Issues in the Measurement of Economic Depreciation
Introductory Remarks
by
Charles R. Hulten and Frank C. Wykoff
April, 1995
Most capital goods are used up in the process of producing output.
Machine tools wear out, trucks break down, electronic equipment becomes
obsolete. When an asset reaches a point at which it is no longer
economical to repair and maintain it, it is withdrawn from service.
And, as asset physical deterioration and retirement cause the productive
capacity to decline to zero, there is a parallel loss in asset financial
value. This depreciation of value is a cost that must be subtracted
from gross revenue in order to determine the income accruing to the asset.
It is also the amount that must be added to the balance sheet in order
to keep wealth intact.
These are relatively straightforward distinctions that are routinely
used in various fields of economics: in studies of economic growth,
particularly in the New Growth Theory with its focus on the role of capital
formation; in environmental economics, with its concerns about sustainable
growth; in production theory with the study of capital formation;
in industrial organization with issues involving the rate of return to
capital; and in public finance, with its interest in the taxation
of income from capital. It is therefore perplexing that these important
distinctions have been the source of much confusion and error. It
is common, for example, to see "deterioration" called "depreciation," though
the former is a quantity concept and the latter refers to financial value.
Other confusions have led to idea that there are two logically separate
concepts of capital, one appropriate for wealth accounting and the other
for the study of productivity and growth.
Part of the problem lies with the historic confusion and controversy
within capital theory itself. This is manifest in academic debates
over the role of capital in economic growth (viz. the Two Cambridges Controversy
in Capital Theory). Another major source of difficulty arises from
the fact that, by definition, a capital good yields its services over the
course of several years, and the fact that capital goods are generally
owner utilized. This leads to a fundamental difference vis a vis
non-capital inputs like labor and materials that complicates the measurement
problem enormously, and necessitates the use of imputational methods and
approximations to get at the underlying economic prices and quantities.
And, with these assumptions and imputations has come yet another layer
of problems and confusions.
On October 10, 1992 the current state of research on capital,
wealth, and depreciation was the subject of a one day Conference on Research
in Income and Wealth symposium, held in Washington D.C. at the Board of
Governors of the Federal Reserve. This symposium ranged over many
of the issues in the measurement of economic depreciation, and presented
both an appraisal of past research and an important set of new results.
The five following papers of this issue of Economic Inquiry are devoted
to proceeding of the workshop, in the hope that further research interest
will be stimulated in this crucial and under-researched branch of economics.
II. Issues in Depreciation Analysis:
Given the history of confusion surrounding the concept of economic
depreciation, it may be useful to proceed the conference papers with a
few
introductory remarks about the problem of depreciation. We will start
with the simple example of a small manufacturing company that owns three
machines: one that was purchased at the beginning of the current
year at a cost of $100,000, on purchased five years ago at a cost of $80,000,
and one purchased twenty years ago for $40,000. The three machines
are intended to perform the same set of tasks, and are essentially the
same, except for wear and tear due to age and design improvements that
have occurred over time. The average useful
life of this type of machine used for accounting purposes is fifteen years,and
the firm uses the straight-line method of accounting depreciation.
The book value of the firm is thus $146,666.67, and annual accounting depreciation
is $12,000. Finally, the operating revenue after expenses is $20,000.1
These data are typical of the information available for analyzing
macro and microeconomic issues that involve capital variables (issues of
growth, production, investment, etc.). The basic question is whether
or not such data are sufficient for the demands made on them. The
answer is, unfortunately, that they are not. Knowledge of the historical
pattern of investment is not sufficient to determine the amount of productive
capacity in a firm, industry, or economy. This becomes appear when
the example above is reworked in analytical form.
The collection of capital goods available for production in year
t may be represented by [It, It-1, ... ,It-T] - in the case of our small
firm, this collection has three elements corresponding to a new capital
good, and one five-year-old and one twenty-year-old capital good.
The historical cost (and gross book value) of the collection is equal to
BVKt = PIt,0I t + PIt,0I t-1 + . . . + PIt-T,0It-T
(1)
where PIt,0 denote the purchase price of a new capital good in year
t. For our example, this is equal to $220,000. The historical
price of new machines PIt,0 is observable, but it tells little about the
value (or shadow price) of a machine that has been in operation for a number
of years, PIt-s. This second price, reflecting the remaining present
value of the income accruing to the machine, is the amount that a rational
investor would be willing to pay to acquire the machine in a second-hand
market. The total value of the collection [It,It-1, ... ,It-T] is
thus equal to
VKt = PIt,0I t + PIt-1It-1 + . . . + PIt-TIt-T
(2)
This is clearly different than the book value measure.
