General Equilibrium Analysis of U.S. 

Taxation Policy 

Don Fullerton 

John B. Shoven 

John Whalley 

Comment 

Arnold C. Harberger 
General Equilibrium Analysis of U.S. 

Taxation Pol icy 

Don Fullerton 

John 8. Shoven 

John Whalley 

In this paper we report work in progress on the construction of 

a medium size general equilibrium model of the U.S. economy and 

taxation system. The model incorporates the full range of taxes 

currently employed in the United States. We identify 19 producer 

good industries, 16 consum~r goods, and 12 consumer types classified by income range. In general, taxes affect the economic behavior of both producers and consumers. The model (outlined in 

chart 1) is being constructed in an interactive, user-oriented form 

in order to allow consideration of many alternative changes in tax 

P<>licy. The model incorporates not only conventional consumer 

and producer behavior, but also savings and investment activity, 

foreign trade activity, and government purchase policies. The 

model is parameterized with 1973 data. The general capability of 

our approach is illustrated with a specific set of calculations performed by the model. We calculate the economic effects of removDON FULLERTON is with the Department of Economics at the University 

of California, Berkeley; JOHN B. SHOVEN is with the Department of 

Economics at Stanford University; and JOHN WHALLEY is with the 

Department of Economics at the University of Western Ontario. This work 

Was supported by the Office of Tax Analysis, U.S. Department of the 

Treasury. However, the views expressed by the authors are not necessarily 

those of the Treasury. We would like to thank the many people at the Commerce and Treasury Departments who have helped us; we are especially 

grateful to A. Thomas King for his assistance in many aspects of this work. 

(23) 
24 COMPENDIUM OF TAX RESEARCH 

C HART 1.- Diagram of the model structure 

Consuml•r side of l'<:onom~· l'rodun·r st<lt• .. r t·l u1 11111~ 

Ownt>rship of faetors I .. l'er-unrt cost minunizatron 

..... el in n1 se ld .. ~ ......... ·, l• 11i' ........ ·~~. ob l't "1 'h du r~ · .. 

i I ncoml· taxes pa id 

Transfers recei,·ed 

llisposablt• incomes 

• l'rodu•·••r taxt•s 

< 'onsunH"'I' tax<.'!-<i 

Fa«tor taXl'S 

Int• rnwd1atl'-USl' taxl•s 

l'•·r-unit fa•·tor dl'mands 

I lemands for consunwr 

products br household 

cit'l;•rmint>d 

Consunwr-good prices I ndust r~ · J!Hlss output,, 

nl·n·ssat·\ to llH'l't market 

dt>man'ils for final ust> 

Total ma rkt>t demands for 

consumer goods obtained 

Competitive e11uil1brium a;·htt·v•·d whl•n: 

1. Dt>ma nds equal supplil's for all )!oods and fattors; 

!\l arket dl'mands 

for product•r J!OOds 

for fi nal use 

llerl\·t·d fattor dt•mands that 

mt•••t market dt•nrnnds for 

product•r J!OOds 

~. Zero profits (net of taxes) pn•vail in all industrit•s; and 

:!. Tax receipts equal total J!m·ern nw'nt t•xp••nditu res. 

ing the distortionary elements of the taxation of income from 

capital. 

One major contribution of the present work is the assembling of 

a recent and consistent microeconomic data set that shows the 

interactive effects of all taxation policies. Such a data set, essential 

for a complete general equilibrium analysis of U.S. taxation policy, has never been constructed. This data set prnvides information 

not only on use of factors by industry (and taxes paid for these 

factors), but also on intermediate usage of products, outputs of 
---

EQUILIBRIUM ANALYSIS OF TAX POLICY 25 

both producer and consumer goods, purchases of consumer goods 

by household types, incomes by source and by household type, income taxes paid, and several other items, including business investment and foreign trade. Inconsistencies between these data 

sets and general equilibrium conditions are resolved using systematic adjustment procedures described in the paper. 

Despite the richness of the present structure in comparison with 

other available analyses, there are a number of ways in which 

further improvements could be made. The present model is motivated by a concern to produce within a reasonable period of time a 

manageable functioning model that provides realistic, if highly 

aggregated, analyses of tax change effects. It should be regarded 

as a pilot model that provides a base for future refinements. For 

instance, if detailed analysis of the effects of a complex reform of 

the personal income tax were to be undertaken, more richness of 

consumer groupings, emphasizing family and age characteristics, 

would be required. The approach draws on and extends that used 

by Whalley ( 1973) and Whalley and Piggott ( 1976) in their work 

on the United Kingdom tax system. 

An outline of our model is given in chart 1. In the next two sections we describe more fully the structure of the model and discuss 

our approach towards its parameterization. In the following sections we outline our data and we present our adjustments to make 

them mutually consistent. We go on to describe computational asI>ects of the solution of the model and we discuss uses of the approach and possible extensions. Finally, to illustrate the capability 

of the model, we analyze the tax change ref erred to above. 

The Structure of the Model 

Production Side 

On the production side of the model 19 industries are identified. 

Each industry produces a single output (or producer good) from 

a combination of primary factor inputs (capital and labor services) and the outputs of other industries. These industries are 

shown in table 1 along with the consumer goods considered. Industry input decisions are assumed to be made on the basis of cost 

minimization, and these decisions are affected by the U.S. tax sys-
26 COMPENDIUM OF TAX RESEARCH 

TABLE 1.-Classification of industries and consumer goods 

Industries Consumer goods 

1. Agriculture, forestry, and 1. Food 

fisheries 2. Alcoholic beverages 

2. Mining 3. Tobacco 

3. Crude petroleum and gas 4. Utilities 

4. Contract construction 5. Housing 

5. Food and tobacco 6. Furnishings 

6. Textiles, apparel, leather 7. Appliances 

products 8. Clothing and jewelry 

7. Paper and printing 9. Transportation 

8. Petroleum refining 10. Motor vehicles 

9. Chemicals and rubber 11. Services 

10. Lumber, furniture, stone 12. Financial services 

11. Metals, machinery, miscella- 13. Reading, recreation, misc. 

neous manufacturing 14. Nondurable-nonfood house12. Transportation equ i pm en t hold items 

13. Motor vehicles 15. Gasoline and other fuels 

14. Transportation, communica- 16. Savings 

tions, and utilities 

15. Trade 

16. Finance and insurance 

17. Real estate 

18. Services 

19. Government enterprises 

tern since the relative producer prices of inputs are altered for 

each industry. 

The decision to select these 19 industries was based on a number 

of considerations. An attempt was made to separate industries for 

which there are important differences in taxation, but the availability of data somewhat constrained this level of detail. The model 

has been kept within an overall dimensionality so that solutions 

can be executed within a reasonable amount of time and so that 

the basic data set can be manipulated. Considerably more detail 

can be considered, but at this stage our concern is to develop a 

manageable model that improves upon those currently available 

for partial or general equilibrium analysis of United States taxation issues. 

The use of primary factors by each industry is described by a 

separate constant elasticity of substitution ( CES) or Cobb-Douglas production function. The model embodies a capability for preselection of functional form in addition to selection of parameter 

values. Later in this paper we outline our procedures for selecting 

parameter values of these functions. 
EQUILIBRIUM ANALYSIS OF TAX POLICY 27 

The intermediate use of products by industries is described by a 

conventional fixed-coefficient input/output (I/0) matrix. The 

matrix is derived from published 1970 input/output data for the 

United States; some of the difficulties with the utilization of this 

data are discussed later. 

A number of taxation instruments are treated as production 

taxes and directly affect the cost structures of industries in the 

model. The corporation income tax, the corporate franchise tax, 

and the property tax are in combination treated as ad valorem 

taxes on capital services by industry. Social security tax, unemployment insurance, and workmen's compensation are treated as 

ad valorem taxes on labor services by industry. There is some discussion in the literature as to the appropriateness of treating each 

of these taxes in this way. For instance, the treatment of social 

security taxation as a set of benefit related contributions and the 

treatment of the corporate income tax as either a lump sum tax or 

a tax on the use of particular financial instruments by firms rather 

than as a tax on capital services have prompted considerable discussion in recent years. Our model abstracts from these problems, 

but we are aware of the controversies. 

In addition to the taxes on the primary factor inputs, we consider taxes on the intermediate usage of producer goods by industry and on the outputs of producer goods. Taxes paid on intermediate inputs include the registration fees paid on motor vehicles for 

business use. Producer output taxes include the federal manufacturers excise tax on tires, which is paid by purchasers for intermediate or final use. Table 2 contains the detailed treatment of all 

these taxes along with an outline of the treatment of the entire 

U.S. tax system. 

Consumption Side 

Within the personal sector, we have identified 12 consumer 

groups defined by their family gross of tax income as reported in 

the 1973 Consumer Expenditure Survey Data published by the 

U.S. Department of Labor. The number of groups has been restricted in order to keep the model to a manageable size, but more 

~nsumer groupings could be considered by the approach. In addition to income, such characteristics as family size, age or marital 

status of household heads, and regional location could be examined. 

Consumer demands are assumed to be generated by a process of 

utility maximization subject to a budget constraint. Any one of 

the conventional functional forms, such as Cobb-Douglas, CES, or 
28 COMPENDIUM OF TAX RESEARCH 

TABLE 2.-United States taxes and their treatment in the model 

Tax 

-corJ)-Orate taxes (including state and 

local) and corporate 

franchise taxes 

Property taxes 

Social Security taxes, 

unemployment insurance, and workmen's 

compensation 

Motor vehicles tax 

Retail sales taxes 

Excise taxes 

Other indirect business 

taxes and nontax 

payments to government 

Personal income taxes 

(including state and 

local) 

Treatment in model 

Ad valorem tax on use 

of capital services by 

industry 

Ad valorem tax on use 

of capital services by 

industry 

Ad valorem tax on us~ 

of labor services by 

industry 

Ad valorem tax on use 

of motor vehicles by 

producers and consumers 

Ad valorem taxes on 

purchase of consumer 

goods 

Ad valorem taxes on 

output of producers 

goods 

Ad valorem tax on ,output of producer goods 

Set of average and 

marginal income tax 

rates differing over 

consumer groups 

Problem areas 

Some argue for treatment as a lump sum 

tax; model treatment 

ignores role of financial instruments 

Differential rates 

across jurisdictions 

ignored 

Benefit-related nature 

of contributions; 

arbitrary distinction 

between public and 

private insurance 

programs 

In practice, a yearly 

registration fee and 

not a purchase tax; 

averaging over jurisdictions 

Averaging of rates 

over states 

Taxes often expressed 

as charge per unit 

physical measure 

such as volume 

Payments depend on 

output levels by industry to only limited 

extent; averaging of 

rates over states 

Detailed deductions and 

exemptions not specifically considered in 

model 

linear expenditure system (LES), can be used for this purpose; 

our computer programs allow preselection.1 From the demands 

for consumer goods, the derived demands for producer goods can 

be generated, and these are used in the solution of the model. 

