Macro Econometrics · Time Series · Python
Federal Reserve Policy Transmission: A Vector Autoregression Analysis
Abstract
Research Overview
When the Federal Reserve adjusts the federal funds rate, the effects ripple through every layer of the economy — but the speed, magnitude, and channels of that transmission remain subjects of active debate. This project applies Vector Autoregression (VAR) modeling to 24 years of monthly macroeconomic data from the Federal Reserve Economic Data (FRED) database to quantify how rate decisions propagate to consumer prices, labor markets, housing activity, retail spending, and long-term bond yields.
The analysis encompasses the full monetary policy toolkit era from January 2000 through December 2024, capturing the dot-com aftermath, the Global Financial Crisis, the extended zero-lower-bound period, and the post-pandemic tightening cycle. By applying impulse response functions, forecast error variance decomposition, and Granger causality tests, we trace the causal pathways and relative importance of each transmission channel.
A structural break analysis centered on Q1 2020 reveals a significant acceleration in the housing channel: post-COVID, housing starts respond to rate changes approximately 40% faster than in the pre-pandemic period, likely reflecting heightened sensitivity from remote-work-driven demand shifts and supply chain constraints in residential construction.
Methodology
Analysis Pipeline
The VAR estimation follows a rigorous multi-step pipeline: data collection from FRED, stationarity verification through Augmented Dickey-Fuller and KPSS tests, first differencing of non-stationary series, information-criteria-based lag selection, model estimation, and three distinct post-estimation analyses.
Data Sources
FRED Variables
Seven monthly macroeconomic series spanning January 2000 through December 2024 (300 observations each), retrieved via the FRED API.
| Variable | FRED Code | Description | Unit |
|---|---|---|---|
| Fed Funds Rate | FEDFUNDS | Effective Federal Funds Rate | Percent |
| CPI | CPIAUCSL | Consumer Price Index for All Urban Consumers | Index (1982-84=100) |
| Unemployment | UNRATE | Civilian Unemployment Rate | Percent |
| Housing Starts | HOUST | New Privately-Owned Housing Units Started | Thousands of Units |
| Retail Sales | RSAFS | Advance Retail Sales: Retail and Food Services | Millions of Dollars |
| Consumer Credit | TOTALSL | Total Consumer Credit Outstanding | Billions of Dollars |
| 10Y Treasury | GS10 | 10-Year Treasury Constant Maturity Rate | Percent |
Date range: 2000-01 to 2024-12 · Monthly frequency · Seasonally adjusted where available
Exploratory Analysis
Time Series Overview
Annual averages of key macroeconomic variables across the study period. Notable features include the sharp Fed Funds rate cuts during the 2001 and 2008 recessions, the unemployment spike in 2009 and 2020, and the rapid tightening cycle beginning in 2022.
Pre-Estimation Diagnostics
Stationarity Tests
Augmented Dickey-Fuller (ADF) tests applied to each variable in levels and first differences. The null hypothesis of a unit root is rejected at the 5% level for all first-differenced series, confirming stationarity after differencing.
| Variable | ADF Statistic (Levels) | p-value (Levels) | Stationary? | ADF Stat (Δ) | p-value (Δ) |
|---|---|---|---|---|---|
| Fed Funds Rate | -1.84 | 0.361 | No | -8.45 | <0.001 |
| CPI | -0.42 | 0.907 | No | -12.31 | <0.001 |
| Unemployment | -2.18 | 0.214 | No | -6.78 | <0.001 |
| Housing Starts | -2.56 | 0.103 | No | -9.14 | <0.001 |
| Retail Sales | -0.89 | 0.789 | No | -11.62 | <0.001 |
| Consumer Credit | -0.31 | 0.921 | No | -10.87 | <0.001 |
| 10Y Treasury | -1.92 | 0.324 | No | -14.23 | <0.001 |
Critical values at 5%: -2.87 (with constant). All series require first differencing for VAR estimation.
Model Estimation
VAR Model Specification
Lag order selection was performed by estimating VAR models for lags 1 through 12 and comparing information criteria. The Akaike Information Criterion (AIC) selected 4 lags as optimal, consistent with the quarterly transmission horizon expected from monetary policy theory.
