Haavelmo's Structural-Equations Agenda And Its Early Critics

          The authoritative statement of conventional econometric modeling is set forth in "The Probability Approach in Econo­metrics", initially a Ph.D. dissertation written in 1941 by Nobel laureate econometrician, Trygve Haavelmo (1911-    ), and then published as a supplement to Econometrica (July, 1944).  Econome­trica is the journal of the Econometric Society, which was founded in 1930, and which described itself as "an interna­tional society for the advancement of economic theory in its relation to statistics and mathematics" and for "the unifi­cation of the theoretical-quantitative and the empirical-­quantitative approach" in economics. The supplement essentially advanced certain fundamental ideas for the application of the Neyman-Pearson theory of statistical testing of mathematical hypotheses expressing neoclassical economic theory.  At the time the supplement was published the society's offices were at the University of Chicago, where econometricians found themselves isolated and unwelcome. Then most economists believed that probability theory is not applicable to economic time series data, partly because the data for successive observations are not statistically indepen­dent, and partly because few economists were competent in the requisite statistical techniques.  In her History of Econometric Ideas (1990) Mary S. Morgan writes that this introduction of probability theory into economics was a "probabilistic revolution" in econometrics, which shifted the role of econometrics from the measuring of the parameters in a theory to the testing of the theory.
          Firstly Haavelmo argued that the time series data are not a set of successive observations, but are one observa­tion with as many dimensions as there are independent vari­ables in the model.  This strategy is not mentioned in textbooks today.  Haavelmo's more lasting agenda consisted of construing the econometric model as a probabilistic statement of the econometric theory, so that the theory is neither held harmless by falsifying data nor immediately and invariably falsified as soon as it is confronted with the data.  He says that the model is an a priori hypothesis about real phenomena that states that every system of values that the economist might observe of the "true" variables, will be one that belongs to the system of numeric values which is admissible within the model.  This attempt to construe the model as a third linguistic entity between theory and data leads him to develop an unusual and compli­cated semantical analysis.  The first chapter titled "Abstract Models and Real­ity” sets forth his theory of the semantics of measurement variables in econometrics.  Haavelmo distinguishes three types of "variables", which actually represent three separate mean­ings associated with each variable symbol that may occur in an empirical economic theory.  The first type is the "theo­retical variable", which is the meaning a variable symbol has simply by virtue of its occurring in the equations of the model, and its values are subject only to the consis­tency of the model as a system of one or several equations.  The second type is the "true variable", which signifies an ideal experimental design that the economist could at least imagine arranging in order to measure those quantities in real economic life, that he thinks might obey the laws imposed by the model on the corresponding theoretical variable.  Haavelmo says that when theoretical variables have ordinary words or names associated with them, these words may merely be vague descriptions that the economist has learned to associate with certain phenomena, or they may signify ideal experimental designs with their descriptions of measurement procedures.  But he also says that there are many indications that the economist nearly always has some such ideal experimental design "in the back of his mind", when the economist builds his theoretical models, and that in the verbal description of his model in economic terms the economist suggests explicitly or implicitly some type of measurement design to obtain the measurements for which he thinks his model would hold.  Thus the theoretical and true variables are distinguished, but are not separated in the fully interpreted theory proposed for estimation and test­ing.  And associated with the true variables there are true or ideal measurements, which are not only error free, but which are collected in accordance with an ideal experimental design.  The third type of variable is the "observational vari­able", which describes the measurements actually used by the economist for his model construction.  Haavelmo says that the economist often must be satisfied with rough and biased measures, and must dig out the measurements he needs from data that were collected for some other purpose.  The true variables are those such that if their behavior should contradict a theory, the theory would be rejected as false.  On the other hand if the behavior of the observational vari­ables contradicts the theory, they leave the possibility that the economist is trying out the theory on facts for which the theory was not meant to hold.  This may cause confusion, when the same names are often used for both types of vari­ables.  To test a theory against facts or to use it for prediction, either the statistical observations available must be corrected or the theory itself must be adjusted, so as to make the facts the economist considers the true vari­ables relevant to the theory.   In Haavelmo's approach to econometrics, probability distributions not only adjust for measurement errors, but also adjust for the deviations between the true and observational values due to their semantical differences.