1 The model can incorporate any continuous set of market demands that 

satisfy Walras law. Other functional forms may be programed in the future, 

but capability now exists to evaluate Cobb-Douglas, CES, or LES demand 

functions. The LES functions include minimum required purchase parameters, 

which must be separately estimated. 
s 

11 

at 

'e, 

1d 

rs, 

EQUILIBRIUM ANALYSIS OF TAX POLICY 29 

Consumer goods 2 are linked to producer goods through a transition matrix termed the G matrix. An element of this matrix, gii, 

is the amount of producer good i needed to produce one unit of 

consumer good j. The producer goods "retail and wholesale trade" 

and "transportation" are needed for the production of all (nonsavings) consumer goods. Savings is treated in the model as a 

separate consumer good that enters demand functions. It is assumed that savings earns a rate of return given by the current 

price of capital services corrected for changes in the price of 

capital goods. 

The model incorporates income taxes using an average rate 

(AR) and a marginal 1·ate (MR) for each consumer group. These 

data are obtained from the U.S. Treasury merged tax file and are 

reported in table 3. The average tax rates are used to estimate the 

group's income tax payments in 1973; however, the marginal tax 

rates are used to examine the effect of the income tax system on 

economic behavior. C()lllsequently, each consumer group's income 

tax liabilities are given by the formula: 

Income tax payments= (ARi) · (1973 Income of group i in 

real terms)+ (MRi) ·(Change in income from 1973 real 

value). 

For present purposes the simplified treatment of the tax code in 

terms of average and marginal rates for each consumer group is 

quite adequate. 3 But a considerable elaboration would be required 

to study the effects of a complex reform of the income tax system. 

State and local income taxes are modeled as "piggyback" or percentage surcharge taxes applying to the Federal levy. 

The model also includes a treatment of consumer taxes as ad 

valorem taxes on household purchases of commodities. Since none 

of the taxes considered in the model has a differential effect across 

households, a single vector of ad valorem consumer tax rates is 

used. These taxes are excise taxes on selected items and retail 

sales taxes. The complete treatment of these taxes appears along 

With other taxes in table 2. 

In addition t;o the consumer groups, there are three special classifications of demand patterns for investment activity, government 

Purchases, and foreign trade. 

~The classification of consumer goods is described in table 1. 3 

At the present stage of model construction, no labor/leisure choice has 

?een incorporated. There are no programing or model difficulties in building 

in such a feature; the difficulties are purely those of data. Even without a 

labor / leisure choice, the marginal tax rates of consumers are important for 

the model treatment of housing. 
30 COMPENDIUM OF TAX RESEARCH 

TABLE 3.-Average and marginal income tax rates by consumer groups 

(b) 

(a) Federal, 'S&L income 

Gross income taxes -;- gross of tax (c) 

including transfers income excluding Average marginal 

(in dollars) transfers (AR) tax rate (MR) 

0- 2,999 .0056 .0100 

3,000- 3,999 .0320 .0608 

4,000- 4,999 .0484 .1019 

5,000- 5,999 .0604 .1228 

6,000- 6,999 .0704 .1346 

7,000- 7,999 .0818 .1570 

8,000- 9,999 .0943 .1813 

10,000-11,999 .1039 .2078 

12,000-14,999 .1158 .2215 

15,000-19,999 .1357 .2618 

20,000-24,999 .1585 .2897 

25,000+ .2556 .4067 

Investment activity is modeled via the transition matrix relating 

producer to consumer goods. Consumer savings made on the basis 

of the anticipated rate of return on capital are converted into derived demands for producer capital goods by type, as appearing in 

the model. This treatment assumes an equality between savings 

and investment. 

Government purchases are derived from a Cobb-Douglas demand function defined over producer goods which holds expenditure shares constant across these items. Government real expenditures are assumed to equal tax receipts plus government net borrowings less transfers, since the general equilibrium approach requires that the government budget must be balanced. 

The foreign trade sector is treated simply so as to close the 

model. The net value of exports less imports for each producer 

good is assumed to be constant. This enables calculation of the net 

quantity transactions at any given vector of producer prices and 

transformation from domestic demands to market demands. The 

constancy in value terms allows for a zero trade balance to be 

maintained at any set of prices if it holds initially. This treatment 

of foreign trade is unsuitable for a detailed analysis of tariff 

policy, but meets our objective of a manageable model for analysis 

of domestic impacts of taxation policy. 
EQUILIBRIUM ANALYSIS OF TAX POLICY 31 

Parameterization 

The broad approach to the parameterization of our model uses 

the concept of a benchmark equilibrium data set. Parameters are 

chosen such that this data set is replicated by the model as an 

equilibrium solution. The technique involves the use of a number 

of detailed data sets that require adjustments to make them mutually consistent in the sense that they satisfy the equilibrium conditions of the general equilibrium model. We describe later the 

adjustments performed to transform our basic data into this form. 

Once arranged in this form, the basic data are used to generate 

parameters for the behavioral equations of our model. This involves a prior step of decomposing our equilibrium observations on 

transactions in value terms into separate observations on equilibrium prices and quantities. For this purpose we follow Harberger 

1959, 1962, 1966) by defining otherwise unobservable physical 

units of both factors and goods as those amounts that can be sold 

for $1 at the observed equilibrium. 5 Thus, our benchmark equilibrium data set can be separated into price and quantity observations; 

all benchmark equilibrium market prices are unity and all benchmark equilibrium quantities are those given by the data in value 

terms. 

From the quantity and price observations and the assumption of 

agent optimization it is possible to infer behavioral equation 

parameter values that are consistent wfth the equilibrium data 

set. For instance, if we assume a given industry has a CobbDouglas production function and cost minimizes, the factor employments observed in that industry are the direct outcome of solving the cost minimization problem at prices of unity. This uniquely 

determines the weighting parameters of the Cobb-Douglas functions. Similarly on the demand side, if a given consumer has a 

Cobb-Douglas utility function his commodity purchases at equilibrium prices of unity imply unique values for the utility function 

exponents. Other equilibrium conditions are used to determine remaining parameters; for example, the zero profit conditions by 

4 These procedures are explained more fully by Whalley and Piggott (1977). 

s We define units of productive factors as those amounts capable of generating $1 of income net of factor taxes rather than net of all taxes. Because different income recipients face different marginal income tax rates, 

units must be defined by factor rewards before income taxes. The imputed 

capital income from home ownership is treated in the model as fully taxable, 

and a subsidy is given at each group's marginal tax rate on purchases of 

owner-occupied housing services. 
32 COMPENDIUM OF TAX RESEARCH 

industry are used to generate the normalization constant in each 

industry's production function. The data together with the equilibrium conditions thus determine all parameter values. 

If more complex functional forms are used, additional parameter values are necessary before the same procedure can be used. In 

the case of constant elasticity of substitution, an extraneous estimate of the elasticity of substitution must be provided for each 

industry or consumer. While we believe there are procedures for 

crudely choosing among these (such as examining implied point 

estimates of the price elasticity of market demand functions at the 

benchmark equilibrium) the degree of arbitrariness in choosing 

any particular set of elasticities should not be ignored. It should 

be added, however, that this difficulty is not a shortcoming of our 

approach alone. It is exactly these elasticity margins which any 

model must specify in order to address the class of issues analyzed 

by our techniques. 

The complexity of our model makes it impossible to estimate 

without a large number of identifying restrictions on parameter 

values. In the face of this identification problem, it might be appropriate to use extraneous econometric estimates of individual 

parameters instead of parameter values generated by the model. 

Such a procedure would require a search of the literature for estimates of production function and demand functions for use in the 

model. However, the implementation of this procedure faces a 

basic methodological difficulty. If extraneous parameter values are 

adopted, there is no test of the overall performance of the model. 

It is quite possible, for instance, that the chosen combination of 

parameters will yield an equilibrium that bears little relation to 

what is known from statistical evidence to occur. Therefore, we 

believe it more appropriate to use the equilibrium solution concept 

as an identifying restriction for the model. 

Our procedures also have a number of practical advantages. 

First, they enable direct use of national accounts data, avoiding 

the difficulty of providing definitions of unit.s in physical form. 

This means that, with the more complex functional forms, we are 

able to use extraneous parameter estimates for unit free elasticity 

parameters and avoid the problem of a conversion between units 

used in our model and extraneous estimation procedures. A further 

point is that extraneous estimates are surprisingly sparse, often 

inconclusive, and usually presented for classifications other than 

those with which we work. 
EQUILIBRIUM ANALYSIS OF TAX POLICY 33 

Data Sources and Procedures 

Much of the production data for our model comes from the July 

1976 Survey of Current Business (SCB) and from disaggregated 

worksheets provided by the National Income Division (NID) of 

the Commerce Department. Some of these data are not compiled in 

a form suitable for this study; therefore, several adjustments must 

be made to obtain the necessary information. The adjustments we 

have made to the national income accounts data are summarized 

below. It should be noted that further adjustments are desirable 

but have not proven feasible. 6 

Labor Income and Tax 

Our definition of labor return gross of tax is the sum of wages, 

salaries, employer contributions for social insurance programs, 

and the estimated return to labor of self-employed persons. This 

last category represents an unobservable fraction of the total 

return to the entrepreneur who invests his time and capital jointly; it is estimated by the product of average employee compensation and the number of proprietors and partners for each industry. 

This component of the return to labor is substantial only for agriculture, construction, services, and trade. 

One difficulty with this handling of the self-employed occurs if 

the estimated labor component exceeds the total unincorporated 

income of an industry. In this case we have set the capital return 

at zero and assigned the total income to labor. 

In the model the tax on labor services includes employer and 

employee contributions for social insurance. As mentioned earlier, 

these contributions are somewhat benefit related, but it is important to include those charges on labor income that discriminate 

among industries. The social security tax, for example, applies a 

fixed rate on wages up to some maximum per employee, so that 

industries with higher than average compensation of employees 

would tend to pay a lower effective rate of social security tax. 

