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Applied General-Equilibrium Models of Taxation and International Trade: An Introduction and Survey Author(s): John B. Shoven and John Whalley Source: Journal of Economic Literature, Vol. 22, No. 3 (Sep., 1984), pp. 1007-1051 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/2725306 Accessed: 04/11/2008 12:16

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http://www.jstor.org Journal of Economic Literature Vol. XXII (September 1984), pp. 1007-1051

Applied General-EquilibriumModels of Taxation and International Trade: An Introduction and Survey

By JOHN B. SHOVEN Stanford University and National Bureau of Economic Research and JOHN WHALLEY University of Western Ontario

We wish to acknowledge the help of three referees and of John Pencavel on several earlier drafts, as well as the assistance of the modelers, whose work is referred to in the paper. They corrected our lack of understanding of their work and provided many other helpful comments. Excellent research and bibliographical assistance have been pro- vided by Debbie Fretz, Radwan Shaban, and Janet Stotsky. Helpful comments have been made by CharlesBallard, Michael Boskin, Lans Bovenberg, Sylvester Damus, Harvey Galper, Glenn Harrison, Gor- don Lenjosek, Jack Mutti, Serena Ng, T. N. Srinivasan, Charles Stuart, and Eric Toder. The authors also acknowledgefinancial sup- port from the National Bureau of Economic Research, the National Science Foundation, International Business Machines, and the Social Sciences and Humanities Research Council: Ottawa, Canada.

I. Introduction to use these models to evaluate policy op- tions by specifying production and de- THE BODY OF RESEARCH discussed here mand parameters and incorporating data is part of a wider series of develop- reflective of real economies. Most contem- ments which, in the last few years, has porary applied general-equilibrium mod- become known as "applied general-equi- els are numerical analogs of traditional librium analysis." The explicit aim of this two-sector general-equilibrium models literature is to convert the Walrasiangen- that James Meade, Harry G. Johnson, Ar- eral-equilibrium structure (formalized in nold Harberger, and others popularized the 1950s by Kenneth Arrow, Gerard De- in the 1950s and 1960s. Earlier analytic breu, and others) from an abstract repre- work with these models has examined the sentation of an economy into realistic distortionary effects of taxes, tariffs and models of actual economies. The idea is other policies, along with functional inci- 1007 1008 Journal of Economic Literature, Vol. XXII (September 1984) dence questions. Recent applied models, work. A final important source of stimulus surveyed here, provide numerical esti- has been an ingenious computer algo- mates of efficiency and distributional ef- rithm for the numerical determination of fects within the same framework. the equilibrium of a Walrasiansystem, de- The Walrasianmodel provides an ideal veloped by Herbert Scarf in 1967. Despite framework for appraising the effects of subsequent extensions to his original al- policy changes on resource allocation and gorithm, and more recently the use of al- for assessing who gains and loses, policy ternative solution techniques, Scarfs work impacts not well covered by empirical has been instrumental in persuading some macro models. We discuss a number of of the recent generation of mathemati- ways in which these models are already cally-trained economists to approach gen- providing fresh insights into long-standing eral equilibrium from a computational policy controversies. Due to space con- and, ultimately, a practical perspective. straints, we will limit our discussion to re- Applied general-equilibrium tax models cent modeling efforts in the fields of taxa- have been used to analyze such policy ini- tion and international trade. tiatives as integrating personal and corpo- The value of these computational mod- rate taxes, the introduction of value-added els is that a computer removes the need taxes, and indexing the tax system. In in- to work in small dimensions: Much more ternational trade models the impacts of detail and complexity can be incorporated trade policy changes on resource alloca- than in simple analytic models. For in- tion within countries, custom union issues, stance, tax policy models can simulta- international trade negotiations under the neously accommodate several taxes. This GATT, and North-South trade questions is important because taxes compound in have been analyzed. effect with other taxes even when evaluat- The plan of this paper is as follows: Sec- ing changes in only one tax. Models involv- tion 2 presents a simple numerical exam- ing 30 or more sectors and industries are ple designed to illustrate how applied gen- commonly employed, providing substan- eral-equilibrium models operate; Section tial detail for policymakers concerned 3 discusses how the methods illustrated with feedback effects of policy initiatives by the numerical example can be imple- directed only at specified products or in- mented (the choice of parameter values dustries. and functional forms, the use of data, solu- The models reported here extend Was- tion methods, and how policy conclusions sily Leontiefs work on empirical Walra- are formulated); Section 4 presents the sian models based on fixed input-output main features of recent tax models and coefficients by incorporating substitution highlights their most important policy im- effects in both production and demand, plications; Section 5 similarly discusses and by including more than one con- trade models; we close with an evaluation sumer. Earlier work by three economists of the approach and outline what could provides background for much of this ac- be useful directions for further research tivity. One is Leif Johansen (1960) who in this area. formulated the first empirically based, multi-sector, price-endogenous model an- II. What Is Applied General-Equilibrium alyzing resource allocation issues. He ap- Analysis? plied this model to policy questions in Norway. Another is Arnold Harberger Applied general-equilibrium analysisin- (1962), who was the first author to investi- volves using a numerically specified gen- gate tax policy questions numerically in eral-equilibrium model for policy evalua- a two-sector general-equilibrium frame- tion. However, despite the widespread Shoven and Whalley: Applied General-Equilibrium Models 1009 use of the term "general equilibrium" in representative of those actually used to modern economics, the precise meaning analyze policy issues. We consider a model of the term is often not fully defined. Ev- with two final goods (manufacturing and eryone seems to agree that a general-equi- nonmanufacturing),two factors of produc- librium model is one in which all markets tion (capital and labor), and two classes clear in equilibrium; there seems to be of consumers. Consumers have initial en- less agreement as to the essential elements dowments of factors, but have no initial of structure which underlie the equilib- endowments of goods. A "rich"consumer rium formulation. group owns all the capital, while a "poor" Our use of the term corresponds to the group owns all the labor. Production of well-known Arrow-Debreu model, elabo- each good takes place according to a con- rated on in Arrow and F. H. Hahn (1971). stant-returns-to-scale, constant-elasticity- The number of consumers in the model of-substitution (CES)production function, is specified. Each of them has an initial and each consumer class has commodity endowment of the N commodities and a demand functions generated by maximiz- set of preferences, resulting in demand ing a CES utility function subject to its functions for each commodity. Market budget constraint. There are no consumer demands are the sum of each consumer's demands for factors (i.e., no labor-leisure demands. Commodity market demands choice). Even though the two consumer- depend on all prices, are continuous, non- two producer nature of this example negative, homogeneous of degree zero means that it is similar to the Harberger (i.e., no money illusion) and satisfy Walras' (1962) tax model and could be solved ana- Law (i.e., that at any set of prices, the total lytically, the solution techniques used value of consumer expenditures equals here are applicable to larger and more consumer incomes). On the production sophisticated models. side, technology is described by either The production functions for the exam- constant returns to scale activities or non- ple are given by increasing returns to scale production functions. Producers maximize profits. The zero homogeneity of demand func- Qi=4 LiL, 1 (1) tions and the linear homogeneity of profits in prices (i.e., doubling all prices doubles (2-1)]1 money profits) implies that only relative + (1 -8i)Ki C , i=1,2 prices are of any significance in such a model; the absolute price level has no im- where Qi denotes output of the ith indus- pact on the equilibrium outcome. try, 4i is the scale or units parameter, FJ Equilibrium in this model is character- is the distribution parameter, Ki and L. ized by a set of prices and levels of produc- are the capital and laborfactorinputs, and tion in each industry such that market de- vi is the elasticity of factor substitution. mand equals supply for all commodities The factor demand functions derived (including disposals if any commodity is from cost minimization for these produc- a free good). Since producers are assumed tion functions (1) are: to maximize profits, this implies that in the constant-returns-to-scalecase no activ- ity (or cost-minimizing techniques for pro- L4 = 4l'Qi [i duction functions) does any better than (2) break even at the equilibrium prices. ] fi To illustrate how these models work, we present a simplified numerical example + (11_ 8i) 3Z)PL jJ(li)J (1 - 1010 Journal of Economic Literature, Vol. XXII (September 1984) and, variables, the four prices P1, P2, PL, PK, and the eight quantities Xl, X2, Xl, X2, and K1, K2, L1, L2 which meet the re- quired conditions for equilibrium. The equilibrium conditions in this O'i model are that market demand equals (1- i) market supply for all inputs and outputs, and that profits are zero in each industry. These can be written out more fully as: where PK and PL are the per-unit factor costs for the industry (including factor (a) Demands equal supply for factors taxes if applicable). The CES utility functions are given by Ki(PL, PK, Qi) (6 + - 1 (Cc-1) - C K2(PL, PK, Q2)=K 2 CC (CC ((CC-1 (4) Li(PL, PK, Qi) (7 + L2(PL, PK, Q2) = ( where Xc is the quantity of good i de- where K1(PL, PK, Qi), K2(PL, PK, Q2), manded by the Cth consumer, ac are share L1(PL, PK, Qi) and L2(PL, PK, Q2) are given parameters, and oc is the substitution elas- by (2) and (3). ticity in consumer c's CES utility function. The consumer's budget equation is P1X (b) Demands equal supply for goods ? P2X2 < PL WL + PK WK = IC, where P1 and P2 are the consumer prices for the Xl (P1, P2, PL, PK) (8) two output commodities, WLand WKare +X (P1, P2, PL, PK) = Q ( consumer c's endowment of labor and Xl P2, PL, capital, and IC is the income of consumer (P1, PK) + = c. If this utility function is maximized, sub- X2(P1, P2, PL, PK) Q2 ject to the budget constraint, the demand functions are: where Xl, Xi, X2, and X2, are given by a- maximizing (4), subject to consumer bud- c~= icIc get constraints, and Q1 and Q2 are given l - - crc)) picc (acP cC)+ acpl (5) by (1). Finally, we have: i 1, 2; c = 1, 2. (c) Zero profit conditions hold in both industries In this simple model, there are ten param- eters whose values need to be specified: PKKi(PL, PK, Qi) (10) six production function parameters which + PLL1(PL,PK, Qi) = P1Q1 affect the supply of the two products (i.e., 8s, and cr- for i = 1, 2), and four utility PKK2(PL, PK, Q2) (P, + = function parameters determining the de- PLL2(PL, PK, Q2) P2Q2. mand for each of the two products by each Given the four commodity and factor of the two consumers (i.e., al, a2, ,r1,and prices, one can evaluate the demands for 0c2). There are four exogenous variables commodities by all consumers because whose values must also be specified: the factor prices determine consumer in- endowment of labor (WL) and capital (WK) comes (which give the position of each for each of the two consumers. The solu- consumer's budget constraint), and com- tion to the model is characterized by 12 modity prices give the slope of the budget Shoven and Whalley: Applied General-Equilibrium Models 1011

