Capital taxation in a dynamic general equilibrium setting

Journal

of Public

Economics

CAPITAL

10 (1978) l-24.

0 North-Holland

Publishing

TAXATION IN A DYNAMIC EQUILIBRIUM SETTING Ann

Massochusett

Company

GENERAL

F. FRIEDLAENDER*

Institute of Technology,

Cambridge

MA 02139, U.S.A.

Adolf F. VANDENDORPE ~!~‘~tr/r.strrCo//rgr, St. Paul, MN 55101, U.S.A. Received

April 1977, revised version

received

April 1978

The familiar two-factor, two-commodity incidence model is extended to a dynamic setting in which the supply of capital is variable and the government can use money or bonds to balance its budget in addition to neutral lump sum taxation. The dynamic incidence effects of a sectoral tax on capital are qualitatively similar to the static incidence effects when the government balances its budget with neutral taxes, but are qualitatively different when the government uses money or bonds. In this case, while capital bears the burden of the tax in the short run, it is able to shift it in the long run.

1. Introduction In analyzing the incidence effects of capital taxation, it is important to distinguish between static incidence and dynamic incidence. Static incidence analysis is concerned with the intratemporal general equilibrium effects of a (marginal) change in taxation upon relative factor and commodity prices, outputs, and welfare. Thus total factor supplies are assumed to be fixed, although intersectoral adjustments in factor allocations are assumed to take place. As its name indicates, dynamic incidence analysis is concerned with similar intertemporal general equilibrium effects of a change in taxation. Because capital is a produced factor of production, it enters the general-equilibrium system not only as a factor input, but also as a produced output. Thus, insofar as any change in the tax structure affects prices, income, interest rates, and real wealth, it will also affect investment demand and the supply of savings and hence the pattern of capital accumulation over time. Consequently, by altering this growth path of the dynamic economy, the *The authors would comments and criticisms experiments.

like to thank in formulating

Geoffrey Woglom and Stanley Fischer for helpful the model. James Paddock performed the simulation

long-run dynamic incidence of any tax-structure change may be quite different from its short-run static incidence,’ and it is this long-run incidence that is ultimately the relevant concept. The accepted general equilibrium analysis of sectoral capital taxation in the public finance literature is based on the model developed by Harberger (1962) and extended by Mieszkowski (1967), hereafter referred to as HM, that treats capital as a fixed factor of production. Using the standard 2(fixed) factor, 2-commodity general equilibrium framework, HM show that a sectoral tax on capital will be borne by capital. From this Harberger (1962) inferred that the corporate income tax is not shifted. More recently, Musgrave (1973) and Aaron (1973, 1975) have used the HM analysis to argue that property taxes are primarily borne by owners of capital and not shifted forward to renters2 While the HM framework is powerful and has formed the basis of generalequilibrium studies of tax incidence in a static setting, it must be extended in two significant ways to enable an in depth analysis of the dynamic aspects of capital taxation. First, the produced nature of capital must be made explicit and specific savings and investment relationships must be introduced. Second, since the nature of the equilibrating adjustments not only depends upon the initial level of taxation but also upon the way in which the government balances its budget, the government budget constraint must be explicitly considered.3 Consequently, in this paper we study the question of the incidence of capital taxation within the context of a general-equilibrium, two-sector model with the following characteristics: (1) capital is treated as a produced factor of production; (2) the government budget constraint is explicitly considered, and in addition to taxes, the government can also use money or bonds to balance its budget.4 Briefly, this paper takes the following form. In section 2 we present such a model, while in section 3 we consider the framework used to analyze questions of dynamic incidence. In section 4 we present some simulation results that enable us to compare the dynamic incidence of sectoral capital taxation under alternative government equilibrating adjustments. Section 5 then gives a brief conclusion and some areas for future research. ‘Feldstein (1974, 1975) has analyzed the dynamic incidence of capital taxation in a single sector model and shown that labor may ultimately bear a large portion of capital taxation if savings are sensitive to the return to capital. Also see Grieson (1975). ‘Musgrave qualities this conclusion, however, by introducing noncompetitive price elements. With respect to the property tax, the analysis of Mieszkowski (1972) is also relevant. sin a static setting, Vandendorpe and Friedlaender (1976) have shown that the government budget constraint can he ignored if there are no initial distorting taxes, but not if the initial tax structure is drsl0rlrn~. ‘Thiz mo&l .rl\o )pcr-m~rs rnr~ral taxes to be set at any al-bitrary nonzero level. Since, however, the implrcattons of an mitial distorting tax structure have been extensively analyzed by Vandendorpe and Friedlaender (1976) they are not explicitly considered in this paper.

A.F. Friedlaender rrnd A.F. Vmdendorpe, Capital taurrtion

3

2. The model The model utilized in the present paper is a hybrid micro-macro model. Following HM, the model is characterized by two factors and two commodities with production subject to constant returns to scale and perfect intersectoral factor mobility. While the HM model is static, however, this model is explicitly dynamic and treats capital as a produced factor of production and introduces money and bonds through the government budget constraint.’ Following HM, we assume that the economy can be characterized by the outputs of a corporate sector (X,) and a non-corporate sector (X2), each of which is produced by the available stocks of labor (I!,) and capital (K) under constant returns to scale.‘j Because of the constant-returns-to-scale assumption, a corporate profits tax is analytically equivalent to a sectoral tax on capital. Like HM, we can infer the incidence of a corporate profits tax by altering the tax rate on capital in the corporate sector. Following Jones’ (1965, 1971) treatment of the two-factor, two-commodity model, the basic production equilibrium relationships consist of the full employment conditions, a,,X,

and the competitive

+a,,x,=lc,

(14

zero profit conditions,

where K and L are respectively the amounts of labor and capital supplied at time t; Xj represents the output of commodity j; rj and wj represent the cost (inclusive of factor taxes and depreciation) of employing respectively one unit of capital or labor in sector j: pj is the producer-price of commodity j; aJj is 5For a similar treatment of a two-sector macro model see Foley and Sidrauski (1971). Our mode1 differs from theirs, however, in two significant ways: first, the corporate sector is assumed to produce both consumer and investment goods; and second, factor and commodity taxes are assumed to be government control variables. Although it is analytically more convenient to utilize a two-sector model with a capital and a consumption goods sector, we have chosen to assume that the corporate sector produces both capital and consumption goods and have thus sacriticed some analytical clarity for realism. 6We refer to K as the number of physical units of capital, intratemporally fixed at time t. Since we assume that capita1 goods are only produced by the corporate sector, on the production side of the model, the concept of physical capital units is clear. On the demand side of the model, however, the term capital will need a careful definition in the context of consumption, investment, and savings.

