Econometrics is the application of statistical methods to economic data, enabling researchers to test theories, estimate relationships, and make causal inferences. It forms the empirical backbone of economics, finance, and policy analysis, bridging theoretical models and real-world data through regression analysis, hypothesis testing, and identification strategies. Ordinary Least Squares (OLS) serves as the foundational estimation method, but violations of its assumptions—endogeneity, heteroskedasticity, autocorrelation—demand corrections and alternative approaches. Modern econometrics emphasizes causal identification through instrumental variables, panel data methods, difference-in-differences, regression discontinuity, and other quasi-experimental designs that recover treatment effects from observational data. A deep working knowledge of diagnostics, robust inference, and model specification is essential for producing credible empirical research.
What This Cheat Sheet Covers
This topic spans 15 focused tables and 87 indexed concepts. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.
Table 1: OLS Assumptions (CLRM)
| Assumption | Example | Description |
|---|---|---|
y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + u | • Model is linear in coefficients \beta, not necessarily in variables• allows transformations like x^2 or \log(x) | |
Draw n independent observations | Each observation (y_i, x_i) is independent and identically distributed (i.i.d.) from the population | |
\text{rank}(X) = k | • No exact linear relationship among regressors • allows estimation of all \beta coefficients uniquely | |
E(u \mid x_1, x_2, \ldots, x_k) = 0 | • Error term has zero mean for any value of regressors • implies exogeneity and no omitted variable bias |