Has Monetary Policy Accelerated Job Polarization Part 3

Table 1: Share of FEV due to monetary shocks — Occupations Horizon (months) Linear Eqn. 2 Baseline Eqn. 3 Quadratic Eqn. 4 Routine 12 Employment 24 36 48 Max. 0.18 0.18 0.11 0.09 0.19 0.23 0.32 0.23 0.16 0.33 0.23 0.33 0.24 0.17 0.33 Nonroutine 12 Employment 24 36 48 Max. 0.03 0.01 0.01 0.01 0.05 0.07 0.04 0.05 0.06 0.10 0.07 0.04 0.03 0.04 0.11 Routine Share 12 24 36 48 Max. 0.16 0.20 0.13 0.10 0.22 0.22 0.38 0.32 0.23 0.40 0.20 0.37 0.32 0.22 0.37 Total 12 Employment 24 36 48 Max. 0.18 0.15 0.08 0.07 0.20 0.24 0.27 0.18 0.11 0.28 0.24 0.29 0.19 0.12 0.29 Note: The table presents the share of the forecast error variance of occupational employment variables due to monetary policy shocks, for both the linear and asymmetric baseline estimates. 28 References Acemoglu, D. (1999), ‘Changes in unemployment and wage inequality: An alternative theory and some evidence’, American Economic Review 89(5), 1259–1278. Angrist, J. D., Jordà, O. and Kuersteiner, G. M. 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Working paper. 31 A Appendix The appendix includes a presentation of alternative monetary policy shock identification techniques; a discussion of the sensitivity of estimates from Equation 3 to different lag specifications; and a FEV analysis for alternative MSFEs. A.1 Alternative shock identification As a robustness check to the linear local projections, as well as to include the post-ZLB period in the estimates, I estimate a VAR, identifying a monetary policy shock using external instruments as in Gertler and Karadi (2015). The Gertler and Karadi (2015) approach to identifying a monetary policy shock is to use “surprise” changes to Fed Funds futures in a thiry-minute window around Federal Open Market Committee (FOMC) policy announcements as instruments for changes in a shortterm interest rate (the Fed Funds Rate, the one-year or two-year treasury); such changes in the short-term rate were unanticipated by markets, and are therefore exogenous and due to policy announcements. The data on the futures contracts used as instruments is only available from the mid-1990s, however. Gertler and Karadi’s (2015) innovation over other high-frequency approaches was to apply the high-frequency identification strategy to a longer horizon. They do so by estimating the linear relationship between the residuals from the reduced form VAR estimates from the shorter period (1991–2012), then assume that this relationship between reduced form residuals and the structural monetary policy shock is the same for the extended period (1979–2012).26 Their baseline VAR includes the one-year treasury rate, (log) industrial productions, (log) consumer price index, and Gilchrist and Zakrajsek’s (2012) excess bond premium, a measure of credit conditions; the time period they consider is July 1979 through June 2012. For the results below, I estimate this same system over a longer period that begins in January 1973,27 but I include additional variables one by one, as in Christiano, Eichenbaum and Evans (1996), reestimating the VAR (including shock identification) each time. The impulse responses to a contractionary Gertler and Karadi (2015) shock that raises the one-year Treasury rate by 100 b.p. impact are displayed in Figure 11. The estimated magnitudes are smaller than, but broadly consistent with, the IRFs estimated in Section 4.1. 26 Since the VARs estimated here are essentially identical to the baseline in Gertler and Karadi (2015), apart from trivially adding an additional variable to the system, for the details of the estimation, the reader is referred to their paper. 27 The results are essentially identical for the Gertler and Karadi time period. 32 Figure 11: Impulse responses of occupation employment to a contractionary Gertler and Karadi (2015) monetary policy shock that increases the one-year rate 100 b.p. on impact. Estimated from the five-variable VAR discussed in Section A.1. Shaded areas are 90 percent bootstrap confidence intervals. 33 The response of routine employment is more than twice as large as the response of nonroutine employment. The difference in magnitudes between responses identified in a VAR and those identified using a narrative approach as in Romer and Romer (2004) are discussed in Coibion (2012). A.2 Alternative lag structures This section considers some alternative lag structures for estimates obtained from Equation 3 to understand the somewhat anomalous responses to expansionary shocks. The results are qualitatively similar to the baseline estimates, aside from the strength of this anomaly. Recall that the baseline estimates include in the vector of controls xt one year of lagged changes in the dependent variable and one quarter of lags of the shocks. Here I consider two alternative sets of controls. Specifically, I consider a vector of controls xt12,1 which includes a year of lags of the dependent variable and no lags of the shock, and another alternative x24,36 , which includes two years of lags of