Econometrics

2019/2020

Academic Year

ENG

Instruction in English

10

ECTS credits

Delivered at:

International College of Economics and Finance

Course type:

Compulsory course

When:

3 year, 1-4 module

Course Syllabus

Abstract

The Elements of Econometrics is an introductory full year course for the 3-rd year ICEF students. The course is taught in English and finally examined by the University of London international programme, or by ICEF final exam. The stress in the course is done on the essence of statements, methods and approaches of econometric analysis. The conclusions and proofs of basic formulas and models are given which allows the students to understand the principles of econometric theory development. The main attention is paid to the economic interpretations and applications of the econometric models. The first part of the course is devoted to the cross-section econometrics; the second part – to the time series and panel data econometrics.

Learning Objectives

• - apply econometric methods to the investigation of economic relationships and processes;
• - verify economic facts, theories and models with real data;
• - evaluate the quality of statistical and econometric analysis;
• - do and evaluate forecasting for time series and cross section data;
• - understand econometric methods, approaches, ideas, results and conclusions met in economic books and articles

Expected Learning Outcomes

• - outline the subject of Econometrics, its approach, the sources for study materials (including online ones), data, software, the course outcomes
• - be able to use theoretical notions, concepts and interpret results using SLR model
• - to analyze and estimate SLR model on real economic data using econometric software
• - to analyze and estimate MLR model on real economic data using econometric software
• - be able to use theoretical notions, concepts and interpret using MLR model
• - to apply variables transformations in econometric models and interpret the results
• - be able to explain the need for variables transformations in Econometric analysis
• - be able to use theoretical notions, concepts and interpret results related to dummy variables
• - to analyze and estimate models with dummy variables on real economic data using econometric software
• - be able to choose and interpret the LRM model specification
• - be able to analyse reasons, consequences, methods of detection and remedial measures for heteroscedasticity
• - to analyze and estimate LRM model in various specifications with real economic data using econometric software
• - to transform and estimate econometrics models with heteroscedasticity on real economic data
• - to apply the Instrumental Variables approach in the models with stochastic explanatory variables on real economic data
• - be able to use theoretical notions, concepts and interpret results on the topic
• - be able to use, interpret and transform the Simultaneous Equations models and the concept of identification
• - to estimate the parameters of Simultaneous Equations model on real economic data using econometric software
• - be able to define and use the maximum likelihood estimation approach
• - to estimate economic models using maximum likelihood approach
• - be able to apply the Binary Choice Models and Limited Dependent Variable Models
• - to analyze and estimate Binary Choice Models and Limited Dependent Variable Models on real economic data using econometric software
• - be able to use theoretical notions, concepts and interpret results of modelling with Time Series Data
• - to analyze and estimate Dynamic Processes models on real economic data using econometric software
• - be able to analyse reasons, consequences, methods of detection and remedial measures for the models with Autocorrelated Disturbance Term
• - to analyze and estimate the models with Autocorrelated Disturbance Term on real economic data using econometric software
• - be able to use theoretical notions, concepts and interpret results on the models with Stationary and Nonstationary Time Series
• - to analyze and estimate the models with Stationary and Nonstationary Time Series on real economic data using econometric software
• - be able to use theoretical notions, concepts and interpret the models with Panel Data
• - to analyze and estimate Panel Data models on real economic data using econometric software

