Life-Cycle Consumption: Can Single Agent Models Get it Right?

In the quantitative macro literature, single agent models are heavily used to explain "per-adult equivalent" household data. In this paper, we study differences between consumption predictions from a single agent model and "adult equivalent" consumption predictions from a model where household size evolves deterministically over the life-cycle and affects individual preferences for consumption. Using a theoretical model we prove that, under mild conditions, these predictions are different. In particular, the single household model cannot explain patterns in life-cycle consumption profiles (the so called 'humps'), nor cross sectional inequality in consumption originating from the second model, even after controlling for household size using equivalence scales. Through a quantitative exercise, we then document that differences in predictions can be substantial: total (per-adult equivalent) consumption over the life-cycle can be up to 5% different, depending on the specific parameterization. We find a similar number for total cross sectional inequality.