Applied General-Equilibrium Tax Modeling
Author: John B Shoven

The general-equilibrium model has long been the centerpiece of economic theory, but its development through this century has been frustratingly slow. Despite its formalization by Leon Walras late in the nineteenth century, a formal proof of the existence of an equilibrium of the model was not established until the 1950s. It is surprising that Marshallian competitive general-equilibrium microeconomics developed so fully in the absence of even a proof that prices existed that simultaneously cleared all markets. The breakthrough of the 1950s was disappointing in one sense—despite demonstrating existence, the proofs did not determine the equilibrium set of prices. It took another decade and breakthrough to develop reliable algorithms for computing equilibria. The work of Herbert E. Scarf and Harold W. Kuhn in the middle to late 1960s provided this capability.

Abstract

The general-equilibrium model has long been the centerpiece of economic theory, but its development through this century has been frustratingly slow. Despite its formalization by Leon Walras late in the nineteenth century, a formal proof of the existence of an equilibrium of the model was not established until the 1950s. It is surprising that Marshallian competitive general-equilibrium microeconomics developed so fully in the absence of even a proof that prices existed that simultaneously cleared all markets. The breakthrough of the 1950s was disappointing in one sense—despite demonstrating existence, the proofs did not determine the equilibrium set of prices. It took another decade and breakthrough to develop reliable algorithms for computing equilibria. The work of Herbert E. Scarf and Harold W. Kuhn in the middle to late 1960s provided this capability.

The general-equilibrium model has long been the centerpiece of economic theory, but its development through this century has been frustratingly slow. Despite its formalization by Leon Walras late in the nineteenth century, a formal proof of the existence of an equilibrium of the model was not established until the 1950s. It is surprising that Marshallian competitive general-equilibrium microeconomics developed so fully in the absence of even a proof that prices existed that simultaneously cleared all markets. The breakthrough of the 1950s was disappointing in one sense—despite demonstrating existence, the proofs did not determine the equilibrium set of prices. It took another decade and breakthrough to develop reliable algorithms for computing equilibria. The work of Herbert E. Scarf and Harold W. Kuhn in the middle to late 1960s provided this capability.

The ability to compute equilibria of relatively complicated general-equilibrium models opened the door to what may be referred to as applied general-equilibrium modeling. It seemed natural to be able to add to these models some features of the real world, such as governments, taxes, tariffs, and transfer payments, specifying them so that they resembled actual economies and performing policy evaluation with them. Before the development of the algorithms, general-equilibrium analysis was limited to the two-by-two analytic or graphic models associated with Harry G. Johnson, James E. Meade, and Arnold C. Harberger. Now, larger and more realistic models were feasible.1 The purpose of this paper is to describe the models and techniques that have been developed for using applied general-equilibrium analysis for evaluating tax policy. The paper also mentions some of the results to date, the shortcomings of current models, and the expected directions of further developments.

I. Fundamental Structure of Applied General-Equilibrium Models

General-equilibrium models have four essential ingredients. There must be a specification of (1) the endowments of consumers, (2) their preferences, (3) the production technology, and (4) the conditions of equilibrium.

In general, consumers may possess endowments of any or all of the commodities in the economy. Often, in practice, consumers are endowed only with factors of production (capital and labor). The preferences of consumers are specified with the demand function for each commodity. Commodity demands are nonnegative and depend on all prices in a continuous manner. They are homogeneous at degree zero in prices, meaning that only relative prices matter. Market demands are the sum of individual household demands, and they satisfy Walras’s law. If some notation is introduced, the consumer side of the model can be specified. Let N be the number of commodities (including factors), Wi be the total endowments of commodity i, and Di (P), i = 1,…, N be the market demand functions. With this notation, Walras’s law now states

Σi=1NPiDi(P)=Σi=1NPiWi

The value of market demands must equal the value of market endowments at all prices. This condition automatically holds if market demands are simply the sum of individual demands when the individuals are subject to their budget constraints.

On the production side of a general-equilibrium model, technology is usually described by a set of constant-returns-to-scale activities or by production functions that exhibit nonincreasing returns to scale. The advantage of the activity-analysis approach is that the conditions for equilibrium are very simple when production is modeled in this way. On the other hand, production functions are more convenient to use in applied work. They are easily given parameters, since most of the relevant econometric literature involves their estimation.

