ECON 589: Seminar in Econometric Theory
Spring 2012

Instructor

Time and place

Monday 5:30-6:45 PM in 403 Kern
Wednesday 5:40-6:55 PM in 403 Kern

Prerequisite level

ECON 501 and ECON 510

Topics: Semi-nonparametric modeling and estimation, and time series econometrics

In view of the preferences of the students, this course will cover two distinct topics:

1. Semi-nonparametric modeling and estimation (on Monday)
2. Time series econometrics (on Wednesday)

Semi-nonparametric modeling and estimation

Objectives

Semi-nonparametric (SNP) models are models where only a part of the model is parametrized, and the non-specified part is an unknown function which is approximated by a series expansion. Therefore, SNP models are in essence models with infinitely many parameters.

The objective of this part of the course is to show how and why unknown functions can be approximated arbitrarily close by series expansions in terms of complete orthonormal functions in Hilbert spaces of square integrable functions, how to model densities and distribution functions semi-nonparametrically using these series expansions, and how to estimate SNP models.

Course material

There is no required textbook. Instead, I will use lecture notes and papers, in particular (but not exclusive):

• Bierens, H. J. (2008), "Semi-Nonparametric Interval-Censored Mixed Proportional Hazard Models: Identification and Consistency Results", Econometric Theory 24, 749-794. [PDF]
• Bierens, H. J. (2011a), Hilbert Space Theory and Its Applications to Semi-Nonparametric Modeling and Inference, incomplete manuscript of a monograph. [PDF]
• Bierens, H. J. (2011b), "The Hilbert Space Theoretical Foundation of Semi-Nonparametric Modeling", draft of a handbook chapter. [PDF]
• Bierens, H. J. (2011c), "Consistency and Asymptotic Normality of Sieve Estimators Under Weak and Verifiable Conditions". [PDF1 (paper), PDF2 (separate appendix)]
• Bierens, H. J. (2012), "Note on the Consistency of Sieve Estimators" [Revised: March 25, 2012] [PDF]
• Bierens, H. J., and J. R. Carvalho (2007), "Semi-Nonparametric Competing Risks Analysis of Recidivism", Journal of Applied Econometrics 22, 971-993. [PDF1 (paper), PDF2 (separate appendix)]
• Bierens, H. J., and H. Song (2012), "Semi-Nonparametric Estimation of Independently and Identically Repeated First-Price Auctions via an Integrated Simulated Moments Method", Journal of Econometrics 168, 108-119. [PDF]
• Bierens, H. J., and H. Song (2011), "Semi-Nonparametric Modeling and Estimation of First-Price Auctions Models with Auction-Specific Heterogeneity", incomplete working paper. [PDF]
• Chen, X. (2007), "Large Sample Sieve Estimation of Semi-Nonparametric Models". In J.J. Heckman & E. Leamer (eds.), Handbook of Econometrics, Vol. 6, Ch. 76. Elsevier. [PDF]
• Shen, X. (1997), "On the Method of Sieves and Penalization", Annals of Statistics 25, 2555-2591. [PDF]

Topics

1. Examples of SNP models. [Bierens (2011b)]
2. Review of Hilbert space theory. [Bierens (2011a, 2011b)]
3. Orthonormal polynomials and the Hilbert spaces they span. [Bierens (2011a, 2011b)]
4. Trigonometric complete orthonormal series. [Bierens (2011a, 2011b)]
5. SNP density and distribution functions. [Bierens (2011a, 2011b)]
6. Sieve estimation
   • Consistency [Bierens (2011c, 2012), Chen (2007)]
   • Asymptotic normality [Bierens (2011c), Chen (2007), Shen (1997)]
   • Applications [Bierens (2008), Bierens and Carvalho (2007), Bierens and Song (2011, 2012)]

Homework assignments

T.B.A.

