This paper introduces a new estimator for the fixed-effects ordered logit model. The proposed method has two advantages over existing estimators. First, it estimates the differences in the cut points along with the regression coefficient, leading to provide bounds on partial effects. Second, the proposed estimator for the regression coefficient is more efficient. I use the fact that the ordered logit model with J outcomes and T observations can be converted to a binary choice logit model in (J - 1)T ways. As an empirical illustration, I examine the income-health gradient for children using the Medical Expenditure Panel Survey.