Advanced Macroeconomics Chapter 19 EXPLAINING BUSINESS CYCLES

Themes of the chapter Explaining business cycles by means of the AS-AD model. The Frisch-Slutzky paradigm: Impulse and propagation. The deterministic versus the stochastic AS-AD model. Supply versus demand shocks. Permanent versus temporary shocks. The theory of real business cycles.

The cyclical components of real GDP and inflation in the United States

Growth in real per capita GDP in the USA, Germany and Japan

The Frisch-Slutzky Paradigm The impulses (demand and supply shocks) initiating business cycles may be unsystematic The propagation of the impulses may generate systematic fluctuations due to the structure of the economy Basic questions  Why do movements in economic activity display persistence? Why do these movements tend to follow a cyclical pattern?

Restating the AS-AD model (1) (2) (3) (4) (5)

The AS-AD Model in compact form Inserting (2), (3) and (5) into (1), we get (6) which may be rearranged to give the aggregate demand curve: (7) Substituting (5) into (4), we obtain the short-run aggregate supply curve: (8)

A short-run macroeconomic equilibrium with cyclical unemployment

The adjustment to long-run equilibrium

How long is the Long Run? Defining (output gap) (inflation gap) and assuming st = zt = 0, we may rewrite (7) and (8) as (9) (10) Inserting (9) into (10), we find

How long is the Long Run? (11) (12) The solutions to these linear first-order difference equations are (13) (14) Note that the long-run equilibrium is stable, since 0 < β < 1.

The speed of convergence (15) According to equation (12) in Chapter 17 we have

Calibrating the model (one time period = one quarter)

Effects of a temporary negative supply shock

Effects of a temporary negative demand shock

The adjustment to a temporary negative supply shock (s1=1)

The adjustment to a temporary negative demand shock (z1= -1)

Permanent Shocks When analyzing permanent shocks, we must account for the fact that such shocks will change the long-run equilibrium real interest rate (the ’natural’ interest rate). Denoting the initial values of natural output and the natural interest rate by zero subscripts, we may write our AS-AD model as (21) (22) Consider an initial equilibrium where and suppose that st permanently changes from zero to some s ≠ 0. The new long-run equilibrium level of output may then be found from (22) by inserting to get

A permanent supply shock The effect of a permanent supply shock on natural output (23) The new equilibrium real interest rate is found from (21) by setting The effect of a permanent supply shock on the equilibrium real interest rate (24)

A permanent demand shock A permanent demand shock does not affect natural output. Hence the effect on the equilibrium real interest rate may be found from (21) by setting The effect of a permanent demand shock on the equilibrium real interest rate (25) To keep inflation close to its target rate and to avoid large deviations of output from trend, the central bank must revise the estimates of natural output and of the equilibrium real interest rate entering the Taylor rule when the economy is hit by permanent shocks. The adjustment of the economy to the new long-run equilibrium will depend on how long it takes the central bank to realize the permanency of the shock. Exercise 19.2 invites you to study these issues further.

The Stochastic AS-AD model The deterministic AS-AD model considered above can explain the persistence in macroeconomic time series, but it cannot explain the recurrent cyclical fluctuations observed in the real world. To generate such fluctuations, we now assume: Stochastic demand and supply shocks (27) (28) Our goal is to calibrate a stochastic AS-AD simulation model which can reproduce the stylized business cycle facts summarized in Table 19.1.

Cyclical components of real GDP and inflation in the USA, 1974-98

Simulation of the stochastic AS-AD model with static expectations and no supply shocks

Expected current inflation and lagged actual inflation in the United States

The Stochastic AS-AD model with static expectations Problems  The model with demand shocks can reproduce the stylized facts regarding output, but it generates far too much persistence of inflation  The model with supply shocks is unable to reproduce the stylized facts of output as well as inflation ● The assumption of static expectations implies greater fluctuations in the expected inflation rate than what we observe in practice (see Figure 19.12) To solve these problems we will now allow for simultaneous demand and supply shocks as well as adaptive expectations.