Time series econometrics

Objectives

The objective of this part of the course is to prepare the Ph.D. students in economics for the study of empirical macroeconomics, by providing a rigorous introduction to the theory and practice of time series analysis (univariate as well as multivariate time series, and stationary as well as non-stationary time series).

Course material

There is no required textbook, except for the Chapters 7 and 8 in

• Bierens, H.J. (2004), Introduction to the Mathematical and Statistical Foundations of Econometrics, Cambridge University Press (2007 paperback edition). See also the ERRATA involved, and the corrected proof of the Wold decomposition.

I will use lecture notes for the other topics.

Topics

1. Stationary time series and limit laws
   • Hilbert spaces of random variables [Bierens (2004), Appendix to Ch. 7]
   • The Wold decomposition [Bierens (2004, Ch. 7), Corrected proof]
   • Weak laws of large numbers and consistency of M-estimators for stationary time series models [Bierens (2004, Ch. 7), Lecture notes]
   • The martingale difference central limit theorem [Bierens (2004, Ch. 7)]
   • Consistency and asymptotic normality of M-estimators of stationary time series models [Bierens (2004, Ch. 7)]
2. Maximum Likelihood estimation of time series models [Bierens (2004, Ch. 8)]
3. ARMA models
   • Stationary ARMA processes [Lecture notes]
   • ARMA model selection on the basis of information criteria [Lecture notes]
4. Vector autoregressions and innovation response analysis [Lecture notes]
5. Unit roots
   • The Augmented Dickey-Fuller (ADF) and Phillips-Perron tests [Lecture notes]
   • The Breitung test [Paper]
6. Cointegration
   • Introduction to cointegration [Lecture notes]

Homework assignments

• Theoretical homework assignments
  • Assignment 1: Skip
  • Assignment 2: Skip
  • Assignment 3, with answer keys.
  • Assignment 4
  • Assignment 5

• Empirical homework assignments
  • Assignment 1: Skip
  • Assignment 2, with answer keys.
  • Assignment 3
  • Assignment 4

The final grade will be determined on the basis of 25% of the midterm score for the time series part, 25% of the midterm score of the SNP part, and 50% of the term paper. Thus, there will be no final exam. As to the term paper, it can be either in the area of (applied) time series, or on an SNP topic. In the latter case the term paper may be a review of an SNP topic, or a computational paper where the approach in an existing SNP paper is replicated. In the time series case the term paper may be empirical, or computational, or a review paper. In which area want you write the term paper is up to you.

Exams

• Midterm:
  • Time series:
    Theoretical homework assignment 3 acts as take-home midterm exam for the time series part.
    Due date: Wednesday March 14.

  • SNP:
    Write a critical review (about 3 pages) of the paper
    Gabler, S, F. Laisney & M. Lechner (1993), ”Seminonparametric Estimation of Binary-Choice Models with an Application to Labor-Force Participation”, Journal of Business & Economic Statistics 11, 61-80. (PDF).
    Due date: Monday March 26.

• Final:
  The official final exam date, time and place is Monday April 30 from 2:30 to 4:20 PM in 107 E E WEST. However, there will be no final exam. Instead, the term paper will act as the final exam. Because I have to submit the grades within 48 hours after the official final exam date, you need to turn in your term paper in on (or before) Monday April 30 from 2:30 to 4:20 PM in my office, 510 Kern.

Messages

• Final Exam Conflict

  Students have the right to file for a final exam conflict, so that their final exam will be held on another day and/or time than the officially scheduled day and time. However, that implies that I have to make two different final exams, which puts an unduly burden on me. Also, in general the separate "conflict exam" will be put together while the instructor is in an upset mood, which is not in your best interest. Therefore, before you file for a final exam conflict, talk to me first!. So far it has always been possible to resolve these conflicts internally.

• Disability Message

  The Pennsylvania State University encourages qualified persons with disabilities to participate in its programs and activities. If you anticipate needing any type of accommodation in this course or have questions about physical access, please tell the instructor as soon as possible.