Auction mechanisms for allocating subsidies for carbon emissions reduction: an experimental investigation

Among similar policies, the Australian government has implemented the Direct Action Plan, in which the Emissions Reduction Fund, designed to provide a direct incentive to reduce emissions, has been extended from 2014 to 2020 and includes initial allocations of $300 million, $500 million and $750 million. The aim of this fund is to allocate funds to select the lowest cost abatement through a reverse auction, as investigated in the present study, and this policy is believed to be “a far more effective means of reducing Australia’s emissions than the carbon tax” (Australian Department of the Environment 2013, page 3).

Furthermore, given the well-known negative consequences—such as traffic restriction, school closure, and the halting of construction sites and industrial production in the entire Beijing region (see, e.g., Smog in China closes schools and construction sites, cuts traffic in Beijing (2015) and the prohibition of straw burning in agricultural production in nearby provinces in response to the severe air pollution, as well as the huge long term and indirect costs associated to this pollution—the local government indeed has the financial capacity and a strong incentive to purchase emission reduction from nearby polluting firms (via, e.g., incentivizing them to cease production or to move far away), at least as a policy choice to improve the air quality.

Periodically held auctions are used to improve the effectiveness of the emission reduction quota allocation and to determine the prices (Cramton and Kerr 2002). For example, the US sulfur dioxide emissions trading program, initiated in 1995, was specifically designed to apply an annual revenue-neutral auction (Burtraw 2000; Carlson et al. 2000). Low prices, thin trading, and large amounts of allowance banking characterized the early market for sulfur dioxide allowances (Ellerman et al. 2000). In the first mandatory emissions control and trading program for GHG emissions in the US, namely, the Regional Greenhouse Gas Initiative (RGGI), carbon dioxide allowances are sold through quarterly auctions using a uniform-price sealed-bid format. California, along with the Canadian provinces of Quebec and Ontario, has initiated a regional cap and trade program and uses quarterly uniform price auctions for allocating most allowances. Auctioning is also the default method to allocate emission allowances in the European Union Emissions Trading System (EU ETS), which operates in 31 countries and accounts for 45% of the EU’s GHG emissions. It is estimated that over half of the allowances will be auctioned during the currently operated third phase (2013–2020), and this auction method has been planned to be expanded to most other emissions sources by 2020 (Ellerman et al. 2016; Salant 2016).

Examples include discriminatory auctions for US sulfur dioxide permits and uniform-price auctions for nitrogen oxide permits in Virginia (Lopomo et al. 2011). See, e.g., Cramton and Kerr (2002), Cramton (2007a), and Betz et al. (2010) in support of discriminatory auctions and Holt et al. (2007, 2008) in support of uniform-price auctions. Lopomo et al. (2011) provide a detailed comparison of different types of auctions based on the case of carbon emissions permits.

In dynamic bid auctions, an auctioneer begins by calling out a low price and raises the price gradually until sufficient emissions reductions are supplied at the announced price, which consumes the entire subsidy. The winning bidders pay their bid prices in discriminatory-price auctions and pay a uniform market-clearing price in uniform-price auction.

Although the equilibrium bidding in Maskin auctions takes the simple form of bidding on cost and eliminating the incentive for strategic bidding behavior, this does not necessarily imply that the auction rules are simple. Therefore, it would be of interest to observe the dynamic bidding behavior.

For example, the performance (e.g., efficiency and increased emissions reductions) of Maskin auctions may not exceed that of other types of auctions in one-shot auctions; however, its performance can be improved gradually when more auctions are conducted.

Regarding the use of a sealed-bid or a dynamic-bid auction design, first, the sealed-bid format does not change the theoretical incentive structure compared to the dynamic-bid format under the independent private information assumption (Krishna 2009). Second, it is widely recognized that the dynamic-bid design increases information transparency, although it does not necessary induce more desirable auction outcomes than a sealed-bid design (Burtraw et al. 2011). Third, dynamic bidding facilitates collusive bidding (Alsemgeest et al. 1998; Holt et al. 2007). Fourth, some scholars argue that ascending-bid auctions outperform sealed-bid auctions in price discovery, especially for multiple products or new assets without established prices (see, e.g., Cramton 1998, 2007b; Cramton and Kerr 2002; and Betz et al. 2010), whereas others observe that sealed-bid uniform-price auctions achieve price discovery equivalent to simultaneous ascending-bid auctions (Burtraw et al. 2009).

