Conditional R&D subsidies

Abstract

This paper introduces a new type of R&D subsidy, which is conditional on the success of the R&D project. In a three-stage model, the government chooses a subsidy(ies), a monopolist chooses R&D effort which determines the size or the probability of success of the R&D project, and the firm chooses output. It is found that conditional subsidies can yield the same level of innovation and welfare as unconditional subsidies. However, when the probability of success is sufficiently low (be it endogenous or exogenous), conditional subsidies yield suboptimal levels of innovation and welfare. When the firm chooses the probability of success, conditional subsidies reduce the expected cost of the subsidy to the government as well as profits. The simultaneous use of conditional and unconditional subsidies is considered. Finally, subsidies conditional on failure are studied. It is found that they yield the same level of innovation and welfare as unconditional subsidies but increase expected subsidy costs and profits.

Keywords:

• R&D subsidies
• innovation
• innovation policy
• R&D

JEL Classification:

• L12
• L52
• O31
• O38

Acknowledgements

I thank two anonymous referees for extremely useful comments which have significantly improved the paper. I am also grateful to the participants in the EARIE conference and seminar participants at the Shanxi University of Finance and Economics for their useful feedback. I also thank Madushi Seneviratne for research assistance.

Notes

1. There is also the possibility that even failed R&D projects are useful, in that the human capital built from such projects is transferred to other firms through employee mobility. Although Mϕen (2004) finds little support for this hypothesis, using Norwegian data.

2. Mansfield et al. (1977) identify three types of success probabilities: technical completion (0.57), commercialization given technical completion (0.65), and financial success given commercialization (0.74). The numbers in brackets represent those probabilities for 16 firms operating in the chemical, pharmaceutical, electronics, and petroleum industries. These numbers show that the probability of failure is significant.

3. He goes even further, suggesting that risky investments should be subsidized, while safer investments should be taxed. This is because in his model, when firms choose the probability of success, they invest too much in safe projects.

4. For a comparison of the tax treatment of R&D across OECD countries, see OECD (2006) and Guellec and van Pottelsberghe de la Potterie (2003).

5. Because θ∈(0, 1), the parameter λ also represents an upper bound on R&D investment when θ is endogenous.

6. When x is endogenous, this means that its arguments are such that x*(.)<α.

7. Note that there are no criteria for selection into the subsidy scheme. There is a single project, and this project automatically qualifies for a subsidy, the level of which is determined by the government, depending on the project risk and the subsidy scheme.

8. The expectation sign is dropped for notational convenience.

9. All second order conditions (s.o.c.) for stages 1 and 2 are given in the appendix.

10. Similar substitutions will be made when writing the welfare function in the other models to be considered.

11. Social optimality here is in a second-best sense, where the output distortion due to monopoly power is beyond the control of the government.

12. Expected subsidy costs, profits, and welfare will be analyzed in more detail in Section 8.

13. Given this solution for s_u, and given the solution for θ from Equation (3), it must be that λ>3[x(2A−α)+x]/16 to get θ<1. This constraint applies to models 5, 6, and 8 below too.

14. In Australia, the equivalent of a subsidy conditional on failure has been used. As the Australian Government Productivity Commission (2008, 6.14) notes: ‘Repayable assistance schemes have been used in Australia \ldots and overseas, partly as a means of limiting assistance to non-induced activity. If the targeted activity proves not to generate sufficient revenue for the firm to cover the costs it incurs (even though it may generate important spillovers), the firm retains the assistance. But where projects prove to be profitable in their own right, the assistance is returned to the government.’ See also Section 3.

15. Basing a subsidy on failure has the advantage of assisting financially strained firms, but may induce firms to claim failure even when the main objectives of the research project have been met. It may also reduce the incentives to increase the probability of success and increase the expected cost of the subsidy to the government; this will be shown to hold here (see below model 8 and also Section 8).

16. Figure 3 is based on the numerical parameterization A=1000, α=50, γ=60.

17. One could also consider a model where the government combines an unconditional subsidy with a reverse conditional subsidy. For example, when the probability of success is exogenous, it is straightforward to verify that the optimal subsidies in this case satisfy .

18. In this paper, the slope of the demand curve is normalized to −1. If we consider a more general demand function, p(y)=A−by, it is easy to verify that for models 1–4, 6, and 7, the optimal subsidies are independent of b. For model 5, ∂ s_c/∂ b>0; in that case, an increase in b, which makes demand less elastic and reduces the gain to the firm from innovating, induces a reduction in θ, which the government counters by increasing the subsidy. While for model 8, ; in that case, a higher b also reduces θ, which increases the chances of failure and therefore of obtaining the subsidy; to counter that effect, the government reduces the subsidy to maintain the expected subsidy constant and induce the socially optimal level of innovation.

19. See Section 2.2.

20. Even though in a more general setting (risk aversion, budget constraints, distortionary taxation, etc.), they could dominate unconditional subsidies.

21. See the work of Kitahara and Matsumura (2006) and Helm and Schöttner (2008) discussed in Section 2.1.

22. One way of alleviating this asymmetry of information would be to let firms bid for the subsidy, to extract information about the firms’ true assessment of their projects (Martin and Scott 2000).