Economic Transition Model

Employment is classified by the user into employment sectors based on aggregations of Standard Industrial Classification codes. Typically 10 to 20 sectors are defined based on the local economic structure. Aggregate annual forecasts of economic activity and sectoral employment are exogenous to UrbanSim, and are used as inputs to the model. These forecasts may be obtained from state economic forecasts or from commercial or in-house sources.

The Economic Transition Model compares these exogenous forecasts of aggregate employment by sector with the UrbanSim employment data, computes the sectoral growth or decline from the preceding year, and either queues jobs to be placed in the employment location choice model for sectors that experience growth, or removes jobs from the database in sectors that are declining. In cases of sectors with employment growth, new jobs are sampled from existing jobs of the same sector with location identifier (grid_id) set to uplaced. While in cases of sectors with employment loss, jobs will be randomly picked to be removed with probability proportional to the number of jobs in the sector. The jobs that are removed vacate the space they were occupying, and this space adds to the pool of vacant space and becomes available for other jobs to occupy in the employment location choice model. This procedure keeps the accounting of land, structures, and occupants up to date.

New jobs are not immediately assigned a location. Instead, new jobs are added to the database and assigned a null location, to be allotted by the Employment Location Choice Model. The model proceeds as follows.

Calculate the number of jobs to be added or removed (a scalar).

$$\Delta J_{st} = C_{st} - \vert J_{s(t-1)}\vert,$$ (1)

where:

$\Delta J_{st}$	is the change from year $t-1$ to $t$ in number of jobs in sector $s$,
$C_{st}$	is the exogenous total employment in sector $s$ in year $t$,
$J_{s(t-1)}$	is the set of all jobs in sector $s$ in year $t-1$,
$\vert.\vert$ returns the number of elements in (cardinality of) the set.

The set of all jobs at year $t$ is defined by one of three cases. Either it is the union of the previous year's jobs and some newly created jobs or the difference between the previous year's jobs and some number of jobs to remove.

$$J_{st} = \begin{cases} J_{s(t-1)} \cup F_{st}, &\text{if $\Delt... ...t} = 0$},\\ J_{s(t-1)} - F_{st}, &\text{if $\Delta J_{st} < 0$}, \end{cases}$$ (2)

where:

$F_{st}$

is the set of jobs in flux in sector $s$ in year $t$,

The set of jobs in flux $F_{st}$ is a set of jobs being added to or removed from sector $s$ in year $t$. It is uniformly sampled from jobs set $J_{s(t-1)}$.

$$F_{st} = \{\, j \in J_{s(t-1)} \,\},$$ (3)

and

$$\vert F_{st} \vert = \vert \Delta J_{st} \vert.$$ (4)

The cardinality of flux jobs is equal to the absolute value of the change in number of jobs.

If we are adding new jobs, then jobs in $F_{st}$ will be unplaced from their current location by changing their location attribute to a pre-defined constant for unplaced.

This set of jobs will be added to the set of unplaced jobs in the previous year and will be allotted to locations by the Employment Location Choice Model later.

$$J^U_{st} = \begin{cases} J^U_{s(t-1)} \cup F_{st}, & \Delta J_{st} > 0,\\ J^U_{s(t-1)}, & \text{otherwise},\\ \end{cases}$$ (5)

where:

$J^U_{st}$

is the set of jobs that do not have a location match at time $t$.

If we are removing jobs, then those jobs in $F_{st}$ will be removed from jobs set $J_{s(t-1)}$, and the space they occupied will be released and become available to unplaced jobs for location choice.

$$S_{lt} = \begin{cases} S_{l(t-1)} + s^l_j \mid j \in F_{st}, (j,... ... (j, l) \vert j \in F_{st}, (j, l) \in M^l_{j(t-1)} \}\, \Delta J_{st} < 0, \\$$ (6)

where:

$S_{lt}$	is the available space for location (gridcell) $l$ at time $t$,
$s^l_j$	is the space job $j$ occupies at location $l$,
$M^l_{j(t-1)}$ is the pair of job/location matching job $j$ to location $l$ at time $t-1$.

So far we assume the space a job takes up depends on space utilization ratio of its location $r_l$.

$$s^l_j = r_l$$ (7)