Mainstream Inventory Theories

If we look at standard macro Dynamic Stochastic General Equilibrium models, inventories do not appear. The modelling focus is on expectation formation – particularly in the household sector – and business sector behavior is stylised. Since the assumption is that products are bought and sold both spot and forward in an optimal fashion, production decisions are just set to give exactly the output needed in the spot market.

Since inventories obviously exist, and are tied to business cycle behaviour, more specialised models have been proposed. My comments here are based on a survey of that literature, “The Role of Inventories in the Business Cycle,” by Aubhik Khan.[i] Even so, the argument is that inventory building is a “mystery.”


(Note: This article is a draft subsection of my latest manuscript. Since my focus in the text is the inventory cycle and recessions, I did not chase after this topic in depth. My argument is that both the mainstream theory and post-Keynesian theory can generate an inventory cycle that can either cause or accentuate recessions, so there was not enough information to really differentiate the approaches. We would need to look at inventory accumulation during the expansion to differentiate the competing approaches.)

The differences between the mainstream approaches and the post-Keynesian perspective can be summarised as the difference between randomness and uncertainty. The mainstream approach is based on the assumption that firms are acting in an optimal fashion in the presence of (unknown) random outcomes – that are described by a known probability distribution. The post-Keynesian approach underlines the importance of fundamental uncertainty – we have no idea what the probability distribution is. As a result, decision-making operates in a fog of uncertainty. From a post-Keynesian perspective, holding inventories is no “mystery”: firms cannot be certain what will happen in the coming months, so stockpiling key inputs and/or produced goods reduces the risks associated with adverse outcomes. As a result, even though it is accepted that firms certainly make plans, they are not blindly following the output of some optimisation. The straightforward way to get a grip on inventory management is to survey managers in industries to see what criteria they use to set target inventories. However, one risks drowning in micro data, and so we probably end up backing out simple macro relationships that match observed data in some sense.

Khan’s article discusses a few classes of inventory models (as well as giving background on inventory behaviour and the cycle).

• Production-smoothing. The model assumes that it is costly to adjust production. Buying new equipment takes time, as would uninstalling unneeded equipment. It takes time to hire and train new employees, while laying them off generates financial costs as well as being bad for morale. The example of toys is given. Christmas sales represent a large chunk of sales, but production levels are normally held steadier to create an inventory to meet the expected surge. The prediction of the model is that production levels should change less than sales. Unfortunately, the model does not really fit the data: observed production is more variable than sales. Another problem is that it is not applicable for input inventories, nor inventory management for intermediary firms (wholesalers, retailers).
• Increasing Returns to Scale. Valerie Ramey suggested that increasing returns to scale would result in inventory management behaviour. (Increasing returns to scale imply that production efficiency increases as total output rises.) This model better fits observed data, but also does not apply to non-manufacturers.
• Random changes to unit costs. This was a modification proposed by Eichenbaum as a way of increasing the volatility of production to better fit the data. Once again, only applicable to manufacturers.
• The (S, s) model. The (S, s) model was developed by Herbert Scarf, and it suggests that firms face large fixed costs when ordering or producing goods. This implies that firms are biased to have large orders infrequently. This creates the needed volatility in production to match the data. Furthermore, the model can be adapted to non-manufacturing firms.

These mainstream models will be attractive to many people, as they provide mathematical models that can be fit to data, and they offer some predictive value. However, the post-Keynesian critique is straightforward: we ought to survey firms and see how the set their target inventory levels. Since different industries will have different preoccupations, it is extremely likely that reality is far more complex than these models suggest. To the extent that the mainstream models work, it is just the reality that we can match almost any plausible simplified model to observed data. This is a debate that is removed from the question of inventory recessions (since both neoclassical models and post-Keynesian models can generate an inventory accumulation cycle), and so there is no value in pursuing the topic herein.

Footnote:

[i] “The Role of Inventories in the Business Cycle,” by Aubik Khan, Business Review, Federal Reserve Bank of Philadelphia, 2003, issue Q3, pages 38-45. URL: https://ideas.repec.org/a/fip/fedpbr/y2003iq3p38-45.html

(c) Brian Romanchuk 2019