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
The real business cycle school 303
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).
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
The real business cycle school 303
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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