COMPETITION AND INNOVATION: AN INVERTED-U RELATIONSHIP* PHILIPPE AGHION NICK BLOOM RICHARD BLUNDELL RACHEL GRIFFITH PETER HOWITT This paper investigates the relationship between product market competition and innovation. We find strong evidence of an inverted-U relationship using panel data. We develop a model where competition discourages laggard firms from innovating but encourages neck-and-neck firms to innovate. Together with the effect of competition on the equilibrium industry structure, these generate an inverted-U. Two additional predictions of the model���that the average technologi- cal distance between leaders and followers increases with competition, and that the inverted-U is steeper when industries are more neck-and-neck���are both supported by the data. I. INTRODUCTION Economists have long been interested in the relationship between competition and innovation, but economic theory seems to be contradicted by the evidence. Theories of industrial organi- zation typically predict that innovation should decline with com- petition1 while empirical work finds that it increases.2 This paper reexamines this relationship using panel data and finds clear nonlinearities in the form of an inverted-U shape, illustrated by Figure I, which plots patents against the Lerner index, with an exponential quadratic overlay. The possibility of an inverted-U relationship between competition and innovation was hinted at by Scherer [1967], who showed a positive relationship between * The authors would like to thank Daron Acemoglu, William Baumol, Timo- thy Bresnahan, Jan Boone, Wendy Carlin, Paul David, Janice Eberly, Edward Glaeser, Dennis Ranque, Mark Shankerman, Robert Solow, Manuel Trajtenberg, Alwyn Young, John Van Reenen, two anonymous referees, and participants at seminars including Canadian Institute of Advance Research, Harvard University, and Massachusetts Institute of Technology. Financial support for this project was provided by the Economic and Social Research Council (ESRC) Centre for the Microeconomic Analysis of Public Policy at the Institute for Fiscal Studies, and the ESRC/EPSRC Advanced Institute of Management (AIM) initiative. The data were developed with funding from the Leverhulme Trust. 1. See our discussion in Section III below. However, the replacement effect in Arrow [1962] and the efficiency effects in Gilbert and Newbury [1982] and Rein- ganum [1983] go in the opposite direction. 2. See Geroski [1995], Nickell [1996], and Blundell, Griffith, and Van Reenen [1999]. �� 2005 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. The Quarterly Journal of Economics, May 2005 701

patenting activity and firm size in the cross section, with a di- minishing impact at larger sizes when allowing for nonlinearities. To our knowledge, no existing model of product market competi- tion and innovation predicts an inverted-U pattern. An explanation for these results could be pieced together by combining agency models3 with Schumpeterian models however, this seems unsatisfactory. Instead, we develop an extension of Aghion, Harris, and Vickers [1997]4 that can fit the entire curve. In this model both current technological leaders and their follow- ers in any industry can innovate, and innovations by leaders and followers all occur step-by-step. Innovation incentives depend not so much upon postinnovation rents, as in previous endogenous growth models where all innovations are made by outsiders, but upon the difference between postinnovation and preinnovation rents of incumbent firms. In this case, more competition may foster innovation and growth, because it may reduce a firm���s preinnovation rents by more than it reduces its postinnovation rents. In other words, competition may increase the incremental profits from innovating, and thereby encourage R&D investments aimed at ���escaping competition.��� This should be particularly true in sectors where incumbent firms are operating at similar tech- nological levels in these ���neck-and-neck��� sectors, preinnovation rents should be especially reduced by product market competi- tion. On the other hand, in sectors where innovations are made by laggard firms with already low initial profits, product market competition will mainly affect postinnovation rents, and therefore the Schumpeterian effect of competition should dominate. The essence of the inverted-U relationship between competi- tion and innovation is that the fraction of sectors with neck-and- neck competitors is itself endogenous, and depends upon equilib- rium innovation intensities in the different types of sectors. More specifically, when competition is low, a larger equilibrium frac- tion of sectors involve neck-and-neck competing incumbents, so that overall the escape-competition effect is more likely to domi- nate the Schumpeterian effect. On the other hand, when compe- tition is high, the Schumpeterian effect is more likely to domi- nate, because a larger fraction of sectors in equilibrium have innovation being performed by laggard firms with low initial profits. The inverted-U shape is confirmed by our U. K. panel 3. Hart [1983], Schmidt [1997], Aghion, Dewatripont, and Rey [1999]. 4. See also Aghion, Harris, Howitt, and Vickers [2001]. 702 QUARTERLY JOURNAL OF ECONOMICS

