Spurious Regression with non stationary time-series

Hi everyone,
I'd like to have a confirmation on the correctness of the following interpretation:
Let say that we want to run a very simple regression like the following one:

We are regressing two I(1) series since x and y are assumed to be both described by a random walk process. The errors of these 2 processes are uncorrelated
Granger and Newbold showed that in this case, we have an excess of rejection of the null hypothesis. This comes from the fact that the t-stat of the estimated
does not converge to a standard normal and the empirical distribution of the estimated
is no concentrated around its true population value. The point is: since the variance is time-dependent because the two time series are I(1), as the sample size increases the empirical distribution of the estimated
becomes fatter and fatter and thus we shall take into account the fact that the critical values are moving to the left. The theoretical critical values of the t-stat are no longer valid.
My doubt is: Granger and Newbold estimated
equal to zero on average. The true population values under this experiment where:

But why
is equal to zero on average?