Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.