* THE EFFECTS OF TAX PARAMETERS ON THE INVESTMENT 

EQUATIONS IN MACROECONOMIC ECONOMETRIC MODELS 

Robert S. Chirinko and Robert Eisner 

Northwestern University 

OTA Paper 47 Janiiary 1981 

OTA Papers are circulated so that the preliminary

findings of tax research conducted by staff members 

and others associated with the Office of Tax Analysis 

may reach a wider audience. The views expressed are 

those of the author, and do not reflect Treasury

policy. Comments are invited, but OTA Papers should 

not be quoted without permission from the authors. -,

Managing editors are Michael Kaufman and Gary Robbins?,’.,,, $5 

Office of Tax Analysis ,.

U.S. Treasury Department, Room -1-116yc ‘* j 

Washington, D.C. 20220 

Issued: Jaamzy 3-981-? * A 

f.J&Lti , ’ r3 ’‘ 
CONTENTS 

Page 

1. Introduction 1 

. 2. A General View of Investment Functions 2 

3. Tax Parameters and Plan of Analysis 6 

4. Tax Parameters in the Structures of the 

Investment Equations 8 

5. Tax Scenarios: Estimates of Direct Effects of 

Tax Parameters 12 

6. Estimated Equations 14 

7. Simulations 22 

8. Summary and Conclusion 29 

Table 1. 

Table 2. 

Table 3. 

Table 4. 

Table 5. 

Table 6. 

.- Table 7. 

Table 8. 

Table 9. 

BEA Equations, Equipment and Structures 32 

Chase Equations, Equipment and Structures 

A. With Autocorrection Coefficient 33 

B. Without Autocorrelation Coefficient 34 

DRI Equations 

A. Equipment 35 

B. Structures 36 

Michigan Equations, Equipment (Production,

Agriculture and Other) and Structures 37 

MPS Equations 

A. Orders for Equipment 39 

B. Structures 40 

Wharton Equations, Total Investment by

Sector i 41 

Tax Scenarios: Direct Effects on 1977-IV 

Investment of tax Credit, Accelerated 

Depreciation Since 1953-IV, and Corporate

Tax Rate Less than 52 percent 42 

BEA Simulations, Equipment and Structures 43 

Chase Simulations, Equipment and Structures 

A. With Autocorrelation Coefficient 44 
B. Without Autocorrelation Coefficient 

Table IO. DRI Simulations 

A. Equipment

B. Structures 

Tab1e 11. M i ch ig an Simu1ations, Eq uipm ent ( Production , Agriculture and Other) and Structures 

Table 12. MPS Simulations 

A. Equipment

B. Structures 

Table 13. Wharton Simulations, Equipment and 

Structures Investment 

Table 14. Comparison of Simulations, Change in 

Investment, 1977-IV, Resulting from 1973-1 

Doubling of Investment Tax Credit for 

Equipment and Institution of 10 Percent 

Credit for Structures, Original and Revised 

Model Specifications, Billions of 1972 

Dollars 

References 

Appendix - Glossary and Variables Used in the Text 

and Tables 

Page 

45 

46 

47 

48 

49 

50 

51 

52 

53 

55 
The Effects of Tax Parameters on The Investment 

Equations in Macroeconomic Econometric Models 

Robert S. Chirinko 

and 

Robert Ei mer* 

1. Introduction 

Large scale econometric models have been used to predict

effects on investment of changes in tax parameters such as 

depreciation charges, investment tax credits and business 

income tax rates. While ultimate results depend upon full 

model specifications, involving the influence of tax changes 

en aggregate demand, prices and interest rates, critical 

points of departure are the investment equations themselves. 

We offer here a study of the specifications, estimated 

parameters and substantive implications of the existing

investment equations and possible alternatives in six models 

of the U.S. economy: BEA, Chase, DRI, Michigan, MPS, and 

Wharton. An analysis of full model simulations will appear

in a subsequent paper. 

'm'uate Research Associate and William R. Kenan 

Professor of Economics, respectively, at Northwestern 

University. An almost identical, earlier version of this 

paper was presented to the Fourth World Congress of the 

Econometric Society in Aix-en-Provence, France, August 28, 

1980. It embodies muyh of the "Phase 1" and "Phase 11" 

reports of Chirinko and Eisner (1980) for the U.S. Department

of Treasury. It has been made possible by the collaboration 

and assistance of responsible officers and staff associated 

with the models under consideration -- BEA, Chase, DRI,

Michigan, MPS and Wharton -- and personnel of the Office of 

Tax Analysis of the Treasury. The authors are particularly

grateful to Allen Sinai for his careful reading of the 

manuscript. They alone, however, are of course solely

responsible for its contents. Fuller documentation and 

details are to be found in the Phase I and Phase I1 reports 

to the Treasury. The analysis of full model simulations is 

to be found in the Phase I11 report, dated August 21, 1980, 

"The Effects of Tax Policies on Investment in Macroeconometric 

Models: Full Model Simulations," or OTA Paper 46. 
-2-

2. A General View of Investment Functions 

Investment equations in the models under consideration 

have a substantial family resemblance. With varying degrees

of aggregation and parametric specifications, they generally

view investment as a distributed lag response or adjustment

of capital to desired or equilibrium levels. These in turn 

relate to expected demand on output, taken explicitly or 

implicitly as a function of capital and labor inputs, and the 

relative prices of output and capital or of capital and 

labor. 

The "rental" price or user cost of capital is in 

principle the rate of economic depreciation, the opportunity 

cost in terms of foregone net earnings, and the capital loss 

(or minus the capital gain) associated with changing prices.

These costs are defined as pure decimals which are then 

applied to the price of capital goods. A general

formulation, which the various model equations only more or 

less approximate, -

1/ would be: 

(1) c = q[ (l-uv) p - (1-UU)4q +6 ] [l-k-uz] 

1-u 

where 

c = the rental price of capital 

q = the supply price of capital goods 

u = the rate of business income taxation 

v = the proportion of the opportunity cost of capital

(such as interest, dividends and foregone earnings)

which is tax deductible 

p = the opportunity cost of capital, presumably an 

appropriately weighted average of nominal interest 

rates and rates of return on equity expected by 

firms 

= the proportion of capital gains and losses 

effectively taxed 

?J = the expected rate of change of prices of capital 

q goods 

6 = the rate of economic depreciation 

k = the effective rate of the investment tax credit and 

z = the original present value of the tax depreciation

expected from a dollar of investment. 

1/ Cf. Jorgenson (1963) and Hall and Jorgenson (1967). -
-3-

. 

The investment equations in most of the models include I 

term such as c but with a number of potentially significant

variations, which we will note. For one thing, allowance is 

made in different ways, if at all, for v, the proportion of 

the opportunity cost of capital which is tax deductible. 

Second, not all of the models allow for expected capital

gains or price inflation and none recognizes the peculiar tax 

treatment of capital gains. Third, the rate of economic 

depreciation is in some instances variable but more usually

held constant, at values which differ somewhat from model to 

model. Fourth, the investment tax credit in equipment

equations is variously taken at its nominal rate and the 

lesser effective rate which reflects, of course, limitations 

on its availability in all or in part. Fifth, the 

determination of z, the original present value of the tax 

depreciation from a dollar of investment, is variously

defined. It should depend upon the rate of discount, t.hc 

length of life of capital for tax purposes, and the met.h(o(l 1 

depreciation (straight-line, declining balance at 200 percoi~l 

or 150 percent of straight-line rates, and sum-of-yearsdigits, as well indeed as special provisions for first year

allowances). In practice, length of life is sometimes taken 

to vary by discrete jumps suggested by shifts to guidelines

and later to ADR (Asset Depreciation Range) without attention 

to actual changes in lives over the years. Shifts in methods 

of depreciation are not always accounted for. Rates of 

discount as well as the extent of their variation differ 

among models. In one case (Michigan) z does net enter 

explicitly at all; rather a tax depreciation rate is used. 

In the great bulk of the investment equations, there is 

no separate estimate of the roles of the rate of business 

taxation, the investment tax credit, or tax depreciation

(however measured). Rather, parameters are estimated for a 

variable like c, the rental price of capital, or mere 

generally, a variable in which c is a component. 

Considerations of cost minimization and profit

maximization with output exogenous suggest that desired 

capital stock will be a function of relative prices and 

output. (This formulation would not apply to a firm 

operating under perfect competition with no perceived limit 

to effective demand for product. For then relative prices

would be exogenous but output would be endogenous.) We may

thus write 

(2) K* = f(P,c,Y), 

where P = the price of output 

c = the rental price or user cost of capital

Y = output. 
-4-

Alternatively, we may substitute w, a measure of the cost of 

labor, for P. The assumption of a Cobb-Douglas production

function, among other things, was offered by Jorgenson as the 

justification for a particular description of the desired 

stock of capital as 

P 

(3) K* = p(c)Y. 

The assumption of the more general CES production function,

with the constraints neither of unitary elasticity of 

substitution nor constant returns to scale, would then fit 

the more general description of the desired stock of capital: 

PO 

(4) K* = B(c) Yr 

where (r is the elasticity of demand for capital with respect 

to the relative price of output and r is the elasticity of 

demand for capital with respect to output. (This last 

elasticity will be more than, equal to or less than unity as 

the returns to scale are decreasing, constant, or 

increasing.) 

The desired capital stock does not of course in itself 

tell us anything about investment, which is the rate of 

replacement of existing capital stock plus the rate of net 

additions. The rate of replacement may well be a variable 

depending upon financial considerations and a general set of 

expectations. The rate of net additions to capital will in 

principle depend upon costs of adjustment, which will in turn 

relate to costs of acquiring information necessary to 

decisions, costs of planning and again financial 

considerations. 

All this leads us to a formulation of investment as a 

distributed lag function of past changes in desired capital

stock plus replacement of some of the existing capital.

Here, however, two underlying theoretical points should be 

noted. First, the speed of adjustment of capital to changes

in its desired or equilibrium value may not be independent of 

the causes and the magnitudes of the changes. If, for 

example, an increase in the demand for output generates an 

increase in the demand for capital, investment may be 

expected to be undertaken with all due speed as expectations

become sufficiently firm with regard to the permanence of the 

increased demand. If the increased demand for capital is 

due, however, to a fall in its relative price due to let us 

say a reduction in the rate of interest, thus generating a 

demand for more durable and hence more substantial and 

expensive capital, the rate of investment will be slowed by

the availability of existing capacity sufficient for current 
-5-

production. These considerations underlie the ttputty-clay"

model. A demand for additional housing services will bring 

on investment in housing as rapidly as cost considerations 

permit. A lower rate of interest, causing substantial 

investment in more durable brick houses to replace less 

durable houses of wood or straw, would cause the rate of 

investment to increase only as existing houses of wood and 

straw wear out and are replaced. 

This suggests that investment equations should in 

principle involve separate distributed lag responses to 

changes in relative prices and to changes in output and 

should also admit the possibility that the lags are not fixed 

and may further vary with other economic parameters. We note 

that our more general expression for the desired stock of 

capital, (4), may be written in a logarithmic transformation 

as 

P 

(5) lnK* = In pt 0 1.nc t r 1nY. 

The ratio of net investment to existing capital stock is then 

approximately equal to the change in the logarithm of capital

which may in turn be written as distributed lag functions of 

changes in the determinants of desired capital as in 

(6) I N- 1 AlnK = o[~l.f~)AlnPI + r[Y2 (L)AlnY] 

K-l C 

where Y1(L) and Y (L) are lag operators which indeed should 

be functions of sucz variables as the rate of interest and 

the cost of capital. 

Finally, since investment equals net investment plus 

replacement, we may write 

I IN +R IN + 

where 6 may vary over time. 

The investment equations in the models under 

consideration most often ignore the possibility that the lag

distributions may vary over time and change, in particular, 

as a consequence of changes in other variables. They also 

ignore in varying degrees the putty-clay hypothesis, either ? assuming a putty-putty model whereby changes in relative 

prices can result in a speedy replacement of all of the 

existing capital stock or assuming that the speed of response

of investment to changes in relative prices and output is the 

same. 
-5-

3. Tax Parameters and Plan of Analysis 

To the extent that there is no differentiation of lag 

responses and to the extent that tax parameters do not enter 

independently we can anticipate, in general, certain peculiar

results in investment equations. First, the response to 

changes in the rate of business taxation, u, or the rate of 

the investment tax credit, k, or changes in the parameters

determining z, the value of tax depreciation, will depend 

upon the estimated parameters of c, the entire rental price 

or user cost of capital, of P/c or w/c, the relative prices

of output or labor and capital, or of the product of P/c and 

Y. Further, the response to tax parameters will depend in a 

number of the models on assumed values of 0, the elasticity

of substitution, or of the demand for capital with respect to 

the relative prices of output and capital. 

Indeed, what the investment equations of the various 

models have to say about the effects of tax incentives for 

investment, and what the models have in fact reported for 

these effects, stem very largely from the way the rental 

price of capital enters the investment equations. To the 

extent that a high value of CI is assumed or estimated, 

changes in tax parameters will appear to have large effects. 

To the extent that estimated lag functions appear shorter or 

faster because the estimated speed of response to changes in 

c, or P/c, or P/c and Y combined are faster, the effects of 

changes in tax parameters will appear to be more speedy.

Conversely, of course, if the speed of reaction to the lagged

variables is estimated as less, the implied or reported speed

of reaction to changes in tax parameters will be less. 

With all of these caveats and before we proceed to 

reporting upon our analysis and estimations of specific

models, we may note finally what may be expected from changes

in the tax parameters designated in equation (1). First, if 

estimated parameters indicate that the partial derivative of 

investment with respect to c, the rental price of capital,

has its expected negative sign, an increase in the investment 

tax credit will have to increase investment since the 

derivative of c with respect to k, the effective rate of the 

investment tax credit, is obviously negative. How much 

investment will be increased will depend upon the 

specification or estimate ofa. How fast it will increase 

will depend upon the distributed lag function relating to c. 

Second, acceleration or other methods of increasing tax 

depreciation which raise the value of z will have to increase 

investment and, again, at speeds determined by the 

distributed lag function on c. 

Third, effects of changes in the rate of direct 

taxation, u, are complicated and ambiguous. Results are 
-7-

affected by assumptions as to what happens to rates of return 

before and after taxes. Further, the higher the values of k 

and z and the higher the rate of expected capital gains, the 

less will decreases in u tend to decrease the value of C. 

With current high rates of inflation it is indeed possible, 

on a priori grounds, that decreases in ut the general

marginal rate of business taxation, may raise c, the rental 

price of capital, and thus at least in this regard, tend to 

reduce investment. -1/ 

Our general strategy in analyzing the investment 

equations of the various models is as follows: 

A. We shall point out how the tax parameters enter ‘in 

each set of equations. 

B. We shall note the direct effects of tax parameters 

on business investment indicated by the investment equation:; 

as currently specified and estimated. This will be 

accomplished, as far as feasible, by setting for the entire? 

period, alternatively, the investment tax credit, the lives 

underlying tax depreciation, 2/ and the rate of business 

taxation at the values assume3 in the last quarter of 1953. 

We shall then note the differences in the predicted values 

for investment brought on by these changes. This, of course 

is only a very partial exercise. It assumes that other 

economic variables within the investment equations and 

feedback from the rest of the system are unaffected. 

C. We shall then relax assumptions, altering

specifications where appropriate, to better ascertain what 

the underlying economic data can tell us about the effects of 

-1/ Effects of other tax parameters, not considered in this 

paper, are also determined by the parameters and lag

functions for c. Thus, a higher value of v, which could be 

obtained by making dividends tax deductible to business would 

lower the value of c and, if the partial derivative of 

investment with respect to c has the expected negative sign, 

will raise investment. The effect of changes in the rate of 

taxation of capital gains, or its rate of inclusion in 

taxable business income, w , is somewhat tricky. Where 

capital gains are positive, lowering the rate of inclusion in 

taxable income will lower the cost of capital and hence 

presumably increase investment. Where capital gains are 

negative, that is, where there are capital losses, however, 

if such losses can be deducted from taxable income, lowering 

the proportion of losses which can be deducted will raise the 

cost of capi’tal and hence lower investment. 

-2/ Furthermore, tax depreciation is calculated using the 

st r a ig h t - 1i ne me t hod . 
-8-

tax parameters on investment without possible biases imposed

by a priori hypotheses. This will generally involve several 

sorts of respecification and reestimation. First, where the 

elasticities of the response of desired capital or investment 

to changes in the cost of capital have been preset or 

constrained, we shall reestimate them freely. Second, where 

response of desired capital or investment to changes in the 

rental price of capital has been tied in part or in whole to 

a measure of the cost of capital based upon earnings-price

ratios, or dividend-price ratios, we shall reestimate with a 

cost of capital based on the rate of interest. A low 

earnings-price ratio on equity may be associated with higher

investment not because it reflects a lower cost of capital

but rather because it reflects, in stock prices, high

expected future earnings. The equity cost of capital to the 

firm is, after all, the ratio of expected future earnings to 

current stock prices. 

D. We shall estimate the effects on investment of 

changes in tax parameters as shown by our reestimated 

equations. 

4. Tax Parameters in the Structures of the Investment 

Equations 

In an effort to facilitate grasping the essential 

ingredients of the investment equations we have, with some 

violence to rigor and detail, set forth equations of each of 

the models in fairly similar notations in Tables 1 through 6. 

Examination of these may be supplemented by consultation with 

the glossary *of text variables presented in the Appendix. -1/ 

-

BEA

Turning first to the BEA model, we note that the tax 

parameters enter directly only in the definition of c, the 

rental price or user cost of capital, which in turn enters 

into the equilibrium or desired capital-output ratio, (P/c)?

The value of 0 is estimated at .74 in the equipment equaticln

but only .36 in the structures equation. The effects for 

equipment of changes in tax parameters can then be seen a 

priori as moderate, at least as against a possible assumed 

value of IS= 1. The effects of tax parameters on structures 

will be small. 

The estimated values of IS reflect, among other things,

the definition of p, the opportunity cost of capital. It 

attempts to adjust for expectations of inflation by an 

-17- Detailed documentation of the six investment sectors is 

available in Chirinko and Eisner (1980), Phase I, Appendix A* 
-9-

adaptive function of current and past price changes and also 

includes as a component a dividend-price ratio. This last, 

in particular, may bias upward the estimates of 0. Sluggish 

movement in dividends in response to changes in expected

earnings will contribute to a bias in the same direction but 

significantly larger than that noted above with regard to 

earnings-price ratios. 

The role of the investment tax credit is somewhat muted 

by recognition of the fact that its effective rate was less 

than the nominal, statutory rate. The investment tax credit 

is scaled down by application of a constant factor of 

proportionality equal to .737379. 

The role of tax depreciation is also somewhat muted in 

the BEA model by calculating z, the present value of the tax 

depreciation from a dollar of investent, on the basis of its 

straight-line formulation. 

Chase 

The Chase model is distinguished by an equation for new 

orders which feeds into the equipment equation. The new 

orders equation permits independent estimation of the tax 

parameters, u, k and z, with which we are concerned. In both 

the equipment and structures equations, the tax parameters 

enter again in c, the rental price of capital. In both 

equations the opportunity cost of capital, p, is based upon 

averages of interest rates and earnings-price ratios with the 

latter more heavily weighted in the equipment equation.

Estimates of the elasticity of response with respect to the 

rental price of capital are not constrained, however, and are 

not assumed constant. 

Economic depreciation is taken as a constant, at a rate 

of .181 for equipment and .095 for structures. In BEA it was 

apparently .38 for equipment and .I6 for structures. The 

present value of tax depreciation is a function of the kind 

of depreciation -- straight-line, sum-of-years digits or 

double-declining balance -- with the length of life varying.

The equipment tax credit, k, enters at its nominal statutory 

rate. 

The Standard and Poor's index of 500 stocks enters 

independently in the structures equation. Thus, it possibly

dilutes the effect of the earnings-price ratio. 

The DRI model enters the expression PY/c as a single set 

of lagged terms in both the equipment and structures 
-10-

equations. Thus elasticities of response are constrained to 

be identical for prices of output, 1/ rates of output and the 

rental cost of capital variable. If accelerator and 

replacement effects dominate and the long-run elasticities of 

demand for capital with respect to output are unity, this 

will have the effect of biasing to unity the estimated 

elasticities of demand for capital with respect to its rental 

pr ice. 

A second major, strategic element in the DRI model is 

the debt service variable, DS, which is the ratio of interest 

obligations to gross cash flsw, where the latter equals 

depreciation plus profits after taxes plus inventory 

valuation adjustment minus dividends. One may expect 

negative coefficients to the debt service variable not merely 

(if Jt all) because of liquidity constraints but also because 

investment will tend to be high in cyclical bGomS when 

profits are high. Variation in gross cash flow will be 

dominated by variations in profits after taxes, quite aside 

from variations in tax parameters. The DRI model will, 

however, imply that changes in tax parameters will have the 

same association with investment as the perhaps spurious 

association of profits and investment. If no feedback is 

allowed in terms of lower prices or pass-through of changes 

in taxes affecting profits before tax, the effects of changes 

in tax parameters will be particularly exaggerated. 

The opportunity cost of capita1,p , is an average of 

interest and equity costs, weighted by the proportions of 

each in business financing. The equity costs consist of a 

dividend-price.ratio plus an estimate of the expected rate of 

growth of earnings per share. 

The rate of economic depreciation is taken from BEA 

series on depreciation and capital stocks and hence varies 

through time. The present value of the tax depreciaticln from 

a dollar of investment, z, takes into account straight-line 

and sum-of-years digits depreciation. 

The DRI model may be expected to indicate particularly 

large impacts of changes in tax parameters because in three 

key areas the tax parameters are constrained to enter with 

coefficients equal to that of other variables expected to 

have a close association with investment: output, profits 

after taxes, and dividend-price ratios. 

IJDefined as final sales less government purchases and 

imputed housing services, with an adjustment for pollutionabatement equipment spending. 
-11-

Michigan 

The Michigan model divides equipment investment into 

three categories: production, agriculture, and other. It is 

unique in having the lagged value of structures enter the 

equation for production investment in equipment. It also 

contains in the "other1' equipment equation a variable 

measuring the difference between long-term and short-term 

interest rates, presumably embodying the effects of expected

changes in long rates. 

Tax depreciation is taken in the Michigan model as a 

rate which varies periodically, apparently with changes in 

allowable lives. The present value of the tax depreciation

for a dollar of investment is not calculated. 

In the structures equation the rental price of capital

is taken simply as the price of structures times .Or>, 

presumably economic depreciation, plus the rate of interest. 

Hence no tax parameters enter. In the equipment equations, 

tax parameters enter through the assumed rate of tax 

depreciation and the assumed nominal rate of investment tax 

credit, k. Economic depreciation is taken at a constant rate 

of one-sixth in the equipment equations. 

The Michigan model uses interest rates minus a'price

change expectations term as its measure of the opportunity 

cost of capital. 

The renta.1 price of capital variable enters as a ratio 

of labor costs in the equipment equations and as a ratio of 

prices in the structures equation. In none of the equations

is its coefficient otherwise constrained. 

The Michigan equations hence offer less a priori support

for the role of tax parameters. They do not enter at all in 

the structures equations. In the equipment equations they 

are constrained to have effects similar to those of other 

components of the rental price of capital. 

MPS 

The MPS investment equations rest heavily on a third 

equation for orders for equipment. This in turn involves 

distributed lag functions of output and changes in output,

each multiplied by (P/c)a . The value of o is constrained at 

unity in the equation for orders for equipment, from which 

actual investment expenditures follow fairly directly. This 

constrains the rental price of capital to have whatever 

effect on investment in equipment is indicated by the 

coefficients of the combined terms (P/c)AY and (P/c)Y,

reflecting accelerator and replacement investment. The value 

of 0 taken identically equal to unity, is apparently 
-12-

derived from a search procedure indicating this to be 

appropriate for a particular form of the equation estimated. 

In the structures equation, however, an estimated value of 0 

equal to ,18629 was used, thus implying a much lesser role in 

structures for the rental price of capital and any tax 

parameters entering into it. 