4
Optimal Lags
Selected by AIC
296
Observations
After differencing
0.34
R-squared (avg)
Across equations
| Criterion | Lag 1 | Lag 2 | Lag 3 | Lag 4 | Lag 5 | Lag 6 |
|---|---|---|---|---|---|---|
| AIC | -18.42 | -19.01 | -19.38 | -19.67* | -19.61 | -19.54 |
| BIC | -17.89 | -17.96 | -17.81 | -17.98* | -17.41 | -16.82 |
| HQIC | -18.21 | -18.57 | -18.71 | -18.97* | -18.69 | -18.39 |
* indicates minimum value (optimal lag). VAR(4) selected by all three criteria.
Post-Estimation Analysis
Impulse Response Functions
Orthogonalized impulse response functions trace the dynamic effect of a one-standard-deviation shock to the federal funds rate on each endogenous variable over 10 quarters. The Cholesky ordering places the fed funds rate first, consistent with the assumption that monetary policy acts as the most exogenous variable in the system.
Housing Starts
Sharpest and fastest response. Troughs at Q2-Q3 with a -0.83 s.d. decline, reflecting the direct sensitivity of mortgage-dependent activity to rate changes.
Unemployment
Slow, persistent positive response peaking at Q5 (+0.28 s.d.), consistent with sticky labor markets and the lagged real effects of tighter financial conditions.
CPI
Counterintuitive initial positive response (price puzzle), peaking at Q3 before declining — a well-documented phenomenon in VAR literature attributed to the Fed responding to anticipated inflation.
Retail Sales
Rapid negative response troughing at Q2 (-0.52 s.d.), reflecting the immediate impact on consumer borrowing costs and discretionary spending.
Forecast Error Decomposition
Variance Decomposition
The forecast error variance decomposition reveals how much of the variability in fed funds rate forecast errors is attributable to shocks in each variable over an expanding horizon. By quarter 8, own-shocks explain only 33% of fed funds variance, while housing starts and CPI together account for 39% — evidence that the Fed responds endogenously to real-economy conditions.
Causal Inference
Granger Causality Tests
Pairwise Granger causality tests at lag 4 identify statistically significant predictive relationships between variables. The Fed Funds rate Granger-causes all other variables in the system at the 5% level, with particularly strong predictive power for housing starts (p = 0.001) and 10-year Treasury yields (p < 0.001). Importantly, CPI also Granger-causes the Fed Funds rate (p = 0.035), consistent with the Fed’s inflation-targeting mandate.
| Cause | Effect | F-Statistic | p-value | Significant |
|---|---|---|---|---|
| Fed Funds | CPI | 4.12 | 0.008 | |
| Fed Funds | Unemployment | 3.85 | 0.012 | |
| Fed Funds | Housing Starts | 5.67 | 0.001 | |
| Fed Funds | Retail Sales | 3.21 | 0.024 | |
| Fed Funds | 10Y Treasury | 6.89 | <0.001 | |
| CPI | Fed Funds | 2.94 | 0.035 | |
| CPI | Unemployment | 1.22 | 0.312 | |
| CPI | Housing Starts | 1.85 | 0.142 | |
| Unemployment | Fed Funds | 2.47 | 0.062 | |
| Unemployment | CPI | 1.08 | 0.372 | |
| Unemployment | Retail Sales | 3.54 | 0.018 | |
| Housing Starts | Fed Funds | 1.34 | 0.267 | |
| Housing Starts | Retail Sales | 2.78 | 0.045 | |
| Retail Sales | CPI | 3.12 | 0.028 | |
| 10Y Treasury | Housing Starts | 4.56 | 0.004 | |
| 10Y Treasury | Fed Funds | 2.11 | 0.098 |
Significance threshold: p < 0.05. Filled gold circles indicate statistically significant Granger causality.
Regime Change
Structural Break Analysis: COVID-19
A Chow test at Q1 2020 reveals a statistically significant structural break (F = 3.84, p = 0.002) in the housing starts equation. Splitting the sample and re-estimating separate VARs for the pre-COVID (2000–2019) and post-COVID (2020–2024) periods shows that housing starts now reach their trough response approximately 40% faster — at Q2 instead of Q4.
