Journal of Accounting and Economics 10 (1988) 111-125. North-Holland

ECONOMIC VS. ACCOUNTING DEPRECIATION*

Moshe KIM

Haifa University, Hai@, Israel University of British Columbia, Vancouver, B.C., Canada V6T 1 W5

Giora MOORE

University of Toronto, Ont., Canada MSS 1 V4

Received November 1986, final version received December 1987

In this paper we present and estimate a model of economic depreciation consistent with producers’ optimization. The estimated economic depreciation, which is a function of the rate of utilization and level of maintenance, is about half of that used according to tax (accounting) depreciation. The difference between the economic and tax rates of depreciation results in a subsidy and earlier capital replacement. The implicit maximum net tax subsidy expressed as a proportion of the acquisition price of the asset is 13.3% for a sample of Canadian trucking firms.

1. Introduction

The divergence between accounting depreciation and economic deprecia- tion’ has given rise to a vigorous controversy concerning the appropriate specification of the neoclassical investment function, tax equity and neutrality, the demand equation for capital, productivity growth, subsidies, and related problems.

It is well known that when tax depreciation exceeds economic depreciation, the effective tax rate on the true income is less than the statutory rate and vice versa [Samuelson (1964)]. Recently Skinner (1982) and Most (1984) addressed

*We are greatly indebted to Peter L. Swan, the referee, for his most valuable contribution to this paper. We are also indebted to the editor, Ray Ball, to Bill Schworm and to Jeremy Rudin for their comments and suggestions. Data were kindly supplied by Statistics Canada. Remaining errors are our sole responsibility.

‘We should distinguish between depreciation for tax purposes and depreciation as reported in the accounting reports. In North America, companies can use different methods for tax purposes than they use in their own accounts. In this paper we focus on the depreciation method used for tax purposes, calling it accounting (tax) depreciation. We note here that in our particular case the depreciation used for tax purposes is identical to book depreciation. Furthermore, we should distinguish between economic (physical) depreciation and economic (value) depreciation. The first refers to the loss in productive capacity of a physical asset, while the second refers to the asset’s loss in monetary value. In this paper we estimate the economic (physical) depreciation rate.

0165-4101/88/$3.50~1988, Elsevier Science Publishers B.V. (North-Holland)

112 M. Kim and G. Moore, Economic vs. accounting depreciation

the divergence issue more closely. They investigated the question of whether the useful asset lives on which historical cost depreciation is based are different than the economic lives of depreciable assets. While Skinner’s find- ings for a sample of U.K. firms suggest that the useful lives selected by accountants are longer than the economic lives, Most’s evidence for U.S. firms indicates the contrary.

As a result of the potential as well as the actual problems emerging from the divergence between these two concepts (and measures) of depreciation there have been considerable efforts to estimate the true rate of economic deprecia- tion in studies such as those by Griliches (1970), Taubman and Rasche (1969), Wykoff (1970) Cagan (1973), Hall (1973) Hulten and Wykoff (1980, 1981), and Epstein and Denny (1980).

There are two basic approaches to the measurement of economic deprecia- tion generally discussed and estimated in the literature. Broadly categorized they include: (i) studies which use market (or rental) price data and (ii) studies that use capital stock data, i.e., use quantities rather than price data. Both approaches use data generated from the history of the particular asset.

In this study we take a more direct approach in that we introduce a model of producer behavior where the producer minimizes the user’s cost-of-capital services by the choice of the optimal rate of utilization and level of mainte- nance applied to the stock of capital equipment, thereby directly affecting the rate of depreciation. The model enables us to estimate the rate of economic depreciation that is consistent with this producer’s optimization program.

To ascertain the difference between economic and accounting depreciation rates, we apply the theoretical model to data taken from trucking firms. It is demonstrated that, by allowing firms to utilize the accounting depreciation rate which is effectively higher than the economic rate, there is an implicit subsidy which the firms can obtain. In order to determine the difference in the said depreciation rates and the implied subsidy we calculate the present value of the emerging subsidy and determine the implied capital replacement which is due to this divergence.

