On page 619 in the paper (please refer to the PDF attachment
DSGEmodelofStockBubblesandBusinessCycles.pdf (522.6 KB)
), for the sentiment shock, its prior standard deviation is 0.1, which is 10 times larger than other prior standard deviation of shocks 0.01, and the posterior standard deviation of the sentiment shock is 0.1839, while remaining posterior standard deviations of the shocks are all less than 0.02,
and if you look at the impulse responses of key observable variables to sentiment shock in the graph on page 626, the responses of consumption, investment and output to 1 standard deviation of sentiment shock are relatively larger in 20 quarters/40 quarters, e.g. greater than 2 percentage in 20 quarters/40 quarters but quite small in instant responses, e.g. around or less than 1 percentage. However, if you have a look at graphs on page 625, the impulse responses of consumption, investment and output to other shocks are much smaller, e.g. smaller instant responses to financial shock at around 1% and also small in 20 quarters/40 quarters. I am curious about the large difference, why these happen? Is it just because the prior and posterior standard deviations of sentiment shocks are relatively larger in comparison with other shocks? and why the large difference does not happen in the instant impulse responses but responses in quarter 20 and quarter 40?
Besides, for hours worked, its responses to sentiment shock and other shocks (e.g. financial shocks) are of similar scale, e.g. within 0.2 percentage, why the effects of the prior and posterior sizes of sentiment shock on hours worked are not obvious?
Thank you very much and look forward to hearing from you.
That is the question of shock size vs transmission. There are no general answers. Given that the estimated shock size is relatively bigger, one would usually also expect the economic effect to be bigger. But the fact that some variables show larger responses while others have similar quantitative sizes suggests that it’s not just the shock size, but also the transmission of the shocks to particular variables. Why that is the case, you have to study the particular model.
Regarding the delayed peaks: most models contain sizable real and nominal rigidities that result in a delayed adjustment (e.g. investment adjustment costs). This will result in hump-shaped responses.