Inequality aversion, macroeconomic objectives and the marginal welfare cost of indirect taxation Does flexibility of prices and wages matter?

EuropeanJournalof POLITICAL ELSEVIER

European Journal of Political Economy Vol. 13 (1997) 315-341

ECONOMY

Inequality aversion, macroeconomic objectives and the marginal welfare cost of indirect taxation Does flexibility of prices and wages matter? Dirk Van de gaer, Erik Schokkaert *, Guido De Bruyne Centrum voor Economische Studi~n, Naamsestraat 69, B-3000 Leuven, Belgium

Received 10 April 1994; revised 9 January 1995; accepted 1 September 1996

Abstract We compare directions of welfare improving marginal tax reform in a situation of involuntary unemployment. We show the role of distributional considerations in assessing these welfare effects: preferences between macroeconomic variables shift with the degree of inequality aversion. To get a better insight into the importance of distributional considerations in different models, we compare the marginal welfare costs of taxation within three different specifications: the Keynesian regime, a flexible prices/fixed wage-model, and a flexible prices/trade union wage-model. These various models are calibrated for Belgian data of 1980. It turns out that the choice of model matters, even in a marginal perspective. The empirical results also show how the welfare costs in the different models vary with the degree of inequality aversion. JEL classification: H21; D58 Keywords: Indirect taxes; Marginal welfare cost

1. Introduction The welfare evaluation of tax reform requires a combination of empirical facts and normative judgments. The first step in the analysis is the computation of the

* Corresponding author. E-mail: [email protected]. 0176-2680/97/$17.00 Copyright © 1997 Elsevier Science B.V. All fights reserved. PI1S0176-2680(97)00007-4

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effects of changes in the instruments on the relevant economic variables. This computation will depend on the model of the economy. For the present Western European economies, we cannot neglect the occurrence of large involuntary unemployment. Therefore, wage rigidities have to be incorporated in the model. The second step is the welfare evaluation of these induced changes, requiring a normative judgment. This judgment will have to integrate efficiency and equity considerations in a consistent welfare framework. It is the purpose of the present paper to investigate the importance of both steps. The theoretical impetus for this framework is the pathbreaking paper in which Drbze (1985) has shown how traditional welfare aspects and macroeconomic considerations related to unemployment can be integrated into second best-analysis. Introducing price rigidities in the general equilibrium framework leads naturally to evaluate costs and benefits by means of the comparative statics approach of macroeconomics, taking all multiplier effects into account (Dr~ze, 1987). We will compute marginal welfare costs in an approach which has been initiated by Ahmad and Stem (1984, 1987). This has the advantage that it allows us to separate clearly the different macroeconomic effects. The non-Walrasian models presented by Dr~ze are more realistic than the traditional stylised Walrasian model of Ahmad and Stem (1984, 1987). But there is a price to be paid for this increase in realism. While the general structure of Drbze's theoretical results remains transparent, the concrete algebraic formulae soon become very complex and the model has to be simplified to yield interpretable results (see, e.g., Marchand et al., 1989). The same problem holds for empirical work: as we need rather complex computations, the theoretical transparency of the empirical results gets lost to some degree. Traditional sensitivity analysis with different parameter values usually is restricted to comparisons within one model of the economy. Yet the choice of model is not straightforward. There is no consensus at all among macro-economists about the degree of price and wage flexibility in the economy. Moreover, this flexibility might change over time. As a consequence several questions arise naturally. Is the ranking of the marginal welfare costs the same, irrespective of the way the economy is modelled? Does a change in the concern for income inequality have a similar effect on the ranking of the marginal welfare costs in all specifications of the economy? Are there any reforms of the system of indirect taxation possible which are welfare improving, irrespective of both the model of the economy and the extent to which one is concerned about income inequality? With this paper we want to get a better insight into the importance of the choice of model and of the distributional aspects. We therefore compare the marginal welfare costs of taxation within three different specifications of an economy with unemployment: the Keynesian case analysed by Wibaut (1987, 1989), the flexible prices/fixed wage-model of Marchand et al. (1989) and a flexible prices/trade union wage-model of Van de gaer et al. (1993). These various models are calibrated for the same Belgian data of 1980: we compute the marginal welfare

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cost of taxes on 15 commodities. W e work within a full general equilibrium structure characterised by different production technologies for the 15 sectors 1. It will turn out that the choice of model and the degree of inequality aversion matter for the evaluation of the marginal costs of taxation 2. The ranking of the macroeconomic objectives, however, is independent of the particular macro model representing different kinds of price rigidities and depends only on the inequality aversion of the social evaluator. A general description of the marginal tax reform framework in a situation of unemployment is given in Section 2. In Section 3 we sketch the structure of our three models of the economy. Section 4 briefly describes the data used for our calculations. Section 5 compares the results for the different specifications and comments on the relationship between the welfare evaluation and the macroeconomic objectives. Section 6 concludes.

2. The welfare cost of taxation in a situation with unemployment W e consider an economy with G commodities, indexed i = 1. . . . . G, with corresponding producer prices Pi, indirect taxes t i and consumer prices qi- In vector notation, we write q=p+t

(1)

The first G - 1 commodities are produced by the private sector, whereas commodity G is supplied by the government. Furthermore, there is a single labour market where the net wage ql is determined. Social security contributions and income taxes, captured by t l, drive a wedge between the net wage ql and the wage cost PI: ql = P l - tl

(2)

The problem of the government is to set the tax rates t i, i = 1. . . . , G and t v In the optimum, a social welfare function is maximised under the constraint that a given government surplus has to be realised. Both the welfare function, W ( ) , and the surplus, R, depend on the vector of tax rates: the exact form of this dependency will be determined by the specification of the economy. In a non-optimal situation, welfare-improving reforms can be determined by using a concept of

i An empirical application of the Drbze-approachfor Belgium has already been presented by Wibaut (1987, 1989). He concentrates only on the Keynesian case, however. Moreover, his model remains a simple representation of the economy with only one aggregate private sector. 2 This is not clear a priori. As Ballard et al. (1985, p. 1) write in the second sentence of their book: "When the policy changes being considered are relatively small, it may be appropriate to neglect the general equilibrium interactions among many different markets".

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the marginal cost (Ahmad and Stern, 1984, 1987) in terms of social welfare of an extra unit of surplus raised via the ith tax rate, defined as: OW/at i

ME/-

-

-

i=1 .....

