1

Economic Policy under Uncertainty and ICT

Advancement

Final Report to Economic and Social Research

Institute

February 2004

Project Leader Kiyohiko G. Nishimura

University of Tokyo

2

List of Participating Researchers

NISHIMURA, Kiyohiko G. (University of Tokyo).

Project Leader

SAITO, Makoto (Hitotsubashi University).

OZAKI, Hiroyuki (Tohoku University).

MIYAZAKI, Kenji (Hosei University).

FUKUTA, Yuichi (Osaka University)

TACHIBANA, Towa (Bank of Japan).

TAKEDA, Yosuke (Sophia University).

TAMAI, Yoshihiro (Kanagawa University).

MINETAKI, Kazunori (Fujitsu Research Institute)

NAGASHIMA, Naoki (Fujitsu Research Institute).

SHINDO, Seiji (Fujitsu Research Institute).

KUROKAWA, Futoshi (University of Tokyo).

3

Chapter 1:

Total Factor Productivity in Japanese Information Service Industries:

Firm-Level Analysis

4

Abstract

We examine factors determining productivity of firms’ information service activities,

using most comprehensive data of information service industries in Japan. We focus on

the degree of modularization and resulting outsourcing, economies/diseconomies of scale in

software development, and firms’ organizational changes. Outsourcing has persistent

negative effects on total factor productivity, suggesting not only productivity-enhancing

modularization is not fully utilized but also productivity-hindering remnants of traditional

main-contractor-subcontractor relations still prevail in information service industries. We

also find diseconomies of scale in software development, suggesting less efficient

communication among development team members. Finally, we find a substantial cost on

firms’ organizational changes on productivity.

5

1. Introduction

Japan has been suffering from the most severe economic stagnation since 1990.

Among possible causes of this prolonged recession, a sharp decline in productivity has

attracted much attention of both economists and policy makers in the past decade.1。In

particular, Nishimura et al. (2002) examine and compare US experience (reported in

Jorgenson et al. (2001)) and Japanese experience (reported in Nishimura and Shirai (2002)).

They find a sharp contrast between productivity-improving manufacturing sectors (though

there is a wide variety among them) and productivity-stagnating non-manufacturing sectors

in Japan. In contrast, no comparable difference of this magnitude is found in the United

States though there is a wide sectoral difference. Japanese ICT hardware-producing

industries are as productive as US counterparts2 but Japanese ICT using industries (finance

and insurance, trade, and other services) show markedly inferior performance compared

with US counterparts.

1 There has been a sizable literature on productivity growth or technological progress. Hayashi and

Prescott (2002) examine the movement of the TFP (total factor productivity) growth relying on neoclassical

framework and argue that declined supply of labor coupled with declined TFP growth is one of the culprits of

disappointing economic growth of Japan. Fukao et al. (2003), based on detailed industry-wise data as well

as macro data, reveal a sharp decline in the TFP growth rate in aggregates and in many industries.

2 In the same token, Ark et al. (2002) show that the labor-productivity growth in Japanese IT-producing

industries in the late 90s is 19.5%, which is roughly in line with 23.7% in the United States and 13.8% in EU.

6

In another piece of evidence, Ark et al. (2002) report that in the latter half of the 90s,

IT-using industries (mostly service industries in a broad sense) show a robust 5.4% increase

in the United States, while the Japanese counterparts exhibit disappointing 0.0%.

Especially, a sharp contrast is notable in Wholesale and Retail Trade industries between

Japan and the United States.3 The White Paper (2001) of the Cabinet Office on the State

of the Economy argues that the TFP growth in Japanese non-manufacturing declines

sharply whereas the decline of TFP growth in manufacturing sectors is not so pronounced.

Thus, disappointing TFP growth in non-manufacturing sectors aggravate, if not cause,

Japan’s economic stagnation of the 1990s.4

Although their importance is apparent in their large share of GDP and the

above-mentioned disappointing performance, non-manufacturing industries have not been a

major subject of large-scale firm-level empirical studies. This is a sharp contrast with

manufacturing industries in which large-scale firm-level as well as plant-level studies are

3 In fact, US wholesale and retail trade sectors contribute greatly to overall productivity. Basu et al.

(2003) claim that almost 70% of the overall TFP growth of the United States can be explained by the TFP

growth of the wholesale and retail trade sectors.

4 However, Fukao and Kwon (2003) report that when they adjust quality of labor inputs and utilization

of capital stocks in the traditional growth accounting framework, TFP growth rates in manufacturing sectors

are rather low compared with rather high TFP growth rates in service sectors. They attribute rather good

performance to deregulation in service industries. However, their procedure of “adjustment” seems

inconsistent with basic assumptions of the growth accounting framework, notably perfect utilization, so that

their result should be evaluated cautiously.

7

commonly undertaken. This scarcity of research is partly due to data availability.5

In this paper, we fill this huge gap between practical importance and scarcity of

firm-level research in non-manufacturing industries. Among a variety of

non-manufacturing industries, we take up information service industries as our target

industries for the following three reasons.

Firstly, information service industries include the software industry that is an

integral part of so-called “IT (information technology) Revolution” alongside with the

hardware industry. Because of a prominent role of IT on recent economic development,

in-depth analysis of information service industries is urgently needed. We should remind

ourselves that the software industry is among non-manufacturing industries while the

hardware industry is by definition among manufacturing industries.6

Secondly, both the Government and business communities consider information

service industries as “strategic” industries. The Japanese government launched an

initiative called “e-Japan Strategy II” in 2003, and clearly targeted information service

5 Ahn (2001) touches service industries briefly in his survey of empirical results in productivity based

on firm dynamics. He points out several problems in productivity analysis of service industries such as

appropriate measurement of outputs, although importance of service industries is obvious in viewing its large

share in GDP.

6 The JSIC (Japanese Standard Industry Classification) System was revised substantially in March 2002

(called 11th Revision). Before this revision, information service industries were classified to service

industries, but after the revision, they now belong to a new 1-digit industry classification called “Information

and Communication Industries”.

8

industries. Some firms in electronic industries are shifting their business emphasis from

computer hardware to software and information services.7

Thirdly, however, there is a seemingly high hurdle for the government and firms to

achieve their goals. There are several pieces of anecdotal evidence of low potential in

Japanese information service industries. For example, according to the so-called

Capability Maturity Model (CMM), 23 Indian firms are in the top rank at the end of 2000,

while no Japanese firm is ranked to this category.8 Similarly, no Japanese firm is in the

top 5 of OECD (2002)’s revenue ranking of software licensing and service fees. Only one

Japanese firm appears among the top 20. Thus, it is of utmost importance to analyze

factors determining productivity in Japanese information service industries including the

software industry and to discern possible impediments to improve efficiency.

Although there is a sizable literature on firm-level productivity in manufacturing

industries, only a few studies have been conducted on non-manufacturing industries and

almost none on information service industries even in the United States, where data are

7 Most prominent is IBM. IBM’s divisional revenues now reveal that revenues from software and

information service divisions exceed those from hardware divisions. IBM’s move prompts several Japanese

firms to follow it.

8 CMM evaluates maturity or capability of software development in five levels. See Conference for

Improving Software Development and Procurement Processes (2001).

9

relatively easily available.9 Ehrlich et al. (1994) examine international airline companies

and find an increase in TFP growth after full privatization. Gort and Sung (1999) show that

increased competition due to deregulation raises TFP growth in telephone companies in the

United States. To our knowledge, there is no empirical study investigating TFP growth of

information service industries at the firm level in the United States. Even case studies that

examine productivity directly are scarce.

One notable exception is Cusmano et al. (2003), who investigate

software-development productivity based on case studies of 104 software development

projects mostly in India, Japan, the United States and the European Union. Their results

indicate that India and Japan are higher development productivity than the United States

and the European Union. However, their productivity measure is not TFP but several

project-oriented measures of performance such as the number of lines of code per

programmer-month, and defects reported per 1000 lines of code in one year after delivery to

customers. To interpret their results, we should take account of “cultural difference,” as

suggested by these authors. They point out that US programmers tend to emphasize

shorter or more innovative programs, and spend more time in optimizing code, which

ultimately reduces the number of lines of code, while simultaneously increasing

programmer-months.

9 Ahn (2001) and Bartelsman and Doms (2000) survey firm-level empirical analyses. Ahn examines

non-manufacturing industries extensively.

10

The research reported here is markedly different from previous researches about

information service industries in Japan and in other countries in two aspects. Firstly, this

research is based on large-scale Census-like survey data on all firms and establishments

engaged in information services, called the Survey on Selected Service Industries, Volume

of Information Services. In contrast, existing studies in this field are at most case studies

(see, for example, Sano (2001)), and in some cases they may be biased to successful firms

(see, for example, Koyama and Takeda (2001)10). These studies are informative, but

insufficient for the purpose of capturing the overall picture of the industry as a whole.

Secondly, we examine total factor (or multi-factor) productivity of firms. Previous

studies using large-scale data are often concerned only with labor productivity (see, for

example, Shintani (1998)). However, it might be misleading to base one’s argument on

labor productivity only, in an industry using sophisticated IT equipments like computers

and servers. The necessity of TFP analysis is obvious in information service industries.

This paper is organized as follows. In Section 2, we examine factors determining

productivity in information service industries, with special emphasis on the software

industry. In section 3, we clarify important characteristics of the Survey of Selected

Service Industries, and explain data construction in some details. Main empirical results

10 Sano (2001) examined the effect of outsourcing on information service industries based on case

studies. Koyama and Takeda (2001) investigated software-development productivity, with special emphasis

on modularization, referring to various cases in the industry.

11

are presented in Section 4. We then discuss these results and examine what factors are

behind these results. Concluding remarks are presented in Section 5.

12

2. Factors Determining Productivity of Information-Service Firms

In this section, we examine possible determinants of productivity of

information-service firms, which will be the basis of empirical analysis of Section 4.

Since software products are major outputs in information service industries, we base our

argument mostly on productivity determinants of software development. 11 In particular,

we consider three possible determinants: the degree of modularization, the scale of software

development, and organizational structure, which have often been considered as most

influential determinants of software development productivity.

2.1. Modularization

Both in popular presses and academic writings, so-called Silicon Valley Model has

attracted much attention. It is often argued that in the Silicon Valley of the State of

California, information companies and engineers form a “community” and collaboration

within the community is common and productive. 12 Based on such collaboration,

outsourcing has been considered as one of the most productivity- enhancing practices.

11 In 1999 the share of custom software and prepackaged software is more than 60% of the total

value-added of information service industries.

12 See Aoki and Okuno (1996) for an example of Japanese academic writing emphasizing this

collaboration positively.

13

However, simple outsourcing is not always likely to be productivity enhancing.

For example, if new products come out with new production design, outsourcing may cause

a serious production problem when readjustment of production process is necessary and

communication between outsourcers and outsourcees are not so smooth. In order to

facilitate such readjustment and communication and to make outsourcing successful,

“modularization” of parts has been considered to play a vital role in the Silicon Valley.13

The concept of “modularization” stems from the development of IBM SYSTEM/360.

Computers before IBM SYSTM/360 had their own specifications with own parts, operating

system, and application software. There were few common parts (both hardware and

software) between each generation of computers. Computer manufacturers developed

idiosyncratic parts and software suitable for each generation of computers virtually from

scratch.

The development of IBM SYSTEM/360 was revolutionary in the sense that its

developers invented the concept of “family” of computers: compatibility within a family

was maintained as much as possible, and in order to do so, “modularization” had been

extensively utilized. The adoption of modularized design and its wide-range application

were considered to be one of the most dramatic driving forces behind the revolutionary

13 Here “modularization” is to design complex products and processes consisting of small-scale

subsystems that are independently designed (see Baldwin and Clark (1997)). The “small subsystems

independently designed” are “modules”. So long as the “integrability” is maintained, each subsystem can be

designed independently.

14

speed of innovations in the computer industry (Baldwin and Clark (1997)).

Modularization has far-reaching consequences. Modularization of product

architecture allows firms to modularize production process, which leads to modularization

of organization. Thus when modularization is “deepened”, firms can outsource a part of

their business. Outsourcees, who are sometimes spinouts of some outsourcer firms, are

then able to get outsourcing contracts from various companies to realize economies of scale

and to slide down the learning curve quite rapidly, so that they become competitive in

prices. This in turn enables outsourcers to procure parts inexpensively.

It should be noted that software was an integral part of computers at the time of IBM

SYSTEM/360. Thus, it may not be far-fetched to assume the same productivity-enhancing

effect of modularization applies to software development.

The successful hardware modularization, however, may not be duplicated in

software and information service industries. Koyama and Takeda (2001) forcefully argue

that production innovation in the software industry is less frequent than the hardware

industry, implying these two industries are not so similar. Thus simple “transplanting” of

modularization may not work well in the software industry. For example, if OS suppliers do

not open source codes of their OS, modularization is far less complete than in the hardware

industry. 14 Furthermore, human factors are relatively important in the software industry,

14 API (application programming interface) is a part of OS that is used in application software

development. Since Microsoft does not make source codes open for its WINDOWS OS, developers of

15

since implicit knowledge of engineers may not be fully “coded” and reproducible.

In sum, there is no theoretically clear-cut conclusion about whether modularization

and resulting outsourcing are productivity enhancing in the software industry. Thus,

whether modularization and outsourcing are productivity improving or not is in essence an

empirical question.

2.2. Scale of Development Organization

The second possible factor determining productivity of information service

industries is the scale of development organization. Here development organization

includes the basic research and development division and system software development

division (including system integration).

Software development is a complex process involving intensive communication

among development team members. Thus, smooth communication among development

team members is vital, especially under continuously changing software development

environment. Development languages are changing quite rapidly, and suppliers have to

cater for ever-changing demand of their customers.

This observation suggests diseconomies, rather than economies, of scale in software

development. In fact, Frederick P. Brooks Jr., who is often referred as the “father of IBM

WINDOWS application software cannot develop their software independently, which implies insufficient

modularization. Such problems do not exist in computer hardware.

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SYSTEM/360”, points out these possible diseconomies of scale, and argues against

large-scale development. He coins the idea that inputs can be measured in man-months as

a “myth” in his renowned book Mythical Man-months (Brooks (1995)). He argues that the

time of one programmer is not substitutable by the time of another programmer, so that

using one hour of 100 programmers cannot finish a project that can be finished by using

100 hours of one programmer. Consequently, programmers’ labor inputs cannot be

measured by man-hours or man-months.15

Thus, when communication is insufficient among development team members, an

increase in the number of development teams may have even negative effects on the

productivity of software development. This possible negative effect may be particularly

keen when the development schedule is suddenly shortened and engineers are added to the

development team to compensate the change.

In contrast, there is one important example of economies of scale in software

development, which is the success of the Linux system development. As is well known,

the development of Linux is made possible by participation of many engineers and

programmers around the world, who form an Internet virtual community. They enhance

communications among them through various means of Internet technology. The most

15 This is a clear warning against common practices that estimate the value of software products by

wage times man-hours of programmers and system engineers who engage in developing these software

products.

17

important characteristics of the development of Linux is that codes are open to their

community and thus coding and debugging are efficiently undertaken in a rapid manner.

The success of Linux suggests that if communication among developers is smooth, there are

notable economies of scale in software development.

In sum, the scale of development may negatively affect productivity as in the case of

the “mythical man-month”, or may positively influence productivity as in the success of

Linux development, depending on the smoothness of communication among development

team members. In the empirical analysis, we see which factor dominates in the Japanese

information service industries.

2.3. Organizational Development and Productivity

We have so far examined a crucial role of communication in software development.

Comparing the phenomenon described in the mythical man-month and the success of Linux,

we understand importance of development-team organization that enhances or hinders

effective communication. In fact, effectiveness of communication is also closely related

to modularization. If software development is modularized in a way to enhance

communication as in the Linux case, we can expect a large productivity gains. If

modularization is pursued by other motivations than communication, we are likely to face

inefficiency described in the mythical man-month. In a similar token, one may argue that

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firm organization may be as important as development team organization.

Innovations in software development are often described as leap-frogging, not

gradual, in which past experiences have relatively less value than in other industries. This

means that firm organization should be sufficiently flexible to accommodate such

leap-frogging innovations. In fact, information service industries are known for a variety

of employment contracts, ranging from standard long-term contracts for regular employees

called “Shain” to short-term ones for workers choosing more flexible work styles.

One typical example is Elysium, a producer of 3D data transformation software

called direct data translator.16 It was divested from Armonicos, which itself was founded

by three spinouts of YAMAHA as a software firm in 1984.17 The packaged software

division was divested in 1999 to become Elysium. The custom software division remains in

Armonicos. Thus, even though Elysium and Armonicos are in the same 3D CAD software

market, they decide to separate in order to seek efficiency and to maximize their

value-making potential.

In the empirical analysis of Section 4, we examine the effect of organizational

changes on productivity explicitly. In particular, we distinguish adjustment costs of firm

organization from those of employment adjustment.

16 See http://www.elysiuminc.com/.

17 See http://www.armonicos.co.jp/english/.

19

20

3. Data: Survey of Selected Service Industries: Volume of Information

Service Industries

In this section, we briefly review and explain our data source, the Survey of

Selected Service Industries, Volume of Information Service Industries. This survey is

conducted by the Ministry of Economy, Trade and Industry (METI). However, before

explaining data source, it may be worthwhile to briefly peruse Japanese information service

industries.

3.1. Japanese Information Service Industries

Survey of Selected Service Industries, Volume of Information Service Industries is

the most comprehensive statistics about the Japanese information service industries. Here

information service industries include information processing service (including application

service providers (ASP))18, custom software, prepackaged software (business prepackaged

software, software game, basic software), system management and administration, data base

service (online and offline), research, and others.

