Expectations hypothesis tests on the Polish sovereign curve
Standard expectations-hypothesis (EH) testing battery applied to the LW-NSS Polish zero-coupon panel and benchmarked against US (GSW) and euro-area AAA. Includes Fama-Bliss FB1 and FB2 regressions, Cochrane-Piazzesi single and seagull tent factors, an out-of-sample STV exercise against a random walk, and the cross-market PL/US/EA pooled robustness.
Fama-Bliss FB1 — β heatmap
Slope coefficient β from y_n(t+h) − y_n(t) = α + β · [(n/(n−h)) · (y_n(t) − y_h(t))] + ε across forecasting horizons (h, in months) and bond maturities (n, in months). Under the pure expectations hypothesis β = 1. Click a cell to see the underlying regression.
Fama-Bliss FB2 — β heatmap
Holding-period type-2 specification: return on n-bond − h-yield = α + β · forward spread + ε. Under EH, β = 0. Strong departures from zero indicate predictable excess returns.
Cochrane-Piazzesi single-factor regressions
Second-stage one-year-ahead excess-return regressions on the CP single factor (one-year-ahead forward-rate combination from the first-stage tent). Coefficients should rise monotonically with maturity if a single factor prices the term structure.
Cross-market FB1 — PL vs US vs EA
Side-by-side β coefficients from FB1 across markets at common (n,h) cells, holding the regression specification constant. Sharp dispersion across markets is the cross-market evidence against EH.
Out-of-sample STV — pure-EH path versus random walk
Diebold-Mariano test of the pure-expectations-hypothesis short-rate path against a random-walk benchmark, h months ahead. Negative DM with low p-value means the EH path beats the random walk; positive DM means the random walk wins. Higher rejection counts mean the EH-implied path is informationally weaker.
FB1 — PL detailed table
Top-20 (n, h) cells from the PL FB1 panel sorted by |β − 1|. Highlighted rows are PEH rejections at 5% Newey-West.
| h (months) | n (months) | n_obs | α | SE(α) | p(α) | β | SE(β) | p(β=1) | R² | NW reject |
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Methodology: FB1 = Fama-Bliss (1987) yield-change regression; FB2 = Fama-Bliss holding-period regression; CP = Cochrane-Piazzesi (2005) single-factor and seagull tent regressions; OOS-STV = expanding-window short-rate prediction comparison à la Sarno-Thornton-Valente (2007). All standard errors are Newey-West with bandwidth = h months. Cross-market cells use the same specification on US (GSW Treasury) and euro-area AAA panels for direct comparison. See about page for the full EH-paper methodology.