TOPICS IN METHODOLOGY OF EMPIRICAL ECONOMICS

Alessio MONETA1

December 4, 2015

Contents

1 Introduction 3

1.1 What is methodology? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Some examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Induction and confirmation 7

2.1 The role of empirical evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Induction vs. deduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Historical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 The problem of induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.5 Induction, deduction and economics . . . . . . . . . . . . . . . . . . . . . . . . 11

2.6 Confirmation and its paradoxes . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Probability 17

3.1 Probability calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Various concepts of probability . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Probability and confirmation 19

4.1 The Bayesian approach to inductive inference . . . . . . . . . . . . . . . . . . . 19

4.2 The frequentist account of statistical inference . . . . . . . . . . . . . . . . . . . 20

5 Causality 21

5.1 The probabilistic account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.2 Conditionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.3 Transmission and mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.4 Manipulability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

6 Explanation and laws 24

7 Models 24

8 Realism and Instrumentalism 25

9 Measurement in Economics 25

1Institute of Economics - LEM, Scuola Superiore Sant’Anna, Piazza Martiri della Liberta 33, 56127 Pisa, Italy.Email: amoneta@sssup.it

1 Introduction

1.1 What is methodology?

What is methodology of economics? Methodology is the analysis of methods used in economics.2

It examines the concepts, arguments and basic principles economists use, in particular when theyjustify their theories and practices.

Reflections on methods are present in the first writings of modern economics, we find indeedimportant pieces of methodological analysis in the works of David Hume, Adam Smith and DavidRicardo. However, the first essays specifically devoted to economic methodology are consideredthose by Nassau William Senior (Introductory Lecture on Political Economy, 1827), John StuartMill (On the Definition of Political Economy and the Method of Investigation Proper to It, 1836)and John Neville Keynes (The Scope and Method of Political Economy, 1891).

As Blaug (Blaug, 1992, p.xii) pointed out “methodology is both a descriptive discipline —‘this is what most economists do’ — and a prescriptive one — ‘this is what economists should doto advance economics’.”

One of the first methodological concern is the definition of the discipline of economics: manyscholars felt the urgency of delimiting the field of economics by specifying both what are theobjects the discipline is talking about and what are the appropriate methods of investigation. Thisis particularly true for J.S. Mill (1836) and, almost one hundred years later, the same concernwas taken up by Lionel Robbins in An Essay on the Nature and Significance of Economic Science(1932)3.

The following notes are hopefully helpful in understanding ‘what economics is’ or ‘what eco-nomics could be’, but the aim here is rather to learn something about the way economic statementsare justified (or should be justified) and phenomena explained by taking into consideration empir-ical observations. The focus on empirical evidence as essential ingredient in theory appraisal isthe reason why I chose to add the word empirical in the title.

What is empirical evidence? What are the possible ways to (empirically) justify theoreti-cal statements, causal claims and laws? What is scientific explanations? These are the typicalquestions which are addressed by the philosophy of science, so that methodology of empiricaleconomics is ultimately philosophy of science as applied to economics. The latter statement, how-ever, should be qualified with at least two further considerations. First, traditional philosophy ofscience, and in particular the strand of literature developed until the 1970s, has been mainly de-veloped having physics as main science of reference. Second, economics is a peculiar scientificdiscipline: on the one hand its objects consist of human behaviour and social phenomena, on theother hand it possesses features which resemble (often imitate) those of the natural sciences (cfr.Hausman, 2013).

Examining the intricate relationships between economics and philosophy of science, Hoover(1995 2001b) maintains the following thesis, which he calls Rosenberg’s continuity thesis: “thereare no defined boundaries between economics as practiced by economists, methodology of eco-nomics, philosophy of science as applied to economics, and philosophy of science. Each dis-cipline blends seamlessly into the other; and the conclusions of each discipline, while they may

2The word method comes from Greek meta (after) and hodos (way, path): way of going after something, way ofinvestigating.

3In this essay Robbins famously defined economics as “the science which studies human behaviour as a relationshipbetween ends and scarce means which have alternative uses”. For a criticism see Pasinetti (1981, chapter 1).

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have different degrees of relevance for the practice of economics, have relevance of the same kind”(Hoover, 2001b, p.6).

1.2 Some examples

The best way to understand the methodological stance is to start with an example.

One of the most famous statement in economics is the so-called laws of demand, which statesthat the quantity demanded of any commodity will vary inversely with its money price. Otherthings being equal, if the unitary price of a commodity drops from 0.50 to 0.20, its quantitydemanded rises by a certain amount, say from 100 to 400 (e.g. kilograms of potatoes), as displayedin Figure 1.

Figure 1: Hypothetical demand curve

In other terms, the law of demand tells us that that the relationship between qx, the quantitydemanded of good x and px, the price of good x can be expressed as qx = f(px), where f is amonotonically strictly decreasing function.

There are several peculiarities in the law of demand, which rise some methodological issues,to be taken up in the subsequent sections.

1. The statement refers to quantity demanded. But who are the subjects? If the law of de-mand refers to individuals, asserting that the quantity demanded of any commodity by anyindividual varies with its price, this claim cannot be a universal law.

2. If the statement refers to the aggregate property (e.g. the average) of a group of consumersin a market, this will be a statistical claim, depending on a statistical model.

3. The law of demand does not specify a functional form of the dependence of quantity onprice and therefore one cannot use it to predict an exact behaviour.

4. It is not obvious whether the statement specifies a causal relation which can be used forintervention.

5. It is not obvious how we learn about the law of demand.

6. The law holds ceteris paribus.

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The English mercantilist economist Charles Davenant (1656-1714), in a work published in16994, claimed that a defect of quantity of harvested corn may rise the prices in the followingproportions:

Defect Above the Common Rate

1 Tenth 3 Tenth

2 Tenth 8 Tenth

3 Tenth Raises the Price 16 Tenth

4 Tenth 28 Tenth

5 Tenth 45 Tenth

Notice that the relationship between quantity and price is not linear (cfr. Yule, 1915) and thatthe implicit causal relation runs from quantity to price. This relationship was later attributed toGregory King (1648-1712) and therefore has usually been known as “King’s law” (cfr. Stigler,1954).

Ernst Engel (1821-1896) made in 1861 an empirical analysis of the relationship between har-vested rye and its price in Prussia, using data from 1846 to 1861 and concluded that there could beno universally valid relationship between price and quantity. In particular King’s law has no claimto validity(cfr. Stigler, 1954, p. 104).

