<figure><img src="image_7.png" /><figcaption>Figure 5: Out-of-Sample Model Validation</figcaption></figure>

<footnote>NOTE: The Figure shows OLS estimates with robust standard errors of the $\theta$ coefficients displayed in equation (37), which capture the effect of receiving the *Seguro Popular* program in 2006 on labor market outcomes both in the data sample and in the simulated sample. The ‘Data’ sample is drawn from the Mexican labor market survey (ENOE 2006) and matched at the municipality-level with the roll-out of the *Seguro Popular* program in the year 2006. The ‘Model’ sample is based on simulated data generated by the estimated model parameters reported in Table 3. The full set of two-sided and one-sided T-tests for the estimated $\beta$ coefficients in the simulated data and in the survey data are reported in Table C.7 in the Appendix.</footnote>
<figure><img src="image_8.png" /><figcaption>Figure 6: Policy Experiments, Changes in Contribution Rate (t)</figcaption></figure>

NOTE: The figures report outcomes from policy experiments that change the social security contribution rate *t* from 0 to 0.66 (a 0.33 change below and above the contribution rate at baseline, represented by the vertical line). *Informality* is the proportion of Informal Employee and Self-employed in the population. *Inequality* is the ratio between the top 90% and the bottom 10% in the wages and self-employment income distribution. *Welfare* is the overall flow welfare in steady state (see Section 6). *Production* is the overall production (*x* and *y*) in steady state. *Schooling* is the proportion of High Schooling in the population. *Selection in Schooling* is the same proportion by ability type.
<figure><img src="image_9.png" /><figcaption>Figure 7: Policy Experiments, Redistribution and Benefits' Valuation</figcaption></figure>

NOTE: The figures report outcomes from the same policy experiments reported in Figure 6 with the addition of three changes in the environment: *Full Redistribution* sets $\tau$ to zero; *Full Valuation* sets $\beta_{1,h}$ to one; *Full Valuation&Redistribution* combines the two experiments. *Informality* is the proportion of Informal Employee and Self-employed in the population. *Inequality* is the ratio between the top 90% and the bottom 10% in the labor income distribution. *Welfare* is the overall flow welfare in steady state (see Section 6). *Schooling* is the proportion of individuals with High Schooling in the population. *Selection in Schooling* is the same proportion by ability type.
# Appendix – Not for Publication

## Table of Contents

A Data and Institutions I

A.1 Data Appendix I

A.2 Institutional Parameters II

B Model II

B.1 Lemmas II

B.2 Proof of Proposition 2 III

B.3 Equilibrium Definition V

B.4 Per-Capita Social Security Benefits: $b_1$ X

C Estimates and Model Fit XI

D Experiments XVII
# A Data and Institutions

## A.1 Data Appendix

This Section provides a more detailed description on how we build the balanced panel of workers we use to extract transitions probabilities and hazard rates. Information contained in the ENOE survey on the consecutive number of the interview (from 1 to 5) allow us to link at the individual level the quarterly waves under the sample selection criteria outlined in Section 2.2. This dataset generates yearly transition probabilities across the four labor market states of formal and informal employment, self-employment and unemployment for individuals entering the survey in each quarter of the year 2005. For instance, an individual who enters in the first quarter of 2005 is observed for five quarters up to the first quarter of 2006, while an individual who first enters in the last quarter of 2005 is observed until the last quarter of 2006.

Since the transition probabilities are potentially affected by attrition in the ENOE survey, we focus on a balanced panel of workers with five consecutive quarterly survey rounds. The relevant time horizon for each observation is a quarter, and hence we cannot detect changes in intertwining spells of employment or job search that are shorter than three months. For instance, the observed transition rates between formal and informal employment may possibly “hide” a short period of unemployment in between. This feature of the data applies to both the ENOE sample and the simulated samples generated by the model from which we construct the moments used in estimation.

We observe a small but significant amount of yearly transitions out of self-employment (see Table 2) but at the same time very long on-going durations in self-employment (not reported in Table 2, median=80 months). We also observe very short on-going durations in unemployment (not reported in Table 2, median=1 month), which are difficult to reconcile with the corresponding transition rates out of unemployment. We claim that the transitions information is more reliable because it is obtained by the labor market state reported in the ENOE survey at the moment of the interview. Retrospective information on the termination date of the last employment spell may be instead prone to recall bias. Indeed, duration spells are on average much longer than those implied by changes in the searching state across contiguous quarters, with severe mismatches for more than half of the individuals in the panel sample.

We thus exclusively use information about changes in labor market states across quarters when constructing the hazard rates out of unemployment. Notably, we focus on the sub-set of workers who become unemployed during the five quarters of observation of the panel (6% of the sample) and generate hazard rates at three and six months by schooling group. Notice that we don't use hazard rates out of the other searching state (self-employment) since the presence of heterogeneous self-employment income ($y$) may generate differences between these exit rates at different time horizons that are unrelated to duration dependence.
## A.2 Institutional Parameters

The parameters {$B_0, \tau, t$} are set to the values determined by the institutional setting of the Mexican labor market. In particular:

$\tau = 0.55$ In order to derive the share of the bundle of additional benefits for Formal employees ($\tau$), we follow calculations reported in Levy (2008), which are based on the current legislation in Mexico. Accordingly, for a worker who earns twice the minimum wage in 2007 (2,931 Pesos), social security contributions amount to 864.30 Pesos (almost 30% of the wage), of which 55% are attributable to spending categories that are proportional to the wage - notably, work-risk insurance (76.2 Pesos), disability and life insurance (69.6 Pesos), retirement pensions (184 Pesos) and housing fund (146.6 Pesos).

$t = 0.33$ We rely on calculations reported in Anton et al. (2012), which are based on official statistics reported by the Mexican Social Security Institute (IMSS). The authors decompose the average tax rate on formal labor (38%) into government subsidies (5%) and firms and workers contributions (33%).

$B_{0,1} = 2.42$ and $B_{0,0} = 1.92$ Total spending in non-contributory social security programs for the year 2005 amounted to 133,090,002,747 Pesos, of which 11,916,448,117 Pesos were devoted to the *Seguro Popular* program. For the same year, we compute the total number of informal workers (25,035,508) and unemployed (1,353,561) by applying sampling weights to the nationally-representative labor market survey used in our empirical analysis (ENOE). Assuming full time working hours over a period of one year (2,080 hours), we can compute the per-capita hourly monetary benefits extended to the part of the labor force that is non-Formally employed, separately for those who reside in municipalities with ($B_{0,1}$) and without ($B_{0,0}$) the *Seguro Popular* program.

