Snowdon & Vane Modern Macroeconomics

evolve as a statistical process known as a random walk. Equation (6.2) shows a random walk with drift for GNP:

In equation (6.2) gt reflects the ‘drift’ of output and, with Yt also being dependent on Yt–1, any shock to zt will raise output permanently. Suppose a shock raises the level of output at time t1 in Figure 6.2. Since output in the next period is determined by output in period t1, the rise in output persists in every future period. In the case of a random walk with drift, output is said to have a ‘unit root’; that is, the coefficient on the lagged output term in equation (6.2) is set equal to unity, b = 1. The identification of unit roots is assumed to be a manifestation of shocks to the production function.

These findings of Nelson and Plosser have radical implications for business cycle theory. If shocks to productivity growth due to technological change are frequent and random, then the path of output following a random walk will exhibit features that resemble a business cycle. In this case, however, the observed fluctuations in GNP are fluctuations in the natural (trend) rate of output, not deviations of output from a smooth deterministic trend. What looks like output fluctuating around a smooth trend is in fact fluctuations in the natural rate of output induced by a series of permanent shocks, with each permanent productivity shock determining a new growth path. Whereas, following Solow’s seminal work, economists have traditionally separated the analysis of growth from the analysis of fluctuations, the work of Nelson and Plosser suggests that the economic forces determining the trend are not different from those causing fluctuations. Since permanent changes in GNP cannot result from monetary shocks in a new classical world because of the neutrality proposition, the main forces causing instability must be real shocks. Nelson and Plosser interpret their findings as placing limits on the importance of monetary theories of the business cycle and that real disturbances are likely to be a much more important source of output fluctuations. If there are important interactions between the process of growth and business cycles, the conventional practice of separating growth theory from the analysis of fluctuations is illegitimate. By ending the distinction between trend and cycle, real business cycle theorists began to integrate the theory of growth and fluctuations (see King et al., 1988a, 1988b; Plosser, 1989).

6.5Supply-side Shocks

Cyclical instability can arise because of shocks to aggregate demand or shocks to aggregate supply, or some combination of the two. On the demand side, the shocks may originate from instability in some component of the IS

curve, as stressed by Keynes and most of the earlier Keynesian models, or they may originate from instability on the monetary side, as described by the LM curve and emphasized by monetarists. On the supply side, we can imagine a variety of shocks which could result in significant changes in productivity:

1.Unfavourable developments in the physical environment which adversely affect agricultural output. This type of shock would include natural disasters such as earthquakes, drought and floods.

2.Significant changes in the price of energy, such as the oil price ‘hikes’ of 1973 and 1979 and the subsequent reduction in 1986. James Hamilton (1983, 1996) has argued that most US recessions since 1945 have been preceded by energy price increases.

3.War, political upheaval, or labour unrest which disrupts the existing performance and structure of the economy, as with the disruption experienced in the former Yugoslavia and Soviet Union, and more recently in Iraq, or the strikes and labour unrest in the UK during the 1970s and 1984.

4.Government regulations, such as import quotas, which damage incentives and divert entrepreneurial talent towards rent-seeking activities.

5.Productivity shocks generated by changes in the quality of the capital and labour inputs, new management practices, the development of new products and the introduction of new techniques of production.

While some or all of the above will be important at specific points in time and space, it is the fifth category, which we can broadly define as ‘technological shocks’, which we can expect under normal circumstances to be the driving force on the supply side over the longer term for advanced industrial economies. It should not be forgotten that politically stable economies, which are normally free from natural disasters, are still characterized by aggregate fluctuations.

Before examining the main features of REBCT we will first review the main features and ‘stylized facts’ that characterize fluctuations in aggregate economic activity (business cycles).

6.6Business Cycles: Main Features and Stylized Facts

As we noted earlier, the main objective of macroeconomic analysis is to provide coherent and robust explanations of aggregate movements of output, employment and the price level, in both the short run and the long run. We have also drawn attention to the major research programmes, or schools of thought which attempt to explain such movements, that emerged following the publication of Keynes’s (1936) General Theory (Snowdon and Vane,

1997a). Any assessment of a particular theory must take into account its ability to explain the main features and ‘stylized facts’ which characterize macroeconomic instability (see Greenwald and Stiglitz, 1988).