In the empirical analysis we use panel data of firms between 1991 and 1998.19

18 ASP is included if they develop software themselves.

19 This is based on the data set supplied by the Statistics Bureau for our empirical study.

21

However, we use the most recent aggregate data (2001) here to review the current state of

Japanese information service industries. The total sales of information service industries

are 13.9 trillion yen, a remarkable 18.2% increase from the previous year. Note that the

Japanese economy was in the deflationary stage in 2001, so that this increase in nominal

terms is all the more impressive. Among all information service industries, custom

software development has the largest share, which is 49.4%, and the third largest is

prepackaged software development’s 10.8%. Thus software development including both

custom and prepackaged accounts for more than 60%. The second largest share is

information processing service’s 19.1%.

Prepackaged software’s growth of sales is an astounding 49.1%, which is the highest

among information service industries. This high rate of growth is the result of extremely

high growth rates of its subcategories, that is, 162.3% growth in software games and

112.6% growth in basic software. System management and administration’s growth rate is

44.8%, which is the second highest. This may be caused by a rapid growth in network

systems in this field. Custom software has a decent growth rate of 8.4%, though its rate

pales before the extremely high growth rate of prepackaged software. Only one category

exhibits negative growth, which is –10.5% of data base service. This category includes

some of Internet businesses, so that this decline may reflect hard time of Internet businesses

after the burst of so-called “Internet Bubble.”

Let us now turn to the demand side of information service industries. In the total

22

contracted sales, the share of manufacturing firms is 22.6% and that of finance and

insurance firms is 17.5%, and these two industries account for more than 40%. As for the

growth rate, transportation and communication have the highest, which grows at the rate of

41.5%. Wholesale and retail trade industries are the second highest, and its growth rate is

30.6%.

3.2. Characteristics of The Survey of Selected Service Industries

The Survey of Selected Service Industries, Volume of Information Service Industries,

is the most comprehensive statistics about Japanese information service industries. This

survey, conducted by the Ministry of Economy, Trade and Industry (METI), is a

Census-like one, in which all firms and establishments engaged in information service

industries are surveyed. Moreover, the coverage of the survey is far wider in its scope of

information service industries than even the Establishment and Enterprise Census. The

Survey collects information about establishments and firms that have some business

activities in information service, while the Census gathers information about establishments

and firms whose major business activities are in information service. This is particularly

important since information service industries are rapidly expanding ones with many entries

from and exits to other industries.

Table 1 shows the number of establishments as a whole and for each sub-categories

based on firms’ organizational structure, according to aggregate figures published by the

23

METI. In our sample period of 1991-1998, the total number of establishments ranges

between the smallest number 5,812 of 1995 and the largest 8248 of 1998. There are three

sub-categories: single establishments (without a branch office), headquarters (with branch

offices), and branch offices. The category of single establishments has the largest share of

50% on the average.

The purpose of our study is to investigate productivity at the firm level and we

examine the effects of firm-level characteristics such as firms’ organizational structure on

firms’ productivity. Thus, our basic units of investigation are firms, rather than

establishments. Among all establishments listed in Table 1, we examine single

establishments and headquarters in our study.

The Survey of Selected Service Industries is particularly suited for firm-level

analysis of information service industries in several respects. Firstly, the Survey

meticulously distinguishes revenues, costs, labor inputs and capital stocks in firms’

information service activities from their other activities. This is important since some

firms in our samples engage only partially in information service activities. In our

empirical analysis, we use these revenues, costs, labor inputs, and capital stocks solely in

their information service activities to construct value-added and other data necessary for

TFP calculation. That is, our value-added, labor input and capital stock data are solely of

firms’ information service activities, and thus they are not “contaminated” by other

24

activities.20

A notable characteristic of capital investment data in this data set is many zeros and

blanks found in the category of “acquisition of structure and buildings” and “acquisition of

machines and equipments”, on the one hand, and relatively large payments of

computer-time lease and other rental payments that are supposedly building rents. This

implies that in some cases a traditional perpetual inventory method may not be appropriate,

especially in the case of capital service inputs of computers, where capitalization is more

appropriate. Thus, in the following analysis, we use the perpetual inventory method as

much as possible, but when it is not appropriate, we resort to other procedures to get capital

service inputs.

Finally, there is no intangible asset data in the Survey. In particular, there is no

data of software assets that firms have. It is inconceivable that firms engaging information

service activities have no software assets. Consequently, we should take this fact in mind

and take measures to correct possible biases stemming from the lack of software asset

20 There are other notable characteristics. First, the Survey asks the headquarters of firms to report the

total fixed capital stocks and the total operating expenses (and their breakdowns) of information service

activities of the firms as a whole. This is very convenient in our constructing firm-level information-service

activities’ value-added and capital stocks. However, categorized information-service activities’ labor input

data (such as the number of system engineers) are available only at the establishment level. Thus, it is

necessary to construct firm-level data of information-service activities’ labor input data from establishment

data.

25

information.

3.3. Framework of TFP Growth Measurement

We follow standard neoclassical growth accounting framework. In particular, we

assume constant returns to scale and flexible factors of production.

3.3.1. Output: Real Value-Added21

Value added of each firm is calculated by the following formula, which follows the

definition of the value-added in the Survey itself.

Real value-added (index) =

(Sales – Operating Expenses + Total Compensation + Rents) / Price Index

Here, as a deflator, we use the Corporate Service Price Index (CSPI) of Information Service

Industry, compiled by the Bank of Japan.

We exclude firms having negative value-added in a particular year from our samples

of that year. However, the number of these firms is very small, accounting only 0.88% of

21 One might argue, as Baily (1986) and Bartelsman and Gray (1996) do, that outputs of firms should be

gross outputs rather than value-added. However, gross outputs seem not so appropriate in information

service industries including the software industry, because outsourcing is prevalent in these indusries.

Outsourcing is not usual inputs in production process and whether to outsource some of their business or not

is a strategic decision rather than a technological constraint. In this case, the framework of gross production

treating outsourcing as usual inputs may lead to misrepresentation of production function. See Hulten

(2001) on this issue.

26

total firm-years, so that this does not cause any significant bias.

3.3.2. Inputs

As for factor inputs, we have labor hours22, equipment stock services, and building

and structure capital services. (As usual, we assume services are proportional to the

amount of stocks throughout this paper.)

We use perpetual inventory methods as much as possible to construct capital stocks

data. For depreciation rates we rely mostly on Fraumeni (1997)’s rates. For deflators, we

construct deflator data based on data supplied by P. Shcreyer of OECD, which are

harmonized price indexes of capital stocks. We construct our depreciation rates and

deflators using weights suitable for Japanese information industries23.

A distinctive characteristic of information service industries is an importance of

computer (and computer time) lease. Fortunately, the Survey has data about computer and

computer-time lease. We capitalize these lease costs to get a computer stock data. (This

conversion is necessary for consistency since we use stock data as inputs assuming service

flows are proportional to stock values.)

One note should be due for buildings and structure. We encounter many zeros in

building and structure investment. This means many small information service firms do

22 Labor hours are estimated by multiplying the number of workers by the average work hours in

information service industries, using the Monthly Labor Survey.

23 As for weights, we use those in the 1995 Input-Output Tables’ fixed-investment matrix data.

27

not own buildings and structure but simply rent them. Since we have information about

building rents, we utilize this information to estimate building and structure capital stocks.24

3.3.3. User Cost

To estimate user costs, we use the following standard formula:

ititt

ittit q

uzu

UCC )(1

1δρ +

−−

=

Here itUCC is the t -th period user cost of the i-th capital stocks, tρ is the t -th

period dividend yields of the First Division of the Tokyo Stock Exchanges,25 iδ is the

depreciation rate of the i -th stocks, tu is the effective marginal corporate tax rate of the

t-th period, and itz is the capital consumption allowance of the i -th capital stocks,26 and

itq is the price of i th capital stocks.

24 Unfortunately however, we do not have an individual firm’s building and structure rent data directly.

We only have information about the percentage of building and structure rents in the total cost on the average.

We construct imputed building rents relying on this average figure assuming individual building rents are not

different from the average.

25 Here we follow Hall (1990).

26 The effective tax rates and the discounted value of future depreciation are calculated by using

information contained in the Annual Report of Incorporated Enterprise Statistics, the Annual Report on

Finance of Local Governments, and the Survey on Incorporated Enterprises. We follow here the procedure

of Homma et al. (1984).

28

3.3.4. TFP Growth

Using data described so far, we calculate TFP growth in the following formula.

{ } ( ) { }5

1 , 1 , , 1 ,1

1ln ln ln ln2t t i t i t i t i t

i

TFPGrowth V V s s F F+ + +=

= − − + ⋅ −∑ ,

where V is real value-added, iF is the i-th inputs and is is their cost share. In particular,

we consider as inputs (a) labor hours, (b) equipment capital stocks, (c) imputed computer

capital stocks by capitalizing lease payments, (d) building and structure stocks estimated by

the perpetual inventory method, and (e) imputed building and structure stocks by

capitalizing building rents.

3.4. “Firms with Well-Established Information Service Activities”

It is not possible to compute TFP growth of all firms because very high turnovers.

For this reason, we restrict our attention on firms whose information service activities are

well established. We set the following two criteria, and firms satisfying all these criteria

are put in the following empirical analysis.

In the first step, if firms whose information service activities yield negative

value-added and/ or hire no worker in a particular year, we exclude these firms from our

sample of the particular year. If these firms show positive value-added after that year,

they are included in our sample thereafter. As reported earlier, actual occurrence of

negative value-added is rather rare, accounting less than 1% of our total firm-years.

29

In the second step, if firms do not have five consecutive years of information

service-related equipment investment, we excluded from our sample. This is necessary

since we use the five-year average investment growth rate to estimate benchmark-year

capital stocks. 27 By doing this, we restrict our attention virtually on firms with

well-established information service activities.

Through this procedure, we get 1,106 firms with well-established information

service activities. Our sample period is 1991-1998, and our sample is an unbalanced

panel.

To discern the characteristics of our samples, “firms with well-established

information service activities”, we compare the whole samples and our truncated samples in

the following tables.

Table 2-1 reports the summary statistics of the whole samples after excluding firms

with negative information-service value-added and/or no information-service worker, while

Table 2-2 shows that of our samples. Here major variables are the ratio of

information-service outsourcing to information-service sales, the number of SE (system

engineers)28, the ratio of SE to the total information-service work force, and the ratio of

27 Here we follow the method of the White Paper of the Cabinet Office. However, this five-year

criterion might be too restrictive, so that we plan to relax this assumption in the future.

28 Although we have information about SE’s in establishments, we cannot aggregate them to get

firm-level SE’s since the Survey does not collect information about what firm a particular establishment

belongs to. Consequently, we are obliged to assume that the ratio of SE’s to the total work force at the

30

information-service profits to information service operating expenses, which we consider

later as determinants of TFP growth.

Comparing Table 2-1 and 2-2, we find that quite a similar picture between the total

samples (excluding abnormal ones) and our “firms with established information services”,

except for the number of SE’s and the number of information service workers. For

example, the ratio of outsourcing to information service sales, the total samples’ average is

0.1378, while 0.1482 in firms with established information activities. Similarly, the ratio

of SE’s is 0.2839 in the total sample, while 0.3789 in our target of investigation. However,

the number of information service workers and SE’s is substantially higher in firms with

established information service activities, so that our target is slanted to larger firms. In

order to interpret our results, these characteristics of our target of investigation should be

kept in mind. 29

Let us now turn to the issue of firms’ organizational dynamics and its effects on TFP

growth in our samples. In order to discern the effects of firm dynamics, we disaggregate

headquarters is on the average its ratio for the firm as a whole. In particular, the firm-level number of SE’s

in our study is calculated by multiplying the firm’s total number of information service workers by the ratio of

SE’s to the information-service work force at the headquarters. The firm-level ratio of SE’s to the total

information-service workers is calculated by using this figure.

29 In addition, we show in Tables 2-3, Table 2-4 and Table 2-5 differences in averages for subcategories

of our samples (custom software, prepackaged software, system management and administration, online

database service) for different thresholds. To make comparison comparable, we results about single

establishments in these tables.

31

our samples further into four segments.30 These four segments are:

Group 1 (Single-Establishment Firms): firms that remain single establishments throughout

the sample period.

Group 2 (Multiple-Establishment Firms): firms with the headquarters and branch offices

throughout the sample period.

Group 3 (Expanded-to-Multi Firms): firms that start as single establishments and become

multi-establishment firms by the end of the sample period.

Group 4 (Shrunk-to-Single Firms): firms that start as multi-establishment firms and become

single establishments by the end of the sample period.

Table 3 reports the average of major variables for each segment. As for the

estimated TFP growth, Group 2 (Multi-Establishment Firms) has the highest TFP growth

rate (2.61%), while Group 4 (Shrunk to-Single Firms) exhibits the lowest (0.51%). We

will consider determinants of the TFP behind these figures. Group 2 (Multi-Establishment

Firms) has the highest outsourcing to sales ratio (17.69%), while Group 1

(Single-Establishment Firms) shows the lowest (13.09%).

30 Firms that do not conform to any of four types are excluded from segment-wise estimations in the

following empirical analysis.

32

4. Models, Estimation Results and Discussion

4.1. Choice of Variables

4.1.1. Modularization and Outsourcing

In Section 2, we have examined possible effects of modularization on information

service productivity. There we have pointed out that modularization enables firms to

outsource parts of their products in an efficient way. If this is the case, the degree of

outsourcing may measure the degree of modularization, although the degree of

modularization itself is not observable. Consequently, in our empirical analysis, we use the

degree of outsourcing, which is the ratio of outsourcing to total sales in information service

activities, as a variable representing modularization and resulting outsourcing.

According to Fujimoto (2002), there are three kinds of modularization: (a)

modularization of product architecture (modularization in development process), (b)

modularization of production process, and (c) modularization of supplier relations.

Outsourcing is a result of (3), which is based on (b) and (a). However, outsourcing may not

solely be motivated by modularization, and other factors may prompt firms to outsource

their business activities. We will explicitly consider the latter possibility in our later

interpretation of empirical results obtained in this paper.

33

4.1.2. Scale of Development Organization and the Number of SE’s

The second determinant we have examined in Section 2 is the scale of software

development. Ideally, if a measure of the average quality-adjusted scale of software

development in a firm is available, this is the variable we should use in our empirical

analysis. However, since the average scale of software development is not directly

observable, we need a proxy for this variable.

Software development is skilled-labor intensive, and thus the scale of development

is likely to be highly correlated with the size of skilled work force. In the context of

information service industries and especially the software industry, skilled work force

include SE’s (system engineers), programmers, and research scientists, about which we

have data in the Survey of Selected Service Industries, Volume of Information Service

Industries. Among them, SE’s have a pivotal role in software development, especially in

custom software one, which dominates Japanese software development.

In custom software development, to tailor software to the demand of customers is of

utmost importance. SE’s in the worker classification of the Survey are those who

responsible to listen customers’ needs and to interpret them into schemes which are

programmable. They are also responsible to select most suitable development languages

and to organize programmers to get the best out of them. Taking account of SE’s

importance in Japanese software development, we use their number as a proxy of the scale

34

of software development.31

4.1.3. Other Possible Determinants

(1) Unobservable Software Capital Stocks and the SE ratio.

As explained before, there is no information about non-tangible software capital

stocks in the Survey. However, it is inconceivable that there is no software capital stock in

information service firms. To ignore this unobservable capital stock may lead to

overestimation of TFP. Thus, we need to control these unobservable software capital

stocks using a proxy variable.

Presumably the more a firm is technology-oriented, the more its unobserved

software capital stocks are. In this sense, the ratio of the number SE’s in the total number of

information service workers, representing the firm’s technological orientation, is likely to

be a good measure of unobserved software capital stocks.

(2) “Profit-driven R&D Investment” Hypothesis and the Profit-to-Sales Ratio.

It has often been argued that the higher a firm’s profits are, the higher the level of

research and development activities is, leading to a higher TFP. This “profit-driven R&D

investment” may be relevant in information service industries in Japan since relatively

small firms in our samples may be liquidity-constrained in our sample period of 1991-1998.

31 We tried the number of programmers and that of research scientists in our preliminary analysis, but

they did not have any significant effects on TFP. Thus, we excluded them in the present analysis.

35

To control this possibility, we consider the ratio of gross profits of information service

activities to their operation costs as one determinant of TFP.

(3) Employment Adjustment Costs

In Section 2, we have pointed out a possibility that changes in firm organization

affect TFP such as transformation from a single-establishment firm to a

multi-establishment-firm. In our empirical analysis, we consider the effects of firms’

organizational dynamics on TFP by disaggregating our samples in four groups explained in

Section 2.

Beside these “adjustment costs” of organizational changes, there are other important

adjustment costs in Japan, which are employment adjustment costs. Although information

service industries are relatively new industries and that we find rather flexible labor

contracts in these industries compared with other industries, there remains a sizable cost of

employment adjustment in information service industries like other Japanese industries.

Such adjustment costs may lower overall productivity of a firm, leading to a lower TFP.

To take account of these employment adjustment costs, we consider the squared rate

of change in the number of information service workers in the following empirical analysis.

4.2. Models and Estimation

Taking account of arguments in previous sections, we formalize that the level of

TFP in information service industries is determined in the following way:

36

(1) , 0 1 , , ,1 1

lnJ T

i t i j ij t k k t i tj k t

TFP t x dα α β γ ε= = +

= + + + +∑ ∑ Ii Λ,1= ; Tt Λ,1=

Here i denotes the i-th firm and t denotes the year. Equation (1) implies that the

total factor productivity of the i-th firm’s information service activities in year t, itTFP , is

determined by a constant 0α , a time trend tt1α , microeconomic variables t,ijx discussed

in the previous sections, time dummy t,kd representing macroeconomic conditions, which

is 1 if t k= otherwise 0, and disturbances t,iε . In this formulation, the time trend is

constant but it varies across firms representing firm heterogeneity.

As for microeconomic determinants t,ijx , we consider the followings.32

1) OUT: the outsourcing-to-sales ratio in information service activities, which is

used as an index of modularization.

2) SE: the number of SE’s, which is used as an index of the scale of development

organization.

