Convergence?

It is natural to conclude that real-business-cycle models probably provide the explanation of some but not all of observed macroeconomic fluctuations. In this view, the appropriate next step is to attempt to integrate real-business-cycle models with other views of fluctuations. Similarly, it is natural to say that both calibration and traditional econometric tests are useful ways of evaluating models, and that we should therefore employ both.

Cho and Cooley (1990) and King (1991) take the first steps toward Integrating real-business-cycle and Keynesian models of fluctuations. These papers introduce rigid nominal prices or wages and monetary disturbances mto real-business-cycle models and analyze the resulting models successes and failures in matching major features of fluctuations. The papers conclude that the models performance is mixed. But they may represent a first step toward a synthesis of real-business-cycle and Keynesian models.

It is possible, however, that attempting to integrate the competing theories is a recipe for obscuring rather than uncovering the truth. To take one extreme, if quarter-to-quarter technology shocks are small, if there is little intertemporal substitution in labor supply, and if markets are highly non-Walrasian-all of which are possible-then real-business-cycle models are essentially irrelevant to actual fluctuations. In this case, by insisting

"There are other Important objections to real-business-cycle theory. For example, Barro and King (1984) and Mankiw, Rotemberg, and Summers (1985) observe that times of high consimption are typically also times of low leisure. But households first-order condition relating current labor supply and consumption (equation [4.26]) implies that this can occur only if the real wage is high. Thus, even when there are sources of shocks other than technology, the models appear to require a highly procyclical real wage. To give another example, Rotemberg and Woodford (1994) argue that the size and characteristics of predictable movements in output differ sharply from the predictions of real-business-cycle models.

These potential problems with calibration suggest that focusing on the components of a model individually may be a better strategy than trying to evaluate its overall ht with macroeconomic data. That is, the most useful way to evaluate real-business-cycle models may be to examine the evidence concerning their assumptions of significant technological shocks, substantial short-run elasticities of labor supply, consumption and labor-supply decisions driven by intertemporal optimization, and so on. If the evidence supports these assumptions, then we should investigate their implications for aggregate fluctuations even if a model based on them alone does not match important features of the data. And if the evidence fails to support the assumptions, the issue of whether a model constructed from them matches the data does not appear particularly important.

"Annual values for all of these series are pubhshed in the Economic Report ofthe President. Quarterly values are available from the Citibase data bank.

on incorporating real-business-cycle ingredients into our models, we would only be making it more difficult to identify the forces that actually drive economic fluctuations. At the other extreme, if the assumptions of, say, the Prescott model are approximately correct-which is also possible-then that model provides a parsimonious representation of the central features of most actual fluctuations. By insisting on complexity we would again be missing the essence of fluctuations. Similar comments apply to the issue of calibration versus traditional statistical procedures: if one approach is more informative than the other, pursuing both is costly.

It is of course possible that actual fluctuations are complicated and involve important elements of both real-business-cycle and Keynesian theories. Thus we cannot rule out the real-business-cycle view, the Keynesian view, or intermediate views of the sources and nature of aggregate fluctuations. As a result, macroeconomists have little choice but to make tentative judgments, based on the currently available models and evidence, about what lines of inquiry are most promising. And they must remain open to the possibility that those judgments will need to be revised.

Problems

4.1. Redo the calculations reported in Table 4.1 for any country other than the United States.

4.2. Redo the calculations reported in Table 4.3 for the foUowing: (a) Employees compensation as a share of national income. ib) The labor force participation rate.

(c) The federal government budget deficit as a share of GDP.

(d) The Standard and Poor 500 composite stock price index.

(e) The difference in yields between Moodys BAA and AAA bonds.

(f) The difference in yields between 10-year and 3-month U.S. Treasury securities.

(g) The weighted average exchange rate of the U.S. dollar against the currencies of other G-10 countries.

4.3. Let InAo denote the value of A in period 0, and let the behavior of InA be given by equations (4.8)-(4.9).

(a) Express InAi, lnA2, and In A3 in terms of 1 , 1, 2, . A and g.

(b) In light of the fact that the expectations of the f zero, what are the expectations of InAi.lnAa, and In A3 given In Ao, A, and g?

4.4. Suppose the period-f utility function, u,, is = InCt -i- b(l - t)~/(l - y), ii > 0, > 0, rather than by (4.7).

(a) Consider the one-period problem analogous to that investigated in (4.12)-(4.15). How, if at all, does labor supply depend on the wage?

(b) Consider the two-period problem analogous to that investigated in (4.16)-(4.21). How does the relative demand for leisure in the two periods depend on the relative wage? How does it depend on the interest rate? Explain intuitively why affects the responsiveness of labor supply to wages and the interest rate.

4.5. Consider the problem investigated in (4.16)-(4.21).

(a) Show that an increase in both wi and W2 that leaves wi/wz unchanged does not affect or 2-

ib) Now assume that the household has initial wealth of amount Z > 0. (i) Does (4.23) continue to hold? Why or why not? (zz) Does the result in (a) continue to hold? Why or why not?

4.6. Suppose an individual lives for two periods and has utility In Ci -i- In C2.

(a) Suppose the individual has labor income of Yi in the first period of life and zero in the second period. Second-period consumption is thus (1 -I- r)(Yi - Cl); r, the rate of return, is potentially random.

(z) Find the first-order condition for the individuals choice of Ci.

(zz) Suppose r changes from being certain to being uncertain, without any change in E[r]. How, if at all, does Ci respond to this change?

(b) Suppose the individual has labor income of zero in the first period and 2 in the second. Second-period consumption is thus 2 - (1 -1- )Ci.y2 is certain; again, r may be random.

(z) Find the first-order condition for the individuals choice of Ci.

(zz) Suppose r changes from being certain to being uncertain, without any change in E[r]. How, if at all, does Ci respond to this change?

4.7. (a) Use an argument analogous to that used to derive equation (4.2 3) to show

that household optimization requires fo/(l = e~Etlw,{l + rf+])fo/

[Wt,i(l-,+l)]].

(b) Show that this condifion is implied by (4.23) and (4.26). (Note that [4.26] must hold in every period.)

4.8. A simpUfied real-business-cycle model with additive technology shocks.

(This follows Blanchard and Fischer, 1989, pp. 329-331.) Consider an economy consisting of a constant population of infinitely-lived individuals. The representative individual maximizes the expected value of = uiCt)/{l+p), p > 0. The instantaneous utility function, u(Cf), is u{C,) = ,- > 0. Assume that is always in the range where u{C) is positive.

Output is linear in capital, plus an additive disturbance: Y, = AK, + e,. There is no depreciation; thus Kt+i = K, + Y, - Ct, and the interest rate is A.