Does the level of a gym's badge affect the gameplay?

Since the last update you can now obtain a badge for a specific gym when you spin its photo disc. It is then possible to level it up by defending it, feeding the Pokemons from your team with berries or attacking it if another team is controlling it. Leveling the badges up apparently awards you with a new badge rarity, going from Bronze to Gold, as you can see from the picture below.

Does the rarity of a badge affect the gym it's linked to? For instance, can you get additional loots, or will your own Pokemon's motivation decrease more slowly?

Solution 1:

Leveling the Gym badge does have an affect on the game play. According to Niantic's post:

You can earn the opportunity to receive bonus items and increased rewards from Gyms by raising the level of your Gym Badge.

Having a higher Gym Badge level will yield more rewards and bonus items from Gyms. At the moment, this appears to be the only thing that the Gym Badges do that I can find.

Solution 2:

My observation is that:

• a bronze gym badge grants you +1 bonus items
• a silver gym badge grants you +2 bonus items
• a gold gym badge grants you +3 bonus items

In addition, you get bonuses if if your team controls the gym:

• If your team controls the gym and you do not have a gold gym badge, you get +1 bonus items.
• If your team controls the gym and you do have a gold gym badge, then you get +2 bonus items (for a total of +5 bonus items, including the gold gym badge bonus).