Discussion Paper No. 772

JAPAN’S INTANGIBLE CAPITALAND VALUATION OF CORPORATIONSIN A NEOCLASSICAL FRAMEWORK

Hiroki Arato
Katsunori Yamada

February 2010
Revised October 2010
Secondly Revised November 2011

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Japan’s Intangible Capital and Valuation of
Corporations in a Neoclassical Framework∗
Hiroki Arato†

Katsunori Yamada‡

Abstract
This paper estimates the economic value in the 1980s and 1990s of corporate
assets in Japan, including both tangible and intangible assets, based on the neoclassical framework of McGrattan and Prescott (2005). Our estimates use a new
micro-data set that comprises the accounting statements of all listed, non-ﬁnancial
companies in Japan. We ﬁnd that in 1981-86, a period that immediately preceded
Japan’s so-called “bubble economy”, our assessed value of corporate productive assets, net of the value of corporate debt, is approximately equal to the actual stock
market value of Japanese corporate equity. The ﬁnding diﬀers from previous results
based on studies of aggregate data sets or based on studies of micro data sets thatneglected intangible capital. We also show that the Japanese ratio of the amountof intangible capital stock to the amount of tangible capital stock is comparable tothe analogous ratios for the U.S. and U.K.

keywords: Intangible capital, Fundamental value of corporations, Accounting
information

JEL classiﬁcation: E01, E22∗This project started when Yamada belonged to KIER, Kyoto University and was ﬁnished after hemoved to ISER, Osaka University. Permission for the usage of the Corporate Financial Databank by
Development Bank of Japan Inc. is greatly appreciated. An earlier version of this study was circulated
under the name “Valuing Japanese Corporations: A New Perspective on Japan’s Stock Market “Bubble”
of the 1980s.” We would like to thank Ellen McGrattan and two anonymous referees for their constructive
and detailed criticism that has substantially improved the study. We are also grateful to Carol Corrado,
Jonathan Haskel, and Tsutomu Miyagawa for their data provisions, and to David Flath, Ronald Harstad,Tae Homma, Ayumi Ikeda, Tomoyuki Nakajima, Fumio Ohtake, Kazuo Ogawa, and Akihisa Shibata
for their helpful comments. Any remaining errors are the sole responsibility of the authors. Yamada
acknowledges the research grant provided by the Global COE program of Osaka University, and Grantin-Aid for Scientiﬁc Research 21830057. Arato acknowledges the research grant provided by the Global
COE program of Hitotsubashi University, and Grant-in-Aid for Scientiﬁc Research 18GS0101 which isheaded by Tsutomu Watanabe.
†
Faculty of Economics, Shinshu University.
‡
Corresponding author: Institute of Social and Economic Research, Osaka University. E-mail:kyamada@iser.osaka-u.ac.jp1

1

Introduction

This paper provides a new assessment of the values in the 1980s and 1990s of corporate
assets in Japan–including both tangible and intangible assets–based on the neoclassicalframework of McGrattan and Prescott (2005). In 1981–86, a period immediately preceding Japan’s “bubble economy”, our assessed value of corporate productive assets, netof the value of corporate debt, closely approximates the actual stock market value ofJapanese corporate equity. The striking implication that equities were correctly priced inJapanese stock markets in 1981–1986 is original, at odds with common perceptions.
As in McGrattan and Prescott, a key assumption of our calculation is that the aftertax rate of return on corporate intangible assets (such as patents, brand names andﬁrm-speciﬁc human capital) is in equilibrium equal to that on tangible corporate assets(such as buildings, machinery and equipment). From a newly available micro-data set
comprising the ﬁnancial statements of all private non-ﬁnancial corporations in Japan, theCorporate Financial Databank (CFD), we extract aggregate measures of corporate pretax proﬁt and investment. Then, these aggregates, observed tax rates, depreciation rates,
and real rates of interest, yield an imputation of the market value of intangible corporate
assets via equilibrium characterization. Construction of aggregate measures of the market
value of tangible corporate assets uses the perpetual inventory method.
This aﬀords a measure of the aggregate ratio of the market value of corporate intangible
assets relative to the market value of corporate tangible assets, during the years 1981–
89, which we argue comported with balanced macroeconomic growth. From this ratio,
estimated for 1981–89 and assuming Cobb-Douglas production technology, measures ofthe market value of corporate intangible assets in the subsequent period 1993–97 are
imputed.
Consequently, our estimate of Japanese corporate intangible capital in the 1980s falls
within a reasonable range. That is, the ratio of aggregate intangible capital stock toaggregate tangible capital stock (0.377) is comparable to the U.S. (0.631 for 1990–2001)
and U.K. (0.352 for 1990–2001) ratios as calculated by McGrattan and Prescott (2005).
Furthermore, incorporating the value of intangible assets, the ratio of actual corporate
market value to the fundamental value of productive capital is approximately one forthe “pre-bubble” period, 1981-86, under a reasonable calibration. This suggests that
intangible assets are important sources of actual values of Japanese corporate equity,
despite being neglected in previous studies of Japanese stock markets.
Yet an unresolved puzzle remains: the Japanese stock price surge during 1987–89
cannot be explained by neoclassical theory (as in McGrattan and Prescott), as the ratioof actual corporate market value to the fundamental values of tangible plus intangible
corporate assets is approximately two. Similarly, the transitory increase in Japanesestock prices during 1993–1997 reaches over-valuations of corporate productive assets ofabout 25 percent.
Our assessment of the values of corporate productive assets in Japan during the 1980s
and 1990s oﬀers two advantages over previous studies. The ﬁrst has been stated: inclusionof intangible assets is original. The market value of intangible corporate capital in Japan isseen to be about one-third that of tangible corporate capital. Neglect of intangible capitalis a primary reason why Hoshi and Kashyap (1990) and Hayashi and Inoue (1991) foundthat the Japanese stock market in 1981–86 was overvalued: their estimates of average2

q were well above one. Hoshi and Kashyap reported that for the period of 1981–87 theq ratio for the median ﬁrm in their sample from the Nikkei Financial Tape, adjustingfor taxes, averages 1.53 when they employ a narrow deﬁnition of capital that should
be costlessly adjustable, and averages 1.445 when they treated all assets as capital (p.
379). Using a dataset from the Japan Development Bank, Hayashi and Inoue report that
tax-adjusted series of Tobin’s q averages 1.245 for the period of 1981–86 (p.740). Theseﬁgures imply over-valuations in the stock markets, since in the long run equilibrium thoseq measures must be one or just enough above one to induce the investment needed tooﬀset depreciation.
The second advantage: our study uses micro-data, the ﬁnancial statements of all corporations, to construct aggregate measures of the value of corporate productive assets,
rather than the less reliable statistics from Japan’s oﬃcial System of National Accounts(SNA). The SNA data are less reliable than micro-data because SNA encompasses theentire private sector including many small proprietorships and non-traded ﬁrms. The assets of these non-traded ﬁrms are subject to errors of measurement an order of magnitude
greater. For example, equity values of non-traded ﬁrms are recorded at par (face value) in
the SNA which is in most instances a substantial underestimate. Reliance on SNA imputations of equity values of non-traded ﬁrms may explain why Ando (2002) and Ando et al.
(2003) claim that the Japanese stock market in 1980 was substantially undervalued compared to corporate productive assets. For example, Ando et al. (2003) calculated that,for the consolidated corporate sector, average q was 0.32 in 1980. Moreover, no clearlystated, consistent deﬁnition of proﬁt is maintained in the SNA dataset proﬁt is, of course,
a key variable in estimating intangible assets. A great merit of accounting informationis that it allows constructing a model-consistent series of proﬁt levels, providing morereliable estimates of intangible assets, as in McGrattan and Prescott.
The next section describes our framework for assessing the Japanese stock market.
Section 3 presents our dataset, describing features such as coverage and relation to the
SNA. Parameter calibrations are also presented. We then provide the main results on
the pricing in the Japanese stock markets, and oﬀer a possible extension of the present
framework. Section 4 concludes.

2

Analytic framework

This section presents, for reference, the equilibrium relations developed by McGrattan
and Prescott (2005) (hereafter MP) to assess stock valuations. Detailed derivations are
in sections 2 and 3 of MP, and a general description is in Appendix B of this paper.
The MP model is a two-sector neo-classical growth model. The production side of theeconomy consists of a representative corporate ﬁrm and a representative non-corporateﬁrm. It is assumed that non-corporate sector has standard production technology whichneeds labor and tangible capital input, and that corporate sector has not only labor andtangible capital but also intangible capital input. The corporate ﬁrm maximizes the net
proﬁt which is used to pay dividend to equity holders. First order conditions of corporate ﬁrm’s problem, together with Euler equation obtained in representative household’s
maximization problem provides the equilibrium condition relating corporate ﬁrm’s actual
value to the sum of fundamental value of tangible capital and that of intangible capital.
3

Speciﬁcally, MP show that under a balanced-growth path the total value of corporations (V ) satisﬁes(1)

V = (1 − τdist )[(1 − τx − τδ )Km + (1 − τcorp )Ku ] + K ∗ ,

where

[

(2)

(

τδ = τcorp δ̂x + (1 − δ̂x ))(δ̂m(i + π + δ̂m )(1 + π)(1 − δm ) − 1 + δ̂m
γ + η + π + δ̂m)].

Km in equation (1) is the tangible capital, and Ku represents the intangible capital. K ∗in the same equation is the tax adjusted value of foreign capital.1 We leave explanationsof parameters in equation (1) and in equation (2) to section 3.2 in order to save the space.
As can be seen from equation (1), the price of tangible capital for the stockholders is
discounted by (1 − τdist )(1 − τx − τδ ), while the price of intangible capital is discountedby (1 − τdist )(1 − τcorp ). Distribution tax aﬀects these prices because a dollar reinvested
is not taxed, but a dollar distributed is. Subsidies to tangible investment reduce theprice of tangible capital because they make investing in tangibles cheaper. The price ofintangible capital depends on the corporate distribution tax, and on the corporate income
tax rate. This is because investments in intangible capital are expensed and reduce taxable
corporate income (MP, p.772).
The intangible capital inputs are not measured; hence we need an estimation formulafor intangible capital. The estimation formula of the reproducible cost of intangible capitalis derived from the equilibrium condition that after tax marginal return to tangible capitaland that to intangible capital are the same. Firm’s proﬁt then can be expressed as thesum of contribution from tangible capital and contribution from intangible capital net ofintangible investments. On a balanced growth path, we obtain that(3)

Ku = [Π −iXm ]/(i − γ − η),(1 − τcorp )(γ + η + δm )where Π is the net proﬁt and Xm is the gross investment in tangible capital.
From equation (1) we obtain the ratio of corporate market value to the predictedfundamental value (RATIO), i.e.:(4)

RAT IO =V,(1 − τdist )[(1 − τx − τδ )Km + (1 − τcorp )Ku ] + K ∗The formula accords with the textbook version of Tobin’s average q, if we do not consider
the reproducible cost of intangible capital Ku and accelerated depreciation allowances τδ .
The quantitative implications of considering the tax-discounted value of intangible capital(1 − τdist )(1 − τcorp )Ku in the denominator are one of the central topics of this paper. In
the following analysis, we normalize these aggregates with output measures of GDP fromthe SNA.
1

Because of the lack of information on the composition of foreign capital and on foreign tax systems,
we use the capital price for Japanese tangible capital. This simplifying assumption and the amount offoreign capital estimated following Hayashi and Prescott (2002) provide the estimate of the predictedfundamental value of foreign capital owned by the private non-ﬁnancial corporations as 0.015 times the
GDP during the 1980s. Note, however, that we will be overestimating the fundamental value of foreign
capital owned by the traded private non-ﬁnancial corporations in the CFD. The coverage of the SNA
private non-ﬁnancial corporate sector is much wider than that of the CFD.