The value of the tax depreciation from a dollar of 

investment, z, takes into account the varying proportions of 

depreciation by straight-line and accelerated methods. The 

investment tax credit is taken at its "effective rate." 

In the forms specified, tax parameters can be expected 

to have a large role in the MPS equipment equations because 

of the constraint that 0 equals unity. It will have a much 

lesser role in the structures equation because of the 

relatively low estimated value of 0. 

Wharton 

The Wharton investment sector involves equations for 

eight separate industry groups, each estimating the sum of 

equipment and structures investment. Aggregate investment is 

then allocated as between equipment and structures. 

The nonagricultural industry investment equations are 

functions of current output, the one-quarter and two-quarter

ahead investment anticipations and, in some cases, the 

current capital stock. The cost of capital affects 

investment by its impact on the investment anticipations

variables. These are generally functions of output, the 

price of industry output relative to the cost of capital,

and, in some cases, the capital stock. The length of the 

lags for these explanatory variables varies by sector. No 

cost of capital term enters the equation for regulated

transportation. 

The industry costs of capital are based on effective 

industry income tax rates and the statutory rate of the 

investment tax credit. The value of z is calculated on the 

assumption that all tax depreciation was sum-of-the-yearsdigits using industry tax lives. 

The lack of constraint on the coefficients of the rental 

price of capital, where it does appear, implies relatively

little presumption in favor of a major role for tax 

parameters in the Wharton investment equations. 

5. Tax Scenarios: Estimates of Direct Effects of Tax 

Parameters 

One measure of the relative direct effects of tax 

parameters in the different models may be derived by setting

the three tax parameters with which we have been concerned at 
-- 

-13-

their essentially l'pre-incentive" values of 1953 and noting

the differences in investment indicated by the investment 

equations. Such a measure is of course very partial,

abstracting from feedback effects on the variables in the 

investment equations. It hence does not offer a reliable 

measure of the total effects of the tax parameters on 

investment. It should, nevertheless, give us a good

preliminary indication of the sensitivity to tax parameters

of the investment equations currently specified and used in 

the models. We do not have such estimates for Wharton. The 

contrasts among the five other models -- BEA, Chase, DRI, 

Michigan, and MPS as shown in Table 7, are striking. 

What we have done first is to set the investment tax 

credit at a rate of zero. Second, we have put the investment 

tax credit back at whatever values it entered the equations

and set the tax depreciation variable at a value which 

assumes continuance of straight-line depreciation at the tax 

lives used or specified in 1953. (In the Michigan model the 

tax depreciation rate was held at the constant value of .08 

for agriculture and .05 for "production" and "other.")

Third, we left the investment tax credit and tax depreciation

variables at whatever values they entered the equations but 

set the corporate profits tax rate at the value of .52 which 

existed in 1953. All comparisons were made for the fourth 

quarter of 1977 for which we had data for all of the models. 

Setting the investment tax credit equal to zero but 

taking all other variables entering the investment equations 

as unaltered, the predicted values of investment in equipment

showed a hugh range of results. The low, for Michigan, was a 

reduction of investment by $1.4 billion. Chase indicated a 

reduction of $4.3 billion. BEA came in with a reduction of 

$7.3 billion and MPS and DRI, as we might have anticipated

from the specification of the investment equations, indicate 

a reduction in investment of $10.9 billion and $12.9 billion, 

respectively. 

On accelerated depreciation Chase is low with an effect 

of $5.2 billion, with Michigan and BEA not far behind with 

estimated effects of $5.8 and $6.3 billion, respectively.

MPS and DRI are again high with investment losses of $14.7 

and $15.5 billion, respectively. 

The corporate profits tax rate, as we have pointed out, 

does not enter as unambiguously in the rental price of 

capital and consequent impact on investment and here the 

differences across the models, while still relatively great, 

are not quite as large. In fact, the results for Michigan

indicate that, by holding the corporate profits tax rate 

equal to its value in the last quarter of 1953, investment 

expenditures on equipment would have been higher by $.94 

billion as compared to the baseline values. All of the ether 

models record declines in investment. C\I,~S~ in(li(:,?t ("; .it1 
-14-

effect of $1.4 billion, but this time BEA ranks ahead of MPS, 

$2.5 billion against $1.8 billion, respectively. Again, DRI 

shows the strongest effects with an estimated decline of $5.7 

billion. 

Tax parameters do not enter the Michigan structures 

equation. As for the other four models, DRI is much higher,

both on accelerated depreciation and on the corporate profits 

tax rate, owing to the constaint that movements in the cost 

of capital or output impact on investment through the same 

set of distributed lag coefficients. The disparities among

the remaining models are relatively small, presumably because 

of the lower estimated value of CJ in the MPS structures 

equation. 

It is of course important to be aware that Table 7 

offers no comparison of the relative effects of variation of 

different tax parameters, even the direct partial effects in 

the investment equations. To measure these we would, at the 

least, have to compare changes in tax parameters that involve 

equal losses of tax revenues, in fact, equal present values 

of losses in tax revenues, since the time pattern of changes

in tax revenues will be different for the investment tax 

credit, tax depreciation, and the corporate profits tax rate. 

6. Estimated Equations 

Differences in results among the models have been 

related generally to explicit or implicit differences in the 

more or less constrained values of 0, the elasticity of 

capital with respect to its rental price. 

The investment tax parameters were most frequently

imbedded in variables measuring that rental price of capital.

Specifications of the components of the rental-price-ofcapital variables as well as constraints imposed upon their 

relations with other variables were of major importance. 

We focused our attention, in reestimating the model 

investment equations, on the coefficients of the rentalprice-of-capital variables and on the specifications which 

affected them. In our new equations we have loosened the 

constraints on variables embodying tax effects and compared

estimates of the original model equations (or our 

representations of them, sometimes trivially different) and 

our new equations. We then proceeded to comparable

simulations of the old and new equations with specified

alterations of the investment tax credit, the tax lives of 

depreciable assets, and the general rate of corporate

taxation. We thus were able to verify the apparent

implications of the various estimated parameters of the 

originally specified equations and our new equations and to 

quantify the results. 
-15-

A major focus of our revised equations has been the 

isolation, as far as possible, of variables presumed to 

embody the effects of tax parameters. This suggested that in 

a number of the models, we revise the definition of p, the 

cost of capital, which is a key, variable component in the 

rental price of capital into which the tax parameters enter. 

In particular, we excluded from the ratio of profits after 

taxes to stock prices or the ratio of dividends to stock 

prices. For high current ratios of profits after taxes to 

stock prices may relate less to the current cost of capital 

than to the state of the business cycle and the relation 

between current profits and expected future profits, which 

latter may play a major role in the value of stock prices.

High current profits may, in fact, stimulate investment 

through their liquidity effects and lower the effective cost 

of capital. 

A low ratio of profits after taxes to stock prices may, 

however, reflect high expected future profits which would be 

positively related to investment and yet not be indicative of 

a low equity cost of raising capital. This is true, a 

fortiori, with regard to the ratio of dividends to stock 

prices. The negative relation between investment and this 

presumed component of the cost of capital may rather reflect 

a positive relation between current investment and the 

expected future returns on this investment which will also be 

positively related to current stock prices. If we are to 

measure the effects of tax parameters on investment in terms 

of their contribution to the rental price of capital we must 

avoid tainting our measure of the rental price of capital 

with spurious rrleasures of p, its cost of capital component. 

A further major revision we have undertaken relates most 

importantly to the DRI model, where the effects of changes in 

relative prices and of output have been constrained to be 

equal in the combined variable, pY/c, where Y is a measure of 

output, p measures the price of output and c denotes the 

rental price of capital. Our major new equations for DRI 

involve estimates of the separate effects of changes in p/c

and changes in Y. Our hypothesis is that, since a strong 

positive relation between capital and output is well 

established, estimating the effects of changes in c, whether 

brought about by changes in tax parameters or changes in 

other components, will be exaggerated by estimates of a 

coefficient of pY/c. We might note as a corollary that, if 

the coefficient of p/c is really lower than that of Y, 

estimating a coefficeint for the combined variable may well 

lead to understatement of the effect of Y. Analogous issues 

of perhaps lesser substance occur with regard to constraints 

which impose similar consequences from changes in the 

relative price of capital goods and output or wages and of 

changes in relative prices due to other changes in the 

components of c. We have explored this with an addikic~niil 

set of equations in the Michigan model. 
-16-

The structures of the investment equations under 

consideration are set forth in fai'rly similar notations, 

along with estimated parameters and associated statistics in 

Tables 1 through 6 (with a glossary of variables in Appendix 

A). We explain them briefly below. 

-

BEA

Critical elements in the BEA model investment equations 

were the definition of the rental price of capital, c, the 

associated estimates of the elasticity of capital with 

respect to the rental price, 0, and the putty-putty form of 

the structures equation. In this equation, the entire 

capital stock, not merely net investment and replacement, was 

specified to change its magnitude with changes in the 

relative values of the implicit price deflator of GNP and the 

rental price of investment in structures. 

We have undertaken two changes in specifications of the 

BEA equations. First, we have altered the definition of p ,

the cost of capital entering the rental price, c. The BEA 

model defines pas a weighted average of an expected interest 

rate term extrapolated from the past change in the rate of 

interest and current and past levels, and a dividend-stock 

price ratio. Interest costs are apparently partially

adjusted for their tax-deductible component. We have defined 

a new PI, modifying the definition of @by excluding the 

dividend-stock price ratio and blowing up the resultant P so 

that its mean is equal to that of p. 

Second, we have added a new structures equation with a 

putty-clay specification, as indicated in Table 1. 

Changing the definition of had only a modest effect in 

the equipment equation. Our estimated value of 0 changed

from .74 to .55, suggesting a slightly lower effect for 

investment tax parameters than in the original equation. 

In the structures equation, our new definition of P 

resulted in lowering the estimate of 0 from .36 to .27 in the 

original putty-putty specification. It should be noted that 

the standard error of the regression based on the 0 

specification was somewhat larger than that with the p 

specification, however. 

The putty-clay specification yields higher estimates of 0, 

both the pand p versions, but again a lower estimate of in 

the p1 equation. We may anticipate though that the higher

values of Din a putty-clay specification will not translate 

themselves into higher short-term effects of tax parameters 

on investment. 
-17-

Chase 

In the Chase model direct effects of investment tax 

parameters are measured in an equation for new orders in all 

manufacturing. Here the values of the corporate tax rate, u, 

of the investment tax credit, k, and of the present value of 

tax depreciation from a dollar of investment in equipment, 

ZE divided by 1-u, all enter linearly. The new orders 

variable in turn enters the equipment investment equation but 

the tax parameters enter this equation again as components of 

cE' the rental price of equipment. The structures equation

does not contain the new orders variable so that the only

effects of the tax parameters there are as components of cs, 

the rental price of investment in structures. 

The rental price in both cases includes the cost of 

capital, p. For equipment this is an average of the interest 

rate on newly issued Aa utility bonds and the ratio of 

profits after taxes in billions of dollars to the Standard 

and Poors index of 500 common stocks. The value of pis

calculated from a similar average in the case of structures, 

but with a lesser weight for PRAT/SP, the ratio of profits to 

the stock price index. The structures equation also enters a 

set of lagged stock price indices as a separate variable. 

Our estimates of the equation involving pl, in which the 

stock price index and profits after taxes are taken out of 

the c/p variable and enter separately, indicate a striking

reduction in the absolute value of the coefficient of c/p,

from 61.4 to 30.3, as shown in Table 2. While leaving intact 

the estimated effects of tax parameters in the curiously

specified equation for new orders, the reduction in the 

coefficient of c/p as we move from the equation to the pl 

equation suggests that an "untainted" estimate of the 

coefficient of the rental price of capital will indicate 

lesser effects of tax parameters on investment in equipment. 

In the structures equation, the coefficient of c/p is 

agsin reduced in absolute size, from 85.6 to 66.5 as we move 

from the P equation to the P' equation. This reduction is 

less in absolute magnitude and still less relatively than the 

corresponding reduction in the case of equipment. The 

structures equation, one may note, has a significantly

positive coefficient for the stock price index but a 

relatively small and insignificant coefficient for the 

PRAT/SP variable. 

