the government as percentage of their wage in the informal sector,<sup>38</sup> and _μ_ is a parameter that measures the workers valuation of the social assistance benefits received, where 0 _≤ μ ≤_ 1.<sup>39</sup> So, informal workers are a “vulnerable” population in the sense that, even if they may have access to partial insurance against health shocks due to a government subsidized health program, they do not have any insurance against unemployment shocks (i.e., severance payments) or aging (i.e., mandatory pension or retirement accounts).

# **3.2 Firms**

The small economy produces two composite goods: tradables and non-tradables. There are two productive sectors in this economy: formal and informal. The formal and informal sectors are assumed to produce tradables and non-tradables, respectively.

Each sector has a continuum of small firms in the unit interval, which are identical in all respects within each sector. Each firm has one job and maximizes the present discounted value of profits and chooses whether to open a job vacancy and hire a worker or not, so the number of jobs/firms is endogenous. Since the profit maximization condition requires that the marginal value of a vacancy must be zero, this is exactly equivalent to a zero-profit condition for firm entry.

Firms can only adjust to meet demand through changes in the extensive margin (number of jobs offered/employed people), but not through the intensive margin.

The main difference between firms across sectors is that informal-sector firms are not affected by labor market regulations such as social security contributions and severance payments. Distributions of productivity and wages are also different.

Let _Vi_ be the present-discounted value of expected profit from a vacant job in sector _i_ , and _Ji_ ( _y_<sup>_′_</sup> _, y_ ) be the present-discounted value of expected profit from a filled job in sector _i_ with a worker of type _y_ and match-specific productivity _y_<sup>_′_</sup> .

Firms in sector _i_ open vacancies and search among the pool of job seekers, which involves a hiring cost _c_ , assumed to be constant.<sup>40</sup> They also face some uncertainty when meeting a job seeker, since they do not know with certainty the type of worker they will meet, and conditional on type, how productive that worker will be at the job.

> 38I assume the benefit from social assistance is proportional to the informal-sector wage. For the case of Colombia, _δ_ 3 corresponds to allocated health expenditures in the Subsidized Regime program as percentage of nominal wage. However, not all workers receive the subsidy: only those workers whose families are categorized as “poor” as determined by a Poverty Index Score, using the Census of the Poor (SISBEN).

> 39I am assuming that employee valuations of these services may be lower, equal or higher than in the SS system ( _μ < τ_ , _μ_ = _τ_ , _μ > τ_ ), depending on the perception of the efficiency of the services provided by the public sector. In the case where _μ_ = 0, informal workers do not value the services offered by the government. In this case, any change in subsidized health expenditures, _δ_ 3, will not change the flow income in the informal sector. If _μ >_ 0, an expansion in subsidized health expenditures will cause a higher flow income in the informal sector with a consequent behavioral impact.

> 40The hiring cost can also depend on productivity or wages over the business cycle, but it is reasonable to assume is constant in the steady state.

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