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Macroeconomic Priorities†

By ROBERT E. LUCAS,JR.*

Macroeconomics was born as a distinct field to give up in return? About one-half of one- in the 1940’s, as a part of the intellectual re- tenth of a percent, I calculate. I will defend this sponse to the Great Depression. The term then estimate as giving the right order of magnitude referred to the body of knowledge and expertise of the potential gain to society from improved that we hoped would prevent the recurrence of stabilization policies, but to do this, many ques- that economic disaster. My thesis in this lecture tions need to be addressed. is that in this original sense How much of aggregate vari- has succeeded: Its central problem of depression ability should be viewed as pathological? How prevention has been solved, for all practical much can or should be removed by monetary purposes, and has in fact been solved for many and fiscal means? Section III reviews evidence decades. There remain important gains in wel- bearing on these questions. Section IV consid- fare from better fiscal policies, but I argue that ers attitudes toward risk: How much do people these are gains from providing people with bet- dislike consumption uncertainty? How much ter incentives to work and to save, not from would they pay to have it reduced? We also better fine-tuning of spending flows. Taking know that business-cycle risk is not evenly dis- U.S. performance over the past 50 years as a tributed or easily diversified, so welfare cost benchmark, the potential for welfare gains from estimates that ignore this fact may badly under- better long-run, supply-side policies exceeds by state the costs of fluctuations. Section V reviews far the potential from further improvements in recently developed models that let us explore short-run demand management. this possibility systematically. These are hard My plan is to review the theory and evidence questions, and definitive answers are too much leading to this conclusion. Section I outlines the to ask for. But I argue in the end that, based on general logic of quantitative welfare analysis, in what we know now, it is unrealistic to hope for which policy comparisons are reduced to differ- gains larger than a tenth of a percent from better ences perceived and valued by individuals. It countercyclical policies. also provides a brief review of some exam- ples—examples that will be familiar to I. Welfare Analysis of Public Policies: many—of changes in long-run monetary and Logic and Results fiscal policies that consumers would view as equivalent to increases of 5–15 percent in their Suppose we want to compare the effects of overall consumption levels. two policies, A and B say, on a single consumer. Section II describes a thought-experiment in Under policy A the consumer’s welfare is which a single consumer is magically relieved U(cA), where cA is the consumption level he of all consumption variability about trend. How enjoys under that policy, and under policy B it Ͻ much average consumption would he be willing is U(cB). Suppose that he prefers cB: U(cA) ␭ Ͼ U(cB). Let 0 solve

† ͑͑ ϩ ␭͒ ͒ ϭ ͑ ͒ Presidential Address delivered at the one-hundred fif- U 1 cA U cB . teenth meeting of the American Economic Association, January 4, 2003, Washington, DC. ␭ * Department of , University of , We call this number —in units of a percentage 1126 East 59th Street, Chicago, IL 60637. I am grateful for of all consumption goods—the welfare gain of discussions with Fernando Alvarez, Gadi Barlevy, Lars a change in policy from A to B. To evaluate the Hansen, Per Krusell, Ellen McGrattan, Chris Phelan, effects of policy change on many different con- Edward Prescott, Esteban Rossi-Hansberg, Tom Sargent, Matthew Shapiro, Tony Smith, Nancy Stokey, Kjetil Stores- sumers, we can calculate welfare gains (perhaps letten, and Tom Tallarini, and for the able assistance of losses, for some) for all of them, one at a time, Adrian Kats and Mikhail Golosov. and add the needed compensations to obtain the 1 2 THE MARCH 2003 welfare gain for the group. We can also specify details, but all were variations on a one-good the compensation in terms of one or a subset growth model in which consumers (either an of goods, rather than all of them: There is no infinitely lived dynasty or a succession of gen- single, right way to carry these comparisons out. erations) maximize the utility of consumption However it is done, we obtain a method for and leisure over time, firms maximize profit, evaluating policies that has comprehensible units and markets are continuously cleared. and is built up from individual preferences. In general, these studies found that reducing There is a great tradition of quantitative pub- capital income taxation from its current U.S. lic finance that applies this general framework level to zero (using other taxes to support an using well-chosen Taylor expansions to calcu- unchanged rate of government spending) would late estimates of the compensation parameter ␭, increase the balanced-growth capital stock by “welfare triangles” as Arnold C. Harberger 30 to 60 percent. With a capital share of around called them. Today we use numerical simula- 0.3, these numbers imply an increase of con- tion of general-equilibrium models, often dy- sumption along a balanced growth path of 7.5 to namic and subject to unpredictable shocks, to 15 percent. Of course, reaching such a balanced carry out welfare analysis with the general logic path involves a period of high investment rates that I have just sketched. Some examples will, I and low consumption. Taking these transition hope, convey the applicability of this approach costs into account, overall welfare gains amount and some of the estimates that have emerged. to perhaps 2 to 4 percent of annual consump- Martin J. Bailey’s (1956) thought-experiment tion, in perpetuity. of a perfectly predictable inflation at a constant Production per adult in France is about 70 rate, induced by sustained growth in the money percent of production per adult in the United supply, was a pioneering example of the quan- States. Edward C. Prescott (2002) observes that titative evaluation of policy. In a replication of hours worked per adult in France, measured as the Bailey study, I estimated the welfare gain a fraction of available hours, are also about 70 from reducing the annual inflation rate from 10 percent of the comparable U.S. figure. Using to 0 percent to be a perpetual consumption flow estimates for France and the of the 1 ϩ ␶ Ϫ ␶ of 1 percent of income. Some take ratio (1 c)/(1 h) that equals the mar- estimates like this to imply that inflation is a ginal rate of substitution between consumption relatively modest problem, but 1 percent of in- and leisure in the neoclassical growth model, he come is a serious amount of money, and in any shows that tax differences can account for the case, the gain depends on how much inflation entire difference in hours worked and, amplified there is. The gain from eliminating a 200- by the indirect effect on capital accumulation, percent annual inflation—well within the range for the entire difference in production. The of recent experience in several South American steady-state welfare gain to French households —is about 7 percent of income. of adopting American tax rates on labor and The development of growth theory, in which consumption would be the equivalent of a con- the evolution of an over time is traced sumption increase of about 20 percent. The con- to its sources in consumer preferences, technol- clusion is not simply that if the French were to ogy, and government policies, opened the way work American hours, they could produce as for extending general-equilibrium policy analy- much as Americans do. It is that the utility sis to a much wider class of dynamic settings. In consequences of doing so would be equivalent the 1980’s, a number of economists used ver- to a 20-percent increase in consumption with no sions of neoclassical growth theory to examine increase in work effort! the effects of taxation on the total stock of The gain from reducing French taxes to U.S. capital, not just the composition of that stock.2 levels can in part be viewed as the gain from The models used in these studies differ in their adopting a flat tax on incomes,3 but it is doubt-

