Inflation and Unit Labor Cost Part 1

Inflation and Unit Labor Cost 1. INTRODUCTION A notable development of early 21st century macroeconomics was the rise of dynamic stochastic general equilibrium models at central banks around the world. Constructed along New Keynesian lines, these DSGE models have been increasingly employed as central banks placed greater weight on inflation targeting frameworks for monetary policy, at times explicitly as in Canada and New Zealand and at times implicitly as in the U.S. and Europe. A price equation stressing unit labor cost, modernizing specifications developed along the lines of Eckstein and Fromm (1968) for an earlier generation of quantitative models, plays a central role in the transmission of shocks from the real sector to inflation in these models. In addition, rational price-setter expectations of unit labor cost also play a key role in the models’ inflation dynamics. This paper provides a transparent accounting of the sources of inflation within the canonical modern macroeconomic policy model, circa 2007, using leading examples of such New Keynesian DSGE modeling. Most modern macroeconomic models feature a structural equation designed along the lines of Gali and Gertler (1999) and Sbordone (2002) that link inflation to fluctuations in expected inflation and real unit labor cost (equivalently, labor's share), which we term the New Keynesian Pricing Equation (NKPE). Notably, a particular NKPE specification is a component of the seven-variable DSGE model that Smets and Wouters (2007) developed for the United States, which we take as our reference DSGE model. The NKPE specifications that we use are of the “hybrid” form common to Gali and Gertler (1999) and Smets and Wouters (2007), in that they contain an inflation lag as well as expected future inflation. They differ in the values and interpretation of the NKPE coefficients in ways that we discuss further below, but are otherwise similar. Both feature a link to a measure of real marginal cost, with Smets and Wouters (2007) making a model-based correction to standard real unit labor cost. To focus attention on the interaction of the unit labor cost data and the models, we do not estimate any structural parameters in our work, but simply use alternative values estimated by Gali and Gertler (1999) and Smets and Wouters (2007). Much of our analysis focuses on the 1960-1999 sample period because this (roughly) coincides with the sample period used by Gali and Gertler, Sbordone, and others, and because it was the behavior of inflation over this period which motivates much of this work. After reviewing the main features of the behavior of inflation and the theory of the NKPE, we make four contributions. The first two involve the accounting focus discussed above. First, we develop and use a four-way decomposition of the hybrid NKPE to break inflation into inflation expectations, inflation inertia, cost, and residual. We show that inflation over 1960-1999 is dominated by the inflation expectations component and that real unit labor cost accounts for only a small part. This first finding is common to the NKPE, when we use the parameter estimates of Gali and Gertler (1999) and those of Smets and Wouters (2007). This decomposition highlights how the NKPE is a double-edged sword for an inflation targeting central bank: the dominance of inflation expectations in inflation shows how important it is to manage these, but the small contribution of real unit labor cost shows that direct management is difficult with temporary changes in aggregate demand. Second, we employ a two-way decomposition based on solving out the NKPE to divide inflation into real cost and residual components, with each being the evolution of an expected present discounted value. Following Gali and Gertler (1999) and Sbordone (2002) who studied similar constructions, we use the label “fundamental inflation” for the marginal cost component. When we implement this decomposition using a bivariate inflation-real unit labor cost VAR to forecast future values of real unit labor cost, we find (like these prior authors) that fundamental inflation comoves strongly with actual inflation. The fundamental inflation decomposition shows that, despite a modest short-run influence of cost, an inflation-targeting central bank could control inflation substantially by having systematic policies to control real activity which smoothed the behavior of real unit labor cost. When we apply our two-way decomposition to the Smets and Wouters (2007) version of the hybrid NKPE using their full general equilibrium model for forecasting marginal cost, we find that fundamental inflation behaves very differently from actual inflation. This decomposition suggests that inflation control would be more problematic, as inflation appears dominated by shocks to the NKPE within the Smets and Wouters (2007) model. More generally, the link between inflation and costs appears very different from an accounting perspective, using the two closely related NKPE frameworks. Third, we undertake detective work aimed at solving this inflation-cost puzzle. Specifically, we consider how