We are all in Scott Sumner’s debt for teaching (or reminding) us never, ever to reason from a price change. The reason is simple. You can’t just posit a price change and then start making inferences from the price change, because price changes don’t just happen spontaneously. If there’s a price change, it’s because something else has caused price to change. Maybe demand has increased; maybe supply has decreased; maybe neither supply nor demand has changed, but the market was in disequilibrium before and is in equilibrium now at the new price; maybe neither supply nor demand has changed, but the market was in equilibrium before and is in disequilibrium now. There could be other scenarios as well, but unless you specify at least one of them, you can’t reason sensibly about the implications of the price change.
There’s another important piece of advice for anyone trying to do economics: never mistake a change in quantity demanded for a change in demand. A change in demand means that the willingness of people to pay for something has changed, so that, everything else held constant, the price has to change. If for some reason, the price of something goes up, the willingness of people to pay for not having changed, then the quantity of the thing that they demand will go down. But here’s the important point: their demand for that something – their willingness to pay for it – has not gone down; the change in the amount demanded is simply a response to the increased price of that something. In other words, a change in the price of something cannot be the cause of a change in the demand for that something; it can only cause a change in the quantity demanded. A change in demand can be caused only by change in something other than price – maybe a change in wealth, or in fashion, or in taste, or in the season, or in the weather.
Why am I engaging in this bit of pedantry? Well, in a recent post, Scott responded to the following question from Dustin in the comment section to one of his posts.
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.
To which Scott responded as follows:
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.
Scott is correct to question the relationship between interest rates and investment. The relationship in the Keynesian model is based on the idea that a reduced interest rate, by reducing the rate at which expected future cash flows are discounted, increases the value of durable assets, so that the optimal size of the capital stock increases, implying a speed up in the rate of capital accumulation (investment). There are a couple of steps missing in the chain of reasoning that goes from a reduced rate of discount to a speed up in the rate of accumulation, but, in the olden days at any rate, economists have usually been willing to rely on their intuition that an increase in the size of the optimal capital stock would translate into an increased rate of capital accumulation.
Alternatively, in the Hawtreyan scheme of things, a reduced rate of interest would increase the optimal size of inventories held by traders and middlemen, causing an increase in orders to manufacturers, and a cycle of rising output and income generated by the attempt to increase inventories. Notice that in the Hawtreyan view, the reduced short-term interest is, in part, a positive supply shock (reducing the costs borne by middlemen and traders of holding inventories financed by short-term borrowing) as long as there are unused resources that can be employed if desired inventories increase in size.
That said, I’m not sure what Scott, in questioning whether a reduction in interesting rates raises investment, meant by his parenthetical remark about reasoning from a price change. Scott was asked about the effect of a Fed policy to reduce interest rates. Why is that reasoning from a price change? And furthermore, if we do posit that investment rises, why is it unclear whether GDP would rise?
Scott continues:
However it’s surprisingly hard to explain why OMPs boost NGDP using the mechanism of interest rates. Dustin is right that lower interest rates increase the demand for money. They also reduce velocity. Higher money demand and lower velocity will, ceteris paribus, reduce NGDP. So why does everyone think that a cut in interest rates increases NGDP? Is it possible that Steve Williamson is right after all?
Sorry, Scott. Lower interest rates don’t increase the demand for money; lower interest rates increase the amount of money demanded. What’s the difference? If an interest-rate reduction increased the demand for money, it would mean that the demand curve had shifted, and the size of that shift would be theoretically unspecified. If that were the case, we would be comparing an unknown increase in investment on the one hand to an unknown increase in money demand on the other hand, the net effect being indeterminate. That’s the argument that Scott seems to be making.
But that’s not, repeat not, what’s going on here. What we have is an interest-rate reduction that triggers an increase investment and also in the amount of money demanded. But there is no shift in the demand curve for money, just a movement along an unchanging demand curve. That imposes a limit on the range of possibilities. What is the limit? It’s the extreme case of a demand curve for money that is perfectly elastic at the current rate of interest — in other words a liquidity trap — so that the slightest reduction in interest rates causes an unlimited increase in the amount of money demanded. But that means that the rate of interest can’t fall, so that investment can’t rise. If the demand for money is less than perfectly elastic, then the rate of interest can in fact be reduced, implying that investment, and therefore NGDP, will increase. The quantity of money demanded increases as well — velocity goes down — but not enough to prevent investment and NGDP from increasing.
So, there’s no ambiguity about the correct answer to Dustin’s question. If Steve Williamson is right, it’s because he has introduced some new analytical element not contained in the old-fashioned macroeconomic analysis. (Note that I use the term “old-fashioned” only as an identifier, not as an expression of preference in either direction.) A policy-induced reduction in the rate of interest must, under standard assumption in the old-fashioned macroeconomics, increase nominal GDP, though the size of the increase depends on specific assumptions about empirical magnitudes. I don’t disagree with Scott’s analysis in terms of the monetary base, I just don’t see a substantive difference between that analysis and the one that I just went through in terms of the interest-rate policy instrument.
