Probability and Stats Review for Econometrics
- Understanding mean, variance, standard deviation, expected value
- Understanding of hypothesis tests: setting up null vs alternate hypothesis
- Understanding Z-score, t-tests, and p-value
- Application of alpha level and confidence intervals
- Understanding of Chi-squared distribution and F-distribution
Regression Analysis
- Correlation vs causation
- Nature of data and the need for best-fit line/regression line
- Terminology and notation
- Concept of population regression function
- Introduction to the idea of residuals and residual sum of squares (RSS)
- Least Squares regression as the minimizing of RSS
- Conceptual understanding and interpretation of regression slope and intercept coefficients
- Gauss Markov properties of Best Linear Unbiased Estimator
- Coefficient of Determination and R squared
Classical Normal Linear Regression Assumptions
- Probability distribution of the disturbance term
- Normality of residuals
- Zero covariance between residuals and explanatory variables
- Assumption of constant variance of residuals or homoscedasticity
Classical Normal Linear Regression Assumptions
- Probability distribution of the disturbance term
- Normality of residuals
- Zero covariance between residuals and explanatory variables
- Assumption of constant variance of residuals or homoscedasticity
Regression Diagnostics
- Checking the goodness of fit or R-squared
- F-test as the joint hypothesis test for the regression model
- Individual t-tests or hypothesis tests for statistical significance of coefficients
- Normality of residuals
- Checking for heteroscedasticity
Multiple linear regression
- Meaning and interpretation of partial regression coefficients
- R squared meaning and interpretation with multiple explanatory variables
- Issue of multicollinearity
- Variance of regression coefficients and the impact on statistical significance
Dummy Variables
- Nature of binary/dummy variables
- Dummy variable trap
- Use of dummy variables in Chow test for structural change
- Piecewise linear regression with dummy variables
- Interaction variables and intercept dummies
Heteroskedasticity
- Issue of heteroscedasticity
- OLS remains unbiased but the variance is no longer the minimum variance
- Detection of heteroscedasticity with graphical method using scatterplots as well as formal tests
- 1. Park’s Test
- 2. Glesjer test
- 3. Breusch-Pagan hettest
- 4. White’s test
- Fixing for heteroscedasticity using weighted least squares or using White’s robust standard errors
Autocorrelation
- Issue of autocorrelation in residuals
- OLS is still unbiased but minimum is no longer minimum variance
- Graphical detection through scatterplot of residuals
- Runs test
- Durbin Watson Test and its limitations
- Breusch-Godfrey test for autocorrelation
- Lagrange multiplier test
- Newey west standard errors to fix the issue of autocorrelation
Binary Dependent Variable models
Panel Data
- Fixed effectsRandom EffectsFirst Differencing
Instrumental Variables
- Endogeneity and finding appropriate instruments
Time Series Data
Financial Econometrics