Shocks and events

Each day, each country draws two values from a standard normal distribution, z^D and z^P, which it receives scaled to its own size:

The demand shock adds to the output gap; the price shock shifts the published price level (x, E5), and this shift fades. A share w of the demand shock is common to the whole world. The value z^W is drawn once a day, the same for all countries. The mix keeps a variance of one for each country, so its volatility stays that of the data, and it makes countries move together. Two advanced countries have shocks correlated at 0.27, an advanced and an emerging country at 0.15. The inflation people see, π^vu = π + 365.25 · (x_t+1 − x_t), feeds their memory of inflation (E3). A price shock passes into expectations, and more so if the central bank has lost its credibility.

Why. The IMF projection model has a shock in each of its equations, independent from one quarter to the next (Berg, Karam and Laxton 2006). This is what brings its world to life. Here, the size of the shocks is not taken from any study. It is computed so that the model, left to itself, varies as much as each country's economy has varied in ordinary times. The calculation is exact near equilibrium and requires no long simulation. One shock of each kind is given to the world on one day, and its trace is followed through output and prices (the impulse responses). This gives how much one unit of shock, falling on any day, moves annual growth and the annual change in inflation, measured as the World Bank measures them, on annual averages. The variances add up over the days and over the two independent shocks. That makes two equations for two sizes, solved country by country. The world is first left for forty years without shocks, so that a country that starts far from its anchors, such as Argentina, is not measured along the way. Checked: over a hundred years with these shocks alone, without the world events (E18), simulated volatility divided by observed volatility is 1.00 at the median for growth and 0.99 for inflation (from 0.90 to 1.10 between the 10th and the 90th percentile).

Recessions, against the data. Measured as the World Bank measures growth, in annual averages, recessions have the right frequency and the right depth: one year of negative growth in five in advanced countries (22% of years, against 18% from 2000 to 2019), 13% in emerging countries (12%); the worst year in twenty falls 4.5 and 4.3 points below median growth (4.5 and 4.2 in the data). Low-income countries vary less than in the data (7% negative years against 12%), because their shocks are clipped at the 90th percentile. These measures count the world events (E18) together with the small shocks. France has more negative years than from 2000 to 2019 (17% against 5%), because its potential growth, 1.1%, is lower than its past growth, 1.8%. Italy, which grew by 0.8% a year over those twenty years, had one negative year in four (25% of years; 27% in the model). From one quarter to the next, growth has the persistence found in the data: its autocorrelation is 0.09 at the median of advanced countries, while it ranges from −0.38 (France) to 0.30 (United States) in the G7, median 0.07 (Campbell and Mankiw 1988, table 6). What does not work: dated quarter by quarter, as Claessens, Kose and Terrones (2008) date them, recessions are three times too frequent in advanced countries (3.5 per decade and 30% of the time, against 1.2 and 11% in 21 OECD countries from 1960 to 2007), with a comparable duration (3 quarters) and a deeper fall (−3.2% against −1.9%). The United States comes closest (2.0 per decade; 1.5 in the data); countries with low potential growth (France, Italy, Japan) have from 3 to 3.5. Daily shocks produce too many short recessions, which the annual average wipes out. Persistent shocks would produce a few fewer, at the cost of quarterly growth that is far too regular. At 0.5 per quarter, there are 2.9 recessions per decade and an autocorrelation of 0.57; at 0.9, 1.8 and 0.81, while the G7 is at 0.07 at the median and the United States at 0.30 (without the events, and 3.6 recessions per decade without persistence). Smaller shocks would also produce fewer, but they would break the annual calibration. This is still to be decided.

Why a robust standard deviation. A crisis or a hyperinflation weighs little on the median absolute deviation, while it would dominate the ordinary standard deviation. The shocks represent ordinary times; crises are the business of the model itself (E16, E17).

Why a price shock that fades. The first version made the shock fall on inflation itself, which kept it in memory. In very volatile countries with a low target (Burkina Faso, Mali, the Central African Republic), this set off deflationary spirals (−29% inflation) that the data never show. In those countries, food prices jump and then fall back.

Randomness comes from a single generator, seeded with the game's seed, which draws the same number of values each day in the same order (one row per use, one column per country), whatever happens in the world. Two games with the same seed are identical to the bit, and one player's decisions do not shift the draws of any other country. The generator is ChaCha8, and the normal values are drawn from it by the Box-Muller transform, with mathematical functions that are identical on all machines.