With the activity-analysis approach, the J activities available to the economy can be listed in an (N × J) matrix A, where the aij elements are negative for inputs and positive for outputs. The first N columns

A=[1000a1,N+1a2,N+1a1,Ja2,J...01aN,N+1aN,J]

of this matrix are disposal activities. Joint products are possible; however, activities are restricted to satisfy the condition of boundedness that AX+W is bounded from above at any nonnegative set of J activity levels X The interpretation of this condition is that the production possibility is finite in all dimensions.2

In the activity-analysis modeling of production, equilibrium is characterized by a nonnegative vector of N prices and J activity levels (P*, X*) so that

(1) demand equals supplies for all commodities

Di(P*)=Σj=iJaijXj*+Wi for i=1,….,N

and

(2) activities in use break even, with those not used having negative economic profits.

Σi=1NPi*aij0(=if Xj*>0) for j=1,….,J

A simplified numerical example may illustrate the general-equilibrium structure. For expositional purposes, consider a model with two final goods (manufacturing and nonmanufacturing), two factors of production (capital and labor), and two classes of consumer. Consumers have initial endowments of factors but no initial endowments of goods. The “rich” consumer group owns capital, while the “poor” group owns labor. Production of each good takes place according to a constant elasticity of substitution (CES) production function, and each consumer class has demands that are derived from maximizing a CES utility function subject to its budget constraint.

The production functions are given by

Qi=Φi[δiLiσi1σi+(1δi)Kiσi1σi]σi1σii=1,2,

where Qi denotes output of the ith industry, Φi is the scale or units parameter, δi is the distribution parameter, Ki and Li are the factor inputs, and σi is the elasticity of factor substitution.

The CES utility functions are given by

Uq=[(α1q)1σq(X1q)σq1αq+(α2q)1σq(X2q)σq1σq]σqαq1q=1,2

where Xiq is the quantity of good i demanded by the qth consumer, af are share parameters, and αiq is the substitution elasticity in consumer class q’s CES utility function.

If consumers maximize these utility functions subject to the constraint that expenditures not exceed income derived from the sale of endowments, the resulting demand functions are

Xiq=αiqIqPiσq(α1qP11σq+α2qP21σq)i=1,2q=1,2

where Iq is individual q’s income level.

With this structure, a “toy” model can be specified, with the following values of the parameters.

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This model has been solved using Merrill’s (1971) algorithm, which is an advanced variant of Scarf’s method. The results are shown in Table 1. At the prices computed, total demand for each output exactly matches the amount produced. It follows that producer revenues equal consumer expenditures. It also is true, to a high degree of approximation, that the labor and capital endowments are fully employed and that consumer factor incomes equal producer factor costs. The cost per unit of output in each sector matches the price, which means that economic profits are zero. The expenditure of each household exhausts its income. Thus, the solution closely approximates all the properties of an equilibrium for this economy. The closeness of the approximation can be enhanced by increasing the amount of computation time allowed for the algorithm used in the solution.

Table 1.

Equilibrium Solution: General Equilibrium for Illustrative Simple Model

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This illustrative example shows the kind of models that can be solved with the relatively new computer-based algorithms. However, it does not indicate how data are collected and incorporated and how taxes and other policy variables are introduced. Also, it is necessary to develop techniques of welfare economics to compare the equilibria that result from alternative policies.

II. Specification of Policy Models

Inclusion of Taxes

The first modification that is desirable in the simple model that was outlined in Section I is the inclusion of a system of taxes and government expenditures. Taxes may be imposed on the purchase of goods and services by consumers, the use of factors and intermediate inputs by producers, the receipt of income by consumers, and the final output of the various production sectors. The tax rates may differ for each good, consumer, and producer. The government uses the tax proceeds to finance transfer payments to consumers and to purchase final goods and services. Most of the models that have been developed to date assume a balanced government budget, but recent work by Feltenstein (1983) incorporates a bond and money market into models of this type.

The method of including taxes and governments in the general-equilibrium framework was first shown in Shoven and Whalley (1973) and Shoven (1974). Conditions for equilibrium become demand equals supply for each commodity, firms in operation break even after taxes, and government receipts (including bond sales and money issuance in Feltenstein’s formulation) equal government expenditure. Walras’s law now states that the gross-of-purchase-tax value of demands equals the value of endowments less personal taxes plus transfer payments. It continues to be the sum of the individual household aftertax budget constraints.

