This post-classical quantitative-functionalist macrosociological theory of social change in the American national society is a recursive, first-degree, higher-order difference-equation system having parameters estimated statistically from time series for the periods 1920 through 1972.  The model is developed by a computerized artificial-intelligence discovery system and implements the contemporary pragmatist philosophy of science.

Post-classical quantitative functionalism is here contrasted with classical functionalism, which is based upon social-psychological motivational mechanisms.  Quantitative functionalism describes outcomes rather than motives, an emphasis also in Merton’s functionalism, and it exhibits the macrosociological outcomes of exogenously initiated endogenous institutional changes.

Quantitative functionalism is here contrasted with classical functionalism based on social-psychological motivational mechanisms.  Quantitative functionalism describes outcomes rather than motives, an emphasis in Merton’s functionalism, and it exhibits the macrosociological outcomes of exogenously initiated endogenous institutional changes.

The macrosociological outcomes are exhibited in static and dynamic analyses.  The static analysis is exhibited by the equilibrium solution of the model, in which all variables are set to the current period t.  The solution shows that the U.S. macrosociety has no stable equilibrium and is thus institutionally malintegrated.  

The dynamic analyses are simulations made by iterating the recursive model.  The simulations show that when per capita real income growth is high and if the national demographic profile is stabilized, the macrosociety tends toward macrosocial consensus equilibrium due to the educational institution, which is a distinctively macrosociological negative feedback mechanism.  And a shock simulation shows that a sudden large internal migration surge from farms into cities disintegrates the institutional social order.


For purposes of contrast the functionalist sociological tradition represented by sociologists such as Durkheim, Parsons and Moore is here referred to as “classical functionalism”.  Classical functionalism is concerned with the institutionalization of rôle concepts, norms and value orientations (Parsons, 1951, p. 552).  It explains social order and stability by the analysis of motivational processes called “integrative mechanisms” consisting paradigmatically of socialization and social control.  These integrate social participants’ need dispositions with sanctioned socially functional values.  Parsons calls this process of integration the “fundamental dynamic theorem of sociology” and the “core phenomenon of the dynamics of social systems” (ibid. p. 42).

The resulting social stability or “equilibrium” is a complementary behavioral interaction of two or more social participants, in which each participant (“ego”) conforms to the cultural value orientations and rôle expectations of the other participant (“alter”), such that alter’s reactions to ego’s actions are reinforcing positive sanctions motivating continued conformity (ibid. p. 204).  When this conformist stability extends throughout the society, the result is a stable consensus equilibrium that characterizes a highly integrated macrosociety. Classical functionalism is social psychology.

Classical functionalist theory does not explain endogenous initiation of social change.  The institutionalization of cultural values, norms and social rôles by the operation of the integrative mechanisms of socialization and social control relate to social change only as forces of resistance except to the degree that the macrosociety is “malintegrated” (ibid. p. 250).  The phenomenon of malitegration is viewed pathologically, because it is a condition of the cultural value system that permits deviant behaviors to have legitimating institutional valuation thereby creating “structured strains”, which are impediments to the emergence of stable macrosocial consensus equilibrium throughout the social system (ibid. p. 493).

Thus in classical functionalism (and contrary to conflict theories) the initiating factors that produce social change are viewed as exogenous to the social system (ibid. p. 219,).  For example Parsons says that he is less interested in the initiating factors than in tracing the repercussions throughout the social system of a change once initiated, including what he calls the “backwash” that modifies the original direction of change, because this shows how the concept of a social system is crucial.  And he advocates more empirical investigation to address this problem (ibid. p. 494).


That needed empirical investigation is implemented by quantitative functionalism. Contrary to Parsons the paradigm of motivational “mechanisms” is not adequate for the analysis of the structure of the social system for the explanation of social change.  It is not possible to trace the interinstitutional pattern of “repercussions” and redirecting “backwash”, what Gustavson (1955, p. 28) calls “social forces”, by focusing on integrative mechanisms viewed as the social-psychological processes by which common value patterns are integrated into the personality.  Quantitative functionalism does not invalidate classical functionalism.  But as in macroeconomics, macrosociological theory has a distinctively macro perspective that is not social-psychological reductionist.

