Spillovers,product innovation and R&D cooperation: a theoretical model

ABSTRACT

We analyze the impact of post-innovation knowledge spillovers on firms’ decisions to invest and cooperate in R&D, forming a research joint venture (RJV). We study the case of two potential investors involved in a non-tournament stochastic competition for developing a new but imitable product. We propose a theoretical model where cooperation may emerge as a subgame perfect Nash equilibrium of a three-stage game. In the first stage, firms decide whether to cooperate; in the second, they decide whether to invest; and in the third, they compete. We show that firms cooperate in R&D when the spillovers are high enough and the fixed costs associated with R&D activities are low enough; however, our analysis suggests that forming an RJV may not always be socially optimal, and subsidizing R&D cooperation may not be efficient. We propose an optimal scheme of subsidies, which should be designed according to the intensity of the spillovers, the level of the R&D costs, and the probability of innovation success. Finally, we show that in the case of mergers the private incentive to invest is maximized, and firms may not need public subsidies to cooperate. When subsidies are costly, not hindering mergers may be the second-best solution.     

Does Firm Size make a Difference? Analysing the Effectiveness of R&D Subsidies in East Germany

We analyse the impact of public subsidies on private sector research and development (R&D) activity for a sample of East German firms. Using propensity score matching, our empirical results indicate that subsidized firms indeed show a higher level of R&D intensity (R&D expenditures relative to total turnover) and a higher probability for patent application compared with non‐subsidized firms. We find that, on average, the R&D intensity increases from 1.5% to 3.9%. The probability of patent application rises from 20% to 40%. These results closely match earlier empirical findings for East Germany. Given the fact that the East German innovation system is particularly driven by small‐ and medium‐sized enterprises (SMEs), we draw special attention to the effectiveness of R&D subsidies for this latter subgroup. Here, no specific empirical evidence is available so far. Our findings indicate that policy effectiveness also holds for private R&D activity of SMEs, with the highest increase in terms of R&D intensity being estimated for microbusinesses with up to ten employees.     

Unsuccessful patent application and cooperative R&;D

We show that uncertainty in patent approvals may induce the firms to do cooperative R&D. With an exogenous probability of success in patent application, we show that, if all firms apply for patents under non-cooperative R&D, the firms prefer cooperative R&D than non-cooperative R&D for moderate (high) probabilities of success in patent applications, if the cost of patenting is small (large). We also show the implications of entry of non-innovating firms and endogenous probability of success in patent applications.      

Cost Signals under Uncertain R&D Outcomes

When it is difficult for firms to differentiate their products from those of their competitors, research and development (R&D) spending on process innovation to lower the cost of production is crucial for profitability. However, the information asymmetry in production costs that results from innovation reduces the efficiency of all firms in a market for a homogeneous good. We employ a signalling game to discuss the feasibility of utilising R&D spending and output levels as cost signals in an environment of quantity competition. The results show that a firm does not spend its money on R&D solely to signal the type of cost. Rather, R&D spending may be chosen as a cost signal over the output level only if expenditures on R&D can lead to a sufficiently high probability of reducing production costs.     

Intellectual Property Rights and Crop-Improving R&D under Adaptive Destruction

This paper studies how the strength of intellectual property rights (IPRs) affects investments in biological innovations when the value of an innovation is stochastically reduced to zero because of the evolution of pest resistance. We frame the problem as a research and development (R&D) investment game in a duopoly model of sequential innovation. We characterize the incentives to invest in R&D under two competing IPR regimes, which differ in their treatment of the follow-on innovations that become necessary because of pest adaptation. Depending on the magnitude of the R&D cost, ex ante firms might prefer an intellectual property regime with or without a “research exemption” provision. The study of the welfare function that also accounts for benefit spillovers to consumers—which is possible analytically under some parametric conditions, and numerically otherwise—shows that the ranking of the two IPR regimes depends critically on the extent of the R&D cost.      

Stochastic innovation and product market organization

Summary This paper analyzes how different types of product market organization affect firms' R&D investments in a stochastic innovation framework. Product market competition determines payoffs to successful and unsuccessful firms. Restrictions on the research project success probability distribution are identified that yield an invariance result for expenditure per R&D project. The impact of the number of firms (n) on the amount of market R&D is shown to be sensitive to product market organization. For a major process innovation, firms undertake more R&D projects under Cournot product market competition than under Bertrand competition, forn sufficiently large. A numerical example is used to illustrate welfare tradeoffs.Tom Lyon, Herman Quirmbach, Ferenc Szidarovszky, Mark Walker and two anonymous referees gave us helpful comments and suggestions on prior versions of this paper. Lucy Atkinson provided expert research assistance on numerical computations. Special thanks to Ted Bergstrom who gave us valuable suggestions about the first proposition.     

On the incentives for cooperative research

This paper analyzes incentives for cooperative research for firms competing in the product market. Contrary to the literature, we portray situations to show that non-cooperative R&D can occur even if the probability of success in R&D is large. We then model synergy in cooperative R&D and show that when the innovation size is large, cooperative research is likely to occur.     

