Modeling Fundamentals: A Novel Approach to Trending Historical Losses

May 18, 2022 / 12 min read

When an event such as the catastrophic July 2021 flooding in Germany caused by the 2021 Bernd low pressure system occurs, it is only natural to compare it to similar historical events to understand it in context. For Germany, the 2002 European flood event, popularly known as the Elbe flood of 2002, was the first to come to mind. While these two events nearly 20 years apart were quite different from a hydrological perspective, the 2002 Elbe flood was, up until July 2021, the benchmark event in terms of insured flood losses for the region. Much has changed since 2002, however, so to make a valid comparison in terms of losses, we must look at the losses from 2002 as if the event had happened today.

Trending historical event losses is not new, but there are different methods we can use to do it; the chosen method can affect how historical events are viewed today. In this article we will discuss two different methods for trending historical losses then apply them to the economic losses from the 2002 Elbe flood. We will then compare these results to the July 2021 flood in Germany. Next, we will look at how the comparison of insured losses for these two events can be affected by changes in insurance penetration. We will conclude by discussing sources of uncertainty.

How Do We Choose a Trending Method?

Normalizing, also known as trending, historical losses can be broken down into two parts: cost inflation and increases in wealth over time. The challenge is when you must use a proxy for one or both parts of the equation. Cost inflation is straightforward when construction indexes are available. When these indexes aren’t available, there are many price deflators (e.g., labor cost index, materials index, or producer output index) that can reasonably approximate the trend.

Capturing the increase in wealth over time is more of a challenge. What we are trying to measure is the increase in the built environment and productive capacity of an economy; this is also known as capital stock, which is, ideally, a complete inventory of what is on the ground, along with its worth at a point in time. Completing such an inventory is labor-intensive, so few national governments go through the effort. Once completed, however, keeping the inventory up to date is less of a challenge, so there is an incentive to keep it current to avoid having to repeat the process of completing an inventory from the very beginning. Few countries go through the massive effort required to conduct an inventory, so researchers often use growth in gross domestic product (GDP) to measure a country’s physical asset wealth and its growth over time.

Internally, we use the Verisk Global Capital Stock Index (VGCSI) for loss trending. This method is based on modeling capital stock for target countries using capital stock investment data from a country’s national accounts and economic equations. Most other researchers use a normalization method based on GDP. Using GDP, however, requires the following two assumptions to get similar results to modeling capital stock:

Growth rates of GDP and capital stock are similar
The ratio of GDP to capital stock is constant over time

Whichever method you use, they both measure changes in wealth by the real growth rate, then capture cost inflation with the corresponding price deflator. In this next section we will provide a high-level look at how these methods support loss trending, and the differences between them using examples from the countries most affected by the European floods of 2002 and 2021.

How Do Methods of Measuring Real Wealth Growth Compare?

We will start by looking at how real capital stock is measured over time. These methods provide a measure of real wealth, meaning wealth that is independent of inflation and relative to a point in time. Figure 1 shows growth in real capital stock and real GDP from 2002 to 2021 for Austria, the Czech Republic, France, and Germany. From 2002 to 2021, capital stock grew 42% in Austria, 82% in the Czech Republic, 41% in France, and 36% in Germany. In contrast, GDP grew 26% in Austria, 59% in the Czech Republic, 22% in France, and 23% in Germany.

From 2002 to 2021, capital stock steadily grew over time. In contrast, GDP had a slower increase but fluctuated during economic cycles (expansions and recessions). Specifically, real GDP growth declined significantly during the global economic recession from 2007 to 2009 and the COVID-19 pandemic in 2020 and 2021.

Figure 1. Growth in real capital stock and GDP (2002-2021). Gray shading indicates the global economic recession from 2007 to 2009 and the global economic recession caused by the COVID-19 pandemic beginning in 2020. (Source: Eurostat, United Nations, Verisk)

Overall, the results from using the two methods are quite different, but to understand how these methods are similar we need to look at the growth rates between the recessionary periods. We will focus on Germany because the bulk of the losses from both the 2002 and 2021 floods were there, but the results are similar for the other countries.

