alternative setup leads to larger values for ηand ρwhich, as discussed above, implies smaller output losses.16 16In particular, under this alternative setup, matching the fraction of employers as well as the firm-size distribution implies values of η= 7.24 and ρ= 0.83. 14 Table 6: Output losses due to employership gender gaps in LAC Short run Long run Output loss (%) Ratio to γ= 0 Output loss (%) Ratio to γ= 0 Benchmark simulation 8.9 1.30 9.4 1.29 Selfemployment gender gap present 11.8 1.23 12.5 1.23 OECD parameters (η, ρ, τ) = (0.79,6.5,0.7) 5.56 1.23 6.32 1.23 Profits as labor inc. (α= 0.41) 6.37 1.30 9.4 1.29 Only necessity selfemployment 6.83 1.30 8.13 1.30 6 Conclusions In this paper we document that in the LAC region only about one-fourth of the total firms are run by women and that female-run firms are around three times smaller than male-run firms. We quantify the output losses caused by these gender gaps using an occupational choice model where women face barriers to becoming firm managers. We allow these barriers to depend on managerial talent in order to be able to replicate the gender differences in firm-size distribution. In our benchmark simulation, we find that the aggregate long-run output loss due to these gender gaps is 8.9% in the short run and 9.4% in the long run, which is due to the drop in average managerial talent and the resulting fall in aggregate productivity. These losses are about 1.3 larger than the ones estimated under a framework with barriers that are independent of talent. Our sensitivity analyses show that the income losses may take values between 5.6% and 11.8% in the short run, and between 6.3% and 12.5% in the long run. In our framework, we explain all the existing differences in firm size between men and women by the presence of exogenous barriers in the occupational choices of women and making these barriers correlate positively with the managerial talent of women. Admittedly, the observed gender gaps in entrepreneurship could be the result of other types of barriers, like discrimination in the labor market, differences in experience or education, or 15 differences in access to credit. Or they could also be also the result of differences in preferences, like a stronger taste for family time or higher risk aversion. More work is clearly needed to determine with precision the fundamental causes behind the difference between male and female-run firm distributions. References Arellano, P, and Peralta, S., 2015. “Informe de resultados: análisis de género en las empresas Tercera Encuesta Longitudinal de Empresas.” Ministerio de Eonomia, Fomento y Turismo. División de Política Comercial e Industrial Agosto. Blau, F. D., and Kahn, L. M., 2016. “The Gender Wage Gap: Extent, Trends, and Explanations.” NBER working paper 21913. Buera, F. J., and Shin, Y., 2011. “Self-Insurance vs. Self-Financing: A Welfare Analysis of the Persistence of Shocks. Journal of Economic Theory 146, 845-862. Buera, F. J., Kaboski, J. P., and Shin, Y., 2011. “Finance and Development: A Tale of Two Sectors.” American Economic Review 101(5), 1964-2002. Cavalcanti, T., and Tavares, J., 2016. “The Output Cost of Gender Discrimination: A Model-Based Macroeconomic Estimate.” The Economic Journal 126(590), 109-134. Cuberes, D., and Teignier, M., 2016. “Aggregate Costs of Gender Gaps in the Labor Market: A Quantitative Estimate.” Journal of Human Capital, 10(1). Cuberes, D., and Teignier, M., 2014. “Gender Inequality and Economic Growth: A Critical Review.” Journal of International Development, 26(2), 260-276. Galor, O., and Weil, D. N., 1996. “The Gender Gap, Fertility, and Growth.” American Economic Review 85(3), 374–387. Greenwood, J., Guner, N., Kocharkov, G., and Santos, C., 2014. “Marry Your Like: Assortative Mating and Income Inequality.” American Economic Review, Papers and Proceedings 104(5), 348-353. Hsieh, C., Hurst, E., Jones, C., and Klenow, P., 2013. “The Allocation of Talent and U.S. Economic Growth.” NBER Working Paper No. 18693. Cambridge, MA. National Bureau of Economic Research. IDB, 2016. Firm Innovation and Productivity in Latin America and the Caribbean.The Engine of Economic Development. Edited by Matteo Grazzi and Carlo Pietrobelli. Washington, DC: Inter-American Development Bank. ILO (2014). “Global Employment Trends.” Geneva: International Labor Organization. Lucas Jr., R. E., 1978. “On the Size Distribution of Business Firms.” The Bell Journal of Economics 9(2), 508-523. 