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Given the following 3 equations: $$ Y^*_t=100+3t \\ Y_t = Y_t^* (1+(0.2 (\sin t)) \\ B_t=B_t^* (1+(0.4 (\sin t)) \\ $$ And take B* to be the following, but is unknown: $$ B_t^*= \alpha Y_t^* \\ $$ I've figured the best way to estimate B* is the following: $$ \hat{B} _t^*=B_t (Y_t^*/Y_t )^{0.4/0.2} \\ $$ But I can't figure how it works. Can anyone provide a step-by-step? Also why is it not a perfect estimate?


3 knowns

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Estimate of unknown

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