The role of diminishing returns in neo-Schumpeterian growth theory

Summary. This paper generalizes Segerstrom [5], a dynamic general equilibrium model of endogenous growth through quality improvements in which innovation and imitation are modeled as the outcomes of research and development (R&D) races. Specific factors introduced into the technologies of both R&D activities achieve diminishing returns to scale in R&D. The comparative-static results of subsidies to R&D activities depend on the degree of diminishing returns to scale in R&D. When there is (is not) a sufficient degree of diminishing returns to R&D, a subsidy to innovative activity increases (decreases) innovative activity. Received: July 8, 1994; revised version: June 9, 1997     

The Evolution of Cooperation in Patent Races:Theory and Experimental Evidence

In a dynamic patent race model we analyze the formation and breakup of joint ventures in relation to: (a) the relative as well as absolute position of the firms in the race; (b) the degree of competition in the ex post market. Fudenberg et al. (1983) studied the main features of a patent race when firms compete in R&D, showing that firms in the same position compete fiercely, dissipating the rent from innovation. By contrast, we show that if firms can cooperate or compete in R&D, and if they start in the same position, they cooperate at the outset but break their agreement in the last stage if they will be serious competitors in the downstream market, while, if they can collude in the ex post market, they cooperate from the outset and they innovate jointly. When the firms are lagged by one step, cooperation does not take place, except in the case the value of the race is negative and the cost saving due to cooperation is large. However, cooperation never occurs if the leader is more than one step ahead. Finally, when the firms cooperate in R&D they proceed to the discovery at low speed. We test these conclusions via experiments on the incentive to cooperate during the course of a race. The results of a sample of 86 races support our theoretical conclusions, although the experimental findings are less clear-cut than the theoretical ones.     

Racing in two dimensions

In this paper we study an industry in which there is an ongoing sequence of R&D races between two firms. Firms are engaged in product innovation. Products are horizontally and vertically differentiated. There are two key characteristics/dimensions to products, and the level at which these are embodied in products can be increased by R&D. At each time firms can spend R&D on improving their product in one or both dimensions. We allow the possibility of economies scope — so R&D undertaken in one dimension can spillover to the other. The question we are interested in is whether a firm that is ahead in a single dimension but behind in another will focus all its R&D effort in the area in which it is ahead (product specialisation), or whether it will try to do R&D in both dimensions in the hope that it might get ahead in both and end up with a superproduct that dominates in both characteristics. The outcome of this R&D competition determines a Markov transition probability matrix determining the evolution of the industry. We show that when the R&D technology is characterized by constant returns then the only steady-state outcome is one in which the economy stays forever in a position in which one firm produces a super-product and the other gives up doing R&D altogether. This outcome is unaffected by the degree of economies of scope. When the R&D technology is characterised by decreasing returns, then the industry will visit all states and so will exhibit both product specialisation and superproduct dominance at various times. Now the extent of economies of scope matters and we show that the greater the extent of economies of scope, the less likely is the industry to exhibit product dominance, and the more likely it is to exhibit product specialisation.     

Process R&;D and Product Line Deletion by a Multiproduct Monopolist

Relative to single-product firms, a multiproduct monopolist can internalize the negative externalities of its R&D investments (the ``cannibalization effect') in two ways: (1) To lower R&D investment for each product; and (2) To delete some of its product lines so as to enlarge the market size for the remaining lines. It is shown that line deletion is profitable if products are close substitutes. If products are not close substitutes, the multiproduct monopolist keeps all product lines and invests less in cost-reducing R&D than single-product firms engaging in Cournot competition with product differentiation. However, it invests more in R&D than single-product firms if there are significant economies of scope in R&D, or if the oligopolistic firms can cooperate in their R&D decisions.      

Effect of piracy on innovation in the presence of network externalities

This paper analyzes the impact of simultaneous increases in piracy (piracy effect) and network externalities (network effect) on R&D investment. A single firm's R&D investment increases (or decreases) if the network effect (or piracy effect) is dominant. With R&D competition, if the firms “significantly” differ with respect to their R&D efficiencies and if the piracy effect dominates the network effect then the less efficient firm's R&D investment increases and that of the more efficient firm's decreases. In this case, the overall probability of successful innovation increases. The reverse holds if the network effect dominates the piracy effect. If the firms are “less” asymmetric then their R&D investment either increases or decreases depending on the relative strengths of the piracy and network effects.     

R&D competition, absorptive capacity, and market shares

This paper deals with an oligopolistic industry where firms are engaged in cost-reducting R&D activity to maximize their market shares. The existence and uniqueness of a feedback-Nash-optimal R&D strategy for each firm are discussed. Our simulations highlight that variations in spillovers hardly influence the firms' R&D investment, if their absorptive capacities to exploit extramural knowledge depend on their R&D efforts. Moreover, extramural knowledge cannot completely replace in-house R&D. However, a high level of public R&D favors the firm with the most restrictive R&D expenditure constraint and/or with the lowest initial R&D stock, provided it invests in R&D.     