Unemployment insurance discriminates by industry since the tax 

depends on the incidence of unemployment in that industry. 

° For example, the establishment basis is used to collect information on 

wages, noncorporate income, and interest paid, while the company basis is 

used for corporate profits and interest paid. A further point is that the 

national income accounts use a "national" definition to measure income to 

factors supplied by U.S. residents, while a "domestic" definition, which 

measures income of factors used domestically, is more appropriate for the 

model. Many of these adjustments are discussed by Rosenberg (1969). 
34 COMPENDIUM OF TAX RESEARCH 

TABLE 4.-Labor income, tax, and effective rates by industry in the 

United States, 1973 1 

(c) 

(a) (b) Effective 

Labor income Tax on tax rate 

Industry net of tax labor (b)+(a) 

All industries 643,040 64,997 .1011 

Ag., for., fish. 16,257 1,141 .0702 

Mining 4,718 464 .0983 

Crude petr. gas 3,415 308 .0902 

Construction 50,908 5,308 .1043 

Food, tobacco 16,964 1,859 .1096 

Textiles, app., lea. 17,447 2,268 .1300 

Paper, printing 18,996 1,948 .1025 

Petrol. refin. 2,834 239 .0843 

Chem., rubber 19,387 1,957 .1009 

Lumber, furn., stone 17,419 1,930 .1108 

Metals, machinery 87,996 9,167 .1042 

Transp. equip. 13,738 1,393 .1014 

Motor vehicles 15,064 1,358 .0901 

Trans., comm., util. 59,086 6,188 .1047 

Trade 130,239 13,745 .1055 

Finance, insurance 32,839 3,161 .0963 

Real estate 7,782 827 .1063 

Services 112,785 10,179 .0903 

Govt. enterprises 15,166 1,557 .1027 

1 All figures in millions of dollars. Component detail available upon request. 

An industry breakdown of each employer payment was provided 

by NID, and the employee share of social security was derived 

from the employer share since they are matching contributions. 

The total for self-employed contributions, is given in the SCB and 

is allocated among industries by the proportion of self-employed 

labor income in each industry. Labor income, taxes, and effective 

rates are shown in table 4. The low rate for agriculture reflects 

noncoverage of employees by insurance programs. The lower than 

average rate for services is due to some nonooverage and some 

salaries above the maximum for the social security tax.7 

Capital Income and Tax 

The return to capital net of tax includes corporate profits after 

tax, the estimated return to noncorporate capital, net rents paid, 

7 The level of aggregation tends to average a\verse rates. Legal services 

alone, for example, have an effective rate of tax of only .0827. At the other 

extreme, the high effective rate for textiles, apparel, and leather includes a 

rate of .1364 for apparel alone. 
EQUILIBRIUM ANALYSIS OF TAX POLICY 35 

and net interest paid. The inventory valuation adjustment (IV A) 

and the capital consumption adjustment (CCA) are applied to 

these figures. Net realized capital gains are not included because 

they refer to accrued gains of earlier years. In fact, accrued gains 

on existing physical capital assets have not been included in our 

capital payments or income figures. This procedure is consistent 

with the assumption that such gains reflect only inflation, and it 

demands less data than alternative approaches. In the current 

model there are no corporate retained earnings: all capital income 

net of business taxes accrues directly to the shareholder. Consequently, real accrued financial capital gains of individuals, reflecting the retained earnings of corporations, are implicitly included. 

The July 1976 SCB gives corporate profits after corporate taxes, 

property taxes, and other indirect business taxes; we aggregate 

these figures for each of our 19 industries. The corporate IV A has 

been obtained in sufficient detail from NID and reduces the corporate profit figures. 8 Wherever negative returns result, we resort 

to an average of several years in order to avoid the implication 

that an industry "supplies" rather than uses capital. Two special 

adjustments are necessary to the data. First, the national accounts 

for finance and insurance include the Federal Reserve Board earnings as corporate income and their payments to the Treasury as 

corporate tax. This government operation is exempt from the 

corporate income tax system, but 'its payments to the Treasury are 

included as a capital tax. Second, IRS corporate profits in extractive industries are understated by the combination of current expensing of exploration and allowances for depletion of reserves. 

We add to SCB income the portion of the percentage depletion 

deduction not included in Commerce Department adjustments. The 

result of these procedures are shown in column (a) of Table 5. 

Unfortunately, the Commerce Department cannot provide the 

disaggregated CCA estimates necessary to measure income net of 

economic depreciation instead of tax depreciation. We use results 

from a study by Coen (1976) for the disaggregated manufacturing CCA, shown in column (b), table 5. The noncorporate farm and 

real estate income figures in the national income accounts include 

CCA adjustments; the remaining industries have no such adjustment because data are lacking. 

Our measure of capital income is meant to approximate a real return 

and thus excludes all inflationary capital gains. The inclusion of the IV A, 

which places all firms on a LIFO inventory accounting basis, is therefore 

appropriate. 
co 

O') 

TABLE 5.-Capital income components by industry in the United States, 1973 1 

(a) (b) (c) (e) (f) 

Corporate Capital Return to (d) Net Total 

profits after consumption noncorporate Net interest capital 

tax with IVA adjustment capital rents paid paid income 

All industries 45,633 8,221 33,541 21,237 65,530 181,973 

Ag., for., fish. 523 5 22,865 4,067 3,323 30,778 (") 

0 

Mining 840 3 37 80 179 1,136 ~ 

Crude Petr., gas 2,446 3 561 304 59 3,370 "'t1 

f::i:j 

Construction 500 0 75 448 1,023 z 

t:i 

Food, tobacco 335 572 0 64 846 1,817 ...... 

~ 

Textiles, app., lea. 428 2 138 0 49 471 1,086 ~ 

Paper, printing 2,376 -96 0 242 199 2,721 0 

Petrol. refin. 3,583 3,578 0 640 481 8,282 1-zj 

Chem., rubber 3,172 132 0 71 535 3,910 ""'3 

> 

Lumber, furn., stone 3,115 3 

>< 

512 0 181 421 4,229 :::ti 

Metals, machinery 5,527 2,144 0 427 2,303 10,401 f::i:j 

r.n 

Trans. equip. -91 ~ 61 0 22 176 168 f::i:j > 

Motor vehicles 2,785 1,180 0 30 852 4,847 :::ti 

Trans., comm., util. 4,292 0 357 8,606 13,255 (") 

::r: 

Trade 7,198 367 898 1,258 9,721 

Finance, insurance 6,843 4 809 188 0 7,840 

Real estate 88 ~ 0 13,013 43,731 56,832 

Services 1,673 8,902 529 1,642 12,746 

Govt. enterprises 7,811 11 

1 In millions of dollars. ~Averaged over 1971, 1972, 1973. J Includes depletion . 4 Includes FRB earnings. ;; CCA already included. n Imputed. 
EQUILIBRIUM ANALYSIS OF TAX POLICY 37 

For noncorporate business, NID provides detailed income and 

IVA data. As with the figures for corporate business, negative income values were avoided by averaging several years together 

when necessary. For each industry, our earlier estimate of the 

labor return is subtracted from total income in order to obtain a 

residual estimate of the return to noncorporate capital. The resulting estimates appear in column (c) of table 5. 

Net rents paid by an industry are payments for borrowed property, buildings, and machinery used in that industry. These payments are treated by the national income accounts as a cost deduction for the renting firm and as income to the owners of the rented 

property. Since we seek to measure all payments to capital used in 

each industry, we count as capital income net rents originating in 

the paying industry. NID has provided net rents for farm realty, 

the imputed net rent from owner occupied dwellings, and the net 

rent from tenant occupied dwellings. We place the first of these 

into agriculture and the latter two into real estate. Net rents paid 

by business are apportioned among the 18 private industries on the 

basis of the data on gross rents paid as given in the 1973 IRS 

Statistics of Income. Finally, in this category, royalties paid for 

natural resources, copyrights, and patents are counted as capital 

income in the industry in which these assets are used. The use of 

natural resources by industry is approximated by the depletion 

deductions taken for tax purposes in 1973. The combination of 

these rental imputations is shown in column ( d) of table 5.9 

The final component of capital income is the net interest paid by 

each industry. These may also be thought of as payments for borrowed capital services used in the industry. NID industry worksheets showing interest flows for 1973 were used. The dollar payments of interest by industry are referred to as net "monetary" 

interest paid. These payments are positive for all industries except 

finance and insurance (F&I), which has a large negative value for 

net monetary interest paid. The receipt of net mooetary interest is 

a return for the financial intermediation services F&I firms provide. If, as for other industries, we add the (negative) net interest 

paid to profits, then the total return to capital in F&I will also be 

negative. We raise the F&I net interest paid figure to zero by imputing additional interest payments to other industr.ies and to 

persons who then pay imputed finance charges to F&I. The Commerce Department NID has made some of these imputations but 

leaves a large negative value for F&I net interest paid. We allo0 Note that the real estate industry no longer encompasses all rental income 

as it does in the national accounts. 
38 COMPENDIUM OF TAX RESEARCH 

cate the remaining imputed interest in the same proportions as 

that already allocated by NID. 10 Net interest paid, both monetary 

and imputed, is shown in column (e) of table 5. The sum of the 

first five columns, the total return to capital used in each industry, 

appears in column (f). 

We consider three components of tax on capital income: the corporation income tax, the corporate franchise tax, and property 

taxes. Information on the corporation income tax by industry is 

given in the SCB; the figures for the 18 private industries in the 

model are shown in column (a) of table 6. The corporation franchise tax is treated as an indirect business tax in the national 

accounts. Data given in unpublished worksheets from NID are 

aggregated to 18 industries; these figures are given in column (b) 

of table 6. The same worksheets provide NID estimates of state 

and local property taxes paid by industry. Our movement of net 

rents paid out of real estate requires a further adjustment to these 

property tax figures. These adjusted property taxes are given in 

column (c) of table 6. Column (d) then gives the total of these 

three taxes on capital income, while column ( e) repeats capital 

income from the previous table. Column (f) reports effective tax 

rates on net of tax income in each industry. 

The low rates of tax in agriculture, real estate, and services 

reflect the discriminatory nature of the corporate tax since these 

industries are largely noncorporate. The low rates in the crude 

petroleum and the petroleum refining industries reflect large depletion deductions in those industries. Depletion deductions also 

play a role in the lumber industry.11 

Intermediate Inputs and Production Taxes 

The Bureau of Economic Analysis 1970 update of the 1967 I/0 

matrix is aggregated for our 19 industries and adjusted to 1973 

levels. We scale up each industry's intermediate use of producer 

goods by the ratio of 1973 to 1970 value added for that industry. 

