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CIAO DATE: 03/02
Critical Review
Winter–Spring 1998 (Vol.12 Nos.1–2)
An Ultra-Keynesian Strikes Back: Rejoinder To Horwitz
By Greg Hill *
Abstract
In real-world markets, individual intentions cannot be brought into perfect harmony before decisions are taken. Choices made without this pre-ordering—choices made in ignorance of one another—produce unwanted outcomes. It is this absence of coordination among plans, not centralized banking, that is the primary cause of macroeconomic market failure. Steven Horwitz’s free-banking alternative would aggravate the collective-action problems inherent in economies without complete markets.
Professor Horwitz describes “the core of the debate” between us as the issue of “what causes the mismatch between saving and investment” (5). I would characterize our disagreement more broadly as a late round in the long-running debate about the effectiveness of real-world market economies in coordinating decentralized decisions. Horwitz is convinced that centralized banking is the chief obstacle to a rational order of individual choices, and that this ideal can be brought within reach through the institution of “free banking.” I shall argue that coordination failures originate mainly in the void created by the absence of complete markets. When decisions must be taken in ignorance of one another, they often give rise to collective action problems that are beyond the power of markets to solve. Free banking would not ameliorate these problems, but exacerbate them.
I. The Act of Saving
In The Moral Economy: Keynes’s Critique of Capitalist Justice (Critical Review 10, no. 1), I developed some of the ramifications of Keynes’s argument that saving and investment are not effectively harmonized in real-world market economies, and I tried to show why this discordance casts doubt upon justifications for unfettered capitalism. In his initial reply to my paper, Horwitz claimed that while “real-world banks and interest rates do not operate perfectly . . . they do effectively facilitate intertemporal coordination day in and day out” (1996, 359). In his present response, Horwitz adds the stunning proviso that “the rate of interest can assure that aggregate saving and investment are effectively harmonized, if the right banking institutions are in place,” viz. free banks that are permitted to create their own currency and deposits (1, Horwitz’s emphasis). The economic arrangement Horwitz wishes to defend—free markets with free banking—comprises a different economic system than the actual capitalist economies Keynes analyzed. In outlining some of the causes of macroeconomic market failure, I shall try to keep before us Horwitz’s claim that these coordination problems would not arise, or would at least be less severe, under laissez-faire banking than under centralized banking.
To begin, let us consider Horwitz’s claim that, with free-banking institutions in place, saving and investment decisions would be effectively coordinated, a contention Horwitz says “Keynesians have rarely addressed” (ibid.). The problem of coordination arises because an individual act of saving—a decision not to buy dinner today—does not necessitate a decision to purchase any particular good at any particular time in the future. Thus, the act of saving—literally, not spending—depresses current demand without stimulating the production of goods that may be consumed in the future (Keynes 1936, 210).
In response to this argument, Horwitz claims “that an increase in savings will (with the right institutions in place) lower interest rates and signal investors to produce outputs that will come into being relatively farther in the future” (1). This reduction in interest rates requires, on Horwitz’s own theory, that the “increase in savings” be an increase in total savings. The question is not whether an individual can increase her own saving by reducing her spending, but whether this act of thrift will increase total saving. The rub, of course, is that when one person reduces her spending, someone else’s income must fall, and there is no guarantee that the increased saving of the former will not be offset by the decreased saving of the latter.
Horwitz no longer denies this, but nevertheless insists that “the increased desire to save on the part of some market actors will cause changes in the relative prices of consumer and producer goods, lowering interest rates” (3). Now, we may grant that when the public reduces its consumption spending, the price of consumer goods may fall. But Horwitz still owes us an explanation of why the relative price of producer goods will rise. To claim that an increase in the flow of saving signals a rising demand for goods in the future begs the question, for it is the assumed increase in total saving that is in doubt. To claim, on the other hand, that the price of producer goods rises because the interest rate has fallen is to reason in a circle, for Horwitz has just argued that lower interest rates are due to the relative rise in producer-goods prices, not vice versa.
Horwitz speaks of “the increased desire to save on the part of some market actors” (ibid., emphasis added), but fails to grasp the difficulty involved in communicating this desire to producers. For an individual, the decision to save involves a reduction in present consumption for the sake of consumption later on. And if, at the time this person reduces her current consumption spending, she were simultaneously to place an order for goods to be delivered in the future, there would be no coordination problem; firms could reduce their output of consumer goods and increase their output of producer goods knowing there would be greater demand in the future. But while a reduction in consumer spending makes possible a shift of resources from consumption to investment, this act of saving provides firms no inducement to expand future output in the absence of an order for future delivery.
