The students will derive the asymptotic properties of the ordinary least squares estimator and will learn how to interpret results, assess the validity of a chosen model, test hypotheses and make predictions. In the second part of the course, the students will learn about methods that can be used when some of the assumptions underlying the linear regression model do not hold. Maximum likelihood estimation is applied to estimate models with binary outcomes (logit, probit) or with censored outcome data (Tobit). Methods that can be used to model stationary time series are also covered in this part.

Throughout the course, students will apply the methods to data from the financial, actuarial and economics domain using statistical programming language R. During these exercises we will discuss principles of modelling, sensitivity analysis, assumption checking, interpretation of the model output and reproducibility of results.

### Entry requirements

It is strongly advised that the student has finished the course PrEMAS 1: Mathematical Methods (or equivalent) and that the student has followed or follows the course PrEMAS 3: Probability Theory and Statistics (or equivalent).

### Learning objectives

Upon successful completion of the module, the student is able to:

- Give examples of the types of questions that can be answered using econometric techniques and the types data that can be used to answer these questions;
- Analyse linear relationships between variables using correlations and regression modelling;
- State the assumptions of the linear regression model and explain when these assumptions may be violated;
- Derive finite sample statistical properties of the ordinary least squares estimator;
- Interpret the results of a linear regression model and explain how variable transformations can be used to alter the interpretation;
- Estimate parameters for these models and perform diagnostic tests including checking assumptions and evaluating model fit;
- Perform variable selection and engineering (e.g. dummy variables, interactions) and test for misspecification of the functional form;
- Perform hypothesis testing on the values of the parameters;
- Explain the impact of omitted variables on the unbiasedness of the least squares estimator;
- Explain the impact of heteroskedasticity, multi-collinearity and autocorrelation on the parameter estimates and their standard errors and propose potential solutions;
- Derive maximum likelihood estimators for the linear regression and for limited dependent variable models (e.g. probit for binary outcomes and Tobit for censored data);
- Apply the likelihood ratio test to compare nested models;
- Describe and apply the main concepts underlying stationary time series models;
- Characterise the stationarity of an autoregressive moving-average (ARMA) process through the roots of lag polynomials;
- Identify when an ARMA model for time-series data is appropriate, estimate the parameters and interpret the results;
- Derive one-step-ahead and multiple-step-ahead forecasts and prediction intervals for an ARMA model;
- Explain the difference between the short-run and long-run properties of a model, and how this may be relevant in deciding whether a model is suitable for any particular application;
- Describe, in general terms, how to decide whether a model is suitable for any particular application;
- Describe, in general terms, how to analyse the potential output from a model, and explain why this is relevant to the choice of model;
- Carry out sensitivity and stress testing of assumptions and explain why this forms an important part of the modelling process;
- Produce an audit trail enabling detailed checking and high-level scrutiny of model;
- Explain the factors that must be considered when communicating the results following the application of a model and produce appropriate documentation;
- Plan and execute a simple empirical research project and document the analysis and the research findings in a scientific paper.

### Literature

Introduction to Econometrics EMEA Edition, 1st Edition, Jeffrey M. Wooldridge, CENGAGE Learning, 2014. ISBN: 978-1-4080-9375-7

### Teacher

Lisanne Sanders

### Software

For the assignments we will use the statistical programming language R (https://www.r-project.org/) and RStudio (https://www.rstudio.com/). It is expected that you have working installations of R and RStudio on your laptop before the start of the first lecture. Please contact the lecturer beforehand if you encounter installation issues.

### Important to know

- The lectures of PrEMAS 4 do not always take place at the same time or on the same weekday, please click here for the complete schedule.
- Assessment: Written exam and take-home assignment.
- Exam – 15 October 2024
- Resit – 19 November 2024
- Deadline paper - 5 November 2024
- Resit deadline paper - to be determined
- The costs for this module are € 3.075.
- Start in study year 2023-2024: 13 May 2024
- Level: the course is taught at the academic level of bachelor Econometrics