It is also different from the value of the services rendered
by the collection of capital goods, as well as from the in-use productive
capacity of the collection. The former is equal to the product of
the annual shadow price that each good in the collection could be rented
for, PKt,s and the quantities It-s, summed over the active vintages
?Kt = PKt,0It-1 + PKt,1It-2 + . . . + PKt,T-1It-T
(3)
This is the total gross rental value of the capital goods in the collection,
or, in other words, property income. Note that it is the sum of past
investments valued using vintage rental prices, while the value of capital
stock is the sum value at vintage asset prices.
The productive capacity of the collection [It, It-1, ... , It-T]
is yet another variant on this theme. The "quantity" of capital associated
with this set of capital goods is defined as the amount of new investment
that would be needed to produce exactly the same amount of output.
The goods in each vintage are assumed to be equivalent to some fraction
of the capital in the newest vintage, regardless of how the characteristics
of the capital goods have changed over time. Given this assumption,
past vintages of capital can be added up to get the total amount of "capital
stock":
Kt = ?0It + ?1It-1 + ... + ?TIt-T. (4)
The weights, ?s, express the productive capacity of s-year-old assets
as a fraction of the productive capacity of a newly produced asset.
The ?'s are thus indexes of a relative efficiency in which in-use efficiency
of a new asset is normalized: ?0=1.
Studies of economic growth and productivity which are based on
production functions with capital as an input clearly need estimates of
the stock (4); studies of income and wealth need estimates of (2)
and the components of (3), adjusted for depreciation. However, what
is available is only (1), and the left and side of (3). The data
which are typically available are thus not sufficient, but what further
steps are needed to bridge the gap? This question has occupied the
field of income and wealth accounting for several decades, and has required
some creative answers. The papers in this issue discuss some of these
answers and provide some new ones. As a back ground for this discussion,
we lay out, in the following section, the basic framework of depreciation
analysis.
III. The Framework of Depreciation Analysis:
The three equations set out above can, and have, been treated
as separate independent entities. However, this leads to potential
inconsistencies that are a problem for economic studiers of production,
growth, taxation, etc., and it is therefore useful to treat the equations
above a part of a unified framework. There are several possible candidates
(Hulten (1990,1995)) for such a framework, the obvious candidate being
that provided by standard economic theory.
Three relationships of the standard framework govern the capital
accounting exercise. The first is the aggregate production function,
which may be expressed as
Qt = AtF(Lt, Kt) = AtF(Lt, [?0It-1 + ?1It-2 + . . . + ?TIt-(T+1)
(5)
Given this aggregate representation technology, the marginal product
of any vintage-s of investment can be expressed as
PKt,s/PQt = ?Qt/?It-s = ?s ?Qt/?Ks
(6)
We have imposed, here, the second key assumption: that rental
prices PKt,s are proportional to marginal products. This is
essential for establishing the link between capital income and the productive
capacity of capital goods, and thus between equation (3) and the aggregate
capital stock (4). This expression is also significant because it
demonstrates that the efficiency index ?s is really nothing more than the
sequence of the ratios of the marginal products of s-year-old assets to
the marginal product of a new asset.
The third economic relation of importance is the link between
marginal products (rents) and the price of capital goods PIt,s. The
price of a capital goods in a fully arbitraged asset market is just equal
to the present value of the income that the asset is expected to generate
over the remainder of its useful life. The general expression for
the remaining present value of an s-year old asset is
PIt,s = ?=0?T PKt+? ,s+? /(1+r)?+1 (7)
where we have assumed for simplicity that discount rate is constant
over time. When s = 0, we have the expression for a new asset.
This expression links the asset financial valuation equation (2) to revenue
equation (3) and to stock equation (4).
This framework lays bare the fundamental economics of the capital
vintage model, and make clear the crucial role of the ?-efficiencies in
the process of depreciation-deterioration. The ?'s are a key determinant
of the rental price, and by extension, of the asset price, which can be
expressed, after some algebraic manipulation, as
PIt,s = ?=0?T ?s+? PKt+?,0 /(1+r)?+1
(8)
The result is a formulation that expresses the remaining present value
of an asset in terms of the rental price of a new asset. This expression
provides an important insight into the link between the production (quantity)
and valuation (price) sides of the capital problem. The marginal
product of capital could be inserted into (7) in place of ?, in which case
it becomes clear that the financial value of the stock of capital derives
from its productivity in generating future output.
