Scott Sumner had two outstanding posts a couple of weeks ago (here and here) discussing the relationship between interest rates and NGDP, making a number of important points, which I largely agree with, even though I have some (mostly semantic) quibbles about the details. I especially liked how in the second post he applied the analysis of Robert Barsky and Larry Summers in their article about Gibson’s Paradox under the gold standard to recent monetary experience. The two posts are so good and cover such a wide range of topics that the best way for me to address them is by cutting and pasting relevant passages and commenting on them.

Scott begins with the equation of exchange *MV* = *PY*. I personally prefer the Cambridge version (*M* = *kPY*) where *k* stands for the fraction of income that people hold as cash, thereby making it clear that the relevant concept is how much money want to hold, not that mysterious metaphysical concept called the velocity of circulation *V* (= 1/*k*). With attention focused on the decision about how much money to hold, it is natural to think of the rate of interest as the opportunity cost of holding non-interest-bearing cash balances. When the rate of interest rate rises, the desired holdings of non-interest-bearing cash tend to fall; in other words *k* falls (and *V* rises). With unchanged *M*, the equation is satisfied only if *PY* increases. So the notion that a reduction in interest rates, in and of itself, is expansionary is based on a misunderstanding. An increase in the amount of money demanded is always contractionary. A reduction in interest rates increases the amount of money demanded (if money is non-interest-bearing). A reduction in interest rates is therefore contractionary (all else equal).

Scott suggests some reasons why this basic relationship seems paradoxical.

Sometimes, not always, reductions in interest rates are caused by an increase in the monetary base. (This was not the case in late 2007 and early 2008, but it is the case on some occasions.) When there is an expansionary monetary policy, specifically an exogenous increase in M, then when interest rates fall, V tends to fall by less than M rises. So the policy as a whole causes NGDP to rise, even as the

specific impact of lower interest rates is to cause NGDP to fall.

To this I would add that, as discussed in my recent posts about Keynes and Fisher, Keynes in the *General Theory* seemed to be advancing a purely monetary theory of the rate of interest. If Keynes meant that the rate of interest is determined exclusively by monetary factors, then a falling rate of interest is a sure sign of an excess supply of money. Of course in the Hicksian world of IS-LM, the rate of interest is simultaneously determined by both equilibrium in the money market and an equilibrium rate of total spending, but Keynes seems to have had trouble with the notion that the rate of interest could be simultaneously determined by not one, but two, equilibrium conditions.

Another problem is the Keynesian model, which hopelessly confuses the transmission mechanism. Any Keynesian model with currency that says low interest rates are expansionary is flat out wrong.

But if Keynes believed that the rate of interest is exclusively determined by money demand and money supply, then the only possible cause of a low or falling interest rate is the state of the money market, the supply side of which is always under the control of the monetary authority. Or stated differently, in the Keynesian model, the money-supply function is perfectly elastic at the target rate of interest, so that the monetary authority supplies whatever amount of money is demanded at that rate of interest. I disagree with the underlying view of what determines the rate of interest, but given that theory of the rate of interest, the model is not incoherent and doesn’t confuse the transmission mechanism.

That’s probably why economists were so confused by 2008. Many people confuse aggregate demand with consumption. Thus they think low rates encourage people to “spend” and that this n somehow boosts AD and NGDP. But it doesn’t, at least not in the way they assume. If by “spend” you mean higher velocity, then yes, spending more boosts NGDP. But we’ve already seen that lower interest rates don’t boost velocity, rather they lower velocity.

But, remember that Keynes believed that the interest rate can be reduced only by increasing the quantity of money, which nullifies the contractionary effect of a reduced interest rate.

Even worse, some assume that “spending” is the same as consumption, hence if low rates encourage people to save less and consume more, then AD will rise. This is reasoning from a price change on steroids! When you don’t spend you save, and saving goes into investment, which is also part of GDP.

But this is reasoning from an accounting identity. The question is what happens if people try to save. The Keynesian argument is that the attempt to save will be self-defeating; instead of increased saving, there is reduced income. Both scenarios are consistent with the accounting identity. The question is which causal mechanism is operating? Does an attempt to increase saving cause investment to increase, or does it cause income to go down? Seemingly aware of the alternative scenario, Scott continues:

Now here’s were amateur Keynesians get hopelessly confused. They recall reading something about the paradox of thrift, about planned vs. actual saving, about the fact that an attempt to save more might depress NGDP, and that in the end people may fail to save more, and instead NGDP will fall. This is possible, but even if true it has no bearing on my claim that low rates are contractionary.

