Figure : The function g(.) 5 3 y y = g(z) y = z 5 3 z 3 5 Notes: Blue curve: the function g(z) = zφ(z) + φ(z). Red dashed line: the 5-degree line. Figure : Forward rates 9 3m 6m y y 5y 7y y 8 7 6 5 3 99 99 99 996 998 6 8 Notes: One-month forward rates monthly from January 99 to December 3, measured in annualized percentage points. Maturities are 3 and 6 months,,, 5, 7 and years. The gray area marks the ZLB period from January 9 to December 3.
3.5 3.5.5.5 fitted observed Figure 3: Observed and fitted forward curves SRTSM 3.5 3.5.5.5 fitted observed GATSM 5 7 5 7 Notes: Average forward curves in. Blue curves: fitted forward curves, from the SRTSM in the left panel and the GATSM in the right panel. Red dots: observed data. X-axis: maturity in years. Figure : The shadow rate and effective federal funds rate 8 shadow rate effective federal funds rate r 6 99 99 99 996 998 6 8 Notes: Blue line: the estimated shadow rate of the SRTSM from January 99 to December 3 in percentage points. Green line: the effective federal funds rate in percentage points. Black line: lower bound r. The gray area marks the ZLB period from January 9 to December 3. 3
Figure 5: Loadings on the macroeconomic factors and policy rate Loadings on macro factor Loadings on macro factor 3 Loadings on macro factor 3 3 Loadings on policy rate 3 5 6 7 8 9 Notes: Loadings of standardized economic variables Yt m on the three macroeconomic factors and the standardized policy rate. X-axis: identification number for economic variables in the Online Appendix. Vertical dashed lines separate variables by groups, and the groups are: real output (-8); employment and hours (9-); consumption (3-6); housing starts and sales (7-53); real inventories, orders and unfilled orders (5-58); stock prices (59-6); exchange rates (6-6); interest rates (63-73); money and credit quantity aggregates (7-79), price indexes (8-9); average hourly earnings (95-96); miscellaneous (97).
Figure 6: Observed and counterfactual macroeconomic variables.5 -.5 - -.5 - Policy rate 5 95 9 85 Industrial production index 5 35 3 5 5 Consumer price index realized counterfactural I counterfactual II -.5 3 8 3 3 78 76 7 7 7 Capacity utilization.5 9.5 9 8.5 8 Unemployment 9 8 7 Housing starts 68 7.5 6 66 7 5 6 3 6.5 3 3 Notes: Blue lines: observed economic variables between July 9 and December 3. Red dashed lines: what would have happened to these macroeconomic variables, if all the monetary policy shocks were shut down. Green dashed lines: what would have happened if the shadow rate was kept at r. 5
Figure 7: Impulse responses with full sample Notes: Impulse responses to a -5 basis-point shock on monetary policy. 9% confidence intervals are shaded. Sample: January 96 - December 3. Model: FAVAR with 3 macro factors and 3 lags. X-axis: response time in months. The policy rate is measured in annualized percentage; the industrial production index, consumer price index and housing starts are measured in percentage deviation from the steady state; the capacity utilization and unemployment rate are measured in percentage points. 6
Figure 8: Impulse responses (full sample vs. ZLB with EFFR) Notes: Impulse responses to a -5 basis-point shock on monetary policy. 9% confidence intervals are shaded. Blue: full sample from January 96 to December 3 with the policy rate in FAVAR (3). Turquoise: ZLB from July 9 to December 3 with the effective federal funds rate in FAVAR (). X-axis: response time in months. The policy rate is measured in annualized percentage; the industrial production index, consumer price index and housing starts are measured in percentage deviation from the steady state; the capacity utilization and unemployment rate are measured in percentage points. 7
Figure 9: Impulse responses (full sample vs. ZLB with new policy rate) Notes: Impulse responses to a -5 basis-point shock on monetary policy. 9% confidence intervals are shaded. Blue: full sample from January 96 to December 3 with the policy rate in FAVAR (3). Turquoise: ZLB from July 9 to December 3 with the policy rate in a FAVAR (). X-axis: response time in months. The policy rate is measured in annualized percentage; the industrial production index, consumer price index and housing starts are measured in percentage deviation from the steady state; the capacity utilization and unemployment rate are measured in percentage points. 8
Figure : the market s expected vs. Fed s announced ZLB lift-off dates 6 5 market anticipation Fed announcement at least through late at least through mid-5 5 3 at least through mid-3 9 3 Notes: Blue dots: the market s expected lift-off dates from January 9 to December 3. Four green vertical lines mark the following months when forward guidance specified explicit lift-off dates for the ZLB: August, January, September and June 3. The corresponding lift-off dates are in red diamonds. Black dashed line: the 5 degree line. 9
Figure : Impulse responses (ZLB with expected duration) ZLB duration Industrial production index.5.5 Consumer price index.5 -.5 -.5 8 -.5 8-8 Capacity utilization. Unemployment 6 Housing starts.5 -. -. -.5 8 -.3 8-8 Notes: Impulse responses to a one year shock to expected ZLB duration. 9% confidence intervals are shaded. Sample: ZLB from July 9 to December 3. Model: FAVAR () with the ZLB duration as the monetary policy measure. X-axis: response time in months. The expected duration is measured in years; the industrial production index, consumer price index and housing starts are measured in percentage deviation from the steady state; the capacity utilization and unemployment rate are measured in percentage points. 5
Figure : Impulse responses at ZLB (policy rate v.s. ZLB duration) ZLB duration Industrial production index.5.5 Consumer price index duration(yr) policy rate(-5bp).5 -.5 8 -.5 8 -.5-8.5 Capacity utilization. Unemployment 6 Housing starts policy rate duration -. -. -.5 8 -.3 8-8 Notes: Turquoise: impulse responses to a -5 basis-point shock on the policy rate. Blue: impulse responses to a one year shock on the ZLB duration. 9% confidence intervals are shaded. Sample: ZLB from July 9 to December 3. Model: FAVAR (). X-axis: response time in months. The policy rate is measured in -5 basis points; the expected duration is measured in years; the industrial production index, consumer price index and housing starts are measured in percentage deviation from the steady state; the capacity utilization and unemployment rate are measured in percentage points. 5
Figure 3: Policy rate and Fed s asset purchases.5.5 QE QE.5 OT QE3.5.5.5 3 8 9 3 5 Notes: Blue line: the extended policy rate in percentage points from our website: http: //faculty.chicagobooth.edu/jing.wu/research/data/wx.html. QE: the first round of quantitative easing from November 8 to March. QE: the second round of quantitative easing from November to June. OT: operation twist from September to December. QE3: the third round of quantitative easing from September to October. 5
Figure : Interest rates responses to Fed s announcements 5 yield QE one day prior forward rate QE one month prior expected path of shadow rate QE one month prior 3 5 5 3 5 6 7 8 9 3 5 6 7 8 9 3 5 6 7 8 9 3 yield Taper tantrum one day prior 6 forward rate Taper tantrum one month prior expected path of shadow rate 6 Taper tantrum one month prior 3 5 6 7 8 9 3 5 6 7 8 9 3 5 6 7 8 9 Notes: Top row: QE announcement on November 5, 8. Bottom row: taper tantrum on May, 3. First column: yield curves. Second column: forward curves. Third column: expected shadow rates. Blue: event dates. Green: one day prior to event dates for yields, one month prior to event dates for forward rates and expected path of shadow rates. X-axis: maturity in years. Y-axis: interest rates in percentage points. 53
Figure 5: Shadow rates 8 r=.5% r estimated 6 99 99 99 996 998 6 8 Notes: Blue line: the shadow rate from the benchmark model with r =.5% in percentage points. Green line: the shadow rate with estimated ˆr =.9% in percentage points. The gray area marks the ZLB period from January 9 to December 3. 5
Figure 6: Liftoff dates r=.5% r estimated 6 5 3 9 3 Notes: Blue dots: lift-off dates from the benchmark model with r =.5%. Green triangles: lift-off dates with estimated ˆr =.9%. Black dashed line: the 5 degree line. 55