A Gentle Introduction to Intertemporal Choice

Lecture notes on consumption, saving, growth, and asset pricing for advanced masters and first-year PhD students in economics.

Authors: Christopher D. Carroll and Alan E. Lujan Solis

1About¶

Almost every question in macroeconomics turns on how people trade off today against tomorrow. How much of a raise gets spent? Why do the rich save so much more than the poor? Why does the stock market move so much more than dividends do? These notes work through the theory that answers such questions, starting with a consumer who lives for two periods and knows everything, and ending with models rich enough to be taken to data.

We keep the arithmetic in view throughout, working each result through in full. Every chapter starts from the simplest case that contains anything interesting and reaches the harder ones by relaxing one assumption at a time. Where a model has no closed form we say so and compute instead, because a formula nobody can interpret teaches less than a number somebody can check.

The notes originated from Christopher Carroll’s graduate macroeconomics lecture notes at Johns Hopkins University. Alan Lujan teaches from these materials in the advanced macroeconomics sequence of JHU’s masters economics program.

2Contents¶

2.1Consumption¶

From perfect foresight through OLG to buffer stock models:

• Perfect foresight consumption under CRRA and CARA utility

• The permanent income hypothesis and consumption smoothing

• Precautionary saving and buffer-stock behavior

• Risk premia and the effects of uncertainty

• Overlapping generations and lifecycle models

• Habits, hyperbolic discounting, and behavioral extensions

2.2Asset Pricing¶

Lucas, Mehra and Prescott, Blanchard, and others:

• CRRA and CARA portfolio allocation

• The consumption-based capital asset pricing model (C-CAPM)

• The equity premium puzzle

2.3Growth¶

Models of economic growth:

• The Ramsey-Cass-Koopmans model

• Fiscal policy in growth models

• Decentralization and competitive equilibrium

• Endogenous growth (Romer, Lucas, Rebelo AK)

• Overlapping generations growth models

2.4Investment¶

From Keynes to imperfections:

• The Hall-Jorgenson neoclassical model

• Tobin’s q and the marginal q model

• Capital market imperfections

• Investment and cash flow sensitivity

2.5DSGE Models¶

Dynamic stochastic general equilibrium frameworks:

• The Brock-Mirman stochastic growth model

• Real business cycle theory

2.6Numerical¶

Derivations and methods useful for macroeconomics:

• Useful facts for graduate macroeconomics

• Aggregation methods

2.7Supplemental Notes¶

Notes that supplement the main chapters, on the website only and not in the PDF:

• Consumption out of risky assets, and with optimal portfolio choice

• Consumption under CARA utility with income risk

• Consumption dynamics with a time-varying interest rate

• CRRA portfolio choice with two risky assets

• An entrepreneur’s problem under perfect foresight

• The q-Ramsey model, and gross saving and growth in the RCK model

• Equiprobable approximations to lognormal distributions

3License¶

• Content: CC BY-NC-ND 4.0

• Code: Apache-2.0

5Citation¶

If you use these materials, please cite:

Carroll, Christopher D. and Alan E. Lujan Solis. A Gentle Introduction to Intertemporal Choice. https://intertemporal-choice.github.io