constraint. The factor requirements to meet commodity demands are given by TABLE 1 (2) and (3). An equilibrium is therefore SPECIFICATION OF PRODUCTION PARAMETERS, DEMAND PARAMETERS, AND ENDOWMENTS FOR characterized by four prices, PL, PK, Pl, P2, such that equations (6)-(11) hold. A SIMPLE GENERAL-EQUILIBRIUM MODEL Once the parameters of these produc- Sector Production Parame- tion and demand functions are specified ters and the factor endowments are known, (Di 8i O'i a complete general-equilibrium model is Manufacturing 1.5 .6 2.0 available. Tax and other policy variables Nonmanufacturing 2.0 .7 .5 can then be added as desired. Demand Parameters By way of example, in Table 1 we list sample numerical values for all the param- Rich Consumers Poor Consumers eters and the exogenous variables in this ac a c qC ac aLc C c model. We have then solved this example 0.5 0.5 1.5 0.3 0.7 0.75 using Olin Merrill's (1972) fixed-point al- Endowments gorithm, a refinement of the Scarf algo- rithm. This algorithm finds a set of market K L clearing prices for goods and factors, pro- Rich Households 25 0 viding a solution to the simultaneous non- Poor Households 0 60 linear equations above, (6)-(11). The equilibrium solution for this exam- revenues. For a given tax program (that ple (the values of the endogenous varia- is, for a specified tax rate imposed on a bles) is shown in Table 2. At the computed particular commodity or factor) tax reve- set of equilibrium prices, total demand for nues will be determined once demands, each output exactly matches the amount production levels, and factor employ- produced, and producer revenues equal ments are known. Demands also depend consumer expenditures. Labor and capital on tax proceeds since these provide in- endowments are fully employed, and con- come to one or more of the agents in the sumer factor incomes equal producer fac- economy. The solution suggested by Sho- tor costs. Because of our assumption of ven and Whalley is to solve not only for constant returns to scale, the per-unit cost equilibrium prices as in the example in each industry equals the selling price, above, but also for equilibrium tax reve- meaning that economic profits are zero. nues. In the simple case where all govern- The expenditures of each household ex- ment revenues are redistributed to con- haust its income. Since only relative prices sumers (i.e., no provision of public goods affect behavior in general-equilibrium and services), this means that in equilib- models such as this, we have chosen labor rium the transfer payments made by gov- as numeraire. ernment to consumers equal taxes col- To illustrate how a general-equilibrium lected by government. This is another model can be adapted for policy evalua- condition that the equilibrium must sat- tion work, we consider the same numeri- isfy. cal example as above, but with a tax policy We assume the same values of the pa- regime added using the approach as in rameters and exogenous variablesas given Shoven and Whalley (1973). The funda- in Table 1, along with an exogenously mental difficulty in modifying the model specified tax rate of 50 percent on each to incorporate taxes is the interdepen- unit of capital income generated in the dence of demands and supplies, and tax manufacturing sector. In the disburse- 1012 Journal of Economic Literature, Vol. XXII (September 1984)

TABLE 2 EQUILIBRIUM SOLUTION FOR ILLUSTRATIVE SIMPLE No TAX GENERAL-EQUILIBRIUM MODEL (PARAMETER VALUES SPECIFIED IN TABLE 1)

EquilibriumPrices ManufacturingOutput 1.399 NonmanufacturingOutput 1.093 Capital 1.373 Labor 1.000

Production Quantity Revenue Capital Capital Cost Manufacturing 24.942 34.898 6.212 8.532 Nonmanufacturing 54.378 59.439 18.788 25.805 Total 94.337 25.000 34.337

Cost Per Labor Labor Cost Total Cost Unit Output Manufacturing 26.366 26.366 34.898 1.399 Nonmanufacturing 33.634 33.634 59.439 1.093 Total 60.000 60.000 94.337

Demands Manufacturing Nonmanufacturing Expenditure Rich Households 11.514 16.674 34.337 Poor Households 13.428 37.704 60.000 Total 24.942 54.378 94.337

Labor Income Capital Income Total Income Rich Households 0 34.337 34.337 Poor Households 60.000 0 60.000 Total 60.000 34.337 94.337 ment of tax revenues, we assume that rium values in Table 2 as the base for the rich households receive 40 percent, with tax. In the no-tax regime the price of capi- the remaining 60 percent going to poor tal is 1.373 and the employment of capital households. The new equilibrium solu- in manufacturing is 6.212. A 50 percent tion is shown in Table 3. tax rate on capital income in manufactur- It is useful to illustrate how a general- ing might therefore be expected to raise equilibrium calculation differs from other 4.265 units of revenue (i.e., 50 percent of less satisfactory methods. One purpose of 1.373 x 6.212). In fact, this would be a such an equilibrium calculation might be seriously misleading estimate of tax reve- to calculate the tax revenues that accrue nues. When all the general-equilibrium to government from the taxes. A naive responses are allowed for, the new reve- revenue estimate might use the equilib- nue is only 2.278. Compared with the no- Shoven and Whalley: Applied General-Equilibrium Models 1013

TABLE 3 EQuILIBRIUM SOLUTION FOR ILLUSTRATIVE SIMPLE GENERAL-EQuILIBRIUM MODEL WITH 50% TAX ON MANUFACTURING CAPITAL

EquilibriumPrices ManufacturingOutput 1.467 NonmanufacturingOutput 1.006 Capital 1.128 Labor 1.000

Production Capital Cost Quantity Revenue Capital (including tax)

Manufacturing 22.387 32.830 4.039 6.832 Nonmanufacturing 57.307 57.639 20.961 23.637 Total 90.469 25.000 30.469

Cost Per Labor Labor Cost Total Cost Unit Output

Manufacturing 25.999 25.999 32.831 1.467 Nonmanufacturing 34.001 34.001 57.638 1.006 Total 60.000 60.000 90.469

Demands Manufacturing Nonmanufacturing Expenditure

Rich Households 8.989 15.827 29.102 Poor Households 13.398 41.480 61.367 Total 22.387 57.307 90.469

