## _wp15114 - References

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### Objective and scope
- Examine how the stance of U.S. monetary policy affects the government spending multiplier, distinguishing accommodative and non-accommodative monetary policy states.
- Provide state-dependent estimates of federal government spending multipliers using U.S. quarterly data (1965Q4–2012Q4), local projections, and identification of spending shocks as forecast errors (SPF/Greenbook) and by Cholesky decomposition.

### Empirical strategy and identification
- Method and state definition:
  - Local projections (Jordà (2005)) with a smooth transition function F(z) = exp(−γ z)/(1+exp(−γ z)), γ>0, F(0) = 1/2.
  - State index z: deviation of the actual Fed funds rate from the Taylor-rule implied rate, normalized to have unit variance (z averages 0 by construction).
- Estimated Taylor-type reduced-form rule (1965Q4–2008Q4):
  - ̂FFR_t = −0.012 (0.167) + 0.897 (0.032) FFR_{t−1} + 0.179 (0.080) π^a_t + 0.138 (0.031) (y_t − y^*_t)
- Calibration of γ:
  - γ calibrated so monetary policy is accommodative about 30 percent of the time; solving Pr(F(z)>0.8)=0.3 yields γ = 5.
- Government spending shock identification:
  - Preferred: forecast errors of the growth rate of real federal spending from SPF and the Greenbook (FE_G_t = ∆log G_t − E_{t−1} ∆log G_t), purged of predictable components.
  - Benchmark comparison: Cholesky decomposition (government spending ranked first).
- Sample treatment of the ZLB:
  - Baseline estimations end in 2008Q4 because the Fed funds rate is constrained by the ZLB thereafter.
  - Extended sample through 2012Q4 uses shadow Fed funds rate estimates (Wu and Xia (2014), Lombardi and Zhu (2014), and an alternative 10-year rate-based proxy).

### Key estimation settings
- Controls: X_t = [G_t, T_t, Y_t]′, 4 lags of X, and a quartic trend.
- Dependent variables in differences relative to lagged levels to construct multipliers consistent with time-varying G/Y:
  - y_{t+h} = (Y_{t+h} − Y_{t−1})/Y_{t−1}
  - g_{t+h} = (G_{t+h} − G_{t−1})/Y_{t−1}
- Transition function F(z) provides smooth probabilistic assignment to accommodative versus non-accommodative states (F(z) in [0,1]).

### Main results — aggregate GDP multipliers (sample ending 2008Q4)
- Table 1 (GDP cumulative and peak multipliers):
  - "Anticipated" shocks (Cholesky decomposition)
    - Linear: 1-year integral 1.53; 2-year integral 2.07; 4-year integral 2.83; Ratio of peak responses 3.27
    - Non accommodative: 1-year 0.60; 2-year 1.46; 4-year 2.12; Ratio of peak 2.59
    - Accommodative: 1-year 2.46; 2-year 2.79; 4-year 3.41; Ratio of peak 4.19
  - "Non-anticipated" shocks (SPF/Greenbook) — preferred specification
    - Linear: 1-year 0.60; 2-year 1.63; 4-year 3.44; Ratio of peak 5.04
    - Non accommodative: 1-year −1.55; 2-year −1.97; 4-year −0.22; Ratio of peak 2.76
    - Accommodative: 1-year 2.50; 2-year 3.96; 4-year 4.48; Ratio of peak 5.51
- Qualitative summary:
  - Federal government spending multipliers are substantially higher under accommodative monetary policy than under non-accommodative policy.
  - Under non-accommodative policy, fiscal shocks can be contractionary on impact (negative 1-year −1.55 for non-anticipated shocks).

### Disaggregated outcomes and crowding effects
- Private consumption:
  - Under accommodative monetary policy, federal spending significantly and persistently crowds-in private consumption (including durable and non-durable/services).
  - Under non-accommodative monetary policy, private consumption is crowded-out.
- Private investment:
  - The state of monetary policy does not strongly discriminate the response of private investment in the estimations reported.

