when x1 is I(1), then the difference should be I(0), they regression of I(0) variable on another I(0) variable is simply a classic regression problem. The asymptotic theory is almost same as iid case. The coinetgration is often refered to such case: two (or more) variable shares common stochatic trend(unit root) such that some linear commination of the variable can be I(0). I.e., y=beta*x+u, x and y are both I(1) but u is I(0). In practice, the coinetgration takes same form as simple regression, but the limit theory is different. waht I mean is, when economic theory suggests that there's relationship between level variables, then it should be cautious in using difference data. However, it's often waht people do in empirical analysis that taking difference to deal with such kind of problem. Because otherwise, there should be a so-called model inconsistence problem. y=beta*x+u, when u is stationary, and x is stationary, it's no way that y is I(1).
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