          An experienced economist, Haavelmo is adequately cogni­zant of the difficulties in the work that makes economics an empirical science.  In contrast, most of his contemporaries in the 1940's were ivory-tower theoreticians.  Today there is much more adequate data available to economists from government agencies.  Nonetheless, economists still sometimes find they must use what they call "proxy" variables, which are recognized as measurements of phenomena other than what the economist is interested in explaining with his models.  And sometimes the government statistical agency will use names to identify data that describe phenomena for which the data are a proxy rather than what the data meas­ure.  For example in their Industrial Production (1986) the Board of Governors of the Federal Reserve System say that when their monthly production index series cannot be based on physical measures of output, such as tons of steel or assemblies of automobiles and trucks, then monthly input measures, such as hours worked or kilowatt hours of electri­city consumed adjusted for the observed long-term trend and cyclical relations between input and output, are used to derive the monthly output series.  Nonetheless, the Federal Reserve Board calls these proxy series "production.”  Except in these explicit cases involving proxy variables, however, it is questionable whether the economist has "in the back of his mind", as Haavelmo says, any specific ideal experimental design setting forth ideal measurement procedures.  Most often the descriptive words associated with theoretical variable symbols in a mathematical model are vague and are just not given semantical resolution until actual measurements are associated with the model.  Then the description of the actual measurement procedures supplies additional information to resolve this vagueness.  Only when economists decide that the actual measurements are proxies for what they wish to investigate, such that there is more deviation involved than just errors of measurement, do they find themselves confronting an equivocation like Haavelmo's "true" and "observational" semantics instead of supplying a resolution to the vagueness in the meanings of the terms in the theory.
          The second chapter titled "The Degree of Permanence of Economic Laws" contains Haavelmo's theory of scientific law in economics, and specifically his treatment of the degree of constancy or permanence in the relations among economic variables in econometric models.  Nonconstancy is manifested by structural breakdown of the traditional structural-equation model, the type that Haavelmo advocates in his monograph.  The rational expecta­tions hypothesis is proposed as an explanation for struc­tural breakdown, and the hypothesis is the basis for a new type of model that is an alternative to the structural-equa­tion model.  The BVAR discovery system constructs a refined version of this new type of model.  Haavelmo says that the constancy in a relationship is a property of real phenomena, as the economist looks upon the phenomena from the viewpoint of a particular theory.  At the very opening of his monograph he states that theoretical models are necessary to understand and explain events in real life, and that even a simple description and classifi­cation of real phenomena would probably not be possible or feasible without viewing reality through the framework of some scheme conceived a priori.  This statement seems similar to Popper's thesis that there is no observation without theory, and to Hanson's characterization of observation as theory-laden.  But the term "theory" in Haavelmo's monograph means specifically the neoclassical economic theory with its rationality postulate, and the basic task of his monograph is to describe his probability approach in econometrics understood as the application of Neyman-Pearson statistical inference theory to neoclassical economic theory for empirical testing.
          In the first chapter of the monograph Haavelmo distin­guished three types of quantitative economic relations.  The first type is the definitional or accounting identity.  A common example is the gross national product, which is merely the summation of its component sectors.  The second type is the technical relation.  The paradigmatic case of the technical relation is the production function, which relates output to inputs such as capital and labor.  Technical engineering equations are more properly the tasks of other sciences, but the practice among econometricians has been to estimate production functions with the same statistical techniques that they use for all econometric equations.  The third type is the relation describing economic actors.  Equations of this type in econometric models are also called behavioral equations or decision functions.  The behavioral equations in conventional econometric models are based on economic theory, and are not like the laws and theories developed in the natural sciences such as physics.  Neoclassical economic theory purports to describe a decision-making process made by economic actors, notably consuming households and producing business firms.  The econometric equation based on neoclassical theory contains independent variables that represent a set of conditions that are considered by the economic actors in relation to their motivating preference schedules or priorities as they make their best or optimized decisions, and the outcome of these optimizing decisions are represented by the dependent variable of the equation.   The system of preference sched­ules is not explicitly contained in the equation, but Haavelmo says that if the system of preference schedules establishes a correspondence between sets of given condi­tions and optimized decision outcomes, such that for each set of conditions there is only one best decision outcome, then the economist may as it were jump over the middle link in the scheme, and say that the decisions of the individuals or firms are determined by the set of independent variables.
