Social surveys generally assume that a sample of units (students, individuals, employees,...) is observed by two-stage selection from a finite population, which is grouped into clusters (schools, household, companies,...). This design involves sampling from two different populations: the population of schools or primary stage units and the population of students or second-stage units. Calibration estimators for student statistics can be defined by using combined information based on school totals and student totals. Auxiliary information from the units at the two stages can be calibrated by integrated weighting, as proposed by Lemaître and Dufour or Estevao and Särndal. Two calibration estimators for the population total based on unit weights are defined. The first estimator satisfies a calibration equation at the unit level, and the second one, at the cluster level. The proposed estimator shrinks the unit estimator toward the cluster. A simulation study based on two real populations is carried out to study the empirical performance of this shrinkage estimator. The populations studied were obtained from the Programme for International Student Assessment database and from the Spanish Household Budget Survey.