Informality and Long-Run Growth

One of the most salient features of developing economies is the existence of a large informal sector. This paper uses quantitative theory to study the dynamic implications of informality on wage inequality, human capital accumulation, child labor and long-run growth. Our model can generate transitory informality equilibria or informality-induced poverty traps. Its calibration reveals that the case for the poverty-trap hypothesis is strong: although informality serves to protect low-skilled workers from extreme poverty in the short-run, it prevents income convergence between developed and developing nations in the long run. Sudden elimination of informality would induce severe welfare losses for several generations on the transition path. Hence, we examine the effectiveness of different development policies to exit the poverty trap. Our numerical experiments show that using means-tested education subsidies is the most cost-effective single policy option. However, for longer time horizons, or as the economy gets closer to the poverty trap threshold, combining means-tested education and wage subsidies is even more effective.


I. Introduction
In this paper, we develop a two-sector growth model to analyze the dynamic implications of informality for long-run growth. The model features bidirectional causal links between informality and human capital accumulation, our source of economic growth. On the one hand, the existence of an informal sector influences the incentive to accumulate human capital; this is because informality lowers the skill premium and facilitates child labor. On the other hand, human capital affects the size of the informal sector; when the number of high-skilled workers is small, labor demand is low in the formal economy and informality increases. First, we theoretically show that these interdependencies between human capital accumulation and informality can be the source of transitory informality equilibria or informality-induced poverty traps. Second, we confront the data to the model to obtain key parameters to match a set of stylized facts that describe the relationships between informality, human capital, child labor and growth. The calibrated model reveals that the case for the poverty trap is strong. In this context, we explore different policies that could enable a developing country to escape the poverty trap.
The informal economy is defined as the part of an economy that is not taxed, monitored by any form of government, or included in gross national product. Although it is difficult to measure precisely, informality is undoubtedly a widespread phenomenon in developing in South Asia. It is usually described as a heterogeneous sector including registered firms' activities hidden from the State, wage employment or self-employment in unregistered smallscale business units, and sometimes home production. We make two clarifications about the concept of informality investigated in this paper. First, our model aims at capturing informal activities that lead to economic transactions between economic agents, not home production. 2

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The size of the informal market has been estimated using direct measurement methods (i.e. household micro surveys) and indirect methods. The latter exploit the correlation between economic activity and monetary indicators (informal activities conduct more transactions in cash), electricity consumption or indicators of aggregate expenditure (Schneider et al., 2010). Second, the nature of the informal economy differs between rich and poor countries.
In developed countries, the informal sector is characterized by unreported employment and sales. Informal activities are governed by the same production technology as in the formal sector and are simply hidden from the state for tax, social security or labor law purposes. 1 The informal economy is of a different nature in developing countries. Although tax evasion also plays a role, developing countries show a dualistic system of production with registered and unregistered firms. The latter are characterized by low-skill intensive technology and provides a precious source of income to many low-skilled individuals in countries where lowskilled wages would fall below subsistence levels in the absence of an informal economy. 2 Our model disregards fiscal informality and focuses on subsistence informality, the overwhelming part of the informal economy in low-income countries.
Subsistence informality is the only way for many people in developing countries to escape extreme poverty and precarious living conditions (Gërxhani, 2004). A large share of informality is tolerated by the State in many developing countries. The reasons are multiple, such as the incapacity of the State to develop or maintain social programs, its incapacity to manage unemployment, the fear of a bankruptcy of the economy, the fear of social tensions, etc. A report by the World Bank (2014, p.23) states that a third of developing economies do not have any social protection policy or strategy, and the number of such countries is growing very recently, meaning that the effects of many of these programs still have to come.
In the absence of social protection, informality is widely tolerated because it provides people with an alternative to live due to absent alternatives such as unemployment insurance (as the elasticity of recorded GDP per capita to human capital is close to unity and school enrolment rates are lower in poor countries. We build a two-sector model, in which people choose to join or not to join the informal sector, and assume the existence of technological differences between sectors (as in Murphy et al. 1989, or Krugman 1991. Then we investigate the implications of subsistence informality on welfare, inequality, growth, and effectiveness of development policies. Our philosophy is to use an abstract economic model, which highlights the major economic mechanisms underlying the formation and persistence of the informal sector and development. Incentives to invest in children's education and opportunities to obtain income from children will play a key role. We then confront the theory to the data, calibrate the parameters of our model and study its dynamic properties. Such a quantitative theory approach is now the dominant research paradigm used by economists incorporating rational expectations and dynamic choice into short-run macroeconomic and monetary economics models (King 1995). Although the sources of poverty traps have been abundantly documented, they have rarely been submitted to a quantitative assessment.
In our framework, the main link between informality and long-run growth operates through the accumulation of human capital. The incentive to accumulate human capital is lowered by the existence of the informal sector for two reasons. On the one hand, since the informal sector absorbs a large share of the less-skilled labor force, the supply of less-skilled workers to the formal sector is reduced, leading to a smaller skill premium. On the other hand, the occurrence of child labor is facilitated by the existence of the informal economy.
Faced with lower skill premia and easier access to child labor, parents tend to choose less schooling for their children.
The model may generate multiple equilibria or a unique equilibrium, depending on the parameter values. In the absence of informality, the model predicts long-run convergence in income across nations. Informality may slow down this convergence process or be the source of a poverty trap. Using the stylized facts above and other consensual parameters from the 5

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This article is protected by copyright. All rights reserved. literature, we calibrate our model and study its quantitative properties. This allows us to discriminate between the poverty-trap and slow-convergence hypotheses. The calibration exercise reveals that the case for the poverty-trap hypothesis arises: although informality serves to protect low-skilled workers in the short run, it prevents income convergence across countries.
On this basis, we assess the effectiveness of different policy options. Coercive policies such as a sudden elimination of child labor would induce large welfare losses for the initial generations of poor people on the transition path. We thus consider different Pigouvian policies (subsidizing education to all families, or to low-income families, subsidizing highskilled formal employment, or low-skilled formal employment) assuming that subsidies are financed by development assistance. Two criteria are used to evaluate these policies: costeffectiveness and the length of the transition required to exit the poverty trap. Among the four subsidies considered, education subsidies paid to low-income families dominate the others in terms of cost efficiency. Moreover, only wage subsidies for low-skill jobs in the formal sector play a distinct and complementary role in the transition to the high-income equilibrium. Whereas the education and the high-skilled formal employment subsidies speed up the accumulation of human capital, the low-skill wage subsidy reduces the threshold at which the informal sector disappears. Therefore, targeted education subsidies are the cheapest single policy, but for medium time horizons, a combination of the two policies is found to be the most cost-efficient choice.
The remainder of this paper is organized as follows. Section II discusses the main stylized facts and Section III describes the model. The implications of informality are examined in Section IV. In Section V, we calibrate the model and study its quantitative properties.
Section VI concludes. 6 Accepted Article

