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(A) Show That yt=β1yt1+uty _ { t } = \beta _ { 1 } y _ { t - 1 } + u _ { t }

question 16

Essay

 Consider the standard AR(1) Yt=β0+β1Yt1+ut, where the usual assumptions hold. \text { Consider the standard AR(1) } Y _ { t } = \beta _ { 0 } + \beta _ { 1 } Y _ { t - 1 } + u _ { t } \text {, where the usual assumptions hold. } (a) Show that yt=β1yt1+uty _ { t } = \beta _ { 1 } y _ { t - 1 } + u _ { t } , where yty _ { t } is YtY _ { t } with the mean removed, i.e., yt=YtE(Yt)y _ { t } = Y _ { t } - E \left( Y _ { t } \right) . Show that E(yt)=0E \left( y _ { t } \right) = 0 .


Definitions:

Money

A medium of exchange that is widely accepted in transactions for goods and services and repayment of debts.

Wealth

The total value of all financial assets and physical possessions owned by an individual or entity, minus any debts.

Required Reserve Ratio

The percentage of deposits that banks are mandated to keep on hand and not lend out, as regulated by central banking authorities.

Money Supply

The total amount of monetary assets available in an economy at any given time, including cash, coins, and balances held in checking and savings accounts.

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