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Inflation is determined by movements in both prices and wages. During the 1990s, price increases remained in check due to rising productivity growth and favorable supply shocks. But since this event occurred during a period of rising productivity growth and declining unemployment, wage stability requires a more nuanced explanation. Macroeconomic theory traditionally has assumed that, in the short run, low unemployment rates give workers a bargaining advantage relative to capital. It is expected that workers should be able to demand and receive higher wages given the scarcity of employable labor and the rising demand for that labor. This process is expected to result in greater rates of inflation, assuming that firms pass on higher labor costs to consumers via a markup over unit labor costs.

Phillips Curve Models of Inflation
Phillips noted an abundance of statistical evidence from the United Kingdom that supported the hypothesis that the rate of change of money wage rates can be explained by the level of unemployment and the rate of change of unemployment (299). When labor is scarce and its demand is high, excess demand is created and market forces will lead to employersbidding more vigorously for the services of labor. During periods when labor is in high supply relative to demand, excess supply is created and employers will be less inclined to grant wage increases, and workers will be in a weaker position to press for them (283). The result of this dynamic is increasing nominal wage growth when unemployment is low or decreasing and declining nominal wage growth when unemployment is high or increasing.

Samuelson and Solow applied Phillips analysis to the United States and found a negative relationship between the unemployment rate and the rates of wage and price inflation. Their findings suggested a menu of choice between different degrees of unemployment and price stability (192). Policy makers could choose the combination of unemployment and inflation that was desired by stimulating or depressing aggregate demand. This could be accomplished by fine-tuning both fiscal and monetary policy to produce the preferred outcome.

In response, Phelps and Friedman augmented Phillips analysis with inflation expectations and argued that Samuelson and Solows menu of choice was only possible in the short run. Friedman forcefully asserted that there is no permanent trade-off in the long run (11). In the long run, the menu of choice disappears as the economy tends toward its natural rate of unemployment or the non-accelerating inflation rate of unemployment (NAIRU). These long-run equilibrium rates of unemployment are identical in that they are consistent with a stable rate of inflation.

Phelps further developed the microeconomic foundations of the natural rate by analyzing labor market frictions that allocate heterogeneous jobs and workers without perfect information (161). Search unemployment creates frictions that lead to deviations from the natural rate of unemployment in the short run. Only when individuals have correct expectations, which is how long-run equilibrium is defined in these models, will the long-run Phillips curve be vertical at the natural rate. The short run is a period of disequilibrium in which individuals make forecast errors about future inflation.  Given enough time and data (i.e., in the long run), they will adjust their expectations and the economy will gravitate to a supply-side determined equilibrium rate of unemployment.

Friedman and Phelps argued that attempts to stimulate aggregate demand could not have a permanent effect on this equilibrium unemployment rate. Policies that target nominal variables, such as monetary policy, can only have temporary effects on real variables, such as output and employment. In a long-run equilibrium, when all expectations are correctly realized, the economy will be unable to deviate from this natural rate. Money illusion, it is assumed, does not exist. Therefore, the actual unemployment rate can deviate from the natural rate only when economic agents have incorrect expectations about future inflation.

The dynamics that lead to a long-run Phillips curve that is vertical at the NAIRU can be explained as follows. Suppose the monetary authorities increase the money supply to stimulate aggregate demand. This expansionary policy then leads to an increase in the aggregate price level. Firms are induced to sell more of their products as they see prices rising. However, they are unable to distinguish between specific price increases for their products and an increase in the general price level. So, initially, they hire more labor to accommodate the rising level of demand and unemployment falls. Nominal wages temporarily rise as firms increase their wage offers to attract more employees.

Since it is assumed that responses to wage changes happen more rapidly than responses to changes in the aggregate price level, workers supply more labor as they believe their real wages have risen. The economy then moves upwards along the short-run Phillips curve to a new, lower level of unemployment but at the cost of higher inflation. Conversely, if monetary authorities reduce the money supply to reign in aggregate demand, this process will operate in reverse. In the short run, then, there is a tradeoff between inflation and unemployment.

In the long run, however, this trade off disappears as inflation expectations are correctly revised. Over time, firms will see that price increases are not specific to their product, but a general phenomenon. They realize that their original strategy of hiring more labor was misinformed due to an erroneous interpretation of the rise in prices. Although firms are bound in the short run by fixed-term contracts for labor, once these contracts expire firms begin to shed unnecessary employees. Workers simultaneously begin to decrease their labor supply as rising inflation lowers their real wage. Their original decision to supply more labor was the result of misperceived (or incorrect) information.