II. Stylized facts
We require our model to be compatible with five major stylized facts (SF1 to SF5) on subsistence informality and development, as illustrated in Figures 1(a) to 1(d). 4 SF1. Informality decreases with development. Figure 1(a) shows the relation between the proportion of tertiary educated (completed college education) and the ratio of the estimated size of the shadow economy over recorded GDP in year 2000. The shadow economy includes both activities hidden from the State for tax purpose and subsistence informality. The share of the shadow economy varies between 10 and 20 percent in high-income countries (an average of 13.5 percent); these informal activities are mainly related to tax evasion.
The share of the shadow economy is much greater in developing countries, which is due to the importance of subsistence informality. Overall, Figure 1(a) shows a downward sloping relationship between informality and the proportion of high-skilled workers. Our model will endogenize the size of the informal sector and be consistent with this fact. The rationale is the following: low-skilled workers are mobile across sectors whereas high-skilled individuals only work in the formal sector. When the number of high-skilled workers is small, there is little demand for low-skilled labor in the formal sector and formal firms pay low wages to the less educated. Many low-skilled workers then move to the informal sector where wages are more attractive. Informality thus serves to protect low-skilled workers against very low levels of income offered in the formal sector and extreme poverty. and Shleifer (2008) find evidence of a substantial difference between the registered and the unregistered firms regarding the skills of their managers, and suggested that this may drive many other differences, including the quality of inputs and access to finance. Rodrik (2013) points out that there is rapid unconditional convergence between rich and poor countries in manufacturing industries, but this phenomenon is hidden by a persistent specialization of poor countries in low-productivity (formal and informal) activities. Based on these facts, our model defines informality as a sector with lower productivity, low-skilled employment, and constant marginal productivity of labor. By contrast, the formal sector combines highskilled and less educated workers, exhibits decreasing marginal productivity, constant returns to scale, and higher total factor productivity.
SF3. Child labor increases with informality. One of the underlying aspects of informality is the existence of child labor. We can think of different forms of child labor, from shoeshine boys to children working in mining extraction. In general, children are not reported as part of the official labor force. Even if formal firms employ children, they are not recorded as part of their formal workers by the state agencies. Figure 1(b) plots the percentage of male children who work against the share of the informal economy, expressed as a percentage of GDP in 2000. 5 We can observe a positive correlation between informality and child labor.
Note that the relation would be much steeper if high-income countries were included. Child labor is more likely to occur in poor families working in the informal economy. As these wealth-constrained families have to rely on the income from child labor, their children are unable to attend school and will therefore have little chance of escaping from poverty.
SF4. Despite very low levels of human capital, returns to schooling are limited in poor countries. The relationship between the rate of return to one year of college (Hendricks 2004) and the proportion of college graduates in the labor force (Barro and Lee 2013) is represented in Figure 1(c). 6 Although returns to education decrease with human capital, they do not 5 More precisely, Figure 1(b) depicts logarithms of percentages on both axes. In the World Bank data, child labor is defined as work by children involved in economic activity for at least one hour in the reference week of the survey. 6 We use the most recent year of information of Mincerian returns in each country from Hendricks (2004).

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This article is protected by copyright. All rights reserved. exceed 15 percent per year of schooling in low-income countries. This is much smaller than the level predicted by the labor market models used to explain wage inequality in highincome countries. Indeed, the CES representation is common in labor markets studies (such as Murphy 1992, Card andLemieux 2001) and in cross-country analysis of relative productivity (Caselli and Coleman 2006). Elasticities of substitution between 1.3 and 2 are obtained in most labor market studies including Angrist (1995), Borjas and Katz (2007) and Katz and Murphy (1992). Assuming that college graduates have ten years more education than the less educated and wages are equal to the marginal productivity of labor, the thin lines in Figure 1(c) represent the prediction of CES models with elasticities of substitution equal to one (Cobb-Douglas), 1.3 or 2.0. None of these models match the data. The average share of college graduates is around 3 percent in low-income countries. For such countries, the models predict a return to schooling comprised between 26 percent and 50 percent. The data provided in Hendricks (2004) show a maximum return to schooling of around 15 percent.
We conclude that either the elasticities of substitution estimated for developed countries do not fit the production function of developing countries (an elasticity of 4.25 would be needed to match observations!), or the structure of the labor market differs across countries. 7 We plead for the second hypothesis and see informality as a key factor limiting the skill premium and wage inequality in poor countries. Informality maintains a large skill ratio (i.e., ratio of college graduates to less educated workers) in the formal sector, thus keeping the return to schooling at a low level (Rodrik, 2013).
SF5. The elasticity of recorded GDP per capita to human capital is close to unity and school enrolment is lower in poor countries. Although many studies point out that education has not generated as much growth as expected in developing countries, it is also reported that education is one of the necessary components for growth. As shown in Figure 1(d), the cross-sectional correlation between the proportion of college graduates in the labor force and GDP per capita is large, and the elasticity is close to unity. Despite scarcity in human 7 Another possibility would be to assume that technologies differ between rich and poor countries, as in Caselli and Coleman (2006).

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III. Model
We develop a two-period overlapping generations model in infinite discrete time with children and working-age adults. In every period, a single homogeneous good can be produced in two different sectors, the formal and informal sectors (labeled f and i). Formal firms employ high-and low-skilled workers whereas the informal sector only employs low-skilled workers.
In each period there is an endogenous number of adults of each type who choose how much to consume and how much to invest in the education of their children. All decisions are made in the adult period of life, i.e., children do not get to decide anything. Below, we describe the technology, preferences, the dynamics, and define the competitive equilibrium path of our economy.

Production
A single good is produced in two sectors. Heterogeneity in firm productivity has been documented in the formal sector (Melitz, 2003) as well as in the informal economy. In particular, Fields (1990Fields ( , 2005 or Günther and Launov (2012) identified the existence of an upper-tier and lower-tier (or easy-entry) parts of the informal economy. 8 The latter consists of employment which is free-entry, low wage, and undesirable relative to formal sector employment. The former consists of (wage or self-) employment which is limited-entry, high wage, and preferred to formal sector employment. Still, the upper-tier sector mainly comprises small-scale, low-productivity, frequently family-based enterprises employing lowskilled workers (Maloney, 2004). Focusing on the interdependencies between informality and human capital accumulation, our model assumes that each sector is characterized by a representative firm. It disregards income heterogeneity between workers of a given type, and productivity heterogeneity between firms of a given sector. The formal sector employs highand low-skilled labor and the informal sector only uses low-skilled labor.

