Investment adjustment costs in annual frequency

General DSGE Modeling
1

Good afternoon,

The standard value of capital investment adjustment cost is near 6. This value is obtained from quarterly data. I would like to know if I have to multiply by 4 this cost in an annual frequency model?

Plus, do you have references on durables investment adjustment costs ? I cannot find any.

Thank you.

Best regards

2
  1. Which type of investment adjustment costs do you have in mind?
  2. Mertens/Ravn (2011) have durables adjustment costs
3

1- I have quadratic convex investment adjustment costs for physical capital and durable goods.
2- The adjustment costs are on the durable stock in the reference, not the durable investments.

Thank you @jpfeifer

Best regards

4

Dear @jpfeifer,

I’m getting back at you on that matter. In order to obtain an adjustment cost in annual frequency, Should I multiply by 4 (4 quarters) an adjustment cost estimated on quarterly data?

Thanks

5

No, usually you have to divide by four, because the same amount of investment is now spread out over four times as many time periods.

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7

Thank you @jpfeifer. So if I find an adjust cost parameter in quarterly data of 10.8, that parameter becomes 2.7 on annual frequency ? Just to make sure, because I mentioned in the previous post adjustment costs instead of “adjustment cost parameter”.

Thanks

8

Yes, according to my experience, this yields similar dynamics in annual values.

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9

Dear Prof. Pfeifier,

May I kindly ask if you know of any books or other resources that discusses conversion of model parameters from annual to quarterly frequency and vice versa. In this thread, I don’t quite understand why we want to spread quarterly investment over the entire year when converting a quarterly investment adjustment cost parameter to annual frequency. What about investment in the other quarters of the year?

With \delta, for example, we have \delta = 0.1 for annual frequency model and \delta = 0.025 for quarterly frequency model. Meaning we multiply \delta by 4 when converting from quarterly to annual frequency.

Is it that each parameter has its own specific procedure when converting it from one frequency to the other? On \beta, why people use \beta=0.9901 for quarterly frequency model and \beta = 0.9605 for annual frequency model? Not sure how the conversion is done.

Would be glad if you know of any resources that discusses these. Many thanks!!

10

Beyond what I wrote in Pfeifer (2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”
I am not aware of anything.
The big difference is whether parameters apply to a flow or a stock and whether they are interest rates or their inverse.
For interest rates, you usually have a geometric product over the respective time period. The discount factor \beta=\frac{1}{1+\rho}, where \rho is the rate of time preference is similar in that you time aggregate the \rho and then compute the discount factor.

11

Do you have any reference on this?

12

For what exactly?

13

Sorry, I ment a reference where it is shown that an annual adjustment cost of 4 times a quarterly value yields similar dynamics in annual values.

I’m trying to understand the logic behind. If an annual adjustment cost is smaller than a quarterly adjustment cost, is it because it is more costly to adjust investment in the short term than in the long term?

14

I am not aware of a reference for that. But the logic with these costs is that it is expensive to change investment in short-run. If you put in a particular cost for adjusting investment at quarterly frequency, then the cost parameter at annual frequency must be lower, because you now allow for 4 quarters time for adjustment to take place.