# Building Models

The real world is too complex. Millions of things move in millions of different ways all the time. Economists try to make sense of all these movements and find the cause-and-effect relationships among these moving things. For example, the general price level, the real GDP, interest rates, the money supply, exports, imports, and stock prices change all the time. But, which one of these changes are the causes and which ones the effects? Is it changes in the interest rates that cause changes in the real GDP or the other way around? Why are we interested in this question in the first place? This is because we want to make policy decisions. What should I do when a recession comes and unemployment increases? What variables under my control have the biggest effect on unemployment rate, if any?

The best way to find the cause of effect relationships is to keep everything constant except the two variables we are interested in. Then change one of them to see how the other responds. But, you cannot do this in social sciences. Laboratory scientists can keep certain things, like the room temperature, constant in order to analyze chemical reactions under different temperatures. Social scientists cannot do that, so they resort to building models.

A model consists of a set of equations relating a number of variables to one another in certain ways. We build models by abstracting from a lot of unnecessary details and focusing on the variables of interest. Models are useful to organize our thinking the same way that area maps are useful to organize our trips. So models are not realistic in the sense of including everything from the real world. In fact such a model would be as useless as the reality itself. Think of an area map that includes all the details in the streets. *A model is a simplified version of the reality that helps us understand the reality.*

However, a model should be realistic description of the world in the sense that the relationships of the model should make sense and the result should be reasonable. For example, it would be stupid to make U.S. national consumption a function of rainfall in Bangladesh.

Any model has the following components:

**Constants.**A constant is a magnitude that does not take different values. What this really means is that while we are solving the model we treat these as constants. Suppose for example in our model we have the corporate tax rate of 35%. This rate is constant. Only the U.S. Congress can change it. So while we are solving the model we treat that as fixed. After we solved the model though, we can ask in what way the results would be different if the tax rate was 30% or 40%. Then we would use 30% or 40% in our models assuming that they are fixed numbers.

2. **Variables**. These can take different values. There are two types:

- Exogenous variables (outside variables). The values of these variables are determined outside the model. In other words, their values are not determined by our models. We are not really willing or able to know how their values are determined and why they change. Exogenous variables are the variables whose values we are not willing or able to explain by our model, but we know that they will affect the values of our endogenous variables. So, in a nutshell, we know the values of our exogenous variables (I could just say this at

the beginning, couldn’t I?) So, the values of the constants and exogenous variables are both known to us. The only difference is, one is fixed and the other is variable.

- Endogenous variables (inside variables). The values of these variables are determined inside our models. In other words, they are the unknowns of the model. These are the variables in whose behavior we are interested in. We what to know how their values are determined and why they change. In fact the reason we build models is just to explain the behavior of endogenous variables. We also know that their values are determined by the values of the constants and exogenous variables. You can see that a model is very similar to a set of simultaneous equations you have seen in high school.

3. **The number of endogenous variables **should equal the number of independent equations of the model; otherwise you cannot solve the model for the values of the endogenous variables. Suppose you want to analyze the behaviors of income and consumption. Then you need two equations. If you change your mind and decide that you also want to analyze the behavior of investment spending, then you need one more equation** to close the model**. A model is said to be closed if it has the same number of endogenous variables and equations.