CONCEPTS PODCAST (1)

Core Concepts

Econometrics

  • Definition: The application of economic theory, mathematics, and statistical inference to analyze economic phenomena.

Theoretical Econometrics

  • Focus: Developing methods to measure economic relationships in econometric models.

Economic Statistics

  • Focus: Collecting, processing, and presenting economic data using charts and tables.

Population Regression Function (PRF)

  • Definition: The set of conditional means of the dependent variable for fixed explanatory variable values.

  • Also called the Conditional Expectation Function (CEF).

Adjusted R-squared

  • Purpose: Adjusts the goodness of fit for the number of variables in the regression model to help prevent overfitting.

Specification Bias

  • Definition: Error that occurs when a key variable is omitted from the regression model.

Coefficient of Partial Determination

  • Definition: Measures the variation in the dependent variable explained by including an additional independent variable.

F-Test (ANOVA)

  • Purpose: Evaluates the overall significance of a regression model.

Covariate

  • Definition: A control variable used in models that combine quantitative and qualitative regressors.

Chow Test

  • Purpose: Tests for structural stability of regression models, identifying if regressions differ, but not specifying the cause.

Data Types

Panel Data

  • Definition: Tracks the same units (e.g., a family or firm) over time.

Pooled Data

  • Definition: Combines cross-sectional and time-series data.

Regression Models

Linear Regression Models

  • Definition: Models linear in parameters, which may not always be linear in regressand or regressors.

Dummy Variables in Regression

  • Purpose: Represent structural changes, with a "slope drifter" indicating how the slope coefficient differs for a specific group.

Assumptions of Classical Linear Regression Model (CLRM)

  1. Linear in Parameters

    • Relationship must be linear in the model's coefficients.

  2. Independent Explanatory Variables from Error Terms

    • Independent variables should not be correlated with the error term.

  3. Zero Mean Value of the Error Term

    • Expected value of the error term for any variable should be zero.

  4. Homoscedasticity

    • Variance of the error term is constant across observations.

  5. No Autocorrelation

    • Error terms should not be correlated across observations.

  6. Sufficient Sample Size (n > k)

    • The number of observations must exceed the number of explanatory variables.

  7. No Exact Collinearity Between Variables

    • There should be no perfect linear relationship among explanatory variables.

  8. Correct Functional Form (No Specification Bias)

    • Model must be correctly specified without missing variables or incorrect functional forms.

Hypothesis Testing

  1. Test of Significance and Confidence Interval

    • Two complementary approaches for testing hypotheses.

Methods of Estimation

Ordinary Least Squares (OLS)

  • Definition: Ensures BLUE (Best Linear Unbiased Estimator) properties.

Maximum Likelihood Method

  • Method assumes normal distribution for parameter estimation.

Types of Regression Comparisons (Chow Test)

  1. Coincidental Regression

    • Same slope, same intercept.

  2. Parallel Regression

    • Same slope, different intercept.

  3. Concurrent Regression

    • Different slope, same intercept.

  4. Dissimilar Regression

    • Different slope and intercept.

True or False Clarifications

  1. r squared in two-variable regression equals the coefficient of determination. — True

  • Indicates the goodness of fit of the model.

  1. r squared works the same way in multiple regression models. — False

  • Adjusted R squared is used instead to account for additional variables.

  1. Zero correlation implies independence. — False

  • Independence is stronger; zero correlation doesn’t imply no relationship.

  1. Correlation is symmetrical (r xy = r yx). — True

  2. Correlation implies cause-effect relationships in strong linear associations. — False

  • Correlation measures association, not causation.

  1. Linear PRFs may not always be linear in variables. — True

  2. Linear in parameters means equations can include nonlinear variables. — True

  3. Sampling fluctuations may lead to PRF over-/under-estimation. — True

  4. Least-squares estimators are BLUE. — True

  5. Zero covariance between variables and error term is essential. — True

  6. Partial regression coefficients are for explanatory variables, not dummy variables. — True

  7. Adjusted R squared increases less than R squared as variables are added. — True

Reasons for Excluding Variables in Regression Models

  1. Vagueness of Theory

    • When the theoretical basis for including a variable is unclear.

  2. Unavailability of Data

    • Data for the variable may not be accessible or reliable.

  3. Core vs. Peripheral Variables

    • Focus on the most relevant variables and exclude less critical ones.

  4. Intrinsic Randomness in Human Behavior

    • Human actions may introduce randomness, making some variables unmeasurable.

  5. Poor Proxy Variable

    • Inability to find a good substitute for an unobservable variable.

  6. Principle of Parsimony

    • Keep the model as simple as possible to avoid overfitting.

  7. Wrong Functional Form

    • Errors in specifying the relationship between variables.

Methods of Estimation in Regression

  1. Ordinary Least Squares (OLS)

    • Minimizes the sum of squared residuals, ensuring estimators are BLUE.

  2. Maximum Likelihood Estimation (MLE)

    • Derives parameter estimates assuming a normal distribution for the error term.

Assumptions of CLRM

  • See above under CLRM assumptions for complete definitions.

Types of Regression Comparisons in Chow Test

  1. Coincidental Regression: Same slope, same intercept.

  2. Parallel Regression: Same slope, different intercept.

  3. Concurrent Regression: Different slope, same intercept.

  4. Dissimilar Regression: Different slope and intercept.