KEO Discussion Paper No.97

Toward Reframing Capital Measurementin Japanese National Accounts∗
Koji Nomura
Keio Economic Observatory, Keio University
nomura@sanken.keio.ac.jp
June 1, 2005

Keywords
age-efficiency profile, age-price profile, gross capital stock, productive capital stock, net capital stock, SNA, NIPA,
BEA, Canberra I & II Group, geometric approach, hyperbolic, consumption of fixed capital, depreciation, constantquality deflator, capitalization of software, information technology, land as capital, price and quantity of capital
service, non-market production

Abstract
The Japanese national accounts are moving toward a sweeping improvement of the measurement of capital, which
is one of the most difficult areas to reframe. The objective of this paper is to recognize current problems on themeasurement of capital in the Japanese national accounts and to examine the direction for catching up and going
forward. Our conclusion that ESRI should introduce capital services at the same time as reframing the measurementof capital stock, thereby anticipating SNA 2008.

∗ This paper was presented at the ESRI (Economic and Social Research Institution) Conference on Next Steps for the Japanese

SNA: ”Towards More Accurate Measurement and More Comprehensive Accounts”, Tokyo, March 25, 2005. I have revised
since this presentation. I am grateful to Dale W. Jorgenson for his valuable comments and Jon D. Samuels for his help at
Harvard University, and Erwin Diewert (University of British Columbia), Steven Landefeld (BEA), and Paul Schreyer (OECD)for useful comments at the conference. This paper is preliminary. Comments welcome.

Contents
1

Introduction

1

2

Capital: Two Aspects of One Entity

2

Concepts of Capital Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

2.1.1 Traditional Gross and Net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

2.1.2 Gross, Productive, and Net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

2.1.3 Geometric vs Hyperbolic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.1

2.2

Price and Quantity of Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.2.1 Price on Investment as Composite Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82.2.2 Constant-Quality Prices in the U.S. and Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.2.3 Possible to Use Harmonized Prices? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.3

Capital Value and Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

2.3.1 Capital Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

2.3.2 BEA’s Revision for Measuring Stock and Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

2.3.3 Possible to Harmonize Depreciation Rate? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

3

Measurement of Capital in Japan

18

Japanese National Accounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.1.1 Net Capital Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.1.2 Consumption of Fixed Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

3.1.3 Gross Capital Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

3.1

3.2

Alternative Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

3.2.1 Price and Quantity of Capital Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

3.2.2 Aggregating Heterogeneous Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

3.2.3 Land as a Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

3.2.4 Capitalization of Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

3.2.5 Impacts of IT Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

3.2.6 Capital for Non-Market Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

4Concluding Remarks: Proposals for the Japanese National Accounts

34

List of Figures
1

Concepts of Capital Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42Capital Stock in the Japanese National Accounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3

Share of Software Investment in GDP: An International Comparison . . . . . . . . . . . . . . . . . . . .

30

4Composition of Software Investment: Comparison between the U.S. and Japan . . . . . . . . . . . . . .

31

5

IT Capital Contribution Share to Total Capital Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

6Additional Capital Service Cost for Non-Market Production . . . . . . . . . . . . . . . . . . . . . . . . .

34

List of Tables
1

Comparison of Capital Stock for Fixed Assets between the JSNA-NCS and Our Estimates . . . . . . . .

20

2Comparison of Capital Stock for Private Fixed Assets between the GCSPE and Our Estimates . . . . . .

21

3Growth Rates of Capital Stock and Services in Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

4Relative Prices of Capital Stock and Services by Industry between the U.S. and Japan . . . . . . . . . . .

28

5Asset Classification and Depreciation Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Toward Reframing of Capital Measurement in Japanese National Accounts
Koji Nomura (Keio University)
June 1, 2005

1

Introduction
The accumulation of theory and empirical studies brought some significant changes to the measurementof capital in national accounts in the 1990s in order to capture rapid changes in the production structure.
Internationally, there are three important events in this area. The first was the clarification and extension
on capital concepts in the United Nations (1993) System of National Accounts (1993 SNA), which wasrevised after an interval of a quarter of a century after 1968. However, the 1993 SNA was not necessarily
a comfortable landing, and triggered intensive discussions on capital measurement. The second event
was the Capital Stock Conferences by the so-called Canberra Group, organized by the Organization
for Economic Cooperation and Development (OECD) in 1997, 1998, and 1999. The third event was the
improvement of the measurement of capital stock and depreciation as a part of the comprehensive revisionof the National Income and Product Accounts (NIPA) by the U.S. Bureau of Economic Analysis (BEA) in
1997.
Although the conceptual expansion of capital recommended in the 1993 SNA was applied in national
accounts of many countries, it was not fully incorporated into the Japanese national accounts. As is widely
well known, the Japanese national accounts still do not capitalize own-account software and prepackaged
software. In international comparisons of economic growth and productivity based on the 1993 SNA,
Japan must be treated as an exception. Can the Japanese stock statistics make up for lost time? Is it
possible to turn the tables in the next revision of the SNA in 2008 (1993 SNA Revision 1)? Our objective inthis paper is to recognize some defects on the measurement of capital in the Japanese national accounts
and to examine the direction for catching up and going forward.
The Japanese economy expended many years eliminating worthless assets and reforming the economic
system after the collapse of the bubble economy in the beginning of the 1990s. The period of the crises
may have passed. For the Japanese national accounts, a turning point may be coming now. In orderto catch up to international standards, Economic and Social Research Institution (ESRI), Cabinet Office,the producer of the Japanese national accounts, officially incorporated the chained index for the national
accounts in the late of 2004. Likewise, ESRI is moving to consider sweeping improvement of the capitalstock statistics, which is one of the most difficult areas for reframing the Japanese national accounts.
The intensive discussions by the Canberra Group and the revision by the BEA in the late of the 1990s
provide valuable insights for improving the measurement of capital in Japan. In order to reframe cap1

ital measurement in the Japanese national accounts, it is appropriate to start with understanding somesignificant concepts. In section 2, we introduce the framework for measuring capital with some practicalissues in this area, based on the theory for measuring capital proposed by Jorgenson and his associates:
Jorgenson (1963, 1974, 1989), Hall and Jorgenson (1967), Jorgenson and Griliches (1972), Hulten (1990),
and Diewert (2001).
In section 3, we briefly introduce the present measurement of capital in the Japanese national accounts
and examine some problems to be overcome. In addition, as an alternative measurement of capital in
Japan, we introduce our measurement for the stocks and services of capital. Our latest estimates forcapital stock and service matrixes are based on 102 assets: 95 fixed assets, 3 types of inventory, and 4 typesof land, and 70 capital holding sectors: 45 industries, government, household, and 23 infrastructures.
One of the most significant conclusions from our measurement of capital is to indicate that there is no
insurmountable obstacles to improve the Japanese capital statistics.
It may be valuable to note that the present defects of capital measurement in the Japanese national
accounts do not necessarily mean that the accuracy of revised capital statistics will be inferior. In fact, theprimary statistics in Japan are well above the international standard. The revised Japanese statistics will
be able to propose an accurate and internally consistent stock measures and consumption of fixed capital.
Moreover, it can contribute to international examination for the further improvement on measurement of
capital, like measurement of price and quantity of capital services, and capital service cost for non-market
production, which are discussed by Canberra II Group (Ahmad 2004; Diewert, Harrison, and Schreyer,2004). We conclude in section 4, summarizing our proposals for sweeping improvement for measuring
capital in the Japanese national accounts.

2

Capital: Two Aspects of One Entity

2.1

Concepts of Capital Stock

What is the role of measurement of capital? Like other factors of production, which are used in
production processes, capital has a productive capacity. Unlike other factors of production, however,capital is not consumed, but used beyond a single accounting period. This durability lets the capital retain
its value so that capital can be used in future production processes. Capturing the two aspects of capital:
the productive capacity and the value of capital, is the main purpose for measuring capital.*1*1

The durability of capital makes the accounting difficult. See Hulten (1990) and Diewert (2001).

22.1.1

Traditional Gross and Net

Traditionally, two distinctive concepts for capital stock, gross capital stock and net capital stock, wereused. The distinction of the two concepts is based on depreciation. Gross capital stock is defined before
the deduction of depreciation and net capital stock is reduced by the depreciation. As the traditional grossconcept still remains in the Japanese statistics of capital stock for production analysis, gross capital stock
may have been sometimes thought suitable to measure the productive capacity of capital.
However, the traditional system of gross and net capital stock is incapable of portraying the two different
aspects of capital, except under unrealistic assumptions. This was finally abandoned by BEA in 1997, aquarter century after the controversy between Jorgenson-Griliches (1972) and Denison, also Jorgenson(1989) had clearly pointed this out.
2.1.2

Gross, Productive, and Net

The intensive works of Dale W. Jorgenson, Robert E. Hall, Zvi Griliches, Charles R. Hulten, Walter E.
Diewert, who marvelously were at the University of California, Berkley in the 1960s,*2 and many otherresearchers and statisticians, have developed the theory for measurement of capital and accumulated
the empirical results. The theory of capital measurement clarifies the distinction of these two aspects ofcapital, based on the concepts of age-efficiency profile and age-price profile. We use three distinctive stock
concepts in this paper. Three concepts are gross, productive, and net capital stocks.*3
Figure 1 represents the three concepts of capital stock and their relationships. The gross capital stock
G,k, j(GCS): St,τ of asset k with age τ in industry j at time t is defined as:
G,k, jk, jSt,τ = At−τ ,

(1)

*2

Griliches was at the University of Chicago in the 1960s, although he has collaborated with Jorgenson.

*3

We use the name of productive capital stock after Triplett (1996a, 1997) and Hill (1998, 1999). Biørn (1989) and Biørn, Holmoy,
and Oystein (1989) call a productive capital stock in this paper as a “gross” capital stock, since they do not need a traditionalgross concept of capital stock. OECD (2001b) does not give a particular name for the productive capital stock.
Net capital stock in this paper is also called “wealth” capital stock, like Triplett (1997). The net capital stock is “generally,a synonym for the wealth capital stock. The “net” language thus distinguishes the depreciated capital stock (the wealthcapital stock) from the undepreciated, or gross capital stock. However, the traditional “gross-net” capital dichotomy does
not encompass the productive capital stock, which could cause confusion (because the productive capital stock is “net” ofdepreciation, compared to the undeteriorated gross stock). Once the distinction between productive and wealth capital stocks
fully enter the lexicon, it will probably be preferable to avoid the net capital stock terminology.” (Triplett, 1997) However, we
use net capital stock in this paper, partly because we cannot find a adequate term in Japanese corresponding to the “wealthcapital stock”, and partly because net capital stock is identical with the traditional net capital stock although the concept isclarified.

3  ! " # "  $%# &'( ) " *       ,% ( -" #           .  / *01

   '( " # +'( ) " * 

Fig. 1 Concepts of Capital Stockk, jwhere At−τ is quantity of investment measured in “efficiency units” among the existing assets with different
vintages: v = t − τ, although the GCS permits the difference of quality of assets with different ages: τ.
In other words, the assets with different ages are evaluated at “as new” prices in the GCS, described inOECD (2001b). The GCS provides the conventional first step for measuring capital stock.
The age-efficiency profile (AEP) gives a schedule for the productive capacity associated with the pureaging of capital at the same point of time, taking an efficiency of a new asset as one to normalize. Assuming
no change of the AEP over time, we write the AEP as dkτ , independently of time t. It satisfies the conditions
below,
dk0 = 1, dk1 > 0, dkτ − dkτ−1 ≤ 0, lim dkτ = 0.
τ→∞

(2)

These four conditions represent, respectively, normalization of AEP at τ = 0, durability of the asset,
monotonic decreases of relative efficiency, and finite durability. Note that the AEP is defined as the
combined distribution of the survival distribution of an asset and the efficiency distribution for thesurviving asset. Triplett (1997) uses the term “deterioration” to define the relative efficiency in the AEP.
Deterioration arises from two sources, “retirement” and “decay” which is defined by the loss of efficiency
of a surviving asset.
Applying the AEP to assets with different ages, the GCS will be transformed to the productive capital4

stock (PCS), as
P,k, jG,k, jSt,τ = dkτ St,τ .

(3)

The PCS is evaluated in the same efficiency unit among assets with different ages. Capital services can beproduced from the PCS, as is discussed later. The AEP transforms assets with different ages to be perfectlyPP,k, jP,k, j *4
substitutable, so that the PCSs with different ages can be simply added: St = ∞By the dual
τ=0 St,τ .
approach of capital, the capital service prices of assets with different ages have perfect complementary, sothat they are equivalent: PtK,k = PK,kt,τ , (Jorgenson, 1989).
The age-price profile (APP) gives a schedule of the capital value associated with its pure aging at thesame point of time, normalizing the capital value of a new asset at one. The schedule of the capital value
in the APP depends on future capital services described in the AEP, the expected capital service price,and the expected discount rate, as defined in Equation (19) later. Here, we write the APP as dP,kt,τ . Assets
with different ages normally have a different value because of a finite service life of the asset, even if the
productive capacity the asset has is exactly same. We assume the conditions for the APP as:
P,k
P,k
dP,k
= 1, dP,k> 0, dP,kt,τ − dt,τ−1 ≤ 0, lim dt,τ = 0,
t,0
t,1
τ→∞

lim dP,k = dkτ .
rt →∞ t,τ(4)

The conditions required for the APP are similar to Equation (2) for the AEP. The fifth condition represents
that the APP converges to the AEP, when the discount rate rt approaches infinity. Applying the APP toassets with different ages, the GCS will be transformed to the net capital stock (NCS):
N,k, jSt,τ

G,k, j= dP,kt,τ St,τ .

