Inflation and Unit Labor Cost Tables

Appendix A: Data All data are from FRED (Federal Reserve Bank of St. Louis). The table below documents the data series used in our analysis. Table A.1 Series FRED Label Desc Units Prices GDP deflator GDPCTPI Gross Domestic Product: Chain-type Price Index NFB Output deflator IPDNBS Household survey employment Employment NFB sector Population (16 and over) CE16OV Total Hours NFB HOANBS Nonfarm Business Sector: Implicit Price Deflator Employment Index 2005=100 Index 2005=100 Thousands Civilian Employment PRS85006013 Nonfarm Business Sector: Employment Civilian Noninstitutional Population (16 and older) : Note CNP16OV is a non-revised series that contains jumps, etc. We have eliminated outliers in growth rates and fitted cubic spline to monthly growth rates, then used this to get adjusted monthly levels, which were temporally aggregated to quarterly series. CNP16OV Nonfarm Business Sector: Hours of All Persons Avg. Weekly Hours NFB PRS85006023 Compensation per hour NFB sector − Nominal COMPNFB Real GDP GDPC96 Real Output NFB OUTNFB Investment − Nominal Consumption − Nominal GPDI Fed Funds Rate FEDFUNDS Nonfarm Business Sector: Average Weekly Hours Wages Index 2005=100 Thousands Index 2005=100 Index 2005=100 Index (2005 = 100) Nonfarm Business Sector: Compensation Per Hour Output, Consumption, and Investment Real Gross Domestic Product, 3 Decimal Nonfarm Business Sector: Output Gross Private Domestic Investment PCEC Personal Consumption Expenditures Interest Rates Effective Federal Funds Rate Billions of Chained 2005 Dollars Index 2005=100 Billions of Dollars Billions of Dollars Percentage points These data were used to construct two measures of real unit labor cost:    COMPNFB  HOANBS  The Gali-Gertler measure of log-real unit cost is GG = ln  .  IPDNBS  OUTNFB  The Smets-Wouters measure of modified real unit labor cost is given by   COMPNFB    PRS 85006023  CE16OV CNP160V a  SW  ln     t   ln     GDPCTPI     GDPC 96 1     ln  a    CNP160V     t   where CNP160Va is the adjusted value of population given in Table A.1, and  and  are parameters estimated by Smets-Wouters (  =0.00432 and  = 1.614980.) The data were also used to construct the seven variables used in the Smets-Wouters DSGE model. Using the notation in their equation (15), the variables are: GDP = GDPC96/ CNP160Va, CONS = (PCEC/ CNP160Va )/GDPCTPI , INV = (GPDI/ CNP160Va )/GDPCTPI, WAG = COMPNFB, HOURS = (PRS85006023/CE160V)/CNP160Va, P = GDPCTPI, and FEDFUNDS = FEDFUNDS. Table 1: NKPE Parameter Values Parameters in equation (2) Model Gali‐ Gertler Smets‐ Wouters Parameters in equation (3) b f     z 0.253 0.682 0.153 0.325 0.876 0.197 5.138 0.186 0.813 0.082 0.228 0.998 0.101 4.911 Notes: Gali-Gertler parameter values are from Gali and Gertler (1999, Table 2, Row 1). SmetsWouters structural parameter values are from Smets and Wouters (2007, Table 1A) and the Dynare replication files for this paper, which are then used to calculate the parameters in equation (6). The values of , , and z reported above are four times the values reported in Gali-Gertler and Smets-Wouters because we measure inflation at annual rate. Table 2: Properties of Fundamental Inflation Using Different Parameters, Forecasting Rules, and Unit Labor Cost Measures Row  1 2 3 4 5 GG SW GG GG SW 6 7 8 9 SW GG SW GG M  (1) (1)  ( ) cor (  ,  ) A. VAR‐Based Measures of Fundamental Inflation MGG‐VAR 1.30 0.26 2.90 GG GG‐VAR GG 1.09 0.99 3.94 M  GG‐VAR SW 1.30 0.26 4.31 M  SW 2.12 ‐0.29 6.31 MSW‐VAR  ‐SW‐VAR SW 4.37 ‐2.11 12.45 M  B. DSGE‐Based Measures of Fundamental Inflation 1.89 ‐0.89 5.22 MSW SW SW SW 1.63 ‐0.34 4.63 M  1.89 ‐0.89 3.46 MSW GG 1.63 ‐0.34 3.01 MSW GG cor ( ,  ) 0.99 0.99 1.00 1.00 1.00 0.61 0.87 0.51 0.28 ‐0.01 0.97 0.99 NA NA 0.02 0.24 ‐0.15 0.20 Notes: GG are the Gali-Gertler parameter values shown in Table 1; SW are the corresponding Smets-Wouters values. MGG-VAR are VAR coefficients estimated from a bivariate (,GG) VAR(4) model over 1960:I-1999:IV; MSW-VAR are VAR coefficients estimated from a bivariate (,SW) VAR(4) model over 1960:I-1999:IV; and MSW is the companion matrix from the SmetsWouters DSGE model. GG is the logarithm of real unit labor cost for the non-farm business sector and SW is the Smets-Wouters modified real unit labor cost measure. See Figure 8 for a visual comparison of the two series. Figure 1: Gali and Gertler Data Inflation and Real Unit Labor Cost Notes: The solid line is inflation in the GDP price deflator measured in percentage points at an annual rate; that is, 400×ln(Pt/Pt−1), where Pt is the value of the GDP deflator. The dashed line is the deviation in real unit labor cost from its value in 1960:I in percentage points; that is, 100×  GG t GG GG is the logarithm of the index of real unit labor cost in the non-farm  1960: I  , where  business sector (see Appendix A). Figure 2: GG inflation breakdown into 4 components Notes: The solid line in each figure is inflation shown in Figure 1. The dotted lines are the components of decomposition 1 (see equation [2]): (a) inertia (bt−1); (b) expectations (f Ett+1); (c) real