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Let h t be the proportion of high-skilled adults at time t, and N t the total labor force of adults. We denote by H t = h t N t and L t = (1 − h t )N t the size of high-and low-skilled labor forces, respectively. Low-skilled workers are assumed to be perfectly mobile across sectors, whereas high-skilled workers have no incentive to join the informal sector. 9 Output Y t is the sum of output Y f,t produced in the formal sector and output Y i,t produced in the informal one. Output produced in each sector is given by: where α is the elasticity of output with respect to high-skilled labor in the formal sector, A t is a time-varying scale factor representing the state of technology, H t is the quantity of high-skilled workers employed in the formal sector, L f,t and L i,t are the quantities of lowskilled workers employed in formal and informal sectors, respectively, and B is a scale factor associated with the technology in the informal sector, which is assumed to be constant.
We assume that total factor productivity (TFP) A t in the formal sector is endogenous. It is a concave function of the skill ratio in the formal sector. 10 For simplicity and in reference to the AK model, the elasticity of TFP with respect to the skill ratio equals 1 − α, i.e., For clarity purposes, we write B = γA 0 , where γ is a parameter that allows us to write B in terms of the scale factor A 0 . 11 Moreover, B also defines the minimum wage that can 9 Our model does not account for brain waste, which may be responsible for employment of educated workers in informality. 10 This assumption implies that the proportion of high-skilled individuals generates a positive externality on aggregate productivity. It is a particular case of Lucas' (1988) model and is also related to other AK models as the ones presented by Romer (1986) and Rebelo (1991). 11 We require γ ∈ [0, α] to be consistent with SF2. Productivity in the informal sector must be low enough (relative to the formal sector) to ensure that wages of low-skilled workers are not higher than wages of high-skilled workers. This condition is satisfied if γ ≤ α (which follows directly from equation (24) below).

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be earned in the informal sector.

Firms choose inputs by maximizing profits
and subject to Y i,t ≥ 0. 12 Under perfect competition, firms in formal and informal sectors choose employment levels by equalizing the marginal productivity of high-and low-skilled workers with their wage rates w h,t and w l,t . In the formal sector, these conditions are The output and employment decisions in the informal sector can be described by the complementary slackness conditions which depict two possible equilibrium regimes: 1. Output in the informal sector is positive and the wage w l,t of low-skilled workers in both sectors is equal to the constant marginal productivity γA 0 of labor in the informal sector. This regime will be referred to as the informality regime henceforth.
2. Firms in the informal sector produce no output and the wage w l,t of low-skilled workers in the formal economy exceeds the marginal productivity of labor in the informal sector.
This regime will be referred to as the formality regime henceforth.
Due to the perfect mobility across sectors, low-skilled wages are identical in the formal and informal sectors in the informality regime. 13 Empirical evidence on the wage differential is mixed. On average formal workers earn more than informal workers. However South Africa). Alternatively, Maloney (2004) argues that the wage differential is explained by the fact that informal workers receive in-kind benefits and part of the payment for young workers also goes to cover implicit training costs.

Preferences
Each adult of type k ∈ {h, l} at period t chooses consumption c k,t and the proportion q k,t ∈ [0, 1] of children sent to college to maximize utility. The utility function is logarithmic and depends on consumption c k,t and the average future wage w k,t+1 of children, where β is the rate of preference for the income of children, and the average future wage of children is which depends on the value of the skill premium σ t+1 = (w h,t+1 − w l,t+1 )/w l,t+1 in the next period.
Educating a child incurs a monetary costẽ. 14 Non-educated children can work in the informal sector as long as the informal sector exists and supply low-skilled labor when adults, whereas educated children go to school, have no time left to work and become high-skilled labor when adults. In the informal sector, children receive a fraction η ∈ [0, 1] of the lowskilled wage rate because they lack experience and physical strength compared to adults.
The budget constraint is where n k is the (exogenous) number of children of a k-type adult, and d t is a dummy variable equal to 1 if some output is produced in the informal sector, and 0 otherwise.
Plugging (10) and (11) into (9) and maximizing utility with respect to q k,t , we obtain Therefore, the optimal level of education is

Dynamics and competitive equilibrium
In the previous section we obtained adults' optimal decision on the proportion of children to be educated. Hence, given the proportion h t of high-skilled workers in period t, fertility rates n h and n l , and the equilibrium condition (13), we can compute the proportion h t+1 of high-skilled workers in the next period. For simplicity, we assume that high-skilled parents educate all their children, i.e., we assume that parameters are such thatq h,t ≥ 1, which implies that q * h,t = 1. 15 By contrast, low-skilled parents only educate an endogenous fraction q l,t ∈ [0, 1) of their children. Therefore, the dynamics of the skill ratio across generations is governed by where n ≡ n h /n l , n ∈ (0, 1) is the fertility ratio of high-to low-skilled workers. And the number N t of adults evolves according to In addition, the labor-market-clearing conditions are the supply and demand of high-skilled workers should be equal in equilibrium. In the next sections, we use H to denote the equilibrium number of high-skilled workers. And demand for low-skilled workers in formal and informal sectors should be equal to supply of low-skilled adults and the efficiency units of children who work. Moreover, we impose the following extra condition: 15 An alternative assumption to ensure thatq h ≥ 1 is to assume that h can not be higher thanh < α and parameters are such that (A 0 α/(ẽn h ) − 1) β ≥ 1 + (1 − α)h/(α −h). de la Croix and Docquier (2012) use the same simplifying assumption.

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Some adult workers are required for the functioning of the informal sector. Indeed, it seems reasonable to assume that children cannot work in the informal sector without a minimum amount of infrastructure provided by adults. We now define the intertemporal equilibrium of our economy: Definition 1 Given an initial population size N 0 and an initial number H 0 of high-skilled workers, an intertemporal equilibrium consists of sequences of prices {w h,t , w l,t }, aggregate and households' decisions {c j,t , q j,t } for j = h, l and for all t such that: 1. the households' decisions c j,t and q j,t maximize utility (9) subject to the constraints (10) and (11); 2. the firms' choices H t , L f,t , and L i,t maximize profits (4) and (5) subject to the constraint 3. the prices w h,t , w l,t , and aggregate quantities H t , L t are such that markets clear, i.e., (16) and (17) hold; 4. aggregate variables N t , H t evolve according to (14) and (15); 5. L t , L i,t , and q l t satisfy (18).

