On the Feasibility of Equating Tax to 

Economic Depreciation 

Charles R. Hulten 

Frank C. Wykoff 

Comment 

Robert M. Coen 
On the Feasibility of Equating Tax to 

Economic Depreciation 

Charles R. Hulten 

Frank C. Wykoff 

In Blueprints for Basic Tax Reform (January 1977) the Treasury proposed, as part of its income-based tax plan, that tax depreciation allowances be set approximately equal t,o real economic 

depreciation of the capital stock. For some time now a number of 

well-known economists, e.g., Samuelson (1964), Eisner (1973), 

Coen (1975), and Break (1974), but by no means all, have been 

recommending that tax depreciation be brought into line with real 

economic depreciation. 1 Because economic depreciation is difficult 

to measure, economists, in order to aid in the assessment of such a 

proposal, should consider its feasibility and implementation, as 

well as its consequences for equity, efficiency, stabilization, and 

growth. 

Economists have, of course, devoted considerable energy to 

studying the consequences of the corporate income tax system, 

including the effects of changes in parameters such as deductions 

for depreciation. Break (1914) has analyzed recent progress in 

this field and identified the major unresolved issues. Considerable 

Professional disagreement as to the precise effects of changing 

deductions remains. Nevertheless, judging from the Treasury's 

Blueprints, realignment of tax deductions for depreciation accord1 For an alternative point of view, see Smith (1963). 

CHARLES R. HULTEN is assistant professor of economics at The Johns 

Hopkins University, and FRANK C. WYKOFF is associate professor of 

economics at Pomona College and the Claremont Graduate School. 

(91) 
~--~~~ - -- - - - - - - --- ~~-~-~ 

92 COMPENDIUM OF TAX RESEARCH 

ing to the economic depreciation norm seems to be a serious possibility. Therefore, we shall take the proposal as given and shall 

address ourselves to two pressing questions we believe have received inadequate attention. First, is the proposal feasible? Specifically, is it possible to measure, with sufficient precision, the 

patterns and rates of economic depreciation to which tax deductions are to conform so that the propooal can be implemented? 

Second, what types of patterns should be adopted so that tax 

deductions approximate economic patterns-straight line, decelerated, or accelerated? 

Many economists seem skeptical about the feasibility of measuring economic depreciation of many classes of assets. The belief 

that used-asset prices are not available because most assets are 

rarely marketed seems to be widespread. 2 Coen (1975), for example, argues: 

Economists have attempted to measure economic depreciation principally 

by examining relationships between market prices of certain types of 

new and used assets-farm tractors, autos, and pick-up trucks, for example, but the absence of active markets for many types of used industrial capital goods greatly limits opportunities for this type of analysis. 

(p.59) 

Discussion at the Department of the Treasury 1975 Conference on 

Tax Research revealed some doubt about the general applicability 

of depreciation studies based on vintage price data. 3 Shoven and 

Bulow ( 1975) also question the practicality of measuring 

depreciation. 

Undoubtedly many assets are rarely traded when used; however, 

we believe many are traded fairly often. Vigorous used-asset markets exist within and across numerous industries, between private 

and public institutions, and even between advanced and less 

developed countries. Recently, for example, the Office of Industrial 

Economics ( OIE) produced a business buildings survey covering 

2 The dependence of economic depreciation on tax depreciation is a closely 

related issue raised by Feldstein and Rothschild (1974) and by Hulten and 

Wykoff (1976). Any change in the tax code will, in general, change asset 

prices and thus change economic depreciation. This dependence suggests that, 

as a practical matter, the two types of depreciation must be brought into line 

by a sequence of tax code changes. The measurement of economic depreciation 

(the topic of this paper) would, in principle, be required at each policy 

iteration. 

:: See U.S. Department of the Treasury, Office of Tax Analysis, Conference 

on Tax Research 1975. 
EQUATING TAX TO ECONOMIC DEPRECIATION 93 

more than 15 classes of commercial and industrial structures and 

containing vintage asset prices.4 Furthermore, numerous equipment categories, in addition to vehicles, are traded in secondhand 

markets: machine to0ls, construction equipment, and office furniture and machinery. While this list is by no means exhaustive, it is 

sufficiently diverse to suggest that further studies along the lines 

of the OIE survey are possible. 5 

Given the availability of used-asset price data-both actual and 

potential-we believe that it is useful to investigate the problems 

involved in estimating economic depreciation from used-asset 

prices. In the next section of this paper we sketch briefly our 

general method for estimating depreciation patterns and rates and 

apply this method to four large classes of commercial and industrial structures : factories, office buildings, retail trade stores, and 

warehouses. This section summarizes research reported in more 

detail elsewhere. Although much remains to be done, we believe 

this approach is worth pursuing. It may be applied to either 

vintage acquisition or rental prices, and, while some assets are 

neither resold when used nor rented, many others are marketed 

one way or another. 

Our principal econometric results are (a) that economic depreciation of the structures studied is accelerated vis-a-vis straightline, and (b) that the rate of economic depreciation is about half 

that allowed under the tax code. The second result is not a major 

surprise. The first, however, may be. Although little actual empirical research has been done in this area, we have encountered 

considerable professional opinion that buildings depreciate as 

"one-hoss shays," i.e., no physical in-place deterioration, merely a 

decline in value due to the approach of retirement. The age-price 

curve of a "one-hoss-shay" asset would be concave, revealing a 

In 1975, commercial and industrial structures accounted for 40 percent 

of the purchases of new private nonresidential structures, and for 14 percent 

of all private nonresidential fixed investment. See tables 1.1, 5.4, and 5.6 of 

the U.S. National Income and Product Accounts, as reported in Survey of 

Current Business (July 1976). 

The Asset Depreciation Range information system must also be mentioned 

as a potentially invaluable source of data. As currently structured, the ADR 

vintage accounts are highly aggregated and are more suited to imputing retirement profiles than to providing data on used-asset values. If the ADR 

system is extended to cover all business taxpayers, as suggested in the 

Treasury's Blueprints for Basic Tax Reform (1977), and is appropriately 

modified, it could ultimately yield data suitable for estimating economic depreciation. 
94 COMPENDIUM OF TAX RESEARCH 

pattern decelerated vis-a-vis straight-line. 6 In their study of office 

buildings, Taubman and Rasche (1969) actually report such a 

concave function. In 1975, Coen reported that " ... structures in 

the majority of industries suffer no loss in productive capacity 

over their service lives (they resemble one-hoss shays)." However, in more recent work, Coen (1976) has found that structures 

appear to depreciate in a convex, or accelerated, pattern. 

Since our results run counter to the conventional wisdom, we 

illustrat-e in a later section the underlying data for the large class 

of office buildings and show that the age-price curve for this data 

is convex. We also analyze the office building class in greater detail 

than in our previous studies. Specifically, our earlier results were 

derived from pooled data on buildings that were purchased at 

different points in time. It is possible that our estimation procedures did not adequately isolate the process of aging from other 

processes associated with the passing of time (inflation, tax code 

changes, etc.) . In order to investigate this possibility, we break 

the office building data into a series of cross sections and analyze 

each cross section separately. The results for the separate cross 

sections are roughly consistent with the results of the pooled 

analysis, and this new evidence indicates that our treatment of the 

date of purchase with the pooled data doe.s not alter our conclusions. In a final section we compare our results with those obtained by Taubman and Rasche (1969) and Coen (1975; 1976). 

The implications of our analysis for tax reform may be briefly 

summarized. We are able to provide tentative conclusions about 

the rate and form of economic depreciation for commercial and 

industrial structures. Accelerated patterns, such as those currently 

allowed by the Federal Tax Code, are warranted ; however, the 

rates of depreciation, implied by the tax lives, appear to be too 

0 To see that an asset with a "one-boss-shay" efficiency pattern has a concave age-price curve, we note that the "one-boss-shay" maintains a constant 

level of efficiency until it is retired. Thus, under the perfect foresight model 

considered in this paper 

T 

Y(t)=f z=I r 

where Y ( t) is the asset's price, C is the (constant) rental price of a new 

dY - asset, and r is the (constant) rate of discount. Differentiating, -=-C e-• 11 - 11 

dt 

<0 (dY/dt is the slope of the age-price curve, which is everywhere negative). 

d2Y - Furthermore, -=-r C e-' 11'-'><0, implying that the age-price curve is 

dt2 

uniformly concave. 
EQUATING TAX TO ECONOMIC DEPRECIATION 95 

rapid. We note that these conclusions are tentative because they 

depend upon only one sample of vintage price data and because, as 

will be seen later, adequate data on asset retirement is not 

"1l.vail.flble. 

On the Theory and Measurement of Economic Depreciation 

Theoretical Framework 

We define economic depreciation as the fall in an asset's price as 

it ages. Following Hotelling (1925), Hall (1968), and Jorgenson 

(1974), we assume efficient and competitive capital markets in 

which, under perfect certainty, the acquisition price of an asset 

will equal the present discounted value of the future flow of aftertax user costs, inclusive of tax credits and depreciation allowances, 

up to retirement plus the present value of any retirement value of 

the asset. Departing from the Hotelling-Hall-Jorgenson model, 

we focus on the average price of an entire cohort, or vintage, of 

homogeneous assets rather than on one single asset. While each 

asset in the cohort is assumed to be identical while in place, each 

has a different, yet certain, retirement date. For purposes of estimating average cohort depreciation, the relevant price, or rental, 

is that of the average asset in the original cohort. For example, if 

all N new assets in a cohort were pooled to form a company in 

which N stock certificates were issued, then the average price 

Would be that of one certificate, and the average rental would be 

the average annual return on a share. 

When dealing with used assets, only the prices of survivors are 

usually available; yet to study the vintage performance of the 

original cohort one must study the average used price both of survivors and of retired assets. Under our assumptions, the average 

cohort used price can be shown to be equivalent to the weighted 

sum of the average price of survivors and that of nonsurvivors, 

where the weights are the probabilities of having survived and 

not survived, respectively. Assuming, as we do, that retired assets 

are worthless, calculation of the average cohort used price merely 

corresponds t.o premultiplying observed vintage prices by their 

Probability of having survived to that age. Some of these assumptions may be relaxed, but, in light of our data, it is pointless to 

relax them. 

Even though in this paper we deal with purchase prices, the fact 

that the same theoretical framework applies to the analysis of 
96 COMPENDIUM OF TAX RESEARCH 

rental prices must be emphasized. The relevant average cohort 

rental prices are simply the observed average used rentals premultiplied by their survival probability. The rental, under our 

assumptions, is equivalent to the sum of the rate of return plus 

depreciation minus revaluation, all calculated on the weighted 

average cohort used prices. Thus, this theory is perfectly general 

in the sense that it may be applied to structures or machinery, 

rental data or purchase data. 

Data on Commercial and Industrial Structures 

The preceding theoretical framework is used to estimate the 

economic depreciation of 16 classes of commercial and industrial 

structures from the vintage acquisition prices reported by owners 

to the Internal Revenue Service's Office of Industrial Economics.' 

The sample, consisting of 8,066 observations taken in 1972, contains reports by current owners of the original prices they paid, 

net of land, to acquire the buildings. About one-third of the buildings were used when purchased, so the acquisition prices per 

square foot can be indexed by age of :structure and date of purchase. In other words, the data can be regarded as a rectangular 

array, by age and date, of the average acquisition prices per square 

foot in each class of structures. 

We report here on our analysis of the four largest classes of 

structures: factories, office buildings, retail trade stores, and 

warehouses. Table 1 contains summary statiistics on these classes, 

illustrating the richness of the data. Each observation also pro7 The survey results are reported by the U.S. Department of the Treasury, 

Office of Industrial Economics (1975). In our research we used unweighted 

price data because the sampling weights employed by the Office of Industrial 

Economics were too variable and appeared to lead to the risk of overemphasizing individual observations. Details are explained in Hulten and Wykoff 

(1977). 

TABLE 1.-Summary statistics by asset class 

Number Bulletin 

of Num- F 

obser- her Price I sq.ft. Age(years) mean 

Class vations used Mean SD Mean SD life 

Large Classes 

Retail trade 1666 1013 7.31 7.89 20.50 24.22 67 

Offices 1654 889 12.20 9.80 16.68 23.84 67 

Warehouse 580 275 5.20 5.10 11.77 19.66 75 

Factory 526 282 5.60 5.92 15.84 22.14 80 
~:..:#"'"-~:~-~-.----• w- . ..... _,, _ _...- _. __ .,,,_..._.__. _. • 

EQUATING TAX TO ECONOMIC DEPRECIATION 97 

FIGURE 1.-Mean asset price by age interval untrans/ undefi. 

Normalized Mean Price/sq. ft.------------------. 

--Retail Trade 

--------- Office Buildings 

- - Factories 

- - - Warehouses 

0.80 

0.60 

0.40 

0.20 

10 20 30 40 50 60 70 80 90 100 110 

vided information on tax depreciation practices and on some distinguishing characteristics of the buildings, such as construction 

quality, primary material, and zip code area. Figure 1 illustrates 

the general age-price pattern of the raw data for each of these 

1arge classes. It depicts the average acquisition price per square 

foot in each 5-year .age interval against age with no adjustments 

for retirement or date of purchase. 

Unfortunately, at this time we do not have actual data on the 

retirement distribution of structures. We therefore apply a Winfrey L0 retirement distribution 8 to the mean life, as approximated 

in Bulletin F, U.S. Department of the Treasury (1942). While the 

choice of the L0 distribution is not based on hard evidence, it has 

the virtue of allowing for the fairly gradual retirement of assets 

with the possibility that some structures survive to very old ages. 

8 See Winfrey (1935). 
98 COMPENDIUM OF TAX RESEARCH 

To illustrate, if a cohort's mean asset life is 50 years, then, according to the Lo distribution, 92 percent sur~ive 10 years, 69 percent 

survive 30 years, 45 percent survive 50 years, and 8 percent survive 100 years. 

When retirement data from the Asset Depreciation Range system become available, it should be possible to incorporate this information into the average asset price model described in this 

section. Use of the data would obviously lead to far more reliable 

estimates of economic depreciation and should help in relaxing the 

assumption of zero scrap value. 

Econometric Procedures 

With sufficient vintage acquisition prices on a reasonably homogeneous class of assets it is possible to construct a rectangular 

array, by age and date, of prices from which depreciation patterns 

and values could be directly observed. Wykoff (1970) applied this 

methodology to user-costs of automobiles. However, here our data 

provides only scattered points in the array, and those are prices of 

rather heterogeneous assets. We therefore must rely on statistical 

inference to estimate economic depreciation: we fit a regression 

plane to the prices, those transformed by the Winfrey distribution and those untransformed taken separately, to obtain a set of 

fitted prices by age and date. These fitted prices provide us with 

depreoiation values from which we estimate qepreciation rates. 

Obviously, a specific functional form for the regression imposes 

restrictions on the age-price patterns and therefore on the form of 

economic depreciation. 9 Since the form of economic depreciation is 

one of the main unknowns of the problem, we must employ a 

highly flexible functional form that includes, as possibilities, patterns such as "one-hoss shay," straight-line, and accelerated depreciation. In our analysis, we used two such specifications : the 

Box-Cox power transformation and the polynomial regression. 

The Box-Cox power transformation, an intrinsically nonlinear 

procedure discussed at some length by Zarembka (1974), permits 

joint estimation of (a) parameters that determine a specific functional form within the Box-Cox class and (b) parameters that 

9 For example, the "one-hoss-shay" age-price pattern is given in footnote 8, 

d h d. te f d . . . . b h d(ln Y) s· -C an t e correspon mg ra o eprec1ation is given y t e . mce 

dt 

and r are constant, this derivative is equivalent to the change in price as the asset ages. The Box-Cox age-price pattern is given by equation (1) of 

the third section of this paper, and the corresponding rate of depreciation can be calculated from equation ( 3) . 
.6 ...... ,.._._ --__ ,,,Ir--- ---_;lflll* ......... -·,J/1- ':""' ,,. . -

EQUATING TAX TO ECONOMIC DEPRECIATION 99 

determine the slope and intercept. Since certain restrictions on the 

unknown form parameters produce "one-hoss-shay," linear, and 

geometric forms, classical hypothesis-testing procedures may be 

employed to evaluate the suitability of these patterns. Estimation 

of the Box-Cox parameters is undertaken using nonlinear maximum likelihood estimation. Asymptotic likelihood ratio tests at 95 

percent levels of significance are used on joint restrictions, and 

asymptotic normal tests are used on individual parameter 

restrictions. 

The polynomial regressions are intrinsically linear and include 

'•one-boss-shay," linear, and accelerated patterns as special cases. 

Linear estimation methods permit the addition of distinguishing 

characteristic variables in a straightforward way (i.e., by using 

multiple regression). The degree of polynomial, and hence the 

functional form, is determined by starting with fourth degree 

polynomials and deleting successive powers by age and year until 

the residual regression variance is minimized. This procedure produces the appropriate specification within the polynomial class. 

Attempts to compare the best polynomial form with semilog forms, 

implying geometric decay, were undertaken as well. 

Statistical Results for Four Large Classes 

As we indicated in the introduction, our statistical findings are 

somewhat surprising : depreciation patterns for factories, offices, 

retail stores, and warehouses appear to be accelerated vis-a-vis 

straight-line, and are perhaps even more accelerated than geometric depreciation. At 95 percent levels of significance, we rejected both the null hypotheses of linear and semilog, or geometric, 

forms within the context of the Box-Cox analysis. Also, a simultaneous test, undertaken at .the 95 percent level of significance, on 

two form parameters only, corresponding to geometric depreciation (a weaker restriction than the semilog constraint), indicates 

rejection in all four classes of the geometric pattern. 

The polynomial tests lead to similar results. Table 2 contains the 

forms of the polynomial price equations. The most common forms 

in the age variable were convex, bowl-shaped, quadratic equations 

and cubic equations that were relatively flat convex forms over 

most of the range of observed ages. When modified sums of 

squared residuals from the semilog equations were compared with 

the best polynomial sums of squares and vice versa, a procedure 

suggested by Theil (1971), the results were inconclusive. The null 

hYPothesis of linear deprecia.tion and of a concave age-price curve 

were rejected at the 95 percent level of significance. 
Class 

Factory 

Offices 

Retail trade 

Warehouse 

Age (s) 

Cubic 

Cubic 

Quadratic 

Quadratic 

TABLE 2.-Polynomial price equations 

Lr.r-Transformed Un transformed 

Year (t) 'IF Age (s) Year ( t) 

Linear .22 Cubic Linear 

Quadratic .34 Cubic Quadratic 

Cubic .24 Cubic Cubic 

Linear .16 Cubic Linear 

No. of n~ Inc/Pop Dummies 

.10 YIN 1 

.20 y 2 

.16 YIN,N 1 

.11 YIN 1 

......... 

0 

0 

(") 

0 

~ 

~ 

t.%j 

z 

t:::i 

-c:: 

~ 

0 

~ 

1-'.3 

> 

>< 

~ 

t:z:j 

rn 

t.%j 

> 

~ 

(") 

~ 
.,., ~~F~ ~- • • -- ~ - •- .I'__.,_--.- --.19- •1.-L_.,...- _,,,. -

EQUATING TAX TO ECONOMIC DEPRECIATION 101 

FIGURE 2.-0f]ice building: fitted vs. actual price by age interval untrans. 

Acquisition Price/sq. ft.----------------~ 

12 

8 

4 

- Actual Values 

------ Box-Cox Fitted Values 

10 20 30 40 50 60 70 80 90 100 110 

Asset Age 

The Box-Cox and polynomial point estimates for one classoffice buildings-are given in the appendix (tables A-1 and 

A-2) .1 ° Figures 2 and 4 summarize the results by 5-year age intervals. It is evident from these figures that (a) the fitted values of 

the dependent variable (acquisition price per square foot) approximate the actual value rather well, and (b) that the fitted ageprice pattern is convex. The convex age--price pattern is clearly 

evident in the underlying data and cannot be attributed to our 

choice of statistical techniques. 

Specific average annual rates of economic depreciation are implied by each of the forms estimated. Table 3 contains some select 

annual percentage decline rates from the Box-Cox analysis. 

The most striking feature of the table 3 rates is that they are 

largest for young buildings and tend to fall throughout assets' 

10 Office buildings were selected for detailed analysis for reasons that will 

become clear in the next section of this paper. Details are given by Hulten 

and Wykoff (1975; 1976; 1977). 
102 COMPENDIUM OF TAX RESEARCH 

TABLE 3.-Selected rates of depreciation from Box-Cox analysis 1 

(percentage decline per year) 

Age Class (transformed) Class (untransformed) 

(years) Fae.~ Off. Ret. War. Fae. Off. Ret. War. 

1 3.02 4.32 3.54 5.77 3.00 5.72 5.39 6.81 

5 2.99 3.07 2.77 3.68 2.02 2.66 2.41 3.23 

10 3.01 2.64 2.47 3.05 1.68 1.84 1.63 2.26 

20 3.07 2.30 2.22 2.55 1.39 1.27 1.09 1.57 

30 3.15 2.15 2.10 2.32 1.25 1.02 0.86 1.27 

40 3.24 2.08 2.03 2.19 1.17 0.88 0.73 1.10 

50 3.34 2.04 1.99 2.11 1.11 0.79 0.64 0.98 

1 Sources: Hulten and Wykoff (1976, 1977) . 2 Fac.=Factory; Off.=Office; Ret.=Retail; War.=Warehousc 

lives. A const.ant percent.age decline per year corresponds to geometric decay, so that a falling annual percent.age decline implies 

depreciation patterns more accelerated than geometric. These accelerated patterns occur both for Winfrey transformed and for 

untransformed prices. The allowance for retirements, with the 

Winfrey transformation, tends to raise depreciation rates from 

the 1 percent to 3 percent to the 3 percent to 4.5 percent range and 

to compress the rate patterns somewhat. 

The polynomial implied depreciation patterns are illustrated in 

table 4. The polynomial regressions produced average annual rates 

of decline that are both smaller and less variable than those of the 

Box-Cox analysis. Furthermore, these rates tend to rise, though 

quite gradually for the transformed <lat.a, over asset life. We calTABLE 4.-Select rates of depreciation from polynomial analysis 1 

(percentage decline per year) 

Age Class (transformed) Class (untransformed) 

(years) Fae. 3 Off. Ret. War. Fae. Off. Ret. War. 

1 2.20 2.39 1.87 2.05 1.32 1.86 1.80 2.33 

5 2.29 2.44 1.92 2.14 1.34 1.90 1.75 2.32 

10 2.42 2.51 2.00 2.27 1.36 2.06 1.68 2.31 

20 2.73 2.64 2.17 2.59 1.38 3.01 1.50 2.26 

30 3.11 2.73 2.34 3.03 1.38 6.17 1.27 2.18 

40 3.58 2.72 2.51 3.67 1.35 31.80 1.02 2.14 

50 4.15 2.54 2.63 4.71 1.27 0.77 2.21 

1 Sources: Hu I ten and Wykoff, ( 1976, 1977) . 

~ Fac.=Factory; Off.=Office; Rct.=Retail; War.= Warehouse. 
EQUATING TAX TO ECONOMIC DEPRECIATION 103 

culated the average annual dollar decline with these rates and 

found that these amounts fell with age. Thus, while five of these 

patterns are less accelerated than geometric, they are more accelerated than straight-line. The untransformed factory pattern 

is nearly geometric, and the untransformed retail store and warehouse patterns are more accelerated than geometric. The rates of 

depreciation range roughly between 1.3 percent and 2.3 percent 

for untransformed and between 2 p€rcent and 3 percent for transformed data. 

We conclude that depreciation of structures is accelerated vis-avis straight-line, and we statistically-reject "one-hoss-shay" decay 

rather decisively. The rates of depreciation our study has produced 

are all considerably lower than those implied by published guideline lives.11 Our rates fall in the 1.5 percent to 3 percent range 

while the guideline lives imply 5 percent to 7 percent rates of 

depreciation. 

Figures 3 and 4 provide a convenient visual illustration of our 

results. Figure 3 plots our basic data for the four largest asset 

classes after this data has been adjusted for (a) retirements using 

the Lo distribution and (b) changes in construction prices over 

time. (This last adjustment is made necessary by the different 

average dates of purchase in each age interval.) The resulting ageprice patterns are unmistakably convex. Figure 4 plots actual Lo 

deflated acquisition prices against the fitted values from the BoxCox analysis. The result, again, strongly supports our conclusion 

that economic depreciation is accelerated relative to a straight-line 

pattern. Our evidence thus suggests rather strongly that the conventional wisdom-that buildings dep;eciate like a "one-hoss 

shay" -is unwarranted. The implication for tax policy is that 

accelerated depreciation ought to be allowed for structures, but 

that the currently allowed implicit guideline rates are probably too 

large. (We are assuming here that economic depreciation is the 

desired norm for tax depreciation allowances.) 

Cross-Sectional Results for Office Buildings 

The results described in the preceding section were obtained by 

Pooling used-asset price data for a number of years. That is, a 5-

year-old office building in 1948 was pooled with a 20 .. year-old 

office building purchased in 1965. Thus, while the pooled analysis 

u U.S. Department of the Treasury, Internal Revenue Service, Depreciation 

Guidelines and Rules, Revenue Procedure 62-21, Revised 1964. 
104 COMPENDIUM OF TAX RESEARCH 

FIGURE 3.-Mean asset price by age interval trans/deft. 

Normalized Mean Price/sq. ft.-------------------, 

--Retail Trade 

1.00 --------- Office Buildings 

- - Warehouses 

--- Factories 

b.80 

0.60 

0.40 

0.20. 

0 ~....___.,__.____._..___,___._____.___..___.__.__._____._..___.__.___.__~...._~~~ 

0 10 20 30 40 50 60 70 80 90 100 110 

Asset Age 

provides a reasonably good statistical fit to the underlying data 

and indicates a convex age-price pattern, as is seen in figures 2 

and 4, the possibility that pooling introduces a systematic bias 

into the results does exist. · The argument that such a bias might 

exist was advanced by Taubman (1976), who argued that there 

have been significant changes over the postwar years in the business tax code (as it relates to tax depreciation) as well as significant variations in the rate of inflation.12 Two identical buildings 

might have different values in different years-and thus different 

observed purchase prices-simply because the present value of the 

net income stream has been altered by changes in the tax code or 

the inflation rate. Thus, if there is a correlation between the age 

of buildings in our sample and the years in which the purchases 

12 Major changes in the depreciation rules occurred in 1954, 1962, and 1971; 

numerous other changes have also occurred. Over the period 1955-1971, the 

average annual growth of the Boechk construction price index was 3.86 percent, for the period 1958-1971, the average annual change of the Bureau of 

Census Composite Index was 2.93 percent. 
~ ... _.,_,,, ______ _,, , ____ -------•.1.-.tl..-...-~~~-

EQUATING TAX TO ECONOMIC DEPRECIATION 105 

FIGURE 4.-0ffice building: fitted vs. actual price by age interval trans. 

Acquisition Price/sq. ft. -------------------, 

16 -Actual Values 

-----Box-Cox Fitted Values 

12 

8 

4 

o.._.....____.___.______. _ _.___.___.____.__.___.__.___.__.____,__.__.______. _ _.___.___.____.___. 

0 10 20 30 40 50 60 70 80 90 100 110 

Asset Age 

occurred, the observed age-price patterns of figures 1 and 3 could 

be biased upward or downward. 

A positive correlation between asset age and date of purchase is 

contained in our sample; for office buildings, the correlation coefficient is 0.13. Furthermore, the estimated Box-Cox parameters 

for the office building class imply that the regressions are cubic in 

date, with very small and statistically insignificant coefficients. 

The possibility of a misspecification associated with the date-ofpurchase variable d0es therefore exist. As noted earlier, we have 

attempted to correct for any bias due to pooling by breaking the 

pooled sample into subsamples corresponding 1:-0 individual yearn, 

and then analyzing each year separately. The effects of time on 

used-asset prices 13 are naturally held constant by this method, and 

13 The use of annual cross sections does not, of course, remove all effects 

associated with the passage of time. Improvements in the quality of buildings 

will introduce a time dimension into the data for any year. To see this in its 

simplest form, assume that depreciation, inflation, and quality change are 
106 COMPENDIUM OF TAX RESEARCH 

if the results are consistent with those obtained from the poole.d 

analysis, then we can conclude tha~ biases in the latter due to 

differing dates of purchase are small. 

The office building class was selected for the cross.,section analysis because it was one of the two classes with over 1,500 observations, and because it was the class studied by Taubman and Rasche 

(1969) .

14 Individual cross-section analyses were conducted for the 

years between 1955 and 1971.15 Linear and semilog regressions 

were calculated for each of these years; the results are reported in 

appendix tab.les A-3 and A-4. All coefficients have the signs and 

magnitude that might be anticipated, implying that depreciation is 

occurring in each year at a plausible rate. Furthermore, all but 

seven of the coefficients are statistically significant at the 95 percent level. We conclude from these cross-section results that the 

pooled sample of office buildings was based on consistent and relatively stable individual annual components. 

Table 5 summarizes the linear and semilog cross-section results 

and compares them with the corresponding pooled estimates. It is 

evident that the average slope coefficients (/3) from the cross sections, given in row ( 1), are almost identi~l to the corresponding 

pooled estimates, given in row ( 4) . Rows ( 2) and ( 3) indicate a 

slight tendency for the cr9ss-sectional 'f3 to increase (in absolute 

value) over time, from the period 1955 to 1963 to the period 1963 

to 1971, indicating the possibility of structural change. However, 

the magnitude of the increase is small relative to the standard 

errors, so it is difficult to discern a significant effect.16 We note, 

occurring at constant, exponential rates /3, 'Y, and <$ respectively. Suppose, 

further, that the price of an S-year-old asset at time tis given by 

Y(t,S)=a eP8 e1 ' e 6<1-s> (A) 

The term li ( t-S) allows for differences in the quality of different vintages. 

