I spent about 2 hours last evening reading through all the catalogs and ran out of time to post anything. Possibly this weekend if I have time I will scan a couple interesting catalog pages for posting to this thread. National Blue paint as DonC3 mentioned is on this bike was National's trade mark color used in all time periods. Once DonC3 posts a good photo of the sprocket side of the bike specifically of the sprocket/crank arm assembly. That may help me somewhat in being more sure of the production year. If DonC3 can determine what the serial number is that would certainly help as well.
What I can say for sure after reading 20 years worth of catalogs is once National decided they had perfected something they did not make many changes. I agree National had a well designed machine (I own a few myself) but that dedication to a single design makes Nationals very difficult to date accurately because they changed so very little between 1899-1916 aside from the components attached to the bike. The earlier models pre-1898 are actually much easier to determine the year of manufacture because something was being changed almost every year during that time period.
As I mentioned previously, this bike has no visible frame lugging as their earlier models did. The disappearance of frame lugging seems to have coincided with when National introduced the collet seat binder in 1899. This makes sense because if you are redesigning the frame to include a new feature, why not make all the changes at once. They even elude in one of the catalogs to their smooth seamless frame (presumably meaning no frame lugs).
Another reason National possibly didn't make many changes beyond 1899 is because as a whole, the bicycle industry by that point was on a downward trend and in the scheme of things National was not a large manufacturer so they probably didn't have the financial capitol to innovate much with new ideas. Stay the course and try to survive is what they appeared to do until finally being bought out by Davis Cycle in late 1916.
So back to this specific bike. The frame is clearly 1899 or later according to the catalogs. Spoked sprocket last appeared in catalog illustrations in 1900 but may have been used beyond that point or possibly it was replaced with a used sprocket at some point due to damage. Only reason I don't wish to date this bike 1899-1900 solely based on frame and sprocket is because all the componentry on this bicycle (handle bars, stem, seat, pedals) are all correct for National bicycles 1913-1916. Even the frame looks correct for 1913-1916 only the sprocket is questionable for that year.
If the components (handle bars, stem, seat, pedals) were all over the place coming from various sources and time periods and not featured in the 1913-1916 National catalogs, than I would be more certain that this bike is 1899-1900 and components were questionable being replaced at some point.
I suppose another possibility does exist though. Since this bicycle is in Bay City MI and has presumably spent its entire life in Bay City where Nationals were produced, possible the original owner of this particular bicycle worked at the National factory or went to a National bicycle dealer to obtain all National correct components of different time periods. In that case I would be more inclined to believe the original 1899-1900 time period for the frame and sprocket with all the components (handle bars, stem, seat, pedals) being added/replaced with later 1913-1916 National correct components.
In the end I suppose we may never know for sure when this bike was manufactured unless the owner can determine the serial number. That would most certainly help point us toward either the earlier 1899-1900 or later 1913-1916 time period.