Inflation and Unit Labor Cost

In‡ation and Unit Labor Cost Abstract We study two decompositions of in‡ation, , motivated by a New Keynesian Pricing Equation. The …rst uses four components: lagged , expected future , real unit labor cost ( ), and a residual. The second uses two components: fundamental in‡ation (discounted expected future ) and a residual. We …nd large low-frequency di¤erences between actual and fundamental in‡ation. From 1999-2011 fundamental in‡ation fell by more than 15 percentage points, while actual in‡ation changed little. We discuss this discrepancy in terms of the data (a large drop in labor’s share of income) and through the lens of a canonical structural model (Smets-Wouters (2007)). 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 were increasingly employed as central banks placed greater weight on in‡ation targeting as a framework for monetary policy, at times explicitly as in Canada and New Zealand and at times more implicitly as in the U.S. and Europe. A price equation stressing unit labor cost, modernizing speci…cations developed by Eckstein and Fromm (1968) and others for an earlier generation of quantitative models, plays a central role in the transmission of shocks from the real sector to in‡ation in these models. In addition, rational price-setter expectations of unit labor cost also play a key role in the models’ in‡ation dynamics. This paper provides a transparent accounting of the sources of in‡ation within the canonical modern macroeconomic policy model, circa 2007, using leading examples of such New 1 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 in‡ation to ‡uctuations in expected in‡ation and real unit labor cost (equivalently, labor’s share), which we term the New Keynesian Pricing Equation (NKPE). Notably, a particular NKPE speci…cation 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 speci…cations that we use are of the "hybrid" form common to Gali and Gertler (1999) and Smets and Wouters (2007), in that they contain an in‡ation lag as well as expected future in‡ation. They di¤er in the values and interpretation of the NKPE coe¢ cients 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 modelbased correction to the standard real unit labor cost. We do not estimate any structural parameters in our work, but simply use alternative values drawn from 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 in‡ation over this period that motivates much of this work. After reviewing the main features of the behavior of in‡ation and the theory of the NKPE, we make four contributions. The …rst two involve the accounting focus discussed above. First, we develop and use a four-way decomposition of the hybrid NKPE directly to break in‡ation into in‡ation expectations, in‡ation inertia, cost, and residual. We show that in‡ation over 1960-1999 is dominated by the in‡ation expectations component and that real unit labor cost accounts for only a small part. This …rst …nding 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 two-edged sword for an in‡ation targeting central bank: the dominance of in‡ation expectations in in‡ation shows how important it is to manage these, but the small contribution of real unit labor cost shows that direct management is di¢ cult with temporary changes in aggregate demand. Second, we employ a two-way decomposition based on solving out the NKPE to divide in‡ation 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 in‡ation" for the marginal cost component. When we implement this decomposition using a bivariate in‡ation-real unit labor cost VAR to forecast future values of real unit labor cost, we …nd (like these prior authors) that fundamental in‡ation comoves strongly with actual in‡ation. This decomposition shows that, despite a modest short-run in‡uence of cost, an in‡ation-targeting central bank could control in‡ation substantially by having systematic policies to control real activity if this smoothed the behavior of real unit labor cost. When we apply our two-way 2 decomposition to the Smets and Wouters (2007) version of the hybrid NKPE using their full general equilibrium model for forecasting marginal cost, we …nd that fundamental in‡ation behaves very di¤erently from actual in‡ation. This decomposition suggests that in‡ation control would be more problematic, as in‡ation appears dominated by shocks to the NKPE within the Smets and Wouters (2007) model. More generally, the NKPE link between in‡ation and costs appears very di¤erent from an accounting perspective, using the two closely related NKPE frameworks. Third, we undertake detective work aimed at solving this in‡ation-cost puzzle. Specifically, we consider how changes in the NKPE parameter values, forecasting methods, and real unit labor costs measures change the behavior of fundamental in‡ation. Fourth, we show how this puzzle manifests itself in the structural interpretation of in‡ation dynamics within the Smets and Wouters DSGE model. Speci…cally we show that the structure of their model implies that in‡ation must be explained primarily by the model’s price shocks and also that these shocks must have opposite e¤ects on in‡ation and marginal cost. Simply put, an important part of in‡ation in the model arises from exogenous price shocks that drive up in‡ation and drive down labor cost. But the in‡ation 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 "…rst generation" sticky price DSGE models driven by highly persistent markup shocks and …nd it interesting that it also appears in the much more elaborate Smets and Wouters model. 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 declines in fundamental in‡ation on the order of 15 percentage points in the 2000s, a period in which actual in‡ation is essentially unchanged. Stepping back, 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 una¤ected 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 e¤ects of trends and productivity shocks that were a major reason for modern pricing analysis to move away from output gaps. Our …ndings highlight the fact that conventional unit labor 1 Fuhrer (1997) argues that the NKPE fails badly when a conventional output gap is employed. However, a class of modern macroeconomic models – those that add nominal frictions to a real business cycle core framework – imply a time-varying level of capacity output due to changes in productivity and other real factors that would make conventional output gaps a poor proxy for pricing pressures, while a measure of real marginal cost (or average markup) would be an appropriate indicator (see, for example, Goodfriend and King (1997)). Gali and Gertler (1999) make an explicit empirical comparison between marginal cost and output gap models of in‡ation dynamics. 