Archive Page 3

Martin Feldstein Just Won’t Stop

Martin Feldstein has been warning about the disasters that would befall us thanks to Fed policy for over five years. His November 2, 2010 op-ed piece in the Financial Times (“QE2 is risky and should be limited”) provoked me to write this letter to the editor in response. Feldstein continued assailing QE in 2013 in a May 9 contribution to the Wall Street Journal to which (having become a blogger in 2011) I responded with this post. Stock prices having dropped steeply so far in 2016, Feldstein seems to think now — five years after pronouncing, with the S&P 500 at 1188, stocks overvalued — is a good time for a victory lap.

The sharp fall in share prices last week was a reminder of the vulnerabilities created by years of monetary policy. While chaos in the Chinese stock market may have been the triggering event, it was inevitable that the artificially high prices of U.S. stocks would eventually decline. Even after last week’s market fall, the S&P 500 stock index remains 30% above its historical average. There is no reason to think the correction is finished.

One would like to know by what criterion Feldstein thinks he can discern when stock prices are “artificially high.” Unlike Scott Sumner, I don’t accept the efficient market hypothesis, but I do agree with Scott that it takes a huge dose of chutzpah to claim to know when the entire market is “artificially” high, and an even bigger dose to continue making the claim more or less continuously for over five years even as prices nearly double. And just what does it mean, I wonder, for the S&P 500 index to be 30% above its historical average? Does it mean that PE ratios are 30% above their historical average? Well PE ratios reflect the rates at which expected future profits are discounted. If discount rates are below their historical average, as they surely are, why shouldn’t PE ratios be above their historical average? Well, because Feldstein believes that discount rates are being held down – artificially held down – by Fed policy. That makes high PE ratios are artificially high. Here’s how Feldstein explains it:

The overpriced share values are a direct result of the Federal Reserve’s quantitative easing (QE) policy. Beginning in November 2008 and running through October 2014, the Fed combined massive bond purchases with a commitment to keep short-term interest rates low as a way to hold down long-term interest rates. Chairman Ben Bernanke explained on several occasions that the Fed’s actions were intended to drive up asset prices, thereby increasing household wealth and consumer spending.

The strategy worked well. Share prices jumped 30% in 2013 alone and house prices rose 13% in that year. The resulting rise in wealth increased consumer spending, leading to higher GDP and lower unemployment.

I have to pause here to note that Feldstein is now actually changing his story a bit from the one he used to tell, because in his 2013 Wall Street Journal piece he said this about how well Bernanke’s strategy of holding down interest rates was working.

But despite the Fed’s current purchases of $85 billion a month and an accumulation of more than $2 trillion of long-term assets, the economy is limping along with per capita gross domestic product rising at less than 1% a year. Although it is impossible to know what would happen without the central bank’s asset purchases, the data imply that very little increase in GDP can be attributed to the so-called portfolio-balance effect of the Fed’s actions.

Even if all of the rise in the value of household equities since quantitative easing began could be attributed to the Fed policy, the implied increase in consumer spending would be quite small. According to the Federal Reserve’s Flow of Funds data, the total value of household stocks and mutual funds rose by $3.6 trillion between the end of 2009 and the end of 2012. Since past experience implies that each dollar of increased wealth raises consumer spending by about four cents, the $3.6 trillion rise in the value of equities would raise the level of consumer spending by about $144 billion over three years, equivalent to an annual increase of $48 billion or 0.3% of nominal GDP.

So in 2013, Feldstein dismissed the possibility that the increase in stock prices had had a significant effect on consumer spending. In my 2013 blog post responding to Feldstein, I noted his failure to understand the sophisticated rationale for QE as opposed to the simplistic one that he (and, in fairness, Bernanke himself) attributed to it.

[A]ll that is irrelevant, because the portfolio balance rationale for QE misrepresents the mechanism whereby QE can have any effect. That mechanism is primarily by preventing inflation expectations from dropping. Each one of the QE episodes has been initiated when expectations of inflation were dropping. In each instance, the announcement or even the expectation of QE succeeded in reversing the downward drift of inflation expectations, thereby contributing to expectations of increased profits and cash flows and thus allowing stock prices to recover from their deeply depressed levels after the 2007-09 downturn and panic.

But now Feldstein says that QE really was effective, even though in 2013 he dismissed as inconsequential the mechanism by which QE could have been effective, failing to acknowledge that there was an alternative mechanism by which QE might work. Nevertheless, in today’s op-ed, Feldstein confirms that he still believes that the only way QE can be effective is via the discredited portfolio-balance mechanism.

But excessively low interest rates have caused investors and lenders, in their reach for yield, to accept excessive risks in equities and fixed-income securities, in commercial real estate, and in the overall quality of loans. There is no doubt that many assets are overpriced, and as the Fed normalizes interest rates these prices will fall. It is difficult to know if this will cause widespread financial and economic declines like those seen in 2008. But the persistence of very low interest rates contributes to that systemic risk and to the possibility of economic instability.

Unfortunately, the recently released minutes of December’s Federal Open Market Committee meeting made no mention of financial-industry risks caused by persistent low interest rates for years to come. There was also no suggestion that the Fed might raise interest rates more rapidly to put a damper on the reach for yield that has led to mispriced assets. Instead the FOMC stressed that the federal-funds rate will creep up very slowly and remain below its equilibrium value even after the economy has achieved full employment and the Fed’s target rate of inflation.

Simply asserting that interest rates are “excessively low” is just question begging. What evidence is there that interest rates are excessively low? Interest rates for Treasuries at maturities of two years or more are lower today, after the Fed raised rates in December than they were for much of 2015. Under the Feldstein view of the world, the Fed had been holding down interest rates before December, so why are they lower now than they were before the Fed stopped suppressing them? The answer of course is that the Fed controls only one interest rate in a very narrow sliver of the entire market economy. Interest rates are embedded in a huge, complex and interconnected array of prices for real capital assets, and financial instruments. The structure of all those prices embodies and reflects the entire spectrum of interest rates affecting the economy. It is simply delusional to believe that the Fed can have more than a marginal effect on interest rates, except insofar as it can affect expectations about future prices – about the future value of the dollar. In the absence of evidence that the Fed is affecting inflation expectations, it is a blatant and demonstrable fallacy to maintain that the Fed is forcing interest rates to deviate from equilibrium values that would, but for Fed intervention, otherwise obtain. No doubt, there are indeed many assets that are overpriced, but, for all Professor Feldstein knows, there are just as many that are underpriced.

So Professor Feldstein might really want to take to heart a salutary maxim of Ludwig Wittgenstein: Whereof one cannot speak, thereof one must be silent.

