Dottorato di Ricerca in
Economia delle Istituzioni e dei Mercati Monetari e Finanziari
Anno Accademico 2001-2002

Programma dei corsi I semestre

PRECORSI

MATEMATICA
Docente: Dr.ssa Maria Elisabetta Tessitore

  • Algebra lineare: vettori e matrici.
  • Studio di funzioni: derivazione, integrazione, massimi e minimi liberi e vincolati.
  • Equazioni differenziali del primo ordine: a variabili separabili, lineari a coefficienti variabili.
  • Equazioni differenziali lineari di ordine superiore a coefficienti costanti.
  • Equazioni alle differenze lineari a coefficienti costanti.
  • Cenni di ottimizzazione dinamica.

Testi di riferimento:

  • F. Cacciafesta, "Lezioni di Matematica generale".
  • Alpha Chiang, "Introduzione all'economia matematica", Bollati Boringhieri.
  • E. Giusti: Analisi matematica 1e2, Boringhieri

Torna all'indice dei Programmi

PROBABILITA'
Docente: Dr. Roberto Monte

  1. Insieme degli esiti di un fenomeno aleatorio, spazio dei campioni, eventi.
  2. Algebre di eventi, l’informazione su un fenomeno aleatorio.
  3. Elementi di calcolo combinatorio.
  4. Misure di probabilità, spazi di probabilità di Kolmogorov.
  5. Probabilità condizionata, formula della probabilità totale, formula di Bayes.
  6. Eventi indipendenti.
  7. Variabili aleatorie e loro proprietà.
  8. Distribuzione di probabilità di una variabile aleatoria.
  9. Funzione di distribuzione e densità di una variabile aleatoria.
  10. Principali funzioni di distribuzione e densità (bernoulliana, binomiale, poissoniana, uniforme, gaussiana, esponenziale, di Cauchy).
  11. Funzioni di distribuzione e densità, teorema di inversione.
  12. Cenni di teoria e tecniche dell’integrazione secondo Riemann.
  13. Speranza e varianza di una variabile aleatoria e loro proprietà.
  14. Speranza e varianza dei principali tipi di variabili aleatorie (bernoulliana, binomiale, poissoniana, uniforme, gaussiana, esponenziale, di Cauchy).
  15. Vettori aleatori e loro proprietà.
  16. Distribuzione di probabilità di un vettore aleatorio.
  17. Funzione di distribuzione e densità, congiunta e marginale, di un vettore aleatorio.
  18. Variabili aleatorie indipendenti, covarianza e correlazione.
  19. Speranza condizionata di una variabile aleatoria e sue proprietà.
  20. Successioni di variabili aleatorie.
  21. Leggi dei grandi numeri.
  22. Teorema del limite centrale.

Testi di riferimento:

  • Baldi Paolo: Calcolo delle Probabilità e Statistica, McGraw-Hill Italia.
  • Baldi Paolo, Giuliano Rita, Ladaelli Lucia: Laboratorio di probabilità e statistica matematica, McGraw-Hill Italia.
  • Chung Kai Lai: A Course in probability theory, Probability and Mathematical Statistics series, Jonh Wiley & Sons.
  • Fagnola Franco, Pistone Giovanni: Primo semestre di probabilità, Clut.
  • Appunti del docente.

Torna all'indice dei Programmi

I SEMESTRE
Gli esami si svolgeranno tra il 17 gennaio 2000 e il 4 Febbraio 2000.

MACROECONOMIA
 Coordinatore: Prof. Giancarlo Marini

Teaching Staff:

  • A.Dalmazzo (University of Siena)
  • G.Marini (University of Rome Tor Vergata)
  • P.Scaramozzino (University of London)

Teaching Assistant:

  • B. Annichiarico (University of Tor Vergata)

Closed Economy Models

  • Expectations, Cycles and the Neutrality of Money: Neo-keynesian Rational Expectations Models. Econometric Policy Evaluation
  • Time consistency and Optimal Monetary Policy
  • Introduction to Real Business Cycle Models
  • Public Debt and Economic Activity
  • Dynamic Optimization
  • Consumption and Investment
  • Growth Theory
  • Externalities, Human Capital and Endogenous Growth
  • Monopolistic Competition and Monetary Policy
  • Monetary transmission mechanisms
  • Strategic Complementarity and Multiple Equilibria

Reference Books:

  • P. Aghion and P. Howitt (1998), Endogenous growth theory, MIT Press
  • F. Bagliano and G.Bertola (1999), Metodi dinamici e fenomeni macroeconomici, Il Mulino
  • R.J.Barro and X. Sala-ì-Martin, Economic Growth (1995), McGraw-Hill
  • O.J.Blanchard and S.Fischer, Lectures in Macroenomics (1989), MIT Press.
  • Chiang, A.C. (1992), Elements of Dynamic Optimization, New York, McGraw-Hill
  • Deaton, A. (1992), Understanding Consumption, Oxford, Clarendon Press
  • D.Romer, Advanced Macroeconomics, McGraw-Hill, 2000
  • Solow, R.M. (1992), Siena Lectures on Endogenous Growth Theory, Università di Siena, Dipartimento di Economia Politica.

Suggested reading list:

  • Aghion, P., e Howitt, P. (1992), "A Model of Growth through Creative Destruction", Econometrica, Vol. 60, No. 2, March, pp. 323-351.
  • Abel, A. (1988), "Consumption and Investment", in B. Friedman and F. Hahn (eds.), Handbook of Monetary Economics, Amsterdam, North-Holland.
  • Akerlof and Yellen (1985), "A Near-Rational Model of the Business Cycle with Wage and Price Inertia", Quarterly Journal of Economics, p.823-838.
  • D. Backus e J. Driffil, (1985), "Inflation and Reputation", American Economic Review
  • R.J. Barro, 1974, "Are Government Bonds Net Wealth?", Journal of Political Economy
  • R.J. Barro e D.B. Gordon, 1983, "Rules, Discretion and Reputation in a Model of Monetary Policy", Journal of Monetary Economics
  • Bernanke B.S. and Gertler M. (1995) Inside the Black Box: the Credit Channel of Monetary TransmissionJournal of Economic Perspectives vol 9. no.4, Fall, 27-48
  • O.J. Blanchard, 1981, "Output, the Stock Market, and Interest Rates", American Economic Review, 71, 132-143
  • O.J. Blanchard, 1985, "Debt, Deficits and Finite Horizons", Journal of Political Economy
  • Blanchard and Kiyotaki (1987), "Monopolistic Competition and the Effects of Aggregate Demand", American Economic Review, p.647-666.
  • A.S, Blinder e S. Fischer, 1981, "Inventories, Rational Expectations and the Business Cycle", Journal of Monetary Economics, 8, 277-304.
  • Blundell, R., S. Bond, M. Devereux and F. Schiantarelli (1992), "Investment and Tobin's Q", Journal of Econometrics, Vol. 51, No. 1/2, Jan./Feb., pp. 233-257.
  • W.H. Buiter, 1988, "Death, Birth, Productivity Growth and Debt Neutrality", Economic Journal
  • W.H. Buiter, 1989, "After the New Classical Macroeconomics", in Macroeconomic Theory and Stabilisation Policy, Manchester University Press.
  • G. Calvo, 1978, "On the Time Consistency of Optimal Policy in a Monetary Economy", Econometrica
  • Chirinko, R.S. (1993), "Business Fixed Investment Spending: Modeling Strategies, Empirical Results, and Policy Implications", Journal of Economic Literature, Vol. 31, December, pp. 1875-1911.
  • Cooper and John (1988), "Coordinating Coordination Failures in Keynesian Models", Quarterly Journal of Economics, p.441-463.
  • Diamond P. (1982), "Aggregate Demand Management in Search Equilibrium", Journal of Political Economy, p.881-894 (Search & Trade Externalities).
  • S. Fischer, 1977, "Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule", Journal of Political Economy, 85, pp. 191-206.
  • Hall, R.E. (1978), "Stochastic Implications of the Life-Cycle - Permanent Income Hypothesis: Theory and Evidence", Journal of Political Economy, Vol. 86, pp. 971-987.
  • Hubbard, R.G. (1998), "Capital-Market Imperfections and Investment", Journal of Economic Literature, Vol. 36, March, pp. 193-225.
  • Kashyap A.K and Stein J.C. (1994) Monetary Policy and Bank Lending, in: Mankiw N.G.(ed) Monetary Policy, University of Chicago Press, Chicago.
  • F.E. Kydland e E.C. Prescott, 1977, "Rules Rather than Discretion: the Inconsistency of Optimal Plans", Journal of Political Economy
  • J.B. Long e C.I. Plosser, 1982, "Trends and Random Walks in Macroeconomic Time Series", Jounal of Monetary Economics
  • R.E. Lucas, 1972, "Expectations and the Neutrality of Money", Journal of Economic Theory, pp. 103-124.
  • R.E. Lucas, 1973, "Some International Evidence on Output-Inflation Trade-Offs", American Economic Review, 63, pp. 326-334.
  • R.E. Lucas, 1976, "Econometric Policy Evaluation - A Critique", Journal of Monetary Economics, Supplemento.
  • Lucas, R.E. Jr. (1988), "On the Mechanics of Economic Development", Journal of Monetary Economics, Vol. 22, pp. 3-42.
  • Lucas, R.E. Jr. (1993), "Making a Miracle", Econometrica, Vol. 61, No. 2, March, pp. 251-272.
  • R.E. Lucas and T.J. Sargent, "After Keynesian Macroeconomics" in Lucas e Sargent (a cura di), op. cit.
  • P.J. Miller (ed.), 1994, The Rational Expectations Revolution, MIT Press.
  • J.F. Muth, 1961, "Rational Expectations and the Theory of Price Movements", Econometrica, 29, pp. 315-355
  • C.R. Nelson e C.I. Plosser, 1983, "Real Business Cycles", Journal of Political Economy
  • C.I. Plosser, 1989, "Understanding Real Business Cycles", Jounal of Economic Perspectives
  • K. Rogoff, 1985, "The Optimal Degree of Commitment to an Intermediate Monetary Target", Quarterly Journal of Economics
  • T.J. Sargent e N. Wallace, 1975, "Rational Expectations, the Optimal Monetary Instrument and the Optimal Money Supply Rule", Journal of Political Economy, 83Scaramozzino, P. (1997), "Investment Irreversibility and Finance Constraints", Oxford Bulletin of Economics and Statistics, Vol. 59, No. 1, pp. 89-108.
  • J. Stiglitz, 1997, "Reflections on the Natural Rate Hypothesis", Journal of Economic Perspectives
  • J. Taylor, 1980, "Aggregate Dynamics and Staggered Contracts", Journal of Political Economy, Febbraio.
  • C.E. Walsh, 1995, "Optimal Contracts for Central Bankers", American Economic Review
  • P. Weil, 1991, "Overlapping Families of Infinitely Lived Agents", Journal of Public Economics

Open Economy Models

  • National and International Money
  • International Monetary Systems: The Gold Standard, Bretton-Woods, The EMS
  • Exchange Rate Volatility and Equilibrium Models
  • The Monetary Approach to the Balance of Payments
  • Sticky Prices and Overshooting
  • Portfolio Models of Exchange Rate Determination
  • Speculative Attacks and Currency Crises

Reference Books:

  • P. De Grauwe, International Money (1996), Oxford University Press
  • B. T. McCallum, International Monetary Economics (1996), Oxford University Press
  • M. Obstfeld and K. Rogoff, Foundations of International Macroeconomics (1996), MIT Press
  • Jones, R.and Kenen, P. (1985), Handbook of International Economics, North Holland, Amsterdam.
  • G. Grossman and Rogoff, K. (eds.) (1996), Handbook of International Economics, vol. III, North Holland, Amsterdam
  • S. Turnovsky, (1997), International Macroeconomics Dynamics, MIT Press, Cambridge (MA)
  • F. Van der Ploeg, (1994), The Handbook of International Macroeconomics, Basil Blackwell, Oxford.