Tax parameters enter the DRI investment equations

through c in the pY/c variable and in the debt service 

variable, DS. The specification is implicitly putty-putty

with direct adjustment of equipment investment to a change in 
-18-

rental price completed over a total of nine quarters. Any

reasonably substantial coefficients of the pY/c variables 

will hence imply a substantial effect on investment. 

The debt service variable, defined as the ratio of 

interest payments to gross cash flow, may also have a 

substantial effect because cyclical increases in profits,

closely related to cash flow, are likely to be positively

associated with cyclical movements in investment. Since 

cyclical movements of interest payments are much less, we may 

expect a considerable negative relation between investment 

and the debt service variable, reflecting essentially the 

positive relation between investment and profits. This 

positive relation of investment to profits will come through

all the more greatly if the role of output is misspecified.

The merging of Y in a combined pY/c variable may then have 

the effect of lowering the constrained coefficient of Y even 

as it raises the constrained coefficient of p/c and raises 

the absolute value of the coefficient of the debt service 

variable. 

The DRI model uses for p a weighted average of interest 

costs and the sum of the dividend stock price ratio and a 

measure of the expected rate of growth of earnings. To the 

extent that the measure of expected earnings growth captures

the earnings-dilution cost of selling new equity as perceived

by firms, the DRI measure of P may be robust against the 

criticisms we have advanced earlier. To the likely extent 

that it is an inadequate measure of these costs in terms of 

expected future earnings, the DRI measure of p may also be 

defective as an indicator of the cost of capital. 

We have thus undertaken two kinds of revisions in the 

DRI equations, both separately and in combination. First, we 

have split the pY/c variables into their separate relative 

price and output components, p/c and Y, or more precisely,

(p/c)Y and Y(p/c). Second, we have redefined p' as the DRI 

measure of the interest rate, blown up to have the same mean 

as the originally defined P. (Thus 13' = i F/T.) We are 

hence able to offer four sets of estimates: 1) the original

DRI equations, with the combined pY/c variable and the 

original p and hence the original c; 2) equations with the 

original P but with (p/c)Y and Y(m entered as separate 

sets of variables; 3) the original D9I specification but with 

p'substituted for p; 4) equations with p' substituted for p , 

and with (p/c)P and Y(p/c) substituted for pY/c. 

The results for equipment appear very much in line with 

our hypotheses. Splitting the pY/c variable lowers the 

constrained coefficient of .0135 to .0055 for p/c and raises 

the coefficient to .0213 for Y. Further, the absolute size 

of the coefficient of the debt service variable was reduced 

from 45.2 to 25.2. The splitting of the pY/c variable thus 

points to a reduction in the implicit effects of all tax 
-19-

parameters in the order of more than 50 percent in the DRT 

equipment equation. 

Substituting p1 for p in itself reduces the estimated 

coefficient of pY/c and the absolute value of the coefficient 

of the debt service variable. The combined effect of both 

alterations, substituting p for p and splitting the pY/c

variable, is most dramatic. The coefficient of the separate

p/c variable is reduced to .0035, little more than one 

quarter of its constrained value in the original DRI equation

and the absolute size of the coefficient of the debt service 

variable is reduced to 14.2, again less than 30 percent of 

its amount in the original DRI equation. 1/-

The DRI equations for structures, however, reveal no 

such dramatic differences. This may relate to the generally 

poor fit of the DRI structures equations. The sum of the 

coefficients of pY/c was not significantly greater than zero 

in the original DRI equation and neither the corresponding

pY/c sum nor the sums of coefficients of the separate p/c and 

Y variables were significantly different from zero in our 

equations. In our revision incorporating both and the 

separate p/c and Y variables, the absolute size of the highly

significant debt service variable was somewhat reduced, from 

45.9 in the original DRI structures equation to 38.3. Our 

revisions have not, however, made very much difference in the 

structures equations. 

Michigan 

The Michigan model, it may be recalled, generates the 

smallest effects of tax parameters on investment. Indeed, 

there is no direct scope for them at all in the structures 

equation. 

We have used the Michigan model to examine a further 

split of the relative price variable in which tax parameters

affecting investment are usually imbedded. What we have done 

is to break out of the relative price of capital and labor 

term, c/w, the price of capital goods and the wage rate. 

This leaves as the residual variation in the rental price of 

capital, c, the interest rate in the structures equation and 

-'1/ An "F" test reveals that the improvement in fit 

resulting from the separation of p/c from Y in the P 

equation for equipment is clearly significant; F(2,76)= 4.83, 

which is just about at the .99 probability level. The "F" 

statistic for the p equation was 2.74, corresponding to a 

probability level of .93. 
-20-

in equipment, in addition, a price change term and the tax 

factors of depreciation, the corporate tax rate and the 

investment tax credit. 

Results were mixed in the three equipment equations -- production, agriculture and other -- and in structures. In 

"production" investment, which had a mean value of almost $15 

billion, the split lowered the absolute value of the 

coefficient of the rental price of capital component

including the interest rate and tax parameters. In the small 

agricultural component (mean investment about $4 billion) the 

absolute value of the coefficient of the rental price of 

capital residual variable was raised considerably and the 

relative price term showed a significant "wrong" positive

sign. (This may have related to interaction with the 

variable measuring relative price changes of farm and nonfarm 

prod ucts.) 

In the equation for "other" equipment investment, the 

mean value of which was $43.5 billion, the split brought

little change in the coefficient of the rental price of 

capital variable. In structures, this split did cut the 

coefficient of the residual rental price of capital variable 

rclughly in half in absolute value and also showed a very

substantial and significant negative coefficient of the new 

variable measuring the relative price of capital goods and 

wages. This may suggest a better formulation of the 

structures equation but is not directly relevant to our 

current work since tax parameters do not enter here. 

__ 

MP S 

In the MPS equations we have reestimated both equipment

and structures equations with focus on the values of 0 , the 

elasticity of demand for capital with respect to the relative 

price cIf output and capital. In the MPS model equation for 

corders fer equipment ais specified as having a value of 

unity. When we reestimate this equation with the MPS 

specification of pand no constant term, we do indeed get a 

maximum likelihood estimate of aof 1.03. When we estimate 3 

without constraining the constant term to be zero, however, 

we find that the constant is signficantly negative, the 

estimated value of ii falls to .70 and the accelerator 

coefficients generally rise. 

Variance in p in the MPS equations relates chiefly tcp

variance in the dividend-stock price ratio and to interaction 

cpf the corporate tax rate and the proportion of capital costs 

which is tax-deductible. There is general allowance for an 

interest rate component but the current MPS model equations

cclnstr3ined its coefficient to be zero. 
-21-

In accordance with our general approach we have defined 

P' so that the interest rate is included and the 

dividend-stock price ratio is excluded. Estimates of the 

equipment equation with substituted for P yield

considerably smaller estimates of the value of 0 . In the 

equation with no constant term, as specified in the MPS 

model, our estimated value of 0 falls from 1.03 to .71. In 

the much better fitting model with the constant term the 

estimated value of in the p1 equations falls from .71 to 

.19. This last value of 0 would suggest a vastly smaller 

role for tax parameters in affecting investment in equipment. 

In the MPS structures equation, the value of 0 provided

in the model is .18629, thus implying only modest effect of 

tax parameters on investment in structures. Our own estimate 

of the structures equation as originally specified including

the MPS definition of p yields a value of 0 of .22. The 

dramatic differences seen in equipment do not appear in our 

different equations in structures. The equation using p with 

a constant term here gives a value of of .29, that using p '

yields a value of cs of .15, and that using P' with a constant 

term gives a value of 0 of .27. 

Wharton 

In the Wharton model, our only modification to the 

original equations is to alter the definition of p. The 

opportunity cost of capital is defined as a fixed-weighted 

average of an estimate of the real rate of interest and the 

dividend-stock'price ratio. As argued above, this latter 

term may be a poor proxy for the true equity costs that the 

firm faces, and we have reestimated the Wharton equations

with pl, equal to the real rate of interest scaled 

appropriately to insure that the means of p and P' are equal. 

The number of equations that were reestimated with the 

new definition of the cost of capital is rather voluminous 

and, in Table 6, we present a representative set of equations

for durable manufacturing. In both the one- and two-quarter

ahead anticipations equations, the sums of estimated 

coefficients are significantly lower for the relative price 

term, and somewhat lower for the output term. This pattern

holds for the majority of the reestimated equations, although

in some cases the sums of coefficients increase relative to 

the original estimates. Given the interrelationships that 

exist in the investment sector of each industry, it is 

somewhat difficult to determine from an examination of the 

coefficients the responsiveness of aggregate investment to 

changes in parameters. The simulation results presented in 

Table 13 provide a convenient means by which to assess the 

differences between the original and modified equaticbns. 
-22-

We may indicate in general that, particularly where the 

original models suggested major effects of tax parameters on 

investment, our revised equations, free of what have seemed 

to us to be critical constraints generating the results, have 

produced parameter estimates suggesting considerably lesser 

effects of tax variables on investment. That story can be 

developed much more clearly and precisely in simulations of 

paths of investment with varying values of the key tax 

parameters of the investment tax credit, tax depreciation and, 

the corporate income tax rate. It is to these simulations 

that we shall now turn. 

7. Simulations 

We report on four basic sets of simulations, similar as 

far as possible for each of the six models. The first is a 

long-run simulation in which the relevant tax parameters are 

held at their fourth quarter, 1953 levels. This means 

setting the investment tax credit at zero, the corporate tax 

rate, effective or statutory as defined in the models, at its 

1953-IV rate, and applying tax depreciation by the straightline method at the length of lives assumed by the models to 

exist in the fourth quarter of 1953. 

Second, we have alternatively changed the investment tax 

credit, the corporate tax rate and the tax depreciation lives 

in the first quarter of 1973 and followed the resultant path 

c~f investment for generally a five-year period through the 

fourth quarter of 1977. For the investment tax credit, we 

have doubled the rate for equipment beginning in the first 

quarter of 1973'and have introduced a credit for structures 

at 10 percent (an effective rate of 8.1 percent in the DRI 

model and 8.5 percent in the MPS model). We have set the 

corporate tax rate at 90 percent of its historical rate 

beginning in the first quarter of 1973. And we have set the 

tax lives for depreciable assets at 50 percent of their 

histerical rates beginning in the first quarter of 1973. 

We have then mapped baseline paths for investment in 

equipment and structures for the original model equations (or 

our approximate rendition of them) and noted the effects upon

investment indicated by each of the specified sets of changes 

in tax parameters. Next, we have constructed similar 

baseline paths for each of our modified equations and noted 

the indicated effects on investment of the changes in tax 

parameters in these equations. Thus we are able to note not 

only how the original model equations indicate changes in tax 

parameters will affect investment but also how the indicated 

effects are dependent upon model specification and how they 

change with the new, less constrained and, in our view, 

better specified equations which we have estimated. 
-23-

To simplify the presentation, we shall offer in our 

tables and concentrate in our discussion on the results for 

the fourth quarter of 1977, in billions of 1972 dollars and 

as a percent of baseline. 

To anticipate in summary fashion, the simulations 

offered generally, and particularly in the results for 

equipment, a striking confirmation of the hypotheses we have 

expressed and of the implications of the estimated equations

indicated above. 

-

BEA

The BEA equipment equations, it will be recalled, were 

only moderately modified by our respecification of p as p'.

The rather substantial effects of tax parameters on 

investment indicated in the BEA model are hence only

moderately reduced with our new specification, With none of 

the "investment incentives" introduced since 1953, the REA 

equipment equation indicates that investment in equipment.

would have been some $15.6 billion in 19'72 dollars less in 

the fourth quarter of 1977, some 17 percent of the baseline. 

Our revised p' equation lowers that effect only to $14 

billion, or 15.1 percent of the baseline. 

Making the equipment tax credit twice its historical 

value beginning in 1973 would have increased equipment

investment by $9 billion or 9.8 percent of baseline according 

to the original BEA equation. According to our pl equation

it would have increased equipment spending by $8 billion or 

5.6 percent of baseline. This latter figure, we may point 

out, indicates that the bang for the buck is not 

expectionally promising. Since a doubling of the investment 

tax credit meant an increase from 10 percent to 20 percent

beginning in 1975, the additional loss of tax revenue equal 

to 10 percent of equipment spending would have increased that 

spending by less than 10 percent. Our single equation

simulations suggest that we could have gotten more added 

investment by paying for the equipment and giving it to 

business free than by the device of a "tax incentive" to 

induce them to buy it on their own. 

