Econometrics Cheat Sheet

The core ideas of Econometrics distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

Ordinary Least Squares (OLS)

The most fundamental estimation technique in econometrics, OLS minimizes the sum of squared residuals between observed and predicted values to find the best-fitting linear relationship between dependent and independent variables.

Endogeneity

A situation in which an explanatory variable is correlated with the error term in a regression model, violating a core OLS assumption and producing biased, inconsistent estimates. Common sources include omitted variable bias, simultaneity, and measurement error.

Instrumental Variables (IV)

A method used to obtain consistent estimates when explanatory variables are endogenous. A valid instrument must be correlated with the endogenous regressor (relevance) but uncorrelated with the error term (exogeneity).

Heteroscedasticity

A condition in which the variance of the error term in a regression model is not constant across observations. While OLS estimates remain unbiased, standard errors become unreliable, leading to incorrect hypothesis tests.

Multicollinearity

A situation in which two or more independent variables in a regression model are highly correlated, making it difficult to isolate the individual effect of each variable and inflating the variance of coefficient estimates.

Time Series Stationarity

A time series is stationary when its statistical properties such as mean, variance, and autocovariance are constant over time. Many econometric techniques require stationarity; non-stationary data can produce spurious regression results.

Panel Data Methods

Techniques for analyzing data that tracks multiple entities (individuals, firms, countries) over multiple time periods. Fixed effects and random effects models exploit both cross-sectional and temporal variation to control for unobserved heterogeneity.

Difference-in-Differences (DiD)

A quasi-experimental research design that estimates causal effects by comparing the change in outcomes over time between a treatment group and a control group. It relies on the parallel trends assumption: absent treatment, both groups would have followed the same trajectory.

Maximum Likelihood Estimation (MLE)

A method that estimates model parameters by finding the values that maximize the likelihood function, which measures the probability of observing the given data under the assumed statistical model. MLE is especially important for nonlinear and limited dependent variable models.

Cointegration

A statistical property of two or more non-stationary time series that share a common stochastic trend, meaning a linear combination of them is stationary. Cointegrated variables have a stable long-run equilibrium relationship even though each individually wanders over time.

Key Terms at a Glance

Econometrics:The branch of economics that applies statistical and mathematical models to economic data to test theories, estimate relationships, and make forecasts.

Ordinary Least Squares (OLS):A regression estimation method that minimizes the sum of squared residuals to find the best linear fit between dependent and independent variables.

Endogeneity:The condition where an independent variable is correlated with the regression error term, leading to biased and inconsistent parameter estimates.

Instrumental Variable:A variable used to obtain consistent estimates when endogeneity is present; it must be correlated with the endogenous regressor and uncorrelated with the error term.

Heteroscedasticity:Non-constant variance of the error term across observations in a regression model.

Homoscedasticity:Constant variance of the error term across all observations, a key assumption for valid OLS inference.

Multicollinearity:High linear correlation among two or more independent variables in a regression model, which inflates the variance of coefficient estimates.

Autocorrelation:Correlation between the error terms at different time periods in a regression, common in time series data and violating the assumption of independent errors.

Stationarity:A property of a time series whose statistical characteristics (mean, variance, autocovariance) do not change over time.

Unit Root:A feature of a non-stationary time series process in which shocks have permanent effects, causing the series to drift without reverting to a mean.

Cointegration:A statistical relationship in which two or more non-stationary series share a common stochastic trend, so a linear combination of them is stationary.

Panel Data:A dataset that tracks multiple cross-sectional entities (individuals, firms, countries) across multiple time periods.

Fixed Effects:A panel data estimation approach that controls for all time-invariant unobserved heterogeneity by demeaning or differencing the data within each entity.

Random Effects:A panel data estimation approach that treats unobserved entity-specific effects as random variables uncorrelated with the regressors, using generalized least squares.

Difference-in-Differences:A quasi-experimental method that estimates causal effects by comparing outcome changes over time between treatment and control groups.

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