Labor Income Capital Income Transfers Total Income

Rich Households 0 28.191 .911 29.102 Poor Households 60.000 0 1.367 61.367 Total 60.000 28.191 2.278 90.469 tax equilibrium, the relative price of man- equilibrium effects, therefore, need to be ufacturing to nonmanufacturing output taken into account in revenue estimation, rises, while the net-of-tax price of capital or in any other policy issue arising from falls. However, the tax-inclusive cost of such a tax. capital in manufacturing increases, lead- A question frequently addressed by ing to a less capital-intensive method of these models is whether any particular production in manufacturing. Less manu- policy change is welfare-improving. In facturing and more nonmanufacturing this instance, policy appraisal using these output is produced because of the tax. techniques usually relies upon a compari- Expenditures of "poor" (labor-owning) son between an existing equilibrium (i.e., households increase, while those of "rich" with unchanged tax policies), and a coun- (capital-owning) households fall. General- terfactual equilibrium computed with 1014 Journal of Economic Literature, Vol. XXII (September 1984) modified policies. Because the underlying theoretical structure of these models is so TABLE 4 firmly rooted in traditional microtheory, WELFARE MEASURES OF THE IMPACT OF A 50% a common procedure is to construct nu- TAX ON CAPITAL ON MANUFACTURING IN merical welfare measures of the gain or TABLE 1 loss. Hicksian Hicksian The measures most widely employed Equivalent Compensating are Hicksian compensating and equiva- Variations Variations lent variations associated with the equilib- Rich Households -4.55 -4.45 rium comparison. The compensating vari- Poor Households +3.99 +3.83 ation (CV) takes the new equilibrium Total -0.56 -0.62 incomes and prices, and asks how much income must be taken away or added in Welfare Loss as a order to return households to their pre- Percent of change utility level. The equivalent varia- National Income 0.62% 0.66% tion (EV) takes the old equilibrium in- Welfare Loss as a comes and prices and computes the Percent of Tax change needed to achieve new equilib- Revenues 24.59% 27.23% rium utilities. For a welfare-improving change, the CV is negative and the EV Decline in Welfare as a Percent of is positive, although it is quite common Marginal Dollar to employ a sign convention so that a posi- of Revenues tive value for either measure indicates a Raised and welfare improvement. For the economy Returned through as a whole, the welfare costs of the taxes Transfers 79.3% 79.3% are measured by aggregating the CVs or EVs across individuals.' where UN, UO and IN, 10 denote the new Because the utility function (4) in our and old levels of utility and income, re- numerical example is linear homoge- spectively. neous, these welfare measures are espe- In Table 4 we report the Hicksian com- cially easy to compute. Adopting the sign pensating and equivalent variations asso- convention that for a welfare-improving ciated with the 50 percent tax on capital change both the CV and EV are positive, income in manufacturing considered in yields Table 3. Here, we compare a no-tax (Pa- reto optimal) equilibrium to an equilib- (UN- CV = UO) IN (12) rium after the imposition of taxes. The fact UN that these taxes are distorting is indicated by the aggregate welfare loss. However, the redistribution caused by the factor UO price change means that poor households ' As noted by John Kay (1980), the sum of EVs is gain and rich households lose. The aggre- a more easily interpreted measure if repeated pair- wise comparisons are being performed. This is be- gate welfare cost of the tax is around 0.6 cause old incomes and prices are used and are typi- percent of national income, a number sim- cally the same in the sequence of pairwise comparisons. Further, aggregation difficulties may ilar to Harberger's (1966) estimate of the arise in using an arithmetic sum of EVs or CVs as cost of the corporate tax in the U.S. where a welfare criterion, even though they are widely the tax discriminant was not so different used elsewhere, including cost-benefit analysis. Some from that used in this example. Although of these difficulties are discussed in Robin Boadway (1974). 0.6 percent of GNP may not seem to be Shoven and Whalley: Applied General-Equilibrium Models 1015 a large number, when measured against policy regimes and to assess impacts of tax revenues the welfare cost appears the change. much larger. The deadweight loss is One point frequently made is that this around one-fourth of tax revenues, sug- approach would not be particularly in- gesting that this distortionary tax is an in- structive if the equilibrium solution in any efficient mechanism for raising revenues. of these models were not unique for any Also, as stressed by Edgar Browning particular tax or tariff policy. Uniqueness, (1976), Dan Usher (1982), Charles Stuart or the lack of it, has been a long-standing (forthcoming), and Charles Ballard, Sho- interest of general-equilibrium theorists ven and Whalley (1982), the marginal (Timothy Kehoe 1980). There is, however, costs of raising an extra dollar in revenues no theoretical argument that guarantees will significantly exceed these average uniqueness in the applied models de- cost estimates; in this case, we find the scribed later. With some of the models, marginal deadweight loss to be 79 cents researchers have conducted ad hoc nu- for each extra dollar raised. merical experimentation (approaching Later in the paper we describe models equilibria from different directions and at constructed to analyze alternative tax and different speeds), but have yet to find a trade policies in a number of countries. case of nonuniqueness. In the case of the The differences between these models tax model of the U.S. due to Ballard, Don and the numerical example above lie in Fullerton, Shoven and Whalley (forthcom- their dimensionality (i.e., in the number ing), uniqueness has been numerically of sectors modeled), their parameter spec- demonstrated by Kehoe and Whalley ification procedures which are based on (1982). The current working hypothesis empirical estimates, and their inclusion of adopted by most modelers seems to be more complex policy regimes than a sim- that uniqueness can be presumed for all ple tax on one factor in one sector. The of the models discussed here until a clear tax models vary in the degree to which case of nonuniqueness is found. they model the whole tax system; some Many other problems beyond the possi- attempt to incorporate the entire tax bility of nonuniqueness are also encoun- structure, while others include only those tered in designing and using these models. portions of the tax system relevant to the What type of model is to be used? Should issues being directly examined. In the it, for instance, be a traditionalfixed-factor trade models, a key difference is between static model, or should it have dynamic those models that are multicountry or features? Once the model form is deter- global in orientation, and those that exam- mined, how are functions and parameter ine how trade with the rest of the world values to be chosen? How are foreign affects individual countries. trade, investment, government expendi- Applied general-equilibrium analyses, tures, and a range of other complicating then, are attempts to assemble and use features to be treated? How is the model models for policy evaluation. In the tax to be solved? And, finally, even after the models, for instance, a proposal may be model has been solved, how are equilibria for the corporate tax to be abolished and to be compared; that is, which summary replaced by a value-added tax. In trade statistics are to be used in evaluating the models, multilateral tariff cuts proposed policy change? These questions apply in a set of international negotiations could equally to all applied general-equilibrium be the issue. Using applied general-equi- modeling efforts whether or not they are librium techniques, it is possible to com- directed towards tax and trade-policy pute alternative equilibria for different evaluation. We therefore now turn to a 1016 Journal of Economic Literature, Vol. XXII (September 1984) discussion of how these issues are dealt natural to retain the same basic theoreti- with in the design of applied models. cal structures. This way researchers can use the intuition gleaned from theoretical III. Implementing Applied General- work to guide numerical investigations of Equilibrium Analysis policy alternatives. Second, most data on which the numeri- A. Choosing the Model cal specifications are based come in a form Although the appropriate general- consistent with two-factor models. For in- equilibrium model for tax or trade policy stance, national accounts data identify analysisdepends partly on the focus of the wages and salaries and operating surpluses model, most models currently in use have as major cost components. This suggests a similar form. They are variants of static, a model with capital and labor as inputs. two-factor models that have long been Input-output data provide intermediate employed in public finance and interna- transactiondata, with value added broken tional trade, and are associated with the down in a similar way. work of Eli Heckscher, Bertil Ohlin, Paul Finally, the partition between goods Samuelson, James Meade, Harry Johnson, and factors can be used in applied models and Arnold Harberger. Most computa- so as to simplify computation and sharply tional models involve more than two reduce the costs of repeated solution. This goods, while aggregating the factors of is done by using factor prices to generate production into two broad types, capital cost-covering goods prices, calculating and labor. In some models, these compos- consumer demands and evaluating the de- ite factors are disaggregated into sub- rived demands for factors (i.e., those groups (e.g., labor, distinguished by skilled amounts needed to meet consumer de- and nonskilled). Intermediate transactions mands). In this way, even a model with are also usually incorporated, either large numbers of goods can be solved by through fixed or flexible coefficient input- working with a system of excess factor de- output matrices. mands only. This simplification not only Perhaps a natural question is: Why have reduces execution costs for solution of most models evolved in this way, when models, but also makes feasible the incor- it is possible to use more general specifica- poration of more detail in the treatment tions, possibly involving joint production2 of households and goods. and more alternative inputs than capital In some cases, static equilibrium models and labor composite factors? Although it have been sequenced through time to re- is possible that in future work these fea- flect changes in an economy's capital stock tures will gradually appear, at the present due to net saving. These models have three reasons seem to account for the pop- been used to analyze intertemporal issues ularity of basic two-factor structure in ap- in tax policy, such as whether a move from plied work. an income tax to a consumption tax (under First, many policy issues have already which saving is less heavily taxed) is desira- been analyzed theoretically using this ble. Under this approach, a series of single- framework. If the major contribution of period equilibria are linked through sav- numerical work is to advance from quali- ing decisions that change the capital stock tative to quantitative analysis, it is clearly of the economy through time. Saving de- pends on the expected future return to 2The ORANI model (Peter Dixon, Brian Parmen- assets acquired in the current period, with ter, John Sutton and D. Vincent 1982) incorporates myopic expectations (i.e., expected future joint production with empirically estimated transfor- mation frontiers. returns on assets equal current returns) Shoven and Whalley: Applied General-Equilibrium Models 1017 frequently assumed to simplify computa- tentions), which are based either on con- tions. At any point in time the economy stant expenditure shares in static models has a stock of capital and a labor endow- or on intertemporal utility maximization ment; saving today augments the capital in dynamic formulations. Government ex- stock in all future periods. In each period penditures are usually broken down into a general equilibrium is computed in transfersand real expenditures. The latter which all markets clear, including that for are frequently determined from utility- newly-produced capital goods. The econ- maximizing behavior for government: i.e., omy thus passes through a sequence the government is treated as a separate of single-period equilibria that change consuming agent that buys public goods through time as the capital stock grows. and services. In a few cases, models have A tax policy that encourages higher saving been used with public goods in household will also cause lowered consumption in utility functions, although this complicates the initial years, with an eventual higher the tax models. consumption level due to the larger capi- B. Choosing Functional Forms tal stock. A further issue in choosing one's model The major constraints on the selection concerns the treatment of external sector of demand and production functions in transactions. In the multicountry trade all the applied models is that they be both models, a common approach is to use the consistent with the theoretical approach so-called "Armington"formulation, which and analytically tractable. The first con- treats similar products produced in differ- straint involves choosing functions that ent countries as different goods. This dif- satisfy the restrictions listed in the presen- fers from theoretical Heckscher-Ohlin tation of general-equilibrium models, models in which it is assumed that prod- above, such as Walras' Law for demand ucts are homogeneous across countries. functions. The second requires that the Among other reasons, the Armington for- demand and supply responses of the econ- mulation is usually adopted in order to omy be reasonably easy to evaluate for accommodate the phenomenon of coun- any price vector considered as a candidate tries both importing and exporting the equilibrium solution for the economy. same good (cross hauling). The external This largely explains why the functional sector specification is also important in the forms used are so often restricted to the tax models, since the effects of tax policies family of "convenient" forms (Cobb- on an economy which is a taker of rental Douglas, Constant Elasticity of Substitu- rates on world capital markets will be sig- tion (CES), Linear Expenditure System nificantly different from those for a closed (LES), Constant Ratios of Elasticities economy. Although international capital of Substitution, Homothetic, (CRESH) mobility is usually ignored, Lawrence Translog, and others). Goulder, Shoven and Whalley (1983) have The choice of a specific functional form shown how its incorporation can change typically depends on how elasticities are the analysisof tax policy options quite sub- to be used in the model. This point is best stantially compared to a model with im- illustrated by considering the demand mobile capital. side of these models. Demands derived Other issues in model design include from Cobb-Douglas utility functions are the treatment of investment and govern- easy to work with, but have the restric- ment expenditures. Investment usu- tions of unitary income and uncompen- ally reflects household-saving decisions sated own-price elasticities, and zero (broadly defined to include corporate re- cross-price elasticities. These restrictions 1018 Journal of Economic Literature, Vol. XXII (September 1984) are typically implausible, given empirical of differentiating products by country is estimates of elasticities applicable to any used. particular model, but can only be relaxed C. Selecting Parameter Values by using more general functional forms. With CES functions, unitary own-price Parameter values for the functional elasticities no longer apply. However, if forms are frequently crucial in determin- all expenditure shares are small, the com- ing results of policy simulationsgenerated pensated own-price elasticities equal the by the applied models. The procedure elasticity of substitution in the prefer- most commonly used to select parameter ences, and it may be unacceptable to values has come to be labeled "cali- model all commodities as having essen- bration" (Ahsan Mansur and Whalley tially the same compensated own-price 1984). This procedure is outlined in Fig- elasticities. A response to this difficulty is ure 1. The economy under consideration to use hierarchical or nested CES func- is assumed to be in equilibrium, a so-called tions, adding further complexity in struc- "benchmark" equilibrium. The parame- ture. The unitary income elasticity feature ters of the model are chosen such that the of the Cobb-Douglas functions can also be model can reproduce this data set as an relaxed. One way is to use LES functions equilibrium solution.3If CES or LES func- with a displaced origin, but then the origin tions are used in the model, exogenously displacements need to be specified. The specified elasticity values (usuallybased on general approach seems to be one of se- literature estimates) are also required in lecting the functional form that best al- this procedure because the benchmark lows key parameter values (e.g., income data only give price and quantity observa- and price elasticities) to be incorporated, tions associated with a single equilibrium. while retaining tractability. On the demand side, for instance, only On the production side, CES value- the slope of the budget constraints at the added functions are usually used to allow equilibrium consumption quantities is for substitution between primary factors. given by the benchmark data. The param- If more than two factors are used, hierar- eter values thus generated can then be chical CES functions are again used. The used to solve for the alternative equilib- intermediate production functions are rium associated with any changed policy sometimes modeled as fixed coefficients; regime. These are usually termed "coun- on other occasions, some intermediate terfactual" or "policy replacement" equi- substitutability is allowed. In the interna- libria. tional trade model one specification used In practice, benchmark equilibria are is to have fixed coefficients in terms of constructed from national accounts and composite goods, but with substitution other government data sources. In gen- possible among the components of the eral, the information will be inconsistent composite. By way of example, a fixed (e.g., payments to labor from firms will steel requirement per car may be speci- not equal labor income received by house- fied, but with substitution between im- ported and domestic steel represented by 3An additionalimportant feature of this procedure CES functions. This may be necessary be- is that once calibrationis complete, it shouldbe possi- ble to reproduce the benchmark equilibrium data cause of the large amount of trade in inter- set as an equilibrium solution of the model. This is mediate products and the unrealistically the replication check referred to in Figure 1, which low import price elasticities that fixed serves as an important accuracy test of a computer code. If the replication check fails, then a program- coefficient intermediate production ming error has been discovered and the coding must would imply if the Armington treatment be investigated further. Shoven and Whalley: Applied General-Equilibrium Models 1019

Basic Data for economy for single year or average of years (national accounts, household income and expenditure, input-output tables, tax data, trade, and balance of payments)

Adjustments for mutual consistency BENCHMARK EQUILIBRIUMDATA SET

Choice of Replication functional form Specification of ai and CALIBRATION Check -* to Exogenous Benchmark Equilibrium Elasticity Values

Policy Change Specified

"Counterfactual"Equili- brium computed for new policy regime

E Further policy Policy Appraisal based on X changes to be pairwise comparison I evaluated between counterfactual T ? and benchmark

