Return to Home Page


Economic Models in Development Economics

I. What is a CGE model?                                                                                                         3

Baseline data                                                                                                                        6

Substantive economic assumptions                                                                                          11

Static versus dynamic simulations                                                                                           13

A sample simulation                                                                                                             14

II. Criteria of adequacy                                                                                                           15

Evaluation                                                                                                                          15

What sorts of knowledge do CGE models purport to offer?                                                         17

Correspondence, abstraction,  and realism                                                                               18

Warrant of economic models                                                                                                  24

Empirical confirmation of a model                                                                                          29

Assessment                                                                                                                             31


            This paper is concerned to explore and evaluate the use of mathematical models in development economics, particularly "computable general equilibrium" (CGE) models. Such models have become an increasingly important tool of analysis in development economics.  They represent an intriguing and powerful device for making predictions about the behavior of complex national economies in response to a variety of kinds of shocks.  They are used to evaluate the probable economic consequences of various policy interventions (e.g. currency devaluation or an increase in food subsidies), as well as to identify the macroeconomic properties of a complex national economy.  Such models permit the economist to run simulations of various macroeconomic scenarios.  They thus represent the opportunity to conduct "experiments" within economics.[1]  And they provide an important basis for policy advice offered to national governments by development consultants and agencies.  My perspective in what follows is the philosophy of social science.  I will try to identify the criteria of validity and consistency that ought to govern the evaluation of such models, and to question the degree to which we can attach rational confidence in their results.

            Consider a schematic example.  Let M be a macroeconomic model of the Mexican economy.  M takes a list of exogenous variables xi and a list of endogenous variables yi and parameters pi.  The model makes a set of causal assumptions about how the exogenous variables affect the endogenous variables and what the intra-system relations are.  These assumptions are represented in the form of a set of equations defining the behavior of the endogenous variables in terms of the parameters and exogenous variables.  The model employs econometric techniques to establish values for exogenous variables and parameters and their trends over time.  And it imposes a set of closure rules.  The equations are solved for a given set of values for the parameters and exogenous variables; this represents the equilibrium condition for the endogenous variables in this setting.  The model can now be used to consider the possible effects of various counterfactual conditions: change in exchange rates, energy price shock, removal of trade barriers, and so on.

            The central attraction of such models is their promise of providing a systematic representation of the inter-relatedness of a modern competitive market economy.  A national economy such as Mexico's is an extremely complex affair, involving dozens of sectors, thousands of industries, millions of workers, a variety of government economic policies, and a fluctuating international economic environment.  And it is desirable to have some way of estimating the probable consequences of possible economic shocks--e.g., increase in international petroleum prices, fall in the price of coffee--and possible government policies--e.g., increase in food subsidies or expenditure on primary education.  Partial equilibrium analysis leads economists to concentrate on a single sector (e.g. agriculture) and ask some or all of these questions; but because of the interconnections within a complex market economy, partial equilibrium analysis is likely to miss important secondary effects. General equilibrium analysis is intended to capture these effects--for example, the effect on agriculture of rising cost of grain leading to higher wages in industry, leading finally to higher input prices for agriculture.

            This paper is primarily concerned with epistemological issues arising in relation to models of this sort.  What standards should be used to assess the validity and reliability of such models?  What are the truth conditions of a model?  What inferences can be drawn from a valid, reliable model?  What is the relation between the model and the underlying economic reality?  How do we determine how good a simulation we have in a particular model?  How well does it represent the underlying economic causal structure?  How reliable are its predictions?  These issues invoke current debates concerning scientific realism and empiricist philosophy of social science: to what extent may we judge that a model is true?  And to what extent does the acceptability of a model turn on its predictive success?


I. What is a CGE model?


            A computable general equilibrium (CGE) model is a distinctive kind of economic model.  It is grounded in the fundamentals of microeconomics: the idea that a competitive market economy reaches an equilibrium of supply and demand, determined by the demand functions and production functions of consumers and firms.  It is a general equilibrium model, in that it is designed to analyze and explore the intersectoral effects of price changes and demand shifts (unlike, for example, the partial equilibrium analysis familiar from microeconomics).  It is an applied model (rather than a purely theoretical model), in two respects: (1) it is based on observed economic data for a particular national economy, and (2) it is designed to simulate the behavior of the modeled economy, permitting predictions and counterfactuals about that particular economy.  It is a simulation model: in contrast to the simple stylized models often constructed to investigate the properties of market systems, CGE models are intended to capture the empirical details and specific economic characteristics of a given economy, with the goal of simulating the response of this economy to a variety of hypothetical shocks and policy interventions.[2]  Though CGE models make use of econometric analysis, they are not econometric models: they are not primarily designed to discern causal regularities through statistical analysis of time-series data, and are instead based on specific theoretical hypotheses about the workings of a market system.[3]  And finally, though CGE models are based on microeconomic mechanisms, they are often employed to probe traditional macroeconomic problems: aggregate effects of taxation, tariffs, and trade; distribution of income; levels of savings and employment; and the causes and effects of price inflation.  CGE models thus bridge micro- and macroeconomics.  These models are generally multi-sectoral representations of the modeled economy.  They use microeconomic laws--essentially, a representation of the demand and supply systems, with a computed equilibrium state--to simulate a whole economic system.  The model thus depends on microeconomic assumptions while leading to macroeconomic analysis and inferences.[4]

            Conceptually a CGE model is fairly simple.  An economy is assumed to be an equilibrium system in which various quantities affect other through competitive market mechanisms.  Economic properties are the effect of large numbers of rational consumers and producers interacting through a system of prices.  The level of income, preferences, and prices jointly determine aggregate demand; while the price of inputs and demand for output determines the profitability (and therefore quantity of output) for each firm and sector.  The system is subject to constraints and conditions.  The system reaches equilibrium through a process of adjustments by consumers and producers to the current price structure. 

            The model is designed to capture the equilibrium conditions and the mechanisms of adjustment for the system as a whole.  Demand is disaggregated into a set of income groups; each group is assumed to have a homogeneous demand and savings function.  Production is disaggregated into a number of sectors; each sector is assumed to have a homogeneous production function and (usually) fixed coefficients of production.  The model takes the form of a system of equations and parameters designed to represent the equilibrium conditions of a market economy: the settings of prices and quantities of product that balance supply and demand given an accounting of all sources of demand (private, export, and government).  If there are as many equations as endogenous variables then it is possible to solve for one (or more) set of values for endogenous variables that satisfy the equilibrium conditions.

            The mathematics involved in solving a large set of independent equations are involved but conceptually simple.  The model consists of a set of equations in n unknowns (endogenous variables), along with m constants and parameters (exogenous variables).  If there are sufficiently many independent equations (n) there may be one or more solutions to the equations: a setting for all n variables that satisfy the equations.[5]  The equations can be solved algebraically or numerically.  There are now computer programs commonly available that will arrive at numerical solutions to large systems of equations.  Numerical programs use various successive approximation algorithms (e.g. the Newton method, the Levenberg-Marquardt method, or the MINPACK algorithms developed by the Argonne National Laboratory) that involve an initial "guess" set of values for the variables, and then successive modification of the variables until a solution is found to a stipulated level of tolerance.  There are various obstacles to finding a solution--e.g. the algorithm may get trapped in a local maximum, or the algorithm may fail to converge to the specified level of tolerance within a reasonable number of iterations.  But these problems do not raise significant conceptual issues.  It is the economics that poses the difficulties.[6]

            The equations of a CGE model fall into two general categories: accounting identities representing the requirement that prices must be such that supply equals demand, investment must equal savings, and so forth; and hypotheses derived from economic theory representing the model-builder's assumptions about the variables that adjust to bring the system into equilibrium.  The latter represent the "closure rules" invoked by the model, and may reflect a variety of economic hypotheses--classical, neo-classical, or structuralist economic theory.  A medium-sized model may involve several hundred equations, variables, and parameters--an algebraic system vastly too large to solve by hand.  However, it is now possible for desktop computers to solve models employing several hundred equations in a reasonable period of time. Whereas first-generation general equilibrium theory was forced to rely on complex algebraic manipulation of small linear systems of equations, it is now possible to compute numerical solutions for large models including both linear and non-linear equations.  It is possible to consider such questions as these:  How would a decrease in the food subsidy in Egypt in the 1970s have affected employment and government deficits?  How will a 10 percent increase in the cost of imported oil affect Argentina's level of employment?  How would currency devaluation affect the nutritional status of Nicaragua's poor?

Baseline data

            Any applied model must incorporate a body of empirical data characterizing the state of the economy at a given time (the base solution of the model).  The model then permits the analyst to run the economy forward in time according to different assumptions about the macroeconomic or policy environment.  Base-year information is generally represented in the form of a "social accounting matrix" (SAM).[7]  This is a multisectoral snapshot of the state of the economy at a point in time, indicating the flows of products and labor between sectors and into consumption and investment.  The rows of the table represent deliveries of commodities or sources of income; the columns are uses of commodities or incomes.  Figure 1 provides a simple example of a three-sector SAM.  In theory the SAM ought to reflect all flows of product and income through the economy.  A SAM incorporates the input-output relations familiar from Leontief and Sraffa (the intersection of columns 1-3 with rows 1-3 in figure 1); data here allow computation of input-output coefficients for each sector (that is, the value of product from sector i used in the production of one dollar of product of sector k; last four lines of figure 1).  A SAM can also represent information concerning the distribution of income across income categories, depending on the level of disaggregation of income represented in the table (peasant, worker, capitalist; columns 4-6 in figure 1).  A SAM is constructed subject to strict rules of accounting consistency.  Totals of corresponding rows and columns must be equal, and all values must be computed in constant prices.  The information in a SAM is derived from a number of sources: input-output tables for sectors or industries; national accounts; and household surveys on patterns of consumer spending.[8]

            The equations in a CGE model are intended to specify the functional relationships that obtain between the economic quantities identified in the SAM.  These equations may be broken down into blocks representing different sorts of economic constraints or processes.  First, we need a set of equations representing sectoral demand‑supply balances.  Imports and domestic production must equal domestic demand plus exports.  Second, there will be a set of equations describing price formation of all goods. Different price rules may be employed, but a common form is the markup pricing rule, in which the price of a good is determined by the cost of all inputs plus a fixed markup rate; another common approach is "flex-price" determination (Taylor, 1979).  Third, the model must represent a set of income distribution rules for different income groups.  Fourth, we need equations defining expenditures by different social groups, breaking down expenditure into savings and consumption (frequently using the assumptions of the "linear expenditure system").  Fifth, since international trade is generally present in modern national economies we need to represent exchange rates, tariffs, and trade balances.  Sixth, since government economic activity is almost always significant it is necessary to represent government revenues and expenditures.  Seventh, the model needs to specify the rules according to which sectors within the economy are postulated to adjust to changes in supply and demand, changes in exchange rates, inflation, and so on.  These are the closure rules of the model; they represent substantive causal hypotheses about how some variables affect others.  Finally, the model needs to sum up savings flows and investment.  Figure 3 summarizes these points.










govt. exp.












































































































Net taxes




















































prod. coef:




















































labor coef:













Figure 1. A social accounting matrix: three sectors and three income groups

Source: derived from Lustig and Taylor, 1990, table 2.1


            Central to the equilibrium analysis are the functions representing demand and supply.  It is common to treat consumer and producer optimization processes separately; this permits separate treatment of demand and supply conditions, which can then be aggregated into a general equilibrium result (Mansur and Whalley, p. 80).  The modeler is forced to make somewhat arbitrary decisions in choosing a functional form in which to represent demand and production.  It is common to use either Cobb-Douglas functions or constant elasticity of substitution (CES) functions to represent utilities (demand) and cost (production).  And consumer demand is often represented in the form of a linear expenditure system (see figure 2 for examples of each).


Cobb-Douglas production function



CES production function


Linear expenditure system

Figure 2.  Examples of functional forms for demand and production


            These equations are formulated in terms of a large number of economic quantities--prices, production levels, income, wages, investment, and so forth.  These quantities can be broken down into variables and parameters.  Variables are the economic quantities whose behavior is either taken to be determined by the equations of the model (endogenous) or to be determined outside the modeled system (exogenous).  Parameters (e.g. elasticities, coefficients, exponents) are quantities that determine the particular "shape" of the economic processes being modeled through the functions.  If there are as many equations as independent variables, then there may be at least one solution of the system of equations for any given set of assignments to the parameters.  Figure 4 represents the relation between parameters, model, and variables; we can look at the model as a super-function that maps settings of the parameters onto settings of the variables that satisfy the model equations given the parameters.  It must be true that the solution values of the model for base-year parameter settings satisfy the SAM for the base year.

            Once the functional form is chosen for production and demand functions, the modeler must arrive at a reasonable assignment of values to parameters.  Roughly, this means setting the slopes, curvature, and intercepts of the respective functions so as to reproduce the SAM.   Input-output coefficients, savings rates, tariffs, taxation rates, exports, and exchange rates are examples of some of the parameters for which it is necessary to provide values.  Some of these are set by government policy--e.g., tariffs, taxation rates, and exchange rates.  Others are intrinsic features of the economy at a given time--e.g., input-output coefficients or savings rates. The SAM permits computation of most of these parameters, while household surveys or other empirical sources must be consulted for others (e.g. the level of subsistence consumption).

            There are two basic approaches to the problem of estimating parameters: calibration and stochastic measurement.  The first approach involves calibrating the model to base-year data.  Here the basic procedure is to assume that the economy is in equilibrium in the base year; substitute base-year observations for the endogenous variables into the equations; and solve for the parameters.  Mansur and Whalley point out, however, that the effectiveness of this procedure depends on the functional form chosen for the production and demand functions.  Cobb-Douglas functions imply a unique set of parameters under this procedure; whereas CES functions require stipulation (or independent measurement) of estimates of elasticities of substitution in order to arrive at a unique set of parameters.  And since the results of the model are highly sensitive to assignments of elasticities, an important possible source of model invalidity occurs at this point.

            The second possible approach for setting the parameters of the model is to provide an independent econometric measurement of the needed parameters.  The econometric approach requires that we use all available data to arrive at statistical estimates of parameters.  On this approach the measurement of parameters requires time-series data--ideally a time series of SAMs for the economy in question.[9]

            The solution of the model describes the setting of the central economic quantities that represent the equilibrium condition for the economy, given the values of the parameters and exogenous variables (figure 4).  These quantities include, first, quantity and price information for each sector.  These variables in turn permit calculation of income, consumption, and savings for each income group; government revenue, expenditure, and savings; and foreign expenditure, savings, and trade balance.



sectoral demand-supply balances


price formation of all goods


income generation rules for different groups


expenditures by different social groups (consumption and savings rates)


exchange rates, tariffs, balance of payments


government revenues and expenditures


sectoral adjustment rules


savings-investment balance


Figure 3. Blocks of equations in typical CGE model


parameters pi                  =>

exogenous variables xi


model equations           =>

solution setting of variables yi

Figure 4. Logic of simulation


Substantive economic assumptions

            A model of any process is only as good as the underlying theory on which it is based, and economic models are no exception.  The principles that underlie economic models are of two broad sorts.  First, there are a host of accounting identities that any economy in equilibrium must satisfy: supply must equal demand, savings must equal investment, income must equal consumption plus investment, and output of consumption-goods industries must equal domestic consumption plus exports.  These identities are formally represented in the social accounting matrix described above.

            Second, an economic model must embody assumptions about economic causation: which economic variables exert primacy within an economic system, and what is the functional form of their influence?  Most broadly assumptions at this level determine how equilibrium is restored after a shock, and represent the economist's assumptions about dynamic processes in the short and medium run.  Assumptions at this level are described as the "closure rules" of the model, and they are critical to the behavior of the model. Adopting different closure rules will lead to substantial differences in the behavior of the model.

            There are a number of different sets of economic assumptions that can serve as closure rules.          Classical models take the wage and the rate of profit as endogenous.  Neo-classical models take the production function as the starting point and determine prices, wages, and profits as the result of profit maximizing within a freely competitive market.  Structuralist models take the institutional context of the economy as a constraining variable; they build into their models assumptions about the functional distribution of income.

            Intermediate between these two levels of assumptions are the mathematics of input-output relations.  Assume that there are n sectors of production and that various sectors use products of other sectors as intermediate goods; what level of production is required in each sector to satisfy intermediate and final demand?  And what set of commodity prices represents an equilibrium in which supply and demand will be equal? It is common to assume linear production functions with fixed coefficients of production. Under these assumptions, it is possible to solve the quantity and price problem formulated above using simple matrix algebra.  This construction takes the wage, the rate of profit (markup rate), and the level of final demand, and computes a price vector and a quantity vector for the n sectors.[10]


Static versus dynamic simulations

            So far we have considered a process of modeling that permits us to extrapolate current economic data forward one period on various counterfactual assumptions.  It establishes the equilibrium conditions that correspond to a new setting of some of the exogenous variables.  This is a static simulation, since it does not build in a representation of the processes of change that the economy is experiencing.  It is possible to introduce dynamic considerations by performing a series of iterations of the model, updating exogenous variables (parameters) on the basis of a hypothesis about their behavior over time.  For example, population change and productivity increase can be built into a dynamic simulation by indexing parameter values over time.  It is possible to use econometric techniques to arrive at an estimate of the rate of increase in factor productivity over time; this regression can then be used to determine parameter values for factor productivity over a number of iterations. Likewise, we may want to build into a dynamic simulation a hypothesis about the direction of change of the real wage; this hypothesis may be based on extra-economic factors such as the political strength of unions within given society.  Chenery et al describe the dynamic features of their model in these terms: "Intertemporal linkage equations update exogenous variables and parameters that are dependent on policy choices and specify cumulative dynamic processes such as factor accumulation and productivity growth.  The intertemporal equations provide all exogenous variables needed for the next period (four years later) by the CGE model, which is then solved for a new equilibrium" (Chenery et al, 1986a, p. 315).  These intertemporal equations describe the behavior of such factors as labor force growth, capital stock growth, productivity growth, world market trends, and trends in savings rates--variables whose behavior is assumed to be independent of the economic processes modeled by the CGE simulation itself.  It should be noted that the intertemporal equations are exterior to the CGE model itself; they represent an effort to model change in exogenous variables over time, which then serve as input to the CGE model for its static equilibrium.  In the Chenery model, the simulation is run over four periods of five years each.  The equilibrium condition for year 0 is solved; the exogenous variables are then updated for year 5 and the equilibrium condition is solved; and so forth through year 20.

            CGE models are particularly common in development economics, and this discipline is centrally concerned with processes of change over time: structural transformation, technological change, population growth, capital formation, growth in educational resources, and economic growth.  So it is essential to be able to provide dynamic analysis within the CGE framework.  However, many of these dynamic processes are not purely economic; they depend on institutional change, political power, and other non-economic factors.


A sample simulation

            We are now ready to consider a sample simulation.  Nora Lustig and Lance Taylor offer a CGE model to examine the effects of various policy interventions in Mexico aimed at improving nutritional status of the poor (Lustig and Taylor, 1990).  Lustig and Taylor aim to compare the effects of a direct income transfer to target groups, and a targeted price subsidy, and a general price subsidy.  They construct a social accounting matrix for the Mexican economy based on 1975 data (a simplified version of which is provided in figure 1 above).  Their model represents eight domestic sectors (corn and beans, other agriculture, petroleum, fertilizers, food processing, industry, services, and commerce) and seven income groups (peasants, agricultural workers, agricultural capitalists, urban workers, urban capitalists, merchants, and urban marginals).  The model is summarized in figure 5.  The model contains 92 equations, but it can be broken into a series of independent blocks.  Given fixed production coefficients and exogenous markup rates, the price equations can be solved independently of quantity information.  Consumer demand depends on prices and income; so blocks II-VII must be solved simultaneously.  Closure is established through adjustment of activity levels, the trade gap, and income distribution to bring savings and investment into balance.  The model is calibrated to reproduce the SAM data as its base solution.  Lustig and Taylor use the model to run three policy experiments: an income transfer to peasants and agricultural workers, a targeted price subsidy, and a general price subsidy.  The central results are described in figure 6; in general, each policy has the effect of increasing incomes flowing to the poor, but at the expense of increasing trade and government budget deficits.  The general price subsidy leads to an explosion in trade and budget deficits and is practically infeasible.  The targeted price subsidy is least costly in terms of fiscal and trade balance, but has only about half the effect on incomes to the poor that are generated by direct income transfer.



prices for eight sectors

flex prices for agriculture; markup pricing for other non-agricultural sectors


sectoral balances for eight sectors



consumer demand

linear expenditure system


total income by income group

income generation rules for each group


total expenditure by income group

income discounted by savings and taxation


final prices

base prices plus commerce margin, subsidies


consumption of commerce



savings (government, foreign, private)



investment-savings balance



Figure 5. Lustig-Taylor model of Mexican food consumption policies



 d real incomes (peasants,

agric. workers and urban


d trade deficit

d govt. savings

income transfer




targeted price subsidy




general price subsidy





Figure 6. Simulation results

II. Criteria of adequacy


            Let us turn to the problem of evaluating a CGE model.  What are the standards of adequacy which should be used to assess CGE models?  And what forms of inference does this technique permit?  Suppose we are presented with a CGE model of the Mexican economy that has been designed to evaluate the probable effects of a targeted food price subsidy.  We are told, let us suppose, that the model predicts that (1) income to the poor will increase by 5.6% over what it would have been absent subsidies; (2) the trade deficit will increase 9.5%; and (3) government savings will fall by 30.6%.  We are to imagine ourselves in the position of the governor of the policy maker with the power to decide whether or not to implement through this subsidy.  What sorts of questions should we entertain about this line of argument?

            First, there is the straightforward policy question.  If we take the simulation as an accurate representation of the economic reality confronting us--that is, we accept that the contemplated action will have these computed economic effects--then it is a question of social policy to determine whether the benefits of the policy outweigh the costs (improved nutrition for the poor versus higher trade and budget deficits).  And here various lines of argument and analysis are available; it might be argued, for example, that the costs are limited to the shortrun, and that the benefits of improved nutrition today will lead to an eventual improvement in workers' productivity that more than offset these costs.  Or it might be held that the resulting trade and budget deficits will so harm future growth as to worsen the welfare of the poor in the next period of time.

            The harder question, however, is how we should determine whether the model can be relied on in the first place: that is, whether it is likely that the predicted effects will in fact occur if the policy is adopted.  This is a general question of scientific rationality; the model, underlying data, associated computations, and predicted outcome constitute a complex scientific hypothesis which needs to be evaluated on rational grounds.  How much confidence can we rationally have in the predictions of the model, given the details of construction and data-gathering on which these rest?  Under what circumstances may we conclude that the model provides a good approximation to the workings of the existing economy?


What sorts of knowledge do CGE models purport to offer?

            Before we can decide what sorts of criteria ought to be used to evaluate a CGE model we need a clearer idea of the purpose of such models.  We have a start on answering this question in the fact that CGE models are applied models: they are designed to analyze the short- and medium-term workings of specific empirically given economies.  Moreover, they are intimately associated with policy concerns; they are commonly used to assess the probable consequences of alternative economic policies (e.g., taxation, tariffs, interest rates, currency devaluation).  These features mean that the empirical standards to be applied to CGE models are stringent; the models are intended to shed quantitative light on existing economies, so it is critical that the results of the model should approximate the behavior of the actual economy being modeled.  And finally, CGE models are concerned with causal relations within a competitive market economy.  Holding a vast range of institutional and situational details fixed, these models generally ask questions of the form: what would be the net effects of policy action A on economic variables X, Y, and Z?  So CGE models are designed to provide causal knowledge about existing economic systems.  This knowledge may take the form of a prediction: If Brazil's national bank devalues its currency by 6%, its coffee exports will increase by 5%.  Or it may take the form of a counterfactual inquiry--what would have happened if (contrary to fact) such and so had occurred?  Seen in this light, CGE models fit a familiar type of causal analysis: an effort to work out particular cause-effect relations based on a theory of the underlying general mechanisms.  The model applies a general theory of the causal properties of a given kind of system (S) to a particular case (s).  The theory is general equilibrium theory, and the causal properties in question are the probable effects on a new economic equilibrium induced by a given set of transformations to price, supply, or demand conditions.

            How much precision is expected of CGE results?  In the Lustig-Taylor model discussed above the simulation results are reported to two decimal points; thus the three policy measures lead to government savings changes of -59.70%, -30.62%, and -269.58% (Lustig and Taylor, table 2.3).  In their model of the aggregate effects of three different development strategies Chenery et al provide estimates of GDP growth rate: import substitution (5.7%), balanced strategy (6.2%), and export promotion (6.5%) (Chenery et al, 1986, table 11.3).  The consumer of such models needs to exercise a skeptical eye, however, at such precision.  Are these advanced as realistic estimates of probable results?  Or are they notional estimates, indicating only order-of-finish comparisons between policies?  The latter seems more plausible than the former; but this means that the actual prediction authorized by the model is that policy x will lead to a higher rate of growth than policy y.[11]

            In some cases CGE models appear to be designed for analytical rather than predictive purposes.  In this kind of application the goal is to trace out the causal consequences of various strategies and shocks at a theoretical level.  Thus Chenery et al write, "We are interested in creating a stylized version of Korea for the purpose of comparative analysis, not in analyzing the strategic choices available to Korea in 1963" (Chenery et al, 1986a, pp. 311-12).


Correspondence, abstraction,  and realism

            Science is generally concerned with two central semantic features of theories: truth of theoretical hypotheses and reliability of observational predictions.[12]  Truth involves a correspondence between hypothesis and the world; while predictions involve statements about the future behavior of a real system.  Science is also concerned with epistemic values: warrant and justification.  The warrant of a hypothesis is a measure of the degree to which available evidence permits us to conclude that the hypothesis is approximately true.  A hypothesis may be true but unwarranted (that is, we may not have adequate evidence available to permit confidence in the truth of the hypothesis).  Likewise, however, a hypothesis may be false but warranted (that is, available evidence may make the hypothesis highly credible, while it is in fact false).  And every science possesses a set of standards of hypothesis evaluation on the basis of which practitioners assess the credibility of their theories--for example, testability, success in prediction, inter-theoretical support, simplicity, and the like.[13]

            The central concern of this article is the epistemology of economic models.  But what does this amount to?  The preceding suggests that there are several questions that fall within the domain of epistemology in this context.  First, we can ask whether the model is a good approximation of the underlying economic reality--that is, the approximate truth of the model.  Likewise, we can ask whether the model gives rise to true predictions about the future behavior of the underlying economic reality (subject to the time frame of the analysis).  Each of these questions falls on the side of the truth value of the model.  Another set of questions concerns the warrant of the model: the strength of the evidence and theoretical grounds available to us on the basis of which we assign a degree of credibility to the model: does available evidence give us reason to believe that the model is approximately true, and does available evidence give us reason to expect that the model's predictions are likely to be true?  These questions are centrally epistemic; answers to them constitute the basis of our scientific confidence in the truth of the model and its predictions.

            It is important to note that the question of the approximate truth of the model is separate from that of the approximate truth of its predictions.  It is possible that the model is approximately true but its predictions are not.  This might be the case because the ceteris paribus conditions are not satisfied, or because low precision of estimates for exogenous variables and parameters leads to indeterminate predictive consequences.  Therefore it is possible that the warrant attaching to the approximate truth of the model and the reliability of its predictions may be different.  It may be that we have good reason to believe that the model is a good approximation of the underlying economic reality, while at the same time we have little reason to rely on its predictions about the future behavior of the system.  The warrant of the model is high on this account, while the warrant of its predictions is low.

            Let us look more closely at the semantic properties of economic models: the relation between a model M and the underlying economic reality S.  Note, to begin, that the relation between analysis and the economic reality is more complex than it first appears.  Models are formulated on the basis of economic theory.  The theory itself bears a referential relation to the world.  That is, it is appropriate to ask whether general equilibrium theory is a true characterization of the workings of competitive market systems.  And it is appropriate to assess the degree of warrant that we can attach to the general theory.  So truth and warrant pertain to the general theory.  Next we have the model of a particular economy.  The model is designed to correspond to the underlying economic reality of the particular economy.  Likewise, it is designed to implement the general theory, in application to the particular case.  So in the case of the model we have several questions to ask--first, with respect to its adequacy as an implementation of the theory, and second, with respect to its correspondence to the underlying economic reality.  Again, there are several distinct epistemic possibilities.  We may attach high warrant to both the theory and the model; or we may have confidence in the theory but not the model.  (The third possibility--confidence in the model but not the underlying theory--is the instrumentalist's position.  But for reasons spelled out below, I find this implausible.)

            Whatever position we arrive at concerning the possible truth or falsity of a given economic model, it is plain that this cannot be understood as literal descriptive truth.[14]  Economic models are not offered as full and detailed representations of the underlying economic reality.  For a model unavoidably involves abstraction, in at least two ways.  First, the model deliberately ignores some empirical characteristics and causal processes of the underlying economic reality.  Just as a Newtonian model of the ballistics of projectiles ignores air resistance in order to focus on gravitational forces and the initial momentum of the projectile, so an economic model ignores differences in consumption behavior among members of functional defined income groups.  Likewise, a model may abstract from regional or sectional differences in prices or wage rates within a national economy.

            The second form of abstraction is more distinctive of economic analysis.  General equilibrium theory represents the general hypothesis underlying CGE models.  But the application of the theory to a particular economy or policy problem is not straightforward.  There is no canonical mode of representing the central economic quantities and processes.  Thus utility functions can be represented in a variety of ways, and likewise with consumption and production functions.  (As we saw above, the linear expenditure system is commonly used in CGE models to represent consumer demand, in large part because this is a highly tractable formulation.  But there are alternative non-equivalent formulations available.)  So a given model represents one out of many different possible ways of implementing the general theory; and in order to arrive at an overall judgment of the credibility of the model we need to assess the adequacy of its particular implementation of supply, demand, savings behavior, and the like.

            It follows from this observation that the specifics of a given model are not deductively entailed by the economic theory that underlies it.  Different model-builders can have equal commitment to the general theory, while providing very different formulations of the central economic processes (e.g., utility functions, production functions, and demand functions).  And the resulting models may have significantly different properties, giving rise to different predictions about the behavior of the economic system in question. 

            Another epistemically significant feature of economic models is the difficulty of isolating causal factors in real social or economic systems.  Models (and economic theories as well, for that matter) are generally subject to ceteris paribus conditions.  Predictions and counterfactual assertions are advanced conditioned by the assumption that no other exogenous causal factors intervene; that is, the assertive content of the model is that the economic processes under analysis will unfold in the described manner absent intervening causal factors.  But if there are intervening causal factors, then the overall behavior of the system may be indeterminate.  In some cases it is possible to specify particularly salient interfering causal factors (e.g. political instability).  But it is often necessary to incorporate open-ended ceteris paribus conditions as well.

            Finally, economic theories and models unavoidably make simplifying or idealizing assumptions about the populations, properties, and processes that they describe.  Consumers are represented as possessing consistent and complete preference rankings; firms are represented as making optimizing choices of products and technologies; product markets are assumed to function perfectly; and so on.  Suppose that our CGE model makes the assumption that the coefficients of production are constant.  This implies that producers do not alter production technologies in the face of different price schedules for inputs.  This assumption abstracts from producers' substitution behavior.  But the model-builder may argue that this is a reasonable approximation in a static model; whatever substitutions occur from one period to the next will be small and will have little effect on aggregate input-output relations.

            Given, then, that models abstract from reality, in what sense does it make sense to ask whether a model is true?  We must distinguish between truth and completeness, to start with.  To say that a description of a system is true is not to say that it is a complete description.  (A complete description provides a specification of the value of all state variables for the system--that is, all variables that have a causal role in the functioning of the system.)  The fact that models are abstractive demonstrates only that they are incomplete, not that they are false.  A description of a hockey puck's trajectory on the ice that assumes a frictionless surface is a true account of some of the causal factors at work: the Newtonian mechanics of the system.  The assumption that the surface of the ice is frictionless is false; but in this particular system the overall behavior of the system (with friction) is sufficiently close to the abstract model (because frictional forces are small relative to other forces affecting the puck).  In this case, then, we can say two things: first, the Newtonian model is exactly true as a description of the forces it directly represents, and second, it is approximately true as a description of the system as a whole (because the forces it ignores are small).

            Consider, then, this account of the truth conditions of theories and models.  An economic theory is true if and only if:


1.   the causal processes the theory identifies are actually at work in the real system, and

2.   the real processes have approximately the causal properties postulated by the theory.


A model is said to be approximately true if and only if:


3.   its characterization of the central economic processes is approximately true, and

4.   the causal processes it ignores have little effect within the scope of analysis of the model.


            This account takes a strongly realist position on economic theory, in that it characterizes truth in terms of correspondence to unobservable entities, processes, or properties.[15]  The presumption here is that social systems generally--and economic systems in particular--have objective unobservable characteristics which it is the task of social science theory to identify.  The realist position is commonly challenged by some economists, however.  Milton Friedman's famous argument for an instrumentalist interpretation of economic theory (Friedman, 1953) is highly unconvincing in this context.[16]  The instrumentalist position maintains that it is a mistake to understand theories as referring to real unobservable entities.  Instead, theories are simply ways of systematizing observable characteristics of the phenomena under study; the only purpose of scientific theory is to serve as an instrument for prediction.  Along these lines, Friedman argues that the realism of economic premises is irrelevant to the warrant of an economic theory; all that matters is the overall predictive success of the theory.  But when we consider general equilibrium models, it is clear that a central part of the overall warrant of the models is the confidence that we have in the approximate truth of general equilibrium theory.  If we were to doubt this theory, then we would have no reason whatsoever to rely on CGE models.  The instrumentalist approach to the interpretation of economic theory, then, is highly unpersuasive as an interpretation of the epistemic standing of economic models.  Instead, the realist position appears to be inescapable: we are forced to treat general equilibrium theory as a substantive empirical hypothesis about the real workings of competitive market systems, and our confidence in general equilibrium models is limited by our confidence in the approximate truth of the general equilibrium theory.


Warrant of economic models

            Turn now to the problem of warrant: what sorts of evidence and theoretical arguments are available to permit us to assess the credibility of a given economic model?  I will approach this problem from two points of view: first, the antecedent warrant of a given model, and second, the a posteriori warrant of the model.  The antecedent warrant of the model is a function of our assessment of its overall adequacy as an implementation of what we know about the causal processes that are being modeled, including particularly the relevant portions of economic theory.  The a posteriori warrant of the model is our evaluation of the credibility of the model on the basis of a comparison between its results and relevant empirical data.

            The general problem of the antecedent credibility of an economic model can be broken down into more specific questions concerning the validity, comprehensiveness, robustness, reliability, and autonomy of the model.  I will define these concepts in the following terms.


    Validity is a measure of the degree to which the assumptions employed in the construction of the model are thought to correspond to the real processes underlying the phenomena represented by the model.

    Comprehensiveness is the degree to which the model is thought to succeed in capturing the major causal factors that influence the features of the behavior of the system in which we are interested.

    Robustness is a measure of the degree to which the results of the model persist under small perturbations in the settings of parameters, formulation of equations, etc.

    Autonomy refers to the stability of the model's results in face of variation of contextual factors.

    Reliability is a measure of the degree of confidence we can have in the data employed in setting the values of the parameters.


These are epistemic features of models that can be investigated more or less independently and prior to examination of the empirical success or failure of the predictions of the model.

