Economic Essay

From Cycles to Shocks: Progress in Business-Cycle Theory Satyajit Chatterjee

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From Cycles to Shocks: Progress in Business-Cycle Theory

Satyajit Chatterjee*

Early analysts of business cycles believed that each cyclical phase of the economy carries within it the seed that generates the next cyclical phase. A boom generates the next recession; that reces- sion generates the next boom; and the economy is caught forever in a self-sustaining cycle. In contrast, modern theories of business cycles at- tribute cyclical fluctuations to the cumulative effects of shocks and disturbances that continu- ally buffet the economy. In other words, without shocks there are no cycles.

The evolution of thought about business cycles from an emphasis on self-sustaining be- havior toward one in which random shocks take center stage is a significant development in mac- roeconomics, and it is an especially important one for policymaking institutions like the Fed- eral Reserve. The view that cycles are self-sus- taining implies that a market economy cannot deliver stable economic performance on a sus- tained basis. Generally speaking, this view points to aggressive countercyclical policies or institutional reform as the appropriate response to cyclical fluctuations.

In contrast, the view that shocks are the ulti- mate sources of business cycles does not point

*Satyajit Chatterjee is an economic advisor in the Re- search Department of the Philadelphia Fed.

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to a particular policy stance. Whether a countercyclical policy should be pursued de- pends on the nature of the shocks. If shocks can be eliminated, macroeconomic policy should endeavor to do so because a more stable eco- nomic environment is preferable to a less stable one. But if shocks cannot be eliminated, it may be in the long-run interests of society to adapt to the shocks. To the extent that countercyclical policies interfere with the necessary adaptations, they may do more harm than good.1

Not surprisingly, the shift of professional opinion toward the shock-based view of busi- ness cycles has been accompanied by increas- ing debate about the sources of cyclical volatil- ity. Few macroeconomists doubt that random shocks underlie business cycles, but they have been unable to agree on which random shocks, historically, have been the main causes of cycli- cal volatility.

To a person not versed in business-cycle theory (including economists who are not macro- economists), this situation must seem somewhat paradoxical: How can macroeconomists be cer- tain that shocks cause cycles, yet not agree on which shocks are responsible for cyclical volatil- ity? Moreover, if a person is told that despite this ignorance, macroeconomists have made great strides in understanding business cycles, his or her perplexity can only increase. How can there be any understanding of business cycles (let alone an improvement in it!) if economists don’t know the causes of cyclical volatility?

This article will answer these questions by sketching the historical evolution of the shock- based theory of business cycles. The answer to the first question delineates the key discoveries that led macroeconomists away from the self-

sustaining view of business cycles and toward the shock-based view. The impetus for the shock- based view of business cycles came in the 1920s when mathematicians made a major break- through in the statistical description of cyclical phenomena. They established that many kinds of irregular cyclical phenomena (in fields as di- verse as economics, geology, and physics) are best explained by random shocks.

This discovery set economists on the search for a shock-based theory of business cycles. Ini- tially, economists thought that observable ran- dom events, such as an unexpected increase in government spending or a financial panic, would turn out to be the shocks causing business cycles. And to some extent they are. But they are not the major source of cyclical volatility. The major source appears to be shocks that manifest them- selves as deviations of macroeconomic variables from their model-predicted values. Such shocks cannot easily be connected to observable real- world events. The unobservable nature of these shocks is the fundamental reason macroecono- mists disagree about the ultimate causes of cy- clical fluctuations. Yet, most macroeconomists agree that some set of unspecified shocks must be ultimately responsible for business cycles.

Although macroeconomists lack firm knowl- edge about the ultimate sources of cyclical vola- tility, they do understand how these shocks, once they occur, contribute to business cycles. Thus, the answer to the second question is that ad- vances in business-cycle theory have provided a better understanding of how industrial econo- mies respond to random shocks. One outcome of these developments is a new appreciation of the role that erratic changes in business-sector productivity play in cyclical fluctuations. Ac- cording to the real business cycle, or RBC, theory (arguably one of the most successful shock- based business-cycle theories to date), random variation in business-sector productivity is the key proximate cause of post-WWII U.S. business cycles.

