¹ Darling, P. G., “Manufacturers' Inventory Investment, 1947–58,” American Economic Review, LXIX (12 1959), 958.Google Scholar

² Lovell, M. C., “Manufacturers' Inventories, Sales Expectations, and the Acceleration Principle,” Econometrica, XXIX (07 1961), 308.Google Scholar

³ Eisner, R. and Strotz, R., “Determinants of Business Investment,” in Impacts of Monetary Policy, a research study prepared for the Commission on Money and Credit (Englewood Cliffs, 1963), p. 106.Google Scholar Italics are in the original.

⁴ Considerable attention is given to it in studies by Abramovitz, M., Inventories and Business Cycles with Special Reference to Manufacturing Inventories, NBER Studies in Business Cycles, 4 (Princeton, 1950)Google Scholar, and by Stanback, T., “Postwar Cycles in Manufacturers' Inventories,” in Inventory Fluctuations and Economic Stabilization, Part I, Joint Economic Committee, 87th Congress, 1st Session 1961, pp. 1–143.Google Scholar However, its greatest proponent in recent years has been Victor Zarnowitz, especially in his paper Unfilled Orders, Price Changes and Business Fluctuations, NBER Occasional Paper 84 (New York, 1962)Google Scholar, also published in the Review of Economics and Statistics, Nov. 1962. This article presents a perceptive analysis of the distinction and is the source of most of the ideas in this section.

⁵ After this article had been accepted for publication, we came across an excellent paper by Belsley, D. A., “Industry Production Behaviour: An Econometric Analysis” (read to the 12, 1966, meetings of the Econometric Society).Google Scholar Belsley develops a theoretical approach to industry production behaviour and in the process emphasizes, and empirically substantiates, the importance of the distinction between production to order and production to stock. This paper is based on his MIT doctoral dissertation of the same title which, since it was completed in 1965, predates our analysis. Even though Belsley does not focus on inventory behaviour per se, his study complements ours in innumerable ways and, in addition, possesses a certain elegance in that it is cast in terms of cost minimization and linear decision rules. It will soon be released in the North-Holland series.

⁶ The ideas (and in some cases the wording itself) in the remainder of this paragraph and the notation in the following are from pp. 5–6 of Zarnowitz, Unfilled Orders.

⁷ Ibid., 6. The level of raw materials that firms deem adequate will, among other things, depend upon whether the supplying firms are characterized by PTS or PTO.

⁸ For this hypothesis to be operational, there must be some degree of predictability in its real-world application, i.e., we must be able to identify some goods as normally produced to order and others as normally produced to stock. The reader interested in the structural characteristics sufficient to lend the PTO-PTS distinction its required degree of stability can consult Zarnowitz, ibid. For our purposes we merely note that fully 60 per cent of Canadian manufacturing industry is engaged in some production to order ( DBS, Inventories, Shipments and Orders in Manufacturing Industries, 12 1960, 85 Google Scholar). In dollar magnitude the monthly unfilled-order backlog during 1962 fluctuated around two billion dollars in book value—an amount approximately equal to the monthly flow of shipments.

⁹ For a discussion of the origin of, and rationale behind, the assumption of 0 < B < 1 see Lovell, “Manufacturers' Inventories,” esp. sections 1 and 2.

¹⁰ For an interesting discussion of this concept see Mack, Ruth, “Characteristics of Inventory Investment: The Aggregate and its Parts,” in Problems in Capital Formation, NBER (New York, 1957), 480–1.Google Scholar We would also like to point out that our approach to adjustment policies for forecast errors is highly simplified. One obvious alternative open to some firms is to alter prices and in this way affect the level of S_t . Note also that the value for j will depend on the length of the time period t, which for our analysis is set at a quarter year.

¹¹ Eisner, and Strotz, , in their review article, “Determinants of Business Investment,” 225 Google Scholar, consider a model such as equation (1) as the “sort of general formulation for an inventory investment equation that one would want to specialize further for econometric research.” The basic model also has desirable theoretical properties. For the conditions under which a model like (1) is consistent with the cost minimization, see Holt, C. and Modigliani, F., “Firm Cost Structures and the Dynamic Response of Inventories, Production, Work Force and Orders to Sales Fluctuations,” Inventory Fluctuations and Economic Stabilization, Part II, JEC, 87th US Congress, 1st Session (12 1961).Google Scholar Michael Lovell has demonstrated that a multi-sector inventory model (with sector equations akin to the “basic inventory model”) is not likely to render the economy dynamically unstable. See Lovell, , “Buffer Stocks, Sales Expectations and Stability: A Multisector Analysis of the Inventory Cycle,” Econometrica, XXX (04 1962), 267–96.CrossRefGoogle Scholar Stability over time for an individual sector (with ΔH_t as the dependent variable) requires that the coefficient of the lagged inventory variable, ΔH _t−1, to be between zero and minus two. The assumption 0 < B < 1 satisfies this.

¹² This classification is from DBS, Inventories Shipments and Orders in Manufacturing Industries.

¹³ This method is adopted from Zarnowitz, , Unfilled Orders, 7.Google Scholar

¹⁴ Actually sector 2A (perishable consumer goods) has the greatest ratio. However, inventory policy for this sector is dominated by conditions of supply and perishability of the product and not governed by future demand as a PTS sector must be.

¹⁵ As Table I indicates, there is a close correlation between the degree of PTO and the length of the production period. In part, this is hardly surprising. The costs involved in producing an item with a long production period would argue strongly for production to order. In part, however, the manner in which we measure the length of the production period biases the ranking in favour of making it similar to the degree of PTO.

¹⁶ The particular seasonal-adjustment method employed allows for both varying seasonal and varying amplitude. For a discussion of the merits of this method, the reader may consult Godfrey, M. D. and Karreman, H. F., “A Spectrum Analysis of Seasonal Adjustment,” Mathematical Economics: Essays in Honor of Oskar Morgenstern, ed. by Shubik, M. (Princeton, 1966).Google Scholar

¹⁷ One of the defects of the “Economic Use Classification” is that price data are not available on a similar classification. To get around this problem in our study (of which the present paper is a summary) we selected a second data set consisting of various SIC industries. While we show no results from this data set in the present paper, we assure the reader that all conclusions we shall draw from nominal data also obtain for price-deflated data. In addition, regression results derived from seasonally unadjusted data are consistent with the empirical results we report below. The interested reader can refer to my thesis for more detailed results in nominal terms as well as the result from price-deflated and seasonally unadjusted data.

¹⁸ We can visualise various effects which might give rise to a positive relationship between H^f and U. 1: U directly affects finished-goods production and to the extent that shipping delays are positively related to may be positively related to U. 2: some sectors may use the backlog of unfilled orders on the order side of the sector to aid in predicting future sales for the stock side, and thereby to determine the effective stock of H^f , etc. None the less, hypothesis II obtains.

¹⁹ One shortcoming of this model is that S_t is used to formulate even before the current period is over, i.e., even before S_t is fully known. This would pose a serious problem were our analysis based on monthly observations. We do not feel it is serious when the time period is a quarter year since the inventory-turnover ratio, , is greater than unity for all sectors, e.g., for sector 2B, = 3.01. We note, however, that equation (8) contains the same variables as does Michael Lovell's familiar inventory model in which both current and past shipments are used to evaluate inventory requirements (see Lovell, “Manufacturers' Inventories,” equation 3.7). The reader can, therefore, interpret our theoretical and empirical results in terms of Lovell's model or can refer to my thesis, Chap. III, where such a comparison is made.

²⁰ This excludes sector 2A. See note 14.

²¹ Stanback, , “Postwar Cycles,” 61–85.Google Scholar

²² This is especially true of the prior-stage inventory variables. Since finished goods products depends upon the existence of goods in process (H_g ) and raw materials (H_r ), it is not unreasonable to assume that stocks of H^f are also related to these prior-stage variables. But we are unable a priori to predict the signs of these variables. As far as lagged inventory investment is concerned, it can be shown that adding to the basic model allows for a more flexible lag pattern than that embodied in the normal flexible-accelerator model.

²³ We also show the value of the multiple-correlation coefficients for the form of the equations having rather than Δ as the dependent variable (see R_L in Table II). In general, they are quite high and give no indication as to how well the equation predicts the changes in the stock, which is the relevant inventory variable for policy purposes. Note also that while we give values for the Durbin-Watson statistics (and shall do so for all equations in this paper), they are hard to interpret since all equations can be shown to contain a lagged dependent variable.

²⁴ “Final Estimates,” as used in this paper, means that variables such as time trend T are allowed to enter the regression equations whenever their t-values are greater than 1.25. The equation for Sector 3A is an exception to this; this was done to emphasize the random-like behaviour of this sector.

²⁵ We do not show these equations here. See Tables III.6 and III.7 of my thesis.

²⁶ This relationship holds for any stock, i.e., the level of a stock will change by the difference between the inflow, K_t + M_t , and the outflow, .

²⁷ Holt, and Modigliani, , “Firm Cost Structures,” 37.Google Scholar

²⁸ It is important to point out that equation (13), with n fixed and k_i and m_i independent of , typifies a production process with a constant production time. An example of this would be a factory operating at a constant speed but having parallel sets of identical machines. Given unused capacity, in-process inventories are proportional to the production rate, Z_f .

