## _wp1020

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---

### Introduction: purpose and framing
- Monetary policy is largely endogenous and should, in theory, react directly to structural shocks rather than only to endogenous consequences such as output and inflation.
- The paper characterizes monetary policy as a reaction function to structural shocks and maps structural response functions from SVARs into behavioral relationships between the policy rate and shock-specific output and inflation movements.
- The derived behavioral relationships are called "new Taylor rules"—analogous to conventional Taylor rules but decomposed by structural shocks.
- Sub-sample estimation is performed for:
  - pre-Volcker / pre-1979 period: 1960:Q1–79:Q2
  - post-1979 period: 1979:Q3–09:Q1
- Key qualitative claims:
  - Post-1979 monetary policy placed more emphasis on fighting inflation than pre-1979.
  - The Fed improved its ability to distinguish demand and supply shocks in the post-1979 period and used greater discretion across shocks.
  - Pre-1979 policy exhibited an excessive initial response to inflation and output growth followed by a sharp decline over longer horizons ("bang-bang" control).
  - Post-1979 policy showed gradual interest-rate responses over horizons of 10 quarters or longer, reflecting optimal control with precautionary learning.

### Econometric framework for new Taylor rules — identification and structure
- Model setup:
  - Three-variable SVAR with variables [Δy, π, i] where:
    - Δy = output growth
    - π = inflation rate
    - i = nominal federal funds rate
  - Assumptions:
    - Fed has complete control of the funds rate; movements in the funds rate reflect monetary authority intentions.
    - All variables are covariance stationary (robustness check with first differences of inflation and nominal interest rate yields qualitatively same results).
- Structural specification (equations preserved in text):
  - Structural representation: equation (1) and Wold MA representation: equation (2).
  - A0 = vε and A0 jj A C = for all j (equation (3) links representations).
  - Normalization: variance of structural shocks set to unity, I = E[εε'].
- Identification: three restrictions to identify aggregate supply, aggregate demand, and monetary policy shocks:
  - R1: Demand shocks have no long-run effects on level of output — the (1,1) element in long-run matrix Σj Aj = 0.
  - R2: Monetary policy shocks have no long-run effects on level of output — the (1,3) element in the long-run matrix Σj Aj = 0.
  - R3: Monetary policy shocks have no contemporaneous effects on output growth — the (1,3) element in contemporaneous matrix A0 is zero.
- Interpretation of R1–R3: only supply shocks affect long-run output; monetary policy shocks affect GDP only with a lag; consistent with standard neoclassical growth and VAR literatures.

### Uncovering new Taylor rules — structural-behavioral mapping
- Definitions and mappings:
  - Average reaction functions (impulse responses) for policy rate and fundamentals defined for arbitrary horizon N ≥ 0 (equations (4a), (4b)).
  - Inversion and substitution yield the new Taylor rule in structural-behavioral form (equation (5)): policy rate expressed as a function of past structural shocks mapped into observed Δy and π over horizons.
  - Short-run (contemporaneous) policy responses obtained by setting N = 0 (equation (6)).
  - Long-run policy responses obtained by setting N = ∞ (equation (7)).
- Decomposition:
  - Define bN matrices (expression preserved as in text) and equation (8) decomposes policy reaction into:
    - demand-side Taylor rule: policy responses to demand-induced inflation and output growth
    - supply-side Taylor rule: policy responses to supply-induced inflation and output growth
- Relation to output gap:
  - Output gap defined as ŷ = y − y*, where y* is potential output determined by long-run technology growth.
  - Supply-induced movements in output growth measure Δy*; demand-induced movements measure Δŷ.
  - Integrating Δŷ over time yields the output gap; Taylor rule coefficients with respect to this output-gap measure can be uncovered from impulse response functions of Δŷ.