The relative magnitude of effects shown in the original

and modified equation are similar for reductions in the 

corporate tax rate and in the lives for tax depreciation, as 

may be seen in Table 8. The equations show modestly 

smaller effects on investment. 

The BEA structures equation, with its distinctly smaller 

value of o, shows markedly smaller effects of changes in tax 

parameters. Using the original BEA putty-putty model, the 

introduction of a 10 percent investment tax credit for 

structures would have increased structures investment by only 
-24-

3.48 percent of baseline by the fourth quarter of 1977. Our 

modified p' equation reduces that effect to 2.64 percent of 

baseline. 

The putty-clay specification which we have introduced 

generates higher estimates of 5 , as might be expected, and 

hence greater long-run and also greater medium-run effects on 

structures investment. By the fourth quarter of 1977, the 

increases in structures investment was some 30 to 40 percent 

greater in the putty-clay equations than in the putty-putty 

equations. The putty-putty result for a 10 percent 

investment tax credit in structures was +S1.13 billion in our 

piequation for 1977-IV as against $1.49 billion in the 

putty-clay pl equation. 1/ Rut in the putty-putty equation 

the indicated added investment in structures had reached a 

peak of about $2.30 billion as early as the third and fourth 

quarters of 1974 and the amount of added investment then 

began to decline. In the putty-clay model the amount of 

additional structures investment rose throughout the 

five-year period but was apparently pretty much at its 

equilibrium level by the fourth quarter of 1977. 

Both the putty-putty model for structures investment and 

the results flowing from it are really implausible. The 

putty-clay models indicate that a reduction in tax revenues 

equal to 10 percent of structures investment would tend to 

increase that investment by some two-thirds of the lost tax 

revenues according to the p equation and some one-half of the 

tax revenues according to the p' equation. All of these 

estimates, we must remind ourselves, are based only upon the 

single investment equations without feedback from the rest of 

the model. Higher interest rates resulting from higher 

investment demand, for example, would tend to reduce the 

effects of these tax incentives. Effects from changes in 

aggregate demand would depend, of course, upon what 

assumptions are made about other offsetting taxes as well as 

whether the economy is or is not at or near full employment. 

Chase 

The original Chase equations do not indicate as large 

effects of tax parameters on equipment investment. The 

simulations with our revised p' equations reduce those 

estimated effects further. Thus, the long-run no tax 

incentive simulation indicates that equipment investment 

would be less by $11.7 billion in 1977-IV, or 12.8 percent of 

baseline. Our p' equation reduces this estimated effect to 

$5.2 billion or 8.9 percent of baseline. The effects of 

-____-

-1/ The BEA model is specified so that a 10 percent statutory 

investment tax credit is transformed into a 7.37 percent 

effective rate. 
-25-

doubling the investment tax credit were only 4.6 percent of 

baseline, less than half of that indicated in the BGA 

equations. Our equation reduced the effects substantially

further to just over 3 percent of baseline. Thus a dollar of 

lost tax revenues from an increase in the investment tax 

credit would generate not much more than 30 cents in 

additional equipment investment, again without feedback from 

the rest of the model. 

The effects in structures were considerably less in the 

original Chase equation, the 10 percent investment credit, 

for example, raising structures investment by only 3.37 

percent of baseline. Our equations here made very little 

difference, as shown in Table 98 and as might have been 

anticipated from Table 2B, which reported the estimated 

equation. 

The Chase equations were estimated without the CocI~i I, 

Orcutt autocorrelation correcticln. When we introduced ttie 

correction the results were about the same in equipment but 

changed somewhat in structures. Here we find simulation of 

the original Chase equation estimated with the autocorrelation correction yielding a somewhat higher structures effect, 

6.38 percent of baseline for a 10 percent investment tax 

credit and similarly greater figures for changes in other tax 

parameters. Simulation of our p' equation, as in equipment,

yields a lesser effect, however, only 4.9 percent of 

baseline. 

The DRI simulations offer the most dramatic confirmation 

of sensitivity of predicted results to equation specification

and estimation. The original DRI model equation, with p 

containing its dividend-stock price component and with the 

combined pY/c variable, indicates that the setting of all tax 

parameters at the levels that existed in 1953-IV would have 

resulted in $36.8 billion 1972 dollars less equipment

investment in 1977-IV, some 40 percent of baseline. 1/

Simulation of the equation estimated with separate p7c and Y 

variables cut this effect by fully three-quarters, to $8.5 

1/ The debt service variable in the DRI model makes it -

extremely difficult to simulate effects of changes in 

depreciation lives. The algorithm which DRI may have used in 

such simulations not proving available, we constructed our 

own. For computational convenience, we used constant tax 

lives for equipment and structures in performing the 

simulations which begain in 1954. The reported results in 

1977-IV would have been changed slightly if historic t TX 

lives had been used. 
-26-

billion, only 9.3 percent of baseline. The pl equation with 

separate p/c and Y reduced this smaller simulated effect by 

half again, to $4.5 billion, or 4.9 percent of baseline. 

The original DRI model equations generate, along with 

MPS, the largest effects of tax incentives on equipment

investment. The doubling of the investment tax credit for 

equipment beginning in 1973-1 results in an increase in 

equipment spending of $13.1 billion 1972 dollars in 1977-IV, 

or 14 percent of baseline, according to our simulation. 

Splitting the pY/c variable again results in a hugh decrease 

in the simulated effect, to $3.7 billion or 4.04 percent of 

baseline. Simulation of the equations makes a lesser 

difference but again reduces the predicted effects, to $2.81 

billion in the equation with separate p/c and Y variables, or 

3.05 percent of baseline. Thus, from a simulated effect of 

$1.42 of added equipment spending for each dollar of tax 

revenues lost through the investment tax credit indicated by 

the original DRI equation, we move to an indicated effect of 

only $0.31 of added equipment investment for each dollar of 

revenues lost from the investment tax credit when we worked 

with our modified p' equation with separate p/c and Y. 

Similarly contrasting effects are to be found with the 

acceleration of depreciation and reduction in the corporate 

tax rate, although in the pl equations the net effect on 

investment of a corporate tax reduction is slightly negative. 

The result stems from the greater effect of the lower u in 

raising the after-tax cost of capital when that is made to 

depend wholely on deductible interest payments. In the 

original formulation the adjusted dividend-stock price ratio 

component was presumably unaffected by changes in the 

corporate tax rate. 

The halving of depreciation lives raised 1977-IV 

equipment investment by $8.0 billion 1972 dollars in the 

original DRI model equation, or 8.69 percent of baseline. 

The simulation with the p/c and Y split reduced the 

accelerated depreciation effect to $2.4 billion, or 2.60 

percent of baseline. And the split with the p' equation

lowered that predicted effect still further, to $1.3 billion, 

1.37 percent of baseline or less than one-sixth of the effect 

shown in the original DRI equation. 

Modification of the structures equation in the DRI model 

does not bring similar changes. As suggested earlier in our 

discussion of those equations, perhaps because structures 

spending is not that closely related to output over the 

preceding nine quarters, the coefficients of the pY/c 

variables in the original DRI structures equation were not 

high (nor were they statistically significant). Reestimated 

equations did not therefore have much scope for reduced 

estimates and, indeed, the free p/c coefficient was slightly 
-27-

higher. Our structures simulation in fact showed somewhat 

greater additions to investment resulting from increasing or 

introducing the investment tax credit. As in equipment, the

6 specification suggested sharply lesser effects of reducing 

the corporate tax rate than the original DRI p equation. 

Michigan 

We have done no simulations with the Michigan structures 

equations because they contain no tax parameters. Taxes 

indeed have mixed effects in the Michigan equipment 

equations. 

Tax depreciation is defined as a rate rather than, as in 

the other models, in terms of length of life and method of 

depreciation which feed into the present value term, z. In 

our Michigan depreciation simulations, therefore, we have 

doubled tax depreciation rates rather than halving lives. 

The particular form of the rental price of capital variable 

in the Michigan model, we may also note, is such that the 

partial derivative of rental price with respect to the rate 

of corporate taxation is negative unless (as was true 

according to the rates assumed in the Michigan model before 

1962) the rate of tax depreciation plus the rate of price

inflation was far less than the assumed rate of economic 

depreciation of one-sixth. 

In all three of the equipment sectors, the Michigan

simulations indicated only very small effects of the 

investment tax credit. In no case did doubling it in 1973 

and thereafter raise equipment spending by more than 2.78 

percent of baseline. 

The corporate tax rate did in fact manifest a "perverse" 

effect. Lowering it to 90 percent of its historical rate 

from 1973 on actually reduced equipment investment in most 

instances. 

Doubling the tax depreciation rate turned out, however, 

to have a very large effect. This would appear to be a 

consequence of the very large assumed tax depreciation rates 

of some 21 percent and 36 percent in recent years. 

Our alternate c' equations, splitting relative price

effects from the rental price variable, did not indicate 

consistent differences in simulated results, in some sectors 

for some parameter changes suggesting lesser effects on 

investment and in some cases greater effects. 

MPS 

The MPS simulations for equipment show extreme 

sensitivity to equation specification. Simulation of the 

original MPS equation with no constant term, and with our 
-28-

estimated CT of 1.03 substituted for the specified 5 of 

unity, indicates very large effects of tax parameters on 

investment. Setting all tax parameters at 1953-IV levels 

leads to a predicted decline of equipment investment of over 

$25 billion by the fourth quarter of 1977, or 30.3 percent

below baseline. When the equation including a constant term 

is used for simulation, that reduction is lessened to 23.3 

percent. The p' equation without a constant term generates a 

predicted drop of 19.7 percent below baseline while the p '

equation with a constant term indicates a drop of only 6.191 

percent, less than one-quarter of that suggeeted by the 

investment in equipment equation specified in the MPS model. 

The other equipment simulations bring similarly

constrasting results. Thus, the original p equation

indicates that doubling the equipment tax credit beginning in 

1973-1 would cause an increase in equipment investment of 

$12.7 billion 1972 dollars, 15.12 percent of the baseline. 

The MPS orders for equipment equation with a constant term, 

however, generates a simulated reduction of only 10.68 

percent of baseline. The 0' equation, in which the interest 

rate is substituted for the dividend-stock price ratio, 

suggests an increase of only 8.28 percent of baseline. And 

the p' equation with a constant term knocks the added 

equipment investment down to 2.78 percent of baseline, only

18.4 percent of the effects indicated in the originally

specified MPS model. Roughly similar, contrasting results 

are found with changes in the corporate tax rate and in the 

lives of assets used in depreciation for tax purposes. 

The results of structure simulations are, as 

anticipated, not nearly as dramatic. Indeed here, since the 

introduction of a constant term somewhat raises the low 

estimates of 0, the simulated results suggest correspondingly somewhat greater effects on investment. Substituting

the interest rate �or the dividend-stock price ratio in the 

definition of P, however, does generally lower the predicted

effects of tax parameters, particularly when the structures 

equation is estimated, as in the MPS model, without a 

constant term. Tn none of the structures equations, it may

be noted, does increased investment come close to equaling

the loss in tax revenues resulting from the tax incentives. 

This can be seen clearly again in the case of introduction of 

an investment tax credit of 10 percent beginning in the first 

quarter of 1973. In that simulation, resultant investment by

the fourth quarter of 1977 increases over a range of from 

3.93 percent of baseline to 7.40 percent of baseline, thus 

generating from 39 cents to 74 cents of added investment for 

each dollar of lost tax revenue. Of course, as in all of 

these simulations, the results relate only to the investment 

equations, without feedback from the rest of the model. 
-29-

Wharton 

The Wharton model calculates total aggregate investment 

expenditure and then divides the estimate between aggregate

equipment and structures. Thus, the effects of alterations 

in tax parameters will tend to have symmetric effects on 

spending for equipment and structures. An increase of 10 

percent in the investment tax credit rate for structures and 

a doubling of the rate for equipment beginning fn 1973-1 

leads to an approximately 4.91 percent increase in 

nonresidential investment in the original Wharton equations

and a 2.95 percent increase in our modified set. In 

performing this simulation, we assumed that these increases 

in investment tax credit rates were such t,hat the relative 

price between equipment and structures was not affected. -1/ 

A 10 percent cut in the corporate income tax rate had 

little effect on either set of estimates, with total 

investment approximately .53 percent and .19 percent higher

than the baseline values in the original and modified 

equations, respectively. This low response is due to the 

recognition of the tax deductability of interest payments in 

the Wharton rental price of capital. Under sufficiently high 

rates of inflation (as exist currently), this term and the 

value of tax depreciation can actually increase the rental 

price of capital in the face of cuts in the corporabe income 

tax rate. 

8. Summary and Conclusion 

Investment equations in the six models under 

consideration, BEA, Chase, DRI, Michigan, MPS and Wharton, 

differ in specification, estimated parameters and results. 

The results in the equipment equations have differed sharply,

primarily as a result of differences in the implicit or 

explicit values of 0 , the elasticity of investment with 

respect to the rental price of capital. Where there were 

high values of 0 , whether due to a constraint tying the 

rental price of capital to output, as in DRI, constrained 

homogeniety (no constant term) in MPS, or use of the ratio of 

earnings or of dividends to stock prices as a component of 

the cost of capital (BEA, Chase, DRI, MPS, and Wharton), even 

with a growth-in-earnings term, the impact of tax parameters 

on investment was high. Where 0 did not have a high value,

the impact was low. 

-1/ We also assumed that the discrepencies between the 

National Income and BEA Survey data remained at their 

historic values. 
-30-

The differences across models are striking. As shown in 

Table 14, our simulations of the original equipment

investment equations indicate that doubling the equipment tax 

credit beginning in 1973 generated a range of effects on 

equipment investment by the fourth quarter of 1977 from a low 

of $1.4 billion 1972 dollars for Michigan to a high of $13.1 

billion for DRI, with MPS not far behind. The BEA simulation 

indicated-a high-middle estimate of $9 billion while Chase 

and Wharton came in fairly low at $4.3 and $5.1 billion, 

respectively. The mean figure from the six simulations was 

$7.6 billion, some 8.3 percent of actual equipment investment 

in 1977-IV. 

Our preferred revised equations, eliminating the 

dividend-stock price ratio from the cost of capital variable, 

splitting output and the rental price of capital into 

separate variables in DRI and removing the homogeneity

constraint in MPS, bring drastic reductions in the effects of 

tax parameters in the original models. The Chase, DRI and 

MPS results of doubling the investment tax credit for 

equipment are knocked down to the range of $2.7 to $2.8 

billion. The BEA estimates remain relatively high, due 

apparently to the persistently high estimate of 5, .65 in 

our revised equation. All in all, simulations of our revised 

equations yield a mean increase in equipment investment of 

$3.5 billion, down to 3.8 percent of actual equipment

investment, and only 45.3 percent of the mean figure derived 

from simulation of the original equations. 

Investment classified in the models as structures 

amounted to less than half of that in the equipment category

and was generally much less responsive to tax parameters in 

simulations of the original model equations. There were no 

tax parameters in the Michigan structures equation, hence 

changing tax parameters could have no effect on structures 

investment there. Over the other models, the range of 

effects from instituting a 10 percent credit for investment 

in structures varied considerably less then effects from the 

analogous doubling of the investment tax credit for 

equipment. Aside from Michigan, the range of predicted added 

investment in the original equations extended from $1.4 

billion for Chase and BEA, to $2.4 billion for MPS and a high

of $2.8 billion for DRI. The mean for all five models was 

$1.7 billion, only 4.3 percent of actual structures 

investment . 

In the case of structures investment, however, with the 

original equations containing explicit values of 0 of ,18629 

and .36 and implicit values also generally low, as indicated 

by coefficients of rental price of capital variables, our 

revised equations offered results which were not 

substantially different from those of the original model 

equations. The mean of predicted increases in structures 
-31-

J 

investment derived from our revised equations was identical 

to that for the original equations, calcul.ated to the first 

decimal. 

Thus, the effects on total business fixed investment of 

essentially adding 10 percentage points of investment credit 

in both equipment and structures ranged, with the original

model equations, from a low of $1.4 billion in the Michigan

model to a high of $15.8 billion in the DRI model, a 

difference of over 1,000 percent. The mean of the disparate

estimates came to $9.3 billion, or 7.07 percent of the actual 

investment figure of $131.7 billion. Because of our 

distinctly lower simulated results in equipment, our revised 

equations yielded, along with a smaller spread, a 

considerably lower mean of $5.2 billion, or 3.98 percent of 

total investment. In either set of equations, but of course 

a fortiori in the revised set, it may be noted that a 10 

percent increase in the tax credit brought considerably less 

than 10 percent in added investment. The results from

the original model 

loss would result 

revised equations 

mean 

equations suggest that each dollar of tax 

in about 71 cents of added investment. The 

offer a comparable figure of only 40 cents. 

All this, it must be recalled again, includes only the 

direct effects of changing tax parameters in the investment 

equations themselves. Full model simulations can alter these 

results, depending in each case on the extent and manner of 

feedback from other equations in the system. -1/ 

-l/ Some of that story, again, is to be found in Chirinko and 

Eisner (1980), Phase I11 or OTA Paper 46 . 
-32-

Table 1. BEA Equations, Equipment and Structures 

(1) (2) (3) (4) (5) (6) (7)

Variable Regression Coefficients and Standard Errors 

or Equipment Structures 

Statistic Putty-Putty Putty-Clay 

P P' P P' P P' 

Constant - - - - - -

Cb (ELAG1; 

jy SLAG1,P-P; .3876 ,4188 1.4961 1.2844 1.5091 1.2792 

SLAGl, P-C) (.0048) ( .0050) (.0447) (.0873) (.0460) (.OS371 

Zb (ELAG2; -.0326 -.0424 -.1586 -.1368 -.1009 -.0813 

jU SLAG2) (. 0056) (.0057) (.0241) (.0453) (. 0278) (. 0317) 

a .74 .65 .36 .27 .48 .36 

Autocor.Coef. .675 .659 .815 .945 .805 .870 

R2 ,997 .997 .979 .975 .978 .976 

S.E.Regression 1.0748 1.0741 ,8126 .8799 .8265 ,8634 

DW 2.009 2.007 2.205 2.079 2.039 2.025 

n 79 79 71 71 71 71 

Means and Standard Deviations 

ELACl, SLAGl 179.103 168.280 32.642 37.517 29.319 34.634 

(51.928) (48.322) (9.786) (7.175) (3.862) (4.272) 

ELAG2, SLAG2 160.069 151.067 56.850 64.780 48.225 57.368 

(85.092) (81.185) (27.903) (32.380) (23.524) (28.583) 

Equip. ,Struct. 60.984 60.984 38.437 38.437 38.437 38.437 

(18.571) (18.571) (5.385) (5.385) (5.385) (5.385) 
-33- i 

Table 2. Chase Equations, Equipment and Structuree 

9 

E = bOE + blE (cd + cnd), + I: a CRED, + bjE NOR, 

j=o 

A. With Autocorrelation Coefficient 

(1) 

Variable 

or 

Statistic 

Constant 

or Investment 

NOR 

CRED­

(cd+cnd) -

Uh 

SPPUT 

PUT/SP 

Autocor .Coef. 

R2 

S. E. Regression 

DW 

. n 

(2) (3) (4 1 (5) (6) (7) 

Regression Coefficients and Standard Errors Means and 

Equipment Structures Standard Deviations . 

1 ?

P P P P Equipment Structures 

-17.161 -21.548 31.720 38.712 62.486 36.068 

(4.897) (2.602) (10.578) (10.173) (17.822) (6. OH?) 

1.290 1.153 - - 45.680 

(.116) (,191) - - (8.908) 

(.433) (.403) - - (.6868) 

.lo14 .0826 .0549 .0427 339.715 324.1 

(.0155) (.0221) (. 0268) (. 0217) (64.696) (71.0) 

-61.381 -30.277 -85.584 -66.539 .225 a .156 

(19.661) (13.953) (39.524) (29.568) (.020) (.039>b 

- - - - (. 336) (. 310) (1.273) 

-

-.912 -.572 - - -.0940 

-.407 -.483 5.318 

b -35.546 -54.083 .2697 

(21.612) (21.094) (.0529) 

- .0775 ,1451 .1461 77.102 - (.0525) (.0327) (.0332) (21.944) 

-

- ,0711 - - 49.912 45.825 

(. 0278) - - (22.089) (22.208) 

- - - - - - (1.607) (.199) (. 183) 

.633 .552 ,823 .810 

.9965 .9970 .9875 .9875 

1.0752 1.0057 .7619 .7645 

2.023 2.045 2.045 2.035 

75 75 90 90 

-1.034 ,574 .572 
-34-

Table 2. Cham Iquatlons, Iqulpmmt and Structures 

(11 

Var lab1e 

or 

Statistic 

Constant 

NOR 

CRED­

(cdkad) -

UIL 

(P/W>­

SP, 

PUT 

PRAT/SP 

Autocor .Coef . 

R2 

S.E. Regression 

DW 

n 

-

E. Without Autocorrelation Coefficient 

(2) (3) (4 1 (5) Begression Coeff icients and Standard Errors 

Equipment 

I

P P 

-14.796 -20,889 

(.2 .54 2 ) US4901 

1.167 1.182 

(.0653) C.1311) 

il. 037 w.5343 

(.2658) (.-28351 

.1155 ,0827 

(.0089) (.0165) 

-67.690 -30.110 

(10.500) (9.506) 

- -

- -

- .0538 

(.0339) 

- -

- -

.9941 .9956 

1.4034 1.2305 

.7429 .8668 

76 76 

Structures 

P 

33.080 

C4.912) 

-

-

3.953 

(1.381) 

-45.071 

(19.505) 

-1.119 

(.1812) 

-32.790 

(9.753) 

,1527 

(.0212) 

-

-

.9689 

1.2125 

.4692 

91 

v P 

31.777 

(6.327) 

-

-

5.0U 

(1.605) 

-44.882 

(14.711) 

-1.033 

(.1767) 

-33.847 

(12.706) 

.1438 

(..0213) 

-2.880 

(1.833) 

-

.9703 

1.1924 

.4934 

91 

N.B. The "minus" subscript alone ("-"), here 8nd in rubsequent tables, 

indicates a general lag operator, of a somewhat varied but usually 

distributed form, as: 
-35-

Table 3. DRI Equations 

A. Equipment 

Variable or Regression Coefficients and Standard Errors Deviations 

Statistic P P, P/c, Y PI P', P/C,Y P P' 

Constant -14.537 -38.863 -15.983 -37.538 63.530 63.530 

or E (4.130) (10.365) (5.891) (12.940) (20.220) (20.220) 

PYIC (2bj) .0135 - ,0084 - 3336.7 4186.5 

(.0038) ( .0040) (952.5) (1065.9) 

( p/dY (Zb - ,0056 - ,0035 3293.9 4165.3 

jP (. 0037) (. 0033) - (245.4) (223.3) 

Y (3) (Tbjy) - ,0213 - .0180 3293.9 4165.4 

( .0091) (.0066) (767.1) (970.1) 

DS (Zd -48.228 -25.248 -38.789 -14.162 .2154 .2154 

j (16.473) (14.876) (18.478) (14.985) (.0917) (.0917) 

KE -.1281 -,0851 -,1337 L .Q784 329.,3 329,3 -1 (. 0698) (. 0564) (.0798) (..0555) (91.3) (91.3) 

KE * UTP .2938 .1503 .3^99 .1231 273.3 273.3 -1 (. 0909) (. 0794) (.1153) (.0857) (75.0) (75.0) 

Y' - Y C.1019 -.0959 -.1148 -.1014 -60.0 -60.0 

(.0203) (. 0192) (. 0211) (. 0180) (22.6) (22.6) 

VNWAR 3.120 3.164 2.752 .0930 .0930 

(. 888) (. 917) (.8861 (.2922) (.2922) 