3) SE-RATIO: the ratio of the number of SE’s to the total information service

workers, which is used to take account for unobservable software capital stocks.

4) PROFIT: the ratio of gross profits to operating expenses in information service

activities.

32 See footnotes in Section 3.4 for the way these variables are constructed.

37

In some cases, we consider the effects of employment adjustment costs on TFP.

There we will add the following variable.

5) ADJUST: the squared rate of employment change.

We use a standard growth accounting procedure to get firms’ TFP growth, so that

we base our analysis in the following “growth” or first-difference formulation (2).33.

(2) , 1, , , ,1 1

lnJ T

i t j j ij t k k t i tj k t

TFP x d eα β γ= = +

∆ = + ∆ + ∆ +∑ ∑ ,

where 1t t tY Y Y+∆ = − and34

, , 1 ,i t i t i te ε ε+= −

In addition, we assume that the time trend, 1,iα , is the sum of a constant and an

unobservable individual specific effect:

1, 1i iuα α= + ,

33 In firm-level panel cases, we can estimate the TFP level using Caves et al (1982) or Good et al

(1997) approach of estimating productivity differentials across the panel. Nishimura et al. (2003) estimate

the TFP level and examine entry-exit dynamics of Japanese manufacturing firms by using a firm-level panel

data based on the Basic Survey of Business Structure and Activities. However, we start here with first

differences for analytic simplicity.

34 In this way, we implicitly assume that TFP levels are non-stationary, which are likely since TFP

changes are in many cases permanent technological changes. However, even if TFP-levels are stationary,

OLS estimators of equation (2) (or (3)) remain consistent. See Maddala (2001).

38

where 1α denotes the constant and iu denotes the unobservable individual

specific effect. Then the equation (2) can be written as ordinary one-way error component

regression model with time dummy (3). 35

(3) , 1 , , ,1 1

lnJ T

i t j ij t k k t i i tj k t

TFP x d u eα β γ= = +

∆ = + ∆ + ∆ + +∑ ∑ ,

It is well known that to apply standard procedures such as OLS causes problems if

variables are non-stationary.36 However, to apply tests of stationarity, we should take into

account our samples’ characteristics of large cross-sectional but small time dimensions (at

most nine years) and a unbalanced panel. To check stationarity of variables in our panel, we

carry unit root tests37 developed by Breitung and Meyer (1994) [BM] and Bond et al.

35 There might be a possibility that lagged ijx may influence TFP in (1) (or (2), (3)). We estimate

correlation matrices of dependent variables and independent variables including lags to check this point.

Estimated correlation matrices, however, suggest that TFP at t is correlated mostly with independent

variables at the same period. Furthermore, preliminary estimation results including these lags show

insignificant coefficients for lagged variables in most cases, so that we ignore them in our baseline empirical

results.

36 However, non-stationarity of the data may not be so problematic. Phillips and Moon (1999) argue

that even if the unit root tests fail to reject the null hypothesis, usual pooled time series and cross section

regression models yield useful information concerning long run regression relationship.

37 Here we should distinguish between unit root tests for panels with large time dimensions and those

for panels with small time dimensions, and between unit roots tests applicable balanced panels and

unbalanced ones. For panel unit root tests with small time dimensions, see Bond et al. (2002). Several

major panel unit root tests, such as those of Levin and Lin (1993) and Im et al. (2003), are not directly

applicable for unbalanced panel data like our samples. For unbalanced panel unit root tests, see Maddala

39

(2002) [OLS1, OLS2 (t-test based on OLS estimation)] for panels with large cross-sectional

dimensions but small time dimensions such as ours. 38 The results of these tests are

reported in Table 4. The unit root hypothesis is soundly rejected in all unit root tests for the

first differenced variables.

It is uncertain that whether , , 1 ,i t i t i te ε ε+= − satisfies standard liner regression model

assumptions about disturbances.39 Consequently, we estimate (3) for cases of (a) error

terms without autocorrelation, and (b) error terms with autocorrelation. For simplicity, we

consider AR (1) in the case of autocorrelation.

Furthermore, there is a good possibility that error terms of each individual firm may

have heteroscedastic structure. To take a proper account of this possibility, we also estimate

(3) by FGLS (Feasible General Least Squares) for the case that error terms in regressions

are autocorrelated and heteroscedasticity is present across firms and years, where

autocorrelation coefficients are not identical across panels.

So, we consider three estimation procedures to take account of them and to check

and Wu (1999).

38 Bond et al. (2002) point out that t-tests based on OLS estimation results provide simple robust tests

with high power in Monte Carlo simulations, in the case that the variance of the unobserved heterogeneity is

relatively small, and in the case of panels with relatively small time series.

39 That is,

( )( ) ( )( ) ( )

,

2 2, ,

, , , ,

0

, 0 for ,

i t

i t i t e

i t r j t s i t r j t s

E e

E e Var e

E e e Var e e i j r s

σ

+ + + +

=

= =

= = ≠ ≠

.

40

robustness.

Panel OLS: (random-effects model/fixed-effects model).

Panel AR1 (random-effects model/fixed-effects model): assuming error terms are

first-order autoregressive.

FGLS (Feasible General Least Squares): assuming error terms are AR (1), where

first-order autocorrelation coefficients are heterogeneous and heteroscedasticity is present

across firms and years.

4.3. Results and Discussion

4.3.1. A Brief Summary

The results of estimation is reported Table 5 through Table 10. Table 5 is the results

of Panel OLS40, Table 6 is those of Panel AR(1), and Table 7 is those of FGLS. Cases with

employment adjustment costs are shown in Table 8 (Panel OLS), Table 9 (Panel AR(1)),

and Table 10 (FLGS). In addition, each table shows the difference among firms with

different organizational dynamics over time. We show the results of all firms in our

samples (“firms with well-established information service activities”) in the column of

“All”. The results of Group 1 (single-establishment firms), Group 2

(multiple-establishment firms), Group 3 (expanded from single to multiple), and Group 4

40 In Table 5, random effect models are selected by the Hausman test.

41

(shrunk from multi to single) are shown respectively in these tables. 41

The Sample period is 1991-1998 for Table 5 through Table 7, and 1991-1997 for

Table 8 through Table 10.42 Although the number of firms varies among tables, roughly

1,100 firms are in our samples.

As shown in Tables 5 and 7, the null hypothesis of no autocorrelation in error terms

is rejected in all cases (see All, Groups 1, 2, 3 and 4) at the 1% significance level, we

hereafter concentrate our discussion mostly on Tables 6 and 9 (Panel AR(1)) and Tables 7

and 10 (FGLS), with some reference to Tables 5 and 7 to check robustness.

Let us consider estimation results of all firms, which are reported in the column

“All” of Tables 5 through 10. In all these tables, we have fairly consistent and significant

results: the coefficient of the d-OUT, d-SE, d-SE-RATIO and d-PROFIT is significant at

the 1% level, where “d-“ means the first difference. The sign of d-OUT and d-SE is

negative, while that of d-SE-RATIO and d-PROFIT is positive. Period dummies are all

significant at the 1% level when employment adjustment costs are not incorporated in

41 One may argue there might be simultaneity between TFP growth and first differences of explanatory

variables. To take this in mind, we conducted an instrument variable estimation and found qualitatively the

same results as in reported Tables 5 through 10. The results of instrumental variable estimation results are

reported in Table 11.

42 Data are available between 1991 and 1999. However, we take first differences so that we lose one

year. In addition, we lose one more year in the case of employment adjustment costs to calculate ADJUST

variables.

42

Tables 5 through 7. However, their effects are substantially reduced when employment

adjustment costs are explicitly considered in Tables 8 through 10.

4.3.2. Outsourcing and Remnants of Traditional Relationship

A remarkable result in these tables is that the outsourcing-to-sales ratio (OUT) has a

significant negative effect on TFP. This result is quite robust in all specifications. This

robust negative effect of outsourcing is striking. As in the Section 2, modularization behind

outsourcing should improve productivity, rather than reduce productivity. Thus, a robust

negative result of outsourcing on TFP suggests that outsourcing in Japanese information

service industries has a different origin from modularization, which hinders productivity.

In fact, in-depth analysis of industrial structure of the Japanese software industry

suggests that the negative effect of outsourcing stems from a remnant of traditional

subcontracting practices found in this industry. In the traditional relationship, there are main

contractors on the one side that get contracts from customers being often large corporations

and/or central as well as local governments. On the other side of the relationship, there are

sub-contractors that depend mostly on main contractors to allocate business to them.

Main contractors outsource their business not to promote the efficiency in software

development but to make sub-contractors as “buffers” of economic fluctuations to reduce

costs of adjustment necessitated by such fluctuations. It is sometimes argued that this cost

consideration of main contractors leads to “over-outsourcing” to sub-contractors in the

sense that programming expertise is not properly retained in these main contractors. If so,

43

they violate the dictum of “do not outsource the core of your competence.”

For sub-contractors, their poor financial positions make them unable to take

advantage of such outsourcing. Outsourced sub-contractors have little human-capital

investment as well as little physical-capital investment.

This inefficient subcontracting system, however, cannot survive if new efficient

firms enter the market. Unfortunately, strong preferences of buyers (consisting of local

and central governments and large corporations) to “established vendors” make entry of

new, especially small, firms very hard and thus this industrial structure is sustained for a

long time.

4.3.3. Mythical Man-Month and Communication Problems

In Section 2, we have argued that the scale of development may affect productivity

positively in some cases and negatively in others, depending on the smoothness of

communication between customers and development team members and among

development team members themselves. The results of our study strongly suggest

diseconomies of scale in software development: the scale of development organization

affects firms’ productivity negatively.

Thus, the phenomenon of mythical man-month dominates Japanese information

service industries. Effective communication to reduce costs between SE’s and their

customers and among SE’s themselves is lacking, and this is likely to be one of major

obstacles of Japanese firms to improve their efficiency in information service provision.

44

In this respect, central and local governments should play an important role to

reverse this tendency. Central and local governments are major customers of information

service firms. However, these governments are often pointed out to be rather incompetent to

articulate their real needs when they place orders to information service firms. Because of

this lack of articulation, communications between these governments as customers and SE’s

in supplier firms are not smooth and in some cases this leads to last-minute specification

changes that are very costly in software development.

To test the magnitude of this “incompetent government” effect, we put a dummy

variable representing a particular firm’s dependency on government contracts as one

explanatory variable in the FGLS estimation of Table 7. Table 12 shows the results for the

case in which the government dummy is 1 when the ratio of government contracts to the

total information service contracts exceeds 30%, 40% and 50%, respectively. In all cases,

the dummy of firms’ dependency on government contracts is statistically significant and

has a negative sign. Clearly, governments themselves should act to rectify this problem.

4.3.4. Other Determinants

As for other determinants, we have statistically significant positive effects of the

SE-RATIO as expected, which is the proxy of unobservable software capital stocks in firms.

We also get statistically significant positive effects of the PROFIT. This suggests many of

information service firms may be liquidity constrained. However, there may be other

possible explanations of these positive effects of profits on productivity, and thus the results

45

should be considered at most as suggestive.

4.3.5. Strong Effects of Employment Adjustment

Let us now turn to the issue of employment adjustment costs. Tables 8, 9 and 10

report the results. For all firms (see “All” category), we see a substantial downward effect

of employment adjustment on productivity. This result is pretty robust across estimation

methods we take, and consistent with the commonly held view of high employment

adjustment costs in Japan.

However, more in-depth analysis of data shows variation across firms’

organizational changes. In particular, while we have a strong negative effect of employment

adjustment for firms of multiple-establishment firms (Group 2) and expanded firms from

single to multiple (Group 3), we obtain no significant effect for single establishment firms

(Group 1) and a significantly positive and large effect for firms shrunk from multiple to a

single establishment (Group 4).

This last finding may be particularly interesting. This shows that when a firm takes

a drastic measure to restructure itself to trim out all subsidiaries to become a single

establishment, the more thoroughly its accompanying employment adjustment (that is,

employment reduction) is, the higher its productivity is.

4.3.6. Effects of Firms’ Organizational Changes (Group1--4)

We now examine the effects of firms’ organizational changes on firms’ productivity.

46

The basic econometric picture of all subcategories (Groups 1 through 4) is qualitatively the

same as “All”: In the OLS Panel, the Hausman test leads to random-effect models, and

there is serial correlation in error terms so that we use AR(1) and FGLS results mostly in

our discussion43.

Group-wise estimation results are similar among these Groups. OUT, SE,

SE-RATIO and PROFIT have mostly statistically significant coefficients at either 1% or

5% level and the same sign as in the case of “All”. However, the magnitude of their

effects varies among these Groups, suggesting a strong effect of firms’ organizational

changes on productivity.

As for the negative effect of outsourcing, Table 6 (Panel AR(1)) shows the

following order of magnitude:

Group 1 (single) < Group 4 (shrunk) < Group 2 (multi) <Group 3 (expanded)

Similarly, Table 7 (FGLS) has comparatively smaller effects and shows the

following order of magnitude

Group 1 (single) < Group 2 (Multi) < Group 4 (shrunk) < Group 3 (expanded).

Thus in both tables, the negative effect of outsourcing is the smallest in single

establishments and the largest in firms expanded from a single establishment to multiple

establishments.

A particularly interesting result is that the negative effect of outsourcing is far less

43 The Wald test leads to the rejection of heteroscedasticity for all Groups in FGLS.

47

pronounced in single establishments (Group 1) than multiple establishment (Group 2). This

result is a piece of supporting evidence for the hypothesis we developed in Section 4.3.2.

There we have argued that traditional relationship between large main contractors and small

subcontractors leads to inefficiency in outsourcing. This argument is more relevant to

large firms in Group 2, than small firms in Group 1, so that this observed sharp difference

strengthens our argument. However, negative effects remain in Group 1 though their

magnitude is far smaller than in Group 2. This may reflect small-scale traditional

subcontracting systems even in Group 1.

Negative effects of outsourcing are the largest in expanded firms (Group 3). When

organization is expanding, there exists larger demand for outsourcing not from efficiency

consideration but from keeping up increasing demand. Since outsourcing here is not from

modularization, resulting effects of outsourcing are rather negative. This shows the

existence of organizational adjustment costs distinct from employment adjustment costs.

Let us now turn to the issue of diseconomies of scale in software development.

Table 6 shows the following ranking in the order of magnitude:

Group 3 (Expanded) < Group 1 (Single) < Group 2 (Multi) < Group 4 (Shrunk),

while Table 7 reveals

Group 3 (Expanded) < Group 1 (Single) < Group 2 (Multi) < Group 4

(Shrunk).

Thus, a consistent picture emerges.

48

A remarkable result is that negative effects diseconomies of scale in development

organization are far less pronounced in single establishments (Group 1). (Group 3, which

are expanded from single establishments, are likely to have much in common with single

establishments with respect to software development organization.) Since single

establishments have the simplest organization structure that facilitate relatively smooth and

efficient communication both inside and outside, this result suggests our communication

argument about the cause of diseconomies of scale is in a right track. Moreover, we find

that negative effects of outsourcing are the largest in expanding organization (Group 3),

where smooth communication is rather difficult. In sum, our results strongly suggest

smooth communication is very important to achieve higher productivity.

5. Concluding Remarks

In this paper, we have examined factors determining productivity of information

service activities of firms, using most comprehensive data of information service industries

in Japan. Among possible determinants, we have focused on (1) the degree of

modularization and resulting outsourcing, (2) economies/diseconomies of scale in software

development, and (3) firms’ organizational changes.

We have found somewhat disturbing results for Japanese government officials

promoting “e-Japan Strategy II” initiatives to revitalize the Japanese economy. Firstly, we

have shown that outsourcing has persistent negative effects on total factor productivity,

49

suggesting not only productivity-enhancing modularization is not fully utilized but also

productivity-hindering remnants of traditional main-contractor-subcontractor relations still

prevail in information service industries. This shows that to increase in productivity is not a

simple task to be achieved by introducing productivity-enhancing modularization into

information service industries. A fundamental restructuring of business practices is

necessary to transform traditional main-contractor-subcontractor relations into modularized,

horizontal as well as vertical, mutually supportive community-like relations. To achieve this

goal, governments as buyers should play a crucial role.

Secondly, we have found diseconomies of scale in software development,

suggesting less efficient communication among development team members.

Communication gaps are also pointed out between information service providers

(particularly system engineers who are in charge of coordinating development) and their

customers. Among these customers, central and local governments are most important,

and our preliminary empirical study shows that these governments hinder information

service firms’ productivity, rather than enhance it, contrary to the presumption of “e-Japan

Strategy II” proponents. Lack of information service expertise on the side of central and

local governments is the cause of these problems, and these governments should rectify

their own problems when they promote productivity-enhancing practices in the industries at

the same time.

Although these tasks seem formidable, these governments have no other choice than

50

transforming themselves into informationally and technologically advanced customers of

information service firms, to promote true modularization and efficient communication

between customers and information service providers.

51

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Table 1 The Numbers of Establishments in Information Service Industries (Survey of Selected Service Industries )

1991 1992 1993 1994 1995 1996 1997 1998Single 3563 3205 3041 2902 2822 3289 3186 4361

Headquarters 1702 1883 1708 1538 1496 1379 1338 1687Branch Offices 1831 1889 1683 1542 1494 1629 1568 2200

Total 7096 6977 6432 5982 5812 6297 6092 8248

58

Table 2-1 Total Samples Excluding Negative Value-Added and Zero Workers: 1991-1998 Summary Statistics of Major Variables: Following variables are those of information service activities of firms.

Average Min. Max. # of Firms # of Firm-Year's

Labor Productivity Growth 0.0311 -8.0988 8.4861 7610 32060(0.4931)

Outsourcing to Sales Ratio 0.1378 0.0000 1.0000 10866 38746(0.1577)

Number of SE 31.7126 0.0000 9425.2220 10866 38746(142.3801)

SE to Total Work Force Ratio 0.2839 0.0000 1.0000 10866 38746(0.2567)

Profit to Operating Cost Rati 0.2827 -0.9608 161.0000 10846 38715(1.7481)

# of Workers 96.2852 1.0000 23668 10866 38746(324.0208)

Notes:

Standard deviations in parenthesis. "# of firms" column reports the number of firms with sufficient informationenabling the calculation.

