Semiparametric　models　are　often　used　to　analyze　panel　data　for　a　good　trade-off　between　parsimony　and　flexibility.　In　this　paper,　we　investigate　a　fixed　effect　model　with　a　possible　varying　coefficient　component.　On　the　basis　of　empirical　likelihood　method,　the　coefficient　functions　are　estimated　as　well　as　their　confidence　intervals.　The　estimation　procedures　are　easily　implemented.　An　important　problem　of　the　statistical　inference　with　the　varying　coefficient　model　is　to　check　the　constant　coefficient　about　the　regression　functions.　We　further　develop　checking　procedures　by　constructing　empirical　likelihood　ratio　statistics　and　establishing　the　Wilks　theorems.　Finally,　some　numerical　simulations　and　a　real　data　analysis　is　presented　to　assess　the　finite　sample　performance.