Inflation and Unit Labor Cost Part 2

3. ACCOUNTING WITH JUST THE NKPE We now investigate how the hybrid NKPE (2) accounts for inflation during the 1960-1999 period, using our two decompositions. For this purpose, we use the parameter values from Gali and Gertler (1999) displayed in Table 1. 3.1 Inflation 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 deflator price inflation (π) and log real unit labor cost ψ (measured as the logarithm of the ratio of nominal compensation per hour to nominal output per hour in the nonfarm business sector). The real unit labor cost series moves together with inflation, notably during the 1970s and 1980s. To operationalize our decompositions, we need to construct Et π+1 for the first and t   j 0  i Et t  j for the second. In each case, we follow Gali and Gertler (1999) and use a  bivariate VAR that includes four lags of  and  to forecast the relevant variables. We consequently call these GG-VAR decompositions. Additional computation details on the fundamental inflation decomposition are provided in section 5 below. 3.2 Results from Decomposition 1 The results of decomposition 1 are displayed in Figure 7. We find that expected inflation is the dominant source of actual inflation in Figure 7 (f Ett+1). A smaller part of inflation is due to inertial effects (bt−1 is shown in panel A). Because the coefficient on real unit labor cost is small ( = 0.15), the real unit labor cost component (t ) accounts for little of the variation in inflation. Finally, residual influences (zt = t – [f Ett+1 + bt−1 + t]) are quantitatively important. 3.3 Results from Decomposition 2 While current real unit labor costs accounted for little of the variation in inflation using decomposition 1, matters are very different when expected future real unit labor costs are included using decomposition 2. Figure 2 displays the fundamental component  t of inflation 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  tz is just the difference between the inflation and its fundamental component (  tz = t −  t ). Our GG fundamental inflation series does a reasonable job of tracking actual inflation during the interval that such expectations-augmented pricing equations were designed to explain: the rise in inflation during the late 1960s, the sustained high inflation of the 1970s, and the unwinding of inflation in the early 1980s. Indeed, it is the close correspondence of fundamental inflation with actual inflation over these periods that many researchers found intriguing when they were first displayed in Gali and Gertler (1999) and Sbordone (2002).9,10 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 inflation targeting, Figures 2 and 7 capture why the NKPE approach was attractive as part of a larger model. Figure 7 is in line with the idea that inflation control requires the management of expectations, while Figure 2 suggests that aggregate demand policies -- which affect inflation 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 study)12. With expected inflation held constant, cutting annualized inflation 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-off if expectations are fixed, while having little long-run trade-off 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 misspecified pricing equation, but rather to other features of these models (that they share with standard real business cycle models).” We now turn to the analysis of a rich DSGE model. 4. ACCOUNTING WITH THE CANONICAL NK-DSGE MODEL While we can learn much about inflation 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 inflation and other variables (output, interest rates, employment, etc.) and questions about the structural sources of variability and covariability. In this paper, we study DSGE inflation 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): they assume that a fraction of firms can dynamically index their prices to the inflation rate, rather than keeping these fixed in nominal terms, a mechanism popularized by Christiano, Eichenbaum and Evans (2005) and developed in detail by Eichenbaum and Fisher (2007).13 While this story provides a different motivation for lagged inflation in the NKPE, the result also takes the form (2), albeit with a different link between that equation's coefficients and structural parameters. The Smets-Wouters study also employs a different sample period, different data, and a different estimation procedure. However, from the structural parameters estimated by Smets and Wouters (2007, table 1), we can calculate the implied values of , f, and b: 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 flexible 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-specific technology.14 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 profits. 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) finding that the model was competitive in fit 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. They specified these as a shock to total factor productivity, an investment specific 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 differently from Gali and Gertler 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 = pzt−1 + pt − ppt−1 (7) with p = 0.89, and p = 0.69.15 Processes with substantial moving average parameters have been used extensively in the literature on forecasting inflation with univariate time series models (see, for example, Nelson and Schwert (1978) and Stock and Watson (2007)). The MA component of the specification allows a forecasting model to capture the fact that there are important high frequency components of inflation 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 = ( − p)pt = 0.21pt). Nevertheless, since Et zt+j – Et−1 zt+j =  j( − p)pt, the implied price markup variations are highly persistent. 