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Contents : Working Paper No. 298 Krugman on the Liquidity Trap: Why Inflation Won't Bring Recovery in Japan by Jan A. Kregel Jerome Levy Economics Institute March 2000 I am grateful to Paul Davidson Rogerio Studart Mario Tonveronachi and Randy Wray for reactions to the argument presented here without implicating them in the final result. INTRODUCTION The failure of the Japanese economy to respond to aggressive monetary easing in the form of a zero bid rate on the Bank of Japan's overnight financing facility has reminded some economists of Hicks's IS-LM rendition of Keynes's "liquidity trap". Those who use Hicks's famous diagram as the point of reference for evaluating monetary policy will recall that at some low rate of interest the horizontal portion of the LM curve emanating from the vertical axis is meant to represent the lack of influence of expanding the money supply on the rate of interest monetary policy thus does not shift the intersection of the LM curve with the IS curve that determines the equilibrium level of output. Since monetary policy has no impact on the level of output along this horizontal portion of the LM curve debt financing of government expenditure remains the only policy capable of influencing output. The explanation that is given of the failure of monetary policy is that interest rates are so low that they cannot be reduced further. In the case of Japan since moving rates below their current zero bid rate would mean negative rates it is considered to be the first known example of an economy facing a liquidity trap. Those who have studied Keynes's original exposition of the influence of changes in the quantity of money on the level of output will recall that there "may be several slips between the cup and the lip" (JMK:VII p. 173) and that his theory of liquidity preference which is the foundation for the liquidity trap as an expression of total liquidity preference challenged the simple mechanical relationship between money creation the price level and the nominal level of economic activity that is the basis of the traditional quantity theory. It is paradoxical that the theoretical explanation of the way in which the liquidity trap is currently producing recession in the Japanese economy is founded on quantity theory models in which the rate of expansion of the quantity of money directly determines the rate of change in the price level. Indeed in canonical quantity theory models money is neutral and has no impact on the long-run equilibrium of real output irrespective of any reference to a liquidity trap since money only affects nominal variables. The failure of a positive rate of change in the quantity of money to reverse the decline in the price level in these traditional quantity theory models is considered to be equivalent to the failure of expansionary money policy to reduce the rate of interest in Keynes's explanation of the liquidity trap. This apparent contradiction is resolved once it is recognised that the liquidity trap in these neo-quantity theory models is seen as an expression of the failure of changes in the quantity of money to influence the "real" rate of return. Thus with the nominal rate of interest bounded at zero the real rate of interest can only be reduced if prices are rising. If on the contrary prices are falling then the real rate is rising and if the Central Bank is nonetheless increasing the money supply and prices are not responding then the real rate is not falling and the economy is said to be in a liquidity trap since monetary policy has no influence on the real rate. The explanation for the existence of the liquidity trap is then the failure of money growth to raise prices as postulated by the traditional quantity theory. This failure is not explained by any shortcomings in the theory but by the failure of the Central Bank to make credible its intention to produce inflation. After decades of urging Central Banks to adopt independent policies and to create credibility in their pledge to keep prices stable by tying their hands and other sorts of sadistic practices it is now argued that in Japan it is precisely the strength of this credibility that makes the attempt to create inflation incredible. Paradoxically the current policy prescription for the Bank of Japan is to make its commitment to price stability incredible in order to convince market participants that it will produce a rate of inflation in nominal output that it sufficient to reduce the real rate of interest to the level that causes domestic savings to fall to the near zero level of real domestic investment expenditures. The modern explanation of liquidity preference is not only couched in the quantity theory tradition it is based on Irving Fisher's version of the theory in which the nominal rate of interest is determined by the real rate of return adjusted for the rate of change in the price level. If instead of rising the price level is falling then nominal rates will have to be below real rates of return and equilibrium may even require negative nominal interest rates if the real rate is less than the deflation rate. But if nominal rates are bounded from below at zero then nominal interest rates cannot be adjusted downwards below zero then the only way to restore savings-investment equilibrium is to reverse the deflation with a policy of inflation. This is precisely the policy that Fisher urged on Franklin Roosevelt during the Great Depression in the United States. It was also the basis of the decision to devalue the dollar by raising the price of gold and the various measures to create the "alphabet soup" US government agencies designed to put floors under domestic prices. The inflation policy that Paul Krugman is recommending for Japan is based on exactly the same principles as Irving Fisher's recommendations during