Does the resolution of the HDRI affect the results in terms of lighting?

I tested Debevec's "dodge" HDRI at 3 different sizes; 1024, 512 and 256 on the same scene. (I resized the HDRI with HDRShop). The lighting changed very noticably in the scene when changing sizes. (as the HDRI got smaller, the lighting got brighter), but as stated, this can be tweaked with Bryce's sliders.

But, the render times of all 3 sizes were all exactly the same.

I believe the reason some HDRI's take longer to render in a scene is due to the amount of exposure levels that were used to create them. I have had HDRI's that were complex looking (sky, buildings, people, ground) and they rendered fairly fast, while an HDRI I made in photoshop (grey background, and a single white square) seemed to render forever. (it had 7 exposure layers)

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