(5)kExcept the case that the AEP declines very rapidly, the APP may be smaller than the AEP: dP,kτ ≤ dτ .

From the conditions for the AEP and APP in Equations (2) and (4), the order of magnitudes in three capitalstocks may be as,
N,k, jSt,τ

P,k, jG,k, j≤ St,τ ≤ St,τ .

(6)
N,k, jFor new assets with τ = 0, the three measures of capital stock are identical: St,0

P,k, jG,k, j= St,0 = St,0 , sincedP,k= dk0 = 1. The difference in the three measures occurs because of the durability of assets.
t,0
The concept of GCS is the same as the traditional gross concept of capital stock. In the three capitalstocks, the GCS may have very limited purposes to be used. If we assume a vintage production function,
the GCS may give an appropriate concept as the factor input. However, for the economic analysis using*4

Diewert and Lawrence (2000) and Diewert (2001) provide new approach in measuring capital and propose the use of asuperlative index number formula to aggregate assets with different ages (or vintages, under the fixed point of time). In thispaper, we assume perfect substitution in the PCSs with different ages, as if the AEP were specified independently.

5

an aggregate measure of capital with different ages, it may be no longer easy to find an appropriate roleof the GCS.*5
The GCS is interpreted as a special case of the PCS, which is an appropriate concept for productive
capacity of capital stock. Only if the AEP is “one-hoss shay”, where the relative efficiency of capital isconstant throughout the lifetime Tk , the GCS is identical with the PCS,
N,k, jSt,τ

P,k, jG,k, j≤ St,τ = St,τ ,

(7)

where
dkτ = 1(τ < Tk ), dkτ = 0(τ = Tk ).

(8)

Only some exceptional assets like electric light bulbs provide an example. The one-hoss shay distribution
can hardly be observed in the empirical studies for measuring the AEP. The clarification on concepts ofcapital stock no longer provide a role for the GCS.
2.1.3

Geometric vs Hyperbolic

In the framework for measuring capital stock, the key idea is the AEP. Based on the comprehensive
empirical studies of Hulten and Wykoff (1981a, 1981b, 1981c), the geometric distribution in the AEP or
APP is approximately accepted for many assets.*6 Theoretically, the geometric distribution alone has thedesirable property that the AEP and the APP are identical. Also, therefore, the PCS and the NCS are
identical, as
N,k, j= St,τ ≤ St,τ ,G,k, j(9)k τdkτ = dP,kt,τ = (1 − δ ) .

(10)

St,τ

P,k, jwhere

This assumption is called as the “best geometric approach” (BGA). The two aspects of one entity ofcapital are captured by only one measure, based on the assumption of the BGA. Accepting the BGA makes*5

Conventionally, GCS is treated as a starting point for the measurement of capital stock, as represented in Equations (3) and(5). However, as the GCS is the same as the quantity of investment in Equation (1), the procedure for the measurement of the
GCS need not be addressed.

*6

Jorgenson (1996) gives a survey of empirical research on depreciation and its applications. There has been considerable debate
about the appropriate depreciation rates for assets with constant-quality deflators. As pointed out by Oliner (1993, 1994) and,more recently, by Whelan (2002), if the quantity of investment is constructed with a constant-quality deflator, the depreciation
rate should be obtained from constant-quality price data by age of asset. This corresponds to “partial depreciation” in Oliner’s
terminology.

6it possible to neglect the age structure for aggregating assets with different ages, like a familiar perpetualinventory method (PIM),
P,k, jSt

P,k, jk, j= (1 − δk )St−1 + At =

∞
X

k, j

(1 − δk )τ At−τ .

(11)

τ=0

On the revised measurement of capital stock and depreciation of the U.S. BEA, the BGA is used as adefault, as discussed in section 2.3.2.
Alternatively, hyperbolic function, which used to be called β-decay, is assumed to describe the AEP. The
hyperbolic function is defined as,dkτ =Tk − τ
,Tk − βkτ(12)where Tk and βkτ (−∞ < βkτ ≤ 1) are parameters for asset k. When βkτ is 0, 0< βkτ < 1, and 1, the hyperbolic
AEP will be straight-line, concave, and one-hoss shay, respectively. When βkτ < 0, the hyperbolic AEP cansimulate geometric distribution.
The advantage of the hyperbolic AEP, relative to the BGA, is that the hyperbolic function is more flexible
and has a upper limit of the service life: dkτ = 0 if τ = Tk , by comparison the efficiency in the BGA
never completely vanishes. On the other hand, the assumption of the hyperbolic AEP does not simplify
the PIM like Equation (11) and some assumptions about real discount rates are required to define thecorresponding APP, unlike the BGA.
The AEP can be determined empirically by modeling a time series of prices of an asset by age. Note that
it is difficult to verify which approximation is most appropriate by the empirical studies to estimate the
APP. As Fraumeni (1997) pointed out, BLS found there was no statistically significant difference between
the geometric and the hyperbolic function, because both have an age-price counterpart that is convex, orbowed towards the origin. An alternative and more direct approach is modeling a time series of rental
prices of an asset by age.
OECD (2001b) reports that the U.S. Bureau of Labor Statistics (BLS) and the Australian Bureau of
Statistics (ABS) use the hyperbolic function and that the U.S. BEA and the Statistics Canada use the
BGA. Although any other flexible functions can be assumed as the AEP, it may be a choice between twoalternatives, geometric and hyperbolic distribution, to reframe the capital measurement in the Japanesenational accounts, in practice.

2.2

Price and Quantity of Investment

Let us go back to the starting point. Prior to measuring capital stock, our starting point is the measurement of nominal investment, which is directly observable and evaluated in current prices at the times they7are produced.*7 We define nominal investment as:
k, j

k, j

It = PA,kt At ,(13)

where PA,kis investment price for acquisition of new assets in time t.
t
The assets invested and produced in different times have different vintages, t = v since v = t − τand τ = 0, so that the technology embodied in the assets may be different. An adjustment for qualityof assets with different vintages, therefore, is required to measure quantity of investment in efficiency
units. Constant-quality prices for investment goods: PA,kt , include the adjustment coefficients. Rapid
technological progress in information technology (IT) and the recent increase in its impact illuminate
anew the importance of constant-quality prices. Here, we introduce the Japanese measurement of prices
and discuss it by the comparison of price measures in the U.S. In center of the discussion, there arecomputer prices, where holding constant-quality has a significant role. First, we examine some issues in
the measurement of investment prices.
2.2.1

Price on Investment as Composite Goods

In Equation (13), the price for acquisition of produced assets is defined not as a producer’s price, but asa purchaser’s price. The nominal investment value is written as the following identity,k, jC,k, jC,kPA,kt At = Pt Xt

k, j

k, j

T,k
+ PW,kt W t + Pt Tt ,

(14)

where
C,k, jPC,kt Xt

D,k, j= PD,kt XtM,k, j+ PM,kt Xt(15)

In Equation (15), PD,kand PM,krepresent constant-quality prices for domestic output and imports of
t
t
M,k
C,k
C D,k
asset k. Using an aggregator function of the two prices: PC,kt = f (Pt , Pt ), the investment price: Pt , canbe defined as the price for composite goods of domestically produced and imported assets, in producer’s
prices. In Equation (14), PtW,k and PT,kare prices for wholesale and transportation costs needed for the
t
W,k
T,k
acquisition of asset k. Using an aggregator function: PA,k
= f A (PC,ktt , Pt , Pt ) of the three prices, the*8investment price: PA,kt , can be defined in purchaser’s prices.
*7

Measurement of nominal investment depends on two approaches: bottom-up and top-down. The bottom-up approachis based on the survey of investment, which depends on the custom in business accounts. On the other hand, top-down
approach is based on the supply of investment goods by domestic production and net imports, as described at the commodity
flow method in national accounts. Reconciling both approaches contributes to recognize the measurement error and theconceptual difference. Although this process has crucial significance to determine the accuracy of measurement of capital, it
is too complicated to describe here. For the case in Japan, see Nomura (2004, Ch.2 and Ch.A-B).

*8

For the prices in Equation (14) and (15), we neglect the difference among industries. In case that one asset at the most detailed

8Surprisingly, as Nomura and Samuels (2004) pointed out, the BEA’s price index for private fixed
investment does not reflect margin rates, margin prices, and transportation costs. The BEA’s investment
price for computers actually falls a little more rapidly than output prices, reflecting import prices that fall
more rapidly than domestically produced prices. For the price of computers during 1980-2000, the average
decline rate of BEA’s output price is 16.1 percent per year and the BEA’s investment price declines 16.5
percent annually. After including the wholesale margins and transportation costs, the decline rate shrinks
to 12.9 percent. During 1995-2000, the decline rates of the output price, investment price, and redefined
investment price are 24.9 percent, 24.4 percent, and 18.7 percent, respectively.*9 The numerous studies
that analyze the contribution of computers to economic growth using this price and harmonized prices
based on the BEA price discussed later, may overestimate declines of the computer prices and increasesof capital inputs from computers.
A possible justification of the BEA’s neglect of margins is that the change of margin price may be same as
the price change of a product treated by a wholesaler, under the assumption of constant nominal margink, jW,k, jrates. Based on the identity in Equation (14), we can get PA,kt At = (1 + vt
T,k, jand vtT,k, j+ vt

C,k, j)PC,kt Xt

W,k, j, where vt

are the nominal rates of margin and transportation cost. As is sometimes assumed, if we thinkk, j

C,k, jquantities of investment are identical: At= Xt, we get the simple relationship on the two prices:

W,k, jT,k, jW,k, jPA,k= (1 + vt+ vt )PC,k
and vT,k, j , the purchaser’s price maytt . Therefore, under the constant rates: v

be proportional to the producer’s price.
Is this identity approach adequate for the asset that has an outstanding quality improvement over time?
W,kT,kUnder a more general aggregator function of prices: PtA,k = f A (PC,kt , Pt , Pt ), quantity of investment

also should be defined to fulfill the price aggregator function and the nominal identity in Equation (14).
k, jC,k, jTherefore, At is defined as not only Xt

C,k, j, but also a composite goods of Xt

W,k, j, XtT,k, j, and Xt

. Moreover,

for a computer, the price changes in margin and transportation: PW,kand PW,ktt , may be more moderateW,kthan the constant-quality prices: PC,kt , in computers. To estimate the margin price: Pt , we have to definelevel consists of some detailed assets corresponding to the commodity flow data, the prices should be reflected the difference
D,k,j

of asset composition invested by industries, as Pt. Moreover, we neglect indirect taxes, here. The indirect tax included in

output prices, like a consumption tax, may be deducted from the purchase of investment goods. The consistent definitions of
indirect taxes in output and investment prices should be of note. In Japan, the consumption tax was introduced in 1989 andthe rate was increased from 3 percent to 5 percent in 1997.
*9

Here, “computers” is defined as US-SIC-357 excluding 3578 and 3579. The wholesale margin rates and transportation costs aretaken from the benchmark Input-Output Tables (1977, 1982, 1987, 1992, 1997), published by BEA. The U.S. prices for wholesale
and transportation are from GDP-by-Industry data. Rates of margin and transportation for computers are 17.1 percent and0.9 percent of the purchaser’s price in 1997, respectively. The rates in the U.S. are similar to that in Japan: 19.0 percent and 0.9
percent in 1995, respectively. See Nomura and Samuels (2004).

9

k, j

the quantity of margin: Wt . Let us think an example. We assume a wholesaler buys in one unit of PC
for one thousand dollar and sells it for two thousand dollar, last year and, also, this year. If the quality of
the PC becomes twofold between the two periods, the constant-quality price for the PC is interpreted as
decreases by fifty percent and the constant-quality quantity is treated as increases twofold. In this case,is quantity of margin unchanged or does it increase twofold also? The adequate answer may be that thequantity of margin is constant, because the quality improvement in the PC as a treated product may notaffect any costs in the wholesaler. The quality change in the computer should not affect the productivityof the wholesaler, so that the quantity of margin, as a real “gross” output of the wholesaler, should beunchanged. Also, the price change of the margin should be zero, in this example. So, in usual, the decline
of PA,kmay be more moderate than that of PC,ktt .
Another important note is on the recognition of investment goods as a compound goods of otherinvestment goods. In practical, an asset is classified as the final goods to be invested. Some investment
goods may be defined including embedded investment goods, which can be also classified as an asset,
separately. For example, the investment of office building is defined including the elevator, lighting,furniture, and operating system, controlled by the computer. Also, computers are defined including theembodied software.
In the 2003 comprehensive revision of the NIPA, the BEA revised the prices for software, so that theprices for own-account software and custom software are defined by a weighted average of the input
cost index for software and the quality-adjusted price for the prepackaged software. The vastly revised
price for software, nevertheless, does not affect the price of computers or operating system of the officebuilding, in which software is partly embedded. If a hedonic function for computer, in which software is
one of characteristics, is estimated, the consistency with the constant-quality price for the software should
be maintained. So far, the revisions of the investment prices are treated separately.