### Empirical framework and data
- Sample: quarterly U.S. time series over 1959:Q1–2009:Q1.
- Variables measured:
  - Output growth Δy = log(Yt)Δ (real GDP)
  - Inflation π = log(Pt)Δ (GDP deflator or CPI)
  - Policy rate it = federal funds rate
- Data sources: series obtained from Federal Reserve Bank of St. Louis (FRED): GDP (nominal GDP), GDPC1 (real GDP), FEDFUNDS (effective federal funds rate, %), CPIAUCSL (consumer price index: all items).
- Figure 1 (described):
  - All rates for 1959:Q1–2009:Q1 are quarterly data in annualized percentage.
  - Output growth and inflation measured by 400 times the log difference of real GDP and the price index (GDP deflator or CPI).
  - Interest rate is the federal funds rate (annual percentage).
  - Vertical lines denote NBER business cycle peaks and troughs.
- Observed patterns:
  - During much of the 1960s and 1970s, the nominal interest rate moved closely with inflation when inflation was high and persistent.
  - When inflation was relatively low and transitory, the association between interest rate and inflation was much weaker or nonexistent (Choi, 2002).
  - Interest rate rose in 1994–95 owing to Fed preemptive tightening but remained steady during 1996–98 despite higher output growth (Sinai, 2004).
  - Interest rate declined after the 2001 recession and remained low before rising in 2005.
  - During the financial turmoil of 2007–09, the interest rate fell to historically low levels, close to zero by end- (text truncated in source).

### Impulse responses and estimation details
- SVAR estimation:
  - SVARs estimated separately for the pre- and post-1979 periods.
  - Responses computed to one-unit structural shocks.
  - One-standard-error bands computed from 10,000 replications of bootstrapping.
  - Lag length k=4 chosen for the SVAR model.
  - Vertical scales: log of output level multiplied by 100, and inflation and interest rates in annualized percentage.
- Use of price indices:
  - Primary presentations use the GDP deflator; robustness checks use CPI.

### Key empirical findings: pre-1979 versus post-1979
- Three primary differences between periods:
  - Demand shock responses:
    - Pre-1979: inflation displays a hump-shaped response.
    - Post-1979: output growth displays a hump-shaped response.
  - Policy shock impact on interest rates:
    - Post-1979: larger and more persistent impact on interest rates (when conduct of monetary policy involved changes in the policy rate).
    - Pre-1979: smaller interest-rate impact (when monetary aggregates were the focus).
  - Inflation response to a policy shock:
    - Post-1979: inflation falls persistently upon the policy shock.
    - Pre-1979: inflation does not fall in the first three quarters following the policy shock.
- Interpretation of positive policy-rate shocks and the “price puzzle”:
  - Positive responses of inflation to positive policy-rate shocks (less persistent than “price puzzles” of 3 or 4 years) can be explained by cost-channel and real-balance-channel effects.
  - Pre-1979: cost-channel and real-balance-channel effects appear to outweigh demand effects, producing positive inflation responses to tighter policy.
  - Post-1979: the price puzzle disappears, possibly because negative demand effects dominate and the real-balance channel is muted when money supply is endogenous under interest-rate policy.

### SVAR responses in the post-1979 period (selected details)
- Aggregate demand shock (positive, one-unit):
  - Output: positive hump-shaped impact over three years.
  - Inflation: upward pressure, with the inflation response reaching a peak immediately.
  - Interest rate: persistent hump-shaped response, reaching a peak in the fourth quarter.
- Aggregate supply shock (positive):
  - Higher output level in the long run and downward pressure on inflation.

### Historical decompositions: contributions to output, inflation, and interest rates
- Output growth:
  - Cyclical fluctuations more attributable to supply shocks than to other shocks (Panel A).
  - Demand shocks clearly contributed to the onset of all recessions; supply shocks contributed to most recessions except for the 1982 recession.
  - Policy shocks tended to reduce output growth before recession onset, implying Fed tightening around business-cycle peaks.
- Inflation:
  - Inflation variability attributable equally to demand and supply shocks (Panel B).
  - Supply shocks show an inverse contribution to inflation relative to demand shocks on output growth.
  - Adverse supply shocks raised inflationary pressures during the 1980, 1990, and 2008 recessions; in 2008 rising energy and material costs induced positive pressure on inflation while negative demand shocks predominated downward pressures.
  - Policy shocks contributed positively to inflationary swings after the mid-1990s; the 2003–05 positive policy contribution may relate to “fear of deflation” and monetary easing.
- Interest rates:
  - Interest rate variability more attributable to demand shocks than to supply shocks (Panel C).
  - Demand shocks drove interest rates; supply shocks often affected rates in opposite directions.
  - Both demand and supply shocks pulled down interest rates during the 2007–09 financial crisis.
  - Policy shocks contributed substantially to interest variability, offsetting demand shocks in the second half of the 1980s and around the mid-1990s.
- Note: historical decompositions expressed in deviations from the historical mean for the post-79 period.

