Suppose we have
$$y = b_1x_1 + b_2x_2 + b_3x_3 + e$$
as our regression model.
Setting a linear restriction, say $b_1 + b_2 + b_3 = 0$, allow us to rewrite the model as,
$$y = (b_1)(x_1 - x_3) + (b_2)(x_2 - x_3) + e$$
Given that such restrictions often improve out of sample performance of estimates (even when the restrictions are wrong), I was wondering if it may be connected to Stein's Paradox? Intuitively, it seems to me that $b_3$ is essentially 'shrunk' to zero with the restriction, and that somehow improves the estimates.
I was wondering if anyone could give a more theoretically robust explanation? Or if I am wrong here, point out where I am wrong.