# B Model

## B.1 Lemmas

**Lemma 4** *The sign of the dependence of $S(y, h)$ on $y$ is ambiguous.*

**Proof.** Consider two values of $y$ such that $y' < y''$. We want to sign the difference:

$$S(y'', h) - S(y', h) \qquad (B.1)$$
By using equation (18), we can show that:

$$[S(y'', h) - S(y', h)] \propto (y'' - y') \tag{B.2} \\ + \gamma_h \left\{ \begin{array}{l} \int_{\neg A(y'', h)} \max\{E_0[w_0(x), y'', h], S(y'', h)\} dG(x|h) \\ + \int_{A(y'', h)} \max\{E_1[w_1(x), y'', h], S(y'', h)\} dG(x|h) \end{array} \right\} \\ - \gamma_h \left\{ \begin{array}{l} \int_{\neg A(y', h)} \max\{E_0[w_0(x), y', h], S(y', h)\} dG(x|h) \\ + \int_{A(y', h)} \max\{E_1[w_1(x), y', h], S(y', h)\} dG(x|h) \end{array} \right\}$$

While the first term $(y'' - y')$ is positive, the difference between the terms in curly brackets is ambiguous. The ambiguity arises from the dependency of the set $A$ on $y$. As shown in equation (13), the set defines the support of the match productivity $x$ over which firms offer formal contracts. Since firms choose this optimally, they may pick ranges that decrease the portion of the surplus going to the worker. In so doing, they may offset some of the advantage that a worker with higher $y$ may have in bargaining, an advantage arising by his higher flow value while searching.

Figure B.1 clarifies the discussion. The figure (a generalization of Figure 2) represents the value functions of a vacancy filled with an informal or a formal job, as defined in equations (10) and (11). These value functions determine the optimal decision rules that affect the continuation value of the worker's searching state. Consider for example the worker with $y = y'$. For $x \in [0, x_0^*(y', h))$, he will continue searching; for $x \in [x_0^*(y', h), \tilde{x}(y', h))$, he will accept to work informally; and for $x \in [\tilde{x}(y', h), \infty)$, he will accept to work formally. The range that creates the ambiguity in the sign is $x \in [\tilde{x}(y', h), \tilde{x}(y'', h))$. Over this range, the $y'$-worker works formally while the $y''$-worker works informally. Since it is the firm that chooses the formality status, we do not know which one of the two types of worker is better off over this range. In other words, for a given $x$ in this range we do not know the sign of:

$$E_0[w_0(x), y'', h] - E_1[w_1(x), y', h] \tag{B.3}$$

This ambiguity does not allow to univocally sign the difference in continuation values between the two types of workers, i.e. the terms in curly brackets in equation (B.2) presented above. As a result, it does not allow to univocally sign expression (B.1). ■

## B.2 Proof of Proposition 2

### Proof.

The result is proved by first observing that, given the wage schedules (24) and (23), the value
<figure><img src="image_10.png" /><figcaption>Figure B.1: Optimal Decision Rules</figcaption></figure>

NOTE: The Figure shows the equilibrium when $\tilde{x}(y, h) > x_1^*(y, h)$ for given $\{y, h\}$. We assume $y'' > y'$. For the definitions of $F_0$, $F_1$, $x_0^*$, $x_1^*$, and $\tilde{x}$, see equations (10), (11), (26), (27), and (25).
functions for a filled informal and formal job are linearly increasing in $x$:

$$F_0[x, y, h] = \frac{(1 - \alpha_h)[x - (1 + \chi_h c_h)[\rho Q(y, h) - \beta_{0,h} B_0]]}{\rho + \eta_h + \chi_h} \quad (B.4)$$

$$F_1[x, y, h] = \frac{(1 - \alpha_h)[x - \phi_h[\rho Q(y, h) - \beta_{1,h} b_1]]}{\rho + \eta_h} \quad (B.5)$$

Since, by equation (22), the cost of posting a vacancy is constant in $x$, $F_0[x, y, h]$ and $F_1[x, y, h]$ will cross that horizontal line and they will cross it only once. This guarantees existence and uniqueness of $x_0^*(y, h)$ and $x_1^*(y, h)$.

Second, the slope of the value function for a filled formal vacancy is steeper than the one for the informal value function since:

$$\frac{\partial F_1[x, y, h]}{\partial x} = \frac{1 - \alpha_h}{\rho + \eta_h} \geq \frac{1 - \alpha_h}{\rho + \eta_h + \chi_h} = \frac{\partial F_0[x, y, h]}{\partial x} > 0$$

As a result $F_0[x, y, h]$ will cross $F_1[x, y, h]$ and will cross it only once, guaranteeing existence and uniqueness of $\tilde{x}(y, h)$.

Finally, the conditions above generate a range of rankings between the three reservations values that depends on parameters. Based on those rankings, one of the four equilibrium cases listed in Proposition 2 is realized. No other equilibrium cases are possible. In addition, given a set of parameters and a choice of $\{y, h\}$, only one of the equilibrium cases is realized.

## B.3 Equilibrium Definition

To provide a formal definition of the equilibrium, we start by reporting the expressions for the equilibrium value functions at given meeting rates. We report only the expressions for Case 2 of Proposition 2. The other cases are straightforward specializations of these expressions. We report all the expressions conditioning on $h$ even if the case $h = 0$ requires a further specialization. We discuss it at the end of the section.

The equilibrium value functions of the filled job states are obtained by inserting the wage schedules (23)–(24) in the value functions expressions (10)–(11) under free-entry:

$$F_0[x, y, h] = \frac{(1 - \alpha_h)[x - x_0^*(y, h)]}{(\rho + \eta_h + \chi_h)} \quad (B.6)$$

$$F_1[x, y, h] = \frac{(1 - \alpha_h)[x - x_1^*(y, h)]}{(\rho + \eta_h)} \quad (B.7)$$

Equating these two expressions and solving for $x$ lead to the reservation value $\tilde{x}(y, h)$ defined in (25). Notice that in these and all the following expressions we use the reservation values $x_0^*(y, h)$ and $x_1^*(y, h)$ defined in equations (26) and (27).

The equilibrium value functions of the employee states are obtained by inserting the wage
schedules (23)–(24) in the value functions expressions (15)–(16):

$$E_0[w_0(x), y, h] = \frac{\alpha_h[x - x_0^*(y, h)]}{(\rho + \eta_h + \chi_h)(1 + \chi_h c_h)} + Q(y, h) \quad (B.8)$$

$$E_1[w_1(x), y, h] = \frac{\alpha_h[x - x_1^*(y, h)]}{(\rho + \eta_h)\phi_h} + Q(y, h) \quad (B.9)$$

The equilibrium value functions of the posted vacancy are obtained by inserting the wage schedules (23)–(24), the equilibrium value functions (B.6)–(B.7) and the optimal decision rules described in Proposition 2 in the value functions expressions (10)–(11):

$$\begin{aligned} 0 = \nu_h & \qquad (B.10) \\ & + \zeta_h \frac{(1 - \alpha_h)}{\psi(h)b(h)} \int_0^{y^*(h)} b(y|h, y < y^*(h)) \left\{ \frac{1}{(\rho + \eta_h + \chi_h)} \int_{x_0^*(0,h)}^{\tilde{x}(0,h)} [x - x_0^*(0,h)] dG(x|h) \right. \\ & \qquad \left. + \frac{1}{(\rho + \eta_h)} \int_{\tilde{x}(0,h)}^{\infty} [x - x_1^*(0,h)] dG(x|h) \right\} dy \\ & + \zeta_h \frac{(1 - \alpha_h)}{\psi(h)b(h)} \int_{y^*(h)}^{\infty} \psi_h b(y|h, y \ge y^*(h)) \left\{ \frac{1}{(\rho + \eta_h + \chi_h)} \int_{x_0^*(y,h)}^{\tilde{x}(y,h)} [x - x_0^*(y,h)] dG(x|h) \right. \\ & \qquad \left. + \frac{1}{(\rho + \eta_h)} \int_{\tilde{x}(y,h)}^{\infty} [x - x_1^*(y,h)] dG(x|h) \right\} dy \end{aligned}$$

