A paradox of thrift or Keynes's misrepresentation of saving in the classical theory of growth?

• Author: Ahiakpor, James C.W.

1. Introduction

   Every year thousands of introductory economics students are made to accept as valid one of Keynes's lasting inversions of classical economics, namely the proposition that saving may be a private virtue, but is a public vice. According to Keynes, a community that seeks to increase its rate of saving would end up impoverishing itself and actually saving less, but the community that increases its consumption at the expense of saving would end up being richer and saving more. This proposition, frequently stated in macroeconomics textbooks as the "paradox of thrift," arises mainly from Keynes's definition of saving to include the hoarding of cash, contrary to the classical definition and language of the marketplace, but has received little recognition or criticism as such.(1) Rather than emphasizing Keynes's misrepresentation of the classical theory of income determination and growth in which hoarding constitutes a reduction in saving, most critics have pointed out only that saving may take other forms besides hoarding.(2) Thus, several reviewers of the General Theory [22], in which Keynes fully develops the argument, criticized it mainly for having assigned too much importance to the hoarding of cash, e.g., Pigou [37], Robertson [40], Viner [51], and Hawtrey [11].

   Some modern textbook writers employ the loanable-funds view of savings to show the limited significance of Keynes's paradox of thrift proposition, but with little reference to the fact that it derives from a fundamental misrepresentation of saving in the classical theory of growth. See, for example, Baird [3], Boyes and Melvin [6], McConnell and Brue [31], and Case and Fair [7]. In the same tradition, Leijonhufvud [26, 196-97] also argues that saving is more than "an antisocial refusal to spend" and calls the paradox of thrift proposition "one of the most dangerous and harmful confusions ever taught as accepted economic doctrine." On the other hand, some other textbook writers insist that Keynes's proposition is logically sound (it can be demonstrated by the use of algebra or a saving-investment diagram), although also conceding that it fails to accord with experience in the real world, e.g., Henderson and Poole [15, 279-81] and Parkin [33, 224-25].

   The principal proponents of the doctrine focus on elaborating Keynes's statement of the obvious (as if it were inconsistent with classical analysis): savings depend on the level of income, and the level of income is determined by the rate of investment, which in turn depends on anticipated consumption demand, e.g., Wonnacott and Wonnacott [52], Samuelson and Nordhaus [47],(3) Heilbroner and Galbraith [14], and Baumol and Blinder [4]. Some claim that the paradox of thrift is a good illustration of the "fallacy of composition" in economics: what is valid at the individual level may not be valid at the group level, e.g., Campagna [8], Bach [2], and Samuelson and Nordhaus [47].(4) Others also suggest that Keynes's argument may be valid only for advanced industrialized economies in certain periods but not for others. But in all these, little reference is made to the classical theory of growth against which Keynes was reacting. Thus, the teaching of Keynes's paradox of thrift proposition continues to thrive in spite of a long history of criticism. And of course, its confusion extends well beyond the level of sophomoric undergraduates, as I document below.

   In this article, I restate the classical savings theory of growth to provide a basis for demonstrating that Keynes misrepresented the classical concept of saving to include the hoarding of cash, a mistake which led to his erroneous conclusions about the classical theory of growth. I use Keynes's arguments mainly in the General Theory to restate the paradox of thrift proposition,(5) and I rely on direct quotations from the classics and Marshall to establish Keynes's misrepresentation of their argument. I conclude that there is no such thing as a paradox of thrift other than Keynes's incorrect substitution of "hoarding" for "saving" in the classical theory of income determination. This recognition may help end the annual ritual of teaching students a fundamental confusion from which they later struggle to escape in courses such as development economics or finance. The discussion also shows that there is much of significance yet to be gained by paying careful attention to what the classics said, especially in assessing Keynes's claims against them. Even among the classics, as Samuelson [45, 1430] has observed, "their quarrels lasted because often they were quarrels over misunderstandings and definitions."