Equal-Yield Tax Comparisons

Often, in consideration of replacement of one system of taxes with an alternative system, the relevant policy constraint is that the replacement set of taxes should generate the same real government revenue as the original set. When economic behavior is itself a function of tax rates, the rates required for matching the yields cannot be easily determined. In fact, a full general-equilibrium analysis is required to determine such rates correctly. The computational algorithms used can easily be extended to calculate not only an equilibrium for a new tax system but also a scaler that determines the level of tax rates. The user has some choice as to whether this scaler is additive or multiplicative to the rates in the tax system under examination and whether the adjustments of the equal-yield rate (determined by the scaler) apply to all agents and taxed activities or just to a subset of them. This technique is described in Shoven and Whalley (1977).

Production

The specification of production is somewhat more complex in the current computational general-equilibrium models than in the illustrative model presented here. The key difference is that intermediate inputs are incorporated, often with a fixed-coefficient technology. Substitution occurs only between primary factors in the production of value added, and then according to a CES or Cobb-Douglas function. The models in use vary in the level of disaggregation, with the number of production sectors varying between 4 and 33. For fixed coefficients for intermediate inputs, the production function for each sector can be written as

Q=Min[1a0VA(K,L),XNa1,,XNaN]

Most empirical models distinguish between industrial outputs and consumer goods for the simple reason that the data are classified differently. Industrial sectors involve such categories as forestry and fisheries, metal mining, and publishing and printing, while consumers purchase furniture, automobiles, and books. This fact is recognized in the models by incorporating a second stage of production, which converts industrial outputs into consumer goods. This technology is usually modeled as a fixed-coefficient conversion matrix.

With some exceptions (for example, Derviş, de Melo, and Robinson (1981) and Fullerton (1982)), capital is modeled as fully mobile between production sectors and thus earns the same aftertax rate of return from each sector. Fullerton’s model allows full mobility to new investment, which earns the same rate of return in all sectors engaged in new investment, but it fixes the industrial locale of capital, once it has been acquired. Derviş, de Melo, and Robinson have a similar “putty-clay” model of capital, although the allocation of investment may be set by arbitrary policy rules rather than by competitive rent seeking.

Consumption and Saving

Computational or applied general-equilibrium models were initially almost always static in nature, possibly including rather artificial saving and investment behavior. In recent years several of the models have been made dynamic, although this remains an area of active model development. The U.S. model with which the author is associated (along with his coinvestigators John Whalley, Don Fullerton, Charles Ballard, and Larry Goulder) now computes a sequence of essentially static equilibria connected by saving and capital formation.

The 12 consumer classes in the U.S. model act as if they were maximizing the nested utility function

U=U[H(Πi=1NXiλi,l),CF]

or some monotonic transformation of it, subject to their income constraint. The X’s are consumer goods (15 in number in the U.S. model), l is leisure, and CF is a composite commodity of future consumption. Both H and U are CES functions. The parameters of those functions determine the shares of income devoted to each commodity, to saving (the provision for CF), and to the “purchase” of leisure. They also determine two key elasticities in the models—the elasticity of labor supply with respect to the real aftertax wage rate, and the elasticity of saving with the real aftertax rate of return to capital.

In the U.S. model, consumers have myopic expectations regarding future prices and, in particular, regarding the future rate of return to capital. Future consumption is “acquired” by buying a fixed composition portfolio of real investments that offer an infinite annuity of returns. There has been some work on incorporating both perfect foresight and limited foresight into this model (Ballard and Goulder (1982)). Work is also being done to incorporate life-cycle behavior where a utility function such as

U=0TH(X,l)eδtdt

is maximized, subject to a lifetime wealth constraint.

Foreign Trade

Applied general-equilibrium modeling is used in the evaluation of customs unions, tariffs, and trade restrictions, and several models focusing on those issues have been developed. (See, for example, Miller and Spencer (1977), Feltenstein (1980; 1982), and Whalley (1982 b).) Here, let us concentrate on the foreign trade specification of models that are designed basically for evaluating domestic tax policies.

International trade is usually modeled extremely simply. In the U.S. model, the standard specification is one that has a constant elasticity of export demand and has import supply equations. Trade balance is imposed, and there is no international mobility of capital. A richer specification of the foreign sector, including international capital markets, was investigated by Goulder, Shoven, and Whalley (1982). The impact of domestic tax policies was shown to be quite sensitive to international capital mobility and to the credit granted in the United States for foreign taxes paid. Other tax models (Ballentine and Thirsk (1979), Keller (1980)) include capital flows, while some (Slemrod (1981) and Auerbach, Kotlikoff, and Skinner (1981)) have no foreign sector at all.

