I_expectations_ho

# I_expectations_ho - ECON110B I Expectations The basic tools...

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1 ECON110B I. Expectations: The basic tools To think about the role of expectations in economic fluctuations Real interest rate and the nominal interest rate Concept of expected present discounted values To build on the distinction between real and nominal interest rates to revisit the effects of money growth on interest rates 1. Nominal versus real interest rates 1) Relation between the nominal interest rate and the real interest rates a. Key idea - How many dollars we shall have to pay in the future in exchange for having one more dollar today - Key interest: We do not consume dollars but goods - How many goods we will have to give up in the future in exchange for the goods we get today - How many goods not how many dollars - The presence of inflation makes the distinction important 2 b. Nominal interest rate - Expressed in terms of dollars: printed in the financial pages of newspapers - i t : Nominal interest rate for year t - Borrowing one dollar this year requires you to pay 1 + i t dollars next year - Observable c. Real interest rate - Expressed in terms of a basket of goods - r t : Real interest rate for year t - Borrowing the equivalent of one basket of goods this year requires you to pay the equivalent of 1 + r t baskets of goods next year - Not observable d. Relation between nominal and real interest rate - Intuition : We must adjust the nominal interest rate to take into account expected inflation - To borrow enough to eat one more pound of bread this year, how much to repay in terms of pounds of bread, next year

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3 Definition and derivation of the Real interest rate - i t = nominal interest rate for year t . - r t = real interest rate for year t . - (1+ i t ): Lending one dollar this year yields (1+ i t ) dollars next year. Alternatively, borrowing one dollar this year implies paying back (1+ i t ) dollars next year. - P t = price this year. - P e t+1 = expected price n ext year. - ( 1 + r t ) : Repayment of one pound of bread next year in terms of the real interest rate - Repayment of one dollar next year for P t dollar borrowing: (1 + i t )P t - Repayment of one pound of bread next year: (1 + i t )P t / P e t+1 4 - e t t t t P P i r 1 ) 1 ( ) 1 ( + + = + - t t e t e t P P P + + 1 1 π - 1 1 1 1 + = + = + + + e t t t t e t t e t P P P P P P - ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 1 1 e t t t e t t e t t t t i P P i P P i r + + + + + = + = + = + - , ) 1 ln( ) 1 ln( ) 1 ( ) 1 ( ln , ) 1 ln( 1 1 1 e t t e t t e t t t t i i i r r + + + + + = + + + when r t , i t , and e t+1 are small. - e t t t i r 1 + = - The real interest rate is equal to the nominal interest rate minus expected inflation e. Implications - e t+1 = 0 r t = i t - e t+1 > 0 r t < i t - Given i t , e t+1 r t
5 2) United States data since 1978 a. Nominal and Real 1-year T-Bill rates in the U.S. since 1978 - Although the nominal interest rate has declined considerably since the early 1980s, the real interest

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## This note was uploaded on 09/18/2008 for the course ECON 100B taught by Professor Rauch during the Winter '07 term at UCSD.

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I_expectations_ho - ECON110B I Expectations The basic tools...

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