• A
• A
• A
• ABC
• ABC
• ABC
• А
• А
• А
• А
• А
Regular version of the site

# Elements of Econometrics

2020/2021
ENG
Instruction in English
10
ECTS credits
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

• The students get in the course basic knowledge and skills of econometric analysis and its application in Economics. They should be able to: - 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.
• The students should understand essential differences between the time series and cross section data and those specific econometric problems met in the work with these types of data (measurement errors, endogeneity, autocorrelation, non-stationarity and others), as well as with panel data, and apply the appropriate econometric methods (instrumental variables, maximum likelihood estimation, models of dynamic processes, etc.). The students should get the skills of construction and development of linear regression models, get acquainted with some non-linear models and special methods of econometric analysis and estimation (binary choice models, , understanding the area of their application in economics. The methods and models should be mastered practically on real economic data sets with modern econometric software.
• The course contributes in the development of the following general competencies: -ability to work with information: to find, evaluate and use information from various sources, necessary to solve scientific and professional problems; - ability to do research, including problem analysis, setting goals and objectives, identifying the object and subject of research, choosing the means and methods of research, assessing its quality; - ability to collect and analyze the data and calculate economic and socio-economic indicators characterizing the activities of economic entities; - ability to choose tools for processing economic data, analyze the results of calculations and substantiate the findings; - ability to analyze and interpret the data of domestic and foreign statistics on socio-economic processes and phenomena, to identify trends in changing of socio-economic indicators; - ability to solve analytical and research problems with modern technical means and information technologies; - ability to organize their activities in the framework of professional tasks.

#### 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
• - be able to use theoretical notions, concepts and interpret using MLR model
• - to analyze and estimate MLR model on real economic data using econometric software
• - be able to explain the need for variables transformations in Econometric analysis
• - to apply variables transformations in econometric models and interpret the results
• - 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
• - to analyze and estimate LRM model in various specifications with real economic data using econometric software
• - be able to analyse reasons, consequences, methods of detection and remedial measures for heteroscedasticity
• - to transform and estimate econometrics models with heteroscedasticity on real economic data
• - be able to use theoretical notions, concepts and interpret results on the topic
• - to apply the Instrumental Variables approach in the models with stochastic explanatory variables on real economic data
• - 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.
• 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.
• 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.
• 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.
• 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.
• 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.

#### Assessment Elements

• Home assignments Semester 1
• October mid-term
• December exam
• March Mid-term
• Final exam
• Applied essay
• Bonus for course activities
• Home assignments Semester 2

#### Interim Assessment

• Interim assessment (2 module)
G=0.25*Goct+0.5*Gdec+0.25*Gha1 ha1 – home assignments in semester; Goct, Gdec - the grades for October mid-term and December ICEF exam out of 100.
• Interim assessment (4 module)
G=0.3*(0.25*Goct+0.5*Gdec+0.25*Gha1)+0.2*Gmarch+0.1*Gha2+0.4Gfin+0.1Gessay+0.05Gbonus ha1 and ha2 – home assignments in semester 1 and 2, Gfin – the grade for final exam of the University of London or ICEF. Goct, Gdec and Gmarch - the grades for October, December and March ICEF exam and mid-terms out of 100. Gessay – bonus points for essay out of 10, Gbonus – bonus points for class participation and contests.