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## Disinflating the economy 2 – the role of expectations

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.

Categories: Macro, Monetary Policy

## 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.

Categories: Macro, Monetary Policy

## Disinflating the economy 1 – the labour market

Getting inflation out of the economy is not an easy task, which is why it is always preferable to prevent inflation getting too high in the first place. When higher inflation gets into the system, eventually the economy will return to a medium run equilibrium in terms of output and unemployment, and inflation will stabilise at a constant, but high level. Inflation stabilises because when the economy is at the natural rate of unemployment, the change in inflation from one year to the next is 0.

Removing inflation usually involves either tightening up the labour market or changing inflationary expectations. Here I will deal with disinflation through tightening the labour market – which is painful as it involves accepting higher unemployment. In 1991 the UK Chancellor Norman Lamont said that “rising unemployment and the recession have been the price that we have had to pay to get inflation down, that price is well worth paying”. This comment has got widespread notoriety and you often hear journalists trying to promote a similar response by asking politicians if they think unemployment is a price worth paying. The basic principle that Lamont was referring to was that if you accept temporarily higher unemployment, you can get inflation out of a system, and then when the economy restabilises at the natural rate of unemployment, inflation will stabilise again at a lower rate.

This common form of the Phillips Curve $\pi_t - \pi_{t-1} = -\alpha (u_t - u_n)$ implies that disinflation can only be obtained at the cost of higher unemployment, however the total amount of unemployment required for a given decrease in inflation does not depend on the speed at which disinflation is achieved – the total amount of higher unemployment can either be spread over a short or longer period of time.

The sacrifice ratio is the number of point-years of excess unemployment needed to achieve a decrease in inflation of 1%. If we consider what would cause inflation to fall by 1% in terms of the Phillips Curve we get $-0.01 = -\alpha (u_t - u_n) \Rightarrow \frac{0.01}{\alpha}=u_t - u_n$. In other words the total amount of excess unemployment (above the natural rate) required for one year, to reduce inflation by 1%, would be $\frac{0.01}{\alpha}$. This ratio does not depend on policy. The total amount of excess unemployment is defined in ‘point years’ so you could disinflate the economy by 1% over 3 years by having an excess level of unemployment of $\frac{0.01}{3\alpha}$ per year.

Categories: Macro, Monetary Policy

## Monetary policy in the short and medium run

There is a very important concept in monetary policy called the neutrality of money. This means that although in the short run, you can use monetary policy – ie the rate at which you grow the money supply – as a tool to influence output and unemployment, monetary policy will have no effect on output and unemployment in the medium run. The only think that the rate of money growth will influence in the medium run is inflation, and if you try to stimulate output for too long through a fast rate of money growth, you will just get punished with a high level of inflation.

This rests on the idea that in the medium run, the economy will return to a natural level of output and natural rate of unemployment. The natural level of output is determined by the supply conditions in the economy, but more realistically, if we are in an economy that is growing over time (its supply potential is steadily increasing) then we will have a natural rate of output growth. The relationship between output growth and unemployment is given in Okun’s Law, and the relationship between unemployment and inflation is given in the Phillips Curve.

If the economy always returns to a natural rate of output growth, then assuming the population growth stays constant, the economy will always return to a natural rate of unemployment. This is where you will get to in the medium run.

However, inflation is not only influenced by the rate of unemployment, but also by expectations of inflation, and here is where money growth influences inflation. When agents in the economy realise that the money supply is increasing faster, and inflation is rising, they will reflect this in their wage bargaining agreements, and it will push inflation up. The rate of money growth is approximately related to inflation and the rate of output growth through the expression $\pi = g_m - g_y$ .

So if in the medium run we know that the growth of output will be $\bar {g_y}$ then in the medium run inflation will be $\pi = g_m - \bar {g_y}$, ie it depends on how much bigger $g_m$ is than $\bar {g_y}$.

This is why money is described as being neutral in the medium run – well, it is neutral in terms of output and unemployment, it is certainly not neutral in terms of inflation!

This is also where the famous Milton Friedman quote “inflation is always and everywhere a monetary phenomenon” comes from – it is saying that in the medium run, inflation solely depends on the rate of money growth, and so if you have a tight grip on your monetary policy you shouldn’t need to worry about inflation getting out of control (in theory anyway).

In the short run, monetary policy does have an effect on output and unemployment – you can trace this easily through using the ISLM model. The ISLM model is a ‘static’ economy model not a model for a growing economy, so you have to use a bit of imagination. When the economy is growing (output is growing) then raising the rate of money growth above the rate of output growth is like raising the money supply in the static ISLM model, which means shifting the LM curve down. This will lower the equilibrium rate of interest, and when interest rates are lower, firms invest more and output rises. In a growing economy this means output rises more than the natural growth rate.

Alternatively, reducing the rate of money growth below the rate of output growth is like cutting the money supply in the static ISLM model, which means shifting the LM curve up. This will raise the equilibrium rate of interest, and when interest rates are higher, firms invest less and output falls. In a growing economy, when the ISLM model tells you that output is falling, it may not actually be falling, it means it is growing below the natural growth rate. So if the natural growth rate of output was 2.5% per year, then a growth of output of 1.8% would show up as a fall of output below the natural level, in the ISLM model. Hope that is not too confusing!

You can read more on this in the sections on the short and medium run effects of a monetary expansion and monetary contraction.

Categories: Macro, Monetary Policy

## An equation linking inflation, output growth, unemployment and money growth

Here we are going to make a single equation out of three other expressions:

1. The Phillips Curve which linked inflation to unemployment: $\pi_t - \pi_{t-1} = \alpha (u_n - u_t)$.

2. Okun’s Law which linked unemployment to output: $u_t - u_{t-1} = -\beta (g_{yt} - \bar{g_y})$

3. The relationship between nominal money growth, output growth and inflation: $g_{yt}=g_{mt}-\pi_t$

You can combine the first two to get:

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

Now you can substitute the value for output growth given in the third equation into that to get:

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

Now for some multiplying out of whats in the brackets:

$\pi_t - \pi_{t-1} = -\alpha (u_{t-1} - u_n - \beta g_{mt} + \beta \pi_t + \beta \bar{g_y})$.
$\Rightarrow \pi_t - \pi_{t-1} = -\alpha u_{t-1} +\alpha u_n + \alpha \beta g_{mt} - \alpha \beta \pi_t - \alpha \beta \bar{g_y}$.
$\Rightarrow \pi_t + \alpha \beta \pi_t - \pi_{t-1} = -\alpha u_{t-1} +\alpha u_n + \alpha \beta g_{mt} - \alpha \beta \bar{g_y}$.
$\Rightarrow \pi_t (1 + \alpha \beta ) - \pi_{t-1} = -\alpha u_{t-1} +\alpha u_n + \alpha \beta g_{mt} - \alpha \beta \bar{g_y}$.
$\Rightarrow \pi_t = \frac{1}{(1 + \alpha \beta )}[\pi_{t-1} -\alpha u_{t-1} +\alpha u_n + \alpha \beta g_{mt} - \alpha \beta \bar{g_y}]$.

We can put the right hand side back in brackets to get:
$\pi_t = \frac{1}{(1 + \alpha \beta )}[\pi_{t-1} -\alpha (u_{t-1} - u_n - \beta (g_{mt} - \bar{g_y}))]$

Categories: Macro, Monetary Policy

## Monetary policy and the AD relation

The AD relation showed a downward sloping relationship between output and prices. The mechanism was really working through real money balances $\frac{M}{P}$, ie when prices rose, if the nominal money stock, M, stayed constant, then real money balances fell.

The opposite of that is what happens if (in the short run) prices stay constant and the money stock rises. Then real money balances will rise, so the analysis used for the AD relation would suggest that output would rise. If prices are constant then increasing the money stock represents a shift up of the LM curve, while decreasing the money stock represents a shift down of the LM curve. This is a simple way to think about monetary policy, a monetary expansion is increasing the money stock, a monetary contraction is decreasing the money stock.

Remember what influences the AD curve:

The AD curve tells you the equilibrium level of output in the goods and money markets, for any given price level. Anything which will change the equilibrium level of output at all price levels, will shift the whole AD curve. So you can basically think of this as anything ‘happening’ in the ISLM model which will cause the equilibrium level of output to change apart from a change in the price level, which is captured in the downward slope of the AD line.

So the AD curve shifts out to the right, if you have a fiscal expansion or a monetary expansion, or anything that will increase consumer confidence to encourage consumers to spend more (which means the IS curve shifts out just like the fiscal expansion)

The AD curve shifts in to the left, if you have a fiscal contraction or a monetary contraction, or anything that will decrease consumer confidence to cause consumers to spend less (which means the IS curve shifts in just like the fiscal contraction)

So we can express a relationship between output and monetary and fiscal policy like this: $Y_t = \gamma[\frac{M_t}{P_t}, G_t, T_t]$.

This is saying output is equal to a parameter multiplied by a function of monetary and fiscal policy. Now if we want to isolate the way monetary policy influences output, keep fiscal policy constant and forget about G and T.