In the I/0 table, the total value of each producer good equals 

the value of intermediate inputs, intermediate input taxes, and 

value added. The latter includes labor services, labor tax, capital 

10 Since individuals receive some of the imputed interest, our accounts show 

greater .national income and greater expenditures on F&I. Consumption-side 

data accomodates the change. 11 At the other extreme, unusually high effective tax rates can be explained 

by low profits in 1973. An industry could include some firms with profits and 

tax liability and other firms with losses. The average income figure could 

even be negative at the same time that taxes are paid by the industry. 
TABLE 6.-Capital taxes by industr y in the United S tates, 1973 1 

(a) (b) (c) (d) (e) (f) 

Corporate Corporate Adjusted Total Capital Effective 

income franchise property tax on income net tax rate 

tax tax tax capital of tax (d) +(e) 

All industries 48,702 1,161 46,033 95,896 181,973 .5270 ~ 

.0 

Ag., for., fish. 309 10 2,420 2,739 30,778 .0890 c 

~ 

Mining 237 8 273 518 1,136 .4560 t"4 

~ 

Crude petr., gas 194 4 804 1,002 3,370 .2973 t::J:I 

~ ~ Construction 1,012 18 334 1,364 1,023 1.3333 c 

Food, tobacco 2,585 45 617 3,247 1,817 1.7870 a:: 

> Textiles, app., lea. 1,221 23 264 1,508 1,086 1.3886 z 

Paper, printing 2,125 31 479 2,635 2,721 .9684 > t"4 Petrol. refin. 1,282 92 256 1,630 8,282 .1968 ~ 

UJ Chem., rubber 3,573 44 574 4,191 3,910 1.0719 ~ 

UJ 

Lumber, furn., stone 1,647 28 422 2,097 4,229 .49591 0 

~ Metals, machinery 8,094 138 1,979 10,211 10,401 .9817 ~ 

Trans. equip. 536 7 542 1,085 168 6.4583 > 

Motor >< vehicles 2,974 19 276 3,269 4,847 .6744 '"C Trans., comm., util. 4,007 319 5,313 9,639 13,255 .7272 0 

t"4 

Trade 7,513 125 3,252 10,890 9,721 1.1203 ~ 

l.) 

Finance, insurance 9,457 2 178 968 10,603 7,840 1.3524 ~ 

Real estate 700 47 25,354 26,101 56,832 .4593 

Services 1,236 25 1,906 3,167 12,746 .2485 

Govt. enterprises 0 0 0 0 7,811 .0000 

1 In millions of dollars. 2 Includes FRB payments to the Treasury. ~ 

c.o 
40 COMPENDIUM OF TAX RESEARCH 

services, capital tax, and the taxes on output. Several of the indirect business taxes have been treated in the model as ad valorem 

taxes cm the output of each industry at appropriate rates. For example, the public utilities taxes, severance taxes, and the business 

and occupation taxes apply to the outputs of particular industries. 

Other tax and nontax payments, although not legally defined as 

taxes on value of output, are so treated. Federal excise and customs duties are treated as ad valorem output taxes on producer 

goods. An adjustment is made to NID data to place retailers' excise taxes on corresponding producer goods instead of on retail 

trade. 

Registration fees on motor vehicles are treated as a tax on their 

intermediate use by industry. This data appears with other indirect business taxes in the worksheets provided by NID. 

Government 

A separate, 19th industry represents the output of government 

enterprises, including the post office, TVA, mass transit, local 

utilities, and other government-run business. Total employee compensation for these Federal, State, and local operations is shown in 

the SCB, as are employer contributions for retirement programs, 

treated as a labor tax. Their use of capital services in 1973 must 

be imputed using a weighted average of the gross of tax capital/ 

labor ratios for the private counterparts of these activities, including services, transportation, finance, and utilities. The weights 

are determined by the proportion of government enterprise value 

added in each of the above activities from the 1967 I/ 0 table. Since 

our value added is greater than the input/ output figure, we treat 

the difference between our .capital use estimates and the recorded 

government enterprise surplus as an output subsidy. The effective 

rate of tax on the use of capital services is zero since no corporate 

income or property taxes are paid by government. 

The intermediate input column for this industry is scaled up 

from 1970 t.o 1973 by the ratio of employee compensation between 

those years instead of value added, since the latter includes the 

"surplus" of government enterprises, which is oft.en negative. The 

only indirect business tax paid by this industry is a Federal nontax payment, modeled as an ad valorem output tax. 

Purchases for general government are modeled as if made by a 

single consumer, with demand functions defined over producer 

goods, capital, and labor. In order to finaince the purchases of this 

consumer, a major fraction of tax revenue is retained in addition 
EQUILIBRIUM ANALYSIS OF TAX POLICY 41 

to government income from ownership of capital services. With 

this income, the government consumer purchases capital and labor 

services and outputs of all 19 industries. The 1970 I/O table shows 

purchases by general government in the four categories of Federal 

defense and nondefense and State and local education and noneducation. Each of these are scaled to 1973 using totals from the 

SCB. An estimation problem is presented by the government use 

of capital services because figures for these are not available. A 

rate of return is imputed to government capital stock data for 

1973. 

Investment and Foreign Trade 

Businesses invest in both capital formation and inventory accumulation. Gross private fixed capital formation requires the 

purchase of our 19 producer goods, scaled from 1970 to 1973 using 

SCB totals. Similar scaling is done for the net inventory change 

column, and the appropriate IV A is subtracted from each industry 

in order to measure only their purchases. Together, these columns 

represent the manner in which savings are spent. As stated earlier, 

one of our 16 consumer goods is savings purchased by each of our 

consumer groups. 

The export column of the 1970 I/0 table is replaced with information for 1973 from U.S. foreign trade statistics, and similar 

information is used on imports for both final and intermediate use. 

Consumer Incomes and Expenditures 

The capital and labor services used by producers and purchased 

by government are endowments of the consumer groups and government. These endowments valued at equilibrium factor prices 

determine factor incomes for each group, and the transfer shares 

applied to equilibrium tax revenue determine transfer incomes. 

Information on factor endowments and tr an sf er shares of each 

consumer group is available on the Treasury Department merged 

tax file compiled from 1973 individual income tax returns. For 

each income range, the capital endowment is indicated by the sum 

of interest and rent receipts, financial capital gains, dividends, and 

the income from unincorporated enterprises. Labor endowments 

are indicated by wage and salary income, while transfers from 

government include a number of items such as social security and 

welfare payments. 

The merged tax file also furnishes average and marginal tax 

rates for each income group. All disposable income after taxes and 
42 COMPENDIUM OF TAX RESEARCH 

transfers is spent by each consumer since one of the purchased 

commodities is savings. Information on consumers' expenditures 

for the other 15 commodities is obtained from the 1973 Survey of 

Consumer Expenditures, which gives data for each income bracket 

used in the model. 

We also require the effective rates of ad valorem tax on each of 

these purchases, since State and local sales tax are modeled as consumer taxes with different rates for each good. The total sales tax 

collections are an indirect business tax available from NID 

sources, and the distribution among commodities is determined 

from a weighted average of State rates scaled so that total collections are matched. The rate for each commodity reflects the proportions of expenditures that on a nationwide basis are exempt. 

In order to estimate coefficients for the G transition matrix between consumer goods and producer goods, we use a February 

1974 publication of the SCB. In the next section we describe our 

adjustments to this and other data to make them consistent. 

The Construction of a Consistent Microeconomic Data Set 

One of the important features of our model is its utilization of a 

consistent microeconomic tax data set, earlier termed our benchmark equilibrium. In this section some of the procedures we have 

used in constructing the data set are reported and described. 

Adjustments must be made to basic data so that the equilibrium 

conditions of the model are satisfied. Total market demand for 

each commodity must equal the amount produced, zero economic 

profits net of tax must be made by each industry, disposable incomes must equal expenditures for each household, payments to 

factors by industry must equal the corresponding income receipts 

by source and by households, the Government's budget must be 

balanced by its receipts, and zero balance (after allowing for capital transactions) should prevail in terms of the value of foreign 

trade. 

As the preceding section indicated, we use detailed national accounts data with a number of adjustments to provide estimates of 

use of capital and labor services by industry. A combination of 

national accounts and 1970 input/ output data then provide the 

five components of final demands for prbducer goods: personal 

consumption expenditure, government purchases, gross private 

fixed capital formation, net inventory change, and net exports. 

The total 1973 final demand facing domestic industries is then 
EQUILIBRIUM ANALYSIS OF TAX POLICY 43 

adjusted so that, in total value terms, the sum of final demand 

equals the sum of value added by industry. 

The RAS method 12 is used to modify our estimate of the aggregated 1973 I/0 matrix into a form consistent with our 1973 value 

added and final demand. The I/0 matrix violates the necessary 

condition that the sum of the value of intermediate inputs and 

value added equals the sum of intermediate uses and final demand 

for each product. The RAS method iterates successively on rows 

and columns of the matrix until the required consistency conditions are satisfied. 

The RAS method is also used to adjust the G transition matrix 

between consumer and producer goods so that it is consistent with 

our 1973 data set. The vector of household purchases of consumer 

goods on our classification is scaled so that in value terms it 

equals the total personal consumption expenditures on producer 

goods. The row sums of the G matrix will not match the vector of 

producer good availabilities, requiring row adjustments to match 

these. In addition, column sums of the matrix will not equal consumer purchases, and the columns of the matrix can be adjusted 

to make these conditions hold. As with the I/O matrix, adjustments are made on rows and columns in turn until both sets of 

conditions are simultaneously satisfied. 

A further set of adjustments is made to produce the component 

of the overall data set that describes the household sector of the 

economy. The total household receipts of income from ownership of capital and labor services are known from the data on the 

production side of the economy, and transfer incomes received 

and income taxes paid are known from the public sector accounts. 

From information on the merged tax file reporting income by 

source and income taxes paid it is possible to apportion these totals 

among our household groups. Total household disposable incomes 

then equal the value of household purchases of consumer goods. 

The 1973 Consumer Expenditure Survey data is aggregated to 

our 16 consumer goods shown in table 1, and where the expenditure data is deficient, other sources are used. The expenditure data 

fail to meet exactly the equilibrium conditions of the model; column sums do not match consumer disposable incomes, and row 

sums do not match aggregate consumer purchases of products. 

