Econometrics and Quantitative Methods
Core Concepts
Econometrics applies statistical methods to economic data. You must understand simple and multiple linear regression, OLS assumptions, hypothesis testing (t-test, F-test), R-squared, multicollinearity, heteroscedasticity, autocorrelation, and endogeneity. Time series concepts (stationarity, cointegration) and panel data are also relevant. For BCS, focus on interpretation of regression output and basic diagnostics.
Common Traps
- Confusing R-squared with adjusted R-squared; adjusted R-squared penalizes for adding variables.
- Forgetting that OLS estimates are BLUE only under Gauss-Markov assumptions.
- Misinterpreting p-values: it is the probability of observing the data given the null hypothesis is true, not the probability that the null is true.
- Overlooking that correlation does not imply causation; endogeneity can bias estimates.
- Assuming heteroscedasticity biases coefficients; it affects standard errors, not coefficients.
Worked Example / Rule of Thumb
Rule of thumb: For a simple regression Y = β0 + β1X + ε, the OLS estimator of β1 is Cov(X,Y)/Var(X). The t-statistic for β1 is (β1_hat - hypothesized value) / SE(β1_hat). If |t| > 1.96 (for large sample at 5% significance), reject the null.
Example: Suppose a regression of consumption (C) on income (Y) yields C = 50 + 0.8Y, with SE(β1) = 0.1 and sample size 100. Test H0: β1 = 1 vs. H1: β1 ≠ 1. t = (0.8 - 1)/0.1 = -2.0. Critical value at 5% is ±1.96. Since |-2.0| > 1.96, reject H0. Conclusion: MPC is significantly different from 1 at 5% level. Also, R-squared = 0.9 means 90% of variation in consumption is explained by income.