10

2.2.2

Constant-Quality Prices in the U.S. and JapanThe hedonic approach has been shown to be an effective technique for capturing quality changes.*10
In the U.S. National Accounts, hedonically adjusted computer prices were introduced in December 1985
representing five types of computer equipment: processors, disk drives, printers, displays, and tapedrives covering 1972-1984, by the work of BEA with IBM (Wasshausen, 2000). In 1987, a hedonic price
was introduced for personal computers, beginning in 1983. BEA later developed estimates of computer
hardware and software prices back to 1959 (Landefeld and Grimm, 2000). Triplett (1989) also extends thecomputer prices backward, based on indexes developed in several independent studies. In the early 1990s,
Bureau of Labor Statistics (BLS), which is the main producer for price statistics in the U.S., began publishingthe quality adjusted Producer Price Index (PPI) for computers. BEA now uses detailed BLS price indexes
for computers, peripherals, parts and for some types of software: these indexes are aggregated using BEA
chain weights to produce chain-type price indexes (Landefeld and Grimm, 2000).
In Japan, the Bank of Japan (BOJ) and the Statistics Bureau, Ministry of Internal Affairs and Communications (MIC) are main producers of price statistics. On the Wholesale Price Index (WPI), the BOJ started
to use the hedonic approach from the 1990 benchmark revision for personal computers (PCs), mainframes,
and magnetic disk devices, modeling the hedonic function on an annual basis. The BOJ’s WPI has been
greatly revised and renamed to the Corporate Goods Price Index (CGPI) in 2000.*11
Compared to the WPI/CGPI, the MIC’s Consumer Price Index (CPI) mainly used the matched modelfor quality adjustment. After the 2000 benchmark revision of the CPI, the MIC began estimating quality*10

Although hedonic approach is widely thought to be suitable to capture quality change, it is not necessarily that the traditional
approach, like a matched model, is inferior to hedonic approach. Aizcorbe, Corrado, and Doms (2000) points out that matchedmodel captures the rapid pace of quality change for high technology goods market, where the life of a product is relatively shortand the varieties of products are sold at once. For computer prices, Landefeld and Grimm (2000) indicates that hedonic priceindexes for computers produce results that are quite robust and that are virtually the same as those produced by a carefully
constructed traditional price index for computers. The use of hedonic price indexes is increasing, and the components thatare deflated by hedonic techniques account for 18 percent of GDP in the U.S. (Landefeld and Grimm, 2000). Also, Moulton(2001) provides the expanding role of hedonic approach in the U.S. and discusses some misconceptions about the technique.

*11

The CGPI is composed of Domestic Corporate Goods Price Index (DCGPI), Export Price Index (EPI), and Import Price Index(IPI). BOJ increased the number of sample prices to be surveyed by 69 percent (63 percent only for DCGPI), from 4902 (3379 fordomestically produced goods) in 1995 benchmark WPI to 8264 (5508) in the 2000 benchmark CGPI. Since the 2000 benchmark
revision, the CGPI uses the hedonic approach for Servers, which is a component of General Purpose Computers & Servers,
Digital Cameras, and Video Cameras, in addition to PCs. On the other hand, BOJ discontinued to use the hedonic approachfor mainframe and magnetic disk devices after 2001, because of a lack of the credible common characteristics data. The BOJ
estimates the hedonic function for two types of PCs, desktop-type and laptop-type below the commodity level, and raises thefrequency twice per year. The functional form, data, and the estimated results by the hedonic approach are in BOJ (2002).

11

improvements for desktop and laptop PCs, adjusting these two items hedonically, using Point of Sales(POS) data, which covers all sales at 3400 major shops across Japan. CPI also starts incorporate hedonics
for digital cameras after 2003.
The significant difference in price statistics of the U.S. and Japan is whether the prices of the commoditythat has an outstanding quality improvement could be extrapolated backward or not. Although thisfunction is carried out by BEA in the U.S., we may not find any similar function in the Japanese statisticalsystem. In the Japanese national accounts, ESRI uses the WPI/CGPI and the CPI. However, ESRI, and BOJ
also, does not extrapolate the prices based on the newly developed methodology backward. This should
be noted as a defect in the Japanese system for price statistics. BOJ also publishes the Corporate Service
Price Index (CSPI). In November 2004, the CSPI began to estimate the price for prepackaged software,
based on cost evaluation method, beginning in 2000.
Another problem in Japan may be found in the index formula. BOJ estimates aggregate price indexes
based on Laspeyres formula as a basic index and chained Laspeyres formula as a reference index in the
WPI/CGPI after 1995. We should note that chained and un-chained versions of the two price indexes of
WPI/CGPI are different even at the most detailed commodity level, reflecting different item weighting
within the detailed commodities. One commodity usually consists of multiple items (“sample prices”),
which are not published. At present, BOJ uses arithmetic aggregation, called a Carli price index by
Diewert, of these item prices for the Laspeyres price index, while geometric aggregation, Jevons priceindex, for the chained version. The difference is large, especially for computers (Nomura and Samuels,
2004). In December of 2004, ESRI officially incorporated the chained Fisher index for the national accounts.
At the most detailed commodities in the Japanese national accounts, however, ESRI uses the BOJ’s basic
index, the Carli index.*12 Fisher and Diewert clearly indicate that the Carli index has a definite upwardbias and urge statistical agencies not to use this formula.
2.2.3

Possible to Use Harmonized Prices?

In studies covering multiple countries, some studies have employed internationally harmonized prices,which translate U.S. prices to comparison country prices in order to control for the quality improvements inthe comparison country.*13 For countries with the statistical agencies, which do not adjust prices for IT for*12

In the Japanese national accounts, the commodity flow data is based on about 2200 commodities at the most detailed level,although commodities have each price index at the level of about 400 commodities.

*13

Price harmonization is an attempt to control for these price differences, under the assumption that the comparison country’s
price data fails to capture quality improvements. Various studies have used different methods to construct harmonized prices,
but the basic idea is the same. The relative price of IT to non-IT in the comparison country is set equal to the IT to non-IT pricerelative in the U.S. The harmonized price is formulated such that: ∆ ln pxIT = ∆ ln pxnIT + (∆ ln pUS− ∆ ln pUS), where the suffix
IT
nIT

12

the quality change, the use of harmonized prices may be one possible approximation for quality-adjusted
prices. However, in a country like Japan, the use of harmonized prices needs further justification.
Nomura-Samuels (2004) examines the IT prices in the U.S. and Japan at the SIC 3-, 4-, 5-digit level.
Comparing the U.S. and Japan data for PCs and General Purpose Computers & Servers at the 5-digit levelfrom 1995 to 2003, there is a small gap between the countries, as a consequence of the definition of index
numbers for aggregation of the most detailed items. At the 4-digit level, after adjustment of the index
numbers and the aggregation weights for the WPI/CGPI to be consistent with the BEA’s output price, theresulting price declines for electronic computers are comparable, as prices fall 29.3 percent per year in
the U.S. compared to 27.0 percent per year in Japan, during 1995-2003. Moving to the 3-digit level, theaggregate price of Electronic Computers and Peripheral Equipment shows that prices fall 23.8 percent per
year in the U.S. compared to 15.5 percent per year in Japan. At the 3-digit level, a significant portion of theremaining price gap can be explained by the Peripheral Equipment price, which falls less rapidly in Japanand has a bigger share of total output when exports are included. After 1995 we conclude the computer
prices at the SIC 3-, 4-, 5-digit level in the U.S. and Japan are appropriate.
During 1980-95, computer prices at the 3-digit level fall 13.1 percent per year in the U.S. based on the
BEA data, while prices fall 7.6 percent per year in Japan. In 1980s, the Japanese PC market was dominatedby the NEC Corporation, which had a 60-70 percent share of domestic demand. On the other hand, theinternational PC market was very competitive, with many manufacturers of IBM-compatible computersentering to combat the dominance of IBM in the early 1980’s. Until 1991, the Japanese PC market was
separated from the international market due to hardware and software differences and incompatibility
issues, but the origin of DOS/V as a new Operating System (OS) in 1991 changed that.
DOS/V is a version of MS-DOS that provides both English and Japanese language command interfaces
and can be used for applications designed for either or both English and Japanese. DOS/V includes all the
English-based commands and specific Japanese DOS/V commands.*14 Because DOS/V works on all IBMcompatible computers, foreign manufacturers were able to enter to the Japanese PC market. Competition
brought prices down for computers. In 1993, NEC Corporation introduced a new model PC, priced 50
percent lower than the previous model. Import share of computer in Japan increased from 7.6 percent in1990 to 14.3 percent in 1995, and it reached to 23.1 percent in 2000. Our observation indicates the use of
the U.S. harmonized price should be rejected for the Japanese economy because of differences in market
conditions.

x means the reference country, pIT is the IT product price, and pnIT is the non-IT price.
*14

DOS/V gets its name because it requires a Video Graphics Array (VGA) display. In 1991, the Open Access Development
Group (OADG), a consortium organized by IBM, developed DOS/V.

13

2.3

Capital Value and Depreciation

For reframing the measurement of capital in the Japanese national accounts, it is important to examine
not only measurement of capital stock, but also the consumption of fixed capital in the production account.
In this section, we start with the framework for describing capital value and depreciation. Based on thisframework, we discuss the improvement in the U.S. National Income and Product Accounts (NIPA) andthe measurement of depreciation rates in the Japanese economy.
2.3.1

Capital Value

The value of a new asset is assumed to be equal to the present value of future capital service income as,PA,k= dk0 PK,ktt +dk1 PK,k
t+1
1 + rt+1+∞X

dk2 PK,kt+2(1 + rt+1 )(1 + rt+2 )+ ··· =
τ=0

dkτ PK,kt+τ
Πτs=0 (1 + rt+s )

,

(16)

where rt = 0 and PK,kt+τ (τ = 0, · · · , ∞) represents future capital service prices. In time t + τ, the capital service
prices of assets with different ages are equivalent. Using the normalized quantity of capital service,*15
represented by the age-efficiency profile (AEP): dkτ , future capital service income is defined by dkτ PK,kt+τ .

The value of a new asset in Equation (16) provides the investment price of the asset, examined in section
2.2.
The nominal value of assets with different ages is written as:
S,k, jN,k, jVt,τ = PA,kt St,τ ,(17)

S,k, jVt,τ represents nominal value of net capital stock, which is capital wealth to be described in the balance
N,k, jsheet of the capital holders. The price for net capital stock St,τ is PA,kt .
Next, we define the value of assets with different ages τ,
k K,k
PA,k
t,τ = dτ Pt +dkτ+1 PK,kt+1
1 + rt+1+(1 + rt+1 )(1 + rt+2 )G,k, jTo measure nominal value of net capital stock, PA,kt,τ St,τ*15∞
X

dkτ+2 PK,kt+2

+ ··· =

dkτ+τ0 PK,k
t+τ0
0

τ0 =0

Πτs=0 (1 + rt+s )

.

(18)

provides alternative definition of equation (17).

In behalf of Equation (16) that is based on the discounted future rentals approach, Diewert (2001) uses the vintage approachas the “fundamental equation” relating the stock value of a new asset to the sequence of cross sectional vintage rental prices.
In the Diewert’s vintage approach, as a matter of form, dkτ in Equation (16) is replaced cross-sectional vintage rental prices:
K,k
k K,k
PK,k
t,τ , which is defined by dτ Pt in our terminology, and Pt+τ in Equation (16) is replaced by the rental price escalation factor:
K,kPK,kt+τ /Pt in our terminology.

14

Using PA,kt,τ , we can define the age-price profile (APP) as,
dP,k
t,τ =

PA,k
t,τ
PA,k
t

.

(19)

The APP depends on the expectation in the future inflation of capital service prices and discount rates.
Under static expectations on PK,kt and rt , the APP depends on the discount rate at time t. Therefore, even
if the AEP is constant over time, the APP can change, associated with the change of rt .
When an asset ages over time: τ → (τ + 1) and (t − 1) → t, the difference in the values: (PA,k− PA,k
), is
t−1,τ
t,τ+1
written as the following identity,
Ekt,τ = Dkt,τ − Πkt,τ ,

(20)

A,k
A,k
A,k
k
Ekt,τ = PA,k
− PA,k, Dkt,τ = PA,kt,τ − Pt,τ+1 , Πt,τ = Pt,τ − Pt−1,τ .
t−1,τ
t,τ+1

(21)

where

Hill (1999) and Diewert (2001) call Ekt,τ and DP,k
τ as (ex post) “time-series depreciation” and “cross-section
depreciation”, respectively.*16 The cross-section depreciation is defined as the difference between the valueof an asset of age τ and an identical asset of age τ + 1 at the same point of time t. The second term of theright hand of Equation (20): Πkt,τ , is the difference between the value of an asset in (t − 1) and an identicalasset in t for the asset with same age. This is called as an asset-specific “revaluation” term. The time-series
depreciation consists of cross-section depreciation and revaluation.
Dividing this identity of price change by PA,k
, we can obtain,t−1,τkkt,τ = (1 + πkt,τ )δP,kt,τ − πt,τ ,wherekt,τ =

δP,k
t,τ =
and
πkt,τ =
*16PA,k
− PA,k
t−1,τ
t,τ+1

,

(23)

,

(24)

.

(25)

PA,k
t−1,τ
A,k
PA,k
t,τ − Pt,τ+1

PA,k
t,τ

(22)

A,k
PA,k
t,τ − Pt−1,τ

PA,k
t−1,τ

Although the importance of the distinction in two concepts of depreciation, the different names are used. Hulten and Wykoff(1981b, 1981c) calls the cross-section depreciation as “economic depreciation”, which is also called as ”Hicksian economic
depreciation” in Hulten (1990), and the time-series depreciation as “economic depreciation and asset inflation”. Oliner (1993,
1994) calls “partial depreciation” and “full depreciation”, respectively.

