The Curve Prices the Fed — the Short End, Not the Long

In an efficient bond market the yield curve embeds the expected path of policy. One regression at three points on the curve: the funds rate is cointegrated with the 2-year Treasury and only spuriously correlated with the 30-year mortgage. Where it lives on the curve is the whole story.

Executive summary

The short end prices the Fed. The 2-year Treasury is cointegrated with the effective federal funds rate ( p = 0.0002); its residuals are stationary and its rolling pass-through coefficient never turns negative in 25 years. In fixed-income terms, the short end of the curve prices the expected policy path — the confirmed on the data, not assumed.
The same method fails on the long end. Regressing the 30-year fixed mortgage rate on the funds rate (monthly, Jan 2000 – Dec 2024, n = 300) yields R² = 0.656 and t = 23.8 — both misleading. A unit root in the residuals cannot be rejected ( p = 0.087) and the pair is (Engle–Granger p = 0.224): a in the Granger–Newbold sense, two persistent series drifting through the same cycle.
The 10-year absorbs whatever the funds rate had to say. Put the 10-year Treasury in the mortgage model and the fed funds coefficient collapses to 0.005 (t = 0.1) while R² does not move. Past the short end, the policy rate carries no information the curve has not already priced.
The mortgage is the foil, not the subject — the most familiar long-end instrument people attribute to the Fed, and precisely the one where the policy rate adds nothing. The 2-year’s rolling coefficient stays positive for 25 years; the mortgage’s swings to −4.77. Out of sample the mortgage-on-funds model is beaten by the most naive benchmark available: expanding-window RMSE of 0.958 versus 0.194 for “next month equals this month.”
The economically coherent reading: an efficient market prices the expected policy path into the short end of the curve, and not into the long end. To read where the Fed is going from the market, read the 2-year — not the 10-year, and not a 30-year mortgage.

Key numbers


Sample	Monthly, Jan 2000 – Dec 2024, n = 300
Baseline	Mortgage = 4.080 + 0.558 × fed funds · R² = 0.656
Cointegration, fed funds ↔ 2-year	p = 0.0002 — long-run relationship
Cointegration, fed funds ↔ 30-year mortgage	p = 0.224 — none
Fed funds β, controlling for the 10-year	0.005 (t = 0.1) — adds nothing
Rolling β range, mortgage	−4.77 to +4.86
Out-of-sample RMSE vs no-change	0.958 vs 0.194
Primary caveat	Observational data. Association, not identified causation.

Introduction and economic background

The federal funds rate is the overnight rate at which depository institutions lend reserves, and it is the FOMC’s primary policy instrument. By moving its target range, the Fed shifts short-term borrowing costs, which propagate into longer-term rates — corporate bonds, auto loans, and residential mortgages. Among those, the 30-year fixed mortgage is arguably the most economically consequential for U.S. households, since housing is the largest asset on most family balance sheets.

Three mechanisms tie policy to long-term rates. First, the of the term structure holds that a long rate reflects the market’s expectation of future short rates plus a ; when the Fed raises the overnight rate, expected future short rates rise and drag long rates with them (Mishkin). Second, the monetary-transmission channel works through originators’ cost of funds and the discount rates used to value , both sensitive to the funds rate (Bernanke and Blinder). Third, the credit channel implies that tightening raises the risk premium lenders demand, widening the spread over the benchmark.

Together these predict a positive relationship — when the funds rate rises, mortgage rates should rise — but not one-for-one, because a long rate also carries inflation expectations, a term premium, and credit spreads the FOMC does not set. And that caveat is where the real question hides. If a yield is roughly the average expected short rate over its life plus a premium, the funds rate should be visible inside the curve — and how visible should depend on where you look:

The 2-year Treasury is, to a first approximation, the market’s forecast of the average funds rate over the next two years, plus a small premium. Over a two-year horizon the Fed does not merely influence it — it substantially is it, so a tight relationship is close to definitional.
The 30-year mortgage is priced off the 10-year Treasury plus a . The 10-year embeds long-run inflation and growth expectations and a term premium the FOMC does not set; the MBS spread moves with and convexity risk, bank funding, origination economics, and the Fed’s balance sheet — none of which is the funds rate.

Schematic yield curve showing where the fed funds rate, the 2-year Treasury, the 10-year Treasury and the 30-year mortgage sit by maturity, and how the Fed's direct control fades from the overnight rate toward the long end

Exhibit A. Where the federal funds rate, the 2-year Treasury, the 10-year Treasury and the 30-year mortgage sit by maturity, and what determines each. Schematic: illustrative shape, not plotted from data — the real curve changes shape over time and can slope downward.

So the sharper question is not whether the funds rate explains the mortgage, but where on the curve the policy rate actually lives. The transmission is real, but it runs through the long end, and the long end has its own drivers — which is why a mortgage is not the policy rate plus a fixed spread. Between June 2004 and June 2006 the FOMC raised the funds rate by 396 while the 30-year mortgage moved 39 bp — and it sits inside this sample. The relationship is topical, too: the 2022–2023 tightening was one of the most aggressive in modern history, and mortgage rates ran from near 2.7% in 2020 to above 7% in 2023.

This note began as a university econometrics assignment pointed at the long end: regress the 30-year mortgage on the funds rate and interpret the output. It ran correctly and received full credit. What sent me back to it was the strength of that output — an R² of 0.66 and a t near 24 look like a finding, and I wanted to know whether they described a stable relationship or two persistent series drifting through the same cycle. Everything past the baseline — the stationarity and cointegration testing, and the 2-year and 10-year comparisons — is new work.

Hypotheses

For the baseline simple regression, Mortgage = β₀ + β₁·FedFunds + ε, the slope is tested at the α = 0.05 level:

H₀: β₁ = 0 — the funds rate has no linear effect on the 30-year mortgage rate.
H₁: β₁ ≠ 0 — a non-zero linear relationship exists.

Rejecting H₀ is evidence — statistical and economic — that the policy rate transmits, at least partly, to the cost of home financing. But a rejection is only the start of a test: on its own it cannot separate a stable, real relationship from a one between two trending series. That harder question is what the diagnostics below are built to answer.

Two schematic sketches: on the left, two wandering series whose gap stays stable around a level (cointegrated); on the right, two series that trend together before drifting apart (spurious)

Exhibit B. Two series whose gap stays stable around a level (), and two that merely trend together before drifting apart (). Schematic: illustrative sketches, not plotted from data. Both shapes can produce a high and a large , which is why fit alone cannot tell them apart.

Data and methodology

Series	FRED ID	Definition	Frequency
Federal funds	`FEDFUNDS`	Effective rate, monthly average	Monthly
30-year mortgage	`MORTGAGE30US`	Freddie Mac PMMS, US average	Weekly → monthly
2-year Treasury	`GS2`	Constant maturity, monthly average	Monthly
10-year Treasury	`GS10`	Constant maturity, monthly average	Monthly

Sample: January 2000 – December 2024, 300 monthly observations, no gaps, no duplicate dates. All series in percent. Estimation in Excel (Data Analysis ToolPak); diagnostics and replication in Python (statsmodels). The baseline was reproduced from the raw spreadsheet data — not copied from the printed output — and matches to seven decimal places.

Inference uses standard errors where reported, because the residuals are both and .

The baseline result

Over the sample the funds rate averaged 1.92% (SD 2.02%), spanning the dot-com, global-financial, and post-pandemic regimes; the 30-year mortgage averaged 5.15% (SD 1.39%). Estimated by OLS in Excel’s Data Analysis ToolPak and reproduced from the raw data, the fit is:

Mortgage rate = 4.08 + 0.56 × federal funds rate

The slope of 0.56 says each one-point rise in the funds rate is associated with a 0.56-point rise in the mortgage rate on average; the intercept of 4.08 is the fitted mortgage rate at a zero funds rate within this sample. R² = 0.66 — about two-thirds of the mortgage’s variation “explained” — with an adjusted R² of 0.65, nearly identical.

Table 1. ANOVA — OLS regression of the 30-year mortgage rate on the federal funds rate, n = 300.

Source of variation	df	SS	MS	F	Significance F
Regression	1	380.65	380.65	568.59	< 0.0001
Residual	298	199.48	0.67
Total	299	580.15

Table 2. Coefficients and significance tests.