,

G

(3)

aR/Ot i

Eq. (3) is easily interpreted. In the optimum the marginal costs have to be the same for all taxes. If MC i < MCj, social welfare will be increased by a lowering of the tax rate tj with an offsetting increase in the tax ti, so as to keep the global government surplus constant 3. W e follow the tradition in the public economics literature on taxation and assume that the social welfare function is of the welfarist form W ( u 1. . . . . vH), where v h is the indirect utility of household h. This traditional specification is sufficiently rich to incorporate macroeconomic objectives in the welfare evaluation of tax reform. To see this, we first have to go deeper into the properties of the indirect utility functions in a situation of unemployment, i.e., an economy where the wage does not clear the labour market. 2.1. Individual welfare and household behaviour

The assumption of a non-equilibrium wage implies that households are rationed on the labour market. Following the standard model of household behaviour, we assume that preferences of household h are represented by a well-behaved utility function uh(x h, --lh), where x h stands for the consumption bundle and I h is the quantity of labour supplied. Household h receives a net wage qh and non-wage income r h. Wage differentiation across households results from exogenous differences in capability or productivity, captured by the efficiency parameters e h, such that qh = ehqv Household h faces a budget constraint q'x h=qlhl h +r h

(ok h)

and a constraint on labour supply 4

= i

(L)

where ~bh and ~ h

are Lagrange multipliers associated with the respective

3 The welfare analysis in this paper must always be interpreted in this surplus-neutral sense. Note that we will use interchangeably the abbreviation MC and the terminology 'marginal welfare cost' to denote the concept, as defined formally in Eq. (3). 4 As in Dr~ze (1985) we assume that unemployment is spread over all households. This assumption is only for analytical and computational convenience. It would have been more realistic to assume that some households keep their job while others become full-time unemployed. More fundamentally, our specification implies that all unemployment is involuntary. Introducing voluntary unemployment in the model would make it much more complex and very difficult to solve.

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319

constraints and L stands for aggregate employment. It is assumed that households willingly supply any demand for labour at the going wage, i.e.

~h Ol h

0-1 h

=h~ ~- = 1

(4)

Non-wage income is made up of an exogenous part p h, a share Oh in private sector profits H (with Eh 0 h = 1) and unemployment compensation:

r h = oh(1 -- t ~ ) I I + bh(l * h - - I h) + ph

(5)

where t~ is the profit tax rate, l * h the full employment level of labour supply and b h the unemployment benefit of household h per unit of unemployment 5. The solution of the constrained utility maximization problem for household h yields the following commodity demand and labour supply functions:

x h = x h ( q , qlh, r h, lh)

(6a)

i h = ~h(L)

(6b)

The indirect utility function, appearing in the social welfare function, can now be written as vh(q, qh, r h, ~h) and the following properties will prove useful: 0/2 h

Oq

O/p h

~)hxh.

0/2 h

__ ~)h; ,

Or h

(9~h

O/) h

__ lIch.

,

Oqh

__ ~)hlh

(7)

Excess supply in the labour market implies that the net wage qh exceeds the reservation wage ~h, defined as

Ouh/Ol h ~h

Ouhl Orh

_ ~h

q_

~)hqh

qbh

(8)

2.2. Macroeconomic objectives and the welfare cost of taxation Let us now return to the social welfare specification. Making use of the indirect utility function and of Eqs. (5), (7) and (8), we can derive immediately that

O~hd g OW= ~h flh --X h' dq + ehl h dql + oh(1 -- t,~ ) d I I + ( ehql - ~h _ b h) _ ~

(9) where flh = ~)h(ow/o1jh ) is the marginal social valuation of one unit of income accruing to household h. These fl's will depend on the concavity of the social

5 In all the derivationswe assume that b h is fixed (although different for the different households), i.e. we neglect the possible link between b h and the labour income of household h.

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welfare function. Eq. (9) can be related in an intuitive way to the traditional macroeconomic objectives. Let us look first at the extreme case of fl h = 1, Vh, which is implied by a social welfare function with zero aversion to inequality in incomes. In that case, Eq. (9) reduces to dW = -

x h dq+~ehlhdqt+(1-t~)d[I

h + ~ , ( ehq, - Oh - b h ) - - d L OL h

(10)

The first term captures the effect of price changes: it is a weighted average of changes in consumer prices, the weights being given by the aggregate consumption of the different commodities. Uniform inflation arises when dq = q dTr with d~r/~" the rate of inflation 6. The second and the third term together give the change in aggregate personal disposable income: the former gives the change in global labour income following from a change in the consumer wage, the latter the development of the income from profits. Finally, the fourth term in Eq. (10) is a monetary measure of the value of changes in (un)employment: individual changes in employment are weighted by the difference between the consumer market wage and the sum of the reservation wage and unemployment benefits. This means that we recover from an explicit social welfare framework in a straightforward way the main macroeconomic objectives: inflation, income, employment. No explicit weighting of these aggregate objectives is necessary. Moreover, income distribution considerations enter in an elegant way, once we allow in Eq. (9) for differences in the /3 's. Eq. (9) immediately shows how the measures of inflation, income and employment have to be adjusted. Households with a larger social marginal valuation of income will get a larger weight 7.

3. The structure of the economy To compute Eq. (3) we have to specify how W and R will be influenced by changes in the vector of tax rates. These effects depend on the specification of the economy. To get a better insight into the impact of the macroeconomic objectives on the welfare evaluation, we will compare three simple specifications. These are first described in general terms. Different assumptions about price flexibility lead to different models of producer behaviour, sketched in Section 3.2. In Section 3.3 we summarize and relate the discussion to the marginal welfare cost of taxation.

6 The use of the word 'inflation' is an abuse of terminologyin a model without monetary sector. We refer to a situation where the prices of all consumer goods increase in the same proportion with respect to the num6raire (which is imported resources). v Analogous interpretations of the link between an individualistic social welfare function and the macroeconomicaggregates have been given by Dr~ze (1985, 1987) and Dr~ze and Stem (1987).

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3.1. Three simple models o f unemployment

The main motivation for leaving the Walrasian framework is the need to take account of unemployment. We therefore did not specify any model with labour market equilibrium 8. On the other hand, we want to keep our structure as manageable as possible and it is not our intention to go deeply into the debate on the causes of unemployment. We will therefore specify three simple models: in each case unemployment follows from the fact that the wage is not sufficiently flexible to clear the labour market. The easiest and most extreme way to model disequilibrium wages is the assumption of fixed wage costs: Pl = P l

(11)

Combined with the assumption of fixed prices and excess supply on the goods markets, Eq. (11) leads to the simple Keynesian model. We will call this model K. Although the assumption of fixed prices may be justified in the case of a small open economy, it probably is too extreme (even in the short run). We therefore will compare model K with a model in which goods markets are in equilibrium (but where Eq. (11) still holds, i.e., the wage cost remains fixed). In this model, which we will call model EQPR, prices are not fixed (or given on the world market) but they adjust and are sufficiently flexible to clear all goods markets. A similar model has been theoretically explored by Dr~ze (1985) and, in a simplified version, by Marchand et al. (1989). The assumption of completely fixed nominal wage costs is also extreme and unrealistic. We therefore will investigate the consequences of relaxing this assumption by introducing some (limited) flexibility of wages. For the specification of the process of wage determination we rely on the work of De Bruyne and Van Rompuy (1991) who derive a rather general wage equation for the private sector of the economy. They consider a 'right to manage'-model of the wage bargaining process as in Nickell and Andrews (1983) or Hoel and Nymoen (1988): the union and the firm bargain over the nominal gross wage rate and once an agreement is reached, the firm sets employment unilaterally. The utility function of an individual union member is defined over leisure and real net income. The latter is just the net consumption wage in case the union member is employed; otherwise it is the real unemployment benefit. The utility function of the union is assumed to be of the utilitarian type and is a weighted average of the utility of the employed and unemployed members. Solving the Nash bargaining problem then yields an

8 A comparison with the traditional Ahmad/Stern-approachis made in Van de gaer et al. (1992). Palokangas (1987) offers a theoretical analysis of optimal taxation and tax reform in a different model of an economywith trade union wages.