### Spectral decompositions: shock contributions to volatility by frequency (Table 1)
- Pre-1979 period (panel A) — shock contributions to volatility (All / High / Business Cycle / Low):
  - Demand shock:
    - Output 0.72 / 0.88 / 0.63 / 0.07
    - Inflation 0.16 / 0.04 / 0.22 / 0.18
    - Interest rate 0.33 / 0.12 / 0.34 / 0.36
  - Supply shock:
    - Output 0.23 / 0.06 / 0.33 / 0.93
    - Inflation 0.36 / 0.12 / 0.42 / 0.61
    - Interest rate 0.65 / 0.86 / 0.63 / 0.63
  - Policy shock:
    - Output 0.05 / 0.06 / 0.04 / 0.00
    - Inflation 0.48 / 0.83 / 0.36 / 0.21
    - Interest rate 0.02 / 0.02 / 0.02 / 0.00
- Post-1979 period (panel B) — shock contributions to volatility (All / High / Business Cycle / Low):
  - Demand shock:
    - Output 0.41 / 0.26 / 0.61 / 0.20
    - Inflation 0.53 / 0.53 / 0.64 / 0.46
    - Interest rate 0.64 / 0.17 / 0.60 / 0.75
  - Supply shock:
    - Output 0.47 / 0.51 / 0.36 / 0.75
    - Inflation 0.42 / 0.45 / 0.32 / 0.44
    - Interest rate 0.05 / 0.02 / 0.02 / 0.07
  - Policy shock:
    - Output 0.12 / 0.23 / 0.03 / 0.05
    - Inflation 0.05 / 0.01 / 0.04 / 0.10
    - Interest rate 0.31 / 0.81 / 0.38 / 0.18
- Interpretation:
  - Pre-1979: supply shocks dominant for output at low frequencies (0.93); demand shocks dominant at business cycle (0.63) and high frequencies (0.88); inflation high-frequency volatility chiefly from policy shocks (0.83); interest rate volatility dominated by supply shocks (over 0.60).
  - Post-1979: supply shocks dominate output volatility at high (0.51) and low (0.75) frequencies; demand shocks dominate business-cycle output volatility (over 0.60); inflation volatility mainly attributable to demand shocks across frequencies; interest rate volatility driven by policy shocks at high frequencies (0.81) and by demand shocks at business cycle and low frequencies (0.60–0.75).

### Uncovered (new) Taylor rules: long-run and contemporaneous coefficients (Table 2 highlights)
- New long-run Taylor rules (GDP deflator as price measure, panel A):
  - Pre-1979 long-run: βπ = 1.93 (0.62), βΔy = 0.32 (0.33).
  - Post-1979 long-run: βπ = 2.23 (0.68), βΔy = 0.97 (0.38).
- Contemporaneous coefficients (GDP deflator):
  - Pre-1979 contemporaneous: βπ = 12.96 (4.87), βΔy = 0.61 (0.24).
  - Post-1979 contemporaneous: βπ = 0.22 (0.20), βΔy = 0.11 (0.04).
- Dissection by shock source (long-run, GDP deflator):
  - Pre-1979 demand-induced: βπ = 1.93 (0.62), βΔy = 0.98 (0.36).
  - Pre-1979 supply-induced: βπ = 0.00 (0.00), βΔy = −0.65 (0.13).
  - Post-1979 demand-induced: βπ = 2.23 (0.68), βΔy = 1.40 (0.56).
  - Post-1979 supply-induced: βπ = 0.00 (0.00), βΔy = −0.43 (0.36).
- Robustness with CPI (panel B) — selected examples:
  - Pre-1979 long-run with CPI: βπ = 1.05 (0.32), βΔy = 0.68 (0.27).
  - Post-1979 long-run with CPI: βπ = 1.80 (0.28), βΔy = 0.72 (0.23).
- Key implications:
  - Monetary policy in both periods was anti-inflationary (long-run inflation coefficient > 1).
  - Pre-1979: small/insignificant contemporaneous output-growth coefficient → Fed lenient toward output pressure; contemporaneous overreaction to inflation ("bang-bang" control).
  - Post-1979: more aggressive stabilization of output growth over the long run; gradual increase in policy intensity over time (gradual control/interest rate smoothing).