4

3

Japanese Economy

3.1

Study Period

The equations presented in Section 2 are applicable to economies on a balanced growthpath. In general, assuming homogeneity of degree one in the production function, an
economy can be said to be on a balanced growth path if the ratio of capital to output
evolves stably over time. Therefore, following Hayashi and Prescott (2002), we calculated
the ratio with respect to the entire Japanese economy using the SNA data for 1980–2009.2
Figure 1 shows the result. The ﬁgure suggests that the capital output ratio evolved in astable manner during 1981–1989, suggesting that we are justiﬁed in applying the equations
to this period. Interestingly, the period includes the so-called “bubble era” (December
1986 – February 1991) when stock prices surged. Therefore, we divide the period 1981–
1989 into two sub-periods, 1981–1986 and 1987–1989, for which we provide RATIO results
separately.
From Figure 1, it may seem that the capital output ratio evolved in a stable manner
during 1993–1997 as well. However, as Hayashi and Prescott (2002) suggested that thewhole 1990s is a part of the transition period, we do not regard this sub-period to be ona steady state. This is because this period is not very separated from the former steadystate in the 80s, and since the transition path to a new steady state would not have been
completed until 2009 as the ﬁgure suggests. Nevertheless, we report RATIO results for
1993–1997, because it is interesting to see what has become of the stock markets valuation
after the stock price surge period of the late 80s.

3.2

Parameters

The tax rate for corporate distributions, τdist , is computed with data of the personal capitalincome tax and of the amount of corporate dividends. Note that Japanese corporations
rarely make distributions by buying back shares or liquidating operations. Therefore, therelevant tax rate is the tax rate on personal income. For the amount of dividends, we use
the “amount of dividends” in the Actual State of Corporate Enterprises Seen from theTaxation Statistics (ASCESTS) published by the National Tax Agency. Similarly, for theamount of dividend tax, we use the “tax on dividends” in the Historical Data publishedby the National Tax Agency. These ﬁgures are on a ﬁscal year basis and are consistent
with the CFD data. We obtain that τdist = 0.226 for the 1980s and τdist = 0.185 for
1993–1997.
Following Japanese studies such as those by Hoshi and Kashyap (1990) and Nomura(2004), the tax rate on corporate proﬁts, τcorp , is computed using corporate tax data fromthe Financial Statements Statistics of Corporations by Industry (FSSCI) published by
the Policy Research Institute, Ministry of Finance. This includes the corporate income
tax, the prefectural residents’ tax, the municipal residents’ tax, and the enterprise tax,
together with the corporate income data from the Historical Data on corporate proﬁts by
the National Tax Agency. These data are available for the private non-ﬁnancial corporate
2

In this paper, the SNA entries are based on SNA93, which became available after publication of thepaper by Hayashi and Prescott (2002), who used data on an SNA68 basis. We use 2009 version of the
SNA.

5sector on a ﬁscal year basis and are consistent with the CFD data. For corporate taxes
we use “corporation tax, residents’ tax and enterprise tax” from the FSSCI, while forcorporate proﬁts we use the “amount of income” from the Historical Data by the National
Tax Agency. We obtain that τcorp = 0.413 for the 1980s and τcorp = 0.392 for 1993–1997.
As Hoshi and Kashyap (1990), Ogawa and Kitasaka (1998), and Nomura (2004) argued, in Japan capital subsidies through investment tax credits for the purchase of newcapital goods are quite small. For this reason and because of the lack of relevant information, we consider the investment tax credits to be negligible. The other important formof subsidies on tangible capital is allowed depreciation in excess of economic depreciation.
In Japan, “special depreciation” is allowed by the Act on Special Measures Concerning
Taxation (Act 26, 1957) in order to promote tangible capital investment. The FSSCI
provides information on “special depreciation.” We obtained the subsidiary rate on tangible capital, τx , by dividing the special depreciation series with “gross tangible capital
investment” for the private non-ﬁnancial sector in the SNA. We obtain that τx = 0.009
for the 1980s and τx = 0.007 for 1993–1997.
As for the allowed rate of immediate expensing of investment, δ̂x , and the allowed
rate of depreciation on book value capital, δ̂m , following MP, we assume that δ̂x = δ̂m /2.
The SNA reports tangible capital depreciation based on the tax code, not the economic
code. Therefore, we obtain the allowed rate of depreciation on a book-value basis using
the SNA data. δ̂m is computed as the ratio of “book value depreciation” minus the“replacement cost adjustment” of the subsequent year to “productive capital excluding
land holdings.” These ﬁgures are available for the private non-ﬁnancial sector in the SNA.
The estimated value of δ̂m is consistent with the coverage of the CFD data. We obtain thatδ̂m = 0.115 for the 1980s and δ̂m = 0.120 for 1993–1997. On the other hand, the economic
rate of depreciation of tangible capital, δm , is computed following Hayashi and Inoue(1991) who provide information on economic tangible capital depreciation rates for six
capital components of (1) buildings; (2) structures; (3) machinery/equipment; (4) ships;(5) autos/trucks; and (6) tools/ﬁxtures. We constructed a weighted average depreciation
rate from the proportions of each capital component in total tangible capital for the period
1981–1989, and set it to the economic depreciation rate, δm . We obtain that δm = 0.076
for the 1980s and δm = 0.076 for 1993–1997. In addition to these depreciation rates,
we construct a capital depreciation rate for later use based on the tax code, and thaton the economic code, taking into account land holdings in the denominator. Because
Hayashi and Inoue (1991) do not report the economic rate of depreciation of tangible
capital including land, we take the ratio of the allowed rate of depreciation on a bookvalue including land to that excluding land. Then we take a product of the ratio and theeconomic rate of depreciation of tangible capital excluding land. Thus, we estimate theeconomic rate of depreciation of tangible capital including land.
Parameters of the growth rate of labor augmenting technology, γ, the inﬂation rate, π,
and the population growth rate, η are calculated following Hayashi and Prescott (2002)
using the SNA information. Notice that we update their series on an SNA68 basis with
the newly available SNA data on an SNA93 basis. The growth rate of labor augmenting
technology is deﬁned as the growth rate of total factor productivity, and is obtained as
γ = 0.053 for the 1980s and γ = 0.012 for 1993–1997. The inﬂation rate is obtained
from the growth rate of the GDP deﬂator as π = 0.012 for the 1980s and π = 0.001 for

6

1993–1997, and the population growth rate is given by the growth rate of the working-age
population as η = 0.008 for the 1980s and η = 0.007 for 1993–1997. Finally, the realinterest rate, i, is obtained using the equilibrium condition. On equilibrium, from the log
preference assumption, the real interest rate i is obtained as i = [(1 + γ)/β] − 1, where β
is the subjective discount factor. We borrow β = 0.98 to obtain i = 0.074 for the 1980s
and i = 0.033 for 1993–1997. These ﬁgures are in line with those in Chen et al. (2006)
and in Braun et al. (2009).

3.3

Capital Prices

Figure 2 presents the price of tangible capital, (1 − τdist )(1 − τx − τδ ), and the price ofintangible capital, (1 − τdist )(1 − τcorp ), during the study period. Interestingly, those prices
evolved in a stable manner, unlike the secular large movements seen in the United States
and Britain. MP explained movements in corporate valuation in the United States andBritain using the changes in those prices. It is noteworthy that in the case of the Japanese
economy, we cannot attribute the surge of actual corporate values in the late 1980s tochanges in capital prices.

3.4

Aggregate Variables

This study mainly employs micro-level accounting data from the Corporate Financial
Databank (CFD) provided by the Development Bank of Japan for the construction ofmacro entries such as the reproducible cost of tangible capital, total proﬁts, total investment, and total actual corporate value. The data set includes accounting data for all
non-ﬁnancial companies listed on the ﬁrst or second section of the stock exchanges ofTokyo, Osaka, and Nagoya. Advantages of using the new data set are (i) it covers all
traded, non-ﬁnancial corporations and (ii) it contains detailed balance sheet information
so that one can construct more accurate measures of tangible capital and net debt thatare evaluated in the stock market, than those calculated using e.g. the aggregate data
(SNA) only. As we will see later, constructed series of aggregate variables from the CFD
and those from the SNA are very diﬀerent in levels, despite their trends being very similar.
Consistent historical data for all entries used in our analysis are available for ﬁscal
1977–2002 from the CFD. (Fiscal years in Japan run from April to March of the next year).
Unfortunately, historical data of detailed tangible capital investment is not available before
1977 FY, while the CFD starts with 1956 FY when merely 414 ﬁrms are listed. We exploit
information for the period of 1956–1976 to obtain the “initial value” of tangible capitalstocks at the beginning of 1977 FY. Because ﬁrms entered and exited during this period,
the number of ﬁrms diﬀers from year to year. All in all, data of 2,771 ﬁrms were used. All
entries in the CFD are based on book value. Therefore, we convert them to a market value
basis for each company and then calculate aggregate variables such as capital, investment,
etc., by aggregating the ﬁrm-level data for each year. The general idea in constructing
macro entries is that we exploit all information listed on the debit and credit sides of thebalance-sheet. We then examine the ratio of corporate actual market value (credit side)
to the predicted fundamental value (debit side) using the MP framework. The detailed
description of how we convert book value entries into market-value entries is in Appendix
A. Below, we will construct current-price time series data for all the entries.
73.4.1

Actual Corporate Value V

Actual corporate value V is deﬁned as the sum of the value of net corporate debt andthe net actual value of outstanding equity. The value of net debt is the diﬀerence of
non-equity ﬁnancial liabilities and non-equity ﬁnancial assets. The net actual value ofoutstanding equity is the diﬀerence of equity liabilities and equity assets, and the valueof cross-holding shares must be subtracted from the value of equity liabilities.3
The top panel of Figure 3 shows the estimated movements of net debt and the net
actual value of outstanding equity for the CFD for 1980–1999. The bottom panel of
Figure 3 shows the time series of the aggregate of the corporate value calculated fromthe CFD data, the movement of the NIKKEI225 stock price index, and the path of the
TOPIX, normalizing the value at 1980 FY being one for each aggregate. For a comparison
purpose, we provide the information calculated from the SNA as well. As it can be seenfrom the ﬁgure, the trends in these four variables are the same for 1980–1999.
3.4.2