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implicit solution for the nominal gross wage, For our purposes, we can work with the following abbreviated version of this structural wage equation:

q1= ql( L, qc, 17, tl)

(12)

where qc = ~,isiqi stands for the consumption price index, si being the average budget share of commodity i. The interpretation of Eq. (12) as the outcome of the 'right to manage'-model of the wage bargaining process will be followed in our model TUW (for 'trade union wage'), where we combine Eq. (12) with the assumption of equilibrium prices on the goods markets. Yet it is clear that Eq. (12) is sufficiently general to fit other models of wage determination 9

3.2. Goods markets and the production side of the economy Let us now turn to a more concrete formulation of the models of the goods markets. In all three models, total consumption of commodity j is derived from Eq. (6a) as follows:

xj =

(13) h

This total consumption xj has to be allocated over imported and domestically produced goods. Following a standard procedure in general equilibrium modeling (see, e.g., De Melo and Robinson, 1985) we assume that this second stage in the decision problem can be operationalised as a cost minimisation problem 10.

min p j x j = dj pdj + mjpmj

xj = x j ( d j , m j ) ,

S.t.

j = 1. . . . .

G - 1

where the composite good xj is a function of two varieties: the imported variety mr with producer price pm r and the domestic variety d r with producer price pd r. This yields

dj = d j ( p d j ,

pmj, x j),

m j = m j ( p d j , pmj, xj), p j = p j ( p d j , pmj),

j = 1. . . . . j=l

j---1 .....

..... G-1

G - 1

(14a)

G-I

(14b) (14c)

9 More specifically, the case of fixed wage costs (as in Eq. (11)) can be imposed in Eq. (12) by assuming that Oql/Off = - 1 and by putting all other partial derivativesequal to zero. 10Since we use producer prices in the formulationof the problem, we implicitly assume that this problem is solved by the (domestic) producers. We could alternatively have specified that the consumers solve this problem. This does not make any differencefor the results and the interpretation of the model. The procedure we followed has the advantage that we can use the data from the input-output table constructedby the Belgian National StatisticalInstitute.

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To get private final demand Dj of domestically produced sector j-goods, we add exports to the resulting domestic demand:

Dj = dj ( pdj, pro j, x j) + exj ( pdj, to),

j = 1..... G - 1

( 15)

where to is an exogenous (and fixed) indicator of demand conditions on the world market. Eq. (15) of final demand holds for all our models. Assumptions about production technology are identical for the different models. Gross output of sector j requires the input of imported resources, our num6raire nj with price Pn, of labour lj with wage cost ejp l, where ej is a sector-specific efficiency parameter, and of a fixed amount of capital. The specification of the gross output production function is characterised by constant returns to scale. Since the capital stock is fixed, decreasing returns to scale result. Total output yj is assumed to be a Leontief function of gross output and of domestically produced intermediate goods purchased at a price pd i, i = 1. . . . . G. Profits of sector j can then be defined as:

IIj = p d j y j -

ejpll j

--Pnnj -

Y'~PdiaijY j,

j = 1. . . . . G - 1

(16)

i

where t h e aij's are the input-output coefficients 11 Good G is supplied by the government. We suppose that the public sector sets the price Pa and that production Ya is then determined by demand: final demand by households, exports and intermediate demand by private producers

y=

y ' x h ( q , qh, r h, ~h) + exG(pdG, oJ) + ~_,acjy j h

(17)

j

Eq. (17) embodies the assumption that household demand for good G is completely met by the (domestic) public sector. Conditional on this demand-determined output level, cost minimisation then leads to the following input demand functions:

IG = lG( YG, Pn, eGPl),

nG= riG( YG, P~, eGPl),

Via = aj6yc,

j = 1. . . . . G

(18)

where V~ stands for the intermediate goods demand by sector G. For the private goods markets, we distinguish the cases of fixed and flexible prices.

3.2.1. Model K: fixed prices In the simple Keynesian model K, prices are fixed and firms are rationed on the goods markets, i.e., output is demand-determined for j = 1. . . . . G - 1:

Y2 = dj( pdj, pmj, xj) -q- exj( pdj, 09) + EajiYi i

11 Profits can be interpreted as the remuneration of the fixed production factor capital.

(19)

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Bringing Eqs. (17) and (19) together and using Eq. (15), we get

y=(I-A)-ID

(20)

where A is the matrix of input-output coefficients aij and D is the vector with elements defined in Eq. (15). The private sector then behaves in the same way as the public sector: profit maximization boils down to cost minimisation, conditional on the demand-determined output level. This leads to

l j = l j ( Y j , Pn, ejPl),

n j = n j ( Y j , Pn, ejpj),

j=l

..... G

..... G-l,i=l

Vij=aijY j, (21)

Note that firms do have substitution possibilities at the input side because of the availability of imported resources n. Total employment, as determined by producer behaviour, then follows from Eqs. (18) and (21): G

L = E l i ( yj, p~, ejPl)

(22)

J

3.2.2. Models EQPR and TUW: Flexible prices Things change when goods prices are flexible. In a situation of clearing goods markets, we no longer have a demand-determined output level. Standard profit maximization now yields the following Walrasian supply and input demand functions (for j = 1. . . . . G - 1):

yj= yj( pd, p,, ejp,)

(23a)

lj = lj( pd, p.. ejp,)

(23b)

nj= nj( pd, p., ejp,)

(23c)

Vij=aijY j,

(23d)

i= l . . . . . G

Domestic prices pdj are determined as equilibrium prices on the goods markets and we have the following market equilibrium conditions for j = 1. . . . . G - 1: G

yj(pd, Pn, e j p l ) = d j ( p d j , pmj, x j ) + e x j ( p d j , t o ) + E a j k y k

(24)

k

where xj is defined in Eq. (13). Aggregate employment then is determined by Eqs. (18) and (23b): G-1

