Olaf Posch
Portrait of Olaf Posch
University of Hamburg

Olaf Posch

Professor of Economics

I am a macroeconomist interested in asset pricing, monetary policy and fiscal policy. My research primarily focuses on economic theory and econometrics at the intersection of macroeconomics, sovereign debt and financial markets with a particular focus on the term structure of interest rate.

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Research

Working Papers

Publications

Code

    Programs
  • Peso Problems in the Estimation of the C-CAPM
    with Juan Carlos Parra-Alvarez and Andreas Schrimpf
    Quantitative Economics 13 (2022): P. 259–313. Link
    [Matlab implementation]
    Notes
    • This folder contains programs to simulate rare disaster and long-run risk (LRR) models and estimate C-CAPM parameters using Matlab.
    • The file main.m simulates the rare disaster and the LRR models and estimates the traditional C-CAPM parameters based on simulated data. The file can be used to replicate the simulation results in Tables A.6 to A.11.

      Type 'help main' for complementary files available in the folder and for details.

    • The file empirical_estimates.m estimates the traditional C-CAPM parameters based on empirical data. The file can be used to replicate the empirical results in Tables A.1 an A.2.

      Type 'help empirical_estimates' for details.

  • Risk Matters: Breaking Certainty Equivalence in Linear Approximations
    with Juan Carlos Parra-Alvarez and Hamza Polattimur
    Journal of Economic Dynamics and Control 133 (2021): 104248. Link
    [Matlab implementation]
    Notes Matlab
    • The file SGM_PPP_2021_Matlab.m computes a first-order perturbation approximation to the Stochastic Growth Model. It builds a first-order Taylor series expansion to the costates variables using Proposition 1, Theorem 2 and Proposition 3 in the paper.

      The model has \( n_x=2 \) state variables (\(x =\) capital, \(K\), and productivity, \(A\)) and \( n_y=2 \) costate variables (\( y = V_K\) and \( V_A \)). The perturbation parameter is denoted by \( \eta \geq 0\).

      The user must provide the following inputs:
      *Input 1: Parameter values
      *Input 2: Symbolic definition of control and state variables
      *Input 3: Coefficients \(a \in \mathbb{R}^{n_x \times 1}\), \(b \in \mathbb{R}^{n_x \times 1}\) and \(c \in \mathbb{R}^{n_x^2 \times 1}\) of the system of quasilinear PDEs
      *Input 4: Deterministic steady state, DSS: \((x,y,\eta) = (x_{ss},y_{ss},0)\).

      Matrices a, b and c define the model class \[H(x,y,y_x,y_{xx}) = a(x,y) + y_x b(x,y) + \eta y_{xx} c = 0\] that summarizes the equilibrium in the economy.

      The solution is given by the policy function \(y = g(x,\eta)\) which is approximated as \[g(x,\eta) = g(x_{ss},0) + g_x (x-x_{ss}) + g_{\eta}\eta.\]

      Using the approximation to the costate functions, the code also reports a first-order approximation to the control variables defined by the first order condition \(u = u(x,y)\). For the Stochastic Growth Model, \(u =\) consumption. Its approximation is given by \[u(x,\eta) = u(x_{ss},0) + u_x (x-x_{ss}) + u_{\eta}\eta.\]

    • The file SGM_PPP_2021_simple_Matlab.m is a simplified version of SGM_PPP_2021_Matlab.m where only the costate for the capital stock \(y = V_K\) is approximated. See Section 3.3 of the paper.
    Notes Mathematica
    • The file SGM_PPP_2021_Mathematica.nb computes a first- and second-order perturbation approximation to the Stochastic Growth Model. The approximations are built using a brute force approach - it successively computes the derivatives of the unknown policy functions \((y,u)=((V_K,V_A),C)\) and evaluates them at the \(D_{SS}, (x,y,\eta) = (x_{ss},y_{ss},0)\).

      The first step is to define the functional \(F(x,\eta) = H(x,g(x,\eta),g_x(x,\eta),g_{xx}(x,\eta)) = 0.\) From there, the code computes successively all the required derivatives to build the approximats to the policy functions:

      "Perfect-foresight" component \[F_x(x,\eta) = F_{xx}(x,\eta) = F_{xxx}(x,\eta) = F_{xxxx}(x,\eta) = 0\] and "Stochastic" component \[F_\eta = F_{x\eta} = F_{xx\eta} = F_{\eta\eta} = 0.\]

  • Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty
    with Timo Trimborn
    Journal of Economic Dynamics and Control 37 (2013): P. 2606-2662. Link
    [Matlab implementation]
    Notes
    • Choose the directory "Waveform" as current Matlab directory.
    • Execute "rbc.m" to start the calculations. The Figures show the policy function, the deviation from the last iteration, and absulte and relative errors (if available).
    • To modify the model open "rbc.m" (main file), "funcODE.m" (set of differential equations), and "findss.m" (steady state conditions).

Contact

Universität Hamburg
Department of Economics
Von-Melle-Park 5
20146 Hamburg
Office
Room 2069, VMP 5

Phone
+49 40 42838 4630

Email
olaf.posch@uni-hamburg.de