Just to offer a non-controversial example, it is possible to reason through the effect of a restriction on imports in terms of a per unit tariff on imports or in terms of a numerical quota on imports. For any per unit tariff, there is a corresponding quota on imports that gives you the same solution. MMT guys often fail to see the symmetry between setting the quantity and the price of bank reserves; in this instance Scott seems to have overlooked the symmetry between the quantity and price of base money.
Uneasy Money 
Years ago I quit using the “change in demand” and “change in quantity demanded” terminology (and similarly “change in supply” and “change in quantity supplied”), because it seemed to me to be unavoidably confusing. I began to talk about a “shift in the demand curve” (to the right or to the left, in the normal demand curve diagram, which results in a movement along the supply curve) and a “movement along a demand curve” (up to the left or down to the right, which is caused by a shift in the supply curve). This seemed to me to be clearer, to describe better what we think is going on. Alas the textbooks have not changed, and so the confusion continues.
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Sumner has recently been drawing supply and demand diagrams for base money with 1/P on the vertical axis. A change in the interest rate shifts that demand curve. A change in the price level is a movement along the curve.
When I read his post, however, I thought much as you that most economists would deal with the question easily, and 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. 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 would 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. The quantity of saving supplied decreases and the quantity of investment demanded increases, making them again equal. There is no impact on nominal GDP.
However, this lower interest rate that coordinates saving and investment also raises the demand to hold money. Think of Sumner (and Patinkin’s) graph. The curve shifts right. 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 curve shifts left due to lower real income.)
In the long run, supposedly the price level falls. Real output recovers, and in the end, the interest rate is lower, saving and investment are both higher, and nominal GDP is unchanged.
And, of course, we could think of the lower interest rate as a price ceiling. The quantity of saving supplied decreases and quantity of investment demanded increases. The short side prevails. People are saving less and consume more. Investment falls to match the quantity of saving supplied. No change in nominal GDP.
The demand for money increases. Some of the frustrated lenders instead just hold money. 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 consumption and less investment than the start. Nominal GDP is the same.
And wasn’t Sumner’s point that you need to say somewhere that the quantity of money changes and that is why a lower interest rate allows for more spending on consumer and capital goods and increased nominal GDP?
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David, Bill is exactly right, I was thinking of the graph with 1/P on the vertical axis. That’s really the only way to get at the issue that puzzled Dustin. I certainly agree that an interest rate reduction that occurs via expansionary monetary policy necessarily boosts NGDP. My point is that the rise in M is essential to the process. If the Fed could wave a magic wand and reduce interest rates without increasing the monetary base, it would reduce NGDP. So trying to evaluate monetary economics by ignoring money and focusing on interest rates is a big mistake.
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Don, That’s a good suggestion, which I sometimes use myself, but I don’t think that there is any single magic bullet for dispelling the confusion.
Bill, Thanks for this clarification. It is correct that we can draw the demand curve for money in terms of the inverse of the price level, in which case it is correct to say that a change in interest rates shifts the demand for money. But I am not sure that it makes things any clearer. Dustin’s original question posits a reduction in the interest rate by the Fed. Doesn’t everyone agree that the Fed operates on interest rates either by offering to lend banks directly at the target interest rate, or by conducting open market operations sufficient to make that interest rate effective in the market for bank reserves? The quantity of base money becomes whatever it takes to achieve the interest rate target. Under some circumstances an interest rate target may be unachievable because market expectations are inconsistent with the target, but for purposes of this exercise, we obviously aren’t considering that possibility.
My guess – and it is just a guess – is that the problem here is that you and Scott are assuming that by “ignoring money,” people are assuming that money is not important. My interpretation is that they are assuming that the money market is always in equilibrium given the interest rate set by the Fed, i.e., the quantity of money supplied equals the amount demanded. I also don’t see how it makes any sense to interpret the Fed’s interest rate target as a price ceiling. As I said earlier, the target is only achievable if it is consistent with market expectations, if it is inconsistent with expectations, the target must be revised.
Scott, Sorry, but I am still having trouble seeing your point. I reject the notion that anyone thinks that the Fed is waving a magic wand to reduce interest rates. I think that changes in the monetary base are simply kept in the background under the assumption that the money market is in equilibrium because the Fed is supplying whatever quantity of reserves is demanded at the target interest rate. Maybe it would help if you could identify for me exactly whose analysis you are trying to rebut.
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David, I’m not claiming that anyone thinks the Fed can reduce interest rates without boosting the base.
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Scott, OK. then we all seem to be basically on the same page.
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