Entrepreneurship, Education and Credit Constraints: A General Equilibrium Model

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1 Entrepreneurship, Education and Credit Constraints: A General Equilibrium Model PRELIMINARY AND INCOMPLETE: Please ask before citing Roberto M. Samaniego Juliana Yu Sun y January 15, 2014 Abstract Credit constraints on entrepreneurs are known to account for the "fat right tail" in the US wealth distribution. Independently, it is known that entrepreneurs are more likely to have college degrees than the general population, and that nancing constraints limit the ability to go to college. This begs the question, is it in fact the inability to borrow for college that leads to a skewed wealth distribution? We develop a lifecycle model where agents decide whether to go to college and whether to be entrepreneurs. In the calibrated economy, we nd that college educated agents are actually less likely to have an entrepreneurial opportunity than average: they nonetheless form a disproportionate share of entrepreneurs because they are less likely to be credit constrained, thanks to the fact that they have higher earnings than agents without college. Although many agents do not go to college because they cannot a ord it, we nd that credit constraints on entrepreneurs are far more important for aggregate outcomes and inequality than credit constraints on earning a college education. Also, removing either kind of credit constraint has a similar e ect on the share of the population that chooses to go to college. Roberto M. Samaniego, George Washington University, 2115 G St NW Suite 340, Washington, DC Tel: (202) Fax: (202) roberto@gwu.edu. y Juliana Y Sun, School of Economics, Singapore Management University, 90 Stamford Road, Singapore Tel: (65) , Fax: (65) , yusun@smu.edu.sg. 1

2 1 Introduction Education and entrepreneurship are important determinants of aggregate outcomes. Education represents the accumulation of human capital, whereas entepreneurship is known to be important for accounting for patterns of physical capital accumulation for example, entrepreneurs account for a disproportionate share of the wealthiest households. 1 In addition, the accumulation of capital through both education and entrepreneurship are thought to be limited by borrowing constraints e.g. see for example Becker (1975) and Evans and Jovanovic (1989). This paper studies the interaction between the borrowing constraints on education and on entrepreneurship. We develop a general equilibrium model featuring both, and will argue that the true impact of either form of nancing constraint on aggregate outcomes cannot be assessed in isolation: the interactions among them are key to understanding the role of nancing constraints on aggregate outcomes, as well as the roles of entrepreneurship and education. That is, nancing constraints on entrepreneurship a ect the decision to become educated, and nancing constraints on education a ect entrepreneurship rates in important ways. To understand these interrelations, consider the following. Borrowing limits on entrepreneurs has been shown to account for the otherwise puzzling fat right tail in the US wealth distribution, since the di culty of raising external funds gives entrepreneurs a powerful incentive to accumulate wealth e.g. Cagetti and De Nardi (2006). 2 At the same time, they nd that wealth is not an important determinant of whether or not most agents become entrepreneurs, consistent with Hurst and Lusardi (2004). Thus, we might conclude that nancing constraints are not important determinants of entrepreneurship rates. However, recent work nds that a disproportionate share of entrepreneurs are college-educated (e.g. Bates (1990), Parker and van Praag (2006) and Mondragon-Velez (2009)). If agents are barred from attending college by the inability to borrow, then nancing constraints may signi cantly lower the number of entrepreneurs even if no agents report being unable to take advantage of en entrepreneurial opportunity because of nancing constraints. Indeed, by limiting entrepreneurial opportunities and high earnings to a subset of the population, 1 See for example Diaz-Gimenez et al (1997) and Cagetti and de Nardi (2006). 2 Holtz-Eakin et al (1994), and more recently Blanch ower (2009), provide evidence that borrowing constraints indeed limit entrepreneurs scale of operation. 2

3 borrowing limits on college could in fact be the main cause of the fat tail in the wealth distribution. Similarly, reductions in the pro tability of entrepreneurship due to borrowing constraints may disproportionately lower the return to college, so that some agents do not nd it optimal to go to college in an environment with nancing constraints even when no agent reports that borrowing constraints limit them from going to college. Such interrelations imply that studies of entrepreneurship that ignore education (and vice versa) might fail to identify important channels through which borrowing constraints might a ect either. Furthermore, are entrepreneurs more likely to become entrepreneurs because they nd it easier and make better entrepreneurs, or because the college educated have higher wealth and are therefore less constrained? Figure 1 Interrelations between nancing constraints on education and on entrepreneurship. To sum up, we ask the following questions: 1. to what extent do nancing constraints on education limit entrepreneurship? 2. to what extent do nancing constraints on entrepreneurship limit educational attainment? 3

