🌍 Week 11 Homework — Feedback

Student: Davide Magnini Assignment: VAR Estimation and Identification

✅ Overall Assessment

Result: ✅ Pass

Solid submission with correct VAR implementation and IRF analysis. The code accurately estimates the VAR parameters, implements the Cholesky identification scheme, and generates the required Impulse Response Functions. The economic interpretation of the results, particularly regarding the delayed effect of monetary policy, is also provided.

🔍 Task-by-Task Check

Task Description Status Notes
1.1 Data Loading & Cleanup ✅ Correctly loads US_macro_data.csv and handles dates
1.2 Data Transformation ✅ Correctly computes annualized growth rates (400 * diff log)
1.3 Construct Data Matrices ✅ Correct setup of Y (LHS) and X (RHS with constant and lags)
1.4 OLS Estimation ✅ Correct equation-by-equation OLS using \ operator
1.5 Extract A1 Matrix ✅ Correctly extracts dynamic coefficients (excluding constants)
1.6 Residuals & Sigma ✅ Correct calculation of residuals and covariance matrix
1.7 Identification (Cholesky) ✅ Correct use of chol(Sigma, 'lower') for recursive identification
1.8 Compute IRFs ✅ Correct iterative computation x_{t+1} = A1 * x_t for 16 periods
1.9 Plot IRFs ✅ Generates all 9 IRF plots in a subplot grid
1.10 Save Figures ✅ Uses exportgraphics to save output

📈 Technical Implementation

  • VAR Estimation: The manual implementation of OLS for each equation is correct.
  • Identification: The structural shocks are correctly identified using the lower triangular Cholesky factor.
  • IRF Generation: The recursive simulation of impulse responses is implemented correctly.
  • File Management: Good practice checking for directory existence and using relative paths.

💬 Style & Clarity

  • Code Structure: The script is well-organized with clear sections (Load Data, VAR Estimation, Identification, Plots).
  • Comments: Good commenting throughout explaining the steps and the model structure ($Y_t = A_0 + A_1 Y_{t-1} + e_t$).
  • Variable Naming: Clear and descriptive names (B_gdp, A1, Sigma, irf_1).

📊 Visual Output Assessment

  • Plots: The 3x3 grid of IRFs is clear and correctly labeled.
  • Styling: Use of grid lines and clear titles helps readability.
  • Economic Interpretation: The comments at the end correctly note the lagged effect of the interest rate shock on inflation (Price Puzzle context) and the contractionary effect on GDP.

✅ Suggestions for Improvement

  1. Generalization: Instead of hardcoding indices 2:4 for A1 extraction, you could use 2:end or 2:1+n_vars to make the code more robust to changes in the number of variables.
  2. Looping: For a larger system, consider using a loop for the OLS estimation and IRF plotting to reduce code repetition.

🎯 Summary

Correct and well-implemented assignment. The student successfully built a VAR model from scratch, estimated it using OLS, and performed structural identification to analyze the effects of monetary policy. The code is clean, efficient, and produces the correct economic insights.

Grade Level: ✅ Pass (10/10 tasks correct)