4

A.F.

Friedhender

ctnd A.F.

Krndendorpe,

Ctrpittrl

ttruatim

the amount of factor f used per unit output of commodity j (that is, czKj -Kj/Xj, and aLj = Lj/Xj).7s ’ All variables are to be understood as dated at time t, unless otherwise specified. Because of the possibility of distorting factor taxes, rl (or wl) need not be equal to r2 (or w2). Indeed, if r and w represent the net rental and wage rates respectively received by capital and labor, which are assumed to be equal in both sectors, then we can define the symbols tfj, zfj, and Trj by wj-w+fLj=w(l+rLj)-wTLj,

j= 1,2,

(3a)

rj-r+t,j+p16=r(l+r,j)+p,6=rTKj+p,6,

j=l,2.

(3b)

Thus tfj represents the specific tax imposed on factor f in sector j, and ~~~ represents the ad ualorem tax rate. The term ‘tax coefficient’ will be used for the symbol Tfj( = 1 + rJj)r it is assumed that 7fj > - 1. We assume that the output of sector 1 (the corporate sector) can be used both as an investment good and as a consumption good, while the output of sector 2 (the non-corporate sector) can be used only as a different consumption good.g Consequently, we shall value capital at pl, the production cost of investment goods. Thus the term p,S represents unit depreciation costs in money terms. lo We assume that capital depreciates at a rate 6 that is independent of the industry in which the machine is used. While the stock of machines, K, is intratemporally fixed, we assume that the labor supply, L, depends upon population, N, and the real wage, w; i.e., L is assumed to be wage elastic within the period: L=L(N,o). The real wage, Q, represents hence we define

(4) the purchasing

power

of the money

wage, w;

wz,

(5)

4 where w represents

the money

wage and q is some index of the general

‘It should be noted that alj is a function isoquant and the cost-minimizing condition.

of the factor

cost ratio

rj/wj, defined

price

by the unlit

‘The subscript j will always refer to commodities (sectors) 1 and 2 while the subscript f will always refer to factors K and I!,. Unless clarity demands it, this range of the subscripts f and j will not be repeated every time. ‘This assumption is made as a compromise between tractability and realism of the model. “‘We implicitly assume that depreciation is deductible. If not, then r, = (r+6p, )TKj. The assumption that each industry has the same depreciation rate is made for expositional simplicity and could easily be relaxed.

A.F. Friedlaender crntl A.F. Vandendorpe, Capital taxation

5

level to be defined precisely within the context of the demand side of the model, which will be discussed below. If we denote by qj the consumer price of commodity j, the relevant commodity taxes (tj, rj, and Tj) are defined by (6)

i.e., tj, TV,and Tj are respectively the specific tax, the ad valorem tax rate, and what we shall label the ‘tax coefficient’ on commodity j. Since the model contains a monetary sector we shall be able to determine some measure of absolute prices. To this end we define (7) Expression (7), a (bilinear) function in the money prices qj and some (as of yet unspecified) constants c(~,can be interpreted as the cost of the commodity basket (xi, ~1~)at prices q1 and q2, or alternatively (if c~i and ~1~were chosen so that c(i +a, = l), as a weighted average of the consumer prices q1 and q2.11

We assume that the government utilizes the output of both sectors and that (as previously indicated) investment goods are only produced by the corporate sector. Hence the aggregate demand for the output of sector 1 consists of government demand (G,), consumption demand (C,), and investment demand (I), while the aggregate demand for the output of sector 2 consists of government demand (G,) and consumer demand (C,). We may therefore write the market clearing equations as X, =C,

+G,

+I,

(84

X,=C,+G,. We assume that consumers base their spending and savings decisions on relative prices (ql/q2), real disposable income (y), and real asset holdings (IV) and thus write the aggregate demand functions12 cj=cj(qllq2,

L’T w)3

(9)

“Setting G(,= 1 and a2 =0 amounts to the customary procedure of choosing good one as the numeraire. The more general definition in terms of arbitrary CI, and CC~seems preferable in the present context. In this analysis we choose the weights a, and a2 to equal the initial share of comsumption of each good. Hence the percentage change in the price of the composite commodity also equals the change in the Laspeyres price index, measured in terms of the base period. ’ %ee Samuelson (1956).

A.F. Friedlaender and A.F. Vandendorpe, Capital taxation

6

and

S=S(L’, w,

(10)

where Cj represents the consumption of good j and S represents real savings. We assume that there are three assets in this economy: physical capital (K): the outstanding stock of money (M); and the stock of outstanding perpetuities (b), each of which has a coupon rate of one dollar. Hence we can define real wealth as

(11) where i, represents the rate of interest in the bond market. We value capital at the price of the capital goods industry, but deflate all money assets by the consumer price index. Total nominal disposable income is defined as Y-wL+rK+b+H, where H is the net lump sum transfer (tax) imposed Total real disposable income is thus defined by I’-

Obviously

(12) by the government.

Y/q.

equations

(13) (12) and (13) satisfy the consumer

budget

constraint (14)

We now turn to the markets for the assets of money, bonds, capital. currently specified, the model yields two interest rates: the rate of interest bonds (ib) and the rate of return on physical capital (ik), defined byr3

As on

(15) If all returns were subjectively certain so that there were no uncertainty, wealth owners would only hold bonds and capital if they yielded the same rate of return. The two assets would be perfect substitutes and equilibrium 13Equation (15) assumes that there is no direct taxation of corporate income and hence neglects the relationships between taxes, depreciation, and investment credits, given by Hall and Jorgenson (1967) in deriving an expression for the cost of capital.

A.F.

Friedlaendrr

and A.F.

Vandendorpe.

Capitol

itruotion

7

uncertainty would require that i, = ib = i.14 In the real world, however, certainly exists and i,#ib. Thus, in terms of empirical relevance, it is probably desirable to permit uncertainty and to let i, differ from ib. The existence of money and bonds introduces a distinctly macro element is important for two into an otherwise micro model. l5 Their introduction reasons, however. First, they permit us to express the model in absolute rather than relative prices and thus to derive measures of the absolute as well as the relative price effects of the corporate profits tax. Second, they extend the permissible range of the government’s equilibrating adjustments in response to a given tax change. Since the government typically adjusts the monetary base or the supply of assets in response to a change in taxes or expenditures, it is important to permit these adjustments for insights into the actual incidence of the corporate profits tax. We assume that the supply of nominal money (M) is determined by the government, while the demand for real money as a proportion of wealth depends upon the ratio of real disposable income to wealth (y/W), and the rates of return on bonds (ib) and capital (ik). l6 Note that we also assume that money and bonds are held by the public as stores of wealth for future consumption. Hence, we measure the real value of money and bonds in terms of q, the price of the composite consumption good. Equilibrium in the money market requires that the money supplied equals the money demanded; hence,

M(t)

-=

W .pM(y/w

i,,

ib).