### Transmission channels
- Substitution (real interest rate) channel:
  - Under accommodative monetary policy, a government spending shock is associated with a decline in the nominal Fed funds rate and a rise in inflation, implying a decline in real interest rates (both ex-ante rr^a_t = FFR_t − π^a_t and ex-post rr^p_t = FFR_t − π_{t+1}).
  - Under non-accommodative policy the nominal rate tends to rise and real rates increase, reducing fiscal effectiveness.
- Funding (wealth) channel:
  - Response of real federal debt: increases under accommodative policy and decreases under non-accommodative policy.
  - Response of real tax revenues does not depend on monetary state (not reported in detail), suggesting financing during accommodative periods relies more on debt at lower real financing costs.

### Results covering the ZLB episode (extended sample through 2012Q4)
- Extended-sample multipliers (Table 2) for SPF/Greenbook shocks, using alternative shadow-rate constructions:
  - ZLB: Wu and Xia (2014)
    - Linear: 1-year −0.58; 2-year −0.29; 4-year 1.61; Ratio of peak 2.79
    - Non accommodative: 1-year −2.89; 2-year −3.97; 4-year −1.16; Ratio of peak 1.63
    - Accommodative: 1-year 1.72; 2-year 2.52; 4-year 2.97; Ratio of peak 3.68
  - ZLB: Own calculations (10-year rate proxy)
    - Linear: 1-year −0.58; 2-year −0.29; 4-year 1.61; Ratio of peak 2.79
    - Non accommodative: 1-year −2.00; 2-year −3.09; 4-year −0.86; Ratio of peak 1.54
    - Accommodative: 1-year 1.47; 2-year 2.45; 4-year 3.01; Ratio of peak 3.77
  - ZLB: Lombardi and Zhu (2014)
    - Linear: 1-year −0.58; 2-year −0.29; 4-year 1.61; Ratio of peak 2.79
    - Non accommodative: 1-year −1.71; 2-year −2.13; 4-year −0.40; Ratio of peak 1.67
    - Accommodative: 1-year 1.01; 2-year 1.84; 4-year 2.76; Ratio of peak 3.57
- Qualitative takeaway:
  - Extending the sample through the ZLB lowers estimated multipliers in the linear model and reduces the accommodative-state multiplier relative to the pre-2008Q4 sample, but the core result—that multipliers are larger under accommodative monetary policy—remains robust across shadow-rate methods.

### Slack versus non-slack episodes (extended sample including ZLB)
- Slack defined by unemployment threshold 6.5 percent (economy in slack about one-third of the time).
- Table 3 (GDP cumulative and peak multipliers at times of slack and non-slack, extended sample):
  - Linear: 1-year −0.58; 2-year −0.29; 4-year 1.61; Ratio of peak 2.79
  - Non-slack: 1-year −1.04; 2-year −0.46; 4-year 1.51; Ratio of peak 3.63
  - Slack: 1-year −0.15; 2-year −0.26; 4-year 1.83; Ratio of peak 2.55
- Interpretation:
  - No broad support for systematically higher multipliers in slack per se when monetary policy is not accounted for.
  - Federal spending is highly effective at times of slack only when monetary policy is accommodative; spending can be contractionary during slack if monetary policy does not accommodate.

### Sensitivity analyses
- Transition parameter γ (speed/steepness):
  - Benchmark γ = 5 (Pr(F(z)>0.8)=0.3). Results robust across different γ values; higher γ reduces the gap between accommodative and non-accommodative multipliers.
- Measure of inflation in the Taylor-rule:
  - Alternatives using SPF one-quarter-ahead inflation, CPI inflation (quarterly and year-on-year), and PCE inflation do not alter qualitative results: multipliers remain larger under accommodative monetary policy.

### Policy implications and suggested extensions
- Policy implications:
  - Fiscal policy is more effective when supported by accommodative monetary policy—fiscal stimulus yields larger GDP multipliers if monetary policy does not tighten in response.
  - Normalization of monetary policy (exit from unconventional tools) would reduce federal spending multipliers even if some slack remains, highlighting timing importance for exit from UMP.
- Suggested empirical extensions:
  - Narrative identification of monetary authority responses using FOMC minutes to better capture the monetary reaction to fiscal actions.
  - Application of the framework to tax policy changes, with attention to identification of exogenous tax variations.
  - Cross-country extensions to OECD and Euro area economies to study monetary-fiscal interactions with different central bank arrangements.