3 cost measure is no longer be a useful construction for in‡ation dynamics and have not been at least since the early 2000s. The organization of the paper is as follows. In section 3, we brie‡y review the in‡ation dynamics developed by Gali and Gertler (1999) and Sbordone (2002), which focuses on the comovement of in‡ation and real unit labor cost. In section 3, we describe the two accounting decompositions discussed above for in‡ation. In section 4, we consider the implications of the NKPE using the parameters and forecasting mechanisms previously developed Gali and Gertler (1999) and then we do the same for the Smets and Wouters (2007) framework in section 5. This isolates the in‡ation-cost puzzle discussed above: a SW fundamental in‡ation measure is very di¤erent from both actual in‡ation and a GG fundamental in‡ation measure.2 In section 6, 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 7, we brie‡y look at in‡ation and labor cost over the longer 1960-2011 interval. We document that a GG fundamental in‡ation measure displays the same aberrant behavior over this extended interval that the SW fundamental in‡ation measure did earlier (and continues to in recent years). The basic di¢ culty is that real unit labor cost or, equivalently, labor’s share has declined dramatically since the mid 1990s with little accompanying change in in‡ation. 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 In this study, which involves replication and extension of prior work, there is potential confusion between the results of the original studies and the results of replications/extensions developed along the lines of the studies. We use full names to indicate material which is exactly taken from prior studies, such as the parameters estimated by Gali and Gertler (1999) and the structural model parameters estimated by Smets-Wouters (2007). When we refer to data, we use the author’s full names because we have carefully reconstructed and extended the data employed these authors, so that the series closely match over the estimation intervals for both prior studies with some small excepections discussed below (see Appendix A for some additional details). Thus, when we discuss the Gali-Gertler and Smets-Wouters measures of labor cost, we are referring to their conceptual constructions and our data set. Fundamental in‡ation plays an important role in our study, as it did in Gali and Gertler (1999) and Sbordonne (2002). We use abbreviations to indicate our FI constructions. When we refer to GG fundamental in‡ation, this is our FI construction along Gali-Gertler lines but it di¤ers in some details that we discuss below. The SW fundamental in‡ation is our construction using Smets-Wouters parameter estimates and our replication/extension of their data set. We think it is an informative construction, but it is not one which they used. 3 This speci…cation is sometimes called the "New Keynesian Phillips Curve." As it links in‡ation to marginal cost rather than output or unemployment, we prefer the terminology of Kurmann (2005). This terminology accurately captures its role in NK-DSGE models as one equation in a wage-price block. 4 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 in‡ation implications of more elaborate models in a tractable manner: there are a small number of parameters to estimate5 . Second, it provides a near-neutral linkage between trend in‡ation and real marginal cost.6 The NKPE may be written as t = bEt t+1 + (1) t 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 speci…cation, Gali and Gertler (1999) develop a more general hybrid model of in‡ation that incorporates a backward-looking component to in‡ation, 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 identi…cation, 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 in‡ation and real variables, as well as on parameter estimates and results of model speci…cation tests. While this literature is valuable, its concerns are not ours: we simply take as given the parameter estimates in two in‡uential 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 di¢ culties that have not been stressed in the literature. 2.2 Decomposing in‡ation In our analysis of the links between pricing and real unit labor cost, we consider two decompositions of the sources of in‡ation. 4 Textbook treatments are provided by Gali (2008), Walsh (2010), and Woodford (2003). See Roberts (1995) for a comparison of speci…cations. 6 This near-neutrality property is shared by many models, as noted, for example, by Roberts (1995) and Goodfriend and King (1997)). It holds for state dependent pricing models (see, Dotsey, King and Wolman (1999). More recently, Cogley and Sbordonne (2008) have considered the consequences of time-varying trend in‡ation within a higher order approximation of the Calvo (1983) model. 5 5 Decomposition 1 involves the elements of (2) directly, which we term inertia ( b t 1 ), expectations ( f Et t+1 ) , real unit labor cost ( t ) and the residual (zt ). For this, we need an estimate of Et t+1 and we have explored several methods for constructing these expectations as we discuss below. Decomposition 2 involves the rational expectations solution of (2), t = t 1 + 1 X j Et t+j + j=0 z 1 X j (3) Et zt+j j=0 Given the parameters b ; f and , the solution parameters ; ; ; z are readily and uniquely determined.7 To make this decomposition operational, we need an estimates of expectations Et t+j and Et zt+j which we compute in various ways as discussed in sections 4 and 5 below. The full time series decomposition that we present involves only two components, z (4) t = t + t in that we solve for the path of in‡ation attributing the is: t z t = = t 1 t 1 1 X + + z j=0 1 X j j Et t+j = (1 Et zt+j = (1 t 1 1 X 1 L) L) separately to 1 j=0 z j=0 1 X j j Et t+j Et zt+j and to z. That (5) (6) j=0 We label t as fundamental in‡ation, using the terminology of Campbell and Shiller (1998) and Gali-Gertler (1999).8 3 Accounting with just the NKPE We now investigate how the hybrid NKPE (2) accounts for in‡ation during the 1960-1999 period, using our two decompositions. For this purpose, we use the parameters from Gali and Gertler (1999) displayed in Table 1. 7 This a second-order expectational di¤erence equation familiar from Sargent (1978). For the speci…c formulas applicable in this case, see Gali and Gertler (1999, page 217). 8 Our measure of fundamental used by Gali and Gertler. Their P1 j in‡ation di¤ers slightly from the measure P1 j measure is E while our measure is + Et t+j , which di¤er in the t 1 + z t z t+j t 1 j=0 j=0 value of lagged in‡ation. We solve out for the e¤ects of past in‡ation so as to make our results more conceptually comparable to historical shock decomposition such as those employed in Smets and Wouters (2007). 6 3.1 In‡ation and RULC The central feature of the New Keynesian pricing theory is a link to real marginal cost, most frequently proxied by real unit labor cost in applied work. Figure 1 shows the comovement of GDP de‡ator price in‡ation ( ) and log real unit labor cost (measured as the logarithm of the ratio of nominal compensation per hour to nominal output per hour in the non-farm business sector). The real unit labor cost series moves together with in‡ation, in both levels and detrended components, notably during the 1970s and 1980s.9 To operationalize our decompositions, we need to construct Et t+1 for the …rst and P1 j Et t+j for the second. In each case, we use a bivariate VAR(4) that includes j=0 and to forecast the relevant variables. We consequently call these GG-VAR decompositions. Additional computation details on the fundamental in‡ation decomposition are provided in section 5 below. 3.2 Results from Decomposition 1 The results of decomposition 1 are displayed in Figure 2. We …nd that expected in‡ation is the dominant source of actual in‡ation in Figure 2 ( f Et t+1 is shown in panel B). A smaller part of in‡ation is due to inertial e¤ects ( b t 1 is shown in panel A). Because the coe¢ cient on real unit labor cost is small ( = 0:15), the real unit labor cost component ( t ) accounts for little of the variation in in‡ation. Finally, residual in‡uences (zt = [ b t 1 + f Et t+1 + t ]) are quantitatively important. t 3.3 Results from Decomposition 2 While real unit labor costs accounted for little of the variation in in‡ation using decomposition 1, matters are very di¤erent for decomposition 2. Figure 3 displays the fundamental component t of in‡ation over 1960-1999 (the comparable Figure 2 in Gali and Gertler (1999) is for a slightly shorter sample period, 1961-1997). Given (4), the residual component zt is just the di¤erence between the in‡ation and its fundamental component ( zt = t t ). Our GG fundamental in‡ation series does a reasonable job of tracking actual in‡ation during the interval that expectations-augmented pricing equations are designed to explain: the rise in in‡ation during the late 1960s, the sustained high in‡ation of the 1970s, and the unwinding of in‡ation in the early 1980s. Indeed, it is the close correspondence of fundamental in‡ation with actual in‡ation over these periods that many researchers found intriguing when they were …rst displayed in Gali and Gertler (1999) and Sbordone (2002).10 9 In appendix B, we display the detrended in‡ation and real unit labor cost series, obtained using a one-sided high pass …lter. 10 The relationship is less strong in the early and late periods of our sample, with much of poor performance 7 3.4 Implications for modeling The tractability and empirical success of the NKPE led it to become a standard, if controversial, element of textbook presentations of the New Keynesian approach to macroeconomics.11 More important for our purposes, the NKPE was imported into modern DSGE models employed by central banks around the world, as discussed in the introduction. With many central banks undertaking some version of in‡ation targeting, Figures 2 and 3 capture why the NKPE approach was attractive as part of a larger model. Figure 2 is in line with the idea that in‡ation control requires the management of expectations, while Figure 3 suggests that aggregate demand policies – which a¤ect in‡ation through real marginal cost in these models – could be used for this purpose. At the same time, the parameter estimates of Table 1 indicate that major movements in real marginal cost must arise because the parameter is small (at 0:15 for the Gali-Gertler studies). With expected in‡ation held constant, cutting annualized in‡ation by one percent in the current quarter thus requires that real marginal costs fall by 6 percent. The NKPE thus incorporated the idea of a challenging short-term trade-o¤ if expectations are …xed, while having little long-run trade-o¤ with changing expectations. Sbordone (2002) highlights the promise of the NKPE single equation estimates as follows: "nominal rigidities are a reasonable component of a complete macroeconomic model. The failure of existing general equilibrium models which incorporate nominal rigidities to account for all features of observed time series (see King and Watson (1996); Christiano et al. (1997)) may not be due to a misspeci…ed pricing equation, but rather to other features of these models (that they share with standard real business cycle models)." It is to analysis with a rich and modern DSGE model that we now turn. 4 Accounting with the canonical NK-DSGE model While we can learn much about in‡ation and its relation to unit labor cost from analyzing the NKPE in isolation, it must be imbedded in a complete structural econometric model to answer questions about interactions of in‡ation and other variables (output, interest rates, employment, etc.) and questions about the structural sources of variability and covariability. In this paper, we study DSGE in‡ation dynamics using the model of Smets and Wouters (2007). Along with many other builders of modern DSGE models, Smets and Wouters employ an alternative route to a hybrid NKPE than that provided by Gali and Gertler (1999): in the later period arising from revisions in the real unit labor cost data that were not available to Gali, Gertler, and Sbordonne. 11 See Gali (2008), Walsh (2010), and Woodford (2003). 8 they assume that a fraction of …rms can dynamically index their prices to the in‡ation rate, rather than keeping these …xed in nominal terms, a mechanism popularized by Christiano, Eichenbaum and Evans (2005) and developed in detail by Eichenbaum and Fisher (2007).12 While this story provides a di¤erent motivation for lagged in‡ation in the NKPE, the result also takes the form (2), albeit with a di¤erent link between that equation’s coe¢ cients and structural parameters. The Smets-Wouters study also employs a di¤erent sample period, di¤erent data, and a di¤erent estimation procedure. However, from the structural parameters estimated by Smets and Wouters estimates (2007, table 1), we can calculate the implied values of , b and f : we list these in Table 1 and use them throughout the paper. The Smets and Wouters (2007) model for the U.S. economy is a medium scale DSGE model. It features a neoclassical ‡exible price "core" that is a real business cycle model augmented with real frictions in investment (cost of changing the rate of investment) and consumption (habit persistence) that is subjected to shocks to general production and investment-speci…c technology.13 Monopolistic competition elements are present in both labor and product markets, with variable elasticity aggregators of the Kimball (1995) form and with overhead costs absorbing pro…ts. Nominal stickiness along Calvo (1983) lines is introduced into both product and labor markets as in Erceg, Henderson, and Levin (2000). As previously discussed, there are additional price and wage inertia mechanisms – partial indexation –embedded in earlier DSGE models. Finally, the model is closed with an interest rate rule for monetary policy in the tradition of Taylor (1993). The Smets-Wouters model is estimated using Bayesian methods along the lines advocated by An and Schorfheide (2007). A major impetus to DSGE model development was provided by the Smets and Wouters (2007) …nding that the model was competitive in …t and forecasting with standard and Bayesian VAR models. As a medium scale DSGE model, the Smets and Wouters framework model contained predictions for a substantial number of macroeconomic variables (about 40). In estimation, the authors sought to match 7 series of major interest to macroeconomists and policymakers: the growth rates of output, consumption, and investment; the growth rates of nominal prices and wages; the level of labor input (aggregate hours); and the short-term nominal interest rate. The authors introduced the minimum number of structural shocks necessary to avoid a stochastic singularity specifying these as a shock to total factor productivity, an investment speci…c technology shock, a government purchase shock, an interest rate spread shock, shocks to price and wage markups, and a monetary policy shock. Importantly for our analysis, Smets and Wouters treat zt di¤erently from Gali and Gertler 12 The fact that actual micro prices are held …xed in nominal terms rather than adjusted mechanically according to an index has led to substantial criticisim of the indexation mechanim (see, for example, Collard and Dellas (2006)). 