# Firms-Jobs Submodule of SMARTPLANS

The jobs-firms submodule predicts the total number of jobs, E_{iG}(t+1), by industrial sectors G in each zone i at time t+1. As in the case of the population-household submodule, zonal future predictions of jobs are based on two process: 1) firm mobility and 2) firm location choice behavior. While the utilized models to describe and imitate these processes consider the behavior of firms, the user can use jobs as proxy for firms. That is, if the user specifies models that predict the mobility and location choice of firms, the results can be converted into jobs by applying exogenous zonal average employment sizes to the predicted firms. Alternatively, the user can model jobs directly to avoid applying exogenous zonal employment sizes.

### 1. Employment Mobility Model

This model is primarily used to identify the number of jobs that belong to industry sector G that stayed in zone i by time t+1. SMARTPLANS allows the user to estimate the number of jobs staying in zone i by either using a : (1) Binary Logit model or (2) Linear Regression model.

A binary logit model will predict the probability, PS_{iG}, of jobs in industry G staying in zone i as follows:

where betas are parameters associated with significant factors that pull the jobs from industry G to stay in zone i by time t+ 1. In this case, the predicted number of zonal jobs in sector G that stayed in zone i by time t +1 is calculated as follows:

Alternatively, the user can choose to use a linear regression model to predict the number of zonal jobs in sector G that stayed in zone i by time t+1. In such case, the mobility model can take the following form:

where betas are the estimated parameters and X’s are the significant covariates pertaining to the characteristics of the zones where the jobs of sector G are staying.

### 2. Employment Mobility Model

The employment location choice model focuses on predicting the probability that a job in a given class C of industry sector G will move to zone i between time t and t+1. This location choice model is implemented in SMARTPLANS using the MNL formulation, that is:

where V_{iG|C} is a linear-in-parameter systematic utility function observed by class C of industry type G and attributes of the zone i. The user can divide the allocation of employment in a specific industry G by class C. These classes could be firm and/or geography specific. That is, the user can define location choice models based on the size of the firm (e.g., small vs. large) and/or based on geographic location (e.g., CBD firms vs. Inner Suburbs vs. Outer Suburbs). Using class C will require the user to provide exogenous shares of the different classes, PC|G, such that the sum of all proportions will add up to 1.

### Zonal Job Simulation Formulas

Once the location choice probabilities are calculated, the total number of jobs to move into zone i can be predicted as follows:

Where ME_{G}(t+1), which represent the total number of jobs seeking a location to move into at time t + 1, is calculated as follows:

The total number of predicted jobs of sector G that will be in zone i at time t+ 1 are then calculated as follows:

Finally, total jobs in zone i at time t + 1 are then calculated by adding the predicted zonal values from all modeled industrial sectors, that is: