Teaching
Computational Macroeconomics, ECON 484, Washington University
Spring 2024
This course provides a more in-depth look into quantitative methods used in contemporary macroeconomic analysis. We will cover numerical methods used in dynamic optimization. In practice, we will apply these methods to solve two major models used in macroeconomic analysis, using Excel and Matlab. The Neoclassical Growth Model and its variants are used to study aggregate trends in output, investment and consumption, as well as the effects of government fiscal policy. The lifecycle model is used to examine questions involving decision-making over one's life cycle, such as how long to attend school, how much to work and when to retire, and the effects of social security policy. We will learn how to use empirical observations for the purpose of calibrating model parameters and how to evaluate various government policies in the context of the calibrated models.
On a side note, this is a great course for learning how to work with Matlab. 82% of Fortune 100 companies use Matlab. It is also widely used in graduate schools.
Lecture: Tuesdays and Thursday, 4-5:20
First class: January 16th (Tuesday)
Spring Break: March 10-16
Last class: April 25th (Thursday)
PRELIMINARY SCHEDULE
Week 1, Jan 16,18
We will start by discussing the general approach to modeling in macroeconomics: Slides
Background reading: Kydland and Prescott 1996 - “The Computational Experiment: An Econometric Tool.” The Journal of Economic Perspectives, 10 (1), pp. 69–85. Kydland and Prescott are the 2004 Nobel laureates.
We will also get familiar with Matlab.
Matlab for Wash U students (follow these instructions and download Matlab to your laptop by next class)
Sample programs - download the entire folder.
An introductory video tutorial on Matlab Basics - optional, it's the official Matlab video
Week 2, Jan 23, 25
We will continue to tool up.
We will review constrained optimization and learn how to solve a system of nonlinear equations in Excel and Matlab ('fsolve'). We will also learn how to perform constrained maximization in Matlab without relying on first order conditions ('fmincon'). See class notes.
Notes on the simple two period model that we will use as an example to solve in Excel and in Matlab:
To solve it in Matlab using the 'fsolve' command, save main_babymodel.m and equations_babymodel.m in the main directory and run the main script.
To solve it in Matlab using the 'fmincon' command, run main_babymodel_fmincon.m. And here is the follow-up exercise we worked out in class where we replaced one constraint with two: main_babymodel_fmincon_2BC.m.
Week 3, Jan 30, Feb 1
Most macroeconomic models involve time dynamics, i.e. aggregate variables such as output, consumption, capital stock, evolve over time and their present levels depend on what happened in the past. This means that the solution to the model reduces to a dynamical system.
In this unit, we will learn how to solve simple dynamical systems. We will do so in the context of modeling long‐run development as in Galor and Weil (2000), "Population, Technology, and Growth: From Malthusian Stagnation to the Demographic Transition and beyond." The American Economic Review 90(4), pp. 806-28. If you want to look at Oded Galor's slides on his broader agenda of unified growth theory, take a look at these. There are lots of interesting data pictures that I used to motivate this topic.
Here is the Excel file that solves the Galor-Weil model.
Here is a practice problem for the Galor-Weil model. After you attempt the question on your own, compare your answer to the solution here.
Week 4, Feb 6, 8
Galor-Weil model -- continued.
HW Assignment 1 is due on Thursday, submit through Canvas.
You may work in groups of 2 on your homework assignments.
Week 5, Feb 13, 15
Discuss the Neoclassical Growth Model (henceforth, NGM) -- a major workhorse of macroeconomic analysis. This model is typically used to study aggregate trends and business cycle fluctuations in output, consumption, investment and wages and business cycles fluctuations.
Notes on the Neoclassical Growth Model -- these cover material through Week 8.
Excel file that solves the NGM.
In order to gain economic intuition for the dynamics produced by the NGM, we will also work out analytically a special case of the model (full depreciation and no utility from leisure). The dynamics produced by this special case is easily understood via graphical tools.
Week 6, Feb 20, 22
We discussed how to solve the Neoclassical Growth Model numerically using first order and terminal conditions. This amounts to solving a large system of non-linear equations.
We discussed the economic intuition behind the model dynamics under various shocks.
We worked out the special case of the NGM -- which implies the constant savings rate. This is essentially the Solow growth model.
Week 7, Feb 27, Feb 29
In order to use our model as a computational lab, we need to assign values to the model parameters, i.e. calibrate the model.
We will learn how to calibrate the Neoclassical Growth Model.
We will also learn the correct mapping between the model variables and data variables reported in the National Income and Product Accounts, available through the Bureau of Economic Analysis website. We will learn how to construct the data moments needed for calibrating the model.
We will discuss how to compute welfare along the equilibrium path of the NGM. This entails learning about computing the sum of tails of geometric time series.
We will also learn how to evaluate macroeconomic policy interventions, i.e. how to compute the welfare impact of various shocks or policy changes. We report welfare impact by citing the equivalent gain/loss in lifetime consumption.
I am also posting Notes on Measurement in Macroeconomics which is a review of measurements you learned in intermediate macroeconomic courses. This resource should help you understand the National Income and Product Accounts variables.
Homework Assignment 2 is due Feb 29 (before lecture)
Data file -- This file contains US data and calculates empirical moments that we use in the calibration of the NGM. See Question 2.
Week 8, March 5, 7
Test 1 on Tuesday, March 5
Computational Experiment: Fiscal Policy in the Neoclassical Growth Model
Now that we know how to solve, calibrate and evaluate policy in the Neoclassical Growth Model, we proceed to introduce the government sector and to evaluate various fiscal policies in the context of our model. What are the pros and cons of taxing labor income or consumption expenditure? When should we tax capital income?
Notes on Fiscal Policy in the Neoclassical Growth Model -- cover the material through week 10
Excel file that solves the NGM with taxes
We derived the first order and terminal conditions and discuss features of the model solution.
We go through the practice problems with answers to solidify our understanding of the NGM with taxes.
March 12, 14 - SPRING BREAK
Weeks 9, March 19, 21
Continue fiscal policy in the neoclassical growth model.
Week 10, March 26, 28
We will employ the NGM with taxes to examine whether or not cross-country differences in tax systems can explain cross-country differences in aggregate labor supply.
Optional reading (my notes already cover the bulk of this info): Prescott (2004). Why Do Americans Work So Much More Than Europeans? Federal Reserve Bank of Minneapolis Quarterly Review vol. 28 (1).
Homework 3, due Tuesday, April 2nd
Week 11, April 2, 4
A General Equilibrium Lifecycle Model
This model will allow us to study data patterns that arise from decision-making that has to do with individual life cycles. Issues like human capital investment, retirement decisions, and social security reform may be studied in the context of this model. We will learn how to solve this model and how to calibrate it so as to get consistency with the relevant data moments (both lifecycle-related and aggregates).
We derive the first order conditions and discuss features of the model solution.
Notes on the Lifecycle Model -- cover material through the rest of the class.
NO CLASS on April 4th, see you at the symposium
Week 12, April 9, 11
Numerical Solution Method for the Lifecycle Model
We discussed the algorithm for solving the lifecycle model and calibrating the Social Security system.
Week 13, April 16, 18
We continue to examine the shape of the age profiles for consumption, labor supply and wealth holding. We analyze the effects of various parameter values on the shape of these profiles. Help with homework and exam.
Week 14, April 23, 25
Help with Homework 4.
To gain some intuition for welfare consequences of a pay-as-you-go (unfunded) social security system in the lifecycle model, we consider a very simple two period lifecycle model. The lecture notes are found here: Social Security.
Homework 4 - lifecycle model, due Th, April 18