Vickrey (1961) first recognizes that the multi-unit discriminatory and uniform-price mechanisms are inefficient due to bidders’ multi-unit demand. Subsequent theoretical studies show that both mechanisms would give rise to underpricing due to the bidders’ market power (Wilson 1979; Back and Zender 1993; Kremer and Nyborg 2004) and further focus on the issue of demand reduction (Ausubel et al. 2014). However, it is noteworthy that bidding on one’s true value is still a weakly dominant strategy in the case of single-unit demand auctions and in the first unit demanded in multi-unit demand auctions. As for empirical evidence, several experimental studies confirm the presence of demand reduction (List and Lucking-Reiley 2000; Kagel and Levin 2001; Engelbrecht‐Wiggans et al. 2006), while other studies find that underpricing in uniform auctions usually does not materialize (Simon 1994; Nyborg and Sundaresan 1996; Keloharju et al. 2005; Goldreich 2007).

The buyer (i.e., the government) in a procurement auction is set to be budget constrained, in line with the common situations in the real world, that is, the emissions abatement schemes using subsidy instruments in Australia, Germany, the UK, etc. (see, e.g., Smith and Swierzbinski 2007; the Australian Department of the Environment 2013; and the Productivity Commission 2011, for a review of carbon emission policies in various countries).

The reasons why we choose discriminatory and uniform-price auctions as the alternative mechanisms are the following: First, in Maskin (2011), the Maskin mechanism is compared with the two auction mechanisms by Erik Maskin himself. Second, discriminatory and uniform-price mechanisms are the most widely used auction mechanisms in Multi-Unit auctions and has attracted attention on the comparisons between them (e.g., Engelbrecht-Wiggans and Kahn 1998a, b; Hortaçsu and McAdams 2010; Ausubel et al. 2014), and they are also the fundamental mechanisms introduced in classical text book (Krishna 2009; Milgrom 2004). Third, both discriminatory and uniform-price auctions have been suggested as the two most commonly employed mechanisms to allocate GHG emission permits (see, e.g., Joskow et al. 1998; Porter et al. 2009; Holt et al. 2007; Benz et al. 2010). Fourth, comparing the two auction mechanisms in the context of GHG emission reduction has attracted considerable attention from the literature while there is not a consensus on which mechanism performs better. For instance, evidence provided by Cramton and Kerr (2002), Cramton (2007a), and Betz et al. (2010) supports discriminatory auctions while Holt et al. (20072008) supports uniform-price auctions.

As noted by a reviewer, the budget is wasted for this purpose only in cases where the leftover budget cannot be rolled over into the future period of the auction. This is a conventional situation in which the government determines the future budget based on the actual spending of the current budget in related fields (Peacock and Wiseman 1961; Payne 1998; Guo and Yang 2007).

$10 is the reserved reduction price, equal to the total $100 subsidy divided by a single firm’s 10 unit reduction capacity.

Up to five winners can be selected in each market given the parameters imposed in this numerical example.

Therefore, compared to the uniform-price mechanism, the Maskin mechanism reduces the gap between transaction prices and a firm’s actual reduction costs, and it provides a theoretically more efficient way to spend a subsidy with the same bid structure.

Following Maskin (2011), Ensthaler and Giebe (2014a, b) and Jarman and Meisner (2017) develop new auction mechanisms which are similar to the Maskin mechanism but guaranteeing the mechanisms to be the optimal ones with soft and ex-post budget constraint.

This background design is commonly used in experiments that investigate auction design for carbon emissions reduction programs (see, e.g., Burtraw et al. 2009; Burtraw et al. 2011; and Shobe et al. 2010).