Figure 1. Flow chart outlining calibration procedures and model use in typical applied general- equilibrium model holds), and a number of adjustments are ally produced in value terms, units must required to the basic data to ensure that be chosen for goods and factors so that equilibrium conditions hold. Some data separate price and quantity observations are taken as correct and others are ad- are obtained. A commonly used units con- justed to be consistent in the process of vention, originally adopted by Harberger, generating a benchmark data set. The is to choose units for both goods and fac- construction of data sets of this type is de- tors so that they have a price of unity in scribed in Kemal Dervis, Jaime de Melo the benchmark equilibrium. and Sherman Robinson (1982), France St. Typically, calibration involves only one Hilaire and Whalley (1983), John Piggott year's data, or a single observation repre- and Whalley (forthcoming), and Ballard, sented as an average over a number of Fullerton, Shoven and Whalley (forthcom- years. A crucial point in using calibration ing). Because the benchmark data are usu- is that because of the reliance on a single 1020 Journal of Economic Literature, Vol. XXII (September 1984) observation, the benchmark data typically work that often simplifies the structure do not identify a unique set of values for of the economic model to allow for sub- the parameters in any model. Particular stantial richness in statistical specification, values for the relevant elasticities are usu- here the procedure is quite the opposite. ally specified on the basis of other re- The richness of the economic structure search, and these serve to identify only allows for a much cruder statistical uniquely the other parameters of the model which, in the case of calibration model along with the equilibrium obser- to a single year's data, becomes determin- vation. This typically places a lot of reli- istic. ance on literature surveys of elasticities Once the calibration procedure is com- and, as many of the modelers have ob- pleted, a fully specified numerical model served in discussing their own work, it is is available that can be used for policy surprising how sparse (and sometimes analysis.As indicated in Figure 1, any pol- contradictory) the literature is on some icy change can be considered and a coun- elasticity values. Also, although this proce- terfactual equilibrium computed for the dure might sound straightforward,it is of- new policy regime. Policy appraisal then ten exceedingly difficult because each proceeds on the basis of pairwise compari- study is different from every other and sons of counterfactual and benchmark recognizing and taking account of these equilibria. If further policy changes are differences is necessary. to be-evaluated, the new policy is incorpo- The specification of elasticities is most rated, and the resulting counterfactual easily thought of as determining the cur- equilibrium is also compared to the vature of isoquants and indifference sur- benchmark. faces, with their position given by the Because the use of deterministic cali- benchmark equilibrium data. For Cobb- bration rather than stochastic estimation Douglas demand or production functions, in these models is often troubling to a single price and quantity observation is econometricians, it is perhaps worthwhile sufficient to determine the parameters of to outline some reasons why this cali- the function uniquely. For CES functions, bration approach is so widely used. First, extraneous values of substitution elastici- in some models many thousandsof param- ties are required, because the curvature eters are involved, and to estimate simul- of indifference curves and isoquants taneously all of the model parameters us- (given by the single elasticity parameter) ing time series methods would require cannot be inferred from the benchmark either unrealistically large numbers of ob- data. Similarly,for LES demand functions, servations or overly severe identifying re- income elasticities are determined once strictions. Although partitioning models the origin coordinates for utility measure- into submodels (such as a demand and pro- ment are known. duction system) may reduce or overcome A further feature of calibration is that this problem, partitioning does not fully no statistical test of the model specifica- incorporate all the equilibrium restric- tion which has been chosen is applied, be- tions that are emphasized in calibration. cause a deterministic procedure of cal- Second, as mentioned, benchmark data culating parameter values from the equi- sets are in value terms, and the decompo- librium observation is employed. The sition into separate price and quantity ob- procedure thus uses the key assumption servations makes it difficult to sequence that the benchmark data represent an equilibrium observations with consistent equilibrium for the economy under inves- units through time as would be required tigation. In contrast to recent econometric for time series estimation. Shoven and Whalley: Applied General-Equilibrium Models 1021

Thus far, these problems have largely analytic solution of models in which all excluded complete econometric estima- substitution elasticities are identical. tion of general-equilibrium systems, al- Another device, originating in Johan- though some progress in this direction has sen's work, is to use a linearized equilib- been made in work by Kenneth Clements rium system to solve for an approximation (1980), Mansur(1980), and Dale Jorgenson to an equilibrium.4 This procedure has (1984). Mansur,for instance, notes the dif- been refined by Dixon, Parmenter, Sutton ficulties in formulating a maximum likeli- and Vincent (1982) who use a multi-step hood procedure incorporating equilib- procedure so that approximation errors rium restrictions. Michael Allingham are eliminated. A similar approach of re- (1973) has also worked on estimation of moving linear approximation errors in a general-equilibrium systems but for a lin- Johansen system by iterated linearization ear system of demand and supply func- is used by Lans Bovenberg and Wouter tions rather than preferences and produc- Keller (1983b). tion functions. Jorgenson provides esti- Execution costs for existing models us- mates for an economy-wide system of cost ing all these techniques currently seem functions. manageable, even on a production run ba- sis. No standard off-the-shelf computer D. Solving Models for Counterfactual routine has yet emerged for the complete Equilibria sequence of data adjustment, calibration, Early applied models either used Her- and equilibrium computation due to the bert Scarfs algorithm (1967, 1973) for so- complexities involved in each application lution or approximated an equilibrium us- of these models. However, what seems ing Johansen's (1960) procedure. Some clear from recent literature is that it is recent models continue to rely on Scarf- no longer the solution methods that con- type methods, but use faster variants of strain model applications, but the availa- his algorithm due to Merrill (1972), Harold bility of data and the ability of modelers Kuhn and James MacKinnon (1975), B. to specify key parameters. Curtis Eaves (1974), and G. van der Laan E. How Are Policy Conclusions Reached? and A. J. Talman (1979). Merrill's refine- ment seems the most widely used. As As has already been noted in discussing work has developed on applied models, the numerical example above, the theo- however, it has become apparent that a retical welfare economics literature is usu- Newton-type method or other local linear- ally followed in making comparisons be- ization techniques can also be used. These tween equilibria in order to arrive at often work as quickly if not more quickly policy conclusions from the tax and trade than the Scarf-type methods listed above, models. For welfare impacts, the most although these methods do not guarantee commonly used summary measures are convergence. Victor Ginsburgh and Jean the Hicksian compensating (CV) and Waelbroeck (1981), for instance, have suc- equivalent variations (EV) discussed cessfully used a tdtonnement procedure above. Welfare measures for the economy in their model work. Also, Glenn Harrison as a whole are computed by simply aggre- and Lawrence Kimbell (1983; also Kim- gating the CVs or EVs over the different bell and Harrison 1983) have developed consumer groups. While this is consistent an iterative procedure based on a Walra- sian factor price revision rule with which 4The Johansen system, however, does not allow for multiple consuming agents and in its application they have experienced rapid conver- it appears to break the income-expenditurelink cen- gence. This corresponds to a method for tral to Walras'Law. 1022 Journal of Economic Literature, Vol. XXII (September 1984) with what is done in cost-benefit studies, ference between national and global wel- theoretical shortcomings of the sum of fare can be important. A tariff, for in- CVs or EVs as a social welfare function stance, may improve the national terms are well known. However, because these of trade and raise national welfare, even models provide a detailed evaluation of though a greater global loss may be in- who gains, who loses, and by how much, volved. As a result, global and national as a result of a policy change, no single welfare considerations can lead to quite summary measure need be chosen if the different policy conclusions. policy analyst using the results is inter- ested in the detailed impacts of a policy IV. Applied General-Equilibrium Tax change. In some models, equilibria are Models computed under the constraint that gov- ernment revenues must remain unaltered In this section we summarize the main which, in the tax models, usually implies features of some recent applied general- replacing one set of taxes with another. equilibrium tax models, highlighting their In other models, government revenues common features as well as the differences are allowed to change. Where this occurs, among them. We emphasize the role however, the welfare impact from played by key parameters, discuss the changes in the level of provision of public strengths and weaknesses of the models, goods and services needs to be added to and outline the main policy implications the economy-wide welfare measures. to be drawn from results obtained thus In addition to welfare impacts, other far. Because these models are complex, differences between equilibria can also be we present much of this information in evaluated. Income distribution effects can a series of tables. Table 5 outlines struc- be examined using the Lorenz curve or tural characteristics; Table 6, the data the Gini coefficient or some other mea- used; Table 7, some of the more significant sure. Distributional effects using alterna- results. tive income concepts (e.g., gross of tax, A. Common Features or net of tax) can be examined. Changes in relative prices can also be examined, The applied general-equilibrium tax and in the international trade models, models all derive in one way or another changes computed in each country's from Harberger's (1959, 1962, 1966) ear- terms of trade. Changes in the use of fac- lier work on United States corporate and tors of production across industries, and capital income taxes. Their common fea- changes in the product composition of tures reflect this heritage. In Harberger's consumer demands are important in some model, two sectors of production are iden- policy evaluations, and can also be ex- tified: the corporate and the noncorporate tracted from the equilibrium computa- sector. The corporate tax is assumed to tions. be an ad valorem partial factor tax, a tax However, the main focus of many (but on capital income generated in the corpo- not all) of the applied models is on the rate sector. Revenues are redistributed to welfare impacts of policy changes, with consumers in lump-sum form, and the particular emphasis on aggregate effi- government budget is balanced. ciency impacts. Although distributional Using linearization and approximation effects may be considered, the bottom line techniques, Harberger (1962) generates in most policy evaluations is whether any an algebraic expression for the change in given policy change raises or reduces ag- the net rental price of capital due to the gregate welfare. In trade models, the dif- introduction of a corporate income tax. Shoven and Whalley: Applied General-Equilibrium Models 1023

He assumes particular values for the sub- ties. Scarf's algorithm enables the exis- stitution elasticities in production func- tence of a tax equilibrium to be shown, tions and for the consumer-demand elas- and also provides a method through which ticities, and he uses United States data for such equilibria can be computed. the mid-1950s on factor and expenditure This method of simultaneously incorpo- shares. His main conclusion is that the re- rating several tax distortions was used by duction in the net return to capital is ap- Whalley (1975) to examine the impact of proximately equal to the tax revenues 1973 tax changes in the United Kingdom, raised and, therefore, capital bears fully and this work was further developed by the burden of the corporate tax. Piggott and Whalley (1977, and forthcom- In this paper, Harberger implicitly out- ing) into a 33-product and 100-household- lines the calibration procedure mentioned type model which has been used to evalu- above. He chooses units for factors of pro- ate structuralcharacteristics of the United duction as those amounts that sell for one Kingdom's tax/subsidy system. They pro- dollar in the presence of the tax (i.e., in duce estimates of the welfare gains and a benchmark equilibrium). His counter- losses for household groups classified by factual experiment involves removing the income, occupation, and family size for corporate tax and replacing it by a nondis- a series of hypothetical tax changes. Sho- torting alternative, the differential tax in- ven (1976) reexamines the Harberger cal- cidence approach of Richard Musgrave culations of the efficiency costs of distor- (1959). tionary capital income taxes, using more Harberger's basic structure has been disaggregated data than Harberger, show- preserved, with embellishments, in most ing how the level of aggregation affects subsequent work. Taxes are modeled as results. ad valorem and the government budget Two models closely related to the Sho- is balanced in equilibrium. The tax instru- ven-Whalley work are those by Piggott ments that make up a typical modern tax (1980) on Australiaand Jaime Serra-Puche system (income, corporate, property, (1984) on Mexico. Piggott's model differs sales, excise, and social security taxes) are from the other tax models in using two- all incorporated in model equivalent stage CES production functions with dif- form. For instance, corporate and prop- fering types of capital and labor. At one erty taxes are usually treated as part of stage, different types of labor "produce" a larger system of taxes on capital income the aggregate labor input and, corre- with rates varying across industries. The spondingly, different types of capital ser- Musgrave and Harberger emphasis on the vices "produce" the aggregate capital in- twin issues of efficiency and distributional put. At the second stage, aggregate labor impacts of taxes appears in most of the and capital combine to produce value work. added. Serra-Puche analyzes tax inci- Shoven and Whalley (1972, 1973) are dence in Mexico in a model with three the first to analyze taxes using a full gen- factors. Subsequent work by Kehoe and eral-equilibrium computational proce- Serra-Puche (1983) has used a similar ap- dure. In their 1972 paper an artificialcom- proach to analyze the 1980 fiscal reform modity is used to incorporate the tax in Mexico, incorporating unemployment distortions,which effectively limits the ap- generated by an exogenously-specified, plicability of the analysis to one tax at a downward-rigid real wage. time. In 1973 they developed a procedure Keller's (1980) tax model of Holland also to deal with several simultaneous tax dis- uses a Harberger structure, but differs tortions without using artificial commodi- from the Shoven-Whalley work in using 1024 Journal of Economic Literature, Vol. XXII (September 1984)

TABLE 5: SUMMARY OF CHARACTERISTICS OF

Demand Model Country(ies) Demand Functions

Ballard, Fullerton, Shoven, U.S. Derived from nested CES/Cobb-Douglasutility Whalley (forthcoming) functions

Ballentine, Thirsk (1979) Canada Differential equations giving quantity changes in terms of elasticities

Keller (1980) The Netherlands Derived from nested CES utility functions

Piggott (1980) Australia Derived from nested CES utility functions

Piggott, Whalley U.K. Derived from nested CES utility functions (forthcoming)

Serra-Puche (1984) Mexico Derived from Cobb-Douglasutility functions

Shoven, Whalley (1972) U.S. Derived from Cobb-Douglasutility functions

Slemrod (1983) U.S. Derived from Cobb-Douglasutility functions

Whalley (1975) U.K. Derived from CES utility functions Shoven and Whalley: Applied General-Equilibrium Models 1025

APPLIED GENERAL-EQUILIBRIUM TAx MODELS

Side Production Side Disaggregation Production Functions Disaggregation

12 consumer income CES or Cobb-Douglasproduction 19 industries groups functions, 16 final demand categories fixed coefficient use of intermediate inputs

12 income classes Differential equations giving quantity 12 production sectors changes in terms of elasticities 7 final productioncategories

4 demand sectors: skilled and Nested CES production functions 4 industries unskilled labor, public, foreign

12 socio-economic household CES value-added production functions 18 domestic and 14 foreign groups, plus government, with intermediate production structure industries foreign and corporate sectors allowing substitutabilitybetween domestic and foreign inputs

100 socio-economic CES value-added production functions, 33 industries household groups, plus fixed coefficient use of intermediate public, investment and goods external sectors

10 rural/urban income Cobb-Douglasproduction functions 14 industries producing groups, plus government, 15 final consumption goods plus the rest of the world

2 income groups CES production functions 2 industries:corporate and noncorporate

9 income groups Cobb-Douglasproduction functions 4 industries, 6 income-generating assets

7 income groups CES production functions 9 industries 1026 Journal of Economic Literature, Vol. XXII (September 1984)

TABLE 6: SOURCES FOR

Base Year Model for Data Extraneous Use of Elasticities

Ballard,Fullerton, Shoven, 1973 Laborsupply, savings (literaturesearch) productionelasticities Whalley (forthcoming) of substitution between capital and labor (literaturesearch)

Ballentine, Thirsk (1979) 1969 Factor substitution, price and income demand elasticities (literaturesearch)

Keller (1980) 1973 Income elasticities of demand (from survey data) elasticities of substitution in production and consumption (best guess)

Piggott (1980) 1972-1973 Elasticities of substitution in production (literaturesearch) elasticities of substitution in demand (literature search and best guess)

Piggott, Whalley 1973 Elasticities of substitution in demand and production (forthcoming) (literature search)

Serra-Puche(1984) 1977 Unitary substitution elasticities in demand and production

Shoven, Whalley (1972) 1953-1959 Elasticitiesof substitutionin production (variousspecifications) (average)

Slemrod (1983) 1977 Unitary substitution elasticities in demand and production

Whalley (1975) 1968-1970 Elasticities of substitution in production and demand (best (average) guess and literature search) Shoven and Whalley: Applied General-Equilibrium Models 1027

DATA AND ELASTICITIES IN TAx MODELS

Production Data Demand Data Taxes Incorporatedin the Model

National Accounts, Input-output Consumer Expenditure survey, All existing U.S. taxes including tables taxation statistics corporate, income, social security, sales and property taxes

Input-outputtables, plus National Budget share Corporate, property and income Accounts data taxes

National Accounts, Input-output National Accounts, Personal Taxes on consumer goods and tables Income Distribution Survey, services, on capital goods, Budget Survey, Savings Survey imports, labor, capital and corporate income; lump-sum taxes

National Income and National Income and All existing Australiantaxes and Expenditure Accounts, Input- Expenditure Accounts, subsidies including income and output tables Household Expenditure Survey sales taxes, production taxes and subsidies, factor taxes and subsidies

National Accounts, Input-output National Accounts, Family All majorU.K. taxes and subsidies tables Expenditure Survey including income, corporate, property, excises, social security and value-added taxes, housing and agriculturalsubsidies

Input-output tables Survey of Family Income and All existing Mexican taxes, Expenditure including turnover taxes, special taxes, income taxes, tariffsand export taxes

Literature source Literature source Taxes on income from capital

Extraneouslyspecified Cobb- Survey of financialcharacteristics Corporate and property taxes Douglas exponents of consumers, income and expenditure data

National Accounts National Accounts MajorU.K. taxes including purchase and excise taxes, income taxes, corporation taxes, rates (property tax) and national insurance (social security) 1028 Journal of Economic Literature, Vol. XXII (September 1984)

TABLE 7: SUMMARY OF MAJOR

Policy Interventions Policy Data Model Incorporated Used Policy Conclusions

Ballard, Fullerton, Integration analysis: four U.S. personal and Total integration of personal and Shoven, Whalley alternative plans for corporate income corporate income taxes yields gains (forthcoming) corporate and personal taxes whose discounted present value is income tax integrations. $500 bil. or 1% of national income. Consumption tax Total integration with scaling to alternatives: change in the preserve tax yields leads to a tax treatment of savings progressive change income distribution even though every class is better off. Consumption tax alternatives yield gains of $650 bil. in present value terms. Ballentine, Thirsk Changes in local Tax and Personal income taxes markedly (1979) government expenditures, expenditure data progressive while property and corporate and property corporate income taxes have a more income taxes, federal mixed incidence pattern. Incidence income taxes, and housing effects of different expenditure subsidies programs small. Keller (1980) Changes in marginal tax Major taxes in the Efficiency effects of taxes generally rates in various production Netherlands small (excepting corporate income and consumption sectors (value-added, tax); only small amounts of tax corporate, social shifting. security and income) Piggott (1980) Total and sectoral abolition Existing Australian Replacing all taxes and subsidies of taxes and subsidies under sectoral taxes and with an equal-yield replacement tax various model parameter subsidies leads to decrease in total domestic specifications final demand: demand for imports rises modestly and world demand for Australian exports rises dramatically. Replacing all taxes and subsidies with an equal-yield export tax leads to total welfare gain of 3.5% of Australian NDP. Piggott, Whalley Variations in U.K. taxes and Existing U.K. taxes Existing U.K. tax system yields (forthcoming) subsidies and subsidies distorting losses of 6-9% of NNP per

a local linearization procedure to solve for (1979) also use a local linearization ap- the tax change equilibria. Four groups of proach along Harberger lines in their gen- agents on the demand side are incorpo- eral-equilibrium tax work on Canada. rated. Government and the foreign sector Their main concern is incidence analysis are separately identified, along with low of changes in financing arrangements (in- income/unskilled labor and high income/ cluding intergovernmental transfers) for skilled labor groups. His incidence analysis local government expenditures, such as concentrates on distributional effects be- increases in federal, personal or corporate tween these two latter groups. taxes to finance increased municipal ex- Greg Ballentine and Wayne Thirsk penditures. No explicit functional forms Shoven and Whalley: Applied General-Equilibrium Models 1029

POLICY FINDINGS OF TAX MODELS

Policy Interventions Policy Data Model Incorporated Used Policy Conclusions

year. Subsidies to local authority housing area are a significantsource of welfare loss. Significant redistributive effects of taxes. Serra-Puche(1984) Replacement of indirect Existing Mexican Resource allocation moved in favor turnover taxes with turnover taxes, of the government target sectors consumption value-added specific goods (agricultureand foodstuffs);income tax (as instituted in Mexico taxes, income taxes, distributionimproved, reducing in 1981) tariffsand export differentialsbetween urban and taxes rural households. Shoven, Whalley Imposition and removal of Existing U.S. In 6 of the 12 cases examined, (1972) existing taxes on income capital income capital bears more than the full from capital under various taxes (corporate, burden of the surtax, while in the model parameter property and remaining 6 cases, labor shares in specifications personal income, the burden. including capital gains) Slemrod (1983) Complete indexation of U.S. Existing U.S. Indexing the U.S. tax system leads tax system for inflation corporate and to aggregate efficiency gains with property taxes the lowest income groups experiencing slight losses and the highest income groups receiving substantialgains. Whalley (1975) 1973 U.K. tax reform 1973 U.K. taxation Welfare gain from 1973 U.K. tax changes changes found to be small and in represented in some cases may be negative. model-equivalent Replacement of purchase tax and form SET by VAT appears to yield welfare losses, while changes made to income tax systems may yield gains.

for demand and production are used, but B. Differences Among Models are implied by the configurationof elastic- ities adopted. On the demand side, for in- The main departures from the basic stance, they are careful to ensure that En- Harberger structure in models appears in gel and Slutsky aggregation conditions are more recent work where two issues not satisfied by the elasticities chosen. Total discussed by Harberger, the modeling of differentials through the equilibrium con- time and the treatment of financial assets, ditions yield approximate estimates of are now beginning to be addressed. The changes between equilibria. An especially model of the United States (Ballard, Full- interesting departure in this model is the erton, Shoven, Whalley: BFSW, forthcom- attempt to incorporate a degree of factor ing) incorporates all major distorting taxes mobility both domestically among regions as in earlier work, but differs from other and internationally. models through the incorporation of time 1030 Journal of Economic Literature, Vol. XXII (September 1984) through dynamic sequencing of single pe- model of the United States, which differs riod Harberger-type equilibria. In the from earlier models in incorporating en- BFSW model, a number of commodities dogenous financial behavior, of both and industries appear as in the static mod- households and firms, into the general- els, but saving decisions in any period are equilibrium approach. His work is moti- made by households based on myopic ex- vated by the extensive literature in recent pectations regarding the future rate of re- years that stresses corporate tax as a tax turn to capital. Household saving deter- on equity returns only, rather than a tax mines the demand for capital goods on all capital income originating in the produced in the period. This treatment corporate sector. The rate of tax on capital allows each period's equilibrium to be income depends not only on the sector computed without requiring information of origin but also on the financial arrange- on future periods' prices. ments that accompany the flow of income. Saving results in an increase in the capi- Slemrod introduces uncertainty into his tal stock, and affects intertemporal behav- model through stochastic production- ior through changed consumption possi- function parameters. A risk-aversion pa- bilities in future periods. Calibration is rameter is introduced into the preference made to an assumed growth path in the functions, which are defined over both ex- presence of existing tax policies, rather pected consumption and the variance of than to a single benchmark equilibrium. income. Both risky and risklessassets yield A change in policy displaces the economy capital income, resulting in a portfolio al- from the balanced growth path. After a location problem for households in addi- transition period,5 the economy settles on tion to the usual budget problem generat- a new growth path with an alternative ing consumption demands. Household capital/labor ratio. The pairwise compari- commodity and asset demands are based son between equilibria in static models is on maximization of a two-stage prefer- replaced by a pairwise comparison be- ence function, the first stage incorporating tween the equilibrium sequences under the risk-aversionparameter. Marketclear- the alternative policy regimes. The re- ing for all goods and assets is incorporated strictive assumption of myopic expecta- with a supply response in financial assets tions can be replaced by a perfect fore- based on an extraneous elasticity which sight approach (or a limited foresight determines the response of firm debt- specification), as shown by Ballard and equity ratios with respect to relative tax Goulder (1982), although significantly costs of debt and equity. The model is more computation costs are involved. Bo- parameterized to represent a "stylized" venberg and Keller (1983a) have also ex- economy rather than calibrated to an ex- tended Keller's model by adding dynamic act benchmark equilibrium, as in the features similar to those introduced by other models. BFSW in order to analyze tax incidence C. Key Parameters over time. The treatment of financial assets has In spite of the extensive detail incorpo- been addressed in Joel Slemrod's (1983) rated into these models, most modelers emphasize the important role played by 5The economy does not instantaneously jump to a few values in determin- the new balanced-growth path because changes in key parameter the capital stock cannot exceed domestic saving in ing results from their policy analyses. the model. As long as saving causes the capital stock These are typically elasticity values and to grow at a rate different from the labor growth ad valorem tax rates. The rate, factor prices will be changing along the transi- the procedure tional path. generally employed is to choose a central Shoven and Whalley: Applied General-Equilibrium Models 1031