Watts and Zimmerman (1986, p. 231) point out that the use of reported profits by regulators provide corporate managers with an incentive to adopt accounting procedures that reduce reported earnings (e.g., accelerated depreci- ation). Lower reported profits reduce the likelihood of adverse government actions against, and increase the likelihood of government subsidies to the firm, if the regulators do not adjust the reported profits to undo management’s earnings-reducing accounting choices. Our empirical findings for the regulated Canadian trucking industry (using the same rate for tax and book purposes) show that the accounting depreciation is larger than the economic depreciation which leads to tax subsidies.

The organization of the paper is as follows: In the following section we develop the theoretical model of economic depreciation, present its properties,

M. Kim and G. Moore, Economic vs. accounting depreciation 113

and discuss the stochastic specification and estimation procedure. Next, we examine the consequences of the economic and accounting depreciation rate differential for the determination of the present value of the implied subsidy and the optimal replacement of the asset. Finally, we describe the data used, present the empirical results, and offer concluding remarks.

2. A model of economic depreciation

Owners of capital assets can alter the amount and rate of depreciation of their assets by varying the rate at which they utilize their assets. The decay of capital assets increases with increases in utilization. On the other hand, owners of capital assets can decrease (or hold constant) the decay of their capital assets by applying maintenance to their capital assets. As a result, the rate of capital depreciation is a function of both utilization and maintenance.

The rate of capital utilization u is defined as the capital services obtained from a unit of capital equipment, i.e., u = E/K, where E represents capital services and K denotes the stock of capital. The quantity of maintenance per unit of capital is similarly defined as m = M/K, with M being the total quantity of maintenance applied during the relevant period.2 The rate of capital decay is specified as a function of both the rate of utilization and the quantity of maintenance per unit capital as 1 r h( U, m) 2 0 with h, > 0, h,,, < 0, h,, > 0, and h,, > 0, where subscripts denote partial differentiation.3

The firm’s technology is described by a concave tranformation function y =j(x, E), where y denotes output and x is a vector of inputs (x,, . . . , x,) other than capital applied during the period.

The basic problem faced by the firm is to choose the optimal levels of maintenance, rate of utilization, and the vector x, given its output constraint and input prices. Formally, the optimization program takes the form

min {C=w~x+{sm+Q[r+h(u,m)]}K}: ~=f(x,E)}, u,m,x,E

0)

where s is the price of a unit maintenance, Q is the acquisition price of a unit of capital stock,4 w is a vector of input prices, and r is the one-period

*See Schworm (1977, 1979) for similar specification.

3We assume that the depreciation function h(u, m) is the same across vintages of capital and therefore utilization rates and levels of maintenance also are equal across vintages. This implies that the depreciated asset is measured in units of the undepreciated asset. This assumption is necessary due to lack of data on asset ‘age and its distribution in our cross-section data set.

4Q = q(l - TD), where 4 is the gross (actual) acquisition price of a unit of capital stock, T is the firm’s income tax rate, and D is the present value of one dollar of depreciation allowances for tax purposes.

114 M. Kim and G. Moore, Economic vs. accounting depreciation

after-tax interest rate. The expression in the inner braces is defined as the user cost of capital services.

The first-order conditions of interest arising from the optimization of (1) are

Qh UK = Xf&, (2)

SK = - Qh,K,

sm + Q[r+ h(u, m)] =Af,u,

(3)

(4

where h # 0 is the Lagrange multiplier. Condition (2) equates the marginal cost of increased utilization Qh, (in the

form of faster decay) with the marginal benefit obtained from higher rate of service flows Af,. Condition (3) equates the marginal benefit from increased maintenance activity, - Qh m > 0, with the price paid for such maintenance activity. Condition (4) equates the user cost of capital with the marginal

productivity of capital services. From (2) and (4) we derive

K/u = Qh,K/{ sm+Q{r+h(u,m)]},

which implies

sm + Q[r+ h(u, m)] = Quh.. (6)

Condition (3) implies

s+ Qh,=O.

