How to shade one side of complicated path?

I would like to be able to reproduce this map, specifically the colored shading of borders (red for Russia, yellow for Ukraine, etc.).

I've tried effects (Glare or Drop Shadow) and gradients but can't make it look like in the example. My problem with Drop Shadow was that it is related to Stroke but in this case I want no stroke, just the shade.

What is the best way to go about it?

Thanks