ulc (t); and (d) residual (zi). The parameter values b, f, and  are from Gali-Gertler and given in Table 1 of this paper. Real unit labor cost, , is from figure 1. Expected inflation, Ett+1, is computed from a bivariate VAR(4) that includes  and . Figure 3: GG Fundamental Inflation Notes: The solid line is inflation shown in Figure 1. The dotted line is fundamental inflation (  t ) from equation (5). The parameter values b, f, and  are from Gali-Gertler and given in Table 1 of this paper. Real unit labor cost, , is from Figure 1. Expected real unit labor cost, Ett+j, is computed from a bivariate VAR(4) that includes  and . Figure 4: Smets-Wouters Data Inflation and Modified Real Unit Labor Cost Notes: The solid line is inflation shown in Figure 1. The dashed line is the deviation of modified real unit labor cost (see equation (8) and Appendix A) from its value in 1960:I in percentage SW SW is the modified unit labor cost measure used by points; that is, 100×  tSW  1960: I  , where  Smets and Wouters (see Appendix A). Figure 5: Historical Decomposition of Inflation in the Smets-Wouters DSGE Model Notes: The solid line is inflation shown in Figure 1, normalized to have a mean of zero over the Smets-Wouter sample period. The dotted lines are the components of inflation attributed to (a) price markup shocks; (b) wage markup shocks; (c) monetary policy shocks; and (d) all other shocks, where these shocks and contributions are computed using the SW-DSGE model evaluated at the posterior mean of the model’s parameters. Figure 6: SW inflation breakdown into 4 components Notes: The solid line in each figure is inflation shown in Figure 1. The dotted lines are the components of decomposition 1 (see equation [2]): (a) inertia (bt−1); (b) expectations (f Ett+1); (c) real ulc (t); and (d) residual (zi). The parameter values b, f, and  are from SmetsWouters and given in Table 1 of this paper. Real unit labor cost, , is from figure 4. Expected inflation, Ett+1, is computed from the SW-DSGE model. Figure 7: SW Fundamental Inflation Notes: The solid line is inflation shown in Figure 1. The dotted line is fundamental inflation,  t , from equation (5). The parameter values b, f, and  are from Smet-Wouters and are given in Table 1 of this paper. Real unit labor cost, , is from Figure 4. Expected real unit labor cost, Ett+j, is computed from the SW-DSGE model. Figure 8: Comparison of Gali-Gertler and Smets-Wouters Measures of Real Unit Labor Cost Notes: The figures shows the values of real unit labor and modified real unit labor cost from Figures 1 and 4. Figure 9: Fundamental Inflation and Its Approximation Notes: Each panel shows inflation and fundamental inflation (from Figures 3 and 7) together with the approximation to fundamental inflation discussed in Section 5.3. Figure 10: Impulse response implications of the Smets-Wouters (2007) model Response to a Price-Markup Shock Notes: The figures show the impulse responses from a price-markup shock in the SmetsWouters model computed using the posterior mean of the model’s parameters. Figure 11: Historical Decomposition of Marginal Cost from Smets-Wouters (2007) model Notes: The solid line is modified real unit labor cost shown in Figure 4, normalized to have a mean of zero over the Smets-Wouters sample period. The dotted lines are the components of inflation attributed to (a) price markup shocks; (b) wage markup shocks; (c) monetary policy shocks; and (d) all other shocks, where these shocks and contributions are computed using the SW-DSGE model evaluated at the posterior mean of the model’s parameters. Figure 12: Two Measures of Real Unit Labor Cost in the Extended Sample Notes: See notes to Figure 8. Figure 13: Actual and Fundamental Inflation Measures in the Extended Sample Notes: See notes to Figures 3 and 7. Fig 14: Decomposition of Fundamental Inflation in the Smets-Wouters Model Notes: The solid line is inflation shown in Figure 1. The dotted line is the price-markup component of the SW fundamental inflation. (The values from 1960-1999 are shown in panel (a) of Figure 11.) The dashed line shows the component of the SW fundamental inflation from shocks other than price-markup shocks . (The values from 1960-1999 are the sum of the components plotted in panels (b)-(d) of Figure 11.) Appendix B: Additional Figures Figure B.1: Gali and Gertler Data Detrended Inflation and Real Unit Labor Cost Notes: This figure shows the detrended values of the series plotted in Figure 1. Detrending was carried out using a one-sided high-pass filter with a cutoff of 40 quarters. Figure B.2: Smets-Wouters Data Detrended Inflation and Modified Real Unit Labor Cost Notes: This figure shows the detrended values of the series plotted in Figure 4. Detrending was carried out using a one-sided high-pass filter with a cutoff of 40 quarters. Figure B.3: Comparison of Gali-Gertler and Smets-Wouters Measures of Real Unit Labor Cost Detrended Data Notes: This figure shows the detrended values of the series plotted in Figure 8. Detrending was carried out using a one-sided high-pass filter with a cutoff of 40 quarters.