Gordon (1997) estimates a time-varying Non-Accelerating Inflation Rate of Unemployment (TV-NAIRU) within the "triangle model" of inflation using state-space maximum likelihood via the Kalman filter. The key innovation is a smoothness prior: is chosen to keep the NAIRU from zig-zagging implausibly quarter-to-quarter, on the economic ground that the no-supply-shock NAIRU reflects slowly-moving microeconomic market structure. Estimated U.S. NAIRU (GDP deflator): 6.0% (mid-1950s) → 5.3% (1962) → 6.2% plateau (1967–72) → 6.5% hump (1978–82) → 5.6% (mid-1996). The inflation-acceleration cost of a sustained 1-percentage-point unemployment gap is only 0.32% per year.
Triangle model of inflation (Gordon 1975, 1982): inflation depends on three sides — inertia, excess demand, and supply shocks: The natural-rate restriction constrains (vertical long-run Phillips curve). Supply shocks include changes in relative import prices, relative food-energy prices, Nixon price-control on/off dummies, and the deviation of productivity growth from trend. No constant is included; the unemployment gap variable absorbs the intercept.
State equation for time-varying NAIRU: The NAIRU is a random walk. is the tuning parameter controlling smoothness. Estimated by maximum likelihood via Hamilton (1994) Kalman filter; sample 1955:Q2–1996:Q2 (165 quarters).
Smoothness prior: is preferred. At : NAIRU constant at 6.0%. At : implausibly volatile, with quarter-to-quarter zig-zags inconsistent with a NAIRU that reflects "the Walrasian microeconomic relations of the economy" (Friedman 1968). The economic argument for slow variation selects the smoothness parameter, bypassing the statistical indistinguishability of alternative NAIRU series.
TV-NAIRU path (GDP deflator, ): declines from 6.0% (mid-1950s) to a minimum of 5.3% (circa 1962), rises to a plateau of ~6.2% (1967–72), declines briefly 1972–75, humps to ~6.5% (1978–82), then drifts down to 5.6% by mid-1996. Supply shocks are essential: without supply variables, the 1970s NAIRU would be estimated at ~7% to absorb the unmodelled oil-price inflation.
Regression results (Table 1, 1955:Q2–1996:Q2):
Dynamic simulation validation: Estimated through 1987:Q3, simulated dynamically 1987:Q4–1996:Q2. root mean squared error (RMSE) = 0.7% (smaller than in-sample SEE = 0.9%); mean error only 0.07% in 1994–96. The stability of the triangle model across 40+ years of data is a central validation claim.
Inflation acceleration: If unemployment falls 1 percentage point below the NAIRU permanently starting 1996:Q3, inflation rises from 2.2% to only 5.3% by 2005 — an acceleration of 0.32% per year. The distributed-lag structure (24 quarterly lags of inflation) substantially slows the adjustment; the effective multiplier is the coefficient divided by the sum of inflation-lag denominators, not itself.
Critique of Staiger-Stock-Watson (SSW, 1996/1997): SSW's 95% confidence interval for the 1990 NAIRU (5.1%–7.7%) "makes no economic sense" — a NAIRU of 5.1% is inconsistent with the 1987–90 inflation acceleration (actual unemployment never fell below 5.1%); a NAIRU of 7.7% is inconsistent with the 1990–93 deceleration (unemployment never exceeded 7.7%). Gordon proposes using an economic criterion (smoothness) rather than a statistical criterion to distinguish among NAIRU series.
NAIRU drivers: Late-1960s rise attributed to labor militancy, high minimum wage, rising labor share. 1990s decline attributed to weak unions, global competition, immigration, and falling computer prices (by mid-1996 cutting ~0.4 pp from the TV-NAIRUs). The NAIRU is a random walk, so the recent decline is not predictable to continue — equal probability of reversing.
Policy assessment: Fed in 1995–96 was "almost precisely on target," with average unemployment 5.6% ≈ TV-NAIRU 5.7% (GDP deflator). NAIRU decline implies potential output growing ~0.1 pp/yr faster than a fixed-6% NAIRU would suggest — far short of "growth hawks" who claim 3%+ potential growth.
"Staiger, Stock and Watson (1996, p. 2) have cast doubt on the enterprise of estimating the NAIRU, concluding that 'a typical 95% confidence interval for the NAIRU in 1990 is 5.1 percent to 7.7 percent. . . . This imprecision suggests caution in using the NAIRU to guide monetary policy.' . . . The recent suggestion . . . that the NAIRU for the year 1990 could range from 5.1 to 7.7 percent makes no economic sense." (pp. 21, 29)
"I propose using a 'smoothness' prior: the NAIRU can move around as much as it likes, subject to the qualification that sharp quarter-to-quarter zig-zags are ruled out." (p. 22)
The key methodological contribution is the smoothness-prior argument: when multiple NAIRU series are statistically indistinguishable, use an economic criterion (slow-moving market structure) to select among them. This is a principled alternative to SSW's statistical criterion (report a wide confidence interval) and predates later Bayesian approaches to the same problem. The Gordon-SSW debate is partly a debate about what the NAIRU concept is for: SSW treat it as a statistical object with well-characterised uncertainty; Gordon treats it as an economic concept with an implied smoothness that the data cannot separately identify. Both are legitimate. The triangle model's extraordinary out-of-sample performance (RMSE 0.7% over 9 years out-of-sample, smaller than in-sample SEE) is genuinely impressive and provides strong validation. The main caveat is that Gordon conditions on one "proper model" and ignores parameter uncertainty, which is precisely what SSW are measuring. The 1997 paper is the lean, policy-oriented companion to the more detailed Gordon (2005) structural decomposition.