Snowdon & Vane Modern Macroeconomics

period, workers will need to consider how much the current real wage offers are above or below the norm. The substitution effect of a higher real wage offer will tend to increase the quantity of labour supplied. However, since higher real wages also make workers feel wealthier, this will tend to suppress the supply of labour. This wealth or income effect works in the opposite direction to the substitution effect. The impact of an increase in the current real wage on the amount of labour supplied will clearly depend on which of the above effects predominates. Real business cycle theorists distinguish between permanent and temporary changes in the real wage in order to analyse how rational maximizing individuals respond over time to changes in their economic circumstances that are brought about by technological shocks. The intertemporal labour substitution hypothesis suggests two things. First, if a technological shock is transitory, so that the current above-normal real wage offers are temporary, workers will ‘make hay while the sun shines’ and substitute work for current leisure. Less work will be offered in the future when the real wage is expected to be lower and hence the decision to supply more labour now is also a decision to consume more leisure in the future and less leisure now. Therefore real business cycle theory predicts a large supply response from temporary changes in the real wage. Permanent technological shocks, by raising the future real wage, induce wealth effects which will tend to lower the current labour supply.

Second, some theorists have stressed the importance of real interest rates on labour supply in flexible price models (see Barro, 1981, 1993). An increase in the real interest rate encourages households to supply more labour in the current period, since the value of income earned from working today relative to tomorrow has risen. This effect would show up as a shift of the labour supply curve to the right.

We can therefore express the general form of the labour supply function in the real business cycle model as equation (6.10), where r = real interest rate:

The appropriate intertemporal relative price (IRP) is given by (6.11):

According to (6.11) any shocks to the economy that cause either the real interest rate to rise or the current real wage (W/P)1 to be temporarily high relative to the future real wage (W/P)2, will increase labour supply and hence employment.

6.9Technology shocks

Although some versions of real business cycle theory allow for real demand shocks, such as changes in preferences or government expenditures, to act as the impulse mechanism, these models are more typically driven by exogenous productivity shocks. These stochastic fluctuations in factor productivity are the result of large random variations in the rate of technological change. The conventional Solow neoclassical growth model postulates that the growth of output per worker over prolonged periods depends on technological progress which is assumed to take place smoothly over time. Real business cycle theorists reject this view and emphasize the erratic nature of technological change which they regard as the major cause of changes in aggregate output.

To see how aggregate output and employment vary in a real business cycle model, consider Figure 6.3. Panel (a) of Figure 6.3 illustrates the impact of a beneficial technology shock, which shifts the production function from Y to Y*. The impact of this shift on the marginal product of labour and hence the demand for labour is shown in panel (b). By increasing the demand for labour a productivity shock raises employment as well as output. How much employment expands will depend on the elasticity of labour supply with respect to the current real wage. The ‘stylized facts’ of the business cycle indicate that small procyclical variations in the real wage are associated with large procyclical variations of employment. Thus a crucial requirement for real business cycle theory to be consistent with these facts is for the labour supply schedule to be highly elastic with respect to the real wage, as indicated in panel (b) by SL2. In this case a technology shock will cause output to expand from Y0 to Y2 with the real wage increasing from (W/P)a to (W/P)c, and employment increasing from L0 to L2. If the labour supply schedule is relatively inelastic, as shown by SL1, large variations of the real wage and small changes in employment would result from a technology shock. However, this does not fit the stylized facts.

It is clear that, in order for real business cycle theories to explain the substantial variations in employment observed during aggregate fluctuations, there must be significant intertemporal substitution of leisure. Since in these models it is assumed that prices and wages are completely flexible, the labour market is always in equilibrium. In such a framework workers choose unemployment or employment in accordance with their preferences and the opportunities that are available. To many economists, especially to those with a Keynesian orientation, this explanation of labour market phenomena remains unconvincing (Mankiw, 1989; Tobin, 1996).