(5)

Hence, (6) and (7) can be solved for the optimal rate of utilization and level of maintenance as functions of the price of maintenance, the acquisition cost

of capital and the interest rate. Thus,

u* = u*(s, Q, r), (8)

m* = m*(s, Q, r), (9)

where asterisks denote optimal values. Using (6), the user cost of capital services is5

P*(s,Q,r)={sm*+Q[r+h(u*,m*)]}/u*. (10)

‘In more detail, we obtain P*(s, Q, r) = (sm* + q[(l - TD)/(l - T)][R(l - T) +

h(u*, m*)l)/u*, where R is the one-period pre-tax interest rate, i.e., r = R(l - T). In the actual estimation we adjusted all appropriate variables to tax rate and depreciation allowances.

M. Kim and G. Moore, Economic vs. accounting depreciation 115

Identical results can be obtained by minimizing the user cost by the choice of the optimal level of maintenance and rate of utilization6

(11)

which is analogous to the result obtained in (10). The user cost P*(s, Q, r) in (10) and (11) is linearly homogeneous in {s, Q}

for a given level of r, it is non-decreasing in { S, Q, r } and is concave in {s, Q } and in {s, r }.’ To estimate the economic rate of depreciation consistent with the producer’s minimization program with respect to its user cost, we have to estimate the user cost function P*(e).

The user cost can be written (making use of the homogeneity property) as

~*=S{(**/U*+~[r+h(u*,m*)]/u*}, 02)

where Q = Q/s is the normalized (by s) asset price of capital. Note that minimizing the user cost P* is equivalent to minimizing the normalized user * cost P*, i.e., the normalized user cost function is*

P*(&,~)=min{(m*/u*)+Q[r+h(u*,m*)]/~*}. 03) U. m

This is so because

P*(~,Q,r)=mins{(m*/u*)+Q[r+h(u*,m*)]/u*} u,m

=.rmin{(m*/u*)+Q[r+h(u*,m*)]/u*) u, m

=,@*($,r).

6This is due to the assumed separability of utilization and maintenance policies from the factor demand decisions. Auerbach (1981) uses a similar approach in which the firm’s behavior is viewed as a two-stage process, where in the first stage it chooses the rate of depreciation to minimize the user cost of capital and in the second stage it invests until the marginal product of capital goods equals this minimized cost.

‘Note that P(s, Q, r, U, m) is pairwise linear in {s, Q} and in (s, r}. Hence, it follows that P*(s, Q, r) is pairwise concave in (s, Q) and in {s, r}. Nothing follows about concavity in {s, Q, r} or (Q, r}. See Kim (1988) for a formal proof.

‘The reason for using the normalized user cost is due to heteroscedasticity. To see that, substitute eqs. (17) and (19) multiplied by Q into the left-hand side of (16) and then ‘unnormalize’ both sides of (16). The result of this exercise gives rise to disturbance terms multiplicatively affected by S. In such a case we get non-constant (s dependent) variance and the classical regression properties are violated. The normalization by s avoids this problem.

116

Thus,

M. Kim and G. Moore, Economic us. accounting depreciation

P*(s,Q,r)=.&*(Q,r). (14

We hypothesize the following flexible functional form for the normalized user cost function: 9

n-1 n-1 n-1

P*(i&.., i?$;,, r) = c aiibci + 2 c c cIij( tiiGj)l’* i=l i=l J=i+l

n-l

+ 2 C fxin$‘*rl/* + an,r, i=l

(15)

where the (Y’S are parameters to be estimated. Note that the normalized user cost function P is a quadratic form in ( iC2,. . . , Gn;,, r).

The normalized user cost is written structurally as

P* = (art + ck2*Q + as3r + 2~xr~&/* + 2a,s( r&)l’* + 2a13r1’2, (16)

with P* as is defined in (13). Assuming minimizing behavior, using the

derivatives of the user cost with respect to ‘capital-use’ equations which are consistent function (15):

dP*/ds = h’P*/i?s = m*/u*

envelope theorem, and taking S, Q, r generates the following with the normalized user cost

= al1 + q3r + q2@/* + a23( rQ) A “* + 2a13r1/*,

dP*/dr = aP*/dr = Q/u*

(17)

= a+ + a,,s(&/r)“” + a13s(1/r)1’2, (18)

d P*/dQ = dP*/ii’Q = (r + h*)/u*

= a2* + ‘~r~(l/Q)l’* + (Y23( r/&l’*. 09)

The system of equations consisting of (16)-(19) constitutes the model to be estimated. Deviations of the user cost (16) and its associated ‘capital-use’

‘This functional form is said to be flexible, since it can attain arbitrary partial elasticities of substitutions and is a version of the Generalized Leontief Function [Diewert (1971)].

