A study uses double sampling (two-phase sampling) to improve estimate precision. The first phase has a large sample size $n'$ to estimate a covariate $x$, and the second phase has a smaller sample $n$ to measure $y$. If the correlation between $x$ and $y$ is $\rho_{xy}$, what happens to the variance of the estimator as $\rho_{xy}^2 \rightarrow 1$?