Fernando Tusell

Statistics Applied to Economics

This is a second quarter in Statistics, for students who have previously taken a quarter in Descriptive Statistics and Probability. It is taught to students in Economics.

Syllabus and bibliography

The syllabus and a collection of past exams can be obtained from Lankopi, in the basement. The syllabus lists several textbooks that can be used in this course.

Class notes, data files, handouts, etc.

All course materials while the course is being taught are in e-Gela; here are old copies.

Slides

Slides used in the classroom. Not all topics included, for some I prefer an old-style presentation, using the blackboard. Slides are offered in three formats, with identical content. This is the version I used when I last taught this course.

• Format 4 to a page
• Format 4 to a page with space for notes
• Format 1 per page (as projected in the classroom)

Class handouts

(In some cases, containing solutions or remarks for my colleagues to ensure teaching homogeneity across different groups; not intended for class distribution.)

• Review (probability distributuions, moment generating function, etc.) .
• Binomial distribution and normal approximation .
• Binomial distribution and normal approximation .
• Binomial, hypergeometric .
• Case studies on common distributions .
• Gamma-derived distributions (exponential, chi-square...) .
• Methods of moments and maximum likelihood estimation .
• Properties of estimators: unbiasedness, consistency .
• Properties of estimators: efficiency, sufficiency .
• Pure significance tests .
• Testing agains an alternative .
• Goodness-of-fit tests .
• Problems: hypothesis testing, normal theory, paired comparisons .
• Problems: sampling .

Other handouts

These are "irregular" handouts. As I recall, most of these were writen to support on-line lectures during the pandemics of 2020-2021.

• Comments on efficiency and the Cramer-Rao lower bound
• Comments on hypothesis testing
• Variance estimator in a paired-comparisons test
• Comments on normal theory hypothesis testing
• A simple example on sampling
• An example of stratified sampling
• An example of stratified sampling
• Comments on sufficiency
• Comments on UMP tests
• Summary of different types of convergence

Seminars and activities

Integral part of the course are "activities", designed to provide hands-on experience on estimation, testing and programming in R. There were two activities during the term, preceded by a seminar in which a similar problem to that proposed in the activity was solved. Below are some problems proposed over the years, some of them sharing a common theme.

• Seminar: A simple example using the Monte Carlo method
  Related activities: bivar.pdf, urgencias.pdf, import.pdf, tadpoles.pdf. S2andVar.pdf.
• Seminar: Estimation and properties of estimators
  Related activities: estim2.pdf, estim3.pdf, estim4.pdf, estim-gamma.pdf, estima-gamma2.pdf, estim-beta.pdf, estim-unif.pdf, Gumbel.pdf, tanks.pdf,
• Seminar: Testing hypothesis
  Related activities: futbol.pdf, IntelMonop.pdf, normreq.pdf,
• Other topics: quincunx.pdf, options.pdf,

Exams with answers

•   First quiz 2011-2012 (binomial, Poisson, gamma, etc.), with answers .
•   Second quiz 2011-2012 (estimation, hypothesis testing etc.), with answers .

Software

The students are responsible to know how to perform all required calculations with the only help of a pocket calculator and statistical tables. However, you are encouraged to use R for homework and everyday use.