Innovation by Heterogeneous Leaders*

Date01 October 2019
Published date01 October 2019
DOIhttp://doi.org/10.1111/sjoe.12347
Scand. J. of Economics 121(4), 1673–1704, 2019
DOI: 10.1111/sjoe.12347
Innovation by Heterogeneous Leaders*
Tatsuro Iwaisako
Osaka University,Osaka 560-0043, Japan
iwaisako@econ.osaka-u.ac.jp
Kazuyoshi Ohki
Kanazawa University, Kanazawa 920-1192, Japan
kazuyoshi.ohki@gmail.com
Abstract
We develop a Schumpeterian growth model in which leaders and followers conduct research
and development (R&D) activities and in which leaders have different-sized quality leads over
their followers, and thus have different profit flows. We show that leaders with larger quality
leads make smaller R&D investments; this result is consistent with the actual behaviorsof some
previous leader firms, such as Sony and Eastman–Kodak.Moreover, we showthat subsidizing the
R&D of followers can promote the aggregate R&D of leaders, because promotion of followers’
R&D decreases (increases) the number of leaders with larger (smaller) quality leads and smaller
(larger) R&D investments.
Keywords: Heterogeneous leaders; R&D subsidies; Schumpeterian growth
JEL classification:L16; O31; O38
I. Introduction
In developed economies, total factor productivity (TFP) growth from
research and development (R&D) activities is the most important source of
sustained economic growth. Since the influential contributions by Grossman
and Helpman (1991) and Aghion and Howitt (1992), many studies have
developed R&D-based growth models and have examined how aggregate
R&D activities and the growth rate of output are determined. However,
most of the earlier studies have two features that are not consistent with
the evidence. First, in most of the earlier studies, innovation is conducted
by new entrants or follower firms, not by the leaders that have state-of-the-
art technology in each industry. In reality, in many industries, the leader
firm conducts R&D activities and contributes to innovation. For example,
*The authors would like to thank two anonymous referees for their helpful comments and
suggestions, which have improved this paper significantly, and Daishoku Kanehara, Akihisa
Shibata, Miho Sunaga, Hitoshi Tanaka, and participants at the JEAAnnual Meeting 2013 and
Kyoto Universityfor their helpful comments on an earlier version of the paper. The authors also
gratefully acknowledge the financial support of a JSPS Grant-in-Aid for Scientific Research (No.
16H02026 and No. 17K03623). Any remaining errors are, of course, our own responsibility.
C
2019The Authors. The Scandinavian Journal of Economics published by John Wiley& Sons Ltd on behalf of F ¨oreningen
or utgivande avthe SJE /The editors of The Scandinavian Journal of Economics.
This is an open access article under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivs License, which
permits use and distribution in any medium, provided the original work is properlycited, the use is non-commercial and no
modifications or adaptations are made.
1674 Innovation by heterogeneous leaders
Bartelsman and Doms (2000) reported that 75 percent of TFP growth results
from R&D activities by incumbent firms. Second, in most of the earlier
studies, profits from innovation are symmetric among firms. However, in
reality, the profits from innovation differ among firms. Commencing with
Scherer (1965), many empirical studies have examined the distribution of
profits among firms.
To construct an R&D-based growth model that is consistent with this
evidence, we assume that the R&D technology of leader firms exhibits
decreasing returns, and that the size of the quality increment is determined
by a random draw from a given distribution. As a result, we develop a
Schumpeterian growth model where leader firms have different profits and
some of them conduct R&D activities.
First, examining this heterogeneous-leaders model, we find the following
interesting tendency in the leader firms’ behaviors. The leader that has
higher quality compared with its followers and earns larger profits makes
smaller R&D investments.1The reason is as follows. The leader whose
quality lead over followers is larger can earn higher profit and thus has
a higher value. Therefore, the net benefit of R&D for the leader with
larger quality lead is lower, and thus a higher-quality leader has lower
R&D expenditure. This theoretical result is consistent with actual firm
behavior. Sony succeeded in developing the high-quality flat cathode-ray
tube TV and did not invest enough in the development of a liquid crystal
TV. Consequently, Sony did not obtain a large share of the market for liquid
crystal TVs. Eastman–Kodak and Polariod were earlier developer of film
cameras. They earned larger gross margins from their existing business (i.e.,
film photography) and did not spend enough on digital photography (see
Carroll and Mui, 2008). Consequently, they went bankrupt because of the
diffusion of digital cameras.