(16)

4

We also assume that the government determines the number of bonds outstanding, each of which is assumed to be a perpetuity with a yield of one dollar. Since bonds are a substitute for money, the demand for bonds as a proportion of welath must also depend upon the ratio of real disposable income to wealth (y/W), and the rate of returns on bonds and stocks (ib and ik). In equilibrium, the demand for bonds must equal their supply; hence b(t)

-=

W

.pb(y/W

i,,

ib).

(17)

&b

“Strictly speaking. this is only true if there is no expected inflation. 15Foley and Sidiauski (1971) also introduce financial variables into their model. They, however, assume that the economy can be characterized by an investment goods and consumption goods sector and, thus, stay within the standard framework of a two-sector growth model. t6We assume that there are static expectations and, hence, no expected capital gains on money, bonds, or capital.

8

A.F. Friedlaender and A.F. Vandendorpe, Capital taxation

From Walras’ Law, we know that if n - 1 markets are in equilibrium, the nth market must also be in equilibrium. In this analysis we, therefore, do not utilize an explicit expression for the asset market for capital. Although the asset market for capital does not appear explicitly in the analysis, it is important to realize that it plays a very important role since it determines the investment demand equation. Thus although we do not state it explicitly, there is an implied investment demand that depends upon interest rates (and hence the rental return to capital), income, and wealth. Equilibrium requires that savings plus taxes equals government expenditures plus investment. Thus, plZ-p,SK(t)+G=qS+T,

(18)

where G and T respectively represent government expenditures and tax revenues. Equilibrium also requires that total government receipts (funds from taxes plus changes in the stock of money and bonds) must equal total government expenditures (purchases of goods and service plus transfers). In this model we assume that the government purchases commodities from both sectors at producers’ prices. In addition, the government makes lump sum transfers (taxes), and pays premiums on any bonds outstanding. Thus, total government expenditures are given by (19a) We assume that the tax instruments available to the government are commodity taxes and sectoral factor taxes. Thus, total tax revenues are given by

T=C tjCj + C j

t,fjU,~ji:

(19b)

f,j

where ulj represents the amount of factor ,f employed in sector j. If the budget is always balanced, G= T and the government budget constraint adds no dynamic element. If, however, the tax receipts and expenditures are not always in balance, the government can balance its budget by issuing money or bonds. Hence, the government budget constraint will generally contain dynamic elements and can be written asl’ “As Hansen (1973) has indicated, this form of the government budget constraint assumes that the government controls both the money suppiy and supply of bonds, as well as the level of taxes and expenditures.

A.F. Friedlaender

and A.F. Vandendorpe,

G-T=M(t+l)-M(t)+

b(t+

Capital

taxation

9

1)-b(t) m.

(19c)

lb

Whether the government’s budget is ‘balanced or not, the growth of the capital stock will always introduce a dynamic element into the model. The expression for the growth of the capital stock is given by K(t+

l)-K@)=Z(t)-C%(t).

(20)

Equations (lt(20) form a full specification of the model, which we assume to be in initial equilibrium. To analyze the incidence of capital taxation, we will specify a change in capital taxation and analyze the general-equilibrium response of the system to this change in a way specified below.

3. Incidence analysis Within the context of any dynamic model, there are three levels at which incidence can be analyzed: comparative statics, comparative dynamics, and a full solution of the dynamic system. As implied by the name, a comparative-static analysis of incidence is purely static and is concerned with the intratemporal effects of a change in the tax structure upon relative prices, output, etc. Thus, in static incidence analysis, a change in the tax structure is postulated to take place at a given time period, and the changes in relative prices are determined that restore the private and government sectors to equilibrium within that time period. This kind of analysis permits us to determine the short-run incidence of a tax and is the kind usually employed in incidence analysis, e.g., Harberger (1962) and Meiszkowski (1967). A comparative-dynamic analysis of incidence is concerned with the comparison of different steady-state equilibria of the dynamic system under different tax structures. Thus, a once and for all change in the tax structure is postulated, and the new steady state values of factor prices, commodity prices, and outputs are derived. By comparing the new steady state values of factcr and commodity prices with their initial steady state values, it is possible to determine the long-run incidence effects of the tax change. This approach has been used by Feldstein (1974, 1975), and is attractive since it permits the analysis of incidence questions in the context of a relatively simple growth model and is algebraically tractable. Because, however, it only yields steady state solutions, it does not give any information about the time path of the adjustment. This is an important deficiency, since a number of studies have indicated that the period of adjustment may be extremely long, e.g., Feldstein (1974) and Sato (1963). Tn so far as we are interested in the time path of the adjustment of the

10

A.F. Friedlaender and A.F. Vandendorpe, Capital taxation

economy to a change in the tax structure, a full solution to the dynamic system is needed, In this context, we can either deal with levels or changes. In the levels case, this analysis requires the derivation of a full solution to the We thus change the tax structure in a model for a given tax structure. specified way and derive a solution for the ensuing periods. This approach is attractive since it enables one to compare the solution values of the endogenous variables over the period of analysis. It is rather unwieldy, however, since it not only requires a full specification of all of the initial values of the relevant variables, but also a full specification of all of the functions and their relevant parameters. Moreover, in so far as nonlinearities are present, this approach is computationally difficult. Thus although Feldstein (1974) was able to use this approach in analyzing the time path of the incidence of a payroll tax in a single sector model, it is not generally feasible. As a more tractable alternative, we can analyze the time path of the changes in the variables in the model. While this approach yields essentially the same results as an analysis of the levels of the relevant variables, it requires considerably less information and is computationally easier to handle since all of the functional forms are linear in percentage changes. Nevertheless, analytic solutions are not generally feasible in this case because the weights attached to the percentage change in the relevant variables are no longer constant but time dependent. Hence the system is inherently nonlinear instead of linear and simulation experiments are necessary in all but the simplest of models.” The differentiation of the model outlined in eqs. (l)-(20) is a straightforward if somewhat tedious task. Since the bulk of the differentiation has been done elsewhere [see Jones (1965), Vandendorpe and Friedlaender (1976)-j, we drive the do not repeat it here. I9 Because > however, the dynamic equations system, it is useful to consider them. An analysis of the relationship between these equations in their levels and percentage change forms will indicate the general approach used in this analysis. If the government balances its budget by adjusting taxes or expenditures, there is no change in the stock of money in bonds. Hence the capital stock eq. (20) introduces the only dynamic element in the model. We can then write the dynamic system in its general reduced form as:

“The nonlinearity of the model raises the question of the uniqueness of the solution. Since the intratemporal system of the equation is linear in percentage changes, the intratemporal solution should be unique in any one period. These solution variables are then used to generate new share variables and the changes in stock variables in the next period; thus given a set of initial conditions, the time path of the solution should be unique since it is essentially based upon a recursive system. “The Appendix gives the differentiation of the government budget constraint. Copies of the full differentiation of the system will be made to interested readers upon request.