By ‘stylized facts’ we mean the broad regularities that have been identified in the statistical property of economic time series. The identification of the major ‘stylized facts’ relating to business cycle phenomena is a legitimate field of enquiry in its own right (see Zarnowitz, 1992a, 1992b). In the USA the National Bureau of Economic Research, founded in 1920, pioneered research into business cycle phenomena, the landmark work being Measuring Business Cycles by Arthur Burns and Wesley Mitchell, published in 1946. In this book Burns and Mitchell provide their classic definition of business cycles:

Business cycles are a type of fluctuation found in the aggregate economic activity of nations that organise their work mainly in business enterprises. A cycle consists of expansions occurring at about the same time in many economic activities, followed by similarly general recessions, contractions, and revivals which merge into the expansion phase of the next cycle; this sequence of changes is recurrent but not periodic, in duration business cycles vary from more than one year to ten or twelve years.

The identification by Burns and Mitchell and subsequent research of comovements of economic variables behaving in a predictable way over the course of the business cycle led Lucas (1977) to claim that ‘with respect to the qualitative behaviour of co-movements among series (economic variables) business cycles are all alike’. This is an attractive characteristic for the economic theorist because ‘it suggests the possibility of a unified explanation of business cycles grounded in the general laws governing market economies, rather than in political or institutional characteristics specific to particular countries or periods’ (Lucas, 1977, p. 10). Although many economists would not go this far, it is obvious that theoretical explanations of business cycle phenomena must be generally guided by the identified statistical properties of the co-movements of deviations from trend of the various economic aggregates with those of real GDP. The co-movement of many important economic variables in a predictable way is an important feature of business cycles. While business cycles are not periodic (that is, they vary in their length and do not occur at predictable intervals), they are recurrent (that is, they repeatedly occur in industrial economies). How well a particular theory is capable of accounting for the major stylized facts of the business cycle will be a principal means of evaluating that theory. As Abel and Bernanke (2001, p. 284) have argued, ‘to be successful, a theory of the business cycle must explain the cyclical behaviour of not just a few variables, such as output and employment, but of a wide range of key economic variables’.

Blanchard and Fischer, 1989; Zarnowitz, 1992a; Danthine and Donaldson, 1993; Simkins, 1994; Els, 1995; Abel and Bernanke, 2001; Ryan, 2002).

Within macroeconomics there is a great deal of controversy about the causes of aggregate fluctuations in economic activity. However, according to Abel and Bernanke (2001), there is a reasonable amount of agreement about the basic empirical business cycle facts. Even though no two business cycles are identical, they do tend to have many features in common. The main ‘stylized facts’, as summarized by Abel and Bernanke, are classified according to both direction and timing relative to the movement of GDP. With respect to the direction of movement, variables that move in the same direction (display positive correlation) as GDP are procyclical; variables that move in the opposite direction (display negative correlation) to GDP are countercyclical; variables that display no clear pattern (display zero correlation) are acyclical. With respect to timing, variables that move ahead of GDP are leading variables; variables that follow GDP are lagging variables; and variables that move at the same time as GDP are coincident variables.

Table 6.1 indicates that the main stylized facts, as set out by Abel and Bernanke (2001), show that output movements tend to be correlated across all sectors of the economy, and that industrial production, consumption and investment are procyclical and coincident. Government purchases also tend to be procyclical. Investment is much more volatile over the course of the business cycle than consumption, although spending on consumer durables is strongly procyclical. Employment is procyclical and unemployment countercyclical. The real wage and average labour productivity are procyclical, although the real wage is only slightly procyclical. The money supply and stock prices are procyclical and lead the cycle. Inflation (and by implication the price level) and nominal interest rates are procyclical and lagging while the real interest rate is acyclical. As we shall see, this ‘agreement’ about the stylized facts has implications for our assessment of the competing theories. However, deciding what are the ‘facts’ is certainly not uncontroversial (see Ryan and Mullineux, 1997; Ryan, 2002).