Suggested reading list:

  • Branson, W.H. (1979), "Exchange Rate Dynamics and Monetary Policy", in Lindbeck A., Inflation and Employment in Open Economies, North-Holland.
  • Brock, P. - Turnovsky, S.J. (1994), "The Dependent Economy Model with Traded and Nontraded Capital Goods", Review of International Economics, 2, 306-325.
  • Burnside, C., Eichenbaum, M., Rebelo, S. (2000),"On the fundamentals of Self-Fulfilling Speculative Attacks", NBER working paper, n.6758.
  • Calvo, G.A. (1985), "Currency Substitution and the Real Exchange Rate: the Utility Maximization Approach", Journal of International Money and Finance, 4, 175-188.
  • Dornbusch, R. (1976), "Expectations and Exchange Rate Dynamics", Journal of Political Economy, 84, 1161-1176.
  • Flood, R.P.-Garber, P. (1984), "Collapsing Exchange Rates Regimes: Some Linear Examples", Journal of International Economics, 17, 1-13.
  • Flood, R.P-Marion, N.P. (1998), "Perspectives on the Recent Currency Crisis Literature", IMF working paper, n.130, sept.
  • Karayalcin, C. (1999), "Temporary and Permanent Government Spending in a Small Open Economy", Journal of Monetary Economics, 43, 125-141.
  • Murphy, R.G. (1991), "Macroeconomic Adjustment under Alternative Lending Arrangements", Journal of Economic Dynamics and Control, 15, 103-127.
  • Obstfeld, M. (1996), "Models of Currency Crises with Self-Fulfilling Features", EER, 40, 1037-1048
  • Obstfeld, M.-Rogoff,K. (1995), "The Mirage of Fixed Exchange Rates", Journal of Economic Perspectives, 9, 73-96.
  • Taylor, M. (1995), "Exchange Rate Behavior", Journal of Economic Literature, 33, 13-47.
  • Turnovsky, S.J.-Sen, P. (1995), "Investment in a Two-Sector Dependent Economy", Journal of Japanese and International Economies, 9, 29-55.
  • Velasco, A. (1997), "When are Fixed Exchange Rates Really Fixed?", Journal of Development Economics, 37, 358-372

 

Torna all'indice dei Programmi

METODI QUANTITATIVI
Coordinatore: Prof. Franco Peracchi
Docenti: Giuseppe Arbia, Simone Borra, Giampaolo Scalia Tomba

Modulo I (Prof. Giuseppe Arbia)

  1. Statistical models. Parametric statistical models. Examples of paramateric models. Conditional parametric models. Non parametric and semi parametric statistical models. Prediction problems. The regression function. Linear predictors. Economic data and statistical models. Typologies of economic data: cross-sections, time series, spatial series, panel data.
  2. Sampling and nonsampling errors. Main sampling schemes (simple, stratified). Nonsampling errors: unobserved heterogeneity, sample selection, nonresponse and missing data, grouped observations, measurement errors. Empirical examples of cross section data.
  3. Typologies of economic time series: low/high frequency data, stock/flows. Stochastic processes and time series. Lag operators. Expected values, stationarity and ergodicity. Non parametric stochastic processes (Martingale, Markovian processes, Brownian motion). Definition and properties of some remarkable parametric stochastic processes (White noise; MA(1), MA(2), AR(1), AR(2), ARMA(1,1), ARMA(p,q), ARMA-ARCH). Autocorrelation and partial autocorrelation. Invertibility and causality. Sample autocorrelation. Nonstationarity. Deterministic trends. Integrated processes. Cointegration. Seasonality. Long-memory processes. Multivariate time series. Example of economic time series data: National account data and high frequency financial data.
  4. Typologies of economic spatial data. Random fields and spatial data. Stationarity and ergodicity in two-dimensions. Spatial autocorrelation. Definition and properties of some remarkable parametric random fields (White noise; Conditional autoregressive). Example of economic spatial data: Regional account data and the European data base REGIO.
  5. Panel data: advantages with respect to pure cross-section or pure time-series. Fixed and random effects models. Attrition and new-entry. Examples of economic panel data: the Europanel.

