Master & PhD in Economics
Institut Polytechnique de Paris

Mathematics, Optimization, Probability, and Statistical Inference36 hours
Nicolas Vieille, Michele Fabi

– Basic calculus.
– Linear algebra.
- Static and dynamic optimization.
– Basic probability theory.
– Statistical inference.

Introduction to R for Economics8 hours
Arnault Chatelain

This crash course is intended to introduce students to the programming language R. The goal is to teach students how to implement simple data science/econometrics projects on R and where to look for for more advanced uses.
We will start with a general overview of R as a programming language and how to install and work with it on one’s own laptop. We will then introduce the tidyverse, a collection of R packages for data science. We will conclude with touching upon a few popular econometrics packages in R.

At the end of the course the student will know:
– What R is
– How to use it for data science/econometrics tasks

Coordinators: Arne Uhlendorff

The applied project ECO511 is a year-long supervised research effort by students designed to complement formal course work. The point of the project is for students to apply what they have learned in class to a real-world research problem. Topics can range in both subject matter and methodology (both empirical and applied theory are possible). Topics are proposed by supervisors at the beginning of the year in a catalogue. Students form groups of twos or threes and then submit ordered rankings of desired topics. Students are then matched to supervisors/topics and work begins. Supervisors should provide some guidance in terms of methodology and data, but students should retain the freedom to be creative in addressing the question. Students are required to submit a midterm report in December describing progress to date. A final written report is due in March, which the students then defend to the supervisor in an oral exam.

Website of the projects

Individual decision-making and market equilibrium50 hours
Tristan Tomala, Bruno Biais, Johan Hombert

– Choice theory and introduction to welfare economics.
– Consumer theory.
– Social choice (preference aggregation and manipulability).
– Producer theory.
– Choice under uncertainty (expected utility, risk aversion).
– General equilibrium, fundamental welfare theorems.
– Asset markets and general equilibrium under uncertainty.
– Externalities and public goods.
– No trade theorem, rational expectations.

Economic Growth50 hours
Antonin Bergeaud, Giovanni Ricco

- Neoclassical growth model.
- Public policies in the neoclassical growth model.
- Structural transformation.
- Inequality, political economy of growth.
- The overlapping generations model.
- Public policies and bubbles in the overlapping-generations model.
- Product variety model.
- Schumpeterian growth.

The Linear Regression Model and Extensions40 hours
Sebastien Roux, Thierry Kamionka

In this course we introduce the linear regression model and its theoretical foundations. We present and discuss the methods to estimate such models, i-e to define the parameters of interest, estimate them and test their statistical significance, under different sets of assumptions (homoskedasticity or heteroscedasticity, exogeneity or endogeneity), specifications (simple or multiple regression) or types of data (cross-sectional, panel data, time series).

Outline:
1. Introduction to econometrics
2. The Simple Regression Model
3. Multiple Regression Analysis:
A. Estimation
B. Inference
C. Asymptotics
4. Qualitative Information in Linear Regression
5. Heteroskedasticity
6. Repeated Cross Section and Panel Data
7. Instrumental Variables

Literature:
Angrist and Pischke: (2009): Mostly Harmless Econometrics, Princeton University Press.
Wooldridge (2013): Introductory Econometrics: A Modern Approach, 5th Edition, South-Western College Publishing.

24 hours
Jean-Michel Zakoian

- Generalities on univariate second-order stationary processes
- Autocovariances, partial autocorrelations
- Innovations
- Wold theorem
- Asymptotic properties of empirical moments.
- AR, MA, ARMA, SARIMA processes
- Canonical representation - Identification, estimation, tests and forecasting
- Model building
- Nonstationary models, Unit root tests.
- Stationary vector processes
- Multivariate AR models
- Statistical Inference
- Causality tests, impulse-response analysis.
- Non-stationary vector processes and definition of cointegration
- Cointegrated VAR models and error-correction models (ECM)
- Estimation of cointegrated VAR
- Testing for Cointegration.

Strategic Interactions and Information50 hours
Yukio Koriyama, Yuki Tamura

– Normal form games, pure and mixed strategies, equilibrium concepts (dominance, rationalizability, Nash).
– Imperfect competition (Cournot, Bertrand, Hotelling).
– Extensive form games with perfect information, backwards induction.
– Extensive form games with imperfect information (information sets), normal form representation.
– Bayesian games, auctions, adverse selection, signaling, screening.
– Equilibrium refinements (Perfect Bayesian equilibrium, sequential equilibrium).
– Social choice and introduction to mechanism design.
– Contract theory, principal agent models, risk sharing.

Business cycles50 hours
Jean-Baptiste Michau

– Traditional macroeconomics: The IS-LM AD-AS model.
– Consumption.
– Investment; The ramsey model.
– Determination of the price level.
– Real business cycle theory.
– The new Keynesian framework.
– Asset pricing; The Aiyagari model.
– Search models of the labor market.
– International macroeconomics.
– The Great Recession.

Nonlinear, Qualitative Data, and Panel Methods40 hours
Christian Belzil, Olivier Allais

– Extremum Estimators 1st part: M-Estimators (Maximum Likelihood, Nonlinear Least squares).
– Extremum Estimators 2nd part: GMM.
– Hypothesis Testing: Wald, Lagrange Multipliers, Likelihood Ratio Statistics.
– Instrumental Variables, 2SLS, Multiple-Equation GMM (if time).
– Dynamic Panel Data: Instrumental Variables and GMM.
– Binary Choice Models.
– Multinomial and Ordered Choice Models.
– Non-linear Panel Data Models.
– Censored Regressions.
– Duration Models.

During the third term, students must complete a research internship of at least 16 weeks. The internship must be either related to Microeconomics, to Macreconomics, or to Finance.