Monetary policy in the presence of asymmetric wage indexation.

• Author: Diana, Giuseppe

1. Introduction

   The study of the reaction functions of central banks has attracted a lot of attention from both academics and practitioners over the recent years, leading to a flourishing literature that has accumulated fresh evidence. Among the newer results is the fact that monetary policy tends to be asymmetric. Namely, it is not adjusted in the same way in the presence of positive or adverse shocks. This observation, initially made by Clarida and Gertler (1997) and Mishkin and Posen (1997), was later confirmed by Dolado, Dolores, and Naveira (2000). It thus appears that major central banks tend to react more aggressively when inflation exceeds its target level than when it is below it.

   This finding is clearly at odds with most of the theoretical work on monetary policy, which, in the spirit of Barro and Gordon (1983), usually assumes that central banks with symmetric preferences face symmetric economies. To depart from the perfect symmetric world that is usually depicted in theoretical contributions and to provide a rationale for observed stylized facts, some authors explicitly introduced an asymmetry in the preferences of the monetary authority. Thus, the recent papers by Cukierman (2000); Dolado, Dolores, and Naveira (2000); Jordan (2001); Cukierman and Gerlach (2003); Gerlach (2003); and Nobay and Peel (2003) all assume that the monetary authorities' loss function is asymmetric. Namely, they assume that positive and negative deviations of economic variables from their target levels impact differently the central banker's utility.

   Asymmetric preferences are, however, not the only asymmetries that may interfere with the conduct of monetary policy. In fact, monetary authorities are confronted with many asymmetries, the most obvious of which is the economy itself. Thus, Cover (1992) observes that negative monetary growth shocks in the United States induce large contractions in real output growth; whereas, positive monetary shocks have only limited expansionary consequences. Kandil (1995, 1998, 2002) also repeatedly observed similar asymmetries in various samples of countries, both developed and developing. This kind of asymmetry was subsequently incorporated in theoretical models by Bean (1997), Nobay and Peel (2000), and Dolado, Dolores, and Naveira (2005), thanks to the assumption of a non-linear Phillips curve. However, those contributions left the asymmetry in the Phillips curve unexplained.

   A likely culprit for those non-linearities is wage indexation, whose macroeconomic impact has been acknowledged since the seminal contributions of Gray (1976), Fisher (1977), or Blanchard (1979). Nominal wages are indeed typically indexed upward but not downward. Card (1986), for instance, observes that since the General Motors--United Auto Workers 1948 agreement, North American contracts in general specify a non-contingent wage schedule, a base price level for the calculation of wage increases, and a wage increase defined as a function of increases, but not decreases, in the consumer price index. In other words, he reports that wages are indexed upward but not downward.

   Moreover, even if one may argue that wage indexation is often implicit rather than explicit, wages indeed behave in a way that is consistent with asymmetric indexation. For instance, Kandil (1995, 1998) observed asymmetric reactions of nominal wages to monetary shocks at the aggregate level. In a more recent paper, Kandil (2002) studies the evolution of the United States' performance in the light of the variations in the downward rigidity and upward flexibility of nominal wages. Furthermore, an ample literature recently surveyed by Gottschalk (2005) emphasizes that nominal wage cuts are rare. That literature reaches the same conclusion while using personnel files, in the case of Fehr and Goette (2005); survey and register data, in the case of Akerlof, Dickens, and Perry (1996) or Dickens et al. (2007); or interviews with wage setters, in the case of Blinder and Choi (1990) or Bewley (1999). Consistent with that evidence, Cover and VanHoose (2002) incorporated asymmetry in a model of wage indexation and concluded that investigating the consequences for the policy implications of macroeconomic models of real-world asymmetrically indexed contracts should be given more attention.

   In this paper, we precisely concentrate on the consequences of asymmetric wage indexation for monetary policy. Our paper therefore bridges the gap between two strands of the literature. The first strand, mentioned above, studies the consequences of an asymmetric economy on monetary policy. The second strand, surveyed by Meon (2004), is devoted to the impact of wage indexation on monetary policy and was pioneered by Ball and Cecchetti (1991), VanHoose and Waller (1991, 1992), and Milesi-Ferretti (1994). Surprisingly, that literature has only focused on symmetric wage indexation. As a result of the policy implications of that strand of research, it is important to check the robustness of its results in the light of a more realistic framework. This is the aim of the present paper.