The equilibrium value functions of the employee states are obtained by inserting the wage schedules (23)–(24), the equilibrium value functions (B.8)–(B.9) and the optimal decision rules described in Proposition 2 in the value functions expressions (17)–(18):

$$\begin{aligned} \rho U(h) = \xi_h + \beta_{0,h} B_0 & \qquad (B.11) \\ & + \frac{\lambda_h \alpha_h}{(\rho + \eta_h + \chi_h)(1 + \chi_h c_h)} \int_{x_0^*(0,h)}^{\tilde{x}(0,h)} [x - x_0^*(0,h)] dG(x|h) \\ & + \frac{\lambda_h \alpha_h}{(\rho + \eta_h)\phi_h} \int_{\tilde{x}(0,h)}^{\infty} [x - x_1^*(0,h)] dG(x|h) \end{aligned}$$

$$\begin{aligned} \rho S(y, h) = y + \beta_{0,h} B_0 & \qquad (B.12) \\ & + \frac{\gamma_h \alpha_h}{(\rho + \eta_h + \chi_h)(1 + \chi_h c_h)} \int_{x_0^*(y,h)}^{\tilde{x}(y,h)} [x - x_0^*(y,h)] dG(x|h) \\ & + \frac{\gamma_h \alpha_h}{(\rho + \eta_h)\phi_h} \int_{\tilde{x}(y,h)}^{\infty} [x - x_1^*(y,h)] dG(x|h) \end{aligned}$$

The equilibrium measures over labor market states conditioning on schooling level h are obtained by imposing the usual steady state conditions equating flows in and out of each state. Flows are governed by the optimal decision rules described in Proposition 2 together with the shocks defined in Section 3. We denote with $b(y|h)$, $e(y|h)$ and $l(y|h)$ the steady state measures for, respectively, searchers, informal employees and formal employees. We start by recalling that they are mutually exclusive states and that the following equalities hold:

$$b(y|h) + e(y|h) + l(y|h) = r(y|h) \qquad (B.13)$$

$$\int_y \{b(y|h) + e(y|h) + l(y|h)\} dy = \int_y r(y|h)dy = 1 \qquad (B.14)$$

$$b(h) + e(h) + l(h) = 1 \qquad (B.15)$$
For each $y|h$, we exploit optimal decision (7), which generates a different behavior if searching as a self-employed ($y \ge y^*(h)$) or as an unemployed ($y < y^*(h)$). To give an example of the flows that this optimal behavior generates, let's focus on the second case:

$$ \dot{b}(y|h, y < y^*(h)) = (\eta_h + \chi_h)e(y|h, y < y^*(h)) + \eta_h l(y|h, y < y^*(h)) - \lambda_h [1 - G(x_0^*(y, h))]b(y|h, y < y^*(h)) $$

$$ \dot{e}(y|h, y < y^*(h)) = \lambda_h[G(\tilde{x}(0, h)) - G(x_0^*(0, h))]b(y|h, y < y^*(h)) - (\eta_h + \chi_h)e(y|h, y < y^*(h)) $$

$$ \dot{l}(y|h, y < y^*(h)) = \lambda_h[1 - G(\tilde{x}(0, h))]b(y|h, y < y^*(h)) - \eta_h l(y|h, y < y^*(h)) $$

The other flows have a similar structure. Imposing steady state and exploiting (B.13) leads to:

$$ b(y|h, y \ge y^*(h)) = \frac{\eta_h(\eta_h + \chi_h)r(y|h)}{\eta_h\gamma_h[G(\tilde{x}(y, h)) - G(x_0^*(y, h))] + (\eta_h + \chi_h)\gamma_h[1 - G(\tilde{x}(y, h))] + \eta_h(\eta_h + \chi_h)} $$

$$ e(y|h, y \ge y^*(h)) = \frac{\eta_h\gamma_h[G(\tilde{x}(y, h)) - G(x_0^*(y, h))]r(y|h)}{\eta_h\gamma_h[G(\tilde{x}(y, h)) - G(x_0^*(y, h))] + (\eta_h + \chi_h)\gamma_h[1 - G(\tilde{x}(y, h))] + \eta_h(\eta_h + \chi_h)} $$

$$ l(y|h, y \ge y^*(h)) = \frac{(\eta_h + \chi_h)\gamma_h[1 - G(\tilde{x}(y, h))]r(y|h)}{\eta_h\gamma_h[G(\tilde{x}(y, h)) - G(x_0^*(y, h))] + (\eta_h + \chi_h)\gamma_h[1 - G(\tilde{x}(y, h))] + \eta_h(\eta_h + \chi_h)} $$

and

$$ b(y|h, y < y^*(h)) = \frac{\eta_h(\eta_h + \chi_h)r(y|h)}{\eta_h\lambda_h[G(\tilde{x}(0, h)) - G(x_0^*(0, h))] + (\eta_h + \chi_h)\lambda_h[1 - G(\tilde{x}(0, h))] + \eta_h(\eta_h + \chi_h)} $$

$$ e(y|h, y < y^*(h)) = \frac{\eta_h\lambda_h[G(\tilde{x}(0, h)) - G(x_0^*(0, h))]r(y|h)}{\eta_h\lambda_h[G(\tilde{x}(0, h)) - G(x_0^*(0, h))] + (\eta_h + \chi_h)\lambda_h[1 - G(\tilde{x}(0, h))] + \eta_h(\eta_h + \chi_h)} $$

$$ l(y|h, y < y^*(h)) = \frac{(\eta_h + \chi_h)\lambda_h[1 - G(\tilde{x}(0, h))]r(y|h)}{\eta_h\lambda_h[G(\tilde{x}(0, h)) - G(x_0^*(0, h))] + (\eta_h + \chi_h)\lambda_h[1 - G(\tilde{x}(0, h))] + \eta_h(\eta_h + \chi_h)} $$

Since each worker is assigned by nature a value of self-employment income $y|h$, we have to integrate the above equations over $r(y|h)$ to find the equilibrium expressions for $b(h)$, $e(h)$, $l(h)$. In other words, we have to insert the above equations in expression (B.14) in order to obtain the three equilibrium components of the left-hand-side of expression (B.15).

The next step is determining the endogenous measure of vacancies by schooling, which is denoted by $v(h)$. It can be found by incorporating in equation (B.10) the workers' side equilibrium measures just defined and by recalling that $\zeta_h$ is a function of $b(h)$ and $v(h)$ through the matching function defined in equation (19).

Finally, the steady measure of individuals with high schooling level is determined by the optimal decision rule described in Section 3.2: we denote this value with $p$.

Since all the optimal decision rules and steady state measures depends only on parameters and on the values $\{U(h), S(y, h)\}$, we can now propose the following:

**Definition 5** *Equilibrium Definition.*

Given the vector of parameters $\{\rho, \xi_h, \lambda_h, \gamma_h, \eta_h, \chi_h, \psi_h, \iota_h, \beta_{0,h}, \beta_{1,h}, \alpha_h, c_h, \nu_h\}$ and the probability distribution functions $\{R(y|h), G(x|h), T(\kappa)\}$ a search model equilibrium in an economy with institutional parameters $\{B_0, \tau, t\}$ is a set of values $\{S(y, h), U(h)\}$ that:

1. solves the equilibrium equations (B.10)–(B.12);
2. satisfies the firms' free-entry condition (22);

3. satisfies the steady state conditions over the measures {$p, b(h), e(h), l(h), v(h)$}.

Two important remarks about Definition 5 are in order. The first remark was mentioned at the beginning of the section: the case for $h = 0$ requires a further specialization that we have not described so far in order to simplify notation. Given the schooling decision stated in Section 3.2, individuals with $h = 0$ are selected over $y$. Therefore, we cannot use the primitive distributions $r(y|0)$ in the equilibrium expressions above. In its place, we use the equilibrium distribution of $y$ for those agents that decide to remain at schooling level $h = 0$. We denote this distribution with $\tilde{r}(y|0)$. The definition is obtained by applying the optimal decision rule derived by problem (4). Recall that each agent extracts a self-employment income $y$ from $R(y|0)$ and a direct cost of schooling $\kappa$ from $T(\kappa)$. Given a direct cost of schooling $\kappa$, the opportunity cost of schooling is increasing in self-employment income $y$. For given $\kappa$, only individuals with self-employment income low enough will decide to acquire additional schooling. We denote this indifference point with $y^{**}(\kappa)$. $\tilde{r}(y|0)$ will then be the $r(y|0)$ distribution truncated at $y^{**}(\kappa)$ and integrated over the $T(\kappa)$ distribution. Formally:

$$ \tilde{r}(y|0) = \int \frac{r(y|0)}{1 - R(y^{**}(\kappa)|0)} dT(\kappa) \qquad (B.16) $$

The second remark is about uniqueness. It is possible that for some parameters combinations the equilibrium defined in (22) is not unique. The sources of multiplicity are the composition effects over education and over self-employment income. Consider the process of firms entering the labor market for schooling level $h = 1$. The direct effect is a tighter market for firms but a better market for workers. Since the labor market for $h = 1$ is now more attractive, more workers acquire schooling level $h = 1$, counter-balancing the direct effect. The extent to which these two opposing forces are enough to create multiple equilibria depends on parameters. Formally, they may lead to more than one value of vacancy rates $v(h)$ such that the free entry condition $V(h) = 0$ is satisfied.

As we discussed in Section 3.5, multiplicity greatly complicates the identification and estimation of the model with the data at our disposal. We have therefore chosen to estimate the model conditioning on two conjectures that deliver uniqueness. We now show that our conjectures hold at our parameter estimates. In section 3.3, we proposed Conjecture 1 stating that the workers' value of search as self-employed ($S(y, h)$) is monotonically increasing in $y$. The conjecture assures the uniqueness of $y^*(h)$. Figure B.2 reports $S(y, h)$ as a function of the self-employed income $y$ for both schooling levels (the dashed lines). Both value functions are monotonically increasing and cross the value of searching as unemployed (the solid lines representing $U(h)$) only once. The intersection points determine the unique $y^*(h)$. The second source of possible equilibrium multiplicity is the value of posting a vacancy: posting externalities together with the endogenous schooling decision rules may lead to non-uniqueness in the vacancy rate that sends the value of
posting to zero. We then proposed Conjecture 3 stating that the firms’ value of posting a vacancy is monotonically decreasing in the vacancy rate $v_h$. Figure B.3 shows that the conjecture holds for both schooling levels at our parameter estimates.

<figure><img src="image_11.png" /><figcaption>Figure B.2: Workers’ Values of Searching: $S(y, h)$ and $U(h)$</figcaption></figure>

NOTE: The figures report the present discounted values of searching as an unemployed ($U(h)$, solid lines) and as a self-employed ($S(y, h)$, dashed lines) as a function of the flow self-employment income $y$. Values approximated using simulated samples of 10,000 worker-level observations for each schooling group. All results based on the parameter estimates reported in Table 3.
<figure><img src="image_12.png" /><figcaption>Figure B.3: Firms’ Values of Posting: $V[h]$</figcaption></figure>

NOTE: The figures report the present discounted values of posting a vacancy $V[h]$ as a function of the vacancy rate $v(h)$. Values approximated using simulated samples of 10,000 worker-level observations for each schooling group. All results based on the parameter estimates reported in Table 3. The vertical lines represent the vacancy rate at baseline.

## B.4 Per-Capita Social Security Benefits: $b_1$

As described in Section 3.1, the common benefit $b_1$ received by formal employees is fully financed by a portion $(1-\tau)$ of the payroll contribution $tw_1(x; y, h)$. As a result, $b_1$ is an equilibrium object that depends on the distribution of formal employees in steady state. In this section, we derive
the equilibrium expression for $b_1$.

Each formal employee contributes $(1-\tau)tw_1(x; y, h)$. The average contribution for a given education level $h$ is obtained by integrating over the equilibrium distribution of accepted productivity $x$ and the distribution over $y$, weighted by the equilibrium measure of formal employee $l(y|h)$:

$$ \text{AvContr}(h) = \int_{S(y)} \int_{S(x)} (1 - \tau)tw_1(x; y, h)l(y|h) \frac{g(x|h)}{[1 - G(\tilde{x}(y, h))]} r(y|h)dxdy \quad (B.17) $$

where $S(y)$ and $S(x)$ denote the equilibrium supports of $y$ and $x$. Due to the schooling decision, the value of $r(y|h)$ is the primitive distribution $r(y|1)$ when the schooling level is high but is the conditional distribution $\tilde{r}(y|0)$ defined in (B.16) when the schooling level is low. Since the benefit is financed by both schooling levels and equally shared between them, the final $b_1$ is the average contribution over the two schooling levels:

$$ b_1 = \text{AvContr}(1)p + \text{AvContr}(0)(1-p) \quad (B.18) $$

where $p$ denotes the equilibrium proportion of agents in the high schooling level $h=1$.

## C Estimates and Model Fit

<table><caption>Table C.1: Demand-side Parameters for Different Values of $\iota$</caption><thead><tr><th colspan="3">Low Schooling: h = 0 High Schooling: h = 1</th></tr></thead><tbody><tr><td colspan="3">i<sub>h</sub> = {0.632, 0.628}</td></tr><tr><td>ζ<sub>h</sub></td><td>6.004</td><td>4.594</td></tr><tr><td>ν<sub>h</sub></td><td>-373.551</td><td>-607.001</td></tr><tr><td colspan="3">i<sub>h</sub> = {0.732, 0.728} (benchmark)</td></tr><tr><td>ζ<sub>h</sub></td><td>7.972</td><td>5.857</td></tr><tr><td>ν<sub>h</sub></td><td>-496.011</td><td>-773.799</td></tr><tr><td colspan="3">i<sub>h</sub> = {0.832, 0.828}</td></tr><tr><td>ζ<sub>h</sub></td><td>10.585</td><td>7.466</td></tr><tr><td>ν<sub>h</sub></td><td>-658.615</td><td>-986.432</td></tr></tbody></table>

NOTE: This table reports alternative values for the arrival rate of workers to firms ($\zeta_h$) and the firms' flow cost of keeping a vacancy open ($\nu_h$) as implied by setting the matching function parameter ($i_h$) at standard values found in the literature. The benchmark case corresponds to the value of the estimated parameters reported in Table 3.
<table><caption>Table C.2: Predicted Values</caption><thead><tr><th></th><th colspan="2">Low Schooling h = 0</th><th colspan="2">High Schooling: h = 1</th></tr><tr><th></th><th>Value</th><th>Std. Error</th><th>Value</th><th>Std. Error</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-weight: bold;">Primitive Distributions</td></tr><tr><td>E(x|h)</td><td>19.231</td><td>0.694</td><td>19.935</td><td>0.750</td></tr><tr><td>SD(x|h)</td><td>13.275</td><td>0.610</td><td>18.779</td><td>0.697</td></tr><tr><td>E(y|h)</td><td>7.188</td><td>0.138</td><td>9.698</td><td>0.887</td></tr><tr><td>SD(y|h)</td><td>6.527</td><td>0.139</td><td>9.224</td><td>1.197</td></tr><tr><td>E(k)</td><td>63.316</td><td>4.086</td><td></td><td></td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">Reservation Values</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">Treatment Group</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">Low Ability: k = 1</td></tr><tr><td>x<sub>0</sub><sup>*</sup>(0, h)</td><td>14.191</td><td>0.665</td><td>21.482</td><td>7.916</td></tr><tr><td>x̃(0, h)</td><td>15.596</td><td>1.062</td><td>22.711</td><td>6.709</td></tr><tr><td>E<sub>y</sub>[x<sub>0</sub><sup>*</sup>(y, h)]</td><td>23.170</td><td>7.810</td><td>33.411</td><td>11.725</td></tr><tr><td>E<sub>y</sub>[x̃(y, h)]</td><td>27.407</td><td>10.874</td><td>34.942</td><td>10.437</td></tr><tr><td>y<sup>*</sup>(h)</td><td>10.448</td><td>4.558</td><td>12.159</td><td>2.826</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">High Ability: k = 2</td></tr><tr><td>x<sub>0</sub><sup>*</sup>(0, h)</td><td>15.693</td><td>0.653</td><td>22.780</td><td>6.658</td></tr><tr><td>x̃(0, h)</td><td>25.649</td><td>1.386</td><td>33.977</td><td>7.751</td></tr><tr><td>E<sub>y</sub>[x<sub>0</sub><sup>*</sup>(y, h)]</td><td>23.555</td><td>7.344</td><td>33.232</td><td>10.349</td></tr><tr><td>E<sub>y</sub>[x̃(y, h)]</td><td>40.333</td><td>14.746</td><td>49.193</td><td>12.833</td></tr><tr><td>y<sup>*</sup>(h)</td><td>12.955</td><td>5.375</td><td>15.676</td><td>3.964</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">Control Group</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">Low Ability: k = 1</td></tr><tr><td>x<sub>0</sub><sup>*</sup>(0, h)</td><td>14.728</td><td>0.676</td><td>22.023</td><td>7.906</td></tr><tr><td>x̃(0, h)</td><td>13.048</td><td>1.163</td><td>21.476</td><td>6.967</td></tr><tr><td>E<sub>y</sub>[x<sub>0</sub><sup>*</sup>(y, h)]</td><td>23.845</td><td>7.661</td><td>32.801</td><td>12.593</td></tr><tr><td>E<sub>y</sub>[x̃(y, h)]</td><td>25.041</td><td>10.615</td><td>32.527</td><td>11.528</td></tr><tr><td>y<sup>*</sup>(h)</td><td>10.468</td><td>4.432</td><td>12.168</td><td>2.757</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">High Ability: k = 2</td></tr><tr><td>x<sub>0</sub><sup>*</sup>(0, h)</td><td>16.247</td><td>0.632</td><td>23.229</td><td>6.636</td></tr><tr><td>x̃(0, h)</td><td>22.806</td><td>1.402</td><td>32.499</td><td>8.028</td></tr><tr><td>E<sub>y</sub>[x<sub>0</sub><sup>*</sup>(y, h)]</td><td>24.936</td><td>7.259</td><td>32.703</td><td>11.228</td></tr><tr><td>E<sub>y</sub>[x̃(y, h)]</td><td>39.033</td><td>14.595</td><td>46.291</td><td>14.317</td></tr><tr><td>y<sup>*</sup>(h)</td><td>13.796</td><td>5.937</td><td>15.697</td><td>3.905</td></tr></tbody></table>

NOTE: Bootstrap standard errors based on 100 replications reported. The Values are obtained from the equilibrium of the model defined in Section 3.5 using the parameter estimates reported in Table 3.
<table><caption>Table C.3: Cross-Sectional Moments and Model Fit – Treated Sample</caption><thead><tr><th rowspan="2">Schooling:</th><th colspan="3">h = 0</th><th colspan="3">h = 1</th></tr><tr><th>Model</th><th>Data</th><th>Weight</th><th>Model</th><th>Data</th><th>Weight</th></tr></thead><tbody><tr><td>Share Formally Employed</td><td>0.512</td><td>0.546</td><td>79.232</td><td>0.572</td><td>0.581</td><td>66.017</td></tr><tr><td>Share Informally Employed</td><td>0.227</td><td>0.253</td><td>43.236</td><td>0.179</td><td>0.216</td><td>29.415</td></tr><tr><td>Share Self-employed</td><td>0.170</td><td>0.162</td><td>31.946</td><td>0.159</td><td>0.155</td><td>23.843</td></tr><tr><td>Share Unemployed</td><td>0.091</td><td>0.040</td><td>14.940</td><td>0.089</td><td>0.048</td><td>12.217</td></tr><tr><td>Mean Formal Wages</td><td>10.126</td><td>12.162</td><td>64.066</td><td>17.241</td><td>15.699</td><td>47.190</td></tr><tr><td>SD Formal Wages</td><td>11.333</td><td>13.873</td><td>79.919</td><td>17.343</td><td>18.436</td><td>48.446</td></tr><tr><td>Mean Informal Wages</td><td>4.370</td><td>4.191</td><td>36.651</td><td>4.547</td><td>4.245</td><td>22.601</td></tr><tr><td>SD Informal Wages</td><td>8.272</td><td>8.436</td><td>49.167</td><td>9.816</td><td>10.392</td><td>24.452</td></tr><tr><td>Mean Self-empl Income</td><td>3.500</td><td>3.566</td><td>25.990</td><td>3.987</td><td>3.796</td><td>19.152</td></tr><tr><td>SD Self-empl Income</td><td>8.696</td><td>9.891</td><td>34.883</td><td>10.767</td><td>11.072</td><td>23.855</td></tr><tr><td>Share Informal Employee - Q1</td><td>0.014</td><td>0.109</td><td>19.915</td><td>0.013</td><td>0.095</td><td>15.246</td></tr><tr><td>Share Informal Employee - Q2</td><td>0.015</td><td>0.063</td><td>12.819</td><td>0.104</td><td>0.046</td><td>8.820</td></tr><tr><td>Share Informal Employee - Q3</td><td>0.119</td><td>0.034</td><td>8.797</td><td>0.058</td><td>0.034</td><td>7.872</td></tr><tr><td>Share Informal Employee - Q4</td><td>0.070</td><td>0.027</td><td>8.497</td><td>0.003</td><td>0.020</td><td>5.690</td></tr><tr><td>Share Informal Employee - Q5</td><td>0.008</td><td>0.020</td><td>9.673</td><td>0.001</td><td>0.021</td><td>7.621</td></tr><tr><td>Mean Formal Wages - Q1</td><td>1.256</td><td>1.096</td><td>50.510</td><td>2.088</td><td>1.246</td><td>41.113</td></tr><tr><td>Mean Formal Wages - Q2</td><td>1.491</td><td>1.714</td><td>51.541</td><td>2.624</td><td>2.032</td><td>40.557</td></tr><tr><td>Mean Formal Wages - Q3</td><td>1.888</td><td>2.209</td><td>41.645</td><td>3.201</td><td>2.464</td><td>35.638</td></tr><tr><td>Mean Formal Wages - Q4</td><td>2.256</td><td>2.781</td><td>33.476</td><td>3.765</td><td>3.690</td><td>34.090</td></tr><tr><td>Mean Formal Wages - Q5</td><td>3.236</td><td>4.362</td><td>47.001</td><td>5.562</td><td>6.267</td><td>31.451</td></tr><tr><td>Mean Informal Wages - Q1</td><td>0.183</td><td>1.086</td><td>15.512</td><td>0.245</td><td>0.967</td><td>13.886</td></tr><tr><td>Mean Informal Wages - Q2</td><td>0.208</td><td>0.984</td><td>12.590</td><td>2.550</td><td>0.780</td><td>7.948</td></tr><tr><td>Mean Informal Wages - Q3</td><td>2.210</td><td>0.679</td><td>7.785</td><td>1.611</td><td>0.775</td><td>8.912</td></tr><tr><td>Mean Informal Wages - Q4</td><td>1.520</td><td>0.684</td><td>9.490</td><td>0.087</td><td>0.598</td><td>5.695</td></tr><tr><td>Mean Informal Wages - Q5</td><td>0.249</td><td>0.758</td><td>10.789</td><td>0.054</td><td>1.125</td><td>6.062</td></tr><tr><td>Share Schooling</td><td>0.614</td><td>0.623</td><td>114.437</td><td>0.386</td><td>0.377</td><td>183.702</td></tr></tbody></table>

<footnote>NOTE: Cross-sectional sample extracted from the Labor Market Survey (ENOE) in 2005:Q1. The treated sample composed by individuals from municipalities receiving the *Seguro Popular* program. The moments are computed unconditionally on the labor market state to guarantee a smoother and well-defined quadratic form during the optimization procedure. The weights in the quadratic form (36) are equal to the inverses of the variance of each sample moment. Additional details on samples and variables definitions are in Section 2.2 and Appendix A.1.</footnote>
<table><caption>Table C.4: Cross-Sectional Moments and Model Fit – Control Sample</caption><thead><tr><th rowspan="2">Schooling:</th><th colspan="3">h = 0</th><th colspan="3">h = 1</th></tr><tr><th>Model</th><th>Data</th><th>Weight</th><th>Model</th><th>Data</th><th>Weight</th></tr></thead><tbody><tr><td>Share Formally Employed</td><td>0.595</td><td>0.585</td><td>71.481</td><td>0.598</td><td>0.601</td><td>54.399</td></tr><tr><td>Share Informally Employed</td><td>0.138</td><td>0.207</td><td>30.460</td><td>0.140</td><td>0.170</td><td>20.134</td></tr><tr><td>Share Self-employed</td><td>0.170</td><td>0.159</td><td>26.772</td><td>0.159</td><td>0.175</td><td>20.422</td></tr><tr><td>Share Unemployed</td><td>0.097</td><td>0.049</td><td>13.760</td><td>0.103</td><td>0.054</td><td>10.874</td></tr><tr><td>Mean Formal Wages</td><td>11.588</td><td>13.055</td><td>56.434</td><td>17.981</td><td>16.454</td><td>40.448</td></tr><tr><td>SD Formal Wages</td><td>11.201</td><td>13.696</td><td>70.433</td><td>18.431</td><td>18.074</td><td>42.787</td></tr><tr><td>Mean Informal Wages</td><td>2.756</td><td>3.512</td><td>25.613</td><td>3.653</td><td>3.526</td><td>15.446</td></tr><tr><td>SD Informal Wages</td><td>6.959</td><td>8.130</td><td>34.817</td><td>9.154</td><td>10.058</td><td>15.573</td></tr><tr><td>Mean Self-empl Income</td><td>3.607</td><td>3.177</td><td>20.646</td><td>3.817</td><td>3.820</td><td>16.609</td></tr><tr><td>SD Self-empl Income</td><td>9.034</td><td>8.929</td><td>24.136</td><td>10.017</td><td>10.489</td><td>22.598</td></tr><tr><td>Share Informal Employee - Q1</td><td>0.000</td><td>0.097</td><td>17.214</td><td>0.000</td><td>0.077</td><td>11.504</td></tr><tr><td>Share Informal Employee - Q2</td><td>0.000</td><td>0.043</td><td>9.782</td><td>0.076</td><td>0.034</td><td>6.495</td></tr><tr><td>Share Informal Employee - Q3</td><td>0.077</td><td>0.025</td><td>6.420</td><td>0.059</td><td>0.029</td><td>6.431</td></tr><tr><td>Share Informal Employee - Q4</td><td>0.055</td><td>0.020</td><td>7.443</td><td>0.002</td><td>0.014</td><td>4.294</td></tr><tr><td>Share Informal Employee - Q5</td><td>0.006</td><td>0.022</td><td>8.506</td><td>0.002</td><td>0.015</td><td>5.196</td></tr><tr><td>Mean Formal Wages - Q1</td><td>1.413</td><td>1.287</td><td>26.576</td><td>2.147</td><td>1.424</td><td>33.632</td></tr><tr><td>Mean Formal Wages - Q2</td><td>1.722</td><td>1.919</td><td>29.433</td><td>2.747</td><td>2.143</td><td>33.154</td></tr><tr><td>Mean Formal Wages - Q3</td><td>2.180</td><td>2.231</td><td>13.881</td><td>3.290</td><td>2.906</td><td>26.222</td></tr><tr><td>Mean Formal Wages - Q4</td><td>2.572</td><td>2.988</td><td>19.474</td><td>3.862</td><td>3.688</td><td>21.520</td></tr><tr><td>Mean Formal Wages - Q5</td><td>3.701</td><td>4.630</td><td>40.220</td><td>5.934</td><td>6.293</td><td>27.282</td></tr><tr><td>Mean Informal Wages - Q1</td><td>0.000</td><td>0.979</td><td>15.061</td><td>0.000</td><td>0.873</td><td>9.843</td></tr><tr><td>Mean Informal Wages - Q2</td><td>0.000</td><td>0.695</td><td>11.703</td><td>1.873</td><td>0.614</td><td>7.102</td></tr><tr><td>Mean Informal Wages - Q3</td><td>1.441</td><td>0.495</td><td>6.586</td><td>1.611</td><td>0.707</td><td>6.523</td></tr><tr><td>Mean Informal Wages - Q4</td><td>1.142</td><td>0.497</td><td>6.430</td><td>0.074</td><td>0.437</td><td>4.105</td></tr><tr><td>Mean Informal Wages - Q5</td><td>0.173</td><td>0.846</td><td>8.353</td><td>0.095</td><td>0.895</td><td>4.890</td></tr><tr><td>Share Schooling</td><td>0.622</td><td>0.639</td><td>100.134</td><td>0.378</td><td>0.361</td><td>56.542</td></tr></tbody></table>

<footnote>NOTE: Cross-sectional sample extracted from the Labor Market Survey (ENOE) in 2005:Q1. The control sample composed by individuals in municipalities *not* receiving the *Seguro Popular* program. The moments are computed unconditionally on the labor market state to guarantee a smoother and well-defined quadratic form during the optimization procedure. The weights in the quadratic form (36) are equal to the inverses of the variance of each sample moment. Additional details on samples and variables definitions are in Section 2.2 and Appendix A.1.</footnote>
<table><caption>Table C.5: Longitudinal Moments and Model Fit</caption><thead><tr><th rowspan="2">Schooling:</th><th colspan="3">h = 0</th><th colspan="3">h = 1</th></tr><tr><th>Model</th><th>Data</th><th>Weight</th><th>Model</th><th>Data</th><th>Weight</th></tr></thead><tbody><tr><td colspan="7"><strong>One-year Transitions:</strong></td></tr><tr><td>Formally E. – Formally E.</td><td>0.427</td><td>0.575</td><td>56.925</td><td>0.490</td><td>0.666</td><td>52.361</td></tr><tr><td>Informally E. – Informally E.</td><td>0.161</td><td>0.138</td><td>19.655</td><td>0.135</td><td>0.118</td><td>13.186</td></tr><tr><td>Self-employed – Self-employed</td><td>0.154</td><td>0.072</td><td>12.855</td><td>0.154</td><td>0.066</td><td>9.682</td></tr><tr><td>Informally E.-Formally E.</td><td>0.024</td><td>0.061</td><td>12.149</td><td>0.018</td><td>0.037</td><td>6.943</td></tr><tr><td>Formally E.-Informally E.</td><td>0.024</td><td>0.057</td><td>11.496</td><td>0.017</td><td>0.040</td><td>7.638</td></tr><tr><td>Unemployed-Formally E.</td><td>0.052</td><td>0.018</td><td>6.546</td><td>0.044</td><td>0.008</td><td>3.107</td></tr><tr><td>Self-employed-Informally E.</td><td>0.006</td><td>0.016</td><td>6.249</td><td>0.004</td><td>0.011</td><td>3.891</td></tr><tr><td>Informally E.-Self-employed</td><td>0.006</td><td>0.015</td><td>6.168</td><td>0.003</td><td>0.011</td><td>3.837</td></tr><tr><td>Formally E.-Unemployed</td><td>0.054</td><td>0.014</td><td>5.781</td><td>0.051</td><td>0.013</td><td>4.085</td></tr><tr><td>Self-employed-Formally E.</td><td>0.010</td><td>0.010</td><td>4.873</td><td>0.008</td><td>0.008</td><td>3.382</td></tr><tr><td>Formally E.-Self-employed</td><td>0.015</td><td>0.009</td><td>4.696</td><td>0.008</td><td>0.010</td><td>3.712</td></tr><tr><td>Unemployed-Informally E.</td><td>0.026</td><td>0.008</td><td>4.274</td><td>0.019</td><td>0.002</td><td>1.717</td></tr><tr><td>Informally E.-Unemployed</td><td>0.025</td><td>0.004</td><td>3.143</td><td>0.022</td><td>0.006</td><td>2.894</td></tr><tr><td>Unemployed – Unemployed</td><td>0.015</td><td>0.003</td><td>2.501</td><td>0.027</td><td>0.005</td><td>2.440</td></tr><tr><td colspan="7"><strong>Hazard rates out of Unemployment:</strong></td></tr><tr><td>At 3 months</td><td>0.744</td><td>0.783</td><td>15.441</td><td>0.627</td><td>0.793</td><td>10.743</td></tr><tr><td>At 6 months</td><td>0.541</td><td>0.667</td><td>5.541</td><td>0.422</td><td>0.667</td><td>3.004</td></tr></tbody></table>

NOTE: Longitudinal sample extracted from a balanced panel of four ENOE cohorts entering in 2005:Q1 through 2005:Q4 and observed over 5 consecutive quarters. The moments are aggregated over municipalities receiving and *not* receiving the *Seguro Popular* program and they are computed unconditionally on the labor market state in order to guarantee a smoother and well-defined quadratic form during the optimization procedure. The weights in the quadratic form (36) are equal to the inverses of the variance of each sample moment. Additional details on the samples and variables definitions are in Section 2.2 and Appendix A.1.
<table><caption>Table C.6: Aggregate Moments and Model Fit</caption><thead><tr><th colspan="3">Labor Share:</th></tr><tr><th>Model</th><th>Data</th><th>Weight</th></tr></thead><tbody><tr><td>0.533</td><td>0.419</td><td>2.000</td></tr></tbody><thead><tr><th colspan="4">Vacancy rate:</th></tr><tr><th colspan="2">Schooling:</th><th colspan="2">h = 0</th></tr><tr><th>Model</th><th>Data</th><th>Model</th><th>Data</th></tr></thead><tbody><tr><td>0.0062</td><td>0.0062</td><td>0.0092</td><td>0.0092</td></tr></tbody></table>

NOTE: Labor share from from AMECO. Vacancy rates from Ministry of Labor's *Bolsa de Trabajo*. Additional details on samples and variables definitions are in Section 2.2 and Appendix A.1.