4 3. to what extent are the educated more likely to be entrepreneurs because they are better entrepreneurs? 4. what is the impact of constraints on di erent activities on inequality, investment and aggregate activity? 5. what is the impact of educational subsidies, or capital subsidies, on inequality, investment and aggregate activity? Since the interrelationships between borrowing constraints involve complex dynamic channels, a dynamic structural framework seems like the appropriate approach for their study. We develop a general equilibrium model in which to analyze the role of borrowing constraints in agents human capital investment decisions and occupational choices. Borrowing constraints arise because of a limited enforcement constraint: agents may simply refuse to pay back their loans, in which case they are subject to punishment. While no default occurs on the equilibrium path, the extent to which agents can borrow is endogenously limited by the possibility of default. 3 We then calibrate the model to match data on inequality and occupational choice in the US. The paper is organized as follows. Section 2 provides some background to the exercise, motivating the model in Section 3. Section 4 explains calibration process and Section 5 reports the results of four quantitative experiments. 2 Background Literature Entrepreneurs are central to many issues in economic theory and in public policy. As a result, the determinants of entrepreneurship have been subject to extensive research. In particular, it is well known that entrepreneurs tend to be wealthy (e.g. Evans and Leighton (1989)). For example, according to Cagetti and De Nardi (2006), 7.5% of the workforce is made up of entrepreneurs (de ned as business owners who manage their rms), yet 54% of the households in the top 1% of the wealth distribution are entrepreneurs. However, do wealth 3 See Quadrini (2000), Cagetti and de Nardi (2006, 2009) or Buera et al (2011) for models with similar constraints. 4

5 and entrepreneurship have joint determinants or is it that, in order to be entrepreneurs, wealth is necessary? Evans and Jovanovic (1989) develop a static model with exogenous borrowing constraints, nding that a lack of wealth excludes some from being entrepreneurs. On the other hand Hurst and Lusardi (2004) challenge the view that wealth is important for entrepreneurial entry, nding that a positive relationship between wealth and entrepreneurship is obvious only among the wealthiest. Consistent with this nding, in a calibrated model of entrepreneurship under nancing constraints, Cagetti and De Nardi (2006, 2009) nd that nancing constraints bar less-wealthy entrepreneurs from achieving the optimal scale of operation, but that they are not important determinants of occupational choice. Independently, the literature regularly nds that agents educational level is also an important determinant of entrepreneurship. Mondragon-Velez (2009) documents using PSID that among entrepreneurs, 41% have college education or higher, while only 28% among the general population have attended college. Bates (1990) nds that rm survival is increasing in the entrepreneur s educational level, with a large increase if the entrepreneur has completed college. Terajima (2006) nds that the earnings of college educated entrepreneurs between 1983 and 2001 was 2.07 to 2.63 times higher than the earnings of non-college educated entrepreneurs. This raises two questions. First, are educated entrepreneurs more successful than the uneducated because education increases their productivity, or simply because they are more wealthy? Diaz-Jimenez et al (1997) nd that the college-educated are 2:6 times as wealthy as the high-school educated, and that their earnings are 2:2 times higher. Since the labor market rewards education, educated entrepreneurs might be more successful simply because they are wealthier, not because they are better entrepreneurs. Parker and van Praag (2006) nd that, not only are the more educated wealthier, but they appear to experience fewer nancing constraints (for example, because if they were to default their foregone earnings would be higher than for the relatively uneducated). Second, it is well known that for some the ability to attend college is limited by wealth see Becker (1975), and more recent work such as Belley and Lochner (2007) and Lochner and Monge-Naranjo (2011). Physical capital, if diverted againts a creditor s wishes, can be con scated and restored or liquidated. On the other hand, the human capital acquired through education is inalienable. Thus, default on an educational loan tends to trigger a harsh punishment regime, including temporary exclusion from capital markets and wage 5

6 garnishment (Ionescu (2009, 2011)), but the human capital itself cannot be retrieved. If the educated are more likely to be entrepreneurs, but education can be limited by nancing constraints, then nancing constraints could in fact limit the number of entrepreneurs in the economy because many agents do not attain the college education that would have increased their likelihood of becoming entrepreneurs in the rst place. Thus, nancing constraints could limit entrepreneurship even if no agents in the data appear to be limited in their occupational choices when an entrepreneurial opportunity does come along. Related quantitative work such as Cagetti and De Nardi (2006, 2009) that studies the role of nance and entrepreneurship in inequality is unable to address these questions, simply because those models do not include an education decision. Terajima (2006) does include an education decision, but educational choice in his model is not subject to nancing constraints, and also the paper focuses on identifying changes in earnings premia for di erent educational or occupational groups rather than on the questions at hand. Furthermore, in Terajima (2006) the nancing constraint takes the form of a simple factor of wealth, as in Evans and Jovanovic (1989). Parker and van Praag (2006) nd that the extent to which rms are nancially constrained appears to matter not just on wealth but also on education. We follow Cagetti and De Nardi (2006, 2009), Buera et al (2011) and others in modeling nancing constraints as being due to a limited enforcement problem, whereby agents may default on their debts. In this case, agents nancing constraints will depend on their wealth but also on their level of education since it a ects both the pro tability of entepreneurship and the foregone income if they default and are punished. 3 The Model We present a general equilibrium model where households choose whether to work or to become entrepreneurs, based on their expected earnings in either activity. These earnings are a function of idiosyncratic productivity shocks and of their capital (wealth). There is incomplete insurance, in that the only way agents may insure against idiosyncratic shocks is by holding capital, as in Aiyagari (1994). Entrepreneurs may also use their capital to produce themlselves, rather than renting it to other agents. Entrepreneurs may also produce using borrowed capital: however, the extent to which they are able to borrow capital is limited by an imperfect enforcement problem. If they refuse to make their interest payments, then 6

