A PERMUTATION-BASED ESTIMATOR FOR MONOTONE INDEX MODELS

This paper shows that the finite-dimensional parameters of a monotone-index model can be estimated by minimizing an objective function based on sorting the data+ The key observation guiding this procedure is that the sum of distances between pairs of adjacent observations is minimized ~over all possible permutations! when the observations are sorted by their values+ The resulting estimator is a generalization of Cavanagh and Sherman’s monotone rank estimator ~MRE! ~Cavanagh and Sherman, 1998, Journal of Econometrics 84, 351–381! and does not require a bandwidth choice+ The estimator is Mn-consistent and asymptotically normal with a consistently estimable covariance matrix+ This least-squares estimator can also be used to estimate monotone-index panel data models+ AMonte Carlo study is presented where the proposed estimator is seen to dominate the MRE in terms of mean-squared error and mean absolute deviation+