Especially if these graduates are unemployed and they can't find a job easily, they would feel unproductive by staying home.

unproductive 是由前缀 un-（表示否定）和形容词 productive（有生产力的）组成的复合词。productive 来自名词 product（产品）加上后缀 -ive（表示"具有...性质的"）。unproductive 字面意思是"不具有生产性质的"，引申为"没有产出的"、"无成效的"。