The　missing　response　problem　in　single-index　models　is　studied,　and　a　bias-correction　method　to　infer　the　index　coefficients　is　developed.　Two　weighted　empirical　log-likelihood　ratios　with　asymptotic　chisquare　are　derived,　and　the　corresponding　empirical　likelihood　confidence　regions　for　the　index　coefficients　are　constructed.　In　addition,　the　estimators　of　the　index　coefficients　and　the　link　function　are　defined,　and　their　asymptotic　normalities　are　proved.　A　simulation　study　is　conducted　to　compare　the　empirical　likelihood　and　the　normal　approximation　based　method　in　terms　of　coverage　probabilities　and　average　lengths　of　confidence　intervals.　A　real　example　illustrates　our　methods.