Some Issues Surrounding the Reduction of Macroeconomics to Microeconomics Author(S): Alan Nelson Source: Philosophy of Science, Vol

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Some Issues Surrounding the Reduction of Macroeconomics to Microeconomics Author(s): Alan Nelson Source: Philosophy of Science, Vol. 51, No. 4 (Dec., 1984), pp. 573-594 Published by: The University of Chicago Press on behalf of the Philosophy of Science Association Stable URL: http://www.jstor.org/stable/187976 Accessed: 25-02-2018 19:34 UTC

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This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms SOME ISSUES SURROUNDING THE REDUCTION OF MACROECONOMICS TO MICROECONOMICS*

ALAN NELSONt

Department of Philosophy University of California, Los Angeles

This paper examines the relationship between modem theories of microeconomics and macroeconomics and, more generally, it evaluates the prospects of theoretically reducing macroeconomics to microeconomics. Many economists have shown strong interest in providing "microfoundations" for macroeconomics and much of their work is germane to the issue of theoretical reduction. Especially relevant is the work that has been done on what is called The Problem of Aggregation. On some accounts, The Problem of Aggregation just is the problem of reducing macroeconomics to microeconomics. I show how to separate these problems and then try to determine to what extent particular kinds of solutions to The Problem of Aggregation succeed in reducing macroeconomics to microeconomics as well. I argue that reduction is not possible by this means given the current state of microeconomics. I also describe how reduction may be possible by means of (dis)aggregation if microeconomics is supple- mented in a certain way with the results of experimental research on individual economic agents.

It is unfortunate that the fertile field of mainstream economic theory has been ignored as a source of insights about what may be involved in reducing one theory to another. 1 This paper is, in part, an attempt to begin remedying this deficiency. In particular, I want to explore the nature of the relationship between the modem mainstream theories of microeconomics and macroeconomics (hereafter just "microeconomics" and "macroeconomics"). The possibility of reducing at least parts of macroeconomic theory to microeconomic theory is especially exciting for two reasons. First, a natural objection to any proposed reduction or reductive program which involves a formal notion of reduction is that one or both of the

*Received July 1983; revised November 1983. tI must thank Gilbert Bassett, Arthur Fine, Daniel Hausman, Alexander Rosenberg, Julius Sensat, referees for Philosophy of Science, and especially Paul Teller for helpful suggestions. Although many of these suggestions have found their way into this paper, I alone am responsible for any remaining errors or misconceptions. 'The very extensive bibliography on reduction in Wimsatt (1978) does not include a single reference to economics despite the fact that "detailed philosophical and historical case studies in the various sciences . . . have grown enormously in the last decade . . ." (p. 353), and the similarly comprehensive bibliography on the philosophy of social science in Michalos (1978) does not cite any work on reduction in economics. Rosenberg (1976) at least mentions the topic of reducing microeconomics to other sciences.

Philosophy of Science, 51 (1984) pp. 573-594. Copyright ( 1984 by the Philosophy of Science Association.

573

This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms 574 ALAN NELSON theories in question cannot be adequately formalized. That is not a problem here because both of these theories are adequately formalizable. Sec- ond, it might be thought that the relationship between microeconomics and macroeconomics ought to be quite transparent just because they are micro- and macrotheories. The formulation of the bridge laws or other mechanisms for relating terms (and entities) has posed substantial obsta- cles in other sciences when "direct" reductions have been considered, ". . . in which the basic terms (and entities) of one theory are related to the basic terms (and entities) of the other and the axioms and laws of the reduced theory are derivable from the reducing theory" (Schaffner 1967, p. 138). It is natural to suppose, however, that bridging mechanisms between microeconomics and macroeconomics may be relatively easy to find. It seems that the large-scale phenomena dealt with in macroeconomics must be the results of the total effects of the small scale phenomena dealt with in microeconomics. Therefore, one might expect that bridges could be built by merely adding up the microeconomic laws describing the microphenomena to obtain the macroeconomic laws describing mac- rophenomena. In fact, the conditions for reduction look so ripe that it is very often assumed that at least parts of macroeconomics have been reduced to microeconomics. John Beare writes in a popular textbook (1978, p. 7):

Macroeconomics deals with relationships between aggregate variables, the rigorous derivation of which now tends to be based on relationships implied by microeconomic theory. (emphasis added)

Although it turns out that this much confidence cannot be based on any available economic results, it does seem that a reduction of macroeconomics to microeconomics would not be plagued with the kind of onto- logical difficulties which might attend schemes for reducing, say, cog- nitive psychology to neurophysiology. Consequently, the manner in which this prima facie highly plausible reduction falls short is particularly re- vealing of the problems facing reductive strategies in general. Before getting started, I want to set aside two issues which will not get any attention in this paper. First, it has been persuasively argued in Fodor (1974), and in Putnam (1973) that successfully reducing one theory to another need not entail that the reducing theory explains what the reduced theory explains. This issue will not arise explicitly in what follows because I shall be arguing that the prospects for a certain form of reduction are not good for other reasons. Second, there is an important dis- tinction between the way in which a theory might reduce a prior theory which it replaces as the most acceptable treatment of some phenomena, and the way in which one theory might reduce a contemporary theory which is not rejected. Although the history of economics provides some excellent case studies of reduction by replacement (including for exam-

This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms REDUCTION OF MACROECONOMICS TO MICROECONOMICS 575 ple, what are referred to as the marginal and Keynesian revolutions), it is the other kind of reduction which will be treated in what follows. Economists use the term microfoundations to refer to schemes which can be broadly regarded as attempting to reduce macroeconomics to microeconomics. I shall follow suit because I want to concentrate on facts about reduction which I think will be of special interest to economists as well as philosophers without becoming embroiled in the standard contro- versies over the precise form that reductions should take. Economists have had a good deal to say about microfoundations; in this paper I want to examine the part of the economic literature which bears most directly on what philosophers have said about theoretical reduction. Let us look at some quotations to help us understand this one reason (described below) why economists are interested in microfoundations. Again, there are other reasons, but they have been less influential among economists and I think that they have less philosophical import. In an influential early paper, Lawrence Klein (1946a, p. 93) stated that

these aggregative theories [i.e., macroeconomic theories] have often been criticized on the grounds that they mislead us by taking attention away from basic individual behavior. The problem of bridging the gap between the traditional theories based on individual behavior and the theories based on community or class behavior is, to a large extent, a problem of proper measurement.