13 Variable depreciation arising from endogenous capacity utilization and overhead production costs also augment the core neoclassical model. 9 along two dimensions. First, they give zt a structural interpretation as the exogenous component of a time-varying markup of price over marginal cost. Second, they specify its evolution as zt = p zt 1 + pt (7) p p;t 1 with p = 0:89, and p = 0:69.14 Processes with substantial moving average parameters have been used extensively in the literature on forecasting in‡ation with univariate time series models (see, for example, Nelson and Schwert (1978) and Stock and Watson (2007)). The MA component of the speci…cation allows a forecasting model to capture the fact that there are important high frequency components of in‡ation since a value of p = 0:69 means a current forecast error induces a forecast revision that is only about 0:2 of the error (Et zt+1 Et 1 zt+1 = ( Et 1 zt+j = p ) pt = 0:21 pt ). Nevertheless, since Et zt+j j ( p ) pt , the implied price markup variations are highly persistent. 4.1 In‡ation and Modi…ed RULC The overhead structure of production in Smets and Wouters (2007) means that standard real unit labor cost does not accurately measure real marginal cost. However, it can be measured by modi…ed real unit labor cost, t = (Wt Pt ) + n t 1 yt , (8) where is the ratio of total cost (including overhead cost) to total output.15 The value of estimated by Smets and Wouters implies that the typical …rm has overhead cost that are approximately 60% of its total cost, so that 1:6. The Gali and Gertler measure of real unit labor cost takes the form as (8), but with = 1. As a practical matter, the Smets and Wouters unit labor cost is thus less responsive to movements in output relative to real compensation . The in‡ation dynamics of the DSGE model obey the NKPE (2) using this modi…ed unit labor cost construction. Figure 4 shows the in‡ation and modi…ed real unit labor cost series which we employ in our analysis of the SW model. (Detrended values are shown in Appendix B.) Note that GDP in‡ation is the same as in Figure 1; it is the labor cost series which is di¤erent.16 14 These numbers are the posterior means of the parameters, provided in Table 2 of Smets and Wouters (2007). In their work, the parameter is called p to distinguish it from the AR parameter of other shock processes. 15 While the SW-DSGE model was not directly …t to match modi…ed real unit labor cost, it was …t to match the joint behavior of its ingredients (W; n; P; y), and modi…ed real unit labor cost is one of the many variables provided by the Smets-Wouters Dynare code that is employed to estimate and simulate the SW-DSGE model. 16 Gali-Gertler and Smets-Wouters also di¤er in some details of their measurements of the components of 10 4.2 Smets-Wouters in‡ation decomposition Smets and Wouters (2007) do not use either of our decompositions, but rather provide a historical decomposition of in‡ation into components arising from the various shocks, as in standard vector autoregression analysis. Figure 5 displays the SW-DSGE model’s decomposition of the historical behavior of in‡ation into price markup shocks, wage markup shocks, monetary policy shocks, and all other shocks.17 The DSGE framework allows a further breakdown of the last panel into consequences of shocks to government purchases, general productivity, investment-speci…c productivity, and an interest rate spread. However, given the focus of the present study and to avoid unwieldy …gures, we opted for a more limited breakdown. Some macroeconomists would surely be surprised by this decomposition, which attributes most of the variation in in‡ation to price and wage shocks. But Keynesian economists have long suggested that most of in‡ation is due to such factors. Other macroeconomists would point to the fact that the DSGE model indicates that monetary policy exerted an important e¤ect on in‡ation –…rst positive and then sharply negative –during the late 1970s and early 1980s. We now turn to the results of our decompositions. 4.3 Decomposition 1 Just as we did for the Gali-Gertler NKPE parameter values, we can use (2) and the SmetsWouters NKPE parameter values to decompose t into a component associated with lagged in‡ation ("inertia"), expected future in‡ation ("expectations"), real unit labor cost ( t , now using the modi…ed unit labor cost series), and residual (z in equation (2). However, to generate in‡ation expectations, we now use the in‡ation forecast from the full Smets and Wouters (2007) DSGE model, so that we label the decompositions as SW-DSGE. The results are shown in Figure 6. Comparing these to the corresponding …gure for our replication of Gali and Gertler (Figure 2) shows little change in decomposition: expected real marginal cost (W; P; n; and y). Gali and Gertler use measures for the non-farm business sector for all of these components. Smets and Wouters use full-economy measures for y and P (real GDP and the GDP de‡ator), nominal compensation per hour in the non-farm business sector for W , and compute n (total hours of employment) using average weekly hours in the non-farm business sector multiplied by employment in the total economy (from the U.S. household survey). Finally, because n and y are in per-capita terms, Smets and Wouters divide hours and output by a measure of population; this adjustment is not necessary for Gali and Gertler (because = 1 for their measurement of ). Edge and Gurkaynak (2010) discuss measurement problems with the population series used by Smets and Wouters. Our analysis is based on a modi…ed version of the series that eliminates these problems. See Appendix A for details. 17 Our Figure 5 conveys similar content to Figure 4 in Smets and Wouters (2007), but is tailored to our purposes. Smets and Wouters (2007) combine price and wage markup shocks in providing the historical decomposition of in‡ation. 11 in‡ation is the dominant force in current level of in‡ation. Evidently this conclusion is robust to the range of parameter values encompassed by Gali-Gertler and Smets-Wouters as well as to the di¤erences in the way real marginal cost ( ) is measured. 4.4 Decomposition 2 Similarly, we can use (5) and (6) to break t into a marginal cost component ("fundamental in‡ation", ) and price mark-up component ( z ) for the DSGE model. Each component depends on current and expected future values: we use the full Smets and Wouters DSGE P j model to construct the forecasts, for example 1 Et t+j in fundamental in‡ation. j=0 Figure 7 provides actual in‡ation and our constructed SW-DSGE fundamental in‡ation . While Figure 3 shows a plausibly close relation between the and the GG-VAR over much of the sample period, no such relation is evident in Figure 7. Notably, since = + z , Figure 7 instead suggests that over the 1960-1999 period, in‡ation was the result of two countervailing trends: a large downward trend in the marginal cost component that was essentially cancelled out by an upward trend in the price markup component z . 