the dependent variable and three years of lags t of the shock. This lag structure is based on Romer and Romer’s (2004) original impulse response estimation for output. As is evident in Figure 12, with fewer lags of the shock included, the contractionary effect of nominally “expansionary” shocks is exacerbated. “Expansionary” shocks are even more contractionary. This naturally leads to easier rejection of the null hypothesis of symmetry, as is evident in the right column. In Figure 13, with more lags, the problem is essentially gone. The effects of contractionary shocks are essentially the same regardless of the lag structure. This result is specific to the linear asymmetric specification in (3); it does not appear in any polynomial specification, regardless of the number of lags included. A.3 Alternative MSFE comparisons The coefficients estimated from (6) suffer from omitted variable bias relative to the estimates that include monetary policy shocks. Although this bias is irrelevant from a pure forecasting perspective, comparing (5) with (6) will understate the contribution of monetary policy shocks relative to the arguably more relevant counterfactual in which the effects of monetary policy shocks are accounted for in the regression, but are assumed to be at their mean values.28 As an alternative, therefore, I consider the forecast error from (5) conditional on 28 That is, zero in the linear or polynomial cases. 34 Figure 12: Fewer lags: Left column: Impulse responses of occupation employment to a 100 b.p. contractionary (red) and expansionary (blue) Romer and Romer (2004) monetary policy shock, no lags of the shock. Estimated from Equation 3. Right column: The same responses estimated from Equation 4. Shaded areas are 90 percent confidence intervals. 35 Figure 13: More lags: Left column: Impulse responses of occupation employment to a 100 b.p. contractionary (red) and expansionary (blue) Romer and Romer (2004) monetary policy shock, with 2 years of lagged dependent variables and 3 years of lagged shocks. Estimated from Equation 3. Right column: The same responses estimated from Equation 4. Shaded areas are 90 percent confidence intervals. 36 et only: x g et ] F E t,h ≡ yt+h − yt − E [yt+h − yt | x et − θ ′ E [e et ] = yt+h − yt − βe′ x ϵt | x h = ut,h + θh′ h et ]] . [e ϵt − E [e ϵt | x (7) h i 2 g Then M^ SF E h = E F E t,h . et ] theoretically should be zero ϵt | x For the linear local projections in (2), the term E [e since the monetary policy shock is unconditionally mean zero and should not be forecastable by macroeconomic variables.29 For the asymmetric projections in (3), however, it will not be − zero since ϵ+ t and ϵt have positive and negative means, respectively. In practice, however, the conditional expectation in (7) is numerically identical to the unconditional mean—that et ] from the linear projection is, the shocks are not forecastable. I estimate E [e ϵt | x ϵet = Γe xt + νt . (8) et includes deterministic terms (in the baseline, a constant and linear time trend). Note that x The conditional expectation in (7) is then just given by Γ̂, the estimate of the coefficient matrix in (8). It is straightforward to verify that both (6) and (7) have a mean of zero, so that for each the MSFE is variance of the forecast error. Therefore, for a given horizon, the relative difference in the FEV between (5) and either (6) or (7) can be interpreted as the share of the FEV explained by the monetary policy shock. Table 2 displays the share of the FEV explained by monetary policy shocks for this alternative specification as well as the baseline in the main text. This alternative modestly increases the explanatory power of monetary policy shocks, but the overall pattern across horizons remains unchanged. 29 I have verified that this is true in practice as well. 37 Table 2: Share of FEV due to monetary shocks — Occupations Horizon (months) Linear Baseline Quadratic (6) (7) (6) (7) (6) (7) Routine 12 Employment 24 36 48 Max. 0.18 0.18 0.11 0.09 0.19 0.19 0.19 0.12 0.10 0.20 0.23 0.32 0.23 0.16 0.33 0.24 0.34 0.24 0.17 0.35 0.23 0.33 0.24 0.17 0.33 0.23 0.33 0.24 0.17 0.34 Nonroutine 12 Employment 24 36 48 Max. 0.03 0.01 0.01 0.01 0.05 0.03 0.01 0.01 0.01 0.05 0.07 0.04 0.05 0.06 0.10 0.07 0.04 0.07 0.08 0.10 0.07 0.04 0.03 0.04 0.11 0.07 0.04 0.04 0.04 0.11 Routine Share 12 24 36 48 Max. 0.16 0.20 0.13 0.10 0.22 0.16 0.20 0.14 0.10 0.23 0.22 0.38 0.32 0.23 0.40 0.22 0.40 0.33 0.23 0.41 0.20 0.37 0.32 0.22 0.37 0.20 0.37 0.32 0.22 0.37 Total 12 Employment 24 36 48 Max. 0.18 0.15 0.08 0.07 0.20 0.19 0.16 0.08 0.07 0.21 0.24 0.27 0.18 0.11 0.28 0.24 0.28 0.18 0.11 0.29 0.24 0.29 0.19 0.12 0.29 0.24 0.29 0.19 0.12 0.29 Note: The table presents the share of the forecast error variance of occupational employment variables due to monetary policy shocks, for both the linear and asymmetric baseline estimates. Within each heading, the number in parentheses indicates the alternative forecasting specification the baseline is compared with, as discussed in Section 5. 38