Land Development Model of SMARTPLANS

The land development model of SMARTPLANS predicts the total amount of developed floorspace that is available to be occupied by land use activities type L. Land use activities could represent households, people, or firms, etc. Let FSiL(t) be the amount of floorspace of type L in zone i. Also, let FSL(t+1) be the region-wide total amount of floorspace type L. The predictions for the land development model depend on running two integrated models:

  1. Building demolition model: This model is used to calculate the probability (or proportion), PDiL, of certain floorspace L being demolished in zone i at time t + 1. The probability is formulated as the following logistic regression model:

    where betas are the estimated parameters to be inputted in the model for type L, and Xki is a set of k zonal characteristics found to have significant influence on the likelihood of that floorspace L being demolished.

  2. Floorspace location choice model: This model is used to calculate the probability of allocating developed floorspace type L to zone i at time t + 1. To account for the heterogeneity that might exist within the one type of floorspace, the location choice model is setup in a way that allows the user to define certain classes C within type L. Here, the user must specify the share P/C|L for each class C within L exogenously. The logit probability for class C belonging to floorspace L to be allocated to zone i at time t + 1 is formulated as follows:

    where ViL|C is a linear-in-parameter systematic utility function observed by class C of land use type L and attributes of the zone i.

Floorspace Simulation Formula

Floorspace of type L in zone i at time t + 1 is calculated as follows:

where FRiL(t+1) represents the amount of floorspace type L in zone i that was not demolished by time t + 1, FNiL(t+1) is the amount of newly developed floorspace type L in zone i at time t +1, PFiL|C is the previously defined logit probability used to allocate newly developed floorspace that is available to class C within type L to zone i at time t +1, PC|L is an exogenous value representing the share of class C within type L. The amount of floorspace type L that was not demolished by time t + 1 is calculated as follows:

where PDiL is the probability of floorspace type L being demolished in zone i by time t +1 (outcome of the building demolition model). Finally, FNiL(t+1) is calculated as follows: