Keith, read what I said. If economic growth led to immigration then the change in immigration would always follow (by a constant-ish margin) the previous change in the economy. It doesn't. I gave the detail above.

Imagine you are investigating the effect of applying flame to a beaker of water. If it gets hot before the flame is applied, or cools while the flame is being applied, the heating effect is being caused by something else.

Are you not aware of the well known happenstance correlation between the number of storks and the birthrate, wherever it was?

And do you not see that there are other factors intended to affect immigration that will be in place when (and if) we climb out of this recession?