Donald McCloskey writes (1982, p. 7):

Although its Greek meaning is "small housekeeping," microeconomics is not the little or trivial portion of economics. On the contrary, it comes close to being the whole. Not all fields of economics are based on microeconomics, but all strive to be. Most of the lasting advances in economic thinking over the past century or so have con- sisted of reducing one or another piece of economic behavior to microeconomics.

Compare Gary Becker (1976, p. 5):

The combined assumptions of maximizing behavior, market equilib- rium, and stable preferences, used relentlessly and unflinchingly, form the heart of the economic approach as I see it.

In the same vein, Arthur Okun writes (1980, p. 818):

Keynes . . . departed from classical microeconomics only by modifying the labor supply function to include a wage floor. But this bridge between micro and macro was defective; none of the explanations flowed directly from the implications of optimization by economic agents. . .

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Finally, Lawrence Boland (1982, p. 80) concludes that

the demonstration of the existence of microfoundations for macrotheories is considered essential by many leading economists. The reason is . . . easy to find. Demonstrating the dependence of all macroeconomics on microeconomic principles is essential for the fulfillment of the (methodological) individualist requirements of neoclassical economics.

The current of thought flowing beneath these remarks seems to be that economics, properly speaking at least, is what is obtained by considering the rational behavior of economic agents. Therefore, since economies are not composed of "macro-agents" who exhibit maximizing behavior,2 it is supposed that the only acceptable way to get macro-results is to consider the interaction of the results obtained for all relevant micro-agents. Then there will be some sense in which macroeconomic theory is "reduced to" microeconomics (McCloskey), or is susceptible to "the economic approach" (Becker), or "flows directly from the implications of optimization" (Okun), or "fulfills the methodological individualist requirements of neoclassical economics" thereby providing a "demonstration of the existence of microfoundations for macrotheories" (Boland). This paper aims to clarify and then to explore the intuitive notion of microfoundations expressed by these phrases. Many economists have thought that a good way (and perhaps the only way) of establishing satisfactory microfoundations would be to solve what is usually called The Problem of Aggregation. In the above quotation from Klein's paper-one of the first to give a mathematically sophisti- cated treatment of The Problem of Aggregation-he indicated that its solution would "to a large extent" serve to "bridge the gap" between macro- and micro-. Alexander Rosenberg (1976, p. 181) actually iden- tifies The Problem of Aggregation with determining "What relationship exists between microeconomic theory and macroeconomic theory cur- rently available." The same view is found frequently in the writings of economists. One of the goals of this paper is to show how to separate The Problem of Aggregation from the question of reduction. This makes it possible to draw out some of the consequences of the work that has been done on The Problem of Aggregation and evaluate their actual im- pact on the issue of providing microfoundations (and hence, indirectly, on philosophical questions about reduction).

2Macroeconomic theories are often presented as describing the interaction of three "sectors": the household; firm, and government sectors. These sectors are then sometimes regarded as jndividual maximizing agents, but this kind of presentation is clearly best regarded as metaphorical and is usually not essential to the theories.

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I should emphasize that the conclusions that I reach are restricted to the issue of providing microfoundations and that no general criticism of the formal economic work on The Problem of Aggregation is intended. This impressive body of economic theory is quite unexceptionable (see Green 1964; Theil 1954; and Deaton and Muellbauer 1980,3 for details). Instead, I'll try to show that these solutions do not serve the purpose of providing microfoundations in the strong sense given in the above quotations (namely, foundations in individual maximizing behavior). Now I am going to try to characterize as succintly as possible The Problem of Aggregation as it is understood by economists.4 There are some quantities at the micro- level which correspond very naturally to certain macroquantities. Examples include consumption, income, quantity demanded for a commodity, and profit. The intuitive correspondence is often made precise by simply adding the values of the microquantity for each individual and taking the sum as the macroquantity; sometimes a more complicated aggregation procedure is appropriate. (These can range from still relatively simple procedures like weighted sums of individual quantities to the very complex functions of individual quantities found in any treatise on index numbers.) There are other cases in which the correspondence is clear intuitively, but no particular aggregation procedure is clearly indicated, for instance, price inflation for a commodity and general price inflation. Of course, it is the business of microtheory to give functional relationships among microquantities and the business of macrotheory to do the same for macroquantities. The Problem of Aggregation arises because macroeconomists generally construct their theories according to the dic- tates of explicitly macroeconomic reasoning and to meet constraints set by macroeconomic data. This leaves open two questions concerning the connection between micro- and macrorelationships. After stating these two questions, I'll try to make them as clear as possible with an example. First, it ought to be determined whether there even exist functional re- lationshps among those macroquantities that could be obtained by aggre-

'I owe this reference to a referee for Philosophy of Science. 4There are other problems concerning aggregation. Most of the prominent ones arise when diverse objects are grouped into "aggregates" and treated as though they were the same. I think these problems are also of philosophical interest, but they are outside the scope of this paper. 5The economics literature tends to be quite careless with nomenclature here because the foundational issues have never been clearly set out. It seems wise to use aggregation procedure to refer to rules for obtaining macrovariables from microvariables and aggregates to refer to the results of applying aggregation procedures. These macrovariables will need to be distinguished from the macrovariables that are singled out for study by those practicing macroeconomics. Keeping these straight will avoid some of the confusion that often riddles treatments of the issues surrounding aggregation and reduction.

