Joaquim Ramalho

By the end of the unit, the student should have achieved the following learning goals (LG):
OA1. Know and apply regression models to cross-sectional or panel data
OA2. Know how to choose and specify econometric models for unlimited or limited continuous dependent variables
OA3. Know how to choose and specify econometric models for discrete dependent variables
OA4. Know how to estimate, evaluate and interpret econometric models
OA5. Know how to evaluate and solve endogeneity problems
OA6. Be able to work with econometric packages

S1. Introduction
S2. Linear Regression Analysis
S3. Nonlinear Regression Analysis
S4. Discrete Choice Models
S5. Models for Limited Dependent Variables

The students are assessed throughout the semester, with the final grade being based on two components: i) two problem sets (weight: 25% each); ii) a written (open book) exam (weight: 50%). To get approval, students must fulfill the following criteria: i) weighted mean of at least 9,5/20; ii) minimum grade at the exam and each problem set of 7,5/20. Students may also be evaluated through a final (open book) exam accounting for 100% of the grade. There are no re-sitting exams.

Alberto Lopez Martin

By the end of this course a student should be able to:
1.1 apply fundamental results of one variable calculus.
1.2 use basic techniques of linear algebra.
1.3 apply fundamental results of vector calculus.
1.4 apply some basic results of measure theory and integration.
The student is also expected to:
2.1 become acquainted with some basic techniques of MATLAB programming.
2.2 be able to identify and apply appropriate numerical methods for the analysis of relevant classes of problems arising in economics and finance.
2.3 implement numerical methods in MATLAB and criticize the results obtained from a mathematical, computational and economical/financial view point.

I. Introduction to MATLAB.
II. Sequences and metric spaces.
a) Facts about the real numbers
b) Sequences of real numbers.
c) Metric spaces.
III. Equations in one variable.
(a) Review of single variable calculus
(b) Numerical solutions of equations in one variable:
IV. Systems of linear and non-linear equations
(a) Some basic notions of linear algebra
(b) Direct and iterative methods for solving linear systems.
(c) Review of vector calculus.
(d) Newton's method for systems of (non-linear) equations.
V. Measure theory, integration and probability
(a) Riemann's integral.
(b) Introduction to Measure theory and the Lebesgue integral.
(c) Applications to Probability theory:

The final grade will be based on homework assignments (50%) and a final exam (50%).
The evaluation of the homework assignments is subjected to oral discussions.
The final exam has a minimum grade of 7.5 out of 20.
Due to the nature of the evaluation in this course, there is no 2nd chance exam.

João António Madeira

The main learning objectives of this course are to develop skills to analyse, summarize and to have a critical opinion about the following items: (i) Solow growth model; (ii) neoclassical view of macroeconomics, focused on the notions of general equilibrium, optimizing behaviour, and real cycles; (iii) Keynesian view of macroeconomics, focused on the notions of imperfect competition, price rigidity, and relevance of economic policy; (iv) simulation and estimation of business cycle models.

Dynamic Macroeconomics: Textbook Models
- Solow growth model
- Dynamic stochastic general equilibrium models
- Real business cycle models
- New-Keynesian macro models
- Simulation and estimation of DSGE models

There are two types of assessment.

The first type consists of assessment throughout the semester, in which the following instruments will be used: individual work (40%) and knowledge assessment exam (60%). This assessment type requires meeting a minimum attendance criterion of 60%. There is no minimum grade requirement for maintenance in assessment throughout the semester.

The second type consists of assessment by exam, in this case the assessment exam has a weight of 100%.

Felipa Sampayo

By the end of the semester the student should have
developed and be able to apply the following
competences:
A. Knowledge and understanding
- Model the behavior of economic agents;
- Be able to follow the relevant theory regarding these subjects.
B. Application of Knowledge
- Implement theoretical results and modelling
techniques fto perform research;
- Choose the appropriate conceptual, mathematical and graphical approaches to provide solutions for specific problems;
C. Learning
- Development of individual study methods, namely
problem solving and understanding of models and modelling techniques.

