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Archive for the ‘Phillips Curve’ Category

## 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.

Categories: Macro, Phillips Curve

## The Long-Run Phillips Curve

The Phillips Curve is a trade-off between inflation and unemployment that holds in the short run.

In the short run you can accept unemployment level $u1$ and inflation level $\pi 1$ at point A or you can move to point B where you lower unemployment to $u2$ at the cost of higher inflation level $\pi 2$.

However, remember the properties of the Phillips Curve:
– It is downward sloping.
– The whole curve shifts up if price expectations rise.
– The curve shifts down if price expectations fall.

If you try to lower unemployment with an expansionary policy, then you move up the Phillips Curve, and have higher inflation. But once workers adjust their expectations of prices upwards, the whole curve will start to shift upwards as well.

So you will get a situation like this:

There are a few things going on here:
1. The government has decided that it wants to lower the rate of unemployment below $u1$, which we will treat here as being the natural rate of unemployment or the NAIRU. So it has used an expansionary policy to move from A to B which meant in the short run, inflation rose from $\pi 1$ to $\pi 2$ as unemployment fell from $u1$ to $u2$.
2. Once workers and firms realised that inflation had risen, this changed price expectations, which meant that the whole Phillips Curve shifted upwards so we went from SRPC1 (Short Run Phillips Curve 1) to SRPC2.
3. Now if the government had abandoned its expansionary policy, then in the medium run output would return to the natural level of output which would mean employment would return to the natural rate of employment hence unemployment would return to the natural rate of unemployment. So we would be at position C. Inflation would now be constant again as we were at $u1$ which here we defined as the NAIRU, but it would be higher than it was at the beginning when we were at point A. Inflation has risen from $\pi 1$ to $\pi 2$.
4. If the government wanted to continue with its expansionary policy to keep unemployment down at $u2$ then it would have to move up the new Phillips Curve SRPC2, to get to point D, where inflation was higher still at $\pi 3$.

Notice how we have a short-run movement up the black curve from A to B, but then if the government wants to maintain the policy for longer, we have a steeper blue curve from A to D. If they wanted to carry on this expansionary policy even longer, then we would have a steeper curve still – the government would have to accept an even higher rate of inflation in order to keep unemployment below the natural rate.

And even if they did, they would be fighting a losing battle, as eventually unemployment would return to the natural rate anyway. The economic intitution here is that basically you are trying to ‘cheat’ the supply conditions of the economy. To lower unemployment below the natural rate of unemployment, you have to increase output above the natural level of output. Now as the economy can’t really sustain this level of output, you will get inflation, this always happens when there is an excess of demand over supply, demand for production is outstripping the capacity of the economy to produce it and so this will drive up prices and drive up wages for a time, but in the end workers cannot produce the impossible, and output will slip back to the natural level eventually, just with a lot of price rises until then.

This is why in the long run, the Long Run Phillips Curve is a vertical line at the NAIRU.

The moral of the story is, you can’t cheat the supply conditions of the economy forever. You can only use the ‘trade-off’ relationship between inflation and unemployment which is held in the Phillips Curve, in the short run, if you try to sustain it for too long unemployment will go back to the natural rate anyway, but you will get a lot of inflation along the way. If you want a permanent reduction in unemployment, you have to change the supply conditions.

Categories: Macro, Phillips Curve

## The NAIRU

Here we’re going to work from two concepts, the natural rate of unemployment and the Expectations-Augmented Phillips Curve.

The natural rate of unemployment is the rate of unemployment where the real wage implied by price-setting equals the real wage implied by wage-setting. The natural rate of unemployment basically corresponds to a natural rate of employment which is associated with the amount of workers needed to produce a natural level of output in the economy (which depends on supply-side conditions in the economy). This was basically the story of the trade-off between inflation and unemployment.

When unemployment is lower than the natural rate of unemployment, then it means output is above the natural rate of output, and more workers need to be hired to produce the extra output.

Because unemployment is now lower than the natural rate, it means workers are becoming more scarce, so firms need to pay more wages to hire them and keep them from moving on to rivals. The labour market becomes more of a ‘sellers’ market – the sellers of labour (workers) have the advantage because workers are scarce and jobs are abundant, so wages are bid up. This leads to an increase in firms’ costs, which are passed on to consumers through the price-setting equation. The increase in prices then leads to an increase in expectations of future prices being higher, which will transfer into higher wage demands at the next round of wage bargaining. So the wage-price spiral causes prices to rise faster.