This causes unemployment to rise to the level that existed prior to the monetary expansion, but this level of unemployment is now accompanied by a new, permanently higher rate of inflation. In order to combat greater unemployment, monetary policy would have to become ever-more expansionary and would cause ever-higher inflation rates. Any attempts to decrease unemployment below its natural rate would therefore lead to perpetually accelerating inflation rates in the long run.

As inflation expectations rise, the short-run Phillips curves shift continuously up and to the right. Once monetary authorities abandon their effort to lower unemployment via monetary stimulus, the economy moves onto the vertical long-run Phillips curve at the natural rate of unemployment.

Alternative Approaches to Estimating Phillips Curves
The malignant behavior of the Phillips curve tradeoff during the 1970s and the benign behavior of this tradeoff during the 1990sespecially for the 1996-2000 periodgenerated a wealth of models that sought to identify the forces that lead to such shifts. Applying an econometrically rigorous Phillips curve analysis to the U.S. economy during the 1990s, Gordon argued that wage inflation followed an upward course given the falling unemployment rate throughout the decade, but price inflation did not behave as predictably as it fell in the face of declining unemployment. He argues that the low inflation of the 1990s was the result of a lower value of the time-varying NAIRU (TV-NAIRU).

Gordon uses what he calls a triangle model of inflation, which summarizes the dependence of the inflation rate on three basic determinants inertia, demand and supply (14). Inflation inertia is measured by lagged values of actual inflation and represents the role played by fixed-term labor and supply contracts. Demand pressures are specified as the difference between actual unemployment and its time-varying natural rate or, alternatively, GDP growth that is above its potential. Supply determinants are exogenous shocks that cause a change in the prices of relevant goods.

Extending his triangle model, Gordon examines the feedback between wages and prices and argues that the low unemployment, low inflation Goldilocks economy of the 1990s was the result of five supply shocks that suppressed the rate of inflation
...between 1993 and 1998 the economy benefited from a powerful and interactive push toward decelerating inflation, resulting from appreciation in the dollar, a decline in real oil prices, an accelerated rate of decline in computer prices, a reduced relative rate of inflation in medical care, and a series of measurement improvements in the official price indexes.

Gordon, alludes to the potential influence of bargaining power on inflation when he notes that price changes were restrained by factors that limited wage changes, for example, worker insecurity (305), but does not explicitly model this in his analysis. Gordon offers additional explanations for declining inflation during the late 1990s, which include the hypothesis that the so-called new economy provided cheap technological goods that rendered obsolete previous capacity constraints associated with the Phillips curve (298). Worldwide financial crises led to an inflow of capital into the U.S., which, in turn, reduced interest rates and import prices. Weak unions, a decline in the real value of the minimum wage, job insecurity, and falling employee benefit costs (primarily due to the presence of cost-minimizing HMOs) also mitigated inflationary pressures.
Other models incorporate forward-looking expectations and sticky prices through fixed-term supply and labor contracts into a Phillips curve model that also includes the unemployment or output gap. Taylor, using rational expectations, finds that staggered wage contracts lead to both unemployment and inflation persistence, which significantly outlasts the duration of the longest contract (2). Calvo and Mankiw, using a sticky-price model, argue that monetary shocks (say, a monetary contraction) will cause firms to shed employees because they cannot sell all the goods they want at prevailing prices. Unemployment results since price adjustment is costly and is thus not immediately responsive to the shock (Mankiw 49). These studies argue that rational expectations do not necessarily imply policy ineffectiveness in the presence of nominal rigidities.

The models of inflation for the United States that are rooted in a Phillips curve approach, in which short-run decreases in inflation must come at the expense of higher unemployment. Since the short-run Phillips curve shifted out during the 1970s and shifted in during the latter half of the 1990s, many studies have attempted to explain what factors led to these shifts.  Mainstream Phillips curve models typically focus their theoretical and empirical analyses on changes in inflation inertia, inflation expectations, demand pressure, supply shocks, and price and wage rigidities.

At low levels of unemployment, workers gain a bargaining advantage relative to capital. When unemployment is high, the relationship is reversed. The short-run Phillips curve is negatively sloped, but in the long run, the equilibrium rate of unemployment is determined by the supply-side of the economy and the Phillips curve is vertical at a unique NAIRU.  On the other hand, when the Phillips curve is horizontal, changes in inflation stem from exogenous shocks, such as commodity prices or import prices, or, possibly, from the institutional structure of the labor market. That is, increases in employment insecurity or the social bargain could offset the inflation-inducing declines in the unemployment rate.