Equation (A) can be written 

Y(t,S)=ae l/J+o>:s e<'Y+6", (B) 

implying that /3, "/, and li cannot be identified using data on asset price, 

Y(t,S). This result is due to Hall (1968), and it should be kept in mind when 

interpreting the results of this paper. 

If quality change varies over time, the appropriate analog to (A) will 

imply cross sections that depend on t. This effect can also arise if past 

changes in the tax code are embodied in the design of assets. 

H Thus we facilitate comparison of our results with those derived by Taubman and Rasche-see the final section of this paper. 

u These years were selected because they contain a reasonably large number of observations. 16 In view of footnote 13, the stability of the cross-sectional estimates indicates that, to the extent that embodied quality changes are important, it is a 

smooth process. 
____ ... - - ----- - - .. -~---_,. - ----~-~ 

EQUATING TAX TO ECONOMIC DEPRECIATION 107 

TABLE 5.-Linear and semilog cross-section results 

Average estimated slope coefficients 

Linear Semilog 

Time period untrans. trans. untrans. trans. 

(1) 1955-1971 -.139 -.198 -.0146 -.0258 

(.053) (.050) (.0043) (.0043) 

(2) 1955-1963 -.136 -.190 -.0142 -.0245 

(.064) (.062) (.0050) (.0050) 

(3 ) 1963-1971 -.143 -.206 -.0156 -.0276 

(.042) (.037) (.0036) (.0036) 

(4) Pooled estimates -.127 -.182 -.015 -.027 

(.010) (.009) (.001) (.002) 

1 Standard errors given in parentheses. 

finally, that the estimates of the intercept coefficients (which are 

not reported in t.able 5) do differ between the pooled and cr08ssectional analyses and increase over time, but that this increase 

Probably reflects the fact that the date-of-purchase variable of 

the pooled analysis is suppressed into the cross-sectional constant 

terms. 

Table 6 gives estimates, for selected years, of the Box-Cox power 

transformational model. In the present context, the Box-Cox model 

takes the form 

TABLE 6.-0ffice buildings: Box-Cox grid search of selected years 

(a) (b) (c) (d) 

Box-Cox Box-Cox 

estimates of adjusted Adjusted 

Year (81, 82) log-likelihoods log-likelihoods 

TRANSFORMED DATA (81=.~12, 82=.714) 

1956 (0.45, 0.40) -144.57 -146.94 

1959 (0.20, 0.80) -171.25 -171.29 

1962 (0.20, 1.20) -211.55 -211.62 

1965 (0.35, 0.80) -349.16 -350.89 

1968 (0.30, 0.80) -333.58 -334.32 

1971 (0.30, 0.80) -221.34 -221.85 

UNTRANSFORMED DATA (81=.247, 82=.384) 

1956 (0.55, 0.20) -149.35 -151.84 

1959 (0.25, 0.40) -178.81 -178.81 

1962 (0.20, 0.60) -221.32 -221.43 

1965 (0.40, 0.00) -365.14 -367.98 

1968 (0.40, 0.60) -350.02 -352.95 

1971 (0.40, 0.60) -238.41 -240.22 
108 COMPENDIUM OF TAX RESEARCH 

solZ-1 

---=a+f3 +e, 01 02 (1) 

where Y denotes acquisition price per square foot and S, the age 

of the building when purchased, 01 and 02 are unknown form parameters, and a and f3 are the respective unknown intercept and 

slope parameter. When (01,02) = (1,1), equation (1) is a linear 

regression model. When Oi-~O, the left-hand side of equation (1) 

becomes ln Y, so that (Oi,02) = (0,1) implies that equation (1) is a 

semilog regression. Other restrictions on ( Oi,02) are possible: for 

example, (Oi,02) = (1,3) yields a cubic regression. 

The parameters of equation ( 1) were estimated using a grid 

search method.17 The resulting estimates of the O's are given in 

column (b) of table 6. Because of the costs involved, the estimates 

were calculated only for every third year of the period 1955 to 

1971. The estimates of (01 ,02) show a high degree of stability and, 

more importantly, are quite close to the pooled estimates of (Oi,02) : 

(.247,.384) for the untransformed data and (.212,.714) for the 

transformed. Intuitively, this means that the age-price patterns 

are relatively stationary over time. 

This last statement can be made statistically precise by considering the adjusted log-likelihood function associated with equation 

( 1) . Assuming that the erroT term e is independently normally 

distributed, the log-likelihood function is given by 

N N 

L= (01 -l) L::ln Yi--(ln 27T+ln (}2+1), i=1. 2 (2) 

where {i is the estimated standard error of the regression and N 

is the number of observations. The normality of e implies the 

approximate normality of L for large N. Furthermore, the statistic,\= -2(L(O*,O*) -L) is approximately chi-square with two 1 2 

degrees of freedom when (Oi,02) = (O*,O*). (Note that L(O*,O*) is 1 2 1 2 

the value of equation ( 1) calculated under the assumption that 

0 =0* and O =0*.) Column (c) of table 6 gives values for L; 1 1 2 2 

column (d) gives values for L(.212,.714) and L(.247,.384)-the 

values of the adjusted log-likelihood function calculated under the 

assumption that the pooled estimates of (01102) are correct. The 

statistic A. is calculated by multiplying the difference between columns (c) and (d) by two, and comparing the result with the 5 

percent critical value of a chi-square variate with two degrees of 

freedom: 5.99. So calculated, ,\is less than 5.99 in all years. Thus, 

17 The parameter 81 was searched in increments of 0.05, and 02 in increments 

of 0.2. 
EQUATING TAX TO ECONOMIC DEPRECIATION 109 

we cannot reject the hypothesis that the pooled estimates and the 

cross-section estimates of the pair ( 811 02 ) are the same. 

This statistical result is of considerable importance. Because the 

cross-sectional and pooled estimates of ( 81 ,82 ) are not significantly 

different under the,\ test,18 and because figures 2 and 4 clearly indicate a convex age-price pattern for the pooled estimates, we conclude that yearly cross-sectional estimates are consistent with the 

convex pattern. This conclusion implies in turn that the convexity 

of the age-price pattern is not a result of the misspecification of 

time in the pooled analysis. 

The conclusion that the age-price pattern is convex can be further assessed by considering the form of the Box-Cox function 

[equation (1)] when e=O. The first derivative is given by 

(3) 

Since Y and Sare nonnegative, the slope of the age-price pattern 

will be nonpositive if, and only if, {3<0. All of our estimates of f3 

are, in fact, less than 1. This result implies that acquisition-price 

per square foot declines with age (Y,S greater than zero). The 

second derivative of equation (1) is given by 

d2Y = 82 -l dY + l-81 ( dY ) 2 

dS2 S dS Y dS . (4) 

Note that when the regression is linear, (8i,82 ) = (1,1), equation 

(3) is constant and equation (4) equals zero; when the regression 

is semilog, the first derivative equals f3 and the second derivative 

equals {32 /Y. {3<0 implies that the second derivative is everywhere 

greater than zero, and the age-price pattern is strictly convex 

whenever 81...::::::::1 and 82...::::::::1. 

BecaUBe of the traditional importance of the "one-hoss-shay" 

hYPOthesis, we pursue the issue of nonconvexity one step further 

and consider the implication of 82> 1. If ~is small and uniformly 

negative, 81> 1 and 82> 1 imply a concave age-price pattern. However 81 > 1 can be strongly rejected in every year considered in 

table 7. Note that the second term on the right-hand side of equation (4) will eventually come to dominate d2Y/dS2 as age S increases. Thus, since this term is positive for 81<1, the age-price 

pattern must ultimately become convex as age increases. If 82 is 

positive and sufficiently large, however, then the first term on the 

right-hand side of equation ( 4) will be negative and will dominate, 

at least in the early years. In this case, the early years of asset life 

18 The term ">.. test" will be used to signify "asymptotic likelihood ratio 

test." 
110 COMPENDIUM OF TAX RESEARCH 

will be characterized by a concave age-price pattern if f3 is small. 

The overall pattern would be shaped like a backward S. While a 

backward S is not consistent with the pure "one-hoss-shay" hypothesis, it is consistent with a variant of the hypothesis in which 

(a) buildings are "one-hoss-shay" in the early years of their life, 

and (b) these buildings are retired at different points of time. 

The preceding discussion suggests a direct t.e.st of convexity 

based on (fj,Oi,02). Note that the estimates of (81 .82) in column (b) 

of table 6 are, with one exception, less than one. Although not 

reported, it is also the case that fi is always negative. Thus, the 

Box-Cox maximum likelihood point estimates consistently imply 

a convex age-price pattern. However, the adjusted likelihood functions are relatively flat over different values of 82 (but not 81). 

When the A. test discussed earlier is applied to the hypothesis that 

82> 1, this hypothesis is rejected only in the 1965 and 1968 cross 

sections. These two years are the ones with the largest number of 

observations, and it is possible that more data points in the other 

years would lead to more precise estimates and thus to the rejection of the alternative hypothesis 82>1 (and therefore to the acceptance of a strictly convex age-price pattern). The data is, unfortunately, not available, and the possibility that the age-price 

pattern is concave over some asset ages must be considered. 

We emphasize, however, that the cross-sectional maximum likelihood point estimates do not indicate the backward-S-shaped ageprice pattern (except in 1962 with the transformed data). On the 

contrary, these estimates imply a strictly convex pattern in most 

years. The point of this discussion is to note that the backward-Sshaped pattern cannot be statistically ruled out in the years 1956, 

1959, 1962, and 1971. 