1 Lucas (2000). My estimates are based on the money demand estimates in Allan H. Meltzer (1963). rence H. Summers (1981), Alan J. Auerbach and Laurence 2 For example, William A. Brock and Stephen J. J. Kotlikoff (1987), and Kenneth L. Judd (1987). Turnovsky (1981), Christophe P. Chamley (1981), Law- 3 See also Robert E. Hall and Alvin Rabushka (1995). VOL. 93 NO. 1 LUCAS: MACROECONOMIC PRIORITIES 3

ful that all of it can be obtained simply by something other than mere units changes. Then rearranging the tax structure. It entails a reduc- it must also be the case that these same rigidities tion in government spending as well, which prevent the economy from responding effi- Prescott interprets as a reduction in the level of ciently to real shocks, raising the possibility that transfer payments, or in the government provi- a that reacts to real shocks in sion of goods that most people would buy any- some way can improve efficiency. way, financed by distorting taxes. Think of If we had a theory that could let us sort these elementary schooling or day care. The gains issues out, we could use it to work out the from eliminating such fiscal “cross-hauling” (as details of an ideal stabilization policy and to [1996] called the Swedish day- evaluate the effects on welfare of adopting it. care system) involve more than eliminating “ex- This seems to me an entirely reasonable re- cess burden,” but they may well be large. search goal—I have been thinking success is The stakes in choosing the right monetary just around the corner for 30 years—but it has and fiscal policies are high. Sustained inflation, not yet been attained. In lieu of such a theory, I tax structures that penalize capital accumulation will try to get quantitative sense of the answer to and work effort, and tax-financed government the thought-experiment I have posed by study- provision of private goods all have uncompen- ing a series of simpler thought-experiments. sated costs amounting to sizeable fractions of In the rest of this section, I ask what the effect income. We can see these costs in differences in on welfare would be if all consumption vari- economic performance across different countries ability could be eliminated.4 To this end, con- and time periods. Even in the United States, sider a single consumer, endowed with the which visibly benefits from the lowest excess stochastic consumption stream burdens in the modern world, economic analy- ϭ ␮t Ϫ͑1/2͒␴2␧ sis has identified large potential gains from fur- (1) ct Ae e t , ther improvements in long-run fiscal policy. ␧ where log( t) is a normally distributed random II. Gains from Stabilization: variable with mean 0 and variance ␴ 2. Under A Baseline Calculation these assumptions

͑ Ϫ͑1/2͒␴2␧ ͒ ϭ In the rest of the lecture, I want to apply the E e t 1 public finance framework just outlined to the assessment of gains from improved stabilization and mean consumption at t is Ae␮t. Preferences policy. Such an exercise presupposes a view of over such consumption paths are assumed to be the workings of the economy in which short-run t monetary and fiscal policies affect resource al- ϱ 1 Ϫ ␥ 1 ct location in ways that are different from the (2) Eͭ ͸ ͩ ͪ ͮ , 1 ϩ ␳ 1 Ϫ ␥ supply side effects I have just been discussing. t ϭ 0 One possibility is that instability in the quan- tity of money or its rate of growth, arising from where ␳ is a subjective discount rate, ␥ is the government or private sources, induces ineffi- coefficient of , and the expectation cient real variability. If that were all there was is taken with respect to the common distribution ␧ ␧ to it, the ideal stabilization policy would be to of the shocks 0 , 1 , ... . fix the money growth rate. (Of course, such a Such a risk-averse consumer would obvi- policy would require the Federal Reserve to ously prefer a deterministic consumption path take an active role in preventing or offsetting to a risky path with the same mean. We quantify instabilities in the private banking system.) But this utility difference by multiplying the risky this cannot be all there is to it, because an path by the constant factor 1 ϩ ␭ in all dates economy in which monetary fluctuations induce and states, choosing ␭ so that the household is real inefficiencies—indeed, any economy in which money has value—must be one that op- erates under missing markets and nominal ri- 4 This calculation replicates the one I carried out in gidities that make changes in money into Lucas (1987, Ch. III). 4 THE AMERICAN ECONOMIC REVIEW MARCH 2003 indifferent between the deterministic stream Many questions have been raised about this and the compensated, risky stream. That is, ␭ is estimate, and subsequent research on this issue chosen to solve has pursued many of them, taking the discus- sion deep into new scientific territory. In the next four sections, I will review some of the ϱ ͑͑ ϩ ␭͒ ͒1 Ϫ ␥ 1 ct main findings. (3) Eͭ ͸ ␤t ͮ Ϫ ␥ ϭ 1 t 0 III. Removeable Variance: Two Estimates

ϱ ͑Ae␮t͒1 Ϫ ␥ Even if we do not know exactly how much ϭ ͸ ␤t , 1 Ϫ ␥ consumption risk would be removed by an op- t ϭ 0 timal monetary and fiscal policy, it is clear that it would fall far short of the removal of all where ct is given by (1). Canceling, taking logs, variability. The major empirical finding in mac- and collecting terms gives roeconomics over the past 25 years was the demonstration by Finn E. Kydland and Prescott 1 (1982), replicated and refined by Gary D. (4) ␭ Х ␥␴2. 