# **4 Model calibration**

We choose values for the model parameters based on econometric estimates in the economic literature on urbanization and development. When econometric estimates are not available, we calibrate the remaining model parameters to match observed patterns of urbanization in developing countries. For most significant model parameters, we conduct a sensitivity analysis over the range of their plausible values. Table 1 lists the model’s parameters and shows the chosen values.

We set the number of economic agents to 5 in order to balance the model’s computational feasibility with tractability. We interpret the number of agents as population quantiles. We consider a uniform distribution of abilities over (0 _,_ 1] with _ai_ = _i/N_ for _i_ = 1 _, ...N_ . Agent _N_ is thus the individual of highest ability _aN_ = 1. We normalize the before-productivity-shock rural wage _w_<sup>_R_</sup> to 1. We set the informal residency penalty on productivity _κ_ equal to .2, consistently with Field (2007). We choose a value of 3 for _σ_ . In developed economies for which state-ofthe-art studies control for sorting according to ability, an increase in city size of 10 percent causes productivity to increase by between .3 and .8 percent (Duranton, 2009). We thus choose a benchmark value of _γ_ of 11, which yields productivity increases of .4 to .7 percent depending on city size.<sup>29</sup> We choose a value of .2 for the rural wage elasticity to adverse shocks, _η_ , based on Jayachandran (2006) who estimated an rural wage elasticity of 17 percent to a weather shock. Wet set the probability of adverse income shock in rural area, _π_<sup>_P_</sup> , to .3 based on Damberg and AghaKouchak (2013), who report 12 episodes between 1979 and 2013 where more than 20 percent of the land in the Southern Hemisphere was under moderate to severe drought. This corresponds to a drought every three years or a yearly probability of a drought of approximately 1/3.<sup>30</sup> As regards the congestion cost parameters, we choose a value of 1 for _b_ and .3 for _δ_ . These numbers are based on the average of Kahn (2010) estimates, who reports city-size elasticities of .14, .25 and .49 for commute times, carbon monoxide pollution and for violent crime respectively. Our choice of _λ_ is based on Malpezzi (1999), who reports a median housing price-to-income ratio in 133 US MSAs of 4.5. Assuming that land represent two-thirds of total housing costs and considering that our period is 10 years, this leaves us with a value of .3.

For the formalization cost parameter, _μ_ , we choose a value of .3. There is a wide variety of situations in terms of formalization contexts, with costs ranging from a few percentages of land value to up to 100 percent or more of the value of the land (see Durand-Lasserve et al _._ , 2015). For _π_<sup>_G_</sup> we assume a value of .1 which is consistent with the high prevalence of conflicts in the cities of developing countries.

> 29In our model, wage elasticity with respect to urban labor force size is _γ._ (1+ _<u>L</u> L_ )<sup>.Since</sup><sup>_L_iscomprisedbetween</sup> 1 and 5, a value of _γ_ comprised between 10.4 and 16.6 ensures that wage elasticities are comprised between 0.03 and 0.08 in any state of the economy.

> 30.3 is a conservative estimate as other shocks affecting incomes such as conflicts, natural disasters or health crises can also occur (see Zceleczky and Yosef, 2014).

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