15kkt,τ , δP,kt,τ , and πt,τ represent rates of time-series depreciation, cross-section depreciation, and revaluation,

respectively. If we assume same inflation rate for assets k with different ages, πkt,τ will be written as πkt .
In case of the geometric approach, δP,kt,τ will be identical for assets with different ages in different points ofktime, so that δP,kt,τ is written as δ . Under this simplification, time-series depreciation is also independent ofage τ, as kt .
2.3.2

BEA’s Revision for Measuring Stock and Depreciation

As a part of the comprehensive revision of NIPA, the U.S. Bureau of Economic Analysis (BEA) revised
the methodology for estimating their capital stock and depreciation in 1997.*17 The revised methodology
reflects the results of empirical studies, which have shown that depreciation for most types of equipment
and structures does not follow a straight-line, but approximates the BGA. The improvement for themeasurement of depreciation involves the use of the BGA as the default, instead of the use of combinationof the straight-line depreciation and the survival distribution.*18 On the other hand, the BEA no longer
produces estimates of gross capital stock and discards.
As a result of their revision, the BEA resolved the internal inconsistency in measures of capital stock in
wealth account and consumption of fixed capital (CFC) in production account. This point was emphasized
by Jorgenson (1989, 1996) as an inconsistency in the NIPA.*19 The importance for sustaining internalconsistency in the measurement of capital stock and CFC became a common objective in the national
accounts, as in the international methodological standards recommended by OECD (2001a, 2001b).
Jorgenson (1999) states that the incorporation of the appropriate definition of CFC is the most importantinnovation in BEA’s revision. Jorgenson indicates that the BEA’s definition of CFC is different from thatin 1993 SNA. This definition identifies CFC as the decline “during the course of the accounting period” inthe value of an asset.*20 However, this decline has two distinct components: “depreciation” due to aging*17

See Fraumeni (1997), Katz and Herman (1997), and BEA (2003). The BEA defines depreciation as “the decline in value due
to wear and tear, obsolescence, accidental damage, and aging”, which included retirements, or discards (Katz and Herman,
1997; Fraumeni, 1997).

*18 Exceptionally, the BEA uses non-geometric patterns of depreciation for autos, computers, missiles, and nuclear fuel (Fraumeni,1997). Therefore, the use of BEA’s stock as the productive capital stock is not appropriate.
*19

Jorgenson (1989) pointed out, “the national accounts fail to provide an internally consistent set of measurement of capitalstock, capital input, and depreciation. This is regrettable, since studies of productivity like those of Denison and Kendrick
will continue to rely on national accounting data.”*20

The 1993 SNA define CFC as, “Consumption of fixed capital is a cost of production. It may be defined in general terms as
the decline, during the course of the accounting period, in the current value of the stock of fixed assets owned and used bya producer as a result of physical deterioration, normal obsolescence or normal accidental damage. It excludes the value of
fixed assets destroyed by acts of war or exceptional events such as major natural disasters, which occur very infrequently.

16and “revaluation” due to a change in the price of an asset of a given age, which is not part of CFC.*21
2.3.3

Possible to Harmonize Depreciation Rate?

As represented in the comprehensive empirical studies of Hulten and Wykoff (1981a, 1981b, 1981c),
there are many empirical studies for measuring the age-price profile or age-efficiency profile. However,almost empirical studies are based on the U.S. data.
There are few empirical studies for the rates of depreciation or deterioration of assets using the Japanesedata. Lee (1978) for fishing fleet and Kuninori (1988) for construction machinery give a few examples.
Many studies of the Japanese economy use the depreciation rates of the BEA (Fraumeni, 1997). However, depreciation rates can differ between the U.S. and Japan, reflecting the difference in natural andenvironmental condition, utilization, maintenance, and composition of capital goods.
Nomura (2004a, Ch-2) estimates age-price profiles based on the Box-Cox transformed function using
the data in the second-hand market for motor vehicle, and age-efficiency profiles based on the data rental
market for housing in Japan. The geometric approach is approximately accepted for these assets. The
estimated depreciation rates are 16.3 percent for passenger motor vehicles, 22.4-23.8 percent for trucks,
and 3.1-4.8 percent for housing. In comparison with the U.S. depreciation rates of BEA, passenger vehicles
and housing are less durable and trucks are more durable in Japan. Even for tradable goods, the differencein the depreciation rates should be considered, if possible. Although empirical studies for measuring
the Japanese depreciation rates are preferable, the use of the U.S. depreciation rates may be acceptable.
Practically, the use of the U.S. harmonized depreciation may not generate a larger bias in measurement of
capital than that caused by the use of the harmonized prices.
We must also estimate the Japanese depreciation rates for other assets. For other assets, we estimate
average service lives Tk based on the Japanese tax-lives and the arbitrary rates to effective service-life ineach fixed asset. Based on the relationship: δk = Rk /Tk , we compute the Japanese depreciation rates using
the declining balance rates Rk originated in Hulten and Wykoff (1981b) and employed by the BEA.
For computer hardware, the BEA depreciation rates incorporate Oliner’s (1993, 1994) estimates for allcomputer components except personal computers (Fraumeni, 1997). Jorgenson, Ho, and Stiroh (2005)
uses 31.5 percent for computers based on the depreciation schedule of the BEA. In Japan, the tax-life is 4
years for personal computer and 5 years for other computers, which are abridged from 6 years after theSuch losses are recorded in the System in the account for “Other changes in the volume of assets”. Consumption of fixed
capital is defined in the System in a way that is intended to be theoretically appropriate and relevant for purposes of economic
analysis. Its value may deviate considerably from depreciation as recorded in business accounts or as allowed for taxation
purposes, especially when there is inflation.” (paragraph 6.179).
*21

See Hill (2000) for the different view of CFC.

17

2001 fiscal year. Based on the tax-lives, we assume 34.7 percent depreciation rate for computers in Japan.
The depreciation rates used in our latest estimates for capital stock and service in Japan are represented
in Table 5.

3

Measurement of Capital in Japan

3.1

Japanese National Accounts

In section 3.1, we briefly introduce the measurement of capital stock and consumption of fixed capitalin the present Japanese national accounts and discuss some problems to be overcome. The Economic
and Social Research Institution (ESRI) of the Cabinet Office (CAO), the producer of the Japanese national
accounts, publishes two main estimates for capital stock. Figure 2 shows the concepts and rough coverageof stock measurement in Japan. The first estimate is net capital stock, which is described in the balance
sheet of the Japanese national accounts. We refer to this measure as ”JSNA-NCS”.*22 The second estimate
is Gross Capital Stock of Private Enterprises (GCSPE), which is the main data source for analysis ofproduction by industry. In addition, the ESRI irregularly publishes gross capital stock for infrastructure.
3.1.1

Net Capital Stock

The JSNA-NCS covers fixed assets, land, inventories, and consumer durables of all capital holders inJapan. Although nominal investment in the JSNA-NCS is consistent with that in the national accounts
commodity flow for certain aggregates, it has only six classifications for tangible assets and one intangible
asset. The tangible assets consist of (1) dwellings, (2) other building, (3) other structures, (4) transport
equipment, (5) other machinery and equipment, and (6) cultivated assets.*23 The only intangible asset
included is custom software.*24 Finally, the JSNA-NCS is not estimated by industry, but by five institutional
sectors. Depreciation in the JSNA-NCS is based on the straight-line method for infrastructure and thegeometric method for other assets. Conceptually, the JSNA-NCS provides total wealth of the Japanese*22

Conventionally in Japan, the Japanese national accounts is also called ”SNA”, which is should be identified with the U.N.’s
recommendation for System of National Accounts.

*23

The classification for consumer durables consists of (1) furniture and floor coverings, (2) household appliances, (3) personaltransport equipment, (4) information transmission equipment, and (5) others.

*24

In the Japanese national accounts, expenditures for plant engineering, mineral exploration, and custom software are treatedas gross fixed capital formation (GFCF) of intangible assets, although plant engineering is not recommended to be treatedas and intangible asset in the 1993 SNA. Furthermore, it is added to ”tangible” assets in the Japanese stock accounts, so thetreatment is a halfway. Also, mineral exploration is not treated in the Japanese stock accounts, based on the assumption thatit has just one-year service life. Both these issues should be reconsidered.

18             ()*#  $ %& '       + ,-  /.
      ! "?  @. A)
0 6 0 & :);$ 1/4 < ' ! & 1 := ' ' 1 < :/! >021 3)3(1/4 & ! 5768 1 9Fig. 2 Capital Stock in the Japanese National Accounts

capital stock. However, the assumed depreciation rates may be too high.*25
Although it is difficult to determine if JSNA-NCS is underestimated because of too high depreciation
rates, Nomura (2004a, Ch.2) gives a comparison of net capital stock for fixed assets at current prices between
the JSNA-NCS and his own estimates with identical nominal values of investment at the aggregate level.*26
In the comparison shown in Table 1, the JSNA-NCS is more than 30 percent lower in the 1990s. Nomura(2004a, Ch.2) defines the average rate of depreciation at the aggregate level as a weighted average ofdepreciation rates by assets, using the capital stock shares as the weights. The average rate of depreciation
has an upward trend from 5.0 percent in the 1960s to 6.0 percent in 2000.*27 In comparison with the U.S., inwhich the average is 6.1 percent based on data from Dale Jorgenson, the computed average depreciationin Japan may be appropriate. The depreciation rates in the JSNA-NCS should be examined.*28*25

Depreciation rates for assets except infrastructure are estimated using the average service life in the Japanese National Wealth
Survey (NWS) from 1970, based on the assumption that the value of capital that has reached the end of its service life is ten
percent of the original value (ESRI, 2000). The depreciation rates used in the JSNA-NCS are not published.

*26

Our estimates of capital stock are based on geometric depreciation for all assets. See Nomura (2004a) for the details.

*27

The capital stock used to estimate the average rate of depreciation is based on all fixed assets in Japan, including infrastructure.
The average rate is 7.8 percent for the secondary industries and 9.2 percent for electric machinery industry in 2000.

*28

Alternative explanations are the differences of constant-quality prices and the benchmark stocks. Our stock estimate uses

19

Table. 1 Comparison of Capital Stock for Fixed Assets between the JSNA-NCS and Our Estimatesa.JSNA-NCS

b.Nomura(2004a)

(a-b)

(a/b)

1990

9364431351431-414987

0.693

1995

1113173

1715143-601970

0.649

2000

1192136

1899239-707103

0.628

Unit: billion yen (current prices), evaluated at the end of the calendar year.
Stock does not include prepackaged and own-account software.

3.1.2

Consumption of Fixed CapitalIn this paper, we call choose ”JSNA-CFC” to label consumption of fixed capital in the ”income andoutlay accounts” and ”capital finance accounts” in the Japanese national accounts. The JSNA-CFC isdefined by historical prices, based on the book value in corporate sector business accounts and on similar
estimates for private unincorporated enterprises and general government. For the estimates by industry,
the JSNA-CFC distributes the total CFC to industries, using the estimated industry shares, which are basedon the share of CFC in gross output and the estimated values of gross output by industry (ESRI, 2000).
Note that the assumptions to estimate the JSNA-CFC are not consistent with that in the JSNA-NCS.
Conceptually, CFC evaluated by historical prices should be revised. To determine the value of the CFC,
the 1993 SNA points out: “Its value may deviate considerably from depreciation as recorded in businessaccounts or as allowed for taxation purposes, especially when there is inflation.” (paragraph 6.179). The
JSNA-CFC evaluated by the historical prices generates a large bias when estimating net domestic product(NDP). NDP is a key economic concept that some argue should replace gross domestic product (GDP) as
the appropriate measure of economic growth in the future.
3.1.3

Gross Capital Stock

For industry analysis of the Japanese economy, the GCSPE is a main data source for the Japanese capitalstock. The GCSPE covers all fixed assets, excluding residential buildings owned by private corporations
and unincorporated enterprises and fixed assets owned by private non-profit institutions. The GCSPE issometimes used as a measure of the productive capacity of the private sector.*29

the Japanese National Wealth Survey (NWS) in 1955 as the benchmark stock. In comparison with the JSNA-NCS, whose
benchmark stock is based on the 1970 NWS, our methodology is close to the perpetual inventory method.
*29

To estimate productive capacity, the GCSPE intentionally excludes the residential capital owned by private sectors. Theremay be no longer any reason to exclude it, since the capital service produced by the residence owned by a company may
be described as the consumption of fixed capital and operating surplus in the company. Also, it is difficult to identify it, in20

However, it is misleading to use this data as a measure of productive capacity, for conceptual andempirical reasons. First, the GCSPE is defined by a traditional gross concept of capital stock. As wediscussed the concepts for capital stock in section 2.1, the gross concept does not provide an appropriate
measure for the productive capacity of capital. Second, the GCSPE does not have asset categories, sothat the nominal investment in the GCSPE is not related to the commodity flow. Therefore, it is difficultk, j

for the GCSPE to measure quantity of investment At in efficiency units and to consider the appropriate
aggregation procedure for heterogeneous capital. Moreover, although the GCSPE publishes the estimatesof gross capital stock and investment by industry at constant prices, it does not publish the nominal
investment or investment prices by industry. The lack of reproducibility of the capital stock data does notallow the users of the GCSPE to test different assumptions for measuring capital.
Table. 2 Comparison of Capital Stock for Private Fixed Assets between the GCSPE and Our Estimates
a.GCSPEb.Nomura(2004a)

(a-b)

(a/b)

1995

971171

838238132934

1.159

1996

1006469862032

144437

1.168

1997

1047554892533155021

1.174

1998

1086240

918990167251

1.182

1999

1120454939743180711

1.192

2000

1160232

965782

1944501.201

Unit: billion yen (1995 constant prices), evaluated at the end of the calendar year.
The values does not include residence, prepackaged and own-account software.
Nomura (2004a) includes fixed assets owned by private non-profit institutions.

