Контрольная работа: Endogenous Cycle Models
Контрольная работа: Endogenous Cycle Models
Contents
Introduction
1. Endogenous Cycle
Models: Kaldor's Non-Linear Cycle
Conclusion
Literature
The multiplier-accelerator
structures reviewed above have linear dynamic structures. As a result, cycles
are generated and maintained only by structurally unstable parameter values (Samuelson)
or dampened dynamics with continuous exogenous shocks (Frisch-Slutsky) or
exogenously-constrained explosive dynamics (Hicks). As a result, early
Keynesian linear multiplier-accelerator fall dangerously close to an "untheoretical"
explanation of the cycle - precisely what the original Oxbridge research
programme was designed to avoid.
However, linear
structures are often adopted because they are simple and the results they yield
are simple. But simplicity is sometimes more a vice than a virtue - particularly
in the case of macrodynamics and economic fluctuations. It is not only unrealistic
to assume linearity, but the very phenomena that we are out to uncover, the
formation of cycles and fluctuations, becomes relegated to the "untheory"
of exogenous shocks, ceilings, floors, etc. The contention of Lowe (1926) and
many Keynesian writers is that theories of fluctuations ought really to explain
how fluctuations arise endogenously from a working system otherwise (paraphrasing
Lowe's title), how is business cycle theory possible at all?
As a result,
many economists have insisted that non-linear structures should be employed
instead. Why interest ourselves with non-linear dynamics? As one famous
scientist answered, for the same reason we are interested in "non-elephant
animals". In short, non-linear dynamical structures are clearly the more
general and common case and restricting attention to linear structures not only
unrealistically limits the scope of analysis, it also limits the type of
dynamics that are possible.
1. Endogenous Cycle Models: Kaldor's
Non-Linear Cycle
One of the most
interesting theories of business cycles in the Keynesian vein is that expounded
in a pioneering article by Nicholas Kaldor (1940). It is distinguishable from
most other contemporary treatments since it utilizes non-linear functions,
which produce endogenous cycles, rather than the linear multiplier-accelerator
kind which rely largely on exogenous factors to maintain regular cycles. We
shall follow Kaldor's simple argument and then proceed to analyze Kaldor in the
light of the rigorous treatment given to it by Chang and Smyth (1971) and
Varian (1979).
What prompted Kaldor's
innovation? Besides the influence of Keynes (1936) and Kalecki (1937), in his
extremely readable article, Kaldor proposed that the treatment of savings and
investment as linear curves simply does not correspond to empirical reality. In
(Harrodian version of) Keynesian theory, investment and savings are both
positive functions of output (income). The savings relationship is cemented by
the income-expenditure theory of Keynes:
S = (1-c) Y
whereas
investment is positively related to income via an accelerator-like
relationship, (which, in Kaldor, is related to the level rather than the
change in income):
I = vY
where v, the Harrod-Kaldor
accelerator coefficient, is merely the capital-output ratio. Over these two
relationships, Kaldor superimposed Keynes's multiplier theory: namely, that
output changes to clear the goods market. Thus, if there is excess goods demand
(which translates to saying that investment exceeds savings, I > S), then
output rises (dY/dt > 0), whereas if there is excess goods supply (which
translates to savings exceeding investment, I < S), then output falls.
The
implications of linearity can be visualized in Figure 1, where we draw two
positively-sloped linear I and S curves. To economize on space, we place
two separate sets of curves in the same diagram. In the left part of Figure 1,
the slope of the savings function is larger than that of the investment
function. Where they intersect (I = S) is the equilibrium Y*. As we can note,
left of Y*, investment is greater than savings (I > S), hence output will
increase by the multiplier dynamic. Right of point Y*, savings is greater than
investment (I < S), hence output will fall. Thus, the equilibrium point Y*
is stable.
In the right
side of Figure 1, we see linear S and I functions again, but this time, the
slope of the investment curve is greater than that of the savings curve. Where
they intersect, Y*, investment equals savings (I = S) and we have equilibrium. However,
note that left of the equilibrium Y*, savings are greater than investment (I
< S), thus output will contract and we will move away from Y*. In contrast,
right of Y*, investment is greater than savings (I > S), so output will
increase and move further to the right of Y*. Thus, equilibrium Y* is unstable.