A.F. Friedlaender

K t+ I K,,

=fw

and A.F. Vandendorpe,

Capital

-6)+4,

taxation

11

(2Oa)

T, given,

where IT; represents the exogenously given vector of tax parameters in period t ; I, represents gross investment in period t; K, represents the capital stock in period t; and 6 represents the depreciation rate. Since K, and To represent the relevant initial conditions, given these, eq. (21) determines the initial level of investment and eq. (20a) determines next period’s capital stock, which, in ’ conjunction with the exogenously given tax parameters, then determines next period’s level of investment. Hence given the reduced-form equation for investment, eqs. (20a) and (21) fully determine the response of the time path of the system to any given vector of tax parameters and the capital stock. The problem is, however, that we cannot obtain the reduced-form investment equation for our model. This is true for two reasons. First, data are unavailable to estimate the relevant demand and production functions on a corporate and non-corporate sectoral basis; and second, since the model presented in eqs. (lt_(20) is likely to be nonlinear, it is unlikely that it would be possible to obtain a tractable reduced-form investment equation, even if the relevant functions were known, By totally differentiating the system and expressing it in terms of percentage changes, it is possible, however, to obtain an intratemporal reducedform equation for the percentage change in investment, and hence to trace out the time path of the changes of the capital stock. Differentiating the simplified system presented in eqs. (20a) and (21) yields

R(t+

-s)rZ(t)+t#ll(t)f(t)-&$KS,

1)=4Jt)(l

Wb)

where the hats denote percentage changes and eIT, .sIh. respectively represent the elasticity of investment with respect to the tax structure and the capital stock. Note that we assume that these elasticities are constant and hence are not time dependent. The variables 4h. and 4I represent share variables that are used to weight the relevant percentage changes and are specifically defined as follows: &(t)f=,

(23a)

K(t+l) &(t)sI(f) K(t+

1)’

Wb)

12

A.F. Friedlaender and A.F. Vandendorpe, Capital raxation

Thus in contrast to the elasticities, which are assumed to be constant, these share variables are permitted to be time dependent. If the system is in initial equilibrium K(t + 1) =K(t) and 4K(t) = 1, $r(t) =6. Moreover, in the next period it is apparent that $h.(t+

l)_lco= K(t+2)

K(t)(l

+m)

K(t+l)[l+R(t+1)]

=Y)K(~)[-l~$)l)]~

Thus once we have determined the initial share variables and elasticities, we can solve for f(t) and R(t + 1) for any given change in the tax structure T(t). k?(t + 1) then becomes a predetermined variable that is used (along with ii(t + 1)) to solve for r^(t+ 1) in the following period, via eq. (22a). Given I^(t + 1 ), R(t + l), we can determine the relevant share variables 4,&t + 1) and 4,(t + l), and thus solve for z(t +2). Thus given the elasticities and the initial share variables, we can trace out the time path of the economy to any given change in the tax structure. If the government uses money or bonds to balance its budget, the government budget constraint drops out as an intratemporal equation and adds an additional dynamic equation. In this case we can write dG-dT ----------~=~:,fi(t+ Y

l)-~,fi(t)+$&+

1)

(25) &here : r;,=iM(t+l)/Y(t), Y,,= M(t)/Y(t), ,j$=b(t+l)/i,(t)Y(t), ?/b= b(t)&(t)Y(t). In this case the changes in the endogenous variables comprising (dG-dT)/Y in period t determine fi(t + 1) or 6(t + l), which are treated as being exogenous in period (t+ 1). Thus, in period (t+ 1) the system reacts to the values of R(t + 1) and ti(t+ 1) or fi(t+ l), determined by the dynamic capital and government budget equations. The introduction of the dynamic eqs. (22b) and (25) raises the question of stability. In our analysis of incidence, we shock the system by changing a

A.F. Friedlaender and A.F. Vandendorpe, Capital

13

taxation

government control variable in period t. This gives rise to a change in savings and investment and, hence, in the capital stock in period (t + 1). If the government balances its budget by changing lump sum taxes and if the government makes no further changes in its control variables, any subsequent adjustments in the system must arise from responses of the system to the changes in the capital stock. Thus, as long as the changes in the capital stock go to zero, the system should be stable and we can analyze the conditions under which jR(t + h + l)/ < IR(t + h)l where h > 1. The situation is more complicated if the government uses money or bonds to balance the budget since two stock variables are now changing. Thus, for stability, not only must the rate of growth of the capital stock be diminishing, but also the rate of growth of money or bonds. Thus, we would generally expect the system to be less stable if the government balanced its budget with money or bonds than if it used taxes (lump sum or otherwise). Analytic treatment of the problem is made difficult by the share variables, introduce nonlinearities into the system. which, as explained above, Nevertheless, a feel for the problem can be obtained by assuming the share variables are constant. Thus, let us compare the conditions needed to ensure stability under lump sum taxation and under money finance.20 If fi is endogenous, the budget OS always balanced with lump sum taxes and there is no change in the stock of money or bonds. If we assume that the rate of depreciation is constant, we can write eq. (22b) as @t+k+l)=[qh,(l-6)]I?(t+k)+&l^(t+k).

(26)

Since the government is assumed to change its policy instrument in period t and keep it at its new level thereafter, as long as k >O, we know that if the economy were in initial equilibrium, the change in investment in period (t + k) depends solely upon the change in the capital stock that occurred at the beginning of that period. Thus we can write (27) where I, represents the reduced-form (27) into eq. (26) we then have

solution

of f(t+ k). Substituting

eq.

