Error band / Confidence interval

[Heidi Ph]

hello,

This question is not really about stata, but i guess it somehow relates, so i post here, just in case has an idea, plz kindly help me.

I am reading a paper that has a figure as below. the figure illustrate the coefficient estimated as well as the 90% error bands. So I am wonder is this the 90% confidence interval?
And at the last quarters where the error band is very large, can i say that the coefficient is not precisely estimated there?


Thank you,

[Matt Warkentin]

Hi Heidi,

It looks like you may have tried to upload a picture, but it does not seem to be working. Perhaps this is a problem on my end, but I will comment without the ability to view the figure you speak of. Yes, a 90% confidence band/error band/confidence interval are terms that can be used interchangeably to describe the variability in point estimates.

In regards to the width of the confidence band, it is usually true that the data are sparse in the extremes of the distribution (i.e. the beginning and end of a distribution) so it is common to see the confidences bands be very wide at the beginning or end, or both. It carries the interpretation you stated, that the intervals are not very precisely estimated in this area.

Hope this is helpful.

[Heidi Ph]

Hi Matt, thanks for your reply.
I reupload the image here. Could you see it now?
If you can see it, I would like to ask you another question relating to it.

[Matt Warkentin]

Hi Heidi,

Yes, I am now able to see the figure. In regards to your initial question, you can see that less data are present at the higher end of the age distribution (visualized by the smaller dot size) and this is reflected by wider confidence intervals.

Happy to try and respond to your additional question.

[Heidi Ph]

Thank you, Matt.

My question is, from the figure, can I say that the trend of log markup is increasing over age?
Actually log markup & age relationship is downward slopping for firms whose age greater than the 7th decile, but as the error band is pretty large in this area, the estimation there is not precise, so can we ignore the trend there, and consider only the trend before 7th decile?

Looking forwards to hear back from you!
Best,

[Matt Warkentin]

Hi Heidi,

I am not sure I can provide any sort of definite answer to this. I do understand your perspective, however, I don't think "ignoring" the latter part of the function is the correct approach, even though it is imprecisely estimated. It certainly does seem that log-markup increases with age for most of the range of age, however, the downward slope at the end provides cause for thought. Is this a real downward slope? Is it actually just a plateau that is shown to decline because of small sample size? Should the trend continue to increase indefinitely with age? I don't know nearly enough about this topic area to provide those sorts of insights.

This is where subject-area knowledge will come in and provide context to the findings (assuming the results have been estimated correctly, using appropriate methods, etc.). It also looks like the panel on the left is the empirical average log-markup within quantiles of age. Perhaps fitting a model to these data would reveal a smoother trend and you could more formally test what the functional form is that best fits the data.

Sorry I can't be more help, I just do not know enough about the background of this figure. I do think you can choose to focus on certain aspects of a function, but I think it is unwise to ignore part of the function entirely only to make the interpretation simpler.

[Heidi Ph]

I got your point. Thanks so much for your help.
Have a nice day, Matt!