Table 1 compares the growth rates of real wealth between the recessions for each method. From 2002 to 2008, the annual growth rates were similar, although the capital stock method was a little higher. From 2012 to 2019, both methods have the same annual growth rates; this is telling us that over a short period of time and during a stable economy both methods can accurately measure growth in wealth.

**Table 1. German growth rates, between recessionary periods 2000 to 2020. (Source: Verisk)**
2002 to 2008		2012 to 2019
GDP	Capital Stock	GDP	Capital Stock
1.5%	1.7%	1.6%	1.6%

The impact of the recessionary periods on measuring the growth of wealth over longer periods of time cannot be overstated. Table 2 shows the effect of taking out the negative growth during the down cycles, indicated by the gray bars in Figure 1. The first two columns show the growth rates we have already seen, using GDP and capital stock. The third column shows what the 2002 to 2021 growth rate would look like if we were to extend the GDP growth rates over the subsequent declines in growth during the global recession and the first year of the pandemic. Without these two recessions, the real growth would have been a lot closer to the capital stock growth rate. The minor difference could be attributed to variation in the ratio of GDP to capital stock or a measurement error.

**Table 2. Comparison of total growth rate in Germany, 2002 to 2021. (Source: Verisk)**
2012 to 2019
GDP	Capital Stock	GDP Trended
22.9%	35.6%	33.6%

Adding the Implicit Price Deflator

Before trending our historical loss example, we need to look at the last component of our method—the implicit price deflator—to account for inflation. The deflator for GDP is not the same as for capital stock. Capital stock is a component of GDP, so the GDP deflator is a weighted average of the capital stock deflator and the deflators of the other components of GDP. Figure 2 shows the nominal growth, which is the combined wealth and price effects for Austria, Czech Republic, France, and Germany. In all cases the growth rate from capital stock (in blue) is higher and the GDP recession-adjusted rate (in gray) is between that and the pure GDP effect (in teal). We are seeing an interesting difference in the Czech Republic where the GDP recession-adjusted rate is the highest. This can be attributed to higher inflation and exchange rate effects.

Figure 2. Loss trending and growth rates for Austria, Czech Republic, France, and Germany based on nominal capital stock and GDP (2002 to 2021). (Source: Eurostat, United Nations, Verisk)

Trending Losses for the 2002 Elbe Floods

In this section we are going to illustrate the effect of loss trending using the Verisk Global Capital Stock Index and GDP methods for the 2002 Elbe floods in Germany, Austria, the Czech Republic, and France. In August 2002, a period of intense rainfall led to widespread flooding across a large portion of central Europe. Flooding along the Elbe River—which flows from the mountains of the Czech Republic, through Germany, and on to the North Sea—resulted in one of the costliest natural flood disasters on record at that time. The worst flooding started in a tributary of the Elbe, Germany's Mulde River, where water levels rose 65 centimeters above the previous record set in 1845. Farther south, in Dresden, the Elbe River swelled from its typical summer level of 2 meters to nearly 9.5 meters—the highest ever recorded. As water continued to accumulate, the Elbe River overflowed—in some cases, bursting levees. The result was ruinous damage in many cities and towns, including Dresden, Wittenberg, Dessau, and Magdeburg. The 2002 flooding had a particularly damaging effect on businesses; more than 12,000 were affected in Germany alone. There were more than 100 deaths associated with the flooding and economic losses were estimated at more than EUR 18.5 billion (in 2002 euros).

Germany, Austria, the Czech Republic, and France were among the countries most affected by this natural catastrophe. Economic losses were obtained from a variety of sources and compiled in a report by the OECD. Economic losses (in 2002 euros) amounted to EUR 9.2 billion in Germany, EUR 3 billion in Austria, EUR 2.2 billion (CZK 70 billion) in the Czech Republic, and EUR 835 million in France. Figure 3 compares normalized catastrophe losses for the 2002 European floods for Austria, the Czech Republic, France, and Germany. Normalized losses (in 2021 euros) range from EUR 1.7 billion to EUR 18.4 billion using the VGCSI and from EUR 1.3 billion to EUR 14.9 billion using GDP normalization.

