Map from measurement equation to state transition equation

Estimation ML/Bayesian estimation
1

Dear Johannes,
In my DSGE model, I use Consumer Sentiment Index growth rate as an observable variable, and I also incorporate a sentiment shock, I have a question about relating consumer sentiment index growth rate to state variables, however, there is no a specific state variable for sentiment in our DSGE model, we use sentiment shock as a way to model growth rate of stock bubbles, based upon equation (3) on page 1354 of the paper ‘Information, Animal Spirits, and the Meaning of Innovations in Consumer Confidence’ (please refer to the PDF attachment), we formulate the following connection:
Consumer Sentiment Growth Rate=sample mean of consumer sentiment growth rate+coefficient1OutputGrowth+coefficient2sentiment shock,
where OutputGrowth is calculated as the growth rate of the state variable of output.
In our Bayesian estimation, I plan to set a Gamma prior distribution for coefficient1 with mean 1 and standard deviation 0.25 and set a Gamma prior distribution for coefficient2 with mean 1 and standard deviation 0.25. My questions are what do you think about our measurement equation, and are our prior mean of Gamma distribution for coefficient1 and coefficient2 appropriate? On page 12, equation (3)
Best regards,
Jesse
BarskySims.pdf (1.4 MB)

2

Dear Johannes,
In my DSGE model, I use Consumer Sentiment Index growth rate as an observable variable, and I also incorporate a sentiment shock, I have a question about relating consumer sentiment index growth rate to state variables, however, there is no a specific state variable for sentiment in our DSGE model, we use sentiment shock as a way to model growth rate of stock bubbles, based upon equation (3) on page 1354 of the paper ‘Information, Animal Spirits, and the Meaning of Innovations in Consumer Confidence’ (please refer to the PDF attachment), we formulate the following connection:
Consumer Sentiment Growth Rate=sample mean of consumer sentiment growth rate+coefficient1OutputGrowth+coefficient2sentiment shock,
where OutputGrowth is calculated as the growth rate of the state variable of output.
In our Bayesian estimation, I plan to set a Gamma prior distribution for coefficient1 with mean 1 and standard deviation 0.25 and set a Gamma prior distribution for coefficient2 with mean 1 and standard deviation 0.25. My questions are what do you think about our measurement equation, and are our prior mean of Gamma
Thank you very much and look forward to hearing from you.
Best regards,
Jesse

3
  1. I would need to see a plot of the prior to judge the shape.
  2. Based on your observation equation, you are giving the sentiment shock a rather straightforward interpretation: a signal for output growth. My understanding is that this is not what the referenced paper actually does. That may be tough to sell to referees.