Course Contents

• Introduction to Econometrics
  Statistical Investigation of Economic Variables' Relationships. Relationships in the economy: examples, problems of estimation and analysis (demand functions, earnings functions, economic growth models). Economic data: cross section data, time series data, panel data. Main statistical concepts and facts used in the course. Data bases. Software. Course materials presentation.
• Simple Linear Regression Model (SLR) with Non-stochastic Explanatory Variables. OLS estimation
  Simple Linear Regression Model: definitions and notation, Model A. SLR Model Estimation using Ordinary Least Squares (OLS). Expressions for the OLS estimators of slope coefficient and intercept: derivation and interpretation. Assumptions of the SLR models and the properties of OLS estimators. Gauss-Markov theorem (formulation). Standard deviations and standard errors of regression coefficients: derivation and interpretation. Statistical significance of OLS estimators: hypotheses testing using t-tests. Derivation and interpretation of confidence intervals. The general quality of regression: determination coefficient R2. F-statistics and F-tests. Relationship of R2 with correlation coefficients. SLR model without intercept. OLS-estimation, properties and applications.
• Multiple Linear Regression Model (MLR): two explanatory variables and k explanatory variables
  Derivation and properties of OLS-estimators of MLR with two explanatory variables. Determination coefficient R2. Adjusted R2. Testing hypotheses using t-tests and F-tests. OLS-estimation of the model with k explanatory variables in vector-matrix form. Properties of coefficients’ estimators. F-test for groups of variables. Multicollinearity. Its consequences, detection and remedial measures. Estimation of production functions in volumes and growth rates' forms as multiple regression models. Making predictions using Multiple Linear Regression Model. Properties of predictors.
• Variables Transformations in Regression Analysis
  Linear and Nonlinear regressions. Linearisation of non-linear functions and their estimation using Ordinary Least Squares. Disturbance term specification. Interpretation of linear, logarithmic and semi-logarithmic relationships. Estimation of functions with constant elasticity and exponential time trends. Comparison of the quality of regression relationships: linear and semi-logarithmic functions. Box-Cox transformation. Models with quadratic and interactive explanatory variables: estimation and interpretation.
• Linear Regression Model Specification
  Consequences of Incorrect Specification. Omitting significant explanatory variable. Including unnecessary explanatory variable in the model. Monte-Carlo method in econometric analysis: general principles, areas of application and examples. Proxy Variables. Testing of linear restrictions on parameters of MLR: single and multiple restrictions, F-tests and t-tests. Role and examples of linear restrictions in economic models. Model reparametrisation: interpretation and examples. Short run and long run effects. Lagged Variables in economic models. SLR model assumptions’ violation. General principles of consequences’ analysis, detection and correction. Generalised Least Squares (GLS).
• Heteroscedasticity
  Concept, consequences and detection of heteroscedasticity. Goldfeld-Quandt and White tests. Model correction. Logarithmic regressions. Weighted Least Squares (WLS) method as a special case of GLS. White’s heteroscedasticity-consistent standard errors. Reasons and examples of heteroscedasticity in economic models.
• Stochastic Explanatory Variables. Measurement Errors. Instrumental Variables
  Stochastic explanatory variables in LR models. Model B assumptions. Properties of OLS-estimators and test statistics of stochastic explanatory variables’ coefficients: finite sample and asymptotic. Measurement errors: reasons and consequences. Milton Friedman's critique on consumption function estimation: Permanent income hypothesis. Instrumental variables. Using instrumental variables in M.Friedman’s consumption model and in other economic models. Asymptotic properties of IV estimators. Durbin-Wu-Hausman (DWH) test.
• Simultaneous Equations Models
  Concept of simultaneous equations model. Exogenous and endogenous variables. Predetermined variables. The simultaneous equations bias. Inconsistency of OLS estimators. Structural and reduced forms of the model. Model of demand and supply and simple Keynesian equilibrium model as simultaneous equations models. Identification problem. Exact identification, underidentification, and overidentification. Rules of identification. Order condition. Testing exogeneity: Durbin-Wu-Hausman test. Methods of estimation. Indirect Least Squares (ILS). Instrumental Variables. Two-Stages Least Squares (TSLS). Examples of simultaneous equations models estimation in Economic Analysis.
• Binary Choice Models, Limited Dependent Variable Models
  Linear probability model: problems of estimation. Logit-analysis. Probit-analysis. Using Maximum Likelihood for logit and probit models' estimation. Models’ interpretation and Marginal effects investigation. Examples of Binary Choice models in Economics. Censored samples. Direct and truncated estimation. Tobit-model: interpretation and ML estimation.
• Maximum Likelihood Estimation
  The idea of maximum likelihood estimation (ML). SLR and MLR Models Estimation using ML. ML Estimators’ properties. Test statistics (z-statistics, pseudo- R2, LR-statistic) and statistical tests.
• Modelling with Time Series Data. Dynamic Processes Models
  Time series data regressions: Model assumptions. Properties of OLS estimators. Distributed lag models: geometrically distributed lags, polynomial lags. Koyck transformation and estimation of geometrical lag’s parameters. Autoregressive Distributed Lag (ADL) models. Interpretation and asymptotic properties. Partial adjustment. Adaptive expectations. Error Correction. Vector autoregression. VAR model. Causality in Economics: Granger test.
• Autocorrelated disturbance term
  Signs and consequences of disturbance term’s autocorrelation in LR model. Durbin-Watson d-test for first order autocorrelation. Breusch-Godfrey (BG) test of higher-order autocorrelation. Autocorrelated disturbance term and model misspecification: apparent autocorrelation. Model correction: Autoregressive transformation. Cochrane-Orcutt (CO) procedure and non-linear estimation. Autoregressive transformation and transformed’ model estimation as a special case of GLS. AR, MA, ARMA models. AR(1) and ADL(1,0) models: Common factor test and model selection. Autocorrelated disturbance term in a model with lagged dependent variable as one of the explanatory variables. Durbin h-statistic and test.
• Time Series Econometrics: Nonstationary Time Series
  Stationary and nonstationary time series. Definitions and examples of stationary and nonstationary time series. Random walk. Drifts and trends. Consequences of nonstationarity. Spurious regressions. Detection of nonstationarity. Correlograms. Unit root tests. Akaike ans Schwarz Information Criteria. Cointegration. Fitting models with nonstationary time series. Detrending. Error Correction models.
• Panel Data Models
  Panel data: economic examples. Unobserved heterogeneity problem. Pooled regressions. Fixed effect regressions. Within-groups regression models. First differences regression models. Least squares dummy variables (LSDV) regression models. Random effect regressions. Fixed effects or random effects: Durbin-Wu-Hausman (DWH) test. Fixed effects or pooled regression: F-test.
• Dummy Variables
  Dummy variables in linear regression models. Reference category and dummy variables’ trap. Effects of change of the reference category. Types of dummy variables: intercept and slope dummies. Interaction dummies. Multiple sets of dummies. Chow test for structural break. Dummy group test. Dummy variables in economic models: earnings functions, production functions. Dummy variables in seasonal adjustment.

