Chapter 18. Explaining business cycles: Aggregate demand and

supply in action

ECON320Prof Mike Kennedy

Overview• We will now use the two aggregate functions we have developed

to examine the business cycle• The model will show how the economy reacts to both demand and

supply shocks• We know that cycles GDP and inflation seem to have regular

features and that they are persistent (next 2 slides)• We will use the so-called Frisch-Slutzky paradigm which

distinguishes between shocks (the impulse) and the propagation mechanism (the response) or how the shock sets off the process we know as the business cycle

• The propagation mechanism reflects the structure of the economy• Among the key questions are:

– Why do we see persistence?– Why do we see a cyclical pattern?– Why do these patterns differ from one another?

Business cycles seem to have regular patterns …

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20152016

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Great recession Canada United States

OECD - Total

Source: OECD Economic Outlook database

… as does inflation, although it varies less that output

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20152016

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Great recession Canada

United States OECD - Total

Source: OECD Economic Outlook database

Our model of AD and AS

• The real rate of interest

• Aggregate demand

• The Taylor rule

• Short-run aggregate supply

• Inflation expectations, which are assumed to be “static”

€

yt − y = α 1(gt − g ) −α 2 (rt − r ) +vt r = r *+ρ

A model of AD and AS con’t

• As noted in the previous lectures, we can combine the first three equations to get the AD curve

• In terms of inflation, the AD becomes

• The AS curve is:

• The next two slides show successively: 1. The short-run equilibrium and 2. The path back to long-run equilibrium, where shocks are zero and

expected and actual inflation are equal to the central bank’s target π*

€

yt − y = α (π *−π ) + z t , α ≡α 2h

1+α 2b, z t ≡

vt +α 1(g − g ) −α 2 (ρ t −ρ t )

1+α 2b

Suppose that the short-run equilibrium is at E0 with cyclical unemployment

The path back to equilibrium

Understanding the path back to equilibrium• To understand the mechanism, remember that expected inflation

(πe = πt-1) will determine where the SRAS curve cuts the long-run supply curve

• In period 0, inflation is π0 and this shifts the SRAS curve down (it cuts the LRAS curve at π0) generating a new SR equilibrium at E1

• At this point, wage setters realise that they have over-estimated inflation and reduce the required rate of wage increases

• Firms now see a lower rate of increase in marginal costs and will lower the rate of increase in their prices and higher more workers

• As inflation falls, the central bank cuts the nominal interest by more that they drop in π insuring that the real interest rate falls – this is key and comes from the Taylor rule where h > 0

• It is not so important that πe = πt-1 , the key is that πe falls with the output gap

How long is the long run?• To answer this question, we need to quantify the model – that is put

some values on key parameters• Let and , and setting all the shocks equal to

zero then the AD and SRAS curves are respectively:

• From the AD curve we have• Putting this into the SRAS curve and using the AD curve again gives:

• Similarly we can get

€

ˆ π t+1 = −1

αˆ y t+1 α ≡

α 2h

1+α 2b

How long does it takes to get back to equilibrium?• The two final equations on the previous slide are linear first order difference

equations which have the following two solutions: • We are interested in the half life of the process which we define as

• Based on estimates for the various coefficients that make up β, its value is

around 0.95 which implies that it takes about 13½ quarters for the economy to return half way back to equilibrium

• Note a lower value of β would imply a faster speed of adjustment (lower half life)

• This is a measure of the persistence of shocks which is related to the slow adjustment of inflation leaving output and unemployment to bear the brunt

• This also seems to be consistent with the empirical evidence

A temporary negative supply shock

A temporary negative supply shock• Initially the SRAS shifts up, resulting in higher inflation and a fall

in output – stagflation– Inflation rises because there is an exogenous increase in production costs– Output falls because the central bank responds to the increase in

inflation by raising the real rate of interest (through the Taylor rule)

• With static inflation expectations, the SRAS shifts down to the point where it intersects the vertical LRAS curve at πe = πt-1

– Note, even though the shock is temporary, the SRAS does not shift back once the shock disappears

• The economy moves from E1 to E2 which is a new short run equilibrium

• This process continues and the economy gradually approaches its long-run equilibrium

• Of importance here is that a temporary shock can create a long-lasting adjustment, because πe adjusts with a lag

