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In economics, a model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified framework designed to illustrate complex processes, often but not always using mathematical techniques. Frequently, economic models posit structural parameters. Structural parameters are underlying parameters in a model or class of models. A model may have various parameters and those parameters may change to create various properties. Methodological uses of models include investigation, theorizing, fitting theories to the world.
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 a paradigm of econometric study.
Simplification is particularly important for economics given the enormous complexity of economic processes. This complexity can be attributed to the diversity of factors that determine economic activity; these factors include: individual and cooperative decision processes, resource limitations, environmental and geographical constraints, institutional and legal requirements and purely random 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 real changes in price, and changes in price which are to be attributed to inflation.
In addition to their professional academic interest, the use of models include:
A model establishes an argumentative framework for applying logic and mathematics 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 the validity of the supporting model.
Economic models in current use do not pretend to be 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 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 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.
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 which illustrate some particularly relevant points of model construction.
Provably unrealistic assumptions are pervasive in neoclassical economic theory (also called the "standard theory" or "neoclassical paradigm"), and those assumptions are inherited by simplified models for that theory. (Any model based on a flawed theory, cannot transcend the limitations of that theory.) Joseph Stiglitz' 2001 Nobel Prize lecture  reviews his work on Information Asymmetries, which contrasts with the assumption, in standard models, of "Perfect Information". Stiglitz surveys many aspects of these faulty standard models, and the faulty policy implications and recommendations that arise from their unrealistic assumptions. Stiglitz writes: (p. 519–520)
"I only varied one assumption – the assumption concerning perfect information – and in ways which seemed highly plausible. ... We succeeded in showing not only that the standard theory was not robust – changing only one assumption in ways which were totally plausible had drastic consequences, but also that an alternative robust paradigm with great explanatory power could be constructed. There were other deficiencies in the theory, some of which were closely connected. The standard theory assumed that technology and preferences were fixed. But changes in technology, R & D, are at the heart of capitalism. ... I similarly became increasingly convinced of the inappropriateness of the assumption of fixed preferences. (Footnote: In addition, much of recent economic theory has assumed that beliefs are, in some sense, rational. As noted earlier, there are many aspects of economic behavior that seem hard to reconcile with this hypothesis.)"
Economic models can be such powerful tools in understanding some economic relationships, that it is easy to ignore their limitations. One tangible example where the limits of Economic Models collided with reality, but were nevertheless accepted as "evidence" in public policy debates, involved models to simulate the effects of NAFTA, the North American Free Trade Agreement. James Stanford published his examination of 10 of these models.  
The fundamental issue is circularity: embedding one's assumptions as foundational "input" axioms in a model, then proceeding to "prove" that, indeed, the model's "output" supports the validity of those assumptions. Such a model is consistent with similar models that have adopted those same assumptions. But is it consistent with reality? As with any scientific theory, empirical validation is needed, if we are to have any confidence in its predictive ability.
If those assumptions are, in fact, fundamental aspects of empirical reality, then the model's output will correctly describe reality (if it is properly "tuned", and if it is not missing any crucial assumptions). But if those assumptions are not valid for the particular aspect of reality one attempts to simulate, then it becomes a case of "GIGO" – Garbage In, Garbage Out".
"..CGE models are circular: if trade theory holds that free trade is mutually beneficial, then a quantitative simulation model based on that theoretical structure will automatically show that free trade is mutually beneficial...if the economy actually behaves in the manner supposed by the modeler, and the model itself sheds no light on this question, then a properly calibrated model may provide a rough empirical estimate of the effects of a policy change. But the validity of the model hangs entirely on the prior, nontested specification of its structural relationships ... [Hence, the apparent consensus of pro-NAFTA modelers] reflects more a consensus of prior theoretical views than a consensus of quantitative evidence."
Commenting on Stanford's analysis, one computer scientist wrote,
"When simulating the impact of a trade agreement on labor, it seems absurd to assume a priori that capital is immobile, that full employment will prevail, that unit labor costs are identical in the U.S. and Mexico, that American consumers will prefer products made in America (even if they are more expensive), and that trade lows between the U.S. and Mexico will exactly balance. Yet a recent examination of ten prominent CGE models showed that nine of them include at least one of those unrealistic assumptions, and two of the CGE models included all the above assumptions.
This situation bears a disturbing resemblance to computer-assisted intellectual dishonesty. Human beings have always been masters of self-deception, and hiding the essential basis of one's deception by embedding it in a computer program surely helps reduce what might otherwise become an intolerable burden of cognitive dissonance."
In commenting on the general phenomenon of embedding unrealistic "GIGO" assumptions in neoclassical economic models, Nobel prizewinner Joseph Stiglitz is only slightly more diplomatic: (p. 507-8)
"But the ... model, by construction, ruled out the information asymmetries which are at the heart of macro-economic problems. Only if an individual has a severe case of schizophrenia is it possible for such problems to arise. If one begins with a model that assumes that markets clear, it is hard to see how one can get much insight into unemployment (the failure of the labor market to clear)."