### Appendix — reported numeric results (selected exact values)
- Table A1 (example rows, benchmark = SPF one-quarter-ahead inflation):
  - Non accommodative / SPF forecast Infl. / 1 year integral −1.55 / 2 years integral −1.97 / 4 years integral −0.22 / Ratio of peak responses 2.76
  - Accommodative / SPF forecast Infl. / 1 year integral 2.50 / 2 years integral 3.96 / 4 years integral 4.48 / Ratio of peak responses 5.51
- Table A2 (smoothing parameter γ examples):
  - γ = 2.5: Non accommodative 1 year integral −2.78; 2 years integral −4.95; 4 years integral −4.39; Ratio of peak responses 2.07
  - γ = 5: Non accommodative 1 year integral −1.55; 2 years integral −1.97; 4 years integral −0.22; Ratio of peak responses 2.76
  - γ = 10: Accommodative 1 year integral 2.10; 2 years integral 3.47; 4 years integral 4.28; Ratio of peak responses 5.53
- Table A3 (sectoral multipliers, surprise federal government spending):
  - Total Consumption
    - Linear / 1-year integral 0.09 / 2-year integral 0.93 / 4-year integral 2.53 / Ratio of peak responses 2.98
    - Non accommodative / 1-year −0.64 / 2-year −0.82 / 4-year −0.01 / Ratio of peak responses 1.63
    - Accommodative / 1-year 1.09 / 2-year 2.27 / 4-year 3.29 / Ratio of peak responses 3.87
  - Cons. of durables
    - Linear / 1-year 0.10 / 2-year 0.32 / 4-year 0.71 / Ratio of peak responses 0.85
    - Non accommodative / 1-year −0.16 / 2-year −0.21 / 4-year −0.04 / Ratio of peak responses 0.49
    - Accommodative / 1-year 0.43 / 2-year 0.76 / 4-year 0.85 / Ratio of peak responses 0.99
  - Private fixed investment
    - Linear / 1-year −0.26 / 2-year −0.42 / 4-year 0.96 / Ratio of peak responses 0.65
    - Non accommodative / 1-year 0.11 / 2-year −0.86 / 4-year −1.11 / Ratio of peak responses 2.30
    - Accommodative / 1-year −0.17 / 2-year 0.02 / 4-year 0.22 / Ratio of peak responses 0.91

*IMF Working Paper content (extracted from _wp15114 - References).*

### References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### _wp15114 - References

### Objective and scope
- Examine how the stance of U.S. monetary policy affects the government spending multiplier, distinguishing accommodative and non-accommodative monetary policy states.
- Provide state-dependent estimates of federal government spending multipliers using U.S. quarterly data (1965Q4–2012Q4), local projections, and identification of spending shocks as forecast errors (SPF/Greenbook) and by Cholesky decomposition.

### Empirical strategy and identification
- Method: local projections (Jordà (2005)) with a smooth transition function F(z) to capture the likelihood of an accommodative monetary state; F(z) = exp(−γ z)/(1+exp(−γ z)), γ>0, F(0) = 1/2.
- State index z: deviation of the actual Fed funds rate from the Taylor-rule implied rate, normalized to have unit variance (z averages 0 by construction).
- Taylor-type reduced-form rule estimated over 1965Q4–2008Q4:
  - ̂FFR_t = −0.012 (0.167) + 0.897 (0.032) FFR_{t−1} + 0.179 (0.080) π^a_t + 0.138 (0.031) (y_t − y^*_t)
- γ calibrated so monetary policy is accommodative about 30 percent of the time; solving Pr(F(z)>0.8)=0.3 yields γ = 5.
- Government spending shocks:
  - Preferred identification: forecast errors of the growth rate of real federal spending from SPF and the Greenbook (FE_G_t = ∆log G_t − E_{t−1} ∆log G_t), further purged of predictable components.
  - Benchmark comparison: Cholesky decomposition (government spending ranked first).
- Sample treatment of ZLB:
  - Baseline estimations end in 2008Q4 because the Fed funds rate is constrained by the ZLB thereafter.
  - Extended sample through 2012Q4 uses shadow Fed funds rate estimates (Wu and Xia (2014), Lombardi and Zhu (2014), and an alternative 10-year rate-based proxy) to characterize policy stance during the ZLB episode.

