unemployed,<sup>24</sup> and _m_ ( _θ_ ) be the endogenous rate at which formal sector offers arrive.<sup>25</sup> Once contact is made between a worker of type _y_ and a potential employer in the formal sector, a productivity for the prospective match, _y_<sup>_′_</sup> , is drawn.

The details of the job creation process are as follows. Because of the existence of a productivity distribution for new matches, not all meetings create a match. Let _RUF_ ( _y_ ) and _RUI_ ( _y_ ) be the minimum productivities in the formal and informal sectors below which neither the firm nor the type-y worker want to start a match (endogenous reservation productivities). If the realization of the productivity draw for a worker of type _y_ is sufficiently ‘high’,<sup>26</sup> the worker and the firm in sector _i_ decide to match, and the worker gets a capital gain of _Ni_ ( _y_<sup>_′_</sup> _, y_ ) _− U_ ( _y_ ); otherwise, the worker returns to the pool of unemployed, and the job remains vacant.<sup>27</sup> The flow value of unemployment for a worker of type _y_ is: Given the assumptions on the match-specific productivity this gives: While employed in sector _i_ , a worker of type _y_ and current productivity _y_<sup>_′_</sup> enjoys flow utility _ui_ ( _y_<sup>_′_</sup> _, y_ ). Then, the match that started at productivity _y_<sup>_′_</sup> may continue or be destroyed. The job destruction rate is endogenized by introducing idiosyncratic shocks to job productivities:<sup>28</sup> productivity shocks arrive to jobs in sector _i_ at Poisson rate _λ_ , changing the productivity to a new level _x_ . These new productivities are _iid_ draws from the conditional distribution _Hi_ ( _x | y_ ).<sup>29</sup>

The same mechanism that governs the job creation process applies to job destruction: a match ends when it is in the mutual interest of the worker and the firm to do so, i.e., when a sufficiently bad draw of _x_ is realized.<sup>30</sup> The threshold productivities for match dissolution in the informal and the formal sector are _RIU_ ( _y_ ) and _RFU_ ( _y_ ), respectively.

> 24I am assuming no congestion effects in the informal sector ( _α_ is not a function of _θ_ ), so the measure of job seekers does not make it harder for an individual to find an informal sector opportunity. It may be the case that while job seekers are eager to find a formal sector job, they are not eager to find an informal sector job.

> 25The matching function has standard properties, so _m_ ( _θ_ ) is increasing and concave in _θ_ . In the calibration I assume a Cobb Douglas matching function given by _m_ ( _θ_ ) = _Aθ_<sup>1</sup><sup>_−αm_</sup> .

> 26 _′ ′_ Sufficiently ‘high’ means _y ≥ RUF_ ( _y_ ) for the formal sector and _y ≥ RUI_ ( _y_ ) for the informal sector.

> 27Another way of modeling this choice is by assuming that workers choose whether or not to accept jobs based on a reservation wage. This is analogous to the reservation productivity concept.

> 28There are two reasons why the productivity of a job may fall below the reservation value: idiosyncratic or aggregate shocks. Previous evidence for Colombia using plant-level data from the Annual Manufacturing survey estimates that the actual impact of reforms through factor adjustment on aggregate productivity was modest (Eslava, Haltiwanger, Kugler and Kugler, 2010), so introducing idiosyncratic shocks instead of aggregate shocks in the model seems more reasonable.

> 29Notice that I assume that productivity shocks affect both sectors symmetrically: workers receive shocks at the same rate, regardless of the sector in which they are in. Also, I assume that the idiosyncratic productivity that is drawn after the shock arrives is independent of the initial productivity _y_<sup>_′_</sup> and is irreversible (the firm must produce at the new productivity or shut down), where _x ∈_ [0 _, ∞_ ].

> 30 This means _x<RIU_ ( _y_ ) for the informal sector, and _x< RF U_ ( _y_ ) for the formal sector.

9