What it simplifies. The common share is that of growth, applied to the shocks. It does not touch price shocks, while inflation also has its world share. The big common blows, such as a pandemic or an El Niño, are the world events (E18). The shocks are symmetric, while real inflation shoots up more often than it drops, and the most volatile countries still go through a few deflations of more than 11% (0.01% of country-months). The demand shock has no persistence of its own. It gets its persistence from the output gap (0.75 per quarter), and that is enough for the persistence of growth from one quarter to the next; but quarterly recessions are too frequent (see above).

Each day, for each kind of event k in the catalogue, a uniform draw u_k decides whether it begins:

where λ_k is its frequency per year in the world, and f_k the frequency multiple chosen in the game settings. For a local event, a second draw picks the country hit, in proportion to its exposure. A third draw picks the severity s, between the weakest and the strongest effect given by the catalogue, and it is the same for all the countries the event hits. The event acts on the same day, through three channels, for each country i:

ΔY is the change in output over the first year, not counting its lasting part. It is the jump in the output gap that, left to close at its own speed s_y (E1), costs ΔY on average over the year (with m̄ = 0.595, a jump of 5.5 points costs 3.3% in the first year). ΔP is the jump in the price level, which fades like price shocks do (E13). ΔY* is the lasting change in potential GDP. What is destroyed is not rebuilt. The total change in the first year is ΔY + ΔY*. An event can act again in the following years (a drought, two years later). Each step acts through the same three channels, on the day it falls, with the event's severity and on the event's country.

The catalogue is part of the game's data:

Why. The small shocks of E13 represent ordinary times. Real fluctuations are also made of a few big blows that can be identified, that are rare and that often hit all countries at once. An anonymous shock tells the player nothing. “Severe pandemic” or “Strong El Niño” tells them why the world has just changed, and gives them a reason to act. No event is caused by a country. Events are natural phenomena, epidemics and accidents, which the player suffers without being able to prevent them.

The calculations. The lasting part of a disaster is the loss of the first year, net of the rebound in the following year. Growth of −1.11 then +0.63 points gives a lasting −0.48% (IMF 2025, emerging countries that are not islands); −1.40 then +1.0 gives −0.4% for an epidemic (Ma et al. 2020). The drought follows the four years of Fomby, Ikeda and Loayza (growth in GDP per head of −1.41, +0.22, −0.51 and +0.03 points in developing countries), which gives a level of −1.41, −1.19, −1.70 and then −1.67%. The first step removes 1.19% of potential GDP and a further 0.22 points over the year. The second, two years later, removes 0.48% of potential GDP and a further 0.03 points over its year. The severe pandemic loses 6.3% in the first year in advanced countries (the gap between growth in 2020 and its forecast of January 2020), of which 3% is lasting (world output in 2024 below its pre-pandemic path, IMF). So ΔY = −3.3 and ΔY* = −3.0. The food price spike keeps the share of the rise in inflation that the World Bank attributes to food. That share is two thirds in low-income countries (+8 and +6 points in 2007-2008 and 2010-2011, hence +4.0 to +5.3), and half in emerging countries (+4 and +1, hence +0.5 to +2.0). The frequencies are counts: 10 strong El Niño episodes in 75 years (a peak of the ONI index of at least 1.5), six spikes in forty years, 190 large isolated disasters in forty years (a lower bound), split by type as in the IMF sample (87 storms, 43 floods, 34 earthquakes, 10 droughts, 16 others), and four epidemics from 2003 to 2016. The frequency of a VEI 6 eruption follows from that of VEI 7 eruptions, one or two per millennium, since each class is 6 to 7 times more frequent than the next.