### Key estimation settings
- Controls X_t = [G_t, T_t, Y_t]′, 4 lags of X, and a quartic trend.
- Dependent variables defined in differences relative to lagged levels to construct multipliers consistent with time-varying G/Y: y_{t+h} = (Y_{t+h} − Y_{t−1})/Y_{t−1}, g_{t+h} = (G_{t+h} − G_{t−1})/Y_{t−1}.
- Transition function F(z) provides smooth probabilistic assignment to accommodative versus non-accommodative states (F(z) in [0,1]).

### Main results — aggregate GDP multipliers (sample ending 2008Q4)
- Table 1 (GDP cumulative and peak multipliers):
  - "Anticipated" shocks (Cholesky decomposition)
    - Linear: 1-year integral 1.53; 2-year integral 2.07; 4-year integral 2.83; Ratio of peak responses 3.27
    - Non accommodative: 1-year 0.60; 2-year 1.46; 4-year 2.12; Ratio of peak 2.59
    - Accommodative: 1-year 2.46; 2-year 2.79; 4-year 3.41; Ratio of peak 4.19
  - "Non-anticipated" shocks (SPF/Greenbook) — preferred specification
    - Linear: 1-year 0.60; 2-year 1.63; 4-year 3.44; Ratio of peak 5.04
    - Non accommodative: 1-year −1.55; 2-year −1.97; 4-year −0.22; Ratio of peak 2.76
    - Accommodative: 1-year 2.50; 2-year 3.96; 4-year 4.48; Ratio of peak 5.51
- Qualitative summary:
  - Federal government spending multipliers are substantially higher under accommodative monetary policy than under non-accommodative policy.
  - Under non-accommodative policy, fiscal shocks can be contractionary on impact (negative 1-year 1.55 for non-anticipated shocks).

### Disaggregated outcomes and crowding effects
- Private consumption:
  - Under accommodative monetary policy, federal spending significantly and persistently crowds-in private consumption (including durable and non-durable/services).
  - Under non-accommodative monetary policy, private consumption is crowded-out.
- Private investment:
  - The state of monetary policy does not strongly discriminate the response of private investment in the estimations reported.

### Transmission channels
- Substitution (real interest rate) channel:
  - Under accommodative monetary policy, a government spending shock is associated with a decline in the nominal Fed funds rate and a rise in inflation, implying a decline in real interest rates (both ex-ante rr^a_t = FFR_t − π^a_t and ex-post rr^p_t = FFR_t − π_{t+1}).
  - Under non-accommodative policy the nominal rate tends to rise and real rates increase, reducing fiscal effectiveness.
- Funding (wealth) channel:
  - Response of real federal debt: increases under accommodative policy and decreases under non-accommodative policy.
  - Response of real tax revenues does not depend on monetary state (not reported in detail), suggesting financing during accommodative periods relies more on debt at lower real financing costs.

### Results covering the ZLB episode (extended sample through 2012Q4)
- Extended-sample multipliers (Table 2) for SPF/Greenbook shocks, using alternative shadow-rate constructions:
  - ZLB: Wu and Xia (2014)
    - Linear: 1-year −0.58; 2-year −0.29; 4-year 1.61; Ratio of peak 2.79
    - Non accommodative: 1-year −2.89; 2-year −3.97; 4-year −1.16; Ratio of peak 1.63
    - Accommodative: 1-year 1.72; 2-year 2.52; 4-year 2.97; Ratio of peak 3.68
  - ZLB: Own calculations (10-year rate proxy)
    - Linear: 1-year −0.58; 2-year −0.29; 4-year 1.61; Ratio of peak 2.79
    - Non accommodative: 1-year −2.00; 2-year −3.09; 4-year −0.86; Ratio of peak 1.54
    - Accommodative: 1-year 1.47; 2-year 2.45; 4-year 3.01; Ratio of peak 3.77
  - ZLB: Lombardi and Zhu (2014)
    - Linear: 1-year −0.58; 2-year −0.29; 4-year 1.61; Ratio of peak 2.79
    - Non accommodative: 1-year −1.71; 2-year −2.13; 4-year −0.40; Ratio of peak 1.67
    - Accommodative: 1-year 1.01; 2-year 1.84; 4-year 2.76; Ratio of peak 3.57
- Qualitative takeaway:
  - Extending the sample through the ZLB lowers estimated multipliers in the linear model and reduces the accommodative-state multiplier relative to the pre-2008Q4 sample, but the core result—that multipliers are larger under accommodative monetary policy—remains robust across shadow-rate methods.

