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Did David Hume Discover the Vertical Phillips Curve?

In my previous post about Nick Rowe and Milton Friedman, I pointed out to Nick Rowe that Friedman (and Phelps) did not discover the argument that the long-run Phillips Curve, defined so that every rate of inflation is correctly expected, is vertical. The argument I suggested can be traced back at least to Hume. My claim on Hume’s behalf was based on my vague recollection that Hume distinguished between the effect of a high price level and a rising price level, a high price level having no effect on output and employment, while a rising price level increases output and employment.

Scott Sumner offered the following comment, leaving it as an exercise for the reader to figure out what he meant by “didn’t quite get there.”:

As you know Friedman is one of the few areas where we disagree. Here I’ll just address one point, the expectations augmented Phillips Curve. Although I love Hume, he didn’t quite get there, although he did discuss the simple Phillips Curve.

I wrote the following response to Scott referring to the quote that I was thinking of without quoting it verbatim (because I couldn’t remember where to find it):

There is a wonderful quote by Hume about how low prices or high prices are irrelevant to total output, profits and employment, but that unexpected increases in prices are a stimulus to profits, output, and employment. I’ll look for it, and post it.

Nick Rowe then obligingly provided the quotation I was thinking of (but not all of it):

Here, to my mind, is the “money quote” (pun not originally intended) from David Hume’s “Of Money”:

“From the whole of this reasoning we may conclude, that it is of no manner of consequence, with regard to the domestic happiness of a state, whether money be in a greater or less quantity. The good policy of the magistrate consists only in keeping it, if possible, still encreasing; because, by that means, he keeps alive a spirit of industry in the nation, and encreases the stock of labour, in which consists all real power and riches.”

The first sentence is fine. But the second sentence is very clearly a problem.

Was it Friedman who said “we have only advanced one derivative since Hume”?

OK, so let’s see the whole relevant quotation from Hume’s essay “Of Money.”

Accordingly we find, that, in every kingdom, into which money begins to flow in greater abundance than formerly, everything takes a new face: labour and industry gain life; the merchant becomes more enterprising, the manufacturer more diligent and skilful, and even the farmer follows his plough with greater alacrity and attention. This is not easily to be accounted for, if we consider only the influence which a greater abundance of coin has in the kingdom itself, by heightening the price of Commodities, and obliging everyone to pay a greater number of these little yellow or white pieces for everything he purchases. And as to foreign trade, it appears, that great plenty of money is rather disadvantageous, by raising the price of every kind of labour.

To account, then, for this phenomenon, we must consider, that though the high price of commodities be a necessary consequence of the encrease of gold and silver, yet it follows not immediately upon that encrease; but some time is required before the money circulates through the whole state, and makes its effect be felt on all ranks of people. At first, no alteration is perceived; by degrees the price rises, first of one commodity, then of another; till the whole at last reaches a just proportion with the new quantity of specie which is in the kingdom. In my opinion, it is only in this interval or intermediate situation, between the acquisition of money and rise of prices, that the encreasing quantity of gold and silver is favourable to industry. When any quantity of money is imported into a nation, it is not at first dispersed into many hands; but is confined to the coffers of a few persons, who immediately seek to employ it to advantage. Here are a set of manufacturers or merchants, we shall suppose, who have received returns of gold and silver for goods which they sent to CADIZ. They are thereby enabled to employ more workmen than formerly, who never dream of demanding higher wages, but are glad of employment from such good paymasters. If workmen become scarce, the manufacturer gives higher wages, but at first requires an encrease of labour; and this is willingly submitted to by the artisan, who can now eat and drink better, to compensate his additional toil and fatigue.

He carries his money to market, where he, finds everything at the same price as formerly, but returns with greater quantity and of better kinds, for the use of his family. The farmer and gardener, finding, that all their commodities are taken off, apply themselves with alacrity to the raising more; and at the same time can afford to take better and more cloths from their tradesmen, whose price is the same as formerly, and their industry only whetted by so much new gain. It is easy to trace the money in its progress through the whole commonwealth; where we shall find, that it must first quicken the diligence of every individual, before it encrease the price of labour. And that the specie may encrease to a considerable pitch, before it have this latter effect, appears, amongst other instances, from the frequent operations of the FRENCH king on the money; where it was always found, that the augmenting of the numerary value did not produce a proportional rise of the prices, at least for some time. In the last year of LOUIS XIV, money was raised three-sevenths, but prices augmented only one. Corn in FRANCE is now sold at the same price, or for the same number of livres, it was in 1683; though silver was then at 30 livres the mark, and is now at 50. Not to mention the great addition of gold and silver, which may have come into that kingdom since the former period.

From the whole of this reasoning we may conclude, that it is of no manner of consequence, with regard to the domestic happiness of a state, whether money be in a greater or less quantity. The good policy of the magistrate consists only in keeping it, if possible, still encreasing; because, by that means, he keeps alive a spirit of industry in the nation, and encreases the stock of labour, in which consists all real power and riches. A nation, whose money decreases, is actually, at that time, weaker and more miserable than another nation, which possesses no more money, but is on the encreasing hand. This will be easily accounted for, if we consider, that the alterations in the quantity of money, either on one side or the other, are not immediately attended with proportionable alterations in the price of commodities. There is always an interval before matters be adjusted to their new situation; and this interval is as pernicious to industry, when gold and silver are diminishing, as it is advantageous when these metals are encreasing. The workman has not the same employment from the manufacturer and merchant; though he pays the same price for everything in the market. The farmer cannot dispose of his corn and cattle; though he must pay the same rent to his landlord. The poverty, and beggary, and sloth, which must ensue, are easily foreseen.

So Hume understands that once-and-for-all increases in the stock of money and in the price level are neutral, and also that in the transition from one price level to another, there will be a transitory effect on output and employment. However, when he says that the good policy of the magistrate consists only in keeping it, if possible, still increasing; because, by that means, he keeps alive a spirit of industry in the nation, he seems to be suggesting that the long-run Phillips Curve is actually positively sloped, thus confirming Milton Friedman (and Nick Rowe and Scott Sumner) in saying that Hume was off by one derivative.

While I think that is a fair reading of Hume, it is not the only one, because Hume really was thinking in terms of price levels, not rates of inflation. The idea that a good magistrate would keep the stock of money increasing could not have meant that the rate of inflation would indefinitely continue at a particular rate, only that the temporary increase in the price level would be extended a while longer. So I don’t think that Hume would ever have imagined that there could be a steady predicted rate of inflation lasting for an indefinite period of time. If he could have imagined a steady rate of inflation, I think he would have understood the simple argument that, once expected, the steady rate of inflation would not permanently increase output and employment.

At any rate, even if Hume did not explicitly anticipate Friedman’s argument for a vertical long-run Phillips Curve, certainly there many economists before Friedman who did. I will quote just one example from a source (Hayek’s Constitution of Liberty) that predates Friedman by about eight years. There is every reason to think that Friedman was familiar with the source, Hayek having been Friedman’s colleague at the University of Chicago between 1950 and 1962. The following excerpt is from p. 331 of the 1960 edition.

Inflation at first merely produces conditions in which more people make profits and in which profits are generally larger than usual. Almost everything succeeds, there are hardly any failures. The fact that profits again and again prove to be greater than had been expected and that an unusual number of ventures turn out to be successful produces a general atmosphere favorable to risk-taking. Even those who would have been driven out of business without the windfalls caused by the unexpected general rise in prices are able to hold on and to keep their employees in the expectation that they will soon share in the general prosperity. This situation will last, however, only until people begin to expect prices to continue to rise at the same rate. Once they begin to count on prices being so many per cent higher in so many months’ time, they will bid up the prices of the factors of production which determine the costs to a level corresponding to the future prices they expect. If prices then rise no more than had been expected, profits will return to normal, and the proportion of those making a profit also will fall; and since, during the period of exceptionally large profits, many have held on who would otherwise have been forced to change the direction of their efforts, a higher proportion than usual will suffer losses.

The stimulating effect of inflation will thus operate only so long as it has not been foreseen; as soon as it comes to be foreseen, only its continuation at an increased rate will maintain the same degree of prosperity. If in such a situation price rose less than expected, the effect would be the same as that of unforeseen deflation. Even if they rose only as much as was generally expected, this would no longer provide the expectational stimulus but would lay bare the whole backlog of adjustments that had been postponed while the temporary stimulus lasted. In order for inflation to retain its initial stimulating effect, it would have to continue at a rate always faster than expected.

This was certainly not the first time that Hayek made the same argument. See his Studies in Philosophy Politics and Economics, p. 295-96 for a 1958 version of the argument. Is there any part of Friedman’s argument in his 1968 essay (“The Role of Monetary Policy“) not contained in the quote from Hayek? Nor is there anything to indicate that Hayek thought he was making an argument that was not already familiar. The logic is so obvious that it is actually pointless to look for someone who “discovered” it. If Friedman somehow gets credit for making the discovery, it is simply because he was the one who made the argument at just the moment when the rest of the profession happened to be paying attention.

The Lucas Critique Revisited

Published January 2, 2013 Phillips Curve , Robert Lucas 27 Comments
Tags: Lucas, natural rate of unemployment, Phillips Curve

After writing my previous post, I reread Robert Lucas’s classic article “Econometric Policy Evaluation: A Critique,” surely one of the most influential economics articles of the last half century. While the main point of the article was not entirely original, as Lucas himself acknowledged in the article, so powerful was his explanation of the point that it soon came to be known simply as the Lucas Critique. The Lucas Critique says that if a certain relationship between two economic variables has been estimated econometrically, policy makers, in formulating a policy for the future, cannot rely on that relationship to persist once a policy aiming to exploit the relationship is adopted. The motivation for the Lucas Critique was the Friedman-Phelps argument that a policy of inflation would fail to reduce the unemployment rate in the long run, because workers would eventually adjust their expectations of inflation, thereby draining inflation of any stimulative effect. By restating the Friedman-Phelps argument as the application of a more general principle, Lucas reinforced and solidified the natural-rate hypothesis, thereby establishing a key principle of modern macroeconomics.

In my previous post I argued that microeconomic relationships, e.g., demand curves and marginal rates of substitution, are, as a matter of pure theory, not independent of the state of the macroeconomy. In an interdependent economy all variables are mutually determined, so there is no warrant for saying that microrelationships are logically prior to, or even independent of, macrorelationships. If so, then the idea of microfoundations for macroeconomics is misleading, because all economic relationships are mutually interdependent; some relationships are not more basic or more fundamental than others. The kernel of truth in the idea of microfoundations is that there are certain basic principles or axioms of behavior that we don’t think an economic model should contradict, e.g., arbitrage opportunities should not be left unexploited – people should not pass up obvious opportunities, such as mutually beneficial offers of exchange, to increase their wealth or otherwise improve their state of well-being.

So I was curious to how see whether Lucas, while addressing the issue of how price expectations affected output and employment, recognized the possibility that a microeconomic relationship could be dependent on the state of the macroeconomy. For my purposes, the relevant passage occurs in section 5.3 (subtitled “Phillips Curves”) of the paper. After working out the basic theory earlier in the page, Lucas, in section 5, provided three examples of how econometric estimates of macroeconomic relationships would mislead policy makers if the effect of expectations on those relationships were not taken into account. The first two subsections treated consumption expenditures and the investment tax credit. The passage that I want to focus on consists of the first two paragraphs of subsection 5.3 (which I now quote verbatim except for minor changes in Lucas’s notation).

A third example is suggested by the recent controversy over the Phelps-Friedman hypothesis that permanent changes in the inflation rate will not alter the average rate of unemployment. Most of the major econometric models have been used in simulation experiments to test this proposition; the results are uniformly negative. Since expectations are involved in an essential way in labor and product market supply behavior, one would presumed, on the basis of the considerations raised in section 4, that these tests are beside the point. This presumption is correct, as the following example illustrates.