Free banking would do nothing to mitigate this difficulty. The coordination problem Horwitz and I have been debating does not arise because real-world banks are constrained by the reserve requirements mandated by a central bank; it arises because the individual act of saving conveys no information to producers about what will be desired in the future or when it will be desired. Allowing banks to create their own currency and deposits would not eliminate this problem because it is the demand for investment loans that is lacking, not the supply!
Horwitz’s explanation of the supply side of the credit market is not quite right either. Although Horwitz has corrected his original oversight, wherein he counted the increased saving of Keynes’s abstinent diner without counting the decreased income and saving of the restaurant owner, he now makes the same mistake with respect to the bank deposits of the two parties. Thus, Horwitz asserts that when the diner foregoes his regular meal at the neighborhood restaurant, “bank deposits are greater than they otherwise would have been” (ibid.). This conclusion, however, is based on an incomplete accounting of the net change in total bank deposits. For while Horwitz recognizes the increase in deposits at the diner’s bank, he fails to take account of the decrease in deposits at the bank of the restaurateur, whose income and savings are lower because the former restaurant patron is no longer buying dinner. Thus the new loans made by the diner’s bank, and the spending and income they generate, which Horwitz notices, must be offset by the decrease in loans made by the restaurateur’s bank and the consequent reduction in spending and income, which Horwitz overlooks.
Finally, let us consider the question Horwitz believes Keynesians have dodged for 50 years, a question that if squarely faced, Horwitz insists, must restore our confidence in the market’s ability to coordinate saving and investment decisions, i.e., “the question of where the savings ‘goes’” (3). As a prelude, it may be noted that this question loses much of its critical force once it has been shown that the individual act of saving ensures neither an increase in total saving, nor an increase in total bank deposits. Bearing these points in mind, let us by all means give Professor Horwitz his answer. When planned saving exceeds planned investment, firms will have produced more goods than households wish to buy at prevailing prices. Consequently, prices will fall, and firms will suffer unexpected losses. Those households that have reduced their spending will have increased savings, and these savings will “go” to firms that must cover their losses. 1 Businesses incurring losses can only meet expenses by drawing down their cash reserves, selling assets, or borrowing. Households with increased savings may acquire these assets or make deposits that support commercial lines of credit. In microcosm, the extra savings of Keynes’s abstinent diner might well be borrowed by the restaurant itself—not for the purpose of investing in a new oven, but to meet expenses that cannot be met following the unforeseen reduction in the restaurant’s sales revenue.
II. Deflation and the Limits of Free Banking
Although I have argued that an individual act of saving will not necessarily increase either aggregate saving or the total stock of bank deposits, this does not mean that the rate of interest will be unaffected by a general reduction in spending. On the contrary, when incomes and prices fall, households and firms require smaller cash balances for transaction purposes. The rate of interest will then decline, not because the price of producer goods has risen in relation to the price of consumer goods, but for the more mundane reason that banks can acquire what is now excess cash by promising lower interest payments than would have been required before the decline in aggregate income.
That said, it must be added that falling interest rates may not be sufficient to revive investment in a deflationary environment. Falling prices reduce profit margins, and it is gross profits, not bank loans, that finance the lion’s share of capital spending. Moreover, deflation causes bankruptcies, which increase the risks of both borrowing and lending. And, finally, there is a lower limit beneath which the rate of interest cannot fall, both because of the large risk involved in holding very high-priced bonds and because investment project risks are “double-counted,” once for the borrower whose project may fail and once for the lender whose loan may not be repaid (Meltzer 1988). Horwitz believes free banking would successfully counterbalance these deflationary forces. If banks were allowed to “produce more currency and deposits when the public wants them,” then, Horwitz claims, “the downward effects on aggregate demand of an excess of planned saving over planned investment will be avoided” (7).