### Conventional Taylor rules (GMM estimates, Table 3)
- GDP deflator as price measure (panel A):
  - Pre-1979 long-run: βπ = 0.68 (0.12), βΔy = 1.39 (0.45), ρ = 0.73 (0.08), R2 = 0.43, DW = 1.73, J-Test = 0.05.
  - Post-1979 long-run: βπ = 3.01 (0.60), βΔy = 1.16 (0.39), ρ = 0.88 (0.04), R2 = 0.28, DW = 2.04, J-Test = 0.05.
- CPI as price measure (panel B):
  - Pre-1979 long-run: βπ = 0.65 (0.12), βΔy = 0.98 (0.41), ρ = 0.77 (0.07), R2 = 0.43, DW = 1.72, J-Test = 0.13.
  - Post-1979 long-run: βπ = 2.30 (0.42), βΔy = 1.96 (0.83), ρ = 0.90 (0.03), R2 = 0.18, DW = 2.12, J-Test = 0.06.
- Interpretation:
  - Pre-1979 conventional rule places relatively smaller weight on inflation than on output growth; long-run inflation coefficient < 1.
  - Post-1979 conventional rule places higher weight on inflation; long-run inflation coefficient > 1 (about 2 or larger), indicating long-run stabilization.
  - Estimated ρ in range 0.7–0.9 implies interest-rate inertia (smoothing), stronger in post-1979 period.
  - Conventional and new Taylor rules differ in dynamic behavior: new rules show short-run overreaction pre-1979; post-1979 new rule closer to conventional smoothing.

### Counterfactual experiments: contemporaneous policy shut-off and impacts
- Experiment design:
  - Shut off only the contemporaneous response of the funds rate to exogenous shocks by setting contemporaneous policy coefficients to zero for one period; compare historical rule (with contemporaneous policy) vs counterfactual (no contemporaneous policy).
- Findings — pre-1979:
  - Contemporaneous policy had substantial impacts on output and inflation.
  - For a positive demand shock, contemporaneous policy response lowered the output level, made inflation and interest rates higher in the short run, and increased volatility over time relative to counterfactual.
  - For a supply shock, historical policy decreased the policy rate with reduced inflation, boosting output; under counterfactual, little change in output and inflation.
  - Spectral decomposition: output volatility at business cycle and low frequencies substantially attributable to contemporaneous policy actions; inflation and interest-rate volatilities substantially attributable to contemporaneous policy reactions to demand and supply shocks.
  - Overall, contemporaneous monetary policy increased output and inflation volatilities substantially in the pre-1979 period.
- Findings — post-1979:
  - Contemporaneous policy had no substantive impacts owing to small contemporaneous coefficients in the historical rule.
  - When the policy rate did increase contemporaneously to demand shocks, output was somewhat lowered over the medium term versus counterfactual.
  - Spectral decomposition: volatilities much less attributable to contemporaneous policy actions than earlier; contemporaneous policy reduced somewhat inflation volatility but affected little output volatility.
  - Shift from bang-bang to gradual control contributed to macroeconomic stability post-1979.

### Major conclusions and policy implications
- Empirical findings on policy style:
  - Policy rate increases over time more strongly in response to demand-induced movements in inflation and output growth than to supply-induced ones.
  - Pre-1979 monetary policy: aggressive short-run tightening (bang-bang control), especially upon inflation pressure.
  - Post-1979 monetary policy: mild initial responsiveness, increasing aggressiveness over time (gradual/precautionary control).
  - Contemporaneous policy actions increased volatilities pre-1979; post-1979 impