# How did (economics) Taylor rule come out mathematically?

There is Taylor rule in economics that shows how to relate nominial interest rate with inflation and GDP.

$i_t = \pi_t + r_t^* + a_\pi ( \pi_t - \pi_t^* ) + a_y ( y_t - \bar y_t )$ In this equation, $\,i_t\,$ is the target short-term nominal interest rate (e.g. the federal funds rate in the US), $\,\pi_t\,$ is the rate of inflation as measured by the GDP deflator, $\pi^*_t$ is the desired rate of inflation, $r_t^*$ is the assumed equilibrium real interest rate, $\,y_t\,$ is the logarithm of real Gross Domestic Product, and $\bar y_t$ is the logarithm of potential output, as determined by a linear trend. In this equation, both a_{\pi} and a_y should be positive. (Wikipedia, Taylor Rule)

So, the question is, how did this equation come up mathematically?

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This is not a nature's law, it is a policy rule that stipulates what should be done. Moreover, since $a_\pi$ and $a_y$ can be chosen freely, virtually any choice of $i_t$ can be justified with it. Please read the section "The Taylor Principle" in the Wikipedia article about why some choices of $a_\pi$ or $a-y$ may be preferred. – Hagen von Eitzen Sep 16 '12 at 8:43
OK, I did get that already, but is it just intuition, not based on empirical data? – Transfinite Lover Sep 16 '12 at 9:26
Well, it states among others that to lower inflation one should raise the federal funds rate above inflaton rate (I have no idea about $r_t^\star$, though). This will drag money from consumption, hence lower inflation. For small values, all continuous dependencies are more or less linear, hence the rule is justified. – Hagen von Eitzen Sep 16 '12 at 10:32