IV. Implications of informality
In this section we characterize the existence of two possible transitory regimes, and then study the implications of informality for human capital accumulation and long-run growth.

The formality and informality regimes
Two regimes arise as a consequence of informality. On the one hand, the formality regime arises if all low-skilled adults opt for the formal sector and the informal sector disappears.
On the other hand, the informality regime arises if the formal and informal sector co-exist. 18

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The formality regime is characterized by the absence of an informal sector. Then, plugging (3) into (6) - (8), wages and the skill premium in the formality regime are Hence, in the formality regime, the skill premium σ t decreases with the proportion of highskilled workers in the economy, and the limit of the skill premium equals infinity when h t tends to zero. A model with a single formal sector predicts huge wage disparities when human capital is low.
Production in the informal sector becomes profitable for low-skilled workers if the wage rate paid in the formal sector does not exceed marginal productivity of labor in the informal sector. Combined with the assumption of perfect mobility of low-skilled workers across sectors, this implies that the number of low-skilled workers in the formal sector is proportional to the number of high-skilled workers in the economy, i.e., Again, plugging (3) into (6) - (8) and taking into account that Y i,t > 0, wages and the skill premium in the informality regime are It clearly appears from (19) and (22) that the wage of high-skilled workers is independent of the economy-wide average level of human capital and of whether informality exists or not.
On the contrary, low-skilled wages are constant in the informality regime (see (23)), whereas they increase with human capital in the formality regime (see (20)).

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The following lemma characterizes the emergence of the informality regime and shows that informality only arises in economies with low levels of human capital: Lemma 1 (The regimes) The informality regime (resp. formality regime) arises when the proportion of high-skilled workers is not too large (resp. large enough), i.e., when h t < Proof. Low-skilled adults work in the informal sector if and only if the wage paid in the formal sector does not exceed marginal productivity of labor in the informal sector.From (20) and (23) we can conclude that the informality regime arises if and only if h t < 1/(1 + γ).
The low-skilled wages in the informality regime are at least as high as in the formality regime if and only if h t /(1 − h t ) < 1/γ, and, by Lemma 1, the informality regime exists if Let us denote GDP per capita and recorded GDP per capita by y t = Y t /N t and y f,t = Y f,t /N t . Consistently with stylized fact SF5, our model predicts that the elasticity of formal output to human capital is equal to unity, as stated in the following proposition: Proposition 1 (Human capital and recorded GDP) In the formality regime, GDP per capita is proportional to the share of high-skilled workers in the labor force, i.e., and recorded GDP is equal to GDP per capita, i.e., y f,t = y t . Meanwhile, in the informality regime, GDP per capita exceeds recorded GDP per capita, y t > y f,t , and recorded GDP per capita is proportional to the share of high-skilled workers, Proof. It follows from equations (1) and (3).
In the informality regime, wages are constant. Hence, q l,t is equal to 20

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Note that in case that next period proportion h t+1 of high-skilled workers is not high enough so as to achieve the threshold proportion 1/(1 + γ) that defines informality, then q l,t is constant and equal to where e =ẽ/A 0 . Moreover, q * l,t ≤ q l when σ t+1 ≤ σ. In line with some empirical papers such as Schneider (2005)  Proof. In the informality regime, we have Note that q l,t is characterized by equation (25). Since (24) and (21) characterize a continuous function σ(h t ) = σ t for h t ∈ [0, 1], thus q l,t defined in equation (25) is continuous. Two cases arise, if h t+1 < 1/(1+γ), then q l,t = q l , and if h t+1 ≥ 1/(1+γ), then q l,t is defined by equation (25). In the former case dq l,t /dh t = 0, whereas in the latter case dq l,t /dh t can be = 0. To compute this derivative let z t be h t /(1−h t ). This monotonic variable transformation enables us to write equations (14) and (25) as

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The vectors (q l,t , z t ) such that H(q l,t , z t ) = 0 characterize the problem. Taking partial derivatives we obtain the Jacobian .
Since DH 1 > 0, by the Implicit Function Theorem there exists a function q l,t (z t ) in a neighborhood of z t and for all h t+1 = 1/(1 + γ). If h t+1 < 1/(1 + γ) then dq l,t /dh t = 0 and dI t /dh t < 0. If

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which implies that the informality level I t always shows a decreasing relationship with respect The existence of the informal sector reduces wage inequality, which can be good for growth because of the negative association between high inequality and long-run growth pointed out by some authors. 16 However, informality allows firms to recruit children from poor households for work. The following result establishes the link between child labor and informality, consistent with stylized fact SF3 : Proof. The proportion of children who work is Hence, taking the derivative with respect to h t we obtain As in the previous Proposition, if h t+1 < 1/(1 + γ) then dq l,t /dh t = 0 and CL ′ (h t ) < 0.

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Effect on long-run growth
We now turn to the analysis of the long-run effects of informality, in particular, we study its effects on human capital accumulation. We distinguish three important channels. First, as informality limits the returns to schooling, it is likely to reduce the incentive to acquire human capital. Second, the existence of an informal economy allows firms to hire children for work. Third, there is an income effect due to informality that may increase the wage of low skilled workers.

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Moreover, the properties of the dynamical system are not modified by this transformation.
The following proposition describes the long-run convergence of human capital in the formality regime: Proposition 3 (Long-run convergence in the formality regime) The dynamical system characterized by (27) and (28)  Proof. The proof is divided into three steps.
Step 1: there exists a function ψ that determines z t+1 given z t and its slope is positive for all z t ≥ 0, i.e., z t+1 = ψ(z t ) and ψ ′ (z t ) > 0.
Let F be a function F : R 2 → R such that F (z t , z t+1 ) = ϕ(z t , z t+1 ) − z t+1 . The vectors (z t , z t+1 ) such that F (z t , z t+1 ) = 0 characterize human capital dynamics. Taking partial derivatives we obtain the Jacobian by the Implicit Function Theorem there exists a function z t+1 (z t ) = ψ(z t ) in a neighborhood of z t (for all z t ) and

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Moreover, ψ is increasing for all z t ≥ 0, i.e., ψ ′ (z t ) > 0, because the numerator is strictly positive if z t ≥ 0, while the denominator is negative.
Step 2: the dynamical system displays two steady state values in z ≥ 0: 0 and z + > 0, and they are the only ones.
The steady state values are the vectors (z t , z t+1 ) such that z t = z t+1 , or the values of z such that F (z, z) = 0. Note that (27) and (28) become and respectively. Plugging (29) into (30) and rearranging terms we obtain F (z, z) = q l (z, z)z + q l (z, z) − (1 − n)z.
Clearly, z = 0 satisfies F (0, 0) = 0 because q l (0, 0) = 0. Since we are interested in the remaining solutions to the problem F (z, z) = 0, we substitute q l , divide by z, and equalize to 0. The solutions to the resulting equation can be rewritten as the roots of the following grade 2 polynomial of z:

