In the last post, we looked at the impact of labor market frictions on unemployment and the various economic theories and models available to measure them. But as with everything, we look beyond economics so this thread is about a system dynamics model of labor market frictions.

If we put all these models together Labor Market Friction is a function of verification, validation, search and march, and on-boarding and exit frictions. This captures not just the supply and demand of vacancies but also the project-level mapping within a company.

System Dynamics’ is a powerful framework for identifying, designing, and implementing solutions for complex challenges. Labour Market frictions are one such complex problem so we are going to use this tool to build a model to run sensitivity analysis.

The building blocks of system dynamics are:

1. Casual Linkages - Mostly non-linear cause and effect relationships.
2. Feedback Loops - Self reinforcing positive loops, while negative loops have a strong touch of control around the status quo, i.e. homeostasis.
3. Rates and Levels - Levels are state variables.
4. Structural-behavioral relationships

A capable system thinker can build a casual loop diagram that lists the requisite number of factors that affect their state variable of interest. Common Mistake: People try & build a system while the thumb rule is to model a problem - & then see what loops emerge.

That ends the intro to #SystemDynamics here is the draft of a casual loop diagram specific to frictions in the labor market we've been exploring.

The Labor Supply Chain and the origin of business cycles basically apply the stock management structure to the human resource supply chain. To begin, aggregate the firm’s labor into a single stock, which is increased by the hiring rate and decreased by the attrition rate.

As you can see there are two stocks

1. Vacancies
2. Labor

Labor ( HumanStock ) = INTEGRAL(Hiring Rate - Quit Rate, labor to).

Vacancies = INTEGRAL(Vacancy Creation Rate - Vacancy Closure Rate, Vacancies (t0)) and Vacancy Closure Rate = Hiring Rate

Note that there is no direct physical flow from the stock of vacancies to the labor force. The labor force is a stock of people, while the stock of vacancies, though measured in people, is information.

In this, the source for the hiring flow is assumed to be outside the boundary of the model. In reality, the pool of unemployed or potentially available workers often limits hiring. In these cases, the delay in filling vacancies will be longer and variable.

Because the labor market is not modeled, the vacancy creation rate is set equal to the desired vacancy creation rate but constrained to be nonnegative (vacancy cancellation will be added later)

The desired vacancy creation rate is formulated using the standard stock management structure: Vacancy Creation Rate = MAX(0, Desired Vacancy Creation Rate), Desired Vacancy Creation Rate = Desired Hiring Rate + Adjustment for Vacancies.

The firm seeks to close the gap between desired and actual vacancies over the time to Adjust Vacancies: Adjustment for Vacancies = (Desired Vacancies - Vacancies)/(Time to Adjust Vacancies).

Desired level of vacancies is the number that will yield the desired hiring rate given the firm’s belief about how long it takes to fill a position. Desired vacancies cannot be less than zero: Desired Vacancies = MAX(0, Expected Time to Fill Vacancies * Desired Hiring Rate)..

Realistically, beliefs about the expected time required to fill positions adjust slowly to changes in the actual time as labor market conditions change. The expected time to fill vacancies could be modeled using an information delay,

If we incorporate the layoff rate and vacancy cancellation rate we can make the system more robust.

These models give us a firm foundation to start building our model for the labor market frictions and their impact on the hiring rate.

In any subsequent iterations, we need to account for these factors -

• Fewer levels to define the problem, a simple structure for hiring is a good reference.
• Factor in the systemic nature of the economy. Some variables like avg period of employment
• Time units should be in weeks, as the average job search period is between a few weeks to some months.
• Need to better identify the physical and infrastructural elements in this system and create smaller causal loops for better understanding.
  • For example - the job search loop captures the behavior of those who want to be employed and the job screening loop captures the behavior of firms that are hiring.
• The stock of labor is central to the problem, add that as a shadow variable within the system, to allow sensitivity analysis.
• A beta model with Unemployment rate = Number of unemployed / Total Labor Force

This is our current state of research w.r.t modeling the labor market frictions. Why go through this process? we'll unravel in the next few threads. Ciao!