Motivation
- Analyse output, unemployment, and inflation both in the short and medium run.
- Combine the IS-LM model with the Philllips curve (PC)
IS-LM-PC Model
IS-LM
From the equilirbrium in the goods market (IS), we derived that in the short run:
where is the real interest rate.
- In the short run, output is determined by demand
- From equilibrium in financial markets, we derived a flat LM curve, showing the interest rate chosen by the central bank
- The intersection of the downward-sloping IS curve and the horizontal LM curve gives us the equilibrium level of output in the short run
- From goods and financial market equilibrium: a lower real interest rate increases demand and output.
PC
From the equilibrium in labour markets, we derived the relation between inflation and unemployment
The relation between the unemployment rate and employment:
where is employment and is the labour force
Reorganising to express as a function of :
Assuming that output is equal to employment, then
when ,
- natural level of employment is
- natural level of output is
The natural level of output is also called potential output
The deviation of output from its natural level is:
This gives us a simple relation between the deviation of output from potential and the deviation of unemployment from its natural rate.
The difference between output and potential output is called the output gap
Okun’s Law
(an empirically observed relationship)
The relation between ouput and unemployment is known as Okun’s law: A higher growth rate of ouput leads to a decrease in unemployment.
We can express the relationship between unemployment and output as
A higher growth rate of output leads to a decrease in
Plug PC () into the deviation of output:
we get:
The output gap is positively related to positive forecast errors , take for example
- If , the output gap is positive ⇒ , inflation exceeds target
- If , the output gap is negative ⇒ , inflation less than target
- If , there is no output gap ⇒ , inflation equals target
From the short to the medium run
Key Dynamics
- Over the medium run (MR), the economy converges to the natural level of output and stable inflation (determined by central bank target and expectations) (a definition of medium run)
- In the short run (SR), output may deviate from its potential and inflation from its target
- If the central bank wants to achieve a constant level of inflation, then the initial boom must be followed by a recession
In the medium run:
- The economy converges to the natural level of output
- Unemployment goes back to
- With unemployment at the natural rate
- The interest rate is such that the demand for goods is equal to potential output
- is called the natural, neutral, or Wicksellian rate of interest
Difficulties when adjusting to the medium run
- It’s difficult for the central bank to know where potential output is exactly and thus how far ouput is from potential
- It takes time for the economic agents and, thus for the economy to adjust
- The change in inflation provides a signal about where is the output gap, but it’s a noisy signal
- The central bank may want to adjust slowly and see what happens
- If the CB goes too fast, it may end up with output below potential
- If the CB goes too slow, it may allow expectations to de-anchored
IS-LM-PC In Action
Fiscal Consolidation
Fiscal consolidation describes government policy intended to reduce deficits and the accumulation of debt. One way is to increase tax as shown below.
Medium-run equilibrium after a fiscal consolidation:
- Composition of Output:
- Consumption is lower than before the policy intervention:
- But consumption is higher than in the short-run equilibrium ()
- Investment is higher than before the policy intervention:
- Lower consumption is offset by higher investment:
- Total demand and output (Y=C+I+G) are unchanged
Note that in many contries, the government and the central banks have separate obligations and targets respectively. Here the government wants to carry out fiscal consolidation while the central banks want to maintain the natural output.
Effects of an Increase in the Price of Oil
To find the effects on the short run and medium run, we use the IS-LM-PC model.
We assume that output is produced only with labour. Capture the increase in the price of oil by an increase in the mark-up (). Intuition: given , an increase in the price of oil increases the cost of production. To maintain the same profit rate, firms should increase prices (by increasing )
Note:
- We have assumed that the IS does not shift
- But the IS may also shift (to the left): e.g. lower investment, lower demand due to income redistribution
- If the IS shifts to the left, output may also decrease in the short run
- If the price increase is not that persistent, the CB may want to let inflation be higher (while the price of oil is high), expecting that inflation will return to the target (so as to avoid a decrease in output)
- But expectations of inflation may de-anchor, thus expectations play a central role in the dynamic effects of shocks
The short and the medium run
Shocks and changes policy typically have different effects in the short run and the medium run
- For example, a fiscal consolidation may be undesirable if the focus is on output and investment in the short run. Typical case: IMF program to refine public debt during a recession
- But a fiscal consolidation may be desirable if the focus is on output and investment in the medium run, as more investment may increase capital accumulation and, thus, growth
The key mechanism is expectations — many disagreements about the effects of various policies depend on how fast people think the economy adjusts to shocks
Monetary Policy Rules
One of the core roles central banks play is to close the “inflation gap” (the difference between actual inflation and the target)
- If inflation is above target, increase the real rate to close the inflation gap
- If inflation is below target, decrease the real rate to close the inflation gap
Shocks and Propagation Mechanisms
Each shock has a dynamic effect on output and its components: propagation mechanisms.
Economic fluctuations: results of shocks and their dynamic effects (propagation mechanisms)
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