# I Term: October - December

### Introduction to econometrics

The course is an introduction to the classical statistical inference theory.

The first half of the course is devoted to Probability theory. Topics include: Elements of set theory. Axiomatic definition of probability. Calculus of probability. Conditional probabaility and Bayes Theorem. Discrete and continuous random variables. Common Family of distributions, Hierarchies and Mixtures. Bivariate Random variables. Transformations and Convolution Integral.

The second part of the course is devoted to Inference. Topics include: Sampling and sampling distribution. Principles of data reduction (sufficiency, Likelihood). Point and interval estimation (methods to find estimators and properties of the estimators). Hypothesis testing. Asymptotic Theory. Linear regression models.

The very last lectures are devoted to an introduction to the use of Stata for applied economic research.

Bibliography:

Casella, G. and Berger, R: *"Statistical Inference"*, Duxbury press.

Stock, J and Watson, M: *"Introduction to Econometrics"*, Addison-Wesley.

### Mathematics for economics and finance

Homogeneous functions and Euler’s formula. Continuous functions and compact sets. Concave and quasi concave functions. The implicit function theorem. Convex sets and separating hyperplanes: separating hyperplanes theorem, supporting hyperplanes theorem. Difference equations. Unconstrained maximization: local and global maximizer (minimizer), maximization theorems. Constrained maximization: the Lagrangian function and constraints qualification, Lagrange multipliers. Inequality constraints: Kuhn Tucker conditions. Comparative statics. Differential equations and systems of differential equations. Dynamic maximization: the calculus of variations and its applications to economic models, Euler equation of maximization problems . Control theory and applications to economic models.

Bibliography:

Alpha C. Chiang and Kevin Wainwright, "Fundamental Methods of Mathematical Economics", New York, Mc-Graw Hill - Irwin.

*"Further Mathematics dor Economic Analysis"*, 2nd Edition, Pearson Education 2008

### Game Theory

Static games with complete information. Simultaneous moves games. Games in strategic form, dominant strategy equilibrium, iterated deletion of strictly dominated strategies. Reaction functions and Nash equilibrium. Finding Nash equilibria with both discrete and continuous action spaces. Supermodular and submodular games. Mixed strategies, domination by a mixed strategy and never-best-response. Rationalisability. Imperfect Information and incomplete information. Risk dominance.

Dynamic games with complete information. Games in extensive forms. Backward induction and information sets, Subgame perfect Nash equilibrium. Repeated games. Folk theorems. Collusion.

Games with incomplete information. Bayesian Nash Equilibrium. Purification. Forward induction. Sequential rationality, consistency of beliefs and perfect Bayesian Nash Equilibrium. Signalling: separating equilibria and pooling equilibria. Spence Signalling Model. Cho and Kreps criterion.

Bibliography:

Robert Gibbons, "A Primer in Game Theory", Harvester-Wheatsheaf, 1992

Martin Osborne, "An introduction to Game Theory", Oxford University Press, 2003

Andreu Mas-Colell, Michael Whinston e Jerry R. Green, "Microeconomic Theory", Oxford University Press, 1995.

### Microeconomics I

Preference and choice: preference relations, choices rules, the consumption set, competitive budgets, demand functions and comparative static. Preference and utility. The utility maximization problem. The expenditure minimization problem. Duality. Indirect utility and expenditure function. Integrability. The weak axiom of revealed preferences. The strong axiom of revealed preference. Welfare evaluation and economic changes. Aggregate demand and wealth. Production: production set, profit maximization and cost minimization, efficient production. Choice under uncertainty: expected utility theory, money lottery and risk aversion, state dependent utility. Monopoly. Oligopoly. General equilibrium theory: pure exchange, Edgeworth box, consumer-producer economy.

Bibliography:

Hal R. Varian, "Microeconomic Analysis", W. W. Norton & Company, 3rd edition, 1993.

Andrew Mas-Colell, Michael D. Whinston and Jerry R. Green, "Microeconomic Theory", Oxford University Press, 1995.