2 Hansen (1985) and by many others since then, that technology shocks measured by the method This compensation parameter ␭—the welfare of Robert M. Solow (1957) can induce a rea- gain from eliminating consumption risk— sonably parameterized stochastic growth model depends, naturally enough, on the amount of to exhibit nearly the same variability in produc- risk that is present, ␴2, and the aversion people tion and consumption as we see in postwar U.S. have for this risk, ␥. time series. In the basic growth model, equilib- We can get an initial idea of the value to the rium and optimal growth are equivalent, so that economy as a whole of removing aggregate risk if technology shocks are all there is to postwar by viewing this agent as representative of U.S. business cycles, resources are already being al- consumers in general. In this case, to estimate ␭ located efficiently and a variance-reducing we need estimates of the variance ␴2 of the log monetary-fiscal policy would be welfare reduc- of consumption about its trend, and of the co- ing. Even if the equilibrium is inefficient, due to efficient ␥ of risk aversion. Using annual U.S. distorting taxes, missing markets or the like, in data for the period 1947–2001, the standard the face of unavoidable technology and prefer- deviation of the log of real, per capita consump- ence shocks an optimal monetary and fiscal tion about a linear trend is 0.032.5 Estimates of the policy will surely be associated with a positive parameter ␥ in use in macroeconomics and pub- level of consumption variance. We need to es- lic finance applications today range from 1 (log timate the size of that part and remove it from utility) to 4. Using log utility, for example, the the estimate of ␴2 used in (4). formula (4) yields the welfare cost estimate Matthew D. Shapiro and Mark W. Watson’s (1988) study is one of several relatively atheo- 1 retical attempts to break down the variance of (5) ␭ ϭ ͑0.032͒2 ϭ 0.0005, 2 production and other variables into a fraction due to what these authors call “demand” shocks about one-twentieth of 1 percent of consumption. (and which I will call “nominal” shocks) and Compared to the examples of welfare gains fractions due to technology and other sources. from fiscal and monetary policy changes that I Their study represents quarterly U.S. time series cited above, this estimate seems trivially small: over the period 1951–1985 as distributed lags of more than an order of magnitude smaller than serially independent shocks. The observables the gain from ending a 10-percent inflation! include first differences of a measure of hours worked, a log real GDP measure, and the cor- responding implicit price deflator. To these 5 The comparable figure using a Hodrick-Prescott trend three rates of change are added an ex post real with the smoothing parameter 400 is 0.022. interest rate (the three-month Treasury bill rate VOL. 93 NO. 1 LUCAS: MACROECONOMIC PRIORITIES 5 minus the inflation rate) and the change in the TABLE 1—PERCENTAGE OF VARIANCE DUE TO NOMINAL relative price of oil. The coefficients of an in- SHOCKS AT DIFFERENT FORECAST HORIZONS vertible vector autoregression are estimated, Quarter Output Hours Inflation Interest rate subject to several restrictions. This procedure ␧ 128368983 yields time series of estimated shocks ˆ t and decompositions of the variance of each of the 428408271 820318272 five variables into the fractions “explained” by 12 17 27 84 74 the most recent k values of each of the five 20 12 20 86 79 shocks. 36 8 12 89 85 Shapiro and Watson apply a variety of the- ϱ 0 0 94 94 oretical principles to the interpretation of their estimates. They do not consistently fol- low the general-equilibrium practice of inter- Shapiro and Watson do with the two nominal preting all shocks as shifts in preferences, shocks, and interpret their paper as partitioning technologies, or the behavior of policy vari- the variance of output and hours into nominal ables, but they have in mind some kind of and real sources. The resulting Table 1 is a monetary growth model that does not have a condensation of their Table 2. long-run .6 Real variables, in The two zeroes for output and hours in the the long run, are determined by real factors last, long-run, row of Table 1 are there by the only. Nominal shocks can affect real variables definition of a nominal shock. But the two 94- and relative prices in the short run but not in percent entries in this row for inflation and the the long run. This idea is not tested: Long-run nominal interest rate could have come out any neutrality is imposed on the statistical model. way. I take the fact that these values are so close In return it becomes possible to estimate sep- to1asaconfirmation of Shapiro and Watson’s arately the importance of nominal shocks to procedure for identifying nominal shocks. Ac- the short- and medium-run variability of out- cording to Table 1, these nominal shocks have put, hours, and real interest rates.7 accounted for something less than 30 percent of In the five-variable scheme that Shapiro and short-run production variability in the postwar Watson use, there are two nominal variables— United States. This effect decays slowly, with the inflation rate and the nominal interest rate— no change after one year, a reduction to 20 and three real ones—output, hours, and the percent after two years, and so on. relative price of oil. They assume as well five One can ask whether a better estimate of the shocks, two of which are nominal in the sense importance of nominal shocks could have ob- of having no effect on real variables in the long tained by using M1 or some other observable run. They are not able to measure the effects of measure of monetary shocks. Many studies the two dimensions of nominal instability sep- have proceeded in this more direct way,8 and arately. The other three shocks are taken to be much has been learned, but in the end one does real. The assumed exogeneity of oil price not know whether the importance of monetary shocks plus a long-run neutrality hypothesis on shocks has been estimated or just the impor- hours are used to estimate the importance of tance of a particular, possibly very defective, three distinct real shocks. This aspect of their measure of them. Information on future prices is identification seems to me questionable, and in conveyed to people by changes in monetary any case it is of an entirely different nature from aggregates, of course, but it is also conveyed by the neutrality of nominal shocks. I will just interest-rate and exchange-rate movements, by lump the effects of the real shocks together, as changes in the fiscal situation that may lead to tighter or easier money later on, by changes in financial regulations, by statements of influen- 6 To remove any doubt on the latter point, they quote tial people, and by many other factors. Shapiro from ’s (1968) Presidential Address. and Watson’s method bypasses these hard 7 A similar, and similarly motivated, identification pro- cedure was used in Olivier J. Blanchard and Danny Quah (1989). Thomas J. Sargent and Christopher A. Sims (1977) is a predecessor in spirit, if not in detail. 8 For example, Lawrence J. Christiano, et al. (1996). 