# Interview | June 16, 2016

# “Forecasts are the ultimate test of whether a theory is correct"

Since April 2016, Roland Rau has been heading the new MPIDR research group Mathematical and Actuarial Demography. In this interview, he explains why it is important to return to the origins of demography.

*Since April you have been heading the new research group "Mathematical and Actuarial Demography". "Mathematical and Actuarial Demography" – that sounds at first like a very broad field, a field where you can fit in almost all kinds of demographic issues. What exactly do you want to do? *

We want to deal with formal demography. In a way, it is the origin but also the core of demography. We want to use mathematical laws to describe mortality. This kind of formal demography is historically very closely tied to insurance mathematics; in fact, you can hardly distinguish between the two research areas. At the end of the 17th century, Edmond Halley – this is the Halley who also discovered the comet named after him – calculated the first life tables in order to derive life annuities from them. That is why we added "Actuarial” to the English name of the research group. We did not do this for the German version because it sounds very strange. It could also lead to misunderstandings because we do not want to calculate contributions and premiums for life and pension insurances. It’s just important to me to show that we use methods from both disciplines.

*Is this more of an "Old School" science then?*

As I said, formal demography is the origin of demographic research. Still, I wouldn’t call it 'old-school'. There have been laments time and again that no-one is any longer interested in it and that everyone is now just doing analyses of micro- and individual data. But it should also be noted that at conferences, presentations and meetings of all issues dealing with formal demography are very well attended. People are probably interested in formal demography, but the hurdle is very high, i.e. you need to understand quite a lot about mathematics.

*Why is formal demography so important for demographic research?*

First it needs to be said that the nice thing about demography is that there are laws that are not exactly found in the social sciences. To give an example: If I live a year longer, I will be one year older after one year. Or: There are no births after age zero. That sounds trivial, but you can derive many mathematical models from such laws. We can see how a population develops, for example whether it shrinks of grows. If we manage to model demographic indicators, such as mortality, we can do forecasts for the future. But you could also say: Only if I understood how certain mechanisms in populations work can I model them. In reverse that means: Prognosis is the ultimate test of whether a theory is correct.

*When you have developed such a model of mortality, do you have to wait for 20, 50 or even 100 years to find out whether it was correct?*

No. Usually, you have data series from the past, i.e., time series. You then take a first time period, and look whether the model matches the actual development. It is relatively easy to make forecasts for one or two years. But when making them for several years, it gets difficult.

*Models do not always have the best reputation, that reason being one of them. Because the forecasts done with them are often wrong …*

That's true. The demographer Nico Keilman has made a similar statement a couple of years ago in an article. He asked the question why the forecasts did not improve even though we have better data sets and better computers we can use. Of course, at first that’s quite a negative statement; but he is right. And I think you can build on this finding. We now need to consider what we can do better. And we need to change our thinking slightly. In forecasting, we have often focused on average values. We have asked ourselves, for example, how many people will be over 80 in year XY. It is important to know that because a certain percentage of them will be in need of care and thus appropriate nursing home capacities must be provided. When we forecast an average value for that, we always get it right in 50% of the cases and in 50% we do not. So, it could be more interesting for policy makers if we could provide probabilistic forecasts that consider fluctuations of certain indicators. We’ll work on this methodology, too.

*Is there a really good model of mortality? *

There are many models, and everyone claims his or hers is the best. We have developed a model, too. I wouldn’t say ours is the best, but it is not worse than other models and it is more suited to fit certain data. What makes it different is that the model does not use mortality rates but instead uses the rates of change in mortality. The models can also include comparative countries, and the whole thing will then be placed into a probabilistic context. Maybe an example will help to explain why this is important: We have recently published an article about the life expectancy of women in Denmark. In Denmark, the life expectancy of women has hardly increased from 1980 to 2000. And the main reason is that these women, who were born between the two World Wars, have smoked a lot. So we have the question: How can you get a case like that into a model? And here our model works well because we could always see how mortality changes from year to year. And we could also enter data from our reference countries, Sweden and Norway. These countries are very similar to Denmark in terms of society and culture, except that the women of the cohorts between the two World Wars have not smoked that much.

*Does that mean that your research group will continue to work on improving the model until it has universal application?*

No. It can be applied only to the so-called High Income Countries. In all countries south of the Sahel, for example, the socio-cultural and economic conditions are so different that the model would probably not work. But what is much more important than the development of the model are the methods that we will develop with that model in parallel. For instance, we have a couple of ideas on how we can check models to see whether the forecasts they provide are realistic or whether they are unrealistic, because they break with all past trends. So, we develop methods that allow us to say today, and not only in 40 or 50 years, whether a forecast is realistic. This is then a kind of tool kit available to anyone who wants to use it.

## More Information

Website of the Research Group Mathematical and Actuarian Demography