Scott Sumner recently responded to a question from a commenter. Dustin asked:
"An elementary question on the topic of interest rates that I’ve been unable to resolve via google: Regarding Fed actions, I understand that reduced interest rates are thought to be expansionary because the resulting decrease in cost of capital induces greater investment. But I also understand that reduced interest rates are thought to be contractionary because the resulting decrease in opportunity cost of holding money increases demand for money.
One? Neither? Both? Little of each? Depends?"
Sumner claimed that it was difficult to answer. He doubted whether most macroeconomists could give a sensible answer. He made a remarkable claim:
"It’s not at all clear that lower interest rates boost investment (never reason from a price change.) And even if they did boost investment it is not at all clear that they would boost GDP."
(On the other hand, he immediately followed that with the statement that open market purchases reduce short term nominal interest rates and boost nominal GDP.)
David Glasner found Sumner's response puzzling and accused Sumner of confusing a change in demand with a change in quantity demanded.
The solution to that puzzle is simple. Sumner has recently been drawing supply and demand diagrams for base money with 1/P on the vertical axis. Patinkin did the same ages ago. A change in the interest rate shifts that demand curve. A change in the price level is a movement along the curve.
And so, if we consider an exogenous decrease in the interest rate, the demand for money curve shifts to the right. The new equilibrium price level is lower. Given real output, that implies lower nominal GDP.
Most economists who teach introductory macro (as opposed to Macroeconomists, I suppose,) would deal with the question easily. I would use it as an opportunity to discuss the difference between a change in demand and a change in quantity demanded using a Keynesian money market diagram–with the interest rate on the vertical axis. In other words, I would answer the question much like Glasner.
If the quantity of money is given, and starting at equilibrium, a lower interest rate leads to a shortage of money. Those short on money sell securities, forcing the interest rate back up. The lower interest rate that might raise investment and nominal GDP is impossible. Unless of course, the quantity of money increased.
Now, consider a more classical framework. An increase in the supply of saving results in a lower interest rate. At the old interest rate, desired saving is greater than desired investment. The lower interest rate causes the quantity of saving supplied to decrease and the quantity of investment demanded to increase, making them again equal. There is no direct impact on nominal GDP. Nominal and real consumption decrease and nominal and real investment increase.
However, this lower interest rate that coordinates saving and investment also raises the demand to hold money. Sumner's (and Patinkin's) curve shifts right. If the price level doesn't fall immediately, due to sticky prices (including wages,) the economy goes into recession. That could very well reduce investment (and saving, for that matter.) It also reduces the demand for money. (Sumner’s and Patinkin's curve shifts back left due to lower real income.)
In the long run, the price level falls. Real output recovers, and in the end, the interest rate is lower, real saving and real investment are both higher, but nominal GDP is lower. Real and nominal consumption are both lower, but nominal investment is ambiguous.
Rather than thinking about a coordinating change in interest rates, we could think of interest rates being lowered through a price ceiling. The quantity of saving supplied decreases and quantity of investment demanded increases. The short side prevails. People are saving less and consuming more. Investment falls to match the quantity of saving supplied. No change in nominal GDP. Real and nominal consumption are higher. Real and nominal investment are lower.
The demand for money increases as before The Sumner/Patinkin demand curve shifts right. Some of the frustrated savers just accumulate money balances since they no longer find it attractive to fund investment by purchasing new debt and equity. The economy goes into recession. This reduces real output and desired saving and investment. But, in the long run, the price level falls.
Given the price ceiling on “the” interest rate, we end up with more real consumption and less real investment than the start. Nominal GDP is lower. Nominal investment is lower, but nominal consumption is ambiguous.
But, of course, Sumner's real point is that an expansionary monetary policy involves an increase in the quantity of money. It is not simply a lower interest rate generated by households saving more or tighter regulations on usury.
Is a lower interest rate expansionary? As Yeager always would say, it depends on what caused it.