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. Inputoutput 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 Meanvalue 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 Comparativestatic 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 Firstorder linear differential equations. Model of partial market equilibrium. Domar model. Harrod model. Sollow model. Inflation. Secondorder linear differential equations. Market model with price expectations. Inflation and unemployment. Consumers' and producers' surplus. System of differential equations. Phase diagrams. Difference equations Firstorder linear difference equations. National income model. Cobweb model. Domar model. Harrod model. Market model with inventory. Secondorder linear difference equations. Inflation and unemployment. Systems of difference equations. Phase diagrams. Game theory Twoplayer zerosum 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. Oneperiod and multiperiod binomial model for asset pricing; noarbitrage conditions. BlackScholes model. Options pricing. Software Mathematics 
Description of general and specific competences (knowledge and skills) to be developed by this course:  Mathematical modelling, analysis, analysisbased 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: 

Additional reading: 

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). GaussMarkov assumptions. Properties of the LS estimator. Goodnessoffit. ANOVA table. Hypothesis testing. Multiple regression model: Specification of the functional relationships. GaussMarkov assumptions. Properties of the LS estimators. Simple, partial and multiple correlation: definition and their interrelationships. Prediction. Goodnessoffit. 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 BreuschPagan test. Solution to the heteroschedasticity problem (weighted least squares and ML method). First order autocorrelation. DurbinWatson (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 (BoxCox). Stationary time series models Autocorrelation function, ACF. Correlogram. Partial autocorrelation function, PACF. Parameters estimation for AR, MA and ARIMA models. The BoxJenkins approach. Forecasting. Goodnessoffit. Nonstationary time series models Spurious regression. Deterministic and stochastic nonstationarity. 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 tasksolving using software. Independent task processing using software. 
Method of assessment/examination  Students themselves opt for the method of assessment which may be through softwareaided empirical research or a written exam 
Required reading: 

Additional reading: 

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)
