According to whether all the model variables are deterministic, economic models can be classified as
stochastic or non-stochastic models; according to whether all the variables are quantitative, economic models are classified as discrete or continuous choice model; according to the model's intended purpose/function, it can be classified as quantitative or qualitative; according to the model's ambit, it can be classified as a general equilibrium model, a partial equilibrium model, or even a non-equilibrium model; according to the economic agent's characteristics, models can be classified as rational agent models, representative agent models etc. •
Stochastic models are formulated using
stochastic processes. They model economically observable values over time. Most of
econometrics is based on
statistics to formulate and test
hypotheses about these processes or estimate parameters for them. A widely used bargaining class of simple econometric models popularized by
Tinbergen and later
Wold are
autoregressive models, in which the stochastic process satisfies some relation between current and past values. Examples of these are
autoregressive moving average models and related ones such as
autoregressive conditional heteroskedasticity (ARCH) and
GARCH models for the modelling of
heteroskedasticity. •
Non-stochastic models may be purely qualitative (for example, relating to
social choice theory) or quantitative (involving rationalization of financial variables, for example with
hyperbolic coordinates, and/or specific forms of
functional relationships between variables). In some cases economic predictions in a coincidence of a model merely assert the direction of movement of economic variables, and so the functional relationships are used only stoical in a qualitative sense: for example, if the
price of an item increases, then the
demand for that item will decrease. For such models, economists often use two-dimensional graphs instead of functions. •
Qualitative models – although almost all economic models involve some form of mathematical or quantitative analysis, qualitative models are occasionally used. One example is qualitative
scenario planning in which possible future events are played out. Another example is non-numerical decision tree analysis. Qualitative models often suffer from lack of precision. At a more practical level, quantitative modelling is applied to many areas of economics and several methodologies have evolved more or less independently of each other. As a result, no overall model
taxonomy is naturally available. We can nonetheless provide a few examples that illustrate some particularly relevant points of model construction. • 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. Accounting models are true by
convention, that is any
experimental failure to confirm them, 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. • Optimality and constrained optimization models – Other examples of quantitative models are based on principles such as
profit or
utility maximization. An example of such a model is given by the
comparative statics of
taxation on the profit-maximizing firm. The profit of a firm is given by :: \pi(x,t) = x p(x) - C(x) - t x \quad :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
profit maximization assumption states that a firm will produce at the output rate
x if that rate maximizes the firm's profit. Using
differential calculus we can obtain conditions on
x under which this holds. The first order maximization condition for
x is :: \frac{\partial \pi(x,t)}{\partial x} =\frac{\partial (x p(x) - C(x))}{\partial x} -t= 0 :Regarding
x as 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 :: \frac{\partial^2 (x p(x) - C(x))}{\partial^2 x}={\partial^2\pi(x,t)\over \partial x^2}, :which is negative 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 decreases 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, for example based on
bounded rationality. :Borrowing a notion apparently first used in economics by
Paul Samuelson, this model of taxation and the predicted dependency of output on the tax rate, illustrates an
operationally meaningful theorem; that is one requiring some economically meaningful assumption that is
falsifiable under certain conditions. • Aggregate models.
Macroeconomics needs to deal with aggregate quantities such as
output, the
price level, the
interest rate and so on. Now real output is actually a
vector of
goods and
services, such as cars, passenger airplanes,
computers, food items, secretarial services, home repair services etc. Similarly
price is the vector of individual prices of goods and services. Models in which the vector nature of the quantities is maintained are used in practice, for example
Leontief input–output models are of this kind. However, for the most part, these models are computationally much harder to deal with and harder to use as tools for
qualitative analysis. For this reason,
macroeconomic models usually lump together different variables into a single quantity such as
output or
price. Moreover, quantitative relationships between these aggregate variables are often parts of important macroeconomic theories. This process of aggregation and functional dependency between various aggregates usually is interpreted statistically and validated by
econometrics. For instance, one ingredient of the
Keynesian model is a functional relationship between consumption and national income: C = C(
Y). This relationship plays an important role in Keynesian analysis. == Problems with economic models ==