Horwitz’s case for “free banking” does not come to grips with the fact that an effective banking system requires the management of collective action problems that, by their nature, cannot be solved by the independent action of many unfettered banks. When an individual bank makes a loan, the borrower will often pay away his deposit to the customers of other banks, which, in turn, will find their position strengthened to the same degree the lending bank is weakened. A bank’s decision as to whether a loan will be approved or disapproved is not, therefore, a strictly private matter between the bank and the loan applicant. Rather, one bank’s lending creates an external benefit for other banks. In Keynes’s words, “every movement forward by an individual bank weakens it, but every such movement by one of its neighbor banks strengthens it; so that if all move forward together, no one is weakened on balance” (1930, 26).
If there is no central bank to manage these externalities, the banking system will be prone to instability because any change in the volume of lending is likely to be self-reinforcing. On the one hand, the increased lending by one bank will increase deposits at other banks, which are then likely to increase their lending, which further increases deposits, and so forth. On the other hand, a reduction in the lending of one bank will reduce the deposits and, therefore, the lending of other banks, which will further reduce total deposits within the system. In the latter case, each bank’s contraction of credit will not only reduce the deposits of other banks, it will also increase the risk of default throughout the economy. Depending on the speed with which this contraction unfolds, a chain reaction of bankruptcies can become a “run” on the banks. Without a central bank standing ready as “the lender of last resort,” the outcome of this cumulative process is unlikely to coincide with Horwitz’s cheerful scenario, which contemplates nothing more than “very minimal, very transient macroeconomic consequences” in response to reductions in aggregate demand (7).
The collectively self-defeating actions of Horwitz’s free banks during a credit crisis exacerbate a parallel collective action problem in the non-financial sector of the economy. Just as one bank’s reduced lending weakens other banks by diminishing their deposits, so one firm’s reduction in investment spending diminishes the sales and income of other firms. If, by contrast, a large number of firms were to increase their level of investment simultaneously during a slump—that is, if their investment decisions were coordinated—all would then benefit from the income and multiplier externalities generated by their cooperative investment expenditure (see Hill 1998). But when each firm, aiming to minimize its risk in a troubled economy, waits for the upswing before investing, the result is the same as when each bank passively waits for an increase in its deposits before increasing its lending: an economy stuck in an underemployment equilibrium.
III. Rationality, Decentralization, and Real-World Price Systems
In his initial reply, Horwitz claimed that “with wage and price flexibility,” real income and output “will not be affected” by an increase in the demand for money (1996, 364). Here, too, Horwitz believes a significant qualification is in order. Thus, he now insists that if “prolonged periods of unemployment” are to be avoided, prices must be “perfectly flexible, where ‘perfectly flexible’ includes perfectly rational agents” (4, Horwitz’s emphasis). A certain sort of Keynesian might be tempted to respond to this astonishing concession by simply saying, “I rest my case.” But I am going to resist the temptation because the concession, itself, is based on a misunderstanding.
The argument of Keynes’s General Theory is not that prolonged unemployment is possible because prices and wages are rigid. Rather, a market economy can get stuck below the full-employment level of output because, among other reasons, unemployed workers have no means of communicating to producers as a whole their willingness to purchase additional goods if they were again employed. 2 The trouble in this instance is not the slow speed of price adjustments, but the absence of a market in which conditional intentions can be pooled, and all mutually advantageous trades revealed and consummated.
In the Austrian theory Horwitz affirms, prices provide the information necessary for rational decision making as well as for the coordination of individual decisions within the economy as a whole. This was, of course, the principal argument of the Austrian school in the great debate over the possibility of rational calculation under socialist planning. The problem illustrated above—that is, the incompleteness of markets in real-world economies and, hence, the absence of prices for many important kinds of goods, including goods to be delivered at future dates under contingent circumstances—dims the action-guiding lights that emanate from the price system. Kenneth Arrow, who described in exquisite mathematical detail the necessary conditions for efficient markets, concludes that “the very concept of rationality is threatened” when markets are incomplete and individuals must predict what a great many other decision makers will do (1986, 203).
The problem of imperfect information in real-world markets is often aggravated by its uneven distribution among market participants. 3 In the credit market, for example, potential borrowers often have better information about their credit-worthiness than do lenders. In this case, two of Horwitz’s main themes collide with ironic force. On the one hand, the development of human capital takes time, which requires the sacrifice of current, for future, income. On the other hand, the credit necessary to meet current expenses may be available only to families that have already accumulated considerable wealth because, in the absence of other reliable information about a borrower’s credit-worthiness, collateral is usually required in order to get a loan. The result is an inefficient pattern of investment in human capital, which also reinforces existing inequalities of wealth and income (see Shah 1992). Government-insured loans can improve upon this outcome by pooling risks, but free banks, operating in markets with information asymmetries, have neither the ability nor the incentive to do so.
IV. Liquidity Preference, Time Preference, and The Rate of Interest
Horwitz’s case for free banking rests on an exceedingly narrow conception of liquidity, which captures almost nothing of what Keynes had in mind by the term. Consider Horwitz’s claim that “the desire for liquidity or availability services is a manifestation of the more fundamental concept of time-preference” (6). “If I choose to sell bonds and acquire cash,” Horwitz says, “this suggests that I am worried about the future and want cash so as to leave my options open. My time preferences have shifted toward the present” (ibid.). This is a muddle. If I suddenly sell bonds to acquire cash for a vacation, then one might plausibly infer that my time preferences “have shifted toward the present.” If, however, I sell bonds because I think interest rates will rise and bond prices will fall, this increase in my liquid holdings does not reflect a change in my time preferences, but a change in my forecast of future bond prices! Even if I were to sell bonds because I have become less confident about the direction of bond prices, this has nothing to do with an increased preference for current versus future consumption. Rather, it reflects my disquietude about the future course of interest rates.
In Keynes’s theory, liquid assets are those that can be used as a means of payment, or can be easily converted into a means of payment, without capital loss. Cash and checks satisfy this requirement, and short-term Treasury Bills come very close. Long-term bonds, stocks, and specialized capital equipment are less liquid by turns. Keynes’s theory of liquidity preference gives an account of the motives that influence decision makers in allocating their wealth among these different kinds of assets. For example, bondholders who become anxious about interest rates will unload their bonds in favor of more liquid assets, provided they can find willing buyers, e.g., other wealth holders who are more bullish about bond values. If, however, a preponderance of the public becomes convinced bond prices are about to tumble, they will tumble because there are too few buyers at the prevailing prices. Interest rates will then rise, some capital goods will no longer be profitable to produce, and unemployment will increase. Horwitz’s free banks would be able to arrest this increase in interest rates, and the unemployment it causes, only if these banks were willing to suffer losses, purchasing bonds even though their prices were being driven down by the public’s self-fulfilling expectations of falling asset values.
Horwitz conceives of the interest rate as an intertemporal price that moves up and down in response to changes in the public’s rate of saving. But households thinking about their future must make two decisions, not one. In addition to deciding how much of their current income to save, households must also decide how to allocate their existing wealth among alternative assets, a decision that will be driven in large measure by expectations regarding future asset prices, as well as by the degree of confidence with which these expectations are held. This asset allocation decision has a much stronger influence on the rate of interest than the decision about current saving, because the stock of existing wealth to be allocated is so much greater than the flow of new saving. At any given time, the quantity of preexisting stocks and bonds that can be released onto the market overwhelms the quantity of new stock and bond issues entering the market. Similarly, the quantity of money and near-money being held in expectation of a fall in securities prices exceeds by many times the volume of new saving. It is because the interest rate is tethered to the expectations, hence the liquidity preferences, of those who hold the massive preexisting stock of financial assets that it cannot, at the same time, balance the flows of saving and investment. There is nothing within the institution of free banking that would emancipate the interest rate from this burden.
V. Saving, Investment, and Finance
Horwitz imagines that production is directed toward consumption and investment goods in proportions determined by the public’s willingness to wait, and that if inflation is to be kept at bay, banks cannot lend more than “the public is willing to save” (10). The hidden premise in this argument (and in many others Horwitz advances) is that income and output are given at the level of full employment. If there are no idle resources, it then follows as a matter of course that any increase in expenditure, whether financed by bank credit or otherwise, will only drive up prices, since output is already at its maximum. If, however, some resources are unemployed, then the relevant question is no longer “How much is the public willing to save at its current level of income?” but rather “How much saving would be forthcoming at a higher level of (real) income?” In an economy with complete futures markets, wherein agents could choose among alternative streams of intertemporal consumption, the equilibrium result would provide a good answer to the question, “How much is the public willing to save?” But, in the absence of such markets, it is unclear how the de facto level of saving even bears on the question.