This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms 578 ALAN NELSON gating the relevant microquantities in an acceptable manner. It is possible that the macroquantities corresponding to members of the domains of the microeconomic functions do not uniquely determine macroquantities corresponding to the ranges of the microeconomic functions. For example, consider

Yi =fi(xi)

Y2 = f2 (X2)

Y= Y1 + Y2

X = X1 X2 where the lowercase letters indicate microeconomic variables and functions and the uppercase letters indicate macroeconomic variables and functions. (This notation will be used throughout.) In this general situation, Y need not be a function of X because it is possible that some values of X are mapped onto more than one value of Y. In other words, once we aggregate both sides of the microfunctions for all of the relevant individual economic agents, the resulting macroquantities may not be functionally related at all. Second, if these macrofunctions do exist, it ought to be determined whether the functions obtained by aggregating the microfunctions (that is, obtained without engaging in any macroeconomic theorizing) are the same ones independently arrived at by macroeconomists doing macroeconomics. In the above example, Y and X are mathematically determined once the values for the y's and the x's are determined using microeconomics. These two questions, which can be regarded as constituting The Prob- lem of Aggregation, may become clearer if we look at a concrete illustration involving consumption functions. This standard illustration incor- porates some gross simplifications (consumption is most likely a function of many variables other than income; time indices need to be considered, etc.), but I do not think that any additional realism will help in the exposition, or affect the results. Moreover, most of the technical work that has been done is at roughly this level of idealization. (See, for example, Theil 1954.) Suppose that microeconomics asserts that for each agentj, consumption is a function of income, that is,

Ci = ci 0;) (1)

Suppose further that macroeconomics asserts the same for the consumption and income of a whole economy of n individuals

C = C(I) (2)

This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms REDUCTION OF MACROECONOMICS TO MICROECONOMICS 579 where

n n C= Cj and I= E i. (3) j=1 j=1

Then there is trouble since this is one of the cases where, in general, there does not exist a functional relationship between EYn=l cj and EYn=l ij because, in order to make certain that (1), (2), and (3) are jointly consistent, certain restrictions upon them must be met. For instance, given (1) and (3), we require that in order to have a single-valued macrorelationship between these quantities in the general case

cj(ij) + Ck(ik) = Cj(ij + Ai) + Ck(ik -/i) AVj,k; Vii,ik (4)

This is a necessary and sufficient condition for each value of I's resulting in a unique value for C. It means that if we add a little income to one agent and take the same little amount away from any other thereby keeping I constant, then C will not change, that is, C = C(I). Arithmetic yields cj(ij) - cj(ij + Ai) = Ck(ik - Ai) - Ck(ik) and taking limits of each side we obtain

dcj (ij ) dCk (ik) dij dik or, expressing cj as a function of ij, cj = a, + bij (5) where aj and b are constants. This well-known result may be interpreted as a partial solution of The Problem of Aggregation for this particular example. It shows that as long as the restrictions (5) on the microfunctions (1) are met we need not worry about the existence of macrofunctions among the aggregates obtained by applying (3) to (1). (It remains to be determined whether these aggregates and the macrofunctions which relate them are the same ones that are obtained by doing macroeconomics.) This partial solution also enables us to see why The Problem of Aggregation has such a strong bite in the first place: (5) is an extremely strong restriction on (1). Even given our sim- plification that cj is to be a function of the single variable ij, it is im- mensely implausible that this function would turn out to be a simple linear one. Nevertheless, in this case the acceptance of (5) is the price that must be paid to rule out the possibility of landing in a contradiction by jointly asserting (1), (2), and (3). Without (5), it would be possible for (1) and (3) to entail that C is not functionally related to I while (2) states that C is functionally related to I and that could happen even when (1), (2), and (3) are each independently well motivated.

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A popular way of summarizing the philosophical import of these considerations has already been indicated in the quotation from Klein. We possess a microtheory which was developed using the highly trusted methodology of treating economic agents as maximizing their individual benefit, and whose successes inspire considerable confidence. This mo- tivates the attempt to give macroeconomics a "foundation" in the ex- emplary microeconomics. An apparently attractive program for accomplishing this is coming up with an appropriate solution of The Problem of Aggregation for every macroeconomic functional relationship thereby effecting one kind of reduction of macrotheory to microtheory. Again, it is one of the aims of this paper to show that actual solutions of The Problems of Aggregation do not provide a foundation-in individual maximizing behavior-for macroeconomics. (Notice that implicit in this framework is part of a version of the "Received View of Theories." It assumes that the content of macroeconomics is exhausted by a list of its lawlike statements. Whether this is true or not does not matter here, although it is often argued that this is an unwarranted assumption for theories in general.) There are, however, at least two distinct ways of accomplishing this. I quote from another paper of Klein's (1946b, p. 305):

There are at least two essentially different approaches to the problem of aggregation. We may accept the traditional theories of microeconomics and the commonly used aggregates . . . and try to determine the structure of a macroeconomic system that is implied by these two sets of information. Alternatively we could proceed differently by assuming the theories of micro- and macroeconomics in advance and then discovering what aggregates are consistent with these two assumptions. In this case, we cannot know in advance the form of the aggregates but must accept those forms which satisfy a mathe- matical requirement.

I read this as identifying two choices of means for providing microfoundations (by solving The Problem of Aggregation):

OPTION 1

Take the antecedently given microtheory concerning the quantities in question. Somehow get satisfactory aggregation procedures. Then use these procedures to derive a macrotheory from the corresponding microquantities.

And

OPTION 2

Take independently determined micro- and macrotheories and then find aggregation procedures that entail the macrotheory when con- joined with the microtheory.