But this is only one of three pure types of factory operation. A second type has invariant to the rate of production. Increases in are reflected by a decrease in the amount of time each item spends in the production process. A third type has an increased production rate accompanied by an increase in the average production time, i.e., in-process inventory rises proportionally more than the production rate. Holt and Modigliani suggest that this latter effect might be captured by a squared- term. An alternative indicator might be some measure of capacity utilization (entering with a positive coefficient, of course). On these points see Holt and Modigliani, ibid., 37–40.

²⁹ In this empirical section, we shall compare the two approaches.

³⁰ On the costs involved in responding to sharply fluctuating orders, see Holt, C., Modigliani, F., Muth, J., and Simon, H., Planning Production, Inventories and Work Force (Englewood Cliffs, 1960), chap. 2.Google Scholar

³¹ We realize that this relationship between unfilled orders and capacity utilization is not unidirectional. The level of the order backlog plus the rate of inflow of orders will certainly determine the rate of capacity utilization. However, the greater the capacity-utilization rate (implying large order backlogs) the longer a new order is likely to remain in this order backlog.

³² It is inappropriate only because we maintain the time period of our analysis at a quarter year. Were we to shorten the time period from a quarter to a month we would be able to retain a specification containing variables lagged more than one time period, as in (18). The collinearity between S_t and NO_t discussed in the next few sentences would likely be less severe for monthly data. However, we have not carried out any empirical work on a monthly basis.

³³ Our reasoning is as follows. If the production period is less than two quarters in length (as the statistics in Table I indicate) some of the new (and therefore, unfilled) orders of period t — 1 will have, by the end of the current period, already passed through the in-process stage and become finished products. This will tend to decrease the U _t−1 coefficient so that the equality b ₂ > b ₃ may not hold. The existence of some PTS in these sectors will, for two reasons, work against the assumption b ₀ > b ₃: the negative relationship between S_t and Δ implied in equation (11) is less direct since = S_t + Δ; the existence of some PTS introduces a positive relationship between S_t and Δ since S_t will be used by PTS industries to approximate (as indicated below).

³⁴ For sector 2B, this ratio is 3.2. Since PTS sectors hold the bulk of their inventory in the form of H^f these ratios are also greater than unity for H^g as well.

³⁵ One contributing factor is that for H^f every shipment directly decreases the level of finished-goods inventories. The relationship between and S_t is not as direct since goods-in-process become finished goods before being shipped.

³⁶ Again most of the equations in this table contain some “V-type” variables (e.g., time-trend, prior-stage variables). Their presence does not affect any of the conclusions drawn from the table. Rather, their effect is primarily in terms of goodness of fit.

³⁷ Note that the regression coefficients in Table IV are “short-run” coefficients. To obtain d ₁, d ₂, and d ₃, these coefficients must be divided by B, the reaction coefficient.

³⁸ In Table IV, blank spaces for the variables discussed in the theoretical section indicate that these variables are not statistically significant when added to the other variables in the equation. Therefore we can say that passive inventory investment is important for the PTS sectors but not important for the PTO sectors—an expected result.

³⁹ We note in passing that goods-in-process inventories for the pure-PTS representative in our “accessory data set” (i.e., the one that has price data available) are not affected by unfilled orders.

⁴⁰ We could have included variables U _t−2 and NO _t−1 in place of U _t−1 in the equation for sector 1. These variables enter the equation with significant positive coefficients and reflect the impact of the PTO end of the spectrum.

⁴¹ This result holds for sector 3A as well.

⁴² H. T. Shapiro, using the same long-term interest rate found that new orders for machinery and equipment were negatively related to the interest rate. See Shapiro, , “The Canadian Monetary Sector: An Econometric Analysis,” unpublished doctoral dissertation, Princeton University, 1964, 116.Google Scholar The question of which rate is appropriate must be viewed in terms of simultaneous model. At a minimum, there should be an equation explaining the inflow of new orders to the firm (in which the long-term interest rate would enter with a negative coefficient) and an equation representing the firm's attempts to supply goods-in-process inventories to meet this demand. In the latter equation the short rate would likely be the more appropriate as proxy for the opportunity cost of tying up funds in inventories. In any case, the use of the long-term rate in the Δ equations combines some elements of both supply and demand for H^g .

⁴³ The multiple-correlation coefficient for equation (26) is very high. However, the dependent variable is s3_inline9, whereas the dependent variable for the sector 3A equation is Δ. In terms of the standard error of estimate, that for equation (26) is twice that of the equation for this sector in Table IV.

The type of specification used in (26) does not fare well at all for sectors other than 3A.

⁴⁴ The last two reasons are from Modigliani, and Holt, , “Firm Cost Structures,” 41.Google Scholar Concerning this last reason we note that if the replenishment period (i.e., the time period elapsing from the moment a purchaser places an order for H^r until he receives these inventories) were instantaneous or if replenishment periods were perfectly predictable, there would be no need for a buffer of H^r . However, conditions conducive to near-zero buffers do not exist. Even if they did, it does not mean that H^r for our sectors would be zero because we are aggregating over firms not all of which will reach re-order points for the same materials at the same time.

⁴⁵ Equation (28) assumes no production smoothing on the part of suppliers—an unlikely assumption in practice but, for the present, convenient in theory. See the previous footnote for the definition of the replenishment period.

⁴⁶ OPO is purchase orders outstanding. The relationship between purchase orders received, placed, and outstanding is OPO_t = OPO _t−1 + OP_t − OPR_t .

⁴⁷ Essentially, this is the crux of the article by Mack, Ruth, “Changes of Ownership of Purchased Materials,” Inventory Fluctuations and Economic Stabilization, Part II (Washington, DC: Joint Economic Committee, 87th Congress, 1st Session, 1962), 57–87.Google Scholar

⁴⁸ For example assume desired stocks, , are larger than actual stocks, Shipping delays may increase replenishment periods in that OPR_t is less than M_t so that will be less than , i.e., the direction of desired change in H^r may differ from the actual change. To be sure, this problem besets all inventory components. However, it is most acute for raw materials.

⁴⁹ The interested reader can refer to Holt, and Modigliani, , “Firm Cost Structures,” 42–4Google Scholar, or to my thesis chap. V for the derivation of this statement. An interesting example that clarifies it (and the references to the replenishment period in the following paragraph) is in Mack, , “Changes in Ownership,” 64–6.Google Scholar

⁵⁰ Holt, and Modigliani, , “Firm Cost Structures,” 41.Google Scholar These authors recognize, of course, that various forms of pressure may be applied by suppliers to purchasers whose orders are excessively erratic (e.g., price discounts in slack periods, reduction of ancillary services).

⁵¹ See the previous note and surrounding text.

⁵² To be sure this is not very obvious from Table V where only the real-world-pure-PTS sector (2B) has = NO_t . However, all the PTS industries in the accessory data set (see note 17) along with sector 2B perform much better with = NO_t than with = S_t .

⁵³ Again blank spaces in Table VI for variables referred to in the theoretical sections for the components indicate that these variables are not statistically significant when added to the existing equation.

⁵⁴ The proportion of total inventory held in the form of H^f , H^g , and H^r for each sector can be found in my thesis, Tables 111.1, IV.1, V.1, and VI.1.

⁵⁵ This holds for most PTS industries. It is not surprising that the ΔH^a results are dominated by the finished-goods and raw-material components since most PTS sectors hold a very small proportion of total inventories in the form of goods in process. For sector 2B, the mean of /s3_inline16 is .15. The one exception to this is sector 6 where this ratio is approximately .40, and this is the only sector in Table VI exhibiting behaviour somewhat out of line with its rank in the stock-order spectrum. The Δ equation for this sector is dominated by results for Δ which in turn reflect a production process explainable more in terms of the PTO model than the PTS model.

⁵⁶ Our seasonal-adjustment procedure does, however, insure that the means of the subsector data equal the means of the aggregate data, the difference being rounding error.

⁵⁷ This is not surprising. Griliches and Grunfeld, analysing the effect of aggregation on goodness of fit conclude: “the aggregate equation may explain the aggregate data better than all the micro equations combined if our micro equations are not ‘perfect’. Since perfection is unlikely, aggregation may result in a ‘net gain’.” Even though our disaggregated equations are not “micro” equations, but rather disaggregated “macro” equations, their conclusion is still relevant. See Grunfeld, Y. and Griliches, Z., “Is Aggregation Necessarily Bad?” Review of Economics and Statistics, XLII (02 1960), 9–10.Google Scholar

⁵⁸ Lovell, M. and Darling, P., “Factors Influencing Investment in Inventories,” in Duesenberry, et at. eds., Brookings Quarterly Econometric Model of the United States (Chicago, 1965), chap. 4.Google Scholar

⁵⁹ Ibid., v (preface by the editors).

⁶⁰ One possible alternative, in a large model like the Brookings model, is to make unfilled orders an endogenous variable so that the impact of government policy on new orders can be traced through to unfilled orders. In fact, unfilled orders is endogenous in the Brookings model, but the specification for it appears to be little more than an identity (ibid., 689). Even if unfilled orders was appropriately integrated into a model, our results indicate new orders are still essential to explaining inventory behaviour, i.e., we have both new-order and unfilled-order terms in our equations, the latter lagged one period behind the new-order term or terms.

⁶¹ Unfilled Orders, 5.

⁶² See Courchene, T. J., “An Analysis of the Price-Inventory Nexus with Empirical Application to the Canadian Manufacturing Sector,” a paper read to the CPSA Conference on Statistics, 06, 1967.Google Scholar