Econometrics

What is Econometrics?

The application of statistical methods to economic data to test hypotheses and estimate causal relationships.

Key challenge in Econometrics

Distinguishing correlation from causation.

Dependent variable in regression analysis

Yi (Y_i), the outcome being predicted.

Independent variable in regression analysis

Xi (X_i), the predictor used to model the outcome.

Error term in regression analysis

εi (ε_i), captures unobserved factors affecting the dependent variable.

Types of Random Variables

Discrete: Limited set of outcomes; Continuous: Infinite possible values.

PDF

Probability Density Function; shows the likelihood of different outcomes.

CDF

Cumulative Distribution Function; shows the probability of observing a value ≤ a given point.

Expected Value (Mean)

E[Y] = ∑ Pi Yi; the average value of a random variable.

Variance

Measures the spread of a distribution.

Covariance

Measures how two variables move together.

Correlation

Standardized covariance; bounded between -1 and 1.

Cross-sectional Data

Data collected from many units at a single time.

Time Series Data

Data collected from a single unit over multiple time periods.

Panel Data

Data that combines cross-sectional and time series data.

Ordinary Least Squares (OLS)

A method to estimate parameters by minimizing the sum of squared residuals.

Key Assumption: Linearity

The model correctly specifies the relationship between the dependent and independent variables.

Key Assumption: Random Sampling

Observations gathered must be independent.

Zero Conditional Mean of Errors

E[ε|X] = 0; no omitted variable bias.

Homoskedasticity

Error variance is constant across values of independent variables.

Threats to Internal Validity

Issues that arise when the estimated relationship between variables is biased.

Omitted Variable Bias (OVB)

Occurs when a variable that affects both independent and dependent variables is left out of the model.

How to Spot Omitted Variable Bias

Ask if there is a missing factor that could influence both variables.

Reverse Causality

Occurs when the dependent variable actually causes the independent variable.

How to Address Measurement Error

Use instrumental variables or better data sources.

Misspecified Functional Form

Occurs when a model assumes a linear relationship when the true relationship is nonlinear.

How to Address Outliers

Winsorizing or using robust regression methods.

Sample Selection Bias

When the sample is not representative of the population.

Randomized Control Trials (RCTs)

The gold standard for causal inference that randomly assigns treatment and control.

Difference-in-Differences (DiD)

Compares treatment and control groups before and after a policy change.

Fixed Effects (FE)

Controls for unobserved characteristics that do not change over time.

Instrumental Variables (IV)

Used when an independent variable is correlated with the error term.

Regression Discontinuity (RD)

Uses a cutoff rule for analysis, relying on specific thresholds.