Nicolas Drouhin



Macroeconomic Modelling (L3 - annual course 24 h+6 h directed studies)

The course is an introduction to macro-dynamics, growth theory and modern economic policy. The aim is twofold. The first objective is to provide students with a deep understanding of consumption, savings and investment, as well as the mecanisms governing long-term evolution of factor productivity and price and the foundations of economic policy. The second objective is to give students strong technical skills and apply them to model concrete economic problems: Optimization with inequality constraints applied to intertemporal choice in discrete time and labor supply; Continuous time optimization: differential equations; phase diagram; optimal control theory (Pontryagin Maximum Principle), etc. These two objectives are complementary, and especially fitted to prepare students of the Ecole normale supérieure Paris-Saclay for graduate studies in the best research institutions.

Course Outline : I. Consumption and savings. II. Investment and financial markets. III. Stylized facts on growth. IV. Growth and capital accumulation.


Intertemporal Choice: Theory and Applications (Master in Economics - M2 24h) (Course delivered at ENSAE)

Intertemporal choice concerns any decision process that involves future consequences.
From a technical point of view, the objective is to provide students with an advanced understanding of dynamic optimization with a focus on continuous time modeling and optimal control theory (Pontryagin maximum principle). The course emphasizes technical difficulties that researchers encounter frequently when they model real economic problems and proposes efficient solutions (free endpoint program, free ending time problem, transversality conditions, discontinuities, constraints on control and state variables, scratch value, endogenous date of regime change, etc.).
As part of the Macroeconomic specialization field, the course emphasizes the life cycle of consumption and savings as the canonical model of intertemporal choice and draws practical examples from this literature and its generalization to health, education and social security. The course also deals with important problems in behavioral economics: memory, addiction and time consistency.
The notions and methods discussed in this course can also be useful for students from other fields than macroeconomics, especially Financial economics, Economic theory, Public economics, Labor Economics or students interested in specific topics, such as dynamic oligopoly or environment.

Outline: I. General introduction (1. Optimal control in economics and management. 2. A two period model of intertemporal Choice. 3. Mathematical prerequisites).II. Optimal control. (1. Basic problem: necessary and sufficient condition for optimality. 2. Free endpoint end free ending time problems, scratch values. 3. Constraints on the state and control variables. 4. Infinite horizon. 5. Multidimensional problem.III. Various topics in life cycle theory. (1. Consumption vs investment : a continuous time Fisherian separation theorem. 2. Education, 3. Health, 4. Uncertain lifetime. 5. Labor and Social security.). III. Various topics in behavioral intertemporal choice. (1 A brief introduction to the axiomatic of intertemporal preferences, 2. Time consistency, 3. Memory and Addiction).