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Instructor: Ciprian NECULA
Course Description
Designed as an entry level statistics and econometrics course, it gives an introduction to probability theory, statistical inference and regression analysis. The main purpose is to provide students with a background in statistics necessary to understand higher level econometrics and applied economics courses.
Econometric Software
Eviews is used in the last part of the course. Students can employ other econometric software (i.e. R, Gauss, Matlab, Octave) if preferred.
Prerequisites
There are no formal prerequisites. However, students are assumed to be familiar with algebra and calculus.
Grading
100% final exam (open book)
Textbooks
There is no required textbook for the course. However, there are some reference books that are recommended:
- DeGroot M.H. and M. J. Schervish, (2001), Probability and Statistics, 3rd Edition, Addison Wesley
- Greene, W.H. (2008), Econometric Analysis, 6th Edition, Prentice Hall
- Mittelhammer, R.C. (1996), Mathematical Statistics for Economics and Business, Springer
- Rohatgi, V.K. (2003), Statistical Inference, Dover Publications
- Wooldridge, J. (2001), Econometric Analysis of Cross Section and Panel Data, MIT Press
Tentative Course Outline
1.Elements of Probability Theory
- events
- axiomatic definition of probability
- conditional probability
- independence
2. Random Variables
- univariate random variables, PDFs, CDFs
- multivariate random variables, PDFs, CDFs
- marginal PDFs and CDFs
- conditional PDFs and CDFs
- independence of random variables
- stochastic proceses
3. Mathematical Expectation and Moments
- expectation of a random variable
- moments of a random variable
- moment generation function
- characteristic function
- conditional expectation
- joint moments, covariance, correlation
4. Parametric Density Functions
- discrete density functions
- continous density functions
5. Asymptotics
- types of random variables convergence
- law of large numbers
- central limit theorem
6. Sampling
- random sampling
- statistics
- sample distribution function
- sample moments
7. Point Estimation Theory
- statistical models
- estimators and estimates
- estimator properties: small sample vs large sample
- sufficient statistics
- MVUE, BLUE, CRLB
- Maximum Likelihood Estimator (MLE): small sample vs large sample properties
- Method of Moments (MM) Estimator
- Generalized Method of Moments (GMM) Estimator
- Least Square Estimator (LSE)
8. Hypothesis Testing Theory
- statistical hypothesis
- statistical hypothesis tests and test statistics
- type I/ type II errors tradeoff
- test size, significance level, the power of a test, p-value
- Generalized Likelihood Ratio Tests
- Lagrange Multiplier Tests
- Wald Tests
- confidence intervals
9. The Classical Linear Regression Model
- the classical assumtions
- the OLS estimator
10. The Generalized Linear Regression Model
- heteroskedasticity and autocorrelation
- Heteroskedasticity and Autocorrelation Consistent (HAC) covariances estimators
- the WLS estimator
- the FGLS estimator
11. Simultaneous Equations Models
- endogeneity
- instrumental variables
- the 2SLS estimator
12. System Estimation
- the SUR estimator
- the 3SLS estimator
- panel data models
Course Materials
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Ciprian Necula - Introduction to Econometrics - Fall 2011