6 THE AMERICAN ECONOMIC REVIEW MARCH 2003 measurement questions and goes directly to an technology shocks, based on comovements of estimation of the importance of nominal shocks production and labor input over the cycle. in general, those we know how to measure and Shapiro and Watson find that at most 30 those we do not, whatever they may be. percent of cyclical output variability can be A second reason for preferring the procedure attributed to nominal shocks. Working from the Shapiro and Watson used is that the effects of opposite direction, Prescott and Aiyagari con- nominal shocks as they estimate them include clude that at least 75 percent of cyclical output the effects of real shocks that could have been variability must be due to technology shocks. offset by monetary policy but were not. What- These findings are not as consistent as they may ever it is that keeps prices from rising in pro- appear, because there are important real factors portion to a given increase in money must also besides technological shocks—shocks to the tax keep relative prices from adjusting as neoclas- system, to the terms of trade, to household tech- sical theory would predict they should to, say, nology, or to preferences—that are cyclically an increase in the OPEC-set price of oil. Effects important but not captured in either of the cat- of either kind—those initiated by monetary egories I have considered so far.10 Even so, on changes and those initiated by real shocks—will the basis of this evidence I find it hard to imag- last only as long as the rigidity or glitch that ine that more than 30 percent of the cyclical gives rise to them lasts, vanishing in the long variability observed in the postwar United run, and will be identified as arising from the States could or should be removed by changes “nominal,” or “demand,” shock under the Sha- in the way monetary and fiscal policy is piro and Watson identification procedure. Thus conducted. I want to interpret the estimates in columns 2 and 3 of Table 1 as upper bounds on the vari- IV. Risk Aversion ance that could have been removed from output and hours at different horizons under some The estimate of the potential gains from sta- monetary policy other than the one actually bilization reviewed in Section II rests on as- pursued. The table gives no information on sumed consumer preferences of the constant what this variance-minimizing monetary policy relative risk aversion (CRRA) family, using but might have been, and there is no presumption two parameters—the subjective discount rate ␳ that it would have been a policy that does not and the risk-aversion coefficient ␥—to charac- respond to real shocks. terize all households. This preference family is Shapiro and Watson applied the theoretical almost universally used in macroeconomic and idea that nominal shocks should be neutral in public finance applications. The familiar for- the long run to obtain an estimate of the fraction mula for an economy’s average return on capital of short-run output variability that can be attrib- under CRRA preferences, uted to such shocks. Prescott (1986a) proceeded in a quite different way to arrive at an estimate (6) r ϭ ␳ ϩ ␥g, of the fraction of output variability that can be attributed to technology shocks. He used actual where g is the growth rate of consumption, Solow residuals to estimate the variance and makes it clear why fairly low ␥ values must be serial correlation of the underlying technology used. Per capita consumption growth in the shocks. Feeding shocks with these properties United States is about 0.02 and the after-tax into a fully calibrated real-business-cycle model return on capital is around 0.05, so the fact that resulted in output variability that was about 84 ␳ must be positive requires that ␥ in (6) be at percent of actual variability.9 In a complemen- most 2.5. Moreover, a value as high as 2.5 tary study, S. Rao Aiyagari (1994) arrived at an would imply much larger interest rate differen- estimate of 79 percent for the contribution of

10 For example, Shapiro and Watson attribute a large 9 Questions of measurement errors are discussed in the share of output variance to a shock which they call “labor paper and by Summers (1986) in the same volume. In supply” [and which I would call “household technology,” Prescott (1986b), estimates of 0.5 to 0.75 for the contribu- following Jess Benhabib et al. (1991) and Jeremy tion of technology shocks to output variance are proposed. Greenwood and Zvi Hercowitz (1991)]. VOL. 93 NO. 1 LUCAS: MACROECONOMIC PRIORITIES 7 tials than those we see between fast-growing of the supply-side gains cited in Section I, and economies like Taiwan and mature economies two orders of magnitude larger than the estimate like the United States. This is the kind of evi- I proposed in Section II.14 As Maurice Obstfeld dence that leads to the use of ␥ values at or near (1994) shows, this result is basically the for- 1 in applications. mula (4) with a coefficient of risk aversion two But the CRRA model has problems. Rajnish orders of magnitude larger than the one I used. Mehra and Prescott (1985) showed that if one Fernando Alvarez and Urban J. Jermann wants to use a stochastic growth model with (2000) take a nonparametric approach to the CRRA preferences to account for the entire evaluation of the potential gains from stabiliza- return differential between stocks and bonds— tion policy, relating the marginal cost of busi- historically about 6 percent—as a premium for ness-cycle risk to observed market prices risk, the parameter ␥ must be enormous, per- without ever committing to a utility function. haps 50 or 100.11 Such values obviously cannot Their estimation procedure is based on the ob- be squared with (6). This “equity premium puz- servation that consumption streams with a wide zle” remains unsolved, and has given rise to a variety of different risk characteristics—or vast literature that is clearly closely related to something very nearly equivalent to them—are the question of assessing the costs of available for sale in securities markets. They instability.12 use a mix of asset-pricing theory and statistical One response to the puzzle is to adopt a methods to infer the prices of a claim to the three- rather than two-parameter description actual, average consumption path and alterna- of preferences. Larry G. Epstein and Stanley tive consumption paths with some of the uncer- E. Zin (1989, 1991) and Philippe Weil (1990) tainty removed. They call the price differentials proposed different forms of recursive utility, so estimated marginal welfare costs, and show preference families in which there is one pa- that they will be upper bounds to the corre- rameter to determine intertemporal substitut- sponding total cost: my compensation parame- ability and a second one to describe risk ter ␭. The basic underlying hypotheses are that aversion. The first corresponds to the param- asset markets are complete and that asset-price eter ␥ in (6), and can be assigned a small differences reflect risk and timing differences value to fit estimated average returns to cap- and nothing else. ital. Then the risk-aversion parameter can be The gain from the removal of all consump- chosen as large as necessary to account for tion variability about trend, estimated in this the equity premium. way, is large—around 30 percent of consump- Thomas D. Tallarini, Jr. (2000) uses prefer- tion.15 This is a reflection of the high risk aver- ences of the Epstein-Zin type, with an intertem- sion needed to match the 6-percent equity poral substitution elasticity of 1, to construct a premium, and can be compared to Tallarini’s real-business-cycle model of the U.S. economy. estimate of 10 percent. But the gain from re- He finds an astonishing separation of quantity moving risk at what Alvarez and Jermann call and asset price determination: The behavior of business-cycle frequencies—cycles of eight aggregate quantities depends hardly at all on attitudes toward risk, so the coefficient of risk 14 aversion is left free to account for the equity James Dolmas (1998) uses still another preference 13 family, obtaining much higher cost estimates than mine. premium perfectly. Tallarini estimates a wel- Like Tallarini, Christopher Otrok (1999) develops and an- fare cost of aggregate consumption risk of 10 alyzes a complete real-business-cycle model. He uses a percent of consumption, comparable to some preference family proposed by John Heaton (1995). His cost estimates are close to mine. A recent paper by Anne Epaulard and Aude Pommeret (2001) contains further results along this line, and provides a very useful quantita- 11 See also and Kenneth J. Singleton tive comparison to earlier findings. (1983). 