Equation (7) also provides an insight into the nature of economic
externalities depreciation. This expression can be made to yield
?t,sPIt,s = PIt,s - PIt,s+1 = ?=0?T (?s+? - ?s+?+1) Pkt+?,0
/ (1+r)?+1 (9)
where ?t,s is the percentage difference in price of capital between
two successive ages in the same year (i.e., ?t,s = 1 - (PIt,s+1/PIt,s).
This expresses the erosion of capital financial value due to the process
of aging. It is also the definition of economic depreciation:
the amount of capital financial value that must be "put back" in order
to keep the real value of the wealth intact. This is the definition
of economic depreciation noted in the introduction, it is seen to be equal
to the present value of the shiftt in asset efficiency from one age to
the next. In other words, when an asset is used in the production
of output over the course of a year, it is the erosion of current and future
productive capacity (?s+t-?s+t+1) that causes the erosion of asset value
(PIt,s-PIt,s+1).
IV. Efficiency and Depreciation Patterns:
There are an infinite number of possible efficiency functions,
and indeed, every piece of capital probably has its own unique pattern.
However, the literature has focused on three efficiency patterns:
(i) The constant efficiency pattern, also known as the 'one-hoss'
shay pattern, which has the form:
?0 = ?1 = ... = ?T-1 = 1,
?T+t = 0 t = 0,1,2, ...
(10)
In the one-hoss shay form, assets retain full efficiency until they
completely fall apart. In this form, the efficiency sequence is completely
characterized by the service life T, and the measurement problem reduces
to the problem of estimating T.
(ii) The straight-line pattern, in which the efficiency
falls off linearly until the date of retirement:
?0 = 1, ?1 = 1-(1/T), ?2 = 1-(2/T) , ..., ?T-1 = 1-[(T-1)/T]
(11)
?T-? = 0 ? = 0,1,2, ...
In this form, efficiency decays in equal increments every year, i.e.
?t-1-?t = 1/T. As with one-hoss shay, T completely determines the
efficiency pattern.
(iii) Geometric decay, in which the productive capacity
of an asset decays at a constant rate ? = (?t-1-?t)/?t-1. This gives
the efficiency sequence
?0 = 1, ?1 = (1-?), ?2 = (1-?)2, ... , ?t = (1-?)t , ... (12)
This form is characterized by a single parameter like the preceding
cases, but the parameter is now the rate ? rather than the service life
T.
These patterns describe the path of efficiency over time, and
should not be confused with the corresponding path of economic depreciation.
Equation (9) makes it clear that the two paths are linked, and it is well
known that one-hoss shay pattern of efficiency implies straight-line depreciation
with a zero rate of discount, and a concave pattern with a positive discount
rate. It is also clear from (9) that straight-line efficiency is
not the same as straight-line depreciation. Indeed, only the geometric
form has this self-dual property, which makes it an attractive alternative
on a priori grounds.
V. Estimation of Efficiency and Depreciation Patterns:
It is clear, given the central importance of the ?-efficiencies,
that any attempt to implement the empirical framework laid out in the preceding
section requires an estimate of the efficiency pattern. The bad news
is that, since the ?'s are ratios of marginal products, they are not directly
observable. The good news is that the association between the rental
prices and the ?'s in (6) means that the former can, in principle, be used
to estimate the latter. In other words, if there were active rental
markets for capital services as there are for labor services, the observed
prices could be used to estimate the marginal products. And, the
rest of the framework would follow from these estimates.
But, again, there is bad news: most capital is owner-utilized,
like much of the stock of single-family houses. This means
that owners of capital, in effect, rent it to themselves, leaving no data
track for the analyst to observe. This leads to the situation
where the rental price must be estimated from the ?'s, not the other way
around. This is accomplished by using the Hall-Jorgenson (1967) "user
cost" formulation, in which (8) is solved to yield:
PKt,s = [r - ?t,s + (1+?t,s ) ?t,s ] PIt,s (13)
This expression has a straight-forward interpretation: the equilibrium
(shadow) rental cost of an asset equalsthe ex post return to the money
invested in the asset r (adjusted for asset revaluation, ? = (PIt+1,s+1/PIt,s+1)+1),
plus the cost of economic depreciation. In this formulation, the
rate of return, r, is measured on an ex post basis and thus includes any
excess returns or rents accruing to the asset (or any deficits).