We chose to use in-context instructions in this experiment because we are interested in the interpretability of the experimental results with respect to specific real-life policy situations regarding reduction in environmental harm (GHG emissions) and the directly related policy implications. The in-context results could differ from those when context-free instructions are used. This choice is in line with several studies that experimentally test auction design for carbon emissions reduction programs (e.g., Burtraw, et al. 2009; Burtraw, et al. 2011; Goeree et al. 2010) as well as experimental studies on procurement auction (e.g., Cummings et al. 2004). Regarding the debate on the usage of in-context versus context-free instructions, although the majority opinion is that context-free instructions should be formulated to avoid connotations caused by non-neutral words that might affect decision behavior (see, e.g., Davis and Holt 1993; Holt 1995; Kachelmeier and Shehata 1997), many scholars argue that the use of neutral instructions may distort the interpretability of experimental results with respect to the real-life situations researchers are interested in. For instance, Eckel and Grossmann (1996) emphasize that the importance of social and psychological factors can only be studied by (at least partially) abandoning abstraction, and similar arguments are put forward by, e.g., Gigerenzer (1996), Ortmann and Gigerenzer (1997), Loewenstein (1999), and Gächter and Riedl (2005). Loomes (1999, f39) comments: “it may be rather more useful to try to study the impact of context than to pursue the impossible goal of eliminating it.” Cummings et al. (2004, P 345–346) comments: “The complexity of the auction procedures being discussed convinced us that a fair amount of context would be useful to reduce confusion…” Zizzo (2010, P 82) also comments: “Context can help subjects’ understanding; it may help external validity for the specific real world context…; if the experiment is complex, context may to some extent be unavoidable.” As for the empirical evidence, Alm et al. (1992) and Abbink and Hennig-Schmidt (2006) respectively find no significant effect for the usage of in-context instructions on decisions regarding tax contributions and bribery, while Baldry (1986) finds that tax payment framed instructions result in subjects paying more taxes.

If the highest (lowest) production costs are drawn for both low and high emitters, the total subsidy needed for all firms to sell their emissions reduction at their costs is 105 (315) yuan; therefore, the actual amount is in the interval [105, 315], depending on the revealed production costs. This tight limitation of the available subsidy reflects real budget constraints.

It is worth noting that although firms have multiple units of emission reductions to sell, each firm is restricted to selling a fixed all-or-nothing quantity of reduction units with a single transaction price. This restriction guarantees that the auctions conducted in our experiment are essentially single-unit demand auctions.

However, learning was more difficult with the varying cost across auctions in each session; therefore, compared to constant cost across all auctions in a session, this experiment will present the lower bounds of learned bidding behavior.

It is noteworthy that although one can use an institution such as a seal-bid format without revealing bids – to prevent bidders seeing others’ actual bids during auctions in hopes of curbing collusion – it is hardly possible to effectively prohibit bidders from knowing this information after each monthly or quarterly held auction, such as in EU-ETS. Thus, revealing the bid after each period can be a natural choice to approach the situation in reality as well as to guarantee that subjects have equal information. This design choice is in line with Cummings et al. (2004), who allow all bidders to know all bids after each auction period, and with Burtraw et al. (2009), who provide an electronic chat room to let bidders explicitly communicate prior to each period of the sealed bid auctions. Moreover, a recent literature survey by Kagel and Levin (2016) shows evidence that collusion is difficult in auction markets when information is asymmetric and incomplete and when competition pressure is high. Additional evidence from literature on collusive behavior in oligopoly markets show that tacit collusion is almost never found in markets with more than four sellers (see, e.g., Huck et al. 2004, and Fonseca and Normmann 2012, and a literature survey by Haan et al. 2009, and Potters and Suetens 2013). Revealing bid information is also a common design feature for experiments on double oral auctions (see, e.g., Smith 1962; Plott and Smith 1978). We thus provide the aforementioned information while maintaining anonymity. We further show evidence in the results section that revealing the information does not have much effect on the bidding behavior in our experiment.

1 US dollar = 6.32 yuan at the time of the experiment.

In addition, the difference between the winner's bid and the winner's indifference price is a useful measure to reflect the role of each auction type in discovering firms’ actual costs of emission reduction. We find that this difference is considerably larger in discriminatory auctions than that in uniform-price and Maskin auctions, and the differences in uniform-price and Maskin auctions decrease significantly across periods, while this is not true in discriminatory auctions. To save space, we do not report the details of these results in this paper, but they can be found in the initial working paper version (He and Chen 2014). The findings thus indicate that both uniform-price and Maskin auctions outperform discriminatory auctions in price discovery, and they play a stronger role in preventing high bids from winning auctions. Consequently, the winner(s) in uniform-price and Maskin auctions is (are) more likely to have lower emissions reduction costs than those in discriminatory auctions, which leads to a more socially desirable outcome.

Because bidders’ bidding behavior depends on the other bidders’ bids in previous periods in the same markets, observations based on individual bidders are not independent. Only the observations based on the mean of all bids in one auction market across all periods are independent, and we will use this statistic for the nonparametric tests.

