To estimate unknown population parameters based on data having nonignorable missing values with a semiparametric exponential tilting propensity, Kim & Yu (2011) assumed that the tilting parameter is known or can be estimated from external data, in order to avoid the identifiability issue. To remove this serious limitation on the methodology, we use an instrument, i.e., a covariate related to the study variable but unrelated to the missing data propensity, to construct some estimating equations. Because these estimating equations are semiparametric, we profile the nonparametric component using a kernel-type estimator and then estimate the tilting parameter based on the profiled estimating equations and the generalized method of moments. Once the tilting parameter is estimated, so is the propensity, and then other population parameters can be estimated using the inverse propensity weighting approach. Consistency and asymptotic normality of the proposed estimators are established. The finite-sample performance of the estimators is studied through simulation, and a real-data example is also presented.