When unemployment is higher than the natural rate, you have the opposite situation, it means output is below the natural level of output and fewer workers are needed. The labour market is a ‘buyers’ market, the buyers of labour (firms) have the advantage because jobs are scarce and unemployed workers are abundant. This will drive down wages and so firms can pay only small wage increases or maybe no increases at all, which keeps their costs from rising and allows them to keep prices lower (to compete with their rivals). This will act as a brake on inflation, so prices will either be stable, rise slowly (more commonly), or if unemployment is very high compared to normal, prices can be driven lower (deflation).

So we have a basic story:
– When unemployment is below the natural rate of unemployment, inflation will rise.
– When unemployment is above the natural rate of unemployment, inflation will fall.

So that implies that when we are at the natural rate of unemployment, inflation will stay constant. This is why the natural rate of unemployment is often called the Non-Accelerating Inflation Rate of Unemployment, or the NAIRU.

We can derive an expression for the natural rate of unemployment from the Expectations-Augmented Phillips Curve: $\pi_t - \pi_{t-1} = (\mu + z) - \alpha u_t$

When inflation is staying constant from one year to the next, then $\pi_t - \pi_{t-1} = 0$ so $0 = (\mu + z) - \alpha u_n \Rightarrow \frac{(\mu + z)}{\alpha} = u_n$

I am using the notation $u_n$, the natural rate of unemployment, for the case where we have a specific $u_t$ such that inflation does not change. The equation above tells us that the NAIRU depends on the profit mark-up, the ‘catch-all’ capturing conditions in the labour market, and the parameter which shows the responsiveness of inflation to unemployment in that economy.

If we have figures over time for an economy’s inflation and unemployment rates, we can form an estimate as to the specific rate of unemployment that would make inflation stable, and so get an estimate of the NAIRU for that economy. Of course if we observe data over a long time period we may find that our estimate of the NAIRU changes, which suggests that supply conditions in the economy are different, ie those parameters above are changing.

$u_n = \frac{(\mu + z)}{\alpha} \Rightarrow \alpha u_n = \mu + z$ so we can substitute this in to $\pi_t - \pi_{t-1} = (\mu + z) - \alpha u_t$ to get $\pi_t - \pi_{t-1} = \alpha u_n - \alpha u_t$.

This can be simplified to $\pi_t - \pi_{t-1} = \alpha (u_n - u_t)$ which we can flip round to give $\pi_t - \pi_{t-1} = -\alpha (u_t - u_n)$.

This is probably the most common and useful form of the Phillips Curve equation. It says that the change in inflation is equal to a negative parameter multiplied by the difference between unemployment in year t, and the natural rate of unemployment.

Categories: Macro, Phillips Curve

## The Expectations-Augmented Phillips Curve

Really any form of the Phillips Curve which has an expression for “expected inflation” in it is an “Expectations-Augmented Phillips Curve” so most of the ones you will see in use today are expectations-augmented. But the early forms of the Phillips Curve didn’t have anything to take account of expectations.

When the Phillips Curve was first ‘discovered’, it was presented in an equation along these lines: $\pi_t = \pi^e + (\mu + z) - \alpha u_t$ where expected inflation was equal to 0, so it was $\pi_t = (\mu + z) - \alpha u_t$. The reason expected inflation was seen as 0 was because prior to the 1970s, inflation didn’t have much of a pattern to it, prices jumped up and down, you had periods of deflation, so agents in the economy didn’t have a very good reference point for forming expectations of inflation from one year to the next.

But during the 1970s, inflation patterns started to change. Instead of jumping around erratically, inflation started to become persistent, ie high inflation one year was a pretty good indicator of a similarly high rate of inflation the next year. Agents in the economy were starting to show evidence of adaptive expectations, ie they based their expectations on inflation this year, on what inflation was last year. In the context of wage-bargaining, this would mean that if workers saw inflation last year was say 6%, they would start their negotiations using that as a reference point.

The Phillips Curve was updated in the form of an Expectations-Augmented Phillips Curve to take account of these adaptive expectations. Setting $\pi^e = \pi_{t-1}$ you get something like this:$\pi_t = \pi_{t-1} + (\mu + z) - \alpha u_t$.

You can rearrange this to $\pi_t - \pi_{t-1} = (\mu + z) - \alpha u_t$. This gives you a key point of the Expectations-Augmented Phillips Curve, it shows the change in inflation from one year to the next in terms of unemployment.

Categories: Macro, Phillips Curve

## An equation for the Phillips Curve

As you do more economics you will start recognising a Phillips Curve equation, it often comes up in slightly different forms, the basic features are always the same, it will be an expression which expresses the rate of inflation in year t, in terms of things like the unemployment rate in year t, the inflation rate in year t-1, the natural rate of unemployment, and a parameter in there which shows how responsive inflation is to unemployment. Often you will get a (+ supply shock) bit stuck on the end.

As usual on this blog I use Olivier Blanchard’s notation, but if you get used to this you will be able to recognise the Phillips Curve as presented in different forms.

