Sets, functions and correspondences; Algebraic structures; Construction of real numbers; Polynomials; Vector spaces and subspaces; linear independence; Basis and dimensions; Matrices; Determinants; Eigenvalues and Eigenvectors; Bilinear and Quadratic Forms; Orthogonal Projection.
Topology and Metric Spaces; Compactness, Connectedness, and Convexity; Differential and Integral calculus.
Probability theory; Univariate random variables; Multivariate random variables; Distribution and density functions; Expectations; Convergence Concepts; Estimation Theory; Maximum Likelihood; Statistical Testing.
Basics of computer programming, numerical differentiation, approximation and interpolation, zero finding and numerical optimization, numerical integration, Monte Carlo methods.
Dynamic Optimization I
Sequential problems and recursive problems, Bellman equations, contraction mappings, solution methods.
Dynamic Optimization II
Markov processes; principle of optimality; stochastic Euler equations; applications to partial equilibrium models; search models.
Investment, consumption, asset pricing, labor supply, optimal taxation, overlapping generations, financial frictions.
Exogenous growth, endogenous growth, empirical findings.
Neoclassical growth models under uncertainty; Dynamic New Keynesian models; optimal fiscal and monetary policy, search and labor market frictions.
Microeconomics I (part 1, part 2)
Decision theory; consumer theory; producer theory; partial equilibrium theory.
Consumer theory; producer theory; general equilibrium theory.
Representation theory; solution theory; applications.
Applied Game Theory
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Algebra of least squares; classical and generalized linear regressions; likelihood function, distributions and testing principles; asymptotic analysis; estimation and testing in generalized regression models.
Stationary stochastic processes; integrated univariate processes; stationary VAR processes; cointegration analysis.
Instrumental variable estimation; generalized method of moments: panel data econometrics.
Empirical project: Application of econometric methods in microeconomics, macroeconomics, or time series econometrics.