We observe, finally, that the hypotheses of linear, geometric, and 

cubic age-price patterns can be rejected using the >..test in every 

year except 1962 (where geometric cannot be rejected). The adjusted log-likelihoods are given in tables 7 and 8. Note also that the 

geometric ( semilog) likelihoods generally outperform the linear 

and cubic cases, although the >.. test is inapplicable because the 

three cases are not nested. The adjusted log-likelihood associated 

with a third degree polynomial in age is also given. The polynomial 

likelihoods cannot be compared with either the Box-Cox or semilog 

functions, since, again, they cannot be derived from restrictions 

on the relevant parameters. We note, however, that the adjusted 

log-likelihoods are uniformly larger under Box-Cox and generally 

larger under the semilog regressions. The linear and cubic functions can be derived from the polynomial functions (using the 
EQUATING TAX TO ECONOMIC DEPRECIATION 111 

TABLE 7.-0/fice buildings (untransformed): adjusted log-likelihoods 

3rd degree 

polynomial 

Semilog Linear Y=a+f318+f3~~ Cubic 

lnY=a+f38+e Y=a+/38+£ +f3a83+e Y=a+/3SJ+( Year (81=0) (81=1) (8=1) (81=1) 

1955 -135.7 -163.0 -162.8 -163.3 

1956 -159.2 -154.9 -153.4 -158.4 

1957 -156.9 -167.7 -166.6 -170.2 

1958 -182.2 -210.4 -210.3 -210.7 

1959 -182.4 -195.3 -194.9 -197.1 

1960 -249.7 -257,2 -256.9 -257.9 

1961 -217.9 -235.7 -235.7 -235.9 

1962 -222.7 -238.9 -238.7 -238.8 

1963 -322.3 -339.2 -338.0 -340.7 

1964 -288.4 -298.6 -298.3 -299.7 

1965 -382.7 -386.8 -384.3 -391.8 

1966 -300.1 -,318.6 -317.5 -321.1 

1967 -302.7 -336.8 ~32.4 -337.3 

1968 -358.8 -363.5 -361.4 -373.1 

1969 -275.9 -284.8 -283.4 -287.5 

1970 -220.0 -216.9 -213.5 -226.6 

1971 -245.2 -248.5 -247.6 -252.8 

TABLE 8.-0/fice buildings (transformed): adjusted log-likelihoods 

3rd degree 

polynomial 

Semilog Linear Y =a+f318+/3~2 Cubic 

Year 

lnY=a+/38+£ Y=a+/38+£ +f3a83+e Y=a+/38'+£ 

(81=0) (81=1) (8=1) (81=1) 

1955 -131.96 -162.90 -162.74 -163.32 

1956 -153.27 -153.32 -151.78 -158.48 

1957 -150.19 -166.95 -165.91 -170.82 

1958 -176.99 -209.75 -209.68 -210.50 

1959 -174.12 -191.48 -191.14 -195.08 

1960 -242.51 -255.02 -218.07 -257.06 

1961 -210.58 -232.07 -232.07 -232.81 

1962 -213.37 -231.82 -231.67 -232.42 

1963 -313.93 -337.20 -336.79 -340.34 

1964 -278.74 -294.91 -294.61 -297.53 

1965 -362.64 -380.23 -378.21 -391.41 

1966 -284.98 -316.36 -314.69 -321.85 

1967 -289.31 -301.96 -297.01 -308.96 

1968 -340.22 -358.52 -355.34 ~374.00 

1969 -260.90 -276.02 -274.05 -282.16 

1970 -198.20 -209.27 -203.47 -225.47 

1971 -226.28 -242.66 -240.69 -251.82 
112 COMPENDIUM OF TAX RESEARCH 

restrictions {32 = f3 a = 0 and {31 ={32=0, respectively) ; surprisingly, 

the corresponding,\ test rejects linear vis-a-vis polynomial in only 

three years. The cubic form is rejected in a majority of the cross 

sections and is uniformly rejected after 1965. 

Summary and Comparison with Other Studies 

Our basic findings can be stated briefly: office buildings appear 

to depreciate at a rate faster than straight-line depreciation, and 

this result holds for both pooled data and for data analyzed as a 

sequence of annual cross sections. The treatment of time (and thus 

inflation, etc.) does not, therefore, appear to bias the pooled office 

building results (to any great extent) on the convexity of the ageprice pattern. · 

These results differ sharply from those reported by Taubman 

and Rasche ( 1969), who studied a sample of average rental income, operating costs, and vacancy rates for 600 office buildings 

between the years 1951 and 1965. Their data distinguish four age 

categories : less than 10 years old, 10 to 25 years old, 25 to 40 years 

old, and over 40 years old. Taubman and Rasche derived an average annual rental series (per square foot) for each age S by an 

elaborate interpolation procedure and then constructed an average 

asset price series, Y, by assuming that asset price equals the present value of the rental income net of operating costs. The asset 

price series constructed in this way yielded a highly concave ageprice pattern. Rates of depreciation-(1/ Y) (dY / dS) in our notation-are continuously increasing and do not exceed 1.00 percent 

until 8>25 in their 1951 cross section, or until 8>39 in their 1960 

cross section.119 

We have fitted the Taubman and Rasche results to the Box-Cox 

model in order to determine the implied values orf (01,02 ) •

20 Using 

the same grid search method applied to our samples, we find that 

in both 1951and1960 .the point estimates of (OH02) are (1.10,2.40). 

These values, when imposed on our data, are strongly rejected using the,\ criterioo. It is worth noting, however, that Taubman and 

Rasche have as a maintained hypothesis the assumption that asset 

value is equal to the present value of the rental income flow. This 

assumption, which is not necessary to1 our statistical estimation of 

10 See Taubman and Rasche (1969), Table Ila. 

~Data from Taubman and Rasche's (1969) Table Ila was, again, used for 

this purpose. We used their estimated present values, which are based on a 

discount rate of 10 percent. 
~~ -- - ----- -- --- ---,-~--- ~ ---

EQUATING TAX TO ECONOMIC DEPRECIATION 113 

economic depreciation/ 1 implies a competitive market equilibrium 

with perfect foresight. Furthermore, Taubman and Rasche have 

average annual data for only four broad a.ge categories and therefore only four points on the age-price curve. Their data consists of 

grossly aggregated averages provided them by a real estate association. Our data, on the other hand; is derived from a stratified 

sample based on the Internal Revenue Service's taxpayers compliance file and has numerous points on the age-price curve. 22 It is, of 

course, true that we do not know the reasons why specific buildings 

in our sample were resold, and, therefore, we cannot be sure that 

they are representative of the entire population of office buildings. 

Furthermore, we note again that we used the raw data unweighted 

by sampling probabilities, for reasons discussed elsewhere 

(Hulten and Wykoff, 1977). We do not, however, have any particular reason to believe that systematic biases are present in 

our sample.23 

The studies reported by Coen (1975; 1976) provide an alternative approach to the measurement of depreciation of nonresidential structures. The neoclassical theory of investment postulates 

that investment depends, in part, on the rental cost of capital. The 

rental, in turn, depends on physical depreciation. Coen models the 

rental price using different assumptions about depreciation-sumof-years-digits, geometric, straight-line, and "one-hoss-shay"-and 

fits a neoclassical investment model using each accounting depreciation variant. The variant yielding the lowest standard error 

(and plausible values for the estimated parameters) was selected 

as the most probable physical depreciation pattern. In the 21 

manufacturing industries s.tudied by Coen ( 1975), "one-boss-shay" 

was found t.o be superior for structures in 11 industries, straightline in 5, and geometric and sum-of-years-digits in 5. However, in 

2

l We do use this assumption (Hulten and Wykoff, 1975) to calculate the 

relative physical efficiency of the various types of buildings in our study. We 

do not, therefore, wish to argue that the assumption is wrong, but only to 

Point out that it is an additional hypothesis not required for the direct 

measurement of economic depreciation from our data. 

2l See U.S. Department of the Treasury, Office of Industrial Economics 

(1975) for a description of the sampling methods underlying the OIE real 

property study. 

::i There may be, for example, a systematic bias resulting from the location 

of older buildings nearer to the centers of the various cities in the OIE 

sample. It might also be the case that buildings appear on the market at a 

discount because they no longer meet the business needs of the sellers. However, while these (and other) possibilities exist, it seems more probable that 

most buildings are sold for reasons related to the general business and financial circumstances of the owners and not to the characteristics of the structures themselves. 
114 COMPENDIUM OF TAX RESEARCH 

a subsequent paper Coen ( 1976) modified these results significantly. "One-hos&-shay" was accepted in only 2 industries, and 

sum-of-years-digits and geometric in 14. The second set of results 

is quite consistent with the results of our work. Although manufacturing structures are primarily factories, and the analysis is 

based on the form of physical depreciation, denoted by the decline 

in relative efficiency or by the mortality sequence, we observe that 

a near geometric form of physical depreciation implies a near 

geometric form of economic depreciation and interpret Coen's 

results as consistent with our own. 

The results of this paper and those of Coen (1976) run counter 

to the intuitive argument made by some people that buildings are 

refurbished and maintained indefinitely at or near their original 

productive capacity. But could the intuitive argument not also be 

applied to automobiles, machine tools, and other equipment? Theoretically, these assets could also be maintained and repaired so 

that they would provide the same productive services as new equipment. Yet studies tend to indicate that equipment also has a convex age-price profile. 24 It may be that intuition has been a misleading guide in understanding economic depreciation. 

~'See, for example, Beidleman (1976) and Wykoff (1970). 

.$ 
Appendix: Detailed Analysis of Office Buildings 

TABLE A-1.-Pooled Box-Cox point estimates: office buildings "' 

01 o. 03 ci /3 'Y LogL (R•) 

UNTRANSFORMED 

Linear 1 1 1 3.63 -.127 .177 -6021.1 

** (.010) (.020) (.123) t_:rj 

Geometric 0 1 1 1.104 -.015 .022 -5583.9 .0 

d 

** (.001) (.002) (.203) > 

Box-Cox ~ 

2 Constraints .277 .277 .277 .105 -.207 .480 -5515.2 -z 

C) 

(.011) (.011) (.011) (.321) (.012) (.043) ~ 

1 Constraint .248 .610 .610 .603 -.083 .153 -5503.5 > 

>< (.011) (.092) (.092) (.339) (.022) (.056) ~ 

0 Constraints .247 .384 3.289 2.452 -.158 .379E-5 -5481.49 0 

(.011) (.098) (.659) (.178) (.039) (.013E-4) t_:rj 

(") 

0 TRANSFORMED z 

Linear 1 1 1 4.517 -.182 .162 -5893.3 0 

** (.009) (,018) (.220) a:: 

Geometric 0 1 1 1.110 -.027 .022 -5302.6 -(") 

t::l ** (.001) (.002) (.403) t_:rj 

Box-Cox 1-'d 

~ 

2 Constraints .294 .294 .294 .231 -.317 .467 -5282.7 ttj 

(") 

(.011) (.011) (.011) (.319) (.011) (.041) -> 1 Constraint .209 .801 .801 1.010 -.071 .069 -5236.2 ~ 

(.011) (.059) (.059) (.208) (.013) (.017) -

0 

z 0 Constraints .212 .714 3.154 2.34 -.094 .6E-5 -5220.4 

(.011) (.060) (.634) (.165) (.017) (.16E-4) 

Y91-l se2_1 t

113-l * Coefficients derived from the equation ~~=ci+~~~+'Y~~· . 01 02 03 ~ 

~ ** A computer program was used which did not provide standard errors of constant terms. Standard errors for other coefficients are Ol 

given in parentheses. 
TABLE A-2.-Pooled polynomial point estimates 1 

n 

a.2 /31 !32 f3a 'Y1 'Y2 0 

~ .,, 

t.'%.:1 

Untransformed 

estimates 12.81 -.271 .0026 -.000001 .270 .002 .000011 z 

(5.4) (2.3) (-1.2) (6.9) (1.7) (0.85) t::I 

1-4 

C! 

~ 

Transformed 

estimates 12.19 -.343 .0031 .000009 .302 .0016 .000009 0 

"'Zj 

(-7.8) (3.1) (1.7) (8.8) (1.6) (0.78) ""'3 

> 

:>< 

~ 

1 t statistics given in parentheses. t.'%.:1 

Ul 2 Estimates derived from the equation. 

Y=a.+f3 S+/32'·sa+-ylt+-y~t~+M. 

t_:l:j 

> 

where I is a variable denoting regional income I. 

~ 

n 

::i:: 
~ ·-·---·-

EQUATING TAX TO ECONOMIC DEPRECIATION 117 

TABLE A-3.-0ffice buildings (transformed): annual regressions 1 

Y=a+.BS+E" lnY =a+,BS+E 

Year a- ~ R" 'Ci' °ff R" 

1955 14.18 -0.207 0.07 2.20 -0.018 0.13 

( 5.29) (-1.709) (12.97) (-2.391) 

1956 13.54 -0.214 0.36 2.48 -0.031 0.42 

(13.62) (-5.176) (19.26) (-5.822) 

1957 12.70 -0.188 0.25 2.34 -0.025 0.38 

(10.58) (-3.984) (19.74) (-5.388) 

1958 17.14 -0.245 0.12 2.65 -0.027 0.38 

( 8.10) (-2.695) (23.40) (-5.556) 

1959 13.21 -0.152 0.20 2.50 -0.026 0.49 

(12.04) (-3.669) (26.28) (-7.212) 

1960 14.75 -0.168 0.13 2.41 -0.021 0.20 

(11.40) (-3.151) (19.36) (-4.075) 

1961 14.90 -0.169 0.11 2.47 -0.019 0.21 

( 9.87) (-2.736) (20.85) (-3.966) 

1962 15.36 -0.177 0.14 2.58 -0.024 0.30 

(10.40) (-3.236) (20.34) (-5.133) 

1963 14.52 -0.187 0.15 2.50 -0.030 0.37 

(13.92) (-4.103) (26.60) (-7.408) 

1964 15.75 -0.195 0.17 2.57 -0.023 0.27 

(13.19) (-4.060) (24.75) (-5.474) 

1965 14.58 -0.161 0.22 2.44 -0.022 0.29 

(14.95) (-5.392) (22.38) (-6.523) 

1966 14.56 -0.147 0.17 2.52 -0.023 0.43 

(13.12) (-4.223) (27.74) (-8.068) 

1967 16.73 -0.184 0.21 2.76 -0.028 0.44 

(15.18) (-4.705) (28.77) (-8.137) 

1968 19.14 -0.266 0.40 2.89 -0.031 0.56 

(19.72) (-8.187) (35.61) (11.409) 

1969 18.52 -0.242 0.28 2.78 -0.027 0.38 

(13.47) (-5.443) (22.46) (-6.750) 

1970 17.56 -0.237 0.57 2.93 -0.035 0.58 

(16.57) (-9.35) (19.33) (-9.550) 

1971 18.04 -0.232 0.38 2.88 -0.029 0.48 

(13.74) (-6.609) (21.07) (-8.05) 

1 t statistics given in parentheses. 

~ Y denotes acquisition price per square foot; S denotes the age of the building 

when purchased. 
118 COMPENDIUM OF TAX RESEARCH 

TABLE A-4.-0ffice buildings (untransformed): annual regressions 1 

Y=a+.BS+E2 lnY=a+.BS+E 

Year 'Ci' If R2 No.obs. -a- 1J R2 

1955 14.14 -0.161 0.04 40 2.18 -0.008 0.03 

( 5.26) (-1.32) (12.87) (-1.09) 

1956 13.50 -0.171 0.25 49 2.46 -0.022 0.25 

(13.14) (-4.01) (18.92) (-4.00) 

1957 12.65 -0.145 0.16 50 2.32 -0.015 0.17 

(10.39) (-3.02) (19.38) (-3.12) 

1958 17.14 -0.191 0.08 53 2.63 -0.017 0.20 

( 8.00) (-2.07) (23.41) (-3.58) 

1959 13.19 -0.102 0.09 57 2.45 -0.014 0.20 

(11.24) (-2.30) (25.34) (-3.70) 

1960 14.71 -0.111 0.06 70 2.38 -0.010 0.05 

(11.03) (-2.01) (19.09) (-1.91) 

1961 14.81 -0.091 0.03 63 2.46 -0.009 0.06 

( 9.26) (-1.38) (20.75) (-1.94) 

1962 15.37 -0.106 0.05 64 2.55 -0.014 0.12 

( 9.32) (-1.73) (20.12) (-2.93) 

1963 14.55 -0.148 0.10 94 2.47 -0.019 0.19 

(13.67) (-3.18) (26.43) (-4.71) 

1964 15.64 -0.121 0.07 82 2.54 -0.012 0.10 

(12.52) (-2.42) (24.57) (-2.91) 

1965 14.50 -0.102 0.09 108 2.39 -0.010 0.07 

(13.98) (-3.22) (21.66) (-2.89) 

1966 14.62 -0.100 0.08 88 2.45 -0.009 0.09 

(12.85) (-2.80) (26.74) (-2.97) 

1967 16.13 -0.061 0.01 86 2.71 -0.016 0.21 

( 9.76) (-1.05) (28.06) (-4.73) 

1968 19.15 -0.212 0.27 104 2.84 -0.019 0.33 

(18.80) (-6.22) (34.54) (-7.07) 

1969 18.42 -0.169 0.13 77 2.72 -0.016 0.17 

(11.95) (-3.40) (21.73) (-3.89) 

1970 17.79 -0.196 0.42 68 2.83 -0.022 0.36 

(15.02) (-6.93) (18.45) (-6.06) 

1971 18.20 -0.178 0.24 72 2.78 -0.017 0.23 

(12.78) (-4.68) (20.25) (-4.60) 

1 t statistics given in parentheses. 2 Y denotes acquisition price per square foot; S denotes the age of the building 

when purchased. 
EQUATIN:G TAX TO ECONOMIC DEPRECIATION 119 

References 

Beidleman, Carl R. "Economic Depreciation in a Capital Goods Industry." 

National Tax Journal 29 :4 (December 1976), pp. 379-390. 

Break, George F. "The Incidence and Economic Effects of Taxation." In 

The Economics of Public Finance, Studies in Government Finance. 

Washington, D.C.: The Brookings Institution, 1974. 

Coen, Robert. "Investment Behaviour, The Measurement of Depreciation 

and Tax Policy." American Economic Review 65 :1 (March 1975), pp. 

59-74. 

Coen, Robert. "Depreciation, and Rates of Return in Manufacturing 

Industries." Paper presented at N .B.E.R. Conference on the Measurement of Capital, October 1976, Toronto. 

Eisner, Robert. Testimony on Tax Treatment of Capital Recovery (Investment Credit, Accelerated Depreciation and Amortization), Committee on Ways and Means, 93rd Congress, Part 3 of 11, February 1, 

1973, pp. 370-391. 

Feldstein, Martin, and Michael Rothschild. "Towards an Economic 

Theory of Replacement Investment." Econometrica 42 (1974), pp. 

393-423. 

Rall, Robert. "Technical Change and Capital from the Point of View of 

the Dual." Review of Economic Studies 35 (1968), 35-46. 

Hotelling, Harold S. "A General Mathematical Theory of Depreciation." 

Journal of the American Statistical Society 20 (1925), pp. 340-353. 

Rulten, Charles R., and Frank C. Wykoff. "Empirical Evidence on Econcmic Depreciation of Structures." In Con/ erence on Tax Research 

1975. Conference sponsored by the Office of Tax Analysis, U.S. Department of the Treasury, July 17-18, 1975. Washington, D.C.: U.S. 

Government Printing Office, 1975, pp. 107-151. 

Rulten, Charles R., and Frank C. Wykoff. "Economic Depreciation and 

the Taxation of Structures in U.S. Manufacturing Industries: An 

Empirical Analysis." Paper presented at N.B.E.R. Conference on 

Measurement of Capital, October 1976, Toronto. 

