What kind of paneling? There are an inifinite number of different ways it can be done, some of which are more expensive than others.

For wainscots its typical to use premade stock e.g. beadboard, pickwick, etc. It's possible (though maybe less common) to run this to the ceiling in a stairway configuration.

More commonly you have some kind of rectangular panel arrangement. There are a number of different ways to do this, some more expensive than others. To achieve the basic look of paneling you can do a simple applied molding which is pretty easy to do. More elaborate recessed paneling would be more material and labor (and correspondingly more expensive). At the high end you get into raised panels with very sophisticated applied moldings.

Complexity in all of these also comes from the fact that the elevation must be carefully designed to look good. There is ideal spacing/balance for the panels vs. the spacing between them. This is something your architect might have done for you, or an interior designer, or maybe even the trim company.

You should get an understanding of the molding profiles being used in that bid, and the general design.

Some pictures from Houzz:

Applied molding:

[Traditional Living Room[(https://www.houzz.com/photos/traditional-living-room-ideas-phbr1-bp~t_718~s_2107)

Recessed panel with an applied molding:

[Traditional Hall[(https://www.houzz.com/photos/traditional-hallway-ideas-phbr1-bp~t_743~s_2107) by Winter Park Interior Designers & Decorators Niemann Interiors

Raised panel:

[Traditional Entry[(https://www.houzz.com/photos/traditional-entryway-ideas-phbr1-bp~t_741~s_2107) by New York Interior Designers & Decorators Robin Baron Design

Search on Houzz for wall paneling, etc. for more images.

Where I live (Louisiana), that's way too much.

This is the type of paneling I asked to be installed. I thought for sure there would have been a high quality pre fabricated panel to limit the costs.

(The photo is on its side....ceiling is on left side, obviously).

I have never heard of a prefabricated block panel.

I guess these 2x2 ceiling tiles are prefabricated panels

If you are talking about paneling the entire stairwell like that than 11k materials and labor seems reasonable.

Here is a link that might be useful: ceiling tile

Oh that kind of panel. No, that doesn't seem too high. I was picturing the old style, fake wood wall paneling. It should be beautiful when you're done.

I have the same idea clipped for my stairway wall to the basement (building a coastal style house), but I hadn't asked for pricing yet. Sounds like it is not going to be in the budget! I wonder if you can achieve the same general feel/look with the prefab beadboard paneling...

The cheapest way to achieve that look for painted trim is to use trim boards (cheap poplar) over your drywall and paint it all the same color.

So the raised wood would be poplar trim, but the flat surface would be drywall finished smooth.

We did it. It's not that expensive. Stripped the drywall and used 1/8"-1/4" high grade plywood, flat stock, and got very creative with mouldings available at Home Depot. We are going to be painting ours.

Before anyone mentions the spindles, yes, I know, they are upside down... That was a bit of an argument but it looks splendid in person.