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We might say that OPTION 1 gives macroeconomics microfoundations by construction. We are just deducing it from microeconomics which is well founded by assumption-neoclassical microeconomics just is the result of the "heart of the economic approach," namely, considering individual maximizing behavior. OPTION 2 is like "discovering" microfoundations; we do not know whether the macrotheory we have actually got has microfoundations until we see whether satisfactory aggregates can be produced to link it up to the microtheory. Furthermore, it is OPTION 2 which bears a striking structural similarity to what Schaffner (1967, p. 139) calls Nagel-Woodger-Quine reduction. Microeconomics is the reducing theory, macroeconomics is the reduced theory, and the aggregation procedures serves as the "reduction function" which provides the connections necessary for the deduction of the latter theory from the former. If one suspected that some theory were reducible to another in this way then, of course, one would have the two theories on the table and the salient question would be: What are the bridge laws? Only rarely would a scientist expect to have a theory and a ready made set of bridge laws which could be used to construct a new theory; this would be the analog of using OPTION 1. In OPTION 1 we deliberately ignore any existing macrotheory and come up with economically well motivated aggregation procedures. We then create a macrotheory by carrying out these procedures. It seems that if one is convinced that in order to be considered well founded any economic theory must be based on individual maximizing behavior, then OPTION 1 is very likely to be preferable. Macroeconomic theory is thereby given the status of a practical aid to computation and there is no need, in principle, to commit ourselves to macroeconomic theoretical entities, to worry about whether nonmaximizing individual behavior might be entailed by the macroeconomic theory, etc. This is the view that introductory texts are appealing to when they suggest that if we only had enough information and a computer powerful enough to handle it, there would not be any real need for macroeconomics. As Klein notes (1946a, p. 94) this view turns out to be too optimistic:

It is very difficult to determine whether a well-defined macrosystem follows from our theories of microeconomics. Consequently, we may be forced to attempt to solve our problem in another way. Instead of assuming the theory of microeconomics and the index numbers, let us assume the theory of micro- and macroeconomics, and then construct aggregates (usually in the form of index numbers) which are consistent with the two theories.

Klein does not clearly indicate why we may be forced to abandon oP- TION 1 in favor of OPTION 2; he seems to think that the computational difficulties posed by OPTION 1 are more stubborn. He also seems to fear

This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms 582 ALAN NELSON the possibility of OPTION l's not involving a solution of The Problem of Aggregation. There may not be enough (or any) functional relationships among the aggregates which we construct from the microtheory to con- stitute an acceptable macrotheory. Additional reasons why a "brute force" approach to OPTION 1 has not attracted more interest are somewhat difficult to fathom. On the face of it, prospects for some measure of success are not entirely lacking. In principle, there are no obviously compelling objections to using economic or psychological experimentation in either the marketplace or the labo- ratory to determine just what microequations like (1) look like for each agent in an economy. With that information in hand, the discovery of the corresponding macroequations and the concomitant provision of microfoundations in the style of OPTION 1 would await only the application of an appropriate aggregation procedure. There would, of course, be insuperable practical difficulties with such an enterprise in any but the smallest and simplest economies. It is vir- tually inconceivable that all of the economically significant agents in an economy could be persuaded into situations in which data sufficiently accurate to determine all the microfunctions could be obtained, or that enough trained experimental economists would be available, etc. It may be an empirical fact that these practical difficulties could be overcome by making principled generalizations from data obtained for individuals from a relatively small, judiciously chosen sample of agents. Economists, however, have generally eschewed this kind of experimental investiga- tion. The reasons for this are no doubt diverse. (For some enlightening speculation, see Coats 1976 and Rosenberg 1980.) I suspect that the chief reason is a conviction that individual economic behavior is too erratic to support an economic theory and that significant microeconomic theorizing must be about some kind of averages. In any event, a final evaluation of the merits of OPTION 1 must await further developments in the experimental study of individual economic behavior.6 The foregoing considerations suggest concentrating attention on OPTION 2. In what follows, it will be argued that even though OPTION 2 appears to require less than OPTION 1 (OPTION 2 permits the use of existing macroeconomics), its chances of successfully providing microfoundations are no greater. In order to make the conclusion of the argument as strong as possible, it will be assumed that the best possible conditions for the success of OPTION 2 obtain: it will be assumed that a powerful solution

6There is a growing body of exploratory efforts in experimental microeconomics. A recent, representative study is Battalio et al. (1981). Nelson (forthcoming) is an attempt to remove some of the methodological barriers that have been placed in the way of this kind of work.

This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms REDUCTION OF MACROECONOMICS TO MICROECONOMICS 583 of The Problem of Aggregation is available in which existing macroeconomics can be used to determine microequations. Thus, the argument is meant to show that even if OPTION 2's recipe for providing microfoundations were successfully followed, macroeconomics would still not have microfoundations; OPTION 2 is not sufficient for microfoundations. Let us begin by considering a schematic example of what this kind of solution to The Problem of Aggregation looks like. (A detailed study is provided in Theil 1954.) Later in this paper, another kind of solution to The Prob- lem of Aggregation, which turns out to be associated with another OPTION for providing microfoundations, will be discussed. This kind of solution to The Problem of Aggregation begins as follows. We start with a set of microfunctions

Yi = f (xi) Vi (6) and the corresponding macrofunction

Y = F(X) (7)

Now specific numerical information is desired for the equations (6) and (7) so that we can eventually actually determine the yi from the xi and the Y from the X. With this information in hand, we can mechanically check candidate aggregation procedures and discard those which do not yield (7) from (6). If we can repeat this procedure for all the relationships like (7) which make up the macrotheory under consideration, then, according to OPTION 2, we will have microfoundations for the whole theory. In most cases there is no problem obtaining enough macroeconomic data to be able to write (7) quite explicitly. Macroeconomists often suffer from an embarrassment of riches when it comes to data. As has already been noted, however, it is usually a practical impossibility to gather a sufficient amount of data for microvariables in economies with large numbers of economic agents. Since the desired information about (6) is often not directly accessible, it is often necessary to relate the available empirical data to these equations. The available empirical data are almost invariably values for macrovariables;7 hence what we need are functions of the form

xi= hi(X) (8) enabling us to determine the values of microvariables from the values of macrovariables. Let me try to show with a concrete example a way that

7There are some good data for some microeconomic agents like households, but even these results tend to be samples of households and not time series for individual households. Therefore, the analysis of these data only yields specifications for "average," "ideal," or "representative" functions-a serious complication. See Rosenberg 1976, pp. 39-45 for discussion.

