Ideal point estimation is a topic of central importance in political science. Published work relying on the ideal point estimates of Poole and Rosenthal for the U.S. Congress is too numerous to list. Recent work has applied ideal point estimation to the state legislatures, Latin American chambers, the Supreme Court, and many other chambers. Although most existing ideal point estimators perform well when the number of voters and the number of bills is large, some important applications involve small chambers. We develop an estimator that does not suffer from the incidental parameters problem and, hence, can be used to estimate ideal points in small chambers. Our Monte Carlo experiments show that our estimator offers an improvement over conventional estimators for small chambers. We apply our estimator to estimate the ideal points of Supreme Court justices in a multidimensional space.
Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters
