The pure expectations hypothesis dies in three different ways in PL, US and EA

The pure expectations hypothesis (PEH) of the term structure says that long-maturity yields are the average of expected future short rates plus a constant term premium. The sharpest empirical implementation of this is the Fama-Bliss type-1 (FB1) regression: regress future yield changes on the appropriately scaled forward-spot spread. Under PEH, the population value of the slope coefficient β is exactly one and the intercept is exactly zero.

Forty years of US evidence has rejected PEH on the FB1 grid, with β estimates that drift toward and even past zero rather than toward one. The Polish question is whether a less-liquid sovereign curve looks more like the US or more like the euro area, the two natural benchmarks. The answer turns out to be different from both: PL drifts mildly anti-PEH (β below zero on most cells), US sits roughly consistent with PEH at long horizons, and EA strongly overshoots β = 1 — but most of the EA rejection vanishes under a wild block bootstrap.

Across 90 individual (h, n) pair tests on each market, the pattern is clean. The Polish curve is the closest of the three to violating PEH on the "wrong side" — βs that cluster around zero or slightly below — while the US drifts toward β = 1 only at horizons of 36 months and longer. The euro area is where the asymptotic-bootstrap gap really matters: 75 of 90 NW rejections collapse to 4 under the wild bootstrap, an 18-fold reduction.

The cross-market table is the headline. The Polish curve never rejects PEH on either inference method — but that is not because PEH holds; it is because the Polish FB1 βs cluster on the "wrong side" of zero with very wide standard errors. The US rejects PEH on six of 90 cells under NW and on zero cells under bootstrap. The euro area rejects on 75 cells under NW and on four under bootstrap, an 18-fold collapse that is the cleanest example in our sample of the Bauer-Hamilton (2018) concern about asymptotic inference in overlapping-return regressions with persistent regressors.

The implication for the Polish curve is that one should not over-interpret the absence of rejection. Polish FB1 βs sit in a regime that is at least as far from PEH as the US ones, just on the other side of zero, and the failure to reject is mostly a function of sample size and persistence of the forward-spread regressor.