4.1 Inflation and Modified 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 modified real unit labor cost, t = (Wt – Pt) + nt − −1yt (8) where  is the ratio of total cost (including overhead cost) to total output.16 The value of  estimated by Smets and Wouters implies that the typical firm 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 inflation dynamics of the DSGE model obey the NKPE (2) using this modified unit labor cost construction. Figure 3 shows the inflation and modified real unit labor cost series which we employ in our analysis of the Smets and Wouters DSGE model. Note that GDP inflation is the same as in Figure 1; it is the labor cost series which is different.17 4.2 Decomposing inflation in the Smets-Wouters model Smets and Wouters (2007) do not use either of our decompositions, but rather provide a historical decomposition of inflation into components arising from the various shocks, as in standard vector autoregression analysis. Figure 8 displays the DSGE model's decomposition of the historical behavior of inflation into price markup shocks, wage markup shocks, monetary policy shocks, and all other shocks.18 The DSGE framework allows a further breakdown of the last panel into consequences of shocks to government purchases, general productivity, investment-specific productivity, and an interest rate spread. However, given the focus of the present study and to avoid unwieldy figures, we opted for a more limited breakdown. Some macroeconomists would surely be surprised by this decomposition, which attributes most of the variation in inflation to price and wage shocks. But Keynesian economists have long suggested that most of inflation is due to such factors. Other macroeconomists would point to the fact that the DSGE model indicates that monetary policy exerted an important effect on inflation -- first 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 Smets-Wouters NKPE parameter values to decompose t into a component associated with lagged inflation (“inertia”), expected future inflation, real unit labor cost (t, now using the modified unit labor cost series), and residual (zt in equation (2)). However, to generate inflation expectations, we now use the inflation 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 9. Comparing these to the corresponding figure for our replication of Gali and Gertler (Figure 7) leads to the same finding: expected inflation is the dominant force in current level of inflation. Evidently this conclusion is robust to the range of parameter values encompassed by Gali-Gertler and Smets-Wouters as well as to the differences 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 inflation,” ) and price mark-up component (z) for the DSE model. Each component depends on current and expected future values: we use the full Smets and Wouters DSGE model to construct the forecasts, for example   j 0  j Et t  j in fundamental inflation. Figure 4 provides actual inflation and our constructed SW-DSGE fundamental inflation . While Figure 2 shows a plausibly close relation between the actual inflation  and the GGVAR  over much of the sample period, no such relation is evident in Figure 4. Notably, since  =  + z, Figure 4 instead suggests that over the 1960-1999 period, inflation 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 Inflation-Unit Labor Cost Puzzle The behavior of inflation 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 inflation so different? Is it because the NKPE parameters in Table 1 are not the same? Is it because unit labor cost, as modified 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 inflation? Or is it something else about the comovement of inflation and real unit labor cost? We now turn from being accountants to being detectives. 19 5. UNDERSTANDING FUNDAMENTAL INFLATION As we have seen, the estimate of fundamental inflation based on the GG-VAR model indicates that much of the variation in inflation over 1960-1999 was associated with variation in expected future marginal cost (i.e., fundamental inflation shown in Figure 2). By contrast, our SW-DSGE construction of fundamental inflation is not close to variations in actual inflation. In this section, we investigate why the two models yield such dramatically different fundamental inflation series over 1960-1999. 5.1 Common computational framework To sort through the sources of differences in the two fundamental inflation measures, it is useful to introduce some notation and a common computational framework. For both the GG fundamental inflation 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 = Mdt−1 + ut (9) where ut is an unforecastable error vector. For the GG measure of fundamental inflation, d contains current and lagged values of inflation 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 = ’dt (10) where, for the GG-VAR model  is a selection vector that extracts  from the state vector d, and for the Smets-Wouters-DSGE model  is a vector of coefficients. Thus, each version of fundamental inflation can be written as  t   t1   '  [ I   M ]1 dt  (1   L)1 '  [ I   M ]1 dt (11) where the expression uses the definition of fundamental inflation in (5) together with the formula for computing expected discounted  familiar from Campbell and Shiller (1988). Equation (11) highlights two important differences in the GG-VAR and SW-DSGE measures of fundamental inflation. The first is that there are a different set of parameters for the hybrid NKPE, that is the values of , , and  in (11).19 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 difference is that there is a different forecasting model, that is the values of M and dt in (11). Finally, a third important difference 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 inflation as (, M, ), indicating its dependence on NKPE parameters, on the forecasting model, and on the empirical measure of marginal cost employed. (Inflation enters, too, but it is a common time series and cannot be the source of any differences given these other elements). Using this notation, we have so far looked at θ(ψπGG, MGG-VAR, ψGG) in Figure 2 and θ(ψπSW, MSW-DSGE, ψSW) in Figure 4.