A Bayesian Method for Macro Scenarios

Bayesian thinking here is not a search for one magical “correct probability.” It forces an analysis to preserve three things: what it believed before an update, which evidence changed that belief, and how its mistakes will later be diagnosed.

1. Define the Question First

Every forecast must specify:

• an observable event, such as “the Bank of Canada overnight target is at or below 2.25% on 2026-12-31”;
• the source and resolution definition;
• information cutoff and resolution date;
• original probability;
• rules for true, false, and void.

“The economy may weaken” cannot be scored. “China's official Q3 2026 real GDP growth is at least 4.0% year over year” can.

2. Make Scenarios Exclusive and Exhaustive

A slice begins with three to five cross-country hypotheses $H_i$, with priors satisfying:

$$\sum_i P(H_i)=1$$

Scenarios describe shared mechanisms rather than giving each country a “good” or “bad” label: divergent growth, synchronized upside, supply-shock inflation, or a trade-shock hard landing. If two scenarios can occur at once, redraw their boundaries.

3. Update Priors into Posteriors

Let $E$ denote the new evidence and $H_i$ one of the scenarios. The prior $P(H_i)$ is its probability before considering $E$. The likelihood $P(E\mid H_i)$ asks how probable that evidence would be if the scenario were true. The posterior $P(H_i\mid E)$ is the updated scenario probability. The denominator sums the weighted likelihoods across all scenarios so that the updated probabilities total one:

$$P(H_i\mid E)=\frac{P(E\mid H_i)P(H_i)}{\sum_j P(E\mid H_j)P(H_j)}$$

The working record uses likelihood ratios rather than pretending to have a high-precision structural model:

Evidence strength	Suggested likelihood ratio	Meaning
Strongly against	0.50	Clearly less likely under the scenario
Mildly against	0.80	Small downgrade
Neutral	1.00	No update
Mildly supportive	1.25	Small upgrade
Strongly supportive	2.00	Clearly more common under the scenario

These are judgment scales, not constants estimated from data. A formal likelihood ratio must compare how likely the same evidence is under two hypotheses. The table does not specify that reference hypothesis or a complete rule for converting its scores into the likelihoods in the equation. Do not calculate numerical posteriors from this table alone: first state the reference and update rule, or supply the scenario likelihoods directly. Weak evidence should not justify a large adjustment; decimal places do not establish accuracy.

4. Avoid Double Counting

Macro variables are highly dependent. GDP, retail sales, employment, and PMIs may be projections of the same demand shock. The control procedure is:

1. group evidence by demand, supply, policy, financial conditions, and external shocks;
2. select one primary signal per mechanism;
3. treat the others as lower-weight confirmation;
4. do not count a revision of the same statistic as new evidence;
5. do not give three votes to Chinese exports, US imports, and Canadian exports when they reflect one cross-border chain.

5. Map Scenarios to Concrete Forecasts

Scenario posteriors are not the final product. Map them into resolvable events:

$$P(A)=\sum_i P(A\mid H_i)P(H_i)$$

Record the assumptions behind the mapping and round the output to five percentage points. Without a calibrated statistical model, 63.7% is usually just 65% wearing a lab coat.

6. Score and Review

Use the Brier score for binary forecasts:

$$BS=\frac{1}{N}\sum_{k=1}^{N}(p_k-y_k)^2$$

Here $y=1$ when the event occurs and $y=0$ otherwise; lower is better. Reviews also classify:

• direction error: the mechanism was wrong;
• probability error: direction was right but confidence was too high or too low;
• definition error: the event was ambiguous;
• timing error: the direction arrived after the deadline;
• data revision: first and final releases imply different outcomes;
• omitted variable: an important shock was absent from the scenario tree.

Use void only when data cease, definitions materially change, or the event cannot be resolved under its original rules—not to pardon an ordinary miss.

7. Updating Discipline

• Put new evidence in a new slice; do not alter an old posterior.
• Lock a probability after publication; append only outcomes and notes.
• For revisions, preserve scores using both first-release and latest data.
• Review calibration buckets quarterly: do events assigned about 70% occur roughly seven times in ten?
• Draw no conclusions from a short winning streak with fewer than 20 forecasts.
• When the method changes, start a new version from that date; do not apply it retroactively.

The goal is not to be perpetually right. It is to give every error an address, a date, and a shape from which to learn.

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