Learning and Efficiency in a Gambling Market

We present a statistical model which uses data on National Football League games and betting lines to study how agents learn from past outcomes and to test market efficiency. Using Kalman Filter estimation, we show that terms' abilities exhibit substantial week-to-week variation during the season. This provides an ideal environment in which to study how agents learn from past information. While we do not find strong evidence of market inefficiency, we are able to make several observations on market learning. In particular, agents have more difficulty learning from “noisy” observations and appear to weight recent observations less that our statistical model suggests is optimal.