$Y_t = \gamma[\frac{M_t}{P_t}]$.

In terms of growth you can use an approximation that if $Y_t = \gamma \frac{M_t}{P_t}$ then $g_{yt} \approx g_{mt} - g_{pt}$. Note that growth in prices in year t is inflation in year t, so $g_{yt} \approx g_{mt} - \pi_t$.

We can rearrange this to say $\pi_t \approx g_{mt} - g_{yt}$. This is a useful way of thinking about the relationship between inflation and money growth, it says that inflation in year 1 will be approximately equal to the rate of money growth minus the rate of output growth. This is basically because if the economy grows, there will be a growing level of transactions, and so a growing demand for real money. The real money stock always grows at the same rate that output grows. As the real money stock is $\frac{M}{P}$ then if M grows at a different rate to output, the difference will be made up by changes in P. If the rate of money growth matches the rate of output growth you will have stable prices and no inflation. This sounds deceptively easy and in reality inflation is easy to stop, if you turn the taps of money growth off, inflation will soon judder to a halt, the reason that isn’t done in practice is that that approach would have a seriously detrimental effect on output as it would mean there was not enough money around to support the level of transactions demanded, so the lack of money would trigger a recession.

## Short and medium run effects of a monetary contraction

We can use the ASAD model to look at the short and medium run effects of a monetary contraction.

You can trace the effects of the monetary contraction through a few of the short run models:
1. In the money supply/money demand diagram the decrease in nominal money shifts the money supply curve to the left, so you get a new (higher) equilibrium interest rate.
2. This means that the money market comes into equilibrium at a higher interest rate for all levels of output, so it is reflected in an upward shift of the LM curve.
3. An upward shift of the LM curve means that, keeping the IS curve constant, the goods and money markets come into equilibrium at a lower level of output in the ISLM model.
4. Anything that causes a lower level of equilibrium output in the ISLM model means the goods and money markets are coming into equilibrium at a lower level of output at all price levels, this is reflected in an inward shift (to the left) of the AD curve.

Here we have started from a medium-run equilibrium in the ASAD with output at the natural level (Yn) and price expectations being level with actual prices. The AD curve has shifted in to the left. The effects are that we have got a lower equilibrium level of output, Y2, and that price expectations are now running above actual prices (Pe<P2). This is our short-run effect.

Now we think about what happens to the AS curve. The AS curve will take us back to the medium run, with the adjustment mechanism being price expectations. As price expectations are above actual prices, they will adjust downwards. When expected prices decrease, the AS curve shifts downwards. Remember that in the medium run, output will be back at the natural level, Yn.

Now the AS curve has shifted downwards to take us back to medium run, we are at the natural level of output again and at a point where expected prices equal actual prices. The only difference is the price level is now lower. I have labelled P1 as the original equilibrium price level. We had a short run fall in prices from P1 to P2, before price expectations caught up with them, and then by the time expected prices had caught up with actual prices it was at P3.

What has really gone on here is that the monetary contraction has reduced output in the short run, which has put downward pressure on prices. When workers have realised that actual prices were below the price expectations they based their last wage claims on, they will adjust their expectations downwards and reflect this in their next round of wage bargaining. The falling prices will be reflected in lower wages which will then decrease firms’ costs, so firms will pass these cost savings onto consumers in the form of lower prices, because they are trying to compete with their rival firms to offer consumers the lowest price. This is why the AS curve is shifting downwards, firms are charging lower prices for the same amount of output, so at all levels of Y, P is lower.

We can also look at the effects on interest rates by tracing out this story in the ISLM model.

The short run effect will be (as described above) that the LM curve shifts up.

Now in the medium run we will go back to the natural level of output, and the ASAD model tells us that it is the price mechanism that will get us there. In the ISLM model, changes in prices are reflected in shifts of the LM curve.

Lower prices will effectively mean an increase of the real money stock, and so this will drive down the interest rate which brings the money market into equilibrium at all levels of output. This is a downwards shift of the LM curve. So the LM curve will shift down to get us back to the medium run where output is at Yn.

So now in the medium run we are back at Yn in terms of output, and we are back in medium run equilibrium with the same interest rate. The interest rate has risen from i1 to i2 in the short run, while output went from Yn to Y2, but then returned to a medium run level of output, Yn, with the interest rate returning to i1.

So the conclusion from this ASAD and ISLM analysis is that a monetary contraction will cause –
A fall in output, a fall in prices and a rise in interest rates in the short run.
No change in output, but a lowe price level and no change in interest rates, in the medium run.

Categories: Macro, Monetary Policy