July 16, 2002

The Production-Smoothing Model of Inventories Bites

Once upon a time economists had a model of inventories and the business cycle. The model was theoretically compelling. It was intuitive. It was easy to explain. There was one problem: the model did not work.

The model was the buffer-stock production-smoothing model of inventory behavior. Its basic premise is that it is difficult and costly for individual business firms or for the economy as a whole to change its scale of operations. When you are downsizing rapidly, firing workers and mothballing capital is expensive and damaging to morale and productivity: it is much better to downsize slowly, letting worker attrition and capital depreciation do the job. When you are expanding rapidly, hiring many new workers is expensive, training them is more so, and these costs of rapid expansion are likely to be smaller than the costs and hassles of finding new locations and ordering and installing new machines: it is much better to expand gradually, so that the burden of growth does not significantly disrupt ongoing operations.

These considerations led economists to hypothesize that when economy-wide demand jumped, production would jump too, but not as rapidly. There would be a time during which demand would run ahead of production, and firms would draw down their inventories of finished goods and goods-in-process, because it would be so much cheaper in the long run to ramp up production slowly. They led economists to hypothesize that when economy-wide demand fell, production would fall too, but not as rapidly. There would be a time during which demand would run behind production, and firms would add to their inventories of finished goods and goods-in-process, because it would be so much cheaper in the long run to shrink production slowly. Thus when production jumped by a lot inventories would be falling, and when production fell by a lot inventories were rising. If one took the variance of production growth--the square of the difference between production growth and its average rate--and decomposed this variance of production growth into three terms:

  • The variance of demand growth.
  • The variance of the change in inventories.
  • The part left over--equal to twice the covariance, that is, twice the difference between demand growth and its average rate multiplied by the difference between the change in inventories and its average change.

Like so:

Variance(Prod Growth) = Variance(Demand Growth) + Variance(Inventory Change) + 2 x Covariance(Demand Growth, Inventory Change)

One would find that the last covariance term was typically negative. Thus inventories were, in this theory, a way to smooth production: a subtraction that would make the variance of production growth less than the variance of demand growth.

But, as I said, the theory bites. The figure below shows, year by year, the contributions of each component in each year to the overall calculated variance of annual growth in real output. Add up the three lines vertically, and you get that year's contribution to business cycle variance. The purple line shows the (dominant) contributions of variability in demand growth. The blue line shows the (relatively small) contributions of variability in the change in inventories. And the yellow line shows the covariance terms, the cross terms, the effect on total variance of the fact that there is a systematic relationship between variation in demand growth and the variation in inventory changes.

If the buffer-stock production-smoothing model of inventories were right, then the yellow line would typically be less than zero: when the change in inventories was positive and the change in demand (relative to trend growth) was negative, their product would be a negative number and hence the covariance would be less than zero. But in only 10 of the past 40 years has the yellow line dipped below zero, and the large extreme observations are the positive ones: 1976 and 1984 when demand and inventories both grew rapidly, and 1980, 1982, and 1991 when both demand and inventories shrank rapidly.

The failure of a good theory to work distressed macroeconomists. Attempts to get around the failure by building another theory--by saying that it really was better and cheaper to expand and shrink production rapidly, or that the economy's production functions were such that a 10% increase in production was possible only with a 20% increase in the flow of goods in process--were unconvincing. It was hard to argue that the costs of rapid expansion and contraction were not costs but net benefits. It was hard to argue that it was more efficient for goods-in-process to move more slowly through the value chain when production was high than when production was low.

So macroeconomists drifted toward a consensus that it was all the result of mistakes. The economy as a whole would run more efficiently if inventories were a buffer stock. However, because one firm cannot figure out what is happening to another firm in a timely fashion at the turning points of the business cycle, and because firms cannot keep good track of what is going on inside their own operations in a timely fashion, and because of managerial biases toward overoptimism and overpessimism in boom and bust, inventories act not as a buffer reducing but as an amplifier magnifying the size of the business cycle.

Hence economists' hope: if this was a problem of information, then perhaps the ongoing revolution in information technology could help. To the extent that information technologies really are information technologies, they should make it easier for firms to gather, transmit, and use information. One prime piece of information that firms need to know is the state of the goods and services moving through its value chain: its inventory, in all stages from goods piling up (or running bare)( on store shelves to the likelihood that its suppliers will successfully make their just-in-time deliveries. To the extent that in the past macroeconomic instability has been driven by mistakes in inventory accumulation and decumulation, themselves the result of a lack of rapid information transmission from final demand to the factory floor, the ongoing revolution in information technology should reduce their magnitude.