   We find that, although the assumption of asymmetric wage indexation leads to greater analytical complexity, it significantly modifies the results of the literature. More precisely, we observe that the monetary authorities do not react to all output shocks and, most of all, that they adopt an asymmetric monetary policy rule. Accordingly, they tend to absorb expansionary shocks more than contractionary ones, which is in line with the stylized fact underlined above. That behavior can, moreover, cause the expected level of income to fall short of its natural level.

   We also find that asymmetric wage indexation lowers expected inflation with respect to a situation with no indexation, which is a standard result of the literature. However, we observe that its impact on average inflation relative to an equivalent symmetric indexation is ambiguous. Similarly, asymmetric wage indexation increases the volatility of output and decreases the volatility of inflation with respect to a situation without indexation, but the comparison of output and inflation volatility with an equivalent symmetric indexation leads to mixed results. Furthermore, we find that it has an ambiguous effect on expected welfare relative to both an equivalent symmetric wage indexation and a situation without indexation. However, when the optimal degree of indexation is used, asymmetric indexation is always outperformed by symmetric indexation.

   To reach those conclusions, the rest of our paper is organized as follows: The next section presents the simple set-up on which our reasoning rests. The third section describes the monetary authorities' behavior. Section 4 closes the model and compares the outcome of monetary policy in the presence of asymmetric wage indexation with the outcomes of monetary policy in the presence of symmetric wage indexation or no indexation. Section 5 offers concluding comments.

2. The Set-Up

   To describe the supply side of our model, we suppose that output is a downward-sloping schedule of the real wage. When all variables are expressed in logs, the supply function reads as follows:

   [y.sub.t] = -([w.sub.t] - [p.sub.t)] + [u.sub.t], (1)

   where [y.sub.t] is output, [w.sub.t] the nominal wage, and [p.sub.t] the price level. The variable [u.sub.t] is a real shock, the magnitude of which is unknown to workers when they sign their wage contracts; [u.sub.t] is independent identically distributed (i.i.d.) and has a zero mean and a well-defined variance [[sigma].sup.2]. Expression 1 implicitly assumes that the natural level of output is zero. (1)

   The nominal wage is supposed to follow a modified Gray (1976) indexation rule: Namely, and following Cover and VanHoose (2002), we assume that wages are indexed upward but not downward. Therefore, the indexation rule reads thus:

   [w.sub.t] = [p.sup.e.sub.t] + [delta]([p.sub.t] - [p.sup.e.sub.t]), (2)

   where 0 [p.sup.e.sub.t] and [delta] = 0 if [p.sub.t] [less than or equal to] [p.sup.e.sub.t].

   [delta] is the indexation parameter and [p.sup.e.sub.t] the rationally expected price level. When the observed price level exceeds the expected price level, the nominal wage is therefore a weighted average of current and expected price levels. It is fully indexed when [delta] = 1. On the other hand, when the expected price level overshoots the observed price level, the nominal wage remains fixed. In other words, we assume that the nominal wage is automatically adjusted upward but is sticky downward. (2)

   In addition, our specification can be viewed as a special case of a more general model that would read [w.sub.t] = [w.sup.*.sub.t] + [delta]([p.sub.t] - [p.sup.e.sub.t]), where [w.sup.*.sub.t] is the base wage. We thus implicitly assume that the base wage is [p.sup.e.sub.t], as is common in the symmetric wage indexation literature. However, Cover and VanHoose (2002) and Calmfors and Johansson (2006) suggest that asymmetric wage indexation may be associated with a lower base wage. In that case, the base wage would be endogenous and would have to be obtained by simulation, then plugged into the model. We leave this strategy for future work and take [p.sup.e.sub.t] as the base wage in this paper in order to facilitate the comparison of our results with the standard symmetric wage indexation literature.

   When Equation 2 is plugged into Equation 1, the supply function is transformed into an expectations-augmented short-run aggregate supply curve, thus:

   [y.sub.t] = (1 - [delta])([[pi].sub.t] - [[pi].sup.e.sub.t]) + [u.sub.t], (3)

   where [[pi].sub.t] [equivalent to] [p.sub.t] - [p.sub.t-1] and [[pi].sup.e.sub.t] [equivalent to] [p.sup.e.sub.t] - [p.sub.t-1] are period t's current and rationally expected inflation. Expression 3 shows that the slope of the trade-off between income and unexpected inflation is a decreasing function of the indexation parameter [delta] whenever current inflation exceeds...