16 Ngai, R. L., and Petrongolo, B., forthcoming. “Gender Gaps and the Rise of the Service Economy.” American Economic Journal-Macroeconomics. Olivetti, C., and Petrongolo, B., 2014. “Gender Gaps across Countries and Skills: Supply, Demand and the Industry Structure.” Review of Economic Dynamics. 17 (4): 842-859. Poschke, M., 2013. “Entrepreneurs Out of Necessity: a Snapshot.” Applied Economics Letters 20(7), 658-663. World Bank, 2012. “World Development Report 2012: Gender Equality and Development.” Washington, DC: World Bank. 17 AAPPENDIX: Model details The economy we consider has a continuum of agents indexed by their entrepreneurial talent x, drawn from a cumulative distribution Γthat takes values between Band ∞. We assume the economy is closed and that it has a workforce of size Nand Kunits of capital. Labor and capital are inelastically supplied in the market by consumers, in exchange for a wage rate wand a capital rental rate r. These inputs are then combined by firms to produce a homogeneous good. Agents decide to become either firm workers, who earn the equilibrium wage rate w—which we assume to be independent of their entrepreneurial talent—, or entrepreneurs, who earn the profits generated by the firm they manage.17 In the model, we also include a fourth category, the out-of-necessity entrepreneurs, who choose this occupation because they have no other occupational choices apart from running their own business. We denote by 1−θthe fraction of both males and females that are out-of-necessity entrepreneurs. An agent with entrepreneurial talent or productivity level xwho chooses to become an employer and hires n(x)units of labor and k(x)units of capital produces y(x)units of output and earns profits π(x) = y(x)−rk (x)−wn (x), where the price of the homogeneous good is normalized to 1. As in Lucas (1978) and Buera and Shin (2011), the production function is given by y(x) = xk(x)αn(x)1−αη,(7) where α∈(0,1) and η∈(0,1). The parameter ηmeasures the span of control of entrepreneurs and, since it is smaller than 1, the entrepreneurial technology involves an element of diminishing returns. On the other hand, an agent with talent xwho chooses to become self-employed uses the amount of capital ˜ k(x), produces ˜y(x)units of output and earns profits ˜π(x) = ˜y(x)−r˜ k(x). The technology he or she operates is ˜y(x) = τx˜ k(x)αη,(8) where τis the self-employed productivity parameter.18 One interpretation of this parameter is that self-employed workers have to spend a fraction of their time on management tasks, which would imply that τis equal to the fraction of time available for work to the power (1 −α)η. As explained below, we estimate this parameter to match the average fraction of self-employed in the data. 17In what follows we will refer to an entrepreneur as someone who works as either an employer or selfemployed. 18The consumption good produced by the self-employed and the capital they use is the same as the one in the employers’ problem. However, it is convenient to denote them ˜yand ˜ kto clarify the exposition. 18 A.1 Agents’ optimization A.1.1 Employers Employers choose the units of labor and capital they hire in order to maximize their current profits π. The optimal number of workers and capital stock, n(x)and k(x), respectively, depend positively on the productivity level x, as equations (9) and (10) show: n(x) = xη(1 −α)α 1−ααη wαη−1 rαη 1/(1−η) ,(9) k(x) = "xηα 1−α αη(1−α)rη(1−α)−1 wη(1−α)#1/(1−η) .(10) A.1.2 Self-employed When we solve for the problem of a self-employed agent with talent xwho wishes to maximize his or her profits, we find ˜ k(x) = τxαη r1 1−αη .