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MASTER in ECONOMICS (II level)
Director: Professor Tommaso Proietti
Academic year 2013/2014
Program
I QUARTER- PRELIMINARY COURSES
(September 16 – October 25, 2013)
MATH (0 credits):
Calculus: Basic Calculus. The Euclidean Space
: Maps between Euclidean Spaces. Calculus for
Maps from
to
. Implicit Functions and Their Derivatives. Ordinary Differential Equations:
Ordinary Differential Equations. Systems of Ordinary Differential Equations.
Linear Algebra: The geometry of linear equations. Elimination with matrices. Matrix operations and
inverses. Transposes and permutations. Column space and nullspace. Solving Ax = 0 and Ax=b.
Independence, basis and dimension. Fundamental subspaces. Orthogonal vectors and subspaces.
Projections onto subspaces. Projection matrices and least squares. Orthogonal matrices and GramSchmidt. Cramer's rule, inverse matrix and volume. Properties of determinants. Determinant formulas
and cofactors. Eigenvalues and eigenvectors. Diagonalization. Differential equations and exp(At).
Symmetric matrices and positive definiteness. Positive definite matrices and minima. Linear
transformations and their matrices. Left and right inverses. Pseudoinverse.
Probability: Elements of a probability space. Algebras of events and information about random
experiments. Introduction to combinatorial calculus. Finite probability spaces, probability measures,
introduction to Kolmogorov theory. Conditional probability, total probability formula, Bayes formula.
Independent events. Random variables and their properties. Probability distribution, distribution function
and densities function of a random variable. Inverse theorem. Expectation and variance of a random
variable and their properties. Expectation and variance for the main kinds of random variables. Random
vectors and their properties. Probability distribution, distribution functions and densities functions of a
random vector. Independent random variables, covariance and correlation. Conditional expectation of a
random variable and its properties. Conditional expectation as best estimator. Geometric approach to the
conditional expectation. Sequences of random variables. Law of large number. Central limit theorem.
Optimization: Quadratic Forms and Their Sign. Unconstrained Optimization. Constrained Optimization.
STATISTICS (3 credits): Properties of a random sample. Principles of data reduction. Point estimation.
Hypothesis testing, Interval estimation.
STATISTICAL COMPUTING 1 (3 credits):
Stata: Introduction to STATA. Dataset management: descriptive statistics. Stata graphics. Random
number generation. Point estimation. Testing hypothesis. Univariate Time Series. Linear regression.
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Introduction to Matlab: Introduction to Matlab. Matrices and operations with matrices. Relations
and Booleans. Scripts and Functions. Controlling the flow: cycles and conditions. Generation of random
numbers. Working with real data: exporting (save) and importing (load) external data. Graphics. LS
estimation of univariate and multivariate linear models.
II QUARTER - CORE COURSES
(November 11 – December 20, 2013)
QUANTITATIVE METHODS:
Static Regression (3 credits): Introduction and review. The classical linear model and the OLS
estimator. Sampling properties of OLS. GLS and feasible GLS. Diagnostic procedures. Hypothesis
testing and model selection.
IV and GMM (3 credits): The method of moments. The instrumental variable (IV) method. Sampling
properties of IV estimators. Hypothesis testing. Testing the validity of IV assumptions. Applications of
the IV method to economics and finance. GMM estimation and testing. Applications of GMM to
economics and finance.
MICROECONOMICS:
Consumption and Production Theory (3 credits): Preferences and Utility. Consumer’s Problem.
Indirect Utility and Expenditure. Consumer Demand. Technology. Profit Maximization. Cost
Minimization. Competitive firm. Choice under uncertainty. Expected Utility.
Equilibrium (3 credits): Existence. Efficiency: First Welfare Theorem, Second Welfare Theorem.
Equilibrium in production. Contingency in GE.
III QUARTER
(February 10 – March 21, 2014)
MACROECONOMICS:
Introduction to Contemporary Macroeconomics (3 credits): The dynamics of aggregate supply and
demand. Rational expectations and the Lucas Critique. Solving rational expectations models. The central
bank and monetary policy rules. Microfoundations of incomplete nominal adjustment.
