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Was Milton Friedman a Closet Keynesian?

Published March 16, 2012 Friedman , Keynes , monetary theory 40 Comments

Commenting on a supremely silly and embarrassingly uninformed (no, Ms. Shlaes, A Monetary History of the United States was not Friedman’s first great work, Essays in Positive Economics, Studies in the Quantity Theory of Money, A Theory of the Consumption Function, A Program for Monetary Stability, and Capitalism and Freedom were all published before A Monetary History of the US was published) column by Amity Shlaes, accusing Ben Bernanke of betraying the teachings of Milton Friedman, teachings that Bernanke had once promised would guide the Fed for ever more, Paul Krugman turned the tables and accused Friedman of having been a crypto-Keynesian.

The truth, although nobody on the right will ever admit it, is that Friedman was basically a Keynesian — or, if you like, a Hicksian. His framework was just IS-LM coupled with an assertion that the LM curve was close enough to vertical — and money demand sufficiently stable — that steady growth in the money supply would do the job of economic stabilization. These were empirical propositions, not basic differences in analysis; and if they turn out to be wrong (as they have), monetarism dissolves back into Keynesianism.

Krugman is being unkind, but he is at least partly right. In his famous introduction to Studies in the Quantity Theory of Money, which he called “The Quantity Theory of Money: A Restatement,” Friedman gave the game away when he called the quantity theory of money a theory of the demand for money, an almost shockingly absurd characterization of what anyone had ever thought the quantity theory of money was. At best one might have said that the quantity theory of money was a non-theory of the demand for money, but Friedman somehow got it into his head that he could get away with repackaging the Cambridge theory of the demand for money — the basis on which Keynes built his theory of liquidity preference — and calling that theory the quantity theory of money, while ascribing it not to Cambridge, but to a largely imaginary oral tradition at the University of Chicago. Friedman was eventually called on this bit of scholarly legerdemain by his old friend from graduate school at Chicago Don Patinkin, and, subsequently, in an increasingly vitriolic series of essays and lectures by his then Chicago colleague Harry Johnson. Friedman never repeated his references to the Chicago oral tradition in his later writings about the quantity theory, e.g., his essay on the quantity theory of money in the International Encyclopedia of the Social Sciences. But the simple fact is that Friedman was never able to set down a monetary or a macroeconomic model that wasn’t grounded in the conventional macroeconomics of his time.

Friedman was above all else a superb applied price theorist who wound up doing a lot of worthwhile empirical work and historical on monetary economics, but his knowledge of the history of monetary theory seems to have been pretty much confined to whatever he learned from his teacher Lloyd Mints’s book, A History of Banking Theory in Great Britain and the United States and probably from a classic book, Studies in the Theory of International Trade, by Jacob Viner, another one of Friedman’s teachers at Chicago That’s why when Friedman finally published an article in two part in the Journal of Political Economy in the early 1970s entitled “A Theoretical Framework for Monetary Analysis,” the papers pretty much flopped, and are now almost completely forgotten (but see here). Actually Friedman’s intellectual forbears were really W. C. Mitchell and Friedman’s teacher at Columbia Arthur Burns from whom Friedman was schooled in the atheoretical, empirical approach of the old NBER founded by Mitchell.

But Krugman is not totally right either. Although Friedman obviously liked the idea that the LM-curve was vertical, and liked the idea that money demand is very stable even more, those ideas were not essential to his theoretical position. (Whether the stability of the demand for money was essential to his position would depend on whether Friedman’s 3-percent growth rule for the money supply is central to his thought. Although Friedman obviously loved the 3-percent rule, I don’t think that objectively it was really that important to his intellectual position, his sentimental attachment to it notwithstanding.) What really mattered was the idea that, in the long run, money is neutral and the long-run Phillips Curve is vertical. Given those assumptions, Friedman could argue that ensuring reasonable monetary stability would lead to better economic performance than discretionary monetary or fiscal policy. But Friedman, as far as I know, never actually considered the possibility of a negative equilibrium real interest rate. That’s why, when we look for guidance from Friedman about the current situation, we can’t be completely sure what he would have said. His comments on Japan suggest that he would have indeed favored quantitative easing. But inasmuch as he did not explicitly advocate inflation, supporters and opponents of QE can make a case that Friedman would have been on their side. My own view is that the argument that Friedman would have supported QE is not one of the five or even ten strongest arguments that could be made on its behalf.

There Are Microfoundations, and There Are Microfoundations; They’re Not the Same

Published March 7, 2012 Keynes , monetary theory , rational expectations 46 Comments

Microfoundations are latest big thing on the econoblogosphere. Krugman, Wren-Lewis (and again), Waldmann, Smith (all two of them!) have weighed in on the subject. So let me take a shot.

The idea of reformulating macroeconomics was all the rage when I studied economics as an undergraduate and graduate student at UCLA in the late 1960s and early 1970s. The UCLA department had largely taken shape in the 1950s and early 1960s around its central figure, Armen Alchian, undoubtedly the greatest pure microeconomist of the second half of the twentieth century in the sense of understanding and applying microeconomics to bring the entire range of economic, financial, legal and social phenomena under its purview, and co-author of the greatest economics textbook ever written. There was simply no problem that he could not attack, using the simple tools one learns in intermediate microeconomics, with a piece of chalk and a blackboard. Alchian’s profound insight (though in this he was anticipated by Coase in his paper on the nature of the firm, and by Hayek’s criticisms of pure equilibrium theory) was that huge chunks of everyday economic activity, such as advertising, the holding of inventories, business firms, contracts, and labor unemployment, simply would not exist in the world characterized by perfect information and zero uncertainty assumed by general-equilibrium theory. For years, Alchian used to say, he could not make sense of Keynes’s General Theory and especially the Keynesian theory of involuntary unemployment, because it seemed to exclude the possibility of equilibration by way of price and wage adjustments, the fundamental mechanism of microeconomic equilibration. It was only when Axel Leijonhufvud arrived on the scene at UCLA, still finishing up his doctoral dissertation, published a few years after his arrival at UCLA as On Keynesian Economics and the Economics of Keynes that Alchian came to understand the deep connections between the Keynesian theory of involuntary unemployment and the kind of informational imperfections that Alchian had been working on for years at the micro-level.

So during my years at UCLA, providing microfoundations for macroeconomics was viewed as an intellectual challenge for gaining a better understanding of Keynesian involuntary unemployment, not as a means of proving that it doesn’t exist. Reformulating macroeconomic theory (I use this phrase in homage to the unpublished paper by the late Earl Thompson, one of Alchian’s very best students) based on microfoundations did not mean simply discarding Keynesian theory into the dustbin of history. Unemployment was viewed as a search process in which workers choose unemployment because it would be irrational to accept the first offer of employment received regardless of the wage being offered. But a big increase in search activity by workers can have feedback effects on aggregate demand preventing a smooth transition to a new equilibrium after an interval of increased search. Alchian, an early member of the Mont Pelerin Society, was able to see the deep connection between Leijonhufvud’s microeconomic rationalization of Keynesian involuntary unemployment and the obscure work, The Theory of Idle Resources, of another member of the MPS, the admirable human being, and unjustly underrated, unfortunately now all but forgotten, economist, W. H. Hutt, who spent most of his professional life engaged in a battle against what he considered the fallacies of J. M. Keynes, especially Keynes’s theory of unemployment.

Unfortunately, this promising approach towards gaining a deeper and richer understanding of the interaction between imperfect information and uncertainty, on the one hand, and, on the other, a process of dynamic macroeconomic adjustment in which both prices and quantities are changing, so that deviations from equilibrium can be cumulative rather than, as conventional equilibrium models assume, self-correcting, has yet to fulfill its promise. Here the story gets complicated, and it would take a much longer explanation than I could possibly reduce to a blog post to tell it adequately. But my own view, in a nutshell, is that the rational-expectations revolution — especially the dogmatic view of how economics ought to be practiced espoused by Robert Lucas and his New Classical, Real Business Cycle and New Keynesian acolytes — has subverted the original aims of the microfoundations project. Rather than relax the informational assumptions underlying conventional equilibrium analysis to allow for a richer and more relevant analysis than is possible when using the tools of standard general-equilibrium theory, Lucas et al. developed sophisticated tools that enabled them to nominally relax the informational assumptions of equilibrium theory while using the tyrannical methodology of rational expectations combined with full market clearing to preserve the essential results of the general-equilibrium model. The combined effect of the faux axiomatic formalism and the narrow conception of microfoundations imposed by the editorial hierarchy of the premier economics journals has been to recreate the gap between the Keynesian theory of involuntary unemployment and rigorous microeconomic reasoning that Alchian, some forty years ago, thought he had found a way to bridge.

Update (1:16PM EST): A commenter points out that the first sentence of my concluding paragraph was left unfinished. That’s what happens when you try to get a post out at 2AM. The sentence is now complete; I hope it’s not to disappointing.

Hawtrey on Competitive Devaluation: Bring It On

Published February 28, 2012 gold standard , Hawtrey , inflation , monetary history , monetary policy , monetary theory 18 Comments

In a comment on my previous post about Ralph Hawtrey’s discussion of the explosive, but short-lived, recovery triggered by FDR’s 1933 suspension of the gold standard and devaluation of the dollar, Greg Ransom queried me as follows:

Is this supposed to be a lesson in international monetary economics . . . or a lesson in closed economy macroeconomics?

To which I responded:

I don’t understand your question. The two are not mutually exclusive; it could be a lesson in either.

To which Greg replied:

I’m pushing you David to make a clearer and cleaner claim about what sort of monetary disequilibrium you are asserting existed in the 1929-1933 period, is this a domestic disequilibrium or an international disequilibrium — or are these temprary effects any nation could achieve via competitive devaluations of the currency, i.e. improving the terms of international trade via unsustainable temporary monetary policy.

Or are a ping pong of competitive devaluations among nations a pure free lunch?

And if so, why?

You can read my response to Greg in the comment section of my post, but I also mentioned that Hawtrey had addressed the issue of competitive devaluation in Trade Depression and the Way Out, hinting that another post discussing Hawtrey’s views on the subject might be in the offing. So let me turn the floor over to Mr. R. G. Hawtrey.

When Great Britain left the gold standard, deflationary measure were everywhere resorted to. Not only did the Bank of England raise its rate, but the tremendous withdrawals of gold from the United States involved an increase of rediscounts and a rise of rates there, and the gold that reached Europe was immobilized or hoarded. . . .

The consequence was that the fall in the price level continued. The British price level rose in the first few weeks after the suspension of the gold standard, but then accompanied the gold price level in its downward trend. This fall of prices calls for no other explanation than the deflationary measures which had been imposed. Indeed what does demand explanation is the moderation of the fall, which was on the whole not so steep after September 1931 as before.

Yet when the commercial and financial world saw that gold prices were falling rather than sterling prices rising, they evolved the purely empirical conclusion that a depreciation of the pound had no effect in raising the price level, but that it caused the price level in terms of gold and of those currencies in relation to which the pound depreciated to fall.

For any such conclusion there was no foundation. Whenever the gold price level tended to fall, the tendency would make itself felt in a fall in the pound concurrently with the fall in commodities. But it would be quite unwarrantable to infer that the fall in the pound was the cause of the fall in commodities.

On the other hand, there is no doubt that the depreciation of any currency, by reducing the cost of manufacture in the country concerned in terms of gold, tends to lower the gold prices of manufactured goods. . . .

But that is quite a different thing from lowering the price level. For the fall in manufacturing costs results in a greater demand for manufactured goods, and therefore the derivative demand for primary products is increased. While the prices of finished goods fall, the prices of primary products rise. Whether the price level as a whole would rise or fall it is not possible to say a priori, but the tendency is toward correcting the disparity between the price levels of finished products and primary products. That is a step towards equilibrium. And there is on the whole an increase of productive activity. The competition of the country which depreciates its currency will result in some reduction of output from the manufacturing industry of other countries. But this reduction will be less than the increase in the country’s output, for if there were no net increase in the world’s output there would be no fall of prices.

In consequence of the competitive advantage gained by a country’s manufacturers from a depreciation of its currency, any such depreciation is only too likely to meet with recriminations and even retaliation from its competitors. . . . Fears are even expressed that if one country starts depreciation, and others follow suit, there may result “a competitive depreciation” to which no end can be seen.

This competitive depreciation is an entirely imaginary danger. The benefit that a country derives from the depreciation of its currency is in the rise of its price level relative to its wage level, and does not depend on its competitive advantage. If other countries depreciate their currencies, its competitive advantage is destroyed, but the advantage of the price level remains both to it and to them. They in turn may carry the depreciation further, and gain a competitive advantage. But this race in depreciation reaches a natural limit when the fall in wages and in the prices of manufactured goods in terms of gold has gone so far in all the countries concerned as to regain the normal relation with the prices of primary products. When that occurs, the depression is over, and industry is everywhere remunerative and fully employed. Any countries that lag behind in the race will suffer from unemployment in their manufacturing industry. But the remedy lies in their own hands; all they have to do is to depreciate their currencies to the extent necessary to make the price level remunerative to their industry. Their tardiness does not benefit their competitors, once these latter are employed up to capacity. Indeed, if the countries that hang back are an important part of the world’s economic system, the result must be to leave the disparity of price levels partly uncorrected, with undesirable consequences to everybody. . . .