In this quantitative theory Merton’s functionalism is more applicable than Parsons’ is, because Merton’s describes observable objective consequences rather than subjective dispositions such as aims, motives, or purposes, and most notably it furthermore describes the effects on the larger macrosociety in which the functions are situated (Merton 1967, p. 51).  In this study the larger macrosociety is the system of different types of internally organized institutional groups in the U.S. national macrosociety.  Attention is therefore directed to another type of integrative mechanism consisting of negative-feedback relations due to the interinstitutional cultural configuration of value orientations that pattern the propagation of social change through the system of types of institutional groups.  And the further empirical investigations required to identify these interinstitutional cultural patterns proceed by examining their effects in aggregate social data using statistical inference by constructing a quantitative theory consisting of a system of equations.  Since the publication in 1939 of “Interactions between the Multiplier Analysis and the Principles of Acceleration” in Review of Economics and Statistics by Nobel-laureate economist Paul Samuelson, such models have become a staple technique in mathematical economics and econometrics, and they apply no less so to sociology.

This quantitative macrosociological theory uses analysis of aggregate data for its method of construction, and does not use Parsonsian motivational analysis as is typically required by classical functionalists.  The constructional process for this model was carried out with the assistance of a computerized discovery system (note: not a stepwise regression), which is described in this author’s Introduction to Metascience (Hickey, 1976).  When the constructed dynamic macrosociometric model is iterated, it propagates a time-series pattern of index numbers of growth rates of per capita rates.  The resulting successive solutions track the progression of growth rates and the directions of changes in degrees of consensus as measured by per capita rates of voluntary institutional-group associations.

Unlike other classical functionalists Merton recognized that social interaction may have consequences that are not intended or even recognized by the members of the social system.  His view of functionalism takes the objective standpoint of the observing social scientist and not the subjective standpoint of participant.  He refers to the unintended beneficial consequences as “latent functions” and attributes them to “latent structures” in contrast to “manifest” functions and structures having consequences that are intended by the members (Merton, ibid.).

Some of the relationships set forth in this functionalist theory seem clearly to be manifest structures enabling manifest functions such as the reinforcing effect of religious affiliation on compliance with criminal laws proscribing homicide.  But there are also latent structures and functions. Latent outcomes are exemplified in Keynesian macroeconomics by the “paradox of thrift”.  And simulations with this macrosociometric model reveal the unintended and unrecognized consequences of social behavior, which are latent for the participants and are furthermore also likely hidden from classical sociologists.  The evidence for the empirical validity of the model is: (1) the satisfactory statistical properties of the equations estimated over more than fifty years of historical sample data, (2) the successful capture of the patterns of the time-series sample data when the model is iterated, and (3) the accurate retrodictive testing performance of the model.


Classical functionalism exemplifies the German romantic philosophy of science that Parsons brought from Weber’s Heidelberg University, while quantitative functionalism exemplifies the contemporary American pragmatist philosophy of science.  In academia contemporary pragmatism has superseded not only the positivist philosophy but also the romantic philosophy.  Some of the relevant differences between the contemporary pragmatist philosophy of science and its predecessors are as follows:

1.  There are different definitions of “theory”.  Romantics and positivists both define “theory” semantically, while pragmatists define “theory” pragmatically by its function in basic research.  As Yale University’s pragmatist philosopher of science Hanson (1958) wrote, ideas such as theory, hypothesis and law, if drawn from what he calls the finished “catalogue-science” found in textbooks will ill prepare one for understanding “research-science”. The pragmatics of theory is empirical testing, and a theory can have any semantics.  Thus while for the romantics sociological “theory” describes subjective motivations, and for the positivists sociological “theory” has a certain formal structure, for the pragmatists all “theory” in research-science is defined as any universally quantified discourse proposed for empirical testing.  With respect to statistical models, for the pragmatist the theory is the model and the model is the theory, so long as it is untested either proposed for empirical testing or actually being tested.  A scientific law is a tested and nonfalsified theory.

