Aneconomic model is atheoretical construct representing economicprocesses by a set ofvariables and a set oflogical and/or quantitative relationships between them. The economicmodel is a simplified, oftenmathematical, framework designed to illustrate complex processes. Frequently, economic models positstructural parameters.[1] A model may have variousexogenous variables, and those variables may change to create various responses by economic variables. Methodological uses of models include investigation, theorizing, and fitting theories to the world.[2]
In general terms, economic models have two functions: first as a simplification of and abstraction from observed data, and second as a means of selection of data based on aparadigm ofeconometric study.
Simplification is particularly important for economics given the enormouscomplexity of economic processes.[3] This complexity can be attributed to the diversity of factors that determine economic activity; these factors include: individual andcooperative decision processes,resource limitations,environmental andgeographical constraints,institutional andlegal requirements and purelyrandom fluctuations. Economists therefore must make a reasoned choice of which variables and which relationships between these variables are relevant and which ways of analyzing and presenting this information are useful.
Selection is important because the nature of an economic model will often determine what facts will be looked at and how they will be compiled. For example,inflation is a general economic concept, but to measure inflation requires a model of behavior, so that an economist can differentiate between changes in relative prices and changes in price that are to be attributed to inflation.
In addition to their professionalacademic interest, uses of models include:
Forecasting economic activity in a way in which conclusions are logically related to assumptions;
Proposingeconomic policy to modify future economic activity;
Presenting reasoned arguments to politically justify economic policy at the national level, to explain and influencecompany strategy at the level of the firm, or to provide intelligent advice for household economic decisions at the level of households.
Infinance, predictive models have been used since the 1980s fortrading (investment andspeculation). For example, emerging marketbonds were often traded based on economic models predicting the growth of thedeveloping nation issuing them. Since the 1990s many long-termrisk management models have incorporated economic relationships between simulated variables in an attempt to detect high-exposure future scenarios (often through aMonte Carlo method).
A model establishes anargumentative framework for applying logic andmathematics that can be independently discussed and tested and that can be applied in various instances. Policies and arguments that rely on economic models have a clear basis for soundness, namely thevalidity of the supporting model.
Economic models in current use do not pretend to betheories of everything economic; any such pretensions would immediately be thwarted bycomputational infeasibility and the incompleteness or lack of theories for various 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 usefulapproximations of key relationships. In this way more can be understood about the relationships in question than by trying to understand the entire economic process.
The details of model construction vary with type of model and its application, but a generic process can be identified. Generally, any modelling process has two steps: generating a model, then checking the model for accuracy (sometimes called diagnostics). The diagnostic step is important because a model is only useful to the extent that it accurately mirrors the relationships that it purports to describe. Creating and diagnosing a model is frequently an iterative process in which the model is modified (and hopefully improved) with each iteration of diagnosis and respecification. Once a satisfactory model is found, it should be double checked by applying it to a different data set.
According to whether all the model variables are deterministic, economic models can be classified asstochastic 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 asquantitative 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.
Non-stochastic models may be purely qualitative (for example, relating tosocial choice theory) or quantitative (involving rationalization of financial variables, for example withhyperbolic coordinates, and/or specific forms offunctional 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 theprice of an item increases, then thedemand 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 qualitativescenario 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 modeltaxonomy is naturally available. We can nonetheless provide a few examples that illustrate some particularly relevant points of model construction.
Anaccounting model is one based on the premise that for everycredit there is adebit. More symbolically, an accounting model expresses some principle of conservation in the form
algebraic sum of inflows = sinks − sources
This principle is certainly true formoney and it is the basis fornational income accounting. Accounting models are true byconvention, that is anyexperimental failure to confirm them, would be attributed tofraud, 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 asprofit orutility maximization. An example of such a model is given by thecomparative statics oftaxation on the profit-maximizing firm. The profit of a firm is given by
where is the price that a product commands in the market if it is supplied at the rate, is the revenue obtained from selling the product, is the cost of bringing the product tomarket at the rate, and is the tax that the firm must pay per unit of the product sold.
Theprofit maximization assumption states that a firm will produce at the output ratex if that rate maximizes the firm's profit. Usingdifferential calculus we can obtain conditions onx under which this holds. The first order maximization condition forx is
Regardingx as an implicitly defined function oft by this equation (seeimplicit function theorem), one concludes that thederivative ofx with respect tot has the same sign as
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 onbounded rationality.
