Bachelor
2020/2021

## Econometrics

Type:
Elective course (Economics)

Area of studies:
Economics

Delivered by:
Department of Economics

When:
3 year, 1, 2 module

Mode of studies:
offline

Language:
English

ECTS credits:
6

### Course Syllabus

#### Abstract

The Econometrics is an introductory course for the 3-rd year students of "Business Economics" track. The course is taught in English. The course aims to give the students the understanding of basic ideas, notions and methods of econometrics. The main attention is paid to the practical applications of econometric models. The first module of the course is devoted to Linear Regression and Ordinary Least Squares; the second module – to Simultaneous Equations Systems, Maximum Likelihood Estimation and Binary Choice.

#### 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
- understand econometric methods, approaches, ideas, results and conclusions met in economic books and articles

#### Expected Learning Outcomes

- students should be able to collect, organize, and analyze data; interpret results from statistical analyses
- construct, test, and analyse econometric models, using variables and relationships commonly found in the studies of economic and management theory
- identify key classical assumptions in the field of econometrics, explain the significance of these assumptions, and describe the effects that violations of the classical assumptions can have
- identify the desirable properties of estimators
- interpret key statistics and diagnostics typically generated by software

#### Course Contents

- Introduction to EconometricsWhat is Econometrics. Connection with Statistics and Machine Learning. Economic data: cross section data, time series data, panel data. Data bases. Software
- Review of StatisticsDistributions. Hypothesis testing. Properties of statistical estimators
- Simple Linear Regression Model (SLR). OLS estimationSimple Linear Regression Model. 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. Goodness-of-fit measures: determination coefficient R2. F-statistics and F-tests. Relationship of R2 with correlation coefficients. Forecasting.
- Multiple Linear Regression Model (MLR)Derivation and properties of OLS-estimators of MLR with two and more 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. Forecasting
- Variables Transformations in Regression AnalysisLinear and Nonlinear regressions. Linearization 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. 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 SpecificationConsequences of misspecification. 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.
- LR Assumptions' ViolationHeteroscedasticity. Goldfeld-Quandt and White tests. Weighted Least Squares. Multicollinearity. Its consequences, detection and remedial measures. Autocorrelation. Durbin-Watson and Breusch-Godfrey tests.
- Dummy VariablesDummy 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.
- Simultaneous Equations ModelsConcept 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).
- Maximum Likelihood EstimationThe idea of maximum likelihood estimation (ML). SLR and MLR Models Estimation using ML. Properties of ML estimators. Test statistics (z-statistics, pseudo- R2, LR-statistic).
- Binary Choice Models, Limited Dependent Variable ModelsLinear probability model: problems of estimation. Logit-analysis. Probit-analysis. Using Maximum Likelihood for logit and probit models' estimation. Models’ interpretation and Marginal effects investigation. Censored samples. Direct and truncated estimation. Tobit-model: interpretation and ML estimation.

#### Assessment Elements

- HomeworkThe homework can be split into several issues during the semester.
- TestThe test can be split into several issues during the semester
- ExamThe exam can be split into two parts and conducted at the end of each module. The exam can be off-line or on-line.

#### Bibliography

#### Recommended Core Bibliography

- Dalenberg, D. (2018). ECNS 403.01: Introduction to Econometrics.

#### Recommended Additional Bibliography

- Kleiber, C., & Zeileis, A. (2008). Applied Econometrics with R. New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=275761
- Wooldridge, J. M. . (DE-588)131680463, (DE-627)512715513, (DE-576)298669293, aut. (2013). Introductory econometrics a modern approach Jeffrey M. Wooldridge.