Archive for the 'multiplier' Category

Traffic Jams and Multipliers

Since my previous post which I closed by quoting the abstract of Brian Arthur’s paper “Complexity Economics: A Different Framework for Economic Thought,” I have been reading his paper and some of the papers he cites, especially Magda Fontana’s paper “The Santa Fe Perspective on Economics: Emerging Patterns in the Science of Complexity,” and Mark Blaug’s paper “The Formalist Revolution of the 1950s.” The papers bring together a number of themes that I have been emphasizing in previous posts on what I consider the misguided focus of modern macroeconomics on rational-expectations equilibrium as the organizing principle of macroeconomic theory. Among these themes are the importance of coordination failures in explaining macroeconomic fluctuations, the inappropriateness of the full general-equilibrium paradigm in macroeconomics, the mistaken transformation of microfoundations from a theoretical problem to be solved into an absolute methodological requirement to be insisted upon (almost exactly analogous to the absurd transformation of the mind-body problem into a dogmatic insistence that the mind is merely a figment of our own imagination), or, stated another way, a recognition that macrofoundations are just as necessary for economics as microfoundations.

Let me quote again from Arthur’s essay; this time a beautiful passage which captures the interdependence between the micro and macro perspectives

To look at the economy, or areas within the economy, from a complexity viewpoint then would mean asking how it evolves, and this means examining in detail how individual agents’ behaviors together form some outcome and how this might in turn alter their behavior as a result. Complexity in other words asks how individual behaviors might react to the pattern they together create, and how that pattern would alter itself as a result. This is often a difficult question; we are asking how a process is created from the purposed actions of multiple agents. And so economics early in its history took a simpler approach, one more amenable to mathematical analysis. It asked not how agents’ behaviors would react to the aggregate patterns these created, but what behaviors (actions, strategies, expectations) would be upheld by — would be consistent with — the aggregate patterns these caused. It asked in other words what patterns would call for no changes in microbehavior, and would therefore be in stasis, or equilibrium. (General equilibrium theory thus asked what prices and quantities of goods produced and consumed would be consistent with — would pose no incentives for change to — the overall pattern of prices and quantities in the economy’s markets. Classical game theory asked what strategies, moves, or allocations would be consistent with — would be the best course of action for an agent (under some criterion) — given the strategies, moves, allocations his rivals might choose. And rational expectations economics asked what expectations would be consistent with — would on average be validated by — the outcomes these expectations together created.)

This equilibrium shortcut was a natural way to examine patterns in the economy and render them open to mathematical analysis. It was an understandable — even proper — way to push economics forward. And it achieved a great deal. Its central construct, general equilibrium theory, is not just mathematically elegant; in modeling the economy it re-composes it in our minds, gives us a way to picture it, a way to comprehend the economy in its wholeness. This is extremely valuable, and the same can be said for other equilibrium modelings: of the theory of the firm, of international trade, of financial markets.

But there has been a price for this equilibrium finesse. Economists have objected to it — to the neoclassical construction it has brought about — on the grounds that it posits an idealized, rationalized world that distorts reality, one whose underlying assumptions are often chosen for analytical convenience. I share these objections. Like many economists, I admire the beauty of the neoclassical economy; but for me the construct is too pure, too brittle — too bled of reality. It lives in a Platonic world of order, stasis, knowableness, and perfection. Absent from it is the ambiguous, the messy, the real. (pp. 2-3)

Later in the essay, Arthur provides a simple example of a non-equilibrium complex process: traffic flow.

A typical model would acknowledge that at close separation from cars in front, cars lower their speed, and at wide separation they raise it. A given high density of traffic of N cars per mile would imply a certain average separation, and cars would slow or accelerate to a speed that corresponds. Trivially, an equilibrium speed emerges, and if we were restricting solutions to equilibrium that is all we would see. But in practice at high density, a nonequilibrium phenomenon occurs. Some car may slow down — its driver may lose concentration or get distracted — and this might cause cars behind to slow down. This immediately compresses the flow, which causes further slowing of the cars behind. The compression propagates backwards, traffic backs up, and a jam emerges. In due course the jam clears. But notice three things. The phenomenon’s onset is spontaneous; each instance of it is unique in time of appearance, length of propagation, and time of clearing. It is therefore not easily captured by closed-form solutions, but best studied by probabilistic or statistical methods. Second, the phenomenon is temporal, it emerges or happens within time, and cannot appear if we insist on equilibrium. And third, the phenomenon occurs neither at the micro-level (individual car level) nor at the macro-level (overall flow on the road) but at a level in between — the meso-level. (p. 9)

This simple example provides an excellent insight into why macroeconomic reasoning can be led badly astray by focusing on the purely equilibrium relationships characterizing what we now think of as microfounded models. In arguing against the Keynesian multiplier analysis supposedly justifying increased government spending as a countercyclical tool, Robert Barro wrote the following in an unfortunate Wall Street Journal op-ed piece, which I have previously commented on here and here.

Keynesian economics argues that incentives and other forces in regular economics are overwhelmed, at least in recessions, by effects involving “aggregate demand.” Recipients of food stamps use their transfers to consume more. Compared to this urge, the negative effects on consumption and investment by taxpayers are viewed as weaker in magnitude, particularly when the transfers are deficit-financed.

Thus, the aggregate demand for goods rises, and businesses respond by selling more goods and then by raising production and employment. The additional wage and profit income leads to further expansions of demand and, hence, to more production and employment. As per Mr. Vilsack, the administration believes that the cumulative effect is a multiplier around two.

If valid, this result would be truly miraculous. The recipients of food stamps get, say, $1 billion but they are not the only ones who benefit. Another $1 billion appears that can make the rest of society better off. Unlike the trade-off in regular economics, that extra $1 billion is the ultimate free lunch.

How can it be right? Where was the market failure that allowed the government to improve things just by borrowing money and giving it to people? Keynes, in his “General Theory” (1936), was not so good at explaining why this worked, and subsequent generations of Keynesian economists (including my own youthful efforts) have not been more successful.

In the disequilibrium environment of a recession, it is at least possible that injecting additional spending into the economy could produce effects that a similar injection of spending, under “normal” macro conditions, would not produce, just as somehow withdrawing a few cars from a congested road could increase the average speed of all the remaining cars on the road, by a much greater amount than would withdrawing a few cars from an uncongested road. In other words, microresponses may be sensitive to macroconditions.

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Barro and Krugman Yet Again on Regular Economics vs. Keynesian Economics

A lot of people have been getting all worked up about Paul Krugman’s acerbic takedown of Robert Barro for suggesting in a Wall Street Journal op-ed in 2011 that increased government spending would not stimulate the economy. Barro’s target was a claim by Agriculture Secretary Tom Vilsack that every additional dollar spent on food stamps would actually result in a net increase of $1.84 in total spending. This statement so annoyed Barro that, in a fit of pique, he wrote the following.

Keynesian economics argues that incentives and other forces in regular economics are overwhelmed, at least in recessions, by effects involving “aggregate demand.” Recipients of food stamps use their transfers to consume more. Compared to this urge, the negative effects on consumption and investment by taxpayers are viewed as weaker in magnitude, particularly when the transfers are deficit-financed.

Thus, the aggregate demand for goods rises, and businesses respond by selling more goods and then by raising production and employment. The additional wage and profit income leads to further expansions of demand and, hence, to more production and employment. As per Mr. Vilsack, the administration believes that the cumulative effect is a multiplier around two.

If valid, this result would be truly miraculous. The recipients of food stamps get, say, $1 billion but they are not the only ones who benefit. Another $1 billion appears that can make the rest of society better off. Unlike the trade-off in regular economics, that extra $1 billion is the ultimate free lunch.

How can it be right? Where was the market failure that allowed the government to improve things just by borrowing money and giving it to people? Keynes, in his “General Theory” (1936), was not so good at explaining why this worked, and subsequent generations of Keynesian economists (including my own youthful efforts) have not been more successful.