Sumner on the Demand for Money, Interest Rates and Barsky and Summers

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 also raising interest 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.

The Free Market Economy Is Awesome and Fragile

Scott Sumner’s three most recent posts (here, here, and here)have been really great, and I’ld like to comment on all of them. I will start with a comment on his post discussing whether the free market economy is stable; perhaps I will get around to the other two next week. Scott uses a 2009 paper by Robert Hetzel as the starting point for his discussion. Hetzel distinguishes between those who view the stabilizing properties of price adjustment as being overwhelmed by real instabilities reflecting fluctuations in consumer and entrepreneurial sentiment – waves of optimism and pessimism – and those who regard the economy as either perpetually in equilibrium (RBC theorists) or just usually in equilibrium (Monetarists) unless destabilized by monetary shocks. Scott classifies himself, along with Hetzel and Milton Friedman, in the latter category.

Scott then brings Paul Krugman into the mix:

Friedman, Hetzel, and I all share the view that the private economy is basically stable, unless disturbed by monetary shocks. Paul Krugman has criticized this view, and indeed accused Friedman of intellectual dishonesty, for claiming that the Fed caused the Great Depression. In Krugman’s view, the account in Friedman and Schwartz’s Monetary History suggests that the Depression was caused by an unstable private economy, which the Fed failed to rescue because of insufficiently interventionist monetary policies. He thinks Friedman was subtly distorting the message to make his broader libertarian ideology seem more appealing.

This is a tricky topic for me to handle, because my own view of what happened in the Great Depression is in one sense similar to Friedman’s – monetary policy, not some spontaneous collapse of the private economy, was what precipitated and prolonged the Great Depression – but Friedman had a partial, simplistic and distorted view of how and why monetary policy failed. And although I believe Friedman was correct to argue that the Great Depression did not prove that the free market economy is inherently unstable and requires comprehensive government intervention to keep it from collapsing, I think that his account of the Great Depression was to some extent informed by his belief that his own simple k-percent rule for monetary growth was a golden bullet that would ensure economic stability and high employment.

I’d like to first ask a basic question: Is this a distinction without a meaningful difference? There are actually two issues here. First, does the Fed always have the ability to stabilize the economy, or does the zero bound sometimes render their policies impotent?  In that case the two views clearly do differ. But the more interesting philosophical question occurs when not at the zero bound, which has been the case for all but one postwar recession. In that case, does it make more sense to say the Fed caused a recession, or failed to prevent it?

Here’s an analogy. Someone might claim that LeBron James is a very weak and frail life form, whose legs will cramp up during basketball games without frequent consumption of fluids. Another might suggest that James is a healthy and powerful athlete, who needs to drink plenty of fluids to perform at his best during basketball games. In a sense, both are describing the same underlying reality, albeit with very different framing techniques. Nonetheless, I think the second description is better. It is a more informative description of LeBron James’s physical condition, relative to average people.

By analogy, I believe the private economy in the US is far more likely to be stable with decent monetary policy than is the economy of Venezuela (which can fall into depression even with sufficiently expansionary monetary policy, or indeed overly expansionary policies.)

I like Scott’s LeBron James analogy, but I have two problems with it. First, although LeBron James is a great player, he’s not perfect. Sometimes, even he messes up. When he messes up, it may not be his fault, in the sense that, with better information or better foresight – say, a little more rest in the second quarter – he might have sunk the game-winning three-pointer at the buzzer. Second, it’s one thing to say that a monetary shock caused the Great Depression, but maybe we just don’t know how to avoid monetary shocks. LeBron can miss shots, so can the Fed. Milton Friedman certainly didn’t know how to avoid monetary shocks, because his pet k-percent rule, as F. A. Hayek shrewdly observed, was a simply a monetary shock waiting to happen. And John Taylor certainly doesn’t know how to avoid monetary shocks, because his pet rule would have caused the Fed to raise interest rates in 2011 with possibly devastating consequences. I agree that a nominal GDP level target would have resulted in a monetary policy superior to the policy the Fed has been conducting since 2008, but do I really know that? I am not sure that I do. The false promise held out by Friedman was that it is easy to get monetary policy right all the time. It certainly wasn’t the case for Friedman’s pet rule, and I don’t think that there is any monetary rule out there that we can be sure will keep us safe and secure and fully employed.

But going beyond the LeBron analogy, I would make a further point. We just have no theoretical basis for saying that the free-market economy is stable. We can prove that, under some assumptions – and it is, to say the least, debatable whether the assumptions could properly be described as reasonable – a model economy corresponding to the basic neoclassical paradigm can be solved for an equilibrium solution. The existence of an equilibrium solution means basically that the neoclassical model is logically coherent, not that it tells us much about how any actual economy works. The pieces of the puzzle could all be put together in a way so that everything fits, but that doesn’t mean that in practice there is any mechanism whereby that equilibrium is ever reached or even approximated.

The argument for the stability of the free market that we learn in our first course in economics, which shows us how price adjusts to balance supply and demand, is an argument that, when every market but one – well, actually two, but we don’t have to quibble about it – is already in equilibrium, price adjustment in the remaining market – if it is small relative to the rest of the economy – will bring that market into equilibrium as well. That’s what I mean when I refer to the macrofoundations of microeconomics. But when many markets are out of equilibrium, even the markets that seem to be equilibrium (with amounts supplied and demanded equal) are not necessarily in equilibrium, because the price adjustments in other markets will disturb the seeming equilibrium of the markets in which supply and demand are momentarily equal. So there is not necessarily any algorithm, either in theory or in practice, by which price adjustments in individual markets would ever lead the economy into a state of general equilibrium. If we believe that the free market economy is stable, our belief is therefore not derived from any theoretical proof of the stability of the free market economy, but simply on an intuition, and some sort of historical assessment that free markets tend to work well most of the time. I would just add that, in his seminal 1937 paper, “Economics and Knowledge,” F. A. Hayek actually made just that observation, though it is not an observation that he, or most of his followers – with the notable and telling exceptions of G. L. S. Shackle and Ludwig Lachmann – made a big fuss about.

Axel Leijonhufvud, who is certainly an admirer of Hayek, addresses the question of the stability of the free-market economy in terms of what he calls a corridor. If you think of an economy moving along a time path, and if you think of the time path that would be followed by the economy if it were operating at a full-employment equilibrium, Leijonjhufvud’s corridor hypothesis is that the actual time path of the economy tends to revert to the equilibrium time path as long as deviations from the equilibrium are kept within certain limits, those limits defining the corridor. However, if the economy, for whatever reasons (exogenous shocks or some other mishaps) leaves the corridor, the spontaneous equilibrating tendencies causing the actual time path to revert back to the equilibrium time path may break down, and there may be no further tendency for the economy to revert back to its equilibrium time path. And as I pointed out recently in my post on Earl Thompson’s “Reformulation of Macroeconomic Theory,” he was able to construct a purely neoclassical model with two potential equilibria, one of which was unstable so that a shock form the lower equilibrium would lead either to a reversion to the higher-level equilibrium or to downward spiral with no endogenous stopping point.

