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31

Empirical Application: Are Modern Economies Dynamically Efficient?

The Diamond model shows that it is possible for a decentralized economy to accumulate capital beyond the golden-rule level, and thus to produce an allocation that is Pareto-inefficient. Given that capital accumulation in actual economies is not dictated by social planners, this raises the issue of whether actual economies might be dynamically inefficient. If they were, there would be important implications for public policy: the great concern about low rates of saving would be entirely misplaced, and there would be an easy way of increasing both present and future consumption.

At first glance, dynamic inefficiency appears to be a possibility for the United States and other major economies. A balanced growth path is dynamically inefficient if the real rate of return, fik*) - S, is less than the growth rate of the economy. A straightforward measure of the real rate of return is the real interest rate on short-term government debt. In the United States over the past fifty years, this interest rate has averaged only a few tenths of a percent; this is much less than the average growth rate of the economy, which is about 3 percent. Similar findings hold for other major industrialized countries. Thus the real interest rate is less than the golden-rule level, which suggests that these economies have overaccumulated capital.

There is a problem with this argument, however. In a world of certainty, all interest rates must be equal; thus there is no ambiguity in what is meant by "the" rate of return. But if there is uncertainty, different assets can have different expected returns. Suppose, for example, we assess dynamic efficiency by examining the marginal product of capital net of depreciation instead of the return on a fairly safe asset. If capital earns its marginal product, the net marginal product can be estimated as the ratio of overall capital income minus total depreciation to the value of the capital stock. For the United States, this ratio is about 10 percent, which is much more than the economys growth rate. Thus, using this approach we would conclude that the U.S. economy is dynamically efficient. Our simple-theoretical model, in which the marginal product of capital and the safe interest rate are the same, provides no guidance concerning which of these contradictory conclusions is correct.

Abel, Mankiw, Summers, and Zeckhauser (1989) tackle the issue of how to assess dynamic efficiency in a world of uncertainty. Their principal theoretical result is that under uncertainty, the condition for dynamic efficiency is that net capital income exceed investment. For the balanced growth path of an economy with certainty, this condition is the same as the usual comparison of the real interest rate with the economys growth rate. In this case, net capital income is the real interest rate times the stock of capital, and investment is the growth rate of the economy times the stock of capital. Thus capital income exceeds investment if and only if the real interest



They argue that adjusting these figures to account for land income and monopoly rents does not change the basic results.

rate exceeds the economys growth rate. But Abel et al. show that under uncertainty these two conditions are not equivalent, and that it is the comparison of capital income and investment that provides the correct way of judging whether there is dynamic efficiency. Intuitively, a capital sector that is on net making resources available by producing more output than it is using for new investment is contributing to consumption, whereas one that is using more in resources than it is producing is not.

Abel et al.s principal empirical result is that the condition for dynamic efficiency seems to be satisfied in practice. They measure capital income as national income minus employees compensation and the part of the income of the self-employed that appears to represent labor income; investment is taken directly from the national income accounts. They find that capital income consistently exceeds investment in the United States and in the six other major industrialized countries they consider. Even in Japan, where investment is remarkably high, the profit rate is so great that the returns to capital comfortably exceed investment. Thus, although decentralized economies can produce dynamically inefficient outcomes in principle, they do not appear to in practice.

2.14 Government in the Diamond Model

As in the infinite-horizon model, a natural question to ask of the Diamond model is what occurs if we introduce a government that makes purchases, levies taxes, and issues debt. For simplicity, we focus on the case of logarithmic utility and Cobb-Douglas production. ....

. . - - - :

The Effects of Covernment Purchases

Let Gf denote the governments purchases of goods per unit of effective labor in period f. Assume for the moment that it finances those purchases by lump-sum taxes on the young.

When the government finances its purchases entirely with taxes, workers after-tax income in period is (1 - a)k" - Gt rather than (1 - a)k". The equation of motion for k, equation (2.61), therefore becomes

A higher Gt therefore reduces kt+i for a given kt.



NEW

FIGURE 2.1 5 The effects of a permanent increase in government purchases

To see the effects of government purchases, suppose that the economy is on a balanced growth path with G constant, and that G increases permanently. From (2.69), this shifts the kt+i function down; this is shown in Figure 2.15. The downward shift of the kt+i function reduces k*. Thus-in contrast to what occurs in the infinite-horizon model-higher government purchases lead to a lower capital stock and a higher equilibrium real interest rate. Intuitively, since individuals live for two periods, they reduce their first-period consumption less than one-for-one with the increase in G. But since taxes are levied only in the first period of life, this means that their saving falls. As usual, the economy moves smoothly from the initial balanced growth path to the new one.

As a second example, consider a temporary increase in government purchases from Gl to Gh, again with the economy initially on its balanced growth path. The dynamics of are thus described by (2.69) with G = Gh during the period that government purchases are high and by (2.69) with G = Gl before and after. That is, the fact that individuals know that govemment purchases will return to Gl does not affect the behavior of the economy during the time that purchases are high. The saving of the young- and hence next periods capital stock-is determined by their after-tax labor income, which is determined by the current capital stock and by the governments current purchases. Thus during the time that government purchases are high, gradually falls and r gradually increases. Once G returns to Gl, rises gradually back to its initial level.

The result that future values of G do not affect the current behavior of the economy



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