What a supply shock might look like:Drilling starts to fall and sharply …

… but production continues at least for a while

A temporary negative demand shock

A temporary negative demand shock• Here the AD curve shifts down from it initial (long-run) equilibrium

point to E1 where it intersects the SRAS curve• In period 2 the shock disappears and the AD curve shifts back to its

original position• However, inflation initially fell from π* to π1 which cause πe to fall,

shifting the SRAS curve downward – it now intersect the LRAS at π1 • In period 2 we end up with the economy at over full employment

which will start to exert upward pressure on π• This will cause the SRAS curve to shift upward restoring equilibrium• Because actual π is below π*, the central bank will keep the real

interest below its equilibrium level – this is key• The interesting (astonishing) point is that a temporary demand

shocks can generate a long lasting cyclical effect• The economy’s propagation mechanism generates a pattern quite

different from the initial shock

The impulse-response function

• This function tells us how the economy responds to a temporary shocks

• We start with the AD and SRAS curves

AD SRAS

• We want to derive as a function of lagged values of itself by writing the SRAS curve solely in terms of

• Start by using the AD curve to eliminate from the SRAS

€

ˆ y t

€

ˆ y t

€

ˆ π t−1

€

ˆ π t =1

α(zt−1 − ˆ y t−1) +γ ˆ y t + s t

The impulse-response function con’t• Next use again the AD curve to write in terms of

• Next multiply through by α, collect the variable to the left hand side we get

– Both the demand (z) and supply (s) shocks are identified– The demand shock enters as a first difference (zt – zt-1), a feature which

explains the over-shooting of output when there is a temporary demand shock

• In a similar fashion we can use the AD curve to eliminate from the SRAS curve to get

• The supply and demand shocks enter directly – there are no lags

€

ˆ π t

€

ˆ y t

€

1

α(zt − ˆ y t ) =

1

α(z t−1 − ˆ y t−1) +γ ˆ y t + st

€

ˆ y t

€

ˆ y t

The impulse-response function con’t• The dynamic versions of the output and inflation gap curves are

reproduced here

• These are the impulse response functions for and• Slide 20 shows the effect of a temporary supply shock

– Initial y falls but inflation rises, leading to stagflation– In the next period the supply shock disappears but the SRAS will not shift back

because πe = πt-1

– The economy will slowly return to equilibrium with πt falling and yt rising

• Slide 21 shows the effect of a temporary demand shock– In the first period, yt falls and so does πt

– In the second period, the AD curve shifts back but πt is slow to adjust– With π < π* the central bank keeps real interest rate below equilibrium levels and

both yt and πt return to their long run values

• Both slides illustrate the economy’s endogenous persistence mechanism

€

ˆ y t

€

ˆ π t

A temporary negative supply shock

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1

Half-life = 3.5 years Output gap π - π*

Parameter values γ = 0.3; α = 0.74; β = 0.82

A temporary negative demand shock

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Half-life = 3.5 years Output gap π - π*

Parameter values γ = 0.3; α = 0.74; β = 0.82

Permanent shocks

• These shocks will change the long-run equilibrium level of the interest rate and output and as such will have monetary policy implications

• Begin by linearising the AD around its long-run equilibrium, where subscripts 0 are initial equilibrium values

• The SRAS curve becomes

• Suppose now that there is a permanent value for the supply shock = s then from the SRAS the new level of equilibrium output will be

• We can use the above with the AD curve to find the new equilibrium interest rate

€

y = y 0 −s

γ

€

y − y 0 = v t −α 2 (rt − r 0 ), v t ≡ vt +α 1(gt − g )

Permanent shocks con’t• The supply shock (in this case negative) has lowered potential output

and as such aggregate demand must fall to maintain the inflation target• To curb aggregate demand, the real interest rate must rise and interest

sensitive sectors of demand will fall

• The central bank must revise up its estimate of the equilibrium real interest rate to

• If the economy is hit by a permanent demand shock (vt  ≠ 0), potential output will be unaffected

• But the central bank will still have to revise its estimate of the equilibrium real rate, which from the AD curve becomes

• If the shock were positive, then the equilibrium real interest rate must rise to bring demand into line with supply

€

r * = r −ρ

The effect of a permanent supply shock

The effect of a permanent supply shock with no change in monetary policy leads to stagflation (higher π and negative output gap)

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5 The supply shock = 1.0 stays in place

Output gap

π - π*

Note the output gap is permanently affected

The effect of a permanent negative demand shock with no change in monetary policy leads to deflation (note the demand shock has no long-

run effect on the output gap)

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2.22044604925031E-16

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The demand shock = 1 and stays in place

Output gap

π - π*

Note that the output gap returns to zero since it has not been affected by the shock

A stochastic version of the AD-AS model of the economy

• So far we have examining a deterministic version of the model• This has yield useful insights into why the economy displays

persistence• That said, we need to understand why cycles are a recurrent

phenomenon• We will use the Frisch-Slutsky paradigm • Slutsky discovered that if we add a stochastic variable (et) to a first-

order difference equation like Xt = aXt-1 + et you can generate a time series that looks remarkably like the business cycle.

