A Leisurely Reading of the Life Cycle Consumption Data

Abstract

A puzzle in consumption theory is the observation of a hump in age-consumption profiles. This paper studies a general equilibrium life-cycle economy with capital in which households include both consumption and leisure in their period utility function. A calibrated version of the model shows that a significant hump in life-cycle consumption is a feature of the equilibrium. Thus inclusion of leisure in household preferences may provide part of the explanation of observed lifecycle consumption humps.

Should We Refinance Unfunded Social Security?

“…Thus we have a standard result where consumption is a function of the ratio of lifetime wealth to area under the discount curve (Caliendo ). Note also that the consumption profile is proportional to the survivorship function, which is intuitive since, in the absence of annuity markets, mortality risk does affect the shape of the consumption profile (Bullard and Feigenbaum ; Feigenbaum ). Further, note from expression (7) that consumption tax does not alter the Euler equation, nor does it enter the individual's optimal capital profile equations (see expressions (A11) and (A12) in Appendix ), therefore it is a fully lump‐sum tax.…”

“…Fifth, because lifetime is uncertain, following Bullard and Feigenbaum () and Feigenbaum (), a deceased agent's wealth is assumed to be spread uniformly across his surviving brethren. Thus at any time, a surviving agent can receive a bequest of size B , determined in a stationary competitive equilibrium to be discussed later.…”

“…A capital–output ratio K/Y is from 2.9 to 3.1. This is a standard range used in this line of research (see, for example, Gourinchas and Parker ; Bullard and Feigenbaum ; Feigenbaum ), and we will target capital–output ratio likewise.…”

“…A gross pre‐tax safe real rate of return r is allowed to take a wider range (preferably close to 3.5%, but not higher than 10%). The lower boundary of this estimate is used in Gourinchas and Parker (), Bullard and Feigenbaum () and Feigenbaum (), and the upper boundary is the Feldstein () estimate of pre‐tax rate of return on corporate capital investment.…”

“…We then choose the non‐payroll labour income tax rate such that the G/Y ratio is close to 21.5%. We set α = 0.34 and δ = 0.07, which are close to the values used in Bullard and Feigenbaum (), Feigenbaum () and Bucciol (). Macroeconomists have traditionally considered a wide range for the discount rate ρ , and also for σ (e.g.…”