Homework 5: Measurement Error and Sample Selection

Flashcards covering the concepts of estimator consistency, measurement error models, classical assumptions, and types of missing data/sample selection.

Consistent Estimator

An estimator whose bias and sampling variance vanish as the sample size grows.

Identifies

The term used to describe when a consistent estimator correctly determines the estimand.

Item Nonresponse

A situation where a respondent (e.g., in the CPS) refuses to report specific information, such as their earnings.

Measurement Error Model

A simple model for unobserved true variables represented as $X = X^{*} + e$, where $X$ is the observed value, $X^{*}$ is the true value, and $e$ is the error.

Classical Measurement-Error Assumptions

The expected value of the measurement error is $0$ and the measurement error is independent of the true variable ($X^{*}$).

Implication of Classical Measurement Error

An effect where the correlation between the observed variable and another random variable is less than the correlation between the true variable and that variable ($corr(X, Y) < corr(X^{*}, Y)$).

Binary Variable Learning

When $X$ is binary, learning about $P(X = 1)$ depends on the false positive and false negative rates.

Attrition

A form of unit nonresponse occurring when participants move away, such as students in Project STAR.

Project STAR Third Grade Retention

Based on Table 3, only $3005$ of the original $5786$ kindergartners remained in the study by third grade.

Missing Completely at Random

A scenario where the selection mechanism is independent of both $X$ and $Y$.

Missing at Random / Exogenous

A selection mechanism $S$ where the conditional expectation of $Y$ satisfies $E(Y|X, S) = E(Y|X)$.

Impute

The process of predicting missing values using a statistical model.