term 2 - lecture 3 - monetary policy rule in the three equation model Flashcards
what is the equation of the central banks loss function?
Lt =(y_t -y^n)^2 + B( π_t - π^T)^2 where B is the relative weight imposed on inflation, y^n is the output target assumed to be the equillibrium level of output) and π^T is the inflation target assumed to equal zero or a small positive number ie 2%
what does a balanced central banks loss function look like on an inflation output graph and what is the value of B?
the value of B is equal to 1 and the loss function is a perfect circle
what does an inflation averse central bank loss function look like on an inflation output graph and what is the value of B?
the value of B is greater than 1 and the loss function is horizontally stretched elipse
what does an unemployment averse central bank loss function look like on an inflation output graph and what is the value of B?
the value of B is less than 1 and the loss function is a vertically stretched ellipse
what is the supply side decribed by the in three model equation?
the supply side is described by a backwards looking phillips curve
what is the equation of the backwards looking phillips curve?
π_t = π_(t-1) +a(y_t - y^n) where π_t is inflation in period t, y^n is ouput target, and a is a fixed positive constant
what is the monetary rule?
the monetary rule is derived by the central bank minimizing their loss function in relation to the backwards looking Phillips curve. this is completed by incomporating the phillips curve inflation formula into the loss function then differentiating the loss function with respect to output. you then rearrange to get it in terms of inflation in period t minus inflation target ie π_t - π^T
how does the steepness of the phillips curve impact the wages?
the steeper the PC (ie the larger a) the more responsive wages to aggregate demand. any reduction in aggregate demand will achieve a greater cut in inflation.
a more inflation averse (ie larger B) central banks will wish to reduce inflation at the expense of a larger output reduction
what is the IS curve?
the IS equation incorporates the lagged effect of real interest rate on output, y_t = A - γr_(t-1)
what is the stabilising interest rate?
the stablising interest rate is the interest rate that produces the equillibrium output y^n = A - γr_s
where y^n is equillibrium output, r_s is the stabilising interest rate
what is the interest rate rule?
the interest rate rule is derived from the monetary rule and the IS curve. by substitution IS curve in its output gap form to the monetary rule, then rarranging to get the interest rate terms as the focus. then have it so the terms are in present period t. this final form is the interest rate rule
what is the interest rate rule if a=b=γ=1?
the interest rate rule is equal to r_t -r_s = 0.5(π_t -π^T)
what are the time lag effects?
“official interest rate decisions have their fullest effect on output with a lag
of around one year, and their fullest effect on inflation with a lag of around
two years.” (see Bank of England Quarterly Bulletin,1999)
the interest rate change will effect output in the next period which will then effect inflation in the next period
what is the taylor rule?
i_t = π_t + π^T +0.5(π_t -π^T) +0.5(y_t -y^n), where y^n is the natural rate of output,π^T is the natural inflation rate, π_t is the rate of inflation over the previous four quaters?
was the taylor rule accurate?
the taylor rule provided a good fir to the actual monetary policy conducted during 1987 to 1992
dynamic stochastic general equilibrium (DSGE) models feature more explicit micro foundations, impose cross-equation restrictions that relate macroeconomic responses to shocks, and provide a closer connection between academic research
and central bank practice.
