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Representation and Structure: The Methodology of Econometric Models of Consumption
Chao, H.K.
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Citation for published version (APA):Chao, H. K. (2002). Representation and Structure: The Methodology of Econometric Models of Consumption.
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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.):
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.
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.
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).
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.
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
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),
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.
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.
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.
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. .
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)
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.
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.
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.
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
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
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.
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).
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—
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)
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
HAAVELMOO AND MEASUREMENT OF ECONOMIC STRUCTURE 57
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. .
588 REPRESENTATION AND STRUCTURE
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"
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.
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. .