          In this traditional neoclassical scheme the econometric model is based on the assumption that indi­vidual consumers’ and firms’ decisions to consume and to produce can be described by certain fundamental behavioral relations, and that there are also certain behavioral and institutional restrictions upon the actor's freedom.  A par­ticular system of such relationships with their equations statistically estimated defines one particular theoretical "structure.”  The problem of finding permanent economic laws becomes the problem of finding permanent structures in this sense; the failure in particular cases to solve this problem is usually manifested by an erroneous forecast with the model, and the failure is called structural breakdown.  Haavelmo then considers several reasons for the structural breakdown of an econometric model.  In all cases the problem is diagnosed as the absence from the model of a variable representing some operative factor that in reality has a significant effect on the dependent variable of the model, and the solution there­fore consists of recognizing the missing factor and then of introducing a variable for it into the model.  In the case of a model of a market one of the reasons for structural breakdown is a structural change due to the irreversibility of economic relations.  It is a shift in a demand curve, such that price-quantity pairs do not repre­sent movements along the demand curve, because the economic actors are revising their preference schedules as prices change.  Haavelmo rejects claims that demand curves cannot be constructed from time series of observed price-quantity pairs, and instead says that the economist should introduce into his model variables representing the factors respons­ible for the revision of preference schedules.  A second explanation for structural breakdown is the simplicity of the model.  Economists like simple models, even though the real world is complex.  Haavelmo distinguishes potential from factual influences in the real world, and says that models can be simple, because only factual influences need be accounted for in the models.   But he says that economists making models may throw away elements of a theory, that would be sufficient to explain apparent struc­tural breakdown that may occur later, because the elements do not exhibit a detectable factual influence over the time series history used to estimate the equation.          Finally a third reason for structural breakdown is the absence of a semantical property that Haavelmo calls "auto­nomy.”  Autonomous equations in a multi-equation model have an independence that is not just the formal independence of axioms in a deductive system.  The semantical independence or autonomy is due to the success of an equation at identifying the preference schedules of just one social group or social role in the economy.  For example the demand equation in a market model represents the decisions of buyers in the market, while the supply equation for the same price-quantity pair represents the decisions of sellers in the same market.  If the supply and demand equations for a market model are autonomous, then a structural breakdown in one equation will not also occur in the other.  An autonomous equation is one that has successfully identified a fundamen­tal behavioral relation described by economic theory.
          In addition to his semantical theory and his theory of scientific law in economics, Haavelmo also gives lengthy consideration to statistical inference.  One statistical topic he considers is the meaning of the phrase "to formu­late theories by looking at the data.”   He is concerned with the problem of whether a well fitting statistically esti­mated model is merely a condensed description of the empiri­cal data, i.e. whether it is ad hoc, or whether it is an effective test of a generalization.  He maintains that how the economist happens to choose a hypothesis to be tested from within a class of a priori admissible theories is irrelevant, and he states that the selection may be made by inspection of the data.  But he says that the class of admissible theories must be fixed a priori to the testing procedure, so that it is possible to calculate the power of the test and to determine the risk of accepting the hypo­thesis tested; he rejects the practice of selecting the whole class of admissible theories by the empirical testing process.  The class of admissible theories cannot be made a function of the sample data, because then the Neyman-Pearson statistical test no longer controls the two types of errors in testing hypotheses, either the error of accepting a wrong hypothesis or the error of rejecting a true hypothesis.  This curious commingling of statistical testing and the investigator's psychology in the Neyman-Pearson statistical inference theory will be ignored by the developers of the new type of model used by rational expectations advocates.