Let’s now examine the historical process by

1For instance, a boom in residential construction could reflect speculative excess or changing demographics. An increase in the interest rate can eliminate speculation, but it cannot change demographics. Thus, policy action is desirable in the former case but probably not in the latter.

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which business-cycle theorists have come to this conclusion.

THE STATISTICAL THEORY OF RANDOM WAVES

The fact that random disturbances may un- derlie business cycles was clearly demonstrated by the Russian statistician and economist Eugen Slutzky. In an article published in Russian in 1927 (and reprinted in English in 1937), Slutzky described in compelling detail how chance events could gen- erate cyclical movements in economic data.2

Slutzky began with a series of many random numbers, each an integer be- tween 0 and 9. If such numbers are plotted on a graph, they produce a line that moves up and down without dis- playing any particular pattern (Figure 1). This simply reflects the fact that the numbers, being drawn at random, don’t bear any relationship to each other. Next, Slutzky constructed a new series by adding the random numbers 10 at a time in the following way. The first number in the new series was the sum of the first 10 random numbers; the second number in the new series was the sum of the second through the 11th random number, and so on. Thus, each member of the new series was a 10-item sum of random num- bers. In the new series, the difference in value between adjacent members could be at most nine, but the differ- ence between widely separated mem-

2Priority of discovery is attributed to the British statistician G. Udny Yule, who made this point in the early 1920s. However, Slutzky went much further than Yule in show- ing how random shocks could lead to ap- parently cyclical movements in economic (and other) data.

bers could be much larger. Slutzky recognized that this combination of

facts—adjacent members of the series are likely to be similar in value, and widely separated members are unlikely to be similar in value— implies wavelike, or cyclical, movement. Indeed, when plotted as a graph, the 10-item moving sums of the random numbers shown in Figure 1 display an unmistakable wavelike pattern (Fig-

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ure 2). While widely separated members of the series may be quite different in value, such as members A and B, the movement from A to B must be gradual because adjacent members of the series cannot be too different from each other. To persuade his readers that random numbers may underlie business-cycle movements, Slutzky compared a segment of his 10-item mov- ing-sum series to an index of English business cycles. As we can see in Figure 3, the similarity is indeed remarkable!

Following Slutzky’s pioneering work, math- ematicians further developed the statistical theory of random waves. This development re- vealed that Slutzky’s random-number-based explanation of irregular cyclical patterns was, in fact, the most compelling explanation of such patterns. This discovery persuaded business- cycle theorists to seek an explanation of busi- ness cycles in the cumulative effects of various random shocks hitting the economic system.

THE GENESIS OF SHOCK-BASED BUSINESS-CYCLE THEORY

Although Slutzky showed that moving sums of random numbers could display business- cycle-like patterns, he didn’t provide any eco- nomic theory as to why macroeconomic variables might behave like moving sums of random num- bers. However, he did point to examples of me- chanical systems, such as a pendulum, whose motion under the influence of random shocks was, mathematically, a moving (weighted) sum of random numbers.

Imagine tapping with a hammer a pendulum whose motion is hampered by friction. If the ham- mer strokes vary randomly in strength, they’ll cause the pendulum to swing about in an ir- regular way. A time-plot of the displacement of the pendulum from its (vertical) resting position (with displacement to the right measured as posi- tive numbers and to the left as negative num- bers) will show an irregular wavy line. The key

From Cycles to Shocks: Progress in Business-Cycle Theory Satyajit Chatterjee

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point is that mathematically (and experimen- tally!), the displacement of the pendulum at any given point in time is a weighted moving sum of random numbers, the random numbers being the strength of each hammer stroke up to that point in time.

In an article published in 1933, the Norwe- gian economist and Nobel laureate Ragnar Frisch described a simple macroeconomic model in which the evolution of output, investment, and consumer spending resembled the motion of a swinging pendulum. Frisch’s model implied that if some transient random event raised out- put above the economy’s normal level, all mac- roeconomic variables (output, investment, and consumer spending) returned to normal in a cy- clical fashion. In other words, the initial periods of above-normal economic activity (analogous to displacements of the pendulum to the right) were followed by periods of below-normal eco- nomic activity (analogous to displacements to the left). These swings in economic activity gradually diminished in strength and eventu- ally died.

Frisch didn’t work out the behavior of his model economy for a sequence of random shocks, but the analogy to the swinging pendulum sug- gested that the resulting behavior would re- semble that of business cycles. In any event, by adopting the swinging pendulum as an anal- ogy for the evolution of a capitalistic economy, Frisch took a step back from the prevailing view that business cycles were self-sustaining. Recall that without the hammer strokes, the force of fric- tion brings the pendulum eventually to rest. And so it is, claimed Frisch, with an economic sys- tem: without shocks, there are no cycles.

Still, by basing his economic model of busi- ness cycles on an analogy to a swinging pendu- lum, Frisch gave inherently cyclical behavior (i.e., pendulum-like movements) a prominent place in business-cycle theory. However, the influence of the pendulum in business-cycle theory re- ceived a severe setback when Irma and Frank Adelman published an article in 1959 showing

that shocks, rather than pendulum-like move- ments, lie at the center of cyclical volatility.

THE DEMISE OF THE PENDULUM AND THE RISE OF SHOCKS

By the mid-1950s, advances in econometrics (the use of statistical methods to determine quan- titative economic relationships from economic data) had progressed to the point where equa- tions describing various sectors of the economy could be inferred from economic data. The Klein- Goldberger model of the U.S. economy was one such model.3 It contained 25 equations describ- ing the evolution of 25 macroeconomic variables for the U.S. economy and was much more de- tailed than the simple economic model used by Frisch.

The question that the Adelmans asked was whether the Klein-Goldberger model could gen- erate business cycles. First, they simulated the model on a computer to see if it displayed inher- ently cyclical behavior. They found that the model did not display appreciable pendulum-like move- ments. If some small to moderate transient shock temporarily raised economic activity, most eco- nomic variables simply returned to normal with- out experiencing any periods of below-normal activity.4

Next, the Adelmans turned to assessing the role of shocks in cyclical fluctuations. The first type of shock they considered was one affecting observable causal factors. In the Klein- Goldberger model, the list of observable causal factors included changes in short-term and long-

3The model was developed by Lawrence Klein and Arthur Goldberger, two well-respected econometricians (Klein received the Nobel Prize in economics in 1980). The model is described in their book published in 1955.

4In their simulations of the Klein-Goldberger model, the Adelmans did find pendulum-like behavior for very large shocks to the economic system. But these shocks were much larger than those actually observed for the U.S. economy.

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term interest rates, an index of hours worked by those employed, government employee compen- sation and government expenditures, agricul- tural exports and agricultural subsidies, and population and labor-force variables. The Adelmans noted that these causal factors didn’t evolve steadily but tended to jump around their respective trend paths “more or less erratically.” The Adelmans treated these erratic movements in causal factors as random shocks and simu- lated the Klein-Goldberger model to see how macroeconomic variables behaved in response to such shocks. They found that these shocks didn’t “produce the sort of cyclical behavior ob- served in the actual economy.” Thus, shocks to observable causal factors did not seem to be re- sponsible for business cycles, either.

The Adelmans then turned to a second type of random shock: the random discrepancies be- tween the predictions of the Klein-Goldberger model and the actual values of macroeconomic variables. These discrepancies arise for several reasons, the most important being that any mac- roeconomic model is likely to omit some relevant factors. For instance, the Klein-Goldberger equa- tion for predicting consumer spending takes into account only the influence of income; the stock of liquid assets (cash as well as checking and savings accounts) held by people; population; and consumer spending from the previous year. It ignores any effects resulting from, say, shifts in the distribution of personal income. If a shift in the distribution of personal income is an im- portant factor in some year, that shift will con- tribute to the discrepancy between the predic- tions of the model and the actual value of con- sumer spending for that year. Macroeconomists refer to such deviations of model-predicted val- ues from actual values as residuals.

When the Adelmans treated the residuals of the Klein-Goldberger model as random shocks, they found that the behavior of macroeconomic variables in the Klein-Goldberger model closely resembled actual U.S. business cycles. In other words, they found that residuals were the prime

source of cyclical volatility! These results were counter to prevailing views

about the role of shocks in cyclical volatility. Recall that Frisch and his contemporaries be- lieved that business cycles resulted from observ- able shocks impinging on an economy prone to pendulum-like movements. But the Adelmans found that business cycles resulted from unex- plained shocks (i.e., residuals) impinging on an economy that displayed no strong tendency to- ward pendulum-like movement.

Why does the Klein-Goldberger model gener- ate business cycles even without any strong ten- dency to pendulum-like movement? The answer lies in the fact that in the Klein-Goldberger model, values of macroeconomic variables are deter- mined, in part, by moving sums of random num- bers. For instance, the Klein-Goldberger equa- tion for consumer spending holds that the level of consumer spending during the previous year has a positive influence on consumer spending in the current year. Thus, if some shock raised consumer spending in the past year, that same shock will raise consumer spending during the current year as well, although not by as much. By the same logic, a shock that raised consumer spending two years ago will also have raised consumer spending during the past year (again, not by as much) and, therefore, will raise it dur- ing the current year as well. In other words, since consumer spending in any year is affected by consumer spending in the previous year, con- sumer spending in any year is determined, in part, by a weighted sum of random shocks af- fecting consumer spending in all previous years.

Now recall Slutzky’s demonstration that a quantity that’s a moving sum of random num- bers will display wavelike movement. Thus, in the presence of random shocks, the link between consumer spending in consecutive years be- comes a source of wavelike movements in con- sumer expenditures.

Most modern macroeconomic models incor- porate links between consecutive values of mac- roeconomic variables. These links imply that

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values of macroeconomic variables are deter- mined, in part, by moving sums of random num- bers, and those random numbers are past unex- plained shocks to macroeconomic variables, i.e., past residuals.5 Thus, while it’s true that macro- economists don’t know which factors cause busi- ness cycles, they do understand how the changes brought about by those factors combine to gen- erate cyclical fluctuations.6

Nevertheless, the fact that residuals cause business cycles is unsettling for business-cycle theory. Macroeconomists would prefer to ex- plain business cycles in terms of observable shocks or, failing that, to develop theories that make minimal use of residuals.

THE POWER OF RESIDUALS Since the 1960s, the evolution of business-

cycle thought has been linked to theoretical de- velopments in economics in general. In particu- lar, advances in dynamic economic theory pro- vided new and powerful tools for tackling prob- lems in business-cycle research. Initially, these new ideas held out hope of reducing the impor- tance of omitted factors in business-cycle mod- els and correspondingly raising that of included factors. Consequently, professional attention

turned to re-assessing the role of factors included in business-cycle models. A great deal of energy was spent in assessing the role of monetary shocks. As it turned out, this assessment failed to produce a compelling case for monetary shocks as an important factor in postwar U.S. business cycles. It also failed to produce com- pelling evidence in favor of other easily identifi- able shocks.7 Since the early 1980s, interest has again shifted to consideration of the role of re- siduals in cyclical fluctuations. Armed with the new advances in dynamic economic theory, Finn Kydland in collaboration with Edward Prescott developed a residual-driven business-cycle model called the real business cycle (RBC) model.8

Recall that a residual is the deviation of a macroeconomic variable from its model-pre- dicted value. In RBC theory, the residual that generates business cycles is the quarterly devia- tion of labor productivity from its model-pre- dicted value. The model of labor productivity used in RBC theory was developed by growth theorists in the 1940s and 1950s. This model holds that average labor productivity (output per worker) is positively related to the amount of capital per worker in the economy. The differ- ence between growth in actual labor productiv- ity and its model-predicted value is called the Solow residual, in honor of Nobel laureate Rob- ert Solow, who developed this idea. A positive Solow residual, i.e., growth in labor productiv- ity in excess of what can be explained by growth in capital per worker, indicates an improvement

5In principle, random shocks to observable causal factors can also be a source of wavelike movements. However, the shocks to observed causal factors are too small to generate realistic business-cycle fluctuations in the Klein-Goldberger model.

6For evidence on the importance of residuals for cycli- cal volatility in modern macroeconomic models, see John Cochrane’s article. Can the omitted factors be discov- ered by relating residuals to observable historical events? Perhaps, but scholars are not sanguine about the pros- pects. To quote the eminent economic historian Peter Temin: “If the goal is to find events that can be repre- sented by the residuals, it may be possible to find events to explain one set of residuals as easily as another. But the variety of models extant today makes that kind of exercise unrealistic as a way to identify causes of mul- tiple cycles.”

7Pre-WWII fluctuations are another matter. In that case, monetary shocks may well have been the decisive factor.

8Prescott’s 1986 article contains an influential state- ment of the RBC model. The antecedents of this article appeared in an earlier 1982 publication by Finn Kydland and Edward Prescott. Two other authors, John Long and Charles Plosser, published a closely related article in 1983; they coined the term real business cycles.

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in the economy’s technological capability (brought on by new inventions). In the theory of economic growth, positive Solow residuals are seen as a major cause of economic growth; in RBC theory, fluctuations in the Solow residual are seen as a major cause of business cycles.9

Two properties of the Solow residual make it possible to base a business-cycle theory on it. First, when the Solow residual rises above its trend path, indicating better-than-average growth in the economy’s technological capabil- ity, firms are motivated to invest in new plant and equipment at a faster-than-average rate. To meet the increased demand for investment goods, businesses hire more than the average number of workers. Above-average employment growth leads, in turn, to faster-than-average growth in consumer spending. Thus, a rise in the Solow residual above its trend path makes investment, employment, and consumer spending rise above their respective trend paths as well. This co- movement of key macroeconomic variables is a central feature of business cycles.

Second, as was the case with consumer spend- ing in the Klein-Goldberger model, there is a strong link between the value of the Solow re- sidual in consecutive years. Therefore, the value of the residual in any given year is determined, in part, by a weighted sum of random shocks affecting the residual in past years. Thus, the observed movements of the Solow residual around its trend path resemble Slutzky’s mov- ing sums of random numbers. Since RBC theory predicts that macroeconomic variables will take on values that are almost proportional to the Solow residual, all macroeconomic variables in the RBC model behave like moving sums of ran- dom numbers as well. Thus, RBC theory can also explain the observed wavelike movement of macroeconomic variables.

RBC theory has had considerable success in explaining cyclical fluctuations. As shown in Charles Plosser ’s 1989 article, values predicted by RBC theory (given the observed movements in the Solow residual) are close to the actual val- ues of key macroeconomic variables during the post-WWII period. For instance, as predicted by the theory, a decline in consumer expenditures, hours worked, investment, and output accom- panied the decline in the Solow residual in 1970. More recently, the faster-than-average growth of the U.S. economy since 1995 has accompanied a faster-than-average growth in the Solow re- sidual. Between 1995 and 1997 (the last year for which the residual can be calculated), the growth in the Solow residual exceeded its average growth rate since 1959 by more than 15 percent.

Still, a natural question to ask about the RBC model is whether it offers a more satisfactory explanation of business cycles than the one of- fered by the Adelmans using the Klein- Goldberger model. After all, given that both ex- planations are residual-based, are there any rea- sons to prefer one to the other?

Quantitatively, the RBC model explains cy- clical fluctuations at least as well as the Klein- Goldberger model, as Robert King and Charles Plosser demonstrated in a 1994 article. However, many macroeconomists prefer the RBC expla- nation for two reasons. First, RBC theory relies on only one residual to generate business cycles whereas the Adelmans relied on a consumer spending residual, an investment residual, and other assorted residuals. Second, the RBC model is based on straightforward economic ideas whereas the theory underlying the Klein- Goldberger model is much more complex and subtle.

WHITHER BUSINESS-CYCLE THEORY? The pioneers of RBC theory have steadfastly

maintained that fluctuations in the Solow re- sidual result from technological and institu- tional changes. Generally speaking, business- cycle theorists don’t view their job as explaining

9For a detailed description of the RBC model and some of its implications, see my 1995 and 1999 articles.

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changes in technology or institutions. So, if the omitted factors that cause fluctuations in the Solow residual are truly technological or insti- tutional in nature, then in one important sense, RBC theory is complete. The phenomenon left unexplained, namely, fluctuations in the Solow residual, falls outside the scope of business-cycle theory and therefore doesn’t need to be explained by it. The intellectual journey begun in 1927 on the pages of an obscure Russian journal has come to an end!

But has it really? Economists, after all, are a curious lot. Confronted with a residual that can explain business cycles, they will want to dig deeper into its ultimate causes. One reason re- searchers are motivated to dig deeper is that some aspects of the Solow residual seem inconsistent with the assertion that only technological or in- stitutional changes cause the residual to fluctu- ate. For instance, during recessions, the residual usually declines. The strict RBC interpretation would hold that some factor caused a decline in the productive potential of the economy and led to the recession. In some cases such an interpre- tation seems plausible (as it does for the decline in the Solow residual during the energy crisis in 1974). However, in other cases (for instance, in 1970) the reason for the decline is not clear. Most macroeconomists find declines in the Solow re- sidual during recessions puzzling, although many now believe the declines are real and not simply the consequence of measurement error.

The future development of shock-based theo- ries of business cycles is almost certainly going to be influenced, in part, by attempts to resolve such puzzles. Indeed, both critics and propo- nents of RBC theory have focused increasingly on the reasons why the Solow residual fluctu- ates.

For instance, critics of RBC theory have pro- posed models in which the Solow residual moves in response to cyclical fluctuations caused by unexplained shifts in investment or consumer spending. In these models, a higher rate of pro- duction enables businesses to produce at a lower

unit cost, which implies that the Solow residual rises during booms and falls during recessions. These induced changes in the Solow residual magnify the effects of the initial change in in- vestment or consumer spending and may lead to excessive cyclical volatility.10

On the other hand, proponents of RBC theory point to evidence from U.S. manufacturing plants that seems to indicate that technological change is an important determinant of fluctuations in the Solow residual. If new plants adopt techno- logical improvements, RBC theory predicts that such improvements will induce old and obso- lete plants to cease production. As the new tech- nology comes into use, both the Solow residual and national output will rise. U.S. data show that, as theory predicts, plant closings precede increases in the Solow residual. Then, as the Solow residual rises, new plants open and na- tional output increases.11

As research on RBC theory progresses, we may expect it to shed light on the questions that vex policymakers. Is there a policy trade-off between the rate of economic growth and its cyclical vola- tility? How can policy contribute to reducing cyclical volatility? What role do existing countercyclical policies play in promoting eco- nomic growth and reducing cyclical volatility? It is to the credit of shock-based business-cycle theories, and to the RBC theory in particular, that progress on these traditional policy concerns can now be made by learning about the factors that underlie fluctuations in the Solow residual.

SUMMARY Early analysts of business cycles believed that

cyclical fluctuations are self-sustaining. But in

10See, for instance, the article by Marianne Baxter and Robert King and the article by Roger Farmer and Jang- Ting Guo.

11This theory is described in Jeffrey Campbell’s ar- ticle.

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the 1920s, statisticians and economists realized that business cycles could result from purely random causes. This discovery moved econo- mists away from the self-sustaining view of busi- ness cycles and toward a shock-based view. The first shock-based business-cycle model gave prominence to both random shocks and inher- ently cyclical behavior as sources of business cycles. But later research demonstrated that shocks were the major source of cyclical fluctua- tions.

However, these shocks turned out to be pecu- liar in nature in that they couldn’t easily be con- nected to observable real-world events. They appeared, instead, as deviations of macroeco- nomic variables from their model-predicted val- ues (i.e., residuals). Then, in the early 1980s, a group of economists greatly refined shock-based (more precisely, residual-based) business-cycle theories by linking cyclical fluctuations to de- viations in labor productivity, the so-called Solow residual. Using the advances made in dynamic economic theory in the 1960s and 1970s, these

economists demonstrated that fluctuations in the Solow residual were powerful enough to gener- ate fluctuations in output that closely resembled post-WWII U.S. business cycles. This remarkable demonstration strengthened the links between business-cycle theory and simple microeconomic principles and reduced the number of residuals from several to just one. For both reasons, RBC theory represents a significant improvement over first-generation shock-based theories.

Nevertheless, RBC theory doesn’t settle the issue of the ultimate sources of cyclical volatility because the random shocks in the RBC model result from variations in unspecified factors that cause erratic movements in business-sector pro- ductivity. However, by focusing attention on the role of the Solow residual in cyclical fluctuations, RBC theory has laid a foundation for better un- derstanding the causes of such fluctuations. As business-cycle researchers look for reasons why the Solow residual fluctuates, they may gain knowledge that will help policymakers fashion better macroeconomic policies.

REFERENCES

Adelman, Irma, and Frank Adelman. “The Dynamic Properties of the Klein-Goldberger Model,” Econometrica, 4 (1959), pp. 596-625.

Baxter, Marianne, and Robert G. King. “Productive Externalities and Business Cycles,” Dis- cussion Paper 53, Institute of Empirical Macroeconomics, Federal Reserve Bank of Min- neapolis, 1991.

Campbell, Jeffrey R. “Entry, Exit, Embodied Technology, and Business Cycles,” Review of Economic Dynamics, 1 (1998), pp. 371-408.

Chatterjee, Satyajit. “Productivity Growth and the American Business Cycle,” Business Re- view, Federal Reserve Bank of Philadelphia, September/October 1995.

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REFERENCES (continued)

Chatterjee, Satyajit. “Real Business Cycles: A Legacy of Countercyclical Policies?” Business Review, Federal Reserve Bank of Philadelphia, January/February 1999.

Cochrane, John. “Shocks,” Carnegie-Rochester Conference Series on Public Policy, 41 (1994), pp. 295-364.

Farmer, Roger E.A., and Jang-Ting Guo. “Real Business Cycles and the Animal Spirits Hy- pothesis,” Journal of Economic Theory, 63 (1994), pp. 42-72.

Frisch, Ragnar. “Propagation Problems and Impulse Problems in Dynamic Economics,”Economic Essays in Honor of Gustav Cassel. London: George Allen & Unwin, 1933.

King, Robert G., and Charles I. Plosser. “Real Business Cycles and the Test of the Adelmans,” Journal of Monetary Economics, 33 (1994), pp. 405-38.

Klein, Lawrence J., and Arthur S. Goldberger. An Econometric Model of the United States, 1929- 1952. Amsterdam: 1955.

Kydland, Finn, and Edward C. Prescott. “Time-to-Build and Aggregate Fluctuations,” Econometrica, 50 (1982), pp. 1345-70.

Long, John, and Charles I. Plosser. “Real Business Cycles,” Journal of Political Economy, 91 (1983), pp. 1345-70.

Plosser, Charles I. “Understanding Real Business Cycles,” Journal of Economic Perspectives, 3 (1989), pp. 51-77.

Prescott, Edward C. “Theory Ahead of Business Cycle Measurement,” Federal Reserve Bank of Minneapolis Quarterly Review 10 (1986), pp. 9-21.

Slutzky, Eugen. “The Summation of Random Causes as the Source of Cyclic Processes,” Econometrica, 5 (1937), pp.19-60.

Solow, Robert M. “Technical Change and Aggregate Production Function,” Review of Econom- ics and Statistics, 39 (1957), pp. 312-20.

Temin, Peter. “The Causes of American Business Cycles: An Essay in Economic Historiogra- phy,” in Jeffrey Fuhrer and Scott Schuh, eds., Beyond Shocks: What Causes Business Cycles? Federal Reserve Bank of Boston, 1998.