Simulation Model

We start with a random set of agents enjoying a randomly drawn personality dis- tribution with a mode drawn from of a uniform distribution between zero and one. Consequently, random tasks are generated from either a uniform distribution or distributions that are skewed to the left or to the right. In order to create unem- ployment, we generate a number of tasks (j) that is smaller than the number of agents (n) in the society and hence the difference of the two absolute numbers gives us the rate of unemployment that will exist in each time cycle.

U nemployment=n−j (2.1)

The number of agents and tasks is kept constant throughout all cycles of the simulation, hence making the unemployment rate constant throughout. One could think of this as the natural rate of unemployment. What varies is the rate of task separation, i.e. the number of agents losing their tasks within a time cycle. This will be explained further below.

Once the agents and the tasks have been generated, we allocate agents to tasks. The allocation process is intended to capture key features of the job-filling process in the real world. Each task is advertised consecutively and for each task the agent that is best for it is found, according to their efficiency at performing the said task. Specifically for each task j we perform the following maximisation:

arg max (αi,βi)

f(j, αi, βi) (2.2)

wherej is the task for which the best agent is being searched for andαi and

βi are the corresponding beta parameters from each available agent being consid-

Figure 2.3: Task Allocation Example

distribution.3

Once the best agent for the task is found this task is considered filled and the agent taking up the task is removed from the available pool of agents for the next task to be filled. This process carries on until all available tasks are filled with the best available agent in each case. Figure 2.3 illustrates five random agents’ personality distributions. The dotted lines indicate the tasks each of these agents have been allocated to. The agent with the green distribution is unemployed and for this reason has no task indicated in the figure. It is important to note that we do not allow for multiple agents to take up the same task.

Once all the available tasks get filled, as explained above, we calculate indi- vidual efficiency and subjective well-being values for each agent. The two measures are given by:

Ef f(xi, αi, βi) =f(xi, αi, βi) (2.3) SW Bi= Ef f(xi, αi, βi) Ef f(x∗_i, αi, βi) (2.4) 3 Beta Distribution PDF:f(x, α, β) = xα−_B1(1_(α,β−x₎)β−1

where xi corresponds to the task each agent i is performing, x∗i represents

the optimal task for each agentiand the functionf(.) is the Beta Distribution PDF (see footnote 3).

Equation 2.4 depicts the calculation made to define the subjective well-being of each agent following from the explanation in the previous section. The closer the job performed is to the peak of their distribution, the greater is their subjective well-being. The range of values for this measure varies between 0 and 1.

The unemployed agents are assumed to be unproductive and hence receive Ef fi equal to zero. All unemployed agents are subsequently replaced by new ran-

dom agents who will be competing in the next task allocation cycle. Unless stated otherwise, the replacement agents are drawn from the uniform distribution.

The number of tasks lost within each cycle varies. The intuition behind this is as follows. Consider an economy which goes through various business cycles. During booms the number of jobs lost are significantly lower than during recession- ary periods. The varying number of tasks lost across different cycles is considered to be a rough approximation of this phenomenon. The probability of each agent losing their task is dependent on their efficiency. The higher efficiency an agent enjoys, the lower is the probability of her losing her allocated task. This allows for well-performing personalities to survive in the population. At the same time this specification allows for some random chance of agents losing their task even if they are good at it. More precisely, once the welfare levels of all agents are computed, they are normalised to be in the range (0,1) using:

Ef f_inorm= Ef fi−Ef f

min

Ef fmax (2.5)

This normalised welfare level of each agent, Ef f_inorm, is then weighted ac- cording to each individual’s subjective well-being and the resulting number is the probability that they will enter an insecure state in their task. Specifically, this

probability is given by:

qi=SW Bi∗Ef finorm (2.6)

This weighting of individual efficiencies to determineqiis included to account

for the fact that if individuals do not feel like they are a good fit to their job this might cause them distress. Given the recent evidence by Oswald, Proto and Sgroi (2015) we believed that it was a fair assumption to make that lower subjective well-being could be detrimental to individual productivity and efficiency at a task - leading to lower likelihood of retaining your job.

Once in the insecure state, agents are offered a further chance to retain their jobs as they will lose their task with probability 10%. This extra chance was included in the simulation model to mirror real life situations where individuals will be warned that their position is in danger but are given a chance to validate themselves, akin to how football managers are given ‘ultimatums’ when their teams are performing below par.

Once the tasks that have become available after task separation are deter- mined, then the task separated and newly introduced agents in the system compete for these. The way allocation works is exactly as explained above, where for each available task the best available agent is selected and so on. We do not allow for agents that lose a task to get re-allocated to it within the same cycle. If this is allowed then we end up having agents losing and being re-allocated to the same task in the same cycle, which did not seem to be a plausible reflection of real life.