Age & Income, Part 1

Background

Economists have done considerable work on the relationship between age and income. They find that (on average) people who are very old or very young have lower incomes than those in between. The question is how exactly to model this relationship.

1. Why does it make sense that the incomes of the old and the young should be lower than the incomes of those whose age is in-between?

The most famous work on this issue is a book by Jacob Mincer [Min], from 1974. Mizner realized that age was less important than the number of years of work experience. This means that we must consider, for example, college graduates separately from workers with only a a high-school diploma.

2. Assuming that a similar relationship between years of work experience and age exists for high-school graduates and college graduates, how do you think the graphs will differ? I.e. what shifts, stretches, etc. might be necessary to transform one graph into the other?

In this project, we will try to develop a reasonable model for the relationship between age and income.

Data

Below is data from the Current Population Survey [CPS] for the year 1999. This table gives the average (mean) income for white male college graduates who worked full-time for the previous year, broken down by age. By restricting to a single educational group (college grads), we can just consider age, rather than years of work experience.

Age	Mean Income
18 to 24 years	31,793
25 to 29 years	42,245
30 to 34 years	57,040
35 to 39 years	70,479
40 to 44 years	76,018
45 to 49 years	78,855
50 to 54 years	82,253
55 to 59 years	92,773
60 to 64 years	85,283
65 to 69 years	80,875
70 to 74 years	73,355
75 years and over	54,329

Problems

1. Graph this data. How are you selecting values for the "age" coordinate of each data point? What is the shape of the graph (roughly)?

2. Mincer suggested that the data should be modeled by a quadratic function (a parabola). Assuming this data is roughly parabolic, estimate the coordinates of the vertex.

3. Now find the parabola which best fits the data (by trial and error). Using linear regression, discuss how well your parabola fits the data.

4. Graph the parabola with the data. Plot the residuals between the model and the data. Discuss the fit of the model with the data in more detail. At what ages is the fit better or worse? Why do you think that is? For what ages do you think your model is valid? Why?

References

[CPS] Current Population Survey website, http://www.bls.census.gov/cps/cpsmain.htm

[Min] Mincer, Jacob. Schooling, Experience and Earnings. New York: National Bureau of Economic Research, 1974.