(28) Stability

requires

that:

IR(t+k+l)/+(t+k)l. “The conditions needed under money finance.

for stability

under

bond

finance

are qualitatively

similar

to those

A.F. Friedlnender

14

und A.F. Vandendorpe, Capital taxtrtion

Thus, as long as ~4J,f&(I-~)~
(29)

the system will be stable.21 If money is endogenous, we must solve the government budget constraint explicitly. By making a full differentiation of the government budget constraint (see Appendix) we can obtain the following solution for the change in the stock of money, assuming fixed government expenditures and an initial budgetary equilibrium. ni(r+h+l)=fIP(t+h)+,,,,i(i+/~)-.(:,, m

+i’,)b,(t+h)

-;‘( ~1’2(t+h)-CYxj8j(t+h)+Y,~(t+h)].

(30)

As long as h >O, and the government control variables are assumed to be constant, each endogenous variable can be expressed as a linear function of the change in the capital stock and money that occurred at the beginning of the period. Thus, if B represents any endogenous variable, then we can express it as

B(t+h)=E,R(t+h)+~,~(t+h),

(31)

expression associated with K where E, and E,, represent the reduced-form and M respectively. Thus, expressing the endogenous variables in eqs. (26) and (30) in terms of their reduced forms, using the notation described in eq. (31), and collecting terms, we can express the two dynamic equations as:

Rtt+h+ l)=A,,R(t+h)+A,,~(t+h),

(32)

A(t+h+l)=A,~,IZ(t+l?)+A,~,~~(t+h),

(33)

where : A,, = c$,z, + (l-6)4,, AK, = 4rZ,,

‘INote, however, that the analysis is actually more complex since the share variables 4, and 4K are themselves nonlinear functions of K(t + h- 1). Moreover, the reduced-form coefficient I, will also generally be a nonlinear function of R(t + h - 1).

A.F. Friedlaender and A.F. Vandendorpe, Capital taxation

Stability

requires

15

that:

Ik(t+h+q+(t+q (A(t+h+1)1+2(t+h)l. Thus, we can write these conditions

as:

ICA,,IZ(t+h)+A,,~(t+h)]l
(344

ICAwsR(t+h)+A,,l\;i(t+h)]l<(~(t+h)l.

Wb)

In contrast, when l? is endogenous be written as:

and A = 0, the stability

I[A..IZ(t+h)]I
condition

can

(35)

and iz will normally be of the same sign, eqs. (34) and (35) the system will be apt to be more stable when the government budget with lump sum taxes than with money (or bonds, since conditions under bond finance are qualitatively similar to those finance).

4. Simulation

analysis of the impact of capital taxation

The model outlined above is quite general and can be used to analyze a number of incidence questions. While the focus of this paper is on the incidence of sectoral capital taxation, we can also analyze the incidence effects of alternative forms of equilibrating adjustments in the government budget constraint. Thus by letting the government balance its budget by using either neutral head taxes, bonds, or money, we can obtain some insights into the question of the ‘burden’ of the national debt.22 To analyze the incidence of a sectoral capital tax, we assume a once and for all increase in the capital tax coefficient in sector 1 and thus set TKl =O.lO in period one and TK1 =0 in subsequent periods. With the exception of the specified change in TKl and the intertemporally determined (induced) change in the stock variables, we will assume that all other exogenous variables remain constant. Thus changes in the endogenous variables can be attributed to the direct change in the tax coefficient and the induced changes in the relevant assets. The change in TK,, in period one leads to equilibrating changes in all of the “See

Diamond

(1965) for a full discussion of the burden of the debt

16

A.F. Friedlaender and A.F. Vandendorpe, Capital taxation

endogenous variables in that period, and thus new share variables to be used in period 2. Moreover, because levels of savings and investment have changed, there will be a change in the capital stock. Similarly, if the budget is balanced through bonds or money, there will be a change in these stock variables. Thus the changes in the stock variables (capital, bonds, and/or money) become the exogenous variables that drive the system in subsequent periods. Consequently the first period response of the system reflects the direct effect of the tax change and corresponds to the usual static analysis. The response of the system in subsequent periods reflects the effect of the asset changes that were induced by the initial tax change. These subsequent effects, of course, represent the dynamic incidence effects. The sum of the first period and subsequent effects therefore represents the net incidence effects of the change in sectoral capital taxation. If the government maintains its budget balance by adjusting lump sum taxes (I?), we can solve for the following variables in terms of the exogenous change in TK, : xi, cifj, Kj, zj, jj, tj, Gj, r*, ti’, f., & ij, cj, i$ t 3, Fb,&, f and 8. In all, there are a total of 31 equations and 31 unknowns. In this case, the only dynamic equation is given by the relationship between the capital stock and investment, eq. (22b). If the government uses bonds or money to balance its budget, A drops out as an endogenous variable. The government budget constraint then drops out as an intratemporal equation and enters as a dynamic equation, eq. (25). In this case, the model consists of 30 intratemporal equations that can be used to solve for the relevant intratemporal variables, and the two dynamic equations that determine the capital stock and the supply of money or bonds. We assume that the relevant elasticities remain constant throughout the period of the analysis. These are given in table 1 and reflect a compromise between empirical realism and consistency with analytical incidence analyses. Following Harberger (1962), we thus assume that the elasticity of substitution (aj) is one in each sector and that the elasticity of demand for each commodity with respect to relative prices (sj) is also one. The elasticities of consumption (sCjy, scjW) and savings (ssy, es+,) with respect to income and wealth, are consistent with generally held views concerning the macroeconomic behavior of these variables, as are the elasticities of demand for money (%fY, EMi,>E,+,J and bonds ‘(s,r, sBib, E& with respect to income and interest rates. The elasticity of the labor supply with respect to the real wage is consistent with empirical labor supply studies.23 Note that since we assume a constant population, we do not give a figure for the elasticity of the labor supply with respect to population. The initial share variables also reflect a compromise between realism and %x

Break

(1974)

A.F. Friedlaender

and A.F. Vandendorpe, Capital

Table Elasticity

values used in simulation 6c2,+.=

0.123

ELo=

0.140

E1 = - 1.000

sMy = - 0.800

EZ=

1.000

ssy=

EsY=

0.300

E+ = - 0.200

sc,y=

1.120

Egik=

sczy=

1.120

-0.533

0.133

EMMlh= -0.200

Es&+, = - 0.700 sCIW=

Es{*=

0.133

0.123

Table Initial values of share variables

2

used in simulation

experiments.