Table 2 compares measure of capital stock of private fixed assets at constant prices between the GCSPE
and estimates based on Nomura (2004, Ch.2). Our estimates include the fixed assets owned by private
non-profit institutions. When GSCPE is interpreted as a special case of the productive capital stock (PCS),
we can compare both estimates. The GCSPE is 16-20 percent higher than our estimates during 1995-2000,
although the coverage of our estimates is broader than that in the GCSPE. However, it is possible tounderstand the overestimates of the GCSPE and bias in using GCS as a measure of PCS.
We can observe this by noting that the average rate of retirement in the GCSPE is 4.6 percent in the 1990s(Nomura, 2004a). The retirement rate is 1.3 percent point lower than the average rate of deterioration,practice. The primary statistics to estimate nominal investment for corporations in the GCSPE is the Annual Report of Financial
Statements of Corporations (ARFSC), by the Ministry of Finance. However, ARFSC does not investigate the investment forresidence the company has, in particular.

21which consists of retirement and decay in Triplett’s terminology, in our estimates of productive capitalstock. To be an appropriate measure of productive capacity, the GCSPE should be reformed to the PCS byasset and industry, sustaining the consistency with the JSNA-NCS in the national accounts.

3.2

Alternative Measurement

One of our aims is to measure productive capital stock (PCS). However, what is the role of productive
capital stock in economic analysis? The direct use of productive capital stock may be limited. The conceptof neoclassical production function, which is used as a basic framework for production analysis, requires
the flow concepts of the factor inputs. Our major concern for measuring the PCS is mainly in measurementof capital services, which are not directly observed in the market because many assets are owned by users.
The most common assumption is that capital stock and capital services are proportional at the mostdetail asset level. Under this assumption, the two growth rates are identical. If we have only an aggregate
measure of capital stock, there is no distinction between capital stock and capital services. The distinction
is generated in the difference in both aggregate measures of heterogeneous capital. In this aggregation
process, if we define Törnqvist quantity indexes for both aggregates, the difference is the weights the nominal cost of capital stock for aggregating capital stock and the nominal cost of capital service
for aggregating capital service. Although the difference is only the weights, the difference of the two
aggregate measures is significant.
Although there is no place for capital service costs in the SNA and the U.S. NIPA at present, only three
countries - Australia, the United States, and Canada - produce time series of capital services as a partof their official statistics; recently, work has also been taken up in the United Kingdom (Schreyer, 2003).
The Canberra II Group supports for introducing measures of the cost of capital services into the national
accounts (Ahmad 2004; Diewert, Harrison, and Schreyer, 2004). Also, they recommend that the valueof capital services should be included as ’of-which’ items in the production account. This introduction
should not change the basic structure of the production account.
In section 3.2, as an alternative measurement of capital stock, we introduce our estimates of capitalstock and capital services in the Japanese economy. Our stock estimates are based on the assumption of
the geometric approach. Therefore, our net capital stock and productive capital stock are identical, as inEquation (9). After we formulate the price and quantity of capital service in addition to the framework
above, we discuss some topics related to the capital measurement, based on Nomura (2004a) and ourlatest estimates in March 2005. Our measurement may provide some clues to consider the reform of thestock measurement in the Japanese national account.

223.2.1Price and Quantity of Capital Servicek
Based on the geometric approach, where δkτ = δP,kt,τ = δ , we start with the perpetual inventory methodk, j

in Equation (11). Since quantity of investment At is defined in terms of progress in construction, theP,k, jproductive capital stock St

defined in Equation (11) includes capital goods that are not yet installed.

For each asset we assume that new investment becomes available for production at the mid-point of theyear so the installed capital stock for each industry and each asset is assumed to the arithmetic averageof the current and lagged capital stock. An exception to this, considering the time lag between progressin construction and installation, is that we assume the installed stock of buildings and structures is thelagged capital stock:P,k, j St−1k, j
Zt = 
 P,k, jP,k, j St−1+ St/2k ∈ buildings and structuresotherwise

(26)

k, j

The installed productive capital stock Zt represents the accumulation of past investments, but we arek, jprimarily interested in Kt , the flow of capital services from that stock over a given period. This distinction
is not critical for individual assets, but becomes essential when we aggregate heterogeneous assets to form
an industry or economy-wide aggregate. We assume the flow of capital services for each industry andeach asset is proportional to the installed stock of capital:
k, j

k, j

Kt = φk, j Zt ,(27)

where φk, j denotes the proportionality constant. The constant coefficient: φk, j , is an ”annualization factor”,
which transform capital stock into capital service.*30
We estimate a price of capital services that corresponds to the quantity of capital input via the costof-capital formula. In equilibrium, with no uncertainty about capital income, investors are indifferent
between earning a nominal rate of return on a different investment or buying a unit of capital, collecting
a rental fee, and then selling the depreciated asset in the next period, as described in Equation (16). For
investors purchasing the asset the cost of capital equals the marginal product of the asset. This implies
the familiar cost of capital, or user cost, for each asset in each industry:
K,k, jPt*30

j= (rt − πkt )PA,k+ δk PA,k
t ,
t−1

(28)

We assume the proportional relationship between productive capital stock and capital service. Hulten (1990) inquires, “Is achair in “service” only when it is occupied? Or, does the availability of the chair for potential occupancy count for something
too? If so, are potential services equivalent to actual services? cdots Is an office building utilized only during business hours,
or is it utilized all the time to keep out thieves and inclement weather?”(Hulten, 1990, p.135).

23

jwhere the asset-specific capital gains term is πkt defined in Equation (25) and rt is the nominal rate of returnin industry j.*31
The cost of capital accounts for the nominal rate of return, asset-specific depreciation, and an assetspecific revaluation term. An asset with a higher depreciation rate has a higher marginal product andmust receive a higher capital service price as compensation. Similarly, if an investor expects a capital loss
( πkt < 0 ), then a higher service price is required. Jorgenson and Stiroh (2000) and Oliner and Sichel (2000)
discuss the importance of incorporating asset-specific revaluation terms for information technology assets
experiencing rapid downward revaluations.
Tax considerations are also a key component of capital service prices, as discussed by Hall and Jorgenson(1967) and developed in detail by Jorgenson and Yun (2001) for the U.S. economy and Nomura (1998,
2004a) for the Japanese economy. Following Nomura (2004a, Ch.3) in accounting for capital consumption
k, j

j

k, j

j

allowances: zt , income allowances and reserves: ζt , special depreciation: µt , corporate income tax:ut ,jjjbusiness income tax: vt , property taxes: κt , acquisition taxes: ωt , debt/equity financing: βt , capital gain
taxes: γt , and dividend tax: θt . We estimate an asset-specific, after-tax real rate of return for each asset ink, jeach industry, rt , that enters the cost-of-capital formula:

j
j
k, j
k, j k, j
1 + ωkt − (ut + vt ) zt + ωkt − µt z̃t +K,k, j
pt =

k, j

µt



k, j

1 + rtj

1 − ψtn kjo(rt − πkt ) + (1 + πkt )δkt pA,k+ κkt PA,k
t ,
t−1

(29)

where
k, j

zt =

∞
X

bkτ
m

k, j τ−1
τ=1 (1 + rt )k, j, z̃t =

∞
X

bkτ+1
m

k, j τ+1
τ=1 (1 + rt )

n
o
k, j
j
rt − πkt = βt (1 − ψt )it − πkt + (1 − βt )

,

(30)
j

ρt − πkt (1 − γt )

,

(31)


j
j
j
j
ψt = 1 + {1 + (ut + vt )(1 − ζt )}it
q

j
j
j
j
j
j
− 1 + 2{1 − (ut + vt )(1 + ζt )}it + {1 − (ut + vt )(1 − ζt )}2 it 2 2it ,

(32)

j

j

(1 − θt )αt + (1 − γt )(1 − αt )

k, j

k, j

where zt is the present value of capital consumption allowance for tax purpose.*32 The rate of return rt
*31

K,k,j
j
= (rt + kt )PA,k. The total capitalt−1
A,kservice cost is the sum of the opportunity cost of financial capital of Pt−1 , and the cost for time-series depreciation, which
consists of cross-section depreciation: δk , and revaluation: πkt .

*32

In the Japanese tax system, a business income tax is levied on revenue for some industries like electricity. A property tax for

Using the time-series depreciation rates in Equation (22), Equation (28) is also written as Pt

depreciable assets except motor vehicles and residence is levied on the book value, rather than the current value. Nomura(2004a, Ch.3) apply different cost-of-capital formulas, which are different from Equation (28), for some assets and industries.

24

is formulated as a weighted average of real, after-tax returns to debt and equity, where the rate of interestjis it and rate of return on equity is ρt . The use of income allowance and reserves could reduce the effectivejtax rate for corporate income: ψt , so that Equation (32) represents effective tax rate for corporate income
after the consideration. Inventories and land have a depreciation rate of zero and do not qualify for acapital consumption allowance for tax purposes, so the cost-of-capital formula is a simplified in Equation(29).
j

We then assume the after-tax rate of return: ρt , to all assets in the corporate sector of each industry is
the same and exhausts the value of payments to capital across all assets in the corporate sector of eachindustry,
K, j

Vt

X
=

K,k, j

Pt

k, j

Kt .

(33)

k
k, j

k, j

The capital service: Kt , is defined by the observable variable: Zt , in Equation (27). From the costK,k, jof-capital formula in Equation (28) for each asset and Equation (33), the capital service prices: (φk, j Pt
jand the after-tax rate of return on equity: ρt , are endogenously imputed.*33),

K,k, jSince Pt represents index

of capital service price, constant annualization factors: φk, j , are computed in each asset and each industry,
K,k, jtaking (φk, j Pt
3.2.2

) as normalized at one in the benchmark year.

Aggregating Heterogeneous Capital

We define the aggregate measure of capital service for the economy as a whole, by means of a Divisia
index as: k, j K̇t X K,k, j  K̇t vt  k, j  ,
=
Kt
K
k, j

(34)

t

K,k, jwhere the weights: vt , are nominal shares of each type of capital income in total capital income:
K,k, j k, j P
K,k, j k, j
Pt Kt / k, j Pt Kt .*34 Similarly, we define the aggregate measure of capital stock by means of a Divisia
index as: k, j Żt X Z,k, j  Żt vt  k, j  ,
=
Zt
Z
k, j

*33

(35)

t

k, j

k,j

In our framework, zt is an endogenous variable, depending on the rate of return rt , which is determined by the imputed
j

k, j

k,j

rate of return on equity: ρt , although Jorgenson and Yun (2001) treat zt as exogenous. zt has significant role to determinek,j
the impacts of corporate income tax to the capital service price. In case of endogenous zt , the elasticity of corporate income
j
K,k,j
k,j
tax ut to Pt
becomes small, in comparison with the case of exogenous zt . See Nomura (2004a, Ch.3) for the details.
*34

Hulten (1990) shows “the existence of a linearly homogeneous aggregator function K(·) allows this expression [Divisia index]
to be integrated to obtain the “level” of the aggregate capital in each year (with one time period arbitrarily normalized atone)”.

25

Z,k, jwhere the weights: vt , are nominal shares of each type of capital stock in total capital stock:k, j PA,k k, j *35
PA,k
The corresponding price index of capital inputs PKt for Kt and of capital stock PZt
t Zt / k, j Pt Zt .
for Zt are defined implicitly to make the value identities hold:
VtK = PKt Kt =X

K,k, j

Kt ,

k, j

(36)

A,k, j

Zt ,

k, j

(37)

Pt
k, j

and
VtZ = PZt Zt =

X

Pt
k, j

respectively. For the comparison of aggregate measures, we also define the simple sum of capital services
and capital stocks,
Kt∗ =

X

Kt ,

k, j

(38)

k, j

(39)

k, j

Z∗t =

X

Zt .
k, j

Among four definitions of aggregate measure of capital in Equations (34)-(35) and (38)-(39), the adequate
measure for capital inputs is only Kt in Equation (34).*36 Note that we need the capital service prices thatare not directly observed, to compute an adequate measure for capital inputs.
Table 3 represents the growth rates of capital stock: Zt and Z∗t , and capital service: Kt and Kt∗ , at theaggregate level in Japan. Here, we compute two cases with the different coverage of capital: fixed assets
and total assets that include land and inventories.*37 In case of fixed assets only, the average annual
growth rate of capital service: Kt , is 7.6 percent during 1960-2000, which is 1.4 percent point higher than
the growth of the simple sum of productive capital stock: Z∗t . In case of total assets, which includes land
and inventories, the growth rates of Kt and Z∗t are 5.9 percent and 3.3 percent per year, respectively. The
difference of two measures is significant. By the quantity index to be normalized as one in 1960, Kt is 10.6
(20.8 in case of fixed assets) and Z∗t is 3.8 (11.8) in 2000. If we use capital stock measures: Z∗t or Zt , as a
*35

k, j

On the assumption of geometric approach, productive capital stock by asset and industry: Zt , is identical with net (wealth)jcapital stock. Zt in Equation (35) may provide the appropriate aggregate measure of real net capital stock. Note that capital
service prices that are not directly observed need not be used, to compute it.
*36

Using the other three inadequate measures, Nomura (2004, Ch.4) defines the three measures of capital quality as Kt /Zt , Kt /Kt∗ ,and Kt /Z∗t . Jorgenson and Stiroh (2000) uses capital quality as Kt /Zt , although they take a simple sum among industries ineach asset. Nomura (2004, Ch.4) uses Kt /Z∗t , analogously with the definition of labor quality.

*37

To keep consistency with the present Japanese national accounts, we do not include custom and prepackaged software in
K,k,j

Table 3. The capital service prices: Pt, used in the two cases with the different coverage of capital are different even forsame asset in same industry, because we impute the ex-post rate of returns in each case.

26

capital input, it underestimates the growth of capital inputs and, therefore, it overestimates the growth of
total factor productivity (TFP).*38
Table. 3 Growth Rates of Capital Stock and Services in Japan
Fixed Assets
Stock

Total Assets
Service

(ref)

Zt

Z∗t

Kt

Service
Kt∗

Zt

Stock
Z∗t

Kt

Kt∗

GCSPE

1960–65

9.11

7.80

13.88

8.25

4.97

3.64

9.85

5.67

11.55

1965–70

10.44

9.53

12.27

10.24

5.94

4.93

9.76

6.86

12.45

1970–75

9.56

9.25

9.96

9.19

5.43

5.05

8.17

5.92

10.10

1975–80

6.15

6.18

5.81

5.95

3.79

3.57

4.67

3.91

6.38

1980–85

4.80

4.69

5.24

4.63

2.73

2.57

3.87

2.92

6.72

1985–90

5.04

4.87

6.02

5.38

2.69

2.68

4.94

3.46

6.79

1990–95

4.42

4.40

5.08

4.75

2.42

2.52

3.82

3.20

5.15

95–2000

2.56

2.60

2.49

2.50

1.74

1.73

2.05

2.06

3.48

60–2000

6.51

6.16

7.59

6.36

3.72

3.34

5.89

4.25

7.83

Unit: average annual percentage (%). “Total Assets” includes fixed assets, land, and inventories.
Assets only for industry use and owner-occupied housing (excluding custom and prepackaged software).
GCSPE is defined by tangible fixed assets, owned by private sectors only, excluding the residence.

Schreyer (2003) estimates capital service inputs for the G7 countries, using a hyperbolic age-efficiency
profile. The estimate of the growth rate in the Japanese aggregate capital service, which is defined by theTörnqvist index of capital services for all fixed assets, is 4.9 percent per year during 1980-2000. This growthrate is close to our estimates (4.7 percent) for the same periods.*39 On the other hand, the GCSPE, which*38

If we define aggregate measures as a simple-sum for labor and value added, like capital inputs: Z∗t , that overestimates by 41
percent (18 percent in case of fixed assets) of average annual growth rate of TFP, at the aggregate level during 1960-2000 in
Japan (Nomura, 2004a, Ch.4).

*39

Schreyer (2004) estimates the multifactor productivity and capital service, for fixed assets only, based on the two assumptions:exogenous rate of return (RoR) and endogenous RoR. In Japan, the growth rate of capital service inputs is reported as annually
4.6 percent by exogenous-RoR approach and 4.5 percent by endogenous-RoR approach during 1985-2000. Although the
Schreyer’s measure includes reallocation bias of capital service, the aggregate growth rate is also 4.5 percent for the same
periods in our estimates, which is based on endogenous-RoR by industry on the Japanese tax structure described in Equation(29).
Although we don’t introduce the details of our estimates of TFP in this paper, however, our TFP (or MFP) measures in
Nomura (2004a, Ch.4) considerably different from Schreyer (2004) at the aggregate level. The main source of the gap is thedefinition of labor input. Schreyer defines the labor inputs as hours worked, in which the increase in labor quality is neglected.
Our estimates based on the KEO (Keio Economic Observatory, Keio University) Database, which has chosen to classify theworkers by sex, age (eleven classes), educational attainment (four classes for male, three classes for female), employment class(three types: employees, self-employed, and unpaid family workers), and industry.

27

is based on the traditional gross concept of capital stock, provides higher growth. During 1980-2000, thegrowth rate of the GCSPE is 5.5 percent per year. If the GCSPE is used as a capital input in production
function, it overestimates the growth of capital inputs and, therefore, it underestimates the growth of TFP.
3.2.3

Land as a Capital

The stocks of land and inventories by industry are estimated in Nomura (2004a, Ch.C-D). In the Japanese
economy, the value of land is particularly notable. In comparison with the 23.6 percent share of land tototal nominal capital stock in the U.S. in 2000 (Jorgenson and Landefeld, 2005), the Japanese land share is43.5 percent in 2000 (Nomura, 2004a, Ch.2), even though the Japanese economy has experienced a record
decline of land prices in the 1990s.
Diewert and Lawrence (2000) indicate that neglecting land and inventories leads to a decline in average
TFP growth rates of 0.1 percent per year in Canada. This is large in relative terms, since the average
growth rate for the Canadian TFP averaged only 0.5-0.6 percent per year during 1963-1996. For theJapanese economy, Nomura (2004a, Ch.4) shows that neglecting land and inventories leads to a declineof 0.7 percent per year in the average TFP growth rate during 1960-2000, compared to 1.5 percent annual
average growth rate for Japanese TFP. TFP growth is underestimated by a factor of almost fifty percent
if land and inventories are ignored. Land has a significant role in the measurement of capital andproductivity in Japan.
Table. 4 Relative Prices of Capital Stock and Services by Industry between the U.S. and Japan
Fixed Assets
Z,jTotal Assets

RPt

RPt

K, j

Rφ j

RPt

Z,j

RPt

K,j

Rφ j

1.Agriculture

1.261

1.829

1.450

5.466

2.620

0.479

18.Machinery

1.120

0.886

0.791

2.009

1.415

0.704

19.Motor Vehicles

1.063

1.300

1.223

1.939

1.411

0.728

23.Transportation

1.267

1.602

1.265

2.252

1.671

0.742

24.Communication

1.262

1.014

0.803

1.694

1.131

0.668

25.Electiric Utilities

1.312

1.569

1.195

1.666

1.655

0.993

27.Trade

1.319

1.410

1.069

2.515

1.646

0.655

29.Other Service

1.282

0.945

0.737

2.738

1.088

0.397

Aggregate

1.314

1.360

1.035

3.050

1.701

0.558

Unit: Ratios of Japanese prices to the U.S. prices, evaluated in 1990 (exchange rate:144.8)
jj

RPZ,T and RPK,T represent relative prices for capital stock and service, respectively.
Rφ j is relative measure of annualization factors.
All indexes are aggregated as Törnqvist index, for all assets within an industry.

In particular, for international level comparison of productivity or capital deepening, the land price has
28

a significant role. Nomura (2004a, Ch.3) estimates relative prices of capital stock and service by asset
Z, jand industry between the U.S. and Japan.*40 Table 4 represents the relative prices for capital stock: RPt ,K, jrelative prices for service: RPt , and relative annualization factors: Rφ j between the U.S. and Japan in
1990, for some selected industries.
In the aggregate measures of the relative prices, defined by Törnqvist index using the average weights
between the U.S. and Japan, if we neglect the land and inventories as capital, the Japanese prices in capitalstock and service are 31.1 percent and 36.0 percent higher than that in the U.S., respectively. However,
if we include land and inventories, the price-gaps increased to about 3 times for capital stock and 1.7
K, jtimes for capital service. The land price-gap explains 56.1 percent of RPt . Especially, for the industries
like Agriculture, the consideration of land price has a big impact to the relative prices. In the aggregate
measure of TFP-gap, Japan is 26.1 percent below to the U.S. in the case of neglecting land and inventories.
The neglect leads to an underestimate of the Japanese TFP level, which is 17.9 percent less than the U.S. in
1990 (Nomura 2004a, Ch.4).
The clarification of the role of land as a capital input in production account is one of the most significant
aspects of Jorgenson system of national accounts.*41 Probably due to the incomplete definition of land
as a capital input in the 1993 SNA, the cost of land has been neglected in many production studies. The
capital service cost of land, however, should be interpreted as implicitly included in value added in the
production account.
3.2.4

Capitalization of Software

The expenditure for own-account and prepackaged software are not capitalized in the official Japanesenational accounts. Nomura (2004b) estimates own-account software investment by industry during 19552000 in Japan, based on the two kinds of methodology in the OECD Task Force on software measurementin the national accounts (Lequiller, Ahmad, Varjonen, Cave, and Ahn, 2003; Ahmad, 2003) and the U.S.
BEA’s methodology for estimating own-account software by industry (Grimm, Moulton, and Wasshausen,
2003).
International comparison of shares of own-account software investment to official GDP is in Figure 3(a)and for total software investment to GDP is in Figure 3(b).*42 In Japan, the share of own-account software*40

Relative price represents the price-gap index in both countries and is not unity even in the base year. To estimate relative
prices for capital stock, we need relative prices for investment by commodity. See Nomura (2004a, Ch.3) for the details offramework and data. The U.S. annualization factors by asset and industry are based on the estimates by Jorgenson. Industry
is classified, based on our common industry classification between the U.S. Jorgenson Data and the KEO Database in Japan.

*41

A brief survey of the history of economic thoughts for land as a factor of production, see Ryan (2002).

*42

In Figure 3, each share in each country is computed, based on the official national accounts. The share in Japan is estimates in29

to the GDP, which is adjusted to include all software investment, is 0.60 percent in 2000. It is higher
than that in the EU countries but Denmark. The U.S. has the highest share of own-account software (0.73
percent) among the countries. As for total software investment in Figure 3(b), Japan has 2.03 percent
GDP attributed to software investment. It is slightly lower than that in the U.S. (2.07 percent). Although
Sweden has the highest share in total software, we may take the difference in economic scales and industry
structures into consideration. The relative scale of software investment between the U.S. and Japan may
be appropriate.
(   $&    $945 

$= #&#

= $". >  

.   $   845 #< " 

< % & #

; $ , 7. 

9!&, :&;#

:'$&$ 

6 04  ,  .+87 #

6%7!4    % 98 

2& 3, 45+

2 $  3 $  "&45 

1 .+

01&% 

/.  0!& #(   $&*)+ ,&-./ 

, -.+   "&' (   )*+

! "#$% 

$%  &'#       !"#

?A@BCD E F GH5H @E D G9I+JKMLN@OQP%R+SUTVMT WXTY ZA[Q\] TZ^G_ `F Ba
Y b'GE adc"CXHe fggfh ] Ti%D jGEU?A@BCD E F GH5Y \*jadcIXe fggkh ] T  
 

 

 

 

 





@BACDE F G HI5I A#F E H8JK#LNMOAP Q.RSUTVNT WXT#Y Z\[^]*_ TZ`H8a bG Cc
Y dHF cfeDXIg hii#hj _ T#k.E lHFU@BACDE F G H8I5Y ]lcfeJXg hiimj _ T  

l 


 >?
 

(a) Own-Account Software Investment



 



 

(b) Total Software Investment

Fig. 3 Share of Software Investment in GDP: An International Comparison

Although the GDP-share of software investment is very close between the U.S. and Japan, the composition by type of software is significantly different. Figure 4 shows the changes of composition of software
investment every five years from 1970 to 2000 in the U.S. and Japan. In 1970, own-account software
has the largest share in software investment and prepackaged software is minor in both countries. The
share of own-account software decreases in both countries through the 1970s and the 1980s. In the U.S.,
the diminution of the share of own-account software is reflected by the rapid expansion of prepackaged
software. On the other hand, in Japan, the diminution is mainly reflected by the expansion of custom
software. In 2000, custom software occupies the largest portion, the share of which is almost two thirds ofthe total software investment in Japan.
One of the reasons why own-account and prepackaged software are avoided to be capitalized in thepresent Japanese national accounts may be that benchmark 1995 input-output (IO) table, which is one
Nomura (2004b). The share in the U.S. is based on the NIPA. The others are based on Hermans (2002) for Belgium and Ahmad(2003) for the other countries.

