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## Okun’s Law

Okun’s Law basically tells you how changes in output cause changes in unemployment.

Before when we’ve looked at the concept of the natural rate of unemployment we’ve talked about it in terms of the natural level of output.

The intuition has basically been:

– At the natural level of output, there is a certain number of workers who need to be employed to produce that output. So there is a natural rate of employment that corresponds to the natural level of output.

– If there is a natural rate of employment, there is obviously a corresponding natural rate of unemployment, eg if you need 95% of those eligible and searching for work to be employed to produce the natural level of output, then there will be a natural rate of unemployment of 5%.

– If output rises over the natural level of output, then you need more workers, so employment rate rises, and unemployment rate falls below the natural rate of unemployment. If output falls below the natural level of output then you need fewer workers so employment rate falls and unemployment rate rises above the natural rate of unemployment.

Okun’s Law tells you how output relates to unemployment. It isn’t a one for one relationship, unemployment responds less than one for one to changes in output. There are a few reasons for this:

1. In any firm, there are usually a set number of employees that the firm will need regardless of output. If a firm is in the construction industry, then when demand falls they might lay off builders and engineers because there is no work for them, but the finance department might still have roughly the same amount of work to do even though the figures don’t look as good. Equally if production expands, they will hire more builders and engineers and keep similar numbers in the finance department.

2. Recruitment costs are expensive anyway, so firms might engage in labour hoarding. This means that rather than just hiring and firing at will, when demand drops off, they might hold back before making too many redundancies, preferring to pay workers to not do much work, in the hope that demand will pick again quickly. If they make a lot of redundancies then not only are they paying redundancy payments but then will have to advertise, go through recruitment processes etc, when it picks up again, so if the fall in demand is short term that could end up more costly than just hanging on to workers in the first place. The more strict the redundancy laws in a country the more this is likely to happen. Labour hoarding is good in the sense that it means unemployment does not rise so much when there is a recession, but the flip side is that when the economy returns to growth, unemployment won’t fall so quickly because the firms can expand production without hiring more, because they had kept workers on the payroll anyway.

3. When the economy starts looking better, labour force participation increases. This means people who previously weren’t looking for work, start looking again. A good example of this is people coming out of higher education – when the economy is bad you get students going on to do Masters degrees or going off travelling rather than looking for work, so they don’t count on the unemployment figures, as the unemployment rate is given by the percentage of those looking for work who can’t find work, rather than just the percentage of the population who can’t find work. When the economy improves, more graduates will apply for jobs straight away rather than going on to postgrad degrees.

There’s another element that you have to factor in with Okun’s Law, it’s that the labour force tends to grow over time, as population grows, higher birth rates, immigration and so on. So in order to keep the natural rate of unemployment constant, you will need the natural level of output to be growing in proportion with labour force growth. This is why Okun’s Law doesn’t think in terms of a natural level of output but a normal growth rate of output.

Okun’s Law can be expressed in this form:

$u_t - u_{t-1} = -\beta (g_{yt} - \bar{g_y})$.

This is saying that the change in unemployment (unemployment in year t minus unemployment in year (t-1) )is equal to a negative parameter, $\beta$ which is less than one, which shows the responsiveness of unemployment to output, multiplied by the difference between output growth in year t and the normal growth rate of output. The parameter is negative because it is saying when output growth goes above the normal growth rate, then unemployment will fall. When output growth is below the normal growth rate, unemployment will rise. That means when output growth is on the normal growth rate then unemployment will be stable.

We can combine Okun’s Law with the Phillips Curve to get a relation between output and inflation.

The Phillips Curve equation was $\pi_t - \pi_{t-1} = -\alpha (u_t - u_n)$. We can rearrange Okun’s Law to $u_t =u_{t-1} -\beta (g_{yt} - \bar{g_y})$ and insert this into the Phillips Curve equation to get:

$\pi_t - \pi_{t-1} = -\alpha (u_{t-1} - u_n - \beta (g_{yt} - \bar{g_y}))$.

This gives us a relation between output and inflation.