Suppose $$ y = aX + \epsilon $$ where $X$ is an extremely weak predictor and estimation of $a$ is dominated by error. Luckily we have another predictor $$ y = bZ + \zeta $$ where $Z$ is very strong, but also correlated to $X$ . My aim is to estimate $a$ better, not necessarily have better prediction error on $y$ . We can use $Z$ to reduce the estimation error. However if I estimate jointly $$ y = cX + dZ + \gamma $$ the procedure does two things: reduce variance of $\gamma$ but also eats from true value of $a$ , that is $c \neq a$ . What kind of estimation procedure do I need to estimate $a$ better hopefully with the help of Z?

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