Rulten, Charles R., and Frank C. Wykoff. "The Economic Depreciation of 

Non-Residential Structures." Johns Hopkins University working paper, 

1977. 

Jorgenson, Dale W. "The Economic Theory of Replacement and Depreciation." In W. Sellykaerts (Ed.), Econometrics and Economw Theory: 

Essays in Honor of Jan Tinbergen. London: Macmillan, 197 4, pp. 189-

221. 

Samuelson, Paul A. "Tax Deductibility of Economic Depreciation to 

Insure Invariant Valuations." Journal of Political Economy 72 (1964), 

pp. 604-606. 

Shoven, John B., and Jeremy I. Bulow. "Inflation Accounting and Nonfinancial Corporate Profits: Physical Assets." Brookings Papers on 

Economic Activity 3 (1975), pp. 557-598. 

Smith, Vernon L. "Tax Depreciation Policy and Investment Theory." 

International Economic Review 4 (1963), pp. 80-91. 

Taubman, Paul. "Discussion of Hulten and Wykoff." Paper presented at 

N.B.E.R. Conference on Measurement of Capital, October 1976, 

Toronto. . 
120 COMPENDIUM OF TAX RESEARCH 

Taubman, Paul, and Robert Rasche. "Economic and Tax Depreciation of 

Office Buildings." National Tax Journal 22 (1969), pp. 334-346. 

Theil, Henri. Principal of Econometrics. New York: John Wiley & Sons, 

Inc., 1971. 

-U.S. Department of Commerce, Bureau of Economic Analysis. Survey of 

Current Business, selected issues. 

U.S. Department of the Treasury. Blueprints for Basic Tax Reform, 

January 17, 1977. 

U.S. Department of the Treasury, Bureau of Internal Revenue. Income 

Tax Depreciation and Obsolescence Estimated Usef'ul Lives and Depreciation Rates, Bulletin F (Rev. ed.). January 1942. 

U.S. Department of the Treasury, Internal Revenue Service. Depreciation 

Guidelines and Rules, Revenue Procedure 62-21 (Rev.). 1964. 

U.S. Department of the Treasury,' Internal Revenue Service. Asset Depreciation Range ( ADR) System. July 1971. 

U.S. Department of the Treasury, Office of Industrial Economics. Business Building Statistics. August 1975. 

U.S. Department of the Treasury, Office of Tax Analysis. Conference on 

Tax Research 1975. Conference sponsored by the Office of Tax Analysis, July 17-18, 1975. Washington, D.C.: U.S. Government Printing 

Office, 1975, pp. 107-151. (Stock No. 048-000-00297-8). 

Winfrey, F. Statistical Analyses of Industrial Property Retirements 

(Bulletin 125). State of Iowa: Engineering Experiment Station, 1935. 

Wykoff, Frank C. "Capital Depreciation in the Postwar Period: Automobiles." Review of Economics and Statistics 52 (1970), 168-172. 

Zarembka, Paul (Ed.). Frontiers in Econometrics. New York: Academic 

Press, 1974. 
~- -- - - ~- ----~-- -- ,._ 

EQUATING TAX TO ECONOMIC DEPRECIATION 121 

COMMENT 

Robert M. Coen, Northwestern University 

If our income tax is to be just that--an income tax-tax depreciation allowances must approximate as closely as possible actual 

changes in the value of capital assets over the accounting period. 

To the extent that tax allowances fall short of actual depreciation, 

the "income tax" becomes a tax on capital itself; and to the extent 

that tax allowances exceed actual depreciation, the "income tax" 

becomes a subsidy to capital. Nearly all tax scholars and practitioners would agree with these propositions and would use them 

to defend proposals for reforming tax depreciation policy. But this 

does not mean that all would arrive at the same reform proposals. 

Some will argue that liberalization of tax allowances has gone too 

far, that the current income tax subsidizes capital, and that reform 

should entail increases in service lives permitted for tax purposes 

and/ or slower write-off methods over these service lives. Others 

hold precisely the opposite view. Still others admit that tax allowances might be liberal but urge us to keep them that way (or even 

liberalize them further) in order to provide incentives for capital 

formation. 

These divergent views on depreciation reform arise not so much 

from differences in conceptual frameworks as from differences in 

perceptions of reality. Are tax allowances currently in excess of 

actual depreciation or are they not? Hulten and Wykoff show that 

it is possible to attack this question in a scientific way, and they 

Present us with empirical applications of their own method. Before 

noting my doubts about their approach and the problems I believe 

they have neglected, let me say that the question addressed is a 

very difficult one for which we need every bit of evidence we can 

get, that no method of estimating actual depreciation is beyond 

reproach, and that applications and comparisons of various methods ought to be enthusiastically encouraged. 

Hulten and Wykoff estimate depreciation rates of nonresidential 

structures by studying the relationshi1ps between market prices of 

new and used buildings. The data employed were collected by the 

Office of Industrial Economics of the Internal Revenue Service. 

Each observation in the sample gives information on a building 

that was traded-the price paid for it, its age at the time of the 
122 COMPENDIUM OF TAX RESEARCH 

trade, and the date of the trade. Contrary to a view I had expressed earlier, evidently there is enough ·trading of some capital 

goods to generate samples of data that are large enough to permit 

statistical analyses; I hope that more surveys of this type will be 

undertaken in the future. 

Hulten and Wykoff begin by positing that the value of a building 

is a function of it.sage and its date of acquisition. The notion that 

the age of a building may affect its value is easily understood. 

Standard capital theory tells us that the value of an asset should 

equal the sum of the discounted net revenues the as.set will generate in the future (net of operating costs but not depreciation). 

Aging will diminish this value even if net revenue is constant in 

each year of an asset's life, because the stream of future net revenues grows shorter. In addition, the asset may lose efficiency or 

become obsolescent as it ages, in which ca.se net revenue will ·decline with age and the value of the asset will fall more rapidly. 

Thus, if we consider two buildings traded in 1970, one 10 years 

old and the other 20 years old, we should expect that the first 

would command a higher price than the second. 

The influence of acquisition date on the value of an asset is less 

apparent. Again consider two buildings, both 10 years old, one 

traded in 1960 and the other in 1970. Why should their purchase 

prices have differed? Perhaps the most important reason is that 

the general level of prices may have changed between 1960 and 

1970, with building prices undergoing the same inflation or deflation as those of other commodities. If inflation has been occurring, 

then we should expect that a 10-year-old building would sell for 

more in 1970 than in 1960; that is, holding age constant, we should 

expect the purchase price of a building to be positively related to 

its date of purchase. Note, however, that the acquisition date is 

serving here as a proxy for inflation and that the estimated effects 

of acquisition date will be determined largely by changes in the 

general price level during the particular sample period being 

studied. 

The Hulten-Wykoff hypothesis can be capsulized by writing 

Y (S,t) as the value of a building of age Sin year t. Assuming that 

the purchase price of a traded building equals its value, · the OIE 

data provide observations from which the general contours of the 

relationship between Y and Sandt can be estimated. The authors 

test their hypothesis using flexible functional forms in S and t, 

such as Box-Cox power transformations and polynomial expressions. The detailed results reported for office buildings confirm 

the expected negative influence of S on Y, with t held constant; 
EQUATING TAX TO ECONOMIC DEPRECIATION 123 

but the influence oft is not so firmly established. In the polynomial 

forms, t has a positive and statistically significant effect on Y, S 

held constant; in the Box-Cox forms (unconstrained), the influence of t is again positive but quite insignificant. In view of 

the inflation that occurred during the sample period (postwar 

Years through 1971), the Box-Cox results are certainly puzzling 

in this respect. 

The next step in the analysis is to calculate depreciation rates 

from the estimated equations relating value to age and acquisition 

date. The results, summarized in tables 3 and 4 of the paper, generally indicate that depreciation of buildings is more accelerated 

than straight-line (in some cases even more accelerated than 

declining-balance), but that the depreciation rates are considerably lower than those consistent with current tax service lives 

(i.e., 1962 guideline lives). The policy implications are, therefore, 

that accelerated depreciation of buildings ought to be maintained 

but that tax service lives ought to be lengthened. Since the little 

evidence we have on actual depreciation practices suggests that 

buildings are being depreciated at lives shorter than the guideline lives, the increase in effective tax lives needed to equate tax 

and actual depreciation may-be much greater than the increase in 

nominal, or statutory, tax lives. For example, Ture's (1967) 

analyses of Treasury survey data indicated that manufacturers 

were depreciating their structures over a 23-year average life 

compared with guideline lives of 45 to 50 years. Regarding the 

basic empirical issue noted at the beginning of my comments, the 

evidence presented by Hulten and Wykoff suggests that tax depreciation allowances have probably been outstripping actual depreciation, although the authors do not provide us in this paper 

with overall annual estimates of these two measures of depreciation. 

The authors do not clearly explain the procedures they followed 

in calculating depreciation rates. It is quite important that readers 

understand the nature of these calculations and the interpretation 

to be given the rates reported. Using their empirical estimates of 

the Y (S,t) relationship, they arrive at their rates by holding t 

(vintage or acquisition date) constant and computing the percentage change in Y as S increases. Thus, the first-year depreciation rate on vintage 1 buildings is [Y (0,1) - Y (1,1) ]/Y (0,1), the 

second-year depreciation rate is [Y (1,1) -Y (2,1) ]/Y (1,1), etc. 

The rates thus derived are specific to a particular vintage of buildings. As in their previous work, Hulten and Wykoff select 1970 as 

the acquisition date for calculating depreciation rates. Had they 
124 COMPENDIUM OF TAX RESEARCH 

selected 1960, 1977, or 1980, the rates would generally not have 

been the same. Given the form and coefficients of the polynomial 

version of the office-buildings equations in the appendix table A-1, 

the calculated depreciation rates will be uniformly lower the later 

the acquisition date. (This is much less true of the estimated BoxCox forms, because the influence of acquisition date is so small.) 

This implies that actual service lives of buildings have been increasing over~ time and will continue to do so-a result that surprises me and deserves some attention by the authors. 