### Slack versus non-slack episodes (extended sample including ZLB)
- Slack defined by unemployment threshold 6.5 percent (economy in slack about one-third of the time).
- Table 3 (GDP cumulative and peak multipliers at times of slack and non-slack, extended sample):
  - Linear: 1-year −0.58; 2-year −0.29; 4-year 1.61; Ratio of peak 2.79
  - Non-slack: 1-year −1.04; 2-year −0.46; 4-year 1.51; Ratio of peak 3.63
  - Slack: 1-year −0.15; 2-year −0.26; 4-year 1.83; Ratio of peak 2.55
- Interpretation:
  - No broad support for systematically higher multipliers in slack per se when monetary policy is not accounted for.
  - Federal spending is highly effective at times of slack only when monetary policy is accommodative; spending can be contractionary during slack if monetary policy does not accommodate.

### Sensitivity analyses
- Transition parameter γ (speed/steepness of smooth transition):
  - Main calibration γ = 5 (Pr(F(z)>0.8)=0.3). Results robust across different γ values; higher γ reduces the gap between accommodative and non-accommodative multipliers (higher γ implies faster movement between states and smaller deviations of interest rate from target).
- Measure of inflation used in the Taylor-rule:
  - Alternative specifications using SPF one-quarter-ahead inflation, CPI inflation (quarterly and year-on-year), and PCE inflation do not alter qualitative results: multipliers remain larger under accommodative monetary policy.

### Policy implications and extensions
- Policy implications:
  - Fiscal policy is more effective when supported by accommodative monetary policy—fiscal stimulus yields larger GDP multipliers if monetary policy does not tighten in response.
  - Normalization of monetary policy (exit from unconventional tools) would reduce federal spending multipliers even if some slack remains, highlighting the importance of carefully timing the exit from UMP.
- Suggested empirical extensions:
  - Narrative identification of monetary authority responses using FOMC minutes to better capture the monetary reaction to fiscal actions.
  - Application of the framework to tax policy changes, with attention to identification of exogenous tax variations.
  - Cross-country extensions to OECD and Euro area economies to study monetary-fiscal interactions with different central bank arrangements.

*Italicized attribution line: IMF Working Paper content (extracted from _wp15114 - References).*