Tangible Capital Km

For tangible capital Km , we consider productive capital, inventories, and land. Figure 4
shows the results of the conversions of the CFD book value entries into the market value
entries. As is expected, the market value of tangible capital exceeds tangible capital ina book value basis. Also, the diﬀerence between the market value of land and the bookvalue of land is large.
3.4.3

Intangible Capital Ku (Xm and Π)

Because we consider the Japanese economy during the 1980s to have been on a steady
growth path, we estimate intangible capital Ku using the equilibrium relation of equation (3). To do so, we need information on gross investment in tangible capital, Xm , andon net operating proﬁts, Π, as explained in Appendix B. For gross investment, we use
gross investment in ﬁxed capital [K6260].4
Regarding net proﬁts, total sales proﬁt [K2960] is given as total sales minus sales
costs. Here, sales costs include labor cost, tangible capital depreciations, R&D investment costs, and ﬁxed asset taxes. However, note that sales costs do not include laborcosts for corporate headquarters, intangible investment, or other miscellaneous tangible
capital cost components. In order to obtain the model-consistent proﬁt series from theaccounting information, from the total sales proﬁts we subtract the sum of tangible capitaldepreciations in the non-operating income section [K3290], in the special account section[K3690], and in the general and administrative expenses (SGA) section [K5810]. We also
exclude the amount of land ownership tax [K3310], the amount of business facility tax[K5850], business tax allowance transfer [k5860], labor costs for corporate headquarters
in the SGA section [K5750; K5760; K5770; K5780; K5782; K5790; K5800],5 intangible
3

In our data set, we cannot distinguish the values of non-cross-holding shares from non-equity longterm ﬁnancial assets. Hence, we count the values of equity assets of non-cross-holding shares as a part ofﬁnancial assets. This manipulation does not aﬀect the results obtained below at all.
4
The square brackets show the CFD codes.
5[K5750] is wages for workers in headquarters oﬃces, [K5760] is provision for accrued bonuses, [K5770]
is the fringe beneﬁt, [K5780] is provision for retirement allowances, [K5782] is retirement beneﬁt expenses,

8capital investment of (i) experiments costs [K5820], (ii) R&D costs [K5822] and (iii) advertisement costs [K5670], and “other SGA costs” [K5910].6 Thereby, we obtain the seriesof net corporate proﬁts that corresponds to the deﬁnition in the MP framework as is given
in equation (24) in Appendix B. These variables are ﬂow variables. Therefore, the bookvalues will be equal to current market values.
3.4.4

Comparison of the CFD with the SNA

Now that we have exploited all the balance sheet information, we are ready to constructaggregate variables from the CFD. These are necessary for examining the ratio of actual
corporate market value to the predicted fundamental value using the framework of MP.
Before we proceed, we characterize more features of the CFD data set, since this data
set is new to the literature. It is usual to gain an overview of the Japanese aggregate
economy using the SNA. We then compare the CFD aggregates with their counterpartsin the SNA for the private non-ﬁnancial sector.
The trend of net actual value of outstanding equity in the SNA resembles that fromthe CFD as the bottom panel of Figure 3 suggests. In terms of trends, the same thingcan be said of other aggregate variables such as tangible capital stocks excluding land, as
can be conﬁrmed in Figure 5. At this point, it seems that the CFD actually resembles the
SNA. Figure 5, however, shows important level diﬀerences between aggregate variables
constructed using the CFD, and the corresponding SNA variables in the private nonﬁnancial sector.
The left top panel of Figure 5 shows the time series of cash holdings by private nonﬁnancial corporations in the SNA and in the CFD. A noteworthy ﬁnding from the panel
is that the levels of cash holdings are very diﬀerent between the two data sets. Because
cash is nominal, the diﬀerences in the levels of cash holdings will reﬂect the diﬀerencesin the coverage of corporations between the data sets. Naturally, the SNA has broader
coverage for the private non-ﬁnancial sector since it includes non-traded corporations. On
the other hand, the average coverage of corporations by the CFD is much smaller, beingaround 20% of the SNA during the period of 1980–1999. Similarly, the top right panelof Figure 5 shows the movements of tangible capital (excluding land) during 1980–1999.
The average coverage of tangible capital of the CFD is around 30% of the SNA.7 The
bottom left panel of the ﬁgure is net debt. Although the trends of the aggregates fromthe two data sets are almost identical, again we see a big gap in levels between the data
sets.
The above ﬁndings conﬁrm that the coverage of private non-ﬁnancial corporations in
the SNA and in the CFD are very diﬀerent from each other. From the FSSCI data, which
is one of the basic statistics for the SNA, we can see that the number of ﬁrms in the sector
is as many as 15 thousands, while the CFD captures only 2,771 traded corporations at
most.
[K5790] is retirement payment, and [K5800] is corporate pension.
6
In a previous version of the paper, we used a diﬀerent set of cost components. We, however, subtract
more of cost components in the SGA section from the proﬁt in this version of the paper. Such components
include for example, advertisement expenses and fringe beneﬁts. Thereby we obtain a model-consistent
proﬁt and investment series.
7
Tangible capital excluding land is on a book value basis for comparison.

9Another remarkable ﬁnding from Figure 5 is found in the bottom right panel, which
depicts the net actual value of outstanding equity for the SNA and that for the CFD. As
can be seen from the ﬁgure, despite the diﬀerences in the coverage of the two statistics,
the levels of net debt equity values are surprisingly comparable between the two data sets.
We can attribute the similarity in these two series to the fact that in the SNA equity
values for non-traded private companies are estimated using face values rather than using
market values, which is previously pointed out by Ando (2002), and by Hayashi (2006).
It is a Japanese business convention that before the major reform of the Commercial
Code in 2001, the majority of stock companies, traded or non-traded, issued equities
in face values of 20JPY, 50JPY, 500JPY, or 50,000JPY for unit equity, irrespective of
their potential market values. The market values of equities were signiﬁcantly greatercompared to the face values, which explains why private corporations no longer issue
equities with face values after the reform in 2001. Evaluating equity values of non-tradedprivate corporations using face values, the SNA equity information is erroneous.
External information from the Flow of Funds (FoF) published by the Bank of Japan
will be helpful in understanding the issue more. Importantly, the FoF is one of the basic
statistics for the SNA, and it provides estimates of debt equity values and cash holdings
for private non-ﬁnancial corporations. It should be emphasized that information of debt
equity values in the FoF covers merely the traded corporations, and also that the FoF
information for cash holdings covers all the corporations. The SNA covers all the corporations for cash holdings and debt equity. Figure 6 shows the movements of cash holdings(top) and that of debt stock values (bottom) for private non-ﬁnancial corporations. As
can be seen in Figure 6, the trends and levels of cash holdings are almost identical between
the SNA and the FoF. On the other hand, it is not natural that the levels of debt equity
values resemble each other given that the coverages of the two data sets diﬀer. These
patterns provide an indirect but important implication that equity values reported in the
SNA are not very useful when researchers would like to examine q-theory: reproducible
costs of capital are reported on a market value basis in the SNA, but in a signiﬁcant part,
equity values are reported on a book value basis. Because the proportion of non-traded
corporations in the private non-ﬁnancial sector is signiﬁcant in the SNA, the total valueof debt equity in the SNA is subject to severe under-estimation.
This measurement issue is absent in the micro accounting data set of the CFD whosebasic statistics are from annual security reports of traded companies. Also, the suggestionof Ando (2002) relying on the SNA that Japanese stock markets undervalued the value ofcorporate capital stocks loses ground. Namely, his undervaluation story can result frommeasurement errors of actual corporate values of non-traded corporations, not from some
malfunction in the stock markets as Ando (2002) argued.

3.5

Estimating Intangible Capital using the MP framework

We begin by explaining how we estimated intangible capital from the CFD data. Given
the calibrated parameters in the top panel of Table 1, and the value of investment relative
to GDP, we estimate the contributions of tangible and intangible capital to domestic
pre-tax proﬁts. The ﬁrst column of Table 1 shows the estimation results for intangible
capital Ku for the period 1981–1989 using the CFD. We ﬁnd that during the 1980s, 96% ofdomestic pre-tax corporate proﬁts are derived from tangible capital. This value is slightly
10

greater than that in the case of the United States shown in Table 2 of MP (90.0% for
1990–2001).
Next, we show the estimate of intangible capital from the SNA data for comparison
purposes. It should be remembered that as stated above, the coverage of private nonﬁnancial corporation sector in the SNA is much wider than the coverage of the CFD.
The estimation of intangible capital from the SNA is possible using the following information on aggregates. In the SNA, inﬂation adjusted proﬁts ΠSN A are given by (i)corporate proﬁts (“3. Operating surplus” in “(21) Income and outlay accounts of private
and public corporations”) minus (ii) adjustments (“Change in assets” in “(2) ReconciliaSN A
tion c account”).8 The gross investment series Xm
are reported in the ﬂow section (“5.
Supporting Tables, (22) Capital Finance Accounts of Private and Public Corporations”)
on a ﬁscal year basis. They are given by (i) investment in tangible capital (“1. Gross
ﬁxed capital formation”). We use GDP for the normalization of these aggregates. The
second column of Table 1 shows the estimation results for intangible capital Ku for theperiod 1981–1989 using the SNA. In this case, we see that about 99% of domestic pre-tax
corporate proﬁts are derived from tangible capital.
Ku is estimated using Equation (3). The bottom row of Table 1 shows the estimatedreproducible cost of intangible capital for each period. Thus, the ﬁrst column indicatesthat during the 1980s, Ku was 0.217 times the GDP level using the CFD information.9
This estimate provides the ratio of reproducible cost of intangible capital to that of tangible capital of around 0.373 for the period of 1981–1989. On the other hand, when werely on the SNA, we obtain that Ku was 1.258 times the GDP level for the same period.
The ratio of reproducible cost of intangible capital to that of tangible capital from the
SNA is around 0.693.
Hence, the estimate of reproducible cost of intangible capital from the SNA information becomes much greater than the CFD correspondence. The diﬀerence between thetwo estimates looks huge, even after taking the diﬀerences in coverage of the two statistics
into account. Mechanically, it happens because the ratio of proﬁts to gross investment in
the SNA information is greater than that in the CFD. Potential reasons for the diﬀerencein the proﬁt to gross investment ratios will be two-fold. The ﬁrst reason is the diﬀerence in the coverage of the two statistics: The CFD data contains only traded private
corporations. However, from the FSSCI information, which is a basic statistic for the
SNA, we can conﬁrm that the proﬁt to gross investment ratios tend to be greater for private non-ﬁnancial corporations with greater amount of net wealth, whatever deﬁnitionsof proﬁts we employ. Hence, the diﬀerence in coverage between two data sets will not be
the relevant reason. The second reason will be the diﬀerence in the deﬁnition of aggregate
variables of “proﬁts” and “gross investments” between the two statistics. We actually ﬁndthat diﬀerences in the deﬁnitions of proﬁts are relevant. Using the detailed accounting
8

