Master 2020/2021

Econometrics (Advanced Level)

Type: Elective course (Applied Economics)

Area of studies: Economics

Delivered by: Department of Applied Economics

Where: Faculty of Economic Sciences

When: 1 year, 1-4 module

Mode of studies: offline

Open to: students of one campus

Instructors: Elena Kotyrlo, Margarita Maximova, Elena Sidorova

Master’s programme: Applied Economics

Language: English

ECTS credits: 11

Contact hours: 136

Course Syllabus

Abstract

The course “Advanced Econometrics” focuses on the estimation, inference and identification of regression models. Particular attention is paid to the econometric theory, to the application of econometrics to real-world problems, and to the interpretation of the estimation results. The first part of the course (Fall term) includes linear regressions and models with limited dependent data. Topics on Gauss-Markov theorem, endogeneity, instrumental variables, maximum likelihood estimation will be covered. The second part of the course (Spring term) is focused on issues in system of equations; time series models; panel data models; nonparametric and semiparametric models; Bayesian estimation. The course will include the use of STATA and MS Excel. Use of R and other statistical analysis software is optional.

Learning Objectives

• The course aims to provide students with: • knowledge on the fundamentals of econometrics and its application • knowledge and proficiency on the use of statistical package STATA for econometric analysis • practice in conducting data analysis and application of econometric tools in research and analytics Prerequisites Course requires knowledge of linear algebra, calculus, probability theory and mathematical statistics.

Expected Learning Outcomes

• knowledge on the fundamentals of econometrics and its application
• knowledge and proficiency on the use of statistical package STATA for econometric analysis
• practice in conducting data analysis and application of econometric tools in research and analytics