Just so. But there is not necessarily any confusion; the issue may be just a difference in how monetary policy is implemented. You can think of the monetary authority as having a choice in setting its policy in terms of the quantity of the monetary base, or in terms of an interest-rate target. Scott characterizes monetary policy in terms of the base, allowing the interest rate to adjust; Keynesians characterize monetary policy in terms of an interest-rate target, allowing the monetary base to adjust. The underlying analysis should not depend on how policy is characterized. I think that this is borne out by Scott’s next paragraph, which is consistent with a policy choice on the part of the Keynesian monetary authority to raise interest rates as needed to curb aggregate demand when aggregate demand is excessive.

To see the problem with this analysis, consider the Keynesian explanations for increases in AD. One theory is that animal spirits propel businesses to invest more. Another is that consumer optimism propels consumers to spend more. Another is that fiscal policy becomes more expansionary, boosting the budget deficit. What do all three of these shocks have in common? In all three cases the shock leads to higher interest rates. (Use the S&I diagram to show this.) Yes, in all three cases the higher interest rates boost velocity, and hence

ceteris paribus(i.e. fixed monetary base) the higher V leads to more NGDP. But that’s not an example of low rates boosting AD, it’s an example of some factor boosting AD, and alsoraisinginterest rates.

In the Keynesian terminology, the shocks do lead to higher rates, but only because excessive aggregate demand, caused by animal spirits, consumer optimism, or government budget deficits, has to be curbed by interest-rate increases. The *ceteris paribus* assumption is ambiguous; it can be interpreted to mean holding the monetary base constant *or* holding the interest-rate target constant. I don’t often cite Milton Friedman as an authority, but one of his early classic papers was “The Marshallian Demand Curve” in which he pointed out that there is an ambiguity in what is held constant along the demand curve: prices of other goods or real income. You can hold only one of the two constant, not both, and you get a different demand curve depending on which *ceteris paribus* assumption you make. So the upshot of my commentary here is that, although Scott is right to point out that the standard reasoning about how a change in interest rates affects NGDP implicitly assumes that the quantity of money is changing, that valid point doesn’t refute the standard reasoning. There is an inherent ambiguity in specifying what is actually held constant in any *ceteris paribus* exercise. It’s good to make these ambiguities explicit, and there might be good reasons to prefer one *ceteris paribus* assumption over another, but a *ceteris paribus* assumption isn’t a sufficient basis for rejecting a model.

Now just to be clear, I agree with Scott that, as a matter of positive economics, the interest rate is not fully under the control of the monetary authority. And one reason that it’s not is that the rate of interest is embedded in the entire price system, not just a particular short-term rate that the central bank may be able to control. So I don’t accept the basic Keynesian premise that monetary authority can always make the rate of interest whatever it wants it to be, though the monetary authority probably does have some control over short-term rates.

Scott also provides an analysis of the effects of interest on reserves, and he is absolutely correct to point out that paying interest on reserves is deflationary.

I will just note that near the end of his post, Scott makes a comment about living “in a Ratex world.” WADR, I don’t think that ratex is at all descriptive of reality, but I will save that discussion for another time.

Scott followed up the post about the contractionary effects of low interest rates with a post about the 1988 Barsky and Summers paper.

Barsky and Summers. . . claim that the “Gibson Paradox” is caused by the fact that low interest rates are deflationary under the gold standard, and that causation runs from falling interest rates to deflation. Note that there was no NGDP data for this period, so they use the price level rather than NGDP as their nominal indicator. But their basic argument is identical to mine.The Gibson Paradox referred to the tendency of prices and interest rates to be highly correlated under the gold standard. Initially some people thought this was due to the Fisher effect, but it turns out that prices were roughly a random walk under the gold standard, and hence the expected rate of inflation was close to zero. So the actual correlation was between prices and both real and nominal interest rates. Nonetheless, the nominal interest rate is the key causal variable in their model, even though changes in that variable are mostly due to changes in the real interest rate.