On the Relationship Between Innovation and Product Market Competition

This paper considers a theoretical model where firms reduce their initial unit costs by spending on R&D activities in a collusive market and where firms are able to coordinate on distinct output levels other than that of the unrestricted joint profit maximization outcome. We show that, in our model, the degree of collusion (captured by the discount factor) reduces the incentive to innovate when innovation is made non‐cooperatively. The reason is that non‐cooperative R&D introduces a negative externality where firms overinvest beyond the effort required to minimize the cost in order to extract profits from the rival firm, and a reduction in product competition helps internalize the externality. In a research joint venture the absence of R&D rivalry leads to contrary results. The main implication is that the validity of the Schumpeterian hypotheses depends on the extent of cooperation at the R&D stage.     

A matching analysis of why some firms in peripheral regions undertake R&D whereas others do not

Many studies have established the importance of investment in R&D to facilitate innovation and consequently improve firm productivity. Firms decide whether or not to undertake R&D depending on a range of factors such as market orientation, business objectives, competitive advantages and absorptive capacity. This paper studies the factors that influence this decision in peripheral locations; and for firms that do not undertake R&D, we analyse the reasons for not doing so. The research is based on data from a survey of some 250 matched firms operating in Northern Ireland, about half undertaking R&D and half not. Northern Ireland is an interesting case study because it exhibits a low level of investment in R&D despite the public subsidies and policy initiatives that have existed over the last 30 years. For firms that undertake R&D, our results mostly confirm the findings of others while for firms that do not undertake R&D the results point to a capabilities-gap rather than a resource-gap as the fundamental problem. Policy conclusions are drawn as to what might be done to boost both the amount of R&D undertaken and the number of firms engaged in R&D in peripheral regions.     

Equal treatment and socially optimal R&D in duopoly with one‐way spillovers

This paper examines the standard symmetric two‐period R&D model with a deterministic one‐way spillover structure: know‐how flows only from the high R&D firm to the low R&D firm (but not vice versa). Though firms are ex ante identical, one obtains a unique asymmetric equilibrium (pair) in R&D investments, leading to interfirm heterogeneity in the industry. R&D cooperation by means of a joint lab is considered and compared to the non cooperative solution. The main part of the paper provides a second‐best welfare analysis in which we show that the joint lab yields a socially optimal R&D level subject to an equal treatment (of firms) constraint, which also coincides with the noncooperative solution in the absence of spillovers. We also investigate the welfare costs of this equal treatment constraint and find that they can be quite significant.     

Rent Protection as a Barrier to Innovation and Growth

We build a model of R&D-based growth in which the discovery of higher-quality products is governed by sequential stochastic innovation contests. We term the costly attempts of incumbent firms to safeguard the monopoly rents from their past innovations rent-protecting activities. Our analysis (1) offers a novel explanation of the observation that the difficulty of conducting R&D has been increasing over time, (2) establishes the emergence of endogenous scale-invariant long-run innovation and growth, and (3) identifies a new structural barrier to innovation and growth. We also show that long-run growth depends positively on proportional R&D subsidies, the population growth rate, and the size of innovations, but negatively on the market interest rate and the effectiveness of rent-protecting activities. An unpublished version of this paper was circulated earlier under the title “Innovation and Rent Protection in the Theory of Schumpeterian Growth.” We thank an anonymous referee and seminar participants in several venues for useful comments and suggestions.     

Timing and Commitment of Environmental Policy,Adoption of New Technology,and Repercussions on R&;D

We investigate the interplay between environmental policy, incentives to adoptnew technology, and repercussions on R&D. We study a model where a monopolistic upstream firm engages in R&D and sells advanced abatement technology to polluting downstream firms. We consider four different timing and commitment regimes of environmental tax and permit policies: ex post taxation (or issuing permits), interim commitment to a tax rate (a quota of permits) after observing R&D success but before adoption, and finally two types of ex antecommitment before R&D activity, one with a unique tax rate (quota of permits), the other one with a menu of tax rates (permit quotas). We study the second best tax and permit policies and rank these with respect to welfare. In particular, we find that commitment to a menu of tax rate dominates all other policy regimes.     

R&D subsidies in a model of growth with dynamic market structure

This paper presents the effects of an R&D subsidy in a Schumpeterian general equilibrium model with rich industry dynamics. R&D subsidies raise the long-run growth rate, but they also raise the level of industry concentration. In the model firms compete for market share through process R&D endogenously determining the market structure within and across industries. Endogeneity of the market structure allows for analysis of changes in the moments of the firm size distribution in response to policy. R&D subsidies primarily benefit large incumbent firms who increase their innovation rates creating a greater technological barrier to entry. Concentration increases with fewer firms and a higher variance in the market shares. In general equilibrium, the greater distortions in the product market cause the wage rate to fall which leads to increased turnover rates. In addition, the analysis demonstrates that the model captures a large number of empirical regularities described in the industrial organization literature, but absent from most endogenous growth models. These features, such as entering firms are small relative to incumbents, the hazard rate of exit is negatively related to firm size, and large firms spend more on R&D than small firms play important roles in understanding the impact of R&D subsidies on the economy.     