Financial Sectors

Current general-equilibrium tax models clearly owe a great deal to the pathfinding work of Arnold Harberger (1959; 1962; 1966). He introduced the two-sector general-equilibrium framework to public finance and was one of the first to investigate the issue of tax incidence as it is known today. In many ways, the proper approach to thinking of the current models is as super-Harberger models.

One severe shortcoming of these models is the total absence of financial markets. They are “real” models solving for relative prices, but there are no debt instruments, money, financial intermediation, or deficits. Integrating financial and real markets in these models is perhaps the current area of greatest research activity. Feltenstein (1983) has added money and government bonds as well as foreign exchange markets to this general model. Slemrod (1981) has attempted to incorporate modern portfolio behavior on the part of consumers, while Fullerton and Gordon (1981) have begun to deal with issues of corporate financial policy and behavior toward risk.

Given that countries experience large government deficits, current account trade imbalances, and sizable accumulated foreign debts, the inclusion of these features in policy models is clearly important. The general issue of the “crowding out” of private sector investment through government borrowing can also be addressed in this framework.

Data Requirements and Parameter Specification

In applying general-equilibrium models, a complete equilibrium data set must be assembled. This includes factor usage by industry, an input/output table, consumer expenditures by commodity and incomes by source, government expenditures and tax collections, and information on foreign trade and investment. The normal practice is to gather this data from available sources for a particular year. In general, such data are inconsistent. For example, total labor payments by employers do not match total labor income. To be useful, the data must be adjusted for consistency. This adjustment requires some judgment as to which data are most reliable and which should be changed so as to be consistent.

The consistent data represents what is often referred to as the “benchmark” equilibrium. The strong assumption is made that the data represent an equilibrium of the economy. The construction of data sets of this type is described in St. Hilaire and Whalley (1980), Piggott and Whalley (1983), and Ballard, Fullerton, Shoven, and Whalley (1983). Since the benchmark data are usually presented in value terms, units must be chosen for goods and factors to obtain separate price and quantity observations. A commonly used type of unit conversion, originally adopted by Harberger, is to choose units for both goods and factors that have a price of unity in the benchmark equilibrium.

With the benchmark observation at hand, parameters are then chosen so that the solution to the model explicitly replicates the benchmark data. This procedure is termed model calibration. Values of the parameters thus generated can then be used to solve for a different equilibrium under alternative policy regimes. This is usually termed a counterfactual or policy replacement equilibrium.

The typical calibration procedure involves only one year’s data or one single observation, which may be an average over a number of years. Depending on the complexity of functional forms used, the data may not uniquely identify the parameters. With Cobb-Douglas functions, a single benchmark observation serves to uniquely identify the values of the parameters, since expenditure and factor shares by sector are known. With other functions, it is typically true that an infinite number of combinations of parameters can replicate the data in the required manner. In such cases, extraneously specified elasticities usually serve as identifying restrictions. Once specified, these allow the other parameters to be determined uniquely from the equilibrium observation.

The extraneous specification of elasticities can be thought of as determining the curvature and position of isoquants and indifferent surfaces. If Cobb-Douglas preference functions are chosen, a single observation of a point and slope at that point of an indifference curve is sufficient to uniquely determine the parameters of the function. If CES functions are used, extraneous values of substitution elasticities are required, since the curvature of indifference curves, described by the single elasticity parameter, is not given by benchmark data. For demand functions of a linear expenditure system, income elasticities are determined, once the origin coordinates for utility measurement are known. The current procedure in setting the additional parameters is to scan empirical literature to select appropriate values of substitution elasticities for the underlying utility and production functions. The primary role of calibration is thus to determine the shares and unit parameters in these functions, once elasticities are known. No statistical test of the chosen model specification is involved, since a deterministic procedure is employed for calculating the values of the parameters from the equilibrium observation. This entire procedure is clearly dependent on both the accuracy of the assembled data and the assumption that it represents an equilibrium. Also, the key role played by elasticities used in these models becomes immediately apparent.

Once the calibration procedure is completed, a full model is available and can be used for policy analysis. As indicated in Figure 1, any policy change can be specified, and a counterfactual equilibrium for a new policy regime can be computed. Policy appraisal then proceeds on the basis of paired comparisons of counterfactual and benchmark equilibria. If further policy changes are to be evaluated, the specification of policy changes is repeated.

Figure 1.
Figure 1.