M. Kim and G. Moore, Economic US. accounting depreciation 117

equations, eqs. (17)-(19) from cost-minimizing levels are assumed to be due to stochastic errors in optimization, and, therefore, we append additive dis- turbance terms to eqs. (16)-(19).

The estimation of the above system could be a conventional matter if we had observed h*, the economic rate of depreciation. However, existing depre- ciation data are inconsistent with our theoretical specification since they are exogenous. Consequently the system (16)-(19) is underidentified.

The solution to this problem adopted here is by postulating an exact relationship between the unobservable variables and other exogenous and endogenous variables in the system.” Specifically, eq. (19) is hypothesized to be exact, and hence, upon rearranging, we can rewrite it as

h* =~*[~,,+~,,(l/&)“‘+cx,,(r/$)“*] --. (20)

Unfortunately, (20) does not resolve matters completely since we lack a value for aZ2. Notice that we can obtain initial values for ai2 and a23 from the initial joint estimation of (17) and (18). In order to arrive at a proxy for a22 we invoke the following assumption: if the price of maintenance would have been zero, i.e., s = 0, then no depreciation would have existed since a firm facing a non-positive price for maintenance would maintain its capital stock up to the level where no depreciation exists, thereby minimizing with respect to its user cost.” This rationale enables us to calculate (y22 as (Y** = l/nC,ri/ui, i.e., the initial value for (Y** is calculated at the sample mean noting that when s = 0 = (l/Q)‘/* = 0 and ( ‘/@I2 = 0.

In order to obtain parameter estimates we initially calculate $* in (16) by substituting the observed variables m*/u* and Q[(r + h*)/u*], where h* is calculated from (20), into the left-hand side of (16). Then we iterate to convergence over the system of equations consisting of (16) and (18) only, since (17) is not independent of (16). At each iteration all the (Y’S are updated [including those of (19)] and as a result the @* is updated accordingly. Parameter estimates are obtained by maximizing the concentrated likelihood function with respect to the parameters of P . * l2 Results of the estimation are given in section 4. In the ensuing section we present a model of the implicit subsidy and optimal capital replacement alluded to earlier.

“See Epstein and Denny (1980) for a similar practice.

“This conceptual treatment views maintenance as analogous to replacement investment. See Betancourt and Clague (1981) for a similar approach.

t2Note that after the substitution of the variables into the right-hand side of (16) as described, the estimated equations become non-linear in the parameters and caution should be taken so as not to confuse local from global maxima of the likelihood function. The reported estimates were obtained using several different starting values. Convergence was rapid and no local, non-global maxima were detected.

J.A.E. B

118 M. Kim and G. Moore, Economic us. accounting depreciation

3. Implicit subsidy and optimal replacement

The annual economic depreciation charges and accounting depreciation charges of an asset are, respectively, h,q and b,q, where q is the purchase price of the asset, t is the time index, and h and b are the economic and accounting rates of depreciation, respectively. Since b,q rather than h,q is allowed to be deducted for tax purposes, the annual implicit tax subsidy emanating from this difference is Tq( b, - h,). The present value of the tax subsidy S is

S = Tqln( b, - ht)eerrdt, 0

(21)

where T is the firm’s income tax rate, r is the appropriate discount rate, and n is the time of replacement of the asset. When the asset is disposed at year n, a capital gain tax is incurred due to the difference between the sale price (L,)

and the book value (II,,) of the asset. The book value of the asset is the purchase price minus the accumulated accounting depreciation, and the sale price can be assumed to be equal to the purchase price minus the economic depreciation. I3 Hence, the pre sent value of the capital gain tax G is

G = Z( L, - Bn)efrn

=Zq (b,-h,)dt eprn, I

where Z is the capital gain tax rate. The net tax subsidy NS due to the depreciation-differential tax subsidy and the recaptured depreciation is simply given by the difference between eqs. (21) and (22):

