Editing Economic model (section)

== Types of models ==

According to whether all the model variables are deterministic, economic models can be classified as [[stochastic process|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 process]]es. 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 [[Jan Tinbergen|Tinbergen]] and later [[Herman Wold|Wold]] are [[autoregressive]] models, in which the stochastic process satisfies some relation between current and past values. Examples of these are [[autoregressive moving average model]]s 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 [[Function (mathematics)|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 (economics)|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 (general)|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 (finance)|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 (norm)|convention]], that is any [[experiment]]al 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 (economics)|profit]] or [[utility maximization]]. An example of such a model is given by the [[comparative statics]] of [[tax]]ation on the profit-maximizing firm. The profit of a firm is given by

::<math> \pi(x,t) = x p(x) - C(x) - t x \quad</math>

:where <math>p(x)</math> is the price that a product commands in the market if it is supplied at the rate <math>x</math>, <math>xp(x)</math> is the revenue obtained from selling the product, <math>C(x)</math> is the cost of bringing the product to [[Market (economics)|market]] at the rate <math>x</math>, and <math>t</math> 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

::<math> \frac{\partial \pi(x,t)}{\partial x} =\frac{\partial (x p(x) - C(x))}{\partial x} -t= 0 </math>

: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

::<math> \frac{\partial^2 (x p(x) - C(x))}{\partial^2 x}={\partial^2\pi(x,t)\over \partial x^2},</math>

:which is negative if the [[Second derivative test|second order condition]]s 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 [[falsifiability|falsifiable]] under certain conditions.

* Aggregate models. [[Macroeconomics]] needs to deal with aggregate quantities such as [[Output (economics)|output]], the [[price level]], the [[interest rate]] and so on. Now real output is actually a [[Vector (geometric)|vector]] of [[good (accounting)|goods]] and [[Service (economics)|service]]s, such as cars, passenger airplanes, [[computer]]s, 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 [[Wassily Leontief|Leontief]] [[input–output model]]s 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 research|qualitative analysis]]. For this reason, [[macroeconomic model]]s 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 economics|Keynesian model]] is a functional relationship between consumption and national income: C = C(''Y''). This relationship plays an important role in Keynesian analysis.