Assessment Elements

• December exam
• October midterm
• home assignments in semester 1
• March midterm
• home assignments
• applied essay
  In the second semester the applied essay is set with the bonus points given equal to 2 regular home assignments.
• class participation, contests, applied essay
  Additional bonus points can be given by the lecturer for class participation during the year (not more than 5 out of 100), and for the Universiade and other contests. In the second semester the applied essay is set with the bonus points given up to 10 out of 100 extra to the year grade.
• the University of London (or ICEF final) exam
  Internal: Экзамен проводится в письменной форме с использованием асинхронного прокторинга. Экзамен проводится на платформе https://hse.student.examus.net). К экзамену необходимо подключиться за 10 минут до начала. Проверку настроек компьютера необходимо провести заранее, чтобы в случае возникших проблем у вас было время для обращения в службу техподдержки и устранения неполадок. Компьютер студента должен удовлетворять требованиям: 1. Стационарный компьютер или ноутбук (мобильные устройства не поддерживаются); 2. Операционная система Windows (версии 7, 8, 8.1, 10) или Mac OS X Yosemite 10.10 и выше; 3. Интернет-браузер Google Chrome последней на момент сдачи экзамена версии (для проверки и обновления версии браузера используйте ссылку chrome://help/); 4. Наличие исправной и включенной веб-камеры (включая встроенные в ноутбуки); 5. Наличие исправного и включенного микрофона (включая встроенные в ноутбуки); 6. Наличие постоянного интернет-соединения со скоростью передачи данных от пользователя не ниже 1 Мбит/сек; 7. Ваш компьютер должен успешно проходить проверку. Проверка доступна только после авторизации. Для доступа к экзамену требуется документ удостоверяющий личность. Его в развернутом виде необходимо будет сфотографировать на камеру после входа на платформу «Экзамус». Также вы должны медленно и плавно продемонстрировать на камеру рабочее место и помещение, в котором Вы пишете экзамен, а также чистые листы для написания экзамена (с двух сторон). Это необходимо для получения чёткого изображения. Во время экзамена запрещается пользоваться любыми материалами (в бумажном / электронном виде), использовать телефон или любые другие устройства (любые функции), открывать на экране посторонние вкладки. В случае выявления факта неприемлемого поведения на экзамене (например, списывание) результат экзамена будет аннулирован, а к студенту будут применены предусмотренные нормативными документами меры дисциплинарного характера вплоть до исключения из НИУ ВШЭ. Если возникают ситуации, когда студент внезапно отключается по любым причинам (камера отключилась, компьютер выключился и др.) или отходит от своего рабочего места на какое-то время, или студент показал неожиданно высокий результат, или будут обнаружены подозрительные действия во время экзамена, будет просмотрена видеозапись выполнения экзамена этим студентом и при необходимости студент будет приглашен на онлайн-собеседование с преподавателем. Об этом студент будет проинформирован заранее в индивидуальном порядке. Во время выполнения задания, не завершайте Интернет-соединения и не отключайте камеры и микрофона. Во время экзамена ведется аудио- и видео-запись. Процедура пересдачи проводится в соотвествии с нормативными документами НИУ ВШЭ.

Interim Assessment

• Interim assessment (2 module)
  0.5 * December exam + 0.25 * home assignments in semester 1 + 0.25 * October midterm
• Interim assessment (4 module)
  0.1 * home assignments + 0.4 * Interim assessment (2 module) + 0.5 * the University of London (or ICEF final) exam

Bibliography

Recommended Core Bibliography

• Dougherty, C. (2016). Introduction to Econometrics. Oxford University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.oxp.obooks.9780199676828
• Introduction to econometrics, Dougherty, C., 2011

Recommended Additional Bibliography

• Wooldridge, J. M. . (DE-588)131680463, (DE-576)298669293. (2010). Econometric analysis of cross section and panel data / Jeffrey M. Wooldridge. Cambridge, Mass. [u.a.]: MIT Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edswao&AN=edswao.263114414