Figure 6.5 The real business cycle aggregate demand and supply model

improvement that shifts the production function will cause the RAS curve to shift to the right and any point on RAS represents a position of equilibrium (full) employment; that is, the RAS curve is a labour market equilibrium curve. Because the price level will automatically adjust so that the LM/P curve will always intersect the RAD curve at the full employment level of output, we need only consider the RAD and RAS curves. However, in Figure 6.4 no account has been taken of the impact of the real interest rate on the supply of labour. A real business cycle aggregate demand and supply model which does incorporate real interest rate effects on the labour supply is shown in Figure 6.5.

The RAS curve is now shown to have a positive slope because an increase in the real rate of interest will also increase the current real wage relative to the expected future real wage, thereby increasing the supply of labour (shifting the labour supply curve to the right), and hence output. Equation (6.11) indicates that the current supply of labour will increase if the real interest rate rises. Several important points are worth noting:

1.This model is entirely real, since the quantity of money and the aggregate price level have no impact on aggregate output or employment.

2.The distinction between the long-run and short-run aggregate supply curves which play an important role in monetarist, early new classical and new Keynesian models is abandoned.

3.The RAS schedule traces out a range of equilibrium positions which are all consistent with ‘full employment’.

4.The assumption of price flexibility allows the real interest rate to equilibrate the goods market, so that RAD = RAS.

5.In explaining fluctuations in output, real business cycle theorists have emphasized shifts of the RAS curve due to technological shocks (see Kydland and Prescott, 1982; Plosser, 1989).

6.Some equilibrium theorists have shown that real aggregate demand shocks can also be important during some periods as an explanation of aggregate fluctuations. For example, Barro has shown how a temporary increase in government expenditure can cause output to expand (see Barro, 1993, chap. 12). He concludes that ‘variations in government purchases play a major role during wartime but not in peacetime business fluctuations’ (see below, Figure 6.7).

In Figure 6.6 we illustrate the impact of a favourable technology shock, taking into account the impact of such a shock on real output (Y), the real rate of interest (r), and the real wage (W/P). In Figure 6.6 we re-label the RAD and RAS curves as Cd and Ys respectively. The initial equilibrium position is at point a in all four quadrants of Figure 6.6. A favourable technology shock shifts the Ys curve from Ys1 to Ys2 in quadrant (d) and the production function up from AF(K,L) to A*F(K,L) in quadrant (b). A favourable technology shock increases the marginal productivity of labour, thereby shifting the labour demand curve (DL) to the right in quadrant (a); that is, from DL1 to DL2. However, the labour supply curve also shifts from SL1 to SL2 in quadrant (a), this decrease in labour supply being a rational intertemporal response to the fall in the real interest rate (from r1 to r2). The new equilibrium taking into account all of these effects is given by point b in all four quadrants of Figure 6.6. Thus a favourable technology shock increases real output (from Y1 to Y2), lowers the real rate of interest (from r1 to r2), increases labour productivity and the real wage (from (W/P)1 to (W/P)2). That is, the real wage and labour productivity are procyclical, as the stylized facts suggest.

Figure 6.7 shows the likely impact of an increase in government purchases. As before the initial equilibrium position is at point a in all four quadrants of Figure 6.7. An increase in government purchases shifts the real aggregate demand curve from Cd1 to Cd2. In this case real output increases (from Y1 to Y2), the real rate of interest rises (from r1 to r2) and the real wage falls (from (W/P)1 to (W/P)2) in response to an increase in labour supply, with the labour supply curve shifting from SL1 to SL2 in quadrant (a). The new equilibrium taking into account all of these effects is given by point b in all four quadrants of Figure 6.7. In the old classical model aggregate supply is perfectly inelastic, as in Figure 6.4, and an increase in government purchases has no

effect on real output. In contrast, in REBCT, an increase in government purchases leads to an increase in real output because the induced rise in the real rate of interest encourages an increase in labour supply, thereby increasing employment and real output.

Finally, we can use the Cd–Ys model to examine the impact of temporary v. permanent technology shocks. In this case we simply reproduce the Cd–Ys diagram on its own, but we also allow for possible wealth effects on the Cd curve.

