مزایده پویا برای تأمین تجهیزات چندهدفه تحت محدودیت بودجه منقبض

This contribution revisits the problem of allocating R&D subsidies by government agencies. Typically, the applicants’ financial constraints are private information. The literature has recommended the use of auctions in order to reduce information rents and thus improve the efficiency of how scarce public funds are allocated. We propose a new open clock auction for this procurement problem. This auction is strategically simple, as it exhibits truthtelling in dominant strategies and satisfies ex-post rationality, while observing the budget constraint. We test the auction in Monte-Carlo simulation and discuss its applicability and limitations. Moreover, we highlight connections to recent advances in computer science.

It is well known that innovation exhibits the classical properties of market failure (indivisibilities, inappropriability and uncertainty, see, e.g., Arrow, 1962), resulting in socially suboptimal R&D investments by private firms. As a response, various policy instruments are being applied, e.g., in order to lower the threshold where socially desirable projects become privately profitable or to step in when markets do not provide sufficient private debt or equity. One of the most important tools is direct subsidization of private R&D.2 For example, the Small Business Innovation Research (SBIR) program in the United States provides funds in excess of $1 billion annually to encourage innovation by small and medium-sized private enterprises.3 Accordingly, the effects of public R&D funding have received considerable attention in the literature (see David et al. (2000) for an extensive discussion). A central question is, to what extent public grants crowd out private R&D. Although the empirical evidence is mixed, the majority of studies seems to speak against the crowding out hypothesis, thus, validating this policy tool. Recent contributions, rejecting (full) crowding out, include Aerts and Schmidt, 2008, Czarnitzki and Lopes-Bento, 2011, Czarnitzki and Lopes-Bento, 2012, Czarnitzki and Lopes-Bento, 2013, Duguet, 2004 and Hall and Maffioli, 2008.4David et al. (2000) is inconclusive, finding that the degree of crowding out depends on the aggregation level and type of industry. Wallsten (2000) finds that subsidies crowd out private R&D dollar for dollar in the SBIR program.5 Apart from the direct effect of enabling socially valuable projects that would have gone unfinanced in the absence of subsidies, public R&D funding has other benefits. Innovation, especially in the area of new technologies, and by small firms or startups, exhibits substantial uncertainty and asymmetric information, making it hard to raise debt or private equity. In this situation, the granting of public funds, following an expert evaluation of the projects in question, might signal the quality or commercial prospects of the firms in questions, thus, enabling access to capital. This ‘halo’ or signaling effect of subsidies has been described and empirically studied by Lerner (1999), followed by Feldman and Kelley (2003) and Meuleman and De Maeseneire (2012), and theoretically analyzed by Kleer (2010) and Takalo and Tanayama (2010). A special form of this effect is known as the ‘certification’ effect. It implies that the fact of getting subsidies is more important than their actual size, see Feldman and Kelley (2003) and Meuleman and De Maeseneire (2012). Another class of ‘soft’ or longer-term benefits of R&D subsidies are spillover effects, the forming of networks and cooperations (especially between firms and research institutions), acquiring expertise, establishing continuous R&D activities in smaller firms. Typically, these benefits are explicit policy aims of the various government programs, see, e.g., Feldman and Kelley, 2003 and Czarnitzki et al., 2007 and Aerts and Schmidt (2008).6 Apart from the inconclusive evidence on the crowding out effect, the literature has pointed out practical problems. Government policy might be distorted, due to lobbying (or ‘regulatory capture’, see Lerner, 1999) or political pressure, resulting in ‘picking-the-winner’ behavior of R&D programs, favoring projects with higher probability of success, rather than more risky, socially desirable projects (see Czarnitzki and Lopes-Bento (2011) and Wallsten (2000) for empirical evidence). Wallsten (2000) is one of a few to stress the need for oversight and evaluation of program managers. Another line of criticism is based on the conjecture that there is room for improvement in the way public funding programs allocate their R&D budgets, e.g., by evaluating programs, resp. allocations, in a different way, and by inducing more competition for funding among applicants.7 The typical procedure in these schemes is that applicants submit a detailed research proposal, stating their goals, expected cost for personnel, equipment, etc. There might be a deadline after which all proposals are evaluated by a panel of experts. This quality evaluation typically includes financial plausibility checks and an evaluation of the commercial, economic or social merits.8 In many programs, cooperation partners and networking efforts are preferred or required.9 Then, the winners receive funding from a given budget. The progress of those projects is then closely monitored and, finally, evaluated by the funding body. The literature has discussed potential improvements on the current practice. First, rather than selecting winners purely on the basis of quality, one needs to take into account that lower-quality projects might make better use of scarce public funds than high-cost, high quality projects.10 Second, the amount of subsidies granted is typically a fixed function of stated project cost (‘matching grant’), and applicants are neither required nor given incentive to reveal to what extend they would pursue their proposals with smaller subsidies or no