7 only a fraction f of their pro ts and remaining capital may be garnished. 4 In equilibrium, agents may only borrow capital up to the point that they are indi erent between repaying and reneging. This inability to obtain the myopic optimum level of capital from external sources is what provides entrepreneurs with an incentive to amass wealth. When born, agents may also choose an education level e 0, at an increasing cost (e; ) 0, where (0; ) = 0 and is a random variable. 5 Agents may borrow to become educated: however, like entrepreneurs, they may renege on repayment. Human capital is inalienable, so there is no way to reduce the agent s chosen value of e. Instead, they are excluded from credit markets for a period of time, during which a share of their wages may also be garnished. This follows the treatment of defaulted college loans documented in Ionescu (2008, 2009 and 2011). If for a given e the agent cannot a ord (e) on her own but would default if she were to borrow, then that level of e is ruled out. As a result, agents have an incentive to accumulate savings so that young agents may be less limited in their educational choices. 3.1 Technology There are two sectors in the economy: entrepreneurial and non-entrepreneurial. The nonentrepreneurial sector represents large publicly traded rms. 6 It operates the standard Cobb- Douglas production function: Y t = AKt L 1 t (1) where Y t is output, K t is capital, L t is labor and A is a productivity term. Entrepreneurial rms are run by single entrepreneur who operates the technology: y t = (e) x t k v t ; 0 < < 1. (2) Here y t is output and k t is capital input. This is similar to the model of Lucas (1978), 4 See Quadrini (2000), Cooley et al. (2004), Cagetti and De Nardi (2006, 2009), Krebs and Wright (2010), Buera et al (2011) and others for similar constraints. 5 The variable captures the idea that a given level of education may be attainable at di erent cost. For example, it is well known that the cost of attending a 4-year college varies signi cantly both across and within private and state universities. 6 See Quadrini (2000) and Cagetti and De Nardi (2006, 2009) for similar models. 7

8 extended to allow for an impact of education. As discussed later, the choice of k t may be limited by a borrowing constraint. 7 Notice there are two productivity terms in this production function. The term x is the entrepreneur s ability. The term (e) re ects the possibility that entrepreneurial productivity may depend on the agent s educational level. We assume that (0) = 1. There is evidence that more educated entrepreneurs tend to have higher earnings, e.g. Terajima (2006). However, that does not necessarily imply that 0 (e) > 0. For example, if more educated agents tend to have higher wealth, then they may display higher earnings simply because they are less nancially constrained, not because they are more productive. The calibration process itself will determine whether or not education boosts entrepreneurial productivity. 3.2 Households There is a continuum of agents in discrete time. Each period a mass of agents called Newborns enters the model. Newborns start life with a wealth inheritance, choosing their level of education e 0. The following period they become Young. The young face a constant probability of remaining young, y, whereas with probability 1 y they become Old. Old agents face a probability o of leaving the model. When an old agent exits the model, it is replaced by a newborn, who inherits the old agent s assets. We normalize the population to equal one. Regardless of their stage of the lifecycle, agents maximize expected discounted utility. Their instantaneous utility function is u(c) = c1 1, > 1, and their discount factor is. Each period an agent is endowed with one unit of labor, which they supply inelastically. At each point in time, agents have two state variables, x t ~F x (x t jx t 1 ; e) and y t ~F y (y t jy t 1 ). The variable x t is the agent s entrepreneurial ability. The variable y t is their labor market earnings ability. These two variables a ect agents earnings power from di erent activities. 7 We could allow entrepreneurs to hire workers. We do not do so to maintain the focus of our work on the accumulation of physical capital. While the impact of entrepreneurship on job creation is a topic of interest, it will not a ect our results, since workers would be paid the same as in the non-entrepreneurial sector so the margin of impact would remain that of occupational choice which is already negatively impacted by the wage because it is the opportunity cost of entrepreneurship. 8