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Since a 0 < 0 and a 2 > 0, the roots of the polynomial are z − < 0 and z + > 0. Hence, the steady state values of the dynamical system are z − , 0, and z + .
Rewrite ψ ′ (z t ) as and note that the denominator goes to infinity when z t goes to infinity whereas the numerator goes to 0 or to a constant because q 1 is a constant, From Steps 1 and 2 we know that the system is well defined and displays two different steady state values in z ≥ 0: 0 and z + > 0. A necessary and sufficient condition for the instability of the 0 steady state is ψ ′ (0) > 1, which is equivalent to (1 + αβ)en l < α((1 − α)β + (1 + β)nen l ). Moreover, Step 1 implies that ψ ′ (z t ) > 0 for all z t > 0. Hence, the series z(t) is monotonic, either increasing or decreasing. Finally, Step 3 ensures that z t+1 = ψ(z t ) < z t for all z t > z + , and we can conclude that z + is globally stable.
In the informality regime, i.e., h t < 1/(1 + γ) or z t < 1/γ, we have q * l,t = q l if h t+1 < 1/(1 + γ), which is satisfied if 1 − n ≥ q l (1 + γ). 17 This condition is satisfied if the fertility ratio n is low enough, and both the relative productivity γ of the informal sector and the education costẽ are sufficiently high. In this case the dynamics of the skill ratio z t are 17 Follows from equation (14).

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Proposition 4 (Long-run effects of informality) There exists a threshold n for the fertility ratio such that, if n is greater than n, the economy converges towards the unique steady state of the formal regime, h stst s . Otherwise, if n ≤ n, there exists a poverty trap in the informality regime. The threshold n is defined as Proof. Human capital dynamics are determined by (31). Thus, a stable poverty trap with informality emerges if and only if φ(1/γ) ≤ 1/γ, and n/(1 − q l ) < 1. The former condition is equivalent to 1−n ≥ q l (1+γ). In addition, this condition ensures that 1 > q l +n. Hence, the former condition is sufficient for the latter condition to be satisfied. Substituting overlineq l by (26) determines n as a function of the other parameters of the model (γ, α, β, e, η, n l ).
When n ≤ n, there exists a steady state level of human capital such that h ss < 1/(1 + γ).
Hence, the key condition on parameters governing the dynamic properties of the model is: As q l is given by (26), this condition virtually involves all the parameters of the model.
If it holds, informality is the source of a poverty trap. Otherwise, informality is a transitory phenomenon. This condition is satisfied if the fertility ratio n is low enough, and both the relative productivity γ of the informal sector and the education costẽ are sufficiently high.
Moreover, it ensures that h t+1 < 1/(1 + γ) in the informality regime from equation (14). We will check in the numerical part whether calibration parameters satisfy this condition or not.

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The previous two propositions characterize the equilibrium path of the skill ratio. Figure   2(a) shows the dynamics with and without informality. The solid line corresponds to an economy with informality if the skill ratio is lower than z 0 = 1/γ, while the dashed line corresponds to one without informality. For high enough levels of human capital there is no informal sector and both lines coincide. As predicted by Proposition 3, without the informal sector the skill ratio converges to the point A 1 as long as the initial skill ratio is larger than 0. However, if the informal sector is at work, Proposition 4 states that there can be poverty traps as the one presented in Figure 2  In all cases there is a jump from the formality to the informality regime due to child labor in the informal sector. Dynamic B is a possible situation without poverty traps. It might arise if condition 1 does not hold. This occurs, for example, if the education costẽ is low enough.
Dynamic A is a case with a poverty trap in the informality regime, and convergence to a high proportion of high-skilled workers in the formality regime. Whereas Dynamic C corresponds to a case where parameters are such that there is no stable steady state without informality.
Because of the existence of the informal sector the poverty trap makes the economy converge to point C, which is characterized by a low proportion of high-skilled workers in the economy.

V. Quantitative assessment
We have shown that informality may slow down income convergence across countries or be the source of a poverty trap depending on the fact that the model exhibit multiple equilibria or uniqueness. In this section, we confront the theory with the data, calibrate the model, and discriminate between these two hypotheses.

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Parametrization
The model is calibrated under the assumption that one period (or generation) represents 30 years, and that individuals are considered high-skilled if they have at least 10 years of education. Our parametrization strategy is based on the following principles: • Parameters are calibrated so as to be compatible with observations for industrialized countries (i.e. the United States or an average of G7 countries) and a representative least developed economy.
• In the benchmark, the situation of the United States is considered as a possible steady state without subsistence informality. Because education statistics vary between the United States and European countries, we also simulate variants in which the average situation of G7 countries (Australia, Canada, France, Germany, Japan, United Kingdom, United States) is a steady state. Least developed countries might be out of steady state and are characterized by the informality regime.
• We require our calibrated model to be compatible with the stylized facts described in the introduction. The underlying assumptions of our model are such that these stylized facts are matched.
• Developing countries and the United States share the same exogenous characteristics: A 0 , e, η, α, γ, β, n h and n l .
• Several scenarios are used to check whether our conclusions are robust to the identifying assumptions.
As for the skill premium in industrialized countries (σ Rich ), we use recent data from Hendricks (2004). The return to schooling observed in the United States is equal to 7.83 percent per year of schooling, implying a skill premium of 112 percent for ten years of education (σ U S t = 1.12). This value will be used in the benchmark scenario. Other values will be used 31

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in robustness scenarios 1 to 5. The average return to schooling in the G7 countries amounts to 6.00 percent per year of schooling, implying σ G7 t = 0.80. In addition, Hendricks (2004) reports a return to schooling between 12 and 15 percent in the least developed countries, or equivalently a level of σ P oor t between 2.5 and 3.0.
As for human capital in industrialized countries (h rich ), we use Barro  As for parameters affecting households' decisions, the fertility ratio n of high-to lowskilled workers is set to 0.57 from Kremer and Chen (1995). They show that n does not vary that much with the level of development, it is stable across countries and over time.
In the benchmark, as we can observe in the United States and other developed economies, we assume no population growth, which implies n h = 0.65 and n l = 1.15. We assume these parameters are constant across countries. This generates a negative relationship between the average fertility rate and development because the proportion of low-fertility, high-skilled households increases with development. Although this underestimates the average fertility rate in the least developed countries, endogenizing fertility would make the occurrence of a poverty trap more likely.
Other parameters are identified to match the above identifying assumptions. Plugging h rich ss and σ Rich into (21), we obtain α = 0.49 in the benchmark. From (24), this requires γ to be equal to 4.24, which implies that γ is 0.12 and the threshold proportion of college graduates below which the informality regime is observed is 19 percent (h thres ). Assuming that the United States economy is in the steady state, we obtain β = 0.19 from (13) and 32