In my initial rejoinder to Horwitz, I argued that an increase in investment need not await an increase in saving because “contemporary banks create credit in excess of savings” (1996, 381). In response, Horwitz claims that “competitive banks themselves create credit . . . only if they have excess reserves to back it up, or if the public is willing to hold balances of the bank’s liabilities” (9–10, Horwitz’s emphasis). Horwitz seems to have forgotten that modern banks operate under a “fractional reserve” system, so that if reserves of 10 percent are required, deposits may expand until they are 10 times as large as reserves. Moreover, “in the real world, a bank’s lending is not normally constrained by the amount of excess reserves it has at any given moment” (Federal Reserve Bank of Chicago 1992, 37). Even if there are no excess reserves, banks can still accommodate an increased demand for investment loans by inducing the public to part with some of its currency in favor of interest-bearing deposits. Since only 10 percent of new deposits must be held in reserve, $100 in new deposits can support $1,000 of additional transaction deposits (ibid., 16). Horwitz may insist that it is only because the public is willing to hold $100 in new savings deposits that banks are able to add an additional $1,000 to the credit lines of borrowers, but there is no doubt that the lion’s share of new investment spending from these accounts is being financed by bank credit, not by “savings proper.”
When we remove the two essential premises of Horwitz’s argument, i.e., full employment and lending no greater than prior savings, the following scenario comes into view: banks lend; firms borrow, invest, and repay their loans out of the increased sales revenue. 4 In part, this is the familiar story of the multiplier. When there are idle resources, an increase in investment spending will increase aggregate income, and out of this increased income, there will be additional saving equal to the additional investment. The finance required for this expansion cannot come from savings that do not yet exist. Hence, the expansion must be facilitated by an extension of credit. Once investment projects have been completed, firms often will repay their short-term bank loans by issuing long-term bonds, which, in turn, will absorb the ex post saving.
Let us now address Horwitz’s objection to this process: his claim that, “without any prior voluntary saving by the public,” an increase in bank lending will lead to inflation and “forced saving” (10). If, by “forced saving,” Horwitz means any saving in excess of the saving that would be forthcoming at full employment, then there is no disagreement between us. But if “forced saving” is taken to mean any addition to saving that results from a rise in prices, then I must object. If total output is increased and prices rise because marginal costs are rising, it is not clear why any additional saving should be called “forced saving.” No one has a natural right to buy at low prices because they are associated with low levels of aggregate output and income (Keynes 1936, 328). Where, after all, is the coercion supposed to occur? The bank is not forced to lend; the firm is not forced to borrow; and the public is not forced to divide its income in a prescribed manner between consumption and investment, nor is it compelled to allocate its wealth among money and other assets in predetermined amounts. If expectations regarding income, prices, and other variables are not satisfied, the disappointment cannot be laid solely at the feet of lenders and borrowers. Rather, it is the natural outcome of decisions taken in ignorance of one another.
VI. Choice, Coordination, and Alternative Economic Arrangements
The implicit premise in many of my arguments is that economic institutions in which decisions can be made with a knowledge of their consequences are generally superior to economic institutions in which agents must choose without this knowledge. The two alternative economic arrangements I outlined in my first rejoinder to Horwitz—an auction mechanism for pooling the investment plans of large firms, and a market in which workers could insure themselves against falling wages—were designed to narrow the range of uncertainty facing market participants, the first by coordinating investment decisions and the second by affording workers an opportunity to choose the level of income risk they wish to bear.
The Walrasian model of general equilibrium, and its perfect coordination of individual plans, is not helpful in understanding real-world market economies because, to achieve its perfect coordination of decisions, it must abolish the uncertainty arising from decisions not yet made. Although Horwitz and I agree on this point, we disagree about whether the range of future outcomes can be narrowed by choices made in the present. Both of the proposals mentioned above assume that some market participants would find it advantageous to enter into binding agreements today in order to reduce the range of future outcomes they would have to contend with tomorrow. It is important to bear in mind, in this regard, that holding liquid assets is not the only way of coping with uncertainty; contracts also serve this purpose, and usually without the adverse social consequences engendered by a heightened demand for money.