6.7Real Business Cycle Theory

The modern new classical research programme starts from the position that ‘growth and fluctuations are not distinct phenomena to be studied with separate data and different analytical tools’ (Cooley, 1995). The REBCT research programme was initiated by Kydland and Prescott (1982), who in effect took up the challenge posed by Lucas (1980a) to build an artificial imitation economy capable of imitating the main features of actual economies. The artificial economy consists of optimizing agents acting in a frictionless perfectly competitive environment that is subject to repeated shocks to productivity. Although

the second phase of new classical macroeconomics has switched emphasis away from monetary explanations of the business cycle, the more recently developed equilibrium models have retained and refined the other new classical building blocks.

Following Frisch (1933) and Lucas (1975, 1977), real business cycle theorists distinguish between impulse and propagation mechanisms. An impulse mechanism is the initial shock which causes a variable to deviate from its steady state value. A propagation mechanism consists of those forces which carry the effects of the shock forward through time and cause the deviation from the steady state to persist. The more recent brand of new classical equilibrium theories have the following general features (Stadler, 1994):

1.REBCT utilizes a representative agent framework where the agent/household/firm aims to maximize their utility or profits, subject to prevailing resource constraints.

2.Agents form expectations rationally and do not suffer informational asymmetries. While expected prices are equal to actual prices, agents may still face a signal extraction problem in deciding whether or not a particular productivity shock is temporary or permanent.

3.Price flexibility ensures continuous market clearing so that equilibrium always prevails. There are no frictions or transaction costs.

4.Fluctuations in aggregate output and employment are driven by large random changes in the available production technology. Exogenous shocks to technology act as the impulse mechanism in these models.

5.A variety of propagation mechanisms carry forward the impact of the initial impulse. These include the effect of consumption smoothing, lags in the investment process (‘time to build’), and intertemporal labour substitution.

6.Fluctuations in employment reflect voluntary changes in the number of hours people choose to work. Work and leisure are assumed to be highly substitutable over time.

7.Monetary policy is irrelevant, having no influence on real variables, that is, money is neutral.

8.The distinction between the short run and the long run in the analysis of economic fluctuations and trends is abandoned.

It can be seen from the above that the major changes from MEBCT are with respect to: (i) the dominant impulse factor, with technological shocks replacing monetary shocks; (ii) the abandonment of the emphasis given to imperfect information as regards the general price level which played such a crucial role in the earlier monetary misperception models inspired by Lucas; and (iii) the breaking down of the short-run/long-run dichotomy in macroeconomic

analysis by integrating the theory of growth with the theory of fluctuations. The lack of clear supporting evidence from econometric work on the causal role of money in economic fluctuations was generally interpreted as providing a strong case for shifting the direction of research towards models where real forces play a crucial role. As we have already seen, this case was further strengthened by the findings of Nelson and Plosser (1982) that most macroeconomic time series are better described as a random walk, rather than as fluctuations or deviations from deterministic trends. Real business cycle theorists also claim that their theories provide a better explanation of the ‘stylized facts’ which characterize aggregate fluctuations. Indeed, they have challenged much of the conventional wisdom with respect to what are the stylized facts (see section 6.14 below).

6.8The Structure of a Real Business Cycle Model

In the typical real business cycle model, aggregate output of a single good, which can be used for both consumption or investment purposes, is produced according to a constant returns to scale neoclassical production function shown by equation (6.3):

where Kt is the capital stock, Lt is the labour input, and At represents a stochastic productivity shift factor (shocks to technology or total factor productivity = TFP). The evolution of the technology parameter, At, is random and takes the form shown in equation (6.4):

Here ρ is large but less than 1, and ε is a random disturbance to technology. Equation (6.4) tells us that the level of technology in any given period depends on the level prevailing in the previous period plus a random disturbance (Kydland and Prescott, 1996). In real business cycle models it is usually assumed that the typical economy is populated by identical individuals. This allows group behaviour to be explained by the behaviour of a representative agent (Plosser, 1989; Hartley, 1997). The representative agent’s utility function takes the general form given by (6.5):