Intensity of R&D competition and the generation of innovations in heterogeneous setting

This paper discusses the role of technological spillovers and technological races in dynamic strategic interactions setup. Two firms invest simultaneously into new products creation and into further development of the quality of these products. Each firm may benefit from the costless technological spillover in case of technological leadership of the other firm. At the same time they cooperate in the joint creation of new products. Three different scenarios emerge: constant technological leadership, the technological leapfrogging and symmetric outcome with or without potential spillovers. R&D is maximal for the first scenario and minimal for the symmetric play under the threat of spillover with endogenous specialization of firms’ activities in cases of constant leadership and leapfrogging. Definition of technological competition intensity as inverse to the technology gap allows to recover inverted-U relationship between those two in a multidimensional context.     

Multistage R&D competition and patent policy

In this paper a model of multistage R&D patent policy is investigated. We study the impact of the duration of patent protection for intermediate products on R&D races when the discovery of the final product requires the accomplishment of an intermediate step. Using a multistage model where firms choose their levels of research investment at each stage, we find all subgame-perfect equilibria of the game. We also determine how competition affects a firm's level of research investment at different stages of the R&D competition.     

R&D competition between public and private sectors

We investigate a mixed market where a welfare-maximizing public research institute competes against profit-maximizing private firms. We investigate R&D competition by using a standard model of patent races where each firm chooses both its innovation size and R&D expenditure. We find that the innovation size (R&D expenditure) chosen by the public institute is too small (too large) from the viewpoint of social welfare, respectively, and so the government should control the public institute appropriately. We also discuss the welfare implications of privatization of public research institutes.     

The impact of public R&D expenditure on business R&D*

This paper attempts to quantify the aggregate net effect of government funding on business R&D in 17 OECD Member countries over the past two decades. Grants, procurement, tax incentives and direct performance of research (in public laboratories or universities) are the major policy tools in the field. The major results of the study are the following: Direct government funding of R&D performed by firms has a positive effect on business financed R&D (except if the funding is targeted towards defence activities). Tax incentives have an immediate and positive effect on business-financed R&D; Direct funding as well as tax incentives are more effective when they are stable over time: firms do not invest in additional R&D if they are uncertain of the durability of the government support; Direct government funding and R&D tax incentives are substitutes: increased intensity of one reduces the effect of the other on business R&D; The stimulating effect of government funding varies with respect to its generosity: it increases up to a certain threshold (about 10% of business R&D) and then decreases beyond; Defence research performed in public laboratories and universities crowds out private R&D; Civilian public research is neutral for business R&D. * We thank the participants to various seminars, including the OECD Committee for Scientific and Technology Policy and the NBER 2000 Summer Institute on Productivity for helpful comments and suggestions. All opinions expressed in this article are those of the authors and do not reflect necessarily the views of the OECD or Université Libre de Bruxelles.     

International Cooperation on Climate-friendly Technologies

We examine international cooperation on technological development as an alternative to international cooperation on emission reductions. We show that without any R&D cooperation, R&D in each country should be increased beyond the non-cooperative level if (i) the technology level in one country is positively affected by R&D in other countries, (ii) the domestic carbon tax is lower than the Pigovian level, or (iii) the domestic carbon tax is set directly through an international tax agreement. We also show that a second-best technology agreement has higher R&D, higher emissions, or both compared with the first-best-outcome. The second-best subsidy always exceeds the subsidy under no international R&D cooperation. Further, when the price of carbon is the same in the second-best technology agreement and in the case without R&D cooperation, welfare is highest, R&D is highest and emissions are lowest in the second-best R&D agreement.     

Preemption,leapfrogging and competition in patent races

This paper investigates when patent races will be characterized by vigorous competition and when they will degenerate into a monopoly. Undersome conditions, a firm with an arbitrarily small headstart can preempt its rivals. Such ‘?-preemption’ is shown to depend on whether a firm that is behind in the patent race, as measured by the expected time remaining until discovery, cant ‘leapfrog’ the competition and become the new leader. An example of an R&D game with random discovery illustrates how ?-preemption can occur when leapfrogging is impossible. A multi-stage R&D process allows leapfrogging and thus permits competition. A similar conclusion emerges in a model of a deterministic patent race with imperfect monitoring of rival firms' R&D investment activities.     

Detecting which firm-specific characteristics impact market-oriented R&D

This paper investigates which firm-specific characteristics lead multinational enterprises (MNEs) to increase their R&D expenditure in host countries as a way of expanding their business into local markets (market-oriented R&D). The literature that addresses this topic is quite limited because of the difficulty of separating market-oriented R&D expenditure from knowledge-sourcing R&D expenditure in the data. We argue that determining the relationship between local sales and R&D expenditure is a better way to identify whether MNEs are investing market-oriented R&D than is separating the two types of R&D. For connecting firm-specific characteristics, local-market sales, and R&D expenditure together, we adapt two-stage regressions. By employing data from Taiwanese multinationals from 2003 to 2006, we found that if an MNE moves its technology toward capital-intensive products, it increases its R&D expenditure to promote its sales in the local markets in the host country.     