4.5 The In‡ation-Unit Labor Cost Puzzle The behavior of in‡ation within the DSGE setup thus provides a puzzle, which we can pose as a series of questions. Why are the single equation and DSGE results for fundamental in‡ation so di¤erent? Is it because the NKPE parameters in Table 1 are not the same? Is it because unit labor cost, as modi…ed by Smets-Wouters, is a poor proxy for marginal cost, while the GGS construction better captures marginal cost? Is it because, as with Sbordone’s (2002) appraisal of an earlier generation of sticky price DSGE models, there is something crucially wrong with the rest of the Smets and Wouters model as a driving process for in‡ation? Or is it something else about the comovement of in‡ation and real unit labor cost? We now turn from being accountants to being detectives. 5 Understanding fundamental in‡ation As we have seen, the estimate of fundamental in‡ation based on the GG-VAR model indicates that much of the variation in in‡ation over 1960-1999 was associated with variation in expected future marginal cost (i.e., fundamental in‡ation shown in Figure 3). By contrast, our SW-DSGE construction of fundamental in‡ation is not close to variations in actual in‡ation. In this section, we investigate why the two models yield such dramatically di¤erent 12 fundamental in‡ation series over 1960-1999. 5.1 Common computational framework To sort through the sources of di¤erences in the two fundamental in‡ation measures, it is useful to introduce some notation and a common computational framework. For both the GG fundamental in‡ation construction (based on a VAR) and the SW construct (based on the DSGE model), future values of are forecast using a state-vector, say dt , which evolves as dt = M dt 1 (9) + ut ; where ut is an unforecastable error vector. For the GG measure of fundamental in‡ation, d contains current and lagged values of in‡ation and real unit labor, when we place their VAR in the companion form (9). For the SW measure, d is the state-vector for the DSGE model. In both models is linearly related to d, that is t = 0 dt , (10) where, for the GG-VAR model is a selection vector that extracts from the state vector d, and for the SW-DSGE model is a vector of coe¢ cients. Thus, each version of fundamental in‡ation can be written as t = t 1 + 0 [I M ] 1 dt = (1 L) 1 0 [I M ] 1 dt (11) where the expression uses the de…nition of fundamental in‡ation in (5) together with the formula for computing expected discounted familiar from Campbell and Shiller (1988). Equation (11) highlights two important di¤erences in the GG-VAR and SW-DSGE measures of fundamental in‡ation. The …rst is that there are a di¤erent set of parameters for the hybrid NKPE, that is the values of , , and in (11).18 In what follows we denote the hybrid NKPE parameters by = ( , , ), with GG and SW denoting the parameter values implied by the Gali-Gertler and Smets-Wouters structural parameter estimates. The second di¤erence is that there is a di¤erent forecasting model, that is the values of M and dt in (11). Finally, a third important di¤erence is that the data used for forecasting (d) is not the same across the two studies, as we discuss further below. More abstractly, based on (11), we can represent fundamental in‡ation as ( ; M; ), indicating its dependence on NKPE parameters, on the forecasting model, and on the empir18 Recall from section 2 above that these parameters are functions of b ; , and are listed in Table 1. In turn, for the Smets-Wouters model, b ; structural parameters. 13 f f and : the implied values of , and are functions of deeper ical measure of marginal cost employed. (In‡ation enters, too, but it is a common time series and cannot be the source of any di¤erences given these other elements). Using this notation, we have so far looked at ( GG ; M GG V AR ; GG ) in Figure 3 and ( SW ; M SW DSGE ; SW ) in Figure 7. 5.2 Di¤erences Cost measures As discussed above, one source of the di¤erence between the fundamental in‡ation measures is the empirical measure of . Figure 8 plots the standard real unit cost measure used by Gali and Gertler and the modi…ed version used by Smets and Wouters. A striking feature of the plot is the di¤erent low-frequency behavior of the two series, particularly post-1980, with the Smets-Wouters modi…ed measure showing a more pronounced decline from 1980 until the mid 1990s. Detrended values of the series are shown in Appendix B; the detrended series generally move together: the correlation between the detrended series is 0:66. Evidently, di¤erences in low-frequency behavior of GG and SW are potential souces of the di¤erences in the two fundamental in‡ation series. 5.3 An approximation to fundamental in‡ation To simplify matters, we …nd it useful to interpret the various versions of using an approximation and a related pair of estimated approximation coe¢ cients. To motivate this approximation, consider the GG-VAR forecasting model in which dt contains current and lagged values of and . From (11), fundamental in‡ation will then depend on a distributed lag of and , (L) t + (L) t (12) t = where the polynomials in the lag operator, (L) and (L), depend on and M . By rearranging the state vector (which one can always do without changing any implications of the model (12)) we create an alternative equivalent form, t = (1) t + (1) t + ! (L) t + ! (L) t: (13) This new formulation (13) pulls out a single level of and together with lags of the …rst di¤erences = t = t t 1 . In (13), the coe¢ cients on the levels of t 1 and and are the sums of the coe¢ cients in distributed lag in the original equation (12), so they can be written as (1) and (1). The rearrangement yielding (13) lets us break up t into a level component, (1) t + (1) t and an additional component that is a distributed lag of changes (! (L) t + ! (L) t ). Because and are persistent and because t depends on long-run forecasts 14 of future , most of the variability in t arises from the level component, (1) t + (1) t , and the distributed lag of changes, ! (L) t and ! (L) t , has relatively little e¤ect on t . Thus, we will approximate t by et , where t et = (1) t + (1) t . (14) The advantage of this approximation is that it allows us to characterize di¤erences in fundamental in‡ation using only the coe¢ cients (1) and (1), as well as the measure of real marginal cost, . This approximation cannot be directly used for the SW-DSGE measure of t because it is based on a state vector d that contains variables other than and , so that (12) does not hold. To overcome this problem, we compute an approximation in two steps for the SW fundamental in‡ation. In the …rst step, we use the DSGE model to compute the model-implied population values of the autocovariances and cross-autocovariances for and : from these, we compute the implied bivariate VAR coe¢ cients for and with the same number of lags used in the GG-VAR fundamental in‡ation. In the second step, we compute the approximation (12) using the model-based bivariate VAR coe¢ cients and data on and . Figure 9 shows the GG-VAR and SW-DSGE measures of fundamental in‡ation ( t , from Figures 3 and 7) together with their approximations (et using (14)) and where each approximation is based on a bivariate VAR, as discussed above. The GG approximation uses the GG measure of (real unit labor cost) and the SW approximation uses the SW measure of (modi…ed real unit labor cost). In panel A of Figure 9, we see that the GG constructs, t and et , essentially coincide: thus, we can capture most of the variation in using to coe¢ cients GG (1) and GG (1) along with the levels of GG and t . In panel B of Figure 9, we see that the approximation t is less than perfect for the SW constructs, but et does capture much of variation in t (the correlation between the two series is 0:97). So, we view the approximation as reasonable in each case. How does the approximation et help us in our detective work? We want to learn about the relative importance of NKPE model parameters , the forecasting model parameters M , and the empirical measure of marginal cost in generating the striking di¤erence between the GG-VAR and SW-DSGE measures of fundamental in‡ation. First, we can see that the distributed lag weights (L) and (L) in (12) depend only on (the parameters in the NKPE) and M (the state-transition matrix that governs the forecastability of future values of real marginal cost), equations (12) and (14): we can thus change and M separately and determine the e¤ect on just two numbers, (1) and (1). Secondly, we see that the particular measure of marginal cost plays a role. Taking these points together, any 15 di¤erences in measures of fundamental in‡ation can be attributed to the choice of , M , and a particular empirical measure of real marginal cost . This allows us to investigate the source of the di¤erences between the two fundamental in‡ation measures by changing the values of , M , and : 5.3.1 Mixing and Matching ; M; and Table 2 summarizes the behavior of ( ; M; ) for various values of , M , and . Five summary statistics are shown for each measure of fundamental in‡ation: (1) and (1) are the coe¢ cients from (14), (e ) is the standard deviation of e over the 1960-1999 sample period, cor( ; e ) is the correlation between fundamental in‡ation and the approximation in (14), and cor( ; e ) is the correlation of actual in‡ation with e . The table highlights two sets of benchmark results, presented in the boldfaced rows 1 and 6. These tabulate information on the fundamental in‡ation and approximation series displayed in Figure 9. First, row 1 of the table shows results for the GG-VAR fundamental in‡ation and its approximation, based on (14) and plotted in Panel A of Figure 9. Row 1 indicates that the approximation depends positively on both and with weights (1) = 1:30 and (1) = 0:26; that it has a volatility just slightly higher than actual in‡ation ( (e ) = 2:90 versus ( ) = 2:53); that the approximation is nearly perfect (cor( ; e ) = 0:99); and that it captures many of the movements in actual in‡ation (cor( ; e ) = 0:61) over the 1960-1999 sample period. Second, row 6 shows the results for the SW-DSGE series plotted in Panel B of Figure 9. In contrast to the results just discussed, row 6 shows that the SW-DSGE approximation places a larger positive weight on ( (1) = 1:89), but a negative weight on ( (1) = 0:89); that it has a volatility much higher than actual in‡ation ( (e ) = 5:22); that it is a good, but not perfect approximation (cor( ; e ) = 0:97); and that it is essentially uncorrelated with actual in‡ation (cor( ; e ) = 0:02). To look behind these stark di¤erences, the other rows of the table summarize the behavior of computed using di¤erent permutations of ; M , and . For example, row 2 shows results for e ( SW ; M GG V AR ; GG ), i.e., an approximation computed using the GG measure of real unit labor cost ( GG ) and forecasting model (M GG V AR ) but using the Smets-Wouters NKPE parameter values ( SW ). Comparing the various rows in the table leads to the conclusion that all of the ( ; M; ) ingredients play complementary roles in explaining the di¤erences between the GG and SW measures of fundamental in‡ation. We discuss each ingredient in turn. To understand the role of the parameter values, compare the row 2 information on e ( SW ; M GG V AR ; GG )) and the benchmark in detail. Note that the Smets-Wouters estimates in Table 1 put more weight on expected future in‡ation (higher ) in the NKPE. In turn, this leads to more weight placed on expected future values of in fundamental 16 in‡ation. (From Table 1, the Smets-Wouters discount factor is SW = :998 while the corresponding Gali-Gertler value is GG = 0:876). Turning to our approximation, with M and held constant (based on GG), (1) is slightly smaller and (1) is substantially larger (rising from 0:26 in row 1 to 0:99 in row 2) computed using SW than with GG . But it cannot be the Smets-Wouters parameters alone that lead to the di¤erence, as row 2 of Table 1 also shows that (i) the approximation becomes more highly correlated with actual in‡ation; and (ii) it also becomes too volatile relative to actual in‡ation. To understand the role of the forecasting model M , start by looking at the …rst three rows of the table: each uses M GG V AR , i.e, constructs that forecasts constructed using a VAR estimated using the GG measure. These measures are di¤erent on some dimensions (such as volatility and correlation with actual in‡ation), but they all place a weight on the measure that is positive and less than the corresponding values using M SW V AR or M SW and a weight on that is positive ( (1) = 0:26 in rows 1 and 3 and is 0:99 is row 2). By contrast, there is a very di¤erent pattern in all of the other rows of the table: the weight placed on is positive and large and the weight placed on is negative ( (1) < 0). Said di¤erently, with t …xed, increases in t predict decreases in future when the SW measure of is used, but predict increases in when the GG measure is used. This …nding holds robustly: (i) it occurs when the forecasting model is estimated using the Smets-Wouters measure of ; either directly in a VAR in rows 4 and 5 (M SW V AR ) or indirectly using the complete Smets-Wouters DSGE model in rows 6 and 7 (M SW ) and (ii) it occurs when the parameters are those of Gali-Gerler (lines 4 and 7) or Smets-Wouters (lines 5 and 6). Finally, to understand the role of the empirical measure of in fundamental in‡ation, notice that cor( ; e ) is close to one for all rows in the table (that is for both the GG and SW measures). This is consistent with the approximation equation (14) that shows, for a given value of (1), the measure of has a direct e¤ect on the approximate measure of fundamental in‡ation. Taken together these results suggest a two-part explanation for the trending behavior of in the SW-DSGE fundamental in‡ation construction displayed in Figures 7 and 9. In the …rst half of the sample period (1960-1980), the steep decline in arises largely from upward trend in actual in‡ation via the (1) t component of our approximation to fundamental in‡ation. This curious result arises because there is a negative value of (1) = 0:89 in line 6 of Table 2. In the second half of the sample period, there is little low frequency variation in in‡ation. However, the Smets-Wouters modi…ed real unit labor cost measure shows a marked decline which, when ampli…ed by (1) = 1:89 in line 6 of Table 2, leads to a steep decline in the measure of fundamental in‡ation that we have constructed for the Smets-Wouters model and data. A pronounced decline does not arise in the benchmark GGVAR measure (displayed in Figure 9A) of fundamental in‡ation, because our approximation indicates that their forecasting model does not imply a negative relationship between and 17 fundamental in‡ation (that is, (1) > 0) and because the Gali-Gertler measure of real unit labor cost does not show the same trend decline evident in the Smets-Wouters cost measure. 