Spillover feedback loops and strategic complements in R&D

This paper studies, in a two‐period model, the effects of knowledge spillovers among product market competitors on R&D levels. It argues that when firms' R&D decisions are strategic complements, in industries in which spillovers increase the marginal productivity of a firm's R&D, both incoming and outgoing spillovers spur R&D in equilibrium. Outgoing spillovers can foster innovation even in a homogeneous‐product industry. In these industries, the intellectual property law should be such that facilitates knowledge diffusion. If firms have power in deciding the level of knowledge spillovers, we show that a firm will choose to disclose its knowledge to its product market competitors.     

An Empirical Evaluation of The Effects of R&D Subsidies

R&D subsidies are a common tool of technology policy, but little is known about the effects they have on the behavior of firms. This paper presents evidence on the effects that R&D subsidies have on the R&D effort of recipients, and on the probability that a firm will participate in a program granting R&D subsidies. The empirical model consists of a system of equations: a participation equation; and an R&D effort equation. Endogeneity of public funding is controlled for. Estimates are obtained with a cross-section sample of Spanish firms. The main findings are that: 1) small firms are more likely to obtain a subsidy than large firms, probably reflecting one of the public agency's goals; 2) overall, public funding induces more private effort, but for some firms (30% of participants) full crowding out effects cannot be ruled out, and 3) firm size remains related to effort, whether or not a firm gets public funding.     

R&D INCENTIVES UNDER BERTRAND COMPETITION: A DIFFERENTIAL GAME*

We investigate dynamic R&D for process innovation in an oligopoly where firms invest in cost‐reducing activities. We focus on the correlation between R&D intensity and market structure, proving that the industry R&D investment at equilibrium monotonically increases in the number of firms. This result contradicts the established wisdom acquired from static games on the same topic. We also prove that, if competition is sufficiently tough, any increase in product substitutability reduces R&D efforts.     

Subsidizing public inputs

If production–cost savings associated with successful research and development are freely disseminated to other firms as soon as they are realized, too few resources may be allocated to this activity. Subsidies to this activity, a public input, can lead to optimal input use. The effectiveness of four alternative subsidy instruments in stimulating firms’ R&D spending are examined. Two are incremental subsidies and two are level subsidies. One of the incremental subsidies and one of the level subsidies crudely capture characteristics of incentive mechanisms used in many countries. A laboratory implementation of these instruments confirms that incremental subsidies are inferior to level subsidies.     

International R&D Networks

This paper considers the Goyal and Moraga‐Gonzalez (2001 ) model of strategic R&D collaboration networks in the open economy framework. The R&D is the d'Aspremont and Jacquemin (1988 ) process innovation and collaboration takes the form of research joint ventures (RJV) in which firms cooperate in R&D but compete in product markets. Countries decide whether to establish free‐trade links while firms decide whether and with whom to form RJVs. A double‐layer pairwise stability concept is introduced to characterize equilibrium network structures. In contrast with conventional wisdom, it is shown that global free trade generally reduces collaborative R&D levels. We give conditions for which pairwise stable R&D networks are welfare maximizing. Stability and efficiency are congruent when R&D cost is either too high or too low. A large public spillover effect is detrimental to an R&D network when trade networks are regional.     

Firm size and types of innovation

We propose a general theory of innovation that illustrates the relative benefits of performing process versus product R&D when firm size is endogenous. A firm's size, scope, and R&D portfolio are shown to reflect the same underlying characteristic of the firm, namely manufacturing efficiency. We demonstrate that efficient firms become larger, have greater scope, and perform more of both process and product R&D. In light of decreasing returns to R&D, this implies small firms obtain more product innovations per dollar of R&D than large firms, which is consistent with evidence we present that small firms are more innovative than large firms as they obtain more patent counts and citations per dollar of R&D.     

Timing of innovation policies when carbon emissions are restricted: An applied general equilibrium analysis

This paper studies the timing of subsidies for emissions-saving research and development (R&D) and how innovation policy is influenced by a carbon tax. We develop a dynamic computable general equilibrium (CGE) model with both general R&D and specific emissions-saving R&D. We find two results that are important when subsidizing emissions-saving R&D in order to target inefficiencies in the research markets. First, the welfare gain from subsidies is larger when the carbon tax is high. This is because a high carbon tax raises the social value of the emissions-saving technology and that this increase in value is not fully appropriated by the private firms. Secondly, the welfare gain is greater when there is a falling time profile of the rate of subsidies for emissions-saving R&D, rather than a constant or increasing profile. The reason is that knowledge spillovers are larger in early periods.