Some Federal Reserve officials apparently have a rule of thumb for thinking about the impact of the Fed’s large-scale asset purchases. I was curious to compare those estimates with the numbers that would come out of my own research.
When principal is repaid on assets currently held by the Federal Reserve, reserve deposits of the payer’s account with the Fed are debited. The result is that the Fed’s balance sheet contracts: both the Fed’s assets (its security holdings) and its liabilities (reserve deposits) decline whenever assets mature. Brian Sack, Executive Vice President of the Federal Reserve Bank of New York, offered this assessment on Wednesday of what it would mean if the Fed were to decide from here on to let the assets it currently holds mature without rolling them over:
If all asset classes in the SOMA were allowed to run off, the portfolio would decline by about $250 billion per year on average over the first several years. Under the interpretation of the policy stance noted earlier, this shrinkage of the balance sheet would amount to a tightening of policy. However, one should realize that this step represents a relatively gradual and limited policy tightening. Indeed, using the mapping that has been discussed by Chairman Bernanke, this path for the balance sheet would, in terms of its effects on the economy, be roughly equivalent to raising the federal funds rate by just over 25 basis point per year over the course of several years.
Sack’s proposed rule of thumb seems to be that each $100 billion decrease in the Fed’s holdings of long-term securities would roughly correspond to what in normal times we’d measure with a 10 basis point increase in the fed funds rate.
I was curious to take a look at what kind of number for this calculation would emerge from my own research. In my research with Cynthia Wu, we estimated that if the Fed were to buy $400 billion of the longest-maturity Treasuries available, it might lower the 10-year yield by about 13 basis points. However, as I noted last December, instead of buying the longest-term securities, instead the Fed has actually been purchasing intermediate-term bonds. In our framework, we estimate that $400 billion in such purchases would only move the 10-year yield by about 10 basis points, or 2.5 basis points for each $100 billion.
The next question is how to relate this change in the 10-year rate to the Fed’s traditional target of the overnight yield. One way to do this is to look at what the relation used to be between changes in the 10-year yield and changes in market expectations about the near-term fed funds rate. In analysis of data over 1988-2006, I found that a one-basis-point increase in the expected fed funds rate was associated with about a 0.4-basis-point increase in the 10-year yield (see Table 2 of Hamilton (2008)). Using that ratio, a $100 billion decrease in the Fed’s assets would roughly correspond to a 6 basis point increase in the fed funds rate, somewhat smaller than the 10 bp rule of thumb invoked by Sack above.
Granted, Cynthia’s and my estimates of the effects of LSAP are somewhat smaller than those obtained by other researchers, and any of these estimates are subject to considerable uncertainty. But these calculations illustrate that the Fed’s rule of thumb could easily be off by a factor of two.