2. There are different aims and criteria for scientific criticism, and different concepts of explanation.  For the romantics the aim for social science is explanation consisting of “interpretative understanding” of the conscious motivations deemed to be the causes of observed behavioral outcomes.  And on the verstehen version the romantic sociologist must furthermore share in the participants’ understanding empathetically, so that it is “convincing” for the sociologist, i.e., folk sociology.  Pragmatists reject all semantical presuppositions as criteria for criticism.  For the pragmatists only empirical adequacy demonstrated in testing may operate as a criterion for the acceptance or rejection of theories.  Unlike positivists, pragmatists permit description of subjective mental states in the semantics of social science explanations, but unlike romantics they never require it.

       3. There are different views about semantics.  For the romantic classical functionalist the semantics of terms such as “values” is fully defined prior to development of his theory.  Indeed, it is defined in social psychology.  For the pragmatists the tested and nonfalsified sociological theory and its test-design language define the semantics of its constituent terms.  This is the pragmatist thesis of “relativized semantics” described by the contemporary pragmatist Quine (1981) and anticipated by both the microphysicist Heisenberg (1971) and the structuralist linguist De Saussure (1959).  Relativized semantics implies that there is a semantical change in the descriptive vocabulary common to an earlier theory and its newer successor, as noted by Kuhn (1962) and Feyerabend (1962).

4. There are different criteria for ontological claims. Ontology is the aspects of extralinguistic reality – including causality – described by the semantics of discourse.  In science the most realistic ontological claims are those described by the semantics of tested and nonfalsified theories.  For the romantic sociologist the participants’ conscious subjective motivations are deemed to be the causes of their observed social behaviors and outcomes.  Thus the romantic believes he firstly knows intuitively or introspectively the operative causal factors, and he then creates and evaluates any constructed theory (or model) accordingly.  In romantic sociology this prior ontological commitment results in the fallacy of social-psychological reductionism.  On the other hand the pragmatist firstly examines the empirical test outcome, and then uses the empirically adequate, i.e., tested and nonfalsified theory to identify the causal factors. This is Quine’s pragmatist thesis of “ontological relativity” (1969), which was anticipated by Heisenberg (1958 and 1974).


Except as otherwise noted the data for the variables in the quantitative functionalist theory are from the U.S. Commerce Department’s Historical Statistics of the United States (1976) for the years 1920 through 1972.  The internal reference series in the source are noted together with the variable symbols used in the equations. Where the data are not released as per capita rates by the source, the aggregates are transformed into per capita rates.

Some of the variables such as technological invention and voluntary exposure to mass media relate to the information content in the culture.  Some others refer to demographic, economic, ecological or international conditions.  But from the viewpoint of functionalist macrosociology the most significant variables in the model are the institutional variables.  These institutional variables represent aggregate voluntary group-associational behaviors in the population, which consist of voluntary membership in, or formation of internally organized characteristically institutional groups, notably a family, a school, a church, a business enterprise, or the civil society.  The fact that they represent voluntary behaviors means that they manifest value orientations. The fact that they represent aggregate behaviors means that the values are cultural values that are widely shared.  And the fact that they represent group-associational behaviors means that the cultural values are characteristic of particular types of institutional groups.

When these institutional data are made per capita rates, they reveal degrees of consensus in the total population about the cultural values of the particular institution, just as per unit price rates reveal economic values about particular products and services according to the “revealed preference” thesis set forth by Nobel-laureate economist Samuelson in his “Consumption Theory in Terms of Revealed Preference” (1966).  Thus the per capita rate for a particular institutional variable is a measure of the population’s level or degree of consensus about the values characteristic of that particular type of institutional group.  When a per capita membership rate is near its maximum, there is a high degree of consensus in the population about the values characteristic of the particular type of institutional group.  And a low per capita membership rate shows a low consensus about the values characteristic of the type of institutional group.

