Editing Phillips curve (section)

====Money wage determination====
The traditional Phillips curve story starts with a wage Phillips curve, of the sort described by Phillips himself. This describes the rate of growth of money wages (''gW''). Here and below, the operator ''g'' is the equivalent of "the percentage rate of growth of" the variable that follows.
:<math>gW = gW^T - f(U)</math>
The "money wage rate" (''W'') is shorthand for total money wage costs per production employee, including benefits and payroll taxes. The focus is on only production workers' money wages, because (as discussed below) these costs are crucial to pricing decisions by the firms.

This equation tells us that the growth of money wages rises with the trend rate of growth of money wages (indicated by the superscript ''T'') and falls with the unemployment rate (''U''). The function ''f'' is assumed to be [[Monotonic function|monotonically]] increasing with ''U'' so that the dampening of money-wage increases by unemployment is shown by the negative sign in the equation above.

There are several possible stories behind this equation. A major one is that money wages are set by ''bilateral negotiations'' under partial [[bilateral monopoly]]: as the unemployment rate rises, ''all else constant'' worker bargaining power falls, so that workers are less able to increase their wages in the face of employer resistance.

During the 1970s, this story had to be modified, because (as the late [[Abba Lerner]] had suggested in the 1940s) workers try to keep up with inflation. Since the 1970s, the  equation has been changed to introduce the role of inflationary expectations (or the expected inflation rate, ''gP''<sup>ex</sup>). This produces the expectations-augmented wage Phillips curve:

:<math>gW = gW^T - f(U) + \lambda gP^\text{ex}.</math>

The introduction of inflationary expectations into the equation implies that actual inflation can ''feed back'' into inflationary expectations and thus cause further inflation. The late economist [[James Tobin]] dubbed the last term "inflationary inertia", because in the current period, inflation exists which represents an inflationary impulse left over from the past.

It also involved much more than expectations, including the price-wage spiral. In this spiral, employers try to protect profits by raising their prices and employees try to keep up with inflation to protect their real wages. This process can feed on itself, becoming a self-fulfilling prophecy.

The parameter '''λ''' (which is presumed constant during any time period) represents the degree to which employees can gain money wage increases to keep up with expected inflation, preventing a fall in expected real wages. It is usually assumed that this parameter equals 1 in the long run.

In addition, the function '''f'''() was modified to introduce the idea of the [[non-accelerating inflation rate of unemployment]] (NAIRU) or what's sometimes called the "natural" rate of unemployment or the
inflation-threshold unemployment rate:
{{NumBlk|:|<math>gW = gW^T-f(U-U^*)+\lambda gP^\text{ex}.</math>|{{EquationRef|1}}}}
Here, ''U*'' is the NAIRU. As discussed below, if ''U'' < ''U''*, inflation tends to accelerate. Similarly, if ''U'' > ''U''*, inflation tends to slow. It is assumed that ''f''(0) = 0, so that when ''U'' = ''U''*, the ''f'' term drops out of the equation.

In equation ({{EquationNote|1}}), the roles of  '''gW<sup>T</sup>''' and '''gP<sup>ex</sup>''' seem to be redundant, playing much the same role. However, assuming that '''λ'''  is equal to unity, it can be seen that they are not. If the trend rate of growth of money wages equals zero, then the case where '''U''' equals '''U*''' implies that '''gW''' equals expected inflation. That is, expected real wages are constant.

In any reasonable economy, however, having constant expected real wages could only be consistent with actual real wages that are constant over the long haul.  This does not fit with economic experience in the U.S. or any other major industrial country. Even though real wages have not risen much in recent years, there have been important increases over the decades.

An alternative is to assume that the trend rate of growth of money wages equals the trend rate of growth of average labor productivity ('''Z'''). That is:
{{NumBlk|:|<math>gW^T=gZ^T.</math>|{{EquationRef|2}}}}

Under assumption ({{EquationNote|2}}), when '''U''' equals '''U*''' and '''λ''' equals unity, expected real wages would increase with labor productivity. This would be consistent with an economy in which actual real wages increase with labor productivity. Deviations of real-wage trends from those of labor productivity might be explained by reference to other variables in the model.