Reading list

  • Anselin, L. (1988) Spatial econometrics, Kluwer Academic publishers, Dordrecht
  • Arbia, G. (1989) Spatial data configuration in the statistical analysis of regional economics, Kluwer Academic publishers, Dordrecht.
  • Arbia, G. (1996) Analisi econometrica di dati spaziali, Quaderni di statistica, Università "G. d'Annunzio".
  • Arbia, G. e G. Espa (1996) Statistica economica territoriale, CEDAM, Padova.
  • Azzalini A. (1996) Statistical inference based on likelihood, Chapman & Hall, London.
  • Baltagi, B. H. (1998) Econometrics, Springer Verlag, Berlin.
  • Greene, W. H. (1997) Econometric analysis, Prentice Hall International, London.
  • Hamilton, J. D. (1994) Time series analysis, Princeton University Press. Traduzione italiana: Econometria delle serie storiche (1995), a cura di B. Sitzia, Monduzzi editore, Bologna.
  • Harvey, A. C. (1994) Forecasting, structural time series models and the Kalman filter, Cambridge University press, Cambridge.
  • Peracchi, F. (2000) Econometrics, Mc Graw Hill.
  • Spanos, A. (1986) Statistical foundations of econometric modelling, Cambridge University Press.

Lecture schedule

  • Weeks 1 to 3. Monday and Tuesday 11.30 to 13.30. Room TBA.

Torna all'indice dei Programmi

Modulo II (Prof. Simone Borra)

Point Estimation (Simone Borra)

The statistical model

  • Parametric
  • Semiparametric
  • Nonparametric

Some general concepts

  • Estimator
  • Sample distribution
  • Likelihood function
  • Sufficiency
    • Definition
    • Factorization theorem
    • Minimal sufficient statistics
  • Exponential families

Same methods of finding estimators

  • Method of moments
  • Method of Maximum likelihood
    • Example: ML estimates of parameters for linear regression model
    • Methods of numerical maximization: direct search method; Newton-Raphson method; Method of scoring.
  • Method of Least Squares
    • Normal equations
    • Example: LS estimates of the linear regression model
  • Minimum Chi-square method
  • Minimum-distance method

Properties of point estimators

  • Closeness (more concentrated estimator, Pitman-closest estimator)
    • Mean Squared Error and Risk Matrix
  • MSE in terms of sampling variance and biased
    • Unbiased estimator
    • Example: linear regression and unbiased estimates of parameters (ML and LS)
    • Consistency (simple and mean-squared-error)
    • Best asymptotically normal estimators (BAN)
  • Uniformly Minimum Variance Unbiased Estimators
    • Definition
    • Cramer-Rao inequality – Fisher’s information
    • Rao-Blackwell Theorem
    • Completeness
    • Lehmann-Scheffé Theorem
  • Optimum properties of ML estimators
  • Location and Scale Invariance
  • Other measures of the closeness of the estimator
    • Mean absolute deviation
    • Prediction problem
  • Loss function, Risk function, Admissible estimator, Minimax
  • Unconditional prediction problem
  • Conditional prediction problem
  • Minimax estimator
  • Bayes approach
    • Bayes posterior estimator
    • Loss-function approach: Bayes estimator