grants at all. Thus, the argument goes, successful applicants on average receive excessive information rents, due to the design of these programs.11 These information rents, in theory, distort the allocation, wasting scarce public funds that could otherwise be used to enable additional innovation (with associated benefits, like the halo effect, spillovers, network effects, etc.). This criticism is related to the crowding-out hypothesis mentioned above.12 In order to address the first issue, the project allocation, Becker et al. (2004) and Giebe et al. (2006) recommend to define fixed quality classes (or grades, such as A, B, C) with associated welfare weights, such that each proposal (that is fundable in principle, by the program's criteria) is given one of the quality grades.13 Then, the allocation of winners is chosen in order to maximize total welfare (according to the welfare weights of each budget-feasible allocation) with the given budget. The second issue, information rents, might be addressed by making the funding decision more competitive, giving applicants the option to increase their chances of funding by lowering the amounts of money they receive in case of being granted a subsidy. This could be done on a sealed-bid basis or in an open auction-like procedure, as recommended by Blum et al., 2001, Blum and Kalus, 2003 and Becker et al., 2004 and Giebe et al. (2006).14 The contributions of Becker et al. (2004) and Giebe et al. (2006) explicitly discuss practical issues arising from the use of auction mechanisms in order to reduce applicants’ requested funding as well as the project selection based on quality classes and welfare weights. This paper is mainly motivated by Giebe et al. (2006). The authors analyze the German R&D subsidy programs for small and medium-sized private businesses (which is similar in spirit to the SBIR program). Firms that satisfy the programs’ various requirements are encouraged to submit their research proposals. The proposals are evaluated by a panel of experts and ranked into one of three quality categories, A, B, and C. Successful applicants typically receive a subsidy of 50% of their stated personnel cost (the matching grant). Current practice allocates subsidies as follows: As many A projects as possible are funded. If there is money left, it is used to fund as many B projects as possible, etc. As mentioned earlier, two major flaws of this procedure have been outlined. First, it puts relatively cheap B and C projects at a disadvantage to expensive A projects even though they might promise much better research output per unit of public funds. Second, it is highly likely that some applicants receive disproportionally more financial support than they require to carry out the project in the promised form. Giebe et al experimentally test open auction mechanisms where applicants bid for funding. In these auctions, the bidders make an initial bid equal to their “status quo” subsidy – the matching grant – which they would recieve in case of a successful application under the current system. Then, in several rounds of bidding, bidders may reduce their requests for funding (which increases the probability of being successful). This enables “lower quality” projects to compete with high quality projects by offering a better value for the public money. The auction would finally select an allocation of research proposals that takes into account the funding agency's preferences as well as the bidders’ requests for funding. Since the auction starts with the status quo subsidies, the final allocation can only reduce the winners’ funding as compared to the status quo, or leave it unchanged. Following, Giebe et al. (2006), our paper addresses two issues: First, spreading the budget among a larger group of recipients by inducing competition for funding using auction mechanisms, and, second, an improvement of the final allocation by basing the funding decision on the ratio of quality of a project per unit of public funding received (rather than the “lexicographic” selection of “highest quality first”). The auctions proposed in Giebe et al. (2006) are theoretically intractable. Thus, it is hard to predict or recommend bidding behavior even for fully rational players. In the present paper we propose a modified design of those auctions that has appealing equilibrium properties, i.e., it implements truthful bidding in weakly dominant strategies and exhibits individual ex post rationality. Therefore, the equilibrium outcome is robust in the sense that it is independent of the knowledge of the underlying distributions of private information. The auction performs favorably in Monte-Carlo simulations as well as in a theoretical worst-case analysis. This auction is an open descending clock auction where the “clock” is a price-per-unit-of-quality clock rather than the usual “money” clock. This enforces competition across quality classes. The auction procedure is related to “greedy” algorithms in the sense that it procures the proposals that have the lowest price per unit of quality.15 We recommend a pragmatic implementation with simple quality classes following Becker et al. (2004) and Giebe et al. (2006). Abstracting from the R&D application, the underlying allocation problem, as well as our mechanism, apply to more general procurement settings. Recently, and following Singer (2010), the computer science literature has studied related, so called “budget feasible” mechanisms, see, e.g., Dobzinski et al. (2011). In the economics literature, Maskin (2010) analyzes the auctioning of pollution permits in a similar framework. The paper is organized as follows. In Section 2, we discuss the problem more formally and present the model. In Section 3 we introduce the auction mechanism. Section 4 presents the results from Monte-Carlo simulations. Section 5 discusses the applicability and limitations of the proposed auction. Section 6 concludes.