See Hayashi (2006) for details on this adjustment of proﬁts.
It is also interesting to see which sector of the economy mainly accumulates the intangible capital.
To do so, we divide the companies into heavy industry and light industry, like Hayashi and Inoue (1991).
In this study, heavy industry includes manufacturing, farm business, mining, construction, and infrastructure. On the other hand, light industry includes sales, ﬁnance (Credit Saison Co. Ltd.), real estate,transportation and communication, and service. For the period of 1981–1989, we see that the heavy
industry is endowed with more than 90% of total intangible capital in the economy. Hence, the intangible
capital estimate is mainly accumulated in the heavy industry.
9

11

information from the CFD, we can construct a model-consistent series of proﬁts as it isgiven in Equation (24). On the other hand, we are kept in the dark about the constructionof proﬁts in the SNA.10
For comparisons, MP estimate that, in 1990–2001, the reproducible costs of domestic
intangible capital and domestic tangible capital were 0.65 times GDP and 1.03 times
GDP, respectively, in the United States (column 5 in Table 1), and 0.51 times GDP and
1.45 times GDP, respectively, in Britain (column 6 in Table 1). Hence, using the CFD
information, we ﬁnd that the production structure of Japanese economy resembles thatof the U.K. (Ku /Km = 0.352 for 1990–2001), whereas it is akin to the U.S. economy(Ku /Km = 0.631 for 1990–2001) when we rely on the SNA. We suggest that the reality
for the production structure lies between the two estimates, despite direct evidence of
Fukao et al. (2009) arguing that intangible capital plays a more minor role in Japan, andthat all of three developed countries are endowed with non-negligible amount of intangible
capital.
We provide other evidence on intangible capital stocks that can be measured directly.
Corrado et al. (2006) and Corrado et al. (2009) (hereafter CHS) suggest a perpetual inventory method of directly measuring the amount of intangible capital using information
on intangible investments and the depreciation rates for intangible stocks. They consider,for intangible investment, (i) categories of business investment in computerized information, (ii) innovative property, (iii) investment in “economic competencies”, and (iv) investment in ﬁrm-speciﬁc human and structural resources.11 According to Corrado et al.
(2009), the average ratio of the reproducible cost of intangible capital to GDP in the U.S.
1990-2001 was 0.375 (column 5 Table 1). MP point out that the amount of intangible
capital from the method in Corrado et al. (2009) is conservative. This is because thedepreciation rates used for R&D investments are too high (33% for Computerized information; 20% for Innovative property; 60% for Brand equity; 40% for Firm-speciﬁc humancapital), and since they may be underestimating some important intangible capital stocks
such as ﬁrm speciﬁc capital. See also Marrano et al. (2009) for U.K. evidence.
Fukao et al. (2009) follow Corrado et al. (2009) and provide a direct measure of intangible capital stock for the Japanese economy. On the last row of Table 1, a direct
measure of intangible capital is reported as 0.28 times GDP level for 1985-1989 in Japanafter we make coverage adjustment to the CFD statistics.12 Unlike the case of the U.S. in
10
We interviewed the national statistical agency of the ESRI about the deﬁnition of proﬁts in the SNA.
We were informed that the proﬁts in the SNA is akin to current proﬁts in the Japanese accounting system,and that the ESRI adds some adjustments to the legal deﬁnition of current proﬁts. Because the way of
the adjustments are not open to economists outside of the agency, it is not clear if the proﬁt series in the
SNA is consistent with the deﬁnition of proﬁts in Equation (24).
11
See Corrado and Hulten (2010) for updates.
12
Notice that Fukao et al. (2009) report a direct measure of intangible capital for the whole economy(0.336 times GDP level). In the ﬁrst column we report intangible capital stock relative to GDP after
we adjust the coverage to the one of the CFD for a comparison purpose. To compare our estimates ofintangible capital stocks in the Japanese corporate sector, we adjust the coverage of their estimates byusing their R&D investment data from Survey of Research and Development (SRD) published by Statistical Bureau, Ministry of Internal Aﬀairs and Communications. The SRD is used for the estimation of
R&D investment by Fukao et al. (2009), and covers all business enterprises, non-proﬁt institutions andpublic organizations, and universities and colleges. We assume that intangible capital stocks produced
from R&D investment by non-proﬁt institutions, public organizations, universities, and colleges are distributed to ﬁrms proportional to the R&D investment each ﬁrm expends. Hence, all R&D investment can

12

McGrattan and Prescott (2005), this ﬁgure and our theoretical prediction of the intangible capital stock resemble each other.

3.6

Estimation of RATIO

Table 2 shows our estimation results for RATIO using equation (4). Notice that we report results from the CFD information only. This is because actual corporate values areunder-estimated in the SNA so that the “undervaluation results” of Ando (2002) are exaggerated when we include the fundamental value of intangible capital in the denominatorof equation (4).13 Interestingly, our study period includes the so-called “bubble era” (December 1986 – February 1991) when stock prices surged. Therefore, we divide the period
1981–1989 into two sub-periods, 1981–1986 and 1987–1989, for which we provide separate
RATIO results, while keeping Ku the same for two sub-periods.
We report the results for the period of 1993–1997, in addition to those for the 1980s,
to provide casual evidence on the stock market situation after the so-called “bubble period.” The tax rates ﬂuctuated only a little during the 1990s as shown in Figure 2, andequation (4) may be justiﬁably exploited for the sub-period. On the other hand, the interest rate and the technological growth rate declined during the 1990s. We do not exploit
Equation (3) in estimating intangible capital for the 1990s, since the equilibrium relation
requires constancy of the interest rate and the technological growth rate.14 Hence, regarding 1993–1997, we infer the re-producible cost of intangible capital using the production
structure of the model. Speciﬁcally, we specify that the homogenous production functionof the ﬁnal goods is of Cobb-Douglas type. Assuming that δm = δu = δ and given the factthat capital prices are stable over the study period, it easy to show that the growth ratesof Km and Ku are the same along a transition path. Hence, we obtain that an expansion
path of tangible capital Km and intangible capital Ku is straight in the (Km , Ku ) planeover the transition period of capital deepening after 1990. Evidence from the U.S. in MP
may support our strategy. In Table 4, MP reported that the Km to Ku ratio was 0.717
for the 1960s, and was 0.631 for the 1990s. From this, we speculate that the production
structure changes only gradually when it happens. Also, notice that the series of capitalshare estimated using the SNA information is highly stable after 1980 around the value of
0.35. We thereby estimate the amount of intangible capital by assuming that the amountsof tangible capital Km and that of intangible capital Ku grow in parallel. This provides
an estimate of Ku for 1993-97 as 0.212 times the GDP level.
In this paper, we provide results with and without land estimations for RATIO, because Japanese economists sometimes prefer not to include land when examining asset
pricings in the macro economy. For example, see Ando (2002).15 However, the results in
be regarded as expended by ﬁrms. Next, to estimate the coverage-adjusted R&D investment in the SRD,
we use data of total sales across ﬁrm size. From the SRD, we can obtain the data on R&D investment
by size of sales. We use the coverage adjusted investment series to obtain the coverage ratio of the CFD
to the SRD. Finally, we assume that intangible capital stocks are proportional to R&D investment andobtain the direct (and corresponding) measure of intangible capital stock.
13
Using the SNA information, we ﬁnd that RAT IO = 0.240 from a without-land-calibration for 1981–
1989 (not shown).
14
See also Chen et al. (2006) and Braun et al. (2009) for the movements of the real interest rates andsavings in Japan after the 80s.
15
Using aggregate data, Ito and Iwaisako (1995) and Nakajima (2008) examined Japanese stock markets

13the left panel and in the right panel of Table 2 suggest that our ﬁndings should remainunchanged, irrespective of inclusion of land into our considerations.
The upper part of Table 2 shows parameter values for the prices of tangible andintangible capital. As shown in Figure 2, the prices of tangible and intangible capital
evolved in a stable manner until the end of the 1990s. The middle part of Table 2 shows
our estimates of reproducible costs and fundamental values of tangible and intangible
capital, as well as our estimates of fundamental values of foreign capital and actual market
values of private non-ﬁnancial corporations in the CFD.16
Finally, the lower part of the table shows the estimates of RATIO for two cases.
RATIO corresponds to the MP framework and takes the fundamental value of intangible
capital into account. On the other hand, the second measure of RATIO is the case when
we do not consider the fundamental value of intangible capital in equation (4). We callit Ando’s RATIO. The ﬁnding here is that our RATIO falls within a reasonable range
around one for the period of 1981–1986. So, the framework of MP works very well using
the Japanese data set as it does in the cases of the U.S. and U.K. applications. We cancompare our results with previous studies on Japanese stock markets that use micro data
sets. Hoshi and Kashyap (1990) and Hayashi and Inoue (1991) have sought to analyze
Japanese stock prices by estimating the ratio of actual corporate market value to thetheoretically-predicted fundamental value, Tobin’s average q. Hoshi and Kashyap (1990)
report that the q ratio for the median ﬁrm in their sample from the Nikkei ﬁnancial tapeis around 1.56 on the average for the period of 1981–1987 when the q ratio is adjusted
for taxes (p. 379, Hoshi and Kashyap 1990). Similarly, using the data set from theJapan Development Bank, Hayashi and Inoue (1991) report that tax adjusted series ofTobin’s average q is around 1.245 on the average for the period of 1981–1986 (p.740,
Hayashi and Inoue 1991). If we rely on these measures, we see that the Japanese stock
markets tended to overassess the fundamental value of corporations. However, our results
show that the ratio of actual market values of corporations to the fundamental values ofcorporations fall within a reasonable range around one, when we consider the fundamental
value of intangible capital. In this sense, our ﬁnding goes on with ﬁne-tuning with respect
to the previous ﬁndings of “over-valuations,” by considering intangible capital.
When we see Ando’s RATIO for the same period, we ﬁnd that the actual market valueof corporations overshoot the predicted fundamental value of corporations. First, this
implies that intangible capital is an important source of corporate values in the Japanesestock markets. Second, this ﬁnding is a sharp contrast with the undervaluation story ofAndo (2002) and Ando et al. (2003). They argue that the market valuation of Japanese
corporations is far below their reproduction costs. For example, Ando et al. (2003) reportthat for the consolidated corporate sector, a measure of Tobin’s average q ranges from alow of 0.32 in 1980 to a high of 0.52 in 1998.17 As stated above, it is well known that thecorporate stock values of private non-listed corporations are severely underestimated inwith special focus on land and secular changes in TFP, corporate taxes, and marginal taxes on landholdings. Stock prices predicted from these models are found not to ﬁt the data well.
16
The estimates of reproducible cost of tangible capital Km are based on the CFD data, the constructionof which is documented in Appendix A. Those of intangible capital Ku are from Table 1.
17
Notice that Ando et al. (2003) do not make tax adjustments in deriving these ﬁgures. If we apply
capital prices and the dividend tax rate of the 1990s calibrated in this paper to the SNA aggregates
reported in Ando et al. (2003), we obtain that Tobin’s average q for 1998 is around 0.717.

14

the SNA (see, e.g., Ando 2002; Hayashi 2006). This is because for un-traded corporations,which are a major component of corporations in the SNA, the value of outstanding stocks
is estimated with a face value basis. Also, the coverage of the private sector in the SNA
includes public enterprises. Because of these features of the SNA, the under-valuation
story loses its grounds. Since we are focusing on the traded companies using the CFD,
our estimates of RATIO from the CFD will provide a reliable view on the Japanese stock
markets phenomena.
So far we employed the framework of MP in investigating the Japanese economy. Thisis because the Japanese tax system has almost the same structures as the U.S. and the
U.K. systems. Here we consider an exceptional tax system that used to be adopted inJapan, but has been absent in the U.S. and the U.K. economies (meaning that MP did
not consider). The tax system is the two tier tax on corporate retained earnings. The twotier tax is the preferential tax on corporate earnings which were paid as dividends. Thistax was introduced in order to encourage ﬁrms’ equity ﬁnances and dividend payments
and was kept lower than the corporate income tax. The tax was abandoned in 1990.18
Following Alpanda (2011) we extend the MP framework to incorporate the two tier tax
rate, and re-assess the ratio of actual market corporate value to the predicted fundamental
value of corporations. When the two tier tax is available for corporations, the amount ofdividend paid by corporations is given as(5) d1,t = p1,t y1,t − x1m,t − x1u,t − wt n1,t − τ1k k1m,tc− τ1 [p1,t y1,t − δ̂1m k̂1m,t − δ̂1x x1m,t − x1u,t − wt n1,t − τ1k k1m,t ] + τx x1m,t + (τ1 − τdist)dt ,cwhere τdistis the preferential tax rate on corporate earnings which were paid as dividends.
c
The last term of (τ1 − τdist)dt is the amount of corporate proﬁts saved by the tax shelter.
With this equation, equation 4 can be rewritten into

(6)0
V = (1 − τdist)[(1 − τx − τδ )Km + (1 − τcorp )Ku ] + K ∗ ,0ccwhere τdist= (τdist + τdist− τcorp )/(1 + τdist− τcorp ).19 In this paper, we borrow the ratioof the corporate tax rate to the two-tier tax rate from Alpanda (2011) to obtain thatc
τdist
= 0.3356 for the 1980s from the corporate tax rate calibrated in this paper. We
then replicate the procedure of estimating RATIO with the modiﬁed eﬀective tax rateon corporate distributions for the sub-periods of 1981–1986. We obtain the modiﬁcation
results at around 17% increase in RATIO, giving a slight impression of “over-valuation.”
Next, regarding the sub-period of 1987–1989 when the stock price surged, RATIO
is found to be too high.20 Hence, as Hoshi and Kashyap (1990) and Hayashi and Inoue(1991), the Japanese stock price surge in the late 1980s remains for us an unsolved puzzle:
we ﬁnd that incorporating intangible capital into a neoclassical model cannot explain thestock price surge in the late 1980s.
18

See Ishi (2001) for the detailed descriptions on the two tier tax system.
0.
See Alpanda (2011) for the derivation of τdist
20
Using aggregate data from the Quarterly Report of Financial Statements of Incorporated Business, Ogawa and Kitasaka (1999) found that after 1986, the discrepancy between Tobin’s average q andmarginal q became large. They argue that this may represent evidence of a stock price bubble during
this period. Fukuta (2002) examined the necessary conditions for the absence of rational bubbles, andshowed that Japanese stock prices and dividends satisfy the necessary conditions.
1915

Regarding the stock price surge during the so-called “bubble-period,” Hoshi and Kashyap(1990) and Hayashi and Inoue (1991) argue that pricing in stock markets was “correct”
both during the pre-bubble period and during the bubble era. They suggested that thereason for this was that the stock price surge during the late 1980s was cancelled out by
the price surge in land (namely, the increase in fundamental value of tangible capital).
These studies, however, leave an open question as to why the land price increased so much.
Recently, Alpanda (2011) has opened a new window to understanding the movement ofJapanese land prices in the framework of a neoclassical growth model akin to MP. He
introduces the role of corporate bonds, and allows the possibility that corporations issueland-collateralized debt to reduce their tax liabilities. The government follows a land taxation policy that is countercyclical to land prices. With these features, the collateral useof land and countercyclical land tax policy introduce a substantial magniﬁcation mechanism for asset prices. The movement of land prices can be partly explained by the model.
The framework of MP abstracts from the role of corporate debts and from the tax shelterrole of the land collateralization. A natural extension of the present framework would be
to introduce corporate debts and the collateral use of land into the framework of MP to
explain the Japanese stock price movement throughout the 1980s.
Finally, we refer to our parsimonious measure of RATIO for the 1990s. We see from
Table 2 that RATIO is around 20% higher compared to the ones for 1981–1986, with orwithout taking land into accounts. The mid 90s is known as the period of recovery in stock
prices after the sharp decline in the early 90s. The recovery will be because of change
in household expectations after the so-called “kouzou-kaikaku” (structural reform) by the
Koizumi cabinet, and after IT revolution as highlighted by Hayashi and Nomura (2005).
We ﬁnd that the stock price increase in the mid 90s was actually a slight over-valuationof the fundamental values of corporate capital stocks.

3.7

Robustness Check

In the above analysis, real interest rates were calibrated with the assumption that β =0.98. It will be useful to provide a sensitivity test on the choice of the subjective discountfactor, or equivalently, of the real interest rate. Here we provide additional results forKu estimation for 1981–1989, using three diﬀerent sources of the real interest rates, (i)a time series of the real interest rate calibrated from the SNA information using themethod in McGrattan and Prescott (2004), (ii) the real interest rate from an externalsource, and (iii) the real interest rate from the method of Hayashi and Prescott (2002).
Regarding (i), we constructed the productivity of capital by dividing after-tax capitalincome by the stock of tangible capital for the private non-ﬁnancial sector in the SNA.
We obtain that i = 0.0791 for 1981–1989. With respect to (ii), we refer to the long term
prime interest rate for city banks in the Bank of Japan Website, and to the CPI inﬂation
rate. We calculate that i = 0.0548. Hayashi and Prescott (2002) estimate the subjective
discount factor with the growth rate of household consumption in the SNA, providingthat β = 0.9693. From this we obtain that i = 0.0858.
When we use the real interest of 0.0791, we obtain that Ku = −0.107 times the GDP
level from the CFD, and is 0.430 times the GDP level from the SNA. The negative valueof Ku does not make any sense, and the SNA estimate is reduced by 70%, compared toour benchmark estimate. Second, when we apply i = 0.0548, we have Ku = −3.401 times
16the GDP level from the CFD and Ku = −7.944 times the GDP level from the SNA.
Third, when we apply i = 0.0858, we have Ku = −0.334 times the GDP level from the
CFD and Ku = −0.151 times the GDP level from the SNA. Obviously, these estimatesof Ku are not encouraging. Hence, a sensitivity issue arises as a limitation of imputation
method using the equilibrium equation (3), which is intrinsically sensitive to changes in
the real interest rate. Here, our claim is not that results from the neo-classical model
are fragile, but that economists should focus on reliable calibrations to obtain convincing
results. Given the plausible results in MP and the results in this paper, we believe that
the MP framework is a nice benchmark model to estimate intangible capital when we
focus on the right periods of steady growth.
Then, given plausible estimates of intangible capital and an assumption of CobbDouglas production function, we can obtain capital share parameters for tangible capitaland that for intangible capital. We think that these are exactly what we want. Whencapital share parameters are available, we can infer the amount of intangible capital forwhen the economies are not on the steady growth path without exploiting the equilibrium
conditions in equation (3). This is a great merit since information of tangible capital iseasily obtained, and usually it takes a long time before the production structure of an
economy has changed.

4Conclusion

A consensus has emerged that intangible capital plays a crucial role in explaining important economic phenomena. Examples include secular movements of stock prices in
the United States and Britain (McGrattan and Prescott 2000, McGrattan and Prescott
2004, McGrattan and Prescott 2005), the diﬀerence of proﬁt performance between domestic and foreign operations of U.S. corporations (McGrattan and Prescott 2010a), andthe business cycles in the United States in the 1990s (McGrattan and Prescott 2010b).
Employing the methodology developed by McGrattan and Prescott (2005), we examined Japanese stock market phenomena in the 1980s and 1990s using a micro data set
from the Corporate Financial Databank, with which we constructed aggregate variables
such as capital stock and actual corporate value in a precise manner. When we consider
the fundamental value of intangible capital, our estimates of the ratio of corporate market
value to the predicted fundamental value falls within a reasonable range of around one,for the period of 1981-1986. This ﬁnding contrasts with previous studies of Japanesestock. Hoshi and Kashyap (1990) and Hayashi and Inoue (1991) who used micro data
sets as in this study reported estimates of Tobin’s average q of 1.56 and 1.25 for the
early 1980s, suggesting that the stock market over-valued corporations relative to theirfundamental values. We show that the previous results overvaluation result is caused byneglecting intangible capital, which is an important component of the capital stock. Ourﬁnding also contrasts with that of Ando (2002) and Ando et al. (2003), who, using datafrom the SNA, argued that the Japanese stock markets undervalued the corporate capitalstock. For example, Ando et al. (2003) calculated that for the consolidated corporate
sector, Tobin’s average q that did not take account of fundamental value of intangible
capital was 0.32 in 1980. We show that the previous result from aggregate SNA data ofundervaluation probably reﬂects errors in measurement of the actual value of smaller and17

non-traded corporations.
However, we ﬁnd that incorporating intangible capital into a neoclassical model cannot
explain the stock price surge in the late 1980s. Regarding the stock price surge during
the so-called “bubble-period,” Hoshi and Kashyap (1990) and Hayashi and Inoue (1991)
argued that pricing in stock markets was correct both during the pre-bubble period and the
bubble era. They suggested that the reason for this was that the stock price surge during
the late 1980s was cancelled out by the price surge in land (namely, the increase in thefundamental value of tangible capital). These studies, however, left an open question as
to why the land price increased so much. A recent study by Alpanda (2011) has suggested
an approach to solve the question. A natural extension of the present framework would
be to introduce corporate debt and the collateral use of land as in Alpanda (2011) into
the framework of McGrattan and Prescott (2005) to explain the Japanese stock pricemovements throughout the 1980s and the 1990s.