This still leaves the question of estimating the ?'s and ?'s.
Fortunately, there are several possibilities besides the use of rental
price. If there is a thick resale market for a particular type of
asset, the ?'s can be estimated from the definition ?t,s = 1 - (PIt,s+1/PIt,s),
and this leads to estimates of ?'s (when depreciation is geometric, both
equal the same constant ?) . However, though more readily available
than rental prices - indeed richly available for many asset types - resale
price data are not available every year for every type of asset and thus
dt,s cannot be computed for the universe of depreciable capital.
This leads to the necessity of approximation methods in order to build
up a picture of the general experience of the entire stock of capital.
We have followed this approach in a series of studies of non-residential
structures and producers' durable equipment in the U.S. (Hulten and Wykoff
(1981a,1981b), Hulten, Robertson, and Wykoff (1989), Wykoff (1989)).
Our basic approach is based on the fact that observation of the price of
capital goods in second-hand resale markets should permit discrimination
between the leading depreciation patterns noted above. If economic
depreciation has the straight-line form, for example, an asset's price
should decline linearly with age; if assets retain their full productive
capacity up to the point of retirement, i.e., are one-hoss shays, price
should decline more slowly than the straight-line pattern when the discount
rate is positive; if depreciation has the geometric form, prices
should decline at a constant rate with age.
We have used this approach to study the depreciation patterns
of a variety of fixed business assets in the United States (e.g., machine
tools, construction equipment, autos and trucks, office equipment, office
buildings, factories, warehouses, and other buildings). The straight-line
and concave patterns are strongly rejected; geometric is also rejected,
but the estimated patterns are extremely close to (though steeper than)
the geometric form, even for structures. Although it is rejected
statistically, the geometric pattern is closer by far to the estimated
pattern than either of the other two candidates. This lead us to
accept the geometric pattern as a reasonable approximation for broad groups
of assets, and to extend our results to assets for which no resale markets
exist be imputing depreciation rates based on an assumption relating the
rate of geometric decline to the useful lives of assets. A
recent paper by Barbara Fraumeni reviews the literature on economic depreciation,
and finds that the weight of evidence strongly supports this form of depreciation.
VI. Criticisms of the Used Asset Price Approach:
The geometric form is a matter of greater controversy (see, for
example, the debate between Feldstein and Rothschild (1974) and Jorgenson
(1973). Feldstein and Rothschild point out that the ?'s and ?'s are
variables that are subject to choices about the degree of utilization and
maintenance, and other factors. They also note that depreciation
can take many forms: increased down time through breakage or repair,
loss in serviceability from wear and tear, wastage of materials, etc.
A theory of ? should capture all of this and, in principle, allow each
asset to be different. Importantly, there is no reasonable
expectation that the pattern is fixed, much less fixed with a geometric
pattern.
Moreover, the geometric form is often regarded as intuitively
implausible because of the rapid loss of efficiency in the early years
of asset life (for example, 34 percent of an asset's productivity is lost
over four years with a 10 percent rate of depreciation). Moreover,
pure geometric decline means that assets are never completely retired and
this implies that the service life is infinite. When viewed from
this intuitive standpoint, the most plausible pattern may well seem to
be "one-hoss shay," in which capital appears to retain the bulk of its
productive capacity throughout its useful life. It is hard to believe
that the productive capacity of desks, chairs, blackboards "evaporates"
at a constant rate every year. It thus would seem that the geometric
pattern is decidedly inappropriate.
Criticism has also been voiced about the viability of used asset
market price data as an indicator of in-use asset values. One argument,
drawing on the Akerlof Lemons Model, is that asset resold in second-hand
markets are not representative of underlying population of assets, because
only poorer quality units are sold when used. Others express concerns about
the thinness of resale markets, believing that it is dominated by dealers
who under-bid.
VII. Evaluation of the Evidence:
Taken together, these intuitive arguments above suggest that
this is case in which econometric evidence leads to wrong result.
However, it may also be true that the intuition, not the econometrics,
is faulty. Intuition tends to be based on personal experience of
individual cases, particularly personal experience of consumer automobiles.
