The Role of Inventories In the

BY AUBHIK KHAN

hanges in the stock of firms’ inventories are INVENTORIES SEEM TO BE IMPORTANT IN THE an important component of the business BUSINESS CYCLE C Figure 1 shows the business- cycle. In fact, discussion about the timing cycle component of real gross domestic of a recovery following economic product (GDP) in the United States often focuses on inventories. Aubhik Khan surveys the over most of the postwar period. We can think of movements in GDP as the sum facts about inventory investment over the business of two components: the trend and the cycle, then discusses two leading theories that may business cycle. The trend represents the average growth rate of the economy explain these observations. across surrounding years. The business cycle reflects short-term deviations from this trend: the expansions and contrac- tions that make up the business cycle.1,2 For comparison, recessions, as dated by Changes in the stock of firms’ that may explain these observations. the National Bureau of Economic inventories are an important component Theory that passes the test of observa- Research, are shaded in the figure. of the business cycle. Alan Blinder, a tion may allow us, with some confi- The figure also includes former Governor of the Federal Reserve dence, to predict future movements in changes in the stock of private nonfarm System, famously remarked that “the the data. Theories that have sought to inventories (private refers to nongovern- business cycle, to a surprisingly large explain macroeconomic changes in ment). The difference between GDP, degree, is an inventory cycle.” Consis- inventory investment have generally the sum of all goods and services tent with this perspective, much of the focused on firms’ attempts to (1) reduce produced in the economy over a given discussion about the timing of a the costs of adjusting their production period, and final sales, the sum of all recovery following economic recessions level or (2) reduce the costs of placing goods and services sold, is known as net focuses on firms’ stocks of inventories. orders for intermediate goods. While inventory investment. Net inventory Pundits suggest that production and much of the research on inventories in employment cannot recover until firms’ the past 50 years has emphasized the inventories fall, relative to their sales. cost of adjusting production, this This article surveys the facts approach has had well-known difficul- 1 about inventory investment over the ties when confronted with the data. Actually, any type of expenditure or output may be broken down into a business-cycle business cycle, then discusses two Recent work that has focused on component and a trend. The process of leading theories of inventory investment reducing the fixed costs of ordering isolating the business-cycle component is known as “detrending” or “filtering.” The goods may provide a framework that is real quarterly series in the figure have been more consistent with the facts. At the detrended with the Hodrick-Prescott filter same time, this recent work may using a smoothing parameter of 1600. For additional details, see Edward C. Prescott’s produce new insights about the paper. interaction between inventories and the Aubhik Khan is a 2 It then follows that a , in this senior economist in macroeconomy. These two theories approach to business cycles, is a period in the Research predict different behavior for aggregate which the economy is growing at rates that Department of the production, sales, and inventory are lower than its trend. This contrasts with Philadelphia Fed. the conventional use of the term recession to investment. describe a period of negative growth.