case specification, around which sensitiv- Having settled on the tax treatment to ity analysis can be performed. be employed, modelers must then select As far as elasticities are concerned, the values for tax rates to be used in the key parameters tend to be labor supply, model-equivalent representation of the saving, and commodity-demand elastici- tax. Following Harberger, the most com- ties. In all of these areas, modelers typi- monly used procedure is to calculate an cally encounter difficulties in selecting average effective tax rate by dividing taxes "appropriate"values due to conflicting lit- paid (as recorded in the benchmark data) erature estimates, and frequent changes by the model tax base. However, as Fuller- in what seems to be the consensus among ton and Roger Gordon (1983) have em- empiricists in the relevant area. With la- phasized, for several taxes there is no a bor supply, for instance, the view for many priori reason to expect average and mar- years seemed to be that wage elasticities ginal tax rates to be the same, and the for prime-age males are small and could marginal rather than the average rate even be negative but values are larger and should be used in a model which evaluates positive for secondary workers. However, resource allocation effects of taxes. Also, some recent work seems to be challenging several alternative marginal rates can be this view. The elasticity of saving with re- calculated which depend on more charac- spect to the rate of interest was also teristics than can adequately be captured thought, for many years, to be small (close by the models. For example, the marginal to zero), but recent work by Michael Bos- tax rates that savers face depend not only kin (1978), and Lawrence Summers (1981) on the savers' income tax rate but also has challenged this view. Commodity-de- on the asset acquired and the financing mand elasticities, on the other hand, have and intermediation vehicles used. Faced typically not accumulated a consensus with these problems, some modelers are view on a product-by-product basis, but averaging across marginal rates calculated significant variations exist among the liter- for a range of circumstances, and incorpo- ature estimates available. As users of elas- rating these into their analysis. Strictly ticity estimates, all of this makes the tax speaking, however, even this is inappro- modelers' task more difficult in that they priate because distortions at the appropri- often have to select among competing es- ate margins are not fully represented. timates, and follow changing literature opinions as to likely ranges for best-guess D. Policy Implications of Results values. On the tax-rate front, the modelers' task Although the ability to apply general- is equally difficult. They must first decide equilibrium techniques to tax policy ques- on the appropriate treatment of each tax tions may strike some readers as an accom- to be modeled, often adjudicating litera- plishment worth noting in itself, ulti- ture disagreements. For instance, is the mately the most important contributions corporate tax to be modeled as a Harber- of the applied models lie in their results, ger partial-factor tax, a lump-sum tax (as and the new insights these offer into policy suggested by Joseph Stiglitz 1973), or as issues. a tax on the return to equity capital in For several years following the original each industry? Is the property tax a tax Harberger work on the resource alloca- on factor incomes or an excise tax? Is the tion effects of taxes in the United States, social security tax a tax on labor or a bene- public finance economists argued that fit-related financing system for transfers deadweight losses from taxes were small to the elderly? (perhaps one percent of GNP per year). 1032 Journal of Economic Literature, Vol. XXII (September 1984)

When combined with the results of inci- to be additive, with the notable exceptions dence studies, such as Joseph Pechman's of corporate and property taxes. They sug- and Benjamin Okner's (1974) suggesting gest that around one-quarter of net reve- little redistribution from the tax system, nues raised by government each year are this often led to a policy stance in favor foregone through the deadweight loss as- of redistributive tax changes with only sociated with the tax subsidy system. limited attention focused on changes de- Sharp distributional gains and losses occur signed to improve allocative efficiency. A through replacing the existing tax system striking feature of the results from the by a yield-preserving neutral sales tax. general-equilibrium tax models is their The welfare gain to the top ten percent suggestion of considerably larger dead- of households is around 25 percent of dis- weight losses from tax distortions, espe- posable income; the loss to the bottom ten cially at the margin. In addition, while dis- percent is around 20 percent of disposable tributional results suffer from some of the income. This, of course, differs from the same problems as in incidence studies traditionalview that tax systems have only (such as Pechman and Okner), they do small distributional impacts. The tax sys- seem to indicate that tax policies may have tem is shown to penalize manufacturing, more redistributive power when their but substantially to protect and promote general-equilibrium effects are taken into housing. Additional welfare costs are cal- account. For example, Harvey Galper and culated from saving and labor-supply dis- Eric Toder (1982) find for the United tortions and are shown to be small or mod- States tax system that the combination of est, although small elasticities are used. a graduated schedule of marginal tax rates Not all models fully endorse these impli- and the existence of a variety of prefer- cations. Slemrod's (1983) results, from ences on assets held by households results fully indexing the United States tax system in a more progressive tax system than for inflation, suggest only small welfare might initially appear, because the gen- gains, while Ballard, Shoven, and Whalley eral-equilibrium solution yields reduced (1982) stress the significance of welfare before-tax returns of the preferred assets, costs of taxes at the margin. They estimate relative to fully taxed assets, thereby low- that welfare losses per extra dollar of reve- ering the after-tax returns available to nues raised from existing United States high-income households. distorting taxes may approach a dollar. A further example of these themes in That is, the private cost of a government results is provided by Piggott and Whalley dollar is almost two dollars. (forthcoming) in their analysis of the There seems little doubt that these tax United Kingdom's taxes and subsidies. models are now being successfully applied They estimate that the 1973 United King- to a range of policy issues and are yielding dom tax/subsidy system yields distorting important insights. Results are helping to losses of between six to nine percent of frame positions on policy issues, especially net national product per year, with subsi- in suggesting which effects of taxes may dies to local authority housing identified be large and which small. In providing as a significant source of welfare loss. The initial null hypotheses until better data costs of distortions from the tax subsidy and model estimates become available, system appear to be heavily concentrated this process clearly advances policy de- in three areas: capital taxes, public-sector bate especially if modelers' conclusions housing subsidies, and excise taxes. Distor- are scrutinized carefully to see which are tionary costs for the most part are shown believable new insights, and which are Shoven and Whalley: Applied General-Equilibrium Models 1033 quirks of unrealistic parameter values or is lightly taxed; some saving is sheltered model specifications. through pensions and IRAs;the tax treat- ment among financial assets differs de- E. Weaknessesof the Models pending upon financing, whether divi- Even though they have a strong claim dends are paid; and human capital to policy applicability, the tax models suf- formation is treated differently from other fer from a number of deficiencies which saving. Inevitably, the applied models reflect problems both endemic to all ap- have to aggregate over some of these mar- plied general-equilibriummodels and spe- gins, raising more concerns regarding the cific to the tax area. In the former are the results. difficultiesof choosing appropriate elastic- A clear weakness of the applied models, ity and other parameter values, and the compared to other empirical work in pub- inevitable feature that a tractable model lic finance, is their incomplete integration abstracts from important details in pro- of the information contained in detailed ducing policy recommendations. In the microdata sets. Although this is an inevita- latter are the inability, as yet, of models ble result of an emphasis on tractability, to incorporate fully detailed microdata the differences can be quite striking. available to public finance economists, Pechman and Okner (1974), for instance, the relatively unsatisfactorydistributional use data on 87,000 households in their tax modeling, and the average/marginal tax incidence work; the most detailed of the rate issue alluded to earlier. tax models covers only 100 households. Our current state of knowledge of elas- However, a start in this direction has been ticity values inevitably means that the de- provided by Slemrod's (forthcoming) im- gree of confidence that both modelers and portant paper. policy analysts have in results is weak- Another, and in some ways related, is- ened. Although the spirit of "doing the sue is the restrictive nature of the distribu- best possible" until better elasticity values tional analysis presently possible with the arrive has much to commend it, the di- tax models. The impacts of taxes on the lemma for modelers is how much confi- personal distribution of income is usually dence to have in such elasticity-depen- calculated through the changes in factor dent estimates of impacts. This partly incomes, transfers, and direct taxes. Little explains why modelers seem content to work has been done on life-cycle tax inci- emphasize the broad themes of results dence, although recent work by Ballard rather than precise point estimates. (1983) is moving in this direction. The level of detail, which ideally should Despite these problems, the contribu- be taken into account in evaluating any tion to policy debate on tax issues that particular tax issue, frequently clashes these models have made seems firmly es- with the limitations imposed by tractabil- tablished, and more contributions seem ity. A good example is provided by at- likely in the years ahead. Models are now tempts to analyze the impact of taxes on being used or contemplated in a number saving. Typically, a single-saving asset is of government agencies in various coun- identified, but as is emphasized in more tries, evidence of the potential contribu- institutional treatments of this issue, the tion that policymakers see. As these mod- range of tax treatments for different sav- els move from the academic development ing vehicles means that, ideally, all the stage closer to the heart of the policy pro- margins need to be separately identified. cess, added realism, more detail, and bet- For example, saving in the form of housing ter data are likely to appear. 1034 Journal of Economic Literature, Vol. XXII (September 1984)