1. Consumer theory
2. Producer Theory
3. Markets

Methods of during the semester Assessment: Final exam (100%)

José Dias Curto

At the end of the course, students must:
1) Know and use dynamic models with stationary and non-stationary variables.
2) Know and use multivariate models.
3) Be able to work with R and RStudio programs.

1) Dynamic models, stationarity and unit root.
2) VARMA models.
3) Univariate and multivariate GARCH models.
4) Cointegration, structural breaks and VECM models.

Assessment takes place through continuous assessment throughout the semester or assessment by exam. Continuous assessment throughout the semester consists of a group work (50%) and a test (50%) that covers the entire subject and whose grade must be greater than or equal to 7.5. Continuous assessment throughout the semester requires a minimum attendance of 66.67% of classes. Assessment by exam consists of carrying out an exam with a weighting of 100%. In the test and exam, students can use a calculator and all the materials provided by the teacher.

João Pedro Ruas

At the end of this course, each student should be able to:
1. Identify the main challenges of choice under uncertainty
2. Price financial assets using an equilibrium approach
3. Price financial assets using an arbitrage approach
4. Read a significant range of research papers in asset pricing and understand the main issues being discussed.

1. Choice theory
2. Portfolio theory
3. Equilibrium Pricing
4. Arbitrage Pricing

Students can choose between assessment throughout the semester or assessment by exam.

The assessment throughout the semester consists of:
- Individual works (50% of the final grade)
- One written test (50% of the final grade)

The assessment by exam consists of:
- One written test (100% of the final grade)

Passing the course depends on obtaining a final grade, rounded to the nearest interest, equal to or greater than 10.

Filipe Alexandre Pedra Aguiar de Moura

By the end of this course a student should be able to:
OA1.1 Determine, analytically and numerically, the solution to nonlinear optimization problems.
OA1.2 Determine and analyze, analytically and numerically, the solution to some difference equations.
OA1.3 Determine and analyze, analytically and numerically, the solution to some ordinary differential equations.
OA1.4 Apply algorithms of dynamic programming.

The student is also expected to:
OA2.1 Become acquainted with the basics of programming in MATLAB.
OA2.2 Be able to identify and apply appropriate numerical methods for the analysis of relevant classes of problems arising in economics and finance.
OA2.3 Implement numerical methods in MATLAB and criticize the results obtained from a mathematical, computational and economical/financial view point.

I. Optimization in R^n.
(a) Unconstrained optimization: Necessary and sufficient conditions. Steepest descent. Newton and quasi-Newton methods.
(b) Non-linear constrained optimization: The Karush-Kuhn-Tucker conditions. Penalty methods.

II. Difference equations.
(a) Linear difference equations.
(b) Some notable non-linear equations.
(c) Equilibrium points.
(d) Markov Chains.
(e) Applications: compound interests and gambler's ruin.

III. Ordinary differential equations.
(a) Some notable ODEs.
(b) Existence, uniqueness and qualitative methods.
(c) Euler's method and friends.
(d) Applications: dynamical interest rates, geometric Brownian motion, demographic models and turbulence.

IV. Dynamic programming.
(a) Dynamic programming in discrete time.
(b) Dynamic programming in continuous time.
(c) Optimal control.
(d) Numerical methods.
(e) Applications: modelling sustainable development and money in the utility.

The final grade will be based on 3 homework assignments in groups of 2 or 3 elements (60%) and a final exam (40%) with a minimum grade of 8/20.
Due to the nature of the evaluation in this course, there is no resitting exam.

Students may have to undertake an oral examination whenever the instructor seems it necessary.

Luís Filipe Martins

At the end of this course the student will:
1. Know the steps involved in the research process;
2. Understand working methodologies;
3. Be able to work autonomously in the production of individual research.
4. Be capable of presenting results, orally and in writing.

Following BRU-IUL and Department of Economics Research Seminars, as well as Research seminars from other Economics Schools where recent Economic research papers are presented and discussed.

In this unit students should develop analytical, information gathering, written and oral communication skills.
Students are encouraged to pick the research they will track as early as possible. They should carefully choose the seminars to attend and prepare ideas to discuss. The active search of new articles in the topics' fields is incited.