Sorry to brag, but it was actually none other than moi that (via Mark Thoma) brought this little gem to Krugman’s attention. In what is still my third most visited blog post, I expressed incredulity that Barro could ask where Is the market failure about a situation in which unemployment suddenly rises to more than double its pre-recession level. I also pointed out that Barro had himself previously acknowledged in a Wall Street Journal op-ed that monetary expansion could alleviate a cyclical increase in unemployment. If monetary policy (printing money on worthless pieces of paper) can miraculously reduce unemployment, why is out of the question that government spending could also reduce unemployment, especially when it is possible to view government spending as a means of transferring cash from people with unlimited demand for money to those unwilling to increase their holdings of cash? So, given Barro’s own explicit statement that monetary policy could be stimulative, it seemed odd for him to suggest, without clarification, that it would be a miracle if fiscal policy were effective.

Apparently, Krugman felt compelled to revisit this argument of Barro’s because of the recent controversy about extending unemployment insurance, an issue to which Barro made only passing reference in his 2011 piece. Krugman again ridiculed the idea that just because regular economics says that a policy will have adverse effects under “normal” conditions, the policy must be wrongheaded even in a recession.

But if you follow right-wing talk — by which I mean not Rush Limbaugh but the Wall Street Journal and famous economists like Robert Barro — you see the notion that aid to the unemployed can create jobs dismissed as self-evidently absurd. You think that you can reduce unemployment by paying people not to work? Hahahaha!

Quite aside from the fact that this ridicule is dead wrong, and has had a malign effect on policy, think about what it represents: it amounts to casually trashing one of the most important discoveries economists have ever made, one of my profession’s main claims to be useful to humanity.

Krugman was subsequently accused of bad faith in making this argument because he, like other Keynesians, has acknowledged that unemployment insurance tends to increase the unemployment rate. Therefore, his critics argue, it was hypocritical of Krugman to criticize Barro and the Wall Street Journal for making precisely the same argument that he himself has made. Well, you can perhaps accuse Krugman of being a bit artful in his argument by not acknowledging explicitly that a full policy assessment might in fact legitimately place some limit on UI benefits, but Krugman’s main point is obviously not to assert that “regular economics” is necessarily wrong, just that Barro and the Wall Street Journal are refusing to acknowledge that countercyclical policy of some type could ever, under any circumstances, be effective. Or, to put it another way, Krugman could (and did) easily agree that increasing UI will increases the natural rate of unemployment, but, in a recession, actual unemployment is above the natural rate, and UI can cause the actual rate to fall even as it causes the natural rate to rise.

Now Barro might respond that all he was really saying in his 2011 piece was that the existence of a government spending multiplier significantly greater than zero is not supported by the empirical evidenc. But there are two problems with that response. First, it would still not resolve the theoretical inconsistency in Barro’s argument that monetary policy does have magical properties in a recession with his position that fiscal policy has no such magical powers. Second, and perhaps less obviously, the empirical evidence on which Barro relies does not necessarily distinguish between periods of severe recession or depression and periods when the economy is close to full employment. If so, the empirical estimates of government spending multipliers are subject to the Lucas critique. Parameter estimates may not be stable over time, because those parameters may change depending on the cyclical phase of the economy. The multiplier at the trough of a deep business cycle may be much greater than the multiplier at close to full employment. The empirical estimates for the multiplier cited by Barro make no real allowance for different cyclical phases in estimating the multiplier.

PS Scott Sumner also comes away from reading Barro’s 2011 piece perplexed by what Barro is really saying and why, and does an excellent job of trying in vain to find some coherent conceptual framework within which to understand Barro. The problem is that there is none. That’s why Barro deserves the rough treatment he got from Krugman.

Keynes and Hawtrey: The Treatise on Money and Discovering the Multiplier

In my previous post on Keynes and Hawtrey, I tried to show the close resemblance between their upbringing and education and early careers. It becomes apparent that Keynes’s brilliance, and perhaps also his more distinguished family connections, had already enabled Keynes to begin overshadowing Hawtrey, four years his senior, as Keynes was approaching his thirties, and by 1919, when Hawtrey was turning 40, Keynes, having achieved something close to superstardom with the publication of The Econoomic Consequences of the Peace, had clearly eclipsed Hawtrey as a public figure, though as a pure monetary theoretician Hawtrey still had a claim to be the more influential of the two. For most of the 1920s, their relative standing did not change greatly, Hawtrey writing prolifically for economics journals as well as several volumes on monetary theory and a general treatise on economics, but without making much of an impression on broader public opinion, while Keynes, who continued to write primarily for a non-professional, though elite, audience, had the much higher public profile.

In the mid-1920s Keynes began writing his first systematic work on monetary theory and policy, the Treatise on Money. The extent to which Keynes communicated with Hawtrey about the Treatise in the five or six years during which he was working on it is unknown to me, but Keynes did send Hawtrey the proofs of the Treatise (totaling over 700 pages) in installments between April and July 1930. Hawtrey sent Keynes detailed comments, which Keynes later called “tremendously useful,” but, except for some minor points, Keynes could not incorporate most of the lengthy comments, criticisms or suggestions he received from Hawtrey before sending the final version of the Treatise to the publisher on September 14. Keynes did not mention Hawtrey in the preface to the Treatise, in which D. H. Robertson, R. F. Kahn, and H. D. Henderson were acknowledged for their assistance. Hawtrey would be mentioned along with Kahn, Joan Robinson, and Roy Harrod in the preface to the General Theory, but Hawtrey’s role in the preparation of the General Theory will be the subject of my next installment in this series. Hawtrey published his comments on the Treatise in his 1932 volume The Art of Central Banking.

Not long after the Treatise was published, and almost immediately subjected to critical reviews by Robertson and Hayek, among others, Keynes made it known that he was dissatisfied with the argument of the Treatise, and began work on what would eventually evolve into the General Theory. Hawtrey’s discussion was especially notable for two criticisms.  First Hawtrey explained that Keynes’s argument that an excess of investment over saving caused prices to rise was in fact a tautology entailed by Keynes’s definition of savings and investment.

[T]he fundamental equations disclose . . . that the price level is composed of two terms, one of which is cost per unit and the other is the difference between price and cost per unit.

Thus the difference between saving and investment is simply another name for the windfall gains or losses or for the difference between prices and costs of output. Throughout the Treatise Mr. Keynes adduces a divergence between saving and investment as the criterion of a departure from monetary equilibrium. But this criterion is nothing more or less than a divergence between prices and costs. Though the criterion ostensibly depends on two economic activities, “investment” and “saving,” it depends in reality not on them but on movements of the price level relative to costs.

That does not mean that the price level may not be influenced by changes in investment or in saving in some sense. But Mr. Keynes’s formula does not record such changes till their effect upon the price level is an accomplished fact. (p. 336)

Hawtrey’s other important criticism was his observation that Keynes assumed that a monetary disequilibrium would manifest itself exclusively in price changes and not at all in changes in output and employment. In fact this criticism followed naturally from Hawtrey’s criticism of Keynes’s definitions of savings and investment, from which the fundamental equations were derived, as not being grounded in the decisions of consumers and entrepreneurs.

With regard to savings, the individual consumers decide what they shall spend (or refrain from spending) on consumption. The balance of their earnings is “savings.” But the balance of their incomes (earnings plus windfall gains) is “investment.” Their decisions determine the amount of investment just as truly and in just the same way as they determine the amount of savings.

For all except entrepreneurs, earnings and income are the same. For entrepreneurs they differ if, and only if, there is a windfall gain or loss. But if there is a windfall gains, the recipients must decide what to do with it exactly as with any other receipt. If there is a windfall loss, the victims are deemed, according to Mr. Keynes’s definition of saving, to “save” the money they do not receive. But this is the result of the definition, not of any “decision.” (p. 345)

Preferring the more natural definition of savings as unconsumed income and of investment as capital outlay, Hawtrey proceeded to suggest an alternative analysis of an increase in saving by consumers. In the alternative analysis both output and prices could vary. It was Hawtrey therefore who provided the impetus for a switch to output and employment, not just prices, as equilibrating variable to a monetary disequilibrium.

It has been pointed out above that a difference between savings and investment [as defined by Keynes] cannot be regarded as the cause of a windfall loss or gain, for it is the windfall loss or gain. To find a causal sequence, we must turn to the decisions relating to consumption and capital outlay. When we do so, we find the windfall loss or gain to be one only among several consequences, and neither the earliest, nor necessarily the most important.

