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UvA-DARE is a service provided by the library of the University of Amsterdam (http://dare.uva.nl) UvA-DARE (Digital Academic Repository) Representation and Structure: The Methodology of Econometric Models of Consumption Chao, H.K. Link to publication Citation for published version (APA): Chao, H. K. (2002). Representation and Structure: The Methodology of Econometric Models of Consumption. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date: 01 Jan 2021

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Page 1: UvA-DARE (Digital Academic Repository) Representation and ... · connectionn to the multiplier. In Keynes's General Theory (Keynes, 1936), an aggregatee consumption function is constructed

UvA-DARE is a service provided by the library of the University of Amsterdam (http://dare.uva.nl)

UvA-DARE (Digital Academic Repository)

Representation and Structure: The Methodology of Econometric Models of Consumption

Chao, H.K.

Link to publication

Citation for published version (APA):Chao, H. K. (2002). Representation and Structure: The Methodology of Econometric Models of Consumption.

General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s),other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons).

Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, statingyour reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Askthe Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam,The Netherlands. You will be contacted as soon as possible.

Download date: 01 Jan 2021

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Chapterr 3

Trygvee Haavelmo and Measurementt of Economic Structure

Thee construction of systems of autonomous relations is, therefore, a matter

off intuition and factual knowledge; it is an art.

[Trygvee Haavelmo, 1944, p. 29]

Itt is my own opinion that the explicit and exact use of the logical concept

off model will turn out to be a highly useful device in clarifying the theory

off experimental design, which many statisticians still think of as an "art"

ratherr than a "science".

[Patrickk Suppes, 1962, p.260]

3.1.. Introduction

Hendryy and Morgan (1995) have pointed out the importance of the notion

off structure in econometrics before the emergence of the new classical

macroeconometrics.. They wrote that "The view of economic world which came to

dominatee econometric ideas and practice in the year from 1940 through to the

1970s,, and continued to hold a strong position thereafter, was associated with the

notionn of structure." (Hendry and Morgan, 1995, p.60). Their interpretation of the

conceptt of structure in econometrics is to make an analogy to a similar notion that

iss to do with physical objects (ibid.):

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366 REPRESENTATION AND STRUCTURE

Itt was believed that the economy consisted of a set of interdependent

relationships,, which linked the economic world and its many agents

togetherr in a network of interactions. It could be envisaged as the main

uprightss and cross beams of a building, anchored into the foundations, and

providingg essential strength and stability to the building, but no longer

directlyy visible in the finished piece of architecture.

Hendryy and Morgan's analogy is familiar to econometricians who accept the

Cowless Commission's a priori specified econometric modeling. This analogy also

indicatess why the Cowles Commission research program is dubbed as "structural

econometrics". .

Thee origin of the Cowles Commission econometrics is Trygve Haavelmo's

TheThe Probability Approach in Econometrics published in 1944. ' One of

Haavelmo'ss legacies to the Cowles Commission research program is the

simultaneouss equations model (Haavelmo, 1943, 1944). Haavelmo advocated the

simultaneouss equations model for several reasons. First, influenced by Walrasian

generall equilibrium, he believed that economic variables are jointly determined.

Thee then-popular single equation approach (e.g., Schultz, 1938) was not able to

representt these "real relations" between variables. Secondly, the Keynesian theory

off macroeconomics suggests studying the macroeconomy in terms of the

constructionn of a system. Finally, the single equation is not an invariant

relationshipp when subject to changes of the system. These arguments involve two

econometricc concepts. The first is structure, denoting the systematic relations

betweenn variables. The other concept is known as autonomy, denoting the

relations'' characteristic of invariance. The concept of autonomy was originated by

Haavelmo'ss teacher Ragner Frisch. However, in the later development of

econometrics,, structure and autonomy have converged into the same concept

indicatingg invariance, especially in the implications of the Lucas critique (Lucas,

1976).22 As Marcel Boumans rightly observed (Boumans, forthcoming), the

convergencee of structure and autonomy can be found as early as in Girshick and

Haavelmoo (1947) (see Section 3.4.2 below). However, structure and autonomy are

bestt regarded as two distinct concepts of econometrics. This chapter investigates

11 See Hendry and Morgan (1995), Morgan (1990) and Qin (1993) for the history of the Haavelmo'ss econometric program.

Chapterr 6 of this thesis investigates the methodology of the Lucas critique in terms of structure.

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HAAVELM OO AND MEASUREMENT OF ECONOMIC STRUCTURE 37

Haavelmo'ss three studies on consumption, which were all published in 1947. Two

off them (Haavelmo, 1947a and 1947b) study the issue of measuring the marginal

propensityy to consume (MPC). The third one, co-authored with Girshick (Girshick

andd Haavelmo, 1947), studies the food consumption of the United States. These

threee papers deal with different concepts of structure and autonomy.

Haavelmo'ss methodology and Patrick Suppes's semantic approach to the

structuree of scientific theories have much in common. Both Haavelmo and Suppes

treatt structure, model and measurement as important concepts. In a recent article,

Daviss (2000) has applied Federick Suppe's Semantic Conception (Suppe, 1989, a

rigorousrigorous version of Patrick Suppes's semantic approach) to interpret Haavelmo's

econometricc methodology. Yet, Davis's discovery of the similarity is no surprise

becausee Suppes was evidently influenced by econometrics when he was

developingg his theory (see Chapter 1). This chapter argues that Haavelmo's

econometricc methodology can be explicitly understood in terms of the semantic

approach.. Haavelmo and the Cowles Commission's structural econometrics aimed

att structural representations in terms of econometric models. Haavelmo used the

simultaneouss equations model to denote a representation for a theoretical structure.

Thiss fits the idea of the representation theorem of the semantic approach (see

Chapterr 2) that models are a kind of representation. In addition, the uniqueness

theoremm can be applied to construe the identification problem in econometrics as

dealingg with the question of yielding a unique representation of the economic

structure.. However, these two approaches - Haavelmo's structural econometrics

andd the semantic approach - are not identical, for as this chapter further argues,

despitee their similarity in discussing experimental design, Haavelmo and Suppes

seekk to explicate their methodologies of modeling in different directions. While

Suppes'ss methodology is concerned with empirical models that related to his

workk in psychological experiment, Haavelmo's account of experimental design in

factt is against the idea of using controlled experiments in econometrics.