### REFERENCES

### _wp15114 - REFERENCES

### Key bibliographic entries
- Alesina, Alberto, and Francesco Giavazzi, 2013, Fiscal Policy After the Financial Crisis (University of Chicago Press, Chicago).
- Anderson, Derek; Benjamin Hunt; Mika Kortelainen; Michael Kumhof; Douglas Laxton; Dirk Muir; Susanna Mursula; and Stephen Snudden, 2013, “Getting to Know GIMF: The Simulation Properties of the Global Integrated Monetary and Fiscal Model,” IMF Working Paper No. 13/55.
- Auerbach, Alan J., and Yuriy Gorodnichenko, 2012, “Measuring the Output Responses to Fiscal Policy,” American Economic Journal: Economic Policy, 4, No. 2, pp. 1–27.
- Auerbach, Alan J., and Yuriy Gorodnichenko, 2013, “Fiscal Multipliers in Recession and Expansion,” in Fiscal Policy after the Financial Crisis, University of Chicago Press.
- Barro, Robert J., and Charles J. Redlick, 2011, “Macroeconomic Effects from Government Purchases and Taxes,” Quarterly Journal of Economics, 126, No. 1, pp. 51–102.
- Baum, Anja; Marcos Poplawski-Ribeiro; and Anke Weber, 2012, “Fiscal Multipliers and the State of the Economy,” International Monetary Fund, No. WP 12/286.
- Belinga, Vincent Tsoungui, 2013, “Effects of Fiscal policy Shocks on a Small Open Economy: Evidence from Canada,” Université de Montréal, Canada, No. Mimeo.
- Blanchard, Olivier, and Roberto Perotti, 2002, “An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output,” The Quarterly Journal of Economics, 114, No. 4, pp. 1329–1368.
- Bouakez, Hafedh, and Nooman Rebei, 2007, “Why does Private Consumption Rise After a Government Spending Shock?” Canadian Journal of Economics, 40, No. 3, pp. 954–979.
- Canova, Fabio, and Evi Pappa, 2011, “Fiscal Policy, Pricing Frictions and Monetary Accommodation,” Economic Policy, pp. 555–598.
- Choi, Woon Gyu, and Michael B. Devereux, 2006, “Asymmetric Effects of Government Spending: Does the Level of Real Interest Rates Matter?” IMF Staff Papers, 53, p. Special Issue.
- Christiano, Lawrence; Martin Eichenbaum; and Sergio Rebelo, 2011, “When is the Government Spending Multiplier Large?” Journal of Political Economy, 119, No. 1, pp. 78–121.
- Christiano, Lawrence J.; Martin Eichenbaum; and Mathias Trabandt, 2014, “Understanding the Great Recession,” Mimeo.
- Clarida, Richard; Jordi Gali; and Mark Gertler, 1998, “Monetary Policy Rules in Practice Some International Evidence,” European Economic Review, 42, No. 6, pp. 1033–1067.
- Coenen, Günter; Christopher Erceg; Charles Freedman; Davide Furceri; Michael Kumhof; René Lalonde; Douglas Laxton; Jesper Lindé; Annabelle Mourougane; Dirk Muir; Susanna Mursula; Carlos de Resende; John Roberts; Werner Roeger; Stephen Snudden; Mathias Trabandt; and Jan in ’t Veld, 2010, “Effects of Fiscal Stimulus in Structural Models,” IMF Working Paper 10/73.
- Davig, Troy, and Eric M. Leeper, 2007, “Fluctuating Macro Policies and the Fiscal Theory,” NBER Macroeconomics Annual 2006, 21, pp. 247–316.
- Davig, Troy, and Eric M. Leeper, 2011, “Monetary-fiscal Policy Interactions and Fiscal Stimulus,” European Economic Review, 55, No. 2, pp. 211–227.
- Freedman, Charles; Michael Kumhof; Douglas Laxton; Dirk Muir; and Susanna Mursula, 2010, “Global Effects of Fiscal Stimulus During the Crisis,” Journal of Monetary Economics, 573, pp. 506–526.
- Gaspar, Vitor, 2015, “Examples of Monetary-Fiscal Interaction at the Zero Lower Bound,” Lecture, MIT Sloan School of Management.
- Jordà, Òscar, 2005, “Estimation and Inference of Impulse Responses by Local Projections,” American Economic Review, 95, No. 1, pp. 161–182.
- Lombardi, Marco, and Feng Zhu, 2014, “A shadow Policy Rate to Calibrate US Monetary Policy at the Zero Lower Bound,” BIS Working Paper No. 425.
- Mertens, Karel R. S. M., and Morten O. Ravn, 2014, “Fiscal Policy in an Expectations-Driven Liquidity Trap,” The Review of Economic Studies, Advanced access, pp. 1–31.
- Morgan, Donald P., 1993, “Asymmetric Effects of Monetary Policy,” Economic Review, Second quarter, pp. 21–33.
- Mountford, Andrew, and Harald Uhlig, 2009, “What are the Effects of Fiscal Policy Shocks?” Journal of Applied Econometrics, 24, No. 6, pp. 960–992.
- Owyang, Michael T.; Valerie Ann Ramey; and Sarah Zubairy, 2013, “Are Government Spending Multipliers Greater During Periods of Slack? Evidence from Twentieth-century Historical Data,” American Economic Review, 103, No. 3, pp. 129–34.
- Perotti, Roberto, 2004, “Estimating the Effects of Fiscal Policy in OECD Countries,” IGIER Working Paper No. 276.
- Ramey, Valerie A., and Matthew D. Shapiro, 1998, “Costly Capital Reallocation and the Effects of Government Spending,” Carnegie-Rochester Conference Series on Public Policy 48, pp. 145–194.
- Ramey, Valery A., 2011, “Identifying Government Spending Shocks: It’s All in the Timing,” The Quarterly Journal of Economics, 126, pp. 1–50.
- Romer, Christina, and David Romer, 1989, “Does Monetary Policy Matter: A New Test in the Spirit of Friedman and Schwartz,” NBER Working Paper No. 3045.
- Romer, Christina, and David Romer, 2010, “The Macroeconomic Effects of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks,” American Economic Review, 100, No. 3.
- Romer, Christina, and David Romer, 2014, “Transfer Payments and the Macroeconomy: The Effects of Social Security Benefit Changes, 1952-1991,” NBER Working Paper No. 20087.
- Taylor, B. J., 1993, “Discretion versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on Public Policy, 39, pp. 195–214.
- Woodford, Michael, 2011, “Simple Analytics of the Government Expenditure Multiplier,” American Economic Journal: Macroeconomics, 3, No. 1, pp. 1–35.
- Wu, Jing Cynthia, and Fan Dora Xia, 2014, “Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound,” NBER Working Paper No. 20117.