In a previous empirical investigation, Engel (1857) showed no hesitation in inferring a univer-sal valid relationship from data. Using Belgian data he pointed out that “the poorer a family is,the larger the budget share it spends on nourishment” and call this general statement law. Engeljustifies the possibility of inferring general laws from particular statements on the basis of ErnstApelt’s (1854) principle of induction. Figure 2 depicts the estimated relationship between foodand household expenditures using household consumption data.

Figure 2: The relationship between food and total expenditure in UK 2005 (household data).

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Engel Curve Food UK 2005 (Budget Shares)

One can start an economic investigation with the analysis of data and attempt to draw outinvariant relations from them, as Engel did. An alternative, but often complementary, approach isto start by making some hypotheses about the mutual influences of the variables of interest andformalize them in an algebraic model.

Macroeconomic models of an economy typically makes hypotheses about the amount of con-sumer spending and income. Consider for example the so-called Keynesian consumption function

4An Essay on the probable means of making the people gainers in the balance of Trade.

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C = a+ bY , where C is total consumption, Y is disposable income, and b is the marginal propen-sity to consume.

Real business cycle models attempt to formulate mathematically specific allocation problemsfaced by households. These models make the simplifying assumptions that the economy consistsof a number of identical, price-taking firms and identical, price-taking households, which live aninfinite number of periods. Output Yt is determined by capital Kt, labour Lt, and technology Atin the following way:

Yt = Kαt (AtLt)

1−α, 0 < α < 1. (1)

The evolution of technology takes the form:

At = ρAAt−1 + εt, 0 < ρA < 1 (2)

The representative household maximizes the expected value of

U =∞∑t=0

e−ρtu(ct, (1− lt))Nt

H, (3)

where u(·) is the instantaneous utility function of the representative member of the household, ρis the discount rate, N is population, H is the number of households, c = C/N , l = L/N , and(1 − lt) is the hours of leisure consumed. These assumptions and hypotheses, together with theassumptions that labour and capital are paid their marginal products (i.e. wage wt = ∂Yt/∂Ltand real interest rate rt = (∂Yt/∂Kt) − δ, where δ is the capital depreciation rate) constitute thestructure of the real business cycle model. From this structure implications about the influenceof changes in At, rt and wt on ct and lt (over time) are deduced. For example, in this modela transitory increase in productivity (measured by At) in period t makes people to work morein period t, reducing their current leisure. Changes in wages make households to shift the laboursupply over time: when real wages are temporally high individuals are more willing to work, whenreal wages are temporally low they work fewer hours (cfr. Snowdon and Vane, 2005, p. 311).

There are several methodological questions that arise from these examples of economic anal-ysis. Here is a non-exhaustive list:

1. Are there invariant laws in economics?

2. How are theoretical statements appraised? What is the role played by empirical observationsand the role of intuition or previous knowledge on human behaviour in theory appraisal?

3. Is it possible to analyse causal relationships in economics? What is the nature of causalityin economics?

4. What is the role of statistical analysis in learning and controlling substantive information?

5. What are models? Should models capture true features of reality? What is the role of modelsassumptions and simplifications?

6. How can we adjudicate between competitive models?

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2 Induction and confirmation

2.1 The role of empirical evidence

The ultimate justification of a scientific claim should be empirical evidence, that is observablefacts. This is, at least, the empiricist stance that is dominant in modern science and in the modernphilosophical discourse of science. This stance is the hallmark of what is normally considereda sound scientific method. A famous example of evidence-based scientific achievement is therevolution in astronomy between the 16th and 17th century, in which the protagonist are TychoBrahe, Galileo Galilei, Johannes Kepler and Isaac Newton. Although there are many historicalinterpretations of the scientific revolution and different concepts of “the scientific method”, itis impossible to deny the importance of the empirical observations collected by Brahe and theexperiments conducted by Galilei for the formulation of general laws by Galilei himself, Keplerand Newton. Moreover, the advantage of basing general claims on empirical evidence insteadof, say, ideological, political, or metaphysical principles is also quite difficult to deny.5 But isit possible to justify general claims on the basis of empirical observations, as Engel (see section1.2) seemed to do? And why are economic models, as the one considered at the end of section1.2, explicitly disregarding or twisting factual observations? To answer these questions we havefirst to understand what the possibilities and limits are when we want to infer general claims fromparticular observation. This is called induction.

2.2 Induction vs. deduction

An inference is a logical process of deriving a conclusion from a set of premises. The field oflogic studies which processes are valid and which one are not valid. Deductive inferences arelogically valid inferences: the conclusion is a logical consequence of the premises. This meansthat if the premises are true, the consequences must be true as well. Inductive inferences areinferences in which the conclusion does not logically follow from the premises (i.e. the inferencesare logically non-valid), but in which nonetheless the premises provide some degree of support forthe conclusion.

In sum, the crucial characteristics of a deductive inference are:

(i) The conclusion necessarily follows from the premises: it is not possible that the premisesare true and the conclusion is false. In other words, the inference is salva veritate.

(ii) All the information contained in the conclusion was already contained, explicitly or implic-itly, in the premises. In other words, the inference is not ampliative: the conclusion does notsay something more or something new, with respect to the premises.6

Example:Premises: All A are B

5An important issue is also the role of value judgement in economics. The doctrine of value-free economics assertsthat we should maintain the positive-normative distinction advocated by Hume (1739) (the so-called Hume’s Guillo-tine).

6Notice however, that, because of our ignorance, we do not always know what the premises imply, i.e. what isimplicitly contained in the premises, so that with deductive reasoning we may actually discover something that we didnot know before. Nevertheless, the conclusion was already contained in the set of true propositions implied by thepremises.

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All C are AConclusion: All C are B

The symbols A, B, and C can be any objects. What counts is the form: if the premises aretrue, the consequences are also true, no matters what objects (predicates) A, B, and C are. Forexample: if it is true that all the ravens are black and that all the birds living in this island areravens, then it must be true that all the birds living in this island are black.

Deductive logic is disciplined by rules of inference, which, by analysing the syntax of thepremises, returns a conclusion. The rules are valid with respect to the semantic of classical logicif they preserve the truth. Modus ponens, modus tollens and contraposition are examples of validrules of inference.

Modus ponens:A −→ BA—————B

Modus tollens:A −→ B¬B—————¬A

Contraposition:A −→ B——————¬B −→ ¬A

Aristotle (384-322 b.C.) considered deductive inference the paradigmatic method of reasoningin science. He provided a systematic analysis of deduction in his theory of syllogism that we findexpounded in the Organum, the collection of his works in logic.

The crucial characteristics of inductive inference are:

(i) The conclusion does not necessarily follow from the premises. The inference is not salvaveritate, even if the premises are true, the conclusion may be wrong.

(ii) The inference is ampliative: the conclusion says something more and new, in fact somethingwhich was not logically entailed by the premises.

With these two characteristics inductive inference is just the opposite of deductive inference. In thenineteenth century, Stanley Jevons suggested indeed that induction is the converse of deduction.As mentioned, deductive reasoning is logically valid and inductive reasoning is logically invalid,because of its lack of truth-preserving. It is important, however, to distinguish, among logicallyinvalid inferences, those who provide some reasons to believe in the truth of the conclusions, andthose who do not. We thus add:

(ii) The premises provide some arguments to support the conclusion.

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The question about the criteria that allow us to support the conclusion is left for the momentopen. This issue will be addressed in the following sections, when we discuss the concept ofprobability. But we can anticipate that in the typical inductive reasoning, if the premises are true,the conclusions are probably true. We may be wrong to claim that the conclusions are true, wecannot exclude an error. The inductive reasoning attempts to control this error and to make thisinference somewhat rigorous. Thus we may have different types of inductive inference, someperhaps stronger, or more credible, than others. Notice also that not only the form (i.e. the syntax)of the inference matters, but also the content of what is said in the premises and conclusions. Onthe contrary, deduction does not come in degrees (it can be only logically valid, otherwise is notdeduction any longer) and is independent of the content of its predicates, as we have seen above.

On the base of the form, however, we can identify different types of inductive inferences.

Induction by enumeration:Premises: The first observed raven is black;

The second observed raven is black;...The nth observed raven is black;

——————————————————————–Conclusion: All raven are black.

This is an inference from particular events to general principles. Traditionally, induction hasbeen associated with this type of inference. But the following type of inference should also con-sidered inductive:

Predictive inference:Premises: The first observed raven is black;

The second observed raven is black;...The nth observed raven is black;

——————————————————————–Conclusion: The (n+ 1)th observed raven is black.

Induction by analogy:Premises: All As are B

As are similar to Cs————————————————Conclusion: All Cs are B

Another case of induction:Premises: These As are B

These As are C————————————————Conclusion: All As that are B are C

Abduction:Premises: All As that are B are C

These As are C————————————————Conclusion: These As are B

Abductive inference is a logically invalid inference, in which the premises provide some de-grees of support for the conclusion, and therefore it should be considered as an inductive inference.

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However, Charles Sanders Peirce (1839-1814), who coined the term, distinguishes abduction frominduction and deduction, as for Peirce induction refers to the inference from particular to generalinstances only. What matters here is to consider deduction as a logically valid (certain) inference,and both induction and abduction as logically invalid but ampliative and probable (uncertain) in-ference.

2.3 Historical background

Francis Bacon (1561-1626) in the Novum organum (1620) emphasized the importance of induc-tive reasoning as method to increase scientific knowledge. He also proposed a method to learncausal relationships from observations. Taking as example the investigation on the nature of heat,he suggested to classify observational data using three tables. In the tabula presentiae all the in-stances of the phenomenon being investigated are listed (e.g. the rays of the sun are hot). In thetabula absentiae in proximo instances are considered in which the phenomenon being investigatedis absent but that are similar to the instances considered in the first table (e.g. the rays of themoon are not hot). In the tabula graduum all the cases are recorded in which the phenomenonbeing investigated is found in varying degrees (e.g. animals increase in heat by motion). At thispoint Bacon suggested to adopt a process of eliminative induction: we can exclude, as cause of thephenomenon all the variables that are not in the first table, all the variables that are in the secondtable, and all the variable that are not in the third table (i.e. instances that do not vary with the phe-nomenon). For example, Bacon excludes that light can be a cause of heat, since it is also presentin the rays of the moon which are not hot. Thus, by elimination (vindemiatio prima), we reacha first hypothesis on the cause of the phenomenon under investigation. In the case of heat, theinduced cause is motion, according to Bacon. This hypothesis has to be tested further by means of(instantiae crucis): crucial experiments capable of adjudicating between rival hypotheses.

David Hume (1711-1776) analysed the problem of finding a justification for the inferenceof an effect from its cause in A Treatise of Human Nature (1739). Predicting an event E from“C causes E” and “C” is a deductive (i.e. certain) inference if “C causes E” is interpreted as“C → E” (since C → E is a true premise, this means that E follows necessarily from C). Butif the causal relation is not reducible to necessary relation, the inference is not certain, we remainin the realm of inductive inference. Hume highlighted two problems: (i) How do we know thatbetween causes and effects there is a necessary relation? (ii) Even if we know that there is anecessary causal relationship between the particular event C and E, how do we know that thecausal relationship will hold also in the future for particular events C ′ and E′ that are similar (ofthe same kind of) C and E? Hume provides a psychological explanation of the belief that theconnection between causes and effects has to be necessary, based on the notion of habituation. Heanswered the second question appealing to the concept of uniformity of nature. In sum, there is noway to justify inductive reasoning in a rational way. Our knowledge is doomed to remain fallible.

John Stuart Mill (1806-1873) in the System of Logic (1843) proposed the five canons of in-duction: (i) method of agreement; (ii) method of difference; (iii) joint method of agreement anddifferences; (iv) method of residue; (v) method of concomitant variation. These canons were notmeant to solve Hume’s problem of induction: any claim based on induction is fallible. But thesecanons guide the researcher to uncover (or confront with the data) possible and probable causalrelationships that were not evident at a first stage.

Rudolf Carnap (1891-1970) in The continuum of inductive methods (1952) proposed to analyseinductive reasoning by specifying the degrees of probability, by which the conclusion follows fromthe premises.

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2.4 The problem of induction

The problem of induction consists of these basic questions:

(i) Why should we accept the conclusion of an inductive inference, although we know that itdoes not logically follow from the premises? (problem of justification)

(ii) Why is a conclusion, that is derived from a set of premises by induction, preferable toanother? (problem of the differential appraisal)

(iii) Are there rules of inductive inference? What are the criteria for deciding that one rule ofinductive inference is superior to another? (problem of the method)

We will consider again issues (ii) and (iii) when we analyse the probabilistic approach to inductiveinference. We focus now on point (i). There are different strategies to tackle this point:

(A) There is no way to justify inductive inferences, therefore we should reject inductive inferencesand rely on deductive reasoning.

• cfr. Karl Popper’s (1934) emphasis on deduction and falsification.

(B) Inductive inferences have an inductive justification.

• cfr. Max Black,“Self-supporting inductive arguments” (1954)

(C) Inductive inferences have a deductive justification, since they are deductive inferences withimplicit or hidden premises.

• Induction as enthymeme, i.e. deductions with unstated general principles (e.g. uniformityof nature in Hume, causality in Mill, and limited independent variety in Keynes).

• Probabilistic approach to deduction (cfr. Carnap and Reichenbach).

(D) Inductive inferences have a pragmatic justification.

• cfr. the role of deduction-induction-abduction in C.S. Peirce.

• cfr. Herbert Feigl’s (1961) notion of vindication of induction, as opposed to validation.

2.5 Induction, deduction and economics

Is there a specific way in which the problem of induction concerns economics? Are there specificstrategies to address the problem of induction in economics? In order to be able to answer thesequestions we should highlight the peculiar features of economics. We should ask how theoreticalstatements like laws and causal relations are learned and justified. Moreover, we should analysewhat defines economic objects and phenomena. A good start point is to look at the manner theseissues were addressed by J.S. Mill.

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• Regularities and laws. In economics many statements are called laws (law of demand,Engel’s law, Okun’s law, etc.). Can some of them be inductively justified from empiricalregularities? This approach seems to have worked out in physics and astronomy, for exam-ple (see above). In economics there are many empirical regularities, somewhat connectedwith the routine-based behaviour of agents and institutions. However, a lot of them are notstable. They break up in a non-predictable fashion. This feature is connected with the flipside of human behaviour: indeterminacy and free will. (Figure 3 and 4 show some exam-ples of economic time series). Another important issue is that many apparent regularitiesare spurious, that is not easily reconcilable with the presence of causal relations. In otherwords, uniformity of nature is a problematic notion in the economic world.

Figure 3: Real 1987 per capita private gross national product (total GNP less real total governmentpurchases of goods and services, in logarithms), US data from Moneta (2008) in levels (chart onthe left) and first differences (chart on the right).

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Figure 4: The chart on the left displays price inflation, log of the implicit price deflator at the timet minus log of the implicit price deflator at the time t - 1), US data from Moneta (2008). The charton the right displays simultaneously price inflation and GNP growth rate.

−5

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• Experiments. The modern scientific paradigm shows the possibility of learning causal re-

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lationships through experiments, or randomized control trials. Notwithstanding the flour-ishing field of experimental economics, and the increasing econometric practice of relyingon natural experiments, the practical difficulties of running economic experiments have notchanged much since Mill’s time:

“There is a property common to almost all the moral sciences, and by whichthey are distinguished from many of the physical; this is, that it is seldom in ourpower to make experiments in them. In chemistry and natural philosophy, wecan not only observe what happens under all the combinations of circumstanceswhich nature brings together, but we may also try an indefinite number of newcombinations. This we can seldom do in ethical, and scarcely ever in politicalscience. We cannot try forms of government and systems of national policy ona diminutive scale in our laboratories, shaping our experiments as we think theymay most conduce to the advancement of knowledge. We therefore study natureunder circumstances of great disadvantage in these sciences; being confined tothe limited number of experiments which take place (if we may so speak) of theirown accord, without any preparation or management of ours; in circumstances,moreover, of great complexity, and never perfectly known to us; and with the fargreater part of the processes concealed from our observation.” (Mill 1836, Onthe definition of Political Economy (And the Method of Investigation Proper toit)).

• Complexity. Mill (1836) points out that the practical difficulty of making experiments ineconomics is due to its “immense multitude of the influencing circumstances.” Multiplicityof causes and over-determination are indeed typical aspects of socio-economic reality. Millproposes a particular strategy to address this problem:

“When an effect depends on a concurrence of causes, these causes must be stud-ied one at a time, and their laws separately investigated, if we wish, through thecauses, to obtain the power of either predicting or controlling the effect; since thelaw of the effect is compounded of the laws of all the causes which determine it.”(Mill 1836, ibidem).

• Homo oeconomicus. In mainstream economics, the usual way to cope with complexity is tofocus on a particular aspect of human behaviour: the desire of improving and maximizingwealth. As Mill (1836) maintained:

“What is now commonly understood by the term ‘Political Economy’ is not thescience of speculative politics, but a branch of that science. It does not treat of thewhole of man’s nature as modified by the social state, nor of the whole conduct ofman in society. It is concerned with him solely as a being who desires to possesswealth, and who is capable of judging of the comparative efficacy of means forobtaining that end. It predicts only such of the phenomena of the social state astake place in consequence of the pursuit of wealth. It makes entire abstractionof every other human passion or motive; except those which may be regardedas perpetually antagonizing principles to the desire of wealth, namely, aversionto labour, and desire of the present enjoyment of costly indulgences. These ittakes, to a certain extent, into its calculations, because these do not merely likeother desires, occasionally conflict with the pursuit of wealth, but accompany italways as a drag, or impediment, and are therefore inseparably mixed up in theconsideration of it. Political Economy considers mankind as occupied solely inacquiring and consuming wealth” (Mill 1836, ibidem).

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• Introspection and deduction How do we know that the desire of acquiring and consumingwealth is a crucial and constant occupation in human behaviour? According to Mill we canknow it by introspection:

“The desires of man, and the nature of the conduct to which they prompt him,are within the reach of our observation. We can also observe what are the objectswhich excite those desires. The materials of this knowledge every one can prin-cipally collect within himself; with reasonable consideration of the differences,of which experience discloses to him the existence, between himself and otherpeople” (Mill 1836, ibidem).

Once we know the first principles of economic phenomena, we can derive the consequencesby deduction. This means that in Mill’s view economics is an a priori science:

“Since, therefore, it is vain to hope that truth can be arrived at, either in PoliticalEconomy or in any other department of the social science, while we look atthe facts in the concrete, clothed in all the complexity with which nature hassurrounded them, and endeavour to elicit a general law by a process of inductionfrom a comparison of details; there remains no other method than the a priorione, or that of ‘abstract speculation’.” (Mill 1836, ibidem).

Mill recognizes a role for the observations, but this is limited to check that we took intoconsiderations all the disturbing causes:

“By the method a priori we mean (what has commonly been meant) reasoningfrom an assumed hypothesis; which is not a practice confined to mathematics,but is of the essence of all science which admits of general reasoning at all. Toverify the hypothesis itself a posteriori, that is, to examine whether the facts ofany actual case are in accordance with it, is no part of the business of science atall, but of the application of science.” (Mill 1836, ibidem).

“When the principles of Political Economy are to be applied to a particular case,then it is necessary to take into account all the individual circumstances of thatcase; not only examining to which of the sets of circumstances contemplated bythe abstract science the circumstances of the case in question correspond, butlikewise what other circumstances may exist in that case, which not being com-mon to it with any large and strongly marked class of cases, have not fallen underthe cognizance of the science. These circumstances have been called disturbingcauses.” (Mill 1836, ibidem).