Remember the basic idea of the Phillips Curve is a relationship between inflation and unemployment.

You can express it in an equation like this: $\pi_t = \pi^e + (\mu + z) - \alpha u_t$

$\mu$ and $z$ have come from the price-setting and wage-setting process. $\mu$ is the mark-up which firms put over and above labour costs in their price-setting, to cover non-labour costs and also, depending on the amount of market power the firm has, a profit margin. $z$ is the ‘catch-all‘ variable referring to conditions in the labour market that influence wage-bargaining power outside of the rate of unemployment (trade union power, employment legislation etc). These two variables don’t change much in the short run so they generally get treated as being static in the short run but they are in the equation because any significant changes in these factors will change the position of the Phillips Curve.

So this equation is saying:
Inflation in year t depends on expected inflation in year t, the pricing mark up, conditions in the labour market and the rate of unemployment in year t. Because the mark up and labour market conditions are treated as static it is really expected inflation and the rate of unemployment that matters here. $\alpha$ is a parameter which shows the responsiveness of inflation to unemployment.

Categories: Macro, Phillips Curve

## The trade-off between inflation and unemployment

The basic idea behind the Phillips Curve is that of a ‘trade-off’ between inflation and unemployment. The trade-off generally holds in the short-run but not in the medium-run. I think the Phillips Curve becomes easier to understand if you start from the concept of a natural rate of unemployment, which will be the opposite of the rate of employment that corresponds to a natural level of output in the economy. This natural level will be determined by supply factors.

When unemployment is lower than the natural rate of unemployment, then it means output is above the natural rate of output, and more workers need to be hired to produce the extra output. This is what will happen if the government uses some form of expansionary policy (fiscal or monetary) to stimulate the economy and push the level of output up above its natural level.

Because unemployment is now lower than the natural rate, it means workers are becoming more scarce, so firms need to pay more wages to hire them and keep them from moving on to rivals. The labour market becomes more of a ‘sellers’ market – the sellers of labour (workers) have the advantage because workers are scarce and jobs are abundant, so wages are bid up. This leads to an increase in firms’ costs, which are passed on to consumers through the price-setting equation. The increase in prices then leads to an increase in expectations of future prices being higher, which will transfer into higher wage demands at the next round of wage bargaining. So the wage-price spiral causes prices to rise faster.

When unemployment is higher than the natural rate, you have the opposite situation, it means output is below the natural level of output and fewer workers are needed. The labour market
is a ‘buyers’ market, the buyers of labour (firms) have the advantage because jobs are scarce and unemployed workers are abundant. This will drive down wages and so firms can pay only small wage increases or maybe no increases at all, which keeps their costs from rising and allows them to keep prices lower (to compete with their rivals). This will act as a brake on inflation, so prices will either be stable, rise slowly (more commonly), or if unemployment is very high compared to normal, prices can be driven lower (deflation).

Remember that although classical economic theory allows for prices to be flexible up and downwards, in practice, you don’t tend to see prices falling downwards very often unless there is a very bad recession. Most workers will be on strike at the first sniff of a nominal pay cut, so when wages need to adjust downwards they tend to do so over a few years, with pay freezes or below inflation pay rises, so that wages end up falling in real terms over a few years. So we don’t tend to equate low unemployment with rising prices and high unemployment with falling prices, in practice it is more like low unemployment means fast rising prices (high inflation) and high unemployment means slowly rising prices (low inflation).

This inverse relationship between inflation and unemployment allows the option of a trade-off (in the short run) for policy makers between inflation and unemployment, it says they can reduce unemployment temporarily by stimulating the economy, but the downside is that it will bring in extra inflation. This is the basis behind the idea of the (short-run) Phillips Curve.

Here you have two choices. In the short run you can accept unemployment level $u1$ and inflation level $\pi 1$ at point A or you can move to point B where you lower unemployment to $u2$ at the cost of higher inflation level $\pi 2$.

The Phillips Curve is downward sloping because unemployment is negatively related to inflation, so a change in unemployment or a change in inflation is represented by a movement along the Phillips Curve. But the wage-setting relation also included expected prices as well as the rate of unemployment. When expected prices are higher, wage demands will be higher at all levels of unemployment. This would be represented by shifting the whole Phillips Curve up. Changes in expected prices shift the Phillips Curve up or down.

So to sum up, the (short-run) Phillips Curve is downward sloping.
The whole curve shifts up if price expectations rise. This has an important implication, because it means that when you move up the curve, and have higher inflation, then if workers adjust their expectations of prices upwards, it means you won’t just move up the curve to get your lower unemployment, but the curve will start to shift upwards as well.
The curve shifts down if price expectations fall.

Categories: Macro, Phillips Curve