Mitchell’s Institutionalist Critique

          Haavelmo's agenda had its Institutionalist critics long before the Rational Expectations advocates.  Morgan notes in her History of Econometric Ideas that Haavelmo's paper was very influential both within the Cowles Commission and with others including Herbert Simon.  She also states that acceptance of Haavelmo's approach made econometrics less creative, because data were taken less seriously as a source of ideas and information for econometric models, and the theory-development role of applied econometrics was downgraded relative to the theory-testing role.  She also notes that Haavelmo's approach was opposed by some econom­ists including the Institutionalist economist, Wesley Clair Mitchell (1874-1948).  Mitchell was instrumental in the founding of the prestigious National Bureau of Economic Research, where he was the Research Director for twenty-five years.  A biographical memorial volume titled Wesley Clair Mitchell: The Economic Scientist edited by Arthur Burns was published by the National Bureau of Economic Research in 1952.  Mitchell's principal interest was the business cycle, and in 1913 he published a descriptive analysis titled Business Cycles.   Haavelmo's proposal to construct models based on existing economic theory may be contrasted with another paper published twenty years earlier by Mitchell in the latter's "Quantitative Analysis in Economic Theory" in American Economic Review (1925).  Mitchell, who studied philosophy under the Pragmatist John Dewey, predicted that quantitative and statistical analyses in economics will result in a radical change in the content of economic theory from the prevailing type such as may be found in the works of Alfred Marshall.  Mitchell said that instead of interpreting the data in terms of subjective motives, which are assumed as constitut­ing an explanation and which are added to the data, quanti­tative economists may either just disregard motives, or more likely they may regard them as problems for investigation rather than assumed explanations and draw any conclusions about them from the data.  In his “Prospects of Economics” in Tugwell’s Trend of Economics (1924) he also said that economists will have a special predilection for the study of institutions, because institutions standardize behavior thus enabling generalizations and facil­itating statistical procedure.  He prognosticated in 1924 that as data becomes more available, economics will become a quantitative science that will be less concerned with puzzles about economic motives and more concerned about the objective validity of the account it gives of economic processes.  While many neoclassical economists view Mitchell's approach as atheoretical, Mitchell had a very erudite knowledge of economic theories as evi­denced in his Types of Economic Theory (1967).
          Mitchell's principal work setting forth the findings from his empirical investigations is his Measuring Business Cycles, which was co-authored with Arthur F. Burns and published by the National Bureau in 1946.  This five-hundred page over-sized book contains no regression-estimated Marshallian supply or demand equations.  Instead it reports on the authors' examination of more than a thousand time series describing the business cycle in four industrialized national economies, namely the U.S., Britain, France and Germany.  The authors explicitly reject the idea of testing business cycle theories, of which there were a great many.  They state that they have surveyed such theories in an effort to identify which time series may be relevant to their interest, but their stated agenda is to concentrate on a systematic examination of the cyclical movements in different economic activities as measured by historical time series data, and to classify the time series with respect to their phasing and amplitude, in order to trace causal relations exhibited in the sequence that different economic activities represented by the time series reveal in the cycle's critical points.  To accomplish this they aggregate the individual time series so that the economic activities represented are not so atomized that the cyclical behavior is obscured by idiosyncrasies of the small individual units.
          The merits and deficiencies of the alternative methodologies used by the Cowles Commission group and the National Bureau were argued in the economics literature in the late 1940's.  Selections from this literature have been reprinted by the American Economic Association in their Readings in Business Cycles (1965).  Defense of Haavelmo's structural-equation approach was given by Tjalling C. Koopmans, who wrote a review of Mitchell's Measuring Business Cycles in the Review of Economic Statistics in 1947 under the title "Measurement without Theory.”  Koopmans compared Burns and Mitchell's findings to Kepler's laws in astronomy and he compared Haavelmo's approach to Newton's theory of gravitation.  He notes that Burns and Mitchell's objective is merely to make generalizing descriptions of the business cycle, while the objective of the structural-equation approach is to develop "genuine explanations" in terms of the behavior of groups of economic agents, such as consumers, workers, entrepreneurs, etc., who with their motives for action are the ultimate determinants of the economic variables.  Then he adds that unlike Newton, economists today already have a systematized body of theory of man's behavior and its motives, and that such theory is indispensable for a quantitative empirical economics.  He furthermore advocates use of the Neyman-Pearson statistical inference theory, and calls Burns and Mitchell's statistical techniques "pedestrian.”
