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Per Krusell

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Chapter 1

Introduction

These lecture notes cover a one-semester course. The overriding goal of the course is

to begin provide methodological tools for advanced research in macroeconomics. The

emphasis is on theory, although data guidesthe theoretical explorations. We build entirely on models with microfoundations, i.e., models where behavior is derived from basic

assumptions on consumers’ preferences, production technologies, information, and so on.

Behavior is always assumed to be rational: given the restrictions imposed by the primitives, all actors in the economic models are assumed to maximize their objectives.Macroeconomic studies emphasize decisions with a time dimension, such as various

forms of investments. Moreover, it is often useful to assume that the time horizon is

inﬁnite. This makes dynamic optimization a necessary part of the tools we need to

cover, and the ﬁrst signiﬁcant fraction of the course goes through, in turn, sequential

maximization and dynamic programming. We assume throughout that timeis discrete,

since it leads to simpler and more intuitive mathematics.

The baseline macroeconomic model we use is based on the assumption of perfect competition. Current research often departs from this assumption in various ways, but it is

important to understand the baseline in order to fully understand the extensions. Therefore, we also spend signiﬁcant time on the concepts of dynamiccompetitive equilibrium,

both expressed in the sequence form and recursively (using dynamic programming). In

this context, the welfare properties of our dynamic equilibria are studied.

Inﬁnite-horizon models can employ diﬀerent assumptions about the time horizon of

each economic actor. We study two extreme cases: (i) all consumers (really, dynasties) live

forever - the inﬁnitely-lived agent model -and (ii) consumers have ﬁnite and deterministic

lifetimes but there are consumers of diﬀerent generations living at any point in time the overlapping-generations model. These two cases share many features but also have

important diﬀerences. Most of the course material is built on inﬁnitely-lived agents, but

we also study the overlapping-generations model in some depth.

Finally, manymacroeconomic issues involve uncertainty. Therefore, we spend some

time on how to introduce it into our models, both mathematically and in terms of economic concepts.

The second part of the course notes goes over some important macroeconomic topics.

These involve growth and business cycle analysis, asset pricing, ﬁscal policy, monetary

economics, unemployment, and inequality. Here, few new tools areintroduced; we instead

simply apply the tools from the ﬁrst part of the course.

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Chapter 2

Motivation: Solow’s growth model

Most modern dynamic models of macroeconomics build on the framework described in

Solow’s (1956) paper.1 To motivate what is to follow, we start with a brief description of

the Solow model. This model was set up to study a closed economy, and we will assumethat there is a constant population.

2.1

The model

The model consists of some simple equations:

Ct + It = Yt = F (Kt, L)

(2.1)

It = Kt+1 − (1 − δ ) Kt

(2.2)

It = sF (Kt , L) .

(2.3)

The equalities in (2.1) are accounting identities, saying that total resources are either

consumed or invested, and that total resources are given by the output of a production

function withcapital and labor as inputs. We take labor input to be constant at this point,

whereas the other variables are allowed to vary over time. The accounting identity can also

be interpreted in terms of technology: this is a one-good, or one-sector, economy, where

the only good can be used both for consumption and as capital (investment). Equation

(2.2) describes capital accumulation: the output...