Suppose that terminal values are conditionally independent given \(\left(Y_{0}, Tight)\) with conditional distribution

\[
Y_{1, i} \sim N\left(\beta_{0}+\beta_{1} Y_{0, i}+\tau T_{i}, \sigma_{1}^{2}ight)
\]

and that \(\tau\) is estimated by ordinary linear regression of \(Y_{1}\) on \(\left(Y_{0}, Tight)\). Compare the asymptotic variance of \(\hat{\tau}\) for three randomization schemes: (i) random permutation with balanced assignment, (ii) independent symmetric Bernoulli, and (iii) the scheme in Exercise 13.1. Hence show that the asymptotic efficiency of the exchangeable randomization scheme relative to either of the others is approximately \(68 \%\).