L = la(y~, Pn, erPl) + ~-, lj(pd, Pn, ejPl) J

(25)

3.3. The marginal welfare cost of taxation Let us now return to the marginal welfare cost of taxation in the various models. The differential effect on the welfare function has already been shown in

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325

Eq. (9): changes in taxes will have an effect via the consumer prices (q), the net wage (q0, the profits ( H ) and aggregate employment (L). The budget surplus (or deficit) of the government is given by

R = Y'~( q i - P i ) X i + ( P l - ql) L + t~ I I + p c y c - ecPll ~ - p . n c i

- Epdjaja Yc - )-~bh( l*h -- ~h(L)) -- d j

(26)

h

Revenues derive from indirect taxes on final demand, the tax on labour income, the tax on profits and the operating surplus of government production. The profit tax rate t= and the labor tax t~ are exogenous and kept fixed in all our calculations. Expenditures consist of an (exogenously given) amount of public good provision G and of unemployment allowances. Hence, we have for the case of fixed producer prices (model K):

dR=(q-p+w~a)'dx+x'dq+

pl-q~+}~bh

+ --eala--eaPlopl --pn--~2-+w _aa~

OL

dL+t,~dFl

dp,

(27)

J

where ~a is a vector with all elements equal to zero except the G-th one which is unity, and w, the change in the public sector surplus due to a change in the public sector output, is given by

Ol~ Onc w =Pc - Y'~pdjaj6 - ecpl-~y~ - P , - j

OYG

When producer prices are flexible (models EQPR and TUW) we get:

dR=(q-p+w~) +

-ecla

dx+x'dq+

pl-ql+~.£,b - - d L + t , ~ d I I h OL

ecp~ oPl --P~-~Pl

w~aaj J

+~_,(wY~ar~ Oy~- - Xj--OPJ )dpdj j \ k Opdj yraj6 Opdj

dPl (28)

Combining Eq. (9) with Eq. (27) or Eq. (28) we see that the relevant endogenous variables for the computation of the marginal welfare cost Eq. (3) are given by (x, q, q~, Pl, L, 1-1, pd). Our different models can then be summarized as in Fig. 1. The different models sketched may be highly nonlinear and difficult to solve. However, to compute the marginal welfare costs a linear approximation is

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VARI-

Model K

Model EOPR

Model TUW

ABLE X

(6a)and (13)

q

(1)

p~

(2)

q~

(ll)

(12)

L

(22)

(25)

H

(16), with ( 19),(21)

(16), with (23)

pd

fixed

(24) Fig. 1. Summary of models.

sufficient, after which we can resort to simple matrix inversion. Indeed, define z as the vector of endogenous variables. These variables are influenced by the policy variables t as described by the respective models. In a very abstract form, the reduced form of each of these models can be written as: Fk(z, t) = 0,

k = K, EQPR, TUW

(29)

If the assumptions underlying the implicit function theorem are met, we can use Eq. (29) to compute the matrix of tax multipliers as at' -

t

z'l

or '

k = K, EQPR, TUW

(30)

and, using this expression in Eq. (3),

- OW/Oz'[ OFJOz']-10FJOt' MC'=-

'

0 ' -1

- a R / a z [aFk/ z ]

aFJar

,

k = K , EQPR, TUW

(31)

The specifications of Fk(z, t) = 0, together with Eqs. (9) and (27) or Eq. (28) give us a complete description of all the elements in Eq. (31) for the marginal welfare cost of taxation. We have applied this framework for an analysis of the Belgian tax system in the reference year 1980. Our data are described in the following section.

4. Application for Belgium For the indirect tax system, overview is given in Table 1. (composed of VAT and excises) second column gives the average

we use a 15 commodities-classification. An The first column gives the indirect tax rate as a percentage of the consumer price and the budget shares in 1980. The tax rate on profits is

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327

Table 1 C o m m o d i t y classification

eq

et

5.7

0.183

0.69 * *

-0.61 *

Beverages (BEVE)

29.3

0.044

1.29 * *

- 0.42 *

0.38 * * -0.81 * *

Tobacco ( T O B A )

65.1

0.016

0.94 *

- 1.20 *

0.06

Clothing ( C L O T ) Rent ( R E N T )

14.7 1.4

0.084 0.103

1.67 * * -0.01

-0.81 * -0.07 *

0.12 - 0.08 *

Heating ( H E A T ) Lighting ( L I G H ) Durables ( D U R A )

7.9 13.8 13.8

0.044 0.018 0.099

1.59 * 0.16 2.18 * *

- 0.30 * -0.64 * - 0.36 *

0.40 -0.28

5.2

0.042

1.02 * *

- 0.93 *

2.1 21.8 28.1 5.7 10.5 1.9

0.104 0.038 0.067 0.011 0.089 0.059

0.83 1.71 0.65 0.12 0.92 0.95

-0.39 -0.73 -0.22 - 0.80 -0.35 - 0.43

Commodities Food ( F O O D )

Maintenance ( M A I N ) Personal care ( H Y G I ) Private transport equipment ( B U Y T ) Use private transport ( U S E T ) Public transportation ( P U B T ) Leisure goods (LEIS) Services (SERV)

t

s

ey

** ** ** ** **

* ** * ** ** *

0.33 0.28 * -0.58 * * - 0.40 -0.31 * 0.98 * * -0.11 -

0.01

t: indirect tax rate ( V A T + e x c i s e s ) as a percentage of c o n s u m e r price; s: budget share; ey: total expenditure elasticity; eq: uncompensated own price elasticity; el: elasticity with respect to rationing variable. * ( * * ) indicates that the estimated coefficient is greater than (twice) its standard error.

put equal to 0.50, and the tax wedge on labour in 1980 is taken to be 0.76 as a percentage of the gross wage 12 To estimate the matrix of tax multipliers, we need information on aggregate behavioural reactions by consumers and producers. This information has been collected from different sources. To introduce it into Eq. (31), estimates of behavioural reactions have been expressed in terms of elasticities. The levels of all variables were calculated (and made consistent) for the year 1980. At the aggregate consumer side, we have estimated a complete demand system for 1953-1988 with National Accounts data, taking into account rationing on the labour market 13. Including the rationing variable in the demand system increased the fit significantly. We compared the results for the Rotterdam, AIDS and CBS-specifications and finally preferred the Rotterdam functional form 14. The last three columns of Table 1 give the income elasticities, uncompensated price

12 This is the figure used by the Belgian Planning Office. R e m e m b e r that our definition of the tax w e d g e includes the social security contributions. 13 The rationing variable is defined as yearly effective man-hours per capita, and hence captures the effect of variations in hours as well as in the rate of unemployment. 14 All estimations were m a d e with the D E M M O D - c o m p u t e r program, constructed by A.P. Barten. The differences between Rotterdam and CBS were rather small, while with AIDS there were problems with the negativity of the Slutsky-matrix.

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Table 2 Production side of the economy Productionsector

o-j

vj

ej

Agriculture Energy Metals Chemical sector Machinery Manufacturingof transportationequipment Food Textile Other manufacturing Construction Retailing services Other transport Other services Railways

1.00 0.78 0.81 5.49 5.62 2.01 0.03 2.20 4.76 1.00 1.00 1.00 1.00 1.00

0.40 0.53 0.48 0.52 0.48 0.44 0.53 0.58 0.52 0.50 0.50 0.50 0.50 0.50

0.60 1.73 1.34 1.28 1.13 1.14 1.07 0.70 1.04 0.96 0.96 1.12 0.91 1.27

o): substitutionelasticitydomestic production-imports(taken from Shiells et al., 1986; missing values put equal to 1.00); vj: substitutionelasticity primary production factors (taken from Ballard et al., 1985; missing values put equal to 0.50); ej: calibratedefficiencyparameter.

elasticities and elasticities with respect to the rationing variable: all these elasticities are evaluated for 1980. Since the classification of commodities at the consumer side is not the same as the sectoral classification at the production side, we need a transition matrix, for which we relied on Van Regemorter (1990). The Belgian data at the sectoral level are not sufficient to estimate all behavioural reactions. We resorted to a calibration of the parameters, assuming CES-functional forms for the specifications of the composite good-function x j ( d j , m1) and the gross output-production functions. A part of the relevant information is shown in Table 2 ~5. Note that 'railways' (closely linked to public transportation in the consumer commodity classification) is the public sector commodity. The elasticities of exports with respect to domestic prices are put equal to minus one. The reference values for the (long run) elasticity of the net wage with respect to its various determinants (used in model TUW) are taken from the empirical study for Belgium of Van Rompuy et al. (1988) and are given in Table 3 t6. Note that, if the change in consumer prices is entirely due to a change in producer prices, then the elasticity of the nominal wage rate with respect to the consumption price should be equal to one. However, if the increase in consumer prices is solely attributable to an increase in indirect taxes, with constant producer prices, then the

15More informationon the calibrationprocedure can be found in Van de gaer et al. (1993). 16In the case of a fixed nominalwage cost (models K and EQPR) the coefficientof the tax on labour equals -0.7056 and all other coefficientsare zero.

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Table 3 Elasticities of the wage equation Elasticity of the net wage with respect to Profits Employment Cost of living index Tax on labor

0.2750 2.1883 0.6900 -0.4410

Reference values are taken from Van Rompuy et al. (1988).

elasticity will be smaller than one. Higher wage demands by the union are no longer matched by an increased willingness to pay by the firm 17 To compute the welfare effects of taxation, we further need household specific information on consumption, employment, profit share, unemployment benefit, reservation wage and efficiency. This information is taken mainly from the Consumer Budget Survey. We consider ten representative households, corresponding to the deciles of that survey. We then have immediately all the necessary information on disposable income and consumption: income data are given in the first column of Table 4. On the basis of the budget survey, we can also easily calculate the profit shares 0 h, shown in the second column of the table. The most difficult part of the exercise was the construction of employment and efficiency data: these had to be consistent with the production side of the model. Starting from the given distribution of unemployment over the deciles and assuming that full time-employment was proportional to the number of active people in the decile, we could derive employment and wage figures from the (given) data on total labour income. Resulting unemployment figures and household efficiency parameters are given in the third and fourth column of Table 4, respectively. The same calibration procedure also yields the efficiency parameters for the different production sectors: these have been given in the last column of Table 2. The reservation wages are put equal to zero ~8 Finally, value judgments incorporated in the parameters /3 h should be made explicit. These are derived from the traditional iso-elastic form of the social welfare function and normalized such that the weight of the poorest decile equals one (see also Ahmad and Stem, 1984). This yields r'h]

e

/3h= 1 ,-vj 17 These observations are confirmed in the study by Nickell and Andrews (1983). 18 This is the most extreme hypothesis, making the impact of changes in unemployment on social welfare as large as possible (see Eq. (9)). Even then it turns out that the unemployment component plays only a minor role in the welfare evaluation of the different tax rates.

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Table 4

Information about households Decile

Disposable income

0h

Unemployment rate

eh

1 2 3 4 5 6 7 8 9 10

171541 270 739 348 663 416209 486 045 555 656 625 792 704 682 815619 1203 589

0.012 0.031 0.061 0.048 0.060 0.044 0.083 0.067 0.176 0.420

0.30 0.23 0.16 0.13 0.11 0.13 0.06 0.07 0.05 0.03

0.343 0.562 0.785 0.813 0.844 0.883 0.887 1.010 1.048 1.473

Disposable income: in Belgian francs per year.

oh: share of decile in total profits (computed on the basis of the Budget Survey); eh: calibrated efficiency parameter. where r* h denotes total income per equivalent adult of household h 19 and s represents the inequality aversion parameter 20

5. Results: Macroeconomic objectives and inequality aversion in marginal tax reform analysis As argued before, the marginal welfare cost of taxation will in general depend on two factors: the value judgments incorporated in the social welfare function, and the prediction of the effects of changes in the tax instruments. The social welfare function determines the evaluation of the various macroeconomic objectives in terms of the effects on individual welfare levels. In Section 5.1, we will derive some useful insights about this interrelationship which are fully independent of the assumptions about the macroeconomic model. In Section 5.2 we analyse the marginal welfare costs and concentrate on the importance of the macroeconomic objectives for the global evaluation. It will turn out that the macroeconomic specification is crucial.

5.1. Inequality aversion and the ranking of the macroeconomic objectives E q . ( 9 ) s h o w s that the evaluative w e i g h t s attached to the different m a c r o e c o -

n o m i c objectives, i.e. the social welfare effects o f c h a n g e s in the v a r i a b l e s d q ,

J9 We use the definition r* h = (q(qh q_ rh)/Tlh, where r/h is the number of equivalent adults in household h. To calculate ~?h, we use the equivalence scales of the League of Nations, also used by the Belgian Statistical Institute for the analysis of the Consumer Budget Survey. 2o The social welfare function will be (strictly) concave in incomes for e >_( > )0. Concavity has been assumed throughout this paper.