Having said all that, I still agree with Scott’s bottom line: if the economy is operating below full employment, and inflation and interest rates are low, there is very likely a problem with monetary policy.

Keynes on the Theory of the Rate of Interest

I have been writing recently about Keynes and his theory of the rate of interest (here, here, here, and here). Perhaps unjustly – but perhaps not — I attribute to him a theory in which the rate of interest is determined exclusively by monetary forces: the interaction of the liquidity preference of the public with the policy of the monetary authorities. In other words, the rate of interest, at least as an approximation, can be modeled in terms of a single market for holding money, the demand to hold money reflecting the liquidity preference of the public and the stock of money being directly controlled by the monetary authority. Because liquidity preference is a function of the rate of interest, the rate of interest adjusts until the stock of money made available by the monetary authority is held willingly by the public.

I have been struggling with Keynes’s liquidity preference theory of interest, which evidently led him to deny the Fisher effect, thus denying that there is a margin of substitution between holding money and holding real assets, because he explicitly recognizes in Chapter 17 of the General Theory that there is a margin of substitution between money and real assets, the expected net returns from holding all assets (including expected appreciation and the net service flows generated by the assets) being equal in equilibrium. And it was that logic which led Keynes to one of his most important pre-General Theory contributions — the covered-interest-arbitrage theorem in chapter 3 of his Tract on Monetary Reform. The equality of expected returns on all assets was the key to Irving Fisher’s 1896 derivation of the Fisher Effect in Appreciation and Interest, restated in 1907 in The Rate of Interest, and in 1930 in The Theory of Interest.

Fisher never asserted that there is complete adjustment of nominal interest rates to expected inflation, actually providing empirical evidence that the adjustment of nominal rates to inflation was only partial, but he did show that in equilibrium a difference in the expected rate of appreciation between alternative assets must correspond to differences in the rates of interest on loans contracted in terms of the two assets. Now there is a difference between the static relationship between the interest rates for two loans contracted in terms of two different assets and a dynamic adjustment in time to a change in the expected rate of appreciation or depreciation of a given asset. The dynamic adjustment does not necessarily coincide with the static relationship.

It is also interesting, as I pointed out in a recent post, that when criticizing the orthodox theory of the rate of interest in the General Theory, Keynes focused not on Fisher, but on his teacher Alfred Marshall as the authoritative representative of the orthodox theory of interest, criticizing Fisher only for the Fisher effect. Keynes reserved is comprehensive criticism for Marshall, attributing to Marshall the notion that rate of interest adjusts to equalize savings and investment. Keynes acknowledged that he could not find textual support in Marshall’s writings for this idea, merely citing his own prior belief that the rate of interest performs that function, consequently attributing a similar belief to Marshall. But even if Marshall did mistakenly believe that the rate of interest adjusts to equalize savings and investment, it does not follow that the orthodox theory of interest is wrong; it just means that Marshall had a defective understanding of the theory. Just because most physicists in the 18th century believed in the phlogiston theory of fire does not prove that classical physics was wrong; it only means that classical physicists had an imperfect understanding of the theory. And if Keynes wanted to establish the content of the most authoritative version of the orthodox theory of interest, he should have been citing Fisher not Marshall.

That is why I wanted to have a look at a not very well known paper by Keynes called “The Theory of the Rate of Interest,” written for a 1937 festschrift in honor of Irving Fisher, The Lessons of Monetary Experience. Keynes began the paper with the following footnote attached to the title acknowledging Fisher as the outstanding authority on the orthodox theory of interest.

I have thought it suitable to offer a short note on this subject in honor of Irving Fisher, since his earliest [presumably Appreciation and Interest, Fisher’s doctoral dissertation] and latest [presumably The Theory of Interest] have been concerned with it, and since during the whole of the thirty years that I have been studying economics he has been the outstanding authority on this problem. (p. 145)

The paper is mostly devoted to spelling out and discussing six propositions that Keynes believes distill the essentials of the orthodox theory of interest. The first four of these propositions Keynes regards as unassailable, but the last two, he maintains, reflect very special, empirically false, assumptions. He therefore replaces them with two substitute propositions, whose implications differ radically from those of orthodox theory. Here are the first four propositions.

1 Interest on money means precisely what the books on arithmetic say it means. . . . [I]t is simply the premium obtainable on current cash over deferred cash, so that it measures the marginal preference . . . for holding cash in hand over cash for deferred delivery. No one would pay this premium unless the possession of cash served some purpose, i.e., has some efficiency. Thus, we can conveniently say that interest on money measures the marginal efficiency of money in terms of itself as a unit.

2 Money is not peculiar in having a marginal efficiency measured in terms of itself. . . . [N]ormally capital assets of all kinds have a positive marginal efficiency measured in terms of themselves. If we know the relation between the present and expected prices of an asset in terms of money we can convert the measure of its marginal efficiency into a measure of its marginal efficiency in terms of money by means of a formula which I have given in my General Theory, p. 227.

3 The effort to obtain the best advantage from the possession of wealth will set up a tendency for capital assets to exchange in equilibrium, at values proportional to their marginal efficiencies in terms of a common unit. . . . [I]f r is the money rate of interest . . . and y is the marginal efficiency of a capital asset A in terms of money, then A will exchange in terms of money at a price such as to make y = r.

4 If the demand price of our capital asset A . . . is not less than its replacement cost, new investment in A will take place, the scale of such investment depending on the capacity available for the production of A, i.e., on its elasticity of supply, and on the rate at which y, its marginal efficiency, declines as the amount of new investment in A increases. At a scale of new investment at which the marginal cost of producing A is equal to its demand price as above, we have a position of equilibrium. Thus the price system resulting from the relationships between the marginal efficiencies of different capital assets including money, measured in terms of a common unit, determines the aggregate rate of investment. (p. 145-46)

Keynes sums up the import of his first four propositions as follows:

These proposition are not . . . inconsistent with the orthodox theory . . . or open to doubt. They establish that relative prices . . . and the scale of output move until the marginal efficiencies of all kinds of assets are equal when measured in a common unit and . . . that the marginal efficiency of capital is equal to the rate of interest. But they tell us nothing as to the forces which determine what this common level of marginal efficiency will tend to be. It is when we proceed to this further discussion that my argument diverges from the orthodox argument.

