Introduction to Bayesian Estimation and Copula Models of Dependence

2 Foundations of Bayesian Analysis

2.1 Education and Wages

Common wisdom states that one’s salary or wages should have something to do with one’s education level. Otherwise, why is higher education so expensive and time consuming? Is it not reasonable that more educated people should be paid more?

Let us define two variables, representing (a) education level of a random person (denote it by E) defined as the number of years of formal education and (b) hourly wage level of the same person (denote it by W) in USD per hour. These variables can be measured for the population of US wage earners. As usual, we will reserve the capital letters E and W for the random variables, while by lowercase e and w we denote particular data: numeric values of these variables. We collect such data for 534 respondents, which constitutes a sample from 1985 census according to Berndt [5].

As we have suggested in the beginning, these two variables must be somewhat related. And if they are, we can use one of these variables measured for a new subject (outside of our sample) to predict the other. For instance, it is logical to believe that if the education level of a person is known, we can make certain predictions regarding their wage. On the other hand, if a person’s wage is known, we can make some suggestions regarding their education level. Let us make the latter our primary objective. We will make statistical inference on an unknown parameter (education level) based on available data (wages).

The ...