Homework 3: Models for Exploration

Vocabulary flashcards covering the Conditional Expectation Function, variance and covariance formulas, and statistical models for career earnings based on March 2009 CPS data.

CEF (Conditional Expectation Function)

A function that gives the expected value of some random variable $Y$ given the value of another random variable $X$.

Gender Pay Gap Variables

In the application of CEF to the gender pay gap, the $Y$ variable represents earnings and the $X$ variable represents gender.

Variance Formula

The expression $E\{[X - E(X)]^2\}$, which is used to define the variance of a random variable.

Covariance Formula

The expression $E\{[X - E(X)][Y - E(Y)]\}$, which defines the covariance between random variables $X$ and $Y$.

Relationship Estimation

To estimate the covariance, sample means for $E(X)$ and $E(Y)$ are plugged in, and the outer expectation is replaced with another sample mean.

Covariance

A measurement that indicates the direction of a relationship between variables but not the strength of that relationship.

Earnings and Age Correlation

The estimated correlation between earnings and age among 23-62 year-olds using the March 2009 CPS is $0.13$.

$E(\text{earnings} | \text{age})$ Estimation

The simplest estimation method is to plug in the sample mean earnings for each specific value of age.

Career Earnings Pattern

According to Figure 6, earnings tend to increase early in a career and plateau after roughly age 40.

Linear Career Earnings Model

A model that assumes the difference in earnings from one age to the next remains constant throughout a career.

Quadratic Career Earnings Model

A model that captures the concave shape of the earnings-age relationship, where the difference in earnings from one age to the next varies with age.

Earnings Peak Prediction

Using March 2009 CPS data, a quadratic model of $E(\text{earnings} | \text{age})$ predicts that earnings increase until approximately age 50.

Human Capital Theory

The theory that provides the justification for using a quadratic model to fit earnings and age data.