How Central Banks View the World
David Andolfatto
November 2003
1 A Basic Model
Earlier in the course, we talked about the theory of consumption and saving.
In the context of a two-period model, where individuals faced a given stream
of income (y1, y2 and could borrow or lend freely at a (gross) real interest
)
rate R, we derived a consumption function cD
1 (y1 , y2 , R). With preferences
given by U = ln(c1 ) + β ln(c2 ), the consumption function took the form:
cD =
1
1
1+
β
y1 +
y2 .
R
This consumption function is consistent both with Friedman’s
Income Hypothesis :
cD
1 = bW,
where b =
function:
where a =
1
1+
(1)
Permanent
β and W equals wealth; as well as the Keynesian consumption
1
1+
β
cD
1 = a + by1 ,
y2 and b = 1 .
R
1+β
In neoclassical theory, the level of output is determined by equilibrium
in the labour market. This concept of equilibrium views the labour market as a centralized market where competition among buyers and sellers of
labour results in a real wage that clears the market. In labour market search
theory, the labour market is viewed as a decentralized market, where the
equilibrium level of employment (and unemployment) is determined by the
search decisions of workers and the recruiting decisions of firms. Neither of
these approaches is the way that central banks (CBs) view the labour market. The viewpoint adopted by the CB is that the labour market resembles a
dysfunctional neoclassical market, where the real wage fails to adjust rapidly
to clear the market. The real wage is viewed as adjusting gradually over
time to clear the market; when the labour market clears, the level of output
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is said to be at ‘potential.’ Let yP denote ‘potential’ output. Because the
labour market is generally not in equilibrium, the level of aggregate demand
is typically either above or below potential output. I’ll return to the concept
of aggregate demand in a moment, but for now, let me talk a little bit more
about consumption.
Let y2e denote the private sector forecast of future GDP. Assume that
the private sector forms an inflation forecast πe and that this expectation
of inflation is also exogenous (central bankers seem inclined to think that
inflation expectations have a life of their own). Let i denote the nominal
interest rate. From the Fisher equation, we know that:
R=
(1 + i)
(1 + π e )
(2)
.
Substituting (2) into (1), we can derive:
cD =
1
y2e
1 + πe 1+β
1+i
+
1
1+β
y1 .
Notice that if we hold πe fixed, then an increase in the nominal interest rate
will lead to an increase in consumer demand (since the real interest rate is
lower).
Now, think back to our lectures on capital and investment. Let x denote
current capital spending (and the future capital stock) and let y2 = z e F (x),
where F is an increasing and concave function and z e > 0 denotes the expected productivity of capital spending. Recall that the investment demand
function xD is determined by equating the expected marginal product of
capital to the real interest rate; i.e.,
ze F (xD ) = R.
For the production function F (x) = xα , 0 < α < 1, we can solve for the
investment demand function:
xD
=
=
ze α 1−α
;
R
e
1−α
e
z α(1 + π )
(1 + i)
2
(3)
.
Notice that investment demand is increasing in ze and πe ; and decreasing
in i. If households have ‘rational expectations’, then their forecast of future
GDP should be consistent with the investment choices made by firms; i.e.,
y2e
=
ze (xD )α.
Observe that y2e is increasing in ze and πe; and is decreasing in i.
We are now ready to construct the aggregate demand function for this
model economy. Aggregate demand is simply the sum of consumer and investment demand (we are abstracting from the government sector and assuming a closed economy); i.e.,
e e
D
e e
y D = cD
(4)
1 (y1 , i, π , z ) + x (i, π , z ).
Notice that yD is increasing in (y1, πe, ze ) and decreasing in i.
Remember now that we (that is, central banks) are viewing (πe , ze ) as
exogenous parameters (they may fluctuate for reasons unknown). The CB
also views itself as being able to influence the nominal interest rate. For
simplicity, let us suppose that the CB can choose i directly. We now turn to
the question of how contemporaneous GDP is determined. Since the labour
market does not clear in the neoclassical sense, the assumption is that workers
and firms will simply supply to the market whatever is demanded from them;
i.e.,
y1 = y D .
(5)
Combining (4) and (5), we derive:
D
e , z e ) + xD (i, πe , z e ).
(6)
You can think of (6) as one equation in the one unknown (y1). The following
diagram provides a diagrammatic representation of the ‘equilibrium’ level of
output in this model economy (note that, in general, yP may be to either the
left or right of y1∗)
y1
= c1 (y1 , i, π
.
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Notice that according to this world view, the CB can influence the level
of GDP by altering the nominal interest. An increase in the nominal interest
rate will (for a given e ) increase the real interest rate, which then serves to
depress both consumer and investment spending. Firms react to this reduction in demand by supplying less output (and contracting their workforce).
The reverse happens if the CB lowers the nominal interest rate.