          The approach of Burns and Mitchell was defended by Rutledge Vining, who wrote a reply to Koopmans in the Review of Economics and Statistics in 1949 under the title "Koopmans on the Choice of Variables to be Studied and the Methods of Measurement.”  Vining argues that Burns and Mitchell's work is one of discovery, search, and hypothesis-seeking rather than one of hypothesis-testing, and that even admitting that observation is always made with some theoretical framework in mind, such exploratory work cannot be confined to theoretical preconceptions having the prescribed form that is tested by use of the Neyman-Pearson technique.  He also argues that the business cycle of a given category of economic activity is a perfectly acceptable unit of analysis, and that many statistical regularities observed in population phenomena involve the behavior of social "organisms" that are distinctively more than simple algebraic aggregates of consciously economizing individuals.  He says that the aggregates have an existence over and above the existence of Koopmans' individual units and their behavior characteristics may not be deducible from the behavior characteristics of the component units.
          Koopmans wrote "A Reply" in the same issue of the same journal.  He admitted that hypothesis-seeking is still an unsolved problem at the very foundations of statistical theory, and that it is doubtful that all hypothesis-seeking activity can be described are formalized as a choice from a pre-assigned range of alternatives.  But he stands by his criticism of Burns and Mitchell's statistical measures, because he says that science has historically progressed by restricting the range of alternative hypotheses, and he advocates crucial experiments.  He maintains that crucial experiments deciding between the wave and particle theories of light in physics were beneficial to the advancement of physics before the modern quantum theory.  He also continues to adhere to his view that it is necessary for economics to seek a basis in theories of individual decisions, and says that he cannot understand what Vining means by saying that the aggregate has an existence apart from its constituent components, and that it has behavior characteristics of its own that are not deducible from the behavior characteristics of the components.  He maintains that individual behavior characteristics are logically equivalent to the group's, and that there is no opening wedge for essentially new group characteristics.  In the same issue of the same journal Vining wrote "A Rejoinder", in which he said that it is gratuitous for anyone to specify any particular entity as necessarily the ultimate unit for a whole range of inquiry in an unexplored field of study.  The question is not a matter of logic, but of fact; the choice of unit for analyses is an empirical matter.
          Contemporary Pragmatist philosophers of science will recognize Vining's appeal to exclusively empirical criteria for deciding the unit of analysis as an application of Quine's principle of ontological relativity.  And students of elementary logic will recognize Koopmans' reductionist requirement as an instance if the fallacy of composition, in which one attributes to a whole the properties of its components.  Thus just as the properties of water waves cannot be described exclusively in terms the physical properties of the water molecules, so too for the economic waves of the business cycles cannot be describe exclusively in terms of the behavior of individuals.  Both types of waves may be described as "real", even if their reality is not easily described as an "entity" as nominalists would require.  As it happens in the history of post-World War II economics a reluctant pluralism has prevailed.  For many years the U.S. Department of Commerce, Bureau of Economic Analysis, assumed the National Bureau's business cycle leading-indicators agenda, and published many cyclical time series with charts in the "yellow pages" of their monthly Survey of Current Business, which is the Federal agency's principal monthly periodical.  In 1996 the function was taken over by the Conference Board, which calculates and releases the monthly Index of Leading Indicators, which is based on Mitchell's approach.  The forecasts are reported monthly in the national news media.  On the other hand the Cowles Commission's structural-equation agenda has effectively conquered the curricula of academic economics.  Today fifty years later in the universities empirical economics has become synonymous with "econometrics” in the sense given to it by Haavelmo.

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