V. Applied General-Equilibrium Trade tions; in "strong" versions, identical pro- Models duction and demand parameters are assumed across countries. Trade is de- Applied trade models differ from tax termined by the relative factor intensity models in being based on a more varied of production, and the relative factor heritage, and in having a more diffuse fo- abundance among countries. cus. Some are multicountry models de- By contrast, the multicountry models signed to analyze global issues. Other listed in Tables 9 and 10 are not assumed single-country models investigate how de- to have identical production and demand velopments abroad affect individual econ- parameters. Thus trade is determined on omies. Some are oriented exclusively to the basis of more than just differences in trade policy questions. Others are general- relative factor endowments. A further purpose modeling efforts, one part being characteristiccommon to most of the mul- the capability to analyze trade questions. ticountry and single-country models is the Some are models of developed economies, use of the so-called Armington assump- while others analyze developing econo- tion, discussed earlier. This treats products mies where trade policy issues are often produced in different regions as qualita- quite different. tively different (i.e., heterogeneous rather In synthesizing experience with these than homogeneous) across countries as in models, we have chosen to follow a similar a traditional Heckscher-Ohlin model. route to that adopted for the tax models, The reasons for this tteatment are mul- namely to display details of models in tifold, revealing the compromises that em- tabular form and then comment in the pirical modelers often have to make. In text. Accordingly, Tables 8 and 9 summa- addition to the problems created by the rize the main characteristics of the mod- presence of "cross hauling" in trade data, els, along with sources for data and elastic- some of the early trade models encoun- ity values. Table 10 presents summaries tered the difficulty that unrealistically of the major policy implications of results strong specialization effects were pro- obtained thus far. To aid presentation in duced when a change in trade policy oc- the tables we divided the models into sep- curred. This reflected the use of homoge- arate multicountry and single-country neous products and production possibility groups. frontiers that were close to linear, so that A. Types of Models a small change in trade policy results in large moves toward specialization. The In analyzing the impacts of trade poli- Armington treatment avoids these diffi- cies, the applied models base themselves culties. on the traditional framework emphasized Also, the key empirical parameters to in pure trade theory. Countries export which many of the models are calibrated commodities in which they have a com- are import- and export-demand elastici- parative advantage. The differences ties; in a model with homogeneous prod- among models reflect the way in which ucts, there is no simple import-demand comparative advantage is incorporated, as elasticity unless the economy is com- well as the modeling of the policy regimes. pletely specialized. Unless the Armington The most prevalent approach in mod- assumption is used, calibration becomes ern trade theory is that associated with difficult because there is only a demand Heckscher and Ohlin. Within this frame- for the imported commodity (some of work, each country involved in trade has which is also domestically produced). production functions and demand func- A major difference between the multi- Shoven and Whalley: Applied General-Equilibrium Models 1035 country and single-country models is the as is evident from the Dervis-de Melo- way in which the determinants of trade Robinson work on Turkey and other coun- are modeled. In the multicountry models, tries, a careful modeling of these policies there is a specification of production and is crucial to an understanding of the policy demand for all of the countries participat- issues involved. ing in trade. In the single-country models, A further issue, emerging in more re- this is not the case because the focus of cent work, concerns modeling the produc- the model is on the implications of trade tion side. Although not summarized in the policy for a single country, and a cruder tables, recent work by Richard Harris modeling is adopted for the rest of the (forthcoming) has emphasized how both world. Usually a closing rule is adopted scale economies and industrial organiza- (i.e., a simple specification of the import tion features, stressed in some of the re- supply and export demand functions) cent international trade theory literature, which countries face in their trade with can have important implications for nu- the rest of the world, along with the speci- merical results of the impacts of trade pol- fication of capital flows and other external icy changes. Harris emphasizes that if sector characteristics.The use of these ex- scale economies are large enough and the ternal sector closing rules in these models trade policy issues involve countries of dif- can be quite important, as has been em- ferent size, as is true in the United States- phasized by Whalley and Bernard Yeung Canadian case, then incorporating scale (1984). Another major difference between economies can substantially change esti- the multicountry and single-country mod- mates of the impact of trade policies. A els is the capability of the multicountry similar theme appears in earlier work by models to analyze multilateral trade pol- Dixon (1978). icy issues such as are involved with cus- toms unions, trade liberalization under B. Exchange Rates and Capital Flows the GATT, or any other trade policy change simultaneously involving a num- Another issue in the trade models con- ber of countries. Single-country models cerns the role of exchange rates and the are typically inappropriate for analyzing related issue of international capital flows this class of policy issues. since the traditional pure theory of inter- The models also use different ap- national trade produces no real effects proaches in their treatments of trade pro- from exchange-rate changes. If a mone- tection policies. Most models incorporate tized extension of a classical general equi- tariffs, but different attempts have been librium model were to be used to analyze made to incorporate the nontariffbarriers. trade policy changes, and a money-de- A simple way to incorporate nontariffbar- mand function by region appeared along riers is through ad valorem tariff equiva- with specified levels of national money lents, but this can be inappropriate in a stocks, neutrality would prevail in the number of cases. For example, the effect sense that the real and financial behavior of a quantity constraint is such that the of the system would be entirely indepen- ad valorem tariff equivalent would not re- dent. Once real side behavior is known, main unchanged as prices change in a specifying national money stocks in each model. In turn, nontariffbarriers in devel- of the regions simply serves to determine oped and developing countries are quite domestic price levels and exchange rates. different. Developing countries typically Alternatively, should a fixed exchange- have import licensing, usually accompa- rate regime be analyzed, one can calculate nied by foreign exchange rationing, and, the national money stocks that are neces- I-i.

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sary to support the equilibrium and study summarizes a number of estimates achieve the desired exchange rates. of trade elasticities, producing best-guess The models summarized in Tables 7 and estimates by product and by region. Many 8 do not all follow this classical approach of the elasticity estimates are relatively to neutrality. This is especially the case low (in the neighborhood of one), and with the single-country models where, in there has been substantial literature over a number of instances, exchange rates ap- the years as to how reasonable these are. pear in the formulation. In some cases, More recently, Chris Alaouze (1977) has these exchange change-rate terms refer worked explicitly on Armington trade to the real exchange rate between traded elasticities. and nontraded goods but, in a number of These elasticity values are important the models, results are reported for because low-trade elasticities tend to pro- changes in exchange rates with the ap- duce strong terms-of-trade effects. The pearance that they have real effects. This work from the 1950s, by Harry Johnson can make the interpretation of results dif- (1954) and William Gorman (1957-1958) ficult from a theoretical point of view. on the optimal tariff emphasizes that a On the capital-flow side, the approach country's optimal tariff is equal to one over in most of the models is to exclude interna- the import price elasticity of the trading tional capital flows. Where capital-flows partner minus one. Import price elastici- are present, an important difference be- ties in the neighborhood of one, therefore, tween models occurs because countries produce very high optimal tariffs, and as- are typically modeled as takers of rental sociated with these are strong terms-of- rates on world capital markets and, there- trade effects. As long ago as 1950, Guy fore, face perfectly elastic capital-supply Orcutt raised the whole question of speci- functions. This issue has been analyzed for fication bias in trade-elasticity estimates, the tax models by Goulder, Shoven and and further contributions to this issue Whalley (1983) who have shown how the have subsequently been made by Murray treatment of international capital flows Kemp (1962), Nanak Kakwani (1972), and can significantly affect results. The intu- Mansur (1982). In spite of disagreements ition from this would be that a similar con- as to the appropriate way to estimate clusion could apply for trade policy analy- these elasticities, literature values con- sis. tinue to be widely used, but with a fair amount of skepticism because of their low C. Key Parameters values. Two sets of key parameters appear in Trade policy parameters break down trade models: international trade elastici- into tariffs and nontariff barriers, with ties, and the trade policy parameters. nontariff barriers representing the major With the widespread use of the Arming- problem. Information on nontariff barri- ton assumption, a common procedure is ers is scarce, and there is not even wide- to relate the elasticities of substitution be- spread agreement as to exactly what the tween the Armington commodities back appropriate list of nontariff measures to empirical estimates of import- and ex- should include. Also, estimates which have port-demand elasticities that countries been made of nontariff barriers are not face. This, in turn, involves the use of liter- particularly satisfactory. While there are ature estimates of trade elasticities. A estimates obtained by the residual method widely-used source is a compendium of of taking the differences between world estimates, due to Robert Stern, Jonathan and domestic prices and subtracting trans- Francis and B. Schumacher (1976). This portation and tariff cost margins, there are Shoven and Whalley: Applied General-Equilibrium Models 1043 conceptual difficulties with this approach. the presence of scale economies and asym- There is a substantial amount of dissatis- metries in the size of the regions in his faction, among the trade modelers at pres- model. Most of the gains from United ent, that the impact of nontariff barriers States-Canadian free trade go to Canada, has been adequately captured. Until more the smaller country; global gains remain data and information are available, this small. sense of discomfort will almost certainly Another strong policy implication from remain. the models is that terms-of-trade effects associated with changes in trade policies D. Major Themes of Results can be significant. Robin Boadway and Policy results obtained thus far yield John Treddenick, for instance, show that a number of strong implications for trade Canada would be made worse off from a policy. One striking conclusion from all tariffreduction due to a terms-of-tradede- the models is that the welfare effects of terioration. This is contrary to the usual changes in trade policy are relatively small perception in Canada of a small, open, compared to the effects of other kinds of price-taking economy, which would sug- policies, such as taxes. As long ago as the gest it could make itself better off by elimi- 1950s, Tibor Scitovsky concluded that nating tariffs. This strength in terms-of- welfare gains from the formation of the trade effects, in turn, suggests that the European Economic Community were threat of a retaliatory trade war (were co- very small, around /o of one percent of operative arrangements in the GATT to GNP per year, and small numbers were break down) could be serious, resulting also produced by Johnson (1958) in his cal- in high optimal tariffs on a global basis. culations of the gain to Britain by joining Another interesting set of policy impli- the EEC. This theme shows through cations refers to geographically discrimi- strongly in the results summarized in Ta- natory trade arrangements of the customs ble 10. The intuition is: distortions that union type. In their work on British entry affect a relatively small portion of total into the EEC, Marcus Miller and John activity, where the distortions themselves Spencer show that the welfare effects are are often relatively mild, can be expected relatively small and tend to be dominated to have small distorting effects. by the direct budget transfersaccompany- This conclusion, however, has been ing the expansion. Their results suggest sharply queried in recent work by Harris that the United Kingdom was made signif- (forthcoming)who also cites earlier studies icantly worse off by joining the EEC. of United States-Canadian free trade by Some of these models have been used RonaldJ. Wonnacott and Paul Wonnacott to look at issues other than trade liberali- (1967), suggesting that the gains to Canada zation. Alan Manne and Paul Preckel pro- from free trade with the United States are duce the interesting result that the im- significant. The essential difference in the pacts of the energy shock of the 1970s Harris work from that summarized in the were relatively small, perhaps less severe tables is the role of scale economies, and than had been thought to be the case at the ability of small economies to realize the time. Future work will also undoubt- large gains when much larger trading edly cover wider dimensions of trade pol- partners reduce their trade barriers. Un- icy than have been taken up thus far, one doubtedly, Harris'results will prompt fur- of these being the regional impacts of ther work along these lines in future trade policy stressed in work by Dixon, model developments, although it seems Parmenter, Sutton, and Vincent on Aus- fair to say that Harris' results reflect both tralia. 1044 Journal of Economic Literature, Vol. XXII (September 1984)

E. Weaknessesof the Models ments will occur in future years, and some of the extensions mentioned above will As with the tax models, the same two be incorporated as these models develop. general weaknesses apply: the problems of the elasticity specification, and the in- VI. Further Issues with the Taxand Trade ability to incorporate completely all detail Models relevant to any particular policy issue. More specific problems relate to the mod- While the applied general-equilibrium eling of production and alternative policy models described in this paper can reason- regimes. The work of Harris has already ably claim to have advanced from the sim- been mentioned as highlighting the im- ple numerical examples of ten to fifteen portance of scale economies and imper- years ago to a stage where quasi-realistic, fect competition. Recent theoretical work larger-dimensional models are yielding in international trade has concentrated new insights into policy debates, it should heavily on these issues, especially the im- be obvious to readers that there is a range perfect competition issue, with models be- of difficulties beyond those mentioned, ing developed to explain cross hauling in which arise with the approach. Our view a way quite different from the manner is, these in no way invalidate the approach in which it is accommodated in the pres- but it is important that policymakers using ent applied models through the Arming- results be aware of these problems so as ton treatment. To some extent, the ap- to form their own judgments to reasona- plied trade models have lagged recent ble policy implications. theoretical developments, and undoubt- A. Robustness of Results edly more work will need to be done in respecifying models. One key issue with the models is how Another major weakness is the model- robust the results are to alternative pa- ing of nontariff barriers. Issues such as the rameter values. Because the calibration operation of voluntary export restraints procedure was used to select parameter where the implicit value of the rent is values, meaningful statistical tests of any transferred to the exporting country have model specification are usually not possi- not been satisfactorily analyzed through ble. Users of model results are often left these models. In current trade policy is- with a sense of discomfort that any given sues between the United States and Japan, results could disappear, or even change this is a crucial question, as a significant sign, if alternative parameter values were amount of United States-Japanese trade chosen. is covered by voluntary restraints. A fea- There seems to be widespread agree- ture neglected in the models of develop- ment among modelers that once policy ing countries is the role of rent seeking, parameters are specified, the elasticity accompanying trade restrictions. This has values are the single most important set been stressed in theoretical work, but not of parameter values in determining re- fully incorporated in the empirical mod- sults. Because of the reliance on empirical els. estimates, one response to the robustness Despite all these problems and difficul- issue is to say that model results are only ties, however, the applied trade models as robust as elasticity estimates appearing have already made contributions both to in the literature. The problem, however, trade policy debates, and to the evaluation is more severe than this for two reasons. of possible changes in the international First, elasticity values combine in both off- trading mechanism. Undoubtedly, refine- setting and compounding ways in these Shoven and Whalley: Applied General-Equilibrium Models 1045

models, and the robustness of any single tion in static models of a closed economy elasticity value in the literature may mean with a fixed amount of capital, Harberger little when used in conjunction with other concludes that capital bears the burden elasticities in a large model. Second, the of the corporate tax. Clearly, if the econ- robustness issue cannot be discussed inde- omy in question is viewed as a participant pendently of the particular features of re- in an international capital market and is sults one has in mind. Some may be very a taker of rental rates on world capital sensitive, while others hardly change. markets, the policy conclusions would Varying trade elasticities, for instance, change. In this case, it is impossible for may make a big difference to projected capital to bear the burden of a capital tax, changes in trade flows from a policy because the effect of the tax would simply change, while leaving welfare impacts be to cause capital to leave the country largely unaffected. until the net-of-tax return is equal to that The response thus far in the applied prevailing on the world markets. Model models has been to take alternative elas- preselection can thus powerfully affect the ticity values to those used in a "central- conclusions that are reached. case" specification, displacing the key The fundamental difficulty is that there values by what seem to the particular are many alternative models in the litera- modeler as "large" changes. Most model- ture, each applicable to the policy ques- ers appear to claim a reasonable degree tion at hand and each yielding different of robustnessfor their results, while admit- policy implications. Applied general-equi- ting the limited nature of the sensitivity librium analysis does not provide a way tests performed. Usually elasticities are of discriminating between alternative varied only singly and not in combination, models because no form of hypothesis test- for the understandable reason that the ing is involved. Thus, a broadly-based sin- volume of results generated is difficult to gle-rate income tax, which is nondistort- digest. Perhaps the best hope for further ing in a static fixed-factor model, becomes insight into this issue is the systematic sen- distorting in a dynamic model due to the sitivity analyses being carried out by double taxation of saving. The effects of Glenn Harrison and Lawrence Kimbell a tariff are different in models with or (1983) who have computed over a million without international factor mobility, or solutions to their model in exploring ro- with or without a downward rigid real bustness. The main difficultyin their work wage. Conflicting economic theories are appears to be synthesizing the results so not resolved merely by putting numerical that a clear judgment on robustness can values on parameters in specified func- be made. Some things are little affected, tional forms, and some degree of summary others more so. Also, how these results judgment by modelers in selecting the translate to other models is unclear. particular theoretical structure to be used seems inevitable in work in this B. Model Preselection area. A related difficulty, common to all A further difficulty with the applied modelers, is that in choosing their models is the set of issues raised by prese- model structure, they have found there is lection (i.e., the necessity to decide on a no single all-purpose, general-equilibrium particularmodel structure before the pol- model that can be used. In order to work icy analysis proceeds). A good way of illus- on a particular policy issue in a particular trating this problem is to consider the clas- country, modelers have had to find some sic Harberger analysis of the impacts of simple way of closing the model with re- corporate tax. Using the standard assump- spect to time (savings and investment), 1046 Journal of Economic Literature, Vol. XXII (September 1984)

space (foreign trade and factor mobility), issue, a significant portion of the model and other issues such as government ex- is often unimportant. With smaller-scale penditures, taxes, and regulatory activity. models, it is clearly much easier to identify Models differ in their methods of closure key parameters that affect results, to work and this makes a comparison among mod- with those parameter values and subse- els difficult. It also presents challenges to quently to trace through the main effects theorists to work out the implications of of the policy change being evaluated. some of these closure rules, which have However, it seems counterproductive to not always been fully thought through. reformulate models repeatedly for each policy application. Also, excessive use of C. "Theoretical"Pedigree small-scale models naturally raises the is- Another issue with applied models de- sue of whether or not the crude level of rives from the attempt to develop models aggregation in the models results in sys- that are consistent with the theoretical tematic biases. Shoven's (1976) work indi- general-equilibrium literature developed cates that disaggregating from 2 to 12 sec- in the 1950s and 1960s, and thus allow tors in his analysis of the impacts of for welfare statements on policy issues. distortionary capital income taxes in the Because of the difficulties in accommodat- United States increases welfare loss esti- ing a wide range of empirical phenomena mates by around 30 percent, but a system- in model building, there is often a ten- atic investigation of the aggregation issue dency to depart from the essential struc- in the models has not yet been done. ture and graft on ad hoc portions of the Perhaps the main point to be kept in model not rooted in traditional theory. mind relates not so much to the use of These include instances where the price existing models but rather the strategy to level affects resource allocation, exchange be followed in developing new models. rates appear to have real effects, and un- Existing models represent sunk costs, and employment is present. Unfortunately, even if they are overly elaborate for the the problem is, the models that make ma- particular issue at hand, it still seems jor departures from known theoretical worthwhile to see what the model has to structures can become difficult to inter- say. For new models, experience gained pret. The conflict between modelers' de- so far does suggest that it is well worth- sires to build realistic models which seek while to consider with care exactly what to capture real features of the policy issue the model will be used for and how much at hand, and to stay within the realm of detail makes sense before embarking on developed economic theory is something model construction. that seems to be increasingly apparent in Despite these problems, models are some of the more recent models. making contributions to policy debate by providing more refined calculations of ef- D. Issue-Specific versus General-Purpose ficiency costs and distributional impacts Models than previously available. The point to be Another issue, raised increasingly by emphasized is not that these models are the modelers themselves, is the design either right or wrong, but that policy deci- question of large-scale, multipurpose sions have to be made and that these mod- models versus smaller-scale, issue-specific els are capable of providing fresh insights models. Models developed in the early on policy options not available from any 1970s have, over time, become larger in other source. Sometimes results will be scale and now provide a multipurpose ca- dismissed as unconvincing; on other occa- pability. However, in analyzing any one sions policymakers may stop and think, Shoven and Whalley: Applied General-Equilibrium Models 1047

and occasions may arise when a policy- cation of a general-equilibrium model maker's prior position will actually be suitable for analyzing the policy issue un- changed. We would never advocate slav- der discussion, and how reliable are results ish mechanistic use of any of these models from this model? The debate in the 1930s in policymaking, but our view clearly is was in many ways the inspiration for the that their potential contribution seems to work in the 1960s on general-equilibrium be large.6 computation. The experiences of model- ers in the 1970s and 1980s may prove to VII. Directions for Future Research be the impetus for a new genre of work on specification of general-equilibrium The directions that seem fruitful for fu- systems. ture research partially reflect our com- Other questions arise from the experi- ments in preceding sections, and partially ence of modelers with model design. One our experience thus far with our own of the most common problems encoun- models. While computing equilibria is no tered by modelers is the necessity to be longer the technical difficulty it seemed simultaneously a "jack of all trades." fifteen years ago, specifying the model for Modelers must know general-equilibrium which the equilibrium is to be computed theory so that their models have a sound remains a challenge. Better data, and es- theoretical basis; they must know how to pecially more and better elasticity esti- solve their models; they need to be able mates seem to be crucial to advancement to program (or at least communicate with of the field. In the past, one of us has gone programmers); they must understand the so far as to argue for the establishment policy issues on which they work; they of an "elasticity bank" in which elasticity have to know about data sources and all estimates would be archived, evaluated by their associated problems; and they have groups of "experts" (even with a quality to be conversant with relevant literature, rating produced) and an on-file compen- especially that on elasticities. Not surpris- dium of these values maintained. While ingly, modelers can at times feel a sense this may be overly ambitious, the general of inadequacy when faced with colleagues direction is one that is sorely needed. specializing in just one of these topics. Equally, the robustness and estimation This need to do several things well can issues are both worthy of considerably also inhibit graduate students from doing more attention. Years ago in the debate thesis work in the area. Perhaps a future on central planning in the 1930s, Lionel direction is teams of modelers, each with Robbins referred to the difficulty of solv- different skills, run on the lines of research ing the millions of equations characteriz- groups in natural sciences. While a "Man- ing a Pareto optimal allocation. In this de- hattan Project" for general-equilibrium bate the prior question (How do you know modeling may be going too far, a team how to write the equations even before built on complementary modeling, com- you worry about solution?) was not fully puting, and data skills would almost cer- discussed. The robustness and estimation tainly be able to make outstanding contri- issues are precisely these questions: What butions to the field. is the most reasonable numerical specifi- A further fruitful direction, as yet unex- 6 A useful survey of the way in which large-scale plored, is to develop more fully the impli- energy models have been used in the Energy cations of the applied work of the last Modelling Forum at Stanford (in ways that are not decade for theoretical work. Joseph dissimilar to what we have in mind) is contained in "Modellingfor Insights, Not Numbers" by H. G. Schumpeter once labeled Walrasian gen- Huntington, J. P. Weyant and J. L. Sweeney (1982). eral equilibrium as the "Magna Carta" of 1048 Journal of Economic Literature, Vol. XXII (September 1984)

economics, and others subsequently ar- of production and preference functions in gued that general-equilibrium analysis has these models is the same as in their theo- no operational content. The theorists retical counterparts, use of the computer might want to make a judgment as to permits the quantitative analysis of large- whether the experience with applied dimensional models. Qualitative analysis models supports or denies this claim and of an issue in a general-equilibrium frame- how they might redirect their work. The work can often only identify potentially experience of modelers in finding they offsetting effects, and this new quantifica- need closing rules, simplified treatment tion offers a way to determine the size of various features and the like, seems to of the net effect. Also, qualitative analysis indicate a need to be more specific rather is frequently unsatisfactory for policymak- than more general in approaching equilib- ers who want quantitative orders of mag- rium modeling. What are the properties nitude to tell them which policy changes of these simplified treatments, and how are significant and worth pursuing. The do they affect results? applied general-equilibrium models in Finally, it is worth raising the issue of these fields seek to help out in both these data organization and their use in applied directions. equilibrium models. Since the work of Si- A number of policy findings have thus mon Kuznets and the early Keynesian far been generated by these models. In macromodels, our national accounting the tax models, a general theme seems procedures have been heavily oriented to- to be that efficiency costs (deadweight ward calculating macroaggregates rather losses) of taxes may be more severe than than subaggregate microeconomic detail. had previously been supposed. This is es- As a result, full Walrasian accounts do not pecially the case with marginal dead- appear in the publications of statistical weight losses from taxes. A further finding agencies. One cannot, for instance, open suggests that tax systems may be pro- a statistical publication and identify sepa- gressive in their distributional impact, rate demand and supply accounts. In con- rather than proportional as often sup- structing their benchmark equilibria to posed. In the trade models, the role of which they calibrate their models, this is terms-of-trade effects and the difference implicitly what the new generation of ap- between national and global interests is plied general-equilibrium modelers is do- an important theme. ing. Perhaps the next ten years might see As with all such modeling efforts, policy further progress in this direction, possibly statements generated by these models through an expansion of the social ac- have to be treated with an appropriate counting matrix approach developed by degree of caution. However, our view is Richard Stone and others. that these models have already con- tributed to policy debate, and if used VIII. Conclusion sensibly can make further important contributions. This is especially so with In this paper we have surveyed some estimates of combined efficiency and dis- recent, applied general-equilibrium mod- tributional effects of policies where, prior eling efforts in the areas of taxation and to these models, no wholly satisfactory international trade. These are most easily way of simultaneously quantifying these understood as attempts to quantify the im- effects existed. pacts of alternative tax and trade policies REFERENCES within the traditional general-equilibrium ALAoUZE, CHRIS M. "Estimates of the Elasticity of framework. Although the basic structure Substitutionbetween Imported and Domestically Shoven and Whalley: Applied General-Equilibrium Models 1049

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