π
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2
Stabilizing Output Fluctuations
Most central bankers appear to hold a view (taught to them in their undergraduate macro courses 20 or 30 years ago) that markets are driven by
‘animal spirits’ (a phrase coined by Keynes). These animal spirits manifest
themselves as wild fluctuations in expectations that are not based on any
change in economic ‘fundamentals.’ These fluctuations in expectations are
sometimes viewed as being ‘irrational.’ It is also possible to take the view
that these fluctuations are ‘rational’ to the extent they become self-fulfilling.
In either case, it seems clear that the CB should try to prevent these animals
spirits from causing ’unwarranted’ fluctuations in GDP. The way the CB can
try to achieve such an objective is by altering the interest rate in response to
what it perceives to be developments that might lead to GDP either falling
below or rising above ’potential’ GDP.
In the context of the model above, one can think of modelling ‘animal
spirits’ as exogenous fluctuations in ze and πe. Let imagine that the economy
is initially at its potential yP . Suppose now, that for some crazy reason, that
individuals become unduly ‘pessimistic’ about future business conditions,
leading to a fall in ze (the expected productivity of current capital spending).
From the model above, we see that the direct effect of this pessimism is a
drop in desired capital spending. This drop in capital spending leads to an
expected decline in future GDP, which serves to reduce household wealth,
which in turn leads to a decline in consumer demand. Together then, this
shock leads to a decline in aggregate demand. Firms react to reduced demand
by contracting the supply of output (and letting go workers). The economy
heads into recession for no good reason.
If the CB observes output declining below potential then, it reacts to
this development by cutting the interest rate in an attempt to stimulate
aggregate demand. Notice that this policy would only work to the extent
that the nominal interest rate is positive. If the nominal interest rate is zero
(as is currently the case in Japan), then the CB is powerless to stimulate
the economy (the economy is said to be in a ‘liquidity trap’). The reverse
would happen should the CB see output rising above potential. In this case,
the CB would view the economy as ‘overheating’ and so would respond by
increasing the interest rate.
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3
Stabilizing Inflation
These days, central banks seem more concerned with stabilizing inflation
rather than output. Perhaps this is because central banks have come to the
realization that they were not especially good at stabilizing output. However,
they do seem to have the power to stabilize the inflation rate. Since fluctuations in inflation are viewed as something undesirable, why not concentrate
on inflation instead of output? In fact, many countries (Canada included)
have recently adopted inflation targets as a primary objective of the CB. In
order to understand how the CB can influence inflation, we need a theory of
the inflation rate.
We have already discussed in class an old theory of inflation (the quantity
theory). According to the quantity theory:
(1 + π ) =
1+µ
1+γ
,
where µ represents the rate of growth of the money supply and γ represents
the rate of growth of money demand (which is assumed to grow at the same
rate as real output). This simple theory holds up remarkably well in terms
of explaining the level of inflation over long periods of time. However, the
theory seems to break down over shorter time intervals.
Consequently, central bankers tend to prefer an alternative theory of inflation that is based on the Phillips curve, which is an alleged empirical
relationship that appears (in the eyes of central bankers, anyway) to hold in
the data. A typical Phillips curve takes the following form:
π = π e + φ(y1 − y P ),
(7)
where φ > 0.
What equation (7) tells us is that if output is at potential, then the actual
inflation rate is determined by the expected inflation rate. If output is above
potential, then the actual inflation rate turns out to be higher than expected.
Conversely, if output is below potential, then inflation turns out to be lower
than expected.
Now, remember that crazy fluctuations in z e induce unwarranted fluctuations in y1 . As a result, actual inflation will fluctuate as well. To the extent
that the CB views these fluctuations in inflation as undesirable, it may want
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to adjust the interest rate to counteract any undesirable movement in z e .
As it turns out, the way that the CB can do this is by stabilizing output at
potential.
However, what if the economy is subject to a different type of shock?
In particular, what if fluctuations are coming not from z e but from πe ? In
this case, stabilizing output at its potential will not minimize fluctuations
in inflation. In fact, if there was a positive ‘inflation shock’ (an increase in
πe , in order to stabilize inflation the CB would have to raise interest rates
sufficiently high in order to send the economy into recession (so that y1 falls
below potential). Alternatively, suppose that π e is currently very high (as it
was in Canada during the 1970s) and suppose that the CB was determined
to lower π e (a policy adopted by the Bank of Canada in the early 1980s).
The way that the CB could try to achieve such an outcome is by raising
interest rates through the roof (in fact, interest rates approached 20% in
the early 1980s). This high interest rate policy would have the effect of
sending the economy into a dramatic recession and (according to the Phillips
curve) result in lower realized rates of inflation. The idea here is that after
observing several periods of low inflation, individuals would eventually revise
downward their expectations of inflation πe . Eventually, this is exactly what
happened in Canada (and many other countries). It was this painful episode
that makes central bankers today so concerned about keeping inflation (and
inflation expectations) at low levels.
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