Campbell-Shiller Yield Curve Regressions

Suppose the ten-year yield sits a full percentage point above the two-year yield. Does that steepness tell you anything about where short-term rates are going over the next couple of years? A trader's gut answer is "yes, rates should rise, otherwise why would anyone lend long at a premium." The Campbell-Shiller regression is the blunt way of checking whether the data agrees.

Think of the yield curve as a market forecast, the way a five-day weather chart implies tomorrow's temperature. If the curve is a good forecaster, a steep slope today should be systematically followed by rising short rates. Campbell and Shiller simply ran that forecast against what actually happened and graded it.

Setting up the test

Start from the expectations hypothesis (EH): a long-term rate is roughly the average of expected future short rates, plus maybe a constant premium. Rearranged, EH makes a sharp prediction — the current slope between an $n$-year yield and a shorter yield should forecast the change in that shorter yield over the life of the spread, one-for-one.

Campbell and Shiller turned this into a regression you can run on a spreadsheet:

$$y_{t+1}^{(n-1)} - y_t^{(n)} = \alpha + \beta \cdot \frac{1}{n-1}\left(y_t^{(n)} - y_t^{(1)}\right) + \varepsilon_{t+1}.$$

In words: take the change in a bond's own yield over the next period, and regress it on today's slope between that bond's yield and the short rate, scaled by the time to maturity. Under EH, the theory says $\beta$ should equal 1. If long rates are unbiased forecasts of future short rates, a steeper curve today should be followed by yield changes that match the slope exactly.

What the data actually says

Run this regression on decades of Treasury data and $\beta$ does not come out near 1. It typically comes out negative, often around $-1$ to $-3$ depending on the maturity pair and sample period. A steep curve tends to be followed not by rising long yields (as EH predicts) but by long yields falling relative to what the slope implied — bond prices rise, i.e. long bonds richen when the curve is steep.

Worked example. Say the two-year yield is 3.5% and the ten-year yield is 5.0%, so the slope term is $(5.0 - 3.5)/8 = 0.19$ per year (scaled by $n-1=8$ years to maturity beyond the short leg, a simplified version of the actual regressor). EH says the ten-year yield should drift up by roughly 0.19 percentage points per year going forward. Suppose instead that, on average across many such steep-curve episodes in the sample, the ten-year yield actually fell by 0.30 points over the following year. Fitting $\beta$ across many such episodes gives something like $\beta \approx -1.5$: not just wrong in size, wrong in sign.

Second example, with numbers you can check by hand. Take five stylized quarters of two-year and ten-year yields: slopes of 0.5%, 1.0%, 1.5%, 0.8%, 0.3%, followed one quarter later by yield changes of $+0.1\%$, $-0.4\%$, $-0.9\%$, $-0.1\%$, $+0.2\%$. Plotting slope on the x-axis and next-quarter change on the y-axis, the best-fit line tilts downward — exactly the sign flip that shows up in the real data, and precisely why the regression, not intuition, is the test that matters.

What this means in practice

A negative $\beta$ does not mean the yield curve is useless — it means the slope is dominated by a time-varying term premium, compensation investors demand for holding duration risk, which moves around for reasons unrelated to expected future rates. When the curve steepens because term premium has risen (not because the market expects hikes), betting on EH loses money. This is the empirical backbone of duration-timing strategies: a steep curve, on average, has historically been a better signal to buy duration than to sell it, the opposite of naive EH intuition.