The choices. 1) The eruption acts through harvests, with the effect of the mildest food price spike. No study puts a figure on its macroeconomic effect (Pinatubo left no trace of one). 2) The solar storm spreads the world loss equally, for lack of a published breakdown, although high latitudes would be hit harder. 3) The “Europe” region of Cashin et al. is carried over to the twenty members of the euro area, and the effect of one standard deviation of their index is carried over to strong episodes. 4) Where disasters strike. Exposure belongs to places, not to countries. It is described province by province, and the model adds it up over the provinces that a country holds on the day of the draw, so a province that changes hands takes its exposure with it. No ready-made exposure index could be redistributed (EM-DAT forbids redistribution and commercial use; INFORM mixes in components under other licences), so exposure is estimated. Each strong, shallow earthquake recorded since 1900 (USGS) and each storm of hurricane force since 1980 (NOAA, IBTrACS) leaves a footprint, made of the provinces it reached (within one degree of the epicentre, or half a degree of the track) and the share of the land of each one that it covered. A footprint counts for a country only if it reaches at least 5% of its population, the inhabitants of a province being spread evenly over its land. This is the threshold at which the IMF finds the same effects as for its disasters with damage above 1% of GDP (Nguyen et al. 2025, figure 9). A cyclone that reaches Guadeloupe is therefore not a major disaster for France. The country hit is drawn in proportion to the number of footprints that count for it, and the event then falls on the provinces of one of them, which the map can show. A drought falls on a country in proportion to the share of its land outside deserts that has a steppe climate (the game's climate map), then on one of its steppe provinces. Floods, other disasters and epidemics fall on a country drawn at random, all countries being equally exposed. The method makes three choices. The reach of an event is the same whatever its strength; “reached” is taken to mean “affected”, which is what the IMF measures; and the population is spread evenly within a province. 5) The effects by type. The drought follows Fomby, Ikeda and Loayza, who measure its effect year by year, and whose results Loayza et al. (2012) confirm; the IMF leaves droughts that last several years out of its sample. The other disasters keep the IMF's average effect by group of countries, because for them the studies contradict one another. Only earthquakes have no effect on prices (Parker 2016).

Checked: when it is forced on its own on a first day, in the middle of its range, each event costs in the model what its source says, to within a few hundredths, even though central banks and budgets react. The severe pandemic costs −6.35% in France (−6.3 expected) and −6.53% in Brazil (−6.6); the solar storm −4.86% (−4.75); El Niño −0.99% in Indonesia (−1.01); an earthquake −1.10% in Vanuatu, the most exposed emerging country (−1.11); a cyclone −1.08% in the Philippines (−1.11); a drought −1.39% in Botswana in the first year (−1.41), and nothing in an advanced country. Over a hundred years, a game draws about as many events as the frequencies predict: 86 earthquakes (85 expected), 244 cyclones (217.5), 25 droughts (25), 154 floods and other disasters (147.5), 11 El Niño episodes (13.3), one severe pandemic (0.8).

What it simplifies. The loss from a cyclone, which Hsiang and Jina (2014) see growing for fifteen years, fits into one year and its rebound, as the IMF measures it. The two sources contradict each other. A footprint that counts for a country hits the whole country, with the IMF's average effect, whatever the share of its population reached beyond the threshold. An epidemic hits only one country, whereas SARS hit twenty-eight. Events are independent of one another, while El Niño and food price spikes often go together. They pass neither through trade nor through commodity prices, which the model does not have. The accidental blocking of a canal is not included, because it has neither a published frequency nor a measurable effect on output.

When an event for which the catalogue provides responses hits a player's country, the player has event_response_days days to respond, between two days. A response goes through the channels the model already has:

• budget lines raised for a time: each by a points of GDP for n months, within the bounds of the line and of its side of the budget (E26), then given back by as much when the day comes. The budget responds to it as to any decision (E1, E8), and the groups according to what the line pays them (E27, E28);
• a larger or smaller cost of the event: the change in output over the first year, ΔY, multiplied by a factor f in the country that responds. The gap (f − 1) ΔY acts on the same day, like an event of that size (E18);
• a change in popularity, at once, which then returns towards its target at the pace of popularity (E12).

The player responds once per event. After the deadline, or if they lose power, they can no longer respond. Non-player countries do not respond, and the world they make is that of E18. Each response is an action recorded in the log, replayed when a save is loaded.

What it simplifies. The responses are few and the same for every country. Their amounts are in points of GDP, not adjusted to the severity of the event. A response goes through no vote, and counts as an emergency decree. The lockdown costs output without saving anything, since the model counts neither the sick nor the dead. All it brings is popularity. Aid does not rebuild the destroyed potential. It supports demand for as long as it lasts.