Thus, by repeatedly operating on the rows and then on the columns 

of the expenditure matrix, the matrix is transformed into a consistent form. This represents the third and final application of the 

RAS consistency technique. 

u See Bacharach (1971) for a complete presentation of this technique. 
44 COMPENDIUM OF TAX RESEARCH 

The major adjustments we make in order to produce a consistent microeconomic data set are outlined in chart 2. Other con-

-ditions must be satisfied by our data, and these involve more minor 

adjustments. The model requires that the total Government budget 

be in balance in equilibrium. Because of this, we incorporate the 

Government deficit or surplus into the model through real transactions, although the surplus involved for 1973 is, at $6 billion, 

small. Foreign trade must also be in overall balance; this involves 

incorporating the trade imbalance. The combination of these adjustments along with other more minor data modifications results 

in our benchmark equilibrium data set. 

CHART 2.-Microeconomic data set modifications to produce overall consistency 

(1) RASonl / Otable 

19 x t9 

Input/ Output 

(initial guess 

Personal consumption and 

savings (busi-

( 2) RAS on G matrix 

19 X16 

G Transition Matrix 

(initial guess 

scaled from ~ 

1970 U.S. 1/ 0 table) 

Final demand 

for 19 producer 

goods (Each of 

five components 

scaled from 1970 ness investment) (Expenditure on' producer goods 

from I 0 table.) 

~ scaled from 191\7 1/ 0 publication) 

t 

Value added by 

industry (from 

national accounts 

with adjustments) 

Net of 

government 

endowments 

1/0 figures to 

1973 totals in 

national accounts) 

t 

value 

Sum 

added 

of t ~ I equals Sums equal 

sum of 

final demand. 

(3) RAS on E matrix 

16 X12 

Expenditure Matrix 

(initial guess from 1973 

Interview Household Survey data) 

.. Column sums 

+ 

Disposable incomes by household 

type (From ownership of capital and labor services plus 

transfers minus income taxes. 

Detailed Treasury tax file 

information scaled to private 

sector endowments.) 

1~ 

Row -

-- --,.. sums 

.. 

rlumn sums 

Personal consumption 

expenditures on consumer goods (from 

national accounts) 

Personal consumption 

expenditures on consumer goods, gross 

of consumer tax 

l 

Sum of 

expenditures 

equals sum 

of disposable 

income 
EQUILIBRIUM ANALYSIS OF TAX POLICY 45 

Computer Software and the Solution of the Model 

The model described above has been programed in a computer 

package that allows users to consider the effects of various tax 

policy changes on the general equilibrium behavior of the economy. 

This computer package embodies a number of features and uses 

particular characteristics of the model in its solution. In this section we explain these points. 

Factor Price Computation 

Although the model involves prices for productive factors, producer goods, and consumer goods, there is a computational saving 

in solving the model by using factor prices alone.1 3 This substantially reduces required execution times. 

The procedure is to use factor prices to generate zero-profit producer good prices, which can then be used (via the G matrix) to 

generate consumer good prices. These consumer good prices are 

used to evaluate individual, and hence aggregate, demands for consumer goods. From these, industry gross output levels, and hence 

the derived demand for factor inputs, can be generated. This allows the computational solution of the model to work in the space 

of factor prices (augmented in one dimension to allow for the 

presence of the tax system), and an equilibrium solution is obt ained by finding a situation in which the excess demand for factors and excess tax receipts are equal to zero. At such a point, all 

other equilibrium conditions are automatically satisfied. 

Equal Yield Computation u 

Our model also embodies a capability for consideration of tax 

changes beyond those described simply by changes in tax rates. On 

many occasions policymakers are primarily concerned with a replacement tax structure (such as an integrated corporate tax) for 

which a tax rate or rates are chosen with the objective of preserving the existing yield from the taxation system. This capability 

has been built into our model by maintaining the yield of the tax 

system in real terms using a Laspeyres price index to correct the 

existing tax revenue. Alternative replacement tax schemes such 

13 This point is also made by Taylor (1975), and the procedure has been 

termed "indirect computation" by Ginsburgh and Waelbroeck (1976). Dixon 

(1974) also uses this approach. 

u These procedures are explained more fully by Shoven and Whalley 

(1977) . 
- - --------

46 COMPENDIUM OF TAX RESEARCH 

as an income tax surcharge or a broadly based sales tax are provided, and the tax rate assuring full equilibrium under the new 

scheme is computed. This capability supplements rather than replaces the examination of the implications of changes in tax rates. 

Tax Modification Capability 

Because of the model form in which we consider the operation 

of the U.S. taxation system, it is necessary to convert tax law 

changes into "model equivalent" tax changes. Thus, were the property tax to be abolished, the effective tax rates on capital services 

by industry implied by the remaining capital taxes need to be 

calculated. This general capability is a part of our programs. 

Solution Procedure 

The user is offered a choice of solution techniques between a 

fixed point algorithm (similar to Scarf, 1973) and a NewtonRaphson method. The reader interested in the details of these approaches is referred to Shoven and Whalley (1972, 1973). Further, 

the current computer package includes a subroutine that compares 

the equilibrium resulting from one tax package with another equilibrium resulting from an alternative policy. 

Nonunique Equilibria 

A further point is that in a model this complex, the possibility 

of non uniqueness of equilibrium solutions cannot be ruled out. We 

believe that equilibrium solutions for our model will be unique on 

the basis of ad hoc tests of approaching equilibria at different 

speeds and from different directions, as done by Whalley ( 1973, 

1975, 1977) with his model of the United Kingdom economy and 

tax system and by Shoven (1973, 1976) with his earlier and simpler model of the U.S. system. Nonunique solutions, however, cannot be ruled out on a priori grounds. 

Uses and Extensions of the Model 

The Range of Proposals That May Be Considered 

In addition to outlining the structure of our model, we seek to 

describe the class of policy issues it is capable of analyzing. While 
EQUILIBRIUM ANALYSIS OF TAX POLICY 47 

in principle all taxation changes generate general equilibrium effects as their induced price changes feed through the economy, 

these effects are clearly more important for some types of tax 

changes than for others. As more specific tax changes are examined by our approach, it may prove desirable to treat in more 

detail those aspects of the model addressed to the issues involved. 

As we have already mentioned, an examination of income tax reform issues with these techniques would require a more sophisticated modeling of the U.S. income taxation system. 

The class of taxation proposals our model can consider are divided into "legal" tax changes and "system" replacements. Legal 

tax changes refer to those proposals raised in public policy debate 

in which actual or proposed legislative changes are at issue; system tax changes refer to replacements of subsystems of taxation 

in our model (such as factor taxation, output taxation, income 

taxation) by some broadly based alternative. In the first case, we 

evaluate legislative proposals; in the second, we seek to provide 

estimates of economy-wide impact by which to evaluate major 

components of the tax system. 

Under legal tax changes, our plan is to consider first the effects 

of integrating personal and corporate income taxes. The proposals 

being actively discussed at the present time include "full integration" and "partial integration." Under full integration the present 

corporate tax would function solely as a withholding tax; individual stockholders in companies would be fully taxed on their 

earnings per share rather than on dividends only and would be 

eligible for an income tax credit for corporate taxes withheld. 

Under the partial integration plan, corporations would be liable 

for corporation income tax as at present, and individual stockholders would receive a dividend tax credit in the amount of corporate taxes attributable to dividends. 

To evaluate each of these integration schemes, it is first necessary to calculate for each industry the new implied effective tax 

rate on use of capital services. This calculation requires an assessment of dividend payout behavior by firms, the likely adjustments 

to this behavior implied by the partial integration scheme, and, 

finally, the implications of these adjustments for effective tax 

rates. Once obtained, these rates can be used to calculate a new 

equilibrium for comparison with the existing equilibrium. 

Other legal tax changes that could be considered in this general 

framework include income tax reform, taxes directed at energy 

conservation, replacement of property taxation by higher sales or 

income taxes, reform of social security tax, and the introduction 
- -- ---- ---

48 COMPENDIUM OF TAX RESEARCH 

of a value-added tax. In each case, the new effective tax rate implied by the change must be calculated and entered in the model. 

System tax replacements are tax changes of a more substantial 

form than are ever likely to be considered by legislative bodies. 

These types of changes may be considered as polar cases that provide results for evaluation of the economic impact of the entire tax 

system. This form of analysis is able, for instance, to complement 

existing incidence studies that assume that no change in relative 

prices will occur as current tax systems are replaced by a broadly 

based alternative tax. 

An important feature of our approach is the capability for 

examining the interactive effects of taxation instruments. It is 

well known that taxes viewed in combination can compound or 

offset the effects they may produce when examined in isolation. It 

is misleading, for example, to consider the discriminatory aspects 

of the corporate tax in isolation from those arising from the property tax. The distortions that each introduces are more satisfactorily examined in combination. 

This aspect of our analysis-that we not only examine the general equilibrium aspects of any tax change on the economy, but 

also take into account interactive aspects with other taxation instruments-is a particular strength of our approach. The preexisting institutional complexity within which all taxation change 

takes place is an important ingredient of our analysis. 

Welfare, Distribution, and Efficiency Aspects of Our Analysis 

Another particular strength of our method is that it can provide 

a wide range of estimates of different effects of tax policy changes. 

Since we are able to compute a complete new competitive equilibrium, we obtain all the detailed·information that describes that equilibrium. We compute not only the new equilibrium prices, but also 

the new equilibrium quantities, the aggregate amount of production of each good, the usage of productive factors and other goods 

in each industry, and the purchases of each product by each consumer group. We also obtain the taxes paid on each transaction. If 

consumer demands are derived by a process of utility maximization subject to a budget constraint, we are able to compute the 

utility level of each household group before and after the tax 

change. The ability to determine numerically these detailed results 

differentiates our approach from those used by other researchers. 

The detail generated by our approach does create a problem: to 

evaluate and compare the overall impacts of tax changes on the 
EQUILIBRIUM ANALYSIS OF TAX POLICY 49 

economy, some set of summary statistics is needed. This obviously 

recalls many of the traditional difficulties of index number theory; 

in our complex model we have no exact properties of indices to 

appeal to. 

Our procedure has been to compute indices of three broad types. 