9 There are incomplete markets: agents may self-insure against di erent forms of idiosyncratic via holdings a t of capital, which pays net interest rate r and depreciates at rate. Notice that we allow the Markov process governing the evolution of x t to depend on the educational level e. Mondragon-Velez (2009) reports that the college-educated form a disproportionate share of entrepreneurs, and we wish to establish whether this is because the college-educated are more likely to have higher values of x t, or because the college-educated tend to be wealthier and thus less nancially-constrained. 3.3 Young agents Young agents can choose whether to be entrepreneurs or workers. Young entrepreneurs use the technology (2) to generate income, using their own capital or borrowing capital from other agents. They also earn income from capital they lend to other agents. With their income they purchase consumption c t, and assets a t+1 for next period. A young entrepreneur has the value function V e (a t ; x t ; y t ; e) = max fu (c t ) + y EV (a t+1 ; x t+1 ; y t+1 ; e) + (1 c t;a t+1 ;k t s:t: c t + a t+1 (e) x t kt wn t + (1 ) k t (1 + r) (k t a t ) k t 0; a t 0 y ) EW (a t+1 ; x t+1 ; e)g (3) where V is the young agent s future expected value in the future if they remain young, to be explained below, and W is their expected value in the future if they become old, in which case they may choose to retire or to continue managing the rm. The expectation E is taken with respect to x t+1 and y t+1. Entrepreneurs are also subject to a borrowing constraint. If k t a t > 0 then the agent is borrowing and must pay (1 + r) (k t a t ) to other agents. If the agent refuses to make this repayment, they are punished by the garnishment of a fraction f of their pro ts and their holdings of undepreciated capital, f [ (e) xkt + (1 )k t ]. Along the equilibrium path the agents will not default. However, the fact that they could 9

10 default introduces an incentive compatibility constraint that can limit the extent to which the rms can borrow. This constraint should compare the value of repaying V e (a t ; x t ; y t ; e) with the value of default, including the possibility that agents might choose di erent values of a t+1 o the equilibrium path. However, Buera et al (2011) show that the incentive compatibility constraint takes the simple form (e) xkt + (1 ) k t (1 + r) (k t a t ) (1 f) [ (e) xkt + (1 )k t ] (4) where f is the fraction of the entrepreneur s pro t that the lender could obtain once default occurs. In other words, what matters is whether or not the pro ts from default are higher now. 8 If the unconstrained optimal capital usage violates this constraint, then the agent will only be able to use the level of capital k t such that equation 4 holds with equality. If the young agent chooses to be a worker, her value is V w (a t ; x t ; y t ; e) = max c t;a t+1 fu (c t ) + y EV (a t+1 ; x t+1 ; y t+1 ; e) + (1 s:t: y ) EW r (a t+1 ; x t+1 ; e)g (5) a t+1 (1 ) (e) wy t + a t (1 + r) c t where w is the wage and y t is her labor productivity shock. The function (e) captures the stylized fact that labor market earnings are higher for more educated people, so we assume (0) = 1, 0 (e) > 0. Labor market earnings are taxed at rate. If the worker ages she retires, earning value W r. is Finally, the agent chooses their occupation optimally. As a result, their value function V V (a t ; x t ; y t ; e) = max fv e (a t ; x t ; y t ; e) ; V w (a t ; x t ; y t ; e)g : (6) 8 As we shall see, the value function V () is strictly increasing in a t, and with higher income agents can attain both higher consumption and higher savings a t+1. Thus, the value of default is higher than that of repayment if and only if the pro ts from default exceed those from repayment. 10

11 3.4 Old agents Most old agents simply retire. The value for a retiree is W r, where W r (a t ) = max fu (c t ) + o W r (a t+1 ) + (1 c t;a t+1 o )EV new (a t+1 ; x t+1 ; y t+1 )g (7) s:t: a t+1 a t (1 + r) c t + p Here, p is a social security payment. Recall that with probablity o the agent exits the model and is replaced by a newborn. There is an altruism parameter 2 [0; 1] which determines the extent to which agents care about their o spring. The function V new is the value function for the newborn. Young entrepreneurs who become old may choose to continue running those rms, if they prefer not to retire. In that case they may become old entrepreneurs, whose value W e is given by: W e (a t ; x t ; e) = max fu (c t ) + o EW (a t+1 ; x t+1 ; e) + (1 o )EV new (a t+1 ; x t+1 ; y t+1 (8) )g s:t: a t+1 (e) xk v t + (1 ) k t (1 + r) (k t a t ) c t k t 0; a t 0 Incentive compatibility constraint (4) : where o 2 (0; 1) is the probability of staying old, and is a measure of altruism, the extent to which you care about your descendants. In two extreme cases: if = 1, it is perfect altruism; if = 0, agents do not care about their children at all. The newborn s value of x t and y t are drawn from distributions Fnew x and Fnew y respectively. Finally, W (a t ; x t ; e) = max fw e (a t ; x t ; e) ; W r (a t )g : (9) 11

12 3.5 The Newborn Newborn agents observe their initial values of x t and y t, and decide on their educational level. If they choose not to become educated, they are identical to young agents for whom e = 0, choosing whether to be workers or entrepreneurs. If they choose e > 0, they may work but they may not become entrepreneurs. 9 In this case, they must also pay a cost (e; ), where (0; ) = 0, e (e; ) and (e; ) > 0. is a random variable that a ects the cost of education for a given agent, drawn from a distribution F. We introduce because later, in our calibration, we will have only a few values of e, so allowing for some noise in the cost of education will ensure that educational decisions are not too "lumpy." 10 The value of an uneducated newborn V noneduc (a t ; x t ; y t ) is: V noneduc (a t ; x t ; y t ) = maxfv m (a t ; x t ; y t ; 0) ; V w (a t ; x t ; y t ; 0)g = V (a t ; x t ; y t ; 0) where V m and V w de ned earlier. are the value functions for entrepreneurs and workers respectively, as For the college educated newborn agents, the value V educ (a t ; x t ; y t ; e) is: V educ (a t ; x t ; y t ; e; ) = max fu (c t ) + EV (a t+1 ; x t+1 ; y t+1 ; e)g c;a 0 s:t: a t+1 (1 ) (e) wy + (a t (e; )) (1 + r) c t The workers must also satisfy an incentive compatibility constraint. (e; ) > a t for any given level of e and then agents must borrow (e; ) a t. Notice that if 9 This is for simplicity. If we allow the newly-educated to be entrepreneurs then there will be two nancing constraints facing certain entrepreneurs, one related to rm size and one related to education, and it would be di cult to specify what occurs if the agent defaults on one type of loan but not the other. Since the very young are unlikely to be entrepreneurs anyway, we simply assume the newborns may not be entrepreneurs. 10 For example, if we let e 2 f0; 1g where e = 1 represents going to college, then can be thought as representing the fact that the college application process is uncertain and that there is signi cant variation in the cost across universities (due to di erent tuition costs, cost of living di erences, etc). 12

13 There is also a credit constraint, such that if an agent does not pay back an educational loan then she enters a "punishment regime" where they earn D educ (a t ; x t ; y t ; e). While being punished the agent is barred from capital markets and from entrepreneurship, and there is a wage garnishment rate (e), as well as a probability (e) that the agent will be forgiven so the punishment ends. Thus we have that D educ (a t ; x t ; y t ; e) = max c t;a t+1 s:t: ( u (ct ) + y [(1 (e))ed educ (a t+1 ; x t+1 ; y t+1 ; e) + (e) EV (a t+1 ; x t+1 ; y t+1 ; e)] + (1 y )W r (a t+1 ) ) a t+1 (1 + r) a t + (1 (e)) (1 ) ewy c t If the agent is forgiven, she can choose occupations and borrow as a normal young agent henceforth. If the agent is still unforgiven when she becomes old, she has to retire. Since at the moment of default the agent would have no assets, the incentive compatibility constraint is V educ (a t ; x t ; y t ; e; ) D educ (0; x t ; y t ; e) : Notice that as! 0 then D educ (0; x t ; y t ; e)! 1, in which case nobody defaults. The value of a newborn is then Z V new (a t ; x t ; y t ) = maxfmax V educ (a t ; x t ; y t ; e; ) ; V noneduc (a t ; x t ; y t )gdf () (10) e 3.6 Equilibrium Let! t be the aggregate state variable, the measure over di erent types of agents. The measure! t is de ned over the quintuple (a; x; y; e; g): the agent s asset holdings, a, entrepreneurial productivity x, labor market productivity y education level e, and a variable g 2 f1; 2; 3; 4g which takes account of the agent s life cycle stage: agents are classi ed as newborn, young, old entrepreneurs or retirees. The measure! t 2 X, where X = R 4 +f1; 2; 3; 4g. There is a transition mapping : X! X, so that! t+1 = (! t ). The mapping is a function of agent s optimal decision rules regarding investment, education and occupational choice, as well as the stochastic processes for x, y, and ageing. 13

14 De nition 1 A stationary equilibrium is a wage w, an interest rate r, a tax rate and a measure! such that: Young agents; consumption, investment, capital use and occupational choices are optimal, solving problems (3), (5) and (6), subject to the incentive compatibility constraint on entrepreneurs. Old agents; consumption, investment, capital use and occupational choices are optimal, solving problems (7) and (8), subject to the incentive compatibility constraint on entrepreneurs. Labor markets clear: total labor supply from workers equals the labor demand from the nonentrepreneurial sector. Capital markets clear: total capital supply from all agent s savings equals capital demand from both entrepreneurial and nonentrepreneurial sectors. Government budget is in balance: total tax receipts equal total social security transfers to retirees. The distribution of agents is invariant:! = (!). 4 Calibration We try to x as many parameters as possible and calibrate the remaining parameters to match various statistics regarding education, entrepreneurship and inequality in the US. Table 1 lists the parameters in our model. The depreciation rate of capital 6% is taken from Stokey and Rebelo (1995). The coe cient of relative risk aversion is 1:5; from Attanasio et al. (1999). Productivity in the non-entrepreneurial sector is normalized to 1. The share of capital is 0:33, as in Gollin (2002). The probabilities of being young and old are taken from Cagetti and De Nardi (2006) who match them with the working life of 45 years and the retirement period of 11 years respectively. The probability of being forgiven in the loan market (education loan) are given 0:1429 so that defaulters are forgiven after 7 years of punishment. The degree of altruism is set to 1 for perfect altruism in our baseline model. The probabilities of ageing and exiting the model imply an average working life of 45 years and an average retirement period of 11 years. 14