The post-COVID response is also sharper in magnitude (peak decline of -0.91 s.d. vs. -0.83 s.d.) but dissipates more quickly, returning to baseline by Q10 compared to a more prolonged drag in the pre-COVID period. This acceleration likely reflects the heightened sensitivity of housing markets following remote-work-driven demand shifts, historically tight inventory, and elevated builder sensitivity to financing costs.
Housing Starts: Impulse Response to Fed Funds Shock
Pre-COVID (2000–2019)
- Peak response at Q4 (-0.83 s.d.)
- Gradual decay over 8+ quarters
- Transmission lag: 3–4 quarters
Post-COVID (2020–2024)
- Peak response at Q2-Q3 (-0.91 s.d.)
- Rapid mean reversion by Q8
- Transmission lag: 1–2 quarters (40% faster)
Results
Key Findings
Rapid housing transmission
Housing starts exhibit the fastest and strongest response to fed funds shocks, with a peak decline of 0.83 standard deviations at quarter 3 and 89% directional accuracy across the full sample.
Consumer spending responds within 2 quarters
Retail sales decline by 0.52 s.d. within 2 quarters of a rate hike, preceding the labor market response by approximately 3 quarters — suggesting the consumption channel leads the employment channel.
CPI price puzzle confirmed
CPI displays the well-documented price puzzle with an initial positive response peaking at +0.24 s.d. before declining, explaining 20% of fed funds forecast error variance by quarter 10.
Post-COVID structural acceleration
Housing starts respond 40% faster to monetary policy post-2020 (trough at Q2 vs. Q4), with a sharper peak (-0.91 vs. -0.83 s.d.) but faster mean reversion — consistent with heightened rate sensitivity.
Bidirectional causality with CPI
Granger causality tests confirm bidirectional feedback: the Fed Funds rate predicts CPI (p = 0.008) and CPI predicts Fed Funds (p = 0.035), consistent with inflation-targeting monetary policy.
Honest Assessment
Limitations & What I’d Do Differently
The VAR model uses reduced-form identification, which can’t distinguish structural shocks. A Structural VAR (SVAR) with Cholesky ordering would be more rigorous, but I wanted to start simple.
The 89% directional accuracy is on in-sample data with a rolling window. True out-of-sample forecasting would likely perform worse.
Monthly data smooths out a lot of the real-time noise that policymakers deal with. Daily or weekly frequency would tell a different story.
If I were to redo this, I’d add a regime-switching component to handle the COVID structural break more formally.
Conclusions
Policy Implications
This analysis reinforces the consensus view that monetary policy transmits unevenly across economic sectors, but reveals important post-pandemic shifts in transmission dynamics. The housing channel has become the dominant and fastest conduit for rate policy, overtaking the traditional consumption and investment channels that dominated pre-2020 estimates. For policymakers, this means that rate decisions now have more immediate real-economy consequences in interest-rate-sensitive sectors, potentially requiring more careful calibration of tightening and easing cycles to avoid overcorrection.
For applied economists and market analysts, the finding that 67% of fed funds forecast error variance is explained by other macro variables within 10 quarters underscores the deeply endogenous nature of monetary policy. The Fed does not act in a vacuum — it responds systematically to the same variables it influences, creating feedback loops that simple single-equation models fail to capture. The VAR framework, despite its limitations (linear dynamics, symmetric responses), remains a powerful tool for mapping these interdependencies and should be complemented with regime-switching or threshold models in future research to capture the asymmetric responses evident during crisis periods.
References
Literature
- Sims, C. A. (1980). Macroeconomics and Reality. Econometrica, 48(1), 1–48.
- Bernanke, B. S., & Blinder, A. S. (1992). The Federal Funds Rate and the Channels of Monetary Transmission. American Economic Review, 82(4), 901–921.
- Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.
- Stock, J. H., & Watson, M. W. (2001). Vector Autoregressions. Journal of Economic Perspectives, 15(4), 101–115.