We compute the changes in national income magnitudes by calculating the total value of production in each equilibrium first at old, 

then at new, equilibrium prices. These measures may be loosely 

interpreted as measures of efficiency gain or loss. Harberger 

( 1976) has recently suggested the calculation of aggregate compensating and equivalent variations as measures of efficiency impact. He has argued that such measures not only provide a more 

useful index than national income-type measures but also largely 

avoid the index number difficulties the latter often raise. Such 

measures can also be computed by our approach. We also compute 

variations in the distribution of income both by comparing points 

on Lorenz curves and by computing traditional summary measures 

such as the Gini coefficient. Implied adjustments in factor usage 

by industry, industry levels, and relative prices are also calculated. 

Our model thus produces a richness of detail and a wide range 

of summary measures of change. Many alternative measures can 

also be computed; for this reason, the techniques we present cannot dispense with personal judgment in deciding which are the 

important elements of change between equilibria. 

Future Extensions of the Model 

The model as presented provides a comparative static analysis 

of changes in tax policy; it does not provide a projection of the 

time path of the economy. A major aspect not captured is that of 

possible adjustments in the capital stock of the economy. At the 

present time the analysis focuses on reallocation rather than on 

accumulation. 

A future extension of our approach will incorporate dynamic 

considerations by calculating the augmentation of the capital stock 

resulting from both individual decisions with respect to savings 

and the depreciation of the aggregate capital stock. Individual 

capital endowments are thus determined by the model for the next 

period, and the model can be solved for a sequence of equilibria 

rather than a single static equilibrium. 

Further elaborations on our approach may also include a detailed analysis of the energy sector, a disaggregation of capital 

and labor into types, and the inclusion of consumer groups dis-
- - - ----------= 

50 COMPENDIUM OF TAX RESEARCH 

tinguished by demographic characteristics. Changes in demographic patterns over time can then be considered in a fashion 

similar to changes in capital stock, by a sequence of equilibria. 

Computational Example 

The calculations presented in tables 7 and 8 are suggestive of 

some of the capabilities of our approach. Not all of the features 

described above have been included here since neither data nor 

programs were complete at the time of these computations. Sales 

and incomes taxes are excluded, as is the distinction between producer and consumer goods. In this particular example, a single 

consumer has Cobb-Douglas demands for 19 goods with a substitution elasticity of 1. Each of the 19 producers uses other outputs as 

intermediate inputs in fixed coefficients, while each uses capital 

and labor in Cobb-Douglas production functions with a substitution elastfoity of 1. 

Table 7 first shows the demand components of each good in the 

replicated 1973 equilibrium. Total consumption now includes general Government purchases and investment since there is only one 

consumer who accrues all income. Final demand plus intermediate 

demand equals total output, which is reproduced on the second page 

of the table along with labor, capital, and tax levels. Given only 

functional parameters and total endowments, the computer has 

solved for levels that replicate our 1973 data, including the data 

shown in tables 4, 5, and 6 of this paper. 

Table 8 shows the percentage changes in all of these levels when 

we calculate a second equilibrium using all of the same functional 

forms and parameters except for the rate of tax on use of capital. 

All industries now pay the same rate, equal to the average tax rate 

in the previous equilibrium. Table 8 also shows the change in 

national income using both Laspeyres and Paasche indices, revealing that income could be higher by $5.85 to $7.77 billion without 

the distortions introduced by the corporate income and property 

taxes' differing effective rates by industry. 

A number of interesting points can be drawn from this set of 

calculations. First, note that all eight industries whose capital tax 

rates have been increased (industries 1, 2, 3, 8, 10, 17, 18, and 19) 

will now use absolutely less capital and absolutely more labor. All 

their output prices also increase. Second, tHe price of capital increases, even though these eight industries have very capitalintensive production processes. One might expect that higher 
TABLE 7.-Equilibrium solution replicating the benchmark equilibrium 

[In millions of dollars] 

Imports Imports 

Good Total for for Final Intermediate 

number 1 consumption Exports consumption production demand production Total 

1 10,405.9 10,313.2 2,368.1 2,339.2 16,011.8 96,308.5 112,320.3 2 1,700.5 1,253.3 140.7 1,080.8 1,732.3 14,270.3 16,002.6 3 367.7 ~ 103.1 311.6 4,879.0 -4,719.8 21,190.4 16,470.6 A:> 

4 132,143.8 0.0 0.0 0.0 132,143.8 27,924.0 160,067.8 c: 

1-4 

5 92,318.5 6,831.7 984.3 4,706.1 93,459.8 37,402.9 130,862.7 t4 

1-4 

6 31,979.2 t:d 3,475.3 3,438.3 2,303.2 29,713.0 35,650.0 65,363.0 ~ 1-4 7 10,230.1 1,405.6 154.4 2,015.6 9,465.7 47,423.2 56,888.9 c: 

8 15,832.1 556.7 144.9 2,994.8 13,249.0 27,906.0 41,155.1 a:: 

9 20,358.0 6,259.0 0.0 3,509.5 23,107.5 66,684.4 89,791.9 > z 10 11,751.3 1,700.9 422.0 2,338.9 10,691.3 55,121.7 65,813.0 > 11 91,677.2 27,499.4 2,537.4 22,712.8 93,926.3 218,863.2 312,789.5 t"4 

t-< 12 24,020.9 4,653.3 664.1 420.1 27,590.0 12,810.5 40,400.6 UJ. 

1-4 13 33,586.4 6,080.0 6,962.5 3,276.4 29,427.5 30,654.3 60,081.8 UJ. 

0 14 62,767.3 8,662.3 6,297.3 5,287.0 59,845.3 111,096.2 170,941.5 l'%j 

15 185,585.0 0.0 0.0 0.0 185,585.0 65,348.9 250,934.0 1--3 

16 37,850.3 > 0.0 0.0 0.0 37,850.3 46,242.5 84,092.8 >< 17 111,252.2 0.0 0.0 0.0 111,252.2 51,906.1 163,158.3 ""Cl 

0 18 132,066.7 5,805.0 280.8 2,028.8 135,562.1 121,578.4 257,140.5 t4 

1-4 19 4,100.7 0.0 0.0 0.0 4,100.7 24,887.8 28,988.4 Cl 

t-< 

CONSUMER INCOME SUMMARY 

Value of Value of 

Before-tax After-tax Sales Income Transfer labor capital income income taxes paid taxes paid income supplied supplied 

CJl 825,013.0 1,099,994.1 0.0 0.0 184,981.1 643,040.0 181,973.0 )-ol 
TABLE 7.-Equilibrium solution replicating the benchmark equilibrium-Continued 

[In millions of dollars] 01 

~ 

PRODUCTION SECTION 

Relative Labor Labor Capital Capital Output 

Producer Output price utilized taxes utilized taxes taxes 

1 112,320.3 1.0000 16,257.0 1,141.0 30,778.0 2,739.0 68.0 

2 16,002.6 1.0000 4,718.0 464.0 1,136.0 518.0 73.0 

3 16,470.6 1.0000 3,415.0 308.0 3,370.0 1,002.0 826.0 

4 160,067.8 1.0000 50,908.0 5,308.0 1,023.0 1,364.0 334.0 n 

5 130,862.7 1.0000 16,964.0 1,859.0 1,817.0 3,247.0 9,407.0 0 

6 65,363.1 1.0000 17,447.0 2,268.0 1,086.0 1,508.0 28.0 is:: 

~ 

7 56,888.9 1.0000 18,996.0 1,948.0 2,721.0 2,635.0 38.0 t2j 

z 

8 41,155.1 1.0000 2,834.0 239.0 8,282.0 1,630.0 4,202.0 t:1 

9 89,791.9 1.0000 19,387.0 1,957.0 3,910.0 4,191.0 926.0 1--4 

c:: 

10 65,813.0 1.0000 17,419.0 1,930.0 4,229.0 2,097.0 24.0 is: 

11 312,789.5 1.0000 87,996.0 9,167.0 10,401.0 10,211.0 199.0 0 

"%j 

12 40,400.6 1.0000 13,738.0 1,393.0 168.0 1,085.0 81.0 t-3 

13 60,081.8 1.0000 15,064.0 1,358.0 4,847.0 3,269.0 629.0 > 

14 170,941.5 1.0000 59,086.0 6,188.0 13,255.0 9,639.0 5,919.0 :>< 

~ 

15 250,934.0 1.0000 130,239.0 13,745.0 9,721.0 10,890.0 3,237.0 t2j 

r.n 

16 84,092.8 1.0000 32,839.0 3,161.0 7,840.0 10,603.0 1,155.0 t2j 

17 163,158.3 1.0000 7,782.0 827.0 56,832.0 26,101.0 2,856.0 > 

~ 

18 257,140.5 1.0000 112,785.0 10,179.0 12,746.0 3,167.0 218.0 0 

::x= 

19 28,988.4 1.0000 15,166.0 1,557.0 7,811.0 0.0 -6,132.0 

20 ~ 0.0 1.0000 0.0 0.0 0.0 0.0 0.0 

21 3 0.0 1.0000 0.0 0.0 0.0 0.0 0.0 

Total 643,040.1 64,997.0 181,973.0 95,896.4 24,088.0 

Government expenditures 184,981.1 

Total tax revenues 184,981.0 

National income 1,009,994.1 

1 Number~ corrcspo11cl to indmtric'i li"tnl in tahlc 2. ~ Lahrn " Capital 
TABLE 8.-Percentage changes from benchma1·k equilibrium when capital tax rates are all set to the average tax rate 

Imports Imports 

Good Total for for Final Intermediate 

number 1 consumption Exports consumption production demand production Total 

1 -15.5H ·-16.37 ~16.37 -16.37 - 15.82 -4.60 -6.20 

3 - 5.66 - 6.70 -6.70 -1.15 - 0.03 1.43 1.25 t:r:l 

.0 4 1.85 0.0 0.0 -6.70 - 6.78 - 2.09 - 0.74 c 

1-4 5 -5.02 -6.08 - 6.08 0.0 1.85 - 1.21 1.32 ~ 1-4 

2 -0.01 -1.18 -1.18 -6.08 -5.04 - 3.30 -4.54 t:1:I 

~ 6 3.30 2.06 2.06 2.06 3.39 2.44 2.87 1-4 

c 7 3.62 2.38 2.38 2.38 3.73 0.86 1.34 a:: 

8 -9.99 -10.95 -10.95 -10.95 -9.81 0.10 -3.09 > 

9 3.52 2.28 0.0 2.28 3.38 0.95 1.57 z 

> 10 -0.13 -1.30 -1.30 -1.30 -0.02 0.99 0.82 t"' 

~ 11 3.68 2.44 2.44 2.44 3.65 2.01 2.50 r:n 12 7.95 6.61 6.61 6.61 7.78 4.82 6.84 r:n 

