Norman B. Ture

English

Research Papers in Economics

This PDF is a selection from an out-of-print volume from the National
Bureau of Economic Research
Volume Title: Accelerated Depreciation in the United States, 1954-60
Volume Author/Editor: Norman B. Ture
Volume Publisher: UMI
Volume ISBN: 0-870-14457-X
Volume URL: http://www.nber.org/books/ture67-1
Publication Date: 1967
Chapter Title: Appendix E
Chapter Author: Norman B. Ture
Chapter URL: http://www.nber.org/chapters/c0933
Chapter pages in book: (p. 227 - 234)APPENDIX EEFFECT OF ACCELERATED
DEPRECiATiON ON CORPORATIONS'
CAPiTAL OUTLAYS IN 1959
In estimating the additional capital outlays in 1959 attributable to the
use of accelerated depreciation, we have represented the demand for
capital goods and the supply of investable funds in the corporate sector
by linear functions of the form:
=ad+ baQd (demand), and
Q, =a8+ b8r8 (supply).'
These functions are presumed to include the effects of the use of ac-
celerated depreciation: in the demand function, this effect is represented
as a higher rate of return with respect to any given amount of capital
outlays than would be obtained by using the straight-line method; and
in the supply function, the effect is represented as an increase in the
amount of investable funds available at any given rate Of interest.2
In equilibrium, of course,
r8 =Td andQ8 =Qt='' t
whichis the estimated volume of corporate expenditures for depreciable
facilities in 1959. According to a preliminary estimate by the Office of
Business Economics, these outlays amounted to $33.8 billion.
Had accelerated depreciation not been available, the functions would
have been
=a—X+ bQ' (demand), and
Q'8 =a8—Y+ b8r'8 (supply),
1Wewish to emphasize the obvious fact that these equations do not imply
specific theories of the demand for capital goods nor of the supply of saving.
They are consistent, however, with the reasoning advanced to explain the effects
of accelerated depreciation on investment, as discussed in Chapter 1.
2SeeChapter 1 above for a discussion of these effects.230ACCELERATED DEPRECIATION, 1954-60
where X and Y are the shifts in the respective functions due to use of
accelerated depreciation. In equilibrium, of course, r'8 ='1d and
, ,a8—Y+b8(ad—X)
Q8 = Q = i 1.8. I —
whichis the estimated volume of capital outlays without accelerated
depreciation. The difference between this amount and observed outlays
for the year is our estimate of the additional outlays attributable to the
use of the declining-balance and SYD depreciation methods. This dif-
Y+b8X ference may be represented as Q— Q 8. I —
Determinationof Q— Q'inthe above equation quite obviously de-
pends on the values of the shift parameters, X and Y, as well as on the
slopes b8 and bd of the supply and demand functions, respectively. We
have estimated the shift in the supply function as Y =$1.265 billion,
i.e., the reduction in tax liabilities, hence the increase in cash flow, for
corporations in 1959 from the use of accelerated depreciation methods.
In estimating X, the shift in the demand function, we referred to Table
2, showing percentage point increases in rates of return realized by
shifting from straight-line to accelerated depreciation at various service
lives and at various rates of return under straight-line depreciation. We
assumed an average service life of ten years for corporate depreciable
property acquisitions in 1959. If we assume a 10 per cent after-tax rate
of return under straight-line for such property, Table 2 shows a 1.1
percentage point increase in rate of return in shifting from straight-line
to declining-balance depreciation and a 1.4 percentage point increase
in shifting to SYD. The table also shows noticeably lower percentage
point increases with respect to ten-year property if the straight-line rate
of return were 5 per cent and noticeably higher increases if the corre-
sponding rater of return were 15 per cent. Properly, therefore, the value
of X should change with the assumed straight-line rate of return. In
the interests of ease of computation, however, we assumed an average
increase of 1.2 percentage points in the rate of return on the property
added to accelerated method accounts in 1959. Little violence is done
by this simplifying assumption, since we are concerned only with a
small section of the demand schedule, within which the range of varia-