=0.667

q,C,/Y

=ycl

=0.476

c,/x,

= fc, =0.490

K2/# =I&., =0.333

q2C,/Y

-ycz

=0.374

GJX,

=

L&E&,

=0.910

qS/Y=ys

=0.150

Lz/L = I,,

= 0.090

p,l/Y-y,

=0.375

pjbK(t),Y

-y,,

=0.225

~,u~,~p, =Br;, =0.167

qlG,/Y

-ycl

=0.120

w,u, ,,p, ~8,~

qtG,,‘Yry,,

=0.833

=e,. =0.500 \z‘LU,.z~pz= e,, =0.500

=O.lflO

VIUh,,Pr

rTh,,hl =pcl =0.810 p,6;r, “q,jP> p,d/r, q,C,/~qjCjry,, q,c,/cq,c,

analyses

1.000

-

17

1

62 = - 1.000

fJ1 =

K,/K=&,

taxation

=pb,

=O.lQO

=&,=0.810 -pa2

=O.lQO =0.560

= y;1* = 0.440

qJ,/Y

=yxl

=0.971

q2X,/Y

-yxz

=0.474

fc, =0.124

I/X, =fr

=0.386

fc2=0.789 G2/X2= fG2=0.211 C,JX, =

M(t)/qW=A,

=0.200

A(t)/qW=A,

=0.300

P&/qW=A,

=0.500

pjr,IiYSy,,,

=O.OOO

i,p,/r=n,

=0.610

M(C)/Y =yM

=0.410

p,&r=n,,

=0.390

M(t+l)/Y-y:,

=0.410

b(t)/i,Y=y,

=0.620

b(t + 1 )/i, Y = yS

= 0.620

rK(t)/Y

=yh.

=0.230

wL/ Y =yL

= 0.670

H/Y -yh

=0.080

b(t)Y=y,

=0.020

K(t)/K(t+l)=4,

r(t)/K(t+l)=(fJ,

=l

=0.05

18

A.F. Friedlaender and A.F. Vandendorpr. Crtpital tourtrim Table 3

Cumulative response of selected endogenous variables to a change in capital taxation in sector 1, head taxes endogenous (T,, =O.lO in period 1, 0 thereafter). Subsequent cumulative changes in periods: Initial change in period 1

2-5

2-10

2-15

2-20

- 0.005383 0.045883 - 0.003309 0.006628 - 0.005799 0.085138 -0.103140 -0.006112 - 0.005697 - 0.045370 -0.023150 - 0.023220 0.056130 -0.011460 0.025530 - 0.005293 - 0.028824 0.011381 0.002386 0.086587 -0.159737 0.0000 0.34854

0.000443 -0.000167 0.002511 0.001163 0.000026 -0.001301 0.002181 -0.000810 - 0.000434 - 0.000323 - 0.00007i 0.001143 - 0.000288 0.000429 - 0.001029 0.000139 0.001560 -0.000432 - 0.000103 - 0.002480 -0.004525 0.00206 - 0.004253

0.000864 -0.000327 0.004888 0.002259 0.000050 - 0.002538 0.004239 -0.001582 - 0.000768 0.000626 - 0.000142 0.002227 - 0.000562 0.000832 - 0.002004 0.000268 0.003039 -0.000837 - 0.000202 - 0.004826 0.008796 0.004008 - 0.008322

0.001175 - 0.000446 0.006634 0.003061 0.000068 - 0.003449 0.005746 -0.002152 - 0.001046 0.000848 - 0.000195 0.003024 -0.000763 0.001127 - 0.002721 0.000361 0.004126 -0.001132 - 0.000274 - 0.006549 0.011924 0.005436 -0.011337

0.001404 - 0.000534 0.007919 0.003649 0.000081 -0.004122 0.006853 - 0.002573 -0.001251 0.001011 - 0.000235 0.003611 -0.000912 0.001343 - 0.003249 0.000429 0.004926 -0.001347 - 0.000327 -0.007815 0.014221 0.006487 -0.013569

consistency with previous analytical incidence studies. The allocation of labor and capital between sectors (A,, A,) and the initial factor shares (tIKj, 0,) are consistent with Harberger’s (1962) study and were chosen for comparative purposes. The allocation of capital payments (pKj, psj, rri, rc6) is consistent with the role of depreciation in the United States economy as are the various income share variables (the y’s).24 However, a certain amount of realism was sacrificed by the assumption that the government does not demand labor and that there is an initial zero tax structure. The allocation of the physical output (fcj, fGj, f,) shares was somewhat arbitrary, but attempted to be consistent with the income shares and relative prices that were assumed to exist. The initial wealth shares (A,, A,, A,) also attempted to reflect current allocation in the United States economy, while the capital allocation (c$~, 4,) was consistent with the assumption of an initial equilibrium.25 Tables 335 illustrate the incidence effects of setting TK, =O.lO in the first

19

A.F. Friedlaender and A.F. Vandendorpe, Capital taxation Table 4

Cumulative response of selected endogenous variables to a change in capital taxation in sector 1, money endogenous (i,., =O.lO in period 1; 0 otherwise). Subsequent cumulative changes in periods: Endogenous variable

Initial change in period 1

2-m5

2-10

2-15

2-20

$1 X2 61 K, 21 L2 i G PI IL q^ c, c2 C s P GV i i $ ‘? K

-0.001699 0.021769 - 0.006803 0.013630 -0.003405 0.057165 - 0.08547 0.002332 0.004037 - 0.033064 -0.012288 -0.050125 0.024077 - 0.029764 0.002543 -0.023010 - 0.008230 0.052044 0.002047 0.034158 -0.146725 o.oooooo

0.005437 -0.016262 0.023334 -0.005081 0.001714 -0.026098. - 0.040033 0.065432 -0.061711 - 0.055683 -0.058978 0.005572 - 0.006484 - 0.005882 0.075846 - 0.048003 -0.103648 0.034027 + 0.000903 0.193031 0.037716 0.014063

0.008277 -0.012981 0.046789 0.007405 0.0013874 -0.031248 - 0.0228 13 0.069437 - 0.062549 -0.051262 -0.057470 0.018766 - 0.003808 - 0.004882 0.065411 -0.041287 -0.086512 0.023259 + 0.001676 0.167324 0.068668 0.029916

0.009893 -0.010137 0.050925 0.015578 0.001101 - 0.033432 -0.010237 0.069282 - 0.060492 - 0.046079 -0.054016 0.027102 -0.001722 - 0.003982 0.055222 - 0.034920 -0.070710 0.014739 +0.002137 0.142167 0.0865 11 0.039421

