Among the several concepts encompassed by the idea of an equilibrium rate of unemployment (labour mismatch, unemployment trend, non inflationary unemployment, structural unemployment), the NAIRU appears as the more interesting one for a central bank since it focuses directly on inflation. Thus, the paper considers the reduced Phillips equation, assuming a stable relationship between inflation and some kind of demand desequilibrium index, as the most promising starting point to estimate an equilibrium rate of unemployment. We adopt a semi-structural method based on a combination of an economic and a statistical approach. The Phillips equation we consider is very close to the so-called "triangle model" suggested by Gordon, where inflation rate is determined by three factors (hence the "triangle") : adaptive expectations and inertia, excess demand or shortage - estimated by the gap between the actual unemployment rate and the NAIRU - and supply shock variables. We regard the NAIRU as a time-varying parameter and estimate a state space model composed of a random walk process that describes its variations over time and of a Phillips equation. Under reasonable assumptions on the innovations to the NAIRU equation, the estimation of the state-space model (using Kalman filter techniques) yields empirical results for France that appear quite convincing: the time varying NAIRU we obtain accounts for the steady increase in the actual unemployment rate during the 1970s and the 1980s and offers the appropriate degree of smoothness. Working on the sample 1986-1999 the time varying NAIRU amounts to 10% in the second quarter of 1999 (with an interval confidence between 9% and 11%). The estimation of the model since 1970 gives information on the path followed by the NAIRU during the last decades. Whereas the NAIRU increased by 2.7 points between 1977 and 1988, its steady rise seems to slow down somewhat since the second part of the 1980s, exhibiting two main deceleration periods: first during the second part of the 1980s and second in the mid-1990s. Though this method exploits the set of information contained in the Phillips curve and provides fairly robust measures of the NAIRU, it gives little insight regarding its underlying determinants. It must therefore be completed by the analysis of the recent developments in French labour market. In the second part of this paper, we provide strong evidence that the changes in the NAIRU in France during these two episodes may be linked to significant shifts in the demographic composition of the workforce together with a break in the evolution of the fiscal-social wedge. Several other factors (such as threshold effects in unemployment benefits or individual abilities) play probably a major role in unemployment variation.