A Simple Average of Monthly GPR is not an Annual GPR Indicator

The geopolitical risk index is often used as a monthly measure of geopolitical tensions. It is tempting to convert it into an annual or fiscal-year variable by taking a simple average of the twelve monthly values. This may look harmless. It is not.

Main point. A simple average of monthly GPR values is not the same object as an annual GPR indicator constructed from article counts. The issue is not that percentages can never be averaged. The issue is that the monthly percentages have different denominators. Averaging them gives each month the same weight, whereas an annual article-share indicator gives each article the same weight.

This distinction matters for empirical work using the geopolitical risk index. The GPR index is based on newspaper articles. Caldara and Iacoviello count articles related to adverse geopolitical events in each newspaper and month as a share of the total number of news articles. The index is therefore a text-based frequency measure. It is not a standard annual accounting variable.

The point is especially important when researchers move from monthly data to annual or fiscal-year data. A fiscal-year average may look more aligned with firm accounts, but it can change the object being measured. It can turn a frequency of articles over a period into an unweighted average of monthly ratios.

1. The measurement issue

Let

G_m = \text{number of geopolitical-risk articles in month } m.

Let

T_m = \text{total number of newspaper articles in month } m.

The raw monthly geopolitical-risk share is

s_m = \frac{G_m}{T_m}.

The raw share s_m is bounded between 0 and 100 percent. The published GPR index can exceed 100 because the raw share is subsequently normalized, typically so that a reference-period average equals 100. A value above 100 therefore does not mean that more than 100 percent of articles are geopolitical-risk articles. It means that geopolitical-risk coverage is above its reference-period average.

Important distinction. The raw article share is a percentage. The published GPR series is an index obtained after normalization. The normalization does not remove the aggregation problem: a simple average of monthly ratios is still not the same as a ratio of annual article counts.

2. Why a simple average is not an annual article share

A simple annual average of the monthly GPR shares is

s_y^{simple} = \frac{1}{12} \sum_{m=1}^{12} s_m = \frac{1}{12} \sum_{m=1}^{12} \frac{G_m}{T_m}.

This object gives exactly the same weight to every month:

w_m^{simple} = \frac{1}{12}.

An annual article-share indicator constructed directly from the underlying counts would instead be

s_y^{direct} = \frac{ \sum_{m=1}^{12} G_m }{ \sum_{m=1}^{12} T_m }.

This can be rewritten as a weighted average of the monthly shares:

s_y^{direct} = \sum_{m=1}^{12} \left( \frac{T_m}{\sum_{k=1}^{12} T_k} \right) \frac{G_m}{T_m}.

The weights are therefore

w_m^{direct} = \frac{T_m}{\sum_{k=1}^{12} T_k}.

The two measures are equal only in the special case where the total number of articles is identical in every month, or where the variation in article volumes is irrelevant for the object being measured. In real newspaper data, this condition should not be assumed.

Core difference. Averaging ratios and taking the ratio of aggregate counts answer different questions. The first gives each month the same weight. The second gives each article the same weight.

3. The intuition

The simple average answers the following question:

\text{What is the average of the twelve monthly geopolitical-risk shares?}

The direct annual article-share indicator answers a different question:

\text{Among all articles published during the year, what fraction concerns geopolitical risk?}

These are not the same question. The difference comes from the denominator. Each monthly share has its own denominator, namely the total number of articles published in that month. If the denominator changes across months, then the average of the monthly percentages is not equal to the percentage computed from the annual totals.

In short, the simple average gives equal weight to months. The direct indicator gives equal weight to articles.

4. A 9/11 example

The difference becomes clear around a major geopolitical event such as 9/11. The GPR index is known to spike after 9/11, which is precisely the kind of event the index is designed to capture.

Suppose that for 11 normal months there are 10 geopolitical-risk articles out of 1,000 total articles. The monthly share is then 1 percent. In September 2001, suppose there are 300 geopolitical-risk articles out of 6,000 total articles. The monthly share is 5 percent.

Month type	GPR articles	Total articles	Monthly share	Simple-average weight	Article-share weight
Normal month, each of 11 months	10	1,000	1.00%	8.33%	5.88% each
September 2001	300	6,000	5.00%	8.33%	35.29%

The simple average is

s_y^{simple} = \frac{11 \times 1\% + 5\%}{12} = 1.33\%.

The direct annual article share is

s_y^{direct} = \frac{11 \times 10 + 300}{11 \times 1000 + 6000} = \frac{410}{17000} = 2.41\%.

The two values are very different:

1.33\% \neq 2.41\%.

The reason is simple. In the simple average, September receives one twelfth of the annual weight. In the direct annual article share, September receives 35.29 percent of the annual weight because it accounts for 35.29 percent of the articles in the year. The annual article share therefore preserves the fact that the news environment itself changed during the shock month.

Interpretation. A simple annual average mechanically treats September 2001 as only one month out of twelve. A direct article-share indicator treats September according to its contribution to the annual volume of news articles. These two operations do not measure the same object.

5. Why the issue is not just “smoothing”

It is correct to say that a fiscal-year or annual average can smooth geopolitical shocks. But the deeper problem is even more basic: the average of monthly percentages does not reconstruct the annual percentage when the monthly denominators differ.

The problem can be written compactly:

\frac{1}{12} \sum_{m=1}^{12} \frac{G_m}{T_m} \neq \frac{ \sum_{m=1}^{12} G_m }{ \sum_{m=1}^{12} T_m }

unless very restrictive conditions hold.

This is the crucial measurement point. A simple average of monthly GPR values may be a useful transformed variable. But it should not be presented as equivalent to an annual GPR indicator constructed from the underlying article counts.

6. The correct label: different objects, not just different formulas

The best classification is therefore:

Object 1: Simple average of monthly GPR shares
Weighting rule: one month, one weight
Interpretation: average monthly geopolitical-risk intensity

Object 2: Annual article-share indicator
Weighting rule: one article, one weight
Interpretation: share of all annual articles related to geopolitical risk

Not equivalent unless: total monthly article counts are constant

This is not a cosmetic distinction. It changes the estimand. The simple average answers: what was the average of the twelve monthly frequencies? The direct annual indicator answers: among all articles published during the year, what fraction was related to geopolitical risk?

7. A simple classification table

Aggregation method	Formula	Implicit weights	Object measured	Defensible use
Simple annual average of monthly GPR	s_y^simple = average of monthly shares	Each month has weight 1/12	Average monthly GPR intensity	Descriptive smoothing or robustness
Direct annual article-share indicator	s_y^direct = sum of GPR articles / sum of total articles	Each month weighted by article volume	Annual share of articles on geopolitical risk	Annual text-based measurement
Simple fiscal-year average	s_i,t^{fiscal simple} = average of monthly shares in firm fiscal year	Each fiscal month has equal weight	Average monthly GPR during a firm fiscal year	Possible robustness if clearly labeled
Direct fiscal-year article-share indicator	s_i,t^{fiscal direct} = fiscal-year GPR articles / fiscal-year total articles	Each fiscal month weighted by article volume	Fiscal-year share of articles on geopolitical risk	Closest fiscal analogue to a period-level article share

8. Why this matters for empirical research

The distinction matters for measurement, identification and interpretation. If the research question is about reactions to geopolitical shocks, then the high-frequency variation is central. A simple fiscal-year average can dilute the very spikes that identify the effect. This is especially problematic when decisions respond quickly to geopolitical news, such as credit decisions, financing conditions, risk premia, market stress or investor sentiment.

The Journal of International Economics article by Caldara, Conlisk, Iacoviello and Penn uses two datasets for different purposes: an annual country panel for long-run macroeconomic effects and monthly global data for rapidly changing transmission channels. The paper explicitly notes that monthly data are better suited for immediate effects on financial conditions, commodity prices and consumer sentiment. That distinction is consistent with the measurement point here: the frequency should match the economic mechanism.

Using an annual variable is not automatically wrong. It is appropriate when the outcome, mechanism and data are annual. But a simple average of monthly GPR is not the same as reconstructing a Caldara-Iacoviello annual article-share measure. If the underlying article counts are not used, the resulting variable should be described as a simple average of monthly GPR, not as the annual GPR indicator.

9. What would make a fiscal aggregation defensible?

A fiscal-year GPR measure can be defended if it is constructed consistently with the object of interest. There are three possibilities.

First, if the goal is to measure average monthly exposure during the fiscal year, then a simple average is admissible, but it must be labeled as such. It is an average of monthly index values.

Second, if the goal is to construct a fiscal-year article-share indicator, the correct approach requires the underlying monthly article counts:

s_{i,t}^{fiscal\ direct} = \frac{ \sum_{m \in FY_{i,t}} G_m }{ \sum_{m \in FY_{i,t}} T_m }.

This means summing the geopolitical-risk articles over the fiscal year and dividing by the sum of all articles over the same fiscal year.

Third, if the goal is to estimate the effect of geopolitical shocks on high-frequency decisions, the monthly GPR value at the relevant decision date, a lagged monthly value, or a peak exposure over a clearly defined window may be more appropriate than a fiscal-year average.

10. A compact rule for GPR aggregation

Rule. Do not treat the average of monthly GPR percentages as equivalent to an annual GPR indicator. A simple average gives each month the same weight. An annual article-share indicator gives each article the same weight. The difference matters when article volumes vary across months, and it is likely to matter most around major geopolitical events.

11. Conclusion

The problem is not that percentages are impossible to average. The problem is that averaging monthly percentages changes the question. A simple mean of monthly GPR values measures the average of monthly ratios. A direct annual indicator measures the ratio of annual counts. These are distinct objects.

For empirical work, the safest wording is therefore precise: a simple fiscal-year mean of monthly GPR is a transformed variable. It may be useful as a robustness check. It should not be presented as equivalent to the Caldara-Iacoviello annual indicator unless it is reconstructed from the underlying article counts and normalized consistently.

References

Caldara, D., and Iacoviello, M. (2022). “Measuring Geopolitical Risk.” American Economic Review, 112(4), 1194–1225. Link.

Economic Policy Uncertainty. “Geopolitical Risk Index.” Link.

Caldara, D., Conlisk, S., Iacoviello, M., and Penn, M. (2026). “Do geopolitical risks raise or lower inflation?” Journal of International Economics, 159, 104188. Link.