We can observe from Fig. 1 that the dynamic pattern of bids shows a reduction towards the indifference price, while it increases in the last three periods. This pattern is determined by the dynamic pattern of the cost of emission reduction, which is randomly drawn from an uniform distribution within certain intervals and the random cost draws were ensure to be balanced across treatments.

The rules in Maskin auctions guarantee transaction prices no higher than those in uniform-price auctions if all bids are the same in both auctions, but we observe higher transaction prices in Maskin auctions. This phenomenon suggests that the function of Maskin auctions in suppressing the transaction price is dominated by its effects on increasing bids.

However, the significant positive differences between bids and indifference prices in uniform-price (Wilcoxon signed-rank tests, p < 0.001) and Maskin auctions (p < 0.001) suggest that bidders are not induced to bid closely at their cost.

We conduct Wilcoxon rank-sum tests for all the performance variables presented in Table 4, with consideration for the correction on the potential family-wise errors following the method introduced by List, Shaikh and Xu (2019) and the clustered data structure of this experiment following the method introduced by Datta and Satten (2005), respectively. Both sets of the robustness check results shown in Tables A1 and A2 in Appendix 4 are qualitatively identical to those shown in Table 4, suggesting that the results in Table 4 are robust with both ways of statistical methodology adjustment.

We further conduct Wilcoxon rank-sum tests for all the performance variables presented in Table 4, but for the last ten and last five periods. The results in Table A3 in Appendix IV show that most of the results are similar compared to those in Table 4 in terms of both quantity and significance, suggesting that most of the significant results over all 20 periods are retained in the last ten periods and the last five periods, while a few results in Table 4 become insignificant mainly due to an increase in variation but without any change in the signs of the differences.

Further analysis provides evidence on the limited effect of revealing bids on bidding behavior in our experiment. First, we compare the bids between the first and second periods of various auction markets, in which bidders either do not know others’ bids or they know others’ bids in the first period when they made bidding decisions. We find no difference for any of the three auction mechanisms or for all data pooled together (Wilcoxon rank-sum tests, p > 0.1 in all cases). Second, given that Kagel and Levin (2016) show that veteran subjects can collude more easily, we conducted an additional experiment with veteran subjects from an experimental economics course. In some sessions, we even tried to provide tips to the subjects to spur them to collude. However, little evidence can be found that indicates the existence of collusion. Third, after the experiment, we asked the veteran subjects, “Did you consider coordinating with the other bidders to make higher profits from the auction market, and if so, how?” We found that no one had considered doing so. Therefore, the differences in bidding behavior across treatments are even less likely to be affected by revealing bids.

We also tried to include an interaction of treatment variables by period in each of the models. However, this analysis does not support the existence of interaction effects.

We compare subjects’ three individual characteristics (i.e., gender, grade and major belonging) recorded when recruiting them, and we find that, for all the three characteristics, the differences in mean of these characteristics across treatments are small (see Table 11 in Appendix IV) and both the p-values of all the Wilcoxon rank-sum tests between any two of the three treatments and the p-values of Kruskal–Wallis tests amongst the three treatments are above the conventional statistical level (see Table A5 in Appendix IV).

Following the criteria introduce in Wooldridge (2016), we choose random effects rather than fixed effects estimator based on the specific structure of our data. On the one hand, given the key independent variables being interested (i.e., the two treatment dummy variables) are constant over periods, these variables cannot be included in the fixed effects model. On the other hand, since the auction mechanisms are randomly assigned, our data satisfy the crucial assumption of the random effects model that the individual time-constant unobservable is independent of the treatment dummy variables. We thus choose the random effects estimator.

For example, as suggested by a reviewer, subsidies may be the only available instrument to incentivize reforestation by small landowners. The small landowners can be included in an emission trading system only when they are treated as the net winners (i.e., are implicitly subsidized by other sectors).

In our experiment setting, all firms have the same \(x\), which is 10. High emitters have 5 capacity and require 2 emission units to operate 1 unit of capacity. And low emitters have 10 capacity and require 1 emission to produce 1 unit. So both two kinds of firms have the same maximum possible emission.

For example, when \(n = 2\), all \(F_{i}\) are the same and \(F^{\prime\prime} < 0,\;F^{\prime\prime} < - 4F^{\prime}(1/2)\;\forall c_{i}\).