Home > Macro, Monetary Policy > Disinflating the economy 1 – a model of disinflation

## Disinflating the economy 1 – a model of disinflation

We can see how disinflation would work in practice by using a fantasy economy. This is a little model economy using the Phillips Curve and Okun’s Law equations, to see how you can disinflate an economy through tighter monetary policy (reducing the rate of nominal money growth). We are using the principle here that $\pi_t = g_{mt} - g_{yt}$.

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. Suppose they decide in Year 1, to reduce nominal money growth down to 4.4%.

You can combine 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 $u_t - u_{t-1} = -\beta (g_{mt}-\pi_t - \bar{g_y})$.

We could substitute our values here to get: $u_t - 0.05 = -0.4 (0.044-\pi_t - 0.025) \Rightarrow u_t = 0.0424 + 0.4\pi_t$.

Now we have got a value for $u_t$ we can sub this into the Phillips Curve to get: $\pi_t - 0.045 = -0.75(0.0424 + 0.4\pi_t - 0.05)$ so $\pi_t = 0.045 -0.75(0.0076 + 0.4\pi_t) \Rightarrow 1.3\pi_t = 0.0507 \Rightarrow \pi_t = 0.039$. So we have found inflation in Year 1 to be 3.9%.

We can sub this value back into the Okun’s Law expression: $u_t = 0.0424 + 0.4(0.039) \Rightarrow u_t = 0.058$. So we have found unemployment in Year 1 to be 5.8%.

We can also sub the value for inflation into the expression $\pi_t = g_{mt} - g_{yt}$ to get $0.039 = 0.044 - g_{yt} \Rightarrow g_{yt} = 0.005$ so output growth is 0.5%.

So lets take stock of what has happened as a result of the central bank’s tightening of monetary policy by reducing nominal money growth to 4.4%. The reduction in money growth has reduced output growth from the normal rate of 2.5% down to 0.5% (the mechanism by which it will have done this will be through the reduction in money growth raising interest rates and reducing investment, it is like a monetary contraction in the ISLM model). The reduction in output growth below the normal rate of output growth has raised unemployment to 5.8% and this has tightened conditions in the labour market so that it has pushed downward pressure on inflation down to 3.9%. Inflation has come down at the cost of some more unemployment, but we are still a way off the target of 2.5%.

Let us suppose in Year 2 the bank chooses a nominal money growth level of 5.15%. I won’t bother going through all the calculations here, I will just show the results. This level of nominal money growth now pushes output growth back up to 2%, but this is still below the normal growth rate of output, so unemployment rises to 6%. This continues to put downward pressure on inflation to bring it down to 3.15%. Remember that any time the unemployment rate is above the natural rate of unemployment, it applies downward pressure to inflation.

In Year 3 suppose the bank chooses a nominal money growth target of 5.35%. Now output growth is allowed to rise to 2.85%, and unemployment rate falls back a little to 5.86%. But as unemployment is still above the natural rate, inflation continues to fall, down to 2.5%. Now the central bank has achieved its target rate of inflation.

If it kept a tight monetary policy then it would carry on forcing inflation down but at the cost of higher unemployment, so suppose the bank relaxes monetary policy and allows money growth of 7.15% in Year 4. This allows the economy to boom, growing at 4.65%, and the extra output growth leads to a surge in firms hiring workers, so unemployment falls to 5%. As this is now the natural rate of unemployment, it keeps inflation constant, so it stays at 2.5% (this is why I chose the level of 7.15% money growth, because it would hit the natural rate of unemployment!). Now the bank is back to equilibrium level of unemployment, all it needs to do is stay there. So in Year 5 it has money growth of 5%, which will return output growth to the normal growth rate of output (as 0.025 = 0.05 – 0.025), and it keeps the rate of unemployment constant at the natural rate, and also keeps inflation constant at 2.5%.

So after this four year policy, we have got inflation down and returned unemployment back down to the natural rate. Inflation was brought down by accepting some higher unemployment in the short term, but once the economy has been disinflated, all that is needed is to keep the economy back on track at its equilibrium levels of output growth and unemployment, to keep that inflation constant.