l.Or

0.8 -

0.6 h 0.4-

0.2 h 0.0

-0.2

I I I

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 Quarters

FIGURE 4.4 The effects of a 15 and the interest rate

technology shock on the paths of the wage

tlie saving rate were to rise by so much that r returned immediately to Its usual level, this would mean that consumption was expected to grow rapidly even though r equaled its normal value; this would violate house-nolds intertemporal first-order condition, (4.23). Thus, instead, households raise the fraction of their income that they save, but not by enough to return r immediately to its usual level. And since the increase in A is persistent, he increase in the saving rate is also persistent. As technology retums to normal, the slow adjustment of the capital stock eventually causes A/K to fall below its initial value, and thus causes r to fall below its usual value, hen this occurs, the saving rate falls below its balanced-growth-path level.

When we allow for variations in labor supply, some of the adjustments of the capital stock occur through changes in labor supply rather than the sa\ ing rate: households build up the capital stock during the early phase partly by increasing labor supply, and bring it back to normal in the later phase partly by decreasing labor supply.

The parameter that the results are most sensitive to is . When technology shocks are less persistent, the wealth effect of a shock is smaller I because its impact is shorter-lived), and its intertemporal-substitution effect is larger. As a result, is increasing in , and Ola and are decreasing; , , and are unaffected. If declines from the

The Effects of Changes in Government Purchases

Our baseline parameter values imply - -0.13, olg - 0-15, and --0.004; , , and are as before. Intuitively, an increase in government purchases causes consumption to faU and labor supply to rise because ofits negative wealth effects. And because the rise in government purchases is not permanent, agents also respond by decreasing their capital holdings.

Since the elasticity of output with respect to I is two-thirds, the value of oiG of 0.15 means that output rises by about 0.1% in response to a 1% government-purchases shock. Since output on the balanced growth path is five times government purchases, this means that Y rises by about one-half as much as G. And since one can show that consumption on the balanced growth path is about two-and-one-half times government purchases, the value of ocG of -0.13 means that falls by about one-third as much as increases. The remaining one-sixth of the adjustment takes the form of lower investment.

Figures 4.5-4.7 trace out the effects of a positive 1% government-purchases shock. The capital stock is only slightly affected; the maximum impact is a dechne of 0.03% after 20 quarters. Employment increases and then gradually returns to normal; in contrast to what occurs with tech-

"See Campbell (1994) and Problem 4.4.

4n addition, Kimball (1991) shows that if we relax the assumption of a Cobb-Douglas production function, the elasticity of substitution between capital and labor has important effects on the economys response to shocks.

baseline value of 0.95 to 0.5, for example, oca falls from 0.38 to 0.11, ola rises from 0.3 5 to 0.66, and rises from 0.08 to 0.12. The result is sharper, shorter output fluctuations. In this case, a 1% technology shock raises output by 1.11% in the period of the shock, but only by 0.30% two periods later. If PA = 1, acA rises to 0.63, ola falls to 0.05, and . falls to 0.04. The result is that employment fluctuations are small and output fluctuations are much more gradual. For example, a 1% shock causes output to increase by 0.70% immediately (only slightly larger than the direct effect of 0.67%), and then to rise very gradually to 1% above its initial level.

In addition, suppose we generahze the way that leisure enters the instantaneous utihty function, (4.7), to allow the intertemporal elasticity of substitution in labor supply to take on values other than 1. With this change, this elasticity also has important effects on the economys response to shocks: the larger the elasticity, the more responsive labor supply is to technology and capital. If the elasticity rises from 1 to 2, for example, ala increases from 0.35 to 0.48, and alk increases from -0.31 to -0.41 (in addition, . acK, , and aU change moderately). As a result, fluctuations are larger when the intertemporal elasticity of substitution is higher.

0.2

0.lh

g 0.0

-0.1

-0.2

I I I I

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 Quarters

K-L-

FIGURE 4.5 The effects of a 1% government-purchases shock on the paths of capital and labor

0.2r

0.0

-0.1b

-0.2

2 4 6

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 Quarters

FIGURE 4.6 The effects of a 1% government-purchases shock on the paths of output and consumption