Figure 6.8 represents the basic market-clearing diagram which is central to the modern new classical equilibrium approach to macroeconomic analysis. Following Barro (1993), the market-clearing condition is given by (6.12):

In equation (6.12) variables omitted and indicated by … include the various wealth and substitution effects which result from shocks to the production function or government expenditure and so on. The response of Cd and Ys to changes in the real rate of interest is illustrated by movements along the aggregate demand and supply curves. The Cd and Ys curves will shift if any of the other variables which influence Cd and Ys change, as with a shock to the production function or an increase in government expenditure.

To see how a technology shock will influence aggregate output in this model, consider Figure 6.8, where, starting from point a, we assume a beneficial technology change takes place of the type considered in Figure 6.3. Such a shock will clearly shift the Ys curve to the right from Ys1 to Ys*. If the technology shock is seen to be temporary, the impact on consumer demand of the wealth effect is likely to be small and the resultant rightward shift of Cd

Figure 6.8 The impact of temporary and permanent technology shocks in the real business cycle model

will be less than the shift of Ys: a movement from point a to b. Output rises from Y1 to Y2 and the real interest rate falls to r2. If the technology shock is seen to be permanent, then the wealth effect of the shock on consumption is more powerful. In this case the rightward shifts of Ys and Cd are likely to be of a similar magnitude, leading to a rise in output from Y1 to Y* but with the real interest rate remaining at r1: a movement from point a to c. According to Barro, this model does reasonably well in accounting for the stylized facts of business fluctuations. For a detailed discussion of these issues, see Barro (1993), especially pp. 232–41.

6.11Calibrating the Model

It was Kydland and Prescott (1982) who first demonstrated that a general equilibrium real business cycle model, driven by exogenous technological shocks, was capable of generating time series data that possessed the statistical properties of US business cycles over the period 1950–79. However, real business cycle theorists have not generally attempted to provide models capable of conventional econometric testing but have instead tended to focus on providing numerical examples of a more general theory of fluctuations. In order to examine the quantitative implications of their mod-

els, real business cycle theorists have developed a method known as ‘calibration’ or ‘computational experiments’. Cooley (1997) defines calibration as ‘a strategy for finding numerical values for the parameters of artificial economies’ and involves a ‘symbiotic relationship between theory and measurement’. The calibration strategy consists of the following steps (see Kydland and Prescott, 1982, 1991, 1996; Plosser, 1989; Backhouse, 1997b; Abel and Bernanke, 2001):

1.Pose a question relating to a specific issue of concern, for example an important policy issue such as ‘What is the quantitative nature of fluctuations caused by technology shocks?’

2.Use a ‘well-tested’ theory, where ‘theory’ is interpreted as a specific set of instructions about how to build the imitation economy.

3.Construct a model economy and select functional forms. Kydland and Prescott (1982) utilize the basic stochastic neoclassical growth model as the cornerstone of their model.

4.Provide specific algebraic forms of the functions used to represent production and consumption decisions. For example, a specific Cobb–Douglas production function is used by Plosser (1989).

5.Calibrate the model economy using data from pre-existing microeconomic studies and knowledge of the ‘stylized facts’. Where no information exists select values for parameters so that the model is capable of mimicking the real-world behaviour of variables.

6.The calibration exercise then involves simulating the effect of subjecting the model to a series of random technology shocks using a computer.

7.The impact that these shocks have on the key macroeconomic variables is then traced out so that the results can be compared with the actual behaviour of the main macroeconomic time series.

8.Run the experiment and compare the equilibrium path of the model economy with the behaviour of the actual economy. Use these types of simulations to answer questions relating to the important issues initially identified under (1).

In their seminal 1982 paper Kydland and Prescott use the neoclassical growth model and follow the calibration/simulation procedure to see if the model can explain aggregate fluctuations when the model economy is subject to technology shocks. As Prescott (1986) recalls, ‘the finding that when uncertainty in the rate of technological change is incorporated into the growth model it displays business cycle phenomena was both dramatic and unanticipated’. The simulations carried out by Kydland, Prescott and Plosser produced some impressive results in that their models are able to mimic an actual economy with respect to some important time series data. These simulations indicate