2. The Classical Theory of Growth

   The classical theory of growth against which Keynes proposed his paradox of thrift argument simply states that economic growth is determined by the rate of saving or capital accumulation. The greater the amount saved out of income, the more capital goods, land, and labour services can be bought or hired for production. As Smith [50, 1:358-59] clearly states the argument,

   Capitals are increased by parsimony,... Whatever a person saves from his revenue he adds to his capital, and either employs it himself in maintaining an additional number of productive hands, or enables some other person to do so, by lending it to him for an interest, that is, for a share of the profits. As the capital of an individual can be increased only by what he saves from his annual revenue or his annual gains, so the capital of society, which is the same with that of all the individuals who compose it, can be increased only in the same manner.(6)

   Earlier, Smith argues that "Every increase or diminution of capital [i.e., saving] . . . naturally tends to increase or diminish the real quantity of industry, the number of productive hands, and consequently the exchangeable value of the annual produce of the land and labour of the country, the real wealth and revenue of all its inhabitants."

   The classics did not presume that every saver was also the ultimate investor or purchaser of investment goods. The classics wrote about an economy in which there was money (cash) as well as financial intermediation by banks and brokers.(7) Also note that the classics used the term "capital" and "savings" interchangeably when discussing the actions of savers, e.g., Smith [50, 1:372-75], Ricardo [38, 1:363, 3:89-94],(8) and Mill [32, 3: ch. 23]. This explains why one typically does not see "saving" cited in the indexes of their works, and when cited, one finds "see capital," e.g., Mill [32, 3:1164].(9) Also see Marshall's Principles. On Keynes's misinterpretation of the classical usage of the term "capital" to mean "funds" or "savings", see Ahiakpor [1](10); also see Hartfield [10] on the widespread misuse of the term "capital" in modern economics.

   Thus, saving or capital in the classical theory of growth refers to nonconsumed income from which revenue is derived, in terms of interest or profits, e.g., Smith [50, 1: Bk 2, ch. 1]; also see Marshall [29, 66]. Non-consumed income hoarded in cash does not constitute saving or capital since it does not earn interest or profits. Malthus, for example, clarifies the place of hoarding well when he argues: "No political economist of the present day can by saving mean mere hoarding." Quoted in Blaug [5, 166]. Rather, hoarding may be regarded as a form of 'spending' income, namely, the purchase of a non-income generating asset, cash.(11) As Smith [50, 1: 458] so well makes the point, "Money, like wine, must always be scarce with those who have neither wherewithal to buy it, nor credit to borrow it." [Emphasis added.] Thus, for those not engaged in the direct purchase of investment goods, there are three forms of spending income (Y), according to the classical argument: consumption (C), purchasing financial assets, i.e., saving ([Delta][FA.sup.d]), and buying or holding cash (pY).(12) Therefore, saving is equal to income less consumption and the proportion (p) of income households desire to hold in cash, i.e., [S.sub.] = [Y.sub.t] - [C.sub.t] - p[Y.sub.t] = [Delta][FA.sup.d].(13)

   Note that pY is not the stock of accumulated cash but a flow within each period. Thus, if p = .1 and Y = $1,000, $100 of a period's income would be the amount desired to be held as cash while $900 would be divided between consumption spending and the purchase of financial assets or current saving. But should p instead be .4, $400 of current income would be the desired cash holding while $600 would be devoted to consumption and saving. Whether the desire to hold a greater proportion of current income in cash is realized or not depends on the existing stock of cash made available by the monetary authorities, less the quantity already being hoarded.

   It is tempting to write the saving equation as S = Y - C - [Delta]H, as some commentators have suggested. But that formulation blurs recognition of the choice variable, p, in affecting the saving decision. Moreover, for the community as a whole, [Delta]H = 0 unless the monetary authorities change H. But the aggregation of [p.sub.i][Y.sub.i] over individuals does not amount to zero. Therefore, households' flow-demand for cash appears better represented by pY in the saving equation rather than [Delta]H, just as kY represents the total demand for money (cash) in the Cambridge equation, H = kY.(14)

   Corresponding to the loaned out savings or accumulated capitals of households ([Delta]FA), is capital acquired by ultimate investors or producers: machinery, equipment, buildings, materials for further processing, produced goods yet to be sold (inventories), and, in a rather small proportion, cash needed to assist transactions of a business enterprise [50, 1:313; 30, esp. 46-47]. These constituents of capital are frequently classified in the classical literature as 'fixed' or 'circulating' depending on whether they yield "a revenue or profit without . . . changing masters" [50, 1:297; 29, 63]. But the...