Borrowing a notion apparently first used in economics byPaul Samuelson, this model of taxation and the predicted dependency of output on the tax rate, illustrates anoperationally meaningful theorem; that is one requiring some economically meaningful assumption that isfalsifiable under certain conditions.
Aggregate models.Macroeconomics needs to deal with aggregate quantities such asoutput, theprice level, theinterest rate and so on. Now real output is actually avector ofgoods andservices, such as cars, passenger airplanes,computers, food items, secretarial services, home repair services etc. Similarlyprice 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 exampleLeontiefinput–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 forqualitative analysis. For this reason,macroeconomic models usually lump together different variables into a single quantity such asoutput orprice. 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 byeconometrics. For instance, one ingredient of theKeynesian model is a functional relationship between consumption and national income: C = C(Y). This relationship plays an important role in Keynesian analysis.
Most economic models rest on a number of assumptions that are not entirely realistic. For example, agents are often assumed to have perfect information, and markets are often assumed to clear without friction. Or, the model may omit issues that are important to the question being considered, such asexternalities. Any analysis of the results of an economic model must therefore consider the extent to which these results may be compromised by inaccuracies in these assumptions, and a large literature has grown up discussingproblems with economic models, or at least asserting that their results are unreliable.
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 Frenchphysiocratic school in the eighteenth century. Among these economists,François Quesnay was known particularly for his development and use of tables he calledTableaux 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 1776Wealth of Nations), simple probabilistic models were used to understand the economics ofinsurance. This was a natural extrapolation of the theory ofgambling, and played an important role both in the development ofprobability theory itself and in the development ofactuarial science. Many of the giants of 18th centurymathematics contributed to this field. Around 1730,De Moivre addressed some of these problems in the 3rd edition ofThe Doctrine of Chances. Even earlier (1709),Nicolas Bernoulli studies problems related to savings and interest in theArs Conjectandi. In 1730,Daniel Bernoulli studied "moral probability" in his bookMensura 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 paradoxicalSaint Petersburg problem. All of these developments were summarized byLaplace in hisAnalytical Theory of Probabilities (1812). Thus, by the timeDavid Ricardo came along he had a well-established mathematical basis to draw from.
In the late 1980s, theBrookings Institution compared 12 leadingmacroeconomic models available at the time. They compared the models' predictions for how the economy would respond to specific economic shocks (allowing the models to control for all the variability in the real world; this was a test of model vs. model, not a test against the actual outcome). Although the models simplified the world and started from a stable, known common parameters the various models gave significantly different answers. For instance, in calculating the impact of amonetary loosening on output some models estimated a 3% change inGDP after one year, and one gave almost no change, with the rest spread between.[4]
Partly as a result of such experiments, modern central bankers no longer have as much confidence that it is possible to 'fine-tune' the economy as they had in the 1960s and early 1970s. Modern policy makers tend to use a less activist approach, explicitly because they lack confidence that their models will actually predict where the economy is going, or the effect of any shock upon it. The new, more humble, approach sees danger in dramatic policy changes based on model predictions, because of several practical and theoretical limitations in current macroeconomic models; in addition to the theoretical pitfalls, (listed above) some problems specific to aggregate modelling are:
Limitations in model construction caused by difficulties in understanding the underlying mechanisms of the real economy. (Hence the profusion of separate models.)
The law ofunintended consequences, on elements of the real economy not yet included in the model.
Thetime lag in both receiving data and the reaction of economic variables to policy makers attempts to 'steer' them (mostly throughmonetary policy) in the direction that central bankers want them to move.Milton Friedman has vigorously argued that these lags are so long and unpredictably variable that effective management of the macroeconomy is impossible.
The difficulty in correctly specifying all of the parameters (througheconometric measurements) even if the structural model and data were perfect.
The fact that all the model's relationships and coefficients are stochastic, so that the error term becomes very large quickly, and the available snapshot of the input parameters is already out of date.
Modern economic models incorporate the reaction of the public and market to the policy maker's actions (throughgame theory), and this feedback is included in modern models (following therational expectations revolution andRobert Lucas, Jr.'sLucas critique of non-microfounded models). If the response to the decision maker's actions (and theircredibility) must be included in the model then it becomes much harder to influence some of the variables simulated.