Our paper starts from the observation that direct public funding of private R&D projects is a widely applied and empirically supported innovation policy instrument. We focus on the way of allocating a given subsidy budget to a given target group of potential recipients. Our contribution is to propose a strategically simple auction mechanism that “levels the playing field” by inducing competition for funding across quality classes of applicants. This is achieved by letting applicants compete not in either the money or the quality dimension, but in both dimensions at once, represented by the subsidy per unit of quality. In contrast to previous work, our auction design is easy to analyze and strategically simple. The dominant strategy is to stay active until one's true reserve price is reached. This property provides a robust equilibrium prediction. Moreover, it is easy to implement since it does not require additional information on the buyer's side (in addition to what the program management knows under the present system). There is empirical evidence that firms are able to calculate their reserve prices. The auction addresses the problem of information rents that represent a deadweight loss in the widely used practice of allocating subsidies. It seems obvious that there must be information rents of some size under the current practice of awarding matching grants regardless of private information. Moreover, if application costs are not prohibitively high, many firms should have an incentive to acquire subsidies for any kind of project, not only those that have insufficient funding.41 The presence of information rents, however, does not imply a one-to-one crowding out or waste of public money.42 The question is, whether or not reducing winner's information rents while increasing the number of winners induces a (net) welfare improvement. It is beneficial if it induces more socially valuable innovation as compared to the status quo allocation. Spreading the given budget among a larger group of recipients has additional positive effects if the fact of getting public funding is important, e.g., in the presence of the ‘certification’ effect, knowledge spillovers, network or cooperation advantages, or other micro-level effects of government contracts, such as developing an R&D infrastructure, learning and training effects, acquisition of durable equipment and skills, see David et al. (2000, p. 505). We have presented simulation results, shedding some light on the theoretical sensitivity of the auction's performance when parameters change. We found that the auction's performance gap as compared to the first-best allocation is mainly due to the presence of information rents and this gap is increasing in the average size of these rents. In contrast, the performance of the status quo mechanism was shown to be very sensitive to parameter changes, which is mainly due to the fundamentally different (‘lexicographic’) way of determining the allocation. All simulated settings confirmed the expectation that the auction clearly outperforms the status quo mechanism, even under the extreme assumption that there are no information rents. Bearing in mind the empirical findings we have discussed above, it is clear that the applicability of the mechanism depends on many factors, such as the kind of innovation, the target group, and the policy aims of the respective funding program. In order to apply our theoretical result in a meaningful way, one would need to test the auction in a realistic setting and empirically evaluate its effects as compared to the status quo. Preferably, the auction should first be tested in a setting where larger improvements are to be expected, e.g., in larger programs, among larger firms who are not severely financially constrained. Our theoretical results might be relevant in settings other than R&D funding. Recent contributions in computer science have analyzed related, so called “budget feasible” mechanisms, see Singer (2010) or Dobzinski et al. (2011). Similar to our contribution, this literature traditionally looks at belief-free settings, i.e., does not make distributional assumptions on the private information, precisely in order to provide for a robust analysis. Singer (2010) analyzes a direct “knapsack”-type mechanism. Our auction can be seen as a simple implementation of such a mechanism.