Working Paper 707

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

Sam Schulhofer-Wohl

Revised June 22, 2016

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).

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Updated version: Federal Reserve Bank of Chicago Working Paper 2017-18.