15 Table 1: Parameters of The Model A. Fixed Parameters Parameter Value 1:5 Attanasio et al. (1999) 6% Stokey and Rebelo (1995) 0:33 Gollin (2002) A 1 Normalization y o 0:978 see text 0:911 see text 0:1429 seven-years punishment 1 Perfect altruism B. Calibrated Parameters Parameter Calibrated value p 0:7764 v 0:7939 x [0 2:1011] F x see text 0:8741 F y see text f 0:4422 (e) 3:3745 F 0 y [0:2039 0:1982 0:1958 0:1982 0:2039] (e) [1 1:2060] y [0:24510:44550:76441:31152:3845] 0:1200 (e) [1:00 1:45] 15

16 We calibrate the rest parameters as follows (see Panel B in table 3). The discount factor is calibrated to match capital a output ratio 3:3 as in Cooley and Prescott (1995). We set the social security transfer p to match a ratio of social security transfers to GDP of 40%, as in Cagetti and De Nardi (2006). The degree of decreasing returns to scale in the entrepreneurial production v is calibrated to pin down the Gini coe cient of wealth of 0:76. The entrepreneurial punishment parameter f is calibrated to match median net worth of entrepreneurs compared to whole population 0:3, in Cagetti and De Nardi (2006). We use a parsimonious speci cation for entrepreneurship, setting x 2 f0; x high g, so that agents either do or do not have an entrepreneurial opportunity, as in Cagetti and De Narti (2006). Unlike that paper, however, it is not the case that all entrepreneurs have the same target level of capital in equilibrium, since entrepreneurial productivity depends both on x and on e. Following that paper, we de ne entrepreneurs as persons who who both own a business and actively manage it. This is because, in our model, it is key that the human capital of the owner be a central determinant of the pro ts of the rm: thus, for example, someone who manages a business but does not own it, or who owns a business but outsources its management, is not an entrepreneur in terms of our model. We also set e 2 f0; 1g, interpreting e = 1 as a college education. We do this because Mondragon-Velez (2009) nds that the probability of being an entrepreneur rises signi cantly with college attendance, whereas Bates (1990) nds that the probability of rm exit drops if the entrepreneur has a college degree. Thus it does not seem useful to allow e to be de ned more nely, while increasing the computational cost. The education cost (e; ) is uniformly distributed over ve values. We set the mean cost to match the share of educated agents in the population. This is 29% in the PSID (see Mondragon-Velez (2009)). The other values are set to cover the range plus or minus 5% of the mean value. The wage garnishment to education loan defaulters, ; is calibrated to match average education loan to GDP per capita of 0:36. We arrive at this value as follows. Reed (2011) nds that two-thirds of college seniors graduating from non-pro t four-year colleges in 2010 had student loan debt, and the average owed was $25; 250. The World Bank reports that US GDP per head in 2010 was $46; 616. Combining these numbers we nd that the average student loan is 0:36 times GDP. 16

17 The college premium for entrepreneurs (1) is calibrated to target average earnings of college educated entrepreneurs over non college educated reported in Terajima (2006), which is 2:35. The college premium for workers (1) is set to match the estimate of 1:4 in Fang (2006). Fang (2006) considers the fact that the observed college premium combines the fact that worker productivity may rise as a result of earning a college education, but that it could also be that college simply provides a signal to employers about worker ability (Spence (1973)). The estimate of 1:4 refers to the productivity increase from going to college, net of any signalling e ects, which is exactly our parameter (1). In our context, this corresponds to the idea that newborns choose whether or not to go to college based on their values of x and y, so the average college premium in the model may also not accurately re ect the productivity increase that comes from going to college. To match the income process F y, we set y t = y t 1 + " t, and set the variance of " t to match the Gini of earnings to be 0:38 as in the PSID. 11 We approximate it over a grid of ve values of y, evenly spaced (in logs) between 1 and 1, rescaled so that the mean value of y equals one. We assume the income and entrepreneurial ability process are independent to each other. Also, we assume the income process is the same for college educated and non-college educated workers. The entrepreneurial ability x takes two values: 0 and a positive shock. The positive shock is calibrated to match fractions of entrepreneurs in the whole population 7:5% in Cagetti and De Nardi (2006). The transition matrix F x is a 222 tensor, since we allow the Markov process governing the evolution of x t to depend on e. This requires in principle four parameters: one each for the probability into and out of entepreneurship for each level of e. 12 We proceed as follows. First, Cagetti and De Nardi (2006) nd an exit rate among 11 In general the earnings process is usually thought of as being mean-reverting. However, estimates indicate that the earnings process is very highly persistent, even if it is not a unit root. In practice since F y is in fact a matrix over ve values of y that approximates this process, it will necessarily display some mean reversion. Thus there is no need to build weak mean reversion into the assumed process. 12 The probability of remaining an entrepreneur for each education group is one minus the probability of going out of entrepreneurship, and the probability of remaining a worker is one minus the probability of going into entrepreneurship. Thus, with these 4 parameters, the entire tensor is determined. 17

18 Table 2: Preliminary Results Target Baseline Model Transfer size as percentage of GDP 40% 40% capital to GDP ratio (Cooley and Prescott 1995) 3:3 3:3 Gini coe cient of wealth 0:76 0:74 fractions of entrepreneurs in the whole population 7:5% 7:5% median net worth of entrepreneurs vs whole population 0:3 0:3 percentage of college educated population 29% 29% education cost over GDP per capita 1:3 1:1 percentage of college educated entrepreneurs 41% 43% ow of workers into entrep, 2:3% 2:5% Gini coe cient of earnings 0:38 0:38 average earnings of college educated entrepreneurs over non college educated 2:35 2:5 average education loan to GDP per capita 0:4 0:4 entrepreneurs of 0:206 in PSID. Bates (1990) reports a logit regression that indicates how the probability of survival varies when an agent earns a college degree. We choose the probabilities of rm survival to match the mean from CDN and the di erences from Bates (see Appendix for details). To match hazard rates into entrepreneurship for college and non-college groups we match two statistics. One is the ow rate of workers into entrepreneurship, which is 2:3% in Cagetti and De Nardi (2006). The other is the share of entreprenurs with college education, which is 41% from Mondragon-Velez (2009). Finally, the newborn s entrepreneurship ability function Fnew x is the ergodic distribution of F x : We also assume the newborn s work ability function Fnew y is the ergodic distribution of F y : Our baseline model results (listed in table 2) match the targets very well, although our gini coe cient of wealth, education cost over GDP per capita and everage earnings of college educated entrepreneurs over non college educated entrepreneurs are slightly lower than the target, and percentage of college educated entrepreneurs and ow of workers into entrepreneurship are slightly higher. 18

19 5 Results Now we compare the behaviors of di erent occupations and education levels. From the upper-left graph in gure 1, we could see that entrepreneurs are in generally wealthier than workers. This result con rms that entrepreneurs tend to save more in face of borrowing constraint, and are wealthier due to high returns to entrepreneurial activities. The upperright graph shows the distributions of college and non-college educated populations. It is very clear that college educated people are wealthier, while the population with zero assets are mainly the non-college educated. Similarly, When comparing the wealth levels between college educated entrepreneurs and workers (the lower-left graph in gure 1), the fraction of entrepreneurs is higher than workers at higher level of wealth. We further compare the wealth of college educated and non-college educated entrepreneurs (the lower-right graph in gure 1). Our results show that college educated entrepreneurs are wealthier, because of higher productivity from education and higher wealth threshold required by creditors due to higher default values. 19

20 fraction of people fraction of people fraction of people fraction of people entrepreneur worker Wealth, in $10, college educated non college educated Wealth, in $10, college entrepreneur college worker college entrepreneur non college entrepreneur Wealth, in $10, Wealth, in $10,000 Figure Policy Experiments We then conduct policy experiments by removing the nancing constraints on education, entreprenerial projects and both, respectively (see table 3). We nd that when removing the education loan constraint, GDP grows by 11%, compared to the benchmark model. Capital to GDP ratio rises by around 1%. This is because educated agents save more to enter entrepreneurship. Both the fraction of entrepreneurs in the whole population and percentage of college educated entrepnreurs go up by 2.6% and 32.4% respectively. However the Gini coe cients of wealth and earnings, indicating that wealth and income are concentrated to 20

21 the entrepreneurs, since the median net worth of entreprenrus over the whole population rises 2.65%. Without surprise, the average education loan to GDP rate goes up by 73%, while education cost falls. Transfer size declines due to the rise in total GDP in the economy. As we can see that relaxing education loan constraint has signi cant impacts on entrepreneurship, capital accumulation and GDP. Next, we relax the nancing constraint on entrepreneurial loan. GDP rises 38% compared to our baseline model. It has signi cant e ects on enterepreneurship. The fraction of entrepreneurs, median net worth of entreprenerus and ow-in rate to entrepreneurship go up by 112.7%, 25.25% and %, respectively. It is noticeable that relaxing the nancing constraint on entrepreneurial loan also has large impacts on education, mainly by making education less expensive and increasing average earning of college educated entrepreneurs. Gini coe cient of wealth declines because entrepreneurs do not need to accumulate wealth to be eligible to borrow. However, gini coe cient of earnings increases by almost 5%. This is because there are more entrepreneurs and more college educated, i.e. more productive, agents in this model. If we remove constraints on both education and entrepreneurial loans (see column 3 in table 3), we nd that the model is very close to the results without entreprenerial constraint only (see column 2). We conclude that nancing constraint on entreprenerus has stronger e ects on aggregate economic performances by changing agents investment and education behaviors. However, in a world with information assymetric, moral hazard and enforcement problem, entrepreneurs face tighter constraints than college loan borrowers. Relaxing education nancing constraint could be an alternative policy choice to promote productivity and entrepreneurship. To further explore how the nancing on college education a ects the aggregate economy, we "forbid" everyone to borrow for education (column 4 of table 3). In this experiment, we can see that GDP declines 8.36%. Similarly, the fraction of entrepreneurs, college educated population and entrepreneurs and ow-in rate all decrease. Inequalities in wealth and earnings are enlarged. This is because the aggregate productivity is lower (due to less educated population) and talented agents have to save more to conqure the borrowing constraints. It is also re ected in higher capital to GDP ratio and net worth ratio of entrepreneurs to the whole population. 21

