DME in Economics     Control questions           190210 

Theoretical economics deals with abstract models. There is no perfect model for any real world phenomenon. Hence, for every abstract model, there is an agenda consisting of desired removals and additions of features. What theoretical economists do is studying the properties of these abstract models by means of mathematical analysis.
Theory development it proceeds by mathematical deduction and proof. The logical form of a proposition of economic theory is:

{C₁,...} IT

That is, a proposition of economic theory proves some interesting theorem IT from a set of conditions {C₁,...}. To a model belongs

• a set of desired IT's and conditions
• a set of undesired theorems and conditions

The task of changing the model such as to get rid of the undesired features while retaining or even extending the desired ones is called deductive model exploration (DME).

There has been quite an extensive discussion among economists about whether one should judge the theory by the realism of the conditions or the truth of its implications (interesting theorems IT). This is known as the Friedman controversy. In practice, economists work both ways, and for both ways employ a number of different methods.

Economists use the terms   "theory" and "model" in different ways. More on this.

Some examples of interesting theorems derived by economists from specific sets of conditions are

• Consumer behaviour: the Law of Demand
• International trade: the Heckscher Ohlin Theorem, The Stolper Samuelson Theorem, the Factor Price Equalisation Theorem
• Economic Growth: the Harrod-Domar theorems on the relation of investment and growth
• Finance: the Modigliani Miller theorem.

Every student of economics is being taught such kinds of theorems, they are the actual substance of the teaching of theoretical economics. In the realm of comparative statics, interesting theorems usually say whether some endogenous variable of the model (often equilibrium price, or equilibrium quantitity traded) moves together up/down with some exogenous variable (like weather temperature) or against it.

Different types of conditions

At their birth, the theorems  are usually proven under  extremely simple, or abstract conditions. There are a number of ways to classify the conditions needed to prove a theorem. The simplest classification is the following:

• Hard core conditions specifying the basic approach of some research programme (school, current) of economics (think of classical, neo-classical, Keynesian, Monetarist) involved. Any such school or current uses these condition in every field of application  (like consumer behaviour, labour market theory, monetary theory, international economics etc.).
• Application conditions, used by a research programme to employ its basic theory for the explanation of phenomena in some special field of application. The standard application conditions of the neo-classical classical theory for international trade are, for instance, that production functions are equal in all countries but available factor endowments (labour, capital) differ -relative- in quantity.
• Special conditions. The third set of conditions is born out of necessity: to prove the desired interesting theorem, hard core and application conditions are usually insufficient, and the gap must be closed by special conditions. These usually have a mathematical technical nature. A good example is that usually nothing can be proven from unspecified production functions. The mathematical problem can be brought under control by making an assumption like linear homogeneity of production functions. Once this is seen to allow the proof of some theorem, research centres around the possibilities to relax such strong special conditions.
• Field. In shaping, in early phases of research, a mathematically manageable model, usually the dimensions of the ideal economy scrutinised are set to limits. For instance, in international trade, there are only two countries, producing only two types of goods with the help of only two types of factors of production. There is no tax, there are zero transport costs etc. This defines the ontology or field of the model.

Strategies of theory development

The basic set up of the different types of conditions and some first key theorems is done by the founders of a "research programme" or "school" of economic research. Some names of such founders are Adam Smith (Classical Economics), Marshall, Jevons (Neo-classical economics, micro-economics), Keynes (Keynesian macro-economics) and Friedman (monetarist macro-economics).

Once some interesting theorems have been proven in some field from some strong set {C₁,...}of conditions, there are  number of ways to proceed in the research programme:

• Proving established theorems (theorems already proven by existing old reserach programmes that adherents of the new programme want to show is inferior).
• Finding new interesting theorems.
• Field extension: you can put more of the relevant things that you know exist in real economies in the ontology of your model (for instance: from two factors of production to three and to any arbitrary number). This is called field extension.
• Weakening of conditions: you can you can check whether all conditions used are really necessary. May be some can be relaxed.
• Finding alternative condition sets: there might be alternative condition sets from which the theorem can be proven as well.
• Deepening, or finding conditions for conditions: special conditions with unclear economic meaning could be scrutinised by considering them like theorems, and finding out whether they can be proven from theorems with a clearer economic meaning.

Finder weaker or alternative conditions means that you discovered additional cases of the model where the theorem holds (see picture right). The research work described is deductive and mathematical. How do theoretical economists judge to what extent a model is a good approximation of existing economic systems? In the natural science, a common strategy is empirical testing: finding some real situation in which the the conditions of the theory are satisfied, or creating such a situation in an experiment. Predictions should come true, if not, the theory is not yet good enough. In economics, there are few possibilities to test by means of controlled observation. Economists have the following alternatives:

1. First, and very often, the plausibility of the conditions used is discussed, referring to general facts of experience. Profit maximisation is defended by stating that in pondering alternatives, an entrepreneur will choose the most profitable one, and those who don't, would be out of business fast. Is this an "observation"? May be yes, but one of a very general kind. The Keynesian consumption function is defended by pointing at the rationality of economic agents to let their consumption be checked by their income, and to maintain that, though this might not hold for every individual, it will hold for the aggregate consumption resulting from the decisions of all consumers in a country. By these plausibility considerations, non-evident claims like the multiplier theory of investment gain credibility because the are derived from plausible assumptions. Plausibility, in these two and in many other examples, is derived from introspection: you are asked to think of  what you would do yourself if you were an entrepreneur, if you were a consumer whose income is changing.
2. Second, work is done to derive a plausible theorem (like the Law of Demand) from a given set of conditions (with the neo-classical utility maximisation as a basic core). There, a core is considered to be a satisfactory tool for explanation only if some key "evident", or plausible truths can be derived from them as theorems. At a somewhat greater distance from the actual theoretical programme is theory evaluation by means of acquiring data relevant to the theory. For example, conditions might be evaluated by questioning agents whether they feel they behave the way supposed by the conditions (one can ask entrepreneurs whether they maximise profit). Or, the theorem might be compared to data (the Heckscher Ohlin theorem implies that a capital rich country like the United State exports capital intensive goods, and the Leontief paradox resulted from trade data indicating that the reverse was, under certain assumptions, the case). If data acquisition leads to conclusions at odds with theorem, conditions or both, a change in the assumptions on how the data relate to the theory is undertaken rather than an abandoning the hard core of the relevant theoretical research programme.