The picture of an endless competition in currency depreciation is completely misleading. The race of depreciation is towards a definite goal; it is a competitive return to equilibrium. The situation is like that of a fishing fleet threatened with a storm; no harm is done if their return to a harbor of refuge is “competitive.” Let them race; the sooner they get there the better. (pp. 154-57)

So yes, Greg, competitive devaluation is a free lunch. Bring it on.

Am I Being Unfair to the Gold Standard?

Published February 12, 2012 Cassel , gold standard , Hawtrey , Hayek , monetary policy , monetary theory 38 Comments

Kurt Schuler takes me (among others) to task in a thoughtful post on the Free-Banking blog for being too harsh in my criticisms of the gold standard, in particular in blaming the gold standard for the Great Depression, when it was really the misguided policies of central banks that were at fault.

Well, I must say that Kurt is a persuasive guy, and he makes a strong case for the gold standard. And, you know, the gold standard really wasn’t fatally flawed, and if the central banks at the time had followed better policies, the gold standard might not have imploded in the way that it did in the early 1930s. So, I have to admit that Kurt is right; the Great Depression was not the inevitable result of the gold standard. If the world’s central banks had not acted so unwisely – in other words, if they had followed the advice of Hawtrey and Cassel about limiting the monetary demand for gold — if the Bank of France had not gone insane, if Benjamin Strong, Governor of the New York Federal Reserve Bank, then the de facto policy-making head of the entire Federal Reserve System, had not taken ill in 1928 and been replaced by the ineffectual George L. Harrison, the Great Depression might very well have been avoided.

So was I being unfair to the gold standard? OK, yes, I admit it, I was being unfair. Gold standard, you really weren’t as bad as I said you were. The Great Depression was really not all your fault. There, I’m sorry if I hurt your feelings. But, do I want to see you restored? No way! At least not while the people backing you are precisely those who, like Hayek, in his 1932 lament for the gold standard defending the insane Bank of France against accusations that it caused the Great Depression, hold Hawtrey and Cassel responsible for the policies that caused the Great Depression. If those are the ideas motivating your backers to want to restore you as a monetary standard, I find the prospect of your restoration pretty scary — as in terrifying.

Now, Kurt suggests that people Ron Paul are not so scary, because all Ron Paul means when he says he wants to restore the gold standard is that the Federal Reserve System be abolished. With no central bank, it will be left up to the market to determine what will serve as money. Here is how Kurt describes what would happen.

If people want the standard to be gold, that’s what free banks will offer to attract their business. But if people want the standard to be silver, copper, a commodity basket, seashells, or cellphone minutes, that’s what free banks will offer. Or if they want several standards side by side, the way that multiple computer operating systems exist side by side, appealing to different niches, that’s what free banks will offer. A pure free banking system would also give people the opportunity to change standards at any time. Historically, though, many free banking systems have used the gold standard, and it is quite possible that gold would re-emerge against other competitors as the generally preferred standard.

Now that’s pretty scary – as in terrifying – too. As I suggested in arecent post, the reason that people in some places, like London, for instance, seem to agree readily on what constitutes money, even without the operation of legal tender laws, is that there are huge advantages to standardization. Economists call these advantages network effects, or network externalities. The demand to use a certain currency increases as other people use it, just as the demand to use a computer operating system or a web browser increases as the number of people already using it increases. Abolishing the dollar as we know it, which is what Kurt’s scenario sounds like to me, would annihilate the huge network effects associated with using the dollar, thereby forcing us to go through an uncertain process of indefinite length to recapture those network effects without knowing how or where the process would end up. If we did actually embark on such a process, there is indeed some chance, perhaps a good chance, that it would lead in the end to a gold standard.

Would a gold standard associated with a system of free banking — without the disruptive interference of central banks — work well? There are strong reasons to doubt that it would. For starters, we have no way of knowing what the demand of such banks to hold gold reserves would be. We also have no way of knowing what would happen to the gold holdings of the US government if the Federal Reserve were abolished. Would the US continue to hold gold reserves if it went out of the money creation business? I have no idea. Thus, the future value of gold in a free-banking system is thus completely unpredictable. What we do know is that under a fractional reserve system, the demand for reserves by the banking system tends to be countercyclical, going up in recessions and going down in expansions. But what tends to cause recessions is an increase in the demand of the public to hold money. So the natural cyclical path of a free-banking system under a gold standard would be an increasing demand for money in recessions, associated with an increasing monetary demand for gold by banks as reserves, causing an increase in the value of gold and a fall in prices. Recessions are generally characterized by declining real interest rates produced by depressed profit expectations. Declining real interest rates increase the demand for an asset like gold under the gold standard with a fixed nominal value, so both the real and the monetary demand for gold would increase in recessions, causing recessions to be deflationary. Recessions with falling asset prices and rising unemployment and, very likely, an increasing number of non-performing loans would impair the profitability and liquidity of banks, perhaps threatening the solvency of at least some banks as well, thereby inducing holders of bank notes and bank deposits to try to shift from holding bank notes and bank deposits to holding gold.

A free-banking system based on a gold standard is thus likely to be subject to a shift in demand from holding bank money to holding gold, when it is least able to accommodate such a shift, making a free-banking system based on a gold standard potentially vulnerable to a the sort of vicious deflationary cycle that characterized the Great Depression. The only way out of such a cycle would be to suspend convertibility. Such suspensions might or might not be tolerated, but it is not at all clear whether or how a mechanism to trigger such a suspension could be created. Insofar as such suspensions were expected, the mere anticipation of a liquidity problem might be sufficient to trigger a shift in demand away from holding bank money toward holding gold, thereby forcing a suspension of convertibility. Chronic suspensions of convertibility would tend to undermine convertibility.

In short, there is a really serious problem inherent in any banking system in which the standard is itself a medium of exchange. The very fact that gold is money means that, in any fractional reserve system based on gold, there is an inherent tendency for the system to implode when there is a loss of confidence in bank money that causes a shift in demand from bank money to gold. In principle, what would be most desirable is a system in which the monetary standard is not itself money. Alternatively, the monetary standard could be an asset whose supply may be increased without limit to meet an increase in demand, an asset like, you guessed it, Federal Reserve notes and reserves. But that very defect is precisely what makes the Ron Pauls of this world think that the gold standard is such a wonderful idea. And that is a scary — as in terrifying — thought.

Ludwig von Mises and the Great Depression

Published February 10, 2012 Cassel , gold standard , Hawtrey , Hayek , monetary history , monetary theory 54 Comments

Many thanks to gliberty who just flagged for me a piece by Mark Spitznagel in today’s (where else?) Wall Street Journal about how Ludwig von Mises, alone among the economists of his day, foresaw the coming of the Great Depression, refusing the offer of a high executive position at the Kredit-Anstalt, Austria’s most important bank, in the summer of 1929, because, as he put it to his fiancée (whom he did not marry till 1938 just before escaping the Nazis), “a great crash is coming, and I don’t want my name in any way connected with it.” Just how going to work for the Kredit Anstalt would have led to Mises’s name being associated with the crash (the result, in Mises’s view, of the inflationary policy of the US Federal Reserve) is left unclear. But it’s such a nice story.

Ludwig von Mises was an extremely well-read and diligent economist, who had some extraordinary insights into economics and business and politics. As a result he made some important contributions to economics, most important the discovery that idea of a fully centrally planned economy is not just an impossibility, it is incoherent. He made other contributions to economics as well, but that insight, perhaps also perceived by Max Weber, was first spelled out and explained by Mises in his book Socialism. That contribution alone is enough to ensure Mises an honorable place in the history of economic thought.

Mises also perceived how the monetary theory of Knut Wicksell, based on a distinction between a market and a natural rate of interest, could be combined with the Austrian theory of capital, developed by his teacher Eugen von Bohm-Bawerk into a theory of business cycles. Von Mises is therefore justly credited with being the father of Austrian business-cycle theory. His own development of the theory was somewhat sketchy, and it was his student F. A. Hayek, who made the great intellectual effort of trying to work out the detailed steps in the argument by which monetary expansion would alter the structure of capital and production, leading to a crisis when the monetary expansion was halted or reversed.

Relying on their newly developed theory of business cycles, Mises and Hayek warned in the late 1920s that the decision of the Federal Reserve to reduce interest rates in 1927, when it appeared that the US economy could be heading into a recession, would distort the structure of production and lead eventually to an even worse downturn than the one the Fed avoided in 1927. That was the basis for Mises’s “prediction” of a “crash” ahead of the Great Depression.

Of course, as I have pointed out previously, Mises and Hayek were not the only ones to have predicted that there could be a downturn. R.G. Hawtrey and Gustav Cassel had been warning about that danger since 1919, should an international return to the gold standard not be managed properly, failing to prevent a rapid deflationary increase in the international monetary demand for gold. When the insane Bank of France began accumulating gold at a breathtaking rate in 1928, and the US reversed its monetary stance in late 1928 and itself began accumulating gold, Hawtrey and Cassel recognized the potential for disaster and warned of the disastrous consequences of the change in Federal Reserve policy.

So Mises and Hayek were not alone in their prediction of a crash; Hawtrey and Cassel were also warning of a looming disaster, and were doing so on the basis of a theory that was both more obvious and more relevant to the situation than theory with which Mises and Hayek were working, a theory that, even giving it the benefit of every doubt, could not possibly have predicted a downturn even remotely approaching the severity of the 1929-31 downturn. Indeed, as I have also pointed out, the irrelevance of the Mises and Hayek “explanation” of the Great Depression is perfectly illustrated by Hayek’s 1932 defense of the insane Bank of France, showing a complete misunderstanding of the international adjustment mechanism and the disastrous consequences of the gold accumulation policy of the insane Bank of France.

Mr. Spitznagel laments that the economics profession somehow ignored Ludwig von Mises. Actually, they didn’t. Some of the greatest economists of the twentieth century were lapsed believers in the Austrian business-cycle theory. A partial list would include, Mises’s own students, Gottfried Haberler and Fritz Machlup; it would include Hayek’s dear friend and colleague, Lionel Robbins who wrote a book on the Great Depression eloquently explaining it in terms of the Austrian theory in a way that even Mises might have approved, a book that Robbins later repudiated and refused to allow to be reprinted in his lifetime (but you can order a new edition here); it would include Hayek’s students, Nobel Laureate J.R. Hicks, Nicholas Kaldor, Abba Lerner, G.L.S. Shackle, and Ludwig Lachmann (who sought a third way incorporating elements of Keynesian and Austrian theory). Hayek himself modified his early views in important ways and admitted that he had given bad policy advice in the 1930s. The only holdout was Mises himself, joined in later years after his arrival in America by a group of more doctrinaire (with at least one notable exception) disciples than Mises had found in Vienna in the 1920s and 1930s. The notion that Austrian theory was ignored by the economics profession and has only lately been rediscovered is just the sort of revisionist history that one tends to find on a lot of wacko Austro-libertarian websites like Lewrockwell.org. Apparently the Wall Street Journal editorial page is providing another, marginally more respectable, venue for such nonsense. Rupert, you’re doing a heckuva job.

John Kay Puts Legal Tender in its Place

Published February 8, 2012 monetary theory 12 Comments

In today’s Financial Times, the always interesting John Kay discusses how it is that Scottish banknotes are accepted as payment for goods and services in London even though, unlike Bank of England notes, the Scottish banknotes are not legal tender in England. And in fitting reciprocity, Bank of England notes are not legal tender in Scotland, but will serve you just as well in Edinburgh as they would in London. Legal tender laws, Kay concludes, are meaningless and irrelevant. What matters, he argues, is convention. When people agree (formally, or, more often, informally by habit and custom) to accept something as money, it is money; when they don’t, it’s not. And legal tender has nothing to do with it. He concludes:

I tip in restaurants or cabs, but not post offices or doctors’ surgeries. Often there is some underlying reason for these practices, although I cannot think of one that applies to the custom of tie-wearing. But in any event it is custom, not reason, that leads me to do it. The Scottish pound is accepted where it is accepted, and not where it is not. There is really no more to it than that.

That paradoxical, and mildly nihilistic, conclusion is, in my view, not quite right. But it contains an important kernel of truth that disposes of the metaphysical delusions of the gold bugs that anything other than gold is not REAL money, and that the only thing that keeps gold from being universally recognized as the one and only true money is the existence of blasphemous legal tender laws. For more on the paradoxical nature of money, see this post from last July.

Krugman on Mistaken Identities

Published January 31, 2012 monetary theory , Uncategorized 75 Comments

Last week I wrote a series of posts (starting with this and ending with this) that were mainly motivated by a single objective: to show how taking the accounting identity between savings and investment seriously can get someone, even a very fine economist, into serious trouble. That, I suggested, is what happened to Scott Sumner when, in a post about whether a temporary increase in government spending and taxes would increase GDP, he relied on the accounting identity between savings and investment to conclude that a reduction in savings necessarily leads to a reduction in investment. Trying to trace Scott’s mistake to misuse of an accounting identity led me a little further than I anticipated into the substance of the argument about how a temporary increase in government spending and taxes affects GDP, an argument that I am still not quite satisfied with, but which – you can relax — I am not going to discuss in this post. My aim in this post is merely to respond to one of Scott’s rejoinders to me, which is that he was just relying on a proposition – the identity of savings and investment – that is taught in just about every macro textbook, including textbooks by Paul Krugman and Greg Mankiw, two of the current heavyweights of the profession. If so, Scott observed, my argument is not really with him, but with the entire profession.

No doubt about it, Scott has a point, though I think that most textbooks and most economists have an intuitive understanding that the accounting identity is basically a fudge, and therefore, unlike Scott, generally do not rely on it for any substantive conclusions. The way that most textbooks try to handle the identity is to say that the identity really just refers to realized (ex post) saving and investment which must be equal, while planned (ex ante) investment and planned (ex ante) saving may not be equal, with the difference between planned investment and planned saving corresponding to unplanned investment (accumulation) of inventories. Equilibrium is determined by the equality of planned investment and planned saving, and any disequilibrium (corresponding to a divergence between planned saving and planned investment) is reflected in unplanned inventory accumulation (either positive or negative) which ensures that the identity between realized investment and realized saving is always satisfied. The usual fudge distinguishing between planned and realized investment and saving and postulating that unplanned inventory investment is what accounts for any difference between planned investment and saving is itself problematic, but it at least puts one on notice that there is a difference between an equilibrium condition and an accounting identity, while nevertheless erroneously suggesting that the accounting identity has some economic significance.

Not entirely coincidentally, Scott having got started on this topic by responding to a post by Paul Krugman, Krugman himself weighed in on the subject of accounting identities last week, enthusiastically citing a post by Noah Smith warning about the misuse of accounting identities in arguments about economics. Now the truth is that there is not too much in Krugman’s post that I disagree with, but there are certain verbal slips or misstatements that betray the confusion between accounting identities and equilibrium conditions that I am trying to get people to recognize and to stay away from. While avoiding any substantive error, Krugman perpetuates the confusion, thus contributing unwittingly to the very problem that motivated his post. Thus, his confusion is not just annoying to compulsive grammarians like me; it is also unnecessary and easily avoidable, and creates the potential for more serious mistakes by the unwary. So there is really no excuse for continuing to pay lip service to the supposed identity between savings and investment, regardless of how deeply entrenched it has become as the result of many decades of unthinking, rote repetition on the part of textbook writers.

Here’s Krugman:

Via Mark Thoma, Noah Smith has a terrific piece on how to argue with economists. All the points are good, but I’d like to focus on Principle 4, “Argument by accounting identity almost never works.”

What he’s referring to, I assume, is arguments like “since savings equals investment, fiscal stimulus can’t affect overall spending”, or “since the current account balance is equal to the difference between domestic saving and domestic investment, exchange rates can’t affect trade”. The first argument is, more or less, Say’s Law and/or the Treasury view. The second argument is what John Williamson called the doctrine of immaculate transfer.

This is pretty straightforward, though I don’t care for the examples that Krugman gives, displaying a conventional misunderstanding of Say’s Law. But Say’s Law is a whole topic unto itself. Nor can the Treasury view be dismissed as nothing more than the misapplication of an accounting identity. So I’m just going to ignore those two specific examples for purposes of this discussion. Back to Krugman.

Why are such arguments so misleading? Noah doesn’t fully explain, so let me put in a further word. As I see it, economic explanations pretty much always have to involve micromotives and macrobehavior (the title of a book by Tom Schelling). That is, when we tell economic stories, they normally involve describing how the actions of individuals, driven by individual motives (and maybe, though not necessarily, by rational self-interest), add up to interesting behavior at the aggregate level.

Again, nothing to argue with there, though the verb “add up” has just faintest whiff of an identity insinuating itself into the discussion.

And the key point is that individuals in general [as opposed to those strange creatures called economists who do care about “aggregate accounting identities?] neither know nor care about aggregate accounting identities.

Ok, now we are starting to have a problem. Individuals in general neither know nor care about aggregate accounting identities. Does that mean that those strange creatures called economist should know or care about aggregate accounting identities? I have yet to hear any cogent reason why they should.

Take the doctrine of immaculate transfer: if you want to claim that a rise in savings translates directly into a fall in the trade deficit, without any depreciation of the currency, you have to tell me how that rise in savings induces domestic consumers to buy fewer foreign goods, or foreign consumers to buy more domestic goods. Don’t tell me about how the identity must hold, tell me about the mechanism that induces the individual decisions that make it hold.

Here is where Krugman, after skating on the edge, finally slips up and begins to talk nonsense — very subtle nonsense, but nonsense nonetheless. What does it mean to say that an identity must hold? It means that, by the very meaning of the terms that one is using, the identity of which one is speaking must be true. It is inconceivable that an identity would not hold. If the difference between investment and savings (in an open economy) is defined to be identitically equal to the trade deficit, then talking about a mechanism that induces individual decisions to make it hold makes as much sense as saying that there must be a mechanism that induces individual decisions to make 2 + 2 equal 4. If, by the very meaning of the terms that I am using, the difference between investment and savings must equal the trade deficit (which, to repeat, is what it means to say that there is an identity between those magnitudes) there is no conceivable set of circumstances in which the two magnitudes would not be equal. If, in the very nature of things, two magnitudes could never possibly be different, it is nonsense to say that there is a mechanism of any kind (much less one describable in terms of the decisions of individual human beings) that operates to bring it about that the equality actually holds.

And once you do that, you realize that something else has to be happening — a slump in the economy, a depreciation of the real exchange rate, it depends on the circumstances, but it can’t be immaculate, with nothing moving to enforce the identity.

No, no! A thousand times no! If we are really talking about an identity, nothing has to be happening to enforce the identity. Identities don’t have to be enforced. Something that could not conceivably be otherwise requires nothing to prevent the inconceivable from happening.

When it comes to confusions about the macro implications of S=I, again the question is how the identity gets reflected in individual motives — is it via the interest rate, via changes in GDP, or what?

There are no macro implications of an identity; an identity has no empirical implications of any kind — period, full stop. If S necessarily equals I, because they have been defined in such a way that they could not possibly be unequal, then there is no conceivable state of the world in which they are unequal. Obviously, if S and I are equal in every conceivable state of the world, the necessary identity between them cannot rule out any conceivable state of the world. That means that the identity between S and I has no empirical implications. It says nothing about what can or cannot be observed in the real world at either the micro or the macro level.

