980916

_{[Note for bibliographic reference: Melberg, Hans O. (1998) Entertaining and
suggestive about the business cycle: A Review of Tvede, www.oocities.org/hmelberg/papers/980916.htm]

Entertaining and suggestive about the business cycle

- Review of Lars Tvede: Business Cycles: From John Law to Chaos theory

by Hans O. Melberg _{English version: Business Cycles

I read the Danish version: Dødsspiralen: Konjunkturproblemet i videnskaben fra John
Law til kaosteori Samfundslitteratur, Frederiksberg, 1993

215 pages, ISBN: 87-593-0383-2}

Introduction

Lars Tvede's book on economic fluctuations is enjoyable, accessible, and relatively
simple. There are three main themes. First, Tvede presents the empirical and intellectual
history of economic fluctuations from John Law to modern chaos theory. Second, he draws on
the historical material to develop a useful list of mechanisms that help explain
fluctuations. Finally, he gives us an introduction to non-linear theories of economic
cycles (chaos theory). Although the style is non-academic and there are no formal
mathematical models, I think students and academics can benefit from this book. The lack
of formal mathematical modeling is partly due to the nature of the book ("popular
science"), but it might also reflect a deeper conviction that equilibrium models
cannot capture the business cycle.

In this review I shall, first, present a list of the mechanisms that I have collected from
Tvede's description of the intellectual history. In the second part, I shall give a closer
account of the concepts used in chaos theory.

Mechanisms

When faced with an empirical phenomena like large economic fluctuations, one might try to
develop a mathematical equilibrium model that can account for the "stylized"
facts. There are at least two potential problems with this approach. First, if there is no
equilibrium or many equilibria in the real world a model with one equilibrium fails to
capture reality. Second, the mathematical tools available and our relative lack of
knowledge may make it more profitable in terms of understanding to focus on mechanisms
instead of spending much time on large models. Before I examine these arguments more
closely, I want to say something about the concept of equilibrium.

An equilibrium is a situation in which nobody wants to change his or her behviour. There
are, in short, no forces for change. There are four main questions one can ask about
equilibrium: Does it exist? Is it unique? Is it stable? Is it efficient? An example of a
real word situation with more than one equilibria, is the choice between driving on the
left or right side of the road. Both are acceptable as long as everybody else does the
same, i.e. we have two equilibria. An example of a situation with no equilibrium, is the
following game: "The person who writes down the highest number wins a prize."
There are always some people who want to write a higher number than they wrote the first
time. Moreover, there are also many games in which there is no equilibrium in "pure
strategies" (there is often several "mixed strategies" equilibria, but one
might argue that these are psychologically unstable).

More seriously, the notion of equilibrium used by most economists relies on rational
choice maximization. The problem with this is that since we live in an uncertain world it
may be impossible to make a rational choice. For instance, the choice of how much
information to collect depends on the expected net benefit of more information. But there
may be no correct mathematical basis for calculating this probability. Similarly, Keynes
argued that there was no way we could form mathematically correct expectations beyond the
immediate future. All this means that equilibrium may fail to exists (since sometimes no
rational choice maximization is possible), and there may be several equilibria. Finally,
we may wonder whether we should revise the dependence between rationality and equilibrium,
for instance using the concept of evolutionary equilibria or psychological equilibria.

The point of the discussion about equilibrium is that is illustrates the complexities of
the real world and the potential shortcomings of macro-models. If there is no equilibrium
mathematical models implying one are misleading. Non-linear dynamics with many equilibria
are also difficult (but not impossible) to handle. Hence, given our limited abilities and
knowledge it may be best simply to search for a verbal description of the mechanisms that
cause economic fluctuations.

SOME MECHANISMS

Tvede's discussion of the intellectual history of the business cycle contains a number of
mechanisms. In this section I simply want to give a short description of these:

Old theories

Saint-Simon: "Nobody could pay since nobody were paid" (p. 12).

Thornton: Increased credit confirms itself as long as activity increases, but when
the economy reaches full capacity the process goes in reverse; contraction decreases
activity which dictate further contraction (p. 43).

Say's law: Supply creates its own demand (so there can be no shortage of money)! If
you produce something you can always sell it to buy something else (given that you adjust
the price). If people do not buy "enough" (i.e. the amount produced) the
interest rate will fall and economic activity will increase.

