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Real wage rigidities and the cost of disinflations.

Article Excerpt
Ball and Romer (1990) show that nominal rigidities need to be complemented by real rigidities in order to generate a suitable endogenous propagation mechanism of monetary policy. Indeed, it is well known that the widely used Calvo price staggering model is not able to generate inflation persistence, and it is believed that this shortcoming can be corrected by introducing real rigidities.

After the influential contribution of Hall (2005) a reduced form of a real wage rigidity assumption began to be incorporated in many dynamic stochastic general equilibrium (DSGE) New Keynesian models, starting with Krause and Lubik (2007) and applied in a number of papers (e.g., Blanchard and Gall 2006, 2007, Christoffel and Linzert 2006). (1) Most of these papers show that real wage rigidities are important to improve the model performance, and to explain the sluggish behavior of inflation.

It is therefore natural to think that real wage rigidities may be useful to explain the output costs of a disinflationary policy because they induce a sluggish real wage adjustment, which is absent in the standard Calvo pricing model. The inertial dynamics of real wages then prevents the immediate adjustment of inflation to the new long run level, causing a recession. For a recent example of this argument see section 4 of Blanchard and Gall (2007). Indeed, this is certainly the case in the log-linearized model.

This paper, however, shows that it is not the case if nonlinearities are taken into account. While real wage rigidities generate an output slump under a disinflation in the log-linearized model, they lead to additional output during the adjustment to the new higher steady state in the nonlinear version of the model. The interaction between long-run effects and short-run dynamics leads, therefore, to completely different results in the linearized and in the nonlinear model. Real wage rigidities can, indeed, even cause an overshooting of output over its higher new steady state level. Hence, real wage rigidities do not imply any output costs after a disinflationary policy.

In contrast, the difference between the log-linear and the nonlinear model is only of quantitative nature when comparing the effects of real wage rigidities under a temporary shock. A temporary shock does not imply movement from one steady state to another. A disinflation, instead, implies a permanent change in the level of inflation. Thus, the effects of such a permanent shock cannot be analyzed using a version of the model that is log-linearized around one particular steady state.

Some papers in the literature (e.g., Ascari 2004, Yun 2005) show that nonlinearities may play an important role in DSGE New Keynesian models. Here, we show that this is the case regarding the effects of real wage rigidities, an increasingly common feature embedded into New Keynesian models. Researchers should be aware of the potentially big mistake of inferring the effects of permanent shocks through log-linearized models.

The rest of this paper is structured as follows. Section 1 presents the model and its calibration. Section 2 compares the steady state effects of a disinflation in the linearized and nonlinear model. Section 3 analyzes the effects of real wage rigidities in a disinflation experiment, and does the same for a temporary shock to the inflation target. Section 4 shortly concludes.

1. THE MODEL AND CALIBRATION

The model is a standard New Keynesian model where:

(i) Firms produce a differentiated product using the following simple constant returns production function

[Y.sub.i,t] = [N.sub.i,t], (1)

where Y is output and N is the labor input. (2)

(ii) Firms' pricing is described by the usual Calvo mechanism, where [theta] is the fraction of firms not adjusting their price in any given period,

(iii) Households have the following instantaneous and separable utility function:

U([C.sub.t],[N.sub.t]) = [C.sup.1-[sigma].sub.t]/1 - [sigma] - [d.sub.n] [N.sup.1+[psi].sub.t]/1 + [psi], (2)

where C is composite consumption (with elasticity of substitution between different types of goods equal to [epsilon]).

(iv) The following partial adjustment model for the real wage is assumed in order to introduce real wage rigidities a la Hall (2005):

[W.sub.t]/[P.sub.t] = [([W.sub.t-1]/[P.sub.t-1]).sup.[gamma]] [([MRS.sub.t]).sup.1-[gamma]], (3)

where MRS is the marginal rate of substitution between labor supply and consumption. For sufficiently big [gamma], this model implies a sluggish adjustment of the real wages. Note that this is the nonlinear counterpart of the partial adjustment model for the real wage employed in many of the references above. For example, Blanchard and Gali (2007) assume [[??].sub.t] - [[??].sub.t] = [gamma]([[??].sub.t-1] - [[??].sub.t-1]) + [(1 - [gamma]).sup.[??]]. (3)

(v) The monetary policy for the nominal interest rate, [i.sub.t], is assumed to be described by a standard Taylor rule:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where [[pi].sub.t] is the gross inflation rate (i.e., [P.sub.t]/[P.sub.t-1]), [bar.[pi]] is the central bank inflation target, and [bar.Y] is the corresponding steady state level of output. (4)

Appendix A describes all model equations in detail, and Appendix C describes our benchmark calibration, which is standard. The qualitative results do not depend on the calibration values chosen.

2. STEADY-STATE EFFECTS

The obvious starting point to analyze a disinflation experiment is to look at the steady state of the full nonlinear model, which is easy to compute, as there is no need for any...