Autocor. Coef . .881 ,748 .911 .720 

R2 ,997 ,997 .997 ,997 

S .E. Regress ion 1.2001 1.1738 1.2447 1.1833 

DW 1.735 1.735 1.647 1.698 

n 85 85 85 85 
-oo26 

-36-

Table 3. DRI Equations 

B. Structures 

Sib 

L 

Variable Regression Coefticients and Standard Errors Standard Deviations 

or Statistic P P, p/c,Y P' p.' ,p/c,Y 

Constant -.255 -29.488 -6.074 -31.229 

or S (7.128) (20.705) (12.378) (30.697) 

- .0022 PY/C (cbj) (. 0017) (.0017) 

.004 5 - .0029 

(.0023) (.0021) 

.0065 - .0027 

(. 0049) (.0031) 

DS (Tdj) -45.927 -49.413 -46.623 -38.321 

(11.745) (14.796) (12.035) (14.826) 

Ys-l* DTP .1308 .0948 .0899 .0771 

(.0610) (. 0712) (. 0862) (. 0932) 

-.0277 -.0349 .0125 .0108 

(. 0490) (. 0560) (. 0698) (. 0801) 

Autocor. Coef. ,871 .873 .882 ,880 

R2 ,979 .979 .978 ,979 

S. E. Regression .9576 -9575 ,9589 .9696 

DW 1.917 2.021 1.873 1.951 

n 85 85 85 85 

P Pt 

37.788 37.788 

(6.354) (6.354) 

5276.7 7764.8 

(750.0) (831.4) 

5427.5 8095.4 

(784.1) (1544.9) 

5427.5 8095.4 

(1264.0) (1885.3) 

.2154 (I 2154 

(.0917) (.0917) 

352.0 352.C 

(78.8) (78.8) 

424.0 424.0 

(94.8) (94.8) 
-37-

Table 4. Michigan Equations, Equipment (Production, Agriculture and Other) 

and Structures 

(1) (2) (3) (41 (5) (6) (7) (8) (9) 

Variable 

or Statistic EX, c 

Regression Coefficients and Standard Errors 

EX, c' FA, c EA, c' EO, c EO, c' S,c S,c' 

Constant 2.132 2.938 -.359 -.084 -2.132 -4.217 1.720 .635 

(.759) (.984) (.239) (. 255) (4.202) (4.867) (. 058) (1.065) 

.049 ,054 ,0143 ,0179 - - - (.010) (.011) (.0055) (.0055) 

Y-1-Y-3 - - - - - - .0250 .0245 

(.0052) ( .OOS2) 

Y- - - ,00103 ,00078 .0106 .0120 .0063 ,0061 

(. 00046) (. 00045) (. 0053) (. 0055) (.0030) (. 003:) 

(c/w>- -4.866 - -3.775 - -9 492 - -32.300 - (1.227) (2.329) (3.485) (13.211) 

-

c 1(q/w)- - -2.771 - -12.908 - -12.634 - -15.15s 

(2.044) (4.341) (5.073) (19.27 3) 

-

(9.018) (27.963) (13.588) (19.65L) 

Pf - p,f - - 1.666 

(.454) 

1.316 

(.459) 

- - - -

' vi* - 1.121 1.101 - - (.153) (.155) 

~AsmIKE - - - - .665 .679 - -

(q/w>- c '- - -16.279 - 64 ..669 -5 1,725 - -50.077 

(6 203) (.204) - E-1 .762 .755 .818 ,807 .732 .715 - (.049) (. 049) (.067) ( .065) (. 073) (.075) 

s-l ,046 .024 - - .121 .161 .882 .862

(.023) (.028) (.053) (.070) (.052) ( .054> 
-38-

Table 4. (continued) 

(3)

Variable Regression Coefficients and Standard Errors 

or Statistic Ex, C EX,C' EA,C EA,C' EO, c E0,c' s,c S,C' 

R2 .981 .982 .965 .968 .993 .993 .987 .987 

S. E. Regresion .4100 ,4079 .2158 .2073 1.0897 1.0921 .8049 ,8025 

DW 1.483 1.532 1.865 1.960 1.714 1.699 1.995 1.986 

n 66 66 66 66 68 68 87 87 

Mean and St. 14.922 14.922 4.161 4.161 43.509 43.509 35.928 35.928 

Dev. of Dep. (2.897) (2.897) (1.113)'(1.113) (12.570) (12.570) (6.799) (6.799) 

Var . 
Table 5. MPS Equations -39-

A. Orders for Equipment 

(11 (2) (3) (4) (5)

Regression Coefficients and Standard Errors 

Variable P p, with P' p ' , with 

or Statistic constant term constant tem 

Constant - -7.457 - -20.471 

(:I U AYl-j'(LbjAy) 25.059 

(7.766) 

47.768 

(12.939) 

77.285 

(8.442) 

152.732 

(25.080) 

(f)' Y1,j (fbjy) 1.7350 

(.0598) 

2,9832 

(. 1615) 

2.3545 

(. 0721) 

6.6801 

(.3106) 

Dk (Edjk) -26.675 -25.341 -21.129 -19.180 

74.672 69.642 110.06 78.250 

or ORE (2.260) (2.984) 

OE 1.03 .70 .71 .19 

Autocor .Coef . 

R2 .957 .958 .927 .948 

S.E. Regr ession 4.6619 4.6072 6.0734 5.1411 

PW 1.54 1.63 1.07 1.47 

n 83 83 83 83 

u by Direct .164 .143 .055 -.023 

E Estimation 

Means and Standard Deviations 

, .2515 .1616 .is86 .0810 

Ayl-j (.3853) (.2498) (.2667) (.1306) 

30.420 19.778 20.036 10.195 

yl-j (9.049) (5.333) (5.700) (2.378) 

Dk .0361 .0361 .0361 .0361 

DP .0723 .0723 .0723 ,0723 

ORE 58.105 58.105 58.105 S8.105 

(20.4 06) (20.406) (20.406) (20.406) 
-40-

Table 5. WPS Equations 

B, Structures 

17 / \Os 

Regression Coefficients and Standard Errors 

Variable P p, with P' p ' , with 

or Statistic constant term constant term 

Constant - -4.676 

(4.516) 

-

- - 15.661 

(4.911) 

(P/C)% Y (zb ) 10.002 8.234 10.650 8.357 

-j jy (1.839) (1.600) (2.174) (1.224) 

Ks-1 -.1778 

(.0482) 

-.1453 

(.0409) 

-.1683 

(.0517) 

-.1142 

(.0265) 

.22 .29 .16 .27 

Autocor. Coef . .8324 .8013 .8792 ,7683 

R2 .980 .980 .980 .981 

S .E. Regression .8311 .8i45 .8431 .8311 

DW 2.08 2.03 2.13 1.99 

n 63 63 63 63 

Means and Standard Deviations 

11.6324 12.9682 10.5896 12.5575 

(1.7465) (1.8642) (1.5346) (1.5943) 

409.935 409.935 409.935 409.935 

(76.657) (76.657) (76.657) (76.657) 

S 38.247 38.247 38.247 38.247 

(5.871) (5.871) (5.871) (5.871) 
-4 1-

Table 6. Uharton Equations, Total Investment by Sector 1 

a (E+SIi - bo,i + bl,1 (E+Sli1 + b2,i (E+S)i 2 

+ b3,i Yi + b4,i K-l,i 

Variable 

or 

StatistIC 

Constant 

Ki' 4 ' -j ,i 

Autocor. Coef. 

R2 

S.E. Regression 

Dw 

(2) (3) (4) (5) (6) 

Selected Regression Coefficients and Standard Errors 

i = Manufacturing, Durables 

0 P' 

(E+Sla (E+S) (E+S) (E+S) (E+S) 

-.1633 -4.4899 -24.807 -3.1106 -9.1792 

*( ,2592) (2.079) (6.125) (1.208) (6.631) 

.6371 - - - - ( ,1083) - - - -

.2727 - - (.0981) 

.5797 

(.08Sl) - .6286 (.0843) -

,0231 .0897 .1578 .0821 ,1230 

( .0070) ( ,0198) (.0119) (.0193) (.0159) 

- ,0202 -.0354 -

- -.0381 -

- (.0052) (.0128) (.0110) 

- 20.168 211.024 12.073 88.115 - (20.531) (58.040) (12.635) (70.572) 

- - - - ,842 

,988 .988 .979 .9a9 a 974 

,4385 .4429 ,6003 ,4298 .6666 

1.263 1.890 2.240 2.122 2.137 
-42-

Table 7. Tax Scenarios: Direct Effects on 1977-IV Investment of Tax Credit, 

Accelerated Depreciation since 1953-IV, and Corporate Tax Rate Less 

than 52 Percent 

Investment Equations Specified in Models, 

Equipment, Predicted, 1977-IV 

Predicted difference due to: 

ITC (k) = 0 

No Accelerated 

Deprec iat ion* 

CPT(u) = .52 

Structures, Predicted, 1977-IV 

Predicted difference due to 

No Accelerated 

Depreciation* 

CPT(u) = .52 

BEA Chase 

92.103 92.125. 

-7.339 -4.281 

-6.346 -5.227 

-2.539 -1.359 

40.255 40.332 

-.473 -1.060 

-.810 -.539 

Billions of Dollars 

DRI Michigan MPS 

92.149 93.903 83.720 

-12.876 -1.406 -10.877 

-16.483 -5.830 -14.745 

-5.720 +.940 -1.753 

43.509 I 42.749 . 

-5.068 I -.729 

-4.194 # -.621 

*Straight-line depreciation, 1953-IV lives. In the Michigan model tax 

depreciation rates held at values in 1953-IV. In the BEA and Chase models, 

the tax lives for structures did not vary from 1953 to the present. In our 

simulation we increased them jn proportion to the increases that occured 

in the DRI and MPS mdels. 

#In the Michigan model, no tax parameters enter the structures equation. 
-4 3-

Table 8. BEA Shulationo, Equipment and Structures 

Change in Investment, 1977-IV 

Tax Parameterr Equation 

Equipment Structures 

Putty-Putty Putty-Clay 

P P' P P' P P' 

Billions of 1972 Dollars 

All always at 1953-IV -15.639 -13.992 -.a10 -.581 ' -1.035 -.747 

levels, SL Dep. 

Changes in 1973-1: 

It'et = 2ket; kit-lOX +9.032 +7.955 +1.399 +1.132 +1.927 +1.485 

u' = .gut +2.752 +2.421 +.a86 M.624 +1.135 M.806 

t 

L; = .5Lt +9.025 +7.931 +1.912 +1'.518 +2.576 +1.981 

As Percent of Baseline 

All always at 

1953-N levels, 

SL Dep. -16.98 -15.08 -2.01 -1.36 -2.56 -1.79 

Changes in 1973-1: - 2ket' kit-lO% +9.81 +8.57 +3.48 +2.64 +4,77 +3.56 

ut - .gut t +2.99 +2.61 +2.20 +1.46 +2.81 +ID93 

L; - .5Lt +9.80 +8.54 +4.75 +3.55 +6.38 +4.74 
-44-

Table 9. Chase Simulations, Equipment and Structures 

Change in Investment, 1977-IV 

A. From Equations With Autocorrelation Coeffi ients 

(1) 

Tax Parameters 

All always at 

1953-IV levels, SL Dep. 

Changes in 1973-1: 

= 2ket; kit=lOX 

u 't = .gut 

L; = .5Lt 

All always at 

1953-I?? levels, SL Dep. 

