Core Course 10: Introductory Econometrics

This course provides the tools to quantify economic relationships, test economic theories, and evaluate policies using real-world data.

Course Content Details

1. The Classical Linear Regression Model (CLRM)

This unit introduces the foundational model of econometrics: the CLRM. We begin with the simple two-variable model and extend it to the multiple regression model. The focus is on understanding the assumptions of the model (e.g., linearity, no perfect multicollinearity, homoskedasticity), which are crucial for the validity of our estimation results.

Key Topics:

  • The Two-Variable and Multiple Regression Models
  • The Assumptions of the CLRM
  • Interpretation of Regression Coefficients
  • Goodness of Fit: R-squared and Adjusted R-squared

2. Ordinary Least Squares (OLS) Estimation

This unit covers the most common method for estimating the parameters of a regression model: Ordinary Least Squares (OLS). We will derive the OLS estimators and study their statistical properties. The Gauss-Markov Theorem is a key result, stating that under the CLRM assumptions, OLS estimators are the "best" (most efficient) among all linear unbiased estimators (BLUE).

Key Topics:

  • Derivation of the OLS estimators
  • Properties of OLS: Unbiasedness and Efficiency
  • The Gauss-Markov Theorem and the BLUE property
  • Variance and Standard Errors of OLS Estimators

3. Hypothesis Testing and Model Specification

Once we have estimated a model, we need to test hypotheses about the population parameters. This unit covers how to test the statistical significance of individual coefficients (using t-tests) and the overall significance of the regression model (using the F-test). We will also discuss issues related to model specification, such as choosing the correct variables and functional form.

Key Topics:

  • Testing Hypotheses about a Single Coefficient (t-test)
  • Confidence Intervals for Coefficients
  • Testing Overall Significance of the Regression (F-test)
  • Testing Linear Restrictions on Coefficients
  • Specification Errors: Omitted and Irrelevant Variables

4. Violations of Classical Assumptions

This unit explores what happens when the assumptions of the CLRM are violated. We will focus on two common problems: heteroskedasticity (non-constant variance of the error term) and multicollinearity (high correlation between independent variables). For each problem, we discuss its consequences for OLS estimation, how to detect it, and potential remedial measures.

Key Topics:

  • Multicollinearity: Consequences, Detection, and Remedies
  • Heteroskedasticity: Consequences, Detection (e.g., White's test), and Remedies
  • Generalized Least Squares (GLS)

5. Dummy Variables and Qualitative Regressors

Economic data often contains qualitative information (e.g., gender, location). This unit introduces dummy variables, which allow us to incorporate such categorical variables into a regression model. We will learn how to use dummy variables to model differences in intercepts and slopes, and how to test for structural breaks in a relationship.

Key Topics:

  • Constructing and Interpreting Dummy Variables
  • Dummy Variable Trap
  • Modeling Differences in Intercepts and Slopes
  • The Chow Test for Structural Stability

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