Here Ct is units of consumption and Let hours of leisure for our representative agent. It is assumed that the objective function of the representative agent

(Robinson Crusoe) is to maximize the expected discounted sum of their current and future utility over an infinite time horizon. This maximization problem is given by equation (6.6):

where Ct is the representative agent’s level of consumption, Lt is the number of hours of work, 1–Lt is the hours of leisure consumed, Et {·} is the mathematical expectations operator, Ω t is the information set on which expectations are based, and β is the representative agent’s discount factor. Equation (6.6) provides a specification of a representative agent’s willingness to substitute consumption for leisure. Thus the choice problem for the representative agent is how to maximize their lifetime (infinite) utility subject to resource constraints shown in equations (6.7) and (6.8):

Equation (6.7) indicates that the total amount of consumption (Ct) plus investment (It) cannot exceed production (Yt), and equation (6.8) limits the total number of hours available to a maximum of 1. The evolution of the capital stock depends on current investment (= saving) and the rate of depreciation, δ , as given in equation (6.9):

In this setting a disturbance to the productivity shift factor At (technological shock) will result in a dynamic response from the utility-maximizing representative agent such that we will observe variations in output, hours worked, consumption and investment over many periods.

To illustrate how a ‘business cycle’ can occur in a world without money or financial institutions, let us take the extreme case of Robinson Crusoe on a desert island. Suppose an exogenous shock occurs (a change in At in equation 6.3), raising Robinson Crusoe’s productivity. In this particular example we can think in terms of an unusual improvement in the weather compared to what Crusoe has been used to over the previous years. With the same number of hours worked Crusoe can now produce much more output given the more favourable weather. Because Crusoe is concerned about consumption in the future as well as the present (see equation 6.6), it is likely that he will choose to reduce current leisure and work more hours

in the current period; that is, Crusoe will engage in intertemporal labour substitution.

The incentive to save and work longer hours will be especially strong if Crusoe believes the shock (better-than-normal weather) is likely to be shortlived. Because some of the increase in output is saved and invested, according to equation (6.9), the capital stock will be higher in the next period, and all future periods. This means that the impact of even a temporary shock on output is carried forward into the future. Moreover, the response of the representative agent to the economic shock is optimal, so that Crusoe’s economy exhibits dynamic Pareto efficiency. When the weather returns to normal the following year Crusoe reverts to his normal working pattern and output declines, although it is now higher than was the case before the shock. Remember, Crusoe now has a higher capital stock due to the accumulation that took place during the previous year. As Plosser (1989) argues, the outcomes we observe in response to a shock are ones chosen by the representative agent. Therefore the social planner should in no way attempt to enforce a different outcome via interventionist policies. Note that throughout this hypothetical example we have just witnessed a fluctuation of output (a business cycle) on Crusoe’s island induced entirely by a supply-side shock and Crusoe’s optimal response to that shock. At no time did money or financial variables play any part.

In the Crusoe story we noted how our representative agent engaged in intertemporal labour substitution when the price of leisure increased (in terms of lost potential current output) due to more favourable weather. According to real business cycle theorists, the large response of the labour supply to small changes in the real wage, resulting from the intertemporal substitution of labour, acts as a powerful propagation mechanism. According to this hypothesis, first introduced by Lucas and Rapping (1969), households shift their labour supply over time, being more willing to work when real wages are temporarily high and working fewer hours when real wages are temporarily low. Why should this be the case?

Since the aggregate supply of labour depends on the labour supply decisions of individuals, we need to consider the various factors which influence the amount of labour individuals choose to supply. The benefits of current employment relate primarily (but obviously not entirely) to the income earned which allows the individual worker to consume goods and services. In order to earn income, workers will need to allocate less of their time to leisure, a term used to encapsulate all non-income-producing activities. The utility function for the representative worker indicates that consumption and leisure both yield utility. But in making their labour supply decisions workers will consider future as well as current consumption and leisure. In taking into account the future when deciding how much labour to supply in the current