Figure 3. Comparison of normalized catastrophe losses for the 2002 European floods. Normalized losses are trended to 2021. For the Czech Republic, losses are converted from local currency at that time, Czech korunas (CZK), to euros (EUR) using annual average exchange rates from the United Nations in 2002 and the International Monetary Fund (IMF) in 2021. (Sources: Eurostat, IMF, United Nations, Verisk)

As expected, trended losses derived using the Verisk Global Capital Stock Index are higher than losses derived using growth in GDP. But how do the trended losses compare with the German flood in July 2021? In January 2022 it was estimated that economic losses may exceed EUR 35 billion. Figure 4 compares the trended economic losses for all countries from 2002 using both methods; the July 2021 event economic losses; and the 2002 loss component attributed to Germany only. If we compare the capital stock (CS)-trended value for the whole 2002 event and the 2021 event economic losses, they are very similar in terms of losses, even though the trended Germany portion is about half the current event. This is important for how to think about demand surge after these events. When a peril, such as flood, has relatively low take-up rates , insured losses alone are not a good indicator for the amount of excess work required to rebuild after the event.

Economic losses for all countries from 2002 using capital stock and GDP methods; July 2021 event economic losses; and the 2002 loss component attributed to Germany. (Sources: GDV, OECD 2002, Verisk)

But how does this compare with the impact on the insurance industry? Estimates of insured loss by the insurance association in Germany (GDV) stood at roughly EUR 8.2 billion (USD 9.3 billion) as of mid-January 2022. Residential take-up rates for flood in Germany have increased significantly since 2002 and the impact on insured losses may be as high as 250%. Figure 5 shows the equivalent insured losses from 2002 using the same trending methods and adjusting the losses for Germany to account for the increased take-up rates. The first two columns show the trended insured losses, the third column shows the 2021 event estimated insured losses for Germany and the fourth column shows just the 2002 insured losses for Germany trended and adjusted for take-up rates.

The clear takeaway here is that whatever your loss trending methodology, the comparison of absolute insured losses for both events are similar after adjusting for take-up rates. This can be attributed to making the adjustment from economic to insured losses. While the 2002 insured loss using the GDP trending matches the 2021 event, this is a coincidence, and it may end up being closer to the capital stock trended losses when all the claims are completed.

Insured losses for all countries from 2002 using capital stock and GDP methods; July 2021 event economic losses; and the 2002 loss component attributed to Germany. (Sources: GDV, OECD 2002, Verisk)

Sources of Uncertainty and the Bottom Line

There are three sources of uncertainty for trending historical losses, and we have looked at two of them here: changes in wealth and inflation. The third is just as important in getting a historical loss number to trend. The challenge is that there is no standard definition of economic or insured losses across the industry. A study done for the OECD in 2009 found that of five sources of historical information, each one used a different definition. This is partly because there is simply no single good source for economic losses, so producing a valid estimate requires additional assumptions and modeling.

A secondary, less well-understood source of uncertainty is accounting for changes in vulnerability over time. This is true whether you use capital stock, GDP, or other methods that employ general consumer price indexes. Changes in vulnerability include the adoption of disaster risk reduction or adaptation efforts, such as building code changes. There is some research on this topic, but the contribution in reducing damage may be offset by climate change effects. Additional research is needed to understand the role of changing vulnerability; changing vulnerability and protection standards, however, are often highly regional, reactive, and slow to be adopted on a broader scale.

Loss trending with the Verisk Global Capital Stock Index provides a new resource to measure changes in exposure value over time. The index provides an internationally consistent data set to measure capital stock. Our novel approach has an advantage over normalization methods that use GDP because it directly measures the value of damageable property, whereas GDP measures annual economic activity. You can learn more about the method behind the index in our paper on U.S. loss trending published in Natural Hazards Review.