Week 11

Week 11 – Macroeconometrics

Learning Outcomes By the end of this week, students will be able to:

1. Import, clean, and transform macroeconomic time series data in MATLAB.
2. Perform basic descriptive statistics and visualisations for time series.
3. Estimate linear regression models using OLS in MATLAB.
4. Implement and estimate a simple Vector Autoregression (VAR).
5. Compute and plot impulse response functions (IRFs) from VAR models.

Suggested Readings

• Stock, J. H., & Watson, M. W. Introduction to Econometrics. (Ch. 17).
• Kilian, L., & Lütkepohl, H. (2017). Structural Vector Autoregressive Analysis. Cambridge University Press. (Advanced reference).

In-Class Activities

• Data Preparation:
  • Import quarterly US data (Real GDP, GDP Deflator, Federal Funds Rate) from FRED.
  • Transform variables: Log-differences for GDP (Growth) and Deflator (Inflation).
• OLS Regression:
  • Estimate a simple Phillips Curve relationship: \(\pi_t = \alpha + \beta \pi_{t-1} + \gamma (y_t - \bar{y}) + u_t\)
  • Compare fitlm results with manual OLS estimator $\hat{\beta} = (X’X)^{-1}X’Y$.
• Vector Autoregression (VAR):
  • Set up a Bivariate VAR(1) for GDP Growth ($y_t$) and Inflation ($\pi_t$): \(\begin{pmatrix} y_t \\ \pi_t \end{pmatrix} = A_0 + A_1 \begin{pmatrix} y_{t-1} \\ \pi_{t-1} \end{pmatrix} + \epsilon_t\)
  • Estimate coefficient matrices equation-by-equation using OLS.
• Impulse Response Functions (IRFs):
  • Compute IRFs by iterating the system forward after a shock.
  • Use the Cholesky decomposition to identify orthogonal shocks (recursive ordering: $y_t \to \pi_t$).

Homework / Practice

• Task 1: 3-Variable VAR
  • Extend the in-class VAR to include the Federal Funds Rate (R).
  • System vector: $X_t = [ \text{GDP Growth}, \text{Inflation}, \text{Interest Rate} ]’$.
• Task 2: Monetary Policy Shock
  • Identify a monetary policy shock using the Cholesky ordering: $y_t \to \pi_t \to R_t$ (Assumption: Output and prices do not respond instantly to interest rates, but rates respond to current output and prices).
  • Compute IRFs for a 1 standard deviation shock to $R_t$.
• Task 3: Interpretation
  • Plot the responses of GDP, Inflation, and Interest Rate over 12-20 quarters.
  • Discuss the results. Do you see a “Price Puzzle” (inflation rising after a rate hike)?

Files

• Slides Week 11 – Lecture slides.
• codes_week11 on Matlab online
  • week11.m – Main lecture script.
  • week11_get_data.m – Script to download and process FRED data.
  • week11_challenge_starter.m – Starter for in-class challenge.

Homework submission

• Submit your homework here
• Please upload your homework as a single zip file. Access is open with any email address! Remember to name your file with your full name and/or student ID.
• The submission should include the .m files used to produce the results.
• You can modify you submission until 9am on Monday of week 12.