5

Appendicies

5.1

Appendix A

5.1.1

Actual Corporate Value V

We obtain the total market value of corporations, V , as follows. In the Japanese accounting system, the debit side of the balance sheet consists of broad categories of quick assets,inventory assets, other liquid assets, allowances for doubtful accounts, tangible capital,
intangible capital, other investment assets, and deferred assets in order of appearance.
Among these entries, the information of inventory assets, tangible capital, and intangible
capital are respectively used in constructing a series of values for tangible and intangible
capital. Hence they are not considered here.
In the CFD data, ﬁnancial assets consist of quick assets [K0870], other liquid assets [K1130], allowances for doubtful accounts [K1270], other investment assets [K1760]
and deferred assets [K1870]. Financial Statements Rules, Act 8 regulates that ﬁnancial
commodity items (except for aﬃliates’ shares) are encouraged to be listed on balancesheets in a market value basis. In this paper we assume for these ﬁnancial asset variables
that the book value variables are equal to the market value variables.21 We aggregate
the above items to obtain the total value of a ﬁnancial asset. In doing so, we need to
exclude the book value of own shares [K0980], shares of parent company [K0990], andaﬃliates’ shares [K1590] from the value of ﬁnancial assets in order to take into accountshare cross-holdings. The Japanese ﬁnancial statements are not consolidated for private
accountings.22
The credit side of the balance sheet consists of the liability part and the net worth part.
Broad categories in the liability part include current liabilities, long term liabilities, and21

See also Hayashi and Inoue (1991).
More precisely, the value of own shares [K0980] is subtracted from the value of ﬁnancial asset, andalso from the actual values of outstanding equity, while the value of parent company [K0990] is subtracted
from the value of ﬁnancial asset, and also from the value of ﬁnancial liability. Own shares [K0980] andshares of parent company [K0990] are included in quick assets [K0870], and aﬃliates’ shares [K1590] is apart of other investment assets [K1760].
22

18

special allowances. Broad categories in the net worth part include shareholders’ equity
and the amount of diﬀerence for reappraisal. As for ﬁnancial debts in the CFD, we consider current liabilities [K2290], long-term liabilities [K2520], special allowances [K2620],
earned reserves [K2670], amount of diﬀerence for land reappraisal [K2672], amount of difference for marketable securities reappraisal [K2674], other surplus [K2680], and amountof diﬀerence for other marketable securities reappraisal [K2782]. Though earned reserves[K2670] and the last four items of amount of diﬀerence for reappraisal come from the net
worth part, we consider them as a part of ﬁnancial debts. Thereby, we can exploit all theinformation listed in the balance sheet. On the other hand, capital fund [K2640], amount
paid for newly issued stocks [K2650], capital reserves [K2660], and change in treasury
stock [K2784] are not counted in the ﬁnancial debts. This is because they are related
to the value of outstanding equity. We have to avoid overlapping valuations when welater estimate the actual values of outstanding equity with information of the stock prices
and the number of shares issued. We assume that the book value variables of ﬁnancial
liabilities are equal to the market value variables.23
Therefore, the value of net debt is given by ﬁnancial liabilities minus total ﬁnancial
assets, multiplied by one less the tax rate on distributions.24 Notice that the value of net
debt thus constructed does not include the value of cross-holding shares.
Regarding equity, we have information on the highest and the lowest stock price within
the ﬁscal year, [K0370] and [K0380], respectively, and information on the number of shares
outstanding [K5440]. Thus, we can estimate the series of actual values of outstanding
equity by using the product of the average of the highest and the lowest prices and thenumber of shares issued in the sample.25 However, as pointed out by Hayashi and Inoue(1991), because the Japanese ﬁnancial statements are not consolidated, the market value
of aﬃliates’ stocks is included in the above estimated total actual value of corporate equity.
We need to subtract the value of cross-holding shares to calculate the actual market valueof non-ﬁnancial listed companies owned by households.
We estimate the value of shares net of the cross-holdings using an external information of “Share-ownership Survey” (SS) which is jointly published by the domestic stock
exchanges (Tokyo, Osaka, Nagoya, Fukuoka, and Sapporo). In this data set, informationof proportions of equity ownership by business sector for the listed non-ﬁnancial corporations is available. Hence, we can obtain a cross-holding proportion by looking at thevalues of shares of non-ﬁnancial corporations held by the same sector. The ratios for the
1980s and for 1993 – 1997 are slightly over 20% and are fairly stable. We can estimate
the actual values of outstanding equity net of cross-holding values as the total actual
value of corporate equity times one minus the cross-holding ratio. It is noteworthy thatthe net equity values thus constructed are underestimating the true values, because the“value of shares of listed nonﬁnancial corporations held by business corporations” in the
23
Hayashi and Inoue (1991) found that for Japanese traded corporations the average maturity period
for long term bank loans, which are the dominant component of long term debt, is relatively short, andthat long term debts are about one half of short term debts. Hence, the discrepancy between the market
value and the book value of ﬁnancial debts will not be an issue.
24
See footnote 23 of MP for details on this point.
25
We subtract the value of self-holdings of shares [K0980] from the above estimated series of actual
values of outstanding equity. [K0980] is recorded in ﬁscal years after 1986, and it accounts for at most
0.1 % of total stock values for each ﬁscal year.

19

SS includes the stock values held by non-traded corporations. This under-estimation issue will be negligible, however, given the small amount of equity holdings by non-traded
corporations.
5.1.2

Tangible Capital Km

For tangible capital Km , we consider productive capital, inventories, and land.
We follow Hori et al. (2006) in considering productive capital. Regarding the CFD
data, we have six categories for productive capital: (i) buildings [K1300], (ii) structures[K1310], (iii) machinery/equipment [K1320], (iv) ships [K1340], (v) autos/trucks [K1350],
and (vi) tools/ﬁxtures [K1360]. We consider ﬁscal 1977 as the benchmark year, because
after the year consistent historical data for tangible capital investment in these six categories is available. Before ﬁscal year 1977, the CFD reports merely the total tangible
capital investment, while it reports the stocks of detailed six tangible capital components
in a book value basis. The CFD starts with 1956 FY and we exploit information before
1977 FY to obtain the initial values of tangible capital stocks and inventory at the beginning of benchmark year of 1977. The following explains our procedure by a run of theitem.
1. The CFD starts with 1956 FY, setting the reported book values of six capital components in this year as the market value. They are aggregated across components
and across companies to form the aggregate tangible capital stock in market value
basis. Note that only 414 companies are listed on the CFD in the year.
2. We construct a simple weighted average depreciation rate to run a perpetual inventory method for total tangible capital from 1956 FY to 1976 FY. The depreciation
rates for six capital components are borrowed from Hayashi and Inoue (1991). The
weights are taken from the proportions of capital components among the total tangible capital in ﬁscal year 1956.
3. With respect to companies that appeared after 1956 FY, the values in the year when
they appear are considered to be the market values.
4. With the price series on investment taken from the Bank of Japan; the weighted
average depreciation rate obtained above (7.88 %); the initial capital stock values in1956 FY; and information regarding the total tangible capital investment [K6260],
we run a perpetual inventory method for the aggregate tangible capital stock. After
we add the real investment in 1976 FY, we are left with the beginning of period
value of total tangible capital in ﬁscal year 1977.
5. We take into account the number of listed companies in the CFD. In 1976 FY, wehave 1,533 companies, whereas in 1977 FY we have 1,544. We assume that the
average sizes of the ﬁrms in these two years are the same, and we obtain our initialvalue of total tangible capital stocks in 1977 FY by multiplying the above obtained
variable by 1544/1533 = 1.0071. Finally, we take the ratio of the total tangible
capital, which is in market value basis, to the sum of the book values of six capitalcomponents in 1977 FY reported in the CFD to obtain the market value to the bookvalue ratio in tangible capital of 2.7601 for the ﬁscal year 1977.
20

6. We then take the products of 2.7601 and the book values of the six capital components in the CFD in the ﬁscal year of 1977, providing the initial values of the six
capital components for the perpetual inventory method after 1977 FY.
7. We repeated the same procedure for all inventories. The multiplier is 2.804.
As for ﬁrms that appear in the CFD data after 1977, the values in the ﬁrst year in which
they appear are assumed to be the market values. These simplifying assumptions areused due to limitations regarding the availability of data. Next, we obtain the book value
gross investment for each category from the CFD for (i) buildings [K6270], (ii) structures[K6280], (iii) machinery/equipment [K6290], (iv) ships [K6300], (v) autos/trucks [K6310],
and (vi) tools/ﬁxtures [K6320]. Then, for each company, we convert the book-value
investment ﬁgures to real investment ﬁgures by dividing the former by the relative priceof capital. The relative price of capital in the benchmark year for the company is set
to one.26 Next, we use the following depreciation rates for the six categories taken from
Hayashi and Inoue (1991) and Hori et al. (2006): (i) 4.7%, (ii) 5.64%, (iii) 9.489%, (iv)14.7%, (v) 14.7%, and (vi) 8.838%. Then for each company, from the capital stockin the benchmark year, we construct the real tangible capital series by the perpetualinventory method using the real investment obtained in the manner described above andthe depreciation rates. We divide the capital series for each company by the relative
price for the appropriate benchmark year. Then we aggregate the real capital obtainedin this way across all companies. Doing so, we obtain the real capital stock historical
data for which the benchmark year for all ﬁrms is set to 1977. Finally, we multiply theaggregate capital stock with the price series for capital, thus obtaining capital stock incurrent prices.
With respect to inventories, we follow Hoshi and Kashyap (1990) to construct themarket value series. We set the benchmark year for each ﬁrm in the same way as we
did for productive capital. Again, the book values in the benchmark year are assumed
to be market values. In general, the book value of inventories can diﬀer greatly from themarket value depending on the method of inventory valuation. Therefore, we divide our
CFD inventory categories into three parts: (i) inventories for which information about thevaluation method is available, (ii) inventories for which information about the method ofvaluation is not available, and (iii) land for sale. Here (i) includes inventories of commercial
goods [K1040], inventories of ﬁnished products [K1060], inventories of half-ﬁnished goods[K1070], inventories of products in progress [K1080], inventories of materials [K1100],and inventories of merchandise and supplies [K1110]. Whereas, (ii) includes inventories
of other goods [K1120]. As stated in Hoshi and Kashyap (1990), when inventories areevaluated in the “last in, ﬁrst out ” (LIFO) manner, the book value diﬀers greatly fromthe market value. Alternatively, if inventories are evaluated in any other manner, thebook value will approximate the market value. Therefore, for inventories in (i), we assume
that the book value equals the market value if ﬁrms do not follow the LIFO method of
inventory valuation.27 We also use this method to calculate category (ii) inventories in
26

The price of capital is taken from the Bank of Japan. Speciﬁcally, we use the price of “construction
materials” for (i) buildings and (ii) structures, the price of “machinery and equipment” for (iii) machinery/equipment and (vi) tools/ﬁxtures, and the price of “transport machinery” for (iv) ships and (v)autos/trucks.
27
We can see how ﬁrms value each inventory item using the CFD information [K4610] – [K4690].

21

current prices. With respect to category (iii), land for sale [K1050], we have neither
information on the inventory valuation method nor on a price index. Hence, we assume
that book values equal market values
On the other hand, when ﬁrms follow the LIFO method with respect to category (i)inventories, we construct market value inventory series as follows. First, if an inventory
item increases from time t − 1 to time t, the addition is assumed to be recorded in thebooks at the current price. Hence, the inventory stock at time t is the sum of the inﬂation
adjusted value of the inventory carried from time t − 1 to time t and the book value of theaddition. Second, when the book value of a ﬁrm’s inventory decreases from time t − 1 totime t, we assume that the cleared inventories are one year old and make the appropriate
correction for inﬂation for the stock of inventory carried from time t − 1 to time t. Finally,
if a ﬁrm uses both the LIFO and another inventory valuation method for an inventory
category, then we assume that half of the inventories are valued using the LIFO method.
Information related to land holdings is available in the CFD under [K1390]. Following Ogawa and Kitasaka (1998), we convert the book value variables into market value
variables as follows. The SNA provides information on the estimated market value landholdings of the private non-ﬁnancial corporate sector. In addition, the Financial Statements Statistics of Corporations by Industry (FSSCI) published by the Policy ResearchInstitute, Ministry of Finance, provides book value information on land holdings for thesector. Theoretically, we could obtain the market-to-book-value ratio by dividing the
SNA values by the FSSCI values if the coverage of corporations were identical in thetwo statistics. However, in practice, the coverage is known to be diﬀerent. Therefore,
we need to adjust the two sets of data by calculating the coverage ratio. Both the SNA
and the FSSCI contain information on cash holdings for the non-ﬁnancial corporate sector. Because cash is nominal, the diﬀerence in the amount of cash holdings between thetwo statistics will reﬂect the diﬀerence in coverage. Consequently, we can adjust for thediﬀerence in coverage and obtain the appropriate market-to-book-value ratios for landholdings. Finally, we obtain our market-value land holding series by multiplying the CFD
land holding with the ratios.
Next, we consider “other capital,” which is the sum of tangible capital for rent [K1370],
other productive capital [K1380] and other tangible capital [K1410]. Because we have no
information to obtain market value series, we assume that the book value variables areequal to the market value variables. We obtain Km for each year by aggregating the above
capital entries across ﬁrms.
Finally, regarding the amount of foreign capital, we have no clues in the CFD data.
Hayashi and Prescott (2002) estimated the amount of foreign capital for the whole Japanese
economy using the SNA, by regarding the current account balance (the sum of net exports
and net factor income from abroad) to accumulations of foreign capital.28 We replicate
the procedure using information on an SNA93 basis. Note that the estimate of foreign
capital thus constructed includes the amount of capital owned by the households, by
the government, and by the private ﬁnancial sector. We estimate the amount of foreign
capital owned by the private non-ﬁnancial sector by using the product of the amount of28

Hayashi and Prescott (2002) assume that the amount of foreign capital in 1989 is 25 times of the net
factor payments of the year. They estimate foreign capital before and after 1989 using information of net
exports and net factor payments of each year recursively.

22

foreign capital and the ratio of domestic capital stock excluding land owned by the private non-ﬁnancial sector to the total domestic capital stock excluding land. We ﬁnd thatthe ratio of foreign capital owned by the private non-ﬁnancial sector to tangible capital,
excluding land owned by the same sector, is around 4% and 13% for the 80s and during
1993-97, respectively.

5.2

Appendix B

This appendix is a reproduction of Section 3 of McGrattan and Prescott (2005) for readers’ reference. The economy consists of two sectors; corporate sector denoted as 1 andnon-corporate sector denoted as 2. The population in period t is denoted by Nt and grows
at rate η, so Nt+1 = (1 + η)Nt . The stand-in household’s preferences are ordered by
∞
∑

(7)

β t U (ct , nt )Nt

t=0

where c and n are per capita consumption and labor supply, respectively. The tangible
capital inputs are measured and are denoted by kjm for sector j. The intangible capital
input in sector 1 is not measured and is denoted by k1u . Note that sector 2 has no
intangible capital input.
The output of sector j is denoted by yj . Sector outputs are combined to produce acomposite good which is used for either private consumption or government consumption
or for one of the categories of investment,
ct + gt + x1m,t + x1u,t + x2m,t ≤ yt = F (y1,t , y2,t )(8)

where g is government consumption, xjm is gross investment in measured tangible capitalin sector j, and x1,u is gross investment in unmeasured intangible capital in sector 1.
The technology of sector 1 is described by
y1,t ≤ f c (k1m,t , k1u,t , zt n1,t )k1m,t+1 = [(1 − δ1m )k1m,t + x1m,t ]/(1 + η)
k1u,t+1 = [(1 − δ1u )k1u,t + x1u,t ]/(1 + η).

(9)
(10)
(11)
Similarly,

y2,t ≤ f nc (k2m,t , zt n2,t )k2m,t+1 = [(1 − δ2m )k2m,t + x2m,t ]/(1 + η).

(12)
(13)

All technologies have constant returns to scale. In (9) and (12), nj is labor services in
sector j and the {zt } are technology parameters that grow at rate γ.
The life time budget constraint of households is written as
(14)

∞
∑

pt {(1 + τc )ct + v1s,t (s1,t+1 − s1,t ) + v2s,t (s2,t+1 − s2,t ) + bt+1 − bt }

t=0

≤

∞
∑

pt {(1 − τd )d1,t s1,t + d2,t s2,t + (1 − τb )rb,t bt + (1 − τn )wt nt + ψt },

t=0

23

where τc is the consumption tax rate, τd is the corporate distributions tax rate, τb is thecapital tax rate, and τn is the labor income tax rate.
The value of shares held in corporate and non-corporate ﬁrms are v1s,t s1,t and v2s,t s2 , t,respectively, where v is the price and s is the number of shares held. The total numberof shares outstanding is normalized to one in each sector. Government bonds are also
held and denoted by b. The interest rate earned on these bonds is rb . Transfers of thegovernment are denoted by ψ.
The distributions paid to households are equal to what ﬁrms have after making newinvestments, paying wages, paying taxes, and receiving subsidies:(15) d1,t = p1,t y1,t − x1m,t − x1u,t − wt n1,t − τ1k k1m,t− τ1 [p1,t y1,t − δ̂1m k̂1m,t − δ̂1x x1m,t − x1u,t − wt n1,t − τ1k k1m,t ] + τx x1m,t(16) d2,t = p2,t y2,t − x2m,t − wt n2,t − τ2k k2m,t− τ2 [p2,t y2,t − δ̂2m k̂2m,t − δ̂2x x2m,t − wt n2,t − τ2k k2m,t ] + τx x2m,twhere pj is the price of goods in sector j, w is the wage rate, τjk is the tax rate on property
in sector j, τj is the tax rate on income in sector j, and τx is the investment tax credit.
The term δ̂1m k̂1m,t + δ̂1x x1m,t is the allowed depreciation on tangible capital in sector j
and is used to compute taxable income. The depreciation rates δjm and δjx are policy
parameters that can be set to eﬀectively lower the price on new capital, as in the cases of
U.S. and U.K.. The rate δ̂jm is the allowed rate of depreciation on sector-j book “capital”,
which has a law of motion,(17)k̂jm,t+1 = [(1 − δ̂jm )k̂jm,t + (1 − δ̂jx )xjm,t ]/[(1 + η)(1 + π)].

The rate δ̂jx is the allowed rate of immediate expensing of investment in sector j.
In equilibrium, ﬁrms in the corporate sector choose capital and labor to solve
(18)

max

∞
∑

pt d1,t (1 − τd )t=0

subject to constraints (9)-(11) and (17) for j = 1. Non-corporate ﬁrms solve a similar
problem
(19)

max

∞
∑

pt d2,tt=0

subject to constraints (12)-(13) and a constraint analogous to (17) for j = 2. Note thatd2,t is non-corporate income net of taxes.
Government production is included in the non-corporate sector. Government purchases and transfers are ﬁnanced by tax receipts and debt issues. The period t government
budget constraint must be satisﬁed each period and is given by(20)

gt + ψt + rb bt = bt+1 − bt + all tax receipts.

Note that all tax rates are proportional in the model economy.
We now derive a estimation formula for the equilibrium value of corporate equity.
24Formula 1 (Proposition 4 in MP) On a balanced-growth path, the total value ofcorporate equity, Vt ≡ v1s,t Nt , satisﬁes
Vt = (1 − τd )[(1 − τx − τδ )K1m,t+1 + (1 − τ1 )K1u,t+1 ],

(21)
where
(22)

[

(

τδ = τ1 δ̂1x + (1 − δ̂1x )

)(

δ̂1m
(i + π + δ̂1m )(1 + π)(1 − δ1m ) − 1 + δ̂1m
γ + η + π + δ̂1m)].

Here, second-order terms are dropped, i is real interest rate, and capital letters denote
aggregates.
The value of intangible capital stock K1u,t+1 is unmeasured and must be estimated.
We follow the MP’s indirect approach. Assuming equal after-tax returns to tangible andintangible assets, we obtain inferred stock of intangible capital.
Formula 2 Then, on a balanced-growth path, the total value of intangible capital stock,
K1u,t , satisﬁes(23)

K1u,t =

1i
Π1,t −
X1m,t .
i−γ−η(1 − τ1 )(γ + η + δ1m )(i − γ − η)

where second-order terms are dropped, capital letters denote aggregates, and Π1,t is aggregate proﬁt in corporate sector. This equilibrium relation is derived from the deﬁnition of
corporate proﬁts as(24)

Proﬁtt = p1,t y1,t − wt n1,t − δ1m k1m,t − τ1k k1m,t − x1u,t .

