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...Journal of econometrics contents lists available at sciencedirect homepage www elsevier com locate jeconom paneldatamethodsforfractionalresponsevariableswithanapplicationtotest passrates leslie e papke jeffrey m wooldridge departmentofeconomics michiganstateuniversity eastlansing mi unitedstates a r t i c l n f o b s article history we revisit the effects spending on student performance using data from state michigan online june in addition to exploiting dramatic change funding mid and subsequent nonsmooth jel classification changes propose nonlinear panel models that recognize bounded nature pass rate importantly show how estimate average partial which can be compared across many different linear under assumptions estimated methods wefindthatspendinghasnontrivialandstatisticallysignificanteffects althoughthe keywords diminishingeffect is not especially pronounced fractional response elsevierb v allrightsreserved paneldata unobservedeffects probit executivesummary todistrictspending in...