# **4. Data sources and parameter estimation**

We apply the theoretical model to a grid of 100 x 80 km that largely encompasses the existing urban footprint of Cape Town. The grid is subdivided into 500m x 500m cells. Each cell represents a location **x** in our theoretical framework. Because the different data sets that we use are available at different spatial resolutions, we either spatially aggregated or disaggregated the information using cell areas as weights.

We make use of a variety of data sets as direct inputs into the model and in order to calibrate parameter values. More specifically, the inputs that are fed into the model consist of the total population in the city at an initial date and its decomposition into income groups ( _Ni_ ), the average income and employment rate (χ _i_ ) by income group, land use constraints ( _Lh_ ( **x** )), and the monetary and time cost of commuting (τ _m_ ) and (δ _m_ ) between cells and job centers, for 5 different modes (walking, minibus/taxi, train, bus, private car).<sup>30</sup> Exogenously chosen parameters include the size of subsidized housing plot ( _qFS_ ), the time lag of housing investment (τ), the housing stock depreciation parameter (θ), the financial depreciation rate of built capital (ρ), and the agricultural land rent ( _PA_ ). Estimated parameters include the gravity equation parameter (λ), wages at workplace ( _wic_ ), housing consumption elasticity in the utility function (β), the minimum housing consumption ( _q_ 0), the land elasticity of housing production ( _a_ ), the scale parameter of housing production (κ), and the index value of amenities _A_ ( **x** ). The disutility parameter of informal housing ( _B_ ) is calibrated to reproduce the distribution between housing types generated by the model.

Below, we describe in more detail data sources and the calibration process.

# _4.1. Data sources_

The spatial distribution of population is taken from National Censuses for the years 2001 and 2011. We define the four income groups by choosing income-group thresholds such that only the lowest income group is eligible for subsidized housing programs, and so that the two highest income groups are not observed to reside informally (see Appendix A for details).<sup>31</sup> We use the transport model used by the City of Cape Town to retrieve transport times between pairs of transport zones for each transport mode and job locations.<sup>32</sup> We also use aggregate statistics on modal shares and residence-workplace distances in Cape Town, that are derived from Cape Town’s 2013 Transport Survey.

Land availability is defined for each housing type. Areas of subsidized housing are identified from the cadastre of the City of Cape Town.<sup>33</sup> The area available for backyard housing is estimated as the yard size of these units. Informal settlement areas are obtained from the Enumerator Area

> 30For simplicity, in what follows, we do not index these variables with time.

> 31 The Census captures annual income, which we assume reflects the employment rate χ _i_ . Households eligible for subsidized housing are the ones with an annual income (χ _iwi,c_ in the model) below the threshold of R38,200.

> 32The origin-destination matrix is produced by the City of Cape Town’s four-step travel demand model, last updated in 2013 using the EMME/2 software. The model was designed by INRO Consultants at the University of Montreal and adopted by the City of Cape Town in 1991. The model implements an equilibrium route assignment based on the distribution of trip origins and destinations in relation to the transport network. The model is calibrated by means of the General Household Transport Survey, on-board surveys and cordon counts.

> 33This corresponds to the category “Single Residential 2 - Incremental Housing”.

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