Advanced Consumption Models - Modeling Macroeconomics

Materials¶

The following computational notebook is a companion to the reading assigned in Lecture 04:

By the end of this lecture, students will be able to:

Derive the Euler equation for a consumer with habit formation and explain why habits reduce current consumption relative to the no-habit case
Apply the envelope theorem with two state variables to obtain the combined Euler equation under habits
Derive the intratemporal condition linking marginal utilities of durable and nondurable goods
Explain why durable goods spending is more volatile than nondurable consumption
Distinguish exponential from quasi-hyperbolic discounting and derive the modified Euler equation for the Laibson model
Describe how the marginal propensity to consume amplifies present bias

Habit formation: Preferences in which past consumption raises the reference point for current utility, producing serial correlation in consumption growth
Envelope theorem with two states: Applying the envelope condition separately for wealth and the habit stock (or durable stock) to characterize the value function
Intratemporal condition: The optimality condition equating the marginal rate of substitution between durables and nondurables to the user cost of durables $(r + \delta)/\mathsf{R}$
Spending volatility: Durable goods expenditure amplifies consumption shocks by the factor $(\epsilon + \delta)/\delta$ , explaining why housing and auto sales are cyclically volatile
Quasi-hyperbolic discounting: A discount structure that applies an extra factor $\delta_h < 1$ to all future periods, capturing the experimental finding that subjects are more impatient about immediate tradeoffs than distant ones
Present-bias and the MPC: The distortion from quasi-hyperbolic preferences scales with the marginal propensity to consume; liquidity-constrained consumers suffer more from present bias