Here is how Keynes describes the divergence between the orthodox theory and his theory:

[T]he orthodox theory maintains that the forces which determine the common value of the marginal efficiency of various assets are independent of money, which has . . . no autonomous influence, and that prices move until the marginal efficiency of money, i.e., the rate of interest, falls into line with the common value of the marginal efficiency of other assets as determined by other forces. My theory . . . maintains that this is a special case and that over a wide range of possible cases almost the opposite is true, namely, that the marginal efficiency of money is determined by forces partly appropriate to itself, and that prices move until the marginal efficiency of other assets fall into line with the rate of interest. (p. 147)

I find Keynes’s description of the difference between the orthodox theory and his own both insightful and problematic. Keynes notes correctly that the orthodox theory, abstracting from all monetary influences, treats the rate of interest as a rate of intertemporal exchange, applicable to exchange between any asset today and any asset in the future, adjusted for differences in rates of appreciation, and in net service flows, across assets. So Keynes was right: the orthodox theory is a special case, corresponding to the special assumptions required for full intertemporal equilibrium. And Keynes was right to emphasize the limitations of the orthodox theory.

But while drawing a sharp contrast between his theory and the orthodox theory (“over a wide range of possible cases almost the opposite is true”), Keynes, to qualify his disagreement, deploys the italicized (by me) weasel words, but without explaining how his seemingly flat rejection of the orthodox theory requires qualification. It is certainly reasonable to say “that the marginal efficiency of capital is determined by forces partly appropriate to itself.” But I don’t see how it follows from that premise “that prices move until the marginal efficiency of other assets fall into line with the rate of interest.” Equilibrium is reached when marginal efficiencies (adjusted for differences in expected rates of appreciation and in net services flows) of all assets are equal, but rejecting the orthodox notion that the marginal efficiency of money adjusts to the common marginal efficiency of all other assets does not establish that the causality is reversed: that the marginal efficiencies of all non-money assets must adjust to whatever the marginal efficiency of money happens to be. The reverse causality also seems like a special case; the general case, it would seem, would be one in which causality could operate, depending on circumstances, in either direction or both directions. An argument about the direction of causality would have been appropriate, but none is made. Keynes just moves on to propositions 5 and 6.

5 The marginal efficiency of money in terms of itself has the peculiarity that it is independent of its quantity. . . . This is a consequence of the Quantity Theory of Money . . . Thus, unless we import considerations from outside, the money rate of interest is indeterminate, for the demand schedule for money is a function solely of its supply [sic, presumably Keynes meant to say “quantity”]. Nevertheless, a determinate value for r can be derived from the condition that the value of an asset A, of which the marginal efficiency in terms of money is y, must be such that y = r. For provided that we know the scale of investment, we know y and the value of A, and hence we can deduce r. In other words, the rate of interest depends on the marginal efficiency of capital assets other than money. This must, however, be supplemented by another proposition; for it requires that we should already know the scale of investment. (p. 147-48)

I pause here, because I am confused. Keynes alludes to the proposition that the neutrality of money implies that any nominal interest rate is compatible with any real interest rate provided that the rate of inflation is correctly anticipated, though without articulating the proposition correctly. Despite getting off to a shaky start with a sloppy allusion to the Fisher effect, Keynes is right in observing that the neutrality of money and the independence of the real rate of interest from monetary factors are extreme assumptions. Given that monetary neutrality is consistent with any nominal interest rate, Keynes then tries to show how the orthodox theory pins down the nominal interest rate. And his attempt does not seem successful; he asserts that the money rate of interest can be deduced from the marginal efficiency of some capital asset A in terms of money. But that marginal efficiency cannot be deduced without knowledge, or an expectation, of the future value of the asset. Instead of couching his analysis in terms of the current and (expected) future values of the asset, i.e., instead of following Fisher’s 1896 own-rate analysis, Keynes brings up the scale of investment in A: “This must . . . be supplemented by another proposition; for it requires that we should already know the scale of investment.” Aside from not knowing what “this” and “it” are referring to, I don’t understand how the scale of investment is relevant to a determination of the marginal efficiency of the capital asset in question.

Now for Keynes’s final proposition:

6 The scale of investment will not reach its equilibrium level until the point is reached at which the elasticity of supply of output as a whole has fallen to zero. (p. 148)

The puzzle only deepens here because proposition 5 is referring to the scale of investment in a particular asset A while proposition 6 seems to be referring to the scale of investment in the aggregate. It is neither a necessary nor a sufficient condition for an equilibrium scale of investment in a particular capital asset to obtain that the elasticity of supply of output as a whole be zero. So the connection between propositions 5 and 6 seems tenuous and superficial. Does Keynes mean to say that, according to orthodox theory, the equality of advantage to asset holders between different kinds of assets cannot be achieved unless the elasticity of supply for output as a whole is zero? Keynes then offers a synthetic restatement of orthodox theory.

The equilibrium rate of aggregate investment, corresponding to the level of output for a further increase in which the elasticity of supply is zero, depends on the readiness of the public to save. But this in turn depends on the rate of interest. Thus for each level of the rate of interest we have a given quantity of saving. This quantity of saving determines the scale of investment. The scale of investment settles the marginal efficiency of capital, to which the rate of interest must be equal. Our system is therefore determinate. To each possible value of the rate of interest there corresponds a given volume of saving; and to each possible value of the marginal efficiency of capital there corresponds a given volume of investment. Now the rate of interest and the marginal efficiency of capital must be equal. Thus the position of equilibrium is given by that common value of the rate of interest and of the marginal efficiency of capital at which saving determined by the former is equal to the investment determined by the latter. (Id.)

This restatement of orthodox theory is remarkably disconnected from the six propositions that Keynes has just identified as the bedrock of the orthodox theory of interest. The word “saving” or “save” is not even mentioned in any of Keynes’s six propositions, so the notion that the orthodox theory asserts that the rate of interest adjusts to equalize saving and investment is inconsistent with his own rendering of the orthodox theory. The rhetorical point that Keynes seems to be making in the form of a strictly analytical discussion is that the orthodox theory held that the equilibrium of an economic system occurs at the rate of interest that equalizes savings and investment at a level of output and income consistent with full employment. Where Keynes was misguided was in characterizing the mechanism by which this equilibrium is reached as an adjustment in the nominal rate of interest. A full equilibrium is achieved by way of a vector of prices (and expected prices) consistent with equilibrium, the rate of interest being implicit in the intertemporal structure of a price vector. Keynes was working with a simplistic misconception of what the rate of interest actually represents and how it affects economic activity.

In place of propositions 5 and 6, which Keynes dismisses as special factual assumptions, he proposes two alternative propositions:

5* The marginal efficiency of money in terms of itself is . . . a function of its quantity (though not of its quantity alone), just as in the case of capital assets.

6* Aggregate investment may reach its equilibrium rate under proposition (4) above, before the elasticity of supply of output as a whole has fallen to zero. (Id.)

So in substituting 5* for 5, all Keynes did was discard a proposition that few if any economists — certainly not Fisher — upholding the orthodox theory ever would have accepted as a factual assertion. The two paragraphs that Keynes devotes to refuting proposition 5 can be safely ignored at almost zero cost. Turning to proposition 6, Keynes restates it as follows:

A zero elasticity of supply for output as a whole means that an increase of demand in terms of money will lead to no change in output; that is to say, prices will rise in the same proportion as the money demand [i.e., nominal aggregate demand, not the demand to hold money] rises. Inflation will have no effect on output or employment, but only on prices. (pp. 149-50)

So, propositions 5 and 6 turn out to be equivalent assertions that money is neutral. Having devoted two separate propositions to identify the orthodox theory of interest with the idea that money is neutral, Keynes spells out the lessons he draws from his reconstruction of the orthodox theory of the rate of interest.

If I am right, the orthodox theory is wholly inapplicable to such problems as those of unemployment and the trade cycle, or, indeed, to any of the day-to-day problems of ordinary life. Nevertheless it is often in fact applied to such problems. . . .

It leads to considerable difficulties to regard the marginal efficiency of money as wholly different in character from the marginal efficiency of other assets. Equilibrium requires . . . that the prices of different kinds of assets measured in the same unit move until their marginal efficiencies measured in that unit are equal. But if the marginal efficiency of money in terms of itself is always equal to the marginal efficiency of other assets, irrespective of the price of the latter, the whole price system in terms of money becomes indeterminate. (150-52)

Keynes is attacking a strawman here, because, even given the extreme assumptions about the neutrality of money that hardly anyone – and certainly not Fisher – accepted as factual, the equality between the marginal efficiency of money and the marginal efficiency of other assets is an equilibrium condition, not an identity, so the charge of indeterminacy is mistaken, as Keynes himself unwittingly acknowledges thereafter.

It is the elements of elasticity (a) in the desire to hold inactive balances and (b) in the supply of output as a whole, which permits a reasonable measure of stability in prices. If these elasticities are zero there is a necessity for the whole body of prices and wages to respond immediately to every change in the quantity of money. (p. 152)

So Keynes is acknowledging that the whole price system in terms of money in not indeterminate, just excessively volatile. But let’s hear him out.

This assumes a state of affairs very different from that in which we live. For the two elasticities named above are highly characteristic of the real world; and the assumption that both of them are zero assumes away three-quarters of the problems in which we are interested. (Id.)

Undoubtedly true, but neither Fisher nor most other economists who accepted the orthodox theory of the rate of interest believed either that money is always neutral or that we live in a world of perpetually full employment. Nor did Keynes show that the theoretical resources of orthodox theory were insufficient to analyze situations of less than full employment. The most obvious example of such an analysis, of course, is one in which a restrictive monetary policy, by creating an excess demand for money, raises the liquidity premium, causing the marginal efficiency of money to exceed the marginal efficiency of other assets, in which case asset prices must fall to restore the equality between the marginal efficiencies of assets and of money.

In principle, the adjustment might be relatively smooth, but if the fall of asset prices triggers bankruptcies or other forms of financial distress, and if the increase in interest rates affects spending flows, the fall in asset prices and in spending flows may become cumulative causing a general downward spiral in income and output. Such an analysis is entirely compatible with orthodox theory even if the orthodox theory, in its emphasis on equilibrium, seems very far removed from the messy dynamic adjustment associated with a sudden increase in liquidity preference.

Eric Rauchway on the Gold Standard

Commenter TravisV recently flagged for me a New York Times review of a new book by Eric Rauchway, Professor of History at the University of California at Davis. The book is called Money Makers: How Roosevelt and Keynes Ended the Depression, Defeated Fascism, and Secured a Prosperous Peace, a history of how FDR, with a bit of encouragement, but no real policy input, from J. M. Keynes, started a recovery from the Great Depression in 1933 by taking the US off the gold standard and devaluing the dollar, and later, with major input from Keynes, was instrumental in creating the post-World War II monetary system which was the result of the historic meeting at Bretton Woods, New Hampshire in 1944.

I had only just learned of Rauchway a week or so before the Times reviewed his book when I read his op-ed piece in the New York Times (“Why Republicans Still Love the Gold Standard” 11/13/15), warning about the curious (and ominous) infatuation that many Republican candidates for President seem to have with the gold standard, an infatuation forthrightly expressed by Ted Cruz in a recent debate among the Republican candidates for President. Rauchway wrote:

In Tuesday’s Republican presidential debate, Senator Ted Cruz reintroduced an idea that had many viewers scratching their heads and nearly all economists pulling out their hair. Mr. Cruz advocated a return to the gold standard — that is, tying the value of a dollar to a set amount of gold — because, he said, it produced prosperity under the Bretton Woods system and it helped “workingmen and -women.”

Mr. Cruz is confused about history and economics. The framers of Bretton Woods specifically designed their new international monetary system not to be a gold standard because they believed gold-based currency was largely responsible for the Great Depression. Their system, named for the New Hampshire town hosting the 1944 international conference that created it, was not a gold standard but “the exact opposite,” according to John Maynard Keynes, one of the system’s principal designers. Under Bretton Woods, nations were not obliged to set monetary policy according to how much gold they had, but rather according to their economic needs.

I thought that Rauchway made an excellent point in distinguishing between the actual gold standard and the Bretton Wood monetary system, in which the price of gold was nominally fixed at $35 dollars an ounce. But Bretton Woods system was very far from being a true gold standard, because the existence of a gold standard is predicated on the existence of a free market in gold, so that gold can be freely bought and sold by anyone at the official price. Under Bretton Woods, however, the market was tightly controlled, and US citizens could not legally own gold, except for industrial or commercial purposes, while the international gold market was under the strict control of the international monetary authorities. The only purchasers to whom the Fed was obligated to sell gold at the official price were other central banks, and it was understood that any request to purchase gold from the US monetary authority beyond what the US government thought appropriate would be considered a hostile act. The only foreign government willing to make such requests was the French government under de Gaulle, who took obvious pleasure in provoking the Anglo-Saxons whenever possible.