Fig.1 - Savings,
Investment and Output Adjustment
Both exclusive
cases, complete stability and complete instability, are implied by linear I and
S curves in figure 1, are incompatible with the empirical reality of cycles and
fluctuations. Hence, Kaldor concluded, it might be sensible to assume that the
S and I curves are non-linear. In general, he assumed I = I (Y, K) and S = S (Y,
K), where investment and savings are non-linear functions of income and capital
as in the Figure 2 below.
We shall focus
the relationship with income first. The logic Kaldor (1940) gave for this is
quite simple.
The non-linear
investment curve, shown in Figure 2 can be explained by simply recognizing that
the rate of investment will be quite low at extreme output levels. Why? Well,
at low output levels (e. g. at YA), there is so much excess capacity
that any increase in aggregate demand will induce very little extra investment.
The extra
demand can be accomodated by existing capacity, so the rate of investment is
low. In contrast, at high rates of output, such as YC, Wicksellian
problems set in. In other words, with such high levels of output and demand,
the cost of expanding capacity is also increasing, capital goods industries are
supply-constrained and thus demand a higher price from entrepreneurs for
producing an extra unit of capital. In addition, the best investment projects
have probably all already been undertaken at this point, so that the only
projects left are low-yielding and simply might not be worth the effort for the
entrepreneur.
Thus, the rate
of investment will also be relatively low. At output levels between YA
and YC (e. g. at YB), the rate of investment is higher. Thus,
the non-linearity of the I curve is reasonably justified.
What about the
non-linear savings curve, S? As shown in Figure 2, it is assumed by Kaldor that
savings rates are high at extreme levels of output. At low levels of output (YA),
income is so low that savings are the first to be cut by individuals in their
household decisions.
Therefore, at
this point, the rate of saving (or rather, in this context, the rate of
dissaving) is extremely high. Slight improvements in income, however, are not
all consumed (perhaps by custom or precaution), but rather much of it is saved.
In contrast, at
high levels of output, YC, income is so high that the consumer is
effectively saturated. Consequently, he will save a far greater portion of his
income - thus, at points like YC, the savings rate is quite high.
Fig.2 - Non-Linear
Investment and Savings
With the
non-linearity of I and S justified, Kaldor (1940) proceeded to analyze cyclical
behavior by superimposing the I and S curves (as in Figure 2). As we can see,
there are three points of intersection (A, B and C) where savings equals
investment (I = S). Let us consider each individually. Left of point A, investment
is greater than savings hence, by the multiplier, Y increases to YA;
to the right of point A, savings is greater than investment (hence Y decreases
to YA). Consequently, it is easy to note that A (and YA) is
a stable point. The same analysis applies to the points to the right and left
of YC, hence C (and YC) is also a stable point.
Intersection
point B (at YB) in Figure 2 is the odd one. Left of B, savings
exceeds investment (so Y falls left of YB) and right of B,
investment exceeds savings (so Y increases right of YB). Thus, B is
an unstable point. Consequently, then, we are faced with two stable equilibria
(A and C) and an unstable equilibrium (B). How can this explain cyclical
phenomenon? If we are at A, we stay at A. If we are at C, we stay at C. If we
are at B, we will move either to A or C with a slight displacement. However, no
cycles are apparent.
The clincher in
Kaldor's system is the phenomenon of capital
accumulation at a given point in time. After all, as Kaldor reminds
us, investment and savings functions are short term. At a high stable level of
output, such as that at point YC in the figure above, if investment
is happening, the stock of capital is increasing. As capital stock increases,
there are some substantial changes in the I and S curves. In the first
instance, as capital stock increases, the return or marginal productivity of
capital declines. Thus, it is not unreasonable to assume that investment will
fall over time. Thus, it is acceptable that dI/dK < 0, i. e. the I curve falls.
However, as
capital goods become more available, a greater proportion of production can be
dedicated to the production of consumer goods. As consumer goods themselves
increase in number, the prices of consumer goods decline. For the individual
consumer, this phenomenon is significant since it implies that less income is
required to purchase the same amount of goods as before. Consequently, there
will be more income left over to be saved. Thus, it is also not unreasonable to
suspect that the savings curve, S, will gradually move upwards, i. e. dS/dK
> 0. This is illustrated in Figure 3.
Страницы: 1, 2, 3 |