59

Table 2-2 Firms with Well-Established Information Service Activities: 1991-1998 Summary Statistics of Major Variables: Following variables are those of information service activities of firms.

Average Min. Max. # of Firms # of Firm-Year's

Labor Productivity Growth 0.0417 -4.1931 4.2479 1106 6117(0.3516)

Outsourcing to Sales Ratio 0.1482 0.0000 0.8898 1106 6117(0.1442)

Number of SE's 79.3533 0.0471 ######## 1106 6117(231.8276)

SE to Total Work Force Ratio 0.3789 0.0031 1.0000 1106 6117(0.2247)

Profit to Operating Cost Rati 0.2332 -0.6533 89.5953 1106 6117(1.3172)

# of Workers 193.2424 1.0000 9430 1106 6117(479.3581)

Notes:

Standard deviations in parenthesis.

60

Table 2-3 Differences in Averages among Subcategories in Single Establishments: Case of 90% CriterionFirms whose particular segment's sales share exceeds more than 90% of their total information service sales

TFP growth 0.0341 0.0644 -0.1051 -0.0545(0.3962) (0.5534) (1.1670) (0.2027)

Labor Productivity Growth 0.0457 0.0471 0.1365 0.0638(0.3177) (0.4748) (1.0241) (0.1124)

Outsourcing to Sales Ratio 0.1626 0.0725 0.0546 0.0635(0.1502) (0.1071) (0.0760) (0.0492)

Number of SE's 42.4845 9.9575 10.2602 3.0500(140.5637) (25.1370) (20.3217) (2.4582)

SE to Total Work Force Rati 0.4912 0.3918 0.3546 0.1921(0.2160) (0.2428) (0.2009) (0.0637)

Profit to Operating Cost Rat 0.1473 0.4267 0.4897 0.0075(0.4017) (0.6632) (0.6779) (0.1306)

# of Workers 69.3514 24.7377 21.4444 16.9000(170.7314) (38.2829) (32.3246) (14.8208)

# of Firms 363 52 6 4# of Firm-Year's 1255 122 9 10

Notes:

The table shows breakdowns of firms with well-established information service activities. Standard deviations are inparenthesis.

Sales Share > 90%

Variable CustomSoftware

PrepackagedSoftware

SystemManagement

and

Online DataBase Service

61

Table 2-4 Differences in Averages among Subcategories in Single Establishments: Case of 70% CriterionFirms whose particular segment's sales share exceeds more than 70% of their total information service sales

TFP growth 0.0281 0.0436 -0.0592 0.0612(0.3987) (0.5782) (0.6637) (0.4613)

Labor Productivity Growth 0.0464 0.0265 0.0980 0.0398(0.3182) (0.4522) (0.5967) (0.2270)

Outsourcing to Sales Ratio 0.1620 0.0805 0.1127 0.0509(0.1575) (0.1126) (0.1472) (0.0517)

Number of SE's 37.3376 12.1866 21.0377 3.0213(124.3926) (30.0798) (44.3199) (2.2421)

SE to Total Work Force Rati 0.4687 0.3836 0.2948 0.1685(0.2164) (0.2385) (0.2249) (0.0710)

Profit to Operating Cost Rati 0.1774 0.4620 0.2234 0.2670(0.5150) (0.7313) (0.4262) (0.8301)

# of Workers 64.4387 27.0452 100.7742 19.3889(153.3472) (40.2962) (136.4685) (13.3907)

# of Firms 458 74 18 10# of Firm-Year's 1680 177 31 18

Sales Share > 70%

Variable CustomSoftware

PrepackagedSoftware

SystemManagement

and

Online DataBase Service

62

Table 2-5 Differences in Averages among Subcategories in Single Establishments: Case of 50% CriterionFirms whose particular segment's sales share exceeds more than 50% of their total information service sales

TFP growth 0.0250 0.0362 0.0810 -0.0010(0.4040) (0.5632) (0.7895) (0.4833)

Labor Productivity Growth 0.0425 0.0264 0.0765 0.0541(0.3202) (0.4457) (0.4346) (0.2134)

Outsourcing to Sales Ratio 0.1542 0.0894 0.1266 0.0487(0.1500) (0.1219) (0.1243) (0.0553)

Number of SE's 35.8617 9.9708 19.5121 3.0284(115.4218) (24.8576) (35.1353) (2.2996)

SE to Total Work Force Rati 0.4532 0.3440 0.2686 0.1723(0.2154) (0.2243) (0.2179) (0.1109)

Profit to Operating Cost Rat 0.1834 0.3748 0.2191 0.4587(0.5186) (0.6261) (0.5663) (1.5229)

# of Workers 64.9219 25.4161 103.2206 19.8184(144.3840) (35.6407) (133.3655) (12.6948)

# of Firms 527 113 35 13# of Firm-Year's 2010 274 68 27

Note:

The table shows breakdowns of firms with well-established information service activities. Standard deviations are inparenthesis.

Sales Share > 50%

Variable CustomSoftware

PrepackagedSoftware

SystemManagement

and

Online DataBase Service

63

Table 3 Differences in Averages Among Different Organizational Changes: 1991-1998

All Group 1(Single) Group 2(Multi) Group 3(Expanded) Group 4(Shrunk)

TFP growth 0.0197 0.0179 0.0261 0.0239 0.0051(0.4631) (0.4164) (0.4139) (0.5017) (0.5198)

Labor Productivity Growth 0.0417 0.0403 0.0433 0.0510 0.0189(0.3516) (0.2972) (0.3079) (0.4273) (0.3943)

Outsourcing to Sales Ratio 0.1482 0.1309 0.1769 0.1549 0.1325(0.1442) (1.4703) (0.1508) (0.1465) (0.1276)

Number of SE's 79.3533 19.7731 174.3493 112.1807 34.6971######## (38.2180) ######## (308.3249) (81.3331)

SE to Total Work Force Ra 0.3789 0.3848 0.3699 0.3713 0.3639(0.2247) (0.2268) (0.2160) (0.2314) (0.2170)

Profit to Operating Cost R 0.2332 0.2048 0.2215 0.3755 0.2095(1.3172) (0.6716) (0.6480) (3.0485) (0.6760)

# of Workers 193.2424 50.0860 445.6522 258.7119 94.4569######## (69.6813) ######## (584.3632) (160.6008)

# of Firm-Year's 6117 1732 1294 899 788

Notes:The table shows breakdowns of firms with well-established information service activities. Standarddeviations are in parenthesis.All: all in our samples, Group 1: firms that remain single establishments throughout the sample period,Group 2: firms that have headquarters and branch offices throughout the sample period, Group 3:firms that start as single establishments and become multi-e4stablishment firms by the end of thesample period, Group 4: firms that start as multi-establishment firms and become singleestablishments by the end of the sample period.Because our samples are an unbalanced panel, the number of firms each year is not equal.

64

Table 4　Unit Root Test：First Difference

TFP Growth d-OUT d-SE d-SE-RATIO d-PROFIT d-ADJUST

BM 0.6264 *** 0.5368 *** 0.7763 *** 0.5402 *** -0.1946 *** 0.9805 **

(0.0180) (0.0138) (0.0111) (0.0138) (0.0147) (0.0083)

OLS1 -0.3467 *** -0.2135 *** -0.1920 *** -0.2982 *** -0.4896 *** -0.0375 ***

(0.0116) (0.0132) (0.0108) (0.0126) (0.0124) (0.0055)

OLS2 -0.6734 *** -0.3474 *** -0.3758 *** -0.5020 *** -1.6247 *** -0.3809 ***

(0.0259) (0.0233) (0.0218) (0.0245) (0.0350) (0.0214)

Notes "d-" denotes the first difference. The null is that there is a unit root and "***", "**", and "*" denote significance at 1%, 5%, and10%, respectively, under the null. Standard deviations are in parenthesis. BM is the unit root test of Breitung and Meyer (1994).OLS1 and OLS2 are those in Bond et al. (2002), where OLS1is without differenced lags, and OLS2 with differenced lags. We testOLS1 and OLS2 both with and without time-dummies, but results are qualitatively similar. Thus we report here only the resultswith time dummies.

65

Table 5 Estimation Results (PANEL OLS): 1991-1998

dependent variable: TFP growthAll Group 1(Single) Group 2(Multi)Group 3(Expanded)Group 4(Shrunk)

d-OUT -0.8310 *** -0.2803 ** -0.6004 *** -1.2221 *** -0.4295 **

(0.0670) (0.1223) (0.1351) (0.1807) (0.1846)

d-SE -0.1008 *** -0.0727 *** -0.1685 *** -0.0809 *** -0.2527 ***

(0.0129) (0.0274) (0.0298) (0.0305) (0.0344)

d-SE-RATIO 0.2838 *** 0.3445 *** 0.2181 * 0.2939 ** 0.6840 ***

(0.0547) (0.0974) (0.1157) (0.1378) (0.1577)

d-PROFIT 0.0753 *** 0.1998 *** 0.1417 *** 0.0494 *** 0.1704 ***

(0.0030) (0.0121) (0.0139) (0.0035) (0.0139)

d-D1992 0.1325 *** 0.0003 0.1902 *** 0.2909 *** -0.3861 ***

(0.0320) (0.0553) (0.0663) (0.0805) (0.0887)

d-D1993 0.0989 ** 0.0102 0.0914 0.2179 *** -0.2886 ***

(0.0313) (0.0540) (0.0640) (0.0785) (0.0902)

d-D1994 0.0402 -0.0652 0.0789 0.1341 * -0.2836 ***

(0.0294) (0.0505) (0.0593) (0.0741) (0.0873)

d-D1995 0.0745 *** 0.0318 0.0844 0.1305 * -0.2235 ***

(0.0267) (0.0455) (0.0534) (0.0682) (0.0796)

d-D1996 0.0869 *** 0.0593 0.0668 0.1047 * -0.1343 *

(0.0235) (0.0396) (0.0466) (0.0604) (0.0704)

d-D1997 0.0630 *** 0.0483 0.0512 0.1620 *** -0.1386 **

(0.0196) (0.0327) (0.0384) (0.0514) (0.0582)

d-D1998 0.0396 *** 0.0216 0.0537 * 0.0976 *** -0.0317(0.0142) (0.0234) (0.0277) (0.0378) (0.0417)

Constant 0.0380 *** 0.0227 ** 0.0512 *** 0.0611 *** -0.0531 ***

(0.0067) (0.0115) (0.0134) (0.0176) (0.0193)

Hausman Test 15.7500 9.3400 12.6300 1.9000 6.2800p-value 0.1508 0.5905 0.3185 0.9988 0.8543

fixed or random random random random random randomLM ####### *** ####### *** 66.9396 *** ####### *** 70.3953 ***

# of Firms 1106 318 231 156 143# of Firm-Year' 6117 1732 1294 899 788

Notes:"d-" denotes the first difference. D-year is a year dummy."***", "**", and "*" denote significance at 1%, 5%, and 10%, respectively.The table shows breakdowns of firms with well-established information service activities. Standard deviations are inparenthesis.All: all in our samples, Group 1: firms that remain single establishments throughout the sample period, Group 2: firmsthat have headquarters and branch offices throughout the sample period, Group 3: firms that start as singleestablishments and become multi-e4stablishment firms by the end of the sample period, Group 4: firms that start asmulti-establishment firms and become single establishments by the end of the sample period.Because our samples are an unbalanced panel, the number of firms each year is not equal.LM is joint LM test for serial correlation and random effects. See Baltagi (1995).

66

Table 6 Estimation Results (PANEL-Random effects with AR1): 1991-1998

dependent variable: TFP growthAll Group 1(Single) Group 2(Multi)Group 3(Expanded)Group 4(Shrunk)

d-OUT -0.8499 *** -0.2765 ** -0.6086 *** -1.2614 *** -0.4255 **

(0.0679) (0.1232) (0.1359) (0.1826) (0.1850)

d-SE -0.1162 *** -0.0894 *** -0.1919 *** -0.0784 ** -0.2686 ***

(0.0132) (0.0278) (0.0306) (0.0311) (0.0348)

d-SE-RATIO 0.3221 *** 0.3841 *** 0.2611 ** 0.2946 ** 0.7199 ***

(0.0553) (0.0982) (0.1167) (0.1389) (0.1580)

d-PROFIT 0.0740 *** 0.2006 *** 0.1464 *** 0.0495 *** 0.1726 ***

(0.0030) (0.0119) (0.0141) (0.0034) (0.0139)

d-D1992 -0.1849 *** -0.0035 -0.2999 *** -0.3672 *** 0.4848 ***

(0.0409) (0.0702) (0.0837) (0.1023) (0.1118)

d-D1993 -0.2090 *** -0.0871 -0.2135 ** -0.3777 *** 0.3929 ***

(0.0412) (0.0702) (0.0851) (0.1039) (0.1123)

d-D1994 -0.1132 *** 0.0883 -0.1926 ** -0.3011 *** 0.4519 ***

(0.0407) (0.0690) (0.0841) (0.1016) (0.1118)

d-D1995 -0.1376 *** 0.0162 -0.2173 *** -0.3195 *** 0.4785 ***

(0.0402) (0.0680) (0.0832) (0.1013) (0.1097)

d-D1996 -0.1730 *** -0.0225 -0.2155 *** -0.2383 *** 0.3863 ***

(0.0402) (0.0680) (0.0832) (0.1003) (0.1114)

d-D1997 -0.1736 *** -0.0391 -0.1972 ** -0.3595 *** 0.4972 ***

(0.0404) (0.0686) (0.0833) (0.1011) (0.1116)

d-D1998 -0.1891 *** -0.0330 -0.2536 *** -0.3908 *** 0.4202 ***

(0.0405) (0.0685) (0.0835) (0.1010) (0.1117)

cosntant 0.1875***

0.0345 0.2513***

0.3557***

-0.4434***

(0.0377) (0.0642) (0.0783) (0.0940) (0.1020)

AR1 Coefficent -0.1273 -0.0991 -0.1454 -0.1107 -0.0869

# of Firms 1106 318 231 156 143# of Firm-Year' 6117 1732 1294 899 788Notes:d- denotes the first difference. D-year is a year dummy.

"***", "**", and "*" denote significance at 1%, 5%, and 10%, respectively.The table shows breakdowns of firms with well-established information service activities. Standard deviations are inparenthesis.All: all in our samples, Group 1: firms that remain single establishments throughout the sample period, Group 2: firmsthat have headquarters and branch offices throughout the sample period, Group 3: firms that start as singleestablishments and become multi-e4stablishment firms by the end of the sample period, Group 4: firms that start asmulti-establishment firms and become single establishments by the end of the sample period.Because our samples are an unbalanced panel, the number of firms each year is not equal.Assuming that the disturbances follow an AR(1) process

67

Table 7 Estimation Results (FGLS): 1991-1998

dependent variable: TFP growthAll Group 1(Single) Group 2(Multi)Group 3(Expanded)Group 4(Shrunk)

d-OUT -0.6283 *** -0.2063 *** -0.3336 *** -1.0684 *** -0.4127 ***

(0.0197) (0.0344) (0.0640) (0.0613) (0.0496)

d-SE -0.0762 *** -0.0880 *** -0.1156 *** -0.0691 *** -0.1877 ***

(0.0050) (0.0104) (0.0132) (0.0158) (0.0191)

d-SE-RATIO 0.2405 *** 0.4207 *** 0.2165 *** 0.2622 *** 0.5558 ***

(0.0153) (0.0371) (0.0436) (0.0579) (0.0637)

d-PROFIT 0.1049 *** 0.2153 *** 0.2058 *** 0.0595 *** 0.2083 ***

(0.0031) (0.0052) (0.0113) (0.0065) (0.0099)

d-D1992 0.0811 *** 0.0239 0.1478 *** 0.1759 *** -0.2940 ***

(0.0113) (0.0294) (0.0120) (0.0411) (0.0441)

d-D1993 0.0512 *** 0.0274 0.0844 *** 0.1122 *** -0.2227 ***

(0.0101) (0.0271) (0.0125) (0.0365) (0.0424)

d-D1994 0.0193 ** -0.0350 0.0624 *** 0.0555 * -0.2289 ***

(0.0092) (0.0237) (0.0118) (0.0308) (0.0365)

d-D1995 0.0601 *** 0.0583 *** 0.0705 *** 0.0682 *** -0.1795 ***

(0.0077) (0.0191) (0.0104) (0.0260) (0.0308)

d-D1996 0.0715 *** 0.0805 *** 0.0471 *** 0.0735 *** -0.1035 ***

(0.0065) (0.0150) (0.0092) (0.0207) (0.0237)

d-D1997 0.0552 *** 0.0543 *** 0.0307 *** 0.1144 *** -0.1186 ***

(0.0050) (0.0118) (0.0055) (0.0163) (0.0184)

d-D1998 0.0302 *** 0.0143 0.0236 *** 0.0725 *** -0.0236 *

(0.0038) (0.0093) (0.0066) (0.0136) (0.0131)

constant 0.0285 *** 0.0237 *** 0.0439 *** 0.0480 *** -0.0387 ***

(0.0020) (0.0050) (0.0026) (0.0076) (0.0075)

Log likelihood ####### ####### ####### 23.4631 #######Wald Test : p-val 0.0000 0.0000 0.0000 0.0000 0.0000

# of Firms 1086 315 226 154 139

# of Firm-Year's 6097 1729 1289 897 784

Note:d- denotes the first difference. D-year is a year dummy.

