Java's checked exceptions can be considered an effect system and coupled with ADTs I suppose we can call it an algebraic effects system. I mean the domino effect in which the exception has to be handled in each method that calls that is what seems to me the effect/handler counterpart that is present in Java. In the end an algebraic effect is just an extension of a type system that supports ADT, or is my memory from university failing me now.
The defining feature of these effect systems is "resumable continuations". Essentially, at the point where you catch an exception, you have the option of resuming the code which threw the exception, and you can tell it how to proceed.
So, whereas exceptions only jump backwards in the stack, resuming a continuation sorta lets you jump forwards again, back to where you were. It's really powerful stuff.
You cannot resume a computation with exceptions. At most, exceptions are a subset of effects. Similarly, a lot of the issues with checked exceptions in Java come from the lack of exception polymorphism in the checked exception type system. Adding the two points, you cannot really call checked exceptions an effect system.
