For a flavor of the basic arguments (more detailed results follow), consider a standard monetary policy game in the spirit of Barro and Gordon (1983), but with two twists:
a) Wage setters are not atomistic; instead, they are organized in unions. These unions set nominal wages on behalf of their membership.
b) Unions dislike inflation, unlike the standard story in which they care only about the expected real wage.
In this context, and for an exogenously fixed price level, it should be clear that the outcome of the game among the unions should be Pareto inefficient, with a real wage that is too high and employment and output that are too low relative to the first best.
Introduce now a central bank that controls the price level (or the rate of inflation, it does not matter which) and that moves after unions have set their nominal wages for the relevant time period. Such a central bank will be tempted to act opportunistically and deflate the real value of set wages to the extent that it cares about employment and output. In the standard model, wage setters anticipate this temptation, so that in equilibrium you get positive inflation with no change in the inefficiently low employment level.
So far nothing is new. But consider now the effects of having non-atomistic wage setters. When deciding upon its desired wage markup, each union will understand that, the higher the average markup and the lower the level of employment, the greater the inflationary temptation faced by the central bank, and the higher the equilibrium inflation rate. Hence, this concern for the resulting inflation may lead unions (which move before the central bank, and are therefore Stackelberg leaders vis a vis the monetary authority) to moderate their real wage claims. And notice: the less conservative (more populist) the central bank is, the greater the inflationary cost of high wage markups, and hence the lower the markups may be in equilibrium.
From the theoretical point of view, this last result follows from the fact that there are two games being played simultaneously: one among the unions and one between the unions as a whole and the central bank. Even if the central bank precommits in its own game (which is what having greater CBC is equivalent to in this setting -see below), the outcome is not necessarily improved since opportunistic behavior can still occur in the other game. This is also the reasoning behind Rogoff’s (1985a) result that international monetary coordination can be counterproductive. The result can also be viewed as an example of the theory of the second best. Introducing a second distortion (opportunistic central bank behavior) into an economy already distorted by monopolistic behavior in the labor market can be welfare improving.