Mathematical Economics and Statistics
Петросян Ованес Леонович
- 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.
- 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
- ProbabilitySet 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
- EstimationMethod of moments. Method of maximum likelihood. Relative efficiency. Common Unbiased Point Estimators. Goodness of a Point Estimator
- Confidence intervalsLarge Sample Confidence Intervals. Small Sample Confidence Intervals (normal). Sample size. Consistency. Sufficiency. The Rao–Blackwell Theorem.
- Hypothesis testingElements 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 modelsIntroduction to time series models. Stationarity. MA, ARMA, ARIMA processes. Dickey-Fuller test.
- Markov chainsIntroduction to Markov chains. Markov property. Examples of Markov chains. Transition probability matrix. Steady-state analysis and limiting distributions
- Introduction to mathematical programmingLinear programming: introduction. Mathematical programming. Geometric Approach.
- Linear programmingLinear programming: Simplex algorithm. Dual problem.
- Nonlinear programmingLagrange theorem. Implicit Function Theorem. The Lagrangean. Kuhn-Tucker conditions. Sufficient Conditions. Concave programming.
- Linear difference equationsIntroduction 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 equationsIntroduction to systems of linear difference equations. First order system of linear difference equations. Stability. Two dimensional systems of linear difference equations
- Dynamic programmingProblem Statement in dynamic programming. Bellman equation. Examples of problems of dynamic programming
- 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
- 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
- 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