Profit-maximizing R&D in response to a random carbon tax

This paper determines a firm’s profit-maximizing R&D response to an uncertain carbon tax, for two different R&D programs: cost reduction of low carbon energy technologies and emissions reductions of currently economic technologies. We find that optimal R&D does not increase monotonically in a carbon tax. R&D into alternative technologies increases only if the firm is flexible enough; R&D into conventional technologies first increases then decreases in a carbon tax. Firms that are very flexible may increase R&D into alternative technologies when the uncertainty surrounding a carbon tax is increased; otherwise firms will generally decrease R&D investment in uncertainty.     

R&;D: A Small Contribution to Productivity Growth

In this article I evaluate the contribution of R&D investments to productivity growth. The basis for the analysis are the free entry condition and the fact that most R&D innovations are embodied. Free entry yields a relationship between the resources devoted to R&D and the growth rate of technology. Since innovators are small, this relationship is not directly affected by the size of R&D externalities, or the presence of aggregate diminishing returns in R&D after controlling for the growth rate of output and the interest rate. The embodiment of R&D-driven innovations bounds the size of the production externalities. The resulting contribution of R&D to productivity growth in the US is smaller than 3–5 tenths of 1% point. This constitutes an upper bound for the case where innovators internalize the consequences of their R&D investments on the cost of conducting future innovations. From a normative perspective, this analysis implies that, if the innovation technology takes the form assumed in the literature, the actual US R&D intensity may be the socially optimal.     

Asymmetric firms,technology sharing and R&D investment

We use a combination of theory and experiment to study the incentives for firms to share knowledge when they engage in research and development (R&D) in an uncertain environment. We consider both symmetric and asymmetric starting points with regards to the amount of initial knowledge firms have before conducting R&D and look at how differences in starting positions affect the willingness of firms to share knowledge. We investigate when and if firms find R&D cooperation beneficial and how investment in R&D is affected by the outcome of the sharing decisions. The experimental evidence shows that overall subjects tend to behave consistently with theoretical predictions for the sharing of knowledge, although leaders who are not compensated by a side payment from laggards are more willing to share than predicted by the theory, and leaders who are compensated are less willing. The data on investment suggests less investment with sharing than without, consistent with theory. Compared to exact numerical predictions, there is overinvestment or underinvestment except for symmetric firms under no sharing. All cases of overinvestment and underinvestment, regardless of sharing or not and regardless of starting positions, are well explained by smoothed-out best (quantal) responses.     

The effect of outward investment to China on domestic R&D: a two-hurdle model with endogenous ODI

Outward direct investment (ODI) and domestic R&D are interrelated, but empirical evidence is affected by the nature of a firm's data, which are heavily censored. Firm data contain a firm's yes/no decision to invest in China, yes/no decision of R&D, and the decision of R&D intensity. We thus adopt a two-hurdle model and allow the China investment decision to be endogenous in an R&D model in order to examine the effect of ODI in China on domestic R&D investment in Taiwan's electronics industry. In the model, a two-equation simultaneous subsystem is formed, in which three regression equations are specified: a decision of R&D intensity, and a yes/no decision of location to conduct R&D together with a yes/no decision to invest in China Our results indicate that China investment and R&D intensity are positively related such that ODI in China helps to raise significantly a firm's R&D intensity as compared to the estimate if the endogeneity of China investment and the nature of data were not properly accounted.     

Strategic Rivalry With Spillovers Within Segmented Versus Integrated Markets

We consider a two-stage game with firms investing in R&D in the first stage while competing [a] la Cournot in the second stage. The firms are located in two countries, which are either segmented or integrated. R&D spillovers occur between firms located in the same country as well as between firms located in different countries.

We first examine the consequences of market integration on the impact of national and international R&D spillovers on innovative efforts, effective R&D, profits and total welfare. Comparing the resulting equilibrium levels, we subsequently conclude that market integration always leads to higher R&D investments and output if international R&D spillovers are limited, while the welfare consequences are ambiguous. Finally, we also analyze the welfare maximization problem of a ‘constrained social planner who can only decide on the level of R&D spillovers.     

The interdependence between FDI and R&D: an application of an endogenous switching model to Taiwan's electronics industry

Foreign direct investment (FDI) and research & development (R&D) are mutually dependent and should be treated as endogenous variables in empirical studies. An endogenous switching regression model is used to examine the mutual effect of FDI and R&D in Taiwan's electronics industry. The empirical results show that FDI and R&D are positively related and do reinforce each other. Unbiased coefficients are obtained as they are compared to those estimates if FDI and R&D are treated as exogenous variables. The results have a strong public policy implication for Taiwan's foreign direct investment and can be further used to estimate the difference in R&D expenditures between FDI and non-FDI firms.     

The effectiveness of R&D subsidies

In this paper, the effectiveness of R&D subsidies is analyzed in an oligopolistic model that we apply to the cases of international R&D competition and cooperation. We find that the existence of asymmetric information among firms on whether a rival (or partner) is being subsidized or not may play a key role in explaining whether subsidies are effective or not in increasing R&D investments. In particular, it is shown that if the existence of the subsidy is made public (e.g. because strict information release regulation about R&D subsidies is enforced) and depending on the strategic relationship between the firms’ R&D efforts, an R&D subsidy could even hurt the subsidized firm.