One of the most widely discussed proposals for depreciation 

reform is a shift from historical-cost accounting to replacementcost (or current-cost) accounting. The authors do not address this 

timely and important issue, and readers might naturally wonder 

to which accounting scheme the reported depreciation rates pertain. At first blush it appears that the rates should be viewed in 

the context of historical-cost accounting, since they are to be 

applied to the depreciated historical costs of assets. This in turn 

suggests that under inflationary circumstances the rates would be 

higher or that the reported rates should be applied to the undepreciated balance revalued to the current price level. 

However, the situation is not quite so straightforward. Consider, for example, the depreciation of a vintage 1 building during 

its first year of service. In terms of the notation introduced above, 

I would define historical-cost depreciation as Y (0,1) - Y (1,1), 

which measures the effect of aging alone on a building's value. But 

if the building were sold at the end of its first year of service, it 

should command a market price of Y ( 1,2). At the same time, a 

new building of a similar type should sell for Y (0,2), so that if 

the owner of the used building were to sell it and replace it with 

a similar new building, the net cost would be Y (0,2) - Y (1,2). 

I would define this last expi:ession as replacement-cost depreciation, consistent with the notion that depreciation should allow 

for the maintenance of real wealth. We can now ask under what 

circumstances the historical-cost and replacement-cost measures 

will differ. The answer is that they will differ if acquisition date 

has some influence on value and if this influence is not purely additive to the influence of aging. 

In the case of the polynomial forms of the price equations, the 

influence of acquisition date is significant but strictly additive, 

and we can therefore view the calculated depreciation measures as 

appropriate to replacement-cost accounting. For the Box-Cox 

forms, the influence of acquisition date is so small that for all 

practical purposes it can be ignored. (If acquisition date were 
"""'.. ------- - - ------ -- -~ ·-

EQUATING TAX TO ECONOMIC DEPRECIATION 125 

significant, its effect would be additive only if 01 were unity, which 

does not appear to be the case.) Thus there is little if any difference between the historical- and replacement-cost measures for 

these forms. (These statements pertain only to the office-building 

equations; equations for the other types of buildings are not given 

in the paper.) 

Raising the replacement-cost issue focuses our attention once 

again on the role of the acquisition-date variables in the estimated 

value equations. I believe that two points need to be stressed. 

First, if, as I suggested earlier, these variables are essentially 

proxies for the general price level, it would be preferable to replace them with an index of prices and not rely on a complex power 

transformation or polynomial in the acquisition date to capture, 

in a possibly very crude way, all of the wiggles in the rate of inflation. This would also facilitate extrapolations of the equations 

into future years when inflation rates might well depart from the 

sample-period cycles and trends that determine the estimated coefficients on the acquisition-date variables. 

Second, it seems unreasonable to introduce either acquisition 

date or a general price index in the value equations in an additive 

way. If there is a general inflation occurring that raises the nominal rate of interest but leaves the real rate of return on physical 

capital unchanged, then the values of all capital goods-new and 

old-should rise at the prevailing rate of inflation (Coen, 1976). 

Accordingly, the value equation should have the multiplicative 

form Y (S,Pt) =Pd (S), where Pt is a general price index and 

f (S) is some general expression in age (polynomial, power transform, or whatever). If one wishes to substitute a general expression in acquisition date for P1, acquisition date would nonetheless 

appear in a multiplicative way with S. When Pt or its proxy appears additively, the implication is that a given rise in the price 

level will produce a larger percentage increase in the value of old 

capital goods than in the value of new capital goods-a phenomenon I can neither justify intuitively nor explain in capitaltheoretic terms. 

Because of these shortcomings in the Hulten-Wykoff specifications of the value equations, I am reluctant to accept any implications of their estimates regarding the relationships between historical-cost and replacement-cost measures of depreciation. 

These specification problems do not apply, of course, to the 

authors' cross-section estimates of the effects of age alone (that is, 

to estimates of the Y (S,t) functions in which t is held constant). 

The cross-section results for office buildings, presented for the first 
126 COMPENDIUM OF TAX RESEARCH 

time in this paper, are a very interesting addition to the authors' 

previous investigations. By and large, they tend to confirm the age 

effects discovered in the pooled time-series, cross-section estimates 

discussed above. Depreciation due to aging alone is again generally 

found to be more accelerated than straight-line and to occur at 

rates substantially lower than those implied by the 1962 guideline 

lives. Thus, although the role of acquisition date may be misspecified in the pooled estimates, this difficulty apparently does not 

lead to serious bias in the coefficients on age in the pooled regressions. 

The Hulten-Wykoff cross-section findings are directly comparable to cross-section estimates of actual depreciation of office buildings derived by Taubman and Rasche ( 1969). The latter authors 

did not use direct observations of :r;esale prices of buildings but 

instead studied the age profile of net rents for a sample of office 

buildings. They computed the present value of net rents for buildings of different ages and defined actual depreciation as the change 

in present value resulting from aging. Contrary to Hulten and 

Wykoff's results, Taubman and Rasche found that depreciation 

was decelerated relative to straight-line. It would certainly be reassuring if these two studies, using different methods and different data sets, arrived at similar conclusions; unfortunately this iR 

not the case. 

How do we explain these diametrically opposed results? One 

possibility is to reject the notion that the value of a buildingits market price-bears any systematic relation to the present 

value of its net rents, i.e., reject the hypothetical market values 

constructed by Taubman and Rasche. But then what does determine capital values, and how does one explain the negative effects 

of aging on value discovered by Hulten and Wykoff? I am not 

ready to forsake this fundamental tenet of capital theory until I 

have a convincing replacement. 

A second possibility is to reject one of the two data sets-perhaps both-as biased. It may be that the used buildings for which 

Hulten and Wykoff have resale prices are not representative of 

"the average building." Many of them might, for example, be the 

remnants of misguided, unprofitable ventures. They might be 

buildings with very high vacancy rates which had to be liquidated 

and could be sold only at substantial discounts to be competitive 

with rates of return being earned on other buildings. If this were 

the case, the authors would overestimate the depreciation rates on 

the preponderance of office buildings that seldom appear on secondhand markets. On the other hand, Taubman and Rasche had 
EQUATING TAX TO ECONOMIC DEPRECIATION 127 

observations on rents only for rather broad age groups, and their 

interpolation scheme to obtain a complete rent-age gradient may 

have been faulty. I must say, though, that the gentle negative slope 

of their gradient seems very plausible. I doubt that anyone would 

pay a substantial premium for office space in Chicago's new Sears 

Tower over similar space in the older John Hancock Building. But 

even if their rent-age relation is correct, their estimates of operating costs by age, which they use to compute net rents, could be in 

error. 

After some rather unrewarding hours of reflection on this 

conundrum, I regret having to revert to banality-more research 

is needed. We need to know more about the resold office buildings 

in the OIE sample to determine to what extent a process of negative selection generated the observations. We need to initiate new, 

more complete surveys of office-building rents and operating costs 

by age of building. We need to combine information on resale 

Prices, rents, and operating costs with building characteristics 

other than age, such as height and location. To the extent that 

height and location are correlated with age, their exclusion from 

price-age or rent-age relations will bias the estimated effects of 

age. 

There are rays of hope here that should not be overlooked. 

Hulten and Wykoff's findings for factories are roughly consistent 

with my recent estimates of loss-of-efficiency patterns for manufacturers' structures (CO€n, 1974), which I arrived at in a way 

totally different from either the present authors or Taubman and 

Rasche. One should not seize on this, however, to make sweeping 

conclusions about the validity of either Hulten and Wykoff's approach or my own, or about the universality of accelerated economic depreciation. For one thing, I suspect that the nature and 

importance of obsolescence are quite different for factory and office 

buildings and the resale markets for the two might be quite 

dissimilar. (For example, factory buildings are rarely used as 

"tax shelters," a practice that has not been uncommon in the case 

of office buildings.) For another thing, I am still at work trying to 

improve my method, and I do not yet know whether the outcome of 

my current refinements will be more in line with my initial findings (Coen, 1975), which are not consistent with those presented 

by Hulten and Wykoff, or with my more recent ones (Coen, 1974). 

I believe that economists are still a long way from having 

definitive estimates of actual depreciation. Various approaches are 

beginning to yield some common results, but there are still many 

instances of opposite findings. And even if agreement could be 
128 COMPENDIUM OF TAX RESEARCH 

reached on service lives and loss-of-efficiency patterns, there would 

remain controversial aspects of replacement-cost accounting that 

need to be resolved. 

Finally, and without intending to downgrade the importance of 

historical investigations of depreciation rates for broad classes of 

assets, I think we should keep in mind that no general tax depreciation formula is likely to do justice to the "facts and circumstances" of individual firms or taxpayers-a point well known to 

Treasury agents in the field but seldom appreciated by scholars. 

Perhaps scholars should begin to devote more of their research 

ingenuity to devising and perfecting-such self-policing accounting 

mechanisms as the defunct reserve-ratio test, which could provide 

more or less automatic checks on whether what taxpayers claim to 

be true is in fact true. This might well turn out to be a more 

promising route to ensuring that tax and economic depreciation 

will someday be equated. 

References 

Coen, Robert M. "Revised Estimates of 'Service Lives and Capacity Depreciation Patterns of Manufacturing Equipment and Structures." 

Research report prepared for the U.S. Department of the Treasury, 

Office of Tax Analysis, June 1974. 

Coen, Robert M. "Investment Behavior, the Measurement of Depreciation, and Tax Policy." American Economic Review 65 :1 (March 

1975), pp. 59-74. 

Coen, Robert M. 4'Alternative Measures of yapital and Its Rate of Return in U. S. Manufacturing." Paper presented at N.B.E.R. Conference 

on the Measurement of Capital, October 1976, Toronto. 

Taubman, Paul, and Robert H. Rasche. "Economic and Ta~ Depreciation 

of Office Buildings." National Tax Journal 22 :3 (September 1969), pp. 

334-346. 

Ture, Norman B. Accelerated Depreciation in the United StatesJ JfJ54-60. 

New York: Columbia University Press, 1967.