Accounting for output fluctuations in manufacturing

Abstract

There is a substantial body of evidence to the effect that output is more volatile than sales among manufacturing industries. Numerous explanations have been advanced to account for this excess output volatility. Some examples are pro-cyclical inventory movements induced by a stockout-avoidance motive, cost and technology shocks and decreasing marginal costs. This article assesses the contribution of these different motives to output volatility for six different manufacturing industries. Linear–quadratic models are estimated for each of the industries and then dynamic simulations are employed to determine the volatility of output when one or more of the factors are removed from the model. Technology shocks provide the most significant contribution to output volatility. The stockout-avoidance motive is also important. Cost shocks provide a very small contribution and marginal production costs are increasing at the margin and thus stabilize output. It is also shown that output volatility declines when current values of sales and material costs are assumed known rather than forecasted from prior periods’ values.

Notes

¹For an overview of the literature on production bunching and other difficulties in accounting for inventory behaviour, see Blinder and Maccini (1991). The evidence on bunching is by no means uncontested. It is derived primarily from a single data base on US manufacturing and authors relying on other data have concluded that production smoothing predominates (Ghali, 1987; Fair, 1989; Miron and Zeldes, 1989). Nevertheless, judging from the amount of literature on the topic, there is a widespread belief that production bunching reflects something other than data problems. Ramey and West (1999) emphasize that bunching has also appeared in studies using less aggregated data than that employed here. West (1988) provides additional support for production bunching using aggregate data from seven industrialized countries.

²Maccini and Zabel (1996) demonstrate that Kahn's conclusions are valid under a broad set of circumstances.

³The results naturally depend upon the model employed. The linear-quadratic model is the obvious choice because of its predominant role in the literature and because the production-smoothing implication of this model is responsible for the emphasis on production variability in the US manufacturing sector (Blinder, 1986a). Bivin (2005) has shown that the myopic flexible-accelerator models out-performs the linear-quadratic model in both explanatory and predictive ability but this model lacks the rigor and intuition of the infinite-horizon model. Sensier (2003) has shown that allowing for asymmetric responses may also improve explanatory power. This possibility is worth pursuing, but is beyond the scope of the approach adopted here.

⁴Details on the construction of the data are provided by Hinrichs and Eckman (1981). More recent data are available under the new North American Classification System back to 1997. We elected to use the older Standard Industrial Classification because it provided longer time series.

⁵The implied sales deflator is the ratio of the nominal sales series produced by the Bureau of the Census to the real sales series produced by the BEA. One could estimate the nominal cost component of the real materials cost series in a similar fashion by dividing nominal inventories provided by the Bureau of the Census by the real inventory series constructed by the BEA. Unfortunately, there is an apparent discontinuity in the nominal inventory series that made this approach unreliable. An earlier version of this article relied on real cost indices for each industry constructed from components of the Producer Price Index and based upon the composition of inputs. Unfortunately, due to the difficulty of constructing these customized cost series, they have not been updated and the ending observation is May 1994. Durlauf and Maccini (1995) employed these data with some success, but in our estimates with these data, the φs were all insignificant and often wrong-signed and the estimated impact of cost shocks on output variability was minimal.

⁶There is evidence of a unit root in each of the series, but imposing this restriction on the estimates is problematic because it reduces the explanatory power of the models that we view as the dominant criterion.

⁷They found the asymptotic standard errors for ML to be between three and 15 times smaller than the asymptotic standard errors for GMM in a linear–quadratic inventory model similar to the one presented here. When Equation 4 was estimated with GMM, the SEs of the regression were always larger than those obtained from ML. Moreover, a larger number of the coefficients were wrong-signed.

⁸The model is not, strictly speaking, maximum likelihood because the sales and cost processes are estimated prior to the decision rule. Full maximum likelihood requires that these models be estimated simultaneously.

⁹A number of authors have noted this persistence. See, for instance, Mack (1964), Carlson and Wehrs (1974), Feldstein and Auerbach (1976), Blinder (1986b) and Ramey and West (1999).

¹⁰Although it is now standard practice to assume that sales forecast errors are fully absorbed by inventories, that has not always been the case. This was a question of considerable interest during the 1960s and 1970s when it was discovered that much of the sales forecast error was absorbed by output instead (Carlson and Wehrs, 1974; Feldstein and Auerbach, 1976). This puzzle has not been resolved and interest has waned with the increased emphasis on the estimation of structural parameters.

¹¹The ratios in Table 1 are constructed from the growth rates of the actual output and sales series. Linear detrending yields very erratic results that were deemed unlikely. By the same token, the variances here were also calculated using growth rates on the simulated values. In some instances, the simulated ratios seemed inordinately small. For instance, when all of the factors that contribute to excess output variability are removed, the variance of the growth rate of output was less than 10% of the variance of the growth rate of sales in the nondurables sector. While this value is possible, we did not feel it was credible and were concerned that the results might overstate the contribution of the factors to output volatility. The values derived from linear-detrending seemed more reasonable. As a check on robustness, we re-calculated the ratios in Tables 5 and 6 with data represented by growth rates (as in Table 1), as well as a data detrended with a quadratic trends, and Hodrick–Prescott filter on the levels and the logs. Both the ratios and the significance levels in Tables 5 and 6 are well within the ranges implied by the other techniques. In fact, linear-detrending yielded extreme results in far fewer cases than one would expect from random chance.