American inventory-to-sales ratios have been declining for nearly a generation. Today, manufacturers of durable goods hold only two-thirds as much inventory relative to their sales as they held in the 1970s. Manufacturers of non-durable goods hold eighty percent as much inventory in proportion to sales as they did in the 1970s. Inventories have also become less volatile. However, much of this reduction in inventory-to-sales ratios is not due to information technology, at least not directly. Before there was a new economy, after all, there was a "Japanese challenge": American firms scrambled to develop and implement "lean production" systems that economized on inventories and achieved much greater control over materials flow and quality.

Managers do claim that one of the principal benefits of new computer-and-communications technologies is better inventory control. But so far the aggregate news about whether this is making a difference for the business cycle is not encouraging, using annual data at least.* A glance back at the first figure above will show you that the overwhelming proportion of inventories' contribution to business-cycle variance comes from the covariance cross-term and comes in the years of recession (and the immediate post-recession bounce-back). Thus there was essentially no information in the aggregate data about whether information technology was moderating the business cycle between the 1991 recession and 2000. And what information we have from the 2001 recession is bad: in fact, the contribution of the covariance cross-term is unusually large relative to the size of the 2001 recession--not that the covariance term in 2001 was unusually large for a recession year, but that the other terms (and indeed the recession itself) were unusually small.

*Quarterly data show a somewhat different but confusing story. I have not yet figured out why. I stick with the annual data, because varition in annual growth rates conforms more closely to my intuition as to what the business cycle really is than does variation in quarter-to-quarter growth rates. See Blanchard and Simon (2001).

Posted by DeLong at July 16, 2002 05:32 PM | TrackBack


Dear Brad

As you know I am very enthusiastic about explaining things with mistakes, but there is a big problem with the mistakes model of inventory investment. As shown by Jeff Miron (and interpreted by Alan Blinder) inventory investment adds to the magnitude of the SEASONAL cycle. Now people may be dumb but I think they have figured out what happens every December 25th.

Also I think your argument against a target inventory (work in progress type) interpretation of the data cheats a little on the difference between levels of inventories and inventory investment. Or maybe I mean you are not boring your web surfers with the fundamental distinction between the variance of innovation forecast errors (rational ignorance) and predictable forecase errors. Hmmm now why have I sometimes been so fascinate by that difference ???

Now you have written a nice paper on well about one data point (I remember you mentioned the troughing of inventories at a conference within a day of the news). I sneer at the number of data points because I want to consider a fancier model. What with information technology and all that, firms manage to detect the drop in demand very quickly and quickly cut inventories. Now demand goes up and too keep the inventory sales ratio above the technological minimum (work in progress roughly) a sharp increase in inventory investment is needed (since they got down all the way to the new target before demand troughed). Note the covariance is on the upswing part of the mini recession.

OK another story. Inventories depend mainly on forecasts of demand but, like all investment they have something to do with interest rates which went waaaay down. Maybe we just saw what happens when the FED finally decides to kick start the economy.



Posted by Robert Waldmann at July 16, 2002 06:27 PM

Posted by: Robert Waldmann on July 16, 2002 06:31 PM

Hah! At least I've said it's a one-data-point regression, and worked hard to produce info-graphics that will show you what is really going on. Others might talk of an extremely low covariance in the 1990s as a sign that inventories are becoming stabilizing without pointing out that the signal comes overwhelmingly from recession and bounce-back years.

It was my belief that you needed unreasonably large expectations of the persistence of jumps in output levels to explain inventory dynamics through the target or work-in-progress model. Am I wrong? But, as you say, Miron's seasonal stuff shoots down the buffer-stock production-smoothing model, at those frequencies at least.


Posted by: Brad DeLong on July 17, 2002 12:10 AM

Think like a retailer. Do you want higher inventories when demand is higher, or when demand is lower?

Posted by: Arnold Kling on July 18, 2002 06:09 AM

Oh, if you're a retailer you want higher inventories when demand is higher: it's the manufacturer who wants the buffer stock. But I've never been able to make the retailer effect dominate in simulations.

Of course, as Robert Waldmann hints above, maybe I've just been running the wrong simulations...

Brad DeLong

Posted by: Brad DeLong on July 18, 2002 09:13 AM
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