the Great Depression. Although mainstream economists have long been sceptical of the existence of the Keynesian liquidity trap Krugman claims to have provided analytical support for the concept within both Hicks's ISLM model and more rigorous traditional theory. This paper will thus start by comparing Keynes's original explanation with Hicks's version and then with Fisher's theory. A final section will assess similarities and differences in terms of the policy that Krugman has recommended for Japan. HICKS'S HORIZONTAL LM CURVE AS LIQUIDITY TRAP Hicks not only claimed to be "a convinced liquidity preference man" (JMK:XIV p. 83) he also claimed that "Keynes accepted the IS-LM diagram as a fair statement of his position" (Hicks 1977 p. 146) However Keynes was not an uncritical reader of Hicks's exposition of his theory in the Economic Journal review of the General Theory and the subsequent derivation of the now famous IS-LL (as it was originally called) diagram. In particular Keynes notes that Hicks inserted two illicit assumptions concerning the elasticity of supply of consumption goods and the income elasticity of the rate of interest in his discussion. Both were important to the derivation of the horizontal portion of the LM curve that represents the liquidity trap for most economists but both were extraneous to Keynes's theory. In his review Hicks notes that even if one accepts Keynes's multiplier proposition that an increase in investment will cause a rise in demand for consumption goods and thus a multiplied increase in aggregate income the empirical magnitude of the increase in real output will be small if the elasticity of supply of consumption goods is low. Hicks thus concludes that Keynes must be implicitly assuming "a high elasticity of supply in the consumption goods industries ... and if things do work out this way it is perfectly intelligible that the increased demand for loans from the investment industries should encounter an increased supply so that there is no reason for the rate of interest to rise" (Hicks CEII pp. 89-91) when investment and output increase. The idea is that the increased output of consumption goods will produce the increased savings necessary to fund the loans for the new investment expenditures. Hicks also argues that if the supply of consumption goods is inelastic during the expansive phase of the cycle: "Mr. Keynes's analysis of this case would evidently lead to the conclusion that there would be an indefinite rise in the prices of consumption goods ... but he would admit on second thoughts that this would lead to a more or less corresponding rise in the demand for money and therefore that unless the supply of money was indefinitely expanded the rate of interest must rise ... I do not think that this differs essentially from what has been said by earlier writers Hicks refers in a footnote to Hayek's Prices and Production they would however begin by assuming the supply of money not indefinitely expansible and so proceed straight to the rise in the rate of interest. But they would admit on their second thoughts that if the supply of money were to be indefinitely expanded the rate of interest could be kept down and the inflation proceed without limit." (Hicks: CEII pp. 93-4). Thus Hicks concludes that Keynes is assuming either a highly elastic supply of consumption goods or an infinitely elastic supply of money and that it is one or the other of these assumptions which allows Keynes's theory to differ from the traditional explanation of the response of the rate of interest to an increase in the level of activity. Thus Hicks's explanation of the stability of the rate of interest in the face of an increase in investment and output which becomes the horizontal range of the LM curve is based on the assumption of either a high elasticity of supply of consumption goods (implicitly loanable funds)or of money. Keynes however rejects any dependence of his theory on the elasticity of supply: "you argue ... that my argument depends on the assumption of a high elasticity of supply of consumption goods' but why high" ... "Towards the end you speak of the imperfect elasticity of supply of consumption goods in a trade cycle leading to a consequent hardening of interest rates.' I do not follow why the one is consequent on the other" (JMK:XIV p.71 72). In answer to this criticism Hicks agrees that the elasticity of supply need only be greater then zero and then goes on "Surely it is quite in accordance with your own theory to speak of the imperfect elasticity of supply of consumption goods in the trade cycle leading to a consequent hardening of interest rates. As investment increases the prices of consumption goods rise this raises the transaction demand for money and if the supply of money is not perfectly elastic interest rates must rise too . The same thing may indeed happen to some extent merely by increasing employment even if the supply of consumption goods is perfectly elastic but imperfect elasticity of supply intensifies it. Is not this orthodox " (JMK:XIV p. 73 italics added). Keynes agrees that this is orthodox but not his own theory replying "I quite misunderstood what you meant ... I quite agree with what you say" (Ibid. p. 75). The reader will note that this discussion confuses two separate points. Hicks's initial statement concerned the low probability of a rise in the rate of interest increasing saving out of a given income in order to balance the failure of the consumption goods industries to expand in step with increased investment the same effect being produced by an elastic supply of consumption goods keeping prices constant and allowing the required increase in the supply of saving. What Hicks had in mind was presumably the availability of stocks to allow the operation of the temporal multiplier process without raising prices. The second argument on