Estimation of the linear model

  • Point estimation
    • ML estimates
  • Properties:Minimal sufficient and jointly complete statistics, UMVUE
    • LS estimates
  • Gauss-Markov theorem
  • Violation of ideal condition of LS
    • Generalized least squares
    • Ridge regression estimators

References

  • Peracchi F. (2001), Econometrics, Wiley
  • Silvey, S.D. (1970), Statistical Inference, Chapman and Hall
  • Azzalini, A. (1996), Statistical Inference based on the Likelihood, Chapman and Hall

Torna all'indice dei Programmi

Modulo III (Prof. Giampaolo Scalia Tomba)

The theory of statistical hypothesis testing.
Various ways of constructing tests. Relations between tests and confidence intervals. The Neyman-Pearson Lemma, tests based on the likelihood function, asymptotic properties.

Tests in various statistical models.
Tests for location and spread parameters, one and two samples. Tests for parameters in the linear model, problems connected with composite hypotheses and multiple tests and hierarchical procedures. Other examples.

Reference books

  • Cox D.R. & Hinkley D.V. (1974) Theoretical Statistics. Chapman and Hall, London.

  • Silvey S.D. (1975) Statistical Inference. Chapman and Hall, London.

 

Torna all'indice dei Programmi

MICROECONOMIA
Docenti: Pietro Reichlin, Sergio Currarini, Robert Waldman

Modulo I (Prof. Pietro Reichlin)

  1. Preferenze e domanda (6 ore).
    Relazioni di preferenza, funzione di utilita', prezzi e vincoli di bilancio, domanda, interpretazione delle condizioni di ottimo, utilita' indiretta, identita'di Roy, scelte intertemporali.
     
  2. Equazione di Slutsky e statica comparata (6 ore).
    Problema di spesa minima, domanda hicksiana e funzione di spesa minima, proprieta' della funzione di spesa minima, equazione di Slutzky, variazione equivalente e compensata, surplus del consumatore.

Testi:

  • A. Mas-Colell, M. Whinston e J. Green, Microeconomic Theory, Oxford U.P., 1995 (cap. 1-3).

Torna all'indice dei Programmi

Modulo II (Prof. Sergio Currarini)

Teoria della Produzione, Teoria dei Giochi

Teoria della produzione
  • Production Sets: Definitions and properties
    Profit maximization and Cost Minimization
    Efficiency in Production
    The case of Leontief Technology

Teoria dei Giochi
  • Games in strategic form
    Equilibrium concepts: Dominance, Rationizability and Nash equilibrium
    Bayesian games and Bayesian equilibrium

Teoria dei Giochi
  • Extensive form games
    Equilibrium concepts: Nash equilibrium and Subgame Perfection
    Sequential Bayesian equilibrium

(Su indicazioni del docente può essere fornita agli studenti una reading list più dettagliata che sarà consultabile presso la segreteria del corso o scaricabile direttamente dal sito web)

Torna all'indice dei Programmi

Modulo III (Prof. Robert Waldman)

Teoria dei giochi

  1.  Teorema di Von Neuman e Morgenstern (Varian capitolo 11)

  2. Misure di avversione al rischio e applicazione (Varian capitolo 11).

  3. Equilibrio di Nash (Varian capitolo 15)

  4. Subgame perfection e giochi con informazione incompleta (Varian capitolo15)

  5. Azzardo morale (Varian ch 25)

  6. selezione avversa (Varian ch 25).

Gli argomenti sono relativamente tecnici e quindi darò poche pagine da leggere in toto capitoli 11, 15 e 25 di Microeconomic Analysis di Varian. 

Anche suggerisco che gli studenti potrebbero leggere in AGGIUNTA Pindyk and Robenfield "Microeconomics" Mazxwell/Macmillan  E3/86 chapter 17 "Markets with asymmetric information.

 

Torna all'indice dei Programmi