Greenslade-Pierse-Saleheen (2003) A Kalman Filter Approach to Estimating the UK NAIRU

Summary

Greenslade, Pierse and Saleheen apply Gordon's (1997) US triangle model to the UK, jointly estimating an accelerationist Phillips curve and a random-walk NAIRU (Non-Accelerating Inflation Rate of Unemployment) via the Kalman filter over 1973 Q1–2000 Q4. The resulting NAIRU profiles peak in the mid-1980s (~9–10%) and decline to ~5–6% by 2000, broadly consistent with structural estimates; the models show UK unemployment below the NAIRU for most of 1997–2000, with temporary import-price deflation offsetting roughly 1 percentage point (pp) of inflation pressure. Confidence intervals are very wide throughout.

Key Claims

• Model: Triangle Phillips curve in first-differences of inflation (to impose dynamic homogeneity); state equation is a random walk for $u^*_t$; signal-to-noise ratio (SNR) restricted to $\sigma^2_\eta = 0.16$ (from Gordon 1997) since free estimation yields implausibly volatile NAIRU.
• Preferred RPIX (Retail Prices Index excluding mortgage interest payments) model (Model 2): $\Delta^2\pi_t = \alpha\Delta\pi_{t-4} + \beta(u_{t-1}-u^*_{t-1}) + \gamma_1\Delta z^{\text{imp}}_{t-1} + \gamma_2\Delta z^{\text{imp}}_{t-4} + \gamma_3\Delta z^{\text{oil}}_{t-4} + \varepsilon_t$; estimated gap coefficient $\beta \approx -0.43$ (t-stat −4.74).
• Unemployment gap dominance: Once lagged gap is included, contemporaneous gap becomes insignificant; further lags also insignificant — lag t-1 dominates across all specifications.
• Supply shocks significant: Real import price inflation (t-1 and t-4) and real oil price inflation (t-3 or t-4) all significant; likelihood-ratio (LR) tests reject exclusion of any supply variable.
• NAIRU profile: Rose from ~7% (1973) to ~9–10% (mid-1985); fell to ~5–6% by 2000. Broadly consistent with Coulton-Cromb (1994) structural estimates. RPIX-based estimates slightly higher than Average Earnings Index (AEI) estimates.
• Supply shock contribution: Falling real import prices post-1996 (sterling appreciation) contributed approximately −1 pp to RPIX inflation 1997–2000, more than offsetting upward unemployment gap pressure.
• Earnings models: AEI and wages-and-salaries per employee give similar NAIRU profiles; productivity growth significant as separate regressor; real oil prices not significant in earnings models.
• Sensitivity to SNR: Signal-to-noise ratio varies profile level but turning points are robust across $\sigma^2_\eta \in \{0.04, 0.09, 0.16, 0.25\}$.
• Wide uncertainty: 90% and 95% confidence intervals from Kalman smoother are very wide, confirming Staiger-Stock-Watson (SSW, 1997) finding; authors caution against any single NAIRU point estimate.
• Distinction natural rate vs. NAIRU: Natural rate determined by structural factors (union density, replacement ratio); NAIRU is reduced-form and may reflect adjustment to shocks. These converge in the long run.

Concepts Introduced or Extended

• NAIRU
• Phillips Curve
• Kalman Filter
• State-Space Representation

Entities Mentioned

• Jennifer Greenslade
• Richard Pierse
• Jumana Saleheen
• Robert J. Gordon

Quotes

"even though there may be uncertainty about the level of the NAIRU, a range of specifications and assumptions tend to suggest that the NAIRU was falling through the 1990s"

"we would not place weight on any particular point estimate for the NAIRU"

My Take

A solid, carefully executed application of Gordon's US framework to UK data. The paper adds value mainly through the multi-model sensitivity analysis and the explicit decomposition of inflation into gap, inertia, and supply-shock contributions. The signal-to-noise restriction choice (copying Gordon's US value of 0.16) is pragmatic but ad hoc for the UK — the paper acknowledges this honestly. The wide confidence intervals underscore that Kalman-filter NAIRU estimates are more useful for directional signals than point estimates. Does not address the Bank of England's move to inflation targeting or the 1997 independence shock, which the authors note may be confounded with the NAIRU path.