The Macroeconomic Determinants of the 10-Year Treasury Yield

This repository contains a quantitative analysis of the long-term interest rate structure of the United States, focusing on the 10-year Treasury yield.
The objective is to identify and quantify the principal macroeconomic forces that explain the historical variation in the yield from 2016 to 2025.

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1. Overview

The model decomposes the 10-year yield into a set of latent macroeconomic factors extracted through Principal Component Analysis (PCA) applied to grouped economic indicators.
Five thematic factor categories are defined:

Category	Variables	Interpretation
Inflation	CPI, CPI_YoY, Inflation Expectations, Oil Prices	Price level and inflationary pressure
Policy	2Y Yield, Federal Funds Rate, Yield Curve Slope	Monetary policy stance
Risk	VIX, USD Index	Market volatility and risk aversion
Fiscal	Federal Debt, Debt-to-GDP Ratio	Fiscal sustainability and leverage
Growth	Real GDP (SAAR)	Real economic activity

Each factor represents the first principal component of its corresponding variable group.
The factors are orthogonal by construction and standardized to mean zero and unit variance.

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2. Methodology

1. Data Collection Data were gathered using the FRED (https://www.stlouisfed.org) API. You can find a script of the data gathering code or the final .csv file in the data folder.

2. Data Standardization
   All variables are standardized to zero mean and unit variance.

3. Principal Component Extraction
   For each thematic group ( G_i ) with variables ( x_{i1}, x_{i2}, \dots, x_{in} ), PCA is applied to obtain the first component: [ F_i = w_{i1}x_{i1} + w_{i2}x_{i2} + \dots + w_{in}x_{in} ] where ( w_{ij} ) are loadings maximizing ( \text{Var}(F_i) ).

4. Regression Framework
   The 10-year yield ( Y_t ) is modeled as: [ Y_t = \beta_0 + \beta_1 F^{(Infl)}_t + \beta_2 F^{(Pol)}_t + \beta_3 F^{(Risk)}_t + \beta_4 F^{(Fiscal)}_t + \beta_5 F^{(Growth)}_t + \epsilon_t ] Estimation is performed via Ordinary Least Squares (OLS).

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3. Results

[ R^2 = 0.816, \quad \text{Adj. } R^2 = 0.807 ]

Factor	Coefficient	t-Statistic	p-Value	Interpretation
Intercept	2.628	54.41	0.000	Baseline yield level
Inflation	0.092	2.16	0.033	Positive sensitivity to inflationary pressure
Policy	0.527	11.86	0.000	Dominant driver: policy stance shifts
Risk	-0.179	-3.30	0.001	Negative relationship (flight-to-safety effect)
Fiscal	-0.059	-0.60	0.551	Insignificant at monthly frequency
Growth	0.265	1.70	0.091	Weakly positive correlation

The model explains approximately 81% of the yield’s historical variation.
Residual variation corresponds to market noise, liquidity effects, and unobserved global drivers.

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4. Interpretation

The regression decomposition aligns with theoretical term structure frameworks.
The Policy Factor dominates yield variation, consistent with the expectations hypothesis.
The Inflation and Risk factors contribute meaningfully, capturing inflation compensation and flight-to-safety dynamics.
Fiscal variables evolve too slowly to exhibit statistical significance at a monthly resolution.

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5. Theoretical Context

This framework is conceptually related to the Nelson–Siegel (1987) and Adrian–Crump–Moench (ACM) (2013) term structure models, but is implemented using a reduced-form, macro–factor representation.
The model captures both expectations of future short-term rates and the term premium through observable macroeconomic dimensions.

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6. Implementation

• Language: Python
• Libraries: pandas, numpy, scikit-learn, statsmodels, matplotlib, plotly
• Data frequency: Monthly (2016–2025)
• Dependent variable: 10-Year Treasury Constant Maturity Rate (FRED: DGS10)

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7. Visualization

The repository includes:

• Time series of standardized macro factors
• Actual vs. model-fitted 10Y yield
• Factor contribution decomposition
• 3D PCA visualization of macro variable space

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8. References

• Diebold, F. X., & Li, C. (2006). Forecasting the Term Structure of Government Bond Yields.
• Adrian, T., Crump, R. K., & Moench, E. (2013). Pricing the Term Structure with Linear Regressions.
• Nelson, C. R., & Siegel, A. F. (1987). Parsimonious Modeling of Yield Curves.

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9. Citation

If this work is referenced, please cite as:

Papakyriakopoulos, Dimitrios. The Macroeconomic Determinants of the 10-Year Treasury Yield. (2025). GitHub Repository.

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Appendix: Figures

Figure 1. Evolution of Macro Factors (2016–2025)

The standardized PCA-derived factors (Inflation, Policy, Risk, Fiscal, Growth) display distinct temporal dynamics.
Notably, the Policy Factor rises sharply post-2021, coinciding with the U.S. monetary tightening cycle.

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Figure 2. Actual vs. Model-Fitted 10-Year Yield

The model’s fitted series tracks the actual 10-year yield with an adjusted ( R^2 = 0.807 ).
Residual deviations correspond to market shocks and structural breaks.