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331

Table 5 Inequality aversion and ranking of macroeconomic objectives 8=0

8=1

¢=2

e=4

¢=9

e=16

PROFI WAGE PRICE EMPLOY

PROFI WAGE PRICE EMPLOY

EMPLOY PRICE WAGE PROFI

EMPLOY PRICE WAGE PROFI

PRICE EMPLOY PROFI WAGE

PRICE EMPLOY PROFI WAGE

dql, d H and dL, will not depend on the macroeconomic model: they immediately follow from observations on the distribution of consumption, employment, efficiency and profits over the different households and are influenced by the inequality aversion, as captured through the /3-vector 21. To get a better insight into this influence, we define changes in the macroeconomic variables dTr * (a uniform change in all consumer prices), dql*, d H * and dL*, such that someone with an intermediate value of the inequality aversion ( e = 1.5) will be indifferent between these changes, i.e., 3W --dlr* O~

OW

=

aql

d aI.

OW ~-dH* OH

OW

=

OL

dL*

where the partial derivatives are calculated as shown in Eq. (9) by combining the /3-vector corresponding to e = 1.5 with observable data on the households. We can now compute the welfare effect of dTr *, dq~*, d H * and dL* for other values of e. Since varying e will lead to another r-vector, these welfare effects will no longer be equal. Table 5 shows the effect of varying e on the ranking of macroeconomic objectives. The pattern in Table 5 is easily understood, by taking into account that the choice of e reflects value judgments about the income distribution. Remember that we consider shifts in macroeconomic variables of a magnitude such that a social evaluator with e = 1.5 considers them as equivalent. The importance attached to the evolution of consumer wages decreases with increasing inequality aversion, because unemployment is relatively more concentrated at the bottom of the income distribution and because the efficiency parameters are much lower for the lower deciles. Profits also become less relevant: they accrue largely to the higher incomes. For very high inequality aversion, price changes (inflation) become the dominant macroeconomic objective. For the lowest deciles, the income gain of employment (wage minus unemployment benefit) becomes rather

21 The only exception is the assumption about the form of the rationing mechanism on the labour market, which may be considered to be a part of the macroeconomic model. However, we make the simple assumption that changes in employment are divided over the households in proportion to actual employment figures.

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small. Uniform inflation hits all households equally. Moreover, for the reasons mentioned above, poor households are less affected by the evolution in the other macroeconomic variables. Hence the finding that the relative importance attached to price changes increases with inequality aversion. While this finding is fully independent of the choice of macroeconomic model, it has immediate implications for the interpretion of the marginal welfare costs. A collection of results for our different models K, EQPR and TUW is shown in the Tables 6-8, respectively 22. Compare the results for e = 0 and e = 16. Since the ranking of the 'price'-component completely dominates the ranking of the welfare cost for a high degree of inequality aversion, we only report the price component for e = 16. In fact, for e--- 16, in the model TUW the ranking of total welfare costs is the same as the ranking on the basis of price changes. For e = 0, however, a more important role is played by changes in the other macroeconomic variables. We will return to the interpretation of these variables in the following subsection. Another straightforward finding follows from Tables 6-8. For all models, increasing the degree of inequality aversion has analogous effects on the ranking of the price component (and hence, the overall ranking) of the marginal welfare costs. For a given model, the predicted changes in economic variables remain the same, and increasing e simply raises the weight attached to the lower deciles. This increases considerably the marginal welfare cost of the tax on food, heating and rent, and decreases the welfare cost of the tax on leisure goods, durables and private transportation (both the purchase and the use of cars). The way changes in influence the ranking of indirect taxes appears to be independent of the way the economy is modelled.

5.2. Results for the different models By way of introduction, it is useful to look at the results for an intermediate value of the inequality aversion ( e = 1.5). These immediately show that the ranking of the welfare costs is very similar for models K and EQPR: the assumption of price flexibility on goods markets does not seem to have an important influence. In both cases a welfare increase could be realised by decreasing the tax on tobacco, services and heating with a compensating increase in the taxes on public transportation, lighting and clothing. However, the introduc-

22 Tables 6 - 8 give point estimates of the marginal welfare costs. The best available method to compute confidence intervals would be to resort to linear approximations (see Decoster and Schokkaert, 1990, for an example). For our model, this approximation would be very crude indeed. Moreover, as noted by Ahmad and Stern (1987, p. 301), if the point estimate of the marginal welfare cost of taxing commodity i is larger than the point estimate of the marginal welfare cost of taxing commodity j, then the expected change in welfare from a switch into j is positive. And if the distribution is symmetric, the probability of an increase in welfare is above 50%. It therefore makes sense to concentrate on these point estimates.

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

FOOD BEVE TOBA CLOT RENT HEAT LIGH DURA MAIN HYGI BUYT USET PUBT LEIS SERV

318986 50548 7830 129372 175291 67301 33138 147296 63622 175638 49571 82941 28706 130371 91568

budget( * )

TOBA SERV MAIN HEAT BEVE LEIS HYGI BUYT DURA RENT USET CLOT FOOD LIGH PUBT

e = 0 price 1.59 1.39 1.38 1.32 1.36 1.34 1.28 1.33 1.28 1.28 1.27 1.22 1.19 1.03 0.81

MC 1.64 1.62 1.53 1.47 1.45 1.45 1.44 1.42 1.41 1.41 1.34 1.28 1.26 0.92 0.91

( * ) Government revenue: in millions Belgian francs.

own price

tax rate

MULTIPLIERS

Table 6 Results for model K

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

wage -0.02 0.01 0.01 0.02 0.00 0.00 0.00 0.02 0.00 -0.01 -0.01 - 0.00 -0.02 0.01 - 0.02

profits 0.08 0.22 0.14 0.14 0.08 0.10 0.16 0.07 0.13 0.13 0.08 0.07 0.08 -0.12 0.11

employment TOBA SERV HEAT MAIN BEVE HYGI LEIS RENT DURA BUYT FOOD USET CLOT LIGH PUBT

e = 1.5

1.13 1.09 1.03 1.00 0.98 0.97 0.95 0.95 0.91 0.88 0.87 0.87 0.84 0.63 0.60

MC HEAT TOBA SERV FOOD BEVE RENT HYGI MAIN LEIS LIGH DURA CLOT PUBT USET BUYT

e=16

0.153 0.116 0.110 0.108 0.107 0.107 0.102 0.099 0.080 0.078 0.068 0.067 0.058 0.053 0.030

MC

0.146 0.113 0.099 0.105 0.103 0.101 0.094 0.092 0.076 0.083 0.062 0.063 0.053 0.050 0.026

price

I

e~

0.95 1.(30 1.00 1.00 0.97 0.99 0.99 1.00 0.99 0.96 1.00 1.00 0.99 1.00 0.96

FOOD BEVE TOBA CLOT RENT HEAT UGH DURA MAIN HYGI BUYT USET PUBT LEIS SERV

301767 48002 7627 125248 165951 63402 32646 139454 61495 166045 47756 79572 26700 125901 85155

budgeff*)

TOBA SERV BEVE MAIN HEAT BUYT LEIS HYGI RENT DURA USET FOOD CLOT LIGH PUBT

e=0

1.72 1.54 1.46 1.46 1.45 1.43 1.42 1.41 1.40 1.40 1.38 1.31 1.31 1.07 1.03

MC

( * ) Government revenue: in millions Belgian francs.