NS=S-G=/“(b,-h,)(Tewr’-Ze-‘“)dl. 0

(23)

In order to obtain the maximum net tax subsidy possible due to the divergence between accounting and the economic rates of depreciation, we assume that the asset (in absence of technological change) performs the same function from one replacement to another. The proper future period over which to examine a number of replacement cycles is represented by an infinite horizon. For the first replacement cycle, where replacement occurs after n

13Note that Samuelson (1964) treats economic depreciation as a negative capital gain

M. Kim and G. Moore, Economic us. accountmg depreciation 119

years, the present value of the net tax subsidy is given by eq. (23); for the second replacement cycle the present value of the net tax gain is NSe-‘“; and for the jth replacement cycle it is NSe-(I-‘jr”. It then follows that the cycles represent an infinite geometric series which reduces to the following expression for the total present value of the net tax subsidy W:

W= NS/(l - eern)

The implied replacement year is determined by the maximization of (24) with respect to n. Using Liebnitz’ theorem, n* can be derived from the following

expression:

F(n) =r/‘(b,-h,)(Z- Te-“)dz 0

+(6,-h,)(l-e-‘“)(T-Z)=O. (25)

Once n* is determined, the asset is replaced every n* years. For a declining balance accounting depreciation method and a constant-rate economic depre- ciation, where b > h, the year of replacing the asset is determined by

+ [b(l - b)‘-l -II](I - e-‘“)(T- Z) = 0. (26)

Note that even when T = Z, the replacement year n* depends on T since the economic depreciation h( .) depends on the tax rate. However, the effects of the tax rate on economic depreciation are ambiguous.14 Economic deprecia- tion depends on the rate of capital utilization u and on the quantity of maintenance per unit of capital m. Schworm (1979) shows that the effects of tax rates on capital utilization and maintenance are ambiguous,15 and Swan (1981) shows that tax can increase as well as lower the durability of assets. In general, little can be said about the qualitative effects of tax rates on optimal replacement policy.

14Differentiate (26) to get dn*/dT= -F’(h)(dh*/dT)/F’(n). F’(h) = -Z(r+ n - e-‘“) < 0 and F’(n) < 0 from the second-order condition. We obtain that sign{dn*/dT} =

sign{dh/dT), but the sign of dh/dTcannot be determined a priori.

-15Notefromeq.() s 8 and (9) that capital utilization and maintenance depend on the tax rate, because Q = q(1 - TD), cf. note 4.

120 M. Kini and G. Moore, Economic OS. accounting depreciation

The maximum present value of the net tax subsidy is

w*=q{[b/(l-b)]{T[(l-b)“-e’“]/[ln(l-b)-r]

-Z[(l-b)“-l]/ln(l-b)}

- hT(e’” - 1)/r + hZn } /(em - 1). (27)

Before we turn to the empirical results, we discuss the effects of inflation in our framework. The user cost P* in a period of inflation at rate p can be derived as follows:

For an asset with an initial purchase price of $1 the present value of the depreciation allowances b in historical cost terms (with exponential decay) is

A= / oaTbee (h+r)rdt = Tb/b + r, (28)

where r is the nominal after-tax interest rate. If R is the pre-tax rate, r = (1 - T)R. The after-tax value of the $1 asset is

l-A= / om[P* _ &](l _ T)e-[r+h(u*,m*)-Plfdt

=[P*-sm*](l- T)/[r+h(u*,m*)-p].

(29)

Now

l-A=[b+r-Tb]/(b+r)=[b(l-T)+r]/(b+r), (30)

so that

[b(l-T)]/(b+r)=[P*-sm*](l-T)/[r+h(u*,m*)-p],

or

P*=[b(l-T)+r][r+h(u*,m*)-p]/(l-T)(b+r)+sm*.