"***", "**", and "*" denote significance at 1%, 5%, and 10%, respectively.The table shows breakdowns of firms with well-established information service activities. Standard deviations are inparenthesis.All: all in our samples, Group 1: firms that remain single establishments throughout the sample period, Group 2: firms thathave headquarters and branch offices throughout the sample period, Group 3: firms that start as single establishments andbecome multi-e4stablishment firms by the end of the sample period, Group 4: firms that start as multi-establishment firmsand become single establishments by the end of the sample period.Because our samples are an unbalanced panel, the number of firms each year is not equal.Wald Test is the test statistic asymptotically distributed as chi-square(k) under the null of heteroscedasticity where k

68

Table 8 Estimation Results with ADJUST (PANEL): 1991-1997

dependent variable: TFP growthAll Group 1(Single) Group 2(Multi)Group 3(Expanded)Group 4(Shrunk)

d-OUT -0.7918 *** -0.2750 ** -0.4778 *** -1.2134 *** -0.3968 **

(0.0737) (0.1374) (0.1469) (0.1941) (0.1873)

d-SE -0.1049 *** -0.0637 ** -0.1891 *** -0.1540 *** -0.3505 ***

(0.0141) (0.0299) (0.0333) (0.0427) (0.0402)

d-SE-RATIO 0.2686 *** 0.3284 *** 0.2789 ** 0.4825 *** 0.9846 ***

(0.0597) (0.1062) (0.1279) (0.1634) (0.1672)

d-PROFIT 0.0714 *** 0.1877 *** 0.1992 *** 0.0451 *** 0.2760 ***

(0.0032) (0.0128) (0.0181) (0.0035) (0.0191)d-ADJUST -0.0231 *** 0.0060 -0.0482 ** -0.0274 ** 0.0827 ***

(0.0063) (0.0204) (0.0236) (0.0113) (0.0191)

d-D1992 0.0628 * 0.0010 0.0761 0.2403 *** -0.2182 **

(0.0358) (0.0626) (0.0814) (0.0810) (0.0915)

d-D1993 0.0329 0.0048 0.0008 0.1584 ** -0.1657 *

(0.0335) (0.0584) (0.0733) (0.0770) (0.0883)

d-D1994 -0.0215 -0.0744 -0.0027 0.0670 -0.1660 **

(0.0301) (0.0520) (0.0648) (0.0705) (0.0812)

d-D1995 0.0166 0.0178 0.0061 0.0604 -0.1428 **

(0.0258) (0.0442) (0.0548) (0.0625) (0.0698)

d-D1996 0.0363 * 0.0422 0.0011 0.0359 -0.0762(0.0209) (0.0354) (0.0431) (0.0520) (0.0572)

d-D1997 0.0181 0.0314 -0.0088 0.0909 ** -0.1000 **

(0.0148) (0.0247) (0.0295) (0.0383) (0.0407)

constant 0.0343 *** 0.0267 * 0.0436 ** 0.0694 *** -0.0314(0.0080) (0.0139) (0.0171) (0.0194) (0.0213)

Hausman Test 9.8200 5.3000 9.6000 4.5900 2.0900p-value 0.5469 0.9157 0.5665 0.9493 0.9982

fixed or random random random random random randomLM ####### *** 78.7613 *** 31.3115 *** 63.4210 *** 18.5245 ***

# of Firms 1096 318 228 155 140# of Firm-Year' 5103 1439 1085 752 656

Note:"d-" denotes the first difference. D-year is a year dummy. ADJUST is the squared rate of change in employment."***", "**", and "*" denote significance at 1%, 5%, and 10%, respectively.The table shows breakdowns of firms with well-established information service activities. Standard deviations are inparenthesis.All: all in our samples, Group 1: firms that remain single establishments throughout the sample period, Group 2: firmsthat have headquarters and branch offices throughout the sample period, Group 3: firms that start as singleestablishments and become multi-e4stablishment firms by the end of the sample period, Group 4: firms that start asmulti-establishment firms and become single establishments by the end of the sample period.Because our samples are an unbalanced panel, the number of firms each year is not equal.LM is joint LM test for serial correlation and random effects. See Baltagi (1995).

69

Table 9 Estimation Results with ADJUST (PANEL-Random Effects with AR1): 1991-1997

dependent variable: TFP growthAll Group 1(Single) Group 2(Multi)Group 3(Expanded)Group 4(Shrunk)

d-OUT -0.8119 *** -0.2701 * -0.4910 *** -1.2519 *** -0.4050 **

(0.0747) (0.1385) (0.1477) (0.1983) (0.1888)

d-SE -0.1184 *** -0.0817 *** -0.2045 *** -0.1423 *** -0.3724 ***

(0.0144) (0.0305) (0.0340) (0.0431) (0.0410)

d-SE-RATIO 0.3009 *** 0.3723 *** 0.3022 ** 0.4573 *** 1.0293 ***

(0.0604) (0.1074) (0.1290) (0.1646) (0.1685)

d-PROFIT 0.0707 *** 0.1879 *** 0.2058 *** 0.0459 *** 0.2708 ***

(0.0031) (0.0127) (0.0184) (0.0035) (0.0188)d-ADJUST -0.0245 *** 0.0069 -0.0508 ** -0.0246 ** 0.0840 ***

(0.0065) (0.0208) (0.0243) (0.0115) (0.0197)

d-D1992 -0.1057 ** -0.0126 -0.1519 -0.3291 *** 0.2730 **

(0.0459) (0.0797) (0.1030) (0.1050) (0.1172)

d-D1993 -0.1294 *** -0.0935 -0.0798 -0.3384 *** 0.2179 *

(0.0461) (0.0799) (0.1020) (0.1071) (0.1188)

d-D1994 -0.0338 0.0813 -0.0663 -0.2593 ** 0.2536 **

(0.0457) (0.0788) (0.1016) (0.1052) (0.1184)

d-D1995 -0.0551 0.0103 -0.0806 -0.2726 *** 0.2894 **

(0.0454) (0.0780) (0.1017) (0.1050) (0.1161)

d-D1996 -0.0914 ** -0.0245 -0.0857 -0.1936 * 0.2013 *

(0.0454) (0.0783) (0.1015) (0.1043) (0.1166)

d-D1997 -0.0927 ** -0.0464 -0.0675 -0.3415 *** 0.3253 ***

(0.0456) (0.0784) (0.1018) (0.1054) (0.1181)

constant 0.1085 ** 0.0413 0.1196 0.3176 *** -0.2548 *

(0.0430) (0.0744) (0.0974) (0.0975) (0.1092)

AR1 Coefficient -0.1263 -0.1083 -0.1082 -0.1525 -0.1230

# of Firms 1096 318 228 155 140

# of Firm-Year' 5103 1439 1085 752 656

Note:"d-" denotes the first difference. D-year is a year dummy. ADJUST is the squared rate of change in employment."***", "**", and "*" denote significance at 1%, 5%, and 10%, respectively.The table shows breakdowns of firms with well-established information service activities. Standard deviations are inparenthesis.All: all in our samples, Group 1: firms that remain single establishments throughout the sample period, Group 2: firmsthat have headquarters and branch offices throughout the sample period, Group 3: firms that start as singleestablishments and become multi-e4stablishment firms by the end of the sample period, Group 4: firms that start asmulti-establishment firms and become single establishments by the end of the sample period.Because our samples are an unbalanced panel, the number of firms each year is not equal.

70

Table 10 Estimation Results with ADJUST (FGLS): 1991-1998

dependent variable: TFP growthAll Group 1(Single) Group 2(Multi)Group 3(Expanded)Group 4(Shrunk)

d-OUT -0.6106 *** -0.3067 *** -0.2908 *** -1.0146 *** -0.2881 ***

(0.0170) (0.0382) (0.0490) (0.0507) (0.0519)

d-SE -0.0951 *** -0.0708 *** -0.1661 *** -0.1667 *** -0.3081 ***

(0.0030) (0.0099) (0.0145) (0.0209) (0.0151)

d-SE-RATIO 0.2669 *** 0.3764 *** 0.2980 *** 0.5281 *** 0.9632 ***

(0.0137) (0.0255) (0.0474) (0.0475) (0.0446)

d-PROFIT 0.0852 *** 0.2146 *** 0.2943 *** 0.0464 *** 0.3653 ***

(0.0025) (0.0079) (0.0173) (0.0057) (0.0162)d-ADJUST -0.0281 *** 0.0160 -0.0499 *** -0.0393 *** 0.1108 ***

(0.0023) (0.0112) (0.0088) (0.0061) (0.0127)

d-D1992 0.0101 0.0331 0.0487 *** 0.0967 *** -0.1802 ***

(0.0106) (0.0305) (0.0181) (0.0361) (0.0343)

d-D1993 -0.0144 0.0340 0.0085 0.0366 -0.1118 ***

(0.0090) (0.0268) (0.0166) (0.0325) (0.0340)

d-D1994 -0.0465 *** -0.0391 * 0.0009 -0.0262 -0.1091 ***

(0.0074) (0.0220) (0.0149) (0.0269) (0.0294)

d-D1995 -0.0014 0.0419 ** 0.0163 -0.0168 -0.0919 ***

(0.0058) (0.0170) (0.0127) (0.0204) (0.0219)

d-D1996 0.0259 *** 0.0657 *** 0.0010 -0.0070 -0.0388 **

(0.0039) (0.0118) (0.0093) (0.0144) (0.0153)

d-D1997 0.0091 *** 0.0467 *** -0.0086 0.0572 *** -0.0763 ***

(0.0028) (0.0079) (0.0072) (0.0101) (0.0110)

constant 0.0281 *** 0.0303 *** 0.0396 *** 0.0494 *** -0.0252 ***

(0.0019) (0.0053) (0.0038) (0.0075) (0.0070)

Log likelihood ####### ####### ####### 67.5614 91.2821Wald Test: p-valu 0.0000 0.0000 0.0000 0.0000 0.0000

# of Firms 1066 310 220 151 137# of Firm-Year's 5073 1431 1077 748 653

Note:"d-" denotes the first difference. D-year is a year dummy. ADJUST is the squared rate of change in employment."***", "**", and "*" denote significance at 1%, 5%, and 10%, respectively.The table shows breakdowns of firms with well-established information service activities. Standard deviations are inparenthesis.All: all in our samples, Group 1: firms that remain single establishments throughout the sample period, Group 2: firms thathave headquarters and branch offices throughout the sample period, Group 3: firms that start as single establishments andbecome multi-e4stablishment firms by the end of the sample period, Group 4: firms that start as multi-establishment firmsand become single establishments by the end of the sample period.Because our samples are an unbalanced panel, the number of firms each year is not equal.Wald Test is the test statistic asymptotically distributed as chi-square(k) under the null of heteroscedasticity, where k

71

Table 11 Estimation Results (IV Method, Random Effects Model): 1992-1998

dependent variable: TFP growthAll Group 1(Single) Group 2(Multi)Group 3(Expanded)Group 4(Shrunk)

d-OUT -1.3809 *** 0.3045 -1.2141 ** -2.4283 ** -0.9453(0.3041) (0.7727) (0.4942) (1.1603) (0.9589)

d-SE -0.8234 *** -1.4139 *** -1.0901 *** -0.0282 -1.6316 ***

(0.1059) (0.3643) (0.2339) (0.3808) (0.3120)

d-SE-RATIO 2.0495 *** 3.8917 *** 2.2545 *** 0.2646 4.0471 ***

(0.3161) (1.0640) (0.6611) (1.1460) (0.9808)

d-PROFIT 0.0404 *** 0.2062 *** 0.1083 *** 0.0404 *** 0.2163 ***

(0.0074) (0.0436) (0.0347) (0.0138) (0.0742)

d-D1993 -0.0910 ** -0.1432 ** -0.0723 -0.0477 -0.1925 *

(0.0289) (0.0641) (0.0665) (0.0556) (0.1087)

d-D1994 -0.1632 -0.2358 *** -0.1497 ** -0.1085 -0.2985 **

(0.0312) (0.0688) (0.0688) (0.0716) (0.1322)

d-D1995 -0.1100 *** -0.1467 ** -0.1380 ** -0.0626 -0.2435 **

(0.0301) (0.0676) (0.0662) (0.0744) (0.1192)

d-D1996 -0.0700 *** -0.1170 * -0.1153 ** -0.0487 -0.2050 *

(0.0268) (0.0615) (0.0580) (0.0750) (0.1105)

d-D1997 -0.0255 -0.0191 -0.0521 0.0534 -0.1296(0.0211) (0.0423) (0.0444) (0.0592) (0.0863)

d-D1998 -0.0079 -0.0320 0.0130 0.0590 0.0186(0.0151) (0.0314) (0.0308) (0.0411) (0.0607)

Constant 0.0218 ** 0.0288 * 0.0263 0.0159 -0.0154(0.0089) (0.0157) (0.0342) (0.0197) (0.0341)

# of Firms 1086 315 226 153 139# of Firm-Year' 5346 1535 1108 786 700

Notes:"d-" denotes the first difference. D-year is a year dummy."***", "**", and "*" denote significance at 1%, 5%, and 10%, respectively.The table shows breakdowns of firms with well-established information service activities. Standard deviations are inparenthesis.All: all in our samples, Group 1: firms that remain single establishments throughout the sample period, Group 2:firms that have headquarters and branch offices throughout the sample period, Group 3: firms that start as singleestablishments and become multi-e4stablishment firms by the end of the sample period, Group 4: firms that start asmulti-establishment firms and become single establishments by the end of the sample period.Because our samples are an unbalanced panel, the number of firms each year is not equal.Instruments are the first lags of explanately variables.

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Table 12 The Government-Dependency Dummy (FGLS): 1991-1998

dependent variable: TFP growth

d-OUT -0.6113 *** -0.6011 *** -0.6072 *** -0.5986 ***

(0.0201) (0.0208) (0.0202) (0.0210)d-SE -0.0780 *** -0.0789 *** -0.0784 *** -0.0787 ***

(0.0050) (0.0050) (0.0050) (0.0050)d-SE-RATIO 0.2481 *** 0.2494 *** 0.2484 *** 0.2497 ***

(0.0154) (0.0155) (0.0154) (0.0155)d-PROFIT 0.1067 *** 0.1075 *** 0.1071 *** 0.1077 ***

(0.0032) (0.0032) (0.0032) (0.0032)d-D1992 0.0828 *** 0.0836 *** 0.0839 *** 0.0831 ***

(0.0113) (0.0113) (0.0114) (0.0114)d-D1993 0.0517 *** 0.0526 *** 0.0528 *** 0.0523 ***

(0.0101) (0.0101) (0.0101) (0.0101)d-D1994 0.0203 ** 0.0210 ** 0.0211 ** 0.0207 **

(0.0092) (0.0091) (0.0092) (0.0092)d-D1995 0.0580 *** 0.0578 *** 0.0584 *** 0.0575 ***

(0.0077) (0.0077) (0.0077) (0.0077)d-D1996 0.0678 *** 0.0673 *** 0.0680 *** 0.0674 ***

(0.0065) (0.0065) (0.0065) (0.0065)d-D1997 0.0510 *** 0.0499 *** 0.0508 *** 0.0497 ***

(0.0051) (0.0052) (0.0051) (0.0052)d-D1998 0.0269 *** 0.0263 *** 0.0268 *** 0.0261 ***

(0.0039) (0.0039) (0.0039) (0.0039)Gov Dummy -0.0174 *** -0.0191 *** -0.0216 *** -0.0141 **

(0.0039) (0.0048) (0.0040) (0.0056)Constant 0.0304 *** 0.0306 *** 0.0302 *** 0.0299 ***

(0.0020) (0.0020) (0.0020) (0.0020)

Log likelihood 610.1253 609.8844 612.0432 610.3230Wald Test: p-valu 0.0000 0.0000 0.0000 0.0000# of Firms withGov_Dummy = 1 111 78 60 44# of Firms 1086 1086 1086 1086# of Firm-Year's 6097 6097 6097 6097Note:"d-" denotes the first difference. D-year is a year dummy. Gov_Dummy is a dummy that indicates large share of salesto government."***", "**", and "*" denote significance at 1%, 5%, and 10%, respectively.The table shows breakdowns of firms with well-established information service activities. Standard deviations are inparenthesis.All: all in our samples, Group 1: firms that remain single establishments throughout the sample period, Group 2: firmsthat have headquarters and branch offices throughout the sample period, Group 3: firms that start as singleestablishments and become multi-e4stablishment firms by the end of the sample period, Group 4: firms that start asmulti-establishment firms and become single establishments by the end of the sample period.Because our samples are an unbalanced panel, the number of firms each year is not equal.Wald Test is the test statistic asymptotically distributed as chi-square(k) under the null of heteroscedasticity, where kdenotes the number of firms.

Gov_Dummy = 1If Gov

Share>20%

Gov_Dummy = 1If Gov

Share>30%

Gov_Dummy = 1If Gov Share >

40%

Gov_Dummy = 1If Gov Share >

50%

73

Chapter 2:

On Possibilities of Macroeconomic Policies

When Financial Markets Are Not Sufficiently Working

74

Abstract

One of the most serious problems that the Japanese economy faces today is that

financial markets are not working very well in allocating funds: household funds stagnate in

liquid/unbacked assets, resulting in grossly insufficient funds for illiquid but profitable

physical investment. This paper investigates possibilities of macroeconomic policies to

rectify (at least partially) this underinvestment problem, given the present partial

dysfunction of financial markets. We have found that policy makers should consider not

only to promote irreversible, productive investment but also to enhance (or at least not to

hamper) self-insuring abilities of consumers using fiat money/government assets, in order

to improve social welfare. Among possible combinations of subsidies and taxes, lump-sum

investment subsidies financed by consumption taxes are found the most preferable, while

proportional investment subsidies financed by large-scale seigniorage revenues are the least

preferable.

75

1. Introduction

One of the most serious problems that the Japanese economy faces today is that

financial markets are not working very well in allocating funds. Non-performing loan

problems have plagued Japanese financial markets so long, and banks have been unable to

play their traditional role of funneling funds from the household sector to the industrial

sector.44 As a result, household funds stagnate in liquid/unbacked assets such as fiat

money and government bonds, and thus there remain grossly insufficient funds for illiquid,

but profitable physical investment. In a sense, financial markets become dysfunctional, at

least partially.

