# How can I test "Pollution causes people move to less polluted cities"?

I want to find an answer for the following question: "Air pollution causes people to move to less polluted cities from 1990 to 1991"?

Assume there are four cities: San Diego, Los Angeles, San Francisco, and New York. And their respective air pollution levels are 0, 1, 2, 100. I have data for 1000 people and the data look like this: if a person lived in Sand Diego in 1990 and in Los Angeles in 1991, Pollution1990 will be 0 and Pollution1991 will be 1.

PersonID    City1990   City1991   Pollution1990   Pollution1991
1        SD         LA             0               1


I thought about checking the following model:

reg Pollution1991   Pollution1990  controls, nocons


and if coefficient is smaller than 1, then I thought I could conclude that people are moving to less-polluted cities.

But then I found that

reg Pollution1990   Pollution1991 controls, nocons


also gives me coefficient smaller than 1. This was strange.

So how can I answer the question "Air pollution causes people to move to less polluted cities from 1990 to 1991"?

Is this even possible to test? Is there a regression towards the mean trap?