Changing the gauge higher or lower will change the resistance. What is your goal?
Inductors are usually just a coil of copper wire, sometimes hundreds of feet long. Copper is the only realistic material to use. One way to lower resistance is to use thicker wire. You can purchase a more expensive coil that uses a heavy gauge wire. Moving from 19g to 14g increases the price by at least 5x's. Using silver increases the cost another 20x's. There are also copper foil inductors which are more expensive, but work somewhat better. Some inductors have iron or ferrite cores in the middle of the coil. This core decreases the amount of copper wire needed for the coil, and therefore lowers the resistance. The problem is that these cores cause some distortion. For smaller inductors, use one without a core - an air core inductor. For the larger inductors required for the woofer's crossover, an air core inductor might not be feasible. In these cases, use a ferrite core. If you want to try to make your own inductor to save money, check out the Inductor Calculator for information on winding your own coils. I hope this helps...
Same person asking about crossover changes?
Iron inductors are OK up until saturation.
Please consult an online inductor calculator. some are pretty good. I'll post one later......
Yes is the answer to your question. You will need MORE of the lower resistance larger wire for the same DCR. Iron core original inductor complicates things, but I was able to design a match for my Magnepan's inductor using aircore formulas and calculators.
Start running some simulations using the calculator I ref'd above.
What do you mean by "higher gauge"? If you intend to use thinner wire (skin effect) and keep the same resistance and inductance you can achieve this by using tape woven inductors. Many good speakers have tape inductors but also many very good speakers don't. I doubt if it makes any difference because skin effect in copper at 20kHz starts at gauge 18 but at this frequency but overall effect is negligible.
It's all about tradeoffs and the original inductor.
If the original inductor is aircore, and larger gauge wire, don't bother.
IF the original inductor is iron core 16 or 18 ga in a fairly low sensitivity speaker, like my Magnepans, than you can get some headroom out of going to larger gauge wire as long as you consider the DCR of the new piece. Changing the DCR will alter the crossover point...but usually not much AND change driver balance and perhaps voicing. 1db would be a large change in my panels.
Inductors in mids and tweets? much less important than in the bass where most of the power goes. That is the best use of a new inductor...in the bass. And than only if you are a 'power user' and routinely crank it up.
Inductor calculators? yep...and plenty on line. Run some 'simulations' My design for my panels new inductor? 14ga......up from 16, aircore and with a DCR within 5% of the original unit. It is also the same number of layers as winds, so the coil is square in cross section AND I designed it to be wound on a standard size of PVC pipe, right from the home store. Outside diameter is a tick over 4" and less than 1" thick, so it is a manageable size.