	Coefficient	Std. error	t Stat	P-value
Intercept	4.08	0.07	62.59	< 0.0001
Federal funds rate	0.56	0.02	23.86	< 0.0001

The F-statistic is 568.59 (1 and 298 df) with Significance F < 0.0001, and the slope’s t is 23.86 — both far past the α = 0.05 threshold. On its face, H₀ is emphatically rejected. Used to forecast, the equation puts the mortgage rate at 4.08 + 0.56 × 4.33 ≈ 6.50% for a 4.33% funds rate — close to observed rates, though actual mortgages have at times run higher on elevated MBS spreads the single variable does not capture.

This is where the coursework version of this analysis stopped — and where the real question begins. Every figure above is correct. What the F-test and the t-statistic cannot tell you is whether the relationship is stable and real or a : two series trending through the same quarter-century will manufacture a high R² and a huge t whether or not any mechanism connects them. The rest of this note runs the diagnostics that separate the two — and then applies the identical method to the 2-year Treasury as a control.

The baseline does not survive the diagnostics

That t of 23.86 is the first casualty. is 0.067 against a healthy 2.0 — near-perfect , which makes the OLS standard errors far too small. Correcting with (HAC, 12 lags):

	OLS	HAC-corrected
Slope	0.558	0.558
Std. error	0.023	0.050
t-statistic	23.86	11.2

The point estimate is untouched; roughly half the apparent precision was an artifact of untreated autocorrelation. The slope still clears any conventional bar — which is why the diagnostics that follow, not the t-statistic, carry the argument.

Federal funds rate, 2-year Treasury and 30-year mortgage rate, monthly, 2000 to 2024

Exhibit 1. Federal funds effective rate, 2-year Treasury, and 30-year fixed mortgage rate. Monthly, January 2000 – December 2024, percent. Source: Federal Reserve Bank of St. Louis (FRED): FEDFUNDS, GS2; Freddie Mac MORTGAGE30US. As of Dec 2024. All three move together over the cycle — which is exactly the impression the levels regression formalises, and exactly what the diagnostics below undermine.

The same method at three points on the curve

The diagnostics on the mortgage look damning in isolation, but the sharper test is comparative: run the identical regression on the 2-year and 10-year Treasuries and see where the funds rate holds up. If the policy rate lives in the short end and not the long, the 2-year should pass the tests the mortgage fails.

Fed funds →	β	R²	Durbin–Watson	Residual ADF (p)	Cointegration (p)	Verdict
2-year Treasury	0.839	0.918	0.150	0.0000	0.0002	Cointegrated
10-year Treasury	0.485	0.566	0.068	0.092	0.234	Spurious
30-year mortgage	0.558	0.656	0.067	0.087	0.224	Spurious

The 2-year passes. The mortgage does not. Same regressor, same sample, same estimator.

In monthly changes — does a policy move actually pass through?

Fed funds →	β	HAC t	R²
2-year Treasury	0.509	8.0	0.202
30-year mortgage	0.127	2.2	0.014

Scatter plots of monthly changes in the 2-year Treasury and in the 30-year mortgage rate against monthly changes in the fed funds rate, with fitted lines

Exhibit 2. Monthly changes in the 2-year Treasury (left) and the 30-year mortgage rate (right) against monthly changes in the federal funds rate, with fitted OLS lines. Percentage points, Jan 2000 – Dec 2024. Source: FRED. HAC (Newey–West, 6 lags). The left panel has a slope you can see; the right is close to a cloud.

Does the funds rate add anything the 10-year doesn’t?

The pass-through coefficient above is small but not zero. The sharper test is whether it survives once the rate the mortgage is actually priced off — the 10-year Treasury — is in the model:

Specification (monthly changes)	R²	Fed funds coefficient
Δ Mortgage ~ Δ FedFunds	0.014	+0.127 (HAC t = 2.2)
Δ Mortgage ~ Δ 10Y	0.707	—
Δ Mortgage ~ Δ 10Y + Δ FedFunds	0.707	+0.005 (t = 0.1)

Scatter plots of monthly changes in the 30-year mortgage rate against changes in the fed funds rate and against changes in the 10-year Treasury, with fitted lines

Exhibit 3. Monthly changes in the 30-year mortgage rate against changes in the fed funds rate (left, R² = 0.014) and against changes in the 10-year Treasury (right, R² = 0.707), with fitted OLS lines. Same data, same period, same dependent variable. Source: FRED. HAC (Newey–West, 6 lags).

The third row is the finding. Add the 10-year and the fed funds coefficient falls to 0.005 with t = 0.1 — indistinguishable from zero, while R² does not move at all. The funds rate carries no information about mortgage rates that the 10-year does not already carry.

This also explains why the levels regression looked strong: fed funds and the 10-year correlate 0.75 in levels. The funds rate was standing in for the 10-year.

Robustness and limitations

Parameter stability is where the mortgage model fails hardest.

Sixty-month rolling coefficient on the fed funds rate for the 2-year Treasury and for the 30-year mortgage, by window end date

Exhibit 4. Coefficient on the federal funds rate from 60-month rolling regressions, plotted against the window’s end date. Shaded where the mortgage coefficient is negative. Source: FRED; author’s calculations. The 2-year coefficient stays positive in every window of the sample. The mortgage coefficient ranges from −4.77 to +4.86 and is negative in 15% of windows — a range of 9.6 around a full-sample “estimate” of 0.558.

The two episodes that matter most. If the 0.558 pass-through were structural, it should hold in large, sustained tightening cycles. It fails in both in the sample — and fails in opposite directions, which is the signature of a relationship that isn’t there rather than one that is merely mismeasured:

Model-predicted versus actual change in the 30-year mortgage rate across the 2004 to 2006 and 2022 to 2023 tightening cycles

Exhibit 5. Model-predicted versus realised change in the 30-year mortgage rate across the two largest tightening episodes in the sample. Source: FRED; author’s calculations. Predicted = 0.558 × Δ fed funds.

	Fed moved	Model predicted	Actual	Error
Jun 2004 – Jun 2006	+396 bp	+221 bp	+39 bp	−182 bp
Jan 2022 – Oct 2023	+525 bp	+293 bp	+417 bp	+124 bp

The first is Greenspan’s conundrum. A model that misses by 182 bp one way and 124 bp the other way in the next cycle is not describing a mechanism.

Structural breaks. reject stability at three of the four policy dates tested — December 2008 (F = 98.6), December 2015 (F = 90.6) and March 2020 (F = 19.3). The fourth, January 2022, does not reject (F = 0.6): the most recent tightening cycle did not itself break the relationship, it inherited one that was already broken.

Those four dates bound five regimes, and the coefficient is different in every one:

Regime	Window	n	β on fed funds
Pre-GFC	Jan 2000 – Nov 2008	107	0.254
	Dec 2008 – Nov 2015	84	3.674
Normalization	Dec 2015 – Feb 2020	51	0.279
COVID ZLB	Mar 2020 – Dec 2021	22	0.733
Tightening	Jan 2022 – Dec 2024	36	0.478

The full-sample 0.558 describes no actual period. It is an average of five regimes that disagree by more than a factor of ten.

Forecasting. Expanding-window validation (train on everything before t, predict t, no shuffling):

	RMSE	MAE
Regression on fed funds	0.958	0.857
No-change benchmark	0.194	0.133
Historical mean	1.673	1.598

The regression is roughly five times worse than assuming next month looks like this month. Directional accuracy is 55.3%. This model should not be used to forecast, and no forecast is offered here.

On the original point estimate. The baseline implies a 6.50% mortgage rate at a 4.33% funds rate. That number reproduces exactly — but its 95% prediction interval is [4.88%, 8.11%], a 3.2-point range spanning “housing boom” to “housing frozen.” A point estimate without that interval overstates what the model knows.

What is clean. Cook’s distance flags zero influential observations (max 0.0130 against a 4/n threshold of 0.0133). The result is not an artifact of outliers or of a single episode. The problem is the specification, not the data.

What this note does not establish. These are observational data with no identification strategy. Cointegration between the funds rate and the 2-year is a statement about a long-run statistical relationship, not a controlled experiment. The theory is consistent with the finding; it does not convert it into proof of causation.

Market implications

For reading policy: the short end is where the market prices the expected path of the funds rate, and it does so cleanly — the 2-year is the place to read policy expectations off the market, not the long end.
For duration: the short end is anchored to policy and is where policy expectations express themselves cleanly. The long end is not, and treating it as a lagged policy rate will misprice it.
For borrowers: watching FOMC meetings to time a mortgage is watching the wrong variable — a stable policy rate is entirely compatible with large moves in mortgage rates, which come from the 10-year, inflation expectations, term premium, and the MBS spread.

Where I’d put weight, and where I wouldn’t.

The 2-year Treasury contains predictive information about the expected policy path. That is closer to definitional than empirical — a 2-year yield is approximately the average federal funds rate the market expects over roughly the next two years, plus a — and the results here are consistent with it. The relationship to the funds rate is materially stronger at the 2-year than at the 10-year or the mortgage. It does not follow that the 2-year anticipates individual FOMC decisions, and I would not use it that way.

On mortgages I’d state it more narrowly. The evidence suggests transmission runs through the long end of the Treasury curve and the rather than from the policy rate directly. The Fed still affects financing conditions — nothing here says otherwise — but the transmission is indirect, variable across regimes, and not one-for-one. A stable policy rate is entirely compatible with large moves in mortgage rates.

The methodological point is the one I’d defend hardest: a high R² in a levels regression is not sufficient evidence of forecasting power. This model explains 66% of the variation in mortgage rates and still loses to “next month equals this month” out of sample by roughly five times. Fit and forecasting are different claims. Only the diagnostics and chronological out-of-sample testing separate them, and they are the part of this note I would run first next time rather than last.

What would change my mind

If the fed funds coefficient held above 0.2 with t > 2 after controlling for the 10-year in a sample excluding the zero-lower-bound years, the “adds nothing” conclusion would need revising.
If the mortgage/fed-funds pair tested cointegrated on a longer sample (1971–2024, spanning Volcker), the spurious-regression verdict would be sample-specific rather than structural.
If an error-correction specification produced stable adjustment coefficients across regimes, the instability shown here would be an artifact of the levels form rather than of the relationship.
If the regression beat a no-change benchmark out of sample at any horizon, the forecasting verdict would change.

Conclusion

The finding that matters most is not that the federal funds rate is irrelevant. It is that monetary policy anchors the short end of the curve far more directly than the long end. The 2-year Treasury largely reflects the expected policy path. A 30-year mortgage absorbs that too, and then adds long-run inflation expectations, growth expectations, a term premium the FOMC does not set, and an MBS spread with drivers of its own. Same regressor, same sample, same estimator — and the answer depends almost entirely on where you point it.

The mortgage earns its place in this note as the counter-case. The coursework model it began as was correct for what it was asked to do: as an exercise in estimating and interpreting a bivariate regression it was executed properly, and I would run it the same way again for that purpose. Held to a research standard it does not survive — a unit root in the residuals cannot be rejected, the two series are not , the coefficient is unstable to the point of changing sign, and out of sample the model loses to the most naive benchmark available. The simple mortgage-levels regression should not be treated as a reliable forecasting model, and I am not treating it as one.

That is the part I’d carry forward. Statistical significance is the start of a test, not the end of one. Before a model is used to forecast anything, or to justify a position, it has to survive the diagnostics that ask whether the relationship it describes is stable and real. This one didn’t — and establishing that was worth more than the original result was.

Methodology appendix

Baseline. OLS, levels: MORTGAGE30US ~ α + β·FEDFUNDS. n = 300. Reproduced from raw data: Multiple R 0.810015, R² 0.656124, Adj R² 0.654970, SE 0.818204, intercept 4.079982, β 0.557938 (SE 0.023398), t 23.845, F 568.591, Significance F 4.78 × 10⁻⁷¹. ANOVA: SS regression 380.6477 (df 1), SS residual 199.4986 (df 298), SS total 580.1463 (df 299). 95% CI on β: [0.512, 0.604].