Accounting identities are important; in fact, they’re the law. But they should inform your stories about how people behave, not act as a substitute for behavioral analysis.

I don’t know what law Krugman is referring to, but usually laws of nature tell us that some conceivable observations are not possible. Accounting identities don’t tell us anything of the sort. They are merely express certain conventional meanings that we are assigning to specific terms that we are using. How an accounting identity that could not be inconsistent with any conceivable state of the world can inform anything is a mystery, but I heartily agree that an accounting identity cannot be “a substitute for behavioral analysis.”

I have been rather (perhaps overly) harsh in my criticism on Krugman, but not to show that I am smarter than he is, which I certainly am not, but to show how easily habitual ways of speaking about macro lead to (easily rectifiable) nonsense statements. The problem is not any real misunderstanding on his part. Indeed, I would be surprised if, should he ever read this, he did not immediately realize that he had been expressing himself sloppily. The point is that macroeconomists have gotten into a lot of bad habits in describing their models and in failing to distinguish properly between accounting identities, which are theoretically unimportant, and equilibrium conditions, which are essential. Everything that Krugman said would have made sense if he had properly distinguished between accounting identities and equilibrium conditions rather than mix them up as he did, and as textbooks have been doing for three generations.

Savings and investment are equal in equilibrium, because that equality is a necessary and sufficient condition for the existence of an equilibrium. If so, being out of equilibrium means that savings and investment are not equal. So if we think that a real economy is ever out of equilibrium, one way to test for the existence of disequilibrium would be to see if actual savings and actual investment are unequal, notwithstanding the presumed accounting identity between savings and investment. That accounting identity is a product of the special definitions assigned to savings and investment by national income accounting practices, not by the meaning that our theory of national income assigns to those terms.

PS I will once again mention (having done so in previous posts on accounting identities) that all the essential points I am making in this post are derived from the really outstanding and unfortunately not very widely known paper by Richard G. Lipsey, “The Foundations of the Theory of National Income” originally published in Essays in Honour of Lord Robbins and reprinted in Macroeconomic Theory and Policy: Selected Essays of Richard G. Lipsey.

Let’s Try Again

Published January 25, 2012 monetary theory 24 Comments

The point is to keep trying until you get it right. I am sorry to say that I got it wrong last time, so I’m taking another shot at it.

Let’s consider, as does Simon Wren-Lewis a two-period model. The first period is in underemployment equilibrium. Let’s say that consumption in period 1 is given by the equation

C0 = 100 + bY0,

where b represents the marginal propensity to consume out of income.

Let’s say that investment is a fixed amount:

I0 = 100.

The expenditure (aggregate demand) equation is thus

E0 = 200 + bY0.

The equilibrium is determined by applying the equilibrium condition E0 = Y0, which gives us

Y0 = 200/(1-b).

Now the case that I posited in my previous post involved b = 0, reflecting income smoothing. This is tricky, because we have to make an assumption about what households expect their income to be in the next period, which can be assumed to be long relative to the initial period, though for simplicity I’m going to let the two periods be equal in length. If households expect income in the next period to reflect full employment, presumably they would try to increase their consumption now, spending more and increasing equilibrium income now, so there is an inherent inconsistency in the model which needs to be resolved, but I am not going to worry about that either. Let’s just take the model at face value.

In this equilibrium, note that consumption, C0, is 100, investment, I0, is 100, and saving, S0, is also 100.

What happens if the government immediately tries to intervene to raise income by increasing government spending, G0, from 0 to 100, and imposes taxes, T0, of 100 to finance its spending? The increased spending is only for this period and the taxation is only for this period, not the next one; in period 1, government spending and taxation go back to zero. What this does is to cause the consumption function to be revised as households choose a uniform level of consumption to be maintained for both periods, reflecting the liability to pay taxes this period, but no obligation to pay taxes next period.

Expecting income next period of 200, households would have chosen to consume 100 this period and 100 next period. But with a tax liability of 100 this period, households will choose, instead of consuming zero this period and 100 next period, to consume 50 this period and 50 next period. They have to borrow 50 this period to be able to pay their tax liability in order to have 50 left over for consumption. Next period, they will have to repay the loan of 50, and will have only 50 left over for consumption (income remaining at 200 with consumption equal to 50 and investment equal to 50, the loan repayment of 50 corresponding, it seems to me, to exports to shipped to foreigners). So the new consumption equation is

C’0 = 50 + bY0, where b is again equal to 0.

Now adding government spending and taxes, we have G = 100 and T = 100, so our new expenditure equation becomes

E’0 = 250 + b(Y’0 – 100).

But since b = 0, this reduces to

E’0 = 250 = Y’0.

We still have I0 = S0 = 100. Since b = MPC = 0, (1-b) = MPS = 1. The increase in income from 200 to 250 is just enough to generate another 50 in savings to offset the 50 in borrowing required to keep consumption level at 50 in period 0 and period 1.

The increase in government spending and taxes of 100 in period 0 raises the period-0 equilibrium (as compared with the case with no government spending and taxes) is 50, so the multiplier is .5.

Of course, this is not a full-equilibrium solution. A full equilibrium should have Y1 also equal to 250 instead of 200, which means that consumption could have been increased by 25 in both periods, but I haven’t worked that solution out yet.

The reason why in this post I arrive at a result different from the result in my previous post is that I made a simple flunk-the-quiz mistake in the previous post, reducing the expenditure curve by 100 to reflect the reduction in disposable income from taxes as if it were a permanent reduction in disposable income rather than a one-period reduction in disposable income. So instead of assuming the MPC was 0 as I wanted to do, I was assuming, for purposes of the effect of taxes on consumption, an MPC of 1. Yikes! My assertion that everything depended on a positive MPC was entirely wrong. In a simple Keynesian model, you get a balanced-budget multiplier of 1 provided that the MPC is less than 1. That was a pretty bad blunder on my part, and I apologize. Scott, himself, seemed to perceive that something was amiss in a comment on the previous post, so I hope that we are now converging toward a solution.

Again my apologies for hastily posting my previous post without checking my work more carefully. I had better get some rest now.

Time to Move On – But Not Before I Explain (Definitively) What it all Means

Published January 24, 2012 monetary theory 20 Comments

Update: Continue reading, but then go to my next post to find out how it all turns out in the end.