There may be two ways to analyze this seeming paralysis of financial markets and

possible remedies to this malaise. The first one is to look at this problem on the ground of

portfolio choice between safe and risky assets. Fiat money and government bonds are safe

assets while physical investment is risky. The second one is to investigate the problem from

portfolio choice between liquid and illiquid assets. Past discussions on this issue have been

concentrated on the first distinction, in particular Japanese investors’ strong preferences of

safe assets over risky ones.45 However, without proper understanding of liquidity when

44 See Nishimura and Kawamoto (2003) and references therein for Japanese banks’ problems in the

1990s and the early 2000s.

45 Japanese households’ strong preferences of safe assets have been singled out as one of major

76

financial markets are not functioning well, we cannot get a balanced diagnosis of the

financial malaise in Japan, since incomplete financial markets are often responsible for

strong demand for liquid assets, independent of risk preferences. In this paper, we pursue

this line of research, and propose welfare-enhancing macroeconomic policies to encourage

a shift of household resources toward illiquid, but productive assets.46

When financial markets are not working very well in the sense that

financial/insurance markets fail to pool idiosyncratic risks effectively among consumers,

fiat money and government bonds, both of which are not backed by productive assets, can

serve as precautionary measures or insurance devices because of their high degree of

liquidity. As a result, such partially dysfunctional financial markets may channel funds to

liquid assets at the expense of productive investment opportunities.

As a starting point of policy analysis, we assume the dysfunctional financial markets

roughly described in the previous paragraph (we later clarify specifics), and that they are

not “normalized” in near future. Then, we consider second-best policies. This

second-best approach by no means implies that measures to normalize these financial

markets are of no interest. We believe that the current seeming paralysis of financial

obstacles to promote productive investment both in popular presses and academic writings.

46 Thus, this paper can be considered as a sequel to Nishimura and Saito (2004), where the authors

examine traditional macroeconomic policies to remedy Japan’s economic problems. Here, we consider

non-traditional macroeconomic policies of directly intervening an economy of which financial markets are not

sufficiently working.

77

markets is not quick to fade away and it is likely to stay for some time. Here we simply

want to be pragmatic.

Taking these partially paralyzed financial markets as given, we explore what

macroeconomic policies, fiscal and monetary, can remedy such undesirable fund allocation,

in which funds are heavily distorted toward liquid/unbacked assets at the expenses of

illiquid/physical assets. We thus investigate measures to promote irreversible, but

productive investment, by reducing funds’ flow into liquid/unbacked assets. Moreover, we

examine analytically welfare implications of financing these measures, especially relative

desirability of various modes of taxes.

To address the issue of not-working-well financial markets formally, we adopt a

theoretical framework proposed by Dutta and Kapur (1998) for the following reasons.

Firstly, thanks to an overlapping-generations setup, this model can incorporate fiat money

or government bonds as an intrinsic intergenerational transfer scheme. Secondly, physical

investments are assumed to be irreversible and in addition, uncollateralizable. The latter

assumption of market participants’ inability to collateralize these investments signifies

(partial) paralysis or dysfunction of financial markets. Thirdly, the model assumes the

absence of insurance markets and the presence of liquidity constraints as another manifesto

of financial markets’ dysfunction. Thus, consumers cannot insure idiosyncratic shocks

directly within their own cohort. Fourthly, under these assumptions, they can only partially

insure idiosyncratic risks by carrying either money or government bonds at the expense of

78

irreversible, but productive investment opportunities. In sum, this simple framework

incorporates portfolio choice between liquid and illiquid assets in the context of incomplete

financial/insurance markets.

Under this formulation of partially dysfunctional financial markets, we explore

policy measures that may rectify these problems and improve social welfare. These

measures consist of subsidies to those who make irreversible investment, and taxes to

finance these subsidies. One of the most important policy implications from our

investigation is that such policies, combinations of subsidies and taxes, should take account

of self-insurance abilities of consumers obtained through holding liquid assets, at the same

time to promote irreversible investment.

In particular, we find that lump-sum subsidies to investors (that is, those who make

commitment to irreversible investment) should be financed not by large-scale inflation

taxes but by broad-based consumption taxes. Large-scale inflation makes insurance

through money holdings more costly to hamper self-insurance abilities of consumers.

Narrowly based taxes, slanted to relatively heavy burdens on low-income earners who are

subject to liquidity constraints, also reduce self-insurance abilities of consumers. Broadly

based consumption taxes are preferable, since under this scheme low-income earners’ (and

thus smaller spenders’) tax burdens are smaller relative to high-income earners’ (and thus

bigger spenders’). In addition, we find that lump-sum subsidies are more preferable than

proportional subsidies in that a portfolio choice between liquid and illiquid assets is less

79

severely distorted in the former than in the latter.

This paper is organized as follows. Section 2 presents a modified version of a

monetary model proposed by Dutta and Kapur (1998), and explores policy measures to

improve social welfare. Section 3 presents several numerical examples to assess qualitative

significance of the results obtained in Section 2. Section 4 contains concluding remarks.

80

2. A Theoretical Setup

This section presents an analytical setup of a simplified version of a monetary model

proposed by Dutta and Kapur (1998) incorporating partly paralyzed financial markets, and

derives properties of various policies in both positive and normative aspects. In particular,

this section establishes several “local” welfare-related propositions: namely, for cases in

which subsidies to those who make irreversible investment are rather small: to be precise, in

the neighborhood of zero. Global properties, that is, those in cases with relative large

subsidies, will be investigated in the next section by examining appropriate numerical

examples.

2. 1. Basic setup

In this paper, we follow Dutta and Kapur (1998)’s monetary model, except that we

assume unobservable income shocks as idiosyncratic risks like in Saito and Takeda (2003),

not preference shocks as in Dutta and Kapur. However, this difference is rather expository

than substantial. Moreover, the assumption of unobservable income is rather realistic,

taking account of various tax evasion schemes existent in the real economy. In addition,

sudden accidents and/or illnesses that reduce income substantially may not easily be

observable with certainty.

Consider an economy of overlapping generations of investor-consumers that

81

consists of three cohorts, young, middle-aged, and old. The population mass of each cohort

is constant over time and standardized to be unity. A young generation is endowed with 0y

units of goods, while a middle-aged generation receives an independently and identically

distributed income shock as described below. There is no endowment or income shock for

an old generation.

Let us explain constraints that each generation faces backwardly as usual. As for

the old generation, their constraints are simple: there is no choice but consume all they

have.

The middle-aged generation receives stochastic income. In the same fashion as Saito

and Takeda (2003), we assume that a middle-aged income takes hy with probability 12

and ly with probability 12 where h ly y> . These independently and identically

distributed income shocks are assumed to be unobservable, and belong to the private

information of each consumer of this generation.47 Because of the unobservability of

middle-age income risks, there exit no standard claims contingent on such risks traded in

insurance markets.

The young generation, and only the young, can make productive investment. In

terms of physical technology, we assume that one unit of investment yields 1 r+ with

47 Individual income may be observed in monetary terms, but there may be health and other problems

that are not observable from outside but change utility levels for the same income. Thus, idiosyncratic income

shocks introduced by this model may be interchangeable with idiosyncratic preference shocks assumed by

Dutta and Kapur (1998).

82

certainty two periods later, where r is assumed to be between zero and one. Let I

hereafter denote the units of investment that an representative young investor makes. As in

Dutta and Kapur (1998), this investment opportunity is assumed to be neither reversible nor

collateralizable, when these investors become middle-aged in the next period.48 Under this

assumption, this illiquid asset cannot serve as self-insurance devices for middle-age

idiosyncratic shocks.

Given the above setup where insurance contracts (standard contingent claims) are

not available and physical investment is illiquid, only liquid assets such as fiat money or

government bonds that are the means of intergenerational resource allocation, may serve as

precautionary measures or self-insurance devices for unobservable idiosyncratic shocks.

Dutta and Kapur (1998) introduce government-issued assets as intergenerational

allocation devices, thereby allowing middle-aged consumers to self-insure idiosyncratic

shocks by holding such assets. In particular, young investors are allowed to hold m units

of government-issued assets, and middle-aged consumers may carry the unspent balance of

government-issued assets up until they are old.

In this framework, on the one hand, when nominal prices are constant over time

without any aggregate shocks, such government-issued assets can be interpreted as

government bonds. With changing nominal prices, on the other hand, they can be

interpreted as fiat money whose value is depreciated by the one-period rate of inflation π .

48 This assumption may be rationalized if an action taken by a young investor is unobservable.

83

While we adopt a fiat money interpretation below, a government-issued asset denoted as

fiat money is interchangeable with government bonds as long as nominal prices are constant

over time without any aggregate risks.

To close the model, we assume that the young do not consume, while both the

middle-aged and the old consume. By constructing a current portfolio choice between liquid

assets m and illiquid assets I , and a future consumption plan, a young investor

maximizes the following lifetime expected utility with logarithmic preferences:

1 2 1 20 5(ln ( ) ln ( )) 0 5(ln ( ) ln ( ))h h l lU c y c y c y c y≡ . + + . + ,

where 1( )c y and 2 ( )c y are middle-aged and old consumption contingent on a realization

of middle-age income y . We denote an indirect lifetime expected utility (1 2

maxc c m I U, , , ) as

W .

Throughout this paper, we restrict ourselves to a steady-state equilibrium without

any attention on a transition to it. To further simplify analysis, we assume that the expected

middle-age income is unity and that the initial endowment 0y satisfies

0(1 ) 0 5( ) 1h lr y y y+ = . + = ,

Then the steady-state first best allocation where idiosyncratic shocks are insured perfectly is

84

that a young investor achieves 1 2 1 2( ) ( ) ( ) ( ) 1h h l lc y c y c y c y= = = = by allocating the whole

young endowment to irreversible investment ( 0I y= ). The corresponding welfare W is

equal to zero. Conversely, if a young investor allocates a part of his initial endowment to

liquid assets for a precautionary purpose in a steady-state equilibrium, the level of physical

investment is less than 1/(1 )r+ ( 0I y< ), and consumers suffer from welfare deterioration

as a result of giving up long-run productive opportunities. As it is later apparent, the latter

is common cases in this type of the economy when insurance is imperfect.

Starting from the above setup, Dutta and Kapur (1998) and Saito and Takeda (2003)

explore possible financial instruments to improve welfare. On the one hand, Dutta and

Kapur introduce several types of financial intermediation to fix the problem of too little

physical investment and thereby to enhance welfare. Saito and Takeda (2003), on the other

hand, examine dynamic insurance contracts with incentive compatibility as a

welfare-enhancing device.

In contrast to Dutta and Kapur and Saito and Takeda, we do not consider new

instruments into the above setting. These instruments are important welfare enhancers in

the long run, but it takes time to introduce and familiarize them to the public. Instead, we

examine possible fiscal and monetary policies enhancing welfare in this context. We

examine how a government should finance subsidies to those who can make a commitment

to irreversible investment (young investors). In particular, we investigate inflation taxes,

85

lump-sum taxes, and consumption taxes.49

2.2. Lump-sum Subsidies Financed by Seigniorage Revenues

We begin with a monetary policy, in which the government redistributes seigniorage

revenues from inflation (inflation taxes) to young investors in a lump-sum manner. In this

case, liquid assets should be interpreted as fiat money. Dutta and Kapur (1998) and Saito

and Takeda (2003) discuss this case extensively.

A young investor chooses a portfolio between fiat money ( m , measured in real

terms) and irreversible investment ( I ) given the budget constraint

0I m y s+ = + , (1)

with 00 m y s≤ ≤ + , where s is the amount of subsidies financed by seigniorage revenues

(measured in real terms). We will later discuss which money supply plan is consistent with

a steady-state level of seigniorage s .

When middle-age income y is realized, a middle-age consumer chooses 1( )c y

subject to liquidity constraints,

49 Note that by definition we cannot use income taxes, since income is assumed to be unobservable.

86

1( ) (1 )c y m yπ≤ − + .

The consumption made by old agents 2 ( )c y is the yield of investment plus any unspent

money balances,

2 1( ) (1 ) (1 )[(1 ) ( )]c y r I m y c yπ π= + + − − + − .

As examined by Saito and Takeda (2003), we concentrate our attention on the most

plausible case where a liquidity constraint is binding for only low-income earners

(consumers with a realization of ly ). We then obtain the following first-order conditions

for an optimal consumption plan given money balances held by young consumers m :

1

2 0

1 0

2 1

( ) (1 )

( ) (1 )( )1( ) 0 5 ( ) (1 )1

( ) (1 ) ( )

l l

l

h h

h h

c y m y

c y r y s mrc y y s m m y

c y c y

π

ππ

π

∗

∗

∗

∗ ∗

= − + ,

= + + − ,

+= . + − + − + ,

−

= − .

Note that for high-income earners free from liquidity constraints, the marginal rate of

intertemporal substitution, or the rate of consumption growth is equal to 1 π− under

logarithmic preferences.

The optimal holding of fiat money m∗ ( 0> ) is derived from the following

87

first-order condition:

2

20 0

1 1 2(1 ) 2(1 )(1 ) (1 )( ) (1 ) (1 )l h

rm y y s m r y s m m yπ π

π π π∗ ∗ ∗ ∗

− + − −= + .

− + + − + + − + − + − (2)

The left-hand side of the above equation is the marginal utility of money from

relaxing a liquidity constraint by one unit, while the right-hand side is the marginal

disutility from giving up one unit of physical investment. As long as 2(1 ) (1 )r π+ − − is

positive, positive subsidies s enhance money demand given an inflation rate. An increase

in steady-state inflation rates, on the other hand, leads to a decrease in money demand. As

suggested by equation (2), if returns on investment r are low, and that middle-age income

volatility ( h ly y− ) is sufficiently large, then money demand m is likely to be positive.50

Because there are only two markets (goods and fiat money) in the cross-sectional

allocation, an equilibrium inflation rate π ∗ is determined by the following equilibrium

condition of goods market (the Walras law);

0 1 1 2 2

0 0

( ) 0 5( ( ) ( )) 0 5( ( ) ( ))

0 5( ) (1 )( )h l h l

h l

y s m c y c y c y c y

y y y r y s m

∗ ∗ ∗ ∗ ∗

∗

+ − + . + + . +

= + . + + + + − .

50 To be precise, lower ly raises the left-hand side of equation (2), while larger hy and lower r

reduces its right-hand side in a way that the equality between both sides holds exactly.

88

The right-hand (left-hand) side of the above market clearing condition represents aggregate

supply (demand). As this clearing condition indicates, an increase in physical investment by

inflation taxes ( s ) improves supply sides.

With respect to monetary policy, nominal money supply M should increase by

(1 )M s Mπ π∆ = + + every period to support the above steady-state monetary equilibrium.

It is straightforward to prove that zero inflation ( 0π ∗ = ) follows immediately from zero

seigniorage revenues ( 0s = ). In other words, lump-sum subsidies can only be financed by

positive inflation taxes.

The following proposition demonstrates global and local properties of such a

money-financing policy on inflation rates, investment in illiquid assets, money demand, and

welfare.

Proposition 1. Consider the case where the government provides young investors with

lump-sum subsidies financed by seigniorage revenues. Suppose that money demand is

positive, and that liquidity constraints are binding for only low-income earners. Then, an

increase in lump-sum subsidies raises inflation rates and productive investment, but reduces

money demand. Zero inflation is suboptimal; an increase in s from 0s = is welfare

improving.

Proof. See Dutta and Kapur (1998) for a formal proof.

89

The above proposition may be interpreted intuitively as follows. An increase in

inflation rate triggered by raising seigniorage revenues leads to an increase in opportunity

costs of money-holdings. It expands productive investment as well as aggregate outputs at

the expense of money demand. As Dutta and Kapur (1998) point out, this exactly

corresponds to the Tobin effect. Thanks to this Tobin effect, an increase in inflation

improves lifetime expected utility W , so long as the size of subsidies is positive but close

to zero.

It should be noted, however, that at the same time, lower levels of money-holdings

by higher inflation rates tighten liquidity constraints for low-income earners, and damage

their self-insurance abilities. Therefore, such a money-financing macroeconomic policy

involves the trade-off between the benefit of investment promotion and the cost of

deteriorated self-insurance abilities. As demonstrated by several numerical examples of the

next section, as the rate of inflation goes up with a larger size of subsidies, the cost starts to

dominate the benefit. In other words, an optimal rate of inflation emerges where the

marginal cost is equal to the marginal benefit.

2.3. Lump-sum Subsidies Financed by Lump-sum Taxes

Next, we consider a tax-financed policy instead of a money-financed policy. To be

precise, the government is assumed to impose lump-sum taxes 0τ on middle-aged and/or

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old consumers to finance lump-sum subsidies to young investors. With constant nominal

prices ( 0π ∗ = ), liquid assets ( m ) may be interpreted as government bonds, although we

still follow fiat money interpretation below.

When a consumer is identifiable in terms of cohort, a government can differentiate

the burden of lump-sum taxes by cohort. The allocation of lump-sum taxes between

middle-aged and old consumers is parameterized by 0 1k≤ ≤ ; in particular, the burden lies

on only old consumers if 0k = , it lies on only middle-aged if 1k = , and it is broad-based

if 0 5k = . .

With this fiscal policy, the budget constraints of households are rewritten as

1 0

2 1 0

( )( ) (1 ) ( ) (1 )

c y m y kc y r I m y c y k

ττ

≤ + − ,= + + + − − − .

The inequality corresponds to the liquidity constraint faced by some middle-aged

consumers.

When liquidity constraints are binding for low-income earners (consumers with a

realization of ly ), the optimal consumption plans given money demand m are

characterized as

1 0

2 0 0

1 2 0 0

( )

( ) (1 )( ) (1 )

( ) ( ) 0 5((1 )( ) )

l l

l

h h h

c y m y k

c y r y s m k

c y c y r y s m m y

τ

τ

τ

∗

∗

∗ ∗

= + − ,

= + + − − − ,

= = . + + − + + − .