            Let us look more closely at these standards of adequacy.  The discussion of realism above suggests that we may attempt to validate the model deductively, by examining each of the assumptions underlying construction of the model for its plausibility or realism.  (This resembles Mill's "deductive method" of theory evaluation.  See Hausman [1981] for a discussion.)  Economists are highly confident in the underlying general equilibrium theory.  The theory is incomplete (or, in Daniel Hausman's language, inexact; Hausman, 1992), in that economic outcomes are not wholly determined by purely economic forces.  But within its scope economists are confident that the theory identifies the main causal processes: an equilibration of supply and demand through market-determined prices. 

            Validity can be assessed through direct inspection of the substantive economic assumptions of the model: the formulation of consumer and firm behavior, the representation of production and consumption functions, the closure rules, and the like.  To the extent that the particular formulation embodied in the model is supported by accepted economic theory, the validity of the model is enhanced.  On the other hand, if particular formulations appear to be ad hoc (introduced, perhaps, to make the problem more tractable), the validity of the model is reduced.  If, for example, the model assumes linear demand functions and we judge that this is a highly unrealistic assumption about the real underlying demand functions, then we will have less confidence in the predictive results of the model. 

            Unfortunately, there can be no fixed standard of evaluation concerning the validity of a model.  All models make simplifying and idealizing assumptions; so to that extent they deviate from literal realism.  And the question of whether a given idealization is felicitous or not cannot always be resolved on antecedent theoretical grounds; instead, it is necessary to look at the overall empirical adequacy of the model.  The adequacy of the assumption of fixed coefficients of production cannot be assessed a priori; in some contexts and for some purposes it is a reasonable approximation of the economic reality, while in other cases it introduces unacceptable distortion of the actual economic processes (when input substitution is extensive).  What can be said concerning the validity of a model's assumptions is rather minimal but not entirely vacuous.  The assumptions should be consistent with existing economic theory; they should be reasonable and motivated formulations of background economic principles; and they should be implemented in a mathematically acceptable fashion.

            Comprehensiveness too is a weak constraint on economic models.  It is plain that all economic theories and models disregard some causal factors in order to isolate the workings of specific economic mechanisms; moreover, there will always be economic forces that have not been represented within the model.  So judgment of the comprehensiveness of a model depends on a qualitative assessment of the relative importance of various economic and non-economic factors in the particular system under analysis.  If a given factor seems to be economically important (e.g. input substitution) but unrepresented within the model, then the model loses points on comprehensiveness.[17]

            Robustness can be directly assessed through a technique widely used by economists, sensitivity analysis.  The model is run a large number of times, varying the values assigned to parameters (reflecting the range of uncertainty in estimates or observations).  If the model continues to have qualitatively similar findings, it is said to be robust.  If solutions vary wildly under small perturbations of the parameter settings, the model is rightly thought to be a poor indicator of the underlying economic mechanisms.

            Autonomy is the theoretical equivalent of robustness.  It is a measure of the stability of the model under changes of assumptions about the causal background of the system.  If the model's results are highly sensitive to changes in the environment within which the modeled processes take place, then we should be suspicious of the results of the model.

            Assessment of reliability is also somewhat more straightforward than comprehensiveness and validity.  The empirical data used to set parameters and exogenous variables have been gathered through specific well-understood procedures, and it is mandatory that we give some account of the precision of the resulting data.

            Note that reliability and robustness interact; if we find that the model is highly robust with respect to a particular set of parameters, then the unreliability of estimates of those parameters will not have much effect on the reliability of the model itself.  In this case it is enough to have "stylized facts" governing the parameters that are used: roughly 60% of workers' income is spent on food, 0% is saved, etc.

            Failures along each of these lines can be illustrated easily.

(1) The model assumes that prices are determined on the basis of markup pricing (costs plus a fixed exogenous markup rate and wage).  In fact, however, we might believe (along neoclassical lines) that prices, wages, and the profit rate are all endogenous, so that markup pricing misrepresents the underlying price mechanism.  This would be a failure of validity; the model is premised on assumptions that may not hold.

(2) The model is premised on a two-sector analysis of the economy.  However, energy production and consumption turn out to be economically crucial factors in the performance of the economy, and these effects are overlooked unless we represent the energy sector separately.  This would be a failure of comprehensiveness; there is an economically significant factor that is not represented in the model.

(3) We rerun the model assuming a slightly altered set of production coefficients, and we find that the predictions are substantially different: the increase in income is only 33% of what it was,  and deficits are only half what they were.  This is a failure of robustness; once we know that the model is extremely sensitive to variations in the parameters, we have strong reason to doubt its predictions.  The accuracy of measurement of parameters is limited, so we can be confident that remeasurement would produce different values.  So we can in turn expect that the simulation will arrive at different values for the endogenous variables.

(4) Suppose that our model of income distribution in a developing economy is premised on the international trading arrangements embodied in GATT.  The model is designed to represent the domestic causal relations between food subsidies and the pattern of income distribution across classes.  If the results of the model change substantially upon dropping the GATT assumption, then the model is not autonomous with respect to international trading arrangements.

(5) Finally, we examine the data underlying the consumption functions and we find that these derive from one household study in one Mexican state, involving 300 households.  Moreover, we determine that the model is sensitive to the parameters defining consumption functions.  On this scenario we have little reason to expect that the estimates derived from the household study are reliable estimates of consumption in all social classes all across Mexico; and therefore we have little reason to depend on the predictions of the model.  This is a failure of reliability. 

            These factors--validity, comprehensiveness, robustness, autonomy, and reliability--figure into our assessment of the antecedent credibility of a given model.  If the model is judged to be reasonably valid and comprehensive; if it appears to be fairly robust and autonomous; and if the empirical data on which it rests appears to be reliable; then we have reason to believe that the model is a reasonable representation of the underlying economic reality.  But this deductive validation of the model does not take us far enough.  These are reasons to have a priori confidence in the model.  But we need as well to have a basis for a posteriori confidence in the particular results of this specific model.  And since there are many well-known ways in which a generally well-constructed model can nonetheless miss the mark--incompleteness of the causal field, failure of ceteris paribus clauses, poor data or poor estimates of the exogenous variables and parameters, proliferation of error to the point where the solution has no value, and path-dependence of the equilibrium solution--we need to have some way of empirically evaluating the results of the model.


Empirical confirmation of a model

            The preceding provides an account of a variety of theoretical arguments and standards that can be employed to assess antecedent credibility for a given model.  But we have seen that there is a substantial gap between a model's being judged adequate on these grounds and our being justified in relying on its predictions.  In order to arrive at a reasonable confidence in the predictive adequacy of a model, therefore, we need to have ways of empirically testing the model.

            Consider an analogy.  Suppose that an engineer has designed a complicated mechanical device to be used in space.  The device has not yet been built, and ipso facto has not been used in space.  The engineer wants to know how the device will behave when subjected to vibration in zero-gravity.  He therefore creates a computer simulation of the device that takes into account the device's known mechanical characteristics and the environmental variables known to be causally relevant to the performance of the device.  The simulation model is validated along the lines suggested above: it is checked for validity, comprehensiveness, robustness, autonomy, and reliability.  The simulation predicts that the device will continue to function according to design even if subjectived to vibrations within a given range.  How much confidence ought we have in this result?  Relatively little, it would seem, until we have had some experience comparing the predicted results of the simulation with the actual behavior of the simulated device.

