1 / 18

Markov Chain and Its Use in Economic Modelling

Markov Chain and Its Use in Economic Modelling . Markov process Transition matrix Convergence Likelihood function Expected values and Policy Decision . A stochastic process . has the Markov process if for all . and all t. A Markov process is characterised by three elements:.

tal
Download Presentation

Markov Chain and Its Use in Economic Modelling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Markov Chain and Its Use in Economic Modelling Markov process Transition matrix Convergence Likelihood function Expected values and Policy Decision Ecocomic Modelling: PG

  2. A stochastic process has the Markov process if for all and all t A Markov process is characterised by three elements: Ecocomic Modelling: PG

  3. A typical Transition matrix Ecocomic Modelling: PG

  4. Chapman-Kolmogorov Equations Ecocomic Modelling: PG

  5. Likelihood Function for a Markov Chain Two uses of likelihood function to study alternative histories of a Markov Chain to estimate the parameter Ecocomic Modelling: PG

  6. Convergence of Markov Process with Finite States A Markov Process Converges when each element of the of the transition matrix approaches to a limit like this. Process is stationary in this example. Reference: Stokey and Lucas (page 321) Ecocomic Modelling: PG

  7. Recurrent or absorbing State or Transient State in a Markov Chain S1 is the recurrent state whenever the process leaves, re-enters in it and stays there forever. It is transient when it does not return to S1 when it leaves it. Here S1 is the recurrent state whenever the process leaves, re-enters in it. S2 and S3 are transient. Ecocomic Modelling: PG

  8. Converging and Non-converging Sequences Even Odd Ecocomic Modelling: PG

  9. One Example of Markov Chain Stochastic life cycle optimisation model (preliminary version of Bhattarai and Perroni) Prob of Transient state Probability of recurrent state If transient High income Low income Ecocomic Modelling: PG Probability of being in Ambiguous state

  10. Impact of Risk Aversion and Ambiguity in Expected Wealth with Markov Process Ecocomic Modelling: PG

  11. Markov Decision problem (refer Ross (187)). Ecocomic Modelling: PG

  12. Use of Markov Chain in analysis of Duopoly Sargent and Ljungqvist (133) Markov perfect equilibrium is the pair of value functions and a pair of policy functions for i=1,2 that satisfies the above Bellman equation. Equilibrium is computed by backward induction and he optimising behaviours of firms by iterating forward for all conceivable future states. Ecocomic Modelling: PG

  13. Other Application of Markov Process • Regime -Switch analysis in economic time series (Hamilton pp. 677-699; Harvey (285)) • Industry investment under uncertainty (SL chap 10) • Stochastic dynamic programming (SL chapter 8,9) • Weak and strong convergence analysis (SLChap 11-13) • Arrow Securities (Ljungqvist and Sargent Chapter 7). • Life cycle consumption and saving: An example • Precautionary saving Ecocomic Modelling: PG

  14. References: Ecocomic Modelling: PG

  15. Markov Chain Example in GAMS Ecocomic Modelling: PG

  16. Markov Chain Example in GAMS Ecocomic Modelling: PG

  17. Markov Chain Example in GAMS: Model Equations Ecocomic Modelling: PG

  18. Calculation of Weight Among Various States Ecocomic Modelling: PG

More Related