data, and it is robust to a number of controls and experiments.5 Our model provides additional testable predictions on the rela- tionship between competition and the composition of industries, and more specifically between competition and the average de- gree of ���neck-and-neckness��� in the economy, which are also vin- dicated by the data. The rest of the paper is structured as follows. Section II displays the empirical evidence on the existence of an inverted-U relationship between competition and innovation. Section III ar- gues that existing models of competition and innovation cannot account for the inverted-U pattern. We develop a theoretical rationale for this relationship, derive some additional empirical predictions, and validate them with data. Finally, Section IV concludes. II. THE IMPACT OF COMPETITION ON INNOVATION The early empirical literature, inspired by Schumpeter [1943], estimated linear cross-sectional relationships and typi- cally found a negative relationship between competition and in- novation, confirming the theoretical prejudices of the era. Scherer [1967] developed this research by allowing for additional nonlin- earities, and in a cross-sectional analysis of Fortune 500 firms discovered a significant inverted-U shape, with higher competi- tion initially increasing then decreasing the rate of innovation. But research since then has returned to estimating linear speci- fications for example, Nickell [1996] and Blundell, Griffith, and Van Reenen [1999] both find a positive linear effect of competition on innovation. In this paper we allow for a nonmonotonic relationship. II.A. Measuring Innovation There is a large literature on measuring innovation inten- sity, with the most commonly used measures being R&D expen- diture and patenting activity. We use the average number of 5. To deal with the possible endogeneity of competition, we use U. K. data and exploit the major policy reforms undertaken over the 1970s and 1980s, which dramatically changed the nature and extent of competition across industries and over time. The radical policies of the Thatcher administration, the introduction of the European Single Market Program (SMP), and the reforms imposed by the Monopolies and Mergers Commission together provide a number of policy changes that vary across time and industries and allow us to identify the causal impact of competition on innovation. 703 COMPETITION AND INNOVATION

patents taken out by firms in an industry, and to reflect the heterogeneous value of patents, we weight each patent by the number of times it has been cited by another patent. These data are generated by matching the NBER patents database6 to ac- counting data on firms listed on the London Stock Exchange (from Datastream). Our sample includes all firms with names beginning ���A��� to ���L��� plus all large R&D firms. After removing firms involved in large mergers or acquisitions and those with missing data, we have an unbalanced panel of 311 firms spanning seventeen two-digit SIC codes over the period 1973���1994. We also have information on citations to and from each patent, which enables us to construct a count of citation-weighted patents. We take the average value of citation-weighted patents of firms within each industry (SIC code) in each year. We do not observe a sufficient number of firms in all industries in all years, so our resulting industry level panel is also unbalanced with 354 industry-year observations. Some descriptive statistics are pro- vided in Appendix 2. II.B. Measuring Competition Our main indicator of product market competition is the Lerner Index, or price cost margin, following Nickell [1996]. This measure has several advantages over indicators such as market share or the Herfindahl concentration index. These other mea- sures rely more directly on precise definitions of geographic and product markets, which is particularly difficult in our application, as many U. K. firms operate in international markets, so that market concentration measures based only on U. K. data may be extremely misleading. The price cost margin we use is measured by operating prof- its net of depreciation, provisions and an estimated financial cost of capital7 divided by sales, liit operating profit financial cost sales . 6. See Hall, Jaffe, and Trajtenberg [2000]. The NBER database contains the patents taken out in the U. S. patent office, which is where innovations are effectively patented internationally, dated by the time of application. 7. The cost of capital is assumed to be 0.085 for all firms and time periods and the capital stock is measured using the perpetual inventory method. The invert- ed-U shape is robust to excluding this financial cost from the Lerner measure, principally because it is relatively small and constant over time. 704 QUARTERLY JOURNAL OF ECONOMICS

Our competition measure is the average of this across firms within the industry, (1) cjt 1 1 Njt i j liit, where i indexes firms, j indexes industry, t indexes time, and Njt is the number of firms in industry j in year t. A value of 1 indicates perfect competition (price equals marginal cost) while values below 1 indicate some degree of market power. In comput- ing this index, we use the entire sample of Stock Market Listed firms in each industry, not only those in the patenting subsample. II.C. A Nonlinear Relationship We use flexible nonlinear estimators to investigate the basic shape of the relationship between competition and innovation. Denoting n as the hazard rate and c as the measure of competi- tion, we start by defining the competition innovation relationship as (2) n eg c , where g( ) is some unknown function. Suppose that the patent process has a Poisson distribution with hazard rate (2), then the expected number of patents satisfies (3) E p c eg c . Parametric models that study count data processes typically base their specification on the Poisson model with a parametric (linear) form for g(c), but they relax the strong assumptions on higher moments.8 We follow this approach in our empirical analy- sis, basing our estimator on the first moment (3). We adopt a flexible specification for g(c), because we are particularly inter- ested in allowing the data to determine the shape of the relation- ship between innovation and product market competition. It is very likely that different industries will have observed levels of patenting activity that have no direct causal relationship with product market competition, but reflect other institutional features of the industry. Consequently, industry fixed effects are essential to remove any spurious correlation or ���endogeneity��� of this type. Time effects are also included to remove common mac- roeconomic shocks. Conditional on industry and time effects, in- 8. See Hausman, Hall, and Griliches [1984], for example. 705 COMPETITION AND INNOVATION