# Why does the Fed's issuance of bank reserves to buy long-term Treasuries, shorten the overall maturity of government debt in private hands?

I quote Kenneth Rogoff, Thomas D. Cabot Professor of Public Policy and Professor of Economics at Harvard University. Is the Fed To Blame for Inequality in America? – Pairagraph Can you economists please simplify and explain this?

Of course, the Federal Reserve does have other levers besides interest rate policy. For example, when the Fed issues bank reserves (a form of short-term debt) to buy long-term Treasuries, it shortens the overall maturity of government debt in private hands. This does have some modest impact, albeit far less than it does through its interest rate policies.

This is actually quite trivial, I think this is best illustrated by an example. Suppose government has \$10000 worth of short-term debt and \$10000 worth of long-term debt all held by private sector. So the ratio of long-term to short-term debt in private hands is 1:1.
Now suppose that Fed creates new reserves and buys \$5000 of the long-term debt on secondary market. Government, now has \$10000 of short-term debt outstanding held in private hands, \$5000 of long-term debt in private hands, and \$5000 owned by Fed, which is a government institution (i.e. government de facto owes that debt to itself). So now the ratio of long-term to short-term debt in private hands is 0.5:1.