Proposed Auction Design/Constraints

Reserve price: Each allowance has a reserve price of $3.00. We will assume that all price values in our simulation are adjusted to equivalent real-money terms so no annual adjustment is required.

Minimum lot size: All bids are submitted in multiples of 1,000, with 1,000 being the minimum lot size. Our model scales so that "1" means a lot of 1,000.

Sealed bid: All bidders are naive to other bidders' value profiles, but can view their own bidding history.

Uniform clearing price: Maximum price floor needed to clear the market above reserve price.

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Model/Simulator Methodology

Here, we attempt to design a simulation environment whereby the environment (market) and agents jointly fulfill the above-stated constraints.

1. The number of agents per simulation and the total number of allowances are determined empirically through the RGGI data.

   • Total number of agents = total number of compliant active accounts (out of: 181 in compliance, 268 active, 610 all-time registered) = 181.

   • Based on the RGGI auction data, 40,000,000, the weighted average number of allowances offered per quarter, seems to be a good starting point. 

2. The auction will be run until at 10 rounds have elapsed. A total of 24 auctions are run, to represent 24 quarterly auctions over 6 years.

3. The budget is randomly determined on a per-agent basis from a fat-tailed distribution (in this case, gamma (Γ) with k = 1, theta = 66.67, mean = 230,000*, scaling with the average distribution of company sizes across sectors, based on an empirical study) to account for the fact that we do not know the true distribution of values, except that they have rather fat tails (not normally distributed).

   • Citation for Empirically-derived Distribution: Sang Sup Cho, (2016) "A study on firm size distribution of the service sector and manufacturing sector", Asia Pacific Journal of Innovation and Entrepreneurship, Vol. 10 Issue: 1, pp.91-100, https://doi.org/10.1108/APJIE-12-2016-011

   • Implicitly, the budget allocated should be a reflection of either allowance requirements or trader size. Therefore, allowance requirements are generated as a heuristically-determined multiple of company wealth.

   • *Aggregate revenue raised from auction distributions (from 24 complete quarters) is: Mean price x Total allowances sold (rounded) = $3.70 * 920,000,000 = $3,404,000,000. If we divide this by the number of quarters and number of all-time registered accounts, we have: $3,404,000,000 / (24*610) = $232,513. So, as a baseline, a mean of $230,000 seems reasonable.

4. Agents have varying strategies depending on whether they are carbon emitters or simply traders – therefore, there will be 2 types of bidding agents.

5. After each auction is finished, by right, secondary model trading should occur:

   • The remaining emitters who still require allowances, as well as the speculative traders, will collectively try to clear the overall market in the secondary market. We will assume that all the remaining transactions are exchange-settled (the data suggests that a vast majority of secondary market transactions are done this way)

   • However, due to difficulties related to implementation, we went with a stylistic choice: the secondary market trading in our model that occurs once after all auctions in a particular model run are done. This is meant to be a proxy for all secondary market trading that has occurred over time – we expect to lose some information this way, but this makes it possible for us to implement, which provides the information we would otherwise miss out on.

   • The secondary market is cleared by settling transactions on the market starting from the endpoints of the bid-ask spread.

6. In addition, after each auction, agents’ budgets and required number of allowances are “replenished” – this is a stylistic choice that reflects company budget planning broken down on a quarterly basis. This also allows for some variation across quarters.

7. Every four auctions (i.e. every “year”), the number of allowances is multiplied by some number less than one (default: 0.9) to reflect the diminishing supply of allowances over time, based on typical cap & trade policy, and specifically, the RGGI’s policies.

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After we got the initial simulation of the auction to work that replicated the RGGI model as closely as possible, we started to manipulate different variables to see how the results would be affected (under Results tab)

 

Model Variables & Rule Variations

Auction Pricing Mechanisms:

1. Default: Uniform Clearing Price

2. Second Price Auction

Reserve Prices:

• Can be varied over a range, but the results are intuitive enough (higher reserve prices = higher floors and higher average prices) that repeated testing is not necessary.

Allowance Reduction Rate:

• Can be varied over a range, but the results should also be quite intuitive – as allowances are reduced, prices go up given a certain allowance requirement profile among agents.

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