definition of the 2011 Census. Land available for formal private development corresponds to all land that is not constrained for construction.<sup>34</sup> The amenities that we consider include natural amenities (such as slope and proximity to the ocean) as well as historical amenities (such as the proximity to the historical center). The data sets used are listed in Appendix C.4.

For the estimation of the model’s parameters (see below), we also use property price data extracted from the City of Cape Town’s geocoded data set on property transactions for 2011, as well as data on dwelling sizes made available to us by the City of Cape Town.

# _4.2. Estimation of the parameters of the model_

The estimation of the model is done in three steps. First, we choose a first set of parameters using available information, without solving the model. These include the minimum dwelling size _qmin_ , the size of subsidized plots _qFS_ and of backyards _Y_ , the construction lag τ, the physical and financial depreciation of housing θ and ρ, the interest rate δ, and the agricultural rent _RA_ . The minimum dwelling-size for formal housing is set at _qmin_ = 31 _._ 6 _m_<sup>2</sup> , which is the minimum dwelling size observed in formal neighborhoods. Backyards of subsidized houses have a size _Y_ = 70 _m_<sup>2</sup> . We choose the time lag of housing investment τ to be 3 years and the physical depreciation time of building stock θ to be 100 years, as in Viguié et al. (2014). The financial depreciation rate of the built capital is ρ=.05 (i.e., 5%). We allow the interest rate δ and the agricultural land rent _PA_ to vary with time. For δ, we use the annual values for South Africa in the World Development Indicator database (World Bank, 2016). We set the agricultural price at the city border _PA_ at 807 _Rands/m_<sup>2</sup> (annual) in 2011, which corresponds to the ninth decile in the sales data sets, when selecting only agricultural properties in rural areas. In the dynamic simulations, we assume that the agricultural land is constant in real terms and have its nominal value increase at the same rate as the average household nominal income.

Second, we calibrate wages, housing production function parameters, utility function parameters and amenities using partial relations from our model. Following Ahlfeldt et al. (2015) and Tsivanidis (2018), we recover the vector of wages ( _wic_ ) using data on job locations and residential locations. The scale parameter in the commuting formula, λ, is estimated using the distribution of residence-workplace distances in Cape Town. We identify the land elasticity of housing production ( _a_ ) and the scale parameter of housing production (κ) by regressing the log of equation (6) (see Appendix B for details) . We then consider equations (9) and (11), which relate utility levels to dwelling sizes, rents and amenities. The amenity term, _A_ ( **x** ) is expressed as a score for all locations, and specified as _A_ ( **x** ) = ∏ _i ai_ ( **x** )<sup>ν</sup><sup>_i_</sup> , where the _ai_ ( **x** ) are measures for each amenity type (see Appendix C.4), and ν _i_ are their marginal valuation, to be estimated. We simultaneously estimate the system of equations by maximum likelihood and recover parameters _{_ β _, q_ 0 _,_ ν _i}_ . Appendix C.4 presents the procedure in more detail.

Third, we calibrate the disutility parameters of informal housing ( _BIB_ and _BIS_ ) by running the entire model to replicate the share of households in informal settlements and backyard housing in the 2011 Census data.

> 34Restrictions include areas used for formal subsidized housing, informal settlements, protected natural areas, large economic or industrial infrastructures (such as the Cape Town airport). A detailed list of sources is presented in Appendix B.3.

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