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are now seen as essentially benign institutions, which reconcile the need for long-term commitment of capital to projects without short-term payoffs with the desire of individual investors to be able to withdraw funds on demand. The problem with such intermediaries, according to the model, is that they are vulnerable to self-fulfilling investor panics: if investors believe that sufficiently many other investors will try to cash in early, they will follow suit-and in so doing force destructive early liquidation of real investments In this section I offer a simplified exposition of a Diamond-Dybvig-type model. It is a highly abstract example, substantially harder to map into real-world developments than the simple Pangloss-collapse model of the previous section, but it does give us at least a first pass at the alternative view financial crises, which must involve an initial investment and then something going wrong wif g As in the crisis model above, we consider a three-period world. (Three periods is the minimum why not an infinite horizon? -my own experience, in which the infinite- horizon Krugman 1998 I expectations rather than or as well as actual earnings. While three-period models may seem artificial actually preceded the finite-horizon Krugman 1998a, suggests that for exploratory theorizing nplicity wins out over the marginal gain in realism). In this case, however, there are real investment bills-that yields a known rate of return r. Or they can back investment projects that yield a higher opportunities, of two kinds. Investors can put their wealth into a short-term asset-say, dollar treasu rate of return, say, but that take two periods to mature. That is, one of these projects takes one unit of initial capital and transforms it into(1+h) 2 units of output in period 3, where h>r Crucially, we assume that for some reason it is not possible to sell a halfway-completed project to some other investor who will finish it. One can imagine a variety of reasons for this- perhaps some kind of lemons problem-but for the purposes of this model we simply take the nonmarketability as a given. Thus an investor who decides to liquidate a long-term asset in period 2 must actually scrap the real investment, realizing only a liquidation value v that we assume less than /+r. The need for financial intermediaries is created, following Diamond and Dybvig, by the need of individuals for liquidity. Each individual starts with one unit of capital, but does not know when he will want to consume: only after investing does he discover whether he wants to consume in period 2 or in period 3. This creates a dilemma: an individual who invests in a long-term project, then discovers a need for short-term consumption, is stuck with only the liquidation value. On the other hand, an individual who invests in the safe asset, then discovers that his consumption will take place in period 3, has foregone an opportunity to achieve a higher standard of living Figure 1 illustrates the dilemma of an individual investor in state space, with consumption in period 2 f he turns out to be a period-2 consumer)on the horizontal axis, consumption in period 3(if he turns out to be a period-3 co r)on the vertical. If he invests only in the short-term asset, he will have consumption of 1+r if he turns out to be a period-2 consumer, (1+r)-(because he must then reinvest his capital short-term) if he turns out to be a period-3 consumer. On the other hand, if he invests only in the long-term asset, he will receive only v if he must consume in period 2, but(1+h)2if he consumes in period 3. And he can, of course, choose any convex combination of the two; say point A But now suppose that there is a financial intermediary which pools the capital of a large number of individuals, investing some in the short-term and some in the long-term asset. Ignoring for a momentare now seen as essentially benign institutions, which reconcile the need for long-term commitment of capital to projects without short-term payoffs with the desire of individual investors to be able to withdraw funds on demand. The problem with such intermediaries, according to the model, is that they are vulnerable to self-fulfilling investor panics: if investors believe that sufficiently many other investors will try to cash in early, they will follow suit - and in so doing force destructive early liquidation of real investments. In this section I offer a simplified exposition of a Diamond-Dybvig-type model. It is a highly abstract example, substantially harder to map into real-world developments than the simple Pangloss-collapse model of the previous section, but it does give us at least a first pass at the alternative view. As in the crisis model above, we consider a three-period world. (Three periods is the minimum for financial crises, which must involve an initial investment and then something going wrong with expectations rather than or as well as actual earnings. While three-period models may seem artificial - why not an infinite horizon? - my own experience, in which the infinite-horizon Krugman 1998b actually preceded the finite-horizon Krugman 1998a, suggests that for exploratory theorizing simplicity wins out over the marginal gain in realism). In this case, however, there are real investment opportunities, of two kinds. Investors can put their wealth into a short-term asset - say, dollar treasury bills - that yields a known rate of return r. Or they can back investment projects that yield a higher rate of return, say , but that take two periods to mature. That is, one of these projects takes one unit of initial capital and transforms it into (1+h)2 units of output in period 3, where h>r. Crucially, we assume that for some reason it is not possible to sell a halfway-completed project to some other investor who will finish it. One can imagine a variety of reasons for this - perhaps some kind of lemons problem - but for the purposes of this model we simply take the nonmarketability as a given. Thus an investor who decides to liquidate a long-term asset in period 2 must actually scrap the real investment, realizing only a liquidation value v that we assume less than 1+r. The need for financial intermediaries is created, following Diamond and Dybvig, by the need of individuals for liquidity. Each individual starts with one unit of capital, but does not know when he will want to consume: only after investing does he discover whether he wants to consume in period 2 or in period 3. This creates a dilemma: an individual who invests in a long-term project, then discovers a need for short-term consumption, is stuck with only the liquidation value. On the other hand, an individual who invests in the safe asset, then discovers that his consumption will take place in period 3, has foregone an opportunity to achieve a higher standard of living. Figure 1 illustrates the dilemma of an individual investor in state space, with consumption in period 2 (if he turns out to be a period-2 consumer) on the horizontal axis, consumption in period 3 (if he turns out to be a period-3 consumer) on the vertical. If he invests only in the short-term asset, he will have consumption of 1+r if he turns out to be a period-2 consumer, (1+r) 2 (because he must then reinvest his capital short-term) if he turns out to be a period-3 consumer. On the other hand, if he invests only in the long-term asset, he will receive only v if he must consume in period 2, but (1+h)2 if he consumes in period 3. And he can, of course, choose any convex combination of the two; say point A. But now suppose that there is a financial intermediary which pools the capital of a large number of individuals, investing some in the short-term and some in the long-term asset. Ignoring for a moment
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