The age-time-cohort problem and the identification of structural parameters in life-cycle models

A 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 this approach is both incorrect and unnecessary: incorrect, because it generally produces inconsistent estimators of the structural parameters, and unnecessary, because consistent estimators can be obtained under weaker assumptions. I derive an estimation method that avoids the problems of the standard approach. I illustrate the method's benefits analytically in a simple model of consumption inequality and numerically by reestimating the classic life-cycle consumption model of Gourinchas and Parker (2002).