22 Table 3: Policy Experiments Compare to the baseline model No const on educ No const on entreps No const No educ loa Y +10:72% +38:00% +37:72% 8:36% Transfer size relative to GDP 7:79% 21:84% 21:73% +8:88% K=Y +0:92% 8:47% 8:52% +0:07% Gini (wealth) +0:47% 4:79% 4:83% +0:18% Entrepreneurs/pop +2:65% +112:72% +112:85% 2:12% median net worth, entreps/whole pop +2:63% +25:25% +25:25% +2:49% percentage of college educated pop +37:45% +25:79% +24:96% 20:78% education cost over GDP per capita 9:68% 27:54% 27:39% +9:12% percentage of entreps with college +32:42% 31:05% 31:52% 19:25% ow of workers into entrep, +1:84% +196:13% +196:34% 1:82% Gini (earnings) +11:70% +10:67% +10:67% 10:80% Average earnings, college/non-college 0:38% +4:66% +4:65% +0:37% average education loan to GDP per capita +73:35% +51:31% +51:52% Next, we compare the wealth distribution of groups by occupation in di erent policy experiments. From gure 2, we can see that for the whole population, the model without constraints on entrepreneurs dominates the baseline model and the model with no constraints on education, i.e. there are more population with higher wealth in the model with no constraints on entrepreneurs. If we focus on the entrepreneurs group, the model without constraints on education bene ts entrepreneurs disproportionately, while the distribution of the model without entrepreneurial borrowing constraint bowls towards the up-left corner and baseline model is in the middle. This is consistent with our conclustions that relaxing entrepreneur s borrowing constraint leads to dissave by entrepreneurs, and relaxing education borrowing constraints promotes productivities and higher wealth inequality. Comparing with the wealth distribution of workers (the lower-left panel), the distribution is similar to the whole population. We then nd that the nancing constraint on education take e ects mainly by changing entrepreneur s behavior (encouraging dissaving). 22

23 population population population 1 whole population 1 entrepreneur 1 W orker baseline 0.1 no constraint no educ constraint Wealth, in $10, Wealth, in $10, Wealth, in $10,000 Figure 2 We also study the distribution di erences by education and occupation (see gure 3). Comparing college educated and non-college educated entrepreneurs, it is noticeable that non-college educated entrepreneurs disave more when borrwoing constraint is relaxed. Unsurprisingly, college educated entrepreneurs are in general richer than the uneducated ones. Similarly, non-college educated workers are concentrated in the low wealth level. It is interesting that relaxing entrepreneurial borrowing constraint encourages non-college workers wealth, thanks to more employment opportunities brought by entrepreneurs. When comparing college educated entreperneurs and workers, the percentage of wealthy (higher than $1000,000) entrepreneurs is higher than workers. 23

24 population population population population 1 college educated entrepreneur 1 non college entrepreneur Wealth, in $10, Wealth, in $10,000 1 college educated worker 1 non college worker baseline No constraints on education No constraints on entreprenerus Wealth, in $10, Wealth, in $10,000 Figure 3 6 References References [1] Attanasio, Orazio P., James Banks, Costas Meghir, and Guglielmo Weber "Humps and Bumps in Lifetime Consumption." Journal of Business and Economic Statistics. 17(1): [2] Aiyagari, S Rao, "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, MIT Press, vol. 109(3), pages , August. 24

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27 [28] Terajima, Yaz "Education and Self-Employment: Changes in Earnings and Wealth Inequality." Bank of Canada working paper The Algorithm The algorithm is the following: 1. Construct A grids for state vectors. The maximum value on the asset grids is set to be higher than household s saving. 2. Set initial guess for interest rate, wage, tax and value functions. 3. Solve c, a 0, and k to maximaize household s problems given interest rate, wage, tax and future value functions. 4. Update value functions using new c, a 0, and k. Go back to step 3 until value functions converge. 5. Use more grids B (B>A) to check borrowing constraints and update constrained agents value functions. 6. Compute measures with grids B, total capital demand and supply, total labor demand and supply. Update new interest rate and wage. 7. Go back to step 3 with new interest rate and wage. Iterate until labor market clears. 8. Compute government budget and update tax rate. 9. Go back to step 3 until government budget is in balance. Note that we can derive the interest rate if we know the wage rate, so we only need to nd the equilibrium wage rate in the labor market. According to Walras Law, when the labor market, capital market are clear, and government budget is balanced, the output market is in equilibrium too. So we do not need to nd the goods market equilibrium. Because our borrowing constraints are endogeous, the maximum investment k is determined by value functions. In step 5, we follow BKS algorithm to nd the "optimal" k by comparing the default and non default value functions and choosing the maximum k at which level entrepreneurs have no incentive to default. 27