            The most obvious approach to empirically evaluating a model is through direct evaluation of its predictions: compare the predictive results of the model with observed data.  It is significant, however, that none of the dozen models contained in Socially Relevant Policy Analysis (Taylor, ed., 1990) provide such post-facto evaluation.

            A second and less direct approach is to attempt to establish the empirical credentials of a class of models.  Here the idea is to consider the predictive successes of a given type of CGE model in application to a range of specific economies.  If a given model has been reasonably accurate in the past, this gives us some basis for confidence in its current application.  (By analogy, suppose there are several different approaches to modeling weather phenomena.  Models have been constructed for particular applications from each of the different approaches.  We might argue inductively that the class of models with the greatest empirical success in the past is likely to continue to succeed in the future.)  The problem with this approach is that each CGE model is tailored to the particular analytical questions the modeler is interested in answering; this means that there will be significant differences in the structure and details of models in different applications.  As a result there will not generally be a track record of previous predictions which might establish the reliability of a given model.[18]

            Another form of direct empirical test of a model or theory is an application of the "bootstrapping method" of confirmation (Glymour 1980).  We may evaluate various components of the model--e.g. its representation of the demand functions--by holding fixed other theoretical hypotheses; deducing demand behavior for the next period; and comparing the predicted results with that predicted by the target demand function.

            It is possible to design an empirical test of a CGE model, then; but very little work has been done along these lines, and CGE models are not generally accompanied by substantial empirical argument designed to support the credibility of the model.  (This stands in marked contrast to the econometrics literature, in which issues of empirical adequacy of findings have received substantial attention.)


            Let us now pull together some general conclusions on the reliability and validity of CGE models. 

            What is the basis for our antecedent confidence in the results of a CGE model?  The most fundamental point concerns the degree of confidence we have in the underlying theory.  Second, a given model can be examined in detail to determine the plausibility of its implementation of the underlying theory: is the functional implementation of demand and supply conditions.  And finally, it is possible to evaluate the empirical core of the model: the SAM on which it depends and the calibration of parameters and exogenous variables.  So there is a general basis for confidence in CGE models: the theory is well-confirmed, a given model can be validated as a reasonable implementation of the theory, and the empirical data used to establish the initial conditions of the simulation can be evaluated independently.

            Epistemically, then, the situation of CGE models is this: If the theory accurately identifies the chief mechanisms of systems of the sort S, and if the model adequately represents the causal hypotheses of the theory, and if the observations of s are accurate and reliable, and if there are no significant countervailing causal factors--then we are justified in attaching credence to the causal assertions, counterfactual claims, and predictions of the model.[19]  But note that each of these qualifications introduces its own uncertainties into the credibility of the resulting assertions.  The theory may be incorrect or incomplete; the model may make damaging simplifications (to make the problem more tractable, perhaps); the description of the existing economy may be incorrect; and there may be unusual causal factors at work in this case that are not generally significant in systems of this sort.

            If we can arrive at a general assessment about the reliability of CGE models, it is this.  CGE models are powerful instruments of analysis that permit economists to represent a good deal of the complexity of a modern multi-sectoral economy.  They permit the economist to explore the consequences of a general-equilibrium representation of an economy, representing the complex interconnections across industries, sectors, and income groups.  As such, they promise to shed a good deal of light on the causal processes within such economies.  At the same time, the predictions of such models are not highly reliable.  This is not a consequence of such models being theoretically ill-conceived; on the contrary, as we saw above, the theoretical motivation for these models is compelling.  But the gap between general theoretical principles, abstract and selective implementation of these principles in a particular model, and the net predictive consequences of the resulting model is substantial.  It is quite possible that the predictions of a model that is antecedently credible will nonetheless be wide from the mark.  The only convincing way of confirming that a given model is a good simulation of a given economy is to empirically test it against data drawn from that economy.  But in many of the contexts in which CGE models are relied on this is not possible; indeed, the whole purpose of formulating a CGE simulation is the difficulty or impossibility of deriving such data.  The level of confidence that policy-makers should attach to such predictions, therefore, is somewhat low.  CGE models are a legitimate and useful way of probing possible economic effects, based on a representation of certain important aspects of the economy in question.  They are most useful when they are used cautiously to explore inter-sectoral effects.  But there is such a wide range of alternative and equally supportable formulations of the general principles, and such a high degree of sensitivity of outcomes to the settings of parameters and exogenous variables, that the predictions of such models must be regarded as speculative.

            Finally, let us return to the idea of simulation as experiment.  Do CGE simulations serve as "experiments" for economics?  They do not, if we understand the idea of an experiment in anything like its usage in the natural sciences.  An experiment involves a theory of the causal processes contained within a system S; a prediction derived from the theory about what effects a given kind of intervention P will produce; a controlled empirical situation which embodies the main characteristics of system S, along with the experimenter's ability to produce P; and an empirical observation of the state of the system following P.  The theory predicts an specific outcome and the experiment allows for an empirical test of that prediction.  CGE simulations differ from this in that they lack the crucial empirical test.  A CGE simulation allows us to formulate a prediction about what would happen to the system if a given intervention occurred.  But this prediction does not have the empirical standing of an observation.   So simulations are thought experiments, not genuine experiments with empirical import.



Boyd, Richard N.  1984.  "The Current Status of Scientific Realism".  In Scientific Realism.  See J. Leplin. 

Brown, Harold I. 1979.  Perception, Commitment, and Theory.  Chicago: University of Chicago Press.

Brown, Harold I. 1987.  Observation and Objectivity.  Oxford: Oxford University Press.

Cartwright, Nancy.  1989.  Nature's Capacities and their Measurement.  Oxford: Oxford University Press.

Chenery, Hollis, Jeffrey Lewis, Jaime de Melo, and Sherman Robinson.  1986a.  "Alternative Routes to Development."  In Industrialization and Growth.  See Chenery et al 1986b.

Chenery, Hollis, Sherman Robinson, and Moshe Syrquin. 1986b.  Industrialization and Growth: A Comparative Study.  New York: Oxford University Press.

Chenery, Hollis, and T. N. Srinivasan, eds.  1988.  The Handbook of Development Economics.  Vol. 1.  Amsterdam: North-Holland Press.

Eatwell, John, Murray Milgate, and Peter Newman, ed.  1989.  The New Palgrave: General Equilibrium.  First American ed.  New York: Norton.

Eatwell, John, Murray Milgate, and Peter Newman, ed.  1990.  The New Palgrave: Econometrics.  First American ed.  New York: Norton.

Friedman, Milton. 1953.  Essays in Positive Economics.  Chicago : University of Chicago Press.

Gibbard, Allan, and Hal Varian.  1978.  "Economic Models."  Journal of Philosophy 25: 664-677.

Glymour, Clark. 1980.  Theory and Evidence.  Princeton: Princeton University Press.

Hausman, Daniel.  1981.  "John Stuart Mill's Philosophy of Economics."  Philosophy of Science 48: 363-85.

Hausman, Daniel. 1992.  The Inexact and Separate Science of Economics.  Cambridge: Cambridge University Press.