Course Contents

• Part I: Fall term. Topic 1. Introduction
  About econometrics and the course program.
• Part I: Topic 2. Vectors and matrices
  Terminology. Matrix manipulations. Properties of matrices and vectors. Inverse matrices. Idempotent matrices. Eigenvalues and eigenvectors. Differentiation. Some least squares manipulations.
• Part I: Topic 3. Statistical and distribution theory
  Discrete random variables. Continuous random variables. Expectations and moments. Multivariate distributions. Conditional distributions. The normal distribution and its properties. tdistribution. Chi squared distribution. F-distribution
• Part I: Topic 4. An introduction to linear regression
  Ordinary least squares (OLS). Simple linear regression. Matrix notation. The linear regression model. Goodness-of-fit
• Part I: Topic 5. The Gauss–Markov assumptions
  Small sample properties of the OLS estimator. Hypothesis testing. A simple t -test. Testing one linear restriction. A joint test of significance of regression coefficients. The general case. Size, power and p-values. Asymptotic properties of the OLS estimator. Consistency. Asymptotic normality.
• Part I: Topic 6. Interpreting and comparing regression models
  Multicollinearity. Interpreting the linear model. Selecting the set of regressors. Misspecifying the set of regressors. Comparing non-nested models. Misspecifying the functional form. Nonlinear models. Testing the functional form. Testing for a structural break. Linear models. Loglinear models.
• Part I: Topic 7. Heteroskedasticity
  Heteroskedasticity. Introduction. Consequences for the OLS estimator. Deriving an alternative estimator. Estimator properties and hypothesis testing. Heteroskedasticity-consistent standard errors for OLS. A model with two unknown variances. Multiplicative heteroskedasticity. Testing for heteroskedasticity. Testing equality of two unknown variances. Testing for multiplicative heteroskedasticity. The Breusch–Pagan test. The White test. The Goldfeld-Quandt test.
• Part I: Topic 8. Autocorrelation
  Autocorrelation. First order autocorrelation. Estimation with a known ρ. Estimation with ρ unknown. Testing for first order autocorrelation. Asymptotic tests. The Durbin–Watson test. What to do when you find autocorrelation? Misspecification. Heteroskedasticity-andautocorrelation-consistent standard errors for OLS.
• Part I: Topic 9. Endogeneity, instrumental variables and GMM
  Cases where the OLS estimator cannot be saved. Autocorrelation with a lagged dependent variable. Measurement error and simultaneity as a cause of endogeneity. The instrumental variables estimator. Estimation with a single endogenous regressor and a single instrument. Multiple endogenous regressors. The generalized instrumental variables estimator. Two-stage least squares. Specification tests. Weak instruments. The generalized method of moments (GMM).
• Part I: Topic 10. Models based on panel data
  Advantages of panel data. Efficiency of parameter estimators. Identification of parameters. The fixed effects model. The random effects model. Fixed effects or random effects. The Hausman test. The Breush-Pagan test. F-test. Goodness-of-fit.
• Part I: Topic 11. Maximum likelihood estimation and specification tests.
  An introduction to maximum likelihood (ML). General properties. The normal linear regression model. Specification tests: the Wald tests, likelihood ratio (LR), the Lagrange multiplier test (LM), Tests in the normal linear regression model. Testing for omitted variables. Testing for heteroskedasticity. Testing for autocorrelation. Quasi-maximum likelihood and moment conditions tests. Quasi-maximum likelihood. Testing for normality.
• Part II. Topic 12. Binary choice models
  Binary choice models. Using linear regression. Introducing binary choice models. An underlying latent model. Estimation. Goodness-of-fit. Specification tests in binary choice models. Relaxing some assumptions in binary choice models
• Part II. Topic 13. Multi-response models. Models for count data
  Ordered response models. About normalization. Multinomial models. Models for count data. The Poisson and negative binomial models.
• Part II. Topic 14. Tobit models
  The standard Tobit model. Estimation. Specification tests in the Tobit model. Extensions of Tobit models. The Tobit II model. Estimation
• Part II. Topic 15. Estimating treatment effects
  Sample selection bias. The nature of the selection problem. The average treatment effect. The average treatment effect for the treated. Difference-in-difference. Switching regression model.
• Part II. Topic 16. Univariate time series models
  Introduction. Stationarity and the autocorrelation function. General autoregressive-moving average (ARMA) processes. Formulating ARMA processes. Invertibility of lag polynomials. Common roots. Stationarity and unit roots. Testing for unit roots. Testing for unit roots in a first order autoregressive model. Testing for unit roots in higher order autoregressive models.
• Part II. Topic 17. Choosing ARMA model and its estimation
  The autocorrelation function. The partial autocorrelation function. Diagnostic checking. Criteria for model selection. Estimation of ARMA models by LS and ML. Predicting with ARMA models. The optimal predictor. Prediction accuracy
• Part II. Topic 18. Autoregressive conditional heteroskedasticity (ARCH)
  ARCH and GARCH models. Estimation and prediction
• Part II. Topic 19. Multivariate time series models
  Dynamic models with stationary variables. Models with nonstationary variables. Spurious regressions. Cointegration. Cointegration and error-correction mechanisms. Vector autoregressive models (VAR). Cointegration: the multivariate case. Cointegration in a VAR. Testing for cointegration.
• Part II. Topic 20. Dynamic linear models
  An autoregressive panel data model. Difference and system GMM. Dynamic models with exogenous variables. Nonstationarity, unit roots and cointegration. Panel data unit root tests. Panel data cointegration tests.
• Part II. Topic 21. Non-parametric and semiparametric methods.
  . Kernel density estimation. Statistical properties of estimators. Kernel functions. Nonparametric regression. Smoothing functions
• Part II. Topic 22. Duration models
  Duration models as an example of semiparametric estimation. Hazard rates and survival functions. Proportional hazards models. Estimation.
• Part II. Topic 23. Simulation-based estimation. Bootstrap standard errors
  Random number generation. Generating pseudo-random numbers. Sampling from a standard uniform population. Sampling from continuous distributions. Sampling from a multivariate normal population. Sampling from discrete populations. Simulation-based statistical inference. Bootstrapping standard errors and confidence intervals.
• Part II. Topic 24. Bayesian estimation and inference
  Bayes theorem and the posterior density. Bayesian analysis of the classical regression model. Analysis with a noninformative prior. Estimation with an informative prior density. Bayesian inference. Point estimation. Interval estimation. Hypothesis testing. Largesample results. Posterior distributions and the Gibbs sampler
• Part II. Topic 25. Spatial econometrics
  Spatial autocorrelation. Contiguity matrix, spatial lags. Spatial error correlation
• Part II. Topic 26. Nonlinear regression models. Quantile regression
  Nonlinear regression models. Assumptions of the nonlinear regression model. The nonlinear least squares estimator. Large sample properties of the nonlinear least squares estimator. Hypothesis testing and parametric restrictions. Quantile regression.
• Part II. Topic 27. Shrinkage methods.
  Big data. Ridge regression, The Lasso, elastic netpenalty