Moreover:

“Having now shown that the method a priori in Political Economy, and in all theother branches of moral science, is the only certain or scientific mode of investi-gation, and that the a posteriors method, or that of specific experience, as a meansof arriving at truth, is inapplicable to these subjects, we shall be able to show thatthe latter method is notwithstanding of great value in the moral sciences; namely,not as means of discovering truth, but of verifying it, and reducing to the low- estpoint that uncertainty before alluded to as arising from the complexity of everyparticular case, and from the difficulty (not to say impossibility) of our being as-sured a priori that we have taken into account all the material circumstances. .”(Mill 1836, ibidem).

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• Ceteris paribus. The disturbing causes have to be considered by the applied economist,according to Mill. The theoretical economist can reason as if these disturbing causes do notexist. Therefore theoretical statements in economics hold ceteris paribus.

“Political Economy considers mankind as occupied solely in acquiring and con-suming wealth; and aims at showing what is the course of action into whichmankind, living in a state of society, would be impelled, if that motive, exceptin the degree in which it is checked by the two perpetual counter-motives aboveadverted to [aversion to labour, and desire of the present enjoyment of costlyindulgences], were absolute ruler of all their actions. ” (Mill 1836, ibidem).

This means that (i) pure economic theory studies economic behaviour in the absence ofnon-economic motives, and (ii) it omits the disturbing (secondary) causes that operate inparticular circumstances only. Maki (1998) points out that this clause could be called ceterisabsentibus instead.

• Tendencies. Economic laws are true in abstract, as tendencies laws, according to Mill(1846):

“The error, when there is error, does not arise from generalizing too extensively;that is, from including too wide a range of particular cases in a single proposition.Doubtless, a man often asserts of an entire class what is only true of a part of it;but his error generally consists not in making too wide an assertion, but in mak-ing the wrong kind of assertion: he predicated an actual result, when he shouldonly have predicated a tendency to that result — a power acting with a certainintensity in that direction. With regard to exceptions; in any tolerably advancedscience there is properly no such thing as an exception. What is thought to be anexception to a principle is always some other and distinct principle cutting intothe former: some other force which impinges against the first force, and deflectsit from its direction. There are not a law and an exception to that law, the lawacting in ninety-nine cases, and the exception in one. There are two laws, eachpossibly acting in the whole hundred cases, and bringing about a common effectby their conjunct operation. If the force which, being the less conspicuous ofthe two, is called the disturbing force, prevails sufficiently over the other force insome one case, to constitute that case what is commonly called an exception, thesame disturbing force probably acts as a modifying cause in many other caseswhich no one will call exceptions.” (Mill 1836, ibidem).

• Additivity vs. non-linearity Tendency laws in economics are additive as in physics, accord-ing to Mill (1843):

“The laws of the phenomena of society are, and can be, nothing but the laws ofthe actions and passions of human beings united together in the social state. Men,however, in a state of society, are still men; their actions and passions are obedi-ent to the laws of individual human nature. Men are not, when brought together,converted into another kind of substance, with different properties; as hydrogenand oxygen are different from water, or as hydrogen, oxygen, carbon, and azoteare different from nerves, muscles, and tendons. Human beings in society haveno properties but those which are derived from, and may be resolved into, thelaws of the nature of individual man. In social phenomena the Composition of

15

Causes is the universal law.” (Mill 1843, A System of Logic, Rationative and In-ductive, Book 6: The Logic of the Moral Sciences, Chapter 7: Of the Chemical,or Experimental, Method in the Social Sciences).

2.6 Confirmation and its paradoxes

Let us consider now the second and third aspect of the problem of induction (see section 2.4). Evenif inductive reasoning is logically invalid, there are many cases in which the premises provides sup-port for the conclusion. In particular, there are cases in which general claims are supported by theempirical evidence. How do we establish which conclusion possesses the best degree of confir-mation and which is the appropriate rule of inference? Probability theory (see next section) offersus a method to measure the “degree of confirmation”, that is the extent to which the hypothesis issupported by the evidence.

Here, we want to point out that some simple rules of inference may raise paradoxes.

Hempel paradox7

Consider the following rules of inductive reasoning:

Generalization principle (GE):Each generalization is confirmed by its positive instances.

Notice that by using the term confirmed we want to emphasize the fact that the generalizationdoes not necessarily (logically) follow from the positive instances, but that the latter provide somesupport for the former. For example the generalization “all the ravens are black” is confirmed byall the examples in which the ravens are black. To what extent is this confirmed? We will considerlater the quantitative aspect of confirmation. Here we limit to analyse the qualitative aspect.

The GE can be expressed in the formal language of first-order logic: a generalization such as(x)(Rx→ Bx) is confirmed by some (Rx ∧Bx)

Equivalence principle (EQ):If two hypotheses H1 and H2 are logically equivalent, then the evidence which confirms H1 willalso confirm H2.

For example, ifH1 is “all the ravens are black” andH2 is “all the non-black things are non-ravens”,then H1 ⇔ H2, since (x)[(Rx → Bx) ⇔ (¬Bx → ¬Rx)]. Therefore — here is the paradox —if the observation of a non-black non-raven (¬Bx→ ¬Rx) confirms H2, then it will confirm H1

as well. Thus the hypothesis that all the ravens are black will be confirmed by an evidence such asthe observation of a red book.

Consider now the hypothesis H3: (x)(¬Rx ∨ Nx), whose positive instances are some ¬Rxor some Nx. Using first-order logic, it can be shown (just consider its possible truth values) thatH3 ⇔ H1. Then, because of EQ, some ¬Rx (observation of a boat) or some Nx (observation ofa hunk of tar) confirms (x)(Rx→ Bx) (all ravens are black).

Possible solutions:

• reject GE;7Cfr. Hempel 1945

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• reject EQ;

• accept the conclusion and show that it is only apparently implausible.

Cfr. Giere (1970) for a statistical resolution of the paradox of confirmation.

Goodman’s paradox8

Consider the following hypothesis: “all emeralds are green”. This is confirmed by the observationof a certain number of green emeralds. Let us now define the new predicate“grue” to express theproperty that an object has if and only if it is green before time t and blue thereafter. Then “Allemeralds are green” and “all emeralds are grue” are equally well supported by the evidence.

An easy answer to this paradox is that “grue” is an artificial predicate, presupposing “green”and “blue” for its definition. But, as Goodman (1965) pointed out, we can also define “bleen” tomean “blue before t” and “green after t”. Let us now define the predicate “green” as “grue beforet” and “bleen after t”. The predicate “green” is now as artificial (and dependent on t) as “grue”.

The predicate “green” is a projectible predicate, involved in lawlike generalization, that sup-ports counterfactuals. On the contrary, “grue” is considered non-projectible. Why is this the case?Goodman explains this fact in terms of the pragmatic notion of entrenchment: “green” is more cru-cially implicated in our theoretical vocabulary and consequently in our scientific and non-scientificpractice than “grue”.