Hempel, Carl.  1965a.  "Studies in the Logic of Confirmation."  In Aspects of Scientific Explanation.  See Hempel 1965b.

Hempel, Carl. 1965b.  Aspects of Scientific Explanation.  New York : The Free Press.

Hoover, Kevin D.  1988.  The new classical macroeconomics: a sceptical inquiry.  Oxford: Basil Blackwell.

Hoover, Kevin D.  1992.  "Calibration and the Methodology of Quantitative Macroeconomics".  Unpublished manuscript.

Kuhn, Thomas. 1970.  The Structure of Scientific Revolutions.   Second ed.  Chicago: Univ. of Chicago Press.

Lakatos, Imre. 1978.  The Methodology of Scientific Research Programmes: Philosophical Papers.  Vol. 1.   Cambridge: Cambridge University Press.

Laudan, Larry. 1977.  Progress and its Problems.  Berkeley: University of California.

Leplin, Jarrett, ed.  1984.  Scientific Realism.  Berkeley: University of California Press.

Lucas, Robert E., Jr.  1987.  Models of Business Cycles.  Oxford: Blackwell.

Lustig, Nora and Lance Taylor.  1990.  "Mexican Food Consumption Policies in a Structuralist CGE Model."  In Socially Relevant Policy Analysis.  See Taylor 1990.

Mansur, Ahsan and John Whalley.  1984.  "Numerican specification of applied general equilibrium models: estimation, calibration, and data."  in Applied General Equilibrium Analysis.  See Scarf and Shoven.

Mathcad.  1992.   Version 3.1.  Cambridge: MathSoft.

Morgenstern, Oskar. 1963.  On the Accuracy of Economic Observations.  Second ed.  Princeton: Princeton University Press.

Newton-Smith, W. H. 1981.  The Rationality of Science.  Boston: Routledge & Kegan Paul.

Putnam, Hilary. 1975.  Mind, Language, and Reality.  Cambridge: Cambridge University Press.

Rosenberg, Alexander. 1976.  Microeconomic Law: A Philosophical Analysis.  Pittsburgh: University of Pittsburgh Press.

Rosenberg, Alexander. 1992.  Economics: Mathematical Politics or Science of Diminishing Returns?  Chicago: University of Chicago Press.

Rosenberg, Nathan. 1982.  Inside the black box: Technology and economics.  Cambridge: Cambridge University Press.

Scarf, Herbert E., and John B. Shoven, eds.  1984.  Applied General Equilibrium Analysis.  Cambridge: Cambridge University Press.

Soritec: Integrated Econometric and Statistical Analysis System.  1990.  Sorites Group. Springfield, Virginia.

Tarski, Alfred. 1983 [1951].  Logic, Semantics and Metamathematics.  Second ed.  Indianapolis: Hackett.

Taylor, Lance. 1979.  Macro Models for Developing Countries.  New York : McGraw-Hill.

Taylor, Lance, ed.  1990.  Socially Relevant Policy Analysis: Structuralist Computable General Equilibrium Models for the Developing World.  Cambridge: MIT Press.

Weintraub, E. 1979.  Microfoundations.  Cambridge: Cambridge University Press.

Weston, Thomas.  1992.  "Approximate Truth and Scientific Realism."  Philosophy of Science 59: 53-74 .


[1] Thus Chenery et al write, "Our approach is to use a CGE model of a single country as a simulation laboratory for doing controlled experiments designed to explore different development strategies" (Chenery et al, 1986a, p. 311).  I will express skepticism about this notion in the concluding section.

[2] See Irma Adelman's useful discussion of simulation models in the New Palgrave: Econometrics (Eatwell, Milgate, and Newman, eds., 1990).

[3] Hausman (1992); Weintraub; Rosenberg.

[4] Sherman Robinson and Laura D'Andrea Tyson address this feature of CGE models in "Modeling structural adjustment: micro and macro elements in a general equilibrium framework;" Scarf and Shoven, eds., 1984.

[5] Herbert Scarf pioneered a solution technique for general equilibrium models based on the Brouwer fixed-point theorem and a method of piecewise-linear approximations of the equilibrium condition.  See Scarf's "Computation of equilibrium prices" for a presentation of the main outlines of his approach, as well as Michael Todd's companion essay "Efficient methods of computing economic equilibria" (Scarf and Shoven, eds.).  Scarf's entry in the New Palgrave: General Equilbrium is useful as well (Eatwell, Milgate, and Newman, 1989).  But since there are now available fast computer algorithms for solving large systems of non-linear equations, it is unnecessary to construct specialized solution techniques for general equilibrium models.

[6] There are various software packages that implement solution algorithms for models involving large systems of equations.  One such package is Soritec: Integrated Econometric and Statistical Analysis System.  Medium-sized models can be implemented in Mathcad, a widely available and intuitive mathematics software package.

[7] Lance Taylor's Macro Models for Developing Countries (1979) provides a detailed description of the structure and construction of social accounting matrix; the discussion here follows Taylor's.

[8] Mansur and Whalley (1984) provide a substantial discussion of the difficulties confronting the construction of a "benchmark data set" for use in a general equilibrium model; see Scarf and Shoven, eds. (1984).

[9] See Lawrence Lau's comments on Mansur and Whalley for defense of the econometric approach; Scarf and Shoven, eds., 1984.  Kevin Hoover has done very interesting work on the underlying epistemological assumptions of calibration methods (Hoover, 1992).

[10] Note, however, the limitations of these assumptions.

[11] Oscar Morgenstern's trenchant criticism of spurious precision in economic analysis is equally pertinent in this context; Morgenstern, 1963.

[12] Philosophers understand the concept of semantics as encompassing the relations between a sentence and the world: truth and reference (Tarski, 1983; Putnam, 1975).  This understanding connects with the ordinary notion of semantics as meaning, in that the truth conditions of a sentence are thought to constitute the meaning of the sentence.  For a good introduction to contemporary philosophy of science see Brown (1979) and Newton-Smith.

[13] See Hempel, Glymour, Lakatos, Kuhn, Newton-Smith, Brown, and Laudan for discussion of the nature of the standards of theory evaluation employed in different scientific disciplines.

[14] Allan Gibbard and Hal Varian explore the idea of approximate truth in "Economic Models" (Gibbard and Varian, 1978).  See also Weston (1992) for a useful analysis of the logic of inference using approximate truths.

[15] See Boyd (1984) and other essays in Leplin (1984) for a statement of scientific realism.

[16] For more extensive discussion of Friedman's view see Rosenberg (1976, 1992) and Gibbard and Varian (1975).  Positions comparable to Friedman's have been argued more recently by Robert Lucas, Jr. (1987, p. 45) and Charles Plott (this volume).

[17] This appears to lie at the heart of the disagreement between neo-classical and structuralist economic theory; the structuralists argue that institutional features of an economy (e.g. features of the property system, historical strength of the labor movement) are causally significant, whereas neo-classical economists abstract from these features.  See Taylor 1990 for extensive discussion of the structuralist viewpoint.

[18] See James MacKinnon's thoughtful suggestions along these lines in his comment on Dale Jorgenson's CGE model of the US economy; Scarf and Shoven, eds., 1984.

[19] Note the correspondence between this procedure and the hypothetico-deductive model of explanation.

Return to Home Page