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

By Sam Schulhofer-Wohl

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 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).

Intriguing paper, especially as one can obtain an age profile that peaks much later than in previous studies, which I find to be more intuitive. But this is not the point of the paper, which is rather that the estimation of the other structural parameters can be severely affected by the difficulties of estimating this age profile. Indeed, as Sam puts it, “To find the effect of age on [income], all else equal, a researcher must collect data at the same instant on two people who were born simultaneously but are now different ages. But this is impossible.” Hence the importance of a method that does not require estimating this.

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