It remains, however, the problem of providing a plausible distinction between accidental andlawlike generalizations. Goodman has shown the impossibility of grounding this distinction on amerely syntactic basis.

In the social sciences, it is particular important to identify invariant empirical generalizationon the basis of which it is possible to evaluate the effects of interventions.

3 Probability

Probability theory provides us a powerful mathematical and logical instrument to address the prob-lems of inductive inference and confirmation. After all inductive reasoning is inferring a probableconclusion from some evidence. Moreover, intuitively confirming evidence for a hypothesis isevidence which should somewhat increase its probability. It is then crucial to possess a methodwhich makes us able to quantify these probability ascriptions.

3.1 Probability calculus

Probability is a function, P , that assigns to specific objects a value ranging in the real number linebetween zero and one (inclusive). The argument-objects are sets or propositions in a formal lan-guage. Since in the first-oder logic predicates can be associated with sets and logical connectives(negation ¬, conjunction ∧, disjunction ∨, implication →) can be associated with operations onsets (complement C, intersection ∩, union ∪, ⊆), we can assign probability values equivalently to

8Cfr. Goodman 1965

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sets and propositions. The set-theoretic approach to probability is more basic and therefore morerigorous. Furthermore it permits us to apply the probability calculus to a much richer context.

We start, however, by specifying the properties of probability when the arguments of the func-tion P are propositions, as those specified in the last section. Let the domain of P be a field or aBoolean algebra F. This means that the domain is closed under negation, conjunction, and dis-junction (i.e. if A ∈ F and B ∈ F, then ¬A ∈ F, ¬B ∈ F, A ∧ B ∈ F and A ∨ B ∈ F). Thefunction P : F 7→ R satisfies the following properties:

1. P ≥ 0, for all A ∈ F (non-negativity).

2. If T is a logical truth (tautology), then P (T ) = 1 (normalization).

3. If A and B are logically incompatible (A ∧ B = ⊥), then P (A ∨ B) = P (A) + P (B)(additivity).9.

Other derived properties or definitions:

• P (A) = 0 if A is logically false.

• P (A) = 1− P (¬A).

• If A⇒ B (i.e. A logically entails B), then P (A) ≤ P (B).

• If A⇔ B (A and B are logically equivalent), then P (A) = P (B).

• P (A|B) = P (A ∧B)|P (B) (definition of conditional probability).

• If B ⇒ A, then P (A|B) = 1.

• If B ⇒ ¬A, then P (A|B) = 0.

The set-theoretic formalization of the probability calculus is expressed in analogous terms.Let Ω be a non-empty set. Let F be a σ−algebra on Ω, that is F is a set of subsets of Ω that isclosed under complementation and countable unions of its members: if A ∈ F, then A ∈ F, ifA1, A2, . . . ∈ F then

⋃∞i=1Ai ∈ F. Let P be a function F 7→ R satisfying:

1. P (A) ≥ 0, for all A ∈ F

2. P (Ω) = 1

3. If A ∩B = ∅, then P (A ∪ B) = P (A) + P (B). If A1, . . . , An is a sequence of countablyinfinite sets such that Ai ∩Aj = ∅ for all i 6= j, then P (

⋃∞i=1Ai) =

∑ni=1 P (Ai).

Other derived properties or definitions:

• P (∅) = 0

• P (A) = 1− P (A).

• If A ⊆ B, then P (A) ≤ P (B).

9An extension of this property, useful in some applications, is countable additivity: if A1, . . . , An is a sequence ofcountably infinite propositions such that Ai ∧Aj = ⊥ for all i 6= j, then P (A1 ∨A2 ∨An) =

∑ni=1 P (Ai)

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• If A = B , then P (A) = P (B).

• P (A|B) = P (A ∩B)|P (B) (definition of conditional probability).

• If B ⊆ A, then P (A|B) = 1.

• If B ⊆ A, then P (A|B) = 0.

Note that if we interpret a proposition E as the set of cases in which E is true, there is no dif-ference between the set-theoretical and the propositional formalization of the probability calculus.

3.2 Various concepts of probability

Classical probability

Probability as frequency

Subjective probability

4 Probability and confirmation

4.1 The Bayesian approach to inductive inference

The tenets of the Bayesian approach to inductive inference are the following:

1. In addition to empirical evidence, derived from experiments or passive observations, back-ground knowledge or initial information plays an explicit role in the inference.

2. The initial information permits the researcher to assign a prior probability distribution tothe possible hypotheses which could explain the phenomena in question. The interpretationof theses probabilities is usually subjective.

3. Once new empirical evidence is collected (through experiments or new observations), priorprobabilities are updated through Bayes’s theorem. The outcome is a probability distributionover the considered hypotheses.

4. The outcome of the inductive inference is represented by the posterior probabilities.

Zellner (1971: 10) represents the Bayesian approach as displayed in Figure (5). Recall Bayes’stheorem:

P (H|e) =P (e|H)P (H)

P (e). (4)

When H and e are logical propositions, using the law of total probabilities, equation (4) isequivalent to:

P (H|e) =P (e|H)P (H)

P (e|H)P (H) + P (e|¬H)P (¬H). (5)

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More in general, for a set of alternative hypotheses H1, . . . ,Hn such that Hi ∧ Hj = ⊥ for anyi 6= j between 1 and n and H1 ∨H2 ∨ . . . ∨Hn = T :

P (Hj |e) =P (e|Hj)P (Hj)∑ni=1 P (e|Hi)P (Hi)

. (6)

#" !

Initialinformation

I0

-

#" !

P (H|I0)prior

probability @@@R

#" !

New datae -

#" !

P (e|H)likelihoodfunction

#" !

Bayes’stheorem

-

#" !

P (H|e, I0)posteriorprobability

Figure 5: The process of revising probabilities, given new data, according to Zellner (1971):10.

It is also possible to write:

P (H|e ∧ I0) =P (e|H ∧ I0)P (H|I0)

P (e|I0). (7)

Let us call P (H|I0) the prior probability; P (e|H ∧ I0) the likelihood; P (H|e ∧ I0) the posteriorprobability.

In this framework (see equation 4), we can say that H is confirmed by e if P (H|e ∧ I0) >P (H|I0); is disconfirmed by e if P (H|e ∧ I0) < P (H|I0); remains indifferent with respect to eif P (H|e ∧ I0) = P (H|I0) (cfr. Howson and Urbach 1989). Possible measures of the degrees ofconfirmation are P (H|e ∧ I0)− P (H|I0) and P (H|e ∧ I0)/P (H|I0).

The problem of initial probability

Subjective vs. objective Bayesianism Some criteria to assign prior probabilities:- non informative priors;- maximum entropy principle (cfr Jaynes 1973);- simplicity.

Bayesian solutions to the paradoxes of confirmation

4.2 The frequentist account of statistical inference

The tenets of this approach are:

1. probability as stable frequency, generated by a chance set up (statistical model)

2. hypothesis testing about some characteristics of the chance set up.

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Fisher’s approach to hypothesis testing

The starting point of the account developed by Ronald A. Fisher (1890 - 1962) in the 1920s is thenotion of null hypothesis:

H0 : θ = θ0,

where the parameter θ determines some important characteristic of the underlying statistical modelon the random variables X. The idea is to test whetherH0 is satisfactory enough. The test consistsin the following steps:

• Choose an estimator θ of θ. For example, θ = 1n

∑ni=1Xi, where Xi is equal to one if some

particular event has occurred (otherwise is equal to zero) and n is the number of realizations.

• Specify a distance and standardize it into a test statistic τ(X). For example, the distance

(θ − θ0) is transformed into τ(X) =√n|θ−θ0|s , where s2 = 1

n

∑ni=1(Xi − θ)2.

• Determine the distribution of τ(X) under H0. For example, τ(X) ∼ t(n− 1) and τ(X) ∼N(0, 1) for n→∞.

• Specify the p-value, i.e. P (|τ(X)| ≥ |τ(x)|;H0 is valid) = p. The p-value indicates howsatisfactory H0 is in view of the observed data (Spanos 1999: 691), or, in other words, howsignificantly close is the estimated value to the hypothesized value. Note that p 6= P (H0)!

The Neyman -Pearson framework

Differently from the Fisher’s approach here the emphasis is on the decision whether to reject ornot the hypothesis H0. The starting point is a null hypothesis H0 and an alternative hypothesisH1. For example:

H0 : θ = θ0, against H1 : θ 6= θ0.

Two types of errors are formulated: (i) type I error: reject H0 when in fact it is valid, (ii) typeII error: accept H0 when in fact it is invalid. The idea of this framework is to fix the probabilityof type I error to α (for example 0.05 or 0.01) and to find a test statistic which minimizes theprobability of type II error. The parameter α is called the significance level (chosen a priori) andthe probability of correctly rejectingH0 when it is invalid is called power of the test. The Neyman-Pearson lemma (1933) proposes a criterion (likelihood ratio) which delivers the most powerful testunder a given α.

5 Causality

We have analysed thus far the difficulties of basing our theoretical hypotheses on empirical ev-idence (cfr. the problem of induction). We have also argued how desirable is that the role ofadjudicating among alternative hypotheses is played by empirical evidence rather than ideology,intuition, etc. (we call this position empirical stance). We pointed out how the theory of proba-bility and statistical inference (both of frequentist and Bayesian mark) provide us a possibility totackle the difficulties of induction in economics. It does not provide a definite solution, becauseprobability and statistics permit us to manage uncertainty, i.e. to minimize the chance of makingerrors, but not to reach certainty.

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We pass now to examine the nature of theoretical knowledge. A philosophical tradition dat-ing back at least to Aristotle claims that scientific knowledge should be causal knowledge, i.e.knowledge about cause-effect relationships. Considerations about causality are indeed pervasivein economics. Knowledge about causes seems particularly important for:

(i) Explanation and understanding of economic phenomena. We claim to understand, for ex-ample, economic fluctuations when we know what triggers them. We explain a phenomenonsuch as a rise in inflation when we elucidate why this happened.

(ii) Intervention. If we want to manipulate a variable X (say, we would like to implement apolicy reducing unemployment), it seems necessary to know what makesX happen in orderto control for the variables influencing X .

(iii) Prediction. Although knowing what causes X does not seem necessary to make forecasts(one could, based on some empirical regularities, guess the approximate value of X , sayGDP next year), such knowledge is surely useful (if not sufficient) for prediction.

Notice also the multifariousness of the occurrence of causal terms in the economic language. AsHoover (2001a, 1) points out, economists pose a variety of causal questions: (i) generic (“donominal or real shocks cause economic fluctuation?”) or singular (“did the 2006 US subprimemortgage crisis cause the 2008-2012 global recession?”); (ii) cause-focused (”what does cause arecession”?) or effect-focused (“what is the effect of raising interest rates on the economy”); (iii)implicit (using terms as “triggering”, “bringing about”, “influencing” etc.) or explicit.

Given the multiplicity of causal terms, one could take into account the philosophical positiondefended by Bertrand Russell and Ernst Mach at the beginning of the XX century, according towhich the concept of causality is dispensable from a properly scientific account of the world (thisposition is rooted in Hume’s view about the impossibility of overcoming the problem of induction)and claim that economics should jettison causal notions from formal economic theorizing. Forexample, one could be content with functional explanations attempting to disentangle the mathe-matical functional dependence among economic variables like consumption and income (withoutadding a further causal interpretation) or be satisfied in discovering statistical associations (cor-relations) among variables like R&D expenditures and profits. Some authoritative economists, asMilton Friedman, have held similar position.

However, this “against-causality” position has been discredited in the philosophy of scienceliterature of the last decades, with the argument that the notion of causality is hardly reducible tonotions like regular associations, functions, conditions, etc. and giving up causal terms amounts toabandoning a crucial modality of reasoning. Moreover, the problem is compounded in economics,where understanding phenomena is intimately connected with the possibility of interventions. Insum, the notion of causality, even if fraught with seemingly daunting problems, is hard to beabandoned. It is, however, important to understand and classify these problems in order not toremain discouraged by them.

There are indeed different orders of issues:

(i) Ontological issues: what are causes? Is there a unique concept of causality?

(ii) Methodological issues: do we need causal notions in the scientific discourse? If we dealwith different concepts which one suits economics?

(iii) Epistemological issues: how do we acquire knowledge of causal relations? What it is therole played, for example, by probabilistic methods in economics?

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(iv) Pragmatic issues: which use can we make of causal relations? If we believe that X causesY , how can we be confident that this relationship will remain stable?

On the basis of different manners of tackling these issues, we can distinguish different ap-proaches to causality based, respectively, on the notions of probability, counterfactual, transmis-sion and manipulability.

5.1 The probabilistic account

“Probabilistic account” designates the attempt of characterizing the relationship between causesand effect using probabilistic tools. This attempt is rooted in the view of causation as regularity.In this perspective, claiming that X causes Y implies that objects sufficiently like X are regularlyassociated with Y . According to David Hume “We may define a cause to be an object, followedby another, and where all the objects similar to the first, are followed by objects similar to thesecond.” (An Enquiry Concerning Human Understanding, 1748, section VII.) The idea behindthis definition is that causation does not consist in a necessary connection between cause andeffect, and nor can causal relations be known a priori.

The regularity view is for many aspects problematic: there could be imperfect regularities; itcan be difficult to distinguish between irrelevant (or spurious) and meaningful regularities; regularassociations are symmetric, while causal relations are asymmetric (if X causes Y it does notfollow that Y causes X). The idea of the probabilistic account is to use probability theory toovercome these difficulties.

Suppes (1970) Reichenbach (1956) definition of causality:

Ct is a cause of Et′ (t < t′) iff:

(i) P (Et′ |Ct) > P (Et′)

(ii) There is no further event Bt′′ , occurring at a time t′′ earlier than or simultaneously with t,such that P (Et′ |Ct ∧ Bt′′) = P (Et′ |Bt′′). If there were such an event Bt′′ we would saythat Bt′′ would screen Et′ off from Ct.

In other words, it is not the case that:

Ct Et′

6

Bt′′

(t′′ ≤ t < t′)

(cfr. Reichenbach, 1956; Suppes, 1970).

5.2 Conditionals

Probabilistic evidence turns out in many cases to be not sufficient for claiming that a particularcausal relation exists. Other approaches analyse the nature of the conditions that makes someobject and its circumstances causes of something else.

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Mackie’s (1974) definition:

C causes E if C is an insufficient but non-redundant part of an unnecessary but sufficientcondition for E (INUS condition):

[(A ∧B ∧C) ∨ (D ∧ F ∧G) ∨ (H ∧ I ∧ J)]⇔ E

(cfr. Mackie, 1974).

Counterfactuals (Lewis, 1973):

C causes E iff C occurs and E occurs and if C had not occurred then E would not haveoccurred.

5.3 Transmission and mechanism

Causal statements as denoting physical processes linking causes and effects. Transmission ofphysical quantity (Salmon, 1984, 2000)

5.4 Manipulability

Causes as handles or devices to manipulate effects (Pearl, 2000; Woodward, 2003): C is a causeof E iff I can manipulate C in such a way that E results to be manipulated.

6 Explanation and laws

7 Models

Nowadays models are pervasive in science. Think of the Bohr model of the atom, the double-helixmodel of DNA, the Lotka-Volterra model of predator-prey interaction, the general equilibriummodel of markets, etc. (cfr. Frigg and Hartmann, 2009). In common parlance, the statement “it’sjust a theory” denotes that a certain hypothesis is not yet validated by the empirical evidence. Butthe statement “it’s just a model” expresses even more strongly the possibility that the hypothesis atstake is only a conjecture or even known to be false. Possibly because of this instrumental power,the capacity of being engine for discovery or intervention, the term model has been proliferated.

In economics we have a variety of models: theoretical models in term of system of equations(cfr. the Real Business Cycle model in section 1.2); verbal model or metaphors (cfr. ‘the pinfactory’, ‘the invisible hand’, etc.); material model (cfr. the Phillips machine); models in terms ofgraphs; simulation models (cfr. agent-based models); statistical models of data; etc.

Different questions arise with respect of models in economics. For the present interest weshould face the issue about semantics: what do models represent? And we want to address theepistemological problem of what and how do we learn with models?

Economic models are most typically meant to represent economic phenomena and their causalrelations in isolation. However, these phenomena are to certain extent idealized and this raises thequestion as to what extent the distortion of reality should be allowed. Realists and instrumentalistshave usually different answers. The former retain that abstraction and idealization are accepted

24

only insofar as essential aspects of the reality are identified (where the danger is taking the notionof essential as given). The goal of idealization is isolation. The instrumentalists defend the viewthat anything goes and that any model is useful as long as it predicts well.

Replication of the data is an important issues for realists and instrumentalists as well. How-ever, some accept that a model, even if does not replicate the data may be useful for conceptualexploration (cfr. minimal models discussed by Grune-Yanoff, 2009). Moreover replication of thedata does not guarantee that the model explicate the data. Econometric and statistical models aimto bridge the gap between data and causal relationships, the problem of induction notwithstanding.

An important issue is the notion of model as surrogate of experiment. Robert Lucas madeexplicit statements about that:

“One of the functions of theoretical economics is to provide fully articulated, artifi-cial economic systems that can serve as laboratories in which policies that would beprohibitively expensive to experiment with in actual economies can be tested out atmuch lower cost” (Lucas, 1980, 696).

“Our task, as I see it ... is to write a FORTRAN program that will accept specificeconomic policy rules as ‘input’ and will generate as ‘output’ statistics describing theoperating characteristics of time series we care about, which are predicted to resultfrom these policies” (Lucas, 1980, 709-710).

But, as mentioned, prediction is not sufficient for explanation, and the tests cited by Lucasin the first quotation are not verification tests based on empirical evidence. Thus the problem ofempirical validation of economic models remains one of the most important unsettled issues in themethodology of economics.

8 Realism and Instrumentalism

9 Measurement in Economics

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Frigg, R. and S. Hartmann (2009). Models in science. Stanford encyclopedia of philosophy.

Grune-Yanoff, T. (2009). Learning from minimal economic models. Erkenntnis 70(1), 81–99.

Hausman, D. M. (2013). Philosophy of economics. In E. N. Zalta (Ed.), The Stanford Encyclope-dia of Philosophy (Winter 2013 ed.).

Hoover, K. D. (1995). Review: Why does methodology matter for economics? The EconomicJournal 105(430), 715–734.

Hoover, K. D. (2001a). Causality in Macroeconomics. Cambridge University Press.

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Hoover, K. D. (2001b). The methodology of empirical macroeconomics. Cambridge UniversityPress.

Lewis, D. (1973). Causation. Journal of Philosophy 70, 556–567.

Lucas, R. E. (1980). Methods and problems in business cycle theory. Journal of Money, Creditand banking, 696–715.

Mackie, J. L. (1974). The cement of the universe. Clarendon Press Oxford.

Pasinetti, L. (1981). Structural change and economic growth: a theoretical essay on the dynamicsof the wealth of nations. Cambridge University Press.

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Salmon, W. C. (2000). Physical Causation. Cambridge University Press.

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Stigler, G. J. (1954). The early history of empirical studies of consumer behavior. The Journal ofPolitical Economy 62(2), 95–113.

Suppes, P. (1970). A Probabilistic Theory of Causality. Amsterdam: North-Holland.

Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford UniversityPress.

Yule, G. U. (1915). Crop production and price: a note on gregory king’s law. Journal of the RoyalStatistical Society 78(2), 296–298.

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