*Optimal* Stockpiles in Everything

Everyone is talking about stockpiles - but how much and when?

There has been a lot of talk of stockpiles to manage price risk in commodities lately. On the left people are rightly concerned about inflation risks due to commodity input prices and on this front Isabella Weber’s work teasing out the key drivers of inflation volatility and pass through has been great and confirmed by work by Bernanke and Blanchard. The key takeaway is that some prices - energy and food commodities in particular - have a special significance for inflation as they are upstream inputs for a lot of things but also form a basis around which other sectors anchor their price formation process. There is likely more to life than monetary policy for price stabilization in the face of certain kinds of supply shocks and there may be cheap insurance strategies by holding precautionary inventories. On the right of politics Heritage has well founded concerns about critical minerals and defence dependence on China and advocates for greater stockpiling.

While you might never see these people in the same room together, they are grappling with the same broad class of problems. These problems are questions of how you optimally consume and store in the face of uncertainty due to supply volatility. Much of this work emerged from the agricultural economics literature where people have since the dawn of agriculture had to think about how much grain to stockpile in the face of uncertain harvests over a long time horizon. With the emergence of dynamic programming and the Bellman Equation formulation in the late 1950s, the tools emerged to solve these challenges for relatively simple stochastic shocks. Solution methods remained numerical - ie, computers are desirable - and that led to these approaches not taking off to any great degree until the advent of personal computers.

Jeffrey Williams and Brian Wright work “Storage and Commodity Markets” is the classic in this area and aggregates much of their work through the 1980s. Using relatively simple stochastic shocks and dynamic programming the key features of commodity locational arbitrage, stockpiling, returns to storage assets and (especially for finance people) the fundamental logic underlying key time series properties of commodities are elucidated. In the interest of brevity, I will not get into the algebra but for any product for which demand is inelastic and especially if it is inelastic and convex - that is, you care a lot more about supply falling below some critical level than having a surplus - then stockpiling to smooth consumption is an option along with trade. Both are options and welfare improving (economist for “good”). These demand curve properties describe things like grain - the focus of much of their work - as nobody likes to starve. It also describes the profound inelasticity in demand for critical materials that can be “golden screws” in industrial processes like Gallium which CSIS wrote about extensively here.

China has an extensive storage and stockpiling program and for the products for which storage is somewhat well documented the impacts are clear. China’s stockpiling of cotton has reduced world price volatility according to one paper, and plenty of more theoretical work has been published by Chinese academics on how much and how China should stockpile for its strategic petroleum reserve including some old friends at Harvard’s China Project which took account of optimal strategy in different shocks in great detail but no consideration of what policy looks like with uncertain shocks. The World Bank FAO has done work on stabilization stocks for food markets globally.

Part of the problem with geopolitical shocks is they tend to be an all or nothing affair. Either your formerly good natured and happy buyer or seller sanctions you or they do not. This kind of regime switching lends itself well to Markov models where you can flip between states (trade war or no trade war, for example) which have distinct distributions for supply shocks that might be described as “China dumps everything it has got as hard as it can” or “best of luck smuggling it out”. I have not found any literature on trade and storage accounting for these kinds of shocks but happily there is a whole field (and software package) for these kinds of problems called Stochastic Dual Dynamic Programming. The implementation for much of this work is in multistage electricity dispatch where you have storage (a hydro reservoir) and uncertain rain, but quite clear rainfall regimes. It will not shock you at this point to learn that one of the developers of this package in the Julia language is based in New Zealand which has a hydro heavy grid and is subject to the vagaries of the El Nino and La Nina weather phenomena or that much of this literature has a seemingly Alps adjacent institution publishing bias.

These models are an effective starting point for estimating how big a stockpile is required and can be extended to provide for optimal domestic subsidies given this risk of trade cut-off in the future especially if that cutoff is persistent. The problem with these models is that multi period lags between decisions like “let’s subsidize some mines” and actually getting the output from those mines is a violation of the Markov property and leads to much more difficult numerical solutions. Similarly, if these interactions are strategic - and they absolutely are - then what the trade counterparty does is not a random process. For example, one country may choose to use export controls less if they can expect them to not work because they are less likely to inflict pain in terms of reduced output or supply constraint. In this scenario stockpiling or domestic capacity payments are doubly effective: they reduce the impact of a shock, but also make it much less likely. This branch of modelling is more along the lines of agent-based modelling and game theory and as far as I can tell broadly unexplored as far as industrial policy and stockpiling go.

More broadly these approaches can provide some guidance on how much should be stockpiled and by whom. They also make explicit and quantitative the trade-offs between security and trade: doing a modest amount of trade with many parties is inherently diversified and less risky than having 70-100% dependency on one party, especially if relations with that party are rocky. If this feels a little like portfolio reliability and finance that is because it largely is - and that is generally something legible to the right of politics. Being able to calibrate around a range of explicit risk parameters might better allow conversations between free traders, national security hawks and industrial policy advocates to be more focussed and coherent as to benefits and trade-offs instead of talking past each other.

Integrating the industrial policy, trade, security and price shock problems into a single objective approach seems ambitious but the work is mostly done for simple models and extensible for more complex ones using existing tools. These objectives often look contradictory because of the political roots of those who advocate for them from one direction or another but there is a common analytic core and broader objective here. I sincerely hope that others take note of the commonalities here and move past the hot political takes phase in this space because these decisions are very consequential.