### Appendix — Tables: reported numeric results (exact values)
- Table A1. GDP Cumulative and Peak Multipliers with Alternative Measures of Inflation in the Taylor Rule
  - Measure of inflation / 1 year integral / 2 years integral / 4 years integral / Ratio of peak responses
  - Non accommodative / SPF forecast Infl. / -1.55 / -1.97 / -0.22 / 2.76
  - Accommodative / SPF forecast Infl. / 2.50 / 3.96 / 4.48 / 5.51
  - Non accommodative / Quarterly CPI Infl. / -1.28 / -1.73 / 0.72 / 2.88
  - Accommodative / Quarterly CPI Infl. / 2.47 / 3.90 / 4.15 / 5.25
  - Non accommodative / Quarterly PCE Infl. / -2.19 / -2.93 / -0.39 / 2.20
  - Accommodative / Quarterly PCE Infl. / 2.78 / 4.09 / 4.22 / 5.21
  - Non accommodative / Year/year CPI infl. / -1.21 / -1.62 / 0.54 / 3.47
  - Accommodative / Year/year CPI infl. / 2.49 / 4.02 / 4.53 / 5.33
  - Non accommodative / Year/year lead CPI Infl. / -1.35 / -2.10 / -0.54 / 2.33
  - Accommodative / Year/year lead CPI Infl. / 2.73 / 4.36 / 4.60 / 5.87
  - Note: The benchmark corresponds to one-quarter ahead inflation forecast from SPF.

- Table A2. GDP Cumulative and Peak Multipliers with Different Values of the Smoothing Parameter, γ
  - γ / 1 year integral / 2 years integral / 4 years integral / Ratio of peak responses
  - Non accommodative / 2.5 / -2.78 / -4.95 / -4.39 / 2.07
  - Accommodative / 2.5 / 3.00 / 4.60 / 4.75 / 5.55
  - Non accommodative / 3.5 / -2.12 / -3.24 / -1.77 / 2.42
  - Accommodative / 3.5 / 2.77 / 4.29 / 4.62 / 5.52
  - Non accommodative / 5 / -1.55 / -1.97 / -0.22 / 2.76
  - Accommodative / 5 / 2.50 / 3.96 / 4.48 / 5.51
  - Non accommodative / 6.5 / -1.21 / -1.28 / 0.52 / 2.97
  - Accommodative / 6.5 / 2.32 / 3.74 / 4.39 / 5.51
  - Non accommodative / 7.5 / -1.06 / -0.99 / 0.82 / 3.07
  - Accommodative / 7.5 / 2.24 / 3.64 / 4.35 / 5.52
  - Non accommodative / 10 / -0.82 / -0.53 / 1.27 / 3.22
  - Accommodative / 10 / 2.10 / 3.47 / 4.28 / 5.53
  - Note: γ=5 corresponds to the benchmark case where monetary policy remains accommodative for about 30 of the time in our sample period.