Since gold is a durable good with a fixed price, the nominal interest rate is the opportunity cost of holding that good. A lower nominal rate tends to increase the demand for gold, for both monetary and non-monetary purposes. And an increased demand for gold is deflationary (and also reduces NGDP.)

Very insightful on Scott’s part to see the connection between the Barsky and Summers analysis and the standard theory of the demand for money. I had previously thought about the Barsky and Summers discussion simply as a present-value problem. The present value of any durable asset, generating a given expected flow of future services, must vary inversely with the interest rate at which those future services are discounted. Since the future price level under the gold standard was expected to be roughly stable, any change in nominal interest rates implied a change in real interest rates. The value of gold, like other durable assets, varied inversely with nominal interest rate. But with the nominal value of gold fixed by the gold standard, changes in the value of gold implied a change in the price level, an increased value of gold being deflationary and a decreased value of gold inflationary. Scott rightly observes that the same idea can be expressed in the language of monetary theory by thinking of the nominal interest rate as the cost of holding any asset, so that a reduction in the nominal interest rate has to increase the demand to own assets, because reducing the cost of holding an asset increases the demand to own it, thereby raising its value in exchange, provided that current output of the asset is small relative to the total stock.

However, the present-value approach does have an advantage over the opportunity-cost approach, because the present-value approach relates the value of gold or money to the entire term structure of interest rates, while the opportunity-cost approach can only handle a single interest rate – presumably the short-term rate – that is relevant to the decision to hold money at any given moment in time. In simple models of the IS-LM ilk, the only interest rate under consideration is the short-term rate, or the term-structure is assumed to have a fixed shape so that all interest rates are equally affected by, or along with, any change in the short-term rate. The latter assumption of course is clearly unrealistic, though Keynes made it without a second thought. However, in his *Century of Bank Rate*, Hawtrey showed that between 1844 and 1938, when the gold standard was in effect in Britain (except 1914-25 and 1931-38) short-term rates and long-term rates often moved by significantly different magnitudes and even in opposite directions.

Scott makes a further interesting observation:

The puzzle of why the economy does poorly when interest rates fall (such as during 2007-09) is in principle just as interesting as the one Barsky and Summers looked at. Just as gold was the medium of account during the gold standard, base money is currently the medium of account. And just as causation went from falling interest rates to higher demand for gold to deflation under the gold standard, causation went from falling interest rates to higher demand for base money to recession in 2007-08.

There is something to this point, but I think Scott may be making too much of it. Falling interest rates in 2007 may have caused the demand for money to increase, but other factors were also important in causing contraction. The problem in 2008 was that the real rate of interest was falling, while the Fed, fixated on commodity (especially energy) prices, kept interest rates too high given the rapidly deteriorating economy. With expected yields from holding real assets falling, the Fed, by not cutting interest rates any further between April and October of 2008, precipitated a financial crisis once inflationary expectations started collapsing in August 2008, the expected yield from holding money dominating the expected yield from holding real assets, bringing about a pathological Fisher effect in which asset values had to collapse for the yields from holding money and from holding assets to be equalized.

Under the gold standard, the value of gold was actually sensitive to two separate interest-rate effects – one reflected in the short-term rate and one reflected in the long-term rate. The latter effect is the one focused on by Barsky and Summers, though they also performed some tests on the short-term rate. However, it was through the short-term rate that the central bank, in particular the Bank of England, the dominant central bank during in the pre-World War I era, manifested its demand for gold reserves, raising the short-term rate when it was trying to accumulate gold and reducing the short-term rate when it was willing to reduce its reserve holdings. Barsky and Summers found the long-term rate to be more highly correlated with the price level than the short-term rate. I conjecture that the reason for that result is that the long-term rate is what captures the theoretical inverse relationship between the interest rate and the value of a durable asset, while the short-term rate would be negatively correlated with the value of gold when (as is usually the case) it moves together with the long-term rate but may sometimes be positively correlated with the value of gold (when the central bank is trying to accumulate gold) and thereby tightening the world market for gold. I don’t know if Barsky and Summers ran regressions using both long-term and short-term rates, but using both long-term and short-term rates in the same regression might have allowed them to find evidence of both effects in the data.

PS I have been too busy and too distracted of late to keep up with comments on earlier posts. Sorry for not responding promptly. In case anyone is still interested, I hope to respond to comments over the next few days, and to post and respond more regularly than I have been doing for the past few weeks.