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In economics, the term model denotes a theoretical construct
that represents economic processes by a set of variables and a set of logical and quantitative relationships between them.
Models are constructed to reason within a idealized logical
framework about economic processes. Their uses include:
- Forecasting economic activity in a way in which conclusions are logically related to assumptions;
- Proposing economic policy to modify future economic activity;
- Presenting reasoned arguments to politically justify economic policy at the national level, to explain and influence company
strategy at the level of the firm, or to provide intelligent advice for household economic decisions at the level of
households.
- Planning and allocation, in the case of centrally planned economies.
Obviously any kind of reasoning about anything uses representations by variables and logical relationships. A model however
establishes an argumentative framework for applying logic
and mathematics that can be independently discussed and that can be applied in various instances.
Economic models in current use have no pretensions of being theories of everything economic; any such pretensions
would immediately be thwarted by computational infeasibility and the paucity of theories for most types of economic behavior.
Therefore conclusions drawn from models will be approximate representations of economic facts. However, properly constructed
models can remove extraneous information and isolate useful approximations of key relationships. In this way more can be
understood about the relationships in question than by trying to understand the entire economic proces.
Types of Models
Borrowing a notion apparently first used in economics by Paul
Samuelson, under the moniker operationally meaningful theorem, we will say a model has empirical content if
the conditions under which the conclusions of the model hold are falsifiable; a model is valid if within the range of
parameters of the model the predictions of the model are satisfied. A model can be valid without having empirical content and
vice-versa. In some cases economic predictions of a model merely assert the direction of movement economic variables; in
econometric models, models propose a statistical hypotheses about economic variables. We illustrate these with some examples.
An accounting model is one based on the premise that for every credit there is a debit. More symbolically, an accounting model
expresses some principle of conservation in the form
- algebraic sum of inflows = sinks - sources
This principle is certainly true for money and it is the basis for national income accounting. Thus in the monetary
interpretation, it is certainly a valid model. However, this model does not have any empirical content since it is not
falsifiable. Any experiment would find that it is true; any deviation from it would be attributed to fraud, arithmetic error or
an extraneous injection (or destruction) of cash which we would interpret as showing the experiment was conducted improperly.
Another kind of model postulates a principle such as profit or utility maximization. An example of this, used by Samuelson as an instance of operationally meaningful
theorem is a model to understand the comparative statics of taxation on the profit-maximizing firm. The model for profit is given by
- π(x,t) = xp(x) - C(x) -
tx
where p(x) is the price that a product commands in the market if it is supplied at
the rate x, xp(x) is the revenue obtained
from selling the product, C(x) is the cost of bringing the product to market at the
rate x, and t is the tax that the firm must pay per unit
of the product sold.
The first order maximization condition for x is
-
Regarding x is an implicitly defined function of t by this equation (see implicit function theorem), one concludes that the
derivative of x with respect to t has the same sign as
-
which is nonpositive if the second order conditions for a local maximum are satisfied.
Thus the profit maximization model predicts something about the effect of taxation on output, namely that output does not
increase with increased taxation. If the predictions of the model fail, we conclude that the profit maximization hypothesis was
false; this should lead to alternate theories of the firm.
The sharp distinction between falsifiable economic models and those that are not is by no means a universally accepted one.
Indeed one can argue that the ceteris paribus qualification that accompanies any claim in economics is nothing more than
an all-purpose escape clause. See the N. de Marchi and M. Blaug collection for a philosophical discussion of these
issues.
Pitfalls
Economic models can be such powerful tools in understanding some economic relationships, that it is easy to ignore their
limitations. An example of this are perfect-competition market equilibrium models. These models are based on perfect information,
an identical product, and inability of individual agents to significantly affect total output or demand. When these assumptions
are met, the resulting static equilibrium conditions will be Pareto
optimal. One can interpret optimality as an ideal situation in which each agent can do no better. When these assumptions
fail, for instance under imperfect information or product differentatition, the model conclusions also fail. Moreover these
models often exclude externalities such as environmental effects.
An economic model that has been established to have some value in explaining a relationship under one set of assumptions, is
useless if the assumptions are not valid. Model assumptions include not only those can be expressed as predicates on model
parameters but others with more qualitative or asymptotic form. This basic concept is however surprisingly often ignored. A
common example is the application of Keynesian economics to government fiscal policy. The simple Keynesian model postulates that
output is a
function of aggregate demand. Government spending is one component
of aggregate demand, so Keynes' model is often applied to conclude that increasing government spending will have the same
positive effect on output as private investment (see Paul Samuelson, Simple Mathematics of Income Determination). This
application of the model is correct in the short run, but the model does not take into account the results of this policy change,
which may affect business cycles, interest and tax rates, private investment, and other factors which could in the long run
either reduce or increase output as a result of the change in fiscal
policy. This example highlights one of the most common failings of the application of economic models, that is differences in
short term and long term effects of economic policy.
History
One of the major problems addressed by economic models has been understanding economic growth. An early attempt to provide a
technique to approach this came from the French physiocratic school in the
Eighteenth century. Among these economists, François Quesnay
should be noted, particularly for his development and use of tables he called Tableaux économiques.
These tables have in fact been interpreted in more modern terminology as a Leontiev model, see the Phillips reference below.
All through the 18th century (that is, well before the founding of modern political economy, conventionally marked by Adam
Smith's 1776 Wealth of Nations) simple probabilistic models were
used to understand the economics of insurance. This was a natural extrapolation
of the theory of gambling, and played an important role both in the development of
probability theory itself and in the development of actuarial science. Many of the giants of 18th century mathematics contributed to this field. Around 1730, De Moivre addressed some of these problems in the 3rd edition of the Doctrine of Chances. Even earlier (1709), Nicolas Bernoulli studies
problems related to savings and interest in the Ars Conjectandi. In 1730, Daniel Bernoulli
studied "moral probability" in his book Mensura Sortis, where he introduced what would today be called "logarithmic utility of money" and applied it
to gambling and insurance problems, including a solution of the paradoxical Saint Petersburg
problem. All of these developments were summarized by Laplace in his Analytical Theory of Probability (1812). Clearly, by the time David Ricardo came along he had a lot of well-established math to draw from.
Examples of Economic Models
References
- N. B. de Marchi and M. Blaug., Appraising Economic Theories, Edward Elgar, 1991.
- A. Phillips, The Tableau Économique of a Simple Leontiev Model, Quarterly Journal of Economics, 69, 1955 pp
137-44.
- Paul Samuelson, Foundations of Economic Analysis, Atheneum, 1965
- Paul Samuelson, The Simple Mathematics of Income Determination, in: Income, Employment and Public Policy; essays
in honor of Alvin Hansen, W. W. Norton, 1948
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