The data are averages over four-year periods.  Like the economists’ price elasticities the coefficients in the equations are dimensionless due to transformation of the per capita time series data into period-to-period change ratios, which also minimizes collinearity in the independent variables of the equations.  Then the change ratios are transformed into index numbers with the base = 1.0 assigned to the out-of-sample last data period in each of the time series.  The system executes each trial model through successive time periods to make predictions of the out-of-sample last period, so that all of the predicted values are compared to the uniform base period to determine accuracy.  Like economists’ elasticities the models’ coefficients measure the impact of change in one institution upon change in another.  The variable with the largest coefficient in an equation dominates the effectiveness of any positive or negative feedbacks.  Also the coefficients’ associated algebraic signs reveal relationships of value reinforcement or value conflict depending on whether the signs are positive or negative respectively.

This quantitative macrosociological functionalist theory contains endogenous variables for groups representing the five basic institutions of a modern macrosociety as follows:

     The family institutional group is represented by the annual change ratio in the marriage rate (Series B3) and denoted MR.  There are several statistical series available that describe group associational behavior relevant to this institution, sich as family size or divorce rates.  The marriage rate represents new family formation.

       The governmental institutional group is represented by the annual change ratio in the reciprocal of the homicide rate (Series H792) and denoted LW.  The group for this institution is not the government apparatus or a political party, but rather the whole civil society and the law governed interaction among the citizens.  What is of interest is the voluntary compliance with criminal law that maintains the minimal and necessary degree of social order, the breach of which is a crime.  Of the various crime statistics available the homicide rate is clearly a measure of deviation from the minimum and necessary conditions for social order.  Homicide is a violent crime and is also the most reliably reported, since there is usually an evident corpse.  The LW variable measures voluntary compliance to criminal law.

     The economic institutional group is represented by the annual change ratio in the per capita rate of the formation of new business enterprises (Series V20) and denoted BE.  This institution offers the greatest range of choice for measurements for the economic sector.  Participation in a business enterprise is selected, because it is the principal group association for the capitalist economy, and business formation is voluntary.

     The religious institutional group is represented by the annual change ratio in the per capita rate of total religious affiliation (Series H793) and denoted RA.

     The educational institutional group is represented by the annual change ratio in the percent of seventeen-year-olds who graduate from high school (Series H599) and denoted HS.  Unlike primary school, high school completion is voluntary, and it is the broadest measure of voluntary educational attainment.

The theory also contains four other endogenous variables representing factors that the discovery system identified as statistically significant.  These other endogenous variables are:

      Urban population is represented by the change ratio in the percent of the population living on farms (Series K2) subtracted from one hundred percent and denoted UR.

       Technological invention is represented by the change ratio in the per capita number of patent applications for inventions (Series W96) and denoted IA.

     Demographic profile is represented by the change ratio in the national crude birth rate (Series B5) and denoted BR.

      Mass communications media is represented by personal consumption expenditures for newspapers, books, periodicals and cinema plus income from radio and television broadcasting companies.  The source is the U.S. Commerce Department’s historical National Income and Product Accounts (1976).  The importance of each medium is weighted by the dollar value of the expenditure or income amounts.  The sum of the dollars is deflated by the consumer price index to remove distortions due to inflation over time, and then the deflated series is made a per capita rate, then a change ratio, and finally an index number.  The result indicates the change rate of voluntary exposure to various mass media and is denoted CM.

There are also three exogenous variables that the discovery system identified as relevant to social change:

      Macroeconomic conditions is represented by the change ratio in the per capita rate of real income, the constant-dollar gross national product (Series F17) and denoted GP.  This variable would not be exogenous were this quantitative functionalist theory integrated with a macroeconometric model of the U.S. national economy.

     Military mobilization is represented by the change ratio in the per capita number of armed forces personnel on active duty (Series Y904) and denoted AF.

     Foreign immigration is represented by the change ratio in the per capita number of immigrants from all countries (Series C120) and denoted IM.

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