5.4 DSGE structural interpretation While this forecasting exercise explains the empirical mechanics underlying the low-frequency behavior of SW fundamental in‡ation, it doesn’t explain how this behavior is manifested in the Smets and Wouters structural DSGE model. For example, what is it in the structural model that explains why high in‡ation today predicts low future values of marginal cost? That is, what is it in the Smets-Wouters model that leads to a negative value of (1)? This negative value is particularly puzzling because the underlying economics of the NKPE indicate just the opposite: if today’s in‡ation arises from expected future values of real marginal cost, then high in‡ation predicts high (not low) values of future marginal cost. To see how the model can generate a value of negative value of (1), recall that in‡ation (fundamental in‡ation, speci…ed in (5)) t is completely decomposed into a component associated with expected future and a component z associated with expected future price markup variations (speci…ed in (6)) . The Smets-Wouters model contains seven exogenous shocks. One of these, p , is a price-markup shock and the six others, which we’ll collect in a vector other , represent shocks to productivity, interest rates, and so forth. The NKPE makes a strong restriction, that other a¤ects only through its e¤ect on . In contrast, the price-markup shock, p , a¤ects in two ways: …rst directly through the e¤ect of p on p 1 current and expected future values of z (zt = (1 p L) (1 p L) t in the Smets-Wouters DSGE model), and indirectly through the general equilibrium e¤ects of these shocks on current and future values of . Thus, consider a other shock that leads to an increase in . Because this arises through , the shock induces a positive correlation between and . Indeed, if was a¤ected other only by shocks, then t = t , so that in the forecasting exercises in the last section (1) = 0 and (1) = 1. Put di¤erently, thinking about other shocks leads one to the conclusion that an increase in in‡ation today should predict higher values of in the future ( (1) > 0). Yet, as we saw in the last section, just the opposite occurs in the Smets-Wouters model. The observation that (1) < 0 therefore leads to two conclusions. First, p must be an important source of variation in both and . Second, a shock to p that leads to an increase in in‡ation must have a persistently negative e¤ect on marginal cost ( ). Using both impulse responses and historical decompositions, we next describe the structural mechanisms that generate this result within the Smets-Wouters model. First, Figure 10 shows the impulse response functions of a price markup shock within the Smets-Wouters model. Panel A shows the model’s implied response of , z, and to 18 a p shock. Panel B decomposes this response into the component arising from and z . Taking the panels together, this …gure shows that a shock to p leads to a relatively shortlived increase in‡ation that is accompanied by much longer-lived but opposite responses of z t and t . What are the economic mechanisms behind this? We consider a real mechanism and an in‡ation mechanism: each discussion essentially involves treating the elaborate Smets and Wouters model as if it were one of the …rst generation DSGE models built around an RBC core (such as in King and Watson (1996), King and Wolman (1996) and Yun (1996)). In this …rst generation of sticky price DSGE models, there is no trade-o¤ between strict in‡ation targeting and maintaining output at its natural level (de…ned as the level of output that arises when there is monopolistic competition and real frictions, but with full nominal price ‡exibility). These …rst generation DSGE models generally also specify production functions for which real marginal cost would be well-captured by real unit labor cost. These models allow us to …rst think about real activity under a "neutral monetary policy" of strict in‡ation targeting, in which the e¤ects of nominal stickiness are absent. An increase in the real price markup is like an increase in taxation of output, the proceeds of which are redistributed as transfer payments (monopoly rents) to households. But, in these models, the real price markup (P= ) is just the inverse of real marginal cost ( = =P ). The highly persistent increase in the price markup (z) thus must lead to a highly persistent decline in real marginal cost : Further, given that the NKPE under strict in‡ation targeting implies that t + zt = 0, a unit increase in zt leads to a 1= decrease in t . Since the real markup shock is highly persistent, there is also a lengthy interval in which the natural rate of output is low due to increases in real distortions. However, if the monetary authority partly accommodates the markup shock by temporarily raising the in‡ation target, price stickiness means that the e¤ect of the markup shock on real marginal cost is partially cushioned and there is a smaller fall in output (output rises relative to the depressed natural rate level). In Figure 10, in‡ation only rises by a small amount (and very temporarily) so that the …rst-round real analysis of the consequence of the markup shock captures the main e¤ects in a …rst generation model which had the same in‡ation response. We …nd this pattern intuitive and broadly compatible with the impulse response functions. Yet, the Smets-Wouters model is more elaborate framework (including a di¤erent marginal cost measure as well additional real and nominal frictions beyond those in the …rst generation models), so this can be at best a reference analysis. Figure 11 uses the historical decomposition approach within the Smets-Wouters model to decompose their measure of into a component associated with price markup shocks (panel A) and all other shocks (panel B). Evidently, the model attributes the trend declines in real unit labor cost (and fundamental in‡ation) to price markup shocks, which as we saw 19 previously in Figure 7 also explained a good part of the variation in the level of in‡ation. The panels of Figure 11 also highlights several major elements of the historical behavior of modi…ed real unit labor cost. Panel A reminds us that the modi…ed real unit labor cost measure displays a downward trend over the 1960-1999 sample period and, as just discussed, most of the ‡uctuations in that trend are accounted for by the price markup shock. Panel B indicates that wage markup shocks also induce quarter-to-quarter variability in modi…ed real unit labor cost. Panel C indicates that monetary policy shocks play an important role in the rise and fall of modi…ed unit labor cost during the late 1970s and early 1980s, when in‡ation rose and fell. Finally, Panel D indicates that other factors also induce variability in modi…ed real unit labor cost. 6 US in‡ation and Real Unit Labor Cost 2000-2011 Thus far we have focused our attention on the 1960-1999 sample period that –through the work of Gali-Gertler, Sbordone, Smets-Wouters and others – played a key role in shaping the economics profession’s views about the potential of the NKPE for explaining in‡ation dynamics. In the section, we extend the data through the 2000s to see how the NKPE instructs us to think about in‡ation during the last decade. This is interesting in its own right and also serves as an out-of-sample external validity check for the in-sample conclusions discussed earlier. Figure 12 plots real unit labor cost and modi…ed real unit labor cost through 2011:I. While in‡ation has remained relatively stable over the past decade, both measures of real unit labor cost show signi…cant declines (between 7 and 8 percent from 1999:IV to 2011:I). Of course, real unit labor cost (in logs, W P + n y) is labor’s share of income in the sector: the stability of this "great ratio" is one of the standard stylized facts of macroeconomics. From a New Keynesian modeling perspective, the constancy is a production function attribute governing low frequency real reactions, but is overlaid by cyclical variations in = W + n P y arising from the interplay of imperfect competition, sticky prices, and shocks. Over the benchmark sample period, 1960-1999, the average value of labor share in the non-farm business sector was 63.8%, while it was 65.1% in 1960.1 and 62.6% in 1999.4. In the last quarter of our data set, 2011.1, it had fallen to 57.8%. The source of this decline in labor’s share (real unit labor cost) is both puzzling and important.19 However, in the context of the NKPE the puzzle about labor’s share is not its source, but rather its predicted e¤ect on in‡ation. Figure 13 plots in‡ation together with measures of fundamental in‡ation computed using the GG-VAR and SW-DSGE models extended with data through 2011:I. Evidently the large declines in real unit labor cost translate into large 19 The decline in labor’s share is discussed, inter alia, in Fleck et al (2011). 20 declines in fundamental in‡ation. While actual in‡ation is essentially unchanged over the post-1999 period, the measure of fundamental in‡ation constructed along Gali-Gertler lines fell by nearly 15 percent and that implied by the Smets-Wouters DSGE model fell by nearly 20 percent. That is, both measures of fundamental in‡ation predicted large de‡ation over the last decade. Our interpretation of this evidence is that real unit labor cost has exhibited important low-frequency variation that is unrelated to in‡ation. The last decade provides a dramatic example of this lack of comovement. However, our earlier analysis using the SW modi…ed real unit labor cost suggests that the pattern of limited low frequency comovement also arose in the earlier sample period (1960-1999) and played out through the Smets and Wouters DSGE model in its estimation period. In this sense, their model was forced to deal with this low-frequency variability in the earlier sample period, and as we discussed above, the model did this by using the price-markup shock to (essentially) explain the trend real unit labor cost. Of course, given the structure of their model, any low-frequency variability in real unit labor cost must be intimately related to variability in in‡ation, so the same shocks the explained the trends in real unit labor cost (the price-markup shock) must also explain some of the variation in in‡ation (see Figure 7, panel A). Figure 14 decomposes our SW fundamental in‡ation measure over the extended sample period into a component associated with the model’s price markup shocks and with all of the other shocks in the model. Given the analysis in the last section, it is not surprising that the price markup shocks explain the trend in fundamental in‡ation. However, it is interesting to note the "detrended" version of fundamental in‡ation (that is, the component of fundamental in‡ation associated with shocks other than the price-markup shock) …ts in‡ation much like our Gali-Gertler measure did over the 1960-1999 sample period. However, this component explains little of the variation in in‡ation since about 1985, following the disin‡ation of the early 1980s. 7 Conclusions An earlier generation of Keynesian macroeconometric models developed in the 1960s featured price and wage sectors that …t well during estimation periods, but that subsequently foundered on episodes of stag‡ation and the implication that there was an important long-run trade-o¤ between in‡ation and unemployment. The Lucas critique led to an abandonment of these models by academics, a deepened skepticism about them within parts of the monetary policy community, and a search for macroeconomic models with stronger microeconomic foundations and better empirical performance. The microeconomic pricing foundations developed along New Keynesian lines incorpo- 21 rate expectations mechanisms that produce a shifting trade-o¤ between in‡ation and real activity. They stressed the role of marginal cost in pricing and in‡ation dynamics, focusing on real unit labor costs as a proxy for marginal cost, and thereby avoided the thorny issue of measuring capacity output. Estimated over the mid 1960s through the early 2000s, these models provide an interpretation of the interval of rising in‡ation in the late 1960s and early 1970s, the subsequent stag‡ation episodes, the Volcker disin‡ation, and the Great Moderation beginning in the mid 1980s. The single equation studies of Gali and Gertler (1999) and Sbordone (2002) that popularized the New Keynesian Pricing Equation had three important properties that we display via replication and decompositions: a minor role of a transitory variation in marginal cost, a major role for expected of in‡ation, and an associated major role for a measure of expected future variations in marginal cost as captured by the construction of "fundamental in‡ation". We show that the DSGE model of Smets and Wouters (2007), which contains a variant of the New Keynesian Pricing Equation, has the …rst two of these properties but is problematic along the third dimension: actual and our SW fundamental in‡ation construction. We trace this di¤erence to the measure of real unit labor cost employed by Smets and Wouters (2007) which has a major downward trend so that their structural model is forced to include a major upward trend in a measure of price markup shocks. We considered how these structural markup shocks likely operate within the Smets-Wouters DSGE model, describing consequences for both real activity and in‡ation. Looking beyond the estimation period of the single equation studies and of the canonical DSGE model, we …nd that all measures of real unit labor costs display major downward trends that not accompanied by similar trends in in‡ation. (Equivalently, labor’s share has fallen dramatically since the late 1990s, while there has been little variation in in‡ation). While it is possible to reconcile this absence of comovement by the introduction of large price markup shocks that are negatively correlated with real unit labor cost, we …nd it more plausible that real factors are in‡uencing labor’s share in ways that are largely unrelated to in‡ation. Tracing the sources of these changes and their implications for speci…cation of pricing equations look to be …rst order topics for macroeconomic research. 22