If Senator Cruz were a little older, or a little better read, or a little more scrupulous in his historical pronouncements, he might have been deterred from identifying the Bretton Woods system with the gold standard, because in the 1950s and 1960s right-wing supporters of the gold standard – I mean people like Ludwig von Mises and Henry Hazlitt — regarded the Bretton Woods as a dreadful engine of inflation, regarding the Bretton Woods system as a sham, embodying only the form, but not the substance, of the gold standard. It was only in the late 1970s that right-wingers began making nostalgic references to Bretton Woods, the very system that they had spent the previous 25 or 30 years denouncing as an abhorrent scheme for currency debasement.

But I stopped nodding my head in agreement with Rauchway when I reached the fifth paragraph of his piece.

Under a gold standard, the amount of gold a nation holds in bank vaults determines how much of its money circulates. If a nation’s gold stock increases through trade, for example, the country issues more currency. Likewise, if its gold stock decreases, it issues less.

Oh dear! Rauchway, like so many others, gets the gold standard all wrong, even though he started off correctly by saying that the gold standard ties “the value of a dollar to a set amount of gold.”

Here’s the point. Given a demand for some product, say, apples, if you can set the quantity of apples, while allowing everyone to trade that fixed amount freely, the equilibrium price for applies will be the price at which the amount demanded exactly matches the fixed quantity available to the market. Alternatively, if you set the price of apples, and can supply exactly as many apples as are demanded, the equilibrium quantity will be whatever quantity is demanded at the fixed price.

The gold standard operates by fixing the price of currency at a certain value in terms of gold (or stated equivalently, defining the currency unit as representing a fixed quantity of gold). The amount of currency under a gold standard is therefore whatever quantity of currency is demanded at the fixed price. That is very different from saying that a gold standard operates by placing a limit on the amount of currency that can be created. It is, to be sure, possible to place a limit on the quantity of currency by imposing a legal gold-reserve requirement on currency issued. But even then, it’s not the amount of reserves that limits the amount of currency; it’s the amount of currency that determines how much gold is held in reserve. Such requirements have existed under a gold standard, but those requirements do not define a gold standard, which is the legal equivalence established between currency and a corresponding amount of gold. A gold-reserve requirement is rather a condition imposed upon the gold standard, not the gold standard itself. Whether reserve requirements are good or bad, wise or unwise, is debatable. But it is a category mistake to confuse the defining characteristic of the gold standard with a separate condition imposed upon the gold standard.

I thought about responding to Rauchway’s erroneous characterization of the gold standard after seeing his op-ed piece, but it didn’t seem quite important enough to make the correction until TravisV pointed me to the review of his new book, which is largely about the gold standard. But then I thought that perhaps Rauchway had just expressed himself sloppily in the Times op-ed, mistakenly trying to convey a somewhat complicated and unfamiliar idea in more easily understood terms. So, without a copy of his book handy, I did a little on-line research, looking up some of the recent – and mostly favorable — reviews of the book. And, to my dismy, I found the following statement in a review in the Economist:

More important, says Mr Rauchway, in 1933 he [FDR] took America off the gold standard, a system whereby the amount of dollars in circulation was determined by the country’s gold reserves.

I am assuming that the reviewer for the Economist did not make this up on his own and is accurately conveying Mr. Rauchway’s understanding of how the gold standard operated. But just to be sure, I checked a few other online reviews, and I found this one by the indefatigable John Tamny in Real Clear Markets. Tamny is listed as editor of Real Clear Markets, which makes sense, because I can’t understand how else his seemingly interminable review of over 4200 words could have gotten published. Luckily for me, I didn’t have to go through the entire review before finding the following comment:

Rauchway lauds FDR for leaving a gold standard that in Rauchway’s words limited money creation to a ratio informed by the “amount of shiny yellow metal a nation had on hand,” but the problem here is that Rauchway’s analysis is spectacularly untrue. As monetary expert Nathan Lewis explained it recently about the U.S. gold standard,

A gold standard system is not, and has never been, a system that “fixes the supply of money to the supply of gold.” Absolutely not. A gold standard system is what I call a fixed-value system. The value of the currency – not the quantity – is linked to gold, for example at 23.2 troy grains of gold per dollar ($20.67/ounce).

It’s too bad that Rauchway had to be corrected by John Tamny and Nathan Lewis, but it is what it is. And don’t forget, even F. A. Hayek and Milton Friedman couldn’t figure out how the gold standard worked. But still, despite its theoretical shortcomings, it seems more than likely that Rauchway’s book is worth reading.

PS Further discussion of GOP nostalgia for the gold standard in today’s New York Times

Once Upon a Time When Keynes Endorsed the Fisher Effect

One of the great puzzles of the General Theory is Keynes’s rejection of the Fisher Effect on pp. 141-42. What is even more difficult to understand than Keynes’s criticism of the Fisher Effect, which I hope to parse in a future post, is that in his Tract on Monetary Reform Keynes had himself reproduced the Fisher Effect, though without crediting the idea to Fisher. Interestingly enough, when he turned against the Fisher Effect in the General Theory, dismissing it almost contemptuously, he explicitly attributed the idea to Fisher.

But here are a couple of quotations from the Tract in which Keynes exactly follows the Fisherian analysis. There are probably other places in which he does so as well, but these two examples seemed the most explicit. Keynes actually cites Fisher several times in the Tract, but those citations are to Fisher’s purely monetary work, in particular The Purchasing Power of Money (1911) which Keynes had reviewed in the Economic Journal. Of course, the distinction between the real and money rates of interest that Fisher made famous was not discovered by Fisher. Marshall had mentioned it and the idea was discussed at length by Henry Thornton, and possibly by other classical economists as well, so Keynes was not necessarily committing a scholarly offense by not mentioning Fisher. Nevertheless, it was Fisher who derived the relationship as a formal theorem, and the idea was already widely associated with him. And, of course, when Keynes criticized the idea, he explicitly attributed the idea to Fisher.

Economists draw an instructive distinction between what are termed the “money” rate of interest and the “real” rate of interest. If a sum of money worth 100 in terms of commodities at the time when the loan is made is lent for a year at 5 per cent interest, and is worth only 90 in terms of commodities at the end of the year, the lender receives back, including interest, what is worth only 94.5. This is expressed by saying that while the money rate of interest was 5 per cent, the real rate of interest had actually been negative and equal to minus 5.5 per cent. . . .