Assessment Elements

• The cumulative score for the Fall term
• The final grade for the Spring term (FG)
  Экзамен проводится в письменной форме. Экзамен проводится на платформе Webinar.ru. К экзамену необходимо подключиться за 5 минут до начала. Компьютер студента должен удовлетворять требованиям: подключение через Google Chrome. Для участия в экзамене студент обязан отправить актуальный e-mail адрес преподавателю за неделю до экзамена. Во время экзамена студентам разрешено пользоваться калькулятором, статистическими программами. Файл с экзаменационными задачами и вставленными в выделенные ячейки ответами и скриншоты с решением должны быть отправлены преподавателю по e-mail не позднее установленного времени. Если возникает проблема отправки или письмо с вложением не было доставлено вовремя, студенту надо будет подтвердить факт своевременной отправки, прислав соответствующие скриншоты. Процедура пересдачи аналогична процедуре сдачи.
• The first intermediate test (Module 1)
  includes tests and problems on the topics 4-6
• The first homework (Module 1)
  the course participants propose a hypothesis and collect their own cross sectional data for a regression model that is going to be analysed further in Module 2.
• The second homework ( Module 2)
  It is based on data collected in Module 1 (and approved by a tutor!). It imposes empirical justification of the stated hypotheses on the base of the material of the topics 4-9. Students are expected to use statistical software STATA or another for data analysis.
• Midterm exam
  it includes tests and problems on the topics 4-11
• Activity on classes
• The second Intermediate Test (Module 3)
  it includes test and problems on the topics 11-15
• The third homework (Module 3)
  The course participants may collect their own data or relay on data given by tutors and use the statistical package STATA (another software is optional) for data analysis. Econometric techniques are based on the topics 10-15).
• The forth homework (Module 4)
  it includes empirical justification of hypotheses relevant to time series analysis and panel data analysis. It is based on the material of the topics 16-19.
• Final exam
  it includes tests and problems on the topics 16-27.

Interim Assessment

• Interim assessment (2 module)
  0.25 * The cumulative score for the Fall term + 0.05 * The final grade for the Spring term (FG) + 0.5 * The first homework (Module 1) + 0.1 * The first intermediate test (Module 1) + 0.1 * The second homework ( Module 2)
• Interim assessment (4 module)
  0.06 * The cumulative score for the Fall term + 0.42 * The final grade for the Spring term (FG) + 0.06 * The first homework (Module 1) + 0.06 * The first intermediate test (Module 1) + 0.4 * The second homework ( Module 2)

Bibliography

Recommended Core Bibliography

• Verbeek, M. (2017). A Guide to Modern Econometrics (Vol. 5th edition). Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1639496

Recommended Additional Bibliography

• Greene, W. H. (2012). Econometric Analysis: International Edition : Global Edition (Vol. 7th ed., International ed). Boston: Pearson Education. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1417839
• Härdle, W., Müller, M., Sperlich, S. A., & Werwatz, A. (2004). Nonparametric and Semiparametric Models. Switzerland, Europe: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.121C8F13
• Hastie, T., Tibshirani, R., & Friedman, J. H. (2009). The Elements of Statistical Learning : Data Mining, Inference, and Prediction (Vol. Second edition, corrected 7th printing). New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=277008
• Keele, L., & Wiley InterScience (Online service). (2008). Semiparametric Regression for the Social Sciences. Chichester, England: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=231580
• Koenker, R. (2005). Quantile Regression. Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=139750