91

Note that the consumption profile of high-income earners is completely flat between

middle-aged and old consumption with zero real interest rates. A shift of tax burden from

middle-aged consumers ( 1)k = to old consumers ( 0k = ) helps to flatten the consumption

profile of low-income earners with relaxed liquidity constraints.

With a balanced budget constraint 0 sτ = , a market clearing condition can be

defined as in the previous subsection. The optimal holding of fiat money (liquid assets) is

the solution of

0 0 0 0 0

1 1 2(1 )( ) (1 ) (1 )( )l h

r rm y k r y s m k r y s m m yτ τ τ∗ ∗ ∗ ∗

+= + .

+ − + + − − − + + − + + − (3)

According to equation (3), with a decrease in s with 0k > , the marginal utility of

holding liquid assets is lowered as a consequence of relaxed liquidity constraints for

low-income earners.

The following proposition demonstrates global properties of the policy of lump-sum

subsidies financed by lump-sum taxes.

Proposition 2. Consider the case where the government provides young investors with

lump-sum subsidies and finances them by taxing on middle-aged and/or old consumers in a

lump-sum manner with an allocation weight k . Suppose that money demand is positive,

92

and that liquidity constraints are binding for only low-income earners. Then:

1. If 0 1k≤ < , then physical investment I is increasing in the size of lump-sum

subsidies. A decrease in k (a shift of tax burdens from middle-aged to old consumers)

increases investment I .

2. If 0 1k≤ < , then lifetime expected utility W is increasing in the size of lump-sum

subsidies s . A decrease in k (a shift from tax burden on middle-aged to old

consumers) is welfare enhancing.

Proof. See the appendix.

To illustrate mechanism behind this proposition, let us now consider a special case

of with 1k = , that is, the case where lump-sum taxes are imposed on only middle-aged

consumers ( 1k = ). With m m s′ ∗= − , equation (3) is rewritten as

0 0

1 1 2(1 )( )l h

rm y y m r y m m y′ ′ ′ ′= + ,

+ − + − + + (4)

which is equivalent to equation (2) with 0s π= = .

Hence, the optimal holding of fiat money (liquid assets) with 1k = increases by the

same amount of lump-sum subsidies. In addition, the amount of productive investment

becomes independent of the size of subsidies. In other words, the lump-sum taxation on

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only middle-aged consumers has no improvement on consumption plans or lifetime

expected utility. This kind of the Ricardian effect is a trivial consequence of the fact that by

construction, liquidity constraints are never binding between young and middle-aged

consumers.

As Proposition 2 implies, except for the above Ricardian case, both physical

investment and lifetime expected utility are monotonically increasing in the size of

lump-sum subsidies. Unlike the case of money-financing, the opportunity cost of holding

liquid assets is independent of the size of subsidies. Therefore, a combination of lump-sum

subsidies and lump-sum taxes promotes irreversible investment, relaxes liquidity

constraints as a result of an increase in money-holdings, and consequently improves welfare,

as long as liquidity constraints are still binding for middle-aged consumers with low

income.

Within this class of lump-sum taxes, taxing on only old consumers is least

“regressive” in the sense that low-income earners (middle-age low-income consumers)

incur the least tax burden. As several numerical examples of the next section shows, the

least regressive tax is most welfare-improving, because it relaxes substantially liquidity

constraints for low-income earners, thereby allowing them to smooth consumption to a

larger extent.

94

2.4. Lump-sum Subsidies Financed by Consumption Taxes

In this subsection, we consider another fiscal policy in which the government

finances lump-sum subsidies to young investors by broad-based consumption taxes.

Obviously, consumption taxes are less “regressive” than lump-sum taxes in the sense that

low-income earners (middle-age low-income consumers) incur comparatively less tax

burden.51 In fact, under our assumption that income taxes are not enforceable due to the

unobservability of income, consumption taxes may be the least regressive among tax

instruments available in this model.

In this case, the budget constraints of consumers are rewritten as

1 1

1 2 1

(1 ) ( )(1 ) ( ) (1 ) ( )

c y m yc y r I m y c y

ττ+ ≤ + ,+ = + + + − ,

where 1τ is a rate of consumption tax. The former equation corresponds to the liquidity

constraint faced by middle-age consumers.

When liquidity constraints are binding for only low-income earners (consumers with

a realization of ly ) as we assume throughout this paper, the optimal consumption plans

given m are

51 They consume less so that they pay less consumption tax than high income consumers.

95

11

2 01

1 2 01

1( ) ( )11( ) ( )10 5( ) ( ) ((1 )( ) )

1

l l

l

h h h

c y m y

rc y y s m

c y c y r y s m m y

τ

τ

τ

∗

∗

∗ ∗

= + ,++

= + − ,+.

= = + + − + + .+

The optimal holding of fiat money (liquid assets) is the solution of

0 0

1 1 2(1 )( )l h

rm y y s m r y s m m y∗ ∗ ∗ ∗= + .

+ + − + + − + + (5)

Under the balanced budget constraint, the equilibrium tax rate is determined by

1 1 2 1 20 5 ( ( ) ( ) ( ) ( ))h h l ls c y c y c y c yτ ∗ ∗ ∗ ∗= . + + + , or

10(1 ) 0 5( ) ( )l h

sr y y y r s m

τ ∗= .+ + . + + −

(6)

The following proposition demonstrates global and local properties of the policy of

lump-sum subsidies financed by consumption taxes.

Proposition 3. Consider the case where a government provides lump-sum subsidies with

young investors and finances them by taxing equally on middle-age and old consumption.

Suppose that money demand is positive, and liquidity constraints are binding for only

low-income earners. Then:

96

1. Physical investment I is increasing in the size of subsidies. The amount of investment

is greater than in the case of the lump-sum taxation on only old consumers, and smaller

than in the case of the lump-sum taxation on only middle-aged consumers.

2. If the parameters of the model are such that money demand m∗ satisfies

0(1 )(1 )( ) (1 ) ( )2(1 ) (1 )

l h lr r y s r r y r y yr r rm + − + − + − +∗

+ + −< , then life-time expected utility W is increasing in the

size of subsidies. The level of welfare is higher than in the case of the lump-sum

taxation only on old consumers in the neighborhood of 0s = .

Proof. See the appendix.

As in the case with lump-sum taxes, an increase in subsidies to young investors

raises both irreversible investment and life-time expected utility (so long as s is not large).

However, this consumption-tax-financed welfare-enhancing policy has an implication

different from the lump-sum-tax-financed policy, with respect to the self-insurance ability

of low-income consumers, especially when the size of subsidies is rather small. That is, the

self-insurance ability of low-income consumers can insure themselves more effectively

under the consumption-tax-financed policy than under lump-sum-tax-financed policy.

In the above proposition, it is shown that if parameters of the model are such that

money demand is less than a certain value then we get a definitive result on utility and

welfare. This technical condition establishes a global property of increasing life-time utility

97

and a local property of the dominance of the consumption-tax-financed polity over the

lump-sum-tax-financed policy around 0s = . The condition may appear a bit restrictive,

but it is a sufficient condition, not a necessary condition. In fact, although we are not able

to establish a necessary condition yet, intensive numerical simulations reveal that, even if

money demand m∗ is larger than 0(1 )(1 )( ) (1 ) ( )2(1 ) (1 )

l h lr r y s r r y r y yr r r

+ − + − + − ++ + − , and even with large-scale

subsidies, these properties are likely to hold true for a wide range of parameters. In the next

section, we will show several numerical examples to confirm this observation.

The welfare advantage of the consumption taxation over lump-sum taxation may be

intuitively explained as follows. Substituting (6) into the optimal consumption plans gives

1 1

2 0 2

1 2 0 3

( )

( ) (1 )( )

( ) ( ) 0 5((1 )( ) )

l l

l

h h h

c y m y k s

c y r y s m k s

c y c y r y s m m y k s

∗

∗

∗ ∗

= + − ,

= + + − − ,

= = . + + − + + − ,

where

10

02

0

03

0

;(1 )( ) 0 5( )

(1 )( ) ;(1 )( ) 0 5( )

(1 )( ) .(1 )( ) 0 5( )

l

l h

l h

h

l h

m ykr y s m m y y

r y s mkr y s m m y y

r y s m m ykr y s m m y y

+=

+ + − + + . +

+ + −=

+ + − + + . ++ + − + +

=+ + − + + . +

,

Here 1k and 2k represent the consumption-tax-financed policy’s sharing rate among

middle-aged and old low-income earners, and 30.5k is that of high-income earners,

respectively, in financing one unit of subsidies s .

98

It is easy to prove that 1 2 1k k< < and that 1 2 30.5( ) 0.5k k k+ < . The former

inequality implies that middle-aged low-income earners bear the least tax burden; while the

latter indicates that tax burden lies more on high-income earners than on low-income

earners. Such less regressive aspects of consumption taxes help make consumption

fluctuations less volatile for low-income earners, thereby maintaining their self-insurance

ability.

The result that less regressive taxes (i.e., smaller tax burdens on lower income

earners) help self-insuring ability of low-income earners may be related to Kimball and

Mankiw (1989)’s finding, where progressive taxes on income work to reduce a need for

self-insurance in the presence of uninsured shocks. In addition, it may be related to Bewley

(1983), where the central bank may not be able to implement an optimal monetary policy by

the lump-sum taxation, because the upper bound of lump-sum taxes is determined by the

lowest income level among consumers in the context of incomplete insurance. In this way,

lump-sum taxes having strong regressive effects (disproportionately higher tax burdens on

lower income earners) may not be suitable for welfare-improving policies.

2.5. Subsidies Proportional to Physical Investment

Lastly, we consider the case where government provides young investors with

subsidies proportional to the amount of their irreversible investment. Let ρ be a

proportional rate of investment subsidies. Thus, a budget constraint for a young investor is

99

rewritten as

0(1 )I m yρ− + = .

Noting that the amount of subsidies s in the previous section is now replaced by

01 ( )y mρρ− − , we can obtain the optimal holding of fiat money (liquid assets) and

consumption plans in this case.

As demonstrated by numerical examples of the next section, in this case of

proportional subsidies, physical investment is increased more than in any cases of

lump-sum subsidies, for a given size of subsidies. Such subsidy policies, designed directly

to the investment promotion, raise opportunity costs of money-holdings in an indirect

manner, and thus these subsidies distort allocation between illiquid and liquid assets.

Consequently, life-time expected utility decreases through this distortion. In particular,

welfare is substantially lower in the case where proportional investment subsidies are

financed by more regressive lump-sum taxes, because of damaged self-insurance abilities

for low-income earners in addition to serious distortion between liquid and illiquid assets.

100

3. Numerical Examples

In the previous section, by establishing analytical propositions including local and

global properties, we have examined qualitative effects of policy combinations of subsidies

to young consumers and taxes on middle-aged and/or old consumers: to be more precise,

lump-sum subsidies to young consumers who make irreversible investment or subsidies

proportional to the amount of investment, that are financed by either of seigniorage

revenues, several types of lump-sum taxes, or consumption taxes. In this section, we

evaluate quantitatively those policy combinations by presenting numerical examples. In

particular, the current section deals with cases where the size of subsidies is not only in the

neighborhood of zero, but also far away from zero.

A set of parameters is chosen as follows. As is assumed in the previous section,

0(1 ) 0 5( ) 1h lr y y y+ = . + = holds so that the level of welfare of the first best allocation is

equal to zero. Numerical examples deal with the case where liquidity constraints are

binding for only middle-aged low-income earners, and money demand is positive. For this

purpose, we choose low returns on irreversible investment ( 0 05r = . ), as well as volatile

income fluctuations ( 1 4hy = . and 0 6ly = . ). Numerical results are presented in Tables 1

and 2 as well as Figures 1 through 13.

101

3.1. Lump-Sum Subsidies to Investors

We begin with cases of relatively small-scale lump-sum subsidies. Figure 1 draws

welfare levels (life-time expected utility) against the size of lump-sum subsidies. These

numerical results confirm the discussion developed in the previous section. There is no

impact on life-time expected utility in the case of lump-sum taxes on only middle-aged

consumers ( 1k = ); the Ricardian effect works perfectly to cancel increases in after-subsidy

income exactly by increases in money-holdings.

Except for this case, welfare is increasing in the size of lump-sum subsidies at 0s = .

Thus, subsidies to young consumers who make irreversible investment tend to rectify

under-investment caused by incomplete markets. As Figure 3 shows, irreversible

investment is indeed increasing in the size of subsidies in all cases except for lump-sum

taxes on only middle-aged consumers.

In the case that lump-sum subsidies increase initially from zero levels, the

seigniorage-revenue financing is most effective in promoting welfare among the five cases.

As a hump-shaped curve demonstrates in Figure 1, however, the seigniorage-revenue

financing’s benefits of fixing under-investment by subsidies is quickly dominated by costs

of money-holdings as a result of higher inflation provoked by larger seigniorage revenues.

In this case, money demand is decreasing substantially in the size of seigniorage revenues

(see Figure 2); this aspect of declining money demand damages the self-insurance ability of

middle-aged consumers who may be subject to liquidity constraints in our assumption. Note

102

that the optimal level of seigniorage is rather low (about 0.8% of average middle-aged

income).

Among the other cases, welfare is monotonically improving in the size of lump-sum

subsidies. A major reason for this is that lump-sum subsidies to young consumers help not

only promote irreversible investment, but also allow for increases in money-holdings

thereby relaxing the liquidity constraint that is faced potentially by middle-aged consumers.

In this regard, the case of broad-based consumption taxes is most effective because

low-income earners, both middle-aged and old, benefit from the least tax burden. In the

case of lump-sum taxes, taxing on only old consumers ( 0k = ) dominates taxing on both

middle-aged and old consumers ( 0 5k = . ) in that liquidity constraints are relaxed to a larger

extent for middle-aged consumers.

The above discussion is confirmed by Table 1 that reports the consumption profile

for these five cases; except for the case of money-financing, the consumption profile of

high-income earners, who are free from liquidity constraints, is completely flat between

middle-aged and old consumption with zero real interest rates. According to this table,

middle-aged low-income consumers are damaged most in the case of money-financing, and

least in the case of consumption taxes.

Combined with Table 2 that reports tax burden rates for each case,52 we find that

52 In the case of consumption taxes, tax burden rates are the same among consumers or equal to

/( 1)τ τ + except for middle-aged high-income consumers who save a part of income.

103

idiosyncratic shocks are self-insured more under less regressive taxation. As Table 2 shows,

our numerical example confirms the observation that, as discussed in the previous section,

consumption taxation is the least regressive among available tax instruments in our model.

3.2. Proportional Investment Subsidies

Next, we turn to the case of small-scale subsidies proportional to the amount of

irreversible investments. Figure 4 draws welfare (life-time expected utility) against the rate

of subsidy ρ ,53 not the size of subsidy s. As these figures demonstrate, the welfare

impact follows the same pattern as in the case of lump-sum subsidies.

In an essential way, however, proportional subsidies differ from lump-sum subsidies,

because the former involves allocation distortion between irreversible investment and liquid

asset (money). According to Figures 7 through 11 that compare the two types of subsidies

on the same scale s , the welfare under proportional subsidies (solid lines) is inferior to the

welfare under lump-sum subsidies (dotted lines).

A major reason for these numerical results is that proportional taxes promote

irreversible investment only at the expense of money demand, thereby making liquidity

53 When m is decreasing in ρ and 0 1ρ≤ < , the corresponding amount of subsidies

01 ( )y mρρ− − is monotonically increasing in ρ . Even if m is increasing in ρ ,

01 ( )y mρρ− − is decreasing except for quite large decrements. An increase in ρ indeed

leads to greater amounts of subsides in all of our numerical examples.

104

constraints more binding for middle-aged low-income earners (see Figures 5 and 6). In

particular, life-time expected utility deteriorates substantially, when proportional subsidies

are financed by either seigniorage revenues or lump-sum taxes on only middle-aged

consumers; that is, the ability of middle-aged consumers to self-share income risks is

damaged seriously due to not only subsidies, but also taxes.

3.3. Large-Scale Subsidies

As examined before, in the case of money-financing, social costs of money-financed

subsidies quickly dominate their social benefits even for small-scale subsidies. Thus, for the

analysis of large-scale subsidies, we concentrate our attention on subsidies financed by

lump-sum taxes (in particular, 0k = ) and consumption taxes.

Let us first consider lump-sum subsidies to physical investment. As shown in

Figure 11, life-time expected utility is monotonically increasing even for large subsidies.

Moreover, this figure shows that consumption-tax-financing has more desirable properties

than lump-sum-tax-financing. For example, while marginal welfare is diminishing, the level

of welfare under consumption-tax financing is still increasing even at 0 5s = . (which

corresponds to 50% of average middle-aged income).

We make two remarks on these cases of lump-sum subsidies. First, this monotonic

property depends crucially on the assumption that middle-aged low-income earners are

subject to liquidity constraints. Second, the welfare level is still far below the first-best

105

welfare (equal to zero).

Turning to proportional subsidies, consumption-tax-financing is again preferable to

lump-sum-tax financing. However, as hump-shaped curves indicate in Figure 12, welfare

begins to deteriorate when subsidies become substantially large. In other words, costs of

allocation distortion of proportional subsidies between money and physical investment

eventually dominate benefits of promoting irreversible investment, as subsidies exceed a

certain threshold.

3.4. Summary

One important implication of the above exercises is that the government may be able

to improve social welfare by certain combinations of subsidies to investors and taxes on

financial asset holders, when financial markets are not sufficiently working, in the sense

consumers are not fully insured against future income fluctuations. These combinations of

policies may increase social welfare in two ways. First, they may increase irreversible

investment. Second, they may reduce welfare-reducing effects of liquidity constraints

through higher money-holdings. Since money-financed subsidies promote irreversible

investment only at the expense of self-insurance abilities, they are proved to be inferior to

tax-financed subsidies. Moreover, by the same token, broad-based

consumption-tax-financed subsidies are shown to be superior to lump-sum-tax-financed

subsidies, since the latter hampers more self-insurance abilities of consumers since relative

106

tax burdens of lump-sum taxes are larger when income is lower, making liquidity

constraints severer.

