# 6.4 Cycles versus Random Walks

During the 1970s, with the rebirth of interest in business cycle research,

economists became more involved with the statistical properties of economic

time series. One of the main problems in this work is to separate trend from

cycle. The conventional approach has been to imagine that the economy

evolves along a path reflecting an underlying trend rate of growth described

by Solow’s neoclassical model (Solow, 1956). This approach assumes that

the long-run trend component of GNP is smooth, with short-run fluctuations

about trend being primarily determined by demand shocks. This conventional

wisdom was accepted by Keynesian, monetarist and new classical economists

alike until the early 1980s. The demand-shock models of all three

groups interpret output deviations from trend as temporary. If business cycles

are temporary events, then recessions create no long-run adverse effects on

GDP. However, whereas Keynesians feel that such deviations could be severe

and prolonged and therefore justify the need for corrective action, monetarists,

and especially new classical economists, reject the need for activist

stabilization policy, having greater faith in the equilibrating power of market

forces and rules-based monetary policy.

In 1982, Nelson and Plosser published an important paper which challenged

this conventional wisdom. Their research into macroeconomic time

series led them to conclude that ‘macroeconomic models that focus on

monetary disturbances as a source of purely transitory fluctuations may

never be successful in explaining a large fraction of output variation and

that stochastic variation due to real factors is an essential element of any

model of macroeconomic fluctuations’. If real factors are behind aggregate

fluctuations, then business cycles should not be viewed as temporary events.

Recessions may well have permanent effects on GDP. The much-discussed

‘productivity slowdown’ after 1973 represents one such example (see Fischer

et al., 1988). Abel and Bernanke (2001) note that GDP in the USA remained

below the levels consistent with the 1947–73 trend throughout the

1980s and 1990s. In an analysis of the UK economy in the interwar period

Solomou (1996) finds that the shock of the First World War, and further

shocks in the immediate post-war period, had a permanent effect on the

path of equilibrium output.

Nelson and Plosser reached their important conclusion because in their

research into US data they were unable to reject the hypothesis that GNP

follows a random walk. How does this conclusion differ from the conventional

approach? The view that reversible cyclical fluctuations can account

for most of the short-term movements of real GNP can be represented by

equation (6.1):

Yt gt bYt−1 zt (6.1)

where t represents time, g and b are constants and z represents random shocks

which have a zero mean. In equation (6.1) gt represents the underlying

average growth rate of GNP which describes the deterministic trend. Suppose

there is some shock to zt that causes output to rise above trend at time t. We

assume that the shock lasts one period only. Since Yt depends on Yt–1, the

shock will be transmitted forward in time, generating serial correlation. But

since in the traditional approach 0 < b < 1, the impact of the shock on output

will eventually die out and output will return to its trend rate of growth. In

this case output is said to be ‘trend-reverting’ or ‘trend-stationary’ (see

Blanchard and Fischer, 1989).

The impact of a shock on the path of income in the trend-stationary case is

illustrated in Figure 6.1, where we assume an expansionary monetary shock

occurs at time t1. Notice that Y eventually reverts to its trend path and

therefore this case is consistent with the natural rate hypothesis, which states

that deviations from the natural level of output caused by unanticipated

monetary shocks will be temporary.

In contrast to the above, Nelson and Plosser argue that most of the changes

in GNP that we observe are permanent, in that there is no tendency for output

to revert to its former trend following a shock. In this case GNP is said to

Figure 6.1 The path of output in the ‘trend-reverting’ case

Figure 6.2 The path of output where shocks have a permanent influence

evolve as a statistical process known as a random walk. Equation (6.2) shows

a random walk with drift for GNP:

Yt gt Yt−1 zt (6.2)

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).

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