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This article is protected by copyright. All rights reserved. (14). Haveman and Wolfe (1995) and Knowles (1999) suggest that the education cost is around 15 percent of time endowment of parents while children live with their parents. This implies that, if children live with their parents for 15 years, e = 0.04 in the benchmark. 18 The relative productivity η of children compared to low-skilled adults matches the empirical evidence presented by Horrell and Humphries (1995). In the benchmark scenario, we use η = 0.34 to have 25 percent of low-skilled families' income coming from child labor in the least developed countries. 19 Table 1 shows the identifying assumptions and provides the fitted values for identified parameters in the benchmark scenario and in 5 variants. Column 1 gives the benchmark values. In Scenario 1, h rich is given by the proportion of individuals with some tertiary education (not necessarily completed). In Scenario 2, the proportion of tertiary and the skill premium in rich countries are calibrated using data for G7 countries. In Scenario 3, we use a lower level for the skill premium in the least developed countries. Scenario 4 combines scenarios 2 and 3. Results for alternative scenarios 1 to 4 are provided in the Appendix.
The case for multiplicity By contrast, countries with an initial proportion of educated above 19 percent converge to 18 For example, de la Croix and Doepke (2003) assume that children live 15 out of 30 years with parents. 19 We obtain a relative productivity of children compared to parents higher than Doepke and Zilibotti (2005) who obtain 0.1 to match the same empirical fact. However, Goldin and Sokoloff (1984) claim that that the relative productivity of children and females compared to males rose from around 0.3 in the North (.58 in the South) to .5 from 1820 to 1850, which is in line with our value.

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This article is protected by copyright. All rights reserved. the high steady state. It can be noticed that some high-income countries are below that threshold. However, the threshold level of human capital must be taken with caution. We will show below that the threshold is divided by 2 when the average of the G7 countries is used as a reference for the good steady state. This also represents about 60 percent of the G7 level. The reason is that the proportion of college graduates is greater in the United States than in the other G7 countries (due to the inclusion of workers with one or two year(s) of college). What is important is that a poverty trap emerges in virtually all calibration scenarios.
As can be seen in Figure 3

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sector reduces the return to education and increases the opportunity cost of sending children to school (since they can only work in the informal sector). Therefore the proportion q l is lower in the informality regime than in the formality regime for proportions h t of high-skilled workers between 4% and 19%. Because agents do not internalize the externality of education on TFP and the low number of highly educated children, the proportion of high-skilled workers remains low and stable over time. For lower levels of human capital (h t < 0.04), the income effect leads to higher education investments in the informality regime.
In the Appendix, we simulate the human capital dynamics under the four alternative sets of identifying assumptions (see figures 8 to 11). In all cases, a poverty trap emerges, except in scenario 2 which shows a "bifurcation" or borderline configuration. In all cases, the threshold level of human capital defining the poverty trap always corresponds to about 60 percent of the steady state proportion of educated in rich countries (the US or the G7 countries). The long-run level of human capital in the poverty trap is particulary low in scenarios 3 and 4. This situation is due to the fact that q l becomes very low in these two scenarios.

Banning child labor
The existence of a poverty trap or low steady state due to informality is partly driven by the fact that children can work in the informal sector. Child labor is responsible for the discontinuity in the dynamics of human capital depicted on Figure 3 Before studying such subsidies in the section, we consider an economy starting from the informality-regime steady state (with child labor) at time 0, and simulate the effect of a sudden elimination of child labor. We look at the transition from the low steady state to the high steady state. The transition occurs because, in the absence of child labor, 36 Accepted Article This article is protected by copyright. All rights reserved. the discontinuity disappears on Figure 3(a) and the formality-regime steady state becomes unique. Figure 4(a) shows the dynamics of human capital using the benchmark parameters except for the relative productivity η of children that we set to 0 to ban child labor. The transition would last around 200 years (or 7 periods) to reach the new steady state. At the same time, we can also observe that the first period after we abolish child labor the proportion of high-skilled individuals is higher than the threshold value that defines the informality regime. Hence, the economy reaches the formality regime if child labor is banned in one period.
The question that follows is how welfare will be affected over time if children cannot work. In Figure 4(b), we compute the welfare loss as percentage of the initial steady state level with child labor and informality. We first compute the new utility level after child labor is banned, and then derive the hypothetical amount of consumption compatible with that level of utility if the average future wage of children was constant at w inf k,ss (this level is denoted by c k,t = exp U k,t − β ln w inf k,ss for a type-k worker). Finally, we compute the percentage deviation of consumption with respect to the initial steady state with informality, ( c k,t − c inf k,ss )/c inf k,ss , and use this as a consumption-equivalent variation in utility. The utility level of high-skilled workers is not modified as their wage is constant along the transition path. For the low-skilled workers, however, consumption falls by about 40% in the first period that child labor vanishes. 20 As time passes, the wage and the utility level of low-skilled workers increase to overcome the consumption level observed in the steady state with informality. Another pattern that we can depict from Figure 4(b) is with regard to the average consumption deviation. In the initial periods, it is relatively closer to the consumption deviation of low-skilled workers than the consumption deviation of high-skilled workers, but it approaches the consumption deviation of the highly skilled over time. Hence, as the economy evolves, the proportion of high-skilled workers increases, and the weight of 20 In a previous version of this paper, we also simulate the effects of a sudden elimination of informality. As in Meghir et al. (2015), this basically implies preventing workers and firms from using an existing technology. For the low-skilled, the welfare loss of such a coercive policy amounts to 80%.

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the low-skilled workers on the average deviation diminishes.
Clearly, part of the first period welfare loss is due to the absent income from children.
Moreover, if children do not work, parents face higher incentives to invest in their children's education. Hence, more income is used to pay for their children's education and consume less. As the economy evolves, the higher proportion of high-skilled adults in the formal sector increases wages of low-skilled workers because the economy leaves the informality regime. Two different effects produce the growth of wages and consumption over time, the complementarity between high-and low-skilled workers, on the one hand, and the increase in TFP, on the other hand. In sum, child labor and informality protect poor and less educated adults from a sharp wage cut in the short run but prevent the accumulation of human capital necessary to observe economic growth in the long run.