- 13 2.86 1.63 1.63 1.63 3.03 2.14 2.58 0 

>'%j 

14 0.93 -0.26 -0.26 -0.26 0.99 0.54 0.70 "'"3 

15 3.07 0.0 0.0 0.0 3.07 0.55 2.41 > 

>< 16 11.70 0.0 0.0 0.0 11.70 1.67 6.18 ~ 

17 -4.18 0.0 0.0 0.0 -4.18 0.41 -2.72 0 

~ 

18 -0.66 -1.81 -1.81 -1.81 -0.69 0.93 0.08 n 

- 19 -9.10 0.0 0.0 0.0 -9.10 0.85 -0.55 ~ 

CONSUMER INCOME SUMMARY 

Value of 

Before-tax After-tax Sales taxes Income taxes Transfer Value of labor capital income income paid paid income supplied supplied 

1.37 1.19 0.0 0.0 0.35 0.0 6.23 01 

Cl:) 
TABLE 8.-Percentage changes from benchmark equilibrium when capital tax rates are all set to the average rate (Cont.) c.n PRODUCTION SECTION ~ 

Relative Labor Labor Capital Capital Output 

Producer Output price utiliized taxes utilized taxes taxes 

1 -6.20 19.5769 20.23 20.23 -17.52 392.28 12.16 

2 1.28 1.1895 3.49 3.49 -5.36 10.25 2.48 

3 -0.74 7.1842 10.80 10.80 -9.61 61.48 6.39 

4 1.32 -0.6403 -0.23 -0.23 45.54 -42.02 0.67 

5 -4.54 6.4753 -15.09 -15.09 47.69 -56.10 1.64 (j 

6 2.87 -~.0216 -1.80 -1.80 46.60 -43.92 0.79 0 

7 1.34 -2.3259 -2.88 -2.88 19.71 -34.34 -1.02 a:: 

8 -3.09 12.2973 20.33 20.33 -9.37 144.59 8.83 "'ti 

t%j 

9 1.57 -2.2303 -5.43 -5.43 22.64 -39.23 -0.69 z 

10 0.82 1.3183 2.39 2.39 -3.82 3.03 2.15 t::I 

1-1 

11 2.50 -2.3789 -1.29 -1.29 22.49 -33.73 0.06 ~ 

12 6.84 -6.2037 -4.86 -4.86 338.53 -63.93 0.21 a:: 

13 2.58 -1.6069 0.93 0.93 6.00 \_16.51 0.93 0 

~ 

14 0.70 0.2563 -1.36 -1.36 6.83 -21.97 0.96 ~ 

15 2.41 -1.8010 -1.15 -1.15 31.16 -37.81 0.57 > 

16 6.18 -9.3215 -6.80 -6.80 37.05 -46.17 -3.71 >< 

17 -2.72 5.5500 5.27 5.27 -3.52 11.59 2.68 ~ 

t:r:j 

18 0.08 1.8442 2.89 2.89 -19.19 72.75 1.92 rn 

t:r:j 

19 -0.55 . 11.2055 15.21 15.21 -27.37 0.0 10.59 > 

20 2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ~ 

(j 

21 3 0.0 6.2336 0.0 0.0 0.0 0.0 0.0 ~ 

Total -0.00 -0.27 -0.00 0.79 0.22 

Government expenditures 0.35 

Total tax revenues 0.35 

National income: at base case prices at revised case prices 

base case 1,009,993.63 base case 1,016,121.56 

revise case 1,017,766.13 revise case 1,021,975.50 

3 change 0.77 3 change 0.58 

1 Numbers correspond to industries listed in table 2. 2 Labor 3 Capital 
EQUILIBRIUM ANALYSIS OF TAX POLICY 55 

prices here would imply lower output, lower demand for capital, 

and thus a lower capital price. But it turns out that these particular outputs are used much more for intermediate purposes than 

for final demand, so that lower prices and greater outputs elsewhere mean that more of these intermediate goods must be produced in spite of their higher prices. Greater output in these capital-intensive industries drives up the price of capital.15 

Third, it should be noted that while the magnitudes of these 

changes depend on the elasticity parameters utilized, the direction 

usually does not. In a separate computation, identical except for a 

.5 substitution elasticity in production, the percentage changes. 

from benchmark were ail smaller. The change in national income 

from removing capital tax distortions in this case was $1.67 to 

3.33 billion. 

Finally, we suggest that by varying the substitution elasticities 

and other parameters across industries or across consumers, we 

can derive relationships relevant to tax incidence analysis in addition to calculating point estimates of likely tax burdens. 

We made four runs in which capital income tax distortions were 

eliminated in stages. Table 9 shows the increase in national income 

measured by old or new prices when part or all of the corporate 

income tax is eliminated. An effort to eliminate the corporate income tax would seem to have some diminishing returns, with gains 

from eliminating the first tenth larger than gains from the last 

tenth. 

Another four runs were made in which the corporate income 

tax was eliminated, but the elasticity of substitution in production 

was varied. Table 10 shows the · increase in national income for 

each case. It appears that the welfare gain is almost linearly related to this elasticity, at least for the case in which consumers' 

elasticity of substitution in the utility function is 1. 

Conclusion 

In this paper we have described a numerical general equilibrium 

model of the U.S. economy and taxation system presently being 

constructed. This model incorporates all the major taxation instruments currently operating in the United States and allows for 

consideration of a wide variety and combination of policy varia15 In a separate calculation in which all capital tax rates were set to a 

higher .7, the price of capital fell below the benchmark price, as we would 

have expected here. 
56 COMPENDIUM OF TAX RESEARCH 

TABLE 9.-Welfare gains in the Cobb-Douglas case 1 

Elimination of 

One-tenth the corporate tax 

One-half the corporate tax 

All corporate income tax 

All capital income tax 

1 In billions of 1973 dollars. 

(a) 

Paasche 

(lower 

bound) 

.67 

2.88 

3.45 

5.85 

- (b) 

Laspeyres 

(upper 

bound) 

.69 

3.28 

5.63 

7.77 

(c) 

Geometric 

mean 

.68 

3.07 

4.41 

6.74 

TABLE 10.-Welfare gains with elimination of the corporate income tax 1 

Elasticity of 

substitution 

in production 

.5 

1.0 

1.5 

2.0 

(a) 

Paasche 

(lower bound) 

1.67 

3.45 

5.51 

7.64 

1 Jn billions of 1973 dollars. 

(b) 

Laspeyres 

(upper bound) 

3.33 

5.63 

7.94 

10.21 

(c) 

Geometric 

mean 

2.36 

4.41 

6.61 

8.83 

tions. At this stage, the focus has been on constructing a manageable, but nonetheless realistic, model that provides a basis for 

further elaboration. 

A major contribution of this work is the assembling, for a recent 

year, of a consistent microeconomic data set for tax analysis. Such 

a data set has not previously been constructed for the U.S. economy and is an indispensable component of a complete general equilibrium analysis of tax policy. Because national accounting at the 

present time is oriented toward production of macroeconomic data, 

we have had to use a number of diverse data sets between which 

there are inconsistencies. We have therefore devoted a portion of 

our paper to a descri.ption of our consistency procedures. 

After construction of this model is complete, the general equilibrium implications of alternative schemes of integration of corporate and personal income taxation will be analyzed. Other investigations using the model are also anticipated. 
...... - ... - -•- -- ~•r -- ..,._ ~ ,___ --~ .._._ -- -------

EQUILIBRIUM ANALYSIS OF TAX POLICY 57 

Ref ere:nces 

Bacharach, Michael. Bi-proportional Matrices and Input-Output Change. 

England: Cambridge University Press, 1971. 

Coen, Robert M. "Alternative Measures of Capital and Its Rate of Return in U.S. Manufacturing." Evanston, Ill.: Northwestern University, 

Department of Economics, 1976. (Mimeo) 

Dixon, Peter B. The Theory of Joint Maximization. Amsterdam: NorthHolland Press, 197 4. 

Ginsburgh, Victor, and Jean Waelbroeck. "Computational Experience 

with a Large General Equilibrium Model." In Computing Equilibria: 

How and Why. Amsterdam: North-Holland Press, 1976. 

Harberger, Arnold C. "The Corporation Income Tax: An Empirical Appraisal." In Tax Revision Compendium, Vol. 1. Washington, D.C.: 

House Committee on Ways and Means, U.S. Government Printing 

Office, 1959. 

Harberger, Arnold C. "The Incidence of the Corporation Income Tax." 

Journal of Political Economy 70 :3 (1962), pp. 215-240. 

Harberger, Arnold C. "Efficiency Effects of Taxes on Income from Capital." In Effects of Corporation Income Tax. Detroit, Mich.: Wayne 

State University Press, 1966. 

Harberger, Arnold C. "The Incidence and Efficiency Effects of Taxes on 

Income from Capital: A Reply." Journal of Political Economy 84 :6 

(1976 ),pp. 1285-1292. 

Piggott, John R., and John Whalley, "General Equilibrium Evaluations 

of U.K. Tax-Subsidy Policy: A Progress Report." Paper presented to 

AUTE meetings, April 1976, Edinburgh, Scotland. In A. R. Nobey and 

M. J. Artis (Eds.), Conference Proceedings, forthcoming. 

Piggott, John R., and John Whalley. "Parameterizing Walrasian Policy 

Models." Paper presented at the North American summer meetings 

of the Econometric 'Society, June 1977. 

Rosenberg, Leonard C. "Taxation of Income from Capital, by Industry 

Group." In The Taxation of Income from Capital. Washington, D.C.: 

The Brookings Institution, 1969. 

Scarf, Herbert E. (with the collaboration of Terje Hansen). The Computation of Economic Equilibria. New Haven, Conn.: Yale University 

Press, 1973. 

Shoven, John B. General Equilibrium with Taxes: Existence, Computation, and a Capital Income Taxation Application. Unpublished doctoral dissertation, Yale University, 1973. 

Shoven, John B. ~'The Incidence and Efficiency Effects of Taxes on Income from Capital." Journal of Political Economy 84:6 (1976), pp. 

1261-1283. 

Shoven, John B., and John Whalley. "A General Equilibrium Calculation 

of the Effects of Differential Taxation of Income from Capital in the 

U.S." Journal of Public Economics 1 (1972), pp. 281-321. 

Shoven, John B., and John Whalley. "General Equilibrium with Taxes: 

A Computational Procedure and an Existence Proof." Re'l:iew of Economic Studies 40 (1973), pp. 475-490. 

