What are we talking about?
When you hear about models it is often about people like Naomi Campbell or Heidi Klum. Yet, there are far more fascinating models out there. They may not dwell in the spotlights but everyone employs them. Scientists are the most heavy users. These models are simplifications or abstractions of reality and are used to explain things or to make predictions.
Indeed these models are as sexy as the scientists using them so a picture might not have drawn your attention. But then again, sexy is just a temporary phase in life. So what kind of models are we talking about? You can think of:
- models to calculate the trajectory of the planets in the solar system
- models to forecast the weather
- models to predict the spread and the mortality of a virus
- models to estimate the impact of a proposed measure on the economy
- models to predict the impact of climate change
In the 1970s weather forecasts were of poor quality compared to today. And they didn’t go a lot farther than the day after tomorrow. Today predictions are more accurate and go up to two weeks in advance, even thougt the longer term predictions are not as good as those for today or tomorrow.
This improvement is the result of weather forecast models and computers. Computer models have improved over time, and a lot of hard work of scientists has gone into them. Usually about 50 different models are used together to make a weather prediction. Models are important tools to make sense of what happens in the world. There has been a course named Model Thinking by Professor Scott E. Page of the University of Michigan on the Internet. Much of what you read here comes from this course.
Why use models?
When making plans for the future, models can be useful. You can ask yourself, what might happen if you choose a particular action. An economist might use models to predict the consequences for economic growth of a proposed policy measure. Predictions made with models do not always come true. For instance, most economists didn’t see the financial crisis of 2008 coming despite all the models they had at their disposal.
In 1972 a group of scientists using a computer model warned that we would have run out of oil and some other crucial natural resources by 2010. They may have been a few decades off the mark but their warning made people and policy makers think about the fact that the resources of our planet are limited.
When models fail people may start to doubt the experts. This can be dangerous. On average experts do better than uneducated guesses. Only, small errors can lead to dramatic misses so an uneducated guess can sometimes be more accurate than an expert calculation. Experts usually don’t make the mistakes laypeople make so they do better on average.
Models can be wrong because they are simplifications and don’t take everything into account. For instance, an economic model to predict demand for goods and services doesn’t include the preferences and budgets of each individual consumer. If you had all that information, you might be able to make very accurate predictions, but that may be impossible.
There are good reasons to become familiar with models and the issues that come with them. Models can make us think clearer. People who use models usually are better decision makers than those who don’t because they have a better understanding of the situation. Models help us to use and understand data. And they assist us with designing solutions for problems and setting out strategies.
Using multiple models together
Proverbs can disagree with each other. Two heads are better than one but too many cooks spoil the broth. And he who hesitates is lost while a stitch in time saves nine. Contradictory statements can’t be true at the same time but they can be true in different situations or times. It may be important to know which advice is best in which situation, or more often, which combination of advice.
Models are better than uneducated guesses and using more models together can lead to better outcomes than using a single model. That is why up to fifty models are used to make a weather prediction. People who use a single model are not good at predicting. They may be right from time to time just like a clock that has stopped sometimes shows the correct time.
Smart people use several models and their personal judgement to determine which models best apply on the situation at hand. Only people using multiple models together make better predictions than mere guessing but they can be wrong. Still, models can help us to think more logically about how the world works, and eliminate a lot of errors we would make otherwise.
When you plan to work with models, you need to think logically from assumptions to conclusions, and then verify the outcomes with the use of experiments or gathered data. This way of working is called model thinking. It gets even more complicated when you use different models together as the outcomes may differ. And so you might have to consider which models apply best on the situation at hand and evaluate the different outcomes. Model thinking usually consists of the following steps:
- name the parts
A model consists of parts. For instance, if you want to figure out which people go to which restaurant, you need to identify the individual people as well as their preferences and budgets. You also need to identify the restaurants and their menus and the price of those menus. And so the parts are the individual people, their preferences, the restaurants, their menus and the price of each of those menus.
- identify the relationships between the parts
A model comes with relationships between the parts. For instance, the financial system is interconnected because financial institutions lend money to each other. If one bank fails, loans may not be repaid, and other institutions may get into trouble too. And so it might be a good idea to identify the relationships between financial institutions and how much they depend on one another.
- work through the logic
Suppose you want to calculate the length of a rope that you want to tie around the earth at one metre above the surface. Assume the Earth’s circumference to be 40,000 kilometres. The formula for circumference C is: C = πD, where D is the diameter of the Earth. In this case C = π(D + 2m) = πD + (π * 2m) = 40,000 km + 6.28m.
- doing experiments
You can design a model on a drawing board and then reality may turn out to be quite different. Model need a reality check. For instance, if people are often jammed near the exit of a room, you could explore the effects of putting a post before the exit to prevent people from pushing each other.
- identify logical boundaries
With the use of models it may be possible to identify boundaries. For instance, if you think of allowing interest rates to go negative, you may want to estimate how low interest rates can go. If interest rates go below a certain level, for instance -3%, most people may stop saving so the interest rate can’t go lower. To estimate that interest rate, you may need a model predicting savings at different interest rates.
- communicate the findings
If you have used a model then you may have to expain your findings, and therefore the use of the model. For instance, to explain why interest rates can’t go below -3%, you may discuss how you have used the model to come to your conclusion. To support your model you may have used a survey asking people at which interest rate they will stop saving.
Models come with different types of outcomes. Models can help us predict which of type of outcomes will materialise in reality. Possible types of outcomes are equilibrium, cycle, random, and complex.
Equilibrium outcomes end at a specific value and stay there until conditions change. For instance, if you set the thermostat of the central heating to 20°C while the room is 17°C, it will turn on the heating until the room is 20°C and stop once the temperature has reached this level. By then the water in the device might be heated to the point that the room will heat up further to 21°C.
But the heater will remain off as long as the temperature is above 20°C so the room will cool down after some time as long as the outside temperature is lower. The heater will only start again once the temperature goes below 20°C. So after some time the temperature will be close to 20°C and remain so until you set the thermostat to another temperature.
Outcomes of the type cycle show a repeating pattern. For instance, there is a business cycle in the economy causing growth to alternate with slumps. Therefore a model for economic growth could identify a trend, which is the average economic growth over a longer period of time as well as cycles of growth and slumps.
Random outcomes are impossible to predict even though there may be boundaries or a limited number of possible outcomes. For instance, if you play a game of cards, it is impossible to know on beforehand which cards you will get even though you may know that you won’t get a joker card if it is not in the game. Likewise, if you throw a dice, you can’t predict the number but it will be between one and six.
Complex outcomes are hard to predict but they are not random. For example, the demand for oil and the supply of oil tend to slope up in a fairly predictable manner. The price of oil depends on all kinds of things, such as reserves, people in markets, and politics, so an oil-price model is probably complex. The model might be wrong quite often too but it may do better than mere guessing.
Using and understanding data
An important application of models is using and understanding data. If you can make sense of data, you may find information that you can use. This can be done in the following ways:
- understand patterns
There may be patterns in the data. For example, there may be fluctuations in economic growth that can be explained by a business cycle model.
- make predictions for individual cases
A model can give a relationship between different variables so you can predict an unknown variable if the other variables are known. For example, the price of a house may depend on the neighbourhood and the number of square metres. So, if you know the neighbourhood and the number of square metres, and the relationship between these variables and price, you can predict the price of a house.
- produce bounds
For example, if you use models to estimate predict the weather two weeks from now, there is too much uncertainty to come up with an exact temperature, so a model will probably produce a range with a lower bound and an upper bound of the temperatures that might occur.
You can use models with the data to ‘predict’ the past. In this way you can test models and check how good they are. For example, if you have the economic data from 1950 to the present, and you have a model that predicts the unemployment rate based on the economic data of previous years, you can use the data from 1950 to 1970 in the model to predict the unemployment in 1972, and then check whether or not the prediction is close to the real unemployment figure of 1972.
- predict other things
For example, you may have made a model that predicts the unemployment rate, but as a side benefit it might also predict the inflation rate. Another example is that early models of the solar system and gravity showed that there must be an unknown planet, which turned out to be Neptune.
- informed data collection
For example, if you want to improve education, and make a model that predicts school results, you have to name the parts, such as teacher quality, the education level of parents, the amount of money spent on the school, and class size. The model determines which data should be collected. There is no reason to collect data on school size if you don’t use it in you model.
- estimate hidden parameters
Data can tell us more about the model and the model can tell us more about reality. For example, a model for the spread of diseases is the Susceptible, Infected, Recovered (SIR) model. If you have the data of how many people are getting the disease, you can predict how the disease will spread over time.
After you have constructed a model, you can use data to improve it and make it closer to the real world.
Making decisions, strategies and designs
Models can help with making decisions, setting out strategies and designing solutions. A few examples can illustrate that:
- decision aides
Models can be used to make decisions. For instance, at the time of the financial crisis of 2008, you could have made a model of financial institutions like Bear Sterns, AIG, CitiGroup, and Morgan Stanley with the relationships between them in terms of how their success depends on another. As some of these companies were starting to fail, the government had to decide whether or not to save them. This model can help to make that decision. The numbers represent how much one institution depends on another.
So, if AIG fails then how likely is it that JP Morgan fails? The number 466 is big. The number 94 represents the link between Wells Fargo and Lehman Brothers. If Lehman Brothers fails, this only has a small effect on Wells Fargo and vice versa. Lehman Brothers only has three lines going in and out and the numbers associated with these lines are relatively small. For the government this can be a reason not to save Lehman Brothers. AIG has much larger numbers associated with AIG and can be a reason to save AIG because a failure of AIG cancause the whole system to fail. This is why some financial institutions were deemed ‘too big to fail’.
- play out different scenarios
History only runs once. But with models of the world, you can play out different scenarios. For example, in April 2009, the Federal Government decided to implement an economic recovery plan. You can run models of the economy and look at the unemployment rate with and without the recovery plan. It doesn’t mean that what a model shows would really have happened without the recovery plan, but at least the model provides some understanding of its effect.
- identify and rank levers
It can be worthwhile to implement the measures that have the most effect. For example, one of the big issues in climate change is the carbon cycle. The total amount of carbon on Earth is fixed. It can be up in the air or down on the earth. If it is down on the earth then it doesn’t contribute to global warming. If you think about intervening, you may ask where in this cycle are there big levers? Surface radiation is a big number. If you think about where to interfere, you want to think about it in terms of where those numbers are large.
- help to choose from policy options
Suppose there will be a market for pollution permits. We can make a simple model and tell which one is going to work better. Suppose a city has to decide about creating more parks. More parks might seem a good thing but if people want to move there and developers build large apartment buildings around them, it might not be such a good idea after all.
Featured image: Naomi Campbell at Festival de Cannes. Georges Biard (2017). Wikimedia Commons. Public Domain.
1. Model Thinking [link]