Flow Chart for Typical Applied General-Equilibrium Model

Citation: IMF Staff Papers 1983, 002; 10.5089/9781451946895.024.A005

There are a number of reasons why this calibration approach, rather than a more direct econometric approach, is so widely used in setting the parameters for applied models. First, in some of the models, many thousands of parameters are involved; to estimate all these parameters of the model simultaneously by using time-series methods would require an unrealistically large number of observations. Second, the way in which benchmark data sets are used to generate the values of the parameters under calibration involves taking an observation in value terms and then decomposing it into separate price and quantity observations. Benchmark equilibrium prices, by construction, represent unity in each benchmark equilibrium, making it difficult to sequence equilibrium observations with consistent units through time, as would be required for time-series estimation. These problems, combined with the difficulty of incorporating equilibrium restrictions into a satisfactory estimation procedure, have thus far largely excluded complete econometric estimation of general-equilibrium systems, although some progress in this direction has been made in recent work by Mansur (1981). Mansur, for instance, notes the difficulties in simply writing down a likelihood function for a maximum-likelihood procedure incorporating full-equilibrium restrictions. He suggests a partitioning approach, using segmented production and demand systems, with a third segment incorporating their equilibrium interdependence. Other attempts at econometric estimation of complete-equilibrium systems occur in the work of Allingham (1973) and Jorgenson (1983).

Welfare Evaluations

A counterfactual equilibrium is computed and is compared with the observed economy (which is assumed to represent an equilibrium). For a dynamic model, a dynamic path of prices and endowments is computed (the capital endowments being endogenous). This path is compared with the path of the economy when there is no policy change. For the U.S. model, the investigators have assumed that the data for the base year (1973) represent not only a static equilibrium but one that lies on a steady-state growth path. Thus, without any policy change, relative prices remain constant, and the economy simply gets larger in a completely balanced manner. When an unanticipated policy change is announced, the economy goes through a transition period but eventually resettles into a new steady-state growth path. The model thus computes both the transition path and the long-run comparative steady states.

Without a social welfare function, it is impossible to state unambiguously that one equilibrium or a path of equilibria is better than an alternative, unless the improvement follows Pareto’s law—that is, everyone is better off. This is, unfortunately, rarely true. What the investigators do in this model in measuring the change in economic efficiency or the welfare of a policy change is analogous to the measurement of costs and benefits in cost-benefit analysis—that is, apply the Kaldor criterion: a situation is superior if the winners could compensate the losers, even if this compensation does not take place. The criterion has well-known theoretical shortcomings (Tibor Scitovsky showed, for instance, that it need not be transitive), but it is widely used for policy evaluation. In the U.S. model, the investigators calculate the dynamic or static compensating variation for each household and sum these for an overall welfare measure. The government’s expenditures do not enter into this calculation—an omission that is less serious owing to the equal revenue-equal expenditure constraint described earlier; that is, the government has the same real resources available to it under both the old and new policy regimes.

The general-equilibrium approach offers a complete description of the economy for alternative policy scenarios. Substantial information is lost in the endeavor to compare the equilibria with a single number. The changes in welfare for each consumer can be computed, and the changes in factor usage, expenditure patterns, and industrial output levels can be examined. It should also be said that, for large policy changes (such as the institution of a new tax regime or the construction of a project such as the Aswan Dam), only a general-equilibrium analysis can capture the interactive effects.

III. Applications

In this section, let us review some of the applications that have been completed using the U.S. model. It should be stated at the outset that a large number of other models have been used for policy evaluation in other countries. These include Whalley’s (1975) evaluation of the major U.K. tax reform package of 1973, Miller and Spencer’s (1977) assessment of the United Kingdom’s entry into the European Economic Community, Piggott’s (1979) evaluation of Australian tax policy, Feltenstein’s (1980) analysis of trade restrictions in Argentina, Whalley’s (1982 b) examination of the effects of the Tokyo Round trade agreement, and Serra-Puché’s (1983) policy model for Mexico. Similar models are being used for energy economics (Hudson and Jorgenson (1978) and Borges and Goulder (1983)), development policy (Derviş, de Melo, and Robinson (1981)), and even economic history (James (1981)).

The U.S. model consists of 19 production sectors, 16 consumer goods, and 12 consumer groups. It is a dynamic model incorporating the complete tax system (federal, state, and local personal income taxes, corporate taxes, sales and excise taxes, social security taxes, etc.). The benchmark data set represents the 1973 economy. The model’s development was financed by the U.S. Treasury Department; it is currently in use there, most recently in evaluating flat-tax proposals.