Throughout the Treatise Mr. Keynes refers to these decisions, and bases his argument upon them. And I think it is true to say that almost everywhere what he says may be interpreted as applying to the modified analysis which we have arrived at just as well as to that embodied in his fundamental equations. (p. 349)

To a large extent, Hawtrey’s criticisms of Keynes were criticisms of Keynes’s choice of definitions and the formal structure of his model rather than of the underlying theoretical intuition motivating Keynes’s theoretical apparatus. Hawtrey made this point in correcting Keynes’s misinterpretation of Hawtrey’s own position.

Mr. Keynes attributes to me (rather tentatively, it is true) acceptance of the view of “Bank rate as acting directly on the quantity of bank credit and so on prices in accordance with the Quantity Equation” (vol. 1., p. 188). But the passage which he quotes from my Currency and Credit contains no reference, explicit or implicit, to the quantity equation. Possibly I have misled him by using the expression “contraction of credit” for what I have sometimes called more accurately a “retardation of the creation of credit.”

The doctrine that I have consistently adhered to, that an acceleration or retardation of the creation of credit acts through changes in consumers’ income and outlay on the price level and on productive activity, and not through changes in the unspent margin [Hawtrey’s term of holdings of cash], is, I think, very close to Mr. Keynees’s theory. (p. 363)

In drawing attention to his belief “that an acceleration or retardation of the creation of credit acts through changes in consumers’ income and outlay . . . not through changes in the unspent margin,” Hawtrey emphasized that his monetary theory was not strictly speaking a quantity-theoretic monetary theory, as Keynes had erroneously suggested. Rather, he shared with Keynes the belief that there is a tendency for changes in expenditure and income to be cumulative. It was Hawtrey’s belief that the most reliable method by which such changes in income and expenditure could be realized was by way of changes in the short-term interest rate, which normally cause businesses and traders to alter their desired stocks of unfinished goods, working capital and inventories. Those changes, in turn, lead to increases in output and income and consumer outlay, which trigger further increases, and so on. In short, as early as 1913, Hawtrey had already sketched out in Good and Bad Trade the essential concept of a multiplier process initiated by changes in short-term interest rates, by way of their effect on desired stocks of working capital and inventories.

Thus, it is a complete misunderstanding of Hawtrey to suggest that, in the words of Peter Clarke (The Keynesian Revolution in the Making  pp. 242-43) that he was “the man who, having stumbled upon [the multiplier], painstakingly suppressed news of its discovery in his subsequent publications.” The multiplier analysis was not stumbled upon, nor was it suppressed. Rather, Hawtrey simply held that, under normal conditions, unless supported by credit expansion (i.e., a lower bank rate), increased government spending would be offset by reduced spending elsewhere producing no net increase in spending and therefore no multiplier effect. In fact, Hawtrey in 1931 in his Trade Depression and the Way Out (or perhaps only in the second 1933 edition of that book) conceded that under conditions of what he called a “credit deadlock” in which businesses could not be induced to borrow to increase spending, monetary policy would not be effective unless it was used to directly finance government spending. In Keynesian terminology, the situation was described as a liquidity trap, and we no refer to it as the zero lower bound. But the formal analysis of the multiplier was a staple of Hawtrey’s cycle theory from the very beginning. It was just kept in the background, not highlighted as in the Keynesian analysis. But it was perfectly natural for Hawtrey to have explained how Keynes could use it in his commentary on the Treatise.

UPDATE (03/12/13): In reading the excellent doctoral thesis of Alan Gaukroger about Hawtrey’s career at the British Treasury (to view and download the thesis click here) to which I refer in my reply to Luis Arroyo’s comment, I realized that Hawtrey did not introduce the terms “consumers’ income” and “consumers’ outlay” in Good and Bad Trade as I asserted in the post.  Those terms were only introduced six years later in Currency and Credit. I will have to reread the relevant passages more carefully to determine to what extent the introduction of the new terms in Currency and Credit represented an actual change in Hawtrey’s conceptual framework as opposed to the introduction of a new term for an a concept that he had previously worked out.


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.

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