Question

First, explain what seigniorage is. Second, write out and explain the expression that represents seigniorage. And finally, what policies can a central bank implement to increase seignorage

Answer 1

(i)

Seigniorage refers to the difference between the value of money and the cost of producing it.

(ii)

Seigniorage can be expressed in three ways:

(1)

As inflation tax:

i.e. $\pi h$ where $\pi$ is inflation rate and $h$ represents real balances, with $m=\frac{H}{p}$ and $H$ is the nominal high powered money.

(2)

Opportunity cost of holding money. i.e. $ih$ with $i$ as the nominal interest rate and $h$ as real balances.

(3)

Total revenues associated with money creation i.e. $\mu h+(r-n)a$

$\mu$ - nominal growth rate of high powered money.

$r-n$ - the difference between real rate of interest and population growth rate.

$a$ - real stock of interest earning government assets.(with $a\le h$ ).

These concepts can be easily combined if one accepts the quantity equation of money and the Fisher effect with perfect foresight:

$\pi.m=(\mu-g_x).m=(i-r).m$

where $x$ is defined as real GDP.

Definition (1) and (2) arise as special cases of (3). During period of high inflation, when the inflation rate $\pi$ , the nominal interest rate, $i$ and nominal money growth, $\mu$ dominate the growth rate of real output, $g_x$ and the real rate of interest, $r$ , the level of seigniorage converges for all the three concepts:$\pi.m\leftrightarrow \mu.m\leftrightarrow i.m.$

(iii)

Monetary policy:

This is used to increase monetary seigniorage and it results in debt monetization. Debt monetization is when the central bank buys interest bearing debt using non interest bearing money. This is a useful tool in the control in the control of the debt level of an economy.

Monetary seigniorage can be used to control interest rates. When the central bank exchanges newly printed banknotes for financial assets, they inject money into the economy. By increasing money supply in the economy, market interest rates decrease resulting in an increase in economic activity.