Second, we examine the effects of subsidizing the R&D of followers,
and we obtain a counterintuitive result. R&D subsidies for followers
naturally promote R&D by followers. However, this promotion of followers’
R&D can also promote aggregate R&D by leaders. The reason is as follows.
The promotion of followers’ R&D impedes R&D by each individual leader.
However, the promotion of followers’ R&D also shifts the distribution of
1Akcigit and Kerr (2018) have shown results similar to ours.They examined the situation where
multi-product incumbents conduct both internal and external R&D. Internal R&D is undertaken
by leaders to improve their product, whereas external R&D is undertaken by both leaders and
followers to obtain a leadership position for products that they do not currently possess. They
showed that larger firms have a smaller ratio of R&D to their size, because internal R&D is
proportional to the firm size while external R&D is constant. They mentioned that the reason
why large firms conduct proportionately less external R&D relates to the difficulty of protecting
their advancedposition while engaging in too many projects, the limits of managerial capabilities,
organizational rigidities, etc.
C
2019The Authors. The Scandinavian Journal of Economics published by John Wiley& Sons Ltd on behalf of F ¨oreningen
or utgivande avthe SJE /The editors of The Scandinavian Journal of Economics.
T. Iwaisako and K. Ohki 1675
leaders. Because of the first result – that is, leaders with larger leads
make only smaller investments – the stationary distribution of leaders with
larger leads and smaller investment is large compared with that of the
distribution from which the quality lead is drawn. Thus, the promotion of
followers’ R&D (i.e., the promotion of R&D by entrants, whose quality lead
is determined by a random draw) reduces the distribution of leaders with
larger leads and smaller R&D investment and increases that of leaders with
smaller leads and larger R&D investment. If this positive effect associated
with the changing distribution outweighs the negative effects on individual
firms’ R&D, then the promotion of followers’ R&D increases leaders’
aggregate R&D. This result implies that R&D subsidies for new entry firms
are effective in raising aggregate productivity growth, and it provides a
rationale for actual promotion policies for R&D activities by new entry
firms.2
Some earlier studies, including Thompson and Waldo (1994),
Segerstrom and Zornierek (1999), and Segerstrom (2007), developed R&D-
based growth models where the leader firms conduct R&D activities, and
re-examined how aggregate R&D is determined. However, in these models,
there is no factor that brings about heterogeneity among the leaders,
and thus the leader firms are symmetric among industries. In contrast,
Minniti et al. (2013) incorporated the uncertainty of innovation size (quality
increment) into Segerstrom (1998) and constructed a Schumpeterian growth
model where the innovation size and profits are different among industry
leaders. However, this study assumes that R&D technology has constant
returns, and focuses the analysis on the equilibrium where the leader firms
do not conduct R&D activities.3Therefore, constructing a realistic model
where heterogeneous leaders innovate is one of the contributions of this
study.
Recently, Denicolo and Zanchettin (2012) developed a quality-ladder
model where leaders can innovate several times, and consequently they
2In this paper, we focus our analysis mainly on the effect of subsidies for followers’ R&D.
There are two reasons for this. First, in reality, subsidy policies for entrants (followers) are
often used. A good example is the Small Business Innovation Research (SBIR) program in
the United States, which intends to help small businesses conduct R&D. In addition, one of
the innovation-promoting policies that the European Commission decided to implement in the
“Innovation Union” was to promote entry and R&D activities by small and medium-sized
enterprises (European Commission, 2010). Second, some empirical studies, such as Blundell
et al. (1995) and Nickell (1996), imply that competition can enhance R&D. We can regard
subsidies for followers’R&D as one type of competition policy, and thus our result can support
the above empirical result partly.
3Chu (2011) developed the quality-ladder model where there are heterogeneous industries and
thus heterogeneous R&D firms. However, he also assumes constant returns of R&D technology
and focuses the analysis on the equilibrium without R&D activities byleaders as in Minniti et al.
(2013).
C
2019The Authors. The Scandinavian Journal of Economics published by John Wiley& Sons Ltd on behalf of F ¨oreningen
or utgivande avthe SJE /The editors of The Scandinavian Journal of Economics.

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