15 Alvarez and Jermann offer many estimates in their 12 Two especially informative surveys are John H. Tables 2A–2D. My summary is based on Table 2D, which Cochrane and Hansen (1992) and Narayana R. Kocherla- uses postwar (1954–1997) data and requires that consump- kota (1996). tion and dividends be cointegrated. From this table, I follow 13 Similar results, obtained in a closely related context, the authors and cite averages over the columns headed “8 were reported by Hansen et al. (1999). years” and “inf.” 8 THE AMERICAN ECONOMIC REVIEW MARCH 2003 years or less—is two orders of magnitude that the welfare costs of cycles are not so high smaller, around 0.3 percent. Most of the high on average, but may be very high for, say, the return on equity is estimated to be compensation very poor or currently unemployed members of for long-term risk only, risk that could not be society.” Several recent studies have pursued much reduced by short-run policies that are this possibility.16 Doing so evidently requires neutral in the long run. models with incomplete risk sharing and differ- Accepting Shapiro and Watson’s finding that ently situated agents. less that 30 percent of output variance at Krusell and Smith (1999, 2002) study a business-cycle frequencies can be attributed to model economy in which individual families nominal shocks, the lower Alvarez and Jermann are subject to three kinds of stochastic shocks. estimate of 0.3 should be reduced to 0.1 if it is There is an aggregate productivity shock that to serve my purpose as an estimate of the value affects everyone, and employment shocks that of potential improvements in stabilization pol- differ from person to person. Families are infi- icy. But it is important to keep in mind that this nitely lived dynasties, but every 40 years or so estimate is not smaller than Tallarini’s because a family draws a new head, whose subjective of a different estimate of risk aversion. Tallarini’s discount rate is drawn from a fixed distribution. estimate of ␥ ϭ 100 is the parametric analogue Dynasties with patient heads will accumulate of Alvarez and Jermann’s “market price of wealth while others will run their wealth risk,” based on exactly the same resolution of down.17 The sizes of these shocks are chosen so the . The different cost that the model economy experiences realistic estimate is entirely due to differences in the GDP fluctuations, spells have consumption paths being compared. realistic properties, and the overall wealth dis- Resolving empirical difficulties by adding tribution matches the U.S. distribution: In the new parameters always works, but often only by model, the wealthiest 5 percent of households raising more problems. The risk-aversion levels own 54 percent of total wealth; in reality, they needed to match the equity premium, under the hold 51 percent. assumption that asset markets are complete, It is essential to the substantive question that ought to show up somewhere besides securities motivates this study that neither the employ- prices, but they do not seem to do so. No one ment shocks nor the uncertainty about the char- has found risk-aversion parameters of 50 or 100 acter of the household head can be diversified in the diversification of individual portfolios, in away. Otherwise, the individual effects of the the level of insurance deductibles, in the wage aggregate productivity shocks would be the premiums associated with occupations with same as in the representative agent models I high earnings risk, or in the revenues raised by have already discussed. One may argue over state-operated lotteries. It would be good to why it is that markets do not permit such diver- have the equity premium resolved, but I think sification, but it seems clear enough that they do we need to look beyond high estimates of risk not: Where is the market where people can be aversion to do it. The great contribution of insured against the risk of having irresponsible Alvarez and Jermann is to show that even using or incompetent parents or children? the highest available estimate of risk aversion, These exogenous forces acting differentially the gain from further reductions in business- across households induce different individual cycle risk is below one-tenth of 1 percent of choices, which in turn lead to differences in consumption. The evidence also leaves one free individual capital holdings. The state space in to believe—asIdo—that the gain is in fact one this economy is very large, much larger than or two orders of magnitude smaller.

V. Incomplete Markets and Distribution Effects 16 For example, Ayse Imrohorog˘lu (1989), Andrew Atkeson and Christopher Phelan (1994), Krusell and Smith The calculations I have described so far treat (1999, 2002), Kjetil Storesletten et al. (2001), and Tom Krebs (2002). households as identical and individual risks as 17 This way of modeling wealth changes within a fixed diversifiable. But as Per Krusell and Anthony A. distribution across families was introduced in John Laitner Smith, Jr. (1999) observe, “it is quite plausible (1992). VOL. 93 NO. 1 LUCAS: MACROECONOMIC PRIORITIES 9 anything people were working with numerically this particular application, removing the vari- 15 years ago, and without the method developed ance of the aggregate shock is estimated to in Krusell and Smith (1998) it would not have reduce the standard deviation of the individual been possible to work out the predictions of this employment shocks by 16 percent.19 model. A key simplification comes from the fact The first such thought-experiment Krusell that the impact on any one family of the shocks and Smith describe involves a comparison be- that hit others has to work through two prices, tween the expected utility drawn from the the real wage and the rental price of capital. steady state of the economy with aggregate These prices in turn depend only on the total shocks and the expected utility from the steady stock of capital, regardless of the way it is state of the economy with aggregate shocks and distributed, and total employment, regardless of their indirect effects removed in the way I have who has a job and who does not. By exploiting just described. The welfare gain from eliminat- these features, solutions can be calculated using ing cycles in this sense turns out to be negative! an iterative procedure that works like a dream: In a model, like this one, in which markets for For determining the behavior of aggregates, risk pooling are incomplete, people will engage they discovered, realistically modeled house- in precautionary savings, overaccumulating hold heterogeneity just does not matter very capital in the effort to self-insure. This implies much. larger average consumption in the more risky For individual behavior and welfare, of economy. Of course, there are costs to accumu- course, heterogeneity is everything. In the lating the higher capital stock, but these costs are thought-experiments that Krusell and Smith run not fully counted in a steady-state comparison. with their model, removal of the business cycle In any case, as Krusell and Smith emphasize, is defined to be equivalent to setting the aggre- there is nothing really distributional about a gate productivity shock equal to a constant. It is steady-state comparison: Every infinitely lived important to be clear on what the effect of such dynasty is assigned a place in the wealth distri- a change would be on the behavior of the em- bution at random, and no one of them can be ployment shocks to which individuals are sub- identified as permanently rich or poor. The ject, but the magical character of the experiment whole motivation of the paper is to focus on the makes it hard to know how this question is best situation of people described as “hand-to-mouth resolved. I will describe what Krusell and Smith consumers,” but a steady-state comparison did, and deal with some other possibilities later on. misses them. This observation motivates a sec- Suppose that a shock y ϭ az ϩ ␧ affects an ond thought-experiment—one with much more individual’s behavior, where z is the aggregate complicated dynamics than the first—in which shock and ␧ is idiosyncratic. We project the an economy is permitted to reach its steady- individual shock on the aggregate, ␧ ϭ cz ϩ ␩, state wealth distribution with realistic aggregate where the residual ␩ is uncorrelated with z, and shocks, and then is relieved of aggregate risk. then think of an ideal stabilization policy as one The full transition to a new steady state is then that replaces worked out and taken into account in the utility comparisons. In this experiment, we can iden- y ϭ az ϩ␧ϭ͑a ϩ c͒z ϩ ␩ tify individuals as “rich” or “poor” by their posi- tion in the initial wealth distribution, and discuss with the effects of risk removal category by category. The average welfare gain in this second ex- yˆ ϭ ͑a ϩ c͒E͑z͒ ϩ ␩. periment is about 0.1 of 1 percent of consump- tion, about twice the estimate in Section II of Not only is the direct effect of the productivity this paper. (Krusell and Smith also assume log shock z removed but also the indirect effects of utility.) But this figure masks a lot of diversity. z on the individual employment shocks ␧.18 In Low wealth, unemployed people—people who

18 This is a linear illustration of the more generally 19 Here and below, the numbers I cite are taken from defined procedure described in Krusell and Smith (1999). Krusell and Smith (2002). 10 THE AMERICAN ECONOMIC REVIEW MARCH 2003 would borrow against future labor income if ence in the way reductions in the variance of they could—enjoy a utility gain equivalent to a aggregate shocks affect risks faced at the indi- 4-percent perpetual increase in consumption. vidual level. In the Storesletten et al. simula- Oddly, the very wealthy can also gain, as much tions, a bad realization of the aggregate as 2 percent. Krusell and Smith conjecture that productivity shock increases the conditional this is due to the higher interest rates implied by variance of the idiosyncratic risk that people the overall decrease in precautionary savings face, so aggregate and individual risks are com- and capital. Finally, there is a large group of pounded in a way that Krusell and Smith rule middle wealth households that are made worse out. A second difference is that idiosyncratic off by eliminating aggregate risk. shocks are assumed to have a random walk These calculations are sensitive—especially at component, so their effects are long lasting. A the poor end of the distribution—to what is as- bad aggregate shock increases the chances that sumed about the incomes of unemployed people. a young worker will draw a bad individual Krusell and Smith calibrate this, roughly, to cur- shock, and if he does he will suffer its effects rent U.S. unemployment insurance replacement throughout his prime working years. rates. If one were estimating the costs of the de- The effects of these two assumptions are pression of the 1930’s, before the current welfare clear: They convert small, transient shocks at system was in place, lower rates would be used the aggregate level into large, persistent shocks and the cost estimates would increase sharply.20 It to the earnings of a small fraction of house- would also be interesting to use a model like this holds. Whether they are realistic is question of to examine the trade-offs between reductions in fact. That individual earnings differences are aggregate risk and an improved welfare system. highly persistent has been clear since Lee Storesletten et al. (2001) study distributional Lillard and Robert Willis’s pioneering (1978) influences on welfare cost estimates with meth- study. The fanning out over time of the earnings ods that are closely related to Krusell and and consumption distributions within a cohort Smith’s, but they obtain larger estimates of the that and (1994) gains from removing all aggregate shocks. They document is striking evidence of a sizeable, use an overlapping generations setup with 43 uninsurable random walk component in earn- working age generations, in which the youngest ings. The relation of the variance of earnings cohort is always credit constrained. In such a shocks to the aggregate state of the economy, setting, the young are helpless in the face of also emphasized by N. Gregory Mankiw (1986) shocks of all kinds and reductions in variance in connection with the equity premium puzzle, can yield large welfare gains. But if the age has only recently been studied empirically. effects are averaged out to reflect the impor- Storesletten et al. find a negative relation over tance of intrafamily lending (as I think they time between cross-section earnings means and should be) the gains estimated by Storesletten et standard deviations in Panel Studies of Income al. under log utility are no larger than Krusell Dynamics data. and Luigi and Smith’s.21 In contrast to earlier studies, Pistaferri (2001) obtain smaller estimates, but however, the Storesletten et al. model implies also conclude that “the unemployment rate and that estimated welfare gains rise faster than the variance of permanent [earnings] shocks proportionately as risk aversion is increased: appear to be quite synchronized” in the 1970’s From Exhibit 2, for example, the average gain and 1980’s. increases from 0.6 of a percent to 2.5 as ␥ is These issues are central to an accurate de- increased from 2 to 4. scription of the risk situation that individual Two features of the theory interact to bring agents face, and hence to the assessment of this about.22 First, and most crucial, is a differ- welfare gains from policies that alter this situ- ation. The development of tractable equilibrium models capable of bringing cross-section and 20 See Satyajit Chatterjee and Dean Corbae (2000). panel evidence to bear on this and other mac- 21 Based on Exhibits 2 and A.3.1. 