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388 REPRESENTATION AND STRUCTURE

3.22 Measuring Marginal Propensity to Consume 3.2.13.2.1 Measuring the least-squares bias

Measuringg the elasticity of consumption to income, or its equivalent, the

marginall propensity to consume, was one of the most important issues in

econometricss in the mid twentieth century. Elasticities are usually regarded as the

measuress of relationships between consumption expenditure and certain variables.

Thiss point is particularly made in the microeconomic studies of commodity

expenditures,, for example, in the linear expenditure models studied in Chapter 2.

Forr this purpose of measuring elasticities, economists had chosen specific

functionall forms, such as linear and log-linear functions, in which elasticities can

bee easily understood and measured. These studies belongs to the "single-equation

approach",, in which a consumption function is proposed to measure the

relationshipp between the expenditure on a particular commodity and income, its

ownn price and price of other commodities.

Inn Keynesian macroeconomics, the MPC is important because of its

connectionn to the multiplier. In Keynes's General Theory (Keynes, 1936), an

aggregatee consumption function is constructed according to the "fundamental

psychologicall law" which asserts that aggregate consumption depends on

aggregatee income. But income is treated as endogenous rather than exogenous, as

incomee is determined by investment. This point was recognized by Haavelmo in

hiss attempt to use the simultaneous equations approach to measure the MPC.

Haavelmoo (1947a) gave two objections to the single-equation, least-square

methodd as follows.

First,, on theoretical grounds, Haavelmo followed Keynesian

macroeconomicc theory to address the importance of measuring the MPC because

off its relation to the multiplier. He continued to argue that investment should be

consideredd when measuring the MPC as the role of investment had been discussed

byy Alvin Hansen and Paul Samuelson (both leading Keynesians at the time).

Givenn the appropriateness of using the Keynesian system to study the

macroeconomy,, Haavelmo was amazed that "it is somewhat surprising to find that

currentt attempts to derive, statistically, the marginal propensity to consume

approachh the problem by correlating consumers' expenditure with income"

(Haavelmo,, 1947a, p. 106).

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HAAVELM OO AND MEASUREMENT OF ECONOMIC STRUCTURE 39

Second,, on statistical grounds, Haavclmo showed that there is an

inconsistencyy bias if we use the ordinary least-squares (OLS) method to measure

thee MPC in a consumption relation that belongs to a simultaneous equations

model.. This error is known as positive "least-squares bias" that has been

introducedd by Haavelmo (1943). In order to illustrate, Haavelmo set up several

completee models of the Keynesian economy and estimated the MPC by using

"indirectt least-square (ILS) method" (that is, first derive the reduced form for

eachh endogenous variable, then use the least-squares method to measure it), then

comparedd ILS estimators with OLS estimators. Haavelmo considered three

versionss of the Keynesian model with different assumptions on investment. The

simplestt one is expressed as follows:

(3.1)) c,=a + Py,+u,

(3.2)) y,=c,+it

(3.3)) i,=J

wheree c, is per capita consumption expenditure, y, is per capita disposable

income,, it is per capita investment expenditure, and ut is the random element. By

assumption,, the investment is fixed (autonomous). The properties of the random elementt are specified as: £(«,) = 0, Var(ut) = o] for all /. E(ut,uM) = 0 for

T * 0 . .

Haavelmoo used US time-series data at per capita level to estimate the MPC

inn his simultaneous equations models and compared them to the OLS estimates of

twoo different models. Model 1 is given in (3.1)-(3.3), model 2 has the similar

frameworkk but private savings are separated from investment, and are a function

off income. His empirical findings are summarized at Table 3.1.

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400 REPRESENTATION AND STRUCTURE

Dataa Period Method Estimate of M PC

Modell 1 1922-19411 OLS 0.732

1922-19411 ILS 0.672 (thee confidence interval of the ILS estimate for p is 0.57 < p < 0.73)

Modell 2

1929-19411 OLS 0.723

1929-19411 ILS 0.712

Tablee 3.1 Comparisons of the OLS and ILS estimates of the MPC

byy using US time-series data for consumption for food

Haavelmo'ss numerical findings confirmed that OLS estimates are larger

thann the ILS estimates. But, as we can observe, the gap is not large. In the first

modell containing equations (3.1)-(3.3), the OLS estimate (0.732) is almost in the

confidencee region of the ILS estimate. However, Haavelmo argued that even

thoughh the gap in the estimates of the MPC is not large, their difference is

"considerable"" in terms of multiplier l / ( l - (3) : 3.731 for the single equation

modell and 3.048 for the simultaneous equations model (see Haavelmo, 1947a,

pp.119-20).. Hence, the interdependence of economic variables should be taken

intoo consideration when measuring the MPC in the macro level.

3.2.23.2.2 False analogy of the Engel curve

Haavelmo'ss other attack on measuring the marginal propensity to consume

inn macroeconomics appeared in Haavelmo (1947b). His criticism here was based

onn his observation that the macro consumption functions were usually built in the

fashionn of the family budget study, in which the elasticity of consumption with

respectt to income is usually measured assuming income is given. Haavelmo

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HAAVELMOO AND MEASUREMENT OF ECONOMIC STRUCTURE 41

arguedd that this is a bad analogy to the Engel curve in the micro consumption

study,, for the reason that there is a gap between the MPC measured by the Engel

curvee type consumption function and the "true" MPC. Assuming that the

aggregatee consumption function is linear, it can be expressed as:

(3.4)) c=py + £aJx,+Y

wheree the x's are "observable characteristics" such as family size, age, location, andd the like, y =Y(/>1,P2,L ,ps) denotes the effects on consumption from

existingg prices. For Haavelmo, p is the true MPC in terms of aggregate variables. Butt the Engel curve considers the average or expected consumption expenditure att the given income level, average income and prices, thus it can be presented in termss of conditional expectation E(c\y;y;pltp2tl ,ps) where y is the average

income.. Haavelmo went on to show that the conditional expected consumption cann be written as

(3.5)) E(c\yiy;pltp2tl ,ps) = g(y;y)+y (p^p^l ,ps)

Therefore,, the MPC measured according to (3.5) is dg/dy. As Haavelmo argued,

dg/dydg/dy is in general not equal to the true MPC p. Haavelmo thought the reason is

thatt the Engel-curve function is not adequate as an aggregate consumption

function.. The Engel-curve function is not able to reflect the effects on

consumptionn expenditure of the changes of those variables which are held

constant.. For example, the change of y. In other words, the Engel curve type

aggregatee consumption function is not autonomous. Therefore, (3.5) does not

representt an invariant relationship between consumption and income with respect

too the changes of other variables.

3.33 Autonomy

Forr Haavelmo, as Hendry and Morgan (1995, p.64) point out, the main

purposee of theoretical models in this case is to highlight the distinction between

contingentt plans (which can be represented by the above Engel-curve method),

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422 REPRESENTATION AND STRUCTURE

andd interdependent relations represented by structural equations. The MPC

obtainedd by measuring the Engel curve is not invariant to the change of the

averagee income and/or income distribution, thus it is only contingent. In this sense,

thee most important criterion of theoretical models is their degree of autonomy.

Autonomyy is defined as invariance under certain changes occurring in economic

systemm (see Haavelmo, 1944).3 Haavelmo (1944) used a mechanical analogy to

illustratee why we need to concentrate on the autonomous relations. He argued that

wee could derive the functional relation between the pressure on the gas throttle

andd the speed of a car on a flat road under usual conditions. But such a relation

wil ll break down as soon as there is a change in any working part of this car

(Haavelmo,, 1944, p.27). To Haavelmo, the throttle-speed relation is less

autonomouss (i.e., it is confluent) because this type of relation is not invariant to

changess of surrounding conditions. Haavelmo criticized the Harvard A-B-C

curvess as being a relation which has littl e autonomy (Haavelmo, 1944, pp.27-8).

Ass this example illustrated, the notion of autonomy is construed as

invariance.invariance. But Haavelmo was less concerned with an empirical regularity such as

throttle-speedd relation or the Harvard A-B-C curves. He believed that measuring

suchh an empirical relation does not say anything about the mechanism behind the

data:: "such a relation leaves the whole inner mechanism of a car in complete

mystery"" (Haavelmo, 1944, p.27). He was concerned with the "theoretical

structuree of the economy", which is defined as "a theoretical set of possible

simultaneouss sets of values or sets of time series for the economic variables"

(p.28).. Despite the emphasis on simultaneity, the notion of structure is proposed

too denote theoretical relations (in contrast with empirical relations), which have a

highh degree of autonomy. Haavelmo's conception of structure can be seen in

Girshickk and Haavelmo (1947).

3.44 Consumption for Food

3.4.13.4.1 The Girshick-Haavelmo model

Haavelmo'ss two studies on the MPC (Haavelmo, 1947a and 1947b) were

onlyy concerned with measuring the parameters of the consumption functions. The

33 Also see Aldrich (1989), Hendry and Morgan (1995), and Boumans, (forthcoming) for methodologicall discussion on autonomy.

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HAAVELM OO AND MEASUREMENT OF ECONOMIC STRUCTURE 43

simultaneouss equations model was not estimated as a whole. Nonetheless

simultaneityy was definitely considered even though only a single consumption

functionn was measured. Besides, these consumption functions are just-identified,

soo that the ILS method applies. It should be noted that a more general technique

forr measuring the simultaneous equations models was not available to

econometricianss in the early 1940s. Only when the limited information maximum

likelihoodd (LIML ) method was invented by the Cowles Commission scholars in

thee mid-1940s did it become possible to measure an overidentified model.

However,, the difficulty of the measurement procedure prevented economists from

usingg the simultaneous equations model, so even though the knowledge of the

simultaneouss equations bias had been accepted by econometricians, it would often

bee too difficult to measure the entire simultaneous equations model. For example,

Richardd Stone's studies on consumption (Stone, 1945, 1954a) mentioned

Haavelmo'ss probability approach and simultaneous equations model, but in

practicee he used Frisch's confluence analysis (or bunch map analysis), which is by

naturee a single equation approach (Stone's objection to the simultaneous

equationss model will be discussed below in Section 3.4.2).4

Thee first application of LIML is found in Girshick and Haavelmo's (1947)

studyy to explain US food consumption at the average per capita level over the

periodd 1922-41. The authors began by re-stating Haavelmo's account of the

simultaneouss equations system. Then the computational procedure of the LIML

methodd was provided. Girshick and Haavelmo went on to set up a five-equation

model,, the so-called Girshick-Haavelmo model, consisting of a demand function

forr food, an income equation, a supply equation in the retail market, a supply

equationn of the food products from farmers, a demand function for food products

byy the retail sector, and a demand function for food products by the commercial

sector.. For each type of equation, Girshick and Haavelmo offered two to three

44 In his interview with Hashem Pesaran, Stone talked about his 1954 work, and says that "It is perhapss surprising that I did not discuss Haavelmo's simultaneous equation system [in Stone (1954)].. In principle I fully agreed with it but in practice I thought that, with many difficulties in timee series regression analysis, this one could perhaps be left over for the time being." (Pesaran, 1991,, p. 103) On the confluence analysis: "... Bunch maps figured largely in my early work as a safeguardd against the appearance of more than one relationship in my small samples. I do not knoww how widely they were used even in the early days. I suppose I was persuaded that they were nott worth the considerable amount of work involved as I gave them up after a time." (Pesaran, ibid.)ibid.) Stone's view on measurement and his consumption expenditure study by using the linear expendituree system can be found in Chapter 2 of this thesis.

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444 REPRESENTATION AND STRUCTURE

alternativess and they chose an equation from each group to constitute their model.

Butt they did not explain their decisions, perhaps for the reason that Girshick and

Haavelmo'ss intention was to use this model "as an illustration" (Girshick and

Haavelmo,, 1947, p.99) for the LIML method. The simultaneous equations model

thatt they chose is presented as follows:

Foodd demand function in the retail market

(3.6)) yi(t)=CLt2y2(t)+a.ïiyi(t)+yut+yi2y3(t-l)+a l{i +ul(t)

Foodd supply function in the retail market

(3.7)) yi(t)=a22y2(t)+a24y4(t)+y2lt+a20+u2(t)

Incomee equation

(3.8)) y3(0=Y3|2(0+Y33>'3(f-1)+a30+"3(0

Farmer'ss supply function

(3.9)) y,(t)=ct4Sy5(t)+yj+y A2y5(t~\)+a40 + u4(t)

Foodd demand by the commercial sector

(3.10)) ^s(0=a52y2(0+Y5i /+a5o+"5(0

where e >>,, =cjpx ; c, denotes annual per capita expenditure for food, /?, denotes the

pricee for food. yy22 = pJP, where P is the total cost-of-living index.

Lett r be per capita disposable income, y3 = r/P then denotes the deflated per

capitaa disposable income.

y4y4 denotes the per capita supply of food by farmers to the commercial sector.

ysys denotes deflated prices paid to farmers.

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HAAVELM OO AND MEASUREMENT OF ECONOMIC STRUCTURE 45

zz(0(0 = ~ = J>3(0 - ——»1(0 denotes per capita investment expenditures.

Thee a's and y's are constants; tn(t) is a random residual; t denotes time.

Finally,, the US time-series data for 1922-1941 were used to estimate the simultaneouss system. The estimate of the marginal propensity to consume was 0.255. .

Thee Girshick-Haavelmo model is a valuable pedagogical device for

econometricianss to understand the LIML method. It is more appreciated given the

factt that the full information maximum likelihood (FIML) method was too

complicatedd to compute because of the lack of capacity in computing facilities at

thatt time. The estimate of MPC of the Girshick-Haavelmo model was taken to

comparee with other empirical measures to show the difference between the

simultaneouss equations approach and the single equation approach. The result

showedd the significant gap between the Girshick-Haavelmo MPC and Haavelmo's

1947bb results shown above; but it was also very different from other measures

takenn around this time. These results are discussed below.

3.4.23.4.2 The measures of MPC

Foodd consumption was an important topic in the 1940s and 1950s. Some

notablee studies, such as Stone (1945, 1954a, see Chapter 2) and Tobin (1950),

however,, did not use the simultaneous equations approach. In addition, Girshick

andd Haavelmo were not concerned with model specification in the sense that they

Thee data used for this model are the following, y, = Food consumption per capita published by thee Bureau of Agricultural Economics (BAE), with an adjustment by the authors to exclude government'ss purchase of meat for relief purposes and distributed through noncommerical channels.. y2 = Retail prices of food products by the BAE, deflated by the Index of Consumer Pricess for Moderate Income Families in Cities published by the Bureau of Labor Statistics (BLS). y33 = Disposable income per capita by the Department of Commerce, deflated by BLS Consumer Pricee Index. y3<t-1) = Disposable income per capita lagged one year. y4 = Production of agriculturall food products per capita by BAE. y5 = Prices received by farmers for food products by BAE,, deflated by BLS Consumer Price Index. ys(t-l ) = Price received by fanners for food products,, lagged one year. z(t) = Net investment per capita = disposable income minus consumers' expenditures,, based on Department of Commerce data, deflated by BLS Consumer Price Index, t = time. .

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466 REPRESENTATION AND STRUCTURE

didd not explain why their model consists of five equations and why each equation

wass chosen from among others. Hence, for economists, Stone's and Tobin's

modelss are more persuasive, at least in the sense that their empirical models were

builtt with the help from the phenomena.

Girshickk and Haavelmo's measure of the MPC (0.25) can be compared

withh the measures from these other consumption expenditure models. In the

discussionn sequel to Tobin's famous 1950 paper on demand for food in the United

States,, Stone (1950) offered a comparison between the measures of the MPC from

thee Girshick-Haavelmo model, Tobin's three estimates in his 1950 paper, and

Stone'ss three estimates in his 1945 paper. They are summarized in Table 3.2.

Girshickk and Haavelmo (1947)

Periodd MPC (orr elasticity to income)

1922-19411 0.25

Tobin(1950) )

(Tl) )

(T2) )

(T3) )

1913-1941 1

1913-1944 4

1913-1944 4

0.44 4

0.45 5

0.27 7

Stonee (1945)

(SI) )

(S2) )

(S3]_ _

1929-1941 1

1929-1941 1

1929-1941 1

0.59 9

0.53 3

0.83 3

Tablee 3.2 Comparison of the marginal propensity to consume for food in the US

(adaptedd from Stone, 1950)

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HAAVELM OO AND MEASUREMENT OF ECONOMIC STRUCTURE 47

Itt can be observed that Stone's first two estimates (SI and S2)were

relativelyy close to Tobin's first two estimates, (Tl) and (T2) but all were

significantlyy larger than Girshick and Haavelmo's estimate. (T3) is very close to

Girshickk and Haavelmo's estimate. Stone suggested that one could object to these

unrestrictedd models on the grounds that "they do not square with what is known

fromfrom budget studies" (Stone, 1950, p. 142). The "unrestricted equation" is in

contrastedd with the "restricted equation", where the former refers to Girshick and

Haavelmoo (1947) and (T3) and the latter refers to (Tl), (T2) and all of Stone's

measuress which were estimated by using extraneous estimators so that the

equationn is restricted, meaning they had used a linear consumption expenditure

functionn in which the sum of two income elasticities was extraneously measured

byy using budget data. In contrast, (T3) and Girshick and Haavelmo's measure

weree unrestricted because they were made based on time-series alone. Stone

obviouslyy believed that (T3) and the Girshick-Haavelmo models should be

rejectedd on the ground that their measures of the MPC were too low.6

Recalll that Haavelmo (1947a) had estimated the least-squares bias in the

measurementt of the MPC and that the estimates of using the simultaneous

equationss model should be smaller than the estimates derived from the single

equation.. In a comparison of the two unrestricted parameter estimates, their

simultaneouss equations version was indeed a littl e smaller than T3, compatible

withh theories and experience of the simultaneous equations bias. Girshick and

Haavelmoo might have faith in their model because it was a simultaneous

equationss model, but there are still some concerns with respect to the empirical

justifications. .

Firstt of all, it should be noted that while in Haavelmo (1947a) the

differencee of MPC between the simultaneous equation method and the single

equationss method is not large, Table 3,1 shows that the Girshick-Haavelmo

estimatee is dramatically smaller than other estimates. Moreover, Haavelmo's

(1947a)) measures of the MPC, even though the data period is similar to that of

Girshickk and Haavelmo (1947), are around 0.7, which is considerably larger than

thee Girshick-Haavelmo's measure of 0.25. But, because the models were not the

same,, the content of the bias cannot be directly compared. Hence it would be

questionablee to use the simultaneity bias to explain this discrepancy.

66 It should be noted that the estimates of the MPC Stone and Stone (1938) by using 1920-1935 dataa were 0.699 and 0.755.

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488 REPRESENTATION AND STRUCTURE

Secondly,, for other economists like Stone, this huge discrepancy would be

evidencee to reject the Girshick-Haavelmo model because they have no reason to

believee their model was better. However, Stone's table shows also the similarity

betweenn Girshick and Haavelmo's estimate and (T3) can also be regarded as a

supportt that both are acceptable estimates for the unrestricted, time-series study of

thee MPC for food. That is to say, the larger discrepancy found between restricted

andd unrestricted models might be explained by the different nature of budget-

studyy and time-series data.

Andd finally, as Christ (1994, p.44) points out, it was not possible to

estimatee the standard deviation of the LIML estimators at that time, hence the

confidencee intervals for parameters are not given in the Girshick and Haavelmo

(1947)) and so comparison of the numerical values of the estimates is problematic.

3.4.33.4.3 Th eoretical models

Inn Haavelmo's methodology, economic theory is believed to be powerful

enoughh to make the model identifiable. Models like the Girshick-Haavelmo model

aree assumed to be well-specified, in the sense that a priori restrictions are imposed

too assume certain parameters are zero, so that the model satisfies the identification

conditions.. This means that, according to theory, certain variables have been

declaredd not have influence on certain variables on the left hand side of the

model.77 This shows that the kind of model that Haavelmo as well as the Cowles

Commissionn were interested in are theoretical models representing economic

theories.. But Haavelmo's a priori restrictions, unlike the Slutsky conditions in the

demandd analysis discussed in Chapter 2, are beyond empirical justification. As

Christt (1994, p.53) puts it, "The Cowles Commission approach to econometrics

wass built on the premise that correct a priori specifications were already available

forr the models that were to be estimated by the methods. Cowles theoretical

econometricc work did not have much to say about the process of specifying

models,, rather taking it for granted that economic theory would do that, or had

Hooverr (1994) called the new classical school's response to the Cowles Commission's a priori restrictionss (especially Cooley and LeRoy, 1985) "strong apriorism", namely, that the basis of thesee identifying restrictions is a well-articulated theory from which restrictions can be derived. Chapterr 6 further discusses this issue.

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HAAVELM OO AND MEASUREMENT OF ECONOMIC STRUCTURE 49

alreadyy done it."8 However, some a priori information is beyond the scope of

economicc theories, for example, lag length, or the "horizon" that distinguishes

permanentt income and transitory income in Friedman's permanent income

hypothesiss (see Chapter 5, Section 4.4). The orthogonality condition in the

simultaneouss equations models has often been criticized in this respect (see

below). .

Theree are two challenges to the simultaneous equations approach and its

identificationn problem. One is Stone's (1954a) argument that identifying the

simultaneouss equations has proven to be "extremely arduous" because in the case

off estimating a single equation like a demand function, other equations, e.g., the

supplyy function, have to be "theoretically specified" and their variables have to be

estimated.. In such a case, in order to satisfy the identification conditions, a new

independentt equation must be added whenever a new endogenous variable is

introducedd to the model. Stone went on to conclude that "The construction of a

systemm around a single equation can only be expected to improve the estimates of

thee parameters in the single equation by bringing into account in a realistic

fashionn some related phenomena with which the relationship under investigation

iss closely connected. A formal system built to satisfy formal conditions for

identifiabilityy is not likely to be helpful." (Stone, 1954a, p.249) For this reason,

thee single equation approach and the bunch map analysis were the major tools of

Stonee (1954a) on the measurement of UK consumption expenditure.

Thee other challenge to the simultaneous equations model is Ta-Chung

Liu'ss criticism on orthogonality conditions (Liu, 1960, 1963). Liu argued that in

thee Cowles Commission's treatment, the simultaneous equations models are

overidentifiedd because variables are excluded from the models according to the

guidancee from theory or a priori information. However, structural models must be

intrinsicallyy underidentified because it seems to be more realistic to include

variabless in the model rather than exclude them. So his critique that most

structurall relationships should contain more variables than those found in the

Cowless Commission models. "The complexity of modern economic society

88 But note that satisfying the identification conditions is not the same as the representation theorem off the semantic axiomatization As has been discussed in Chapter 2, models are representations if andd only if they satisfy a certain set of axioms. Later in this chapter, identification will be discussedd showing that it is not concerned with how to construct a model, rather it is concerned withh yielding a unique representation thus can be understood in terms of the uniqueness theorem off the representational approach to measurement.

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500 REPRESENTATION AND STRUCTURE

makess it much more likely that the true structural relationships are underidentified

ratherr than overidentified." (Liu, 1960, p.856.) Sims (1980) shared Liu's critique

onn the Cowles Commission method and established the VAR method that is

knownn as a "non-structural" approach to econometric modeling.

Despitee the controversies over the role of theory and a priori restrictions,

thee simultaneous equations models, exemplified by the Girshick-Haavelmo model

off food consumption, did emphasize the econometric concepts of structure and

autonomy.. But these concepts are not identical. The next section analyses the

Girshick-Haavelmoo model further in this respect and discusses the difference

betweenn structure and autonomy.

3.55 Structures and Autonomy: A Clarification

Thee objective of statistical inference is to find a simultaneous system in

whichh the endogenous variables are determined as functions of the predetermined

andd random variables. It implies a procedure of inferring from data to the "true

structure"" of the system. While there can be many possible versions of the

Girshick-Haavelmoo model (162 possible models according to the setups), they

thinkk there is a "true model". For this true model, "there exists a set of values of

thee parameters such that, for the assumed distribution of the H'S, the resulting joint

probabilityy distribution of the v's is identical with the true distribution of the

observablee / s, for all values of the predetermined variables" (Girshick and

Haavelmo,, 1947, p.92). This true model represents autonomous relations.

Therefore,, although the role of statistical inference is to find the true structure, at

thee same time it also identifies an autonomous system. As Girshick and Haavelmo

(1947,p.93)putit, ,

Whyy is it that we are interested in one particular member of this infinite set

off true systems? It is because, in setting up the original model, we believe

thatt there is one particular system of equations that is a system of

autonomous,autonomous, or structural equations, that is, equations such that it is

possiblee that the parameters in any one of the equations could in fact

change,, e.g., by the introduction of some new economic policy, without

anyy change taking place in any of the parameters of the other equations. If

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HAAVELM OO AND MEASUREMENT OF ECONOMIC STRUCTURE 51

theree is one system for which this is true, the other systems that can be

derivedd from it will not have this property. The parameters of equations in

derivedd systems will be functions of the parameters in two or more of the

equationss in the original system. (Original emphases.)

Thee purpose of finding the true model is such that we can use the true model to

analyzee economic policies' affects on structural changes (ibid.):

Thee results could be used to judge, in advance, the effects of various

policiess that might be considered. If the policy considered represents a

knownknown change in the structure, e.g., a known absolute or relative change in

onee or more of the parameters or variables involved and if the structure

beforebefore the change is known, then obviously the structure after the change

iss also known, and we can compare the two.

Bothh quotations emphasize the conception that a "true model" is a system of

autonomouss relations, and somehow autonomy and structure become the same

notion,, indeed, Girshick and Haavelmo called the true model "a system of

autonomous,autonomous, or structural equations". Boumans (forthcoming) observes this and

concludess that autonomy and structure have converged to the same concept.

However,, in the content of Haavelmo's econometric approach, structure and

autonomyy must be regarded as two distinct concepts. Autonomy is equivalent to

invariance,, and does not say anything about the constitution of a system. Structure

iss better understood as referring to Haavelmo's econometric task of constructing

thee simultaneous equations model, or what we nowadays call "structural

econometrics"" because it refers to the constitution of the relationships between

economicc variables, like Hendry and Morgan's analogy mentioned in the first

sectionn of this chapter. To know such a constitution is important in econometrics,

andd statistical inference can be understood as to achieve the task of knowing the

uniquee structure. It can be summarized by Girshick and Haavelmo's declaration

(1947,, p.93):

Itt is clear, then, that the fundamental objective of statistical inference with

respectt to economic models is to derive estimates of the structural

parameters.. Knowing the structural parameters, all the relations implied by

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522 REPRESENTATION AND STRUCTURE

thee model can be derived. In a sense these structural parameters play a role

similarr to that of the elements in chemistry.

Thee structure-autonomy distinction can be further explained by discussing

identification.. Identification has various meanings (see Aldrich, 1994, Hendry,

1995,, Hendry and Morgan, 1995, and Qin 1993). Aldrich (1994, p.200) argues

thatt Haavelmo's identification is the inference from sample to structure, which is

differentt from two other types of identification: sample to population and

populationn to structure.9 Yet all three have something in common: identification

yieldss a unique representation.

Inn the context of simultaneous equations models, as Haavelmo puts it,

modell building represents economists' effort of reconstructing "the mechanisms

whichh we think lie behind the phenomena we observe in the real world"

(Haavelmo,, 1944, p.27). Nonetheless, identifiability does not merely indicate a

model'ss representation of a mechanism that produces data, but it must be

understoodd as a feature of model's unique representation of the mechanism behind

thee phenomena. This is because, for a given system autonomous relations, there

existt many other systems which are equivalent to the autonomous system, but are

(linear)) combinations of the autonomous relations. The latter are confluent

relations,, and can be reduced to the autonomous relations. Identifiability thus

meanss a feature of yielding a unique representation of the econometric model's

structure.. Haavelmo (1944) offered the following argument:

Supposee that it be possible to define a class Q, of structure, such that one

numberr or another of this class would, approximately, describe economic

realityy in any particularly conceivable situation. And suppose that we

definee some nonnegative measure of the "size" (or of the "importance" or

credibility")) of any subclass, co in Q, including Q itself, such that, if a

subclasss contains completely another subclass, the measure of the former

iss greater than, or at least equal to, that of the latter, and such that the

measuree of Q is positive. Now consider a particular subclass (of Q),

containingg all those—and only those—structures that satisfy a particular

relationn "A." Let co be this particular subclass. (E.g., co might be the

subclasss of all those structures that satisfy a particular demand function

99 See Aldrich (1994) for further discussions.

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HAAVELM OO AND MEASUREMENT OF ECONOMIC STRUCTURE 53

"A.")"A.") We then say that the relation "A" is autonomous with respect to the

subclasss of structure v>A. And we say that "A" has a degree of autonomy

whichh is the greater the larger be the "size" of a>A as compared with that of

Q.. (Haavelmo, 1944, pp.28-9)

Theree can be many subsets of structures containing the same autonomous

relations.. The measure of autonomy indicates the direction of reduction, that is to

say,, the structure with lesser autonomy can be reduced to the structure with

greaterr autonomy. Therefore, all alternative structures eventually are reduced to a

uniquee structure: the structure with the greatest degree of autonomy.

Itt has to be emphasized that the meanings of identification vary. Here

identificationn is restricted to the sense of uniqueness, whose formal account was

developedd by Koopmans, Rubin and Leipnik (1950) in the famous Cowles

Commissionn Monograph 10. They provided the rank and order conditions for

derivingg the unique coefficients in simultaneous systems. Nevertheless the idea of

usingg econometric models, as Koopmans et al. stated, involved the sense of

representation.. They explicitly referred to models as representations: "Let a 'way

off writing' the system be called a representation of the distribution of variables."

(Koopmans,, Rubin and Leipnik, 1950, pp.62-3.) Two representations are

equivalentt if these representations define the same joint probability distribution of

thee variables. However, there exists only one "representation according to

economicc structure" or "structural representation", as Koopmans et al. called it

(Koopmans,, Rubin and Leipnik, 1950, p.63), which contains a set of equations

andd each equation corresponds either to a specified law of behavior, a specified

laww of technology of a specified identity.10 The problem that econometricians face

iss that such a model written down is only one mathematical specification of the

jointt probability of the variables. Any linear transformation of this model

mathematicallyy equivalently defines the probability distribution. In a sense, this is

aa uniqueness theorem: a linear transformation of the structural representation is

alsoo a permitted structural representation, thus econometricians need to identify

thee desired structural representation among all linear combinations of the

equations.. This kind of discussion on identification, that is, whether a structure is

uniquelyuniquely identifiable among all available structures, can also be found in

Koopmanss (1949a) and Marshack (1950).

Thiss categorization of equations in a system appeared first in Haavelmo (1944).

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544 REPRESENTATION AND STRUCTURE

Onee has to bear in mind that the common understanding of identification is

too yield a unique structure, or a unique representation of the economy, while we

cann recall that structure has been specifically analogized to elements in chemistry,

nott just simply invariant relations. So long as the meaning of "autonomous" and

"structural"" are understood as identical and denote invariance, uniqueness, as a

criterionn of model specification, is thereby ignored. Reemphasizing the different

characteristicss of uniqueness and invariance is thus helpful to understand the

meaningg of structure in Haavelmo's structural approach to econometrics.

Usingg the methodologies concerning representation, structure and

uniquenesss discussed above, we can reinterpret Haavelmo's three studies on

consumptionn in terms of autonomy and structure. In Haavelmo (1947b), the

conceptt of autonomy is applied to criticize the use of Engel curve consumption

functionn in macroeconomics. Because consumption is influenced by many

variabless other than income, the MPC measured by relating consumption with

givenn income is proven not an autonomous relation. This consumption-income

relationn is not invariant when other variable changes. Yet structure is not specified

inn this article.

Inn contrast, Haavelmo (1947a) and Girshick and Haavelmo (1947) are

concernedd with identifying unique structures. In the light of the structural

modelingg strategy, they indicate how a (true) structure is measured. A (true)

structuree is measured when its parameters are measured for this means that the

econometricc model is a unique representation of the network of the economy.

Ass discussed in the previous chapter, the uniqueness theorem states that,

givenn a set of models which all have the same relational structure, these models

cann be reduced to a unique model. This is consistent with the identifiability

conditions.. In Suppes's semantic approach, it is crucial to present a model set-

theoretically.. A model can be understood as a relational structure because the

propertiess and relations are all specified. Econometric structure can also be

understoodd as a relational structure for there is no problem to present econometric

modelss in terms of set-theoretical entities. But relational structure in the semantic

approachh does not concern autonomy in Haavelmo's sense. That is to say

philosopherss do not ask whether their relational structure will remain invariant

duee to the change from the variables that are already included in the relational

structure.. Rather they would like to ask whether our model has the same structure

ass that being investigated, so we can use our model to represent the phenomena—

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HAAVELMOO AND MEASUREMENT OF ECONOMIC STRUCTURE 55

thee representation theorem; and whether the structure is uniquely represented—

thee uniqueness theorem. In this sense, the semantic approach's concern of

uniquenesss is identical to identifiability in econometrics.

3.66 Experimental Design: Uaavelmo versus Suppes

Haavelmo'ss econometric methodology has an historical connection with

thee semantic approach. This similarity is not just because econometric models can

bee represented set-theoretically. Suppes's semantic approach was greatly

influencedd by the Cowles Commission people (e.g., M. A. Girshick and Herman

Rubin,, see his autobiography) and both used the language of the Hubert Program.

Thuss it is no accident that Haavelmo's conceptions on models and structures look

familiarr to those in the semantic approach u . We have argued that the

representationn and uniqueness theorems can help us to understand the key

conceptss in Haavelmo's econometric program: structure, autonomy and

identification.. But the Cowles's and the Suppes's views on models and modeling

havee different interpretations in the sense that their models represent different

entities. .

3.6.13.6.1 Models of data

Inn philosophy of science, the theory of models in the semantic approach is

exemplifiedd in Patrick Suppes's seminal paper "Models of Data". This paper

providess an account for the logical notion of models of data, in analogy to the

moree familiar notion of models of theory. The objective of Suppes's paper, in his

word,, was "to show that exact analysis of the relation between empirical theories

andd relevant data calls for a hierarchy of models of different logical type"

(Suppes,, 1962, p.260). The practical purpose of the hierarchy of models is to

providee a procedure for deriving models in experimental science. This procedure

Suppess once put it: "There is also a certain technical usage in econometrics of the word 'model* thatt needs to be noted. In the sense of the econometricians a model is a class of models in the sensee of logicians, and what logicians call a model is called by econometricians a structure." (Suppes,, 1960, p. 12)

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566 REPRESENTATION AND STRUCTURE

camee from Suppes's experience of constructing a model for experimental science

relatedd to his work of learning theory in psychology experiments. For example,

seee his learning theory (Estes and Suppes, 1959, Suppes, 1959). Therefore,

Suppess regarded this account as a "theory of experimental design" (Suppes, 1962,

p.260).. Mayo (1996, p. 140) provides a general and detailed interpretation of

Suppes'ss hierarchy of models of data in the context of experimental work:

Ceteriss Paribus Conditions

Insuree the adequate control of extraneous factors or estimate their

influencee to subtract them out in the analysis.

Dataa Generation and Experimental Design

Applyy systematic procedures for producing data satisfying the assumptions

off the experimental data model. Introduce statistical considerations via

simulationss and manipulations on paper or on computer.

Modelss of Data

Putt raw data into a canonical form to apply analytical methods and run

hypothesiss test. Test whether assumptions of the experimental model hold

forr the actual data, test for robustness.

Modelss of Experiments

Breakk down questions into test of experimental hypotheses, select relevant

canonicall models of error for performing primary tests. Specify

experimentss and specify analytical methods to answer questions framed in

termss of the experiment.

Primaryy Models

Breakk down inquiry into questions that can be addressed by canonical

modelss for testing hypotheses and estimating values of parameters in

equationss and theories. Test hypotheses by applying procedures of testing

andd estimation to models of data.

Tablee 3.3 Models of data (adapted from Mayo, 1996)12

Thee order of these models in the above table is reversed from Suppes's and Mayo's illustrations. Suppess and Mayo put "primary models" on the top and "ceteris paribus conditions at the bottom" inn order to show the hierarchy of the sophistication of models. I reverse the order to show the

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Suppess was confident in constructing models for experimental data, as

longg as we follow the procedure he suggested. It should be kept in mind that

Suppes'ss theory of models intrinsically deals with experimental science (what he

calledd empirical science). Although he expressed the ambition to apply his theory

off models to science in general, and to replace the syntactic approach to structure

att the pragmatic level (Suppes, 1962, pp.260-1), his optimism might not be shared

byy econometricians like Haavelmo. The econometricians' point of view

representedd by Haavelmo is rather pessimistic.

Haavelmoo also talked about experimental design. His experimental design

iss in fact an alternative to experiments in natural science. Morgan (1998, p.218)

pointss out a twofold injunction of Haavelmo's experimental design:

1.. To adapt the theoretical model so that it was about what could be in

principlee observed.

2.. To incorporate a probabilistic format such that the model becomes a

hypothesiss about statistical data.

Haavelmo'ss approach is different from Suppes's approach in the respect

thatt Suppes wanted to give an account of experiments in which observed data are

producedd by experiments themselves. The task in such cases is to find the

relationall structures and the scale so that experimental data can be measured. In

contrast,, Haavelmo objected to the idea of using controlled experiments in

economics.. For Haavelmo, econometricians are merely passive observers of data:

dataa are the results of passive observation of Nature's experiment, not the kind of

productss of experiments controlled in laboratory. Haavelmo defined passive

observationn in terms of positive statements in contrast to theory's normative role

off suggesting what economic phenomena might occur (Haavelmo, 1944, p. 16). In

thiss sense, models come along as a bridge between theory and data. Models are

built,, with the help from economic theory, to match data. So that models are

statisticallyy testable hypotheses of the theory.

proceduree of empirical modeling: starting from ceteris paribus conditions and ending at primary models. .

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Butt in the full-scale account of the semantic approach, in addition to the

modelss of data, there are models of theory or theoretical models and isomorphism

ass discussed in Chapter 2. That is to say, there are two types of models in science.

Theoreticall models do not directly confront data. Rather they match empirical

modelss up to an isomorphism. "Models of Data" only account for one side of the

semanticc approach: the construction of empirical models. Haavelmo is concerned

withh adapting theoretical models to the empirical level, but it is questionable, as

havee seen in his three studies on consumption, whether the empirical information

helpss to justify Haavelmo's models. Model specifications are mainly based on a

priorii information. The Cowles Commission, going a step further, were only

concernedd with constructing theoretical models. And, most importantly, how to

uniquelyy identify the structure. The nature of passive observation and

experimentall design are crucially related to the identification methodology. Since

econometricianss are not able to control the experiments and are only passive

observers,, they have to rely on a priori information to help them to specify the

simultaneouss equations model. Koopmans, Rubin and Leipnik (1950, p.64) stated

that: :

Underr no circumstances whatever will passive statistical observation

permitt him [the econometrician] to distinguish between different

mathematicallyy equivalent ways of writing down that distribution. Because

hee has no experimental control over economic variables, the simultaneous

validityy of all the structural equations prevents him from isolating and

individuallyy observing any one of them on a statistical basis alone. The

onlyy way in which he can hope to identify and measure individual

structurall equations implied in that system is with the help of a priori

specificationn of the form of each structural equation.

Apriorismm is evidence of the Cowles Commission's strong view on

economicc theories and addressed in the "Measurement Without Theory" debate

betweenn Koopmans and Vining (Koopmans, 1947, 1949b, Vining 1949a and

1949b).. The modeling procedure is from theory to model, then to use data to

measuree the model. Nonetheless, to know the true structure for Haavelmo

remainedd difficult. He thought the real problem is "actually knowing something

aboutt real phenomena and of making realistic assumptions about them"

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HAAVELMOO AND MEASUREMENT OF ECONOMIC STRUCTURE 59

(Haavelmo,, 1944, p.29). Like Girshick and Haavelmo's structure-as-chemical-

elementt view, if we know the real combination of elements, then we know the real

chemicall compounds or the real economy. By using Ian Hacking's terminology,

wee can say that Haavelmo subscribed to realism about entities: n economic

structuress and autonomous relations. But epistemologically speaking, they cannot

bee precisely known or understood. The model's probability format also speaks of

thiss concern, as the error term stands for all other variables not included in the

equation.144 Had we actually know the real phenomena, we would have not need

thee probability format. Therefore, he concluded that "The construction of systems

off autonomous relations is, therefore, a matter of intuition and factual knowledge;

itt is an art."

3.77 Conclusion

Haavelmoo and the Cowles Commission take very seriously the

philosophicall issues of modeling and measurement. However, their account of

macroeconomicc consumption, though significantly related to the Keynesian

theory,, was excluded from what J. J. Thomas called his "stylized history" of the

consumptionn function (Thomas, 1989, 1992).I5 The stylized history of the

consumptionn function starts from Keynes's (1936) "fundamental psychological

law"" or the absolute income hypothesis (AIH), moving to Duesenberry's (1949)

relativee income hypothesis (RIH), Modigliani and Brumberg's (1954) life cycle

hypothesiss (LCH) and the permanent income hypothesis by Friedman (1957).

Thesee approaches all are concerned with theorization of the consumption-income

relationn and the use of theoretical entities—relative income, life cycle income and

permanentt income—to explain the consumption phenomena, and hence can be

interpretedd in terms of the syntactic approach that has discussed in Chapter 2. In

contrast,, Haavelmo's studies on MPC, which are regarded as in the tradition of

econometricss rather than the stylized history of theorizing the consumption-

incomee relation, are concerned with model construction and identifying the

Hacking'ss realism about entity and realism about theory are discussed in Chapter 5, Section 7. Qinn and Gilbert (2001) discuss different meanings of the error term in the history of time-series

econometrics. . ISS Cook (2000) provides a reconsideration of the "stylized history" of consumption function.

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600 REPRESENTATION AND STRUCTURE

structure.. They can be interpreted in terms of the uniqueness theorem within the

semanticc approach.

Neverthelesss the accounts included in the stylized history of the

consumptionn do relate to explanations and measurements of consumption in terms

off models. The next chapter studies the different models and the empirical

meaningss of the constructed long-term income in Friedman's permanent income

hypothesis. .