| Vose Software

Industry: Agriculture and Food Supply Chain
Product: ModelRisk
Application: Food security


Average Supply of 2,547 kcal, and a One-in-Six Chance of Falling Short

A net food-importing country of 50 million people plans against an average per-capita supply of 2,547 kcal per person per day — comfortably above the 2,100 kcal undernourishment floor. On paper the country is food-secure by a 21% margin. Run the supply system as a Monte Carlo simulation — four growing regions whose yields share a national climate factor, imports drawn from a world market, post-harvest losses Beta-distributed — and the comfortable average dissolves: there is a 16.2% probability that supply falls below the requirement floor in any given year, and in the worst 1% of years per-capita supply averages just 1,525 kcal, a deficit of nearly 575 kcal per person per day. The average is reassuring precisely because it averages over the bad years it is meant to warn about.

The danger is not that a single region has a poor harvest. It is that the same drought or heat year suppresses every region at once, and that the global bad year which cuts the domestic harvest is the same year world prices spike and exporters restrict — so imports shrink exactly when domestic output fails. Plan against the average and that compounding failure is invisible; it lives entirely in the left tail.

The supply distribution crosses the requirement floor

The headline is the full distribution of national per-capita supply against the undernourishment floor:

Distribution of national per-capita food supply versus the requirement floor

The mean supply is 2,547 kcal, but the distribution has a long left tail: the P10 is 1,989 kcal, already below the 2,100 kcal floor, and 16.2% of years fall short. The shaded region below the floor is the food-security risk a single average erases entirely. The distinction the chart forces is between "the country has a 21% supply surplus" and "the country has a one-in-six chance of undernourishment in any year" — and only the second is a number a food-security ministry can build a strategic reserve against.

Why a point estimate fails here

An average per-capita supply discards the two facts that decide adequacy. First, the variability: yields, imports and losses all swing year to year, so the realised supply ranges far wider than the mean implies. Second, the correlation: regional yields move together under a shared climate, and imports are coupled to the same global signal, so the bad outcomes stack rather than diversify. A deterministic balance sheet that nets average supply against average demand reports a safe margin in exactly the years the system is most exposed.

Correlation is imposed, and it doubles the shortfall risk

The model drives all four regional yields from one national climate factor (plus regional noise), and links import availability to the same factor — a good global year brings high yields and plentiful imports; a bad year cuts both. This coupling is real in the simulation, not asserted: the empirical correlation between domestic output and imports is +0.51 with the coupling on, versus 0.00 with it off. The joint-failure corner shows what that does:

Joint density of domestic output and import availability

The probability of a year with both low domestic output (bottom 15%) and low imports (bottom 15%) is 5.9%. If domestic output and imports were independent — the assumption behind treating "grow more" and "import more" as separate, substitutable levers — the joint probability would be just 2.3%. The real joint-crisis risk is 2.6 times the independence estimate. Diversifying between domestic production and imports only helps if the two are not driven by the same climate; this model shows they are.

The compounding shows up in the gap probability itself: with correlated yields and coupled imports the chance of a supply gap is 16.2%, against just 6.9% in a world of independent regions and uncoupled imports — correlation multiplies the shortfall risk by ×2.3.

Sizing the strategic grain reserve

The policy lever is the strategic reserve, measured in days of national consumption. Sweeping its size shows how much buffer is needed to push the shortfall risk below a policy target — and how badly that requirement is under-sized if correlation is ignored:

Strategic buffer-stock sizing to close the supply-gap risk

Reading off the correlated curve, reaching a 99% probability of no supply gap requires more than 90 days of reserve. The independent-world curve reaches the same target at about 60 days — so a planner who assumes regions and imports are independent would under-size the strategic reserve by roughly a month of national consumption, leaving the country exposed in precisely the correlated bad years the reserve exists to cover. The correlated curve sits below the independent one at every reserve level: correlation makes every day of buffer buy less risk reduction.

What drives the worst years

Tornado of drivers of the worst-5% per-capita supply

Ranking inputs by their effect on the P5 (worst-5%) supply of 1,859 kcal puts the national climate factor — the correlated-yield driver — at the top, ahead of the import-availability coupling. Individual regional yields and population level matter far less. The message for policy is direct: the worst years are made by system-wide climate and trade coupling, so resilience comes from buffer stocks and diversified import partners that break the coupling, not from marginal yield gains in any one region.

What the model changed

  • The strategic reserve was sized at over 90 days of consumption, not the ~60 days an independence assumption implied — closing a month-long under-reserve in the correlated bad years.
  • Correlation was made explicit and verified — a +0.51 empirical link between domestic output and imports — so "grow more" and "import more" were no longer treated as independent, substitutable levers.
  • The shortfall risk was reported as a probability (16.2%), not a margin, giving the ministry a 1-in-6 exposure to plan against instead of a reassuring average surplus.
  • Resilience investment was aimed at breaking the climate-trade coupling — diversified import partners and buffer stock — following the tornado's verdict that the national climate factor and import coupling own the tail.

ModelRisk Functionality Used

  • LogNormal regional yields and import availability, with Beta-distributed post-harvest losses — the building blocks of a national food-balance model.
  • A one-factor national climate copula correlating all four regional yields and coupling import availability to the same global signal, verified by the +0.51 empirical domestic-import correlation.
  • A buffer-stock sizing sweep reading the reserve days required to hit a 99% no-gap target directly off the supply distribution, separately for the correlated and independent worlds.
  • Joint-density output quantifying the low-domestic / low-import crisis corner at 2.6 times the independence estimate.
  • Sensitivity tornado ranking the national climate factor and import coupling above individual regional yields as drivers of the worst-5% supply.

A food-security plan built on average supply is a claim that the bad year looks like the average year. Monte Carlo simulation in ModelRisk replaces that claim with a distribution — turning "we have a 21% supply surplus" into "we have a one-in-six chance of undernourishment, the bad years hit domestic output and imports together, and closing the gap to 99% safety takes more than 90 days of strategic reserve."