Simon Wren-Lewis has a post discussing the NAIRU. He acknowledges that it has its problems but struggles to find a good alternative.
The idea with the NAIRU is that, when unemployment falls below that level, we don't simply have a higher rate of inflation, we have an ever increasing rate of inflation.
The theory here is that wage inflation reflects an attempt by workers to secure a particular real wage, based on their expectations of price inflation. If they are thwarted by price inflation higher than expected they will revise their expectations and increase their demands.
However, whilst wage inflation may sometimes be driven by real wage concerns, it is not clear this should generally the case. Particularly at lower levels of inflation, changes in aggregate wages may have little to do with real wage considerations.
First of all, it is worth noting that the inflation rate, and the rate of wage inflation, are aggregate figures. At any time, some firms will be facing supply constraints and will be bidding up wages. Others will find themselves with excess capacity and will be holding wages constant (or in rare cases, cutting them). The balance will vary with the level of aggregate demand. There isn't a single labour market and a single wage.
One of the reasons why the idea of a single wage might be unhelpful is to do with nominal wage rigidity. On the whole, wages are not subject to constant revision. An individual worker's wage is fixed when he is first employed and then only changed when there is sufficient reason to do so.
At low inflation rates, therefore, most wage inflation arises from the turnover in jobs, where some firms are hiring and others are firing. The lower the level of unemployment, the more that turnover requires hiring firms tempting workers to change jobs, rather than simply drawing on the pool of unemployed. This requires greater wage differentials.
Actual cuts in nominal wages are unusual. Having greater wage differentials therefore requires having a higher minimum average level wage inflation when unemployment is lower. The higher average means the wages that are growing the least are not actually falling.
Real wages play no role in this. It is all to do with relative wages. So there's no question of foiled expectations or any reason to think that this inflation should accelerate.
All this means that, at low rates of inflation, we may well have some kind of trade-off between unemployment and inflation, rather than the accelerating inflation dictated by the NAIRU. However, if higher rates of inflation become the norm, this kind of relationship may break down. If the average rate of wage inflation is high, then cuts in relative wages can be easily achieved simply by holding some nominal wages fixed for longer. The pay-off between inflation and unemployment depends on the reluctance to cut nominal wages being relevant.
Furthermore, if it becomes normal to frequently adjust wages to compensate for price inflation, then some measure of indexed wages starts to replace the fixed nominal anchor as the benchmark for relative wage competition.
So, accelerating inflation may still be a trap to fall into. However, as conceived here, this does not simply arise from venturing past the NAIRU. It comes from allowing inflation to persist at too high a level and for too long. It is true that this could come from trying to achieve excessively low unemployment. But wages are not the only factor in determining price inflation. Things like exchange rates and world commodity prices also play a role. On the whole, it should be no surprise that it is difficult for advocates of the NAIRU to pin down what the level of the NAIRU actually is.