Implications for development policy
In the previous sections we established the result that the existence of an informal sector combined with human capital externalities can generate a poverty trap. We also showed that without informal activities such as child labor, low-skilled workers would suffer initially a quite dramatic drop in wages. In this section, we analyze alternative (Pigouvian) policies that could help the economy to escape the poverty trap and converge towards the high-income steady state, without banning child labor or informality. We examine the cost efficiency of such policies under the constraint that wage losses during the transition should be avoided.
We consider the situation of a developing country trapped in the low-income steady state and assume that it will obtain a windfall gain (which might come from different sources, e.g. foreign aid or the discovery of natural resources). 21 How can the country use such a windfall gain in the most efficient way in order to escape the poverty trap? To answer this question, we analyze different policy instruments that address the human capital externality and the child labor trap, and compare their discounted costs. We first consider each instrument in 21 In the case of a resource-rich country, it would have to be assumed that the natural resource sector operates independently from the rest of the economy, excluding thereby Dutch disease effects.

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isolation and then examine whether a combination of two instruments may be a cheaper alternative.
Alternative Pigouvian policies. On one hand, we consider the introduction of education subsidies that are either paid unconditionally to all families or targeted to low-skill parents.
The latter policy can be interpreted as the education component of existing conditional cash transfers. 22 On the other hand, we analyze wage subsidies for jobs in the formal sector, allowing for different subsidy rates for low-skill and high-skill jobs. 23 To sum up, we introduce the following policy variables in the model: • an education subsidy at rate s e t (paid to all families or targeted to low-skilled parents); • a wage subsidy for low-skilled workers in the formal sector at rate s l t ; • a wage subsidy for high-skilled workers in the formal sector at rate s h t .
From the assumptions of the model it is immediately clear that it would be inefficient to pay education subsidies to high-skilled parents since they educate all their children even without receiving any subsidies. Hence, the general education subsidy is less cost-efficient than the targeted education subsidy. As we will show below, the wage subsidy for highskilled workers has similar effects as an education subsidy to all parents. This type of wage subsidy is therefore also dominated by the targeted education subsidy.
Policy effects in the informality regime. In the informality regime, the introduction of subsidies does not change the income of low-skilled workers. Subsidizing low-skilled workers draws them into the formal sector but as long as the informal sector exists, the low-skill 22 E.g., the Oportunidades/Progresa program in Mexico or the Bolsa Familia scheme in Brazil. These programs are targeted towards low-income families and provide grants for children conditional on school attendance. 23 Equivalently the government could implement a combination of an output subsidy in the formal sector and a (progressive) tax on income from the formal sector. An output subsidy has the same effect as subsidizing high-skilled and low-skilled workers in the formal sector at the same rate. Adding a progressive income tax would be equivalent to differentiating the effective subsidy rates received by high and low-skilled workers.

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wage is determined by the (exogenous) productivity in the informal sector. By contrast, the income of high-skilled workers is increased one-by-one by the subsidy. Hence, wages (including subsidies) and the skill premium in the informality regime are The number of low-skilled workers in the formal sector is given by L f,t = (1 + s l t )γH t . The informal sector disappears if marginal productivity of low-skilled workers in the formal sector exceeds the minimum wage in the informal economy, i.e., if L f,t /H t ≤ (1 + s l t )γ. This condition is equivalent to .
The role of the two types of wage subsidies in the formal sector can now be made clear.
Subsidizing high-wage jobs increases the skill premium but has no effect on the allocation of workers between sectors. By contrast, a subsidy for low-wage jobs in the formal sector does not affect the skill premium but lowers the critical human capital level at which the economy leaves the informality regime.
In turn, the budget constraint of adults is modified by the introduction of an education subsidy as follows: The proportion of children who go to school is therefore equal to

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Subsidizing high-skilled workers in the next generation (t + 1) has similar qualitative effects as subsidizing education for the current generation t. Obviously, an expected rise in the future skill premium increases the incentive to send children to school. There is, however, a decisive difference between the two types of subsidies: an education subsidy can be targeted towards low-skilled parents and is therefore more cost-effective (since high-skilled parents educate all their children even without subsidies). Moreover, subsidizing the wages of relatively rich workers rather than the education of poor children seems politically less feasible.
The preceding results enable us to highlight the different (and possibly complementary) roles of the two most promising policies: targeted education subsidies and wage subsidies for low-skilled workers in the formal sector (see Figure 5). If the economy is initially stuck in the inferior steady-state (B 2 ), the introduction of targeted education subsidies increases the incentive of low-skilled parents to invest in their children's education and the informal sector schedule shifts upwards in Figure 5. If the subsidy rate is sufficiently high, the country can escape the poverty trap with the help of this single policy instrument; the new situation of the economy could then be described by Dynamic A in Figure 2(b).
By contrast, the subsidy for low-skilled workers in the formal sector pulls workers out of the informal sector and decreases the critical skill ratio from z 0 to z 1 in Figure 5 without changing the informality schedule. It is clear that such a low-wage subsidy has no effect on human capital accumulation if it is too small or if the economy is too far below the critical skill ratio; the subsidy rate must be sufficiently high to eliminate informal sector employment entirely. Wage subsidies should therefore only be used as a temporary policy allowing the transition to the formality regime to accelerate.
As the two types of subsidies address different aspects of the transition to the high income equilibrium, they can be implemented jointly and their combined use might possibly reduce the overall cost of escaping the poverty trap. This issue will be taken up below in the simulations. In any case, we assume that subsidies are abolished as soon as the economy 42 Accepted Article This article is protected by copyright. All rights reserved. Cost-efficient policies. The calibrated model can now be used to calculate, for each policy, the minimum windfall gain necessary to enable the country to escape the poverty trap. This windfall gain (or discounted cost of policy) depends on the time horizon within which the economy leaves the informality regime. Consider a constant subsidy of each type, s k t ≡ s k for k ∈ {e, l, h}. The horizontal axis of Figure 6 indicates the time needed to achieve a level of human capital that ensures convergence to the high steady state, or equivalently, the number of periods T needed to achieve a proportion of high-skilled workers higher than 24 To avoid clutter, Figure 5 does not depict the policy-induced change in the dynamics of the formality regime. The two policies have different effects on the formality schedule. Whereas education subsidies shift the formality schedule unambiguously upwards, the introduction of low-skill wage subsidies has ambiguous effects: a positive income effect (low-skill parents receive a higher income which is partly spent on education of their children) and a negative substitution effect (low-wage subsidies decrease the future wage differential, diminishing the incentive for education). These changes do not seem to have a decisive influence on the transition from the informality to the formality regime.