Ricardo's gold standard argument: The gold standard is self-stabilizing because a)
if you try to increase the money supply you will run a deficit which has to be financed by
exporting gold which will reduce the money supply. And b) Low money supply leads to a
balance of payment surplus which in turn increases the gold supply and hence the money
supply (p. 46).

John S. Mill: Confidence and competitive investment: Changes in the saving rate is
an important determinant of the cycle (so Says law does not apply) and this saving rate is
determined by the degree of confidence people have in the future. Confidence is governed
partly by trend-extrapolation, so if prices increase people buy more to avoid the expected
future price increase. This leads to even higher prices. The argument that the money
supply is stable (and hence should limit the cycle as argued by Cantillion) does not work
because the money supply is endogenous; velocity and bank credit can increase the
effective supply. In addition to the importance of confidence, Mill also introduced the
concept of "competitive investment" to explain business cycles. The concept
applies to a situation in which a new innovation creates a new market. It may be difficult
to form correct expectations about this market and this may lead to over-investment.
(Basing their investment on the belief that the initially high price will continue - i.e.
trend-extrapolation - they will all invest but this will increase the productive capacity
so much that the price will decrease.) A concrete example of this is railroad-investment
in the US in the nineteenth century. Initially very profitable the over-investment led to
a drastic decrease in the price and finally bankrupt railroad companies (p. 50).

Modern theories

Tvede distinguishes the following main categories of business cycle theories (p. 77):

Over-investment (Wicksell, Robertson): One mechanism that can create
over-investment is the so-called accelerator principle. This simply means that investment
is very sensitive to changes in sales. Small changes in sales can greatly increase or
decrease investment. Another mechanism that can create over-investment is when the
interest rate is below its "natural rate" - that is below the rate of return
people earn in business.

Business conditions. For instance, during a boom productivity may decrease as
inefficient capital is used, while the reverse happens during a recession; productivity
increases as one sheds the least efficient capital/workers.

Psychology (contageous fear and optimism) (A. C. Pigou): When many people go
skating on a pond you may think the ice must be safe and joint the people skating. Yet,
the more people on the ice, the less safe it is. People may "imitate" other
people's behaviour and this creates a herd-behaviour that leads to ups and downs.

Monetary theories (Fisher, Friedman): In short, fluctuations are always caused by
changes in the money supply (especially unexpected changes). Underconsumption (Keynes):
Increased uncertainty leads to increased saving and not enough demand to maintain full
employment. Says argument that people will buy when prices fall does not apply because
people may expect further price decreases and hence delay their purchases. Moreover, the
saving that ocurred after the first uncertainty, may increase uncertainty even more (more
people may be threatened by layoffs) and hence increase the demand for liquid reserves
even more (increase saving even more) which in turn increases uncertainty even more and so
on (p. 102).

CHAOS AND NON-LINEAR MECHANISMS

In addition to the traditional theories of economic fluctuations - Tvede spends quite a
few pages on modern chaos theory. He is very good at giving short and intuitive
explanations of the central concepts:

Fractals: Self-replicating patterns i.e. the small part of a large picture tends to
show the same patterns as the large picture.

Feigenbaum threes: A figure which shows the number of solutions that a model
converges to after repetition (for some parameter values this is one, then two, then four,
then eight and so on, there are also intervals of no stable solution (chaos).

Hurst exponent: In a system with positive feedback the range (difference between
the highest and lowest value) will increase more than the square root of the number of
observations (which is the rule for normal observations). Hence, by observing the range as
one increases the number of observations we can measure the amount of positive feedback. A
number above 0.5 indicates positive feedback. 1.0 is maximium feedback (see p. 142).

Attractors (and strange attractors): These are the stable situations in the
phase-space. They are either "point-attractors" which is s stable situation with
no change (no movement in our case), or a stable cycle (repeated over and over again).
Strange attractors occur when the object moves within a limited "area" in the
phase-space, but never repeats its old cycle.

Phase-space: Imagine a pendelum going back and forth in a space with no fricton. We
could plot time on one axis and the position of the pendulum on the other. This graph is
readily understood by most people. However, in a phase space we plot the position of the
pendelum on the horizontal axis and speed on the vertical axis (for more see Tvede p.
151).