- Table A3. Cumulative and Peak Sectoral Multipliers (surprise federal government spending)
  - 1-year integral / 2-year integral / 4-year integral / Ratio of peak responses
  - Total Consumption
    - Linear / 0.09 / 0.93 / 2.53 / 2.98
    - Non accommodative / -0.64 / -0.82 / -0.01 / 1.63
    - Accommodative / 1.09 / 2.27 / 3.29 / 3.87
  - Cons. of durables
    - Linear / 0.10 / 0.32 / 0.71 / 0.85
    - Non accommodative / -0.16 / -0.21 / -0.04 / 0.49
    - Accommodative / 0.43 / 0.76 / 0.85 / 0.99
  - Cons. of non durables & serv.
    - Linear / -0.11 / 0.22 / 1.27 / 1.71
    - Non accommodative / -0.57 / -0.60 / -0.00 / 0.79
    - Accommodative / 0.47 / 0.91 / 1.69 / 2.43
  - Private fixed investment
    - Linear / -0.26 / -0.42 / 0.96 / 0.65
    - Non accommodative / 0.11 / -0.86 / -1.11 / 2.30
    - Accommodative / -0.17 / 0.02 / 0.22 / 0.91
  - Note: Cumulative multipliers are computed as the ratio of the sum of responses of GDP and government spending. The peak measure is the ratio of the IRFs at their respective peaks.

### Appendix — Figures: captions, notes, and figure-specific observations
- Figure A1. Federal Spending-to-GDP Ratio (in percent) Over the Sample Period.
- Figure A2. Shadow Fed Funds Rate Near the ZLB (2008Q1–2012Q4).
- Figure A3. IRFs of Federal Government Spending and Output to Federal Government Spending Shocks Using the Cholesky Decomposition.
  - Notes: Shaded areas represent the 95 percent confidence bands around the estimates.
  - Panels shown for: G: Linear case; GDP: Linear case; G: Accommodative Monetary Policy; GDP: Accommodative Monetary Policy; G: Non−accommodative Monetary Policy; GDP: Non−accommodative Monetary Policy. Horizontal axis in Quarters; vertical axes labeled Dollars.
- Figure A4. IRFs of Private Investment (SPF/Greenbook).
  - Notes: Shaded areas represent the 95 percent confidence bands around estimates.
  - Panels shown for: G: Linear case; I: Linear case; G: Accommodative Monetary Policy; I: Accommodative Monetary Policy; G: Non−accommodative Monetary Policy; I: Non−accommodative Monetary Policy. Horizontal axis in Quarters; vertical axes labeled Dollars.
- Figure A5. IRFs of Federal Debt (SPF/Greenbook).
  - Panels shown for: G: linear case; Debt: linear case; G: Accommodative Monetary Policy; Debt: Accommodative Monetary Policy; G: Non−accommodative Monetary Policy; Debt: Non−accommodative Monetary Policy. Horizontal axis in Quarters; vertical axes labeled Percent.
- Figure A6. IRFs of Output (SPF/Greenbook): Extended Sample Through 2012Q4.
  - Panels shown for: G: Linear case; GDP: Linear case; G: Accommodative Monetary Policy; GDP: Accommodative Monetary Policy; G: Non−accommodative Monetary Policy; GDP: Non−accommodative Monetary Policy. Horizontal axis in Quarters; vertical axes labeled Dollars.
- Figure A7. IRFs of Employment at Times of Slack (SPF/Greenbook): Extended Sample, Including the ZLB Episode.
  - Panels shown for: G: Linear case (Slack); Empl. ratio: Linear case (Slack); G: Accommodative Monetary policy (Slack); Empl. ratio: Accommodative Mon. Policy (Slack); G: Non−accommodative Monetary policy (Slack); Empl. ratio: Non−accommodative Mon. Policy (Slack). Horizontal axis in Quarters; vertical axes labeled Percent.
- Figure A8. The Fed Funds Rate, the Shadow Fed Funds Rate, and the Likelihood of Being in the Accommodative State (extended sample, including the recent ZLB episode).
- Figure A9. Historical Cumulative Fiscal Multipliers Over the Sample Period.
  - Notes: The multiplier in each quarter is cumulative over 16 quarters ahead (4-year integral).

*Source: _wp15114 - REFERENCES (IMF PDF)._

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15114.pdf_