Real business cycle in emerging countries

Thank you so much!

  1. I reset the upper bound to 50% of std.dev of observable and estimate under following scenarios:
    a) mode compute : 4 and uniform prior. This yields the following error:
    matrix must be positive definite with real diagonal

b) Then I change the mode compute to 6 and use inverse gamma prior (also uniform prior). Both give me similar results in terms of variance decomposition. Here’s the inverse gamma version
Posterior mean variance decomposition (in percent)

           eps_al      eps_vl      eps_ga      eps_gv      eps_xi  eps_tby_ME
g_y         31.85        3.61       42.05        8.29       14.20        0.00
g_c         15.42        0.06       45.10        2.38       37.02        0.00
g_x         24.51       16.83       18.41       11.80       28.45        0.00
tby          7.66        0.91       37.52       19.81       24.24        9.86

As you can see, the contribution of tby_ME comes down to less than 10%. However, the priors and posteriors for eps_tby_y look unusual.

  1. Did you ask me to check the following plot?

    Both actually observed data and smoothed series are identical. Do you want me to check somethingelse?

My original concern was the value of the the debt sensitivity of interest rate (psi) parameter. When I set it to a low value of 0.001, the contribution is trivial. However, either calibrating psi with a relatively high value (0.0355) or estimating it makes the contributions of measurement error and preference shocks to variance decomposition very high.

  1. Obviously your mode-finding runs into the upper bound for the measurement error. That corner solution explains the graph. GPU encountered something similar.
  2. Of course the oberved tby is identical to the data. But when you specify
    tby = nx_linear + eps_tby_ME;, then eps_tby_ME explains the difference between the measured tby and the true nx_linear in the model dynamics. You should compare these two.
  1. What else can I do to minimize the error?

  2. Could you please tell me what exactly I should compare? I checked the observation equation relating tby and nx_linear carefully and found okay according to my understanding. Do I need to subtract the steady state of nx_linear from the right hand side since I used demeaned series?

  3. This point is unrelated to ongoing discussion but related to my study. May I request you for clarification about observation equations defined in your paper titled “Fiscal News and Macroeconomic Volatility “? I have derived the equation for relative price of investment as attached here.
    Observation equation.pdf (144.8 KB)
    In the paper a minus (-) sign appears before the constant (log(mu_a)). But my derivation results in a positive sign. Would you mind giving a brief clarification?
    I am thinking about using the relative price as another observable.

  1. One way is to have a more informative prior that moves the measurement error towards zero. After all, the high measurement error seems to be inconsistent with your prior intuition on what it’s supposed to be.
  2. The difference between the smoothed values for tby and nx_linear is the measurement error. Sometimes one can spot in their different dynamics why the measurement error is needed.
  3. You did not explain your notation. If the left is the undemeaned growth rate in the data and all object with a time index on the right are mean zero, then there must be the constant on the right, because only then will the left and the right have a positive mean.

Thank you so much!

  1. I’ll work on it and see if changing the prior gives me better results.
    FYI, when I estimated parameters excluding psi, I obtained the following decomposition.
Posterior mean variance decomposition (in percent)
           eps_al      eps_vl      eps_ga      eps_gv      eps_xi  eps_tby_ME
g_y         22.80        2.90       43.33       26.21        4.76        0.00
g_c          4.25        0.16       61.17       24.30       10.12        0.00
g_x          7.88       14.90       40.03       35.44        1.75        0.00
tby          0.67        0.19       10.70       84.28        2.58        1.57
  1. I used exactly the same notation you used in your paper. My derivation results in a positive sign with the constant term while the paper has a negative sign. The non-demeaned series has been applied.
  1. But in our paper we imposed cointegration, i.e. subtracted the mean growth rate of output from the observed data. Thus, the data are essentially demeaned and you need to subtract the steady state from the \log \mu_t to remove the mean.

Appreciate you for patiently addressing my all questions posted in this thread and elsewhere.

Many thanks, Johannes. Your disclaimers in code are all very helpful.

thanks, Johannes. Your disclaimers in code are all very helpful..

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