What may be true on a case by case basis may not be true of an entire population
of assets. If so, this has important implications for evaluating
econometric ersults, which typically reflect the average experience of
whole populations not individual units.
The problem with intuition here may lie in a basic fallacy of
composition: it may well be true that every single asset in a group
of 1000 assets depreciates as a one-hoss shay, but the that the group as
a whole experiences near-geometric depreciation. This arises from
the fact that different assets in the group are retired at different dates:
some may last only a year or two, other ten to fifteen years. When
the experience of the short-lived assets is averaged against the experience
of the long-lived assets, and the average cohort experience is graphed,
it will look nearly geometric if the 1000 assets have a retirement distribution
of the sort used by BEA (i.e., one of the Winfrey distributions).
Thus, the average asset (in the sense of an asset that embodies the experience
of 1/1000 each of 1000 assets in the group) is not one-hoss shay, but something
that is much closer to the geometric pattern. This can easily be
verified by performing this experiment using the parameters of the BEA
capital stock program.
There are, of course, applications in which the experience of
one individual asset is at issue. However, most applications in growth,
production analysis, environmental economics, industry studies, and tax
analysis, concern primarily the average experience of a heterogeneous population
of capital, and not with the idiosyncratic behavior of each individual
asset. In this regard, the Feldstein and Rothschild critique may
well be correct about the complexity of the depreciation process for individual
assets, while, at the same time, the idiosyncracies of individual experience
actually average out in the population, so that one observes comparatively
stable and predictable depreciation patterns over all. Such stability
was found in our 1989 study with James Robertson.
Intuition about the lemons problem also may be potentially faulty.
Business capital, unlike personal autos, is resold for reasons not associated
with asset quality per se, but because of events like plant closings, shifts
in product demand, or decisions related to tax optimization, inventory
control or liquidity requirements. Structures, similarly, may be
sold for the same reasons that any piece of real estate is sold.
There is thus no strong basis for believing that only "lemons" come on
to the market. Moreover, it is by no means clear that asymmetrical
information is a problem: the decision to buy a used asset like a
building is usually made by experts in the resale market whose economic
survival depends on the ability to spot defective assets. Akerlof himself
explains that sellers have economic incentive to help potential buyers
overcome the asymmetric information problem. Indeed, were this not so,
the logic of the lemons argument itself would imply no (or very tiny)
used-asset markets.
VIII. Technical Change and Obsolescence:
When new vintages of capital are introduced into the market,
they contain new “state of the art” technology. If this new technology
is superior, then the arrival of new, better vintages of capital will depress
prices of existing old vintages of capital which do not contain the new
technology. This decline in value of old vintages is obsolescence.: the
decline in price resulting from the introduction of new vintages of capital.
Thus, obsolescence is the effect on older vintages of capital of the introduction
of new technology embodied in new vintages of capital. In other words,
embodied technical change results in obsolescence of older vintages
of capital if the new change cannot be grafted on to the older assets.
Until now, we have not tried to identify the obsolescence term. We now
turn to that problem.
This is important because Robert J. Gordon (1990) reported measures
of the rate of technical change embodied in computers through out the 1960s,
1970s and early 1980s. His new measures of obsolescence have dramatic implications
for valuation of computers. He argues that they significantly lower the
rate of increase in computer price indexes and raise the corresponding
rate of growth of stock measures. Gordon also reports new measures of obsolescence
for the general class of producer durable equipment.
The key to conceptually disentangling and identifying the obsolescence
and deterioration components of depreciation begins by observing that the
Jorgenson model of depreciation folds both components into economic depreciation.
Consider the total differential of asset price pIt,s:
dpIt,s = (dpIt,s/ds) - (dpIt,s/dt) (14)
This decomposition of an asset’s price change is illustrated visually
in age-price profiles by Hulten and Wykoff in (1981). Because we will be
dealing only with asset prices and not service prices in this section,
we delete the I superscrips which designate asset prices, either observed
or shadow prices. Furthermore, since we are emphasising variations in age-s
and date-t indexes, we express these in parentheses rather than as subscripts.
Writing the right hand side of equation (14) in discrete differences yields:
dp = [p(s,t) - p(s+1,t)] - [p(s+1,t+1) - p(s+1,t)] (15)
The first square-bracketed term on the right hand side of (15)
is economic depreciation, ??, the change in asset price as a result of
advancing the age index-s, holding the time index-t constant. Economic
depreciation can be further decomposed. First, we need new notation in
order to identify assets by vintage. Let v=t-s and replicate the economic
depreciation term of (15):
?? = p(v,s,t) + p(v-1, s+1,t) (16)
If age advances one integer term then v ? t-(s+1) becomes v-1; thus
two distinct forces combine to yield economic depreciation, one an aging
effect that occurs as the age index advances from s to s+1; and the other
a technological effect that occurs as the vintage index goes from v to
v-1, implying that a new vintage embodying new technology has entered the
market. We name these two effects deterioration, which is the decline is
asset value as a result of aging, and obsolescence, which is the decline
in asset value as a result of the technical change embodied in new vintages
of capital. Both effects are folded into depreciation measures produced
by used asset prices.
That this is so may be seen by introducing the term, q(v-1,s,t).
This would be the period-t price of a vintage v-1=t-(s+1) asset of age-s
. To clarify what is going on here, we take the discrete total differential
of a new asset age-0 in period-t in equation (15). The price is q(t,0,t),
because when s = 0, v = t. Economic depreciation is:
?? = [p(t,0,t) - p(t-1,1, t)] (17)
The new term we would insert is q(t,1,t), which is a contemporary vintage
asset that was produced in one-period ago, and so is now one year old.
Inserting q(t,1,t) into (17) yields:
?? = [p(t,0,t) - p(t,1,t)] + [p(t,1,t) - p(t-1,1,t)] (18)
Clearly (18) and (17) are identical and both equal economic depreciation.
Equation (18) breaks economic depreciation into its two discrete elements,
deterioration, the change in asset price with age, fixing both date and
vintage, and obsolescence, the change in asset price with vintage fixing
age and date.
If depreciation, deterioration, and obsolescence, each occur
at constant geometric rates, say ?, ?, and ? respectively, then combining
(17’) and (18) yields:
??(0,t) = ? p(0,t) = (? + ?) p(0,t) (19)
The rate of economic depreciation is the sum of the deterioration rate
and the obsolescence rate. By successive substitution of ?, ?, and
? into q(s,t) one can measure various aspects of the capital stock from
new investment flows and estimates of ?, ?, and ?.
Unless the same vintages of assets are produced in different
periods, however, then one cannot from price data alone identify ? and
?, even though we know that two distinct processes are causing economic
depreciation - an aging process and a vintage (or technological) process.
This measurement problem is called the Hall identification problem from
his seminal recognition of it in (1968). Hall suggested an arbitrary normalization,
so that one could identify depreciation and inter-temporal revaluation
subject to this arbitrary normalization. Nonetheless, the consequences
for capital asset values and yields as a result of changes in the two may
not be the same. Thus separate identification of deterioration and of obsolescence
is essential to understanding technological change, capital stock, productivity
and investment and rates of return. Gordon (1990) argued that his allowance
for obsolescence resulted in a three fold measurement correction in computer
prices.
While actual identification of the two separate terms that comprise
depreciation, deterioration and obsolescence, is impossible from price
data alone without additional information, Hall (1968) actually suggested
a solution using the price hedonic methods. Basically the hedonic approach
identifies the incremental contribution to asset price of each characteristic
of the asset. One then can isolate the prices of the characteristics which
constitute the new vintage and construct a latent price for a hypothetical
one-year-old contemporary vintage asset, q(t,1,t). The difference between
this latent price and the observed q(t-1,1,t) is the obsolescence component
of economic depreciation.
IX. Hulten-Wykoff Rates Vintage 1981 and 1995:
Jorgenson reproduces in his Table 2 the industry depreciation
rates we produced in 1981. While no one had claimed that these rates were
the last word on depreciation, they have been widely used by empirical
researchers in the US and abroad. Recently new evidence has emerged that
causes one to rethink the use of these rates. Should these rates be updated
and if so how? BEA has produced new asset lives by asset category. In addition,
as Jorgenson announced in this volume, new data has been produced by the
Treasury Department. Finally, new research by Oliner and others on used
asset prices of computers and other specific assets, provides potential
new evidence as to the appropriate rates and levels of assets that are
completely new since our earlier research effort.
This is welcome news. The introduction of new information will
be an on-going process and a strategy for integrating new evidence needs
to be developed. We do not presume to have the entire answer to this very
complex question at this time. The nature of revisions will depend on the
nature of the new data. At times, new evidence is not easy to integrate
into the rates. For example, new studies that fail to account for retirement
bias are simply not comparable to state of the art procedures. If new information
could cause a twist of relative rates, but is based only upon part of the
assets, then we have to decide whether to respond at all.