This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms 584 ALAN NELSON economists have proposed to circumvent this problem. (For a more complicated and general example see Theil 1954, p. 35ff.) Suppose we some how know that for a certain desert-island economy with only three consumers that (1) is the set of equations

cl = 0.1i3 - l5if + 300

C2= i2 + 200 (9)

C3= 2i3 - 200 and suppose that (2) is determined to be

C =2I-100 (10)

Now aggregating (9) by some appropriate procedure (simple summation is used here, but only to simplify the exposition)8 gives

c1+ c2 + c3 = 0.1i3 - 15i2 + 2+ 2i3+ 300

Now if (9) and (10) and aggregation by simple summation are to be consistent, then the question that must be answered is whether

cl + c2 + c3=C (11) and O.1i3 - 15i2 + i2+ 26 + 300 = 2I- 100 (12) hold. We cannot answer this question unless we have values for the i's and the c's. In this very simple illustration, we may be able to actually get these numbers and substitute them into (11) and (12) to see whether those equations are satisfied. When we are examining economies with very large numbers of agents, however, the values of these microvariables will not be available. The only numbers we have access to are values for the macrovariables like I and C. Therefore, to solve the problem what is needed is a way of obtaining values for the i's from I. Then we could check an equation like (12) outright and check (11) after obtaining the c's from the i's (and C from I if necessary). Applying this general procedure to the simple illustration already given, we can see that if we had il = 0.31 i2= 0.21 (13) i3= 0.51 and we empirically determined I to be, say, 500 then it follows from (13)

'We will avoid violating the constraint (5) by restricting the possible income distribu- tions.

This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms REDUCTION OF MACROECONOMICS TO MICROECONOMICS 585 that i = 150, i = 100, and i = 250. Now (9) gives us that cl = 300, c2 = 300, and C3 = 300 and both (11) and (12) are satisfied. Clearly it is (13) that does the work here and it is just these kinds of functions that are provided by (8). Returning to the general case, if we chose the h so that values for X are included among the measurable macroquantities, (8) can give us

yi = fi (hi (X)) (14) by substitution into (6) or

yi= ki(X) (15) by composing functions in (14). In most cases, we would not expect microvariables to be functions of a single macrovariable like they are in (8) and in (15); but even in these somewhat more realistic cases it is assumed that there will be similar functions which will do the job like

Yi =li (X,X1 S I I . ,Xr gX1. . . ,Xs ) ( 16) where the X's are macroquantities (probably including the corresponding macroquantity X, as indicated) and the x's are microquantities. In these general cases, we may need the additional conditions that r is much smaller than n9 and that the x's are subject to some simplifications; for example, they are constant or have a known probability distribution. Without conditions like these each x will be as problematic as the yi. It is now assumed that more or less reasonable attempts to specify the functions ki or 1i and to estimate their parameters can be made. Once we explicitly have an expression like (15) or (16), OPTION 2 tells us that we get microfoundations just by applying an appropriate aggregation procedure. To illustrate, if simple summation is the correct procedure, we get

n n

Y = Yi = E ki(X) = F(X) or i=l i=l1

n n Y = Yi = li(X,Xl ,. . . ,X.,X1 * *,xs) (17) i=l i-l

- F (X,X1,. . .*Xr .Xl., . * Xs

This might appear to provide microfoundations according to OPTION 2 because the macrofunction (7) or its multivariate analog is mathematically derived from the microfunctions (6). But already we can see that what has been done here in solving The

90therwise the amount of data gathering necessary to obtain values for the macrovariables will be just as great as for the microvariables.

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Problem of Aggregation is not in accord with OPTION 2. The problem is with (8), which plays a crucial role in the kind of solution we began above. Equations like (8) appear to be ordinary, economic relationships, but what is their status? It is convenient to regard them as formal, cal- culational devices applied en route to destinations like (17). Theil (1954, p. 13), for instance, asserts that relationships like (8) have no economic significance whatsoever (that is, that they do not tell us anything about economic phenomena). But given an expression like (8) which actually fits the data, is it not reasonable to suppose that there is an economic explanation of this fact? Why are the x's related to the X in this way? It is certainly to be hoped that economics is complete enough to provide an answer to this question. We want (8) to be a set of real causal relationships, not just the result of a fabulous statistical fluctuation in the values of the x's and the X which have been observed. The provision of microfoundations ought not be based on our good fortune in having an expe- dient set of fortuitous correlations. If I am right about this and (8) does express causal relationships, then it provides a means of determining a microquantity from a macroquantity. That fact lands us in a surprising dilemma. If we regard (8) as somehow having sound theoretical support and as being empirically accurate, then most of the motivation for providing microfoundations for (7) is removed. If we are willing to accept (8) as a true macro-description of microeconomic events, why not accept (7), a macro-description of macroeconomic events, on the same grounds, whatever those may be? I suppose that one of the things that makes those who worry about missing microfoundations uncomfortable is the explicit use of macroeconomic methods and con- cepts. But if we could get an accurate macro-description of microeconomic phenomena, one which really did transfer well-explained facts in the macro-domain to less clearly explained facts in the micro-domain, then a fortiori there is a strong sense in which macroeconomics is methodologically at least as sound as microeconomics is. And, ironically, there is a sense in which macroeconomics is at least as well founded as microeconomics is, even if the foundations are not built on the same ground. Anyway, in this situation it seems that no foundations in microeconomics are required. On the other hand, if we try to rule out that conclusion by assuming instead that all macroeconomic relationships really do need microfoundations to ensure that they perform well empirically or to ensure that they are methodologically sound, then (8) will not be entirely satisfactory. After all, it employs the now suspect macro-concept X and using it to provide microfoundations as outlined in OPTION 2 will import its unsat- isfactory qualities into the supposedly micro-founded macrorelationship (17). To see how this happens, let us recall in what respect (17) is sup-