Thus, when prices are rising, the business man who borrows money is able to repay the lender with what, in terms of real value, not only represents no interest, but is even less than the capital originally advanced; that is the borrower reaps a corresponding benefit. It is true that , in so far as a rise in prices is foreseen, attempts to get advantage from this by increased borrowing force the money rates of interest to move upwards. It is for this reason, amongst others, that a high bank rate should be associated with a period of rising prices, and a low bank rate with a period of faling prices. The apparent abnormality of the money rate of interest at such times is merely the other side of the attempt of the real rate of interest to steady itself. Nevertheless in a period of rapidly changing prices, the money rate of interest seldom adjusts itself adequately or fast enough to prevent the real rate from becoming abnormal. For it is not the fact of a given rise of prices, but the expectation of a rise compounded of the various possible price movements and the estimated probability of each, which affects money rates. (pp. 20-22)

Like Fisher, Keynes, allowed for the possibility that inflation will not be fully anticipated so that the rise in the nominal rate will not fully compensate for the effect of inflation, suggesting that it is generally unlikely that inflation will be fully anticipated so that, in practice, inflation tends to reduce the real rate of interest. So Keynes seems fully on board with Fisher in the Tract.

Then there is Keynes’s celebrated theorem of covered interest arbitrage, perhaps his most important and enduring contribution to economics before writing the General Theory. He demonstrates the theorem in chapter 3 of the Tract.

If dollars one month forward are quoted cheaper than spot dollars to a London buyer in terms of sterling, this indicates a preference by the market, on balance, in favour of holding funds in New York during the month in question rather than in London – a preference the degree of which is measured by the discount on forward dollars. For if spot dollars are worth $4.40 to the pound and dollars one month forward $4.405 to the pound, then the owner of $4.40 can, by selling the dollars spot and buying them back one month forward, find himself at the end of the month with $4.405, merely by being during the month the owner of £1 in London instead of $4.40 in New York. That he should require and can obtain half a cent, which, earned in one month, is equal to about 1.5 per cent per annum, to induce him to do the transaction, shows, and is, under conditions of competition, a measure of, the market’s preference for holding funds during the month in question in New York rather than in London. . . .

The difference between the spot and forward rates is, therefore, precisely and exactly the measure of the preference of the money and exchange market for holding funds in one international centre rather than in another, the exchange risk apart, that is to say under conditions in which the exchange risk is covered. What is it that determines these preferences?

1. The most fundamental cause is to be found in the interest rates obtainable on “short” money – that is to say, on money lent or deposited for short periods of time in the money markets of the two centres under consideration. If by lending dollars in New York for one month the lender could earn interest at the rate of 5.5 per cent per annum, whereas by lending sterling in London for one month he could only earn interest at the rate of 4 per cent, then the preference observed above for holding funds in New York rather than London is wholly explained. That is to say, the forward quotations for the purchase of the currency of the dearer money market tend to be cheaper than spot quotations by a percentage per month equal to the excess of the interest which can be earned in a month in the dearer market over what can be earned in the cheaper. (pp. 123-34)

Compare Keynes’s discussion in the Tract to Fisher’s discussion in Appreciation and Interest, written over a quarter of a century before the Tract.

Suppose gold is to appreciate relatively to wheat a certain known amount in one year. What will be the relation between the rates of interest in the two standards? Let wheat fall in gold price (or gold rise in wheat price) so that the quantity of gold which would buy one bushel of wheat at the beginning of the year will buy 1 + a bushels at the end, a being therefore the rate of appreciation of gold in terms of wheat. Let the rate of interest in gold be i, and in wheat be j, and let the principal of the loan be D dollars or its equivalent B bushels. Our alternative contracts are then:

For D dollars borrowed D + Di or D(1 + i) dollars are due in one yr.

For B bushels     “       B + Bj or B(1 + j) bushels  ”   “    “   “   “

and our problem is to find the relation between i and j, which will make the D(1 + i) dollars equal the B(1 + j) bushels.

At first, D dollars equals B bushels.

At the end of the year D dollars equals B(1 + a) bushels

Hence at the end of one year D(1 + i) dollars equals B(1 + a) (1 + i) bushels

Since D(1 + i) dollars is the number of dollars necessary to liquidate the debt, its equivalent B(1 + a) (1 + i) bushels is the number of bushels necessary to liquidate it. But we have already designated this number of bushels by B(1 + j). Our result, therefore, is:

At the end of 1 year D(1 + i) dollars equals B(1 + j) equals B(1 + a) (1 + i) bushels

which, after B is canceled, discloses the formula:

1 + j = (1 + a) (1 + i)

Or,

j = i + a + ia

Or, in words: The rate of interest in the (relatively) depreciating standard is equal to the sum of three terms, viz., the rate of interest in the appreciating standard, the rate of appreciation itself and the product of these two elements. (pp. 8-9)

So, it’s clear that Keynes’s theorem of covered interest arbitrage in the Tract is a straightforward application of Fisher’s analysis in Appreciation and Interest. Now it is quite possible that Keynes was unaware of Fisher’s analysis in Appreciation and Interest, though it was reproduced in Fisher’s better known 1907 classic The Rate of Interest, so that Keynes’s covered-interest-arbitrage theorem may have been subjectively original, even though it had been anticipated in its essentials a quarter of a century earlier by Fisher. Nevertheless, Keynes’s failure to acknowledge, when he criticized the Fisher effect in the General Theory, how profoundly indebted he had been, in his own celebrated work on the foreign-exchange markets, to the Fisherian analysis was a serious lapse in scholarship, if not in scholarly ethics.

Thompson’s Reformulation of Macroeconomic Theory, Part V: A Neoclassical Black Hole

It’s been over three years since I posted the fourth of my four previous installments in this series about Earl Thompson’s unpublished paper “A Reformulation of Macroeconomic Theory,” Thompson’s strictly neoclassical alternative to the standard Keynesian IS-LM model. Given the long hiatus, a short recapitulation seems in order.

The first installment was an introduction summarizing Thompson’s two main criticisms of the Keynesian model: 1) the disconnect between the standard neoclassical marginal productivity theory of production and factor pricing and the Keynesian assertion that labor receives a wage equal to its marginal product, thereby implying the existence of a second scarce factor of production (capital), but with the market for capital services replaced in the IS-LM model by the Keynesian expenditure functions, creating a potential inconsistency between the IS-LM model and a deep property of neoclassical theory; 2) the market for capital services having been excluded from the IS-LM model, the model lacks a variable that equilibrates the choice between holding money or real assets, so that the Keynesian investment function is incompletely specified, the Keynesian equilibrium condition for spending – equality between savings and investment – taking no account of the incentive for capital accumulation or the relationship, explicitly discussed by Keynes, between current investment and the (expected) future price level. Excluding the dependence of the equilibrium rate of spending on (expected) inflation from the IS-LM model renders the model logically incomplete.

