Question

Consider the Taylor-Rule equation and the following values given:

         

            π $8ky9IbbwfJw4ijAAAAABJRU5ErkJggg==$ t = the actual annual expected inflation rate at time t =?        

                π $IXr8dMK4LcQAAAABJRU5ErkJggg==$ * = the target annual expected inflation rate = 2.0%

     yt = the actual annual GDP growth rate at time t = 3.5%

      y* = the economy’s potential annual GDP growth rate = 2.5%

              r * = the neutral real fed funds rate = 2.0%

             β = .5

             iFFt = the nominal Fed Funds target rate at time t = 6.5%

Let’s say that we know that: (iFFt) the nominal Fed Funds target rate at time t is = 6.5%, (β) is = .5, (r *) the neutral real fed funds rate is = 2%, (yt) actual annual GDP growth rate at time t is = 3.5%, and (y*) the economy’s potential annual GDP growth rate is = 2.5%.

*Given the aforementioned information, derive the previously unknown π t, the actual annual inflation expectations rate at time t, through utilizing some simple algebra. Instead of plugging in the values and deriving the nominal fed funds target rate, like usual, plug in all the previously given numeric values and algebraically solve for, again, the unknown value for π t $QJhVu5J16DynwAAAABJRU5ErkJggg==$ , the actual annual inflation expectations rate at time t. Just remember to combine like terms when solving.

Answer 1

Use the following taylore rule formula

iFFt = r* + $\pi$ t + B($\pi$t - $\pi$ *) + (1-B)(yt -y*)  

6.5% = 2% + $\pi$ t + [0.5($\pi$t - 2%)] + [(1-0.5)( 3.5%-2.5%)]

6.5% = 2% + $\pi$ t + [0.5$\pi$t - 1%] + 0.5%

6.5% - 2% - 0.5% = $\pi$ t + 0.5$\pi$t - 1%

6.5%-2%-0.5% + 1% = 1.5$\pi$t

5% = 1.5$\pi$t

$\pi$t = 5%/1.5

$\pi$t = 3.33%

where,

B = 0.5

iFFt is nominal fed funds rate

r* is the real federal funds rate

$\pi$* is the target inflation rate

$\pi$t is the actual inflation rate

yt is actual GDP rate

y* is potential GDP rate

Hence actual inflation will be 3.33%