Week 11 Homework Feedback: Ignazio Nunzi

Overall Assessment

Grade: ✅ (Pass)

Correct submission. You successfully estimated the VAR and generated impulse responses. You went above and beyond by calculating and plotting the full matrix of IRFs (responses of all variables to all shocks), which demonstrates a deeper understanding of the method.

Task-by-Task Check

Data Preparation

  1. Transformations: ✅ Correct transformations. Note: For Interest Rate, you calculated diff(T.FEDFUNDS). While this makes the series stationary (change in rate), the standard monetary VAR typically uses the level of the interest rate (as per the solution and lecture). This interpretation difference affects the scale and persistence of the IRF but is a valid econometric choice.
  2. Alignment: ✅ Data alignment handled correctly.

Estimation & Identification

  1. VAR Estimation: ✅ Correct OLS estimation.
  2. Covariance: ✅ Residual covariance calculated.
  3. Cholesky: ✅ Correct lower triangular decomposition.
  4. Ordering: ✅ Correct ordering.

Impulse Response Functions

  1. Shock Selection: ✅ You correctly identified the 3rd shock as the interest rate shock (and plotted all others too).
  2. IRF Computation: ✅ Correct simulation loop.
  3. Plotting: ✅ Extensive plotting (3x3 grid) covering all shock-response pairs.
  4. Interpretation: ✅ Detailed and thoughtful analysis of the recessionary effects and inflationary pressure.

Technical Implementation

  • Robustness: Good use of NaN checks (any(isnan(Y), 2)).
  • Code Structure: Well-organized script.

Suggestions for Improvement

  1. Interest Rate Variable: Standard practice in this specific VAR (Christiano, Eichenbaum, Evans) is to use the level of the Federal Funds Rate rather than the first difference. Using the difference implies the shock is to the change in the rate, and the rate itself would have a permanent unit root component if reconstructed.

Summary

10/10 tasks correct (with a valid alternative choice for the interest rate variable). Correct work.