The policy that has received the most attention in the United States from general-equilibrium modelers is the integration of the U.S. corporate and personal income tax, probably because Harberger originally examined the incidence and efficiency consequences of the corporate income tax with his two-sector model. Corporate equity capital is taxed twice in the United States in that the earnings of firms are subject to the 46 percent corporate income tax. Aftertax earnings are either distributed as dividends and taxed at the personal level or retained. If retained, the earnings may lead to partially taxable capital gains. Capital income from other sectors, particularly real estate and to some extent agriculture, is lightly taxed. The result is an inefficient allocation of capital across sectors and, quite possibly, a distortion of the consumption/saving decision.

Another policy that has been evaluated with the U.S. general-equilibrium model is the possibility of taxing consumption rather than income at the personal level. This result could be accomplished by first establishing the household’s income and then allowing a deduction for all saving. As the tax would be direct, special exemptions could be granted the blind, the elderly, those with large families, etc., and the tax could have increasing marginal rates. The advocates of a consumption tax argue that it does not distort the consumption/saving decision, as does an income tax, and that it is better to base taxes on a household’s withdrawals from the social product (consumption) than on a rough approximation of their contribution to it (income).

Before evaluating the consumption tax, it is important to recognize that the United States already has a partial consumption tax, since roughly half of saving is not subject to tax: 30 percent through retirement plans and life insurance, where the tax is deferred until withdrawal (as with a consumption tax), and 20 percent in the form of new housing construction. Housing must be purchased with aftertax dollars (i.e., the saving/investment is not deductible), but the return on it, imputed or otherwise, is very lightly taxed. Thus, it is not taxed twice, as with an income tax; its treatment is more nearly analogous to a consumption tax.

Table 2 presents the dynamic efficiency gains for a consumption tax and corporate tax integration. The figures are in 1973 dollars. The key parameters of the model are set at 0.4 for the saving elasticity and 0.15 for the labor supply elasticity. The elasticity for factor substitution in value added varies by industry, but it is generally slightly less than unity. The gain in efficiency depends on how the lost revenue is compensated for. For example, if a consumption tax is instituted by making 80 percent of saving deductible (over and above the 20 percent currently saved through new housing acquisition), row (1) of Table 2 shows the gain to be $686 billion if the revenue shortfall was made up with lump-sum tax increases. However, if marginal tax rates are increased in a multiplicate manner (everyone’s ratio is multiplied by a common X > 1.0), the gain is $621 billion, while if they increased in an additive manner (t’ = t + X), the welfare measure increases by $636 billion. These numbers are about 1.25 percent of the present value of future national income, expanded to include the value of leisure. The discount rate used is each consumer’s aftertax rate of return to capital before the tax change, which averaged a real rate of return of 4 percent.

Table 2.

United States: Dynamic Welfare Effects in Present Value of Compensating Variations over Time

(In billions of 1973 dollars) 1

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The numbers in parentheses represent the gain as a percentage of the present discounted value of consumption plus leisure in the base sequence. This number is $49,863 trillion for all comparisons and accounts for only the initial population.

Row (2) of Table 2 shows the welfare gains of integrating the two income tax systems. The results are more sensitive to the replacement tax used for maintaining government revenues, both because integration involves the loss of more tax receipts and because it does not stimulate saving, capital formation, and growth as much as does the consumption tax. Row (3) combines the policies of the first two systems and shows that the efficiency improvement is approximately additive.

Since 80 percent of total savings is deductible under the plans of rows (1) and (3) and 20 percent of total savings flow into tax-favored housing, these plans capture the intertemporal effects of a full consumption tax. However, since any savings can be used for housing, these plans leave an intersectoral distortion in favor of owner occupancy. The plan of row (4) allows full deductibility of savings and eliminates the preference for housing. Gains are larger, as expected. The efficiency gain of the plan in row (4) relative to the current tax system is roughly $1.5 trillion with lump-sum revenue replacement, $1,350 billion with multiplicative marginal rate surcharges, and $1,390 billion with additive marginal rate surcharges. Row (5) examines a partial move toward a consumption tax—halfway between the current 30 percent sheltering of retirement plans and the 80 percent of row (1)—while row (6) exempts all saving from taxation, leaves the housing preference unchanged, and results in a personal income tax subsidy to saving. However, since this subsidy offsets the corporate income tax, which is left in place, total efficiency is enhanced relative to the plan shown in row (1).

