The target for the federal funds rate is low-- a range between .25% and zero. At the end of December, the effective federal funds rate was .11%.
The interest rates on 4 week T-bills is even lower, .03%. Clearly, the zero nominal bound is near. Right?
The interest rate on one year T-bills was .44% at the end of December, quite low, but not zero. Government bonds maturing in two years had a 1.1% yield. Those maturing in three years had a 1.66% yield. And for 5 years, the yield was 2.64%
Interest rates on bonds with longer terms to maturity surely "depend" on expectations of future yields on bonds with shorter terms to maturity. There is a very plausible market process of substituting between short term and long term securities, and changes in market yields to clear markets.
However, the notion that the Fed can only impact the yields on bonds maturing in 2 years, by influencing expectations of 4 week T-bills two years from now, is implausible. Because the Fed can create money and people will accept money in exchange even if they don't intend to hold it, the Fed can target the price of bonds maturing in 2 years in a way that will fix the yield where it wants. It is possible that the result would be that the everyone would sell to the Fed, and so market price would be a Fed bid and offer price with no one transacting, but that is still the price. There is no doubt that the Fed can peg long term interest rates by directly purchasing them.
The only live question is whether lower longer term interest rates would either directly or indirectly result in increase expenditures on goods and services. Will everyone currently holding government bonds maturing in 2 years, instead switch to 4 week T-bills, planning to roll them over as they mature for the next 2 years? Or will at least some currently satisfied with a 1.1% yield instead switch to AAA corporate bonds, equity, commodities, or buying that new washing machine?
The Fed should target a growth path for nominal expenditure. It should buy assets and increase base money whatever amount is necessary to get nominal expenditure to target. There is little point in purchasing securities that already have a zero nominal yield, and so, this implies purchasing assets, such as government bonds, with progressively longer terms to maturity or levels of risk. What this does to the yields on these securities is secondary, but as any class of security has its yield driven to zero, some other security with a positive yield should be purchased.