We develop a fixed-effects estimation framework for fractional-outcome panel models with a logit conditional mean. Pairwise quasi-differencing eliminates individual effects from the moment conditions, yielding a generalized method of moments estimator that is consistent under the stated moment restrictions even when the number of time period is finite and fixed. The framework allows unrestricted dependence between individual effects and covariates, accommodates endogenous regressors through instrumental variables, and extends to multivariate shares that sum to one. Boundary observations require no adjustment, and average semi-elasticities can be estimated without recovering the individual effects. We apply the framework to Australia's National Disability Insurance Scheme (NDIS), using HILDA (Household, Income and Labour Dynamics in Australia) survey data for 2011-2023 and instruments based on the scheme's staggered geographic rollout. We examine how NDIS receipt affects the allocation of time across paid work, housework, disability care, and remaining activities for recipients and other household members. The estimates indicate that recipients reduce work and disability care, while other household members increase disability care.