Day 1: Monday
Introduction
to Dynamic Macroeconomics: Analysis of Saving and Investment
Required
reading: This
day will concern the neoclassical growth model with an infinite horizon
behavior of saving. An excellent textbook presentation of this model is given
by David Romer, Advanced
Macroeconomics, chapters 1 and 2. The first chapter discusses economic
growth facts (PDF) and the
second chapter discusses the "Ramsey-Cass-Koomans"
infinite horizon model in continuous time as well as the two period overlapping
generations model in discrete time (PDF).
The two course lectures will discuss some macroeconomic facts and describe the Ramsey-Cass-Koopmans model in discrete time.
Lecture 1: Basic facts and core concepts (PDF of slides)
Lecture 2: Capital accumulation in general
equilibrium (PDF of slides)
Required reading: Lecture notes
on " Introduction
to dynamic macroeconomics: Analysis of saving and investment" (PDF: document)
Study
Problems
Problem
1: The Stationary State:
We are interested in the stationary state
of the basic model of capital accumulation for two reasons. First, it is the
long-run position to which the model economy ultimately moves, so that it
provides the long-run positions of the model economy. Second, its form is
reveals how the long-run positions of many models with discounted utility can
be analyzed: one first can determine elements of the production side of the
economy consistent with the long-run interest rate implied by time preference;
then one can determine the additional features of the economy from preferences.
PROBLEM (ANSWERS) Related classic
paper by Brock
Problem
2: Revenue from Money Creation.
We will be studying dynamic optimization
for several reasons. One is to understand the nature of optimal individual and
firm behavior over time and under uncertainty. Another is to understand how
optimal public policy might be determined and whether observed public policy is
according to a particular model. In his classic study of the German
hyperinflation, Cagan observed that the country
appeared to be creating money "too fast" even if its objective was to
maximize a measure of the revenue from money creation. We study an intertemporal optization problem
for such a government. PROBLEM (ANSWERS) Related
classic paper by Cagan
These two problems are
tied together by a basic point about the maximization of "present
discounted values". There are two
reasons that the optimal long-run policy will not generally maximize the static
flow objective (utility in problem 1, revenue in problem 2). One is that there
may be a state variable (capital in problem 1) that ties together periods; the
other is that there may be a forward-looking constraints (expected inflation in
problem 2) that ties together periods. These connections generalize to models
with multiple state variables and multiple forward-looking constraints.
Note that the two
classic papers are not additional required reading. However, they
provide background for students that are interested in looking at how the study
problem materials are related to research in aggregative economics (as diverse
as capital theory and economic history)
MACROLAB
Materials
LAB1: Introductory materials
Plotting
LAB2: Stochastic Systems (developed in lecture 5)