References
Alpanda, S. (2011): “Taxation, Collateral Use of Land and Japanese Asset Prices,”
Empirical Economics, forthcoming.
Ando, A. (2002): “Missing Household Saving and Valuation of Corporations: Inquiry into Japanese National Accounts I,” Journal of the Japanese and International
Economies, 16, 147–176.
Ando, A., D. Christelis, and T. Miyagawa (2003): “Ineﬃciency of Corporate
Investment and Distortion of Savings Behavior in Japan,” in Structural Impediments
to Growth in Japan, ed. by M. Blomstrom, J. Corbett, F. Hayashi, and A. Kashyap,
Chicago: University of Chicago Press, 155–190.
Braun, R. A., D. Ikeda, and D. H. Joines (2009): “Saving and interest rates inJapan: Why they have fallen and why they will remain low,” International Economic
Review, 50, 291–321.
Chen, K., A. Imrohoroglu, and S. Imrohoroglu (2006): “The Japanese Saving
Rate,” American Economic Review, 96, 1850–1858.
25

Corrado, C. and C. Hulten (2010): “How Do You Measure a “Technological Revolution”?” American Economic Review, 100, 99–104.
Corrado, C. A., C. Hulten, and D. Sichel (2009): “Intangible Capital and U.S.
Economic Growth,” Review of Income and Wealth, 55, 661–685.
Corrado, C. A., C. R. Hulten, and D. E. Sichel (2006): “Intangible Capitaland Economic Growth,” NBER Working Papers 11948, National Bureau of Economic
Research, Inc.
Fukao, K., T. Miyagawa, K. Mukai, Y. Shinoda, and K. Tonogi (2009): “Intangible Investment In Japan: Measurement And Contribution To Economic Growth,”
Review of Income and Wealth, 55, 717–736.
Fukuta, Y. (2002): “A test for rational bubbles in stock prices,” Empirical Economics,
27, 587–600.
Hayashi, F. (2006): “The Over-Investment Hypothesis,” in Long-Run Growth and ShortRun Stabilization: Essays in Memory of Albert Ando, ed. by L. R. Klein, Cheltenham:
Edward Elgar Publishing.
Hayashi, F. and T. Inoue (1991): “The Relation between Firm Growth and q with
Multiple Capital Goods: Theory and Evidence from Panel Data on Japanese Firms,”
Econometrica, 59, 731–53.
Hayashi, F. and K. Nomura (2005): “Can IT be Japan’s savior?” Journal of theJapanese and International Economies, 19, 543–567.
Hayashi, F. and E. C. Prescott (2002): “The 1990s in Japan: A Lost Decade,”
Review of Economic Dynamics, 5, 206–235.
Hori, K., M. Saito, and K. Ando (2006): “What Caused Fixed Investment to Stagnate During the 1990s in Japan? Evidence from Panel Data of Listed Companies,” The
Japanese Economic Review, 57, 283–306.
Hoshi, T. and A. K. Kashyap (1990): “Evidence on q and Investment for JapaneseFirms,” Journal of the Japanese and International Economies, 4, 371–400.
Ishi, H. (2001): The Japanese Tax System, New York: Oxford University Press.
Ito, T. and T. Iwaisako (1995): “Explaining Asset Bubbles in Japan,” NBER Working
Papers 5358, National Bureau of Economic Research, Inc.
Marrano, M. G., J. Haskel, and G. Wallis (2009): “What Happened To The
Knowledge Economy? Ict, Intangible Investment, And Britain’S Productivity Record
Revisited,” Review of Income and Wealth, 55, 686–716.
McGrattan, E. R. and E. C. Prescott (2000): “Is the Stock Market Overvalued?”
Quarterly Review, Federal Reserve Bank of Minneapolis, 20–40.

26

——— (2004): “The 1929 Stock Market: Irving Fisher Was Right,” International Economic Review, 45, 991–1009.
——— (2005): “Taxes, Regulations, and the Value of U.S. and U.K. Corporations,”
Review of Economic Studies, 72, 767–796.
——— (2010a): “Technology Capital and the U.S. Current Account,” American Economic
Review.
——— (2010b): “Unmeasured Investment and the Puzzling U.S. Boom in the 1990s,”
American Economic Journal: Macroeconomics.
Nakajima, T. (2008): “Asset Price Fluctuations in Japan: 1980-2000,” Japan and theWorld Economy, 20, 129–153.
Nomura, K. (2004): The Measurement of Capital, Tokyo: Keio-Gijuku-DaigakuShuppan (in Japanese).
Ogawa, K. and S. Kitasaka (1998): Capital Markets and Business Cycles: An Empirical Analysis of the Modern Japanese Economy, Tokyo: Nihon-Keizai-Shimbun-Sha(in Japanese).
——— (1999): “Market Valuation and the q Theory of Investment,” Japanese Economic
Review, 50, 191–211.

27

Figure 1: Capital-Output Ratio in Japan3

2.8

Capital/Output Ratio from the SNA

2.6

2.4

2.2

2

1.8

1.6

1.4

1.2

1
1980

1985

1990

1995

2000

2005

2010

Calender Year

Note: The ﬁgure shows the capital-output ratio for Japan following the method of Hayashi and Prescott (2002) using 93SNA
data.

Figure 2: Prices of Tangible and Intangible Capital

Prices of Tangible Capital and Intangible Capital

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0
1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

Year

Note: The line with square dots shows the movement of the price of tangible capital, (1 − τdist )(1 − τx − τδ ). The line withround dots shows the movement of the price of intangible capital, (1 − τdist )(1 − τcorp ).

28

Figure 3: Net Debt and Stock Value Movements in the CFD
Net Debt and Net Equity Value in the CFD
350

Trillion Yen

300
250
200
150
100
50
1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

1994

1996

1998

2000

Fiscal Year
Movements of Stock Value
8

1980 Value = 1

7
6
5
4
3
2
1
1980

1982

1984

1986

1988

1990

1992

Fiscal Year

Top; The real line shows the movement of actual stock values net of the value of cross holding share and equity assets.
The dashed line shows the movement of net debt value as non-equity ﬁnancial liabilities minus non-equity ﬁnancial assets.
These aggregates are constructed using the CFD information.
Bottom; The line with square dots shows the movement of total actual value of outstanding equity from the CFD. We
do not exclude the value of cross-holding shares. The line with triangle dots shows the movement of the same series fromthe SNA. The line with + dots shows the movement of Nikkei 225, and the line with round dots is for TOPIX. They arenormalized to one for 1980 values.

29

Figure 4: The Conversions of the CFD Book-Value Entries into the Market-Value Entries
Tangible Capital Excl. Land

Trillion Yen

250

200

150

100

50
1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

1992

1994

1996

1998

2000

Fiscal Year
Land
120

Trillion Yen

100
80
60
40
20
0
1980

1982

1984

1986

1988

1990
Fiscal Year

Note: Lines with square dots are for the movements of aggregates in a market-value basis. Dashed lines with round dots
depict the movements of aggregates in a book-value basis.

30

Figure 5: The diﬀerence in Coverage between the CFD and the SNA
Cash Holdings

Tangible Capital Excl. Land

200

600

Trillion Yen

Trillion Yen

500
150

100

400
300
200

50
100
0
1980

1985

1990

1995

0
1980

2000

1985

Year
Net Debt

2000

Net Equity Value
500

300

400
Trillion Yen

Trillion Yen

1995

Year

350

250
200
150

300
200
100

100
50
1980

1990

1985

1990

1995

0
1980

2000

Year

1985

1990

1995

2000

Year

Note: Lines with triangle dots show variables from the SNA and the lines with square dots show variables from the CFD.
The SNA data variables are in an end-of-calendar-year basis, and the CFD variables are in a ﬁscal year basis.

31

Figure 6: Comparison the SNA with the FoF
Cash Holdings
180

Trillion Yen

160
140
120
100
80
60
1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

1994

1996

1998

2000

Year
Equity Liabilities

Trillion Yen

800

600

400

200

0
1980

1982

1984

1986

1988

1990

1992

Year

Note: Lines with triangle dots show variables from the SNA and the lines with ∗ dots show variables from the FoF. The
SNA data variables are in an end-of-calendar-year basis, and the FoF variables are in a ﬁscal year basis. The coverage forcash holdings are the same for two data sets; all private non-ﬁnancial corporations. The coverage of debt equity for the
SNA is also all private non-ﬁnancial corporations, where as that for the FoF is traded private non-ﬁnancial corporations.

32

33
0.575
0.377
0.28d

Domestic tangible capital Km
Ku /KmEstimate of intangible capital from the CHS methodc

1.03
0.631
0.375 f

0.063
0.007
0.070
0.650

(3)
US
Whole
1990-2001
NIPA/BEA
0.349
0.030
0.041
0.067
0.097

(4)
UK

estimated Ku for the U.K., using the ratio of U.K. to U.S. investments in R&D as the ratio of the intangible capital stocks to the U.S.
economy.
c See Corrado et al. (2009) for technical details.
d For this ﬁgure, the coverage of corporations is adjusted to that of the CFD. For the whole economy, Fukao et al. (2009) reports that
intangible capital stock is 0.336 times the GDP level for 1985-1989.
e See Fukao et al. (2009) for technical details.
f Marrano et al. (2009) report real investment on intangible capital for the whole sector excluding for the government sector. When theytake the ratio of intangible capital stock to output, they use market sector gross value added as a proxy of output. Hence, the ratio can beused for direct comparisons with U.S. evidence by Corrado et al. (2009) who estimated the whole sector stock of intangible capital.
* These values are relative to GDP

1.45
0.352

0.51b

1990-2001b With lack of information for consistent time series of after-tax proﬁts, tangible capital, growth rates, and depreciation rates, MP

a The private non-ﬁnancial corporation sector in the SNA.

0.127
0.016
0.144
1.258

0.070
0.003
0.073
0.217

Country
Coverage
PeriodData
Corporate tax rate τcorp
Growth of real GDP γ + ηReal interest rate i
Tangible depreciation rate δm
Average corporate investment* Xm
Contributions to domestic pre-tax proﬁts*
Tangible assets iXm /[(1 − τcorp )(γ + η + δm )]Intangible assets (i − γ − η)Ku
Total ΠEstimate of intangible capital* Ku
1.815
0.693
0.336 e(2)
JPN
P. N. F.a
1981-1989
SNA
0.413
0.061
0.074
0.076
0.129

(1)
JPN
Traded non-ﬁnancial corporations
1981-1989
CFD
0.413
0.061
0.074
0.076
0.076

Table 1: Estimating Intangible Capital using the MP method

34
0.442
0.455
1.030
1.401

Total fundamental value*

Actual market values *RATIO
Ando’s RATIO

1.987
2.727

0.773

0.389

0.014

1993−97 = K 1981−89 K 1993−97 /K 1981−89 .
u in the period is obtained as Kummu* These values are relative to GDP

aK

0.015

1.268
1.891

0.564

0.445

0.041

Without land
1981-1986 1987-1989 1993-1997
0.405
0.428
0.392
0.211
0.257
0.185
0.009
0.007
0.008
0.082
0.085
0.116
0.217
0.217
0.213a
0.469
0.425
0.496
0.102
0.092
0.106
0.454
0.421
0.417
0.717
0.674
0.715
0.325
0.284
0.298

Fundamental value of foreign capital*

Corporate tax rate
Tax on distributions
Investment subsidy rate
Tax credit due to depreciation allowance
Estimate of intangible capital*
Price of intangible capital
Fundamental value of intangible capital*
Tangible capital*
Price of tangible capital
Fundamental value of tangible capital*

JPN values

1.064
1.367

0.561

0.527

0.015

1981-1986
0.405
0.211
0.009
0.061
0.217
0.469
0.102
0.559
0.734
0.410

1.796
2.239

0.960

0.534

0.014

With land
1987-1989
0.428
0.257
0.008
0.042
0.217
0.425
0.092
0.607
0.706
0.429

Table 2: Predicted and Actual Corporate Values and RATIO (CFD)

1.266
1.702

0.724

0.572

0.041

1993-1997
0.392
0.185
0.007
0.089
0.213a
0.496
0.106
0.577
0.737
0.425