This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms REDUCTION OF MACROECONOMICS TO MICROECONOMICS 587 posed to be preferable to (better founded than) (7). Evidently, the only advantage of (17) is that a macroquantity appears as a dependent variable, and an empirically determinable microquantity, in whose credentials we are supposed to have no doubt, appears (indirectly) as the independent variable. To see this, recall that ki(X) = f(hi(X)) = f (xi). Unfortunately, this advantage of (17) is seen to evaporate when it is realized that the value of the microvariable xi is not actually obtainable by the procedure which makes it well-founded, namely, examining utility maximization by an individual. Instead, (17) is obtained from an "unfounded" macrovariable using (8) with the result that it is not built upon the intended foundation. Incidentally, this discussion suggests another critical difficulty with (8). It was introduced as a mechanism for obtaining information about n individuals when n is too large for the information to be directly available. Obviously, (8) must contain n equations, one for each agent i, and we may now well wonder how we are going to specify and estimate these equations. There may not be a problem if many of the equations are the same. If X is the amount of land in the economy and there is an institutional constraint to the effect that everyone gets X/n units of land, then all the equations in (8) are the same and are obtained by mere division. If, however, X is a quantity like number of avocados for which a helpful institutional constraint is not likely to be forthcoming, then differences in preferences for avocados will render the equations in (8) just as problematic as those in (6). (There is also a problem with using institutional constraints in the process of providing microfoundations if these constraints are not themselves explicit consequences of individual maximizing behavior; but we will have to let this thicket remain untangled at present.) This difficulty with obtaining (8) may be easy to overlook given the unreasonable notion that it has no economic significance. These arguments leave us with an extraordinary result. If OPTION 2 is to provide microfoundations through a solution of The Problem of Ag- gregation, then there is a strong sense in which this undertaking presup- poses the existence of macrofoundations for microeconomics; namely, it requires the existence of some macroexplanations of some microphenomena (or, perhaps more modestly, determinations of some microquantities by some macroquantities) in the form of equations like (8). This circularity entails that no microfoundations are provided in the way that the economists quoted earlier intended. It may be worth noting here that the unfortunate circularity does not arise because (8) relates macrovariables like the aggregate demand for avocados to corresponding microvariables like individual demands for avocados. It is even imaginable that we could have equations like (8) relating individual demands for avocados to aggregate demand for bananas and individual demands for bananas to aggregate demands for cantaloupes etc. Instead, the circularity infects oP-

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TION 2 when supposed microfoundations for macroeconomics themselves involve a macroeconomic underpinning. One might wonder whether the problem encountered here is any worse than the one which arises in other attempts to effect theoretical reductions like the putative reduction of thermodynamics to statistical mechanics. It is also true that empirical information about individual particles is not available, but is only deduced from macroscopic properties of aggregates of particles. Nevertheless, it is commonly supposed that thermodynamics can be deduced from the statistical mechanics with the empirical data filled in, and that this is all that is required for the reduction. Whether or not this reduction succeeds, there is at least one important disanalogy between the physical case and the economic example being discussed. The laws of motion upon which statistical mechanics is based have a very wide range of application outside of statistical mechanics. They describe the orbits of planets and the motion of billiard balls on a table, for example, and in these cases it is very easy to get useful empirical results. This naturally gives us a more or less reasonable expectation that the same laws apply to very small particles as well. Once we are quite confident that the laws of motion for very small particles have a particular form, there is correspondingly little risk involved in using data about macro- phenomena to fill in numerical details in the laws describing microphenomena. In economics, however, this kind of evidence is much weaker or missing altogether. If the aggregate demand for ice cubes is a quadratic function of some measure of temperature, that by itself would provide little reason to believe that individual demands for ice cubes were quadratic in temperature. The way of breaking out of the circularity in physics does not seem to have a viable analog in economics. All this discussion points to the nature of microeconomics as the stum- bling block in the attempt to use OPTION 2 to provide microfoundations. I shall try to bring this out more clearly by considering some more important facts about aggregation and reduction. Economists working on The Problem of Aggregation are usually not explicitly concerned with constructing aggregation procedures-the crux of OPTION 2. The reason for this is that in many cases the aggregation procedure to use is antecedently quite obvious. For example, in the treatment outlined above for the case of the consumption function (3),

n n C= E Cj and I=Eij j=1 j=1 gave the indicated aggregation procedures. No one would actually check these procedures to see whether they yielded the right numbers. In fact, any solution of The Problem for this case which did not use these aggregation procedures would probably be rejected out of hand. Values of

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C and I obtained by other means would not even count as the macroquantities aggregate consumption and aggregate income because it is ex- ceedingly natural to regard (3) as giving identities. Consumption and income are just amounts of some standard commodity (like money) and it is hard to see how they could be affected by a bookkeeping operation like addition. It is of course possible that we might discover lawlike connections between some aggregates which were somewhat different from (3). That would be interesting, but it would not show that we were mistaken about considering (3) as giving identities. It would just show that aggregate consumption and aggregate income were not as important as we thought for understanding macroeconomics. Naturally, the temptation to use simple summation is always strong. As I suggested before, if the x's are some bulk quantity like income, consumption, or amount of land owned, then

n X=xj j=1 is plausibly viewed as an identity. How could one add the area of some plots of adjacent (or even nonadjacent) plots of land and get a result which differed from the total area? (Rosenberg has argued [1976, p. 171] that all aggregation procedures are "synthetic," i.e., not identities. As I have indicated, this seems too strong although it is certainly true that not all aggregation procedures are "analytic.") (One need only consider the common disputes over measuring the overall inflation rate [a macroquantity] by means of the Consumer Price Index [the result of applying a certain set of aggregation procedures].) Now, given that OPTION 2 is supposed to be a technique for determining aggregation procedures given micro- and macrotheories, what are we supposed to make of these cases where we know the aggregation procedure in advance? There are two possibilities. One possibility is that in these cases where the aggregation procedure is stipulated beforehand, existing or tentative microtheory and macrotheory are shown to be mutually inconsistent, and at least one of them needs to be modified or have restrictions placed upon it. This is what happened in the example of consumption functions given earlier. It turns out that much of the research done on microfoundations proceeds in just this way. For example, Edmund Phelps writes in the introduction to an anthology on the subject (Phelps 1970, p. 1):

The conventional neoclassical theory of the supply decisions of the household and of the firm, the theory we all teach though rarely prac- tice, is well known to be inconsistent with Keynesian models of employment and with Post-Keynesian models of inflation. It contains

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no road from the fall of aggregate demand to the fall of output and employment airily reached by Keynes.