38 Q3 2003 Business Review www.phil.frb.org investment is a measure of goods that sures the size of the variable’s total that a common view of inventories — have been made but not sold to fluctuation over the business cycle.3 that they are goods that firms were consumers nor used by a firm as an Economic variables differ considerably unable to sell — can’t explain most of intermediate input into production. in their volatility. For example, consump- the movements in inventories. In an A car made by Honda in Ohio, tion of nondurable goods and services is expansion, inventories grow as consump- completed but retained unused in the far less volatile than GDP, while business tion and investment grow. That is, when factory, adds to Honda’s stock of investment and consumption of sales rise, inventories also rise. If inventories. Steel bought by the same consumer durable goods are more inventories were mainly goods that firms manufacturer but left unused is a raw volatile — i.e., they have bigger swings. couldn’t sell, they would tend to rise material that also adds to Honda’s stock Thus, investment fluctuates a lot more when sales fell. of inventories. Nonfarm private than does the consumption of nondu- By definition GDP = Final inventories are essentially stocks of these rables and services as output rises and Sales + Net Inventory Investment. final goods, intermediate inputs, falls. Thus, any change in GDP must be materials, or supplies held by businesses. Net inventory investment is attributable to either a change in final Changes in this component of total pro-cyclical (Figure 1). It moves along sales or a change in net inventory inventory investment account for most with GDP, rising during expansions and investment. Let’s look at the fraction of of the change in total inventories over falling during recessions. This is a very the change in GDP that can be the business cycle. important observation because it means accounted for by changes in net Cyclicality and Volatility. In inventory investment. To accomplish organizing their thinking about the role this, we divide the change in inventories of an economic variable such as during recessions by the corresponding 3 inventory investment over the business Formally, we define volatility as the change in GDP. The result is a number standard deviation of the business-cycle cycle, economists focus on the cyclicality component of the quarterly data. around one-half. Almost half of the fall and volatility of the variable. A variable’s cyclicality — formally, its correlation with real GDP — is a measure of how the variable changes over the business cycle. For example, net FIGURE 1 — that is, exports minus imports GDP, Final Sales, and Changes in Nonfarm In- — are countercyclical: they fall as GDP rises during an expansion, and they rise ventories as GDP declines in a recession. In contrast, consumption and investment are pro-cyclical: they rise during expansions and fall, alongside GDP, in recessions. A significant correlation, whether positive or negative, between any economic variable and GDP suggests that the variable is cyclical in that it varies in a systematic way with GDP over the business cycle. This is not true of all economic variables. For example, is acyclical: it shows no significant correlation with economy activity over the business cycle, neither rising nor falling systematically. While the cyclicality of a variable measures the extent to which it rises or falls with GDP, volatility mea-

www.phil.frb.org Business Review Q3 2003 39 in production experienced by the U.S. THE MYSTERY known as the (S, s) model of inventories, economy during a recession may be OF INVENTORIES emphasizes the costs of accepting explained by a reduction in net Economists are not satisfied deliveries. While each of these theories inventory investment. This is a merely to uncover the facts about can explain why firms hold inventories, surprisingly large fraction when one inventories and the business cycle. they are commonly applied to different considers that net inventory investment Their primary goal is to explain these types of inventories. Thus, the two is, on average, only around 0.5 percent findings. Before we may begin to theories are not mutually exclusive; both of GDP. It indicates that inventory understand why firms change their may be relevant to an understanding of investment is extremely volatile. holdings of inventories over the business the overall stock of inventories. Adding to the Volatility of cycle, we must have an understanding However, as with all science, Output. The pro-cyclicality and of why firms hold inventories at all. For the empirical relevance of these extreme volatility of inventory invest- economic theory, this has been more of a alternative theories can be assessed by ment have led researchers to suggest mystery than you might suppose. evaluating their predictions against the that inventories are a destabilizing force. Why would a firm produce data. The production-smoothing model At its simplest, their argument is as goods but not sell them? Sales com- and the (S, s) model generally have follows. Inventory investment and final pleted today give the firm income that it distinct predictions about the joint sales tend to move together: both rise may invest. For example, even if the behavior of production, sales, and during expansions, and both fall during firm has no other immediate use for the inventory investment. recessions. Consequently, GDP varies funds, it might deposit them in an by more than it would if inventory interest-earning account. A firm would THE PRODUCTION- investment were constant or negatively forgo this interest income if it chooses SMOOTHING MODEL correlated with final sales. not to sell its goods immediately. The production-smoothing To understand this better, But perhaps it isn’t voluntary. model explains why a manufacturing consider the following simple example. If You may think firms hold inventories firm holds stocks of goods produced but final sales rise during odd years and fall only of finished goods they have been unsold. The model assumes that it is during even years, while inventory unable to sell. While firms do sometimes costly for the manufacturing firm to investment rises (by the same amount) accumulate inventories of unsold goods adjust production. during even years and falls during odd because of weaker-than-expected It is costly to buy and install years, there’s no effect on GDP. demand, this can’t be the central new equipment or to uninstall and sell Inventory investment and final sales explanation of inventory holdings. First, off previously installed equipment. move in opposite directions; they are remember that inventories rise when Workers are costly to hire and train, and negatively correlated. As a result, each sales do. Second, goods that have been layoffs are also expensive. Since chang- offsets the change in the other. Produc- produced but not yet sold are only a ing levels of output often involve tion is smoothed. fraction of the total stock of inventories. changing the size of the labor force and Now, consider an alternative Firms also hold inventories of inputs they purchasing new capital equipment, case in which both series rise during odd use to produce their goods, buying them these adjustment costs are inevitable for a years. Since inventory investment moves before they need them. firm that changes its level of output over with output, and since it’s highly The answer to the question of time. It’s reasonable to assume that these volatile, inventories substantially raise why firms forgo interest income must costs of changing production levels the volatility of GDP. Since final sales involve benefits derived from holding actually increase with the size of the and inventory investment are indeed inventories. Holding stocks of invento- change. For example, a large increase in positively correlated, typically rising and ries must somehow reduce a firm’s cost production requires hiring more workers falling at the same time, researchers of production, and these cost savings and, thus, involves higher training costs. have concluded that inventories are a must exceed the forgone interest. In any case, given these costs of adjust- destabilizing force in the economy. (See There are two theories of how ing production, if sales are volatile, a Are Inventories Becoming Less Promi- production costs induce firms to hold firm may prefer not to vary production nent?) Changes in inventories magnify stocks of inventories. The first, known to match the variation in sales. Instead, the effect of a change in final sales on as the production-smoothing model of it may use inventories of already domestic production. inventories, emphasizes the costs of produced goods to offset the difference adjusting production. The second, between production and sales.

40 Q3 2003 Business Review www.phil.frb.org ARE INVENTORIES BECOMING LESS PROMINENT?

If inventories are indeed a destabilizing element intermediate inputs and materials and supplies, both of aggregate economic activity, perhaps the much heralded components of the overall stock of inventories but not part improvements in technology that have led to sharp declines of final sales, must account for the divergence between the in the inventory to sales ratio will eventually yield a less real and nominal ratios of inventories to sales. severe business cycle. Since inventories seem to explain so While I cannot suggest which ratio is more much of the decline in output during recessions, and since sensible, Figure 2 casts some doubt on some of the discus- they amplify the effect of changes in final sales on GDP, as sion of technological improvements’ role in reducing inventory levels decline, perhaps GDP will be subject to less demand for inventories. While both the financial press and severe fluctuations. policymakers have repeatedly mentioned the important Arguments such as this have led economists to role of improved management techniques, such as just-in- emphasize the decline in the inventory to sales ratio. In time production methods, in reducing firms’ dependence Figure 2, we see the nominal stock of inventories as a ratio on inventories, the real inventory to sales ratio in Figure 2 of final sales. Clearly, it has declined sharply since the early suggests caution before making sweeping generalizations. 1980s. Many observers have regarded this decline as the When examining the nominal inventory to sales ratio, we result of improvements in technology and management see that it rose before it fell, something that is hard to methods that have allowed firms to reduce their holdings explain using technological improvement. The real ratio of inventories relative to their sales. This is less clear from has not declined consistently over the past 20 years. the figure. First, we see that the inventory to sales ratio rose sharply in the 1970s. If technological innovation has reduced the ratio FIGURE 2 since the 1980s, what was the sharp Quarterly Nominal and Real Inventory technological regress in the 1970s? to Sales Ratios Second, and related, is the finding that the inventory to sales ratio was as low in the late 1960s as it was in the mid 1980s. Even the decline in the importance of inventories is less clear than is commonly acknowledged. The figure also plots the real inventory to sales ratio, that is, the ratio when both inventories and sales figures have been divided by their price indexes. While the nominal inventory to sales ratio shows a clear negative trend over the past 20 to 25 years, the real inventory to sales ratio displays no corresponding decline! This implies that the price index for inventories has fallen more slowly than that for final sales. It would seem that changes in the relative price of

www.phil.frb.org Business Review Q3 2003 41 For example, a toy maker volatility of final sales is the ratio of the In her paper, Ramey suggests knows that sales are always higher standard deviation of final sales divided that firms may actually prefer to bunch during the Christmas season. However, by that of GDP itself. This gives us a their production because unit costs fall since it is expensive to hire a large measure of how much sales fluctuate as they produce more. This is known as number of workers in the last quarter of relative to GDP. For example, we see increasing returns. Ramey and Daniel the year, the toy company may produce that the relative volatility of final sales is Vine studied an interesting example of more toys than it sells over the first nine 82 percent of that of GDP. At least at increasing returns in the automobile months. During these nine months, the aggregate level, production is more industry that is a result of contracts production exceeds sales, and the toy volatile than sales. between manufacturers and labor company accumulates inventories. At In the third row of the second unions. They argued that these the end of the year, when demand rises, column, we also find that the correlation contracts broadly imply that if an the toy factory has fewer workers than it between final sales and inventory automobile manufacturer employs needs to satisfy sales. But even though investment is actually positive. Both the workers for less than 40 hours in any production is lower than Christmas sales, higher variability of production and this given week, it must also pay them 85 the company can sell off its accumu- correlation contradict the predictions of percent of the earnings lost in working lated inventories to meet the increased the basic production-smoothing model less than a full week, but only if the demand. Accumulating inventories described above. If production is more workers work at all.4 from January through September lets volatile than sales, inventories are not Consider the following the toy maker smooth production effective in smoothing production. This example, which highlights the implica- relative to sales; that is, production is less evidence — which also holds for tions of such a wage contract. Assume volatile than sales, and when sales rise, countries other than the U.S. and for that an automobile manufacturer sells inventories fall. individual industries and even for firms 75 cars a week. If its workers work a full The defining assumption of — offers no support for the view that week (40 hours), they produce 100 cars. the production-smoothing model is that smoothing production is an important there are costs of adjusting the level of motive for holding inventories. production in a firm and that these costs Attempts to Adapt the rise in proportion to the extent of the Model to Fit the Facts. By adjusting 4 Thus, if a worker is paid $10 an hour and is adjustment. The central prediction of the production- smoothing model to fit employed full time for 40 hours, he is paid $400 for the week. However, if he is employed the production-smoothing model is that, the data, both Valerie Ramey and for 35 hours, he is paid $350 for the time he at least to the extent that there are Martin Eichenbaum have developed worked and 85 percent of the $50 he would solutions to the problems with the basic have earned for the five hours he did not fluctuations in the demand for a firm’s work or $392.50 in total. Finally, if he does products, its production will vary less production-smoothing model. not work at all in a week, he is not paid at all. than its sales, and when its sales are high, inventories will be reduced. If all firms behave this way, we should see, for the economy as a whole: (1) GDP less TABLE 1 volatile than final sales and (2) a GDP, Final Sales, and Inventory Investment negative correlation between final sales and inventory investment. Net Inventory The Dilemma with Invento- GDP Final Sales Investment ries as a Buffer Against Changes in Sales. There are two difficulties with Percent Standard Deviation Relative to GDP 1.675 0.824 0.282 the production-smoothing model (Table 1). The first row of the first column Correlation with GDP 1.000 0.951 0.653 shows a measure of the volatility — the standard deviation — of the business- Correlation with NII 0.653 0.410 1.000 cycle component of GDP. The first rows Data are quarterly U.S., 1954.1 – 2002.4, seasonally adjusted and chained in 1996 dollars. GDP of the next two columns report the and final sales are reported as percentage standard deviations, detrended using a Hodrick- relative volatility of final sales and net Prescott filter with a weight of 1600. Net inventory investment in private nonfarm inventories x , is detrended relative to GDP; the detrended series is (x -x ) / y , where x is the HP-trend inventory investment. The relative t t t t t of the series and yt is the trend for GDP.

42 Q3 2003 Business Review www.phil.frb.org One possible production plan would be as a rise in oil prices, and poor weather. finished goods that it will sell later. to employ all workers for only 30 hours A sudden rise in oil prices that is not Inventories of finished manu- a week. But if, instead, they are expected to last very long may give a factured goods are only 13 percent of employed full time for three weeks, transportation company an incentive to the total stock of inventories in the then laid off every fourth week, the temporarily reduce its shipments. An economy (Table 2). The remaining manufacturer will have lower labor unexpectedly cold winter will lead two-thirds of inventories held in the costs. Moreover, this second option construction companies to defer as manufacturing sector are intermediate implies that production varies across much building as they can. Such inputs into production. The inventories weeks, while sales do not. Production random changes in costs lead to random held in the wholesale and retail sectors has become more variable than sales changes in production and do so are largely finished goods, but produc- because of increasing returns.5 independently of fluctuations in sales. tion smoothing may not be best suited Martin Eichenbaum considers Thus, production becomes more volatile, to explain the inventories held in these an alternative: the effect of random and if these cost shocks are sufficiently sectors. One reason is that firms in changes in unit costs that are indepen- large, it may become more volatile than these sectors do not produce the goods dent of the quantity produced. This sales. they sell.6 theory is different from the assumption Both Ramey’s increasing of increasing returns; it does not assume returns model and Eichenbaum’s cost THE (S,s) MODEL OF that unit costs fall with quantity shocks model modify the production- INVENTORY ACCUMULATION produced but that they rise and fall smoothing model, making it more Surprisingly, given its wide- unexpectedly over time. Examples of consistent with the data. In each spread use by macroeconomists studying such unexpected changes in firms’ instance, the positive co-movement inventory accumulation, the original production costs include, but are not between final sales and inventory model developed by economists to limited to, changes in input prices, such investment is restored, and production becomes more variable than sales. Regardless of whether the 6 However, V.V. Chari of the University of Minnesota and the Federal Reserve Bank of 5 If the firm chooses to employ its workers for production-smoothing model can be Minneapolis and Mitchell Berlin of the four weeks, having them work just 30 hours reconciled to observation, a second Federal Reserve Bank of Philadelphia have each week, it will have to pay them for 38.5 difficulty remains. This model may independently noted, in separate discussions hours a week, or 154 hours in total, for a with me, that long-term relationships between total cost of $1540. If, instead, the firm has apply to a relatively small fraction of the sellers and manufacturers may imply that the them work full time for 40 hours during the firms that hold inventories because the production-smoothing model is applicable to first three weeks, then lays them off during retail and wholesale inventories. In such the fourth week, it has to pay them for only model is based on a manufacturing firm settings, manufacturers may store their 120 hours, or $1200 in total. that produces, then stores as inventories, finished goods with sellers.

TABLE 2 Sectoral Distribution of Private Nonfarm Inventories

Percentage of Total STD Correlation (Inventory Stock of Inventories (Inventory Investment) Investment, GDP)

Manufacturing 37 0.14 0.65 finished goods 13 work in process 12 materials & supplies 12 Trade retail 26 0.12 0.32 wholesale 26 0.09 0.35 Other 11

Column 3, the percentages of the total stock of inventories, is taken from Ramey and West, 869, Table 4.

www.phil.frb.org Business Review Q3 2003 43 explain firms’ holdings of inventories was inventories to fluctuate between an words, inventories will tend to move not the production-smoothing model. It upper level labeled S and a lower level with sales when the change in sales itself was the (S, s) model first formulated by labeled s — hence, the conventional is large. Smaller increases in sales may be Herbert Scarf of Yale University. While label (S, s). S represents the level of associated with a net reduction in total macroeconomists do not commonly use inventories held by the firm after it has inventory holdings. Thus, the model this model, Alan Blinder and Louis restocked. It then allows its stock to fall predicts an interesting nonlinearity: we Maccini have argued that the (S, s) over time until it reaches the threshold s. should expect inventories and sales to model provides a natural resolution to At that time, another order is placed. rise together when sales rise by a large the empirical inconsistencies of the basic Sometimes, the order costs are called amount, but the correlation may be production-smoothing model without adjustment costs. negative for a small rise in sales. relying on increasing returns or cost The (S, s) model is flexible In a formal analysis of (S, s) shocks. enough to be consistent with either retail inventories, Andrew Caplin The (S,s) model obtains very positive or negative correlations between proved a positive correlation between different predictions because adjust- sales and inventories. To see this, assume final sales and inventory investment. For ment costs operate differently. Instead of there’s a short-term increase in sales the reasons described above, this positive assuming that adjustment costs increase across a large number of firms selling the correlation raised the variability of smoothly with changes in production, in same product. Firms will reduce their production above that of sales. Caplin the (S, s) model, adjustments lead to inventories to meet the rise in sales. For concluded, “The (S, s) theory thus fixed costs. Moreover, instead of arising some firms, the net effect is to reduce contradicts the widely held notion that during production, these costs are inventories. For firms with already low retail sector inventories act as a buffer, incurred when a firm either orders or protecting manufacturers from fluctuat- undertakes delivery of goods. A firm facing such costs will tend to order the relevant goods in large Overall, some firms will increase inventories quantities but infrequently. By ordering when sales increase, while others will more than is needed at any one time, the firm can hold stocks of the goods, reduce them. thereby avoiding fixed order costs because the firm orders less frequently. levels of inventories, this initial reduc- ing sales.”7 Caplin’s work suggests that By holding these stocks of goods, the tion means they reach their order inventories may indeed destabilize the firm reduces the overall cost of ordering. threshold, s. As a result, they will adjust economy. However, his seminal analysis For example, consider Honda their inventories upward, raising them to of retail sector inventories took final again. In deciding the size of the S. Overall, some firms will increase sales as given, rather than allowing them quarterly steel order for Honda’s Ohio inventories when sales increase, while to be determined along with inventories, plant, a manager must go over last others will reduce them. On average, in general equilibrium. In general quarter’s production and forecast future the rise in sales could be associated with equilibrium, a complete assessment of sales. This takes a certain amount of either an increase or a decrease in net the role of inventories would have to managerial time that is largely indepen- inventory investment, depending on the allow for feedback effects from the rest dent of the size of the steel order. As size of the demand shock and different of the economy, which may change the such, the costs of ordering steel, which firms’ current levels of inventories. behavior of final sales. include the labor costs associated with There is an interesting subtlety (S, s) Inventories in a Model the manager’s efforts, are fixed costs. to the reasoning outlined above. A rise of the Business Cycle. The (S, s) These costs are reduced when the firm in the typical firm’s inventories along model of inventories provides us with a orders infrequently — that is, when it with a rise in sales is more likely if many framework, broadly consistent with places orders of sufficient size so as to firms hit their re-ordering level. This is observation, to study the role of not have to order again for some time. In more likely to be the case when the inventories over the business cycle. For other words, Honda will hold inventories increase in sales itself is large. Such of steel to reduce the fixed costs of large increases in sales move most firms ordering. As Herbert Scarf proved, a to their lower threshold for inventories, 7 See page 1396, paragraph 2, of Caplin’s firm facing such fixed costs will allow its causing them to readjust. In other article.

44 Q3 2003 Business Review www.phil.frb.org example, it allows us to examine the (S, s) rule, as described above. In this second effect dominates, higher levels of central question of whether inventories setting, we asked the question: If an inventories actually reduce the volatility destabilize the economy and exacerbate economist were to observe two econo- of sales and, thus, GDP. Which effect the movements in GDP. In a recent mies with firms and consumers that dominates depends on how the many paper, Julia Thomas and I did just that. were essentially identical, but firms in parameters of our model interact; Our approach, in common one economy held higher inventory however, we often found cases where with other modern macroeconomic levels than firms in another economy, increases in the level of inventories analysis, relied on building a model of should we expect to observe more reduced the variability of GDP. the macroeconomy in which aggregate volatile sales in the economy with economic variables, such as production, inventories? CONCLUSION consumption, investment, and employ- Our answer is that there are Economics is full of puzzles, ment, are the result of interactions really two effects. The first is straight- some of which take the form of between households and firms, much as forward. Remember the relationship disparities between the best available in the actual economy. The essential GDP = Final Sales + Net Inventory models and macroeconomic data. The feature of our model is that, in keeping Investment. As we discussed above, net production-smoothing model of with modern practice, we model the inventory investment in the data is inventory investment is an example of decisions of individual households and procyclical and volatile. It is also such a puzzle. firms, summing these decisions to arrive positively correlated with final sales. Inventory investment is pro- at aggregate variables for the economy This tends to raise the variability of GDP cyclical and very volatile. Furthermore, as a whole. above that of final sales. Increases in it is positively correlated with final sales. Our model included an (S, s) final sales are associated with increases As a result, the sum of these two objects, model of a firm’s inventory investment. in inventory investment, and given that GDP, is more volatile than sales. The Simulating our model to produce both rise simultaneously, GDP rises more production-smoothing model assumes artificial business cycles, we were able to than final sales. This effect is in our that since production is costly to adjust, explain roughly one-half of the observed model. firms hold inventories to smooth volatility of inventory investment. More However, our model identified fluctuations in sales. The result is that important, inventory investment and a second effect: the introduction of simple versions of the model predict that final sales moved together, as in the inventories reduces the volatility of final production is less volatile than sales. data, and production, as a result, was sales. Firms facing adjustment costs — Some recent research has more volatile than sales. We also found the reason for the inventories in the first focused on alternative explanations of that the relationship between invento- place — change production levels less why firms hold inventories, and this has ries and GDP is not as straightforward as frequently. This tends to offset the led to a renewed emphasis on the (S, s) you might expect. increase in the variability of GDP. model of inventory investment. The We compared two model Certainly, the introduction of invento- (S, s) model, which replaces the economies, identical in most fundamen- ries raised the variability of GDP assumption that production is costly to tals, but with one difference. Firms in directly, but there was an offsetting adjust with the alternative assumption one economy had no adjustment costs change in the volatility of final sales. that there are costs of ordering goods, and, thus, no need to hold inventories. When the first effect domi- may overturn our thinking of inventories Firms in the second economy faced the nates, more inventories lead to more as existing to buffer changes in sales. BR costs of purchasing inputs and, thus, had volatile sales and increases in the an incentive to hold inventories using an variability of GDP. In contrast, when the

www.phil.frb.org Business Review Q3 2003 45 REFERENCES

Blinder, Alan S. and Louis J. Maccini. Prescott, Edward C. “Theory Ahead of Ramey, Valerie A., and K.D. West. “Taking Stock: A Critical Assessment of Business Cycle Measurement,” Federal “Inventories,” in M. Woodford and J. Taylor, Recent Research on Inventories,” Journal of Reserve Bank of Minneapolis Quarterly eds., Handbook of IB. Economic Perspectives, 5, 1991, pp. 73-96. Review, 10, 1986, pp. 9-22. Amsterdam: Elsevier Science, 1999, pp. 863-927. Caplin, Andrew S. “The Variability of Ramey, Valerie A. “Nonconvex Costs and Aggregate Demand with (S, s) Inventory the Behavior of Inventories,” Scarf, Herbert E. “The Optimality of Policies,” Econometrica, 53, 1985, pp. Journal of Political Economy, 99, 1991, (S, s) Policies in the Dynamic Inventory 1395-1410. pp. 306-34. Problem,” In Mathematical Methods in the Social Sciences 1959. Proceedings of the First Eichenbaum, Martin S. “Rational Expecta- Ramey, Valerie A., and Daniel J. Vine. Stanford Symposium. Stanford, Calif.: tions and the Smoothing Properties of “Tracking the Source of the Decline in GDP Stanford University Press, 1959. Inventories and Finished Goods,” Journal of Volatility: An Analysis of the Automobile Monetary Economics, 14, 1984, pp. 71-96. Industry,” University of California, San Diego Economics Department Working Khan, Aubhik, and Julia K. Thomas. Paper, 2001. “Inventories and the Business Cycle: An Equilibrium Analysis of (S, s) Policies,” Federal Reserve Bank of Philadelphia Working Paper 02-20 (2002).

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