Signs of fatigue are clearly evident and multiplying rapidly, so we had all better figure out and start executing our exit strategies from this convoluted, and at times acrimonious, debate about consumption smoothing. Things got started (two whole weeks ago!) when Simon Wren-Lewis picked on Robert Lucas for the following statement:

But, if we do build the bridge by taking tax money away from somebody else, and using that to pay the bridge builder — the guys who work on the bridge — then it’s just a wash. It has no first-starter effect. There’s no reason to expect any stimulation. And, in some sense, there’s nothing to apply a multiplier to. (Laughs.) You apply a multiplier to the bridge builders, then you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge.

and on John Cochrane for this statement:

Before we spend a trillion dollars or so, it’s important to understand how it’s supposed to work. Spending supported by taxes pretty obviously won’t work: If the government taxes A by $1 and gives the money to B, B can spend $1 more. But A spends $1 less and we are not collectively any better off.

Wren-Lewis made the following accusation:

Imagine a Nobel Prize winner in physics, who in public debate makes elementary errors that would embarrass a good undergraduate. Now imagine other academic colleagues, from one of the best faculties in the world, making the same errors. It could not happen. However that is exactly what has happened in macro over the last few years.

Paul Krugman followed up with a blast of his own at both Cochrane and Lucas, and John Cochrane weighed in, defending himself and Lucas. The battles among the principals were accompanied by various interventions on either (or neither) side by Brad DeLong, Scott Sumner, Nick Rowe, Karl Smith (to name just a few) and by responses and rejoinders by Cochrane, Wren-Lewis and Krugman. I got involved mainly because I was upset that my friend Scott Sumner seemed to be making arguments invoking accounting identities in ways that I thought were illegitimate and even nonsensical. Scott, though apparently intervening on the side of Lucas and Cochrane, denied that he was supporting their substantive position, a denial that I, though apparently intervening on the side of Wren-Lewis and Krugman, also made.

I am not going to repeat my previous arguments against Scott, which mostly involved denials that any useful implication can be inferred from an accounting identity. I will merely reiterate that I hate – despise — all accounting identities, and deny that they can ever have any substantive implications about anything, serving only one function, namely, to force us to obey the laws of arithmetic. OK, I got that out of my system, and now I feel well enough to go on.

The key passage that we have all been arguing was this one from Wren-Lewis’s original post:

Both make the same simple error. If you spend X at time t to build a bridge, aggregate demand increases by X at time t. If you raise taxes by X at time t, consumers will smooth this effect over time, so their spending at time t will fall by much less than X. Put the two together and aggregate demand rises.

But surely very clever people cannot make simple errors of this kind? Perhaps there is some way to re-interpret such statements so that they make sense. They would make sense, for example, if the extra government spending was permanent. The only trouble is that both statements were made about a temporary fiscal stimulus package.

My next step is a bit tricky because I am going to have to refer to Scott’s criticism of Wren-Lewis, which, I must admit, I still do not fully understand. But the gist of at least part of what Scott was trying to say — and he, as well as Karl Smith, has repeated it in responding to me several times — is that Wren-Lewis was trying to force Lucas and Cochrane to accept the validity of the Keynesian model, when they simply don’t accept the model. My basic response to that has been that you can’t have a discussion about the effects of a policy unless you have some (at least implicit) model from which you are deriving your conclusions. It is not enough to invoke an accounting identity from which no conclusions (as Scott agrees) can be deduced. My first attempt to specify some model from which we could deduce the position adopted by Lucas and Cochrane was not too successful. I suggested that what they had in mind was some sort of crowding-out effect, the increase in government spending and taxes causing private investment to fall. I then combined this effect with a consumption-smoothing effect to produce a small short-term increase in Y as a result of building the bridge. This was unsatisfactory, because it was ad hoc, and because, as commenter John Hall pointed out, the change in consumption ought to (and could) have been derived rather than just assumed as I had done.

But I realized when responding to Scott’s comment on my previous post, that there is a simple way to reconcile what Lucas and Cochrane are saying with the basic Keynesian model, which, after all, is just a tool of analysis compatible with a variety of substantive assertions about the real world. So it is not correct to say that it is an unfair imposition on Lucas and Cochrane to require their position to be expressed in terms of a Keynesian model that they obviously reject. The Keynesian model is pretty flexible, and, by appropriate assumptions, you can get almost any substantive implication you want. So how does one interpret Lucas and Cochrane? Simple. They believe that households are rational maximizers basin their consumption decisions on their expected future income stream and expected future tax liabilities. They therefore engage in consumption smoothing, so that current consumption is fixed and independent of variations in current income, such variations being capitalized into their expected future income streams. Thus, the MPC out of current income in such a model is 0.

In terms of the Keynesian cross, you have an aggregate expenditure line that is horizontal (reflecting a 0 MPC). The multiplier with respect to a change in autonomous expenditure is one. However, since all government spending must be financed eventually by taxes, Ricardian equivalence implies that the increase in G is offset by an equal reduction in C, reflecting the effect on consumption of expected future taxes. That is precisely what Lucas and Cochrane were saying in the quotations above. Wren-Lewis, in his criticism, accepted that position. His point was that if the increase in government spending is temporary, the increase in government spending in the current period will rise by more than the fall in consumption this period due to the effect of expected future taxes (or borrowing this period to pay part of the current tax bill). This is not necessarily the end of the story (though, with a bit of luck, perhaps it will be), but this is the framework within which the argument must be carried out. It has nothing to do with accounting identities.

PS By the way Nick Rowe apparently had this all figured out almost two weeks ago. He could have saved us all this agony. But the truth is we loved every minute of it.

Advice to Scott: Avoid Accounting Identities at ALL Costs

Published January 22, 2012 Keynes , monetary theory 33 Comments

It must have been a good feeling when Scott Sumner saw Karl Smith’s blog post last Thursday announcing that he had proved that Scott was right in asserting that Simon Wren-Lewis had committed a logical blunder in his demonstration that Robert Lucas and John Cochrane made a logical blunder in denying, on the basis of Ricardian equivalence, that government spending to build a bridge would be stimulative. I don’t begrudge Scott such innocent pleasures, and I feel slightly guilty for depriving him of that good feeling, but, you know the old saying: a blogger’s gotta do what a blogger’s gotta do. For any new readers who haven’t been following this twisted tale of claim and counterclaim, charge and countercharge, response and rejoinder, see my three previous posts (here, here, and here, and the far from comprehensive array of links in them to other posts on the topic).