Horwitz argues that the provision of insurance against wage reductions that are beyond the control of individual workers would require the same sort of actuarial certainty that underlies conventional home and life insurance. But if by “insurance,” we mean, more broadly, contracts in which one party agrees to bear the risk of another in exchange for a premium, then Horwitz’s assertion does not fit the facts. There is, in principle, no difference between a futures market in corn where farmers can transfer price risk to commodity brokers, and a futures market in wages where workers could transfer income risk to either a private firm or to society as a whole (see Shiller 1993). A firm that is willing to bet on wage increases and, hence, to pay claims in the event of wage decreases, is not unlike a commodity broker who bets on an increase in corn prices and incurs losses if prices should happen to fall. Similarly, firms that would benefit from falling wages and wished to hedge their bets could do so by accepting premiums now in exchange for a commitment to pay claims in the event of decreasing wages. All of the uncertainties Horwitz cites as obstacles to this insurance scheme—uncertainty about “new inventions,” the introduction of “computer and robotics technology,” the “rise of Japanese competitors” (14–15), etc.—already confront investors who buy and sell any asset with an extended life.
The same point can be made in response to many of the objections Horwitz raises against the auction scheme for coordinating investment decisions. In listing all the complexities and tacit knowledge that go into a firm’s investment decisions, Horwitz seems to have forgotten that these decisions must be made in any case. Firms must already decide how much to invest without knowing how interest rates will change or how much the public plans to save. One of the main sources of uncertainty facing firms considering investment projects is the future level of aggregate demand, which, in turn, is strongly influenced by the level of aggregate investment. Providing a framework within which the investment plans of large firms could be coordinated with respect to aggregate expenditure, if not with regard to composition, is a “discovery procedure” (14) that would generate useful information about aggregate spending.
In concluding, I want to return to my original point: in real-world capitalist economies, incomes are determined in significant measure by a game of chance. Without markets in which plans can be coordinated before final commitments are made, individual choices will produce outcomes that are inefficient and unfair. This result would not be improved upon by the establishment of free banking, an institutional arrangement that is ill designed for the solution of collective action problems. Macro insurance markets are better suited to the twin purposes of coordinating investment plans and affording market participants greater opportunity to insure themselves against outcomes that are beyond their individual control.
References
Arrow, Kenneth J. 1986. “Rationality of Self and Others in an Economic System.” In Rational Choice, ed. Robin M. Hogarth and Melvin W. Reder. Chicago: University of Chicago Press.
Clower, R. W. 1969. “The Keynesian Counter-Revolution: A Theoretical Appraisal.” In idem, Monetary Theory. Middlesex: Penguin Books.
Federal Reserve Bank of Chicago. 1992. Modern Money Mechanics. Chicago: Federal Reserve Bank.
Hill, Greg. 1996a. “The Moral Economy: Keynes’s Critique of Capitalist Justice.” Critical Review 10(1): 33–61.
Hill, Greg. 1996b. “Capitalism, Coordination, and Keynes: Rejoinder to Horwitz.” Critical Review 10(3): 373–87.
Hill, Greg. 1998. “The Socialization of Investment: Comment on Meltzer.” Journal of Post Keynesian Economics 20: 309–13.
Horwitz, Steven. 1996. “Keynes on Capitalism: Reply to Hill,” Critical Review 10(3): 353–72.
Leijonhufvud, Axel. 1968. On Keynesian Economics and the Economics of Keynes. New York: Oxford University Press.
Keynes, John Maynard. 1930. A Treatise on Money. New York: Harcourt Brace.
Keynes, John Maynard. 1936. The General Theory of Employment, Interest, and Money. New York: Harcourt Brace.
Meltzer, Allan H. 1988. Keynes’s Monetary Theory: A Different Interpretation. Cambridge: Cambridge University Press.
Shah, Anup. 1992. Credit Markets and the Distribution of Income. London: Academic Press.
Shiller, Robert. 1993. Macro Markets. New York: Oxford University Press.
Stiglitz, Joseph E. 1994. Wither Socialism? Cambridge, Mass.: MIT Press.
Endotes
*: Greg Hill, Seattle Office of Management and Planning, 300 Municipal Bldg., Seattle, WA 98104, telephone (206) 684-8049, telefax (206) 233-0085, e-mail greg.hill@ci.seattle.wa.us. Back.
Note 1: For simplicity, I assume that households are net savers and firms are net borrowers. Back.
Note 2: This point is developed in Clower 1969 and in Leijonhufvud 1968. Back.
Note 3: See, for example, Stiglitz 1994. Back.
Note 4: For present purposes, I assume that the forecasts of the borrowing firms are validated. Back.