own price

tax rate

MULTIPLIERS

Table 7 Results for model EQPR

1.64 1.20 1.32 1.26 1.22 1.30 1.28 1.17 1.21 1.20 1.27 1.19 1.22 1.19 0.88

price 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

wage -0.02 0.23 0.10 0.12 0.16 0.09 0.09 0.14 0.11 0.12 0.05 0.05 0.04 - 0.06 0.04

profits 0.09 0.11 0.04 0.08 0.07 0.04 0.06 0.09 0.08 0.07 0.06 0.06 0.05 - 0.05 0.10

employment TOBA SERV HEAT BEVE MAIN HYGI RENT LEIS DURA FOOD USET BUYT CLOT LIGH PUBT

e=l.5

1.18 1.02 1.00 0.98 0.94 0.94 0.93 0.93 0.90 0.89 0.89 0.87 0.85 0.73 0.68

MC HEAT TOBA FOOD BEVE RENT SERV HYGI MAIN LIGH LEIS CLOT PUBT DURA USET BUYT

e=16

0.150 0.121 0.110 0.104 0.103 0.098 0.095 0.091 0.089 0.075 0.066 0.064 0.062 0.052 0.025

MC

0.142 0.117 0.105 0.099 0.096 0.086 0.087 0.083 0.094 0.070 0.062 0.058 0.055 0.047 0.020

price

I

e~

4~

0.95 1.00 1.00 1.00 0.97 0.99 0.99 1.00 0.99 0.96 1.00 1.00 0.99 1.00 0.96

FOOD BEVE TOBA CLOT RENT HEAT LIGH DURA MAIN HYGI BUYT USET PUBT LEIS SERV

260850 32106 513 99013 155877 57684 16217 122327 56077 163681 34319 57401 27894 103393 91891

budget( * )

TOBA LIGH BEVE BUYT USET LEIS CLOT DURA MAIN HEAT FOOD RENT HYGI SERV PUBT

~=0

30.69 2.54 2.36 2.13 2.06 1.81 1.75 1.64 1.64 1.63 1.57 1.51 1.43 1.40 0.97

MC

( * ) Government revenue: in millions Belgian francs.

own price

tax rate

MULTIPLIERS

Table 8 Results for model TUW

25.68 2.48 2.01 1.84 1.80 1.57 1.56 1.38 1.39 1.35 1.40 1.29 1.19 1.10 0.84

price - 8.43 - 0.62 - 0.30 -0.24 -0.23 -0.13 -0.16 - 0.09 -0.06 - 0.06 -0.10 - 0.04 -0.01 0.04 0.03

wage 10.18 0.64 0.52 0.43 0.36 0.27 0.25 0.25 0.21 0.25 0.18 0.17 0.16 0.16 0.01

profits 3.26 0.03 0.13 0.11 0.13 0.10 0.10 0.10 0.10 0.09 0.09 0.09 0.09 0.10 0.09

employment TOBA LIGH BEVE USET BUYT LEIS CLOT HEAT FOOD MAIN DURA RENT HYGI SERV PUBT

e=l.5

20.63 1.70 1.57 1.32 1.30 1.17 1.14 1.12 1.07 1.06 1.05 1.00 0.96 0.93 0.64

MC TOBA LIGH HEAT BEVE FOOD RENT MAIN HYGI LEIS CLOT SERV USET DURA PUBT BUYT

s=16 price 1.833 0.195 0.157 0.152 0.123 0.103 0.092 0.088 0.086 0.081 0.079 0.068 0.063 0.055 0.031

MC 2.100 0.202 0.167 0.167 0.130 0.111 0.102 0.097 0.096 0.089 0.089 0.080 0.074 0.060 0.044

J

g~

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tion of a trade union wage specification (model TUW) does change the ranking of the marginal welfare costs considerably. Although the welfare cost of tobacco remains the highest, the welfare costs are now relatively lower for services and heating. Lighting on the other hand gets a higher welfare cost. Analogous differences are found for other values of 6. To get a better insight into the importance of the different macroeconomic objectives for the explanation of these differences, we have given a detailed overview of the different components for e = 0, i.e., the case where inequality aversion is zero and the monetary effects play in the most direct way. Even here, however, one has to be careful with the comparison of the different effects: the components of the welfare cost are not only influenced by the expression in the numerator but also by the budget effect in the denominator (see Eqs. (3), (9), (27) and (28)). These budget multipliers are given in Tables 6-8. Of course, to understand these multipliers one has to consider the complete general equilibrium process, but at this point we already want to stress an important finding: the budget effects are strongly influenced by the actual magnitude of the tax rates. Compare the pattern of tax rates in Table 1 with the pattern of the budget multipliers: if the tax rates are already high, a change in these tax rates will have a smaller effect on tax revenue and this raises the marginal welfare cost (because it decreases the budget multiplier). Let us now consider each model in turn. In the Keynesian case (Table 6) producer prices and wage costs are fixed and the changes in indirect taxes are completely shifted on the consumers. Therefore there is hardly any effect on profits. Unemployment increases because the demand effect of the price changes induces a lower production level (with the notable exception of lighting). These changes in unemployment have some influence on the welfare costs (e.g. for heating and the purchase of cars) but the overall ranking is still mainly determined by the price component. Things look different in the EQPR-model (Table 7). At first sight the multiplier effects on consumer prices in the first column seem remarkably close to 1. Note that this result here follows from a quite complex general equilibrium structure. In general, the magnitude of these multiplier effects is determined by two forces: the supply elasticities, mainly determined by the degree of decreasing returns to scale, and the price elasticities of demand for the domestic varieties of the goods, determined by the overall price elasticity of demand and by the relative importance of the domestic variety in total consumption 23. Those goods for which the fraction of domestic goods is high (food, services, heating and lighting) and that have strongly decreasing returns to scale (services, heating and lighting) have a price multiplier smaller than one. The fact that, generally speaking, the multipliers

23This is of course a simple extension of well-knownpartial equilibrium results.