The contributors to the Phelps volume try to resolve these inconsistencies by strengthening the microtheory by removing idealization in favor of more detail until its results are more in line with macroeconomic facts (or at least with the macroeconomic theory which attempts to deal with these facts). This is done by modifying conventional neoclassical theory to include considerations of uncertainty, expectations, and information costs. Insofar as such an augmented microtheory could be aggregated to agree with what we know about macrotheory, the result might reasonably be construed as having provided some kind of microfoundations. (For some discussion of the economic problems involved with this approach, see Weintraub 1979.) It is significant, however, that this work is done in areas where the aggregation procedures are not sensibly regarded as obvious before the fact. The other possibility is that the theories are guaranteed to be mutually consistent. But this possibility is never realized. Given a microtheory and a macrotheory which are consistent in the sense that we have an aggregation procedure which enables us to deduce the latter from the former, we actually have microfoundations according to OPTION 2. Moreover, there would be no Problem of Aggregation whatsoever. The reason that we have never really been this lucky lies with the microtheory, specifically with our lack of microeconomic information. A reasonable reaction to these arguments would be to point out that requiring equations like (8) may be overly stringent for either solving The Problem of Aggregation or for providing microfoundations. It seems that there ought to be weaker yet still interesting ways of establishing connections between microeconomics and macroeconomics. In fact, there are such ways. For example, Deaton and Muellbauer (1980) refer to solutions of The Problem of Aggregation which "provide the necessary conditions under which it is possible to treat aggregate consumer behavior as if it were the outcome of decisions of a single maximizing consumer; this case we shall refer to as exact aggregation." What this "exact aggregation" involves then, is discovering conditions upon the microtheory which must hold if macrofunctions are to be such that they could be derived from the maximizing behavior of an idealized consumer described by an average microfunction. For example, it would be interesting if the aggregate demand, Q, for some commodity, h, were a function of aggregate income and the price of h:

Q= Qh (I, ph) (18)

and that this could be derived by just summing an average demand qh:

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n Q = E h(- ph) (19)

j=1 where

( (ij)) j=1

Now we can essentially repeat the argument given earlier in the example of the consumption functions to conclude that an analogous condition holds on the individual demands if the average demand functions are to exist: qh(i ph) = Aj(ph) + Bh(ph)ij Vj (20) where Aj(ph) and Bh(ph) are linear homogeneous functions. Now we can proceed to use macroeconomic data for aggregate demand to econometri- cally estimate the parameters of (20). The availability of this kind of solution to The Problem of Aggregation points toward a third option for providing microfoundations:

OPTION 3

Take macrotheory as antecedently given. Stipulate satisfactory aggregation procedures. Then try to find restrictions on the form of the microtheory such that the macrotheory can be derived after the fact from the microtheory and the aggregation procedures.

It is significant that this option bears little resemblance to popular philosophical models of reduction. Something quite different is going on here. It may even be hard to see how OPTION 3 could ever be counted as providing microfoundations. I suspect that some are impressed with the fact that economists have had some success with OPTION 3, but that they have not clearly distinguished OPTION 3 from OPTION 1 or OPTION 2. This can lead to the mistaken assumption that the success attaches to something like OPTION 1 or OPTION 2. Let us, however, examine the question of whether OPTION 3 can provide microfoundations in the sense envisioned by the economists quoted above. It can if all that is required is to exhibit some microrelationships or other which can be aggregated to obtain the best available macrotheory. But even leaving aside qualms about the use of "average" consumers, there is a difficulty with the nature of the particular microrelationships used. The reason that microeconomics inspires so much confidence is that it is obtained by the method of examining individual maximizing behavior,

This content downloaded from 152.3.10.159 on Sun, 25 Feb 2018 19:34:59 UTC All use subject to http://about.jstor.org/terms 592 ALAN NELSON which itself inspires great confidence. It is hard to avoid the inference that the transferring of this confidence to macrotheory by providing microfoundations ought to take place by showing how macrotheory is a con- sequence of microrelationships obtained from the maximization hypoth- esis. Since OPTION 3 uses a given macrotheory to fairly rigidly determine what the microtheory must look like, those microrelationships cannot plausibly be viewed as providing secure microfoundations. The restrictions on these relationships which come from the macrotheory are not obtained by maximization methodology, the basis for microfoundations. Instead, they are obtained indirectly from the macrotheory and aggregation procedures. Therefore, I do not think that the kind of procedure which I just described would satisfy most of those who want macroeconomics to be somehow based on individual maximizing behavior. There is more evidence of this. Donald F. Gordon and Allan Hynes write the following concerning Samuelson's correspondence principle, a different but related means of obtaining restrictions on microeconomic theory (1970, p. 371):

This methodology is anomalous, and may not yield powerful oper- ational theorems, precisely because the adjustment mechanisms [the source of the restrictions] are not linked to the analysis of utility or profit maximization behavior of the relevant economic units. (emphasis added)

