[Econometrics] Incorporating Ordinal Information by using dummy variables

 

Y = β0 + β1x + other factors,

 

under the condition of x1 is an ordinal variable.

- x1 has a range from zero to four, with zero being the worst and four being the best. 

 

The problem in this case is that the difference between four and three is not always the same as the difference between one and zero. In order to resolve it, we need to take a single credit rating and turn it into five categories.

 

Let x1 = 1 if x = 1, and x1 = 0 otherwise....

Then the model is established as

Y = β0 + δ1x1 + δ2x2 + δ3x1 + δ4x1 +  δ5x5 + other factors

 

Following our rule for including dummy variables in a model, we include four dummy variables because we have five categories. The omitted category here is a credit rating of zero, which is the base group.

If this model has a constant partial effect, there is one way to write the three restrictions that imply a constant partial effect. δ2 = 2*δ1, δ3 = 3*δ1, δ4 = 4*δ4

So the model can be reestablished as

Y = β0 + δ1(x1 + x2 + x3 + x4) + other factors

 

In some cases, the ordinal variable takes on too many values so that a dummy variable cannot be included for each value. For example, if one of the key IDV is the rank of the law school. Because each law school has a different rank, we clearly cannot include a dummy variable for each rank(너무 많아). If we do not wish to put the rank directly in the function, we can break it down into categories.

 

Resource : Jeffrey M. Woolderfige, "Introductory Econometrics : A Modern Approach 5th edition"