22 Storesletten et al. do a good job of breaking the roeconomic questions is an enormous step for- differences into intelligible pieces. I also found the example ward. But Krusell and Smith find only modest explicitly solved in Krebs (2002) very helpful in this regard. effects of heterogeneity on the estimates of wel- VOL. 93 NO. 1 LUCAS: MACROECONOMIC PRIORITIES 11 fare gains from the elimination of aggregate average level of investment. He obtains welfare risk, and even accepting the Storesletten et al. gains as large as 7 percent of consumption in view entails an upward revision of a factor of models based on this idea, but everything only about 5. hinges on a curvature parameter on which there The real promise of the Krusell-Smith model is little evidence. This is a promising frontier on and related formulations, I think, will be in the which there is much to be done. Surely there are study of the relation of policies that reduce the others. impact of risk by reducing the variance of shocks (like aggregate stabilization policies) to VII. Conclusions those that act by reallocating risks (like social insurance policies). Traditionally, these two If business cycles were simply efficient re- kinds of policies have been studied by different sponses of quantities and prices to unpredict- economists, using unrelated models and differ- able shifts in technology and preferences, there ent data sets. But both appear explicitly in the would be no need for distinct stabilization or models I have reviewed here, and it is clear that demand management policies and certainly no it will soon be possible to provide a unified point to such legislation as the Employment Act analysis of their costs and benefits. of 1946. If, on the other hand, rigidities of some kind prevent the economy from reacting effi- VI. Other Directions ciently to nominal or real shocks, or both, there is a need to design suitable policies and to My plan was to go down a list of all the assess their performance. In my opinion, this is things that could have gone wrong with my the case: I think the stability of monetary ag- 1987 calculations but, as I should have antici- gregates and nominal spending in the postwar pated, possibilities were added to the list faster United States is a major reason for the stability than I could eliminate them. I will just note of aggregate production and consumption dur- some of the more interesting of these possibil- ing these years, relative to the experience of the ities, and then conclude. The level of consump- interwar period and the contemporary experi- tion risk in a society is, in part, subject to ence of other economies. If so, this stability choice. When in an economy that is subject to must be seen in part as an achievement of the larger shocks, people will live with more con- economists, Keynesian and monetarist, who sumption variability and the associated loss in guided economic policy over these years. welfare, but they may also substitute into risk- The question I have addressed in this lecture avoiding technologies, accepting reduced aver- is whether stabilization policies that go beyond age levels of production. This possibility shows the general stabilization of spending that char- up in the precautionary savings—overaccumu- acterizes the last 50 years, whatever form they lation of capital—that Krusell and Smith (1999, might take, promise important increases in wel- 2002) found. As Garey Ramey and Valerie A. fare. The answer to this question is “No”: The Ramey (1991) suggested, this kind of substitu- potential gains from improved stabilization pol- tion surely shows up in other forms as well. icies are on the order of hundredths of a percent In an endogenous growth framework, substi- of consumption, perhaps two orders of magni- tution against risky technologies can affect rates tude smaller than the potential benefits of avail- of growth as well as output levels. Larry E. able “supply-side”fiscal reforms. This answer Jones et al. (1999) and Epaulard and Pommeret does depend, certainly, on the degree of risk (2001) explore some of these possibilities, aversion. It does not appear to be very sensitive though neither study attributes large welfare to the way distribution effects are dealt with, gains to volatility-induced reductions in growth though it does presuppose a system of unem- rates. Gadi Barlevy (2001) proposes a convex ployment insurance at postwar U.S. levels. I adjustment cost that makes an erratic path of have been as explicit as I can be on the way investment in knowledge less effective than a theory and evidence bear on these conclusions. smooth path at the same average level. In such When gave his Money, Interest, a setting, reducing shock variability can lead to and Prices the subtitle “An Integration of Mon- higher growth even without an effect on the etary and Value Theory,” value theory meant, to 12 THE AMERICAN ECONOMIC REVIEW MARCH 2003 him, a purely static theory of general equilib- and Supply Disturbances.” American Eco- rium. Fluctuations in production and employ- nomic Review, September 1989, 79(4), pp. ment, due to monetary disturbances or to shocks 655–73. of any other kind, were viewed as inducing Brock, William A. and Turnovsky, Stephen J. disequilibrium adjustments, unrelated to any- “The Analysis of Macroeconomic Policies in one’s purposeful behavior, modeled with vast Perfect Foresight Equilibrium.” International numbers of free parameters. For us, today, value Economic Review, February 1981, 22(1), pp. theory refers to models of dynamic economies 179–209. subject to unpredictable shocks, populated by Chamley, Christophe P. “The Welfare Cost of agents who are good at processing information Capital Income Taxation in a Growing Econ- and making choices over time. The macroeco- omy.” Journal of Political Economy, June nomic research I have discussed today makes 1981, 89(3), pp. 468–96. essential use of value theory in this modern Chatterjee, Satyajit and Corbae, Dean. “On the sense: formulating explicit models, computing Welfare Gains of Reducing the Likelihood of solutions, comparing their behavior quantita- Economic Crises.” Federal Reserve Bank of tively to observed time series and other data Philadelphia Research Working Paper No. sets. As a result, we are able to form a much 00/14, November 2000. sharper quantitative view of the potential of Christiano, Lawrence J.; Eichenbaum, Martin changes in policy to improve peoples’ lives than and Evans, Charles. “The Effects of Monetary was possible a generation ago. Policy Shocks: Evidence from the Flow of Funds.” Review of Economics and Statistics, REFERENCES February 1996, 78(1), pp. 16–34. Cochrane, John H. and Hansen, Lars Peter. “As- Aiyagari, S. Rao. “On the Contribution of Tech- set Pricing Explorations for Macroeconom- nology Shocks to Business Cycles.” Federal ics.” NBER macroeconomics annual, 1992. Reserve Bank of Minneapolis Quarterly Re- Cambridge, MA: MIT Press, 1992, pp. 115–65. view, Summer 1994, 18(3), pp. 22–34. Deaton, Angus and Paxson, Christina. “Intertem- Alvarez, Fernando and Jermann, Urban J. “Us- poral Choice and Inequality.” Journal of Po- ing Asset Prices to Measure the Cost of Busi- litical Economy, June 1994, 102(3), pp. 437– ness Cycles.” Working paper, University of 67. Chicago, 2000. Dolmas, James. “Risk Preferences and the Wel- Atkeson, Andrew and Phelan, Christopher. “Re- fare Cost of Business Cycles.” Review of considering the Costs of Business Cycles Economic Dynamics, July 1998, 1(3), pp. with Incomplete Markets.” NBER macroeco- 646–76. nomics annual, 1994. Cambridge, MA: MIT Epaulard, Anne and Pommeret, Aude. “Recur- Press, 1994, pp. 187–207. sive Utility, Endogenous Growth, and the Auerbach, Alan J. and Kotlikoff, Laurence J. Dy- Welfare Cost of Volatility.” International namic fiscal policy. Cambridge: Cambridge Monetary Fund Working Paper No. WP/01/ University Press, 1987. 05, 2001. Bailey, Martin J. “The Welfare Cost of Inflation- Epstein, Larry G. and Zin, Stanley E. “Substitu- ary .” Journal of Political Economy, tion, Risk Aversion, and the Temporal Be- April 1956, 64(2), pp. 93–110. havior of Consumption Growth and Asset Barlevy, Gadi. “The Cost of Business Cycles Returns I: A Theoretical Framework.” Under Endogenous Growth.” Working paper, , July 1989, 57(4), pp. 937–69. Northwestern University, 2001. . “Substitution, Risk Aversion, and the Benhabib, Jess; Rogerson, Richard and Wright, Temporal Behavior of Consumption Growth Randall. “Homework in Macroeconomics: and Asset Returns II: An Empirical Analy- Household Production and Aggregate Fluctu- sis.” Journal of Political Economy, April ations.” Journal of Political Economy, De- 1991, 99(2), pp. 263–86. cember 1991, 99(6), pp. 1166–87. Friedman, Milton. “The Role of Monetary Poli- Blanchard, Olivier J. and Quah, Danny. “The cy.” American Economic Review, March Dynamic Effects of Aggregate Demand 1968, 58(1), pp. 1–17. VOL. 93 NO. 1 LUCAS: MACROECONOMIC PRIORITIES 13

Greenwood, Jeremy and Hercowitz, Zvi. “The Eliminating Business Cycles.” Working pa- Allocation of Capital and Time over the Busi- per, Carnegie Mellon University, 2002. ness Cycle.” Journal of Political Economy, Kydland, Finn E. and Prescott, Edward C. “Time December 1991, 99(6), pp. 1188–214. to Build and Aggregate Fluctuations.” Hall, Robert E. and Rabushka, Alvin. The flat tax, Econometrica, November 1982, 50(6), pp. 2nd Ed. Stanford, CA: 1345–70. Press. 1995. Laitner, John. “Random Earnings Differences, Hansen, Gary D. “Indivisible Labor and the Lifetime Liquidity Constraints, and Altruistic Business Cycle.” Journal of Monetary Eco- Intergenerational Transfers.” Journal of Eco- nomics, November 1985, 16(3), pp. 309–27. nomic Theory, December 1992, 58(2), pp. Hansen, Lars Peter; Sargent, Thomas J. and 135–70. Tallarini, Thomas D., Jr. “Robust Permanent Lillard, Lee and Willis, Robert. “Dynamic As- Income and Pricing.” Review of Economic pects of Earnings Mobility.” Econometrica, Studies, October 1999, 66(4), pp. 873–908. September 1978, 46(5), pp. 985–1012. Hansen, Lars Peter and Singleton, Kenneth J. Lucas, Robert E., Jr. Models of business cycles. “Stochastic Consumption, Risk Aversion, New York: Basil Blackwell, 1987. and the Temporal Behavior of Asset Re- . “Inflation and Welfare.” Economet- turns.” Journal of Political Economy, April rica, March 2000, 68(2), pp. 247–74. 1983, 91(2), pp. 249–65. Mankiw, N. Gregory. “The Equity Premium and Heaton, John. “An Empirical Investigation of the Concentration of Aggregate Shocks.” Asset Pricing with Temporally Dependent Journal of Financial Economics, September Preference Specifications.” Econometrica, 1986, 17(1), pp. 211–19. May 1995, 63(3), pp. 681–717. Meghir, Costas and Pistaferri, Luigi. “Income Imrohorogùlu, Ayse. “The Cost of Business Cy- Variance Dynamics and Heterogeneity.” cles with Indivisibilities and Liquidity Con- Working paper, Institute for Fiscal Studies, straints.” Journal of Political Economy, 2001. December 1989, 97(6), pp. 1364–83. Mehra, Rajnish and Prescott, Edward C. “The Jones, Larry E.; Manuelli, Rodolfo E. and Equity Premium: A Puzzle.” Journal of Mon- Stacchetti, Ennio. “Technology (and Policy) etary Economics, March 1985, 15(2), pp. Shocks in Models of Endogenous Growth.” 145–61. National Bureau of Economic Research Meltzer, Allan H. “The Demand for Money: The (Cambridge, MA) Working Paper No. Evidence from Time Series.” Journal of Po- 7063, April 1999. litical Economy, June 1963, 71(3), pp. 219– Judd, Kenneth L. “The Welfare Cost of Factor 46. Taxation in a Perfect Foresight Model.” Jour- Obstfeld, Maurice. “Evaluating Risky Consump- nal of Political Economy, August 1987, tion Paths: The Role of Intertemporal Substi- 95(4), pp. 675–709. tutability.” European Economic Review, Kocherlakota, Narayana R. “The Equity Premi- August 1994, 38(7), pp. 1471–86. um: It’s Still a Puzzle.” Journal of Economic Otrok, Christopher. “On Measuring the Welfare Literature, March 1996, 34(1), pp. 42–71. Cost of Business Cycles.” Working paper, Krebs, Tom. “Growth and Welfare Effects of University of Virginia, 1999. Business Cycles in Economies with Idiosyn- Prescott, Edward C. “Theory Ahead of Business cratic Human Capital Risk.” Working paper, Cycle Measurement.” Federal Reserve Bank Brown University, 2002. of Minneapolis Quarterly Review, Fall Krusell, Per and Smith, Anthony A., Jr. “Income 1986a, 10(4), pp. 9–21. and Wealth Heterogeneity in the Macro- . “Response to a Skeptic.” Federal Re- economy.” Journal of Political Economy, serve Bank of Minneapolis Quarterly Review, October 1998, 106(5), pp. 867–96. Fall 1986b, 10(4), pp. 28–33. . “On the Welfare Effects of Eliminat- . “Richard T. Ely Lecture: Prosperity ing Business Cycles.” Review of Economic and Depression.” American Economic Re- Dynamics, January 1999, 2(2), pp. 245–72. view, May 2002 (Papers and Proceedings), . “Revisiting the Welfare Effects of 92(2), pp. 1–15. 14 THE AMERICAN ECONOMIC REVIEW MARCH 2003

Ramey, Garey and Ramey, Valerie A. “Technol- Economics and Statistics, August 1957, ogy Commitment and the Cost of Economic 39(3), pp. 312–20. Fluctuation.” National Bureau of Economic Storesletten, Kjetil; Telmer, Chris I. and Yaron, Research (Cambridge, MA) Working Paper Amir. “The Welfare Cost of Business Cycles No. 3755, June 1991. Revisited: Finite Lives and Cyclical Varia- Rosen, Sherwin. “Public Employment and the tion in Idiosyncratic Risk.” European Eco- Welfare State in Sweden.” Journal of Eco- nomic Review, June 2001, 45(7), pp. 1311– nomic Literature, June 1996, 34(2), pp. 729– 39. 40. Summers, Lawrence H. “Capital Taxation and Sargent, Thomas J. and Sims, Christopher A. Accumulation in a Life Cycle Growth Mod- “Business Cycle Modeling without Pretend- el.” American Economic Review, September ing to Have Too Much A-Priori Economic 1981, 71(4), pp. 533–44. Theory,” in New methods in business cycle . “Some Skeptical Observations on Real research. Proceedings from a Conference, Business Cycle Theory.” Federal Reserve Federal Reserve Bank of Minneapolis, 1977, Bank of Minneapolis Quarterly Review, Fall pp. 45–109. 1986, 10(4), pp. 22–27. Shapiro, Matthew D. and Watson, Mark W. Tallarini, Thomas D., Jr. “Risk-Sensitive Real “Sources of Business Cycle Fluctuations.” Business Cycles.” Journal of Monetary Eco- NBER macroeconomics annual, 1988. Cam- nomics, June 2000, 45(3), pp. 507–32. bridge, MA: MIT Press, 1988, pp. 111–48. Weil, Philippe. “Non-Expected Utility in Macro- Solow, Robert M. “Technical Change and the economics.” Quarterly Journal of Econom- Aggregate Production Function.” Review of ics, February 1990, 105(1), pp. 27–42.