The latter point may be worth emphasizing. When financial markets are

insufficiently working in the sense that consumers are not fully insured against future

income fluctuations, less regressive taxes are preferable in terms of risk-sharing. In our

context, consumption taxes are the least regressive, while lump-sum taxes on only

middle-aged consumers are the most regressive. Both lump-sum taxes only on old

consumers and broad-based lump-sum taxes are mildly regressive in that old low-income

earners still bear relatively heavy tax burdens.

In sum, a policy in which less distortionary subsidies (lump-sum subsidies) are

financed by less regressive taxes (consumption taxes) is the best policy combination in our

model. Money-financed subsidies are preferable only for rather small-scale subsidies;

otherwise, high inflation triggered by large seigniorage revenues makes money-holdings

quite costly, thereby deteriorating self-insurance abilities substantially.

107

4. Concluding Remarks

This paper has adopted an overlapping generations framework proposed by Dutta

and Kapur (1998) to formalize not-well-functioned financial markets of the 1990s and the

early 2000s in Japan, in which there are too much funds in liquid assets such as both money

and government bonds, and too little for irreversible investment. Assuming that the

problems are not rectified soon, we have investigated possible second-best policy measures

to improve social welfare, in the form of subsidies and taxes. We have found that under this

set up, policy makers should consider not only to promote irreversible, productive

investment but also at least not to hamper self-insuring abilities of consumers through fiat

money/government assets, in order to improve social welfare.

Our findings include that (i) unlike in models with complete markets, broad-based

consumption taxes are preferable to broad-based lump-sum taxes because middle-aged

low-income earners, who are subject to liquidity constraints, incur the least tax burden, (ii)

in the case of money-financing, costs of money-holdings from inflation dominate benefits

of promoting irreversible investment except for rather small-scale subsidies, and (iii)

lump-sum subsidies are better than proportional subsidies because allocation distortion

between liquid and illiquid assets hampers welfare greatly in the latter case.

Among possible combinations of subsidies and taxes, lump-sum investment

subsidies financed by consumption taxes are found the most preferable, while proportional

108

investment subsidies financed by large-scale seigniorage revenues are the least preferable.

This result suggests that a policy combination putting the first priority on the promotion of

irreversible productive investment is not necessarily most desirable. A macroeconomic

policy, which is designed to promote irreversible investment, should also take account of

self-insurance abilities of consumers who are likely to face liquidity constraints, in order to

improve social welfare. Here the “regressiveness” of taxes is the issue, since regressive

taxes, in which low income consumers heavily burdened by the taxes, hamper self-insuring

abilities of consumers.

109

Appendix

Proof of Proposition 2.

1. First, we show that investment is increasing in s and decreasing in k when

0 1k≤ < . We have already shown that an increase in s has no effect with investment in

the case of 1k = . Let m∗ be the optimal money demand in the case of lump-sum taxation.

Substituting m m s′ ∗= − and 0s τ= into (3) yields

1

0 01

1 1 2(1 ) (1 )( )k

l hr

rm y k s y m s r y m m y′ ′ ′ ′−

+

= + .+ + − − − + − + +

The left-hand side is decreasing in m′ . The right-hand side is, on the other hand, increasing

in m′ when 0r > . An increase in s or a decrease in k lowers the left-hand side and

raises the right-hand side. In order to equate both sides, m′ should be reduced. Thus

investment 0I y m′= − is increasing in s and decreasing in k .

2. Next we will show that welfare is increasing in s and decreasing in k using

the marginal welfare with respect to s or k . The level of welfare is

{ }

{ }00 5( ) 0 5ln (1 )( ) (1 )

ln 0 5 (1 )( )

l

h

W m y ks r y s m k s

r y s m m y s

∗ ∗

∗ ∗

= . + − + . + + − − −

+ . + + − + + − .

110

Then the envelope theorem implies that

* * * *0 0

0 5 0 5( )(1 )( ) ( ) (1 )( )l h

dW k r k rds m y ks r y m r k s r y m m y rs

. . += − + +

+ − + − + + + − + + +

* *0

1 10 5 0 5 0,(1 )( ) ( )l

k km y ks r y m r k s

− −= . + . >

+ − + − + + (7)

as long as 0 1k< < , 1( ) 0lc y > , and 2 ( ) 0lc y > . The last equality is derived from the

first-order condition (3). Thus, welfare is increasing in s .

The envelope theorem also indicates that

0

0 5 0 5 0(1 )( ) ( )l

dW s sdk m y ks r y m r k s

. .= − + < ,

+ − + − + +

as long as middle-aged liquidity constraints of low-income earners are binding

( 1 2( ) ( )l lc y c y< , or

(1 )( ) (1 )l lm y ks r y s m k s∗ ∗− − < + + − − −

for each s and k ). Thus, welfare is decreasing in k .

Proof of Proposition 3.

1. Given Proposition 2 and 0I m y s+ = + , it suffices to demonstrate that the money

demand under the consumption taxation is equal to that under the lump-sum taxation case

111

with some k . The first order conditions (3) and (5) indicate that the right-hand (left-hand)

side is increasing (decreasing) in m∗ (optimal money demand).

Consider the following two extreme cases. When 0k = , the left-hand side of

equations (3) and (5) are equal to each other for each m∗ , while the right-hand side of

equation (3) is always greater than that of equation (5). Thus the optimal money demand

under the consumption taxation is larger than that under the lump-sum taxation with 0k = .

When 1k = , the right-hand (left-hand) side of equation (3) is greater than that of

equation (5). However, the increment of the left-hand side ( 1 1l lm y s m y∗ ∗+ − +

− ) is greater than

that of the right-hand side (0

2(1 )( ) h

rr y s m m y s∗ ∗+ + − + + −

-0

2(1 )( ) h

rr y s m m y∗ ∗+ + − + +

) for each 0s ≥ , because

returns of investment are between zero and one by assumption, and because the

consumption of middle-aged low-income earners is lower than that of high-income earners

( 1 1 1( ) ( )hc y c y< , or

00 5{(1 )( ) }l hm y s r y s m m y s∗ ∗ ∗+ − < . + + − + + −

for each 0s ≥ ). Hence, the optimal money demand under the consumption taxation is

smaller than that under the lump-sum taxation with 1k = .

As is shown by the proof of Proposition 2, the money demand in the lump-sum case

is monotonically decreasing in k . Hence, there exists some k such that the optimal

money demand under the lump-sum taxation is equal to that under the consumption

112

taxation.

2. Next, we will prove that the marginal welfare with respect to s in the

consumption tax case is positive, and that the marginal welfare at 0s = is greater than that

in the lump-sum tax case with 0k = . Let m∗ the optimal money demand in the

consumption tax case. The level of welfare is

0

1

0 5( ) 0 5ln(1 )( )

ln 0 5 (1 )( ) 2 ln(1 )l

h

W m y r y s m

r y s m m y τ

∗ ∗

∗ ∗

= . + + . + + −

+ . + + − + + − + .

By equation (6) and the envelope theorem, the marginal welfare in the consumption

case is

0 0

0 5 (1 )( ) (1 )( ) h

dW rds y s m r y s m m y∗ ∗ ∗

. += +

+ − + + − + +

0

2(1 )(1 )( ) 0 5( )l h

rr y s m m y y∗ ∗

+−

+ + − + + . +

0

2(1 )( ) 0 5( )l h

rr y s m m y y s∗ ∗+ .

+ + − + + . + − (8)

The last term is positive. Using equation (5), we obtain

113

0

0

0 0 0

1 12( ) (1 )( )

2(1 )(1 )( ) 0 5( )

1 1 1 12( ) 0 5( )

l h

l h

l h l

dWds m y r y s m m y

rr y s m m y y

r rm y x x y y x

∗ ∗ ∗

∗ ∗

∗

> ++ + + − + +

+−

+ + − + + . ++ +

= − + − ,+ + . −

where 0 0(1 )( ) 0 5( )l hx r y s m m y y∗ ∗≡ + + − + + . + >0.

Since 0 001 12( ) 0 5( ) 0x x

l h lr rm y x y y∗+ +− + > + . − − > by the assumption

0(1 )(1 )( ) (1 ) ( )2(1 ) (1 )

l h lr r y s r r y r y yr r rm + − + − + − +∗

+ + −< ,

0 0 0

1 1 1 1 02( ) 0 5( )l h l

r rm y x x x y y∗

+ +− > − > .

+ + . −

Therefore, 0dWds > .

On the other hand, by equation (7), the marginal welfare in the lump-sum tax case

with 0k = ,

0

0 5(1 )( ) (1 )( ) h

r rr y s m s r y s m m y s

.+ ,

′ ′ ′+ + − − + + − + + −

is increasing in m′ (optimal money demand) in the case of the lump-sum tax. Since the

optimal money demand in the case of the consumption taxation m∗ is greater than m′ , it

suffices to show that the following function is positive at 0s = :

114

10 0

0

0

0 0

0 5 (1 )( )(1 )( )2(1 )

(1 )( ) 0 5( )2

(1 )( ) 0 5( )0 5

(1 )( ) (1 )( )

h

l h

l h

h

rV sy s m r y s m m y

rr y s m m y y

rr y s m m y y s

r rr y s m s r y s m m y s

∗ ∗ ∗

∗ ∗

∗ ∗

∗ ∗ ∗

. +≡ +

+ − + + − + ++

−+ + − + + . +

++ + − + + . + −

.− − .

+ + − − + + − + + −

When 0s = , 1(0)V is written as

1

0 0

0

0 5 1(0)(1 )( ) (1 )( )

2(1 )( ) 0 5( )

h

l h

Vr y m r y m m y

r y m m y y

∗ ∗ ∗

∗ ∗

.= +

+ − + − + +

− .+ − + + . +

The right-hand side corresponds to the collection of the first three terms of equation (8) that

are divided by 1 r+ with 0s = . Hence, 1(0)V is positive similarly.

115

References

Bewley, T. (1983) “A Difficulty with the Optimum Quantity of Money,” Econometrica

51,1485-1504.

Dutta, J. and S. Kapur (1998) “Liquidity Preference and Financial Intermediation,” Review

of Economic Studies 65, 551-571.

Kimball, M. and G. Mankiw (1989) “Precautionary Saving and the Timing of Taxes,”

Journal of Political Economy 97, 863-879.

Nishimura, K. G., and Y. Kawamoto (2003) “Why Does the Problem Persist?: ‘Rational

Rigidity’ and the Plight of Japanese Banks,” The World Economy, 26, 301-324,

reprinted in: Saxonhouse, G. R., and R. M. Stern, eds., Japan’s Lost Decade,

Oxford: Blackwell, 2004, 35-58.

Nishimura, K. G., and M. Saito (2004) “On Alternatives to Aggregate Demand Policy to

Revitalize the Japanese Economy,” forthcoming in Asian Economic Papers 2 (2).

Saito, M. and Y. Takeda (2003) “On an Interaction between Monetary Environment and

Incentive Compatibility: A Case of Dynamic Insurance Contracts,” mimeographed.

116

Table 2.1. Consumption profiles in the case of lump-sum subsidiesseigniorage revenues

0.764 0.751 0.736 0.7150.828 0.844 0.863 0.8881.196 1.204 1.214 1.2281.196 1.186 1.174 1.159

lump-sum tax (k=0)0.764 0.764 0.764 0.7640.828 0.828 0.829 0.8291.196 1.196 1.196 1.196

lump-sum tax (k=0.5)0.764 0.764 0.764 0.7640.828 0.828 0.828 0.8281.196 1.196 1.196 1.196

lump-sum tax (k=1)0.764 0.764 0.764 0.7640.828 0.828 0.828 0.8281.196 1.196 1.196 1.196

consumption tax0.764 0.764 0.765 0.7650.828 0.829 0.829 0.831.196 1.196 1.195 1.195

0.000s = 0.005s = 0.010s = 0.015s =1( )lc y2( )lc y1( )hc y2( )hc y

0k =

0.000s = 0.005s = 0.010s = 0.015s =1( )lc y2( )lc y1 2( ) ( )h hc y c y=

0.000s = 0.005s = 0.010s = 0.015s =1( )lc y2( )lc y1 2( ) ( )h hc y c y=

1k =

0.000s = 0.005s = 0.010s = 0.015s =1( )lc y2( )lc y1 2( ) ( )h hc y c y=

0.000s = 0.005s = 0.010s = 0.015s =1( )lc y2( )lc y1 2( ) ( )h hc y c y=

117

Table 2.2Tax burden rates in the case of tax-financing and lump-sum subsidies

(unit: %)lump-sum tax (k=0)

middle-aged low-income 0 0 0 0old low-income 0 0.6 1.19 1.78middle-aged high-income 0 0 0 0old high-income 0 0.42 0.83 1.24

lump-sum tax (k=0.5)middle-aged low-income 0 0.33 0.65 0.97old low-income 0 0.3 0.6 0.9middle-aged high-income 0 0.16 0.32 0.48old high-income 0 0.21 0.42 0.62

lump-sum tax (k=1)middle-aged low-income 0 0.65 1.29 1.93old low-income 0 0 0 0middle-aged high-income 0 0.32 0.64 0.95old high-income 0 0 0 0

consumption taxmiddle-aged low-income 0 0.25 0.5 0.75old low-income 0 0.25 0.5 0.75middle-aged high-income 0 0.19 0.38 0.57old high-income 0 0.25 0.5 0.75

0.000s = 0.005s = 0.010s = 0.015s =

0 . 5k =

0.000s = 0.005s = 0.010s = 0.015s =

0.000s = 0.005s = 0.010s = 0.015s =

0.000s = 0.005s = 0.010s = 0.015s =

(1) The tax burden rate is defined as the ratio of tax payment relative to total income

including endowment as well as saving balances held in terms of fiat money or government

bonds.

118

-5 0 5 10 15

x 10-3

-0.0508

-0.0506

-0.0504

-0.0502

-0.05

-0.0498

-0.0496

-0.0494

-0.0492

-0.049

s

welfare

inflation tax lump-sum tax (k=0) lump-sum tax (k=0.5)lump-sum tax (k=1) consumption tax

Figure 1.

Welfare comparison in the case of constant subsidies

119

-5 0 5 10 15

x 10-3

0.12

0.13

0.14

0.15

0.16

0.17

0.18

s

money

inflation tax lump-sum tax (k=0) lump-sum tax (k=0.5)lump-sum tax (k=1) consumption tax

Figure 2.

Money demand comparison in the case of constant subsidies

120

-5 0 5 10 15

x 10-3

0.77

0.78

0.79

0.8

0.81

0.82

0.83

0.84

0.85

s

investment

inflation tax lump-sum tax (k=0) lump-sum tax (k=0.5)lump-sum tax (k=1) consumption tax

Figure 3.

Physical investment comparison in the case of constant subsidies

121

-5 0 5 10 15

x 10-3

-0.0508

-0.0506

-0.0504

-0.0502

-0.05

-0.0498

-0.0496

-0.0494

-0.0492

-0.049

rho

welfare

inflation tax lump-sum tax (k=0) lump-sum tax (k=0.5)lump-sum tax (k=1) consumption tax

Figure 4.

Welfare comparison in the case of subsidies proportional to investment

122

-5 0 5 10 15

x 10-3

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

rho

money

inflation tax lump-sum tax (k=0) lump-sum tax (k=0.5)lump-sum tax (k=1) consumption tax

Figure 5.

Money demand comparison in the case of subsidies proportional to investment

123

-5 0 5 10 15

x 10-3

0.77

0.78

0.79

0.8

0.81

0.82

0.83

0.84

0.85

rho

investment

inflation tax lump-sum tax (k=0) lump-sum tax (k=0.5)lump-sum tax (k=1) consumption tax

Figure 6.

Physical investment comparison in the case of subsidies proportional to investment

124

-5 0 5 10 15

x 10-3

-0.0508

-0.0506

-0.0504

-0.0502

-0.05

-0.0498

-0.0496

-0.0494

-0.0492

-0.049

s

welfare

lump-sum subsidies proportional subsidies

Figure 7.

Welfare comparison in the case of seigniorage revenues

125

-5 0 5 10 15

x 10-3

-0.0508

-0.0506

-0.0504

-0.0502

-0.05

-0.0498

-0.0496

-0.0494

-0.0492

-0.049

s

welfare

lump-sum subsidies proportional subsidies

Figure 8.

Welfare comparison in the case of lump-sum taxes (k=0)

126

-5 0 5 10 15

x 10-3

-0.0508

-0.0506

-0.0504

-0.0502

-0.05

-0.0498

-0.0496

-0.0494

-0.0492

-0.049

s

welfare

lump-sum subsidies proportional subsidies

Figure 9.

Welfare comparison in the case of lump-sum taxes (k=0.5)

127

-5 0 5 10 15

x 10-3

-0.0508

-0.0506

-0.0504

-0.0502

-0.05

-0.0498

-0.0496

-0.0494

-0.0492

-0.049

s

welfare

lump-sum subsidies proportional subsidies

Figure 10.

Welfare comparison in the case of lump-sum taxes (k=1)

128

-5 0 5 10 15

x 10-3

-0.0508

-0.0506

-0.0504

-0.0502

-0.05

-0.0498

-0.0496

-0.0494

-0.0492

-0.049

s

welfare

lump-sum subsidies proportional subsidies

Figure 11.

Welfare comparison in the case of consumption taxes

129

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-0.055

-0.05

-0.045

-0.04

-0.035

-0.03

-0.025

-0.02

s

welfare

lump-sum tax (k=0)consumption tax

Figure 12.

Welfare comparison between consumption taxes and lump-sum taxes (k=0) in the case of constant

subsidies

130

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

rho

welfare

lump-sum tax (k=0)consumption tax

Figure 13.

Welfare comparison between consumption taxes and lump-sum taxes (k=0) in the case of subsidies

proportional subsidies