0.010860 -0.008387 0.056929 0.020463 0.000924 - 0.03469 1 - 0.002689 0.069089 -0.059153 - 0.042877 -0.051848 0.032132 -0.000417 - 0.003428 0.048849 -0.031004 - 0.06085 1 0.009505 +0.002414 0.126517 0.096979 0.045067

period and zero thereafter. The first column shows the direct impact of the tax change, while columns (2t(5) show the response of the system to equilibrating changes in the capital stock alone (table 3), the capital stock and money (table 4), and the capital stock and bonds (table 5). Table 3 permits us to analyze the impact of capital taxation with a neutral head tax adjustment. Column (2) shows the short-run static incidence effects with a fixed capital stock and is analogous to the traditional static incidence analysis. The results of this simulation experiment are consistent with the results of Harberger (1962) and Mieszkowski (1967) and indicate that capital bears virtually the entire burden of the tax in the short run. Thus the increase in the tax causes capital and labor to move from sector 1 to sector 2 and leads to a rise in the real wage and a fall in the real return to capital. The tax also causes a fall in the price level. Consequently, although money disposable income falls, real disposable income rises, as do savings and investment. Hence the capital stock rises as does the labor force. The change in the capital stock then leads to further adjustments in the economy, which tend to counteract the impact of the initial tax change. Subsequent adjustments cause the rate of investment to fall relative to the

20

A.F. Friedlaender

and A.F. Vandendorpe, Capital taxation Table

Cumulative

response

5

of selected endogenous variables to a change in capital bonds endogenous (Fk, =O.lO in period 1; 0 otherwise). Subsequent

cumulative

changes

taxation

in sector

1,

in periods:

Endogenous variable

Initial change in period 1

2-5

2-10

2215

2-20

$1 X-2 K_’ Kz 4, L, i 6 PI PZ 4^ CL C-2 C s P iv i L 5 ‘* K

-0.001699 0.021769 0.006803 0.013630 - 0.003405 0.057165 -0.085470 0.002332 0.004037 - 0,033064 - 0.012288 -0.050125 0.024077 - 0.029764 0.002543 - 0.023010 -0.008230 0.052044 0.002047 0.034158 -0.146725 0.000000

0.002890 - 0.004791 0.014349 0.002471 0.000522 -0.011143 - 0.000029 -0.016501 -0.014133 -0.010171 - 0.012348 0.004408 -0.003516 -0.001150 0.011303 - 0.001027 -0.015258 0.006978 -0.000581 - 0.093289 0.024585 0.010459

0.006004 -0.008918 0.030017 0.006239 0.000962 - 0.022379 0.001004 - 0.033559 -0.028518 -0.020142 - 0.02475 1 0.010489 - 0.006263 -0.002177 0.021909 - 0.001967 -0.029119 0.012412 -0.001233 -0.183707 0.051172 0.022261

0.008524 -0.011392 0.042861 0.010210 0.001221 - 0.030822 0.00303 1 - 0.04645 1 - 0.039149 - 0.027083 -0.033728 0.016442 - 0.007689 -0.002810 0.028837 - 0.002568 - 0.037745 0.015028 -0.001781 a.246947 0.072774 0.032243

0.010472 - 0.012672 0.052923 0.013965 0.001351 - 0.036872 - 0.005660 - 0.055574 -0.046453 - 0.03 1448 -0.039718 0.021755 -0.008255 -0.003140 0.032773 - 0.002905 -0.042247 0.015713 - 0.002219 - 0.287763 0.089592 0.040282

growth of the labor force and thus the return to capital rises relative to that of labor. The magnitude of these counteracting adjustments is quite small, however. By the end of the 20th period, capital has only recovered some six percent of its initial losses in absolute terms. Relative to labor, however, it has fared somewhat better, Initially, I:- GJ= -0.097, while in periods 2-20, r^- G =0.008. Thus the cumulative impact is still that i--G= -0.089, which indicates that capital still bears the brunt of the tax. Thus in a world of neutral lump sum adjustments, the dynamic incidence effects do not appear to differ substantially from the static incidence effectsz6 Of course, neutral lump sum tax adjustments are not available in the real world where the government has to balance its budget by other means; and when the government balances its budget using bonds or money the story is quite different from the one in which the government uses neutral taxes. 26Although these findings are somewhat at variance with those of Feldstein (1974, 1975), it is important to realize that it may take a very long time to reach the new equilibrium. Thus, although Feldstein argued that labor could shift the burden of a payroll tax in the long run, after 20 periods only 50 percent of the total shift had taken place, with the remaining shift occurring over an additional 140 periods.

A.F. Friedlaender

and A.F. Vrcndendorpe.

Ctrpital tccmtion

21

Table 4 shows the incidence effects of setting TKl =O.lO when the government balances the budget using money and table 5 shows the incidence effects when the government uses bonds. Since neither money nor bonds can change within the first period, column (1) of both tables is the same and differs from column (1) of table 3 in that no offsetting transfers are assumed. Nevertheless, the results of column (1) in all three tables are qualitatively similar, and indicate that, in the short run, capital bears the burden of a sector tax on capital. When money or bonds adjust endogenously, in subsequent periods the system must not only react to the changes in the capital stock, but also to the changes in the stock of money or bonds. In the case where the government uses money to balance its budget, i--G = -0.087 initially, indicating that capital bears the brunt of the tax increase. In subsequent periods, however, the return to capital rises relative to that of labor. Thus in periods 2-20, the cumulative change of F - ti = 0.066 indicates that capital has regained much of its position relative to labor. The results are qualitatively similar when the government balances the budget by buying bonds. The initial i-G= -0.087, while during periods 220, the cumulative F-Q =0.050. Thus in the long run, capital bears considerably less of the tax than it does in the short run. A comparison of the incidence effects of capital taxation financed by money and bonds is instructive, and yields some insights into the burden of the debt, which considers the incidence effects of increased government expenditure under bond or money finance. Because bond finance reduces capital formation, income (and presumably utility) are lower under bond finance than under money finance. In this case, we postulate an increase in distorting taxes, and hence a reduction in money or bonds. Thus we would expect more capital formation under bond finance, which indeed occurs. With money finance, there is a cumulative increase of I^= 0.0615, while under bond finance there is a cumulative increase of 1^=0.0677. However, the cumulative changes in real income are virtually the same in both cases; for period l-20, under money finance, ? -$ =O.OlO, while under bond finance ? - 4 =0.008. Thus in terms of income changes, the impacts of money and bond finance appear to be qualitatively similar. As we have indicated previously, the size and complexity of this model do not permit it to yield analytical solutions to the question of dynamic incidence. Nevertheless, it is important to consider the robustness of our findings. If, for example, we found that the incidence patterns changed dramatically with different initial share variables or elasticities, we would clearly have to modify our conclusion with respect to the ability of capital to shift a sectoral capital tax. We have consequently run a number of simulation experiments using a relatively wide range of share variables and elasticities and found that when

22

A.F. Friedlaender and A.F. Vandendorpe, Capital taxation

the model was stable, it generated results that were qualitatively similar to those described above. However, the model did not always generate stable solutions in the case of money or bond finance. In particular, although the stability of the solutions was generally insensitive to the values of the initial share variables,” it was rather sensitive to the chosen elasticities on the savings and asset demand variables, with the stability of the system being reduced as these elasticities increased. 28 These results are not surprising since our stability discussion indicated that the system is inherently less stable under money or bond finance. Given this, we would expect increasing the sensitivity of the savings and the asset demands to their relevant arguments to tend to reduce the stability of the system.