Changes in 1973-1: 

k:t = 2ket; kkt= 10% 

u' = .9u 

t t 

L' = .5Lt 

t 

(2) (3) (41 (5) 

Equa t ion 

Equipment Struc tures 

Billions of 1972 Dollars 

-11.736 -8.094 -2.547 -1.962 

i-4.218 +2.804 +2.584 +l.990 

+1.806 +1.480 +le037 +e799 

+3.192 

-12.80 

i-4.60 

+1.97 

+3.48 

+2.211 +2.380 +l.833 

As Percent of Baseline 

-8.74 -6.29 -4.86 

+3.03 +6.38 i-4.93 

+1.60 +2.56 +l.98 

+2.39 +5.88 +4.54 
-4 5-

Table 9. Chase Slmulations, Equipment and Structures 

Change in Iwoitment, 1977-N 

B. From Equations Without Autocorrelation Coefficients 

(1) 

Tax Parameters Equat Ions 

Equipment Structures 

P P' P P' 

Billions of 1972 Dollars 

All always at 

1953-IV levels, SL Dep. -11.768 -8.213 -1.341 -1.323 

Changes in 1973-1: 

k:t = 2ket; kAt = 10% +4.281 +2.840 +1.361 +1.342 

u't = .gut +l.699 +l.513 + .546 + .539 

L; = .5Lt +3.197 +2.244 +l.253 +l.236 

As Percent of Baseline 

All always at 

1953-IV levels, SL Dep. -12.77 -8.86 -3.33 t3.29 

Changes in 1973-1: 

kHt = 2ket ; k'st = 10% +4.65 +3.07 +3.37 +3.34 

u' - .9u t t +l.84 +l.63 +l.35 +l.34 

L; = .5Lt +3.47 +2.42 +3.11 +3.08 
-46-

Table 10. DRI Simulations 

Change in Investment, 1977-IV 

All always at 

1953-IV levels, 

Changes in 1973-1: 

k:t = 2ket 

u't = .gut 

L; - .5Lt 

All always at 

1953-IV levels, 

Changes in 1973-1: 

k'et = 2ket 

u' - .9u

t t 

L' = .5Lt 

t 

A. Equipment 

Billions of 

-36- 769 -81 518 

+U.075 +3.719 

+1.585 +. 509 

+8.010 +2.395 

1972 Dollars 

-26.013 

a1.333 

,283 

+5.208 

-4.475 

+2807 

-.074 

+l.265 

As Percent of Baseline 

-39.90 -9.26 -28.38 -4.86 

t14.19 4.04 +12.36 +3.05 

t1.72 + .55 -.31 - .08 

+8.69 +2.60 + 5.68 +1.37 
-47-

Table 10, DRI Simulations 

Change in Invcrtment, 1977-IV 

B. Structures 

Changes in 1973-1: 

kit 0 8.1% 

u' = .gut t 

L; - .5Lt 

All always at 

1953-IV levels,SL Dep 

Changes in 1973-1: 

kHt - 8.1% 

u' - .gut t 

L; = .5Lt 

Bllllonr of 1972 Dollars 

+2.754 +3.080 +3.396 4-3.164 

+1.107 +1.132 +. 386 +. 248 

+3.335 +3.549 +3.333 +2.923 

As Percent of Baseline 

-27.53 -23.74 -22.87 -19.76 

+6.33 +7.09 +7.74 +7.21 

+2.54 +2.61 +. 88 +. 57 

+7.67 +8.17 +7.60 +6.66 
-48-

Table 11. Michigan Simulations, Equipment (Production, Agriculture and 

Other) and Structures 

Change in Investment, 1977-IV 

(1) (2) (3) (4) (5) (6) (7) ($1 (9) 

Tax Parameters Equations 

Equipment Strue tures 

M,c M,c' EA,c EA,c' EO,c E0,c' S,c S,c' 

Billions of 1972,Dollars 

All always at 

1953-IV levels,

SL Dep. -2.870 -1.142 -.053 +.239 -4.501 -6.900 0 0 

Changes in 1973-1: 

+.523 +.218 +.029 +.078 +.839 +1.298 0 0 

kLt 2ket 

u' -.9u -.363 -.145 -.008 +.022 -.579 -.890 0 0 

t t 

TD; = 2TDt +2.890 +1.150 +.lo3 -.043 +4.570 +7.034 0 0 . 

As Percent of Baseline 

All always at 

1953-IV levels,

SL Dep. -15.24 -6.18 -1.01 +5.00 -6.45 -9.84 0 0 

k' - 2ket Changes In 1973-1: +2.78 +1.18 +.55 +1.62 +1.20 +1.85 0 0 

et 

u' - .9u -1.93 -.79 -.15 + .45 -.83 -1.27 0 0 

t t 

TD; = 2TDt +15.34 +6.22 +1.95 - .91 .+6.55 +10.03 0 0 
Table 12. MPS Simulations 

Change in InvertPcnt, 1977-IV 

A. Equipment 

(1)

Tax Parameters 

(2) (3) (4) (5)

Equat ions 

P P with p' p ', with 

Constant Constant 

Term Term 

Billions of 1972 Dollars 

All always at 

1953-IV levels, SL Dep, -25.383 -20.273 -19.365 -6.621 

Changes in 1973-1:

k' - et 2ket +12.656 M.304 +8.133 +2.707 

u't = .gut +l.605 +l. 190 +l.117 +. 372 

L; = .5Lt +7.790 +5.730 +4.967 +l.658 

As Percent of Baseline 

All always at 

1953-IV levels, SL Dep. -30.32 -23.26 -19.73 -6.81 

Changes in 1973-1: 

k;t = 2ket +15.12 +lo. 68 +8.28 +2.78 

u' = .9u +1.92 +1.37 +l.14 +. 38 t t 

L; = .5Lt +9.30 +6.57 +5.06 +1.71 
-50-

Table 12. KPS Simulations 

Cbaage in Investment, 1977-IV 

E. Structures 

(11 

Tax Parameters 

All always at 

1953-IV, SL Dep. 

Channes in 1973-1: 

kit - 8.5% 

u't =.gut 

L; = .5Lt 

All always at 

1953-IV levels, 

Equations 

P P, with P' p ', with 

Constant Constant 

Term term 

Billions of 1972 Dollars 

-1.449 -1.928 -1.141 -2.145 

+2.420 +3.094 +l.824 +3.171 

+. 957 +l.222 +. 716 +l.240 

+2.452 +3.137 +1.840 +3.197 

As Percent of Baseline 

SL Dep. -3.39 -4.61 -2.46 -4.60 

Changes in 1973-1: 

kAt = 8.5% 

u' - .gut t 

L; - .5Lt 

+S. 66 +7.40 +3.93 +6.80 

+2.24 +2.92 . +1.54 +2.66 

+5.74 +7.50 +3.96 +6.86 
-51-

Table 13. Wharton Simulations, Equipment and Structures Investment 

Change in Investment , 1977- IV 

(1) 

Tax Parameters 

Changes in 1973-1: 

= 2ket; kit = 10% 

u' - .9u

t t 

L; - .5Lt 

Changes in 1973-1: kA - 2ket; kit - 10% 

u'

t = .gut 

L; - .5Lt 

F 

(2) (3) (4) (5) 

Equation 

Equipment Structures 

P P' P P' 

Billions of 1972 Dollars 

+5.100 +3.200 +2.400 +1,500 

+. 500 +. 200 +.300 +.lo0 

As Percent of Baseline 

+4.88 +2.94 +4.96 +2.98 

+. 48 +. 18 +.62 +. 20 

+2.01 +1.01 +2.07 +. 99 
-52-

1972 Dollore 

(1) (2) (3) (4 1 (5)

Hodel Equipment Structures 

Original Revised Original Revised 

Table 14. Comparison of Simulations, Change in Investment, 1977-IV, 

Resulting from 1973-1 Doubling of Investment Tax Credit 

for Equipment end Institution of 10 Percent Credit for 

Structures, Original 8nd Rwised Hodel Specifications, 

Billions of 

BEA 9.032 

Chase 4.281 

DRI (ki = 8.1%) 13.075 

Michigan 1.391 

KPS (ki - 8.5%) 12.656 

Wharton 5.100 

Hean 7.589 

Actual 

Investment 91.507 

Mean Difference 

as Percent 

of Actual 

Investment 8.29% 

7.955 1*399 1.132 

2.840 1.361 1.342 

2.807 2 754 3.164 

1.594 0 0 

2.707 2.420 3.171 

3.200 2.400 1.500 

3.513 1.722 1.718 

91,507 40.149 40.149 

3.84% 4.29% 4.28% 

(6) (7 1 

Total 

Original Revised 

10.431 9.087 

5.642 4.182 

15.829 5.971 

1.391 1.594 

15.076 5.878 

7.500 4.7CO 

9.312 5.235 

131.656 131.656 

7.07% 3.98% 
-53-

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Bischoff, C.W. 1971. "Business Investment in the 1970s: A CompnrIson of Modc:I!~." 

Brookings Papers on Economic Activity,l971-1: 13-63. 

Clark, P.K. 1979. "Investment in the 1970s: Theory, Performance and Prediction." 

Brookings Papers on Economic Activity, 1979-1: 73-124. 

Coen, R. M. 1968. "Effects of Tax Policy on Investment in Manufacturing." 

American Economic Review 58 (May): 200-11. 

. 1969. "Tax Policy and Investment Behavior: Comment." American 

Economic Review 59 (June): 370-79. 

Eisner, R. 1969a. "Investment and the Frustrations of Econometricians." 

American Economic Review 59 (May): 50-64. 

. 1969b. "Tax Policy and Investment Behavior: Comment .'I Amer!j:il)r 

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the National Bureau of Economic Research. 

and P. J. Lawler. 1975. "Tax Policy and Investment: An Analysis of 

Survey Responses." American Economi Review 65 (March) : 

206-12. 

and PI. I. Nadiri. 1968. "On Investment Behavior and Neoclassical 

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369-82. 

. 1970. "Once More on that 'Neoclassical Theory 

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and R. H. Strotz. 1963. "Determinants of Business Investment." 

in Commission on Money and Credit, Impacts of Monetary 

Policy: 60-337. Englewood Cliffs, N.J.: Prentice-Hall. 

From, G. ed. 1971. Tax Incentives and Capital Spending. Washington, D.C.: 

Brookings, including papers by R.E. Hall and D.W. Jorgenson, 

C.W. Bischoff, R. M. Coen, L.R. Klein and P. Taubman, and 

discussion by F. M. Fisher and A.C. Harberger. 

Green, R.J. 1980. "Investment Determinants and Tax Factors in Major 

Macroeconometric Models." In G.M. von Furstenberg, The 

Government and Capital Formation, pp. 337-381. Cambridge: 

Ballinger. 

Hall, R.E. and D.W. Jorgenson. 1967. "Tax Policy and Investment Behavior." 

American Economic Review 57 (June):391-414. 
-54-

Hendershott, P.H. and S-C Hu. 1980. "The Relative Impactsof Various Proposals 

to Stimulate Business Investment." In G.M. von Furstenberg, 

The Government and Capital Formation, pp.321-336. Cambridge: 

Ballinger. 

Hirsch, A.A., S.H. Hymans and H.T. Shapiro. 1978. "Econometric Review of 

Alternative Fiscal and Monetary Policies, 1971-75." 

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Joint Economic Committee. 1978. Economic Stabilization Policies: The 

Historical Record, 1962-76, Including "Data Resources, Inc. - Fiscal Policy: The Scoreboard Between 1962 and 1976," and 

"Wharton Econometric Forecasting Associates, Inc. - A Study 

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and Alan Greenspan. 

Jorgenson, D. W. 1963. "Capital Theory and Investment Behavior.'' 

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August 4, from the Office of Management and Budget, on 

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-5 5-

GLOSSARY 

-CCCA Capital Consumption Adjustment, Corporate 

CTR Federal Corporate Tax Receipts 

D Tax Depreciation Allowances, Current Law 

DA Tax Depreciation Allowances, 10-5-3 

DB Tax Depreciation Allowances, OTA Alternative 

E Investment Expenditures on Producers' Durable Equipment, Constant Dollars 

E$ Investment Expenditures on Producers' Durable Equipment, Current Dollars 

I.$ Producers' Investment Expenditures for Sector j , Current Dollars 

J 

k Rate of Investment Tax Credit, Equipment e 

k 

S 

Rate of Investment Tax Credit, Structures 

Effective Rate of Investment Tax Credit for Sector j 

Le Tax Life of Equipment 

Tax Life of Structures

S 

-PCCA Capital Consumption Adjustment, Proprietors 

PTR Federal Personal Tax Receipts 

S Corporate Share of Nonresidential Business Capital Consumption Allowances 

S Investment Expenditures on Producers' Structures, Constant Dollars 

S$ Investment Expenditures on Producers' Structures, Current Dollars 

TD Tax Depreciation for Sector j j 

U Rate of Federal Business Income Taxation 

L