28176 - STATISTICAL METHODS FOR ECONOMIC ANALYSIS

Learning outcomes

At the end of the course students are expected to have a deep knowledge of main concepts and tool of inferential statistics - estimation, confidence intervals, hypothesis testing – for the probabilistic models that are exploited in advanced economic and econometric courses of the master degree. Moreover, students should be able to apply these models not only in univariate scenarios both also in a multivariate framework.

Course contents

1. Introduction to data analysis and Monte Carlo simulations with R
   
   
2. Discrete Cumulative Distribution Functions (CDF)
   
   Binomial CDF; Poisson CDF; Negative Binomial CDF; Guided Analysis of Voting Results and Road Traffic Accidents
   
   
3. Continuous Probability Distribution Functions
   
   Probability Density Function (PDF); Uniform CDF; Exponential CDF; Guided Analysis of Time Between Earthquakes; The Inspection Paradox with a Simulation Study
   
   
4. The Normal Probability Distribution
   
   Normal PDF; Guided Analysis of Opinions Monitoring; Approximation to the Binomial PDF; Galton Board; Regression Towards the Mean
   
   
5. Empirical Data Analysis
   
   Empirical CDF; Summary Statistics for CDF; Descriptive Data Analysis; Guided Simulation Study with QQ-plots
   
   
6. Estimation Methods
   
   Statistical Inference; Estimators; Maximum Likelihood Estimator; Guided Derivation of the MLE for the Normal and Negative Binomial Models; General Classes of Estimators; Guided Simulation Study for Estimator's Properties
   
   
7. Testing Hypotheses
   
   Statistical Hypotheses; Statistical Tests; Size of a Test; Guided Simulation Study for Test's Properties; Confidence Intervals; The Bootstrap; Guided Example on Computing CI with Bootstrapping Methods; Coverage; Guided Example on Computing Coverage for CI
   
   
8. Regression Models I
   
   Introduction to Regression Models; OLS and MLE (with derivation); Significance Testing; Residual Analysis; Guided Analysis of Crime Data
   
   
9. Regression Models II
   
   Lasso Linear Regression; Estimation Bias of the Lasso; Robust Estimation and Inference; Guided Analysis of Crime Data; Covariate Transformations; Interactions; Guided Analysis of Literacy Data

Readings/Bibliography

Recommended reading:

• James, G., Witten, D., Hastie, T. and Tibshirani, R. An Introduction to Statistical Learning with Applications in R. Springer Texts in Statistics 103, 2013. Chapters 3,5,6.
  
  
• Available at: https://www.stat.berkeley.edu/~rabbee/s154/ISLR_First_Printing.pdf

Teaching material:

• Rmarkdown documents in HTML including R scripts, fully analyzed data sets and simulation studies.
  
  
• Data sets.
  
  
• Materials released on Unibo Virtuale.

Teaching methods

• Interactive lectures using Rmarkdown documents that include access to R scripts.
  
  
• Systematic question–answer dialogue between lecturer and students.
  
  
• Class material available in advance.

Assessment methods

The assessments aim at verifting the following detailed learning outcomes:

Knowledge (KNOW):

1. Understand and manipulate PDF, discrete and continuous.
2. Learn about counterintuitive results in probability and statistics (inspection paradox, regression towards the mean).
3. Study empirical distribution functions and associated population and finite sample moments.
4. Study different visualization tools for descriptive data analysis.
5. Study classical estimation principles (OLS, MLE) and study their finite-sample properties using simulations.
6. Study classical inference method (confidence intervals, hypothesis testing, p-value) as well as resampling methods (bootstrap).
7. Learn simulation-based validation methods (Monte Carlo) for finite sample properties of estimators and inferential methods.
8. Study the linear regression model and associated estimation methods (OLS, MLE, Lasso, M-estimator), with transformation of variables and interactions.
9. Study residual analysis for model and estimation method selection.

Skills (DO):

1. Use PDF to model a variety of data.
2. Analyze data using descriptive analysis for modelling purposes.
3. Analyze data using R for linear regression models (OLS, Lasso and M-estimator).
4. Analyze regression residuals using R for modelling purposes.
5. Evaluate the finite sample properties of estimators and inferential methods via Monte Carlo simulation, using R.
6. Use sampling based procedures (bootstrap) to construct confidence intervals, using R.
7. Perform a complete statistical analysis of regression models.

The methods:

• Term project provided two weeks before the end of the semester, consisting on a data analysis.
  
  
• The term project is unmarked and does not need to be handed in, but the final exams is based (not exclusively) on the analysis of the data for the term project.
  
  
• The final exam has 3 intakes of 2-hours, with open book and closed questions format.
  
  
• The final exam yields a grade between 0 and 32, with 31 and 32 graded as 30 cum laude.
  
  
• The final grade is averaged with the grade obtained for the class “Mathematical Methods for Economists” (B2198).
  
  
• Learning outcomes: KNOW 1–9, DO 1–7.
  
  
• Registration to a chosen exam session is mandatory through the AlamaEsami web site.
  
  
• The classes allow students to practice data analysis, learn the different methods and ask questions to the professor.

Teaching tools

The teaching material presented in class is conveniently made available to the student through Unibo Virtuale.

This digital access, with a username and password reserved for students enrolled at the University of Bologna, ensures students can study at their own pace and convenience.

Office hours can be delivered using Teams.

The instructor responds to e-mail messages duly signed by the student with Name, Surname and enrollment number, which concern appointment requests for clarifications about the subjets presented during the class.

Links to further information

https://virtuale.unibo.it/course/view.php?id=55903

Office hours

See the website of Maria Pia Victoria Feser