Adaptive expectations (29) Eq. (29) may be rewritten as (33) The AS-AD model with adaptive expectations (34) (35) (36)

The AS-AD model with adaptive expectations The model (34) through (36) may be condensed to: (41) (42) The third row in Table 19.1 shows that this model reproduces the U.S. business cycle reasonably well, given its simplicity.

The AS-AD model with adaptive expectations (top diagram) versus the actual U.S. business cycle (bottom diagram)

The theory of real business cycles Our AS-AD model of the business cycle emphasizes the role of expectational errors and sluggish wage and price adjustment, and the microfoundation for the SRAS curve implies that business fluctuations are associated with fluctuations in involuntary unemployment. The model also assigns an important role to demand shocks. A very different theory is: Real business cycle theory (basic version) ● The business cycle is mainly driven by fluctuations in the rate of productivity growth ● The employment fluctuations observed during business cycles reflect voluntary movements along individual labour supply curves (intertemporal substitution in labour supply, no involuntary unemployment) ● Economic growth and business cycles can and should be explained within a unified model framework. To explain business cycles, there is no need to postulate nominal and/or real rigidities.

A simple RBC model: technology (44) (45) (46) (47) For simplicity, we will assume that δ = 1.

A simple RBC model: economic behaviour (48) (49) (50) (51) (52)

A simple RBC model As shown on pp. 585-86 in the text, the model (44) through (52) may be reduced to (59) (60) Propagation mechanism in the model: A positive productivity shock raises current income which in turn raises saving and capital accumulation. This leads to a higher capital stock in the next period, which in turn raises next period’s income and saving, and so on. In this way a temporary productivity shock generates persistence in output and employment. Indeed, we see from Table 19.3 that the calibrated version of the model generates too much persistence compared to the persistence observed in the U.S. data.

Table 19.3: The RBC model versus the U.S. economy   Standard deviation of Autocorrelation Standard deviation (%) output relative to standard in output in hours worked Output Hours worked deviation of hours worked t-1 t-2 t-3 RBC model1 3.42 2.84 0.83 0.75 0.50 0.23 The U.S economy2 3.47 2.88 0.76 0.38 0.08 0.73 0.29 0.06 1 α = 0.33, η = 0.83, ω = 0.1, σc = 0.015 2 Annual data for the business sector. Note: The cyclical components of output and employment have been estimated via linear OLS detrending of annual data. Source: Economic Outlook Database, OECD. Table 19.3: The RBC model versus the U.S. economy

Some problems with basic RBC theory The virtue of the basic RBC model is that it is simple and fully integrates the theory of business cycles with the theory of economic growth. However, critics object to the theory by raising the following questions: Is technological progress really so uneven as postulated in the RBC model? Is it really plausible that recessions are periods of technological regress? (Alternative hypothesis: the observed fluctuations in productivity reflect fluctuations in capacity utilization caused by demand shocks).

Some problems with basic RBC theory Are the observed fluctuations in employment really a reflection of intertemporal substitution in labour supply? To reproduce the observed volatility of employment relative to the volatility of output, the wage elasticity of labour supply in our simple RBC model (ε) has to be set at 4.9 which is much higher than the elasticity estimated by labour economists. More generally: Is all recorded unemployment really voluntary? The RBC model predicts that the real wage is procyclical. This is in line with U.S. data, but it is not consistent with European data.

The lasting contribution of real business cycle theory In response to these criticisms, real business cycle theorists have recently tried to make their models more realistic by allowing for various frictions and rigidities, including (in some cases) nominal rigidities. At the methodological level RBC theorists have made a lasting contribution by pointing out that supply shocks may play an important part in the explanation of business cycles, and by insisting that a satisfactory theory of the business cycle should consist of a dynamic stochastic general equilibrium model which is able to reproduce the most important stylized facts of the business cycle reasonably well.