(31)

If we can crudely think of the real after-tax cost of capital, r - p, as being independent of the inflation rate p (at least as an approximation), then the influence of p on P* arises via its influence in raising the nominal after-tax cost r. Thus, aP*/Jr > 0; that is, inflation raises the user cost, and we would expect the rate of economic depreciation to be higher. The average inflation

M. Kim and G. Moore, Economic us. accounting depreciarion 121

rate expressed in terms of the consumer price index was 9.53 percent for 1975. The (low) after-tax value of the nominal interest rate was 4.75 percent, suggesting that inflation was not a severe problem during the sample period.16

4. Data and empirical results

In order to estimate the user cost of capital services and its associated rate of depreciation we used data on Canadian trucking firms. Canadian trucking is a regulated industry and most of these data were derived from the confidential tapes compiled by Statistics Canada from the 1975 Motor Carrier’s Freight (MCF) Survey and the For-Hire Trucking Origin and Destination (TOD) Survey. The MCF records mainly financial data collected from trucking firms and includes 2756 carriers. The TOD survey records information pertaining to the shipments carried by a subsample of carriers appearing in the MCF

survey. Trucking firms differ significantly as to the type of commodities they haul,

and as a result use varying types of equipment (e.g., vans, trailers, straight trucks). Thus, in order to select a relatively homogeneous group of carriers we selected carriers whose predominant activity is the haulage of general freight. We arrived at a sample consisting of 99 firms drawn from five Canadian provinces. The calculation of the specific variables is discussed next.

The one-period interest rate was taken from the Bank of Canada Review (1977) as the average of the (monthly) prime interest on business loans. This rate should be viewed as a rough estimate of the true rate of interest since, in general, interest rates vary according to risk classes. This rate then was adjusted to account for the various tax rates. The acquisition cost of capital was arrived at by the use of a Divisia price index accounting for the fact that firms have different composition of equipment types. Here again, the com- posite acquisition price of equipment was adjusted to tax rate and depreciation allowance for tax purposes.

Maintenance expenditures include several categories such as: mechanics and their supervisors, tires and tubes, lubricants, parts, purchased repairs and garage. Price indexes for these categories were taken from Statistics Canada, industry price indexes and the employment earnings and hours were aggre- gated using the Divisia price index. The quantity of maintenance was the implicit quantity, that is, maintenance expenditure divided by the Divisia price index. The rate of utilization was specified as miles driven per vehicle.”

The model described in section 2 was estimated for the sample of 99 firms using a full information maximum likelihood method. Parameter estimates

16See Moore (1987) for the effects of inflation on optimal replacement policy

“See Parks (1979) for a similar measure.

JAE. C

122 M. Kim und G. Moore, Economic us. accounting depreciation

Table 1 L

Summary of parameter estimates of the user cost function: P* = aIt + a12Q + assr + 2a,,i)‘/*

+2a,,(ri))‘/‘+ 2a,,r’/’ + error (all entries were multiplied by 104).”

Parameter a11 a22 a33 a12 a23 a13

Value - 0.0181 0.0065 - 0.4382 0.9660 0.1179 0.0936 Standard error 0.2365 0.0803 0.0324 0.0324 0.0434 0.0028

aLog of likelihood function = 1014.25, sum of squares residuals (SSR) = 0.5138 x lo-“, stan- dard error of regression (SER) = 0.7704 x 10m6.

were obtained by maximizing the concentrated likelihood function with re- spect to the parameters of @* and are given in table 1.l’

Using these estimates we checked for curvature properties. Monotonicity requires that P,* 2 0, P; 2 0 and P,* 2 0, these conditions were fulfilled. Concavity was not violated as P,: I 0, P&I 0, P3:P& - P,$Pp*, 2 0 and P,: 5 0, P,T 2 0, P,fP,'f - P,:P,: 2 0. The F value for (6; 92) is 6.503, and the 1% level of significance is 3.12, thus pointing to the high predictive power of the model.”

The estimated rate of economic depreciation for the sampled firms was 0.148 at the sample mean, with standard deviation of 0.139. One of the sampled firms had its rate of economic depreciation equal to -0.14 which should be viewed as a statistical anomaly. 2o Theory dictates that we should restrict the model to parameters which imply a value for h* between 0 and 1. If, in fact, the unconstrained parameters which maximize the likelihood function result in 0 I h* I 1, there is no need to constraint h* to the [0, l] interval. As it happens, only one out of the 99 observations exhibited the statistical anomaly of a negative rate of economic depreciation. This single

‘“Since our data consist of a cross-section of firms drawn from five Canadian provinces, we specified regional dummy variables X,, where i indexes the particular equation and k indexes the particular province. These regional dummies were statistically insignificant.

