How much should someone pay to use another person’s property without permission? The question sounds like a law school hypothetical (ok, it already is one), but it is anything but hypothetical in several real-world licensing markets. Music streaming, natural gas transportation, and standard-essential patents all operate under legal regimes that permit parties to negotiate licensing terms privately, while offering would-be users a fallback option to obtain access at a “recourse” rate determined (or overseen) by a court or regulator. AI training data may be the next frontier of such liability-rule background regimes.
These arrangements are attractive for good reasons. By providing an alternative to protracted negotiations, they can reduce transaction costs, mitigate hold-up, and facilitate socially valuable exchanges. But they also create a vexing problem for the authorities charged with setting the fallback price: How does one determine a fair market rate when the market transactions used to estimate it are themselves influenced by the very rate being set?
In a new paper, we tackle this problem head on, developing a structural economic model and a statistical approach for recovering fair market prices from negotiations conducted in the shadow of a regulatory fallback.
The Problem: Bargaining in the Shadow of the Law
Consider the market for digital performances of copyrighted sound recordings. The Copyright Royalty Board (CRB) periodically sets compulsory licensing rates that permit qualifying music services to stream recordings without negotiating directly with copyright owners. The statutory benchmark generally asks what a hypothetical willing buyer and willing seller (WBWS) would agree upon in a competitive market without the compulsory license.
In practice, however, the CRB frequently relies on actual negotiated licensing agreements to construct this hypothetical market. And therein lies the rub.
A music service negotiating with a record label knows that it can walk away and invoke the compulsory license instead. That option influences which agreements are struck, which are abandoned, and what prices emerge from successful negotiations. Treating these observed prices as unalloyed evidence of an unconstrained market is therefore inherently self-referential: The prevailing regulatory rate distorts the very evidence that is then used to set the successor rate.
This circularity is not merely theoretical. In prior CRB proceedings, adjudicators acknowledged the potential distortion but declined to correct for it, largely because no reliable method existed to quantify the adjustment. The same problem arises in natural gas pipeline regulation and in fair, reasonable, and non-discriminatory (FRAND) licensing of standard-essential patents.
A Statistical Way Out
Our paper offers two principal contributions.
First, we develop a structural bargaining model that formally characterizes how a background compulsory rate distorts observed negotiated prices. Under relatively weak conditions, the resulting bias is systematically downward. Indeed, the effect extends beyond average prices: The entire distribution of negotiated rates shifts downward relative to the hypothetical WBWS benchmark, including its median and other quantiles.
The intuition is straightforward. A compulsory rate gives prospective buyers an option to bypass negotiations, disproportionately removing higher-valued transactions from the pool of observed negotiated deals. An adjudicator relying exclusively on those surviving deals consequently receives a distorted picture of what unconstrained bargaining would produce.
Second, and more importantly, we propose a method for correcting this distortion through maximum likelihood estimation (MLE). Our approach uses two sources of information: the prices of successfully negotiated agreements and the relative frequency of transactions consummated at the compulsory rate. Together, these observations help recover the underlying distribution of buyer and seller valuations, which can then be used to simulate the hypothetical market without the regulatory fallback.
The initial results are encouraging. In simulations using a conventional Gaussian valuation model, observed negotiated prices understate the true WBWS mean by approximately 11.5 percent. Our MLE correction reduces that shortfall to approximately 3 percent, eliminating roughly 72 percent of the original bias. Parallel exercises using lognormal distributions produce similarly promising estimates of counterfactual prices.
To be sure, the method is not a statistical panacea. It requires assumptions about the underlying valuation distributions, and the estimation of certain structural parameters can prove challenging. Yet the counterfactual prices that adjudicators ultimately care about remain surprisingly robust. Moreover, several seemingly complicating institutional features—including bundled licenses and multiple fallback rates—actually improve statistical identification.
Beyond Music Licensing
Although our motivating example comes from copyright licensing, the implications extend considerably further. The framework can accommodate natural gas pipeline recourse rates, judicially determined FRAND royalties for standard-essential patents, and potentially even proposed compulsory licensing arrangements for generative AI training data.
More broadly, the analysis speaks to a recurring tension between markets and regulation. Regulators frequently seek to harness the informational advantages of private bargaining while simultaneously constraining the terms on which it occurs. Yet in doing so, they inevitably alter the very market signals they hope to learn from.
Our approach offers a way to disentangle these effects, allowing adjudicators to look beyond the regulatory shadow rather than simply perpetuating it. The next step is to put the method to work on actual licensing transactions, where its practical utility can be assessed outside the controlled environment of simulations.
When the key regulatory task requires one to determine what the “market” would do without regulatory intervention, it helps to have a method that can allow regulators to avoid stumbling over their own shadows.
This post comes to us from Eric Talley, the Marc & Eva Stern Professor of Law and Business at Columbia Law School, and Rhys Lester Talley, an M.S. candidate in computer science at Columbia University’s Fu Foundation School of Engineering and Applied Science. It is based on their new working paper, “You’ve Got a FRAND in MLE: Coaxing Fair Prices from the Shadow of a Liability Rule,” available here.