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Course Syllabus

Master 2020/2021

Mathematical Economics and Statistics

Type: Compulsory course (Applied Economics and Mathematical Methods)
Area of studies: Economics
Delivered by: Department of Mathematics
Where: St.Petersburg School of Economics and Management
When: 1 year, 1, 2 module
Mode of studies: offline
Instructors: Yaroslavna Pankratova
Master’s programme: Applied Economics and Mathematical Methods
Language: English
ECTS credits: 6
Contact hours: 52

Course Syllabus

Full Syllabus

Abstract

Course Mathematical Economics and Statistics is aimed for master students who are willing to obtain a basic knowledge of applied mathematics that is used in Economics. The course consists of Probability Theory, Statistics, Optimization and Dynamical Systems. Topics: 1. Basis of Probability Theory. 2. Statistics: estimation, confidence intervals, hypotheses testing, stochastic processes, time series. 3. Mathematical programming: problem statement, classification mathematical programming problems, linear programming, convex analysis, Kuhn-Tucker theorem. 4. Dynamical systems: difference equations, systems of difference equations, stochastic linear difference equations, basic methods for solving differential equations, dynamic optimization.
Learning Objectives

Learning Objectives

  • Being able to perform probabilistic and statistical calculations in standard formulations, give a meaningful interpretation of the results of calculations, process empirical and experimental data.
  • Being able to investigate the local behavior and stability of nonlinear dynamical systems in the vicinity of a hyperbolic stationary point.
  • Have the skills of probabilistic statistical thinking, have an idea about basic concepts of nonlinear dynamics.
Expected Learning Outcomes

Expected Learning Outcomes

  • can compute conditional and total probabilities, knows basic laws of probabilities
  • can use method of moments and method of of maximum likelihood
  • can compute large sample and small sample confidence interval
  • can test hypothesis on defined significance level
  • able to define MA, ARMA, ARIMA processes
  • knows properties of Markov chains, can solve problems
  • know key concepts of mathematical programming
  • can use simplex algorithm to solve linear programming problem
  • can solve nonlinear programming using Lagrange theorem and Kuhn-Tucker conditions
  • can solve first order linear difference equations and LDE of order p
  • can solve system of linear difference equations
  • can solve problems of dynamic programming using Bellman equation
Course Contents

Course Contents

  • Probability
    Set of events. Probability function. Tools for computing sample points. Conditional probability. Total probability. Bayes rule. Discrete random variables. Discrete random distribution: binomial, Poisson, geometric. Continuous random variables: normal, uniform, gamma, exponential, chi-squared. Basic laws of probabilities. Convergences. Law of large numbers. Central limit theorem
  • Estimation
    Method of moments. Method of maximum likelihood. Relative efficiency. Common Unbiased Point Estimators. Goodness of a Point Estimator
  • Confidence intervals
    Large Sample Confidence Intervals. Small Sample Confidence Intervals (normal). Sample size. Consistency. Sufficiency. The Rao–Blackwell Theorem.
  • Hypothesis testing
    Elements of Statistical Test. Common Large Sample Test. Type II Error Probabilities. Attained Significance Level. Neyman-Pearson Lemma. Likelihood Ratio Tests. Student's t-test. Chi-square Test.
  • Time series models
    Introduction to time series models. Stationarity. MA, ARMA, ARIMA processes. Dickey-Fuller test.
  • Markov chains
    Introduction to Markov chains. Markov property. Examples of Markov chains. Transition probability matrix. Steady-state analysis and limiting distributions
  • Introduction to mathematical programming
    Linear programming: introduction. Mathematical programming. Geometric Approach.
  • Linear programming
    Linear programming: Simplex algorithm. Dual problem.
  • Nonlinear programming
    Lagrange theorem. Implicit Function Theorem. The Lagrangean. Kuhn-Tucker conditions. Sufficient Conditions. Concave programming.
  • Linear difference equations
    Introduction to linear difference equations. First order linear difference equations. Solution Algorithm. Steady State and Stability. Linear Difference Equations of Order p. Stability.
  • System of linear difference equations
    Introduction to systems of linear difference equations. First order system of linear difference equations. Stability. Two dimensional systems of linear difference equations
  • Dynamic programming
    Problem Statement in dynamic programming. Bellman equation. Examples of problems of dynamic programming
Assessment Elements

Assessment Elements

  • non-blocking Test 1
  • non-blocking Test 2
  • non-blocking Homework 1
  • non-blocking Homework 2
  • non-blocking Activity
  • non-blocking Exam
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    0.12 * Activity + 0.4 * Exam + 0.12 * Homework 1 + 0.12 * Homework 2 + 0.12 * Test 1 + 0.12 * Test 2
Bibliography

Bibliography

Recommended Core Bibliography

  • Ljungqvist, L., & Sargent, T. J. (2012). Recursive Macroeconomic Theory (Vol. 3rd ed). Cambridge, Mass: The MIT Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=550665

Recommended Additional Bibliography

  • Takayama,Akira. (1985). Mathematical Economics. Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.cup.cbooks.9780521314985