<table><caption>Table C.7: Out-of-Sample Model Validation</caption><thead><tr><th rowspan="3"></th><th colspan="3">Hourly Labor Income (log)</th><th colspan="4">Labor Market Proportions</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th></tr><tr><th>Formal</th><th>Informal</th><th>Self</th><th>Formal</th><th>Informal</th><th>Self</th><th>Unemployed</th></tr></thead><tbody><tr><td colspan="8">One-Sided T-Tests (P-values)</td></tr><tr><td>H<sub>0</sub>: β<sub>Data</sub> &lt; 0</td><td>0.031</td><td>0.524</td><td>0.441</td><td>0.925</td><td>0.026</td><td>0.451</td><td>0.667</td></tr><tr><td>H<sub>0</sub>: β<sub>Model</sub> &lt; 0</td><td>0.000</td><td>1.000</td><td>0.822</td><td>1.000</td><td>0.000</td><td>0.520</td><td>0.871</td></tr><tr><td>H<sub>0</sub>: β<sub>Data</sub> &gt; 0</td><td>0.969</td><td>0.476</td><td>0.559</td><td>0.075</td><td>0.974</td><td>0.549</td><td>0.333</td></tr><tr><td>H<sub>0</sub>: β<sub>Model</sub> &gt; 0</td><td>1.000</td><td>0.000</td><td>0.178</td><td>0.000</td><td>1.000</td><td>0.480</td><td>0.129</td></tr><tr><td colspan="8">Two-Sided T-Tests (P-values)</td></tr><tr><td>H<sub>0</sub>: β<sub>Data</sub> = β<sub>Model</sub></td><td>0.424</td><td>0.539</td><td>0.809</td><td>0.002</td><td>0.000</td><td>0.895</td><td>0.941</td></tr></tbody></table>

NOTE: The Table reports p-values of one-sided and two-sided T-Tests for the estimated θ coefficients displayed in equation (37), which capture the effect of receiving the *Seguro Popular* program in 2006 on labor market outcomes both in the data sample and in the simulated sample. The data sample is drawn from the Mexican labor market survey (ENOE 2006) and matched at the municipality-level with the roll-out of the *Seguro Popular* program in the year 2006. The simulated sample is based on simulated data generated by the estimated model parameters reported in Table 3. The full set of OLS coefficients with robust standard errors are reported in Figure 5.
# D Experiments

In our model, the distortions introduced by the institutional parameters and by the presence of multiple labor market contracts interact with the three sources of inefficiency and externality discussed in Section 6. This interaction introduces an additional layer of complexity that prevents the model from delivering such clean theoretical result as the ones provided in Acemoglu and Shimer (1999) for the hold-up problem, in Hosios (1990) for the posting externality or Charlot and Decreuse (2010) for the selection over ability. However, in this Appendix we can still study the joint importance of these channels by focusing on the two crucial parameters governing the extent of their impact: $\alpha$ and $\iota$. Similarly to what we performed in Section 6.2, we study a range of outcomes resulting from counterfactual experiments obtained by changing the parameters of interest. In this case, the parameter of interest is the workers’ bargaining weight in the Nash product $\alpha$: the higher $\alpha$, the higher the share of the surplus going to the worker (see equation (21)). We vary $\alpha$ over a broad range of values, including the “Hosios condition” value corresponding to the estimated $\iota_h$.<fnref n="81" />

Figure D.1 reports welfare and schooling obtained by varying the workers’ bargaining weight $\alpha$. In the first row, we perform the exercise at the average estimated value of $\iota$ (0.73). Panel (a) shows that overall welfare is quite sensitive to $\alpha$. If $\alpha$ were set to 0.1 (giving most of the surplus to firms), welfare would decrease by about 7% with respect to benchmark. If $\alpha$ were set to 0.9 (giving most of the surplus to workers), welfare would decrease by about 31% with respect to benchmark. Two implications are of interest. First, the asymmetry of the impact signals that the importance of externalities and inefficiencies are different between the two sides of the market: transferring bargaining power to the workers is relatively more costly than transferring it to the firms. Second, the concavity implies that it must exists an optimal value of $\alpha$ that maximizes welfare. This value is equal to about 0.325 and it is lower than the one estimated in the model (equal to 0.563 and denoted by the vertical solid line in the figure), suggesting that workers receive a too high share of the surplus and firms do not post enough vacancies. Panel (b) shows that the education decision – and the related externalities and inefficiencies – are not very sensitive to the way the surplus is split. Over a large range of $\alpha$, a range that includes both the optimal and the baseline value, the overall optimal proportion of High Schooling agents is very similar. Only for extreme values of $\alpha$ (higher than 0.8 and smaller than 0.2), education starts to significantly decrease, mimicking the loss of welfare. Finally, it is interesting to note that the optimal $\alpha$ is much lower than the optimal value suggested by the Hosios condition. The optimal $\alpha$ is equal to 0.325, a value much lower than the average estimated $\iota_h$ which is equal to 0.73 and denoted by the vertical dashed line in the figure. Under the conjecture that the Hosios condition is a good approximation of efficiency in our setting, this result would suggest that the institutional framework adds inefficiencies above and beyond the standard inefficiencies affecting this class of models.

<footnote n="81">⁸¹In estimation, we allow matching elasticities to differ by education. Since the estimated values are very similar for both schooling group (see Table 3), we just report one value equal to 0.73 (the mean of the estimated 0.732 and 0.728) to avoid cluttering the figures.</footnote>
<figure><img src="image_13.png" /><figcaption>Figure D.1: Robustness for Different Values of the Bargaining Parameter ($\alpha$) and the Matching function Parameter ($\iota$)</figcaption></figure>

NOTE: The figures report outcomes from counterfactual experiments that change the bargaining power parameter $\alpha$ from 0.1 to 0.9. The vertical continuous lines are set at the estimated value of the bargaining power parameter ($\hat{\alpha}$) and the vertical dashed lines are set at the estimated value of the matching elasticity parameter ($\hat{\iota}$). *Welfare* is the overall flow welfare in steady state (see Section 6). *Schooling* is the proportion of individuals with High Schooling in the population.
We further investigate this point by focusing on the matching elasticity $\iota$ and asking if the observed result is sensitive to its estimated value.<fnref n="82" /> The third and second rows of Figure D.1 reports the same exercise for values of $\iota$ higher and lower than benchmark. The main result is confirmed: the optimal $\alpha$ is much lower than the optimal value suggested by the Hosios condition. The departure from Hosios is larger for the lower value of $\iota$ (0.63) than for the higher one (0.83). The relative low elasticity of schooling with respect to $\alpha$ is also qualitatively robust to changes in $\iota$. The range of low elasticity is large in all cases but its support and location change for different values of $\iota$: the lower $\iota$, the higher the range of $\alpha$ for which schooling is increasing.

We draw two main conclusions from this partial efficiency analysis. First, the distortions introduced by the institutional features that generate informality also seem to magnify the inefficiencies already present in our non-competitive model of the labor market. Second, given the institutional setting, workers’ bargaining power may be too high to induce firms to post an efficient amount of vacancies in the two schooling markets.

<footnote n="82">⁸²Our estimated value is similar to what found by Arroyo Miranda et al. (2014) using macro data on Mexico and it is within the range of standard measures reported in the Petrongolo and Pissarides (2001)'s review.</footnote>