It will be helpful to utilize a simple, parametric model which captures the main features of the expectational view of aggregate supply – rational agents, cleared markets, incomplete information. We imagine suppliers of goods to be distributed over N distinct markets i, I = 1, . . ., N. To avoid index number problems, suppose that the same (except for location) good is traded in each market, and let y_it be the log of quantity supplied in market i in period t. Assume, further, that the supply y_it is composed of two factors

y_it = Py_it + Cy_it,

where Py_it denotes normal or permanent supply, and Cy_it cyclical or transitory supply (both again in logs). We take Py_it to be unresponsive to all but permanent relative price changes or, since the latter have been defined away by assuming a single good, simply unresponsive to price changes. Transitory supply Cy_it varies with perceived changes in the relative price of goods in i:

Cy_it = β(p_it – Ep_it),

where p_it is the log of the actual price in i at time t, and Ep_it is the log of the general (geometric average) price level in the economy as a whole, as perceived in market i.

Let’s take a moment to ponder the meaning of Lucas’s simplifying assumption that there is just one good. Relative prices (except for spatial differences in an otherwise identical good) are fixed by assumption; a disequilibrium (or suboptimal outcome) can arise only because of misperceptions of the aggregate price level. So, by explicit assumption, Lucas rules out the possibility that any microeconomic relationship depends on macroeconomic conditions. Note also that Lucas does not provide an account of the process by which market prices are established at each location, nothing being said about demand conditions. For example, if suppliers at location i perceive a price (transitorily) above the equilibrium price, and respond by (mistakenly) increasing output, thereby increasing their earnings, do those suppliers increase their demand to consume output? Suppose suppliers live and purchase at locations other than where they are supplying product, so that a supplier at location i purchases at location j, where i does not equal j. If a supplier at location i perceives an increase in price at location i, will his demand to purchase the good at location j increase as well? Will the increase in demand at location j cause an increase in the price at location j? What if there is a one-period lag between supplier receipts and their consumption demands? Lucas provides no insight into these possible ambiguities in his model.

Stated more generally, the problem with Lucas’s example is that it seems to be designed to exclude a priori the possibility of every type of disequilibrium but one, a disequilibrium corresponding to a single type of informational imperfection. Reasoning on the basis of that narrow premise, Lucas shows that, under a given expectation of the future price level, an econometrician would find a positive correlation between the price level and output — a negatively sloped Phillips Curve. Yet, under the same assumptions, Lucas also shows that an anticipated policy to raise the rate of inflation would fail to raise output (or, by implication, increase employment). But, given his very narrow underlying assumptions, it seems plausible to doubt the robustness of Lucas’s conclusion. Proving the validity of a proposition requires more than constructing an example in which the proposition is shown to be valid. That would be like trying to prove that the sides of every triangle are equal in length by constructing a triangle whose angles are all equal to 60 degrees, and then claiming that, because the sides of that triangle are equal in length, the sides of all triangles are equal in length.

Perhaps a better model than the one Lucas posited would have been one in which the amount supplied in each market was positively correlated with the amount supplied in every other market, inasmuch as an increase (decrease) in the amount supplied in one market will tend to increase (decrease) demand in other markets. In that case, I conjecture, deviations from permanent supply would tend to be cumulative (though not necessarily permanent), implying a more complex propagation mechanism than Lucas’s simple model does. Nor is it obvious to me how the equilibrium of such a model would compare to the equilibrium in the Lucas model. It does not seem inconceivable that a model could be constructed in which equilibrium output depended on the average price level. But this is just conjecture on my part, because I haven’t tried to write out and solve such a model. Perhaps an interested reader out there will try to work it out and report back to us on the results.

PS: Congratulations to Scott Sumner on his excellent op-ed on nominal GDP level targeting in today’s Financial Times.

About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. 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.

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

Follow me on Twitter @david_glasner

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The Lucas Critique Revisited

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