One costly possibility is to replicate our studies using retirement
distributions that center on the new lives. This would be a costly research
effort. A simpler procedure to conveniently update our vintage nineteen
seventies is suggested by Fraumeni in (1995).
A related problem is that new industrial classification methods
are contemplated as are new raw data sources and new individual asset class
studies. Each of these new types of information suggests different measurement
strategies. One strategy would be a census approach, compile a new industry
classification of depreciation rates every five, ten, or twenty five years,
building in whatever possible new information on technical change, asset
mix, and industry classification has evolved.
Instead of one single strategy, here we suggest several options.
The chosen option will depend upon resources available for capital measurement.
As noted above, estimation options could range from entirely new Hulten-Wykoff
econometric analysis complete with new retirement patterns, new asset lives,
and new price data, on the one hand, to simple extrapolation of old rates
with minor adjustments to certain classes if new data calls for this, on
the other. Alternatively, one might alter the basic class structure so
as to compress different asset classes even more than they are in Jorgenson’s
Table 1. We shall illustrate the rates that result from th simple modification
suggested in Fraumeni (1995).
___________________________________________________________________
Table 1
Rates of Economic Depreciation (d)
__________________________________________________________________
Approximate
Asset
Depreciation
Class
Rate
___________________________________________________________________
Producers' Durable Equipment:
Furniture & Fixtures
12%
Agricultural Machinery
12%
Industrial Machinery and Equipment
12%
Construction Tractors and Equipment
18%
Farm Tractors
18%
Service Industry Equipment
18%
Electrical Equipment
18%
Aircraft
18%
Trucks and Autos
30%
Office and Computing Equipment
30%
Non-Residential Structures:
3%
___________________________________________________________________
Source: Based on more detailed estimates by Hulten and Wykoff
(1981), revised and updated in Fraumeni (1995).
One example of a new strategy is presented in Table 1 which contains
comparatively direct imputation to our original rate adjusted only superficially
for the new asset lives. Our approach is to employ the procedure used in
(1978) to extrapolate evidence mula is:
? = x?T (20)
where ? is the depreciation rate, T is the asset-class life and the
x-factor is the Hulten-Wykoff conversion rate. This x-factor is calculated
from the classes for which we have independent estimates of Box-Cox best
geometric approximations of economic depreciation. These are called class
A assets. Thus x is endogenous to the class A estimation process:
xA = ?A ? LA (21)
From class A assets lives and depreciation rates we calculate xA. We
then extrapolate rates for class C assets assuming the value of xC is identical
to xA. Thus from LC and xC, we calculate ?C. This gives us depreciation
rates for class-C assets.
Now that BEA has altered asset lives, we could use the new lives
to map new rates from type A assets, that we had studied relatively carefully,
into class C assets. It appears to us, though, that some of the life adjustments
are more radical than others. Another approach would be to simply compress
asset classes into a smaller number of categories reflecting the level
of our ignorance. This compression causes a good deal of lost information,
but when aggregating to the degree necessary, one may not be able to utilize
evidence for each individual class or type of asset. One possible, and
severe compression appears in Table 2. While we feel our more detailed
rates may give a more accurate picture of each asset class and assets in
each industry vintage US 1970s, this less detailed compression may of more
practical use to statistical agencies world wide until better studies can
be undertaken by the leading agencies.
X. Contents Review:
As we noted at the outset, heated argument has marked much of
the debate on capital measurement. Jack Triplett’s paper deals with the
famous 1970s debate between Edward Denison on the one hand and Dale Jorgenson
and Zvi Griliches on the other. Triplett argues that the disagreement boiled
down to a different perspective on the role of capital in the income accounting
literature of Denison from the growth and productivity literature of Jorgenson
and Griliches. Triplett bridges the intellectual gap between Denison and
thus BEA to the model we have outlined above. Triplett’s equation (3a)
goes to the heart of the dispute that had stymied reconciliation. Triplett’s
equation (3a) links the Jorgenson definition of economic depreciation to
the Denison concepts of exhaustion and decay. Triplett’s expression k(1,s)
- k(2,s) in his equation (3a) is simply the Jorgenson term, ?s - ?s+1,
the decline in efficiency which Jorgenson calls the mortality function:
ms = ?s - ?s+1 (22)
The mortality function appears in equation (9) above as a key aspect
of economic depreciation. Triplett’s contribution is to explain and thus
reconcile a major dispute, paving the way for construction of a coherent
measure of capital in the SNAs.