tion in r is likely to be small. We estimate that roughly two-thirds of
1959's property additions were added to accelerated method accountsAPPENDIX E 231
and one-third to straight-line. Accordingly, with respect to the function
representing aggregate corporate demand for depreciable facilities in
1959, we have assumed the shift parameter X0.008.
Determination of Q— Q'alsorequires that we find the slopes of the
respective functions, i.e., b8 and bd, which in turn depend on the as-
sumed values of randthe assumed elasticities for the respective func-
tions, given the actual Qobservedin 1959. By experiment, we deter-
mined that given = $33.81billion, we could vary the assumed
value of rovera wide range without significant effect on the solution
of the equation incorporating the shift parameters. With a given value
for Q,differencesin r,ofcourse, result in differences in the values of
b in the respective functions, for any assumed elasticity, since the elas-
ticities of the functions may be expressed as
rd = ----— (demand),and
b8r8 =-— (supply).
In other words, specification of the actual value of r makes relatively
little difference for the outcome, given, Q1959andthe assumed elasticities
of the functions.
This is evident in Table E-1. With a demand elasticity of —.5,for ex-
ample, the computed value of Q— Q'(theestimated volume of addi-
tional capital outlays due to accelerated depreciation) varies narrowly
over a wide range of assumed values of r, for any given elasticity of sup-
ply. With a demand elasticity of —1.0,a narrow range of estimate of
Q— Q'isalso observable. The spread between computed values of
Q— Q'fromone r to another tends to increase as the demand and
supply elasticities increase.
The more significant variance in Q— Q' appearsin respect to differ-
ences in the assumed elasticities of the demand and supply functions,
with any given r. With a low elasticity of demand, the difference in
Q— Q'isquite small from one supply elasticity to another. With
=—2.5,however, an appreciable difference appears.
Accordingly, we concluded that precise determination of r would not
materially increase the reliability of our estimates. We have, therefore,
based these estimates on the assumption that the $33.81 billion of
capital outlays in 1959 involved an after-tax rate of return of 10.0232ACCELERATED DEPRECIATION, 1954-60
per cent. As shown in Table E-1, depending on the assumed elasticities
of the supply and demand functions, these capital outlays were between
$1.3 billion and $5.7 billion more than would have been forthcoming
in the absence of accelerated depreciation.
The shift in the demand function resulting from use of accelerated
depreciation acounts for a substantial part of the estimated increase
in outlays, as seen in Table E-2. Only when the elasticity of supply is
very low, e.g., 0.5, is the increase in outlays due to the shift in the sup-
ply of investable funds of about the same magnitude as that resulting
from the demand shift. Moreover, the greater the elasticity of supply,
the greater is the proportion of the total estimated increase attributable
to the shift in the demand function.APPENDIX E 233
TABLE E-1
Estimated Additional Corporate Outlays for Depreciable Facilities,
1959, Attributable to the Use of Accelerated Depreciation, at
Selected Rates of Return (r) and Elasticities
(billion dollars)
Elasticity
of Supply
Elasticity of Demand
—0.5 —1.0 —2.5
. r.05
0.5 1.43 1.90 2.38
1.6 1.48 2.22 3.17
2.5 1.54 2.63 4.61
5.0 1.56 2.86 5.72
10.0 1.57 3.00 6.61
r = .10
0.5 1.31 1.75 2.17
1.0 • 1.32 1.99 2.84 •
2.5 1.34 2.29 4.01
5.0 1.34 2.47 4.93
10.0 1.35 2.57 5.66
0.5 1.24
r=.15
1.65 2.06
1.0 1.23 1.84 2.63
2.5 1.22 •2.08 3.65
5.0 1.21 2.20 4.44
10.0 1.21 2.31 5.08234ACCELERATED DEPRECIATiON, 1954-60
TABLEE-2
Estimated Additional Corporate Outlays forDepreciableFacilities,
1959, Attributable totheShift in the Demand and Supply
Functions, at Selected F2lasticitiesa
(billion dollars)
Elasticity
of Supply
Elasticity of Demand
—0.5 —1.0 —2.5
Supply Shift Only
0.5 0.63 0.84 1.05
1.0 0.42 0.63 0.90
2.5 0.21 0.36 0.63
5.0 • 0.12 0.21 0.42
10.0 0.06 0.12 0.25
Demand Shift Only
0.5 0.68 0.90 1.13
1.0 0.90 1.35 1.93
2.5 1.13 1.93 3.38
5.0 1.23 2.25 4.51
10.0 1.29 2.46 5.41
ar = .10.

Accelerated Depreciation in the United States, 1954-60

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