The results shown in rows (7) and (8) indicate that the United States could move to a pure income tax and integrate the corporate tax with no loss in efficiency, but that a pure income tax alone would lose efficiency. For row (7), the tax base is increased, since imputed income from housing is included and existing savings deductions are eliminated. Thus, the tax rate can be lowered, rather than raised, to maintain government revenues. Results in row (7) show that moving to a pure income tax alone involves an efficiency loss of $579 billion if marginal tax rates are not lowered—primarily because the intertemporal distortions of the current system are worsened. However, if the marginal rates are reduced, the efficiency loss to the economy is lowered to roughly $470 billion. The improvement in the interindustry allocation of capital (resulting primarily from the taxation of the return to owner-occupied housing) tends to offset the deterioration in the intertemporal efficiency (now reduced by the marginal rate adjustments). Row (8) shows the results from a comprehensive single-level income tax plan involving corporate tax integration as well. Such a tax system lowers revenues and thus necessitates a rate increase to maintain the yield. When the rates are adjusted either multiplicatively or additively, the net efficiency impact of the package is negligible.

The results in Table 2 are sensitive to the elasticities incorporated in the model. For example, the $621 billion from row (1), with a multiplicative scaling of the marginal tax rates, becomes $411 billion if the uncompensated saving elasticity is zero and $1,279 billion if this elasticity is 2.0. A more thorough evaluation of these results appears in Fullerton, Shoven, and Whalley (1983).

Table 3 provides information on how long the economy takes to resettle into a steady-state growth path after a tax change occurs. Once the economy has completely adjusted to the new policy regime, all relative prices will again remain constant. For consumption tax proposals, the new steady state is characterized by a higher capital intensity and a lower relative return to capital. The results of Table 3 indicate that, for the cases with a savings elasticity of 0.4, roughly 40 percent of the adjustment is completed after 10 years and 80 percent after 30 years. The economy then asymptotically approaches the new steady-state growth path. The transition is accomplished much more rapidly with a savings elasticity of 2.0, despite the fact that the total adjustment is larger. Adjustments in capital/labor ratios proceed in patterns similar to the adjustments of the price ratios in Table 3.

Table 3.

United States: Time Path for Ratio of Rental Price of Capital to Wage Rate

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Refers to the number of the row in Table 2.

Interestingly, Ballard and Goulder (1982) find that the adjustment to a new steady state is slightly slower with perfect foresight and the institution of a consumption tax, since consumers are deterred from additional saving by the recognition that future capital deepening will depress the rate of return to capital.

In previous literature, estimates of the length of the long run have varied widely. Sato (1963) finds the adjustment to be extremely long (more than 100 years), while Hall (1968) and Summers (1981) find it to be surprisingly short (about 5 years). It is difficult to reconcile these various findings completely, but it is clear that a prime determinant is the strength of substitution effects in the model used for the analysis.

Ballard, Shoven, and Whalley (1982) made another set of computer runs, asking a question of more theoretical interest: What are the efficiency costs of the entire U.S. tax system? This question is of interest because efficiency issues are often treated as minor ones, relative to those of economic stability. The aim here was also to estimate the marginal cost of a government dollar raised by increasing taxes. In the past, efficiency costs have frequently been quoted as fractions of gross national product or as the deadweight loss relative to the revenue raised. The former measure is ridiculous if the question is whether a tax on automobile tires or restrictions on steel imports are inefficient. The latter measure—the average distortion per dollar raised—does not often give the right answer either (average figures seldom do in economics). What has been computed, therefore, is the marginal distortionary cost per marginal dollar raised for each of the major tax systems in the United States.

The estimate here for the hypothetical experiment of removing the entire tax system and replacing it with a set of lump-sum levies (proportional to income and with sales taxes actually paid so as to minimize income and wealth transfers) is that the present value of welfare would increase by $3.3 trillion, which is roughly 6.7 percent of national income plus leisure, or 10 percent of national income. The primary result of removing all marginal taxes is tremendous capital deepening. The net of tax rental/wage ratio immediately climbs by 113 percent and gradually sinks from there to become 30 percent higher than its present value in the new steady-state growth path. The capital/labor ratio is 50 percent higher after 50 years. The labor supply also grows, being 19 percent higher in the first period, because leisure is no longer the ultimate tax shelter that it is under the current system.

These results are sensitive to the values of the key elasticity parameters, as shown in Table 4, although the general picture is preserved. The standard case is shown in row (2). The total loss represents 3.55 percent of expanded national income, even when both the uncompensated labor supply and saving elasticities are zero.

Table 4.