Complex systems specialist and mathematicianDavid Orrell wrote on this issue in his bookApollo's Arrow and explained that the weather, human health and economics use similar methods of prediction (mathematical models). Their systems—the atmosphere, the human body and the economy—also have similar levels of complexity. He found that forecasts fail because the models suffer from two problems: (i) they cannot capture the full detail of the underlying system, so rely on approximate equations; (ii) they are sensitive to small changes in the exact form of these equations. This is because complex systems like the economy or the climate consist of a delicate balance of opposing forces, so a slight imbalance in their representation has big effects. Thus, predictions of things like economic recessions are still highly inaccurate, despite the use of enormous models running on fast computers.[5]SeeUnreasonable ineffectiveness of mathematics § Economics and finance.
Economic and meteorological simulations may share a fundamental limit to their predictive powers:chaos. Although the modern mathematical work onchaotic systems began in the 1970s the danger of chaos had been identified and defined inEconometrica as early as 1958:
"Good theorising consists to a large extent in avoiding assumptions ... [with the property that] a small change in what is posited will seriously affect the conclusions."
It is straightforward to design economic models susceptible tobutterfly effects of initial-condition sensitivity.[6][7]
However, theeconometric research program to identify which variables are chaotic (if any) has largely concluded that aggregate macroeconomic variables probably do not behave chaotically.[citation needed] This would mean that refinements to the models could ultimately produce reliable long-term forecasts. However, the validity of this conclusion has generated two challenges:
In 2004Philip Mirowski challenged this view and those who hold it, saying that chaos in economics is suffering from a biased "crusade" against it byneo-classical economics in order to preserve their mathematical models.
The variables infinance may well be subject to chaos. Also in 2004, theUniversity of Canterbury studyEconomics on the Edge of Chaos concludes that after noise is removed fromS&P 500 returns, evidence ofdeterministic chaosis found.
More recently, chaos (or the butterfly effect) has been identified as less significant than previously thought to explain prediction errors. Rather, the predictive power of economics and meteorology would mostly be limited by the models themselves and the nature of their underlying systems (seeComparison with models in other sciences above).
A key strand offree market economic thinking is that the market'sinvisible hand guides an economy to prosperity more efficiently thancentral planning using an economic model. One reason, emphasized byFriedrich Hayek, is the claim that many of the true forces shaping the economy can never be captured in a single plan. This is an argument that cannot be made through a conventional (mathematical) economic model because it says that there are critical systemic-elements that will always be omitted from any top-down analysis of the economy.[8]
Caldwell, Bruce (1994),Beyond Positivism: Economic Methodology in the Twentieth Century (Revised ed.), New York: Routledge,ISBN0-415-10911-6.
Holcombe, R. (1989),Economic Models and Methodology, New York: Greenwood Press,ISBN0-313-26679-4.Defines model by analogy with maps, an idea borrowed from Baumol and Blinder. Discusses deduction within models, and logical derivation of one model from another. Chapter 9 compares the neoclassical school and theAustrian School, in particular in relation to falsifiability.
Lange, Oskar (1945), "The Scope and Method of Economics",Review of Economic Studies,13 (1), The Review of Economic Studies Ltd.:19–32,doi:10.2307/2296113,JSTOR2296113,S2CID4140287.One of the earliest studies on methodology of economics, analysing the postulate of rationality.
Samuelson, Paul A. (1948), "The Simple Mathematics of Income Determination", inMetzler, Lloyd A. (ed.),Income, Employment and Public Policy; essays in honor of Alvin Hansen, New York: W. W. Norton.
Samuelson, Paul A. (1983),Foundations of Economic Analysis (Enlarged ed.), Cambridge: Harvard University Press,ISBN0-674-31301-1.This is a classic book carefully discussing comparative statics in microeconomics, though some dynamics is studied as well as some macroeconomic theory. This should not be confused with Samuelson's popular textbook.
Tinbergen, Jan (1939),Statistical Testing of Business Cycle Theories, Geneva: League of Nations.
R. Frigg and S. Hartmann,Models in Science. Entry in theStanford Encyclopedia of Philosophy.
H. VarianHow to build a model in your spare time The author makes several unexpected suggestions: Look for a model in the real world, not in journals. Look at the literature later, not sooner.