30+     B+    +  !   "#  $  %  &  'C   
 3 

: ;< =

2 3 3 @ A ;A =687 97.+D E#F#0#1)+* ,* . D+E#F#01< > ;? =    

3 4        !   "#  $  %  &  '(     
 4 5 

2 +    
687 97. /!0!0#01)+* ,* . /!0#0#01

  2+3   

Fig. 4 Composition of Software Investment: Comparison between the U.S. and Japanof basic statistics for estimating the national accounts, did treat only custom software as a software
investment. In the summer of 2004, the benchmark 2000 IO table was published and began to treat
prepackaged software as GFCF, in addition to custom software. However, capitalization of own-accountsoftware was postponed even in the benchmark 2000 IO table. ESRI (2000) pointed out that, in the Japanesestatistics, it is difficult to identify own-account software and that R&D activity that is not recommended
to be capitalized by the 1993 SNA. As the OECD Task Force on software measurement in the national
accounts (Lequiller, Ahmad, Varjonen, Cave, and Ahn, 2003; Ahmad, 2003) also discusses, the difficulty
is not peculiar to Japan. It is possible to estimate own-account software investment by industry in Japan,
applying similar methodology as that the recommendation of the OECD Task Force on software and the
BEA.
3.2.5

Impacts of IT Capital

To capture the impacts of capital related to information technology (IT), our latest estimates of capitalstock and service have detailed asset classification. The capital stock and service matrixes are based on 102
assets shown in Table 5: 95 fixed assets, 3 types of inventory, and 4 types of land, and 70 capital holding
sectors: 45 industries, government, household, and 23 infrastructures.*43*43 Although Nomura (2004a) estimated time-series capital formation matrixes during 1955-2000 with detailed asset classification,

the assets were aggregated for the measurement of capital stock mainly because of the lack of the long-term investment prices.
Author newly developed the prices and revised capital formation matrixes using 2000 benchmark capital formation matrix.
Also, to compute the long-term CFC for infrastructure, the classification for assets and capital holding sectors was reformed.
The productivity analysis in the Japanese industries, separately treating the IT-producing industries, is described in Jorgenson

31



  !"$#&% ')() +*,'-/.0'-21435 +*61798: #&; <  => $"$#@? * /'A"$B+CD" B = 17#@"$FE  $G

 
 
 
 




 

 

 

 

  



 



Fig. 5 IT Capital Contribution Share to Total Capital Service

Figure 5 shows the contribution share of IT capital to the growth of total capital service in the U.S.
and Japan at the aggregate level. The U.S. measurement is from Jorgenson, Ho, and Stiroh (2005). Here,the IT capital is defined by computer hardware, computer software (custom, prepackaged, own-account),and communications equipment (37-40 and 93-95 in Table 5). The total capital consists of fixed assets,
consumer durables, land, and inventories of all capital holders in each country. The growth rates areaggregated for the economies as a whole, based on the Törnqvist index, in both countries. In Japan,
although the contribution share of IT capital gradually increases during 1960-1986, however, it still about
10 percent lower than that in the U.S. The share decreases in the bubble economy periods. As mentioned
in section 2.2.3, the DOS/V as a operating system in PC was newly developed in 1991. The year of theintroduction of the DOS/V is a turning point. Especially, after 1995, the IT contribution rapidly expands.
In 2000, the contribution of the IT capital is 42.0 percent, approaching to the 46.0 percent in the U.S.
In nominal value of total capital stock, the share of IT capital is only 1.7 percent (3.2 percent of fixed
capital) in Japan in 2000. However, the capital service cost of IT capital gradually increased to 9.8 percent
in 2000 and the IT capital contributes more than 40 percent of the growth in total capital service inputs.
Note that the deep impacts of IT capital can be found only in the measurement of capital service withdetailed classification of assets, because the capital service prices, reflecting their marginal products, inIT capital is higher than that of other Non-IT capital due to the large depreciation rate and the rapid
downward revaluation of the IT capital, as described in Equation (28).

and Nomura (forthcoming).

32

3.2.6

Capital for Non-Market Production

As the final topics related to capital measurement, we introduce our evaluation of capital service cost for
non-market production. In the 1993 SNA and also in NIPA by the U.S. BEA, for non-market production,
only consumption of fixed capital (CFC) is described in their production accounts. The CFC is only apart of the capital cost. Here, our accounting is based on the Jorgenson system of national accounts.*44
The extension to the Jorgenson system of national accounts means the replacement of the CFC to theappropriate measure of capital service cost in non-market production, which will be considered in thenext revision of SNA in 2008 (1993 SNA Revision 1) as also proposed by the Canberra II Group (Ahmad,
2004).
First, let us adjust the GDP in the present Japanese national accounts to the 1993 concepts of GDP.
Figure 6(a) gives the capital service cost to be added, associated with the revision from the 1968 SNA
to the 1993 SNA concepts of GDP. The custom software investment and the CFC for infrastructure isalready considered in the present Japanese national accounts, and valued at 14.7 trillion yen in 2000.*45
Capitalizing own-account and prepackaged software leads to an increase of 3.8 trillion yen in 2000 in theJapanese GDP. *46
Our measurement of capital service cost for non-market production includes capital services of public
capital, land for owner-occupied housing by households, and consumer durables. Based on author’s
estimates, Figure 6(b) shows the cost of the three capital services, which is added to the 1993 SNA concepts
of GDP. In the figure, the capital service cost of public capital that excludes the CFC for public capital,
because it is already included in the estimates of the GDP. Introducing the three capital service costs leads
to an increase 41.8 trillion yen in 2000 in the Japanese GDP.*47 The largest part is the capital service costof consumer durables, which is 25.5 trillion yen and accounts for 4.6 percent in the Jorgenson concepts*44

See Christensen and Jorgenson (1996), Fraumeni (2000), and Jorgenson and Landefeld (2005).

*45

The Japanese national accounts does not still estimated before 1980, so far. Here, the CFC for infrastructure in Figure 6(a) is
author’s estimates, based on our capital stock estimates in 23 kinds of infrastructure during 1955-2000 (Nomura, 2004a).

*46

Including this leads to a rebalancing of the IO tables with some difficulties to keep consistency with other data. See Nomura(2004b) for the detail. Since output of government sector is defined by the total costs, capitalization of software leads to thechange of the government output. In the total economy, increase of the GDP is the sum of the increase of investment for
own-account software and prepackaged software, the increase of consumption for both capitals in the government, and thedecrease of own-account software produced and prepackaged software purchased by the government. The consumption forsoftware capital is computed to be consistent with our estimates of software stock government sector holds.

*47

We impute the capital service cost for non-market production using the average rate of return of all industries, weighted by
the nominal share of capital stock in the industries. The rate of return in each industry is defined by the weighted average ofrate of interest and the rate of return on equity. See Jorgenson and Nomura (forthcoming).

33



 

  "! #%$'&()
* &,+"-/.0!21 + $3"! #4$5&()

B $%&7A42C"6+7EDF"%G.)H+456DIKJLKM

6 178$/!29:"! #4$'&()



6<;=6

 !#"$%&'( ")+*-,.0/213+0/3454 6+7&'*389#7:;<$=>89?)@+ %A* #>!2@?/+"#4)78$'>1"$51 







 





 








A $'B5C'C'B'!2+(D"+E
 

 

 

 

 







GND&O7P%&%&7&-=+M


 

 

(a) for 93 SNA Concepts



 



 



 



(b) for Non-Market Production

Fig. 6 Additional Capital Service Cost for Non-Market Productionof GDP in 2000. In comparison with the U.S., the scale is about twofold, as Jorgenson and Landefeld(2005) estimates the consumer durables account for 9.6 percent in 2002, reflecting the difference the rates
of return in both countries.

4

Concluding Remarks: Proposals for the Japanese National Accounts
As concluding remarks of this paper, we summarize our proposals for sweeping improvement formeasuring capital in the Japanese national accounts. Our proposals are assorted into two groups. The
first group: (i)-(v), is the proposals to catch up the international standard. The second: (vi)-(viii), is the
proposals to be prepared for the next revision of SNA in 2008 (1993 SNA Revision 1) or for measurementof productivity. For the second group, we attach the mark of ∗. Each proposal may be ordered by urgency,
rather than importance or ease of implementation.
(i)Capitalization of Software (related to section 3.2.4)(ii)

Reframing Net Capital Stock and CFC (related to section 2.3 & 3.1)

(iii)

Gross Capital Stock to Productive Capital Stock (related to section 2.1 & 3.1.3)(iv)

Constant-Quality Prices in Japan (related to section 2.2)

(v)
(vi)

Empirical Studies for AEP and APP in Japan (related to section 2.3.3)∗

Measurement of Price and Quantity of Capital Service (related to section 3.2)(vii)∗(viii)

Land as a Capital (related to section 3.2.3)∗

Capital Service Cost for Non-Market Production (related to section 3.2.6)

34

First, (i) capitalization of own-account and prepackaged software is the most urgent requirement. As
Nomura (2004b) pointed out, it is possible to estimate own-account software investment by industry inJapan, applying similar methodology as that recommended by the OECD Task Force on software and theindustry approach used by the BEA.
Our proposals: (ii) and (iii), are highly desired to improve the measurement of capital in the Japanesenational accounts. The traditional system of gross and net capital stock is incapable of portraying thetwo different aspects of capital: the productive capacity and the value of capital, except under unrealistic
assumptions. A quarter century after the controversy between Jorgenson-Griliches (1972) and Denison,measuring internally consistent estimates of capital stock, capital input, and depreciation became a common objective in the national accounts, as in the international methodological standards recommended
by OECD (2001a, 2001b). Fortunately, ESRI can learn a lot from the BEA’s revision in 1997.
The ESRI has a plan to spend the following three years reframing measurement of capital in the Japanesenational accounts. Over this time, it is important to estimate the long-term constant-quality prices, as in our
proposal (iv). The main purpose of price statistics is to measure of current movement of prices, which can
only be captured with constant-quality prices. However, the national accounts, in particular measurementof capital, requires the constant-quality prices be extrapolate backward, sustaining the consistency with
newly developed methodology, if possible. Although this function is carried out by BEA in the U.S., we
may not find any similar function in the Japanese statistical system.
Empirical studies for estimating depreciation or deterioration in the Japanese economy is also required.
In the framework for measuring capital stock, the key idea is the age-efficiency profile. The AEP canbe determined empirically by modeling a time series of prices of an asset by age. An alternative andmore direct approach is modeling a time series of rental prices of an asset by age. Although Nomura(2004a, Ch.2) accepted the geometric distribution as approximation based on Japanese data, passenger
vehicles and housing are less durable and trucks are more durable in Japan, in comparison with the BEA
depreciation rates. Further empirical studies for the Japanese economy are required.
The theory for measuring capital, proposed by Jorgenson and his associates, can provide a consistentframework for measures of both capital stock and capital services. As Jorgenson (1989) clearly pointed
out, measures of net capital stock and asset prices can be employed in the national wealth accounts, whilemeasures of capital service input and capital service prices can be utilized in national production accounts.
At present, although there is still no place for capital service cost in the SNA and the U.S. NIPA, only three
countries - Australia, the United States, and Canada - produce time series of capital services as a part oftheir official statistics. Recently, work has also been taken up in the United Kingdom (Schreyer, 2003).

35

We recommend that ESRI should introduce capital services at the same time as reframing the measurement of capital stock. In addition, the capital service cost of land should be evaluated. Land as a capital
has a significant role in the measurement of capital and productivity in Japan, although almost empirical studies for the Japanese economy do not fully recognize the importance. Measuring capital service
leads the additional imputation of capital service cost for non-market production. ESRI can accomplish
sweeping improvement by overcoming all our proposals, thereby anticipating the SNA 2008 (1993 SNA
Revision 1). The Canberra II Group supports for introducing measures of the cost of capital services into
the national accounts, as ‘of-which’ items in the production account (Ahmad 2004; Diewert, Harrison, andSchreyer, 2004). The time has come to turn the tables!

36

Table. 5 Asset Classification and Depreciation Rates
Assets1.Trees
2.Livestock
3.Textile products
4.Wooded products
5.Wooden furniture and fixtures
6.Metallic furniture and fixtures
7.Nuclear fuel rods
8.Metallic products
9.Boilers and turbines
10.Engines
11.Conveyors
12.Refrigerators and air conditioning apparatus
13.Pumps and compressors
14.Sewing machines
15.Other general industrial machinery and equipment
16.Mining, civil engineering and construction machinery
17.Chemical machinery
18.Industrial robots
19.Metal machine tools
20.Metal processing machinery
21.Agricultural machinery
22.Textile machinery
23.Food processing machinery
24.Sawmill, wood working, veneer & plywood machinery
25.Pulp equipment and paper machinery
26.Printing, bookbinding and paper processing machinery
27.Casting equipment
28.Plastic processing machinery
29.Other special industrial machinery & nec
30.Other general machines and parts
31.Office machines
32.Vending, amusement and other service machinery
33.Electric audio equipment
34.Radio and television sets
35.Video recording and playback equipment
36.Household electric appliance
37.Electronic computer and peripheral equipment
38.Wired communication equipment
39.Radio communication equipment
40.Other communication equipment
41.Applied electronic equipment
42.Electric measuring instruments
43.Generators
44.Electric motors
45.Relay switches and switchboards
46.Other industrial heavy electrical equipment
47.Electric lighting fixtures and apparatus
48.Passenger motor vehicles
49.Trucks, buses and other vehicles
50.Two-wheel motor vehicles
51.Motor vehicle partsδ

Assets

0.200
0.309
0.347
0.236
0.171
0.098
0.413
0.086
0.102
0.112
0.098
0.116
0.118
0.112
0.142
0.171
0.143
0.150
0.127
0.111
0.098
0.117
0.113
0.137
0.104
0.127
0.107
0.122
0.130
0.208
0.347
0.210
0.236
0.236
0.236
0.196
0.347
0.206
0.275
0.118
0.196
0.196
0.079
0.079
0.079
0.109
0.079
0.163
0.228
0.218
0.208

52.Steel ships
53.Other ships
54.Railway vehicles
55.Aircraft
56.Bicycles
57.Transport equipment for industrial use
58.Other transport equipment
59.Camera
60.Other photographic and optical instruments
61.Watches and clocks
62.Physics and chemistry instruments
63.Analytical, measuring instruments & testing machines
64.Medical instruments
65.Miscellaneous manufacturing products
66.Residential construction (wooden)
67.Residential construction (non-wooden)
68.Non-residential construction (wooden)
69.Non-residential construction (non-wooden)
70.Road construction
71.Street construction
72.Bridge construction
73.Toll road construction
74.River improvement
75.Erosion control
76.Seashore improvement
77.Park construction
78.Sewer construction
79.Sewage disposal facilities
80.Waste disposal facilities
81.Harbor construction
82.Fishing port construction
83.Airport construction
84.Agricultural construction
85.Forest road construction
86.Forestry protection
87.Railway construction
88.Electric power facilities
89.Telecommunication facilities
90.Other civil engineering and construction
91.Plant engineering
92.Mineral exploration
93.Custom software
94.Pre-packaged software
95.Own-account software
96.Finished-goods inventory
97.Work-in-process inventory
98.Material inventory
99.Land for agricultural use
100.Land for industrial use
101.Land for commercial use
102.Land for residential use

δ
0.108
0.166
0.068
0.135
0.498
0.217
0.332
0.210
0.218
0.118
0.236
0.236
0.199
0.274
0.048
0.031
0.057
0.039
0.020
0.020
0.020
0.020
0.019
0.019
0.018
0.048
0.027
0.027
0.061
0.018
0.018
0.054
0.028
0.034
0.019
0.030
0.025
0.035
0.025
0.025
0.550
0.330
0.330
0.330
0.000
0.000
0.000
0.000
0.000
0.000
0.000

Represents geometric depreciation rates used in our latest estimates of capital stock and service.
Assets 48-49 and 66-67: estimates in Nomura(2004, Ch-2).
For other assets: author’s estimates based the Japanese tax-lives, converting rates to effective service life, and the BEA’s declining balance rates.