The second installment was a discussion of the Hicksian temporary-equilibrium method used by Thompson to rationalize the existence of involuntary unemployment. For Thompson involuntary unemployment means unemployment caused by overly optimistic expectations by workers of wage offers, leading them to mistakenly set reservation wages too high. The key idea of advantage of the temporary-equilibrium method is that it reconciles the convention of allowing a market-clearing price to equilibrate supply and demand with the phenomenon of substantial involuntary unemployment in business-cycle downturns. Because workers have an incentive to withhold their services in order to engage in further job search or job training or leisure, their actual short-run supply of labor services in a given time period is highly elastic at the expected wage. If wage offers are below expectations, workers (mistakenly = involuntarily) choose unemployment, but given those mistaken expectations, the labor market is cleared with the observed wage equilibrating the demand for labor services and supply of labor services. There are clearly problems with this way of modeling the labor market, but it does provide an analytical technique that can account for cyclical fluctuations in unemployment within a standard microeconomic framework.

In the third installment, I showed how Thompson derived his FF curve, representing combinations of price levels and interest rates consistent with (temporary) equilibrium in both factor markets (labor services and capital services) and two versions of the LM curve, representing price levels and interest rates consistent with equilibrium in the money market. The two versions of the LM curve (analogous, but not identical, to the Keynesian LM curve) correspond to different monetary regimes. In what Thompson called the classical case, the price level is fixed by convertibility of output into cash at a fixed exchange rate, with money being supplied by a competitive banking system paying competitive interest on cash balances. The LM curve in this case is vertical at the fixed price level, with any nominal rate of interest being consistent with equilibrium in the money market, inasmuch as the amount of money demanded depends not on the nominal interest rate, but on the difference between the nominal interest rate and the competitively determined interest rate paid on cash. In the modern case, cash is non-interest bearing and supplied monopolistically by the monetary authority, so the LM curve is upward-sloping, with the cost of holding cash rising with the rate of interest, thereby reducing the amount of money demanded and increasing the price level for a given quantity of money supplied by the monetary authority. The solution of the model corresponds to the intersection of the FF and LM curves. For the classical case, the intersection is unique, but in the modern case since both curves are upward sloping, multiple intersections are possible.

The focus of the fourth installment was on setting up a model analogous to the Keynesian model by replacing the market for capital services excluded by Walras’s Law with something similar to the Keynesian expenditure functions (consumption, investment, government spending, etc.). The key point is that the FF and LM curves implicitly define a corresponding CC curve (shown in Figure 4 of the third installment) with the property that, at all points on the CC curve, the excess demand for (supply of) money exactly equals the excess supply of (demand for) labor. Thus, the CC curve represents a stock equilibrium in the market for commodities (i.e., a single consumption/capital good) rather than a flow rate of expenditure and income as represented by the conventional IS curve. But the inconsistency between the upward-sloping CC curve and the downward sloping IS curve reflects the underlying inconsistency between the neoclassical and the Keynesian paradigms.

In this installment, I am going to work through Thompson’s argument about the potential for an unstable equilibrium in the version of his model with an upward-sloping LM curve corresponding to the case in which non-interest bearing money is monopolistically supplied by a central bank. Thompson makes the argument using Figure 5, a phase diagram showing the potential equilibria for such an economy in terms of the FF curve (representing price levels and nominal interest rates consistent with equilibrium in the markets for labor and capital services) and the CC curve (representing price levels and nominal interest rates consistent with equilibrium in the output market).

Thompson_Figure5A phase diagram shows the direction of price adjustment when the economy is not in equilibrium (one of the two points of intersection between the FF and the CC curves). A disequilibrium implies a price change in response to an excess supply or excess demand in some market. All points above and to the left of the FF curve correspond to an excess supply of capital services, implying a falling nominal interest rate; points below and to the right of the FF curve correspond to excess demand for capital services, implying a rising interest rate. Points above and to the left of the CC curve correspond to an excess demand for output, implying a rising price level; points below and to the right of the CC curve correspond to an excess supply of output, implying a falling price level. Points in between the FF and CC curves correspond either to an excess demand for commodities and for capital services, implying a rising price level and a rising nominal interest rate (in the region between the two points of intersection – Eu and Es — between the CC and FF curves) or to an excess supply of both capital services and commodities, implying a falling interest rate and a falling price level (in the regions below the lower intersection Eu and above the upper intersection Es). The arrows in the diagram indicate the direction in which the price level and the nominal interest rate are changing at any point in the diagram.

Given the direction of price change corresponding to points off the CC and FF curves, the upper intersection is shown to be a stable equilibrium, while the lower intersection is unstable. Moreover, the instability corresponding to the lower intersection is very dangerous, because entering the region between the CC and FF curves below Eu means getting sucked into a vicious downward spiral of prices and interest rates that can only be prevented by a policy intervention to shift the CC curve to the right, either directly by way of increased government spending or tax cuts, or indirectly, through monetary policy aimed at raising the price level and expected inflation, shifting the LM curve, and thereby the CC curve, to the right. It’s like stepping off a cliff into a black hole.

Although I have a lot of reservations about the practical relevance of this model as an analytical tool for understanding cyclical fluctuations and counter-cyclical policy, which I plan to discuss in a future post, the model does resonate with me, and it does so especially after my recent posts about the representative-agent modeling strategy in New Classical economics (here, here, and here). Representative-agent models, I argued, are inherently unable to serve as analytical tools in macroeconomics, because their reductionist approach implies that all relevant decision making can be reduced to the optimization of a single agent, insulating the analysis from any interactions between decision-makers. But it is precisely the interaction effects between decision makers that create analytical problems that constitute the subject matter of the discipline or sub-discipline known as macroeconomics. That Robert Lucas has made it his life’s work to annihilate this field of study is a sad commentary on his contribution, Nobel Prize or no Nobel Prize, as an economic theorist.

That is one reason why I regard Thompson’s model, despite its oversimplifications, as important: it is constructed on a highly aggregated, yet strictly neoclassical, foundation, including continuous market-clearing, arriving at the remarkable conclusion that not only is there an unstable equilibrium, but it is at least possible for an economy in the neighborhood of the unstable equilibrium to be caught in a vicious downward deflationary spiral in which falling prices do not restore equilibrium but, instead, suck the economy into a zero-output black hole. That result seems to me to be a major conceptual breakthrough, showing that the strict rationality assumptions of neoclassical theory can lead to aoutcome that is totally at odds with the usual presumption that the standard neoclassical assumptions inevitably generate a unique stable equilibrium and render macroeconomics superfluous.


About Me

David Glasner
Washington, DC

I am an economist at the Federal Trade Commission. Nothing that you read on this blog necessarily reflects the views of the FTC or the individual commissioners. Although I work at the FTC as an antitrust economist, most of my research and writing has been on monetary economics and policy and the history of monetary theory. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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