Inflation and unemployment
Inflation and unemployment
Recall the wage-setting relation:
\[
W = P^e \cdot F(u,z)
\]
So far, we have not explicitly assumed a form to the function F.
Let us start by a linear form:
\[
F(u,z) = 1 - \alpha u + z
\]
Inflation and unemployment
\[
F(u,z) = 1 - \alpha u + z
\]
where α captures the strength of the effect of unemployment on wages.
Then, the price-setting relation becomes:
\[
W = P^e (1 - \alpha u + z)
\]
Inflation and unemployment
And recall the price-setting relation:
\[
P = (1+m)W
\]
Using the wage- and price-setting equations together:
\[
P = P^e(1+m)(1 - \alpha u + z)
\]
… And this expression gives us a relation between the price level, the expected price level, and the unemployment rate.
Inflation and unemployment
In case we want to replace the price level by the inflation rate, π, and the expected inflation rate, πe, we end up with
\[
\pi = \pi^e + (m+z) - \alpha u
\]
What are the effects of:
A rise in the markup rate, m?
An increase in expected inflation, πe?
A decrease in the unemployment rate, u?
The Phillips curve
For a better understanding of what is to come, it will be convenient to include time indexes in our previous inflation equation:
\[
\pi_t = \pi_t^e + (m+z) - \alpha u_t
\]
where the subscript t refers to the present period; t-1 to the previous period, and so on.
The Phillips curve
In 1958, A. W. Phillips (1914–1975) empirically found that low rates of unemployment were associated with high rates of inflation, and high unemployment with low inflation.
This relationship has since been referred to as the Phillips curve.
The Phillips curve
From the Phillips curve equation:
\[
\pi_t = \pi_t^e + (m+z) - \alpha u_t
\]
Assume, first, a stable scenario, with no persistent change in the price level.
This can be represented by πe = 0.
Then, it becomes
\[
\pi_t = (m+z) - \alpha u_t
\]
The Phillips curve
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The Phillips curve
But then…
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The Phillips curve
Why did the original Phillips curve change?
We need to bring back πe.
Now,
\[
\pi_t^e = (1-\theta)\bar{\pi} + \theta \pi_{t-1}
\]
The Phillips curve
When θ = 1, we have:
\[
\Delta \pi_t = (m + z) - \alpha u_t
\]
where Δπt = πt - πt-1 is the change in the inflation rate.
High unemployment leads to decreasing inflation; low unemployment leads to increasing inflation.
This version is known as the accelerationist Phillips curve.
The Phillips curve
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The Phillips curve
![]()
The Phillips curve
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