 Course title: MATHEMATICS FOR ECONOMIC ANALYSES Type of course: Compulsory Number of contact hours 45 hours ECTS: 5 ECTS Course coordinator: Professor Zrinka Lukač, Ph.D. Course instructors (in case of more instructors): Professor Zrinka Lukač, Ph.D. Course content: Linear algebra System of linear equations. Gaussian method of solving linear equations. Linear dependence and independence, rank of a matrix, inverse matrix, determinants. Solving a system of linear equations with the inverse matrices and determinants. Eigenvalues of a matrix. Eigenvectors of a matrix. Input-output analysis. Functions of one variable Elementary functions: polynomials, rational functions, irrational functions, exponential function, logarithmic functions, trigonometric functions. Domain, range, increasing functions, decreasing functions, convexity, concavity. Limit of a function. Differential calculus of functions of one variable Mean-value theorems. Taylor's formula. Rate of change. Elasticity of function. Point elasticity. Total, average and marginal values. Extremum of function. Differential calculus of multivariable functions Comparative-static analysis of equilibrium.  Extremum of multivariable functions without constraints, necessary and sufficient conditions. Extremum of multivariable functions without constraints, Lagrange multipliers. Production function, isoquants, factor substitution, elasticity of substitution. Optimal combination of production factors. Utility function, indifference curves, optimal choice of consumers with a given budget. Integral calculus First-order linear differential equations. Model of partial market equilibrium. Domar model. Harrod model.  Sollow model. Inflation. Second-order linear differential equations. Market model with price expectations. Inflation and unemployment. Consumers' and producers' surplus. System of differential equations. Phase diagrams. Difference equations First-order linear difference equations. National income model. Cobweb model. Domar model. Harrod model. Market model with inventory. Second-order linear difference equations. Inflation and unemployment. Systems of difference equations. Phase diagrams. Game theory Two-player zero-sum games. Static and dynamic games of complete information. Static and dynamic games of incomplete information. Mathematics of finance Accumulation and present value of an investment, discrete and continuous case. Efficiency of an investment project. One-period and multiperiod binomial model for asset pricing; no-arbitrage conditions. Black-Scholes model. Options pricing. Software Mathematics Description of general and specific competences (knowledge and skills) to be developed by this course: Mathematical modelling, analysis, analysis-based conclusions Teaching methods: Lectures, exercises, seminars, computer work, individual assignments Requirements for students and ways to participate: Class attendance, computer work, homework, seminar papers, working on articles from literature Method of assessment/examination Written and oral part of the exam, homework assignments Required reading: M Anthony & N L Biggs, Mathematics for Economics and Finance: Methods and Modelling, Cambridge University Press, 1996.A Ostaszewski, Mathematics for Economics: Models and Methods, Blackwell, 1993. Additional reading: Carl. P. Simon, Lawrence Blume, «Mathematics for Economists», W.W. Norton & Company, New York, 1994. Basis for credit allocation: The number of ECTS credits is determined by the complexity of the programme, the number of hours needed for lectures, student obligations in class and autonomous work. Course and teaching quality assurance: - Student surveys on the quality of the course and teaching - Occasional observation and evaluation of teaching by the head of the study programme - External evaluation provided by the Croatian Agency for Science and Higher Education (Agencija za znanost i visoko obrazovanje) Course title: INTRODUCTION TO ECONOMETRICS Type of course: Compulsory Number of contact hours 45 hours ECTS: 5 ECTS Course coordinator: Professor Nataša Erjavec, Ph.D. Course instructors (in case of more instructors): Professor Nataša Erjavec, Ph.D. Course content: Review: Basic statistical concepts. Basics in matrix algebra. Introduction: Definition of econometrics. Concepts and types of models. Special characteristics of economic data. Econometric model concretization data. Data types and sources. Testing data quality, data transformation. Statistical and theoretical concepts of econometric modelling. Selected statistical software. Simple regression model: Specification of the functional relationships. Methods of parameter estimation: method of moments (MM), method of least squares (LS) and maximum likelihood method (ML). Gauss-Markov assumptions.  Properties of the LS estimator. Goodness-of-fit. ANOVA table. Hypothesis testing. Multiple regression model: Specification of the functional relationships. Gauss-Markov assumptions. Properties of the LS estimators. Simple, partial and multiple correlation: definition and their interrelationships. Prediction.  Goodness-of-fit. ANOVA . Hypothesis testing. LR (likelihood ratio) test. Waldov test and LM (Lagrange multiplier) test. Multicollinearity. Regression model with qualitative variables Qualitative variables: binary, indicator, dummy and categorical variables. Dummy variables for changes in the intercept term. Dummy variables for changes in slope coefficients.  Dummy variables for testing stability of regression coefficients. Dummy variable as a dependent variable. Logit model. Probit model. Tobit model. Heteroschedasticity and Autocorrelation Definition of heteroschedasticity. Consequences of heteroschedasticity. Testing for heteroschedasticity: RESET test, LR test, Goldfeld and Quandt test and Breusch-Pagan test. Solution to the heteroschedasticity problem (weighted least squares and ML method). First order autocorrelation. Durbin-Watson (DW) test. High order autocorrelation. LM test. Introduction to Time Series Analysis Time series: definition, problems and opportunities. General form of the model. Time series graphs with different components. Methods of time series analysis: frequency domain and time domain. Stationary and nonstationary time series. Selected time series models: pure random model, autoregressive AR (p) model, moving average MA (q) model, mixed ARIMA (p,q) model, ARIMA (p,d,q), random walk model, random walk model with drift. Variance stabilizing transformations (Box-Cox). Stationary time series models Autocorrelation function, ACF. Correlogram. Partial autocorrelation function, PACF. Parameters estimation for AR, MA and ARIMA models. The Box-Jenkins approach. Forecasting. Goodness-of-fit. Non-stationary time series models Spurious regression. Deterministic and stochastic non-stationarity. Unit root. Unit root tests: DF, ADF, KPSS and PP test. Granger causality. Error correction model. Description of general and specific competences (knowledge and skills) to be developed by this course: The course is an introduction to the theory and practical application of econometrics with the purpose of acquiring the knowledge of econometric theory and mastering practical skills required for appropriate statistical analysis and interpretation of the results obtained. Teaching methods: Lectures, case analysis, software use Requirements for students and ways to participate: Individual task-solving using software. Independent task processing using software. Method of assessment/examination Students themselves opt for the method of assessment which may be through software-aided empirical research or a written exam Required reading: Wooldridge, J.M. (2006). Introductory Econometrics: A Modern Approach, 3nd Ed. Thomson, South-Western College, Cincinnati., OH. Additional reading: Verbeek, M. (2000). A Guide to Modern Econometrics,  John Wiley & Sons, New York. Dinardo, J., Johnston, J. and Johnston, J. (1996). Econometric Methods, 4th Ed., McGraw-Hill/Irwin.Maddala, G.S. (2002). Introduction to Econometrics, 3rd Ed., John Wiley & Sons, Chichester, UK.Wei, W. W. S. (2005). Time Series Analysis: Univariate and Multivariate Methods, Addison Wesley Publishing Company, USA. Basis for credit allocation: The number of ECTS credits is determined by the complexity of the programme, the number of hours needed for lectures, student obligations in class and autonomous work. Course and teaching quality assurance: - Student surveys on the quality of the course and teaching - Occasional observation and evaluation of teaching by the head of the study programme - External evaluation provided by the Croatian Agency for Science and Higher Education (Agencija za znanost i visoko obrazovanje)
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