My main problem with Scott’s argument against Wren-Lewis was that, at a crucial stage in his argument, he relied on the national income accounts identity that savings equals investment. Now in the General Theory, Keynes himself also asserted that savings and investment were identically equal and made a rather strange argument that the identity between savings and investment had a deep economic significance because there had to be an economic mechanism operating to ensure the ultimate satisfaction of the identity. That was a nonsense statement by Keynes, as pointed out by Robertson, Haberler, Hawtrey, Lutz and others, because if two magnitudes are identically equal, there is no possible state of the world in which the two magnitudes would not be equal, so there obviously is no mechanism required (or possible) to ensure equality between the magnitudes. The equality is simply a consequence of how we have defined the terms we are using, not a statement about what can or cannot happen in the world. The nonsense statement by Keynes did not invalidate his theory, it merely meant that Keynes was confused about how to interpret his theory.

I cannot resist observing that this is just one example of many showing that the notion that the original intent of the Framers of the Constitution has any special authority in Constitutional interpretation and adjudication is totally wrong, based on the misconception that the original inventor, discoverer, or articulator of a concept has any power to control its meaning and interpretation. Keynes, let us posit, invented the income-expenditure theory. But his understanding of the savings-equals-investment equilibrium condition of the theory was obviously wrong and defective. The Framers of the Constitution may have invented or may have first articulated any number of concepts mentioned in the Constitution, e.g., the prohibition against cruel and unusual punishment, due process of law, the right to bear arms, equal protection. That they invented or articulated those terms first does not give the Framers ownership over the meaning of those terms in the sense that their understanding of the meaning of those terms cannot establish an immutable understanding of what the terms mean any more than Keynes could impose the notion that savings is identically equal to investment simply because he provided the first articulation of a model that hinged on the equality of savings and investment. Sorry for that digression, but I just couldn’t help myself.

Now back to Scott. Based on the presumed identity between savings and investment, Scott asserted that the reduction in savings by which households would seek to smooth their consumption in response to a temporary increase in taxes would necessarily imply a reduction in spending on capital goods (i.e., a reduction in investment). But savings and investment are not identical; their equality is a condition of equilibrium. If savings fall, there has to be an economic mechanism (perhaps, but not necessarily, the one posited by the Keynesian model) that restores equality between saving and investment. The equality cannot be established by invoking an identity between savings and investment that is purely conventional and is the result of a special definition that ensures the equality of savings and investment in every conceivable state of the world, a definition that drains the identity of any and all empirical content.

Here’s what Karl Smith had to say on the subject on his blog:

Scott says

In a perfect world I’d lay out a concise logical proof that Simon Wren-Lewis and Paul Krugman are wrong. And number each point. They’d respond saying which of my points were wrong, and why. Then I’d reply. . . .

Perhaps I can help.

Wren-Lewis said:

DY = DC + DS + DT = DC + DS + DG Λ DG > 0 Λ -DC < DT ==> DY > 0

Karl’s notation is a bit cryptic. This is how I understand it:

DY = change in Y (income)

DC = change in C (consumption)

DS = change in S (saving)

DT= change in T (taxes)

DG = change in G (government spending)

The first equation says that a change in income can be decomposed into a change in consumption plus a change in savings plus a change in tax payments. This is derived from the definition of income in the income-expenditure model, namely that income is disposed of either by spending it on consumption, paying taxes or saving it. There is nothing else (in the model) that one can do with his income.

The next equation simply makes the substitution of G for T, which in the example under consideration were assumed to change by equal amounts.

The symbol “Λ” means something like “and furthermore,” so that we are supposed to assume that DG > 0, i.e., that government spending has increased. Then we are given another assumption, -DC < DT, which means that, because of consumption smoothing, the temporary increase in taxes is not financed entirely by a reduction in consumption, but partly by a reduction in consumption and partly by a reduction in savings, so that the reduction in consumption is less than the increase in taxes. This is Karl’s rendition of Simon Wren-Lewis’s argument that a temporary increase in taxes to finance the construction of a bridge would imply an increase in Y because G will increase by more than C falls. Karl continues:

Which is false.

Proof by example:

Let DG = DT = 2, DC = -1, and DS = –1

Here Karl is saying let us assume that G and T both increase by 2. That part is fine. The problem is what comes next. He assumes that to finance the increase in taxes, consumption goes down by 1 and savings goes down by 1. Why is that a problem? Because he is reasoning in terms of an accounting identity rather than in terms of an economic model. Wren-Lewis was making an argument in terms of the implications of the income-expenditure model which consists of (yes!) definitions, causal or empirical functions (consumption, investment, etc.) and an equilibrium condition. The change in income cannot be derived from a simple definition, it is derived from the solution of the model. The model has a solution. You can solve for Y by taking the initial conditions and the empirical functions and applying the equilibrium condition. You can also express the equilibrium value of Y in a single equation as a reduced form in terms of all the parameters and initial conditions. If you want to solve for DY in terms of a change in one of the other initial conditions, like G and T or consumption function, you have to do so in terms of the reduced-form equation for Y, not in terms of the definition of Y. Doing that leads to the nonsense result that, I am sorry to say, Karl arrives at below.

Then both inequalities are satisfied and by the first equation.

DY = –1 –1 + 2 = 0

Which is what we were required to show.

It’s a nonsense result, because his solution does not correspond to the equilibrium condition of the model, which is either savings equals investment or expenditure equals income. In Karl’s nonsense result, savings is not equal to investment (because investment has not changed while savings has fallen by 1) and expenditure is not equal to income (because DC + DG + DI > DC + DS + DT). This is just the ABCs of comparative-statics analysis.

Now in a subsequent post, Karl seems to have retracted his “proof,” admitting:

S = –1 is not allowed [because investment has not changed].

Karl actually has interesting things to say about how to think about the effects of an increase in government spending and taxes in terms of a neo-classical analysis which is worth reading and thinking about. But the point is that to make any statement about the consequences of a change in the initial conditions or parameters of a model, one must reason in terms of the equilibrium solution of the model, not in terms of the definitions within the model, and certainly not in accounting identities that are completely separate from the model.

Finally, just one comment about Lucas and Cochrane. As Karl points out in his more recent post, Lucas and Cochrane offered reasons for rejecting the stimulative effect of building a bridge that were themselves couched in the very terms of the Keynesian income-expenditure model that they were criticizing. Thus, Lucas offered as his explanation for why building the bridge would have no stimulative effect that the increase in spending associated with building the bridge would be offset by a reduction in consumption associated with the taxes needed to finance the bridge as if that were an obvious internal contradiction within the model. Karl suggests a better response that Lucas and Cochrane might have given, but their response was simply an attempt to show that there was some gap in the logic of the model. That is why they invited such a brutal counter-attack from the Keynesians.

PS Have a look as well at Brad DeLong who has a new post quoting Paul Krugman quoting Noah Smith on the dangers of accounting identities, and also quoting moi.

PPS Just to be clear, as Scott notes in a comment below, Noah did not mention Scott in his post.

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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

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