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This article is protected by copyright. All rights reserved. the threshold value h T > 1/(1 + γ) delimiting the two regimes. For each value of T , we compute the subsidy rate required to exit the poverty trap and the discounted cost of the policy using a discount factor equal to .99 120 ∼ = 0.2994. The vertical axis of Figure 6 shows the total discounted cost of policies for a country with an initial population of 20 million inhabitants and a scale factor A 0 of 112900. 25 As expected, targeted education subsidies are more cost-efficient than unconditional education subsidies or high-skill wage subsidies at any time horizon. A windfall of 1.5 to 2 billion 2005 US$ (PPP adjusted) per year is needed to help a country of around 20 million inhabitants escape from the poverty trap within one or two generations (30 or 60 years). As the initial skill ratio of this economy is far below the critical level, low-skill wage subsidies are not efficient if they are used as a single policy instrument.
Moreover, as Figure 6 makes clear, policies that take more time to leave the informality regime have lower discounted costs. Consider for example education subsidies targeted to low-skilled parents. The total discounted cost of attaining the critical human capital ratio is lower if the policy is implemented over several generations using a low subsidy rate (by opposition to a high-subsidy policy which operates within one generation). The reason for this result is twofold. First, within a generation the marginal cost of subsidizing education increases with the proportion of children that are educated. Second, targeted education subsidies have a cumulative impact over time: in each generation, they provide an incentive for low-skilled adults to educate a larger proportion of their children. In the following generation, these high-skilled children will provide education to all their offspring although they do not receive the (targeted) education subsidy.
Combination of policies. The preceding results leave scope for a cost-reducing combination of policies. As the marginal cost of a single policy increases with its rate, it might be more cost-efficient to combine two instruments using lower rates. We explore this possibility 25 Parameter A 0 is set to 112900 to obtain that GDP per capita in the United States is 35000 in 2005 US$ PPP adjusted, which is close to the value in PWT 7.0. The discount factor is obtained from the literature taking into account that a period lasts 30 years and the discount factor of a quarter of year is .99.

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This article is protected by copyright. All rights reserved. by combining targeted education subsidies and low-skill wage subsidies. As we have argued above, the latter should only be used as a transitory measure. Hence, in the simulations reported in Figure 7, while education subsidies are used in all periods, low-skill wage subsidies are only used in one period, i.e., when they enable the economy to reach the formality regime within the next generation. 26 Therefore, education subsidies are implemented in all generations, whereas low-skill wage subsidies are only implemented during one generation.
Moreover, the subsidy rate of low-skill wages is set such as to make the informal sector disappear within this generation. Figure 7 shows that using both instruments is cheaper than using a single instrument for time horizons that exceed four generations (150 years). Note that for slightly richer countries (that are closer to the critical skill ratio), a combination of the two policy instruments is likely to be more cost-efficient even for shorter time horizons.
Our policy findings can be summarized as follows. First, among four possible education and wage subsidy schemes, two policies dominate the others in terms of cost efficiency: education subsidies to low-income families and wage subsidies for low-skill jobs in the formal sector. Second, these two policies play distinct and possibly complementary roles in the transition to the high-income equilibrium. Whereas the education subsidy speeds up the accumulation of human capital, the low-skill wage subsidy reduces the threshold at which the informal sector disappears. Third, targeted education subsidies are the cheapest single policy but for longer time horizons a combination of the two policies turns out to be the most cost-efficient choice.

VI. Conclusion
This paper establishes a theoretical relation between education, child labor and the informal sector. In the data we observe a direct relation between informality and education, countries with high proportions of tertiary educated workers tend to show lower levels of informality than countries with low proportions. Moreover, child labor is part of the informal sector, and the data shows that countries with more informality have more children involved in production activities. With these facts in mind we construct an overlapping generations model that is able to reproduce these relations in line with previous findings of other authors.
The model is able to explain, or to give a complementary view of, the documented fact that less-developed countries present higher levels of inequality than developed countries but much lower levels than standard models predict. The introduction of the informal sector in a model with complementarity between high-and low-skilled workers lowers the skill premium (and makes it constant). In other words, we view informality as a possible channel to reduce the skill premium in developing countries.
The reduction in inequality due to informality generates several effects in the short and the long run. On one hand, low-skilled workers may obtain a higher salary with the existence of an informal sector than in its absence, because there is an alternative sector where they can supply their working hours. However, this sector is not controlled by state agencies and enables children to use their time to work and generate an extra source of income for the household. Hence, the model is able to replicate the relations between informality and education, and between child labor and education in line with the data: the share of high-skilled workers is negatively correlated with informality, and informality is positively correlated with child labor. On the other hand, the model has several predictions for the long run. The trade-off between child income and future education of children is taken into account and is key to generate poverty traps due to informality and child labor. The "low" inequality observed in developing countries and the opportunity cost of sending children to school can have a pernicious effect on parents. They may not provide enough education for their children so as to increase the aggregate proportion of educated workers in the labor force. Parents do not internalize the positive externality of aggregate education on firms' productivity. Therefore, the informal sector can prevent the economy from developing as it would in the absence of informality.

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The model is calibrated to reproduce several facts observed in the data. The model is also calibrated to evaluate different policies considered to reduce the size and effects of informality. The calibration exercise reveals that the case for the poverty-trap hypothesis is strong: although informality serves to protect low-skilled workers from extreme poverty in the short-run, it prevents income convergence between developed and developing nations.
Sudden elimination of child labor or informal activities would induce severe welfare losses for poor people on the transition path.
Hence, we analyze noncoercive policies that could help the economy to escape the poverty trap and converge towards the high-income steady state. We analyze the cost efficiency of Pigouvian policies under the constraint that wage losses during the transition should be avoided. Assuming that an inflow of resources is provided to a developing country, for example in the form of foreign aid, we analyze the effects of different subsidies. Informality can be reduced by diminishing education costs or by making the formal sector more attractive.
Hence we consider four possible subsidies on education and formal firms wages. Subsidizing education is the most cost-efficient policy, and it can be targeted towards low-skilled parents to reduce costs. Subsidizing high-wage jobs increases the skill premium but has no effect on the allocation of workers between sectors. Moreover, the increase in the skill premium gives similar incentives to parents on children's education than reducing education costs. By contrast, a subsidy for low-wage jobs in the formal sector does not affect the skill premium but lowers the critical human capital level necessary to skip the poverty trap. Because of the possible complementary effect of different subsidies, we turn to analyze the cost-efficiency of a combination of subsidies on education to low-income parents and low-skilled formal firms wages. Although targeted education subsidies are the cheapest single policy, for longer time horizons, or as the economy gets closer to the poverty trap threshold, a combination of the two policies is found to be the most cost-efficient choice.

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