The Age-Time-Cohort Problem and the Identification of Structural Parameters in Life-Cycle Models

The standard approach to estimating structural parameters in life-cycle models imposes sufficient assumptions on the data to identify the "age profile" of outcomes, then chooses model parameters so that the model's age profile matches this empirical age profile. I show that the standard approach is both incorrect and unnecessary: incorrect, because it generically produces inconsistent estimators of the structural parameters, and unnecessary, because consistent estimators can be obtained under weaker fewer assumptions. I derive an identification method that avoids the problems of the standard approach and illustrate its benefits in a simple model of consumption inequality.