Monetary stability
and the Taylor principle

Gregor Boehl
Uni Bonn
Teaching talk
University of Vienna

Context


(link)

Monetary stability
and the Taylor principle


  • Target group: advanced bachelor

  • Learning objectives:
    • Key concepts of monetary policy
    • Monetary policy works through demand side
    • Monetary policy must always be active

Recap: The Central Bank

  • Policy institution
  • Mandate: stabilize inflation
  • Tool: control nominal interest rates

Question:
How to set interest rates to stabilize inflation?

A simple Model: demand

$$ \definecolor{sgreen}{RGB}{78, 126, 100} \definecolor{syellow}{RGB}{225, 231, 75} \definecolor{sred}{RGB}{231, 127, 75} \definecolor{sblue}{RGB}{112, 174, 255} y = D(r)$$
($D'<0$, output $y$, real interest rate $r$)
  • households' demand: consumption vs. saving
  • the IS curve!
  • By definition: $r = i - \pi$
    (nominal interest rate $i$,
    inflation rate $\pi$)
    • $$ \large \hookrightarrow y = D( \color{syellow} i - \pi \color{white}) $$
Monetary policy: $\color{syellow} i \uparrow$

A simple Model: supply

$$\pi = S(y, z_\pi)$$
($S' > 0$, price shock $z_\pi$)

  • pricing decision
  • the Phillips curve!

A price/cost-push shock

$$ \begin{align} y &= D(i - \pi) \\ \pi &= S(y, z_\pi ) \end{align} $$
$$ \begin{align} y &= D(i - \pi) \\ \pi &= S(y, \color{sred} z_\pi \color{white} ) \end{align} $$
$$ \begin{align} y &= D(i - \pi) \\ \pi &= S(y, \color{sred} z_\pi \color{white} ) \end{align} $$
$$ \begin{align} y &= D(i - \color{sred} \pi \color{white}) \\ \color{sred} \pi \color{white} &= S(y, \color{sred} z_\pi \color{white} ) \end{align} $$
$$ \begin{align} y &= D(i - \color{sred} \pi \color{white}) \\ \color{sred} \pi \color{white} &= S(y, \color{sred} z_\pi \color{white} ) \end{align} $$
$$ \begin{align} y &= D( \color{sblue} i \color{white} - \color{sred} \pi \color{white} ) \\ \color{sred} \pi \color{white} &= S(y, \color{sred} z_\pi \color{white} ) \end{align} $$
$$ \begin{align} \color{sblue} y \color{white} &= D( \color{sblue} i \color{white} - \color{sred} \pi \color{white}) \\ \color{sred} \pi \color{white} &= S( \color{sblue} y \color{white} , \color{sred} z_\pi \color{white} ) \end{align} $$
$$ \begin{align} \color{sblue} y \color{white} &= D( \color{sblue} i \color{white} - \color{sred} \pi \color{white}) \\ \color{syellow} \pi \color{white} &= S( \color{sblue} y \color{white} , \color{sred} z_\pi \color{white} ) \end{align} $$
$$ \begin{align} \color{sblue} y \color{white} &= D( \color{sblue} i \color{white} - \color{sred} \pi \color{white}) \\ \color{syellow} \pi \color{white} &= S( \color{sblue} y \color{white} , \color{sred} z_\pi \color{white} ) \end{align} $$
  • price shock: $ \color{sred} z_\pi \color{white} \uparrow$
    • $\hookrightarrow$ PC shifts upwards
  • CB raises interest rate
    • $\hookrightarrow$ Demand shifts left

The taylor Principle

$$ \begin{align} y \color{sgreen} \uparrow \color{white} &= D(i \color{sgreen} \Uparrow \color{white} - \pi \color{sgreen} \uparrow \color{white} ) \\ \pi \color{sgreen} \uparrow \color{white} &= S(y \color{sgreen} \uparrow \color{white} , z_\pi \color{sgreen} \uparrow \color{white} ) \end{align} $$
$$ \begin{align} y \color{sgreen} \uparrow \color{white} &= D(i \color{sgreen} \Uparrow \color{white} - \pi \color{sgreen} \uparrow \color{white} ) \\ \pi \color{sgreen} \uparrow \color{white} &= S(y \color{sgreen} \uparrow \color{white} , z_\pi \color{sred} \uparrow \color{white} ) \end{align} $$
$$ \begin{align} y \color{sgreen} \uparrow \color{white} &= D(i \color{sgreen} \Uparrow \color{white} - \pi \color{sred} \uparrow \color{white} ) \\ \pi \color{sred} \uparrow \color{white} &= S(y \color{sgreen} \uparrow \color{white} , z_\pi \color{sred} \uparrow \color{white} ) \end{align} $$
$$ \begin{align} y \color{sred} \uparrow \color{white} &= D(i \color{sgreen} \Uparrow \color{white} - \pi \color{sred} \uparrow \color{white} ) \\ \pi \color{sred} \uparrow \color{white} &= S(y \color{sred} \uparrow \color{white} , z_\pi \color{sred} \uparrow \color{white} ) \end{align} $$
$$ \begin{align} y \color{sred} \uparrow \color{white} &= D(i \color{sgreen} \Uparrow \color{white} - \pi \color{sred} \uparrow \color{white} ) \\ \pi \color{sred} \Uparrow \color{white} &= S(y \color{sred} \uparrow \color{white} , z_\pi \color{sred} \uparrow \color{white} ) \end{align} $$
$$ \begin{align} y \color{sred} \uparrow \color{white} &= D(i \color{sblue} \Uparrow \color{white} - \pi \color{sred} \uparrow \color{white} ) \\ \pi \color{sred} \Uparrow \color{white} &= S(y \color{sred} \uparrow \color{white} , z_\pi \color{sred} \uparrow \color{white} ) \end{align} $$
$$ \begin{align} y \color{syellow} \downarrow \color{white} &= D(i \color{sblue} \Uparrow \color{white} - \pi \color{sred} \uparrow \color{white} ) \\ \pi \color{sred} \Uparrow \color{white} &= S(y \color{syellow} \downarrow \color{white} , z_\pi \color{sred} \uparrow \color{white} ) \end{align} $$
$$ \begin{align} y \color{syellow} \downarrow \color{white} &= D(i \color{sblue} \Uparrow \color{white} - \pi \color{sred} \uparrow \color{white} ) \\ \pi \color{syellow} \uparrow \color{white} &= S(y \color{syellow} \downarrow \color{white} , z_\pi \color{sred} \uparrow \color{white} ) \end{align} $$
  • Statement:
    Always set $\Delta i > \Delta \pi$
  • Intuition: counteract real-rate effect on demand

  • Disclaimer:
    In a dynamic economy, (often) sufficient for dynamic stability

Current inflation

Taylor principle: Always set $\Delta i > \Delta \pi$

Thanks!