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# Chapter 18. Explaining business cycles: Aggregate demand and supply in action ECON320 Prof Mike Kennedy.

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Chapter 18. Explaining business cycles: Aggregate demand and supply in action ECON320 Prof 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 …

… as does inflation, although it varies less that output

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”

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 *

Suppose that the short-run equilibrium is at E 0 with cyclical unemployment

The path back to equilibrium

Understanding the path back to equilibrium To understand the mechanism, remember that expected inflation (π e = π t-1 ) will determine where the SRAS curve cuts the long-run supply curve In period 0, inflation is π 0 and this shifts the SRAS curve down (it cuts the LRAS curve at π 0 ) generating a new SR equilibrium at E 1 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 π e = π t-1, the key is that π e 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

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

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 π e = π t-1 – Note, even though the shock is temporary, the SRAS does not shift back once the shock disappears The economy moves from E 1 to E 2 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 π e 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

Here the AD curve shifts down from it initial (long-run) equilibrium point to E 1 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 π 1 which cause π e to fall, shifting the SRAS curve downward – it now intersect the LRAS at π 1 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

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 ( z t – z t-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

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 π e = π t-1 – The economy will slowly return to equilibrium with π t falling and y t rising Slide 21 shows the effect of a temporary demand shock – In the first period, y t falls and so does π t – In the second period, the AD curve shifts back but π t is slow to adjust – With π < π * the central bank keeps real interest rate below equilibrium levels and both y t and π t return to their long run values Both slides illustrate the economy’s endogenous persistence mechanism

A temporary negative supply shock

A temporary negative demand shock

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

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 ( v t ≠ 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

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)

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)

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 (e t ) to a first- order difference equation like X t = aX t-1 + e t 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

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: z t+1 = δz t + x t+1 s t+1 = ωs t + c t+1 The variables x t+1 and c t+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

An economy hit by only supply shocks with ω = 0.15

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 π e = π t-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 π e = π t-1 and that errors on gradually get incorporated into changes in π e 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

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

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

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