Zhao-Hogan (2011) Measuring the NAIRU – A Structural VAR Approach

Summary

Zhao applies the Blanchard-Quah (1989) long-run identifying restriction to a bivariate vector autoregression (VAR) in first-differenced inflation and unemployment to estimate the time-varying U.S. Non-Accelerating Inflation Rate of Unemployment (NAIRU) over 1960–2000. The NAIRU disturbance is defined as the component of unemployment with no long-run effect on inflation; it explains less than 10% of inflation variation but pins down a NAIRU that fell sharply from roughly 7% to 3% between 1993 and 2000, implying a long-run Phillips Curve shift from 6.8% to 4% around 1997. Bootstrap standard error bands are tighter than those from simpler approaches.

Key Claims

• NAIRU is identified as the component of unemployment uncorrelated with inflation in the long run: the NAIRU structural disturbance has zero cumulated (long-run) effect on inflation.
• Bivariate system $(\Delta\pi_t, u_t)$: inflation enters first-differenced ($I(1)$ by Augmented Dickey-Fuller (ADF) test); unemployment stationary; 4 annual lags by Likelihood Ratio (LR) test; exogenous controls absorb supply shocks (constant, linear and quadratic time trend, $\Delta$import prices, $\Delta$unit labour costs).
• Long-run Vector Moving Average (VMA) representation $X_t = C(L)\varepsilon_t$ recovered from VAR; long-run restriction gives the 4th equation needed to exactly identify $C(0)$.
• Two uncorrelated unit-variance structural disturbances: $\varepsilon_1$ (NAIRU disturbance, $\approx$ aggregate supply; no long-run inflation effect) and $\varepsilon_2$ (gap disturbance, $\approx$ aggregate demand; permanent inflation effect).
• NAIRU = counterfactual path of $u_t$ when $\varepsilon_2 \equiv 0$; core inflation = counterfactual path of $\pi_t$ when $\varepsilon_1 \equiv 0$.
• U.S. NAIRU stable at 6–8% through 1993; falls sharply to ~3% by 2000. Long-run Phillips Curve shifts from 6.8% (pre-1997) to 4% (post-1997).
• NAIRU disturbance explains < 10% of inflation forecast-error variance; gap disturbance dominates.
• NAIRU shock Impulse Response Function (IRF): inflation initially falls 0.4%, rises and peaks at year 3, then returns to baseline — oscillatory but long-run neutral. Gap shock: permanent +0.8% inflation (peak year 1); unemployment takes 4+ years to recover.
• 95% bootstrap bands ~1.6–2% wide (1,000 replications) — tighter than univariate Phillips Curve (2.6%) or plain bivariate model (2.3%).
• Core inflation path (when $\varepsilon_1 = 0$) closely parallels the Quah-Vahey (1995) decomposition.

Concepts Introduced or Extended

• NAIRU
• Phillips Curve
• Structural Identification
• Vector Autoregression
• Impulse Response Function
• Variance Decomposition

Entities Mentioned

• Hongmei Zhao

Quotes

"The NAIRU is defined as the level of unemployment that would occur if there were no demand shocks — that is, the level consistent with stable inflation in the long run."

My Take

A clean, textbook-level application of Blanchard-Quah identification to the inflation-unemployment system. The long-run restriction is economically compelling given a vertical long-run Phillips Curve and requires minimal auxiliary assumptions. The dramatic NAIRU decline in the 1990s is the headline finding, though the wide uncertainty bands (1.6–2%) remind us that real-time NAIRU estimation is highly imprecise. No author affiliation or date is given; the paper appears to be an unpublished working paper and may be a student exercise, but the methodology and results are internally consistent.