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Students should present a revision of a published paper (50%) and a research paper project (50%).
There is no re-sitting exam.

Thomas Greve

At the end of the course, the student should be able to:
LG1. Analyse the main theoretical models of mechanism design and auction theory;
LG2. Apply the theoretical concepts to practical applications; and
LG3. Develop a critical assessment of research articles in the area of microeconomics with a focus on topics in mechanism design and auction theory.

P1. Auctions with single unit sale
P2. Mechanism Design
P3. Interdependent values
P4. Multi-unit (identical) auctions
P5. Multiple Object auctions
P6. Applications

The assessment elements and their respective weightings are as follows:
a) 40% presentation of a scientific article (preferably still in an unpublished working paper version) and a peer-review report on the chosen article.
b) 60% final exam (with a minimum mark of 8).

Luís Filipe Martins

By the end of the unit, the student should have achieved the following learning outcomes (LO):
LO1. To identify research questions from a specific field that can contribute to solving a problem and expanding the knowledge base.
LO2. Relate the research questions previously identified with the state of the art in the chosen field of inquiry.
LO3. Identify the most adequate methodologies to tackle the research questions.
LO4. To present and discuss her/his ideas in front of an evaluation committee.

Development of a PhD research proposal.

Performance assessment is accomplished by the presentation and discussion of the research project before a committee composed by the student supervisor, the Director of the PhD Program and an additional evaluator. The jury grade accounts for 100% of the final grade and the grade range is 0-20.

João Silva

At the end of this course the student will:
1. Understand working methodologies in the domain of Political Economy;
2. Be able to work autonomously in the production of individual research.
3. Relate the research questions previously identified with the state of the art in the chosen field of inquiry.
4. Be capable of presenting results.

1.Industrial Policy
2.Innovation and Knowledge
3.Governance, economy and society

The assessment will be based on the presentation of two critical reviews, each counting 50% of the final grade.
There is no alternative form of evaluation.
Students should attend at least 80% of the seminars.

Sérgio Chilra Lagoa

Vivaldo Manuel Mendes

The module's goal is to develop the following competences:

1. Knowledge and comprehension of the main modern macroeconomic models, notably the ones of the monetary area.

2. Capacity to compute, simulate and estimate the models studied.

3. Capacity to elaborate arguments and justify them from a theoretical and empirical point of view, and be able to communicate them, namely through an academic paper.

Part I - Computation and policy
1. Introduction to computation: Python, Julia, Jupyter Notebooks
2. Modeling techniques for Dynamic Stochastic General Equilibrium Models (DSGEM)
3. Numerical simulation using linearization methods: the Jordan decomposition and the QZ factorization
4. Numerical simulation using projection methods

Part II - Empirical evidence and extensions

5. Empirical evidence on the relationship between money, inflation and output.
6. Extensions to the NKM: the cost channel. Model simulation.
7. Financial frictions and the credit market
8. Estimating DGSE models
9. Recent topics on monetary policy and its empirical methods.

The student can choose between:
- Assessment throughout the semester: individual assignments (50%), and final test (“frequência”) (50%)
- Final exam (100%)
To participate in the assessment throughout the semester, the student needs to have a rate of attendance to classes equal or larger than 80%.

Students who successfully complete this course should be able to:
1. Design, plan, adapt and perform original research that meets the requirements of academic quality and integrity and contribute to expand the frontiers of knowledge in Economics.
2. Communicate the results of that research to peers and the academic community in general, including their dissemination through national or international scientific conferences and publications.

The nature of the Course does not allow the delineation of a syllabus with explicit subjects. More important than the transmission of new knowledge, this course aims to apply the skills previously acquired to achieve the ultimate goal of completing the thesis. Thus, the syllabus will be set each year based on research projects presented and implemented by Phd students, with the aim of providing the foundations for a better and updated methodological, theoretical and empirical contextualization of their work.

The process of developing the thesis is continuously evaluated by the supervisor. From the third year of the PhD Program onwards, students should write a progress report yearly, which will be subject to review and comment by an evaluation panel.