Econometrics

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

  • Logit
  • Probit

Panel Data

  • Fixed effectsRandom EffectsFirst Differencing 

Instrumental Variables

  • Endogeneity and finding appropriate instruments

Time Series Data

Financial Econometrics