Shoven, John B., and John Whalley. "Equal Yield Tax Alternatives: General Equilibrium Computational Techniques." Journal of Public Economics, 8 (1977), pp. 211-224. 
58 COMPENDIUM OF TAX RESEARCH 

Taylor, Lance L. "The Theoretical Foundations and Technical Implications." In Economy-wide Models and Development Planning. England: 

Oxford University Press, 1975. 

Whalley, John. A Numerical Assessment of the April 1.973 Tax Changes 

in the United Kingdom. Unpublished doctoral dissertation, Yale University, 1973. 

Whalley, John. "A General Equilibrium Assessment of the 1973 United 

Kingdom Tax Reform." Economics 42 (1975), pp. 139-161. 

Whalley, John. "The U.K. Tax System 1968-1970: Some Fixed Point Indications of Its Economic Impact." Econometrica, 45 :8 (1977), pp. 

1837-1858. 
EQUILIBRIUM ANALYSIS OF TAX POLICY 59 

COMMENT 

Arnold C. Harberger, University of Chicago 

The present paper is so much in the "tradition" of my own work 

on related topics that I faced something of a dilemma in framing 

my comments on it. Should I frankly recognize the similarity (at 

the risk of intruding myself into,the.authors' story) or should I 

couch my comments in a more "objective" tone, dissimulating my 

long involvement in the field? For better or worse, I have taken the 

first option. In the final analysis, this choke could not be avoided, 

for the structure of my own thinking on economic problems, as it 

has evolved through time, is simply too much a part of me to be 

hidden behind any plausible di~guise. 

That said, let me straightforwardly take the role of an intellectual grandfather in approaching the paper. It does not really matter to what degree my work had a direct influence on the evolution 

of the paper; indeed, if many of the j udgmen'ts on which the 

authors and I coincide were reached .independently, it is in some 

sense even more impressive. After all, grandparents should prefer 

it when grandchildren come to share their views via an independent route rather than through direct inculcation. 

So it is with pleasure that I note 

1. that the authors present a general equilibrium framework I 

for taxation ; 

2. that they amalgamate property taxes with corporation income (and franchise) taxes in each sector and treat the result as 

a single tax on capital income (the percentage rate of tax differing 

by sector according to the weight of these combined taxes in total 

(gross-of-tax) income from capital) ; 

3. that they similarly amalgamate social security, workmen's 

compensation, and unemployment compensation contributions (regardless of whether they are allocated to employer or employee) 

as a single tax on labor input, with rates varying by sector according to the weight of these taxes in total (gross-of-tax) income 

from labor; 

4. that they use a production-function framework that allows 

for substitution between labor and capital at the industry level, 

but not between these primary factors on the one hand and ma-
60 COMPENDIUM OF TAX RESEARCH 

terial inputs on the other (fixed coefficients are assumed for material inputs) ; 

5. that the principle of aggregation used (separately) for the 

capital and labor inputs was that the unit of capital (labor) was 

the amount that generated one dollar of income in the base (equilibrium) period; 

6. that, as tax changes and other disturbances are introduced 

into the system; capital and labor are assumed to be reallocated so 

as to maintain equality in the net-of-tax rate of return (and netof-tax wage) across different industries and sectors; and 

7. that consumer demand is assumed to obey a specified functional form (e.g., CES), with consumer prices reflecting, in equilibrium, the rewards paid to primary factors plus factor taxes 

paid (see items 2 and 3) plus indirect taxes (on both intermediate 

and final products). 

All of the above are close enough to assumptions used in my own 

work (both in the papers cited by the authors and in others 1 ) that 

I would be embarrassed were I now to find fault With them. 

The same goes for some of the technical procedures adopted in 

the process of reducing an infinitely complex reality down to the 

dimensions of the model : 

8. Income of unincorporated enterprises is divided between 

labor and capital on the assumption that the labor of the selfemployed (proprietors, partners, etc.) in any industry has a value 

(per person) equal to the average compensation of employees in 

that industry. 

9. Capital's return is defined to include net interest paid (after 

imputing to financial intermediaries a payment of interest from 

them to their depositors, balanced by an imputed service charge 

from their depositors to them), plus net rents paid, plus corporate 

profits plus the part of the income of unincorporated enterprises 

that remains after the labor allocation specified in h) has been 

made. 

10. The equalization of the net-of-tax return to capital is assumed to take place at the level where the market meets-Le., after 

corporation and property taxes but before personal taxes. This 

means that corporate savings are automatically counted as part of 

the net return to capital and that the subsidy to owner-occupied 

housing occasioned by the nontaxation of imputed income from it 

is treated as if it were explicit (and divorced from the personal 

1 Especially "The Measurement of Waste," American Economic Review 54:3 

(May 1964) , pp. 58- 76. 
- - -- --•--- -....._ .- -------2---=--=- .,,. -- r- ,__ -----~ ~ - - - ~~ --~-~-~- - -

EQUILIBRIUM ANALYSIS OF TAX POLICY 61 

tax), with housing income (including such subsidy) then being 

subject to full personal taxation at normal r~tes. 

These are not the only ways of handling the specific problems 

the authors address; but, while being arbitrary in a sense, these 

procedures nonetheless reflect what I consider to be sound and 

sensible judgment. 

The specific application of the model reported in the section 

titled "Computational Example" and dealing with the hypothetical 

equalization of the tax rates applying to income from capital generated in different industries, is unexceptionable. It shows what 

the model can do when it is used to analyze one of the specific class 

of problems for which it was built. 

My only quarrel is with the authors' penchant for reporting 

changes in welfare by calculating the total value of production in 

each equilibrium first at old, and then at new, equilibrium prices. 

I have suggested elsewhere that far better measures are available, 

and the authors are kind enough to cite me to this effect; but they 

proceed (stubbornly in my view) to compute and report inferior 

rather than superior measures. (Actually, they give in tables 9 

and 10 the geometric mean measure of welfare gain, which is far 

better than either of the two component measures they report, but 

they neither explain what it does, nor encourag~ its use by others.) 

Lest the&e grandfatherly remarks be interpreted as signs of 

senility, let me justify them by an appeal to the very simple and 

familiar example ofi;he welfare loss from an excise tax. Assuming 

the tax in question to be the only distortion, and production costs 

to be constant (linear production possibility locus for the economy 

as a whole) , the familiar triangle between the demand and supply 

curves (ABC in figure 1) gives the "right" measure of the loss. 

The authors' preference, however, seems to be .to report an upper 

bound of the rectangle ABCD and a lower bound of zero (~p~~x =0 1 't 

for movements along the linear production constraint ~p~x . =K). 't 1 

Why, I ask, be so inelegant in reporting results after going to all 

the work of constructing a very elegant model? 

If I were they, having gone so far as to produce the model, I 

would program it to approximate a Divisia measure of welfare 

change. The basic measure of such a change is 

· J ~Ti(z) oxi dz. i oz 

For a change in a vootor of taxes from T~ to T~, let Ti(z) be equal 1 't 

to ~ + z ( T~ - T~) , and let the line integral then be taken from 1 1 't 
62 COMPENDIUM OF TAX RESEARCH 

FIGURE 1 

Price 

C D Po+ T t---------__,..-- - - - - ·- - -I 

I 

I 

I 

I 

IA Po1--~~~~~~~~~~~-....--~-....-.-.....->io.-~....._~~--

0 a, quantity 

z = 0 to z = 1. To approximate this, I would suggest programing 

the calculation of ten steps, the first going from z = 0 1:o z = 0.1, the 

second going from z=0.1 to z=0.2, etc.; we might even have only 

four or five steps-but I feel that having more than ten would be 

gilding the lily. And within each step I would evaluate the change 

in welfare at Ti(z) for z at the midpoint of the step. Actually, the 

authors report in table 9 calculations that bear a family resemblance 1:o what I have here suggested-they measure the welfare 

gains of eliminating a) one-tenth of the corporation income tax, 

b) one-half of the corporation income tax, c) all of the corporation 

income tax, and finally d) all taxes on income from capital. However, they do not evaluate the change in increments, at prices corresponding to each step, and they continue to pay far too much 

attention to their upper and lower bounds. 

My main criticism (if it can be called that) of the paper is really 

a sort of warning, perhaps directed more to the authors than to 

their readers. It concerns the possibilities of getting interesting or 

useful results out of applications of the model to problems connected with the size distribution o.f income. 

So far as I can see, the division of consumers into 12 income 

groups is an interesting frill but not a fundamental feature of the 

model. So long as the model itself discriminates only between two 
- -- --- - - - - ~_r-~_-_....._-~-___,,.._------~~- ---

EQUILIBRIUM ANALYSIS OF TAX POLICY 63 

primary factors, Land K, it cannot really explain why some families are in group 1, others in group 6, and others in group 12. 

What the model can and does do is show how a given change in 

relative factor rewards will affect the size distribution of income. 

If the net return to capital rises by 10 percent while that to labor 

falls by 5 percent, a group whose income comes 80 percent from 

capital will enjoy a rise of 7 percent, while a group whose income 

comes 90 percent from labor will suffer a fall of 3.5 percent. 

It is easy to appreciate that this information adds to the richness of our understanding of the effects of a disturbance like the 

reduction of the corporation tax rate. However, the model is not 

built to help decide how progressive the tax system ought to be or 

to analyze the effects of changes in, say, the progressivity of the 

personal income tax. 

For such matters one would want to know much more than this 

model tells about the anatomy of income distribution-how education and skills are distributed, how their economic rewards are 

determined, how various tax provisions (e.g., those relating to 

capital gains, gifts, trusts, estates) impinge differentially on different layers of the income distribution. 

To my mind, this model does not provide what is needed, nor is 

it the proper starting point from which to build what is needed. 

The division of the economy into 19 industries is a sensible classification for answering certain questions; it is not so for answering 

others. Serious work focusing on Gini coefficients and Lorenz 

curves would call for a totally different model. 

This simply calls attention to a general proposition that is widely-but perhaps not widely enough-appreciated among practitioners of empirical economics. That proposition is that it is never 

worthwhile to build a model to replicate the economy. All models 

are partial in the sense that they fail at this impossible task. To be 

useful, a model must be well suited to the problem being addressed 

(even though the model may. not be explicitly built for that problem). More generally, however, the advice that economic models 

~hould in principle be separately tuned (if not built) for each 

problem is clearly better than the suggestion that one grand model 

that will handle a broad gamut of questions (many not even perceived by the builders) should be sought.