Home > Macro, Monetary Policy > Disinflating the economy 2 – the role of expectations

Disinflating the economy 2 – the role of expectations

December 3, 2011

The model of disinflation I created here relied on the concept of using unemployment to place downward pressure on inflation through tightening conditions in the labour market.

As such it was using a Phillips Curve like this: $\pi_t - \pi_{t-1} = -\alpha (u_t - u_n)$. This is an Expectations-Augmented Phillips Curve that assumes that agents in the economy base their expectations of inflation one year on what inflation was the previous year, ie $\pi^e = \pi_{t-1}$.

What about if we don’t make that assumption? Without that assumption, expected inflation replaces the term for inflation last year, so you have a Phillips Curve of $\pi_t - \pi^e = -\alpha (u_t - u_n) \Rightarrow \pi_t = \pi^e -\alpha (u_t - u_n)$. Now we can consider what would happen if agents expectations were based on something other than just inflation last year.

This economy has the following properties:

Normal output growth rate is 2.5%: $\bar {g_y} =0.025$.
Natural rate of unemployment is 5%: $u_n = 0.05$.
Okun’s Law parameter is 0.4 so $u_t - u_{t-1} = -0.4(g_{yt}-0.025)$.
Phillips Curve parameter is 0.75 so $\pi_t - \pi_{t-1} = -0.75(u_t - 0.05)$.

Lets say we start off in Year 0 with a medium run equilibrium, with nominal money growth at 7%. Inflation equals nominal money growth minus the growth rate of output so Year 0 inflation is 0.07 – 0.025 = 0.045, we are starting off with inflation at 4.5%.

Suppose the target is to bring inflation down to 2.5%, so the central bank will want to tighten monetary policy.

Lets say that this time, the central bank’s promise to bring inflation down to 2.5% was taken credibly by the agents in the economy. So their expectation of inflation in Year 1 was not simply that it would be 4.5% like last year, lets suppose everyone thought that they would probably be able to drive inflation down to something like 3%. So expected inflation was 3%. This means the Phillips Curve is actually $\pi_t = 0.03 -0.75(u_t - 0.05)$

In the model last time, the central bank started off by reducing money growth to 4.4% which meant output growth fell to 0.5% and unemployment rose to 5.8% in Year 1, in order to start getting inflation down (it fell to 3.9% in year 1, so there was still much work to be done).

Now this time because of the ‘credibility’ that the bank has, and the fact agents’ expectations are lower, it can be a little less drastic in its approach.

Remember we combined the equation that links nominal money growth, output growth and inflation: $g_{yt}=g_{mt}-\pi_t$ with Okun’s Law $u_t - u_{t-1} = -\beta (g_{yt} - \bar{g_y})$ to get $u_t - u_{t-1} = -\beta (g_{mt}-\pi_t - \bar{g_y})$.

Then substituted the values to get: $u_t - 0.05 = -0.4 (0.044-\pi_t - 0.025) \Rightarrow u_t = 0.0424 + 0.4\pi_t$.

So we have a value for $u_t$ that we can sub into the new Phillips Curve to get:
$\pi_t = 0.03 - 0.75(0.0424 + 0.4\pi_t - 0.05)$ so $\pi_t = 0.03 - 0.75(0.4\pi_t - 0.0076) \Rightarrow \pi_t = 0.0275$. Inflation has fallen to 2.75%. This is much further than the fall to 3.9% it had done in the first example.

Now subbing that in to the expression we had for unemployment we get that $u_t = 0.0424 + 0.4 (0.0275) = 0.0534$ so unemployment is rising to 5.34%. Compare this to 5.8% in the first example.

We can also sub the value for inflation into the expression $\pi_t = g_{mt} - g_{yt}$ to get $0.0275 = 0.044 - g_{yt} \Rightarrow g_{yt} = 0.0165$ so output growth is 1.65%. Compare this to 0.5% in the first example.

So lets take stock of what has happened this time as a result of the central bank’s tightening of monetary policy by reducing nominal money growth to 4.4%. Because agents in the economy were expecting inflation to fall anyway (to 3%), the tightening of monetary policy worked much more effectively and involved less of a trade off with unemployment and output growth. Growth did not fall by as much and unemployment did not rise by as much. And with inflation already down to 2.75%, it would not take much more tightening next year to hit the 2.5% target.

The moral of the story is that if you can establish credibility and get agents in the economy to believe that you are going to bring down inflation, you can do it with much less pain in terms of unemployment and output growth. This is part of the reason why a stated central bank target can be a good idea – it lends some credibility to the fact you are working your monetary policy towards a target. But if you keep missing the target, then that credibility will disappear.