### Spanish Unemployment – No Rapid Road Down

I saw this graph in the article ‘Spain is Beyond Doomed‘ by Matthew O’Brien at The Atlantic. It shows the dramatic upswing in unemployment in Spain during the past few years, especially among those who have been unemployed for 2 or more years.

*(click image to enlarge)*

As a chemical engineer, though, one thing that struck me about the graph is that it resembles a simple model of the behavior of the flow of liquid through a leaky pipeline. Say that we have a pipeline made of segments representing people who have been unemployed for a certain number of months. Each month, everyone in each segment can find work (but not yet start working) and thus, leak out of the pipeline into a bin called ‘Already Found Work’. One month later, these people will join the ranks of the Employed. Alternatively, if you do not leak out of the pipe, you simply advance to the next step down the line.

Also, each month each Employed person has a chance of becoming unemployed, thereby getting put into the start of the pipeline.

Here’s what the model looks like visually:

If we assume:

(1) that the ‘**finding work probability’** is such that 2/3rds of the people who enter the blue, red and green sections (that is, 0-6 months, 6-12 months unemployed, and 1-2 years unemployed) leak out at some before reaching the end of that section,

(2) that the ‘**becoming unemployed probability**‘ – the chance of an Employed person becoming unemployed each month – is 1%, and

(3) Anyone in the purple (2+ years unemployed) section has a 5% chance per month of finding work,

then the behavior of the model looks like what we see in the graph below:

This scenario also assumes that, 20 months after the start of 2005 the ‘**becoming unemployed probability’** doubled over the next 20 months from 1% to 2%. Over the same time period, the ‘**finding work probability**‘ dropped (for everyone unemployed less than 2 years) from 2/3rds to 1/3rd.

The model does not fit the observed data precisely, but it does not take into account things like emigration, an aging population, dropping out of the labor force and differences in education, experience, age and gender.

If these ‘becoming unemployed’ and ‘finding work’ probabilities, starting right now – essentially May 2013 – return to their previous values (1% and 2/3rds) over the next 20 months, then we can see from the graph that it might still take years for Spanish unemployment to return to anything resembling pre-crash levels. In this scenario, it would take until 2015 for unemployment to drop below 20%.

These probabilities are shown in the graphs below:

*(click image to enlarge)*

In the graph below, I show the total unemployment rate under this ‘gradual restoration’ scenario and also for the case where conditions do not deteriorate any further from the current parameter values of 2% and 1/3. If the current parameters persist, then unemployment should level out at just under 30%.

*(click image to enlarge)*

It is sort of a truism that if conditions do not deteriorate any further, then the unemployment situation should not get worse. But this simple model suggests that, without a recovery of the ‘becoming unemployed probability’ and the ‘finding work probability’, the unemployment rate might not go below 20% at any foreseeable time in the future.

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