The adjustment mechanisms referred to by Gordon and Hynes are analogous to the macroeconomic theory in OPTION 3. They are both a source of restrictions on the microeconomic theory and they both themselves lack foundations in maximizing behavior. Moreover, they both might be regarded as defective insofar as they are imposed without a microeconomic reason for their being imposed. This view is not really very strange; in physics it is not permissible to specify boundary conditions unless there is a physical reason for the given conditions, if one wants to retain the explanatory power of the physical description. Some of the gloom generated by the tenor of these remarks can be dissipated. I think it is possible to cast a somewhat more optimistic light on OPTION 3. One might try to employ OPTION 3 as a kind of indirect regulatory device. One could take a macrotheory and aggregation procedures as given and see what restrictions one gets on microtheory. Now, if we also had an independently motivated set of microrelationships and these did not conform to the restrictions we obtained using OPTION 3, we might conclude that the offending macrotheory should be discarded. For example, if we were confident in the microrelationship (5) from above,

c - aj + b but we were able to derive the restriction

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Cj= ajVij from a proposed macrotheory, then we could conclude that the macrotheory was defective. Perhaps it is worth mentioning that most economists would not be inclined to use OPTION 3 to regulate proposed microtheories. It is assumed that the status of questionable microrelationships ought to be settled with principles of microeconomic methodology. I do not share this inclination; unfortunately, a careful treatment of this issue is outside the scope of the present paper. Nevertheless, as we have seen, OPTION 3 does give us a method for discovering inconsistencies between microeconomic theory and macroeconomic theory. It might be noted here that the regarding of technical economic results on The Problem of Aggregation as solutions need not be incompatible with Rosenberg's claim (1976, p. 200) that we have not got a "final" solution. His view is that a "final" solution would require 4"reasonably detailed versions of the relevant macro- and microtheories" which he does not think that we possess. There is a sense (to be avoided, I think) in which this is surely right; it is the sense in which solving The Problem of Aggregation involves providing microfoundations through oP- TION 1 or OPTION 2. I cannot agree, however, that even "addressing entire aggregation problems is very premature indeed' (p. 201, emphasis added), or that The Problem of Aggregation is not even "relevant" at this time (p. 202). On the contrary, I think it is now clear that the availability of OPTION 3 shows that addressing The Problem of Aggregation can yield economic results which can be of relevance in evaluating the acceptability of economic theories (the "indirect regulatory device"). Also, I hope to have shown how clarifying the nature and ramifications of The Problem of Aggregation can yield results which are relevant to both

(i) the important economic issue of providing microfoundations: I have argued that those economists whose work has been directed towards executing OPTION 1 and/or OPTION 2 are most unlikely to accomplish at this time what they set out to do, and that those economists who see themselves as working on OPTION 3 have little prospect of providing anything which deserves to be called microfoundations, and

(ii) the philosophical issue of reduction: Despite the congeniality of the micro- and macrotheoretical frameworks, it is unlikely that we will see any progress in reducing macroeconomics to microeconomics.

Finally, I hope to have indicated in what direction future research should go if the project of providing strong microfoundations in individual maximizing behavior is not to be abandoned. Successful execution of the strong

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OPTIONS I and 2 requires specific information about the nature of microfunctions, but I have argued that the common procedure of using econo- metric techniques to obtain this information from macroeconomic data about aggregates is circular.10 The way to break out of this circularity is to obtain the microeconomic information directly, and a potentially fruit- ful way of accomplishing that is to energetically pursue research programs in experimental microeconomics.

REFERENCES

Battalio, R.; Kagel, J.; Rachlin, H.; and Green, L. (1981), "Commodity Choice Behavior with Pigeons as Subjects", The Journal of Political Economy 89: 67-91. Beare, J. (1978), Macroeconomics. New York: Macmillan. Becker, G. (1976), The Economic Approach to Human Behavior. Chicago: University of Chicago Press. Boland, L. (1982), The Foundations of Economic Method. Boston: Allen & Unwin. Coats, A. (1976), "Economics and Psychology: The Death and Resurrection of a Research Programme", in Method and Appraisal in Economics, S. Latsis (ed.), pp. 43-64. Cambridge: Cambridge University Press. Deaton, A., and Muellbauer, J. (1980), Economics and Consumer Behavior. Cambridge: Cambridge University Press. Fodor, J. (1974), "Special Sciences: (or The Disunity of Science as a Working Hypoth- esis)", Synthese 28: 97-115. Gordon, D., and Hynes, A. (1970), "On the Theory of Price Dynamics", in Microecon- omic Foundations of Employment and Inflation, E. Phelps (ed.), pp. 369-93. New York: Norton. Green, H. A. J. (1964), Aggregation in Economic Analysis. Princeton: Princeton Univer- sity Press. Klein, L. (1946a), "Macroeconomics and the Theory of Rational Behavior", Econometrica 14: 93-108. .(1946b), "Remarks on the Theory of Aggregation", Econometrica 14: 303-12. McCloskey, D. (1982), The Applied Theory of Price. New York: Macmillan. Michalos, A. (1978), "Philosophy of Social Science", in Current Research in Philosophy of Science, P. Asquith and H. Kyburg (eds.), pp. 463-502. East Lansing: Philosophy of Science Association. Nelson, A. (forthcoming), "New Individualistic Foundations for Economics", Noas. Okun, A. (1980), "Rational-expectations-with-misperceptions as a Theory of the Business Cycle", Journal of Money, Credit, and Banking 12: 817-25. Phelps, E. (ed.) (1970), Microeconomic Foundations of Employment and Inflation Theory. New York: Norton. Putnam, H. (1973), "Reductionism and the Nature of Psychology", Cognition 2: 131-45. Rosenberg, A. (1976), Microeconomic Laws: A Philosophical Analysis. Pittsburgh: Uni- versity of Pittsburgh Press. . (1980), "A Skeptical History of Microeconomic Theory", Theory and Decision 12: 75-83. Schaffner, K. (1967), "Approaches to Reduction", Philosophy of Science 34: 137-47. Theil, H. (1954), Linear Aggregation of Economic Relations. Amsterdam: North-Holland. Weintraub, E. R. (1979), Microfoundations. Cambridge: Cambridge University Press. Wimsatt, W. (1978), "Reduction and Reductionism", in Current Research in Philosophy of Science, P. Asquith and H. Kyburg (eds.), pp. 352-77. East Lansing: Philosophy of Science Association.

"0To repeat, this circularity arises in the attempt to provide microfoundations. The techniques referred to are perfectly acceptable in other contexts.

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