“The parameters orI and az2 are statistically insignificant. A zero estimated value for a,, is consistent with the i* eq. (16) being actually an index number. The insignificance of az2 arises from high correlation of Q and Q “’ The omission of Q from the estimation would have produced biased results for the included parameters. See Theil (1975).

“This high standard deviation is due to the fact that one of the sampled firms had its rate of economic depreciation negative as reported above. We note that our model admits a zero rate. However, negative rate is related to the nature of the data. Specifically, we are forced to assume that all vehicles and equipment are of the same age. In addition, we use a Divisia price aggregate for Q which is a price index aggregating the various types of equipment actually used by the sampled firms. This practice may have contributed to the statistical anomaly reported above. Cf. footnote 3 and the following discussion in the text.

M. Kim and G. Moore, Economic US. accounting depreciation 123

peculiarity hardly justifies the complexities involved in constraining h* to the [0, l] interval.

Given our method for estimating the rate of economic depreciation and its results, it is useful to provide an additional perspective on the estimates by giving an overview of other related studies of depreciation. Transport Canada (1974, 1976) reports a 12% depreciation rate for trailers and 16% for truck tractors. Hall (1973) reports a 17% rate for trucks, and Griliches (1970) reports ll%-12% for tractors. These studies (except Transport Canada) use price- oriented data. Thus, albeit the differences in methodologies, our results are in the range of results documented in the literature, with the important caviat that our depreciation estimates emanate directly from a behavioral model of producer optimization.

The maximum net tax subsidy and the implied replacement policy depend, as demonstrated in the previous section, on 4, h, r, b, Z and T. The average acquisition price of a truck in our sample was $26,844, with an estimated economic rate of depreciation of 14.8%. The value of the after-tax nominal interest rate Y was 4.75%, the corporate tax rate T was 50%, and the capital gain tax rate Z was 50%. The accounting depreciation rate used was 30%, which is the maximum depreciation rate that Canadian trucking companies can declare for tax purposes. This is also the depreciation used in the companies’ books. Inserting these values into eq. (27) and changing the values of n to obtain a solution, yielded a maximum net tax subsidy W* = $3,581. This maximum W* was achieved when the asset was replaced every n* = 4.9 years. Hence, the implicit maximum net tax subsidy expressed as a proportion of the acquisition price of the asset was 13.3%.

5. Concluding remarks

In this paper we have introduced and estimated a model of a producer who minimizes the user’s cost-of-capital services by choosing the optimal rate of utilization and level of maintenance applied to the stock of capital equipment, thereby achieving an optimal rate of economic depreciation. This model enabled us to estimate the rate of economic depreciation which is a decision variable for the firm, and not a technological or tax datum as generally used in empirical work. 21 Using data from the Canadian trucking industry we have shown that estimated economic depreciation is lower than the maximum allowed accounting rate used for tax purposes. Thus, the divergence between the actual economic rate and the accounting rate gives rise to implicit subsidy. We calculated this subsidy and in addition calculated the inferred optimal replacement time for capital, and we found that the proportion of subsidy

*ISee Hawkins and Leggett (1983).

124 M. Kim and G. Moore, Economic us. accounting depreciation

out of the acquisition price of the asset was 13.3% and that the implied replacement period was about 4.9 years.22

Our empirical work used data from the Canadian trucking industry which is regulated. In regulated industries firms want to appear as unprofitable as possible [Watts and Zimmerman (1986)].23 There are two types of possible subsidy arising from depreciation methods: (1) subsidy due to tax depreciation differing from economic depreciation, thus influencing tax payments and then influencing after-tax cash flows, and (2) subsidy due to book ‘depreciation differing from economic depreciation, thus influencing the regulatory author- ity’s decisions on price and entry to routes and then influencing pre-tax flows. In this paper we were looking at the incentive to over-depreciate for tax purposes, although our empirical data is from a regulated industry, and we calculated the subsidy due to tax depreciation differing from economic depre- ciation. In order to generalize our conclusions, future research should examine the issues raised in this paper in the context of unregulated industries and should examine the incentive to over-depreciate for regulatory purposes.

References

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