Gold's duration

In the Barsky–Summers model, $p_g = \delta/(\rho - g)$. (a) With $g = 0$, compute the proportional change in $p_g$ when the real rate rises from 0.5% to 2.5%. (b) With $g = -2.5\%$ (a "service flow" that decays), recompute. (c) Use (a) and (b) to explain why estimated gold–real-yield betas are unstable, and why the model's sign is more reliable than its size.