37

References[1] Aizcorde, Ana, Carol Corrado, and Mark Doms (2000). Constructing Price and Quality Indexes for High Technology Goods,
CRIW workshop on Price Measurement, August, 39p.
[2] Ahmad, Nadim (2003), Measuring Investment in Software, STI Working Paper Series, OECD, May.
[3]

(2004). Introducing Capital Services into the Production Account, Meeting of the Advisory Expert Group on National
Accounts, December.

[4] Bank of Japan (2002). Publication of “Domestic Corporate Goods Price Index using chain-weighted index formula”, Nihon
Ginkou Chosa Geppou, Research and Statistics Department, Bank of Japan, (in Japanese).
[5] Biørn, Erik (1989). Taxation, Technology and the User Cost of Capital, Amsterdam: North-Holland, 325p.
[6] Biørn, Erik, Erling Holmoy, and Oystein Olsen (1989). Gross and Net Capital, and the Form of the Survival Function: Theory
and Some Norwegian Evidence, Review of Income and Wealth, 35, 133-149.
[7] Bureau of Economic Analysis (1997). Note on Alternative Measures of Gross Product by Industry, Survey of Current Business,
November, 84-85.
[8][9](1999). Fixed Reproducible Tangible Wealth in the United States, 1925-94, Washington, U.S. Department of Commerce.
(2003), Fixed Assets and Consumer Durable Goods in the United States, 1925-99, Washington, DC: U.S. Government
Printing Office, September.

[10] Christensen, Laurits R. and Dale W. Jorgenson (1996). Measuring Economic Performance in the Private Sector, in D.W. Jorgenson,
Postwar U.S. Economic Growth, Cambridge, The MIT Press.
[11] Corrado, Carol, John Haltiwanger, and Dan Sicherl, eds. (2005), Measuring Capital in the New Economy, Chicago, University of
Chicago Press.
[12] Diewert, Erwin W. (1980). Aggregation Problems in the Measurement of Capital, in D.Usher eds., The Measurement of Capital,
Chicago, University of Chicago Press, 433-528.
[13](2001). Measuring the Price and Quantity as Capital Service Under Alternative Assumptions, Department of Economics,
University of British Columbia, Discussion Paper No.01-24, June.

[14] Diewert, Erwin W. and Denis Lawrence A. (2000). Progress in Measuring the Price and Quantity of Capital, in Lawrence J. Lau
eds., Econometrics and the Cost of Capital: Essays in honor of Dale W. Jorgenson, Chapter 11, Cambridge, The MIT Press, 273-326.
[15] Diewert, Erwin W. Anne Harrison, and Paul Schreyer (2004). Cost of Capital Services in the Production Account, 20p.
[16] Doms, Mark E., Wendy E. Dunn, Stephen D. Oliner, and Daniel E. Sichel. (2003). How Fast Do Personal Computers Depreciate?
Concepts and New Estimates, FRBSF Working Paper 2003-20, Novenmber, 57p.
[17] Economic and Social Research Institution (2000). The Explanation of the Japanese National Accounts Based on the 1993 SNA,
November (in Japanese).
[18] Fraumeni, Barbara (1997). The Measurement of Depreciation in the U.S. National Income and Product Accounts, Survey ofCurrent Business, July, 7-23.
[19](2000). The Jorgenson System of National Accounts, in Lawrence J. Lau eds., Econometrics and the Cost of Capital: Essays inhonor of Dale W. Jorgenson, Chapter 6, Cambridge, The MIT Press, 111-142.

[20] Grimm, Bruce T., Brent R. Moulton, and David B. Wasshausen (2003). Information Processing Equipment and Software in the
National Accounts, revision of the paper prepared for Conference on Measuring Capital in the New Economy, NBER/CRIW,
April 26-27, 2002, Federal Reserve Board, Washington, D.C., March.
[21] Hall, Robert E. and Dale W. Jorgenson (1967). Tax Policy and Investment Behavior. Amrican Economic Review, Vol.57, 391-414.
[22] Hermans, Tim (2002). Measurement of GFCF in Software in the Belgian National Accounts, Joint ECE/Eurostat/OECD Meetingon National Accounts, April.
[23] Hill, Peter (1998). Gross, Productive, Net Capital Stock, Second Meeting of the Canberra Group on Capital Stock Statistics, 20p.
[24]

(1999). The Productive Capital Stock and the Quantity Index for Flow of Capital, Third Meeting of the Canberra Groupon Capital Stock Statistics, 5p.

[25](2000). Economic Depreciation and the SNA, Paper Prepared for the 26th General Conference of The International
Association for Research in Income and Wealth, Cracow, Poland, 27 August to 2 September, 19p.

38

[26] Hulten, Charles (1990). The Measurement of Capital, in E. R. Berndt and J. E Triplett eds., Fifty Years of Economic Measurement:
The Jubilee of the Conference on Research in Income and Wealth, Chicago: University of Chicago Press, 119-158.
[27] Hulten, Charles R. and Frank C. Wykoff (1981a), Economic Depreciation and the Taxation of Structures in United States
Manufacturing Industries: An Empirical Analysis, in D. Usher eds., The Measurement of Capital, Chicago: University of Chicago
Press, 83-120.
[28](1981b), The Estimation of Economic Depreciation Using Vintage Asset Prices: An Application of the Box-Cox Power
Transformation, Journal of Econometrics, April, 367-396.

[29](1981c), The Measurement of Economic Depreciation, in C. R. Hulten eds., Depreciation, Inflation, and the Taxation ofIncome from Capital, Washington, D.C.: The Urban Institute Press, 81-125.

[30] Jorgenson, Dale W. (1963). Capital Theory and Investment Behavior, American Economic Review, Vol.53, No.2, 247-274.
[31](1974). The Economic Theory of Replacement and Depreciation, in W. Sellekaerts, eds., Econometrics and Economic Theory:
Essays in Honour of Jan Tinbergen, New York: Macmillan, 189-221.

[32](1989). Capital as a Factor of Production, in D. W. Jorgenson and R. Landau, eds., Technology and Capital Formation,
Cambridge: The MIT Press, 1-35.

[33](1996). Empirical Studies of Depreciation, Economic Inquiry, 34, 24-42.

[34](1999). New Methods for Measuring Capital, Third Meeting of the Canberra Group on Capital Stock Statistics, 17p.

[35] Jorgenson, Dale W., and Zvi Griliches (1967). The Explanation of Productivity Change, Review of Economic Studies, Vol.34,
249-283.
[36](1972). Issues in Growth Accounting: A Reply to Edward F. Denison, Survey of Current Business, Vol.52, No.4, 65-94.

[37] Jorgenson, Dale W., Mun S. Ho, and Kevin J. Stiroh (2005). Growth of U.S. Industries and Investments in Information Technology
and Higher Education, in Corrado, Haltiwanger, and Sichel (2005).
[38] Jorgenson, Dale W. and J. Steven Landefeld (2005). Blueprint for Expanded and Integrated U.S. National Accounts: Review,
Assessment, and Next Steps, in D.W. Jorgenson, J.S. Landefeld, and W.D. Nordhaus, eds., A New Architecture for the U.S. National
Accounts, Chicago, University of Chicago Press.
[39] Jorgenson, Dale W. and Koji Nomura (forthcoming). Growth of Japanese Industries and Investment in Information Technology,
mimeo.
[40] Jorgenson, Dale W. and Kevin J. Stiroh (2000). Raising the Speed Limit: U.S. Economic Growth in the Information Age, in D.W.
Jorgenson, Economic Growth in the Information Age, Cambridge, The MIT Press.
[41] Jorgenson, Dale W. and Kun-Young Yun (2001). Lifting the Burden: Tax Reform, the Cost of Capital and U.S. Economic Growth,
Cambridge, The MIT Press.
[42] Kuninori, Morio (1988). Measurement of Depreciation of Japanese Construction Machinery, Keizai Keiei Kenkyu, Vol.9 (inJapanese).
[43] Lee, Bun S. (1978). Measurement of Capital Depreciation within the Japanese Fishing Fleet, Review of Economics and Statistics,
255-273.
[44] Lequiller, Francois, Nadim Ahmad, Seppo Varjonen, William Cave, and Kil-Hyo Ahn (2003): Report of the OECD Task Forceon Software Measurement in the National Accounts, OECD Statistics Working Paper Series, OECD, March.
[45] Moulton, Brent R. (2001). The Expanding Role of Hedonic Methods in the Official Statistics of the United States, 15p.
[46] Nomura, Koji (1998). Measurement of Capital Service Price Based on Japanese Tax Structure, KEO Discussion Paper, No.53, (inJapanese), 56p.
[47]
[48]

(2004a). Measurement of Capital and Productivity, Tokyo: Keio University Press. (in Japanese) , 633p.
(2004b). Capitalizing Own-Account Software in Japan, Program on Technology and Economic Policy (PTEP), John F.
Kennedy School of Government, Harvard University, 35p.

[49] Nomura, Koji and Jon D. Samuels (2004). Can We Go Back to Data? Reconsideration of U.S.-Harmonized Computer Prices inJapan, Program on Technology and Economic Policy (PTEP), John F. Kennedy School of Government, Harvard University, 43p.
[50] OECD (2001a), OECD Productivity Manual: A Guide to the Measurement of Industry-Level and Aggregate Productivity Growth, OECD,
Paris, March.
[51] OECD (2001b), Measuring Capital: A Manual on the Measurement of Capital Stocks, Consumption of Fixed Capital, and Capital Services,
Paris, OECD, April.

39

[52] Oliner, Stephen D. (1993). Constant-Quality Price Change, Depreciation, and the Retirement of Mainframe Computers, inMurray F. Foss, Marilyn E. Manser, and Allan H. Young, eds., Price Measurement and Their Uses, Chicago: University of Chicago
Press, 19-61.
[53](1994). Measuring Stocks of Computer Peripheral Equipment: Theory and Application, Washington, Board of Governorsof the Federal Reserve System, May.

[54] Oliner, Stephen D. and Daniel E. Sichel (2000). The Resurgence of Growth in the Late 1990s: Is Information Technology the
Story?, Journal of Economic Perspectives, 14, 3-22.
[55](2002). Information Technology and Productivity: Where are We Now and Where are We Going?, Economic Review, Federal
Reserve Bank of Atlanta, 87(3), Quarter Three, 15-44.

[56] Parker, Robert P. and Bruce T. Grimm (2000). Recognition of Business and Government Expenditures for Software Investment:
Methodology and Quantitative Impacts, 1958-98, paper presented for BEA’s Advisory Committee, May.
[57] Ryan, Christopher K. (2002). Land as a Factor of Production, American Journal of Economics and Sociology, Vol.61, Issue 5, Nov.,
7-25.
[58] Schreyer, Paul (2003). Capital Stocks, Capital Services and Multi-Factor Productivity Measures, OECD Draft Paper Economic
Studies , 22p.
(2004). Measuring Multi-factor Productivity When Rates of Return are Exogenous, Paper presented at the SSHRC Inter-[59]

national Conference on Index Number Theory and the Measurement of Prices and Productivity, Vancouver, 30 June-3 July,35p.
[60] Triplett, Jack E. (1989). Price and Technological Change in a Capital Good: A survey of Research on Computers, in D. W.
Jorgenson and R. Landau, eds., Technology and Capital Formation, Cambridge: The MIT Press, 127-213.
[61](1996a). Depreciation in Production Analysis and in Income and Wealth Accounts: Resolution of an OLD Debate, Economic
Inquiry, 34(1), 93-115.

[62](1996b). High-Tech Industry Productivity and Hedonic Price Indices, Industry Productivity, International Comparisonand Measurement Issues, Paris, OECD, 119-142.

[63](1997). Concepts of Capital for Production Accounts and for Wealth Accounts: The Implications for Statistical Programs,
First Meeting of the Canberra Group on Capital Stock Statistics, 57p.

[64] United Nations (1993). System of National Accounts 1993, New York, United Nations.
[65] Wasshausen, David (2000), Computer Prices in the National Income and Product Accounts, Draft Methodology Paper, Bureau
of Economic Analysis, 24p.
[66] Whelan, Karl (2002), Computers, Obsolescence, and Productivity, Review of Economics and Statistics, 84, 445-62.

40