(11) A.1.3 Occupational choice Figure 2displays the shape of the profit functions of employers, πe(x), and self-employed, πs(x), as well as the wage earned by workers as a function of talent x. The agents’ optimization determines the relevant talent cutoffs for the occupational choices. Here we present the equations that define these thresholds. The first one, z1, defines the earnings such that agents are indifferent between becoming workers or self-employed and it is given by w=τz1˜ k(z1)αη −r˜ k(z1).(12) If x≤z1agents choose to become workers, while if x>z1they become self-employed or employers. The second cutoff, z2, determines the choice between being a self-employed or an employer and it is given by τz2˜ k(z2)αη −r˜ k(z2) = z2xk(z2)αn(z2)1−αη−rk (z2)−wn(z2)(13) so that if x>z2an agent wants to become an employer. 19 A.2 Competitive equilibrium We assume that women represent half of the population in the economy and that there is no unemployment. Moreover, any agent in the economy can potentially participate in the labor market, except for the restrictions on women described above. Under these assumptions, in equilibrium, the total demand for capital from employers and self-employed must be equal to the aggregate capital endowment (in per capita terms) k: k=1 2  ∞ ˆ z2 k(x)dΓ(x) + z2 ˆ z1 ˜ k(x)dΓ(x) + (1 −θ) z1 ˆ B ˜ k(x)dΓ(x)  +1 2  ∞ ˆ z2 µ(x)k(x)dΓ(x) + z2 ˆ z1 ˜ k(x)dΓ(x) + ∞ ˆ z2 (1 −µ(x))˜ k(x)dΓ(x) + (1 −θ) z1 ˆ B ˜ k(x)dΓ(x) . The upper term is the demand for capital from men and the two lower terms are the women’s demand for capital. The demand for capital from male-run firms has three components: the first one represents capital demand from employers, while the second and third terms represent the demand from self-employed (i.e. those who have the right ability to be selfemployed plus capital demand by those who become self-employed because they could not find a job as workers).19 These out-of-necessity self-employed demand the optimal amount of capital given their talent or ability. The demand for capital from female-run firms has four components. The first represents capital demand from female employers (i.e. those with enough ability to be employers and who are allowed to be so). The second term represents capital demand from women who have the right ability to be self-employed and are allowed to work. The third term shows capital demand from women who become self-employed because they are excluded from employership. Finally, the last term shows the fraction of females who would like to be workers but, since they are “excluded” from this occupation, they choose to become out-ofnecessity self-employed if they are not excluded from entrepreneurship. Similarly, the labor market-clearing condition is given by 1 2  ∞ ˆ z2 n(x)dΓ(x) +1 2  ∞ ˆ z2 µ(x)n(x)dΓ(x) =θΓ(z1), which shows that, in equilibrium, aggregate labor demand is equal to aggregate labor supply. The first term is labor demand from male employers and the second one corresponds 19As explained in Section 3, a fraction (1 −θ)of both males and females with ability below z1become selfemployed because they would like to be workers but are not allowed to do so and choose their second-best option. 20 to labor demand from female employers (i.e. those women with enough ability to be employers who are allowed to choose their occupation freely). The labor supply shows the fraction of men and women who choose to become workers and are not forced to be necessity self-employed. A competitive equilibrium in this economy is a pair of cutoff levels (z1, z2), a set of quantities hn(x), k (x),˜ k(x)i,∀x, and prices (w, r)such that entrepreneurs choose the amount of capital and labor to maximize their profits, and labor and capital markets clear. BAPPENDIX: Details on size-distribution calculations Given a level of talent x, firms choose to have n(x) = hxη(1 −α)α 1−ααη wαη−1 rαη i1/(1−η) workers. We can invert this function to find x=n1−ηη(1 −α)α 1−ααη wαη−1 rαη −1 Substituting this expression into the cumulative density function 2gives us S(n) = 1 −n−ρ(1−η)Bρ ηα rαη 1−α w1−αη!ρ . 21