5. Summary and conclusions Perhaps the most striking finding of this paper is the differential incidence effects of sectoral capital taxation when the government uses neutral head taxes to balance its budget and when the government uses either money or bonds to balance its budget. In the first case, the long-run incidence effects are quite similar to the short-run incidence effects and indicate that capital bears the brunt of an increase in a sectoral capital tax. Thus this analysis corroborates the static incidence analysis of Harberger and Mieszkowski. When the government uses either money or bonds to balance its budget, however, the conclusions change substantially. While capital still bears the tax in the short run, in the long run, it is able to shift a major portion of the tax to labor. In the case of money finance, capital ultimately bears only some 20 percent of the tax burden, while in the case of bond linance, capital ultimately bears somewhat less than 40 percent of the tax burden. Hence under the more realistic assumptions concerning budgetary balance, we find that labor shares a major portion of the tax with capital. Thus this paper not only illustrates the importance of analyzing the incidence of capital taxation in a dynamic framework, but also the importance of considering a range of equilibrating adjustments on the part of government. Since the government typically cannot use lump sum adjustments to balance its budget, it is important to analyze tax incidence under a range of realistic budgetary adjustments. It is clear that the incidence effects under realistic budgetary adjustments may be quite different from those under lump sum tax adjustments. “For example, the results were fundamentally the same with i,, =0.64, I.,, =0.36, i.,, =0.56, i,,=OW 0,,=0.39, S;,=O.61, QKz=0.41, H,,=0.59, pyz=0.75, pSz=0.25, f,,=O.376, fG,= 0.490, f, = 0.124. “For example, under money and bond finance the system was not stable with the following elasticities: ESY=O.l, t&+r= - 1.0, EM),= - 1.0, EBY= - 1.0, Eq= - 1.0, E+= - 1.0, Ebi =0.55, Ebi =0.55.

h

A.F. Friedlaender

23

and A.F. Vmule~do~pe, Ctrpitcrl tmtrtion

It would, of course, be rash to draw any firm conclusions about the incidence of the corporate profits tax (or any form of capital taxation) from this highly simplified analysis. Nevertheless, it does indicate that a static framework that assumes lump sum tax adjustments may lead to quite different incidence conclusions than a dynamic framework that assumes adjustments in the stock of money or bonds. Consequently, until we know more about the general equilibrium characteristics of the economy, it is probably well to remain agnostic concerning the incidence effects of capital taxation.

Appendix Differentiation of the expression for taxes and expenditures, (19b), readily yields the following expression:

dG-dT=

~pjdGj+~Gjdpj+dH+db(t) [ i i -

C tjdCj+CCjdtj+ j j

eqs. (19a) and

1 C f/jdUfj+ S.j

C Urjdt,j S,j

I

.

(A.l)

The first term in brackets on the left hand side represents the change in expenditures, while the second term in brackets on the left hand side represents the change in revenues. We can simplify eq. (A.l) by making use of the following relationships:’

1 Vrjdt/j=CXjdpj-(Kdr+Ldw), J,j j

(A.2a)

(A.2b)

(A.2c)

(A.2d)

By substituting expressing the ‘See Vandendorpe

eqs. (A.2a)-(A.2d) into equation (A.l), collecting terms, resulting expressions in percentage terms, and dividing and Friedlaender

(1976) for a full discussion.

24

through

A.F. Friedlaender

by disposable dG-dT Y

income

nntl A.F. Vond~ndorpr,

Cripitol rtrlration

Y, we obtain:

_ ^ _. =yclG,+y,,Gz-yxlX~-~xzxz-yrr,f

_.

-(Ycl+yr)P^1-yC2P12-yCI~-YYC2~++

(A.31

where :

References Aaron, H.J., 1974, New views on property tax incidence, American Economic Association, Papers and Proceedings, May. Aaron, H.J., 1975, Who pays the property tax? (The Brookings Institution, Washington, D.C.). Break, G.F., 1974, The incidence and economic effects of taxation, in Blinder et al., Economics of Public Finance (The Brookings Institution Washington, D.C.). Diamond, P.A., 1965, The national debt in a neoclassical growth model, American Economic Review, Dec. Feldstein, M., 1974, Tax incidence in a growing economy with variable labor supply, Quarterly Journal of Economics, Nov. Feldstein, M., 1975, Incidence of a capital income tax in a growing economy with variable savings rates, Review of Economic Studies. Foley, D.K. and M. Sidrauski, 1971, Monetary and fiscal policy in a growing economy (Macmillan, New York). Grieson, R.E., 1975, The incidence of profits taxes in a neoclassical growth model, Journal of Public Economics, Feb. Hall, R.J. and D.W. Jorgenson, 1967, Tax policy and investment behavior, American Economic Review, June. Hansen, B., 1973. On the ettects of fiscal and monetary policy, American Economic Review, Sept. Harberger, AC., 1962, The incidence of the corporate income tax, Journal of Political Economy, June. Jones, R.W., 1965, The structure of simple general equilibrium models, Journal of Political Economics, Dec. Jones, R.W., 1971, Distortion in factor markets and the general equilibrium mode1 of production, Journal of Political Economics, May/June. Mieszkowski, P., 1967, On the theory of tax incidence, Journal of Political Economics, June. Mieszkowski, P., 1972, The property tax: An excise or a profits tax?, Journal of Public Economics, Jan. Musgrave, R.A., 1974, The property tax on housing: Progressive or regressive?, American Economic Association, Papers and Proceedings, May. Samuelson, P.A., 1956, Social indifference curves, Quarterly Journal of Economics. Feb. Sato, R., 1963, Fiscal policy in a neoclassical growth model, Review of Economic Studies, Feb., 16-23. Vandendorpe, A. and A.F. Friedlaender, 1976, Differential incidence and distorting taxes in a static general equilibrium framework, Journal of Public Economics, Oct.