differences in the NKPE parameter values, forecasting methods, and real unit labor costs measures alter the behavior of fundamental inflation. Fourth, we explore how this inflation-cost puzzle manifests itself in the structural interpretation of inflation dynamics within the Smets and Wouters DSGE model. Specifically we highlight how the structure of their model implies that inflation must be explained primarily by the model's price shocks and also that these shocks must have opposite effects on inflation and marginal cost. Simply put, an important part of inflation in the model arises from exogenous price shocks that drive up inflation and drive down labor cost. But the inflation generated by these shocks is fairly temporary given the monetary policy rule, while the price markup shocks and the labor cost responses are highly persistent and move in opposite directions. We describe why this negative comovement is an inevitable part of basic "first generation" sticky price DSGE models driven by highly persistent markup shocks and find it interesting that it also appears in the much more elaborate Smets and Wouters model. We then look forward from the end of the basic data interval in 1999 to examine the inflation cost puzzle in more recent times, finding that it intensifies, and then look back to consider how the evolving behavior of unit labor costs undermines a key motivation for the NKPE. When we extend the sample through 2010, the real unit labor cost series used by Gali, Gertler, and Sbordone -- as well as the measure used by Smets and Wouters -- exhibit large trend declines at the end of the sample. This leads to a collapse in fundamental inflation on the order of 15 percentage points in the 2000s, a period in which actual inflation is essentially unchanged. Stepping back, we recall that the NKPE focus on cost measures was developed partly to avoid challenges raised by the modeling of capacity output for empirical analysis of price dynamics: unit labor cost could potentially be unaffected by real trends, while output would not be.1 Ironically, it seems that the marginal cost approach now faces the same issues of identifying the effects of trends and productivity shocks that were a major reason for modern pricing analysis to move away from output gaps. Our findings highlight the fact that conventional unit labor cost measure is no longer a useful construction for inflation dynamics and has not been at least since the early 2000s. The organization of the paper is as follows. In section 2, we briefly review the inflation dynamics developed by Gali and Gertler (1999) and Sbordone (2002), which focuses on the comovement of inflation and real unit labor cost. In section 3, we describe the two accounting decompositions discussed above for inflation. In section 4, we consider the implications of the NKPE using the parameter values and forecasting mechanisms previously developed in Gali and Gertler (1999) and then we do the same for the Smets and Wouters (2007) framework. This isolates the inflation-cost puzzle discussed above: a SW fundamental inflation measure is very different from both actual inflation and a GG fundamental inflation measure.2 In section 5, we conduct our detective work and solve the puzzle, at least in a mechanical empirical sense, and then we describe how it is manifested in the structural impulse response of the Smets and Wouters DSGE model. In section 6, we briefly look at inflation and labor cost over the longer 1960-2011 interval. We document that a GG fundamental inflation measure displays the same aberrant behavior over this extended interval that the SW fundamental inflation measure did earlier (and continues to in recent years). The basic difficulty is that real unit labor cost or, equivalently, labor's share has declined dramatically since the mid 1990s with little accompanying change in inflation. In section 7, we provide a summary, conclusion, and discussion of directions for further work. 2. THE NEW KEYNESIAN PRICE EQUATION We start by providing a brief account of the motivations for the New Keynesian pricing equation (NKPE) studied in this paper.3 2.1 Forward-Looking Pricing The standard New Keynesian modeling of price dynamics is attractive on two dimensions. First, as widely noted, it is an implication of optimization in the Calvo setting, stressing the impact of current and expected future marginal cost on pricing.4 Importantly, it captures key dynamic inflation implications of more elaborate models in a tractable manner: there are a small number of parameters to estimate.5 Second, it provides a near-neutral linkage between trend inflation and real marginal cost.6 The NKPE may be written as t = bEtt+1 + t (1) where t is a measure of real marginal cost, b is a discount factor and  is a nonlinear combination of the discount factor, the expected frequency of price adjustment opportunities, and other structural parameters in various versions of (1). After discussing this benchmark specification, Gali and Gertler (1999) develop a more general hybrid model of inflation that incorporates a backward-looking component to inflation, t = bt−1 + f Ett+1 + t + zt (2) rationalized by the introduction of some price-setters who adopt imitative strategies. In this expression, zt is a residual term, with traditional ambiguity in interpretation. There is an extensive literature on identification, estimation and testing of (2). Macroeconomists are widely divided on whether the frictions embedded in (2) are the most important ones for understanding the interaction of inflation and real variables, as well as on parameter estimates and results of model specification tests. While this literature is valuable, its concerns are not ours: we simply take the parameter estimates in two influential studies and undertake accounting exercises based on these parameter values. These exercises highlight dimensions of success, as in the prior literature, but also substantial empirical difficulties that have not been stressed in the literature. 2.2 Decomposing inflation In our analysis of the links between pricing and real unit labor cost, we consider two decompositions of the sources of inflation. Decomposition 1 involves the elements of (2) directly, which we term inertia (bt−1 ), expected inflation (f Ett−1 ), real unit labor cost (t ) and the residual (zt). For this, we need an estimate of Ett+1 which we construct using two models: (1) an estimated bivariate vector autoregression using  and  and (2) the estimated Smets-Wouters DSGE model. Decomposition 2 involves the rational expectations solution of (2)   j 0 j 0  t   t 1     i Et t  j  z   i Et zt  j (3) Given the parameters b, f, and  the solution parameters (, , , z) are readily and uniquely determined.7 To make this decomposition operational, we need estimates of the expectation terms Ett+j and Et zt+j which are computed using a vector autoregression and the Smets- Wouters model. The full time series decomposition that we present involves only two components, t =  t +  tz (4) in that we solve for the path of inflation attributing the t−1 separately to  and z. That is:   j 0 j 0  t   t1     i Et t  j  (1   L)1    i Et t  j (5)   j 0 j 0  tz   tz1  z   i Et zt  j  (1   L)1 z   i Et zt  j We label  t as fundamental inflation, using the terminology of Campbell and Shiller (1998) and Gali-Gertler (1999).8 2.3 A preview of the data and our main results Armed with this framework, we can summarize the main results in the paper before going into the details of the models and our analysis. Decomposition 2 uses fundamental inflation () to summarize the relation between real unit labor costs () and inflation (). Because  is the discounted sum of expected future , and because  is highly serially correlated (as we will see), the low frequency movements in  mimic the low frequency (6) movements in . Thus, an implication of the NKPE is that inflation inherits the low frequency movements of real unit labor costs. The model is useful, in the sense that it explains inflation using real unit labor costs, if these two time series share the same low-frequency behavior. Put differently, if the low-frequency behavior of inflation differs markedly from the low frequency behavior of real unit labor costs, then variables other than real unit labor cost (z in equation (2)) must be important for explaining inflation. Figure 1 plots inflation and Gali and Gertler’s  measure. The two series move together over low frequencies, and the implied fundamental inflation series in Figure 2 captures important movements in inflation. Figure 3 plots inflation and the Smets-Wouters  measure. They have different low-frequency behavior, and the fundamental inflation which we construct for the Smets-Wouters model and displayed in Figure 4 differs markedly from actual inflation. Thus, Gali and Gertler’s model suggests that real unit labor costs are the main drivers of inflation, while Smets and Wouter’s model suggests that other factors (z) play a dominant role. These figures cover the 1960-1999, the (approximate) sample period of interest in early work on the NKPE. Figure 5 extends both  measures through 2010, and shows large post1999 declines in both measures. Figure 6 shows that these declines in  led to large falls in the corresponding measures of fundamental inflation, but that actual inflation changed little. Thus, the NKPE implies that these measures of  have important low-frequency movements unrelated to the real marginal costs important for aggregate inflation or that other factors (z) conspired to prevent a dramatic fall in inflation during the 2000s. This preview raises many questions. Why do the  measures used by Gali and Gertler and Smets and Wouters differ? What role do the specific parameter values in (2) play in these conclusions? Do these differences in fundamental inflation (decomposition 2) lead to different 10 conclusions about the importance of expected inflation (decomposition 1) in the inflation process? What is the structural interpretation of the z-variable in the Smets and Wouters model and how does it interact with ψ? Why have real unit labor costs fallen so dramatically over the past decade? And finally, given these results, is the NKPE a useful empirical model for inflation? The remainder of the paper takes up these questions.