Dale Jorgenson, the founder of this literature, in his up-to-date
summary in this volume of the econometrics of economic depreciation links
the Hall approach to the various econometric models for estimating depreciation
taking into consideration both in-use depreciation and retirement.
Jorgenson reviews major new data provided by the statistical agencies in
the US and recent attempts to estimate obsolescence as well as a
summary of the empirical depreciation literature itself. Thus, combined
with this introduction, Triplett’s reconciliation and Jogenson’s linkage
of the theory of depreciation to empirical research we have a comprehensive
and coherent research agenda into measurement of capital stocks.
Ishaq Nadiri and Ingmar Prucha significantly advance the measurement
of capital by solving three problems. These are the problem of permitting
endogenous depreciation, the problem of limited used-asset price data,
and the problem of estimating the stocks of intangible assets, such as
goodwill and research and development (R&D). When one considers measurement
of depreciation of large fixed capital assets like dams, paper mills, nuclear
reactors, and missile silos, it is obvious that a measurement solution
that does not rely on used-asset prices must be found.
Nadiri and Prucha implement their framework for the total US
manufacturing industry. By assuming that a period-t cost function, dual
to the production function, yields conventional output from the period-t
input mix, and simultaneously yields the new period-t+1 values for these
inputs, they render depreciation as an endogenous byproduct of cost minimization.
Since their assets include expenditures on (R&D), they are able to
extend the analysis to measure the stock of endogenous R&D capital.
In a related contribution, Mark Domes exploits production function
analysis to directly infer efficiency sequences, ?s, for plant level data
in which capital assets are held in-place between periods. This is a two
fold contribution. Jorgenson in (1976) suggested that the efficiency sequence
could be thought of as an efficiency “function” whose form would depend
upon the decline over age and time of marginal products of various
vintage of capital, so that rather than try to measure ?s from relative
rental prices for each individual vintage t-s, one could estimate a pattern
which would represent the path of efficiency decline throughout the life
of a cohort of capital.
Domes, like Nadiri and Prucha, does not require used-asset market
prices to obtain his endogenously driven efficiency function estimates.
This not only enlarges the scope of measurable depreciable capital but
provides a check on inferences about depreciation drawn from used asset
market prices. Domes applies his methodology to steel plant capital. Again
we have an illustration of a new method for estimating Jorgenson’s efficiency
sequence, and thus the mortality sequence in Triplett’s equation (3a).
Another major problem confronted by estimators of depreciation
involves correcting used-asset prices for early asset retirement. We showed
in Hulten and Wykoff (1981) that without a correction for retirement, a
censored sample would result in downward-biased estimates of the true depreciation
rates. Steve Oliner studies the consequences for vintage capital of new
computerized technology that favors newer vintages of machine tools by
allowing them to receive numerical instructions. this technological innovation
replaces the need for a machinist, thus reducing risk, increasing quality
control, and making newer vintages of capital technologically superior
to the older vintages by reducing labor input costs. Oliner develops a
framework for estimating obsolescence of capital while at the same time
integrating a new set of retirement figures into the analysis.
One important aspect of the Oliner paper is its analysis of retirements.
In theory, retirement should occur as soon as quasi-rents fall so low that
the present discounted value of the remainder is less than scrap value.
Until Oliner’s work we had only one or two actual empirical studies of
retirement. BEA still uses the Winfrey studies from the 1930s.
Oliner’s paper is important for another reason. The role of technical
change is absolutely central to growth, capital measurement and productivity.
How does one measure technical change, the impact of new goods and
the separable effects of obsolescence and deterioration? This is another
topic that has been a subject of much debate in recent years and to considerable
confusion. Diewert (1989), Griliches in CRIW, Berndt and Griliches, Gordon
(1990) and Hulten (1992?) have all started to deal with a special case
of new technology - the new goods problem. The apparent acceleration in
new goods production resulting from the technological advances of computer,
electronic, telecommunications and biotechnology has wrecked havoc in measurement
of quantity and price measures. The very definition of a good comes in
to question. Is a VCR a mere technical advance over recording devices or
is I an entirely new product without predecessors. Regardless of how one
answers this question the modeling of technical change and its impact on
capital values is closely related to these problems and concerns.