Consumption and Investment (3 credits): Stochastic implications of the Permanent Income
Hypothesis. The overlapping generations model with money. Fixed Capital Investment. Inventory
investment. Credit Rationing.
* Growth Theory (3 credits): Solow Model Review. The Ramsey Cass Koopmans Model I and II. The
Diamond Model. The Romer 86 model. The Romer 90 model I and II. Human Capital and Growth.
* Business Cycle (3 credits): Business Cycle facts. Real Business Cycles theory. Critiques and
extensions. Money and business cycles. Business cycles and the labor market.
* International Economics (3 credits): International Finance and European Economics: Exchange
Rate Regimes; Currency Crises; Financial and Sovereign Debt Crises; The Sub-Prime Crisis.
International Trade: Comparative Advantages and New Economic Geography; European
Income Inequality and Specialization.
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* Empirics in Growth Theory (3 credits): The course aims to provide a discussion about some
important questions related to the empirical investigation of some economic growth theories.
Convergence versus multiple equilibria models. Model uncertainty. Production functions and unobserved
heterogeneity. Empirical methods.
MICROECONOMICS:
* Labor Economics (3 credits): Causal Effects. Supply in the Labor Market. Family policies. Demand
in the labor market. Labor market equilibrium. Discrimination.
* Games and Imperfect Markets (3 credits): Monopoly, price discrimination. Market structure and
imperfect competition, collusion. Dynamic games of perfect and imperfect information.
FINANCE:
* Credit Risk Models (3 credits): Poisson processes. Credit risk modelling: structural approach
(endogenous default). Credit risk modelling: reduced form approach (exogenous default). Applications
to bond evaluation.
* Theory of Banking (3 credits): Introduction to time, uncertainty and liquidity. Microeconomic
foundations for financial intermediation. Why do banks exist. The effects of banks on financial
markets: credit rationing; transmission mechanisms from the financial to the real sector. Bank
runs and remedies to instability. An analysis of the interbank market.
* Theory of Banking part 2 (3 credits): Banks can fail: history and institutions. A discussion on
the emergence of a financial crisis: the causes, the consequences and policy issues related to a
crisis. Financial market regulation as it has been designed before the current crisis. Analysis of
the features of the financial crisis of 2007-2009 in comparison with past crises’ episodes: the
causes, the transmission mechanisms, the consequences. A focus on the ongoing academic and
policy debate on current issues in banking regulation.
QUANTITATIVE METHODS:
Univariate Time-Series (3 credits): Univariate time series analysis: Basic concepts. Stationarity,
autocorrelation, Linear indeterministic processes. Nonstationary time series analysis: ARIMA models.
Seasonal models. Unit root tests. The Beveridge-Nelson decomposition. Forecasting and the evaluation
of forecasts. Univariate analysis of financial time series: Volatility and conditional heteroscedasticity.
GARCH and IGARCH models.
* Multivariate Time Series (3 credits): Vector processes. Stationarity of a vector process. Examples:
Vector white noise, vector ARMA, linear processes. Wold representation and spectral representation for
vector processes. Granger causality and exogeneity. VAR approximations to stationary vector processes.
Estimation of VAR models. Structural VAR models. The debate on the relative importance of permanent
and transitory shocks in explaining macroeconomic fluctuations.
IV QUARTER
(March 31 – May 09, 2014)
MACROECONOMICS :
* Advanced Topics in Macroeconomics and Growth (2 credits): The deterministic and stochastic
Solow Model. The Ramsey Kass-Koopmans Model. TheBrock –Mirman Model and the Hansen Model.
Linearization Techniques: Uhlig’s and Blanchard-Kahn methods. Deterministic Dynamic Programming.
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Stochastic Differential Equations and Markov Chains. Stochastic Dynamic Programming. Introduction
to Dynare.
* Applied Health Economics (3 credits): The course focuses on the analysis of health care demand
and provision, with special emphasis on the empirical aspects. The goal is to provide students with the
tools, knowledge, and understanding necessary to carry out original applied researches in the field.
Apart from an introductory lecture on the main problems and unresolved questions faced by the health
economists today, the remaining lectures will focus on the estimation and measurement of the
behavioral aspects in the health care field, by means of the most recent advances in health econometrics.
* Computational Macroeconomics (2 credits): Dynamic Stochastic General Equilibrium (DSGE).
Macro models of monetary policy with forward looking behaviour are solved using traditional
techniques, such as Blanchard and Kahn’s (1980). Numerical solution methods: QR technique
(Anderson and Moore, 1985; King and Watson, 1998) and the QZ method (Sims, 1996; Uhlig, 1999;
Christiano, 2002). Application on a linear rational expectation model with financial frictions using
MATLAB.
MICROECONOMICS :
* Uncertainty and Information (3 credits): Choice under uncertainty. Game theory (introduction).
Adverse selection, screening, signalling. Insurance. Moral hazard, principal agent.
* Public Economics (2 credits): Financing of G with distortionary taxation: Production public
goods (the McGuire-Olson model); Consumption public goods (the Atkinson-Stern model).
Public choice and voting: Rationality and democracy (Arrow); Median voter (singlepeakedness, single crossing, multidimensionality). The failures of collective action. The Olson
theory in game-theoretic terms: Free cooperation; Enforced cooperation.
* Topics on Procurement of Public Services (3 credits): Contracting out versus in house
provision. Incentives and Contractual issues. Relational contracts and Reputation in
Procurement. Corruption and Transparency. Group presentations.
FINANCE:
* Theory of Finance, part 1 (3 credits): Expected Utility Theory and Economic Theory of Choice;
Financial Markets and Financial Securities; Efficient Portfolios and Efficient Frontier.
* Theory of Finance, part 2 (3 credits): Correlation Structure of Securities and CAPM; Efficient
Markets and Event Study Approach.
* Financial Econometrics, part 1 (3 credits): Modeling of financial returns. Random walk, normality
tests, volatility persistence. ARCH and GARCH models. Long memory and fractionally integrated
models. Stochastic volatility modeling in discrete time. Realized volatility. Volatility forecasting.
* Financial Econometrics, part 2 (3 credits): MIDAS: MIxed DAta Sampling. Introduction.
Forecasting with mixed (and high) frequency data. Forecasting accuracy. Introduction: schemes, number
of observations, why out of sample, measures of accuracy (MSFE, MAFE, forecast encompassing in.
Comparing small number of models, nested models, non-nested models. Comparing large number of
models. Applications: Business Cycle, Exchange Rates, Interest rates. Econometrics with option prices.
QUANTITATIVE METHODS:
* Dynamic Regression (3 credits): Interdependence. Weak exogeneity. Granger causality. Strong
exogeneity. Autoregressive distributed lag models. Error (equilibrium) correction. Cointegration
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(bivariate case). Inference on cointegration: Single equation methods. Vector autoregressive and vector
error correction models.
* State Space Models for Business Cycle Analysis (3 credits): Review of main concepts in time series
(stationarity, autocorrelation, frequency domain analysis). State space models. Unobserved components
models for the analysis of economic time series (trends and cycles in macroeconomic time series).
Inference for state space models: the Kalman filter, smoothing filter, maximum likelihood estimation.
Forecasting with state space models. Topics in business cycle analysis. Filtering economic time series.
* Microeconometrics using STATA (3 credits): Linear Regression: Policy Evaluation. The Linear
Regression Model. Endogeneity and Instrumental Variable Estimation. Robust Inference. Programme
Evaluation and Treatment Effects. Applications of Treatment Models. Linear Unobserved Effects Panel
Data Models. Stata Session Re and Fe. Generalised Method of Moments I & II. Generalised Method of
Moments III: Testing. Dynamic Panel Data Models. Applications. Nonlinear regression: STATA
session: Nonlinear regression and the Poisson model. Discrete Choice I: Binary Choice; Endogeneity in
Binary Choice. (depending on time constraints: Discrete Choice II: Multinomial Choice Models;
Applications of Multinomial Choice Models. Discrete Choice III - The Mixed Logit Model. Discrete
Choice III - The Mixed Logit Model. Dynamic Binary Choice. Applications of Dynamic Binary Choice
Models. Count Data and Related Models.)
Matlab (1,5 credits): ARMA model, integration test, VAR model, cointegrazion test, ECM model.
* Elective Courses
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