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337

are not far below 1 can largely be explained by our assumption of relatively large supply elasticities. This reasoning could suggest that the flexibility of the prices does not play an important role for the calculation of the marginal welfare costs. But this is not true: the increased price flexibility has a strong impact on profits and the important profits component leads to a smaller rank correlation between the overall welfare costs and the price component. Look at the results for services, heating and personal care (HYGI) on the one hand and clothing, and the use of private transport on the other hand. The reason here is that the price decrease holds for all units sold and that in our open economy there may be large quantity effects, even if the price effect is relatively small. The differences in these quantity effects (linked to the own-price elasticities of demand) largely explain, e.g., the different rankings for rent and services, two goods which are basically related to the same production sector. Note also that, compared to the K-model, the employment component in the welfare cost becomes smaller and is more uniformly distributed over the different taxes. The reason is clear: the increase in price flexibility leads to smaller effects on domestic production and hence (with constant relative factor prices) a lower effect on employment. The interaction between price changes and substitution effects at the consumer side leads to a more uniform distribution of that effect over the different sectors. Although the differences for the macroeconomic variables are clear, the overall ranking of the marginal welfare costs in model EQPR is about the same as in model K. And the reason is easily understood: there is a negative correlation between the changes in the price component and in the profit component for the two models. If prices in a sector go down, profits in the sector decrease: this leads to a smaller welfare cost because of price changes but a higher welfare cost due to the change in profits. The two effects compensate each other to a large extent. Of course, this result will depend on the pattern of elasticities, as explained above. Sensitivity analysis 24 reveals that the differences between the models EQPR and K grow larger if we impose larger demand elasticities a n d / o r smaller supply elasticities. Let us now turn to model TUW (Table 8). The nominal wage cost is no longer fixed in this model: a part of the burden of the tax increase will be borne by the firms, because there is an increase in the nominal consumer wages. This increase in itself has a negative effect on the marginal welfare cost. Compared to model K we now have two additional but opposite effects on employment. As in model EQPR, price flexibility leads to a smaller increase in unemployment (and a more uniform distribution over the sectors). In addition, however, the increase in wage costs in model TUW leads to an increase in unemployment through the process of

24 The results of this sensitivity analysis are available from the authors on request.

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factor substitution (more imports, less labour). The net effect differs from sector to sector, but in general the demand effect is stronger than the factor substitution effect (and, hence, the effect on unemployment is smaller in model TUW than in model K but larger than in model EQPR). The combination of the downwards price flexibility and the increase in wage costs leads to a very pronounced effect on profits. All this does n o t imply that the correlation between the ranking of the overall welfare costs and the price component would be low. Quite the contrary: although the other macroeconomic components are large in absolute value, they hardly change the welfare ranking on the basis of the price change. The reason is threefold. Firstly, the employment effect is rather uniformly distributed over the different commodities. Secondly, the wage effect and the profits effect tend to compensate each other. The reason is obvious: the higher the increase in wage costs (i.e., the lower the effect on the consumer wage), the larger the decrease in profits. Thirdly, and contrary to what was observed in model EQPR, there is now a highly positive correlation between price increases and decreases in profits. To understand this latter phenomenon, it is important to realise that there is a common labour market in the model. If prices increase more, the increase in the net wage through the wage indexation process will be higher. The resulting wage increase will have an influence on profits in all sectors: this general equilibrium effect was absent in model EQPR. Since there is a high correlation between the overall welfare cost and the price component in both models K and TUW but at the same time a much lower correlation between the marginal welfare costs in both models, these different rankings must be explained by the differences in the price components themselves. The most striking changes in going from model K to model TUW are the decrease in the relative marginal welfare cost of services and personal care and rent and the increase in the relative welfare cost of lighting, clothing and the use and purchase of private transportation. The former commodities are characterised by a large share of domestic production in total consumption: there will be a rather strong negative effect on the prices in these sectors (as is also clear from the multipliers). Therefore the influence on wage costs and, hence, on employment and profits in all domestic sectors will be smaller. Note that these effects can also be seen in the multipliers of government revenue. This again reminds us of the importance of the budget effects to get a clear insight into the pattern of marginal welfare costs. 6. Conclusion

In this paper, we started from the framework of Dr~ze (1985) to integrate macroeconomic objectives and distributional considerations in the welfare evaluation of tax changes. Two distinct types of judgment are indispensable to assess the desirability of a policy change. First, there is a normative judgment with respect to the choice of differential weights attached to individuals in a welfaristic context.

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This choice of weights will also influence the evaluation of the trade-off between the different macroeconomic objectives. Second, there is a positive judgment with respect to the specification and parameterization of the economy. Differences in both types of judgment lead to different policy prescriptions. With this paper we tried to get a better insight into these different relations. We have indicated how differences in inequality aversion lead to differences in the importance attached to the different macroeconomic objectives. People with a low aversion to inequality tend to stress the evolution of profits and net wages, while those which are highly averse to inequality will emphasize inflation and unemployment. To analyse the effects of changes in the tax instruments, one has to specify the structure of the economy. We worked with three simple specifications of unemployment and price and wage setting behavior in order to investigate whether the result of marginal tax reform calculations depend on the assumptions about price and wage flexibility. They do. Assumptions about the general equilibrium structure of the economy have a crucial impact on the results. Introducing flexible prices on the goods markets in a model with a fixed wage does not change the rankings of the welfare costs very much, because the development of profits compensates for the differences in price changes. But the ranking does change considerably if we add the assumption of a common labour market where a trade union wage is determined. All this implies that the analyst must be very careful when he makes assumptions about the macroeconomic model. Alternatively, one could look for directions of reform which imply a welfare improvement for all specifications of the economy. Our tables offer the straightforward possibility of defining welfare improving directions of tax reform in the Belgian tax system. As the degree of inequality aversion increases, the relative marginal welfare cost of heating, food and rent increases, while the relative cost for leisure, durables, and both the purchase and use of private transportation decreases. Our analysis shows that these findings are robust with respect to the model of the economy. Yet for other commodities the specification of the model does matter and, as indicated above, the introduction of a trade union wage is very important. This stands out most clearly when one considers the rankings of services and lighting. The former has a high welfare cost in models K and EQPR, while it has a low welfare cost in model TUW. The reverse holds for the latter. Despite the substantial influence of inequality aversion and the specification of the model of the economy, it is possible to find directions of tax reform which are welfare improving, irrespective of the model used or the normative judgement adhered to. Decreasing the tax rate on tobacco (or beverages) and at the same time increasing the tax on public transportation is an example of such a reform. Given the simplicity of our specifications, these conclusions should be interpreted cautiously. Surely it would have been preferable to work with a general assumption of price-setting behaviour, possibly containing the variants of fixed

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and equilibrium prices as special cases. Our m o d e l s o f u n e m p l o y m e n t remain rather simple: in all three specifications u n e m p l o y m e n t follows f r o m the assumption o f a n o n - m a r k e t clearing w a g e and is essentially involuntary. W i t h the available data and g i v e n the present state o f our empirical k n o w l e d g e , it is difficult to apply such m o r e c o m p l i c a t e d models for Belgium.

Acknowledgements W e thank L e o n Bettendorf, Stef Proost and Denise Van R e g e m o r t e r for their valuable c o m m e n t s and for their indispensable help with the data. W e also thank two a n o n y m o u s referees, w h o s e useful c o m m e n t s led to a considerable revision o f a previous version o f the paper.

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