the other hand refers to the impact of higher consumption goods prices in increasing the demand for money and thus raising interest rates even when the multiplier is able to proceed without encountering supply shortages. Thus it is the assumption of the infinitely elastic supply of money which is crucial to the presumed constant rate of interest. But this proposition Keynes clearly accepted as being consistent with classical theory and as such was not a distinguishing feature of this own theory or of any relation to the liquidity trap as defined above. Having agreed that in his theory as in any other an increase in investment would in general cause an increase in output and probably prices and via an increase in transactions demands for money an increase in the rate of interest irrespective of the value of the elasticity of supply above zero Keynes must have been perplexed by Hicks's statement in the article that set out the IS-LL analysis "Mr Keynes and the Classics" that Keynes's theory leads to the "startling conclusion that an increase in the inducement to invest or in the propensity to consume will not tend to raise the rate of interest but only to increase employment" (Hicks: CEII p. l07 italics supplied) and that " the most important thing in Mr Keynes's book" is that "It is not only possible to show that a given supply of money determines a certain relation between Income and interest (which we have expressed here by the curve LL) it is also possible to say something about the shape of the curve. It will probably tend to be nearly horizontal on the left and nearly vertical on the right" (Ibid. p. 109 italics supplied) implying that the rate of interest would not rise as investment and output expanded until full employment was reached. But given the above discussion the horizontal behaviour of the LL curve "on the left" could only take place even in the presence of a perfectly elastic supply of money while its behaviour "on the right" could only result from a less than perfectly elastic supply of money. Keynes was quick to note his disagreement with Hicks's clearly ad hoc representation of the behaviour of the rate of interest as the "most important thing" in Keynes's theory: "From my point of view it is important to insist that my remark is to the effect that an increase in the inducement to invest need not raise the rate of interest. I should agree that unless the monetary policy is appropriate it is quite likely to. In this respect I consider that the difference between myself and the classicals lies in the fact that they regard the rate of interest as a non-monetary phenomenon so that an increase in the inducement to invest would raise the rate of interest irrespective of monetary policy " (JMK:XIV p. 80 italics added). Thus Keynes rejects the argument that the difference between his theory and the Classics lies in the restrictions placed on the money supply function in particular the existence of a horizontal portion usually known as the "liquidity trap" or in any restriction on the elasticity of supply. Keynes clearly stated that liquidity trap conditions while possible had not yet been experienced they thus could not not serve as an explanation for the Great Depression. Nonetheless Hicks's formulation of liquidity preference led to a presentation of Keynes's theory which implicitly required either 1) the operation of the liquidity trap due to the elasticity of supply of money or 2) the assumption of unchanging prices of consumption goods for a horizontal LM curve represented stable prices in conditions of perfectly elastic supply of consumption goods. However the IS-LM framework makes no reference to any supply conditions for money or consumption goods output only the supply of savings. Even though this representation was never accepted by Keynes -Hicks's suggestions to the contrary -- it has become the standard representation. Tobin for example comments "In terms of the Hicksian language ... I thought (and I still think) ... the main issue ...is the shape of the LM locus" (Tobin 1972 p. 853). Indeed both Friedman and Tobin accept a positive slope for the LM curve rejecting a vertical or horizontal curve. But as Hicks's article pointed out here there is no difference between Keynes's and the "ordinary method of economic theory." Clearly Hicks's explanation of the liquidity trap as the horizontal portion of the LM curve is consistent with traditional theory as Keynes agreed. But it cannot be considered as an analytical foundation for the failure of the rate of interest to respond to policy changes in the amount of base money created by the central bank for it deals with the behaviour of rates when output is increasing with perfectly elastic money supply not the behaviour of rates when the quantity of money is increasing with perfectly elastic supply of output. THE MODERN THEORY OF THE LIQUIDITY TRAP Although Krugman considers Hicks's model as a "very useful heuristic" (Krugman p. 7) he notes that it is considered too ad hoc and thus not the best vehicle for presenting the traditional version of the liquidity trap. In his view "A liquidity trap may be defined as a situation in which conventional monetary policies have become impotent because nominal rates are at or near zero - so that injecting monetary base into the economy has no effect because base and bonds are viewed by the private sector as perfect substitutes." He notes that an alternative "way of stating the liquidity trap problem is to say that it occurs when the equilibrium real interest rate the rate at which savings and investment would be equal at potential output is negative" (op. cit. p. 16) As noted above in traditional theory if the nominal interest rate is determined by adjusting the real rate of return for depreciation in the monetary standard a rise in the inflation rate given the nominal rate should cause the real rate to decline. If a rise in the growth of base money causes a rise in the rate of inflation then it should be possible for monetary policy to achieve the required equilibrium real rate. This raises the question of "how is the liquidity trap possible The answer lies in a little-noticed escape clause in the standard argument for monetary neutrality: ... there is no ... argument that says that a rise in the money supply that is not expected to be sustained will raise prices equiproportionally - or indeed at all. In short to approach the question from this level of abstraction already suggests that a liquidity trap involves a kind of credibility problem ... if monetary expansion does not work if there is a liquidity trap it must be because the public does not expect it to be sustained" (op. cit. p. 7). Although a one-shot increase in base money will lead to a once over increase in the price level this should have no impact on the rate of inflation and leave the nominal rate of interest unchanged if the real rate of interest is unchanged. The liquidity trap thus occurs because the central bank cannot make individuals with rational expectations believe that it will keep money growing in perpetuum at the new higher rate so as to ensure a higher rate of inflation in perpetuum. This looks just the opposite of Hicks's theory which is based on stable prices of consumer goods and belief in the perfect elasticity of the money supply. Krugman argues that investors do not believe that the money supply will be perfectly elastic indeed the increases that occur in the present period will be reversed in future. Thus monetary policy cannot influence the real rate of interest to make it adjust to the level that will lower private sector savings to equality with the voluntary investment decisions of the private sector. "The easiest way to think about this is to say that there is an equilibrium real interest rate which the economy will deliver whatever the behaviour of nominal prices." (op. cit p. 10) Thus the liquidity trap occurs because the real rate cannot be influenced by monetary policy. As already noted this is a perfectly standard result within Fisher's version of the quantity theory and formed the basis for Keynes's belief that Hicks had not captured his essential difference from classical theory: "Put shortly the orthodox theory maintains that the forces which determine the common value of the marginal efficiency of various assets are independent of money which has so to speak no autonomous influence and that prices move until the marginal efficiency of money i.e. the rate of interest falls into line with the common value of the marginal efficiency of other assets as determined by other forces. My theory on the other hand maintains that this is a special case and that over a wide range of possible cases almost the opposite is true namely that the marginal efficiency of money is determined by forces partly appropriate to itself and that prices move until the marginal efficiency of other assets fall into line with the rate of interest" (JMK:XIV p. 101). LIQUIDITY PREFERENCE AND THE LIQUIDITY TRAP Krugman notes that unlike Hicks's ad hoc version his explanation of the liquidity trap depends on the modern theory of intertemporal choice. But it is precisely in the exposition of this intertemporal relation that Keynes differed from Fisher. Fisher's explanation -- which is the one used by Krugman -- of the determination of nominal interest rates is based on expectations of future goods prices relative to present goods prices as expressed in the expected rate of inflation or deflation of goods prices. The theory is based on a proposition presented in Irving Fisher's The Theory of Interest (1930) which on Fisher's own admission only applied to conditions in which "rational tendencies" based on "rational and empirical laws ... analogous to rational and empirical laws of physics and astronomy" (Fisher 1930 p. 321). However Fisher notes that where actuarial risk cannot be applied and "uncertain" conditions make the value of money unstable "We must ... give up as a bad job any attempt to formulate completely the influences which really determine the rate of interest" (ibid). These are precisely the conditions which Keynes believed to be normal and thus the basis for this theory. Both Fisher and Keynes specify the rate of interest as an intertemporal relationship represented by a spot-forward swap or by the excess of the forward price over the par or spot price. However In Fisher's time preference approach the rate of interest is the discount of future over present income that makes their utility equal at the margin while for Keynes liquidity preference represents the return that must be paid on illiquid assets to make investors indifferent to holding more liquid assets. Since time preference is a relation between real income today and in the future it would be disturbed by changes in relative prices thus Fisher argues that the money rate of interest that allows individuals to transfer income from the present to the future r must be corrected for the rate of inflation p in order to leave the time transformation of income undisturbed: thus the Fisher relation: (1+p)(1+r) (1+i) and i (1+r)(1+p) - 1 1 + r + p + rp -1 which is usually written i r + p when rp is small and p is the rate of inflation r the rate of increase in real income and i the rate of interest on money. In the case of Japan the problem is not inflation but deflation and p 0. Then if i is constrained to be non-negative r must be positive and it is impossible for the competitive market system to achieve an equilibrium which requires r to be negative. In simple terms this is Krugman's version of the liquidity trap. In Krugman's simple monetary view p should be determined by the rate of growth of base money but if money growth is indeed positive