Dimensions: The dimension depends on how the object fills the phase-space. The more
uneven it is the higher the dimension. A straight line has dimesion 1, an uneven coastline
is close to 2 (2 is the dimension of a plane).

Lyapunov exponent and hyperchaos: If a small change leads to large differences over
time, the Lyapunov exponent is positive in that dimension. A negative exponent means that
a small initial difference does not affect the result over time (convergence). A zero
exponent means that there neither the "butterfly" effect or the stabilizing
dampening effect. Hyperchaos exists, for instance, with the following Lyapunov exponents
in the four dimansial room: (+,+,0,-). This kind of behaviour was discovered by O.E.
Rossler (in 1979) in a system with four differential equation. In "real life" it
was later discovered that the "beer" game could lead to this kind of behaviour.

Rescaled Range Analysis: If there is a change in the feedback process this should
be reflected in the Hurst-exponent. By drawing a line which shows how the Hurst exponent
of a time series changes over time, one can observe when there are significant changes.
This is called rescaled range analysis.

Tvede also also presents a summary of the five general mechanisms he thinks are the key
causes of non-linear behaviour. These are (135-136):

1. Loops (x cause y which in turn stimulate x) (e.g Mill and Marshall: Price up =
people buy more (expect price to go up more so rational to buy now = price up (since many
buy) which starts the cycle all over again.)

2. Eccho (e.g. re-investment in the shipping industry or baby-booms after wars
which may lead to building booms that are repated when the baby-boomers get their own
babies).

3. Cascade-reactions (for instance information often spreads like cascades; two
people known something who each tell it to one person, then four people know this, and if
they all tell it to one and so on we have: 2, 4, 8, 16, 32, 64, 128 ...).

4. Lags (It often takes some time before the cause is present until we see the
consequences and this leads to non-linear behaviour evident in cob-web cycles and the
accelerator theory).

5. Disinhibitions (potential negative feedback processes temporarily hindered by
positive feed-back processes. Evident in many psychological theories - for instance we
want to leave a room when we see smoke, but if nobody around us did showed sign of
discomfort most people tend to stay too - they do not want to be the first to panic).

Tvede then goes on to give some examples of the mechanisms that creates these five
non-linearities in the stock-market/the financial sector (p. 165-) and in the real sector
of the economy (see the discussion of the beer game, p. 175-).

Short criticism

Tvede gives us a part of the picture, but sometimes the presentations is characterized by
speculation. For instance, the argument that "phase lock-in" makes the many
non-linearities unite to cause large collapses (like in 1930), is speculatative (p.
195). Two clocks on the same wall may tend to become synchronized and synchronization may
be large problem for car designers, but this does not explain synchronization of waves in
the economy or prove that we have a synchronization problem. We need to know why
synchronization occurs and Tvede does not give us a convincing account of this. Maybe, for
instance, there is little synchronizations, only random accidents? This could explain
stability as well as occasional breakdowns; In general the economy works fine but when we accidentially
have several bad effects at the same time they are magnified through the mechanisms he
describes.

Second, consider Tvede's entertaining comment that after E. Peters had discovered the
periodicity of economic cycles (using the Hurst exponenet and rescaled range analysis) he
"turned his attention to the stock-market" (p. 158). It seems to me that this
innocent comment shows that as soon as we "discover" the rules, the rules will
change. If people know when the market will turn, they will use this information to buy
stocks when they are low and sell when they are high (as Tvede says about E. Peter). But
this very process will lead to stabilization; buying drives the price us (when the market
is down) and selling drives the price down (when the market is top). And, knowing that
others know what E. Peters know we may try to be slightly smarter and sell/buy right
before him (which in turn is right before the market turns), but this kind of reasoning
would lead to a stable market.

Conclusion

Tvede is entertaining and he has a gift for intuitive explanations. The book, correctly
focuses on mechanism instead of large theories and models. In so doing he covers a large
terrain. As a result there are simplifications and popularizations but judged by its own
pretensions this is a good book that even academics can benefit from. Everything he says
is not covered by a footnote or a reference, but as long as one discounts for this (i.e.
remain critical e.g. of the ability of chaos theory to explain economic crisis), it is a
valuable book.

_{[Note for bibliographic reference: Melberg, Hans O. (1998) Entertaining and
suggestive about the business cycle: A Review of Tvede, www.oocities.org/hmelberg/papers/980916.htm]}}