United States: Sensitivity Analysis with Respect to Key Parameters of Deadweight Loss of Total Tax System

article image

The figures in parentheses express the welfare gains as a percentage of the total present value of welfare from consumption and leisure, which is $49,863 trillion.

Table 5 contains the results of computing the marginal distortionary costs of the U.S. tax system. If all marginal tax rates were multiplied by 1.01, the effect would be to raise government receipts by $3,331 billion. Transfers to consumers amount to just under one third of government revenues; the question is whether this fraction of a marginal tax increase would also be returned to households as transfers. Table 5 computes the marginal cost of funds for exhaustive expenditures under the assumptions that transfers are adjusted when receipts increase and that they are held fixed.

Table 5.

United States: Relationship Between First-Period Marginal Tax Revenue Collections and Marginal Change in Welfare (Annualized to First Period) for Various Parts of Tax System

article image

If transfers increase, then $1,101 billion is returned to households. Further, of the $3,331 billion raised, the government itself pays $0,233 billion. Netting out the transfers and the government’s own tax payments, the funds available for a public project are $1,997 billion, shown in column (5). The decrease in consumer welfare is $3,520 billion, 1.76 times as much as the money available for the government project. Column (7) reflects this distortionary cost ($0.76) per dollar transferred to the public sector. If transfer payments are not increased, the government ends up with more net revenue and households have a larger decrease in utility, with the net result that consumers lose 1.52 times as much as the government raises. This fact is reflected in column (8).

The implications of these numbers, if accepted, are great. The $1.76 or $1.52 private cost of a marginal government dollar means that cost-benefit studies that use unity as the critical benefit/cost ratio support projects that are socially inefficient. They do this by not taking into account the resource waste caused by the distortionary taxes that are used to raise the additional revenues. The correct critical ratio would be 1.76 or 1.52, depending on how transfer payments react to the enlarged government budget. At a more theoretical level, the results indicate that Paul Samuelson’s conditions for the optimal provision of public goods should include

ΣconsMRSX,G=λMRTX,G

where λ is 1.76 or 1.52. Public goods not only use up resources in their manufacture but also are a cost to economic welfare in the distortionary taxes that they necessitate.

Rows (2)–(7) of Table 5 compute the marginal cost of each major type of tax. If these tax types were used in a third-best optimal manner, they would each have the same marginal distortionary cost per dollar raised. This cost would minimize the total deadweight loss for a given revenue using this given set of instruments. The results of columns (7) and (8) show that the U.S. tax system is far from this condition of optimality. An additional flat tax on labor by industry (payroll tax) could raise one dollar for as little as $1.19 in private welfare, whereas increasing the 1973 personal income tax rates would result in government dollars that cost $1.57 each at the margin, even if transfer payments are frozen.

The results of this table are elaborated on in Ballard, Shoven, and Whalley (1982). They illustrate a kind of analysis that cannot be carried out appropriately with partial equilibrium techniques.

IV. Conclusion

General-equilibrium analysis has developed from an abstract economic theory to a computational procedure and now to a tool that can be used for policy purposes. It is not always the appropriate technique; certainly, many issues are best examined at a very fine level of detail by using partial-equilibrium methods. The model also is inappropriate for very short-run forecasting of business and the business cycle and does not yet have the many rigidities (unions, rent controls, monopolies, transactions costs, etc.) that characterize real economies. Nonetheless, for analyzing the likely medium-run to long-run adjustments of an economy to a large policy change, the applied general-equilibrium model seems to be appropriate and to be ready for application.

*

Mr. Shoven, Professor of Economics at Stanford University and Research Associate of the National Bureau of Economic Research, was a consultant in the Fund’s Fiscal Affairs Department when this paper was prepared. He is a graduate of Yale University. The work described was supported by the National Science Foundation and the U.S. Treasury Department. The views are the author’s and do not necessarily represent the views of these organizations.

1

It is perhaps ironic that once the applied general-equilibrium models were developed, it was found that they could usually be solved with Newton-type methods that have long been available. Despite this finding, the expanding interest in computational general-equilibrium models is clearly due to the work of Kuhn and Scarf. Improved versions of their algorithms are now competitive with Newton methods in terms of computational speed, even in cases where the Newton algorithms converge.

2

Continuous constant-returns-to-scale production functions are similar to an infinite listing of activities to produce each output. For any set of input prices, one can compute the cost-minimizing method of producing a unit output for each output. This is the technique or activity that will be used at those prices (if output prices are sufficient for production to take place).

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