ECON 589: Topics in Advanced Econometrics (Fall 1997)

Instructor: Prof. Herman J.Bierens

Time and place: TTH 11:15-12:30, 413 Kern

Required Text:

[BT] H.J. Bierens: Topics in Advanced Econometrics, Cambridge University Press, 1994

This course consists of two parts: a core part that covers the first four chapters of Bierens' book as listed below, and an elective part consisting of a coherent choice of other topics/chapters from my textbook and/or the elective topics listed below. These other topics will be decided upon in consultation with the students. Each week a number of exercises will be assigned as homework. The final grade is determined by the homework (20%), a written mid-term exam (30%), a written final exam (30%), and a term paper (20%).

Core topics (50%) [BT]:

  1. BASIC PROBABILITY THEORY
    1. Measure-theoretical foundation of probability theory
    2. Independence
    3. Borel measurable functions
    4. Mathematical expectation
    5. Characteristic functions
    6. Random functions
  2. CONVERGENCE
    1. Weak and strong convergence of random variables
    2. Convergence of mathematical expectations
    3. Convergence of distributions
    4. Central limit theorems
    5. Further convergence results, stochastic boundedness, and the Op and op notation
    6. Convergence of random functions
    7. Uniform strong and weak laws of large numbers
  3. INTRODUCTION TO CONDITIONING
    1. Definition of conditional expectation
    2. Basic properties of conditional expectations
  4. NONLINEAR PARAMETRIC REGRESSION ANALYSIS, AND MAXIMUM LIKELIHOOD THEORY
    1. Nonlinear regression models and the nonlinear least squares estimator
    2. Consistency and asymptotic normality: General theory
    3. Consistency and asymptotic normality of nonlinear least squares estimators in the i.i.d. case
    4. Maximum likelihood theory
    5. Testing parameter restrictions

Elective topics (50%):

  1. TIME SERIES MODELS:
    1. Conditioning on infinitely many random variables. [BT, Ch.6, pp. 1-5]
    2. Functional specification of time series models. [BT, Ch.7, pp. 1-7]
    3. VAR models, Granger causality and innovation response analysis. [SI + lecture notes]
    4. Unit roots [NP; BT, Ch. 9, pp. 1 - 38]
    5. Cointegration [BT, Ch.9, pp.38-50; JJ]
    6. ARMAX modelling [BT, Ch.8; BB]
    7. ARMA Memory Index Modelling [BT, Ch. 7]
  2. NONPARAMETRIC REGRESSION: [BT, Ch.10, pp.1-42; BP; B2]
  3. GMM ESTIMATORS: [BT, Ch.5; HA]
  4. APPLICATIONS OF MAXIMUM LIKELIHOOD METHODS:
    1. Concentrating the likelihood function [CR, Ch.5, pp.59-62]
    2. Generalized classical regression, SURE and GLS [CR, Ch.6-7, pp. 79-108]
    3. Discrete choice models [CR, Ch. 10, pp.150-171]
    4. Limited dependent variables models [CR, Ch. 11; AM]
    5. Duration models [CR, Ch. 12, pp. 186-193]
  5. INTEGRATED CONDITIONAL MOMENT TESTS [BT, Ch.3(rest); BP2; DJ; B1; B3]
  6. ANY OTHER TOPIC YOU WANT TO KNOW MORE ABOUT

Literature (tentative):

[AM]
Amemiya (1981): "Qualitative Response Models: A Survey", Journal of Economic Literature XIX, 1483-1536
[B1]
Bierens (1982): "Consistent Model Specification Tests", Journal of Econometrics 20, 105-134.
[B2]
Bierens (1987): "Kernel Estimators of Regression Functions", in: Truman F.Bewley (ed.), Advances in Econometrics: Fifth World Congress, Vol.I, New York: Cambridge University Press, 99-144.
[B3]
Bierens (1990): "A Consistent Conditional Moment Test of Functional Form", Econometrica 58, 1443-1458.
[BB]
Bierens and Broersma (1993): "The relation between unemployment and interest rate: some international evidence", Econometric Reviews 12, 217-256.
[BP1]
Bierens and Pott-Buter (1990): "Specification of Household Engel Curves by Nonparametric Regression", Econometric Reviews 9, 123-184
[BP2]
Bierens and W.Ploberger (1997), "Asymptotic Theory of Integrated Conditional Moment Tests", Econometrica 65, 1129-1152
[CR]
Cramer (1986): Econometric Applications of Maximum Likelihood Methods, Cambridge University Press (May be out of print. If so, we will work with lecture notes)
[DJ]
De Jong (1996), "The Bierens test under data dependence", Journal of Econometrics 72, 1-32.
[HA]
Hansen (1982): "Large Sample Properties of Generalized Method of Moments Estimators", Econometrica 50, 1029-1054
[JJ]
Johansen and Juselius (1990): "Maximum likelihood estimation and inference on cointegration: with application to the demand for money", Oxford Bulletin of Economics and Statistics 52, 169-210
[NP]
Nelson and Plosser (1982): "Trends and random walks in macroeconomic time series", Journal of Monetary Economics 10 (1982), 139-162
[SI]
Sims (1980): "Macroeconomics and Reality", Econometrica 48, 1-48
Sims (1982): "Policy Analysis with Econometric Models", Brookings Papers on Economics Activity 1, 107-152