Loss Functions for Predicted Click-Through Rates in Auctions for Online Advertising

Article Source: Journal of Applied Econometrics, 2017 (forthcoming)
Publication Date:
Time to Read: 2 minute read
Written By:

 Patrick Hummel

Patrick Hummel

Search for the full article on Bing



Online ads are usually purchased in auctions. Auction participants sometimes misestimate the likelihood that users will click on an ad, resulting in economic loss. This paper develops a new method of estimating such losses called the “empirical loss function.”


Policy Relevance:

The empirical loss function calculates losses more accurately than the standard methods used by most applications.


Key Takeaways:
  • Ads on search engine result pages and other online ads are often purchased in auctions; usually, the advertiser only pays if the user click on the ad (cost-per-click or CPC pricing).
  • An ad with a bid of $2 is worth more than an ad with a bid of $4, if users are twice as likely to click on the $2 ad; auction participants must estimate the probability that users will click on ads.
  • Estimation is done by using machine learning to develop reliable models of user behavior involving hundreds or even billions of variables, known as features.
    • Features include the ad, the page on which it will be shown, and qualities of the user that influence click-through rates (CTRs).
    • The machine is trained using billions of data points collected from users.
  • When the CTR of an ad is wrongly predicted, users might see an ad other than the best ad, resulting in a loss; a loss function shows the amount of loss from an error in estimation.
  • Usually, losses from misestimation are calculated using methods known as mean squared error (MSE) or log likelihood, but these methods do not reflect the actual losses from misestimation.
  • This paper develops a better method of adjusting the models by considering the true economic losses that result from mistakes in estimating predicted CTRs; this method is called the “empirical loss function.”
  • Both the MSE and LL methods impose penalties that increase with the size of the mis-prediction, thus imposing much greater penalties for large mispredictions than small ones, but the empirical loss function imposes significant penalties for small mispredictions and only slightly larger penalties for large mispredictions.
  • The empirical loss function is more accurate; if a predicted CTR is much too high, further errors will not matter, because the ad will win the auction, and if a predicted CTR is much too low, the ad will lose the auction, and further errors will not matter.
  • Using the empirical loss function method reduces losses from estimation errors compared to the standard method, even when models adjusted using the standard method are given large amounts of training data.



R. Preston McAfee

About R. Preston McAfee

R. Preston McAfee was the Chief Economist and Corporate Vice President at Microsoft from June 2014 until February 2018. His research has concentrated on microeconomics and industrial organization, on topics such as auctions, bundling, price discrimination, antitrust, contracting, and mechanism design. His recent research interests involve machine learning, user generated content, and exchange design, and he has recently been publishing research at the interface between microeconomics and computer science.