and p remains negative this can only be explained by the expectation that money growth will not remain positive and the expansionary monetary policy will be reversed in the medium run. Thus the system is stuck in a liquidity trap with a real rate of interest that is too high or a nominal rate of interest that is too high because the rate of inflation is too low when nominal interest rates are fixed at zero. The reason can only be the failure of the central bank to convince the public that p will be permanently higher. Overcoming the liquidity trap thus requires permanent and perfectly anticipated inflation in the form of a positive value of p sufficient to allow r to be negative when i is constrained to be non-negative. Keynes has a very simple objection to Fisher's relation between the rate of interest and the rate of inflation. First pace Krugman's emphasis on the lack of central bank credibility he objected because it relied on the assumption of perfect foresight over the path of future incomes and prices (cf.1930 pp. 202-3 and JMK:VII pp. 142-3). Second he objected because Fisher's argument that the money rate of interest should automatically reflect a perfectly foreseen rise or fall in the price level overlooks the impact of a rise or fall in interest rates on the capital value of existing stocks of financial assets. While it is true that if a rise in the price level for the coming year of 2% is perfectly foreseen interest rates must be 2% higher to keep real returns for investors in one-year bills constant the same would not be true for an investor holding fixed-interest assets of longer maturity in order to sell after one year since there would be a positive or negative change in its capital value if interest rates change. Since market arbitrage should ensure that the one- year holding period rate of return should be the same for any instrument (even 30-year bonds sold one year after purchase) held for one year longer-dated instruments should have a larger adjustment in their interest rates to offset the fall in capital value due to the rise in interest rates. A change in the rate of inflation should then have a differential impact on the rate of interest along the maturity spectrum rising with time to maturity. Keynes noted that a rise in the rate of interest from 10% to 12.2% will cause the price of a 100 par value British consol paying a 10 coupon to fall from 100 to 81.96 a decline of 1.8% and a capital loss of over 18. While the "variations in the rate of interest earned during the year in question are too small to make much difference" (e.g. the extra 2.2% earned on the reinvestment of the 10 coupon) relative to the much more substantial capital loss since the benefit of being able to invest the future 10 interest coupon payments at the higher rate of 12.2% will be swamped by the 18 decline in the capital value of the bond. The rise in the rate of interest equal to the rise in the rate of inflation could by no means be considered as sufficient to compensate for the loss in purchasing power. Thus Keynes argues Fisher's relation goes in the wrong direction for existing bondholders since the higher yields required to preserve real yields cause capital losses that will more than offset the increased interest earnings. What change in the rate of interest would be required to keep the capital position of the bond holder unchanged Since the impact of the rate of interest will increase interest earned on reinvestment of coupon interest while it changes capital values in the opposite direction the breakeven condition for a perpetual bond will be P-C 0 where P is the annual cumulative change in price and C its annual coupon payment. The price or present value of a perpetual bond is C/i where 'i' is its current yield to maturity and C the annual coupon. The change in price P of a perpetual bond is given by the product of its market price the change in the rate of interest i and the modified duration of the bond. For a perpetual bond duration is given by D (1+i)/i and modified duration by D/(1+i) which simplifies to 1/r. Thus P P * i * MD which can be expressed P (C/i) * i * (1/i) i * (C/i2 ). Substituting in P-C 0 gives i * (C/i2) - C 0 which simplifies to P C and is Keynes's square rule. Thus for increases in the rate of interest equal to the increase in the rate of inflation to leave capital values unchanged they must be equal to i 2. Thus the Fisher relation will hold only for an increase in the rate of inflation p i2 but this only keeps capital values constant and does not provide any adjustment for inflation. For the Fisher relation to hold interest rates must rise by more than this but this means that capital value will fall further etc which illustrates Keynes's point that in general it is impossible for a simple adjustment in the interest rate to keep purchasing power unchanged once the impact of the interest rate on the value of existing stocks of assets is taken into account. There is thus no reason to expect the Fisher relation to hold as has indeed turned out to be the case empirically. But Keynes's calculation also served another purpose. It can also be represented as the "breakeven" point for the two opposing forces working on the value of the bond that is the point at which the change in capital value is just offset by the opposite change in interest income from reinvesting coupon interest at the higher or lower interest rate over the remaining time to maturity of the bond. This point is called the "duration" of the bond in the finance literature. The lower the rate of interest the higher the bond's "duration" and the longer it takes to recover the fall in capital values from the increased reinvestment earnings due to higher reinvestment interest rates. At a 3% nominal interest rate i i 2 as the condition under which

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