Econometrics

Heteroskedasticity

(posted: 20 Nov 2025)

On Thu 20 Nov, we'll continue our discussion of heteroskedasticity focusing the discussion on the case of heteroskedasticity in the logit model. To prepare, please read my notes, Studenmund chap. 10 and Kennedy chap. 8.

Midterm Exam

(posted: 20 Nov 2025)

On Tue 25 Nov, we'll hold a short midterm exam. Please prepare written answers to the questions below. Then I'll test you on your knowledge during our session on Tue 25 Nov.

What is Ordinary Least Squares? What is Maximum Likelihood Estimation?
What are the Gauss-Markov assumptions?
Why are the OLS estimates of regression coefficients equal to the MLE estimates?
Why doesn’t OLS provide an estimate of the standard error?
What is the standard error of regression? What is the standard error of a regression coefficient?
Why do the MLE first-order conditions provide an estimate of the standard error of the regression?
Why do the MLE second-order conditions provide estimates of the standard error of the regression coefficents?
Why is the standard error of a parameter estimate smaller when the log-likelihood surface comes to a sharp peak along its dimension?

links and files

course syllabus
message board

problem set (PDF)

monopsonist and minimum wage

answers

datasets

datasets for course project

my Analysis of the "Biagi Law" (PDF)
Teaching with the "Biagi Law" Data

Italian data: CSV file R script Gretl data
OECD data: CSV file R script Gretl data
Phillips Curve: wikipedia doviak.net

OECD Indicators of Employment Protection

EPL dataset description (PDF)

Wikipedia. Minimum Wage
Schmitt (CEPR, 2013). effect on employment

course outline

introductory discussions

statistics vs. machine learning
Bender and Koller (2020). "Climbing towards NLU"

the octopus test – notes on Bender and Koller's paper

Wdowiak. monopsonist and minimum wage
Wdowiak (2017). minimum wage, employment and annual pay

background -- statistics and probability

bivariate normal distribution, (wxM) (PDF)

lecture 1 -- ordinary least squares

Studenmund, chaps. 1, 2 and 3
notes on regression, (PDF)
OLS regression, (PDF)
OLS regression, (R script)
OLS regression, (wxM) (PDF)
problems #4 and #1

lecture 2 -- maximum likelihood

Kennedy, chaps. 1, 2 and 3
MLE mean-variance, (wxM) (PDF)
MLE regression, (wxM) (PDF)
MLE 2nd o.c., (wxM) (PDF)
problem #2

lecture 3 -- hypothesis testing

Studenmund, chaps. 4 and 5
Kennedy, chap. 4
MLE explanations, (wxM) (PDF)
distribution of beta hat, (R script)
problems #3 and #4

lecture 4 -- violations of the Gauss-Markov assumptions

Kennedy, chaps. 5, 6 and 7

lecture 5 -- panel data

Studenmund, chap. 16
Kennedy, chap. 18

lecture 6 -- heteroskedascity

Studenmund, chap. 10
Kennedy, chap. 8
heteroskedascity in the logit model

lecture 7 -- probability models

Studenmund, chap. 13
Kennedy, chaps. 16 and 17
logit model, (wxM) (PDF)

lecture 8 -- time-series

Studenmund, chaps. 9, 12 and 15
Kennedy, chaps. 10, 19 and 20
non-stationary residuals, (wxM) (PDF)

lecture 9 -- simultaneous equations

Studenmund, chap. 14
Kennedy, chap. 11

references and software

statistics

my statistics course
L.&H. Friedman's statistics course

statistical software

the R language

LearnEconometrics.com

mathematical software

Maxima and wxMaxima

wxMaxima installation instructions (U. New Haven)

Josef Leydold's Maxima for Economics
Zachary Hannan's wxMaxima for Calculus

textbooks

required:
- A.H. Studenmund. Using Econometrics: A Practical Guide.
- P. Kennedy. A Guide to Econometrics.
other suggestions:
- L. Adkins (2018). Using gretl for Principles of Econometrics.
- DeGroot and Schervish. Probability and Statistics.
- Pearce. The MIT Dictionary of Modern Economics.

Copyright © 2002-2025 Eryk Wdowiak