• The key is the coefficient, a, has to be close to but less that one – in fact not far off the value we have calculated for β in the impulse response function

• The following slides shows the Slutsky equation for two different values of the coefficient a.

Business cycles in a stochastic world:The Slutsky equation

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Green line Xt = 1.0Xt-1 + et; Var = 5.0Blue line Xt = 0.9Xt-1 + et ; Var = 3.8Red line Xt = 0.6Xt-1 + et; Var = 1.5

Note that the variance (Var) of the series rises the higher the coefficient on Xt-1 The longer the “memory” of a series, the higher the variance

The stochastic version of the AD-AS model• We can use the impulse-response functions we have already

developed and treat the shock variables (z and s) as stochastic processes

• In particular we will assume that z and s evolve as follows:zt+1 = δzt + xt+1

st+1 = ωst + ct+1

• The variables xt+1 and ct+1 are random variables with 0 means and constant variances while the coefficients δ and ω are between less that one and positive

• We are assuming that both demand and supply shocks have some persistence

• We will now use the model to answer the question: – Are fluctuations in output and inflation due to purely demand or

supply shocks?

An economy hit by only demand shocks with δ = 0.8

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Output gap π - π*

Assumes no supply shocks

An economy hit by only supply shocks with ω = 0.15

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Output gap π - π*

Assumes no demand shocks

Examining the two cases• The economy we have modelled here is closed to trade

– As such we will compare it broad features of the US economy– Over time the US business has a standard deviation of 1.64, while that for inflation

(minus its trend) is 0.21– The correlation between the inflation and output gaps is 0.31– Other features of the US economy can be found in Table 18.1 in the text

• In the case of only demand shocks (slide 30) – The model so calibrated produces a standard deviation of the output gap of 1.41

somewhat close to that of the US– Inflation however appears to be too persistent and its standard deviation at 0.85 is too

high– Finally the correlation between inflation and GDP at 0.27 is low but close

• In the case of only supply shocks– The standard deviation of output at 1.59 is close enough – The standard deviation of inflation at 2.14 is too high– The correlation between inflation and output is a perfect -1.0, something not seen in the

data

• For other information on simulations similar to this see Table 18.1

Some further modifications to the model• We need to modify are assumption about πe = πt-1

• Now we will assume that agents update the expectations base on the errors that they make forecasting inflation

• Note that if ϕ = 0, then we would have πe = πt-1 and that errors on gradually get incorporated into changes in πe

• We can re-write the above as

• By successively substituting into the lagged values of expected inflation we can get

• This says that expected inflation is a weighted average of past inflation

Some further modifications to the model, con’t• The AD curve remains the same since it is π* that counts

• The SRAS curve will change because of the different way in which inflation expectations are formed

• Using the simplified definition of the output and inflation gaps (variables with ˆs) and substituting the new expectations equation into the SRAS curve

• We can write each equation in a form to be simulated

Main message: The importance of both supply and demand shocks• When the model is simulated with both supply and demand

shock the key statistical measures more closer to actual values• Now the standard deviation of the output gap is 1.62 while

that for inflation is 0.23, very close to actual values of 1.64 and 0.21

• The correlation between inflation and the output gap is still low at 0.22 versus an actual of 0.31

• The main message is that we need both types of shocks to explain the observed movement in the output gap and inflation

• The general pattern of the cycle and inflation that emerges is similar to what is observed in the US economy (see next two slides)

• Note the importance of having lags in the model

What the model simulates for the business cycle and inflation

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Output gap π - π*

The actual US business cycle looks similar to the simulated version in the previous slide

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Output gap π-π*

Note that inflation is the price of consumer expenditures (CPE) less food and energy

An alternative theory: Real Business Cycles (RBC)

• The other view of macroeconomic fluctuations is that they are caused by productivity shocks – changes in TFP

• Because the economy is always in equilibrium, changes in employment represent workers voluntarily withdrawing or entering the labour market when their real wages change

• Two important problems with this view are that: – the models need an implausibly high elasticity of labour supply

wrt a change in real wages and– all shocks are due to productivity changes

• The important contribution that these economists have made is the integration of growth and business cycle theory