On the intercept. 4.080 is the model’s fitted value at a zero funds rate within this sample. It is not a structural “natural” mortgage rate, and the sample contains only the 2009–15 and 2020–21 episodes near zero to inform it.

Diagnostics. Durbin–Watson 0.067; residual AR(1) 0.966; Ljung–Box rejects at lags 1, 6, 12 (p < 1e-60). Breusch–Pagan p = 0.002 and White p = 2.2e-09 (heteroskedastic). Jarque–Bera p = 0.012 (skew 0.291, kurtosis 2.396). ADF: FEDFUNDS stationary (p = 0.001), MORTGAGE30US non-stationary (p = 0.223); KPSS agrees on both. Regressing an I(1) series on an I(0) series is unbalanced. Engle–Granger: mortgage p = 0.224, 2-year p = 0.0002.

Robustness. First differences; 3-lag distributed lag (cumulative 4-month pass-through 0.172, no individual lag significant); multiple regression including GS10; 60-month rolling windows; Chow tests at four policy dates; five regime subsamples; expanding-window out-of-sample validation against no-change and historical-mean benchmarks.

Specifications, stated so the figures above can be reproduced rather than taken on trust. Cointegration is Engle–Granger with the target regressed on the funds rate — the test is not symmetric, and reversing the arguments changes the mortgage p-value from 0.224 to 0.070. Residual AR(1) is the lag-1 autocorrelation of the residual series (0.9664), consistent with the 1 − DW/2 approximation. Regime subsamples are bounded by the Chow break dates, not by calendar years: pre-GFC is Jan 2000 – Nov 2008, the zero-lower-bound era is Dec 2008 – Nov 2015, and the tightening cycle is Jan 2022 – Dec 2024. Out-of-sample validation uses a 120-month burn-in and then expands one month at a time — train on everything strictly before t, predict t, never shuffle — giving 180 chronological predictions. Directional accuracy compares the sign of the change in the model’s prediction against the sign of the change in the realised rate, on the same 180 predictions.

Reproducibility. Every series is public and free from FRED — no paid data, no API key. Both workbooks are downloadable:

Original regression workbook (.xlsx) — the estimation as first run, in Excel, unmodified.
Methodology workbook (.xlsx) — README, raw data, baseline (live formulas), diagnostics, robustness, and sources.

Sources

Board of Governors of the Federal Reserve System. Federal Funds Effective Rate [FEDFUNDS]. FRED, Federal Reserve Bank of St. Louis. https://fred.stlouisfed.org/series/FEDFUNDS
Freddie Mac. 30-Year Fixed Rate Mortgage Average in the United States [MORTGAGE30US]. FRED. https://fred.stlouisfed.org/series/MORTGAGE30US
Board of Governors. Market Yield on U.S. Treasury Securities at 2-Year Constant Maturity [GS2]. FRED. https://fred.stlouisfed.org/series/GS2
Board of Governors. Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity [GS10]. FRED. https://fred.stlouisfed.org/series/GS10
Bernanke, Ben S., and Alan S. Blinder. “The Federal Funds Rate and the Channels of Monetary Transmission.” American Economic Review, vol. 82, no. 4, 1992, pp. 901–921.
Granger, C.W.J., and P. Newbold. “Spurious Regressions in Econometrics.” Journal of Econometrics, vol. 2, no. 2, 1974, pp. 111–120.
Engle, Robert F., and C.W.J. Granger. “Co-Integration and Error Correction: Representation, Estimation, and Testing.” Econometrica, vol. 55, no. 2, 1987, pp. 251–276.
Newey, Whitney K., and Kenneth D. West. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, vol. 55, no. 3, 1987, pp. 703–708.

This note revises an earlier version of my own analysis — a university econometrics assignment from March 2026 — which reported the levels regression without stationarity or autocorrelation diagnostics and concluded that changes in the funds rate “reliably translate” into mortgage costs. The data does not support that conclusion, and this note supersedes it. The assignment contained the baseline regression only; the diagnostics, the cointegration testing and the Treasury comparisons are new work.

Ken Capital is an independent investment-research portfolio. This note is personal research and not investment advice. Estimation sample ends December 2024; no current-market values are stated.