Despite the prominence of Stiglitz' 2001 Nobel prize lecture, the use of misleading (perhaps intentionally) neoclassical models persisted in 2007, according to these authors:
" ... projected welfare gains from trade liberalization are derived from global computable general equilibrium (CGE) models, which are based on highly unrealistic assumptions. CGE models have become the main tool for economic analysis of the benefits of multilateral trade liberalization; therefore, it is essential that these models be scrutinized for their realism and relevance. ... we analyze the foundation of CGE models and argue that their predictions are often misleading. ... We appeal for more honest simulation strategies that produce a variety of plausible outcomes."
The working paper, "Debunking the Myths of Computable General Equilibrium Models",  provides both a history, and a readable theoretical analysis of what CGE models are, and are not. In particular, despite their name, CGE models use neither the Walrass general equilibrium, nor the Arrow-Debreus General Equilibrium frameworks. Thus, CGE models are highly distorted simplifications of theoretical frameworks—collectively called "the neoclassical economic paradigm" – which—themselves—were largely discredited by Joseph Stiglitz.
In the "Concluding Remarks" (p. 524) of his 2001 Nobel Prize lecture, Stiglitz examined why the neoclassical paradigm—and models based on it—persists, despite his publication, over a decade earlier, of some of his seminal results showing that Information Asymmetries invalidated core Assumptions of that paradigm and its models:
"One might ask, how can we explain the persistence of the paradigm for so long? Partly, it must be because, in spite of its deficiencies, it did provide insights into many economic phenomena. ... But one cannot ignore the possibility that the survival of the [neoclassical] paradigm was partly because the belief in that paradigm, and the policy prescriptions, has served certain interests."
In the aftermath of the 2007–2009 global economic meltdown, the profession's attachment to unrealistic models is increasingly being questioned and criticized. After a weeklong workshop, one group of economists released a paper highly critical of their own profession's unethical use of unrealistic models. Their Abstract offers an indictment of fundamental practices:
"The economics profession appears to have been unaware of the long build-up to the current worldwide financial crisis and to have significantly underestimated its dimensions once it started to unfold. In our view, this lack of understanding is due to a misallocation of research efforts in economics. We trace the deeper roots of this failure to the profession’s focus on models that, by design, disregard key elements driving outcomes in real-world markets. The economics profession has failed in communicating the imitations, weaknesses, and even dangers of its preferred models to the public. This state of affairs makes clear the need for a major reorientation of focus in the research economists undertake, as well as for the establishment of an ethical code that would ask economists to understand and communicate the limitations and potential misuses of their models."
A great danger inherent in the simplification required to fit the entire economy into a model is omitting critical elements. Some economists believe that making the model as simple as possible is an art form, but the details left out are often contentious. For instance:
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 (all else being equal) qualification that accompanies any claim in economics is nothing more than an all-purpose escape clause (See N. de Marchi and M. Blaug.) The all else being equal claim allows holding all variables constant except the few that the model is attempting to reason about. This allows the separation and clarification of the specific relationship. However, in reality all else is never equal, so economic models are guaranteed to not be perfect. The goal of the model is that the isolated and simplified relationship has some predictive power that can be tested, mainly that it is a theory capable of being applied to reality. To qualify as a theory, a model should arguably answer three questions: Theory of what?, Why should we care?, What merit is in your explanation? If the model fails to do so, it is probably too detached from reality and meaningful societal issues to qualify as theory. Research conducted according to this three-question test finds that in the 2004 edition of the Journal of Economic Theory, only 12% of the articles satisfy the three requirements.” Ignoring the fact that the ceteris paribus assumption is being made is another big failure often made when a model is applied. At the minimum an attempt must be made to look at the various factors that may not be equal and take those into account.
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 Probabilities (1812). Clearly, by the time David Ricardo came along he had a lot of well-established math to draw from.
In the late 1980s the Brookings institute compared 12 leading macroeconomic 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 a monetary loosening on output some models estimated a 3% change in GDP after one year, and one gave almost no change, with the rest spread between.
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:
Complex systems specialist and mathematician David Orrell wrote on this issue 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. 
Economic and meteorological simulations may share a fundamental limit to their predictive powers: chaos. Although the modern mathematical work on chaotic systems began in the 1970s the danger of chaos had been identified and defined in Econometrica as early as 1958:
However, the econometric research program to identify which variables are chaotic (if any) has largely concluded that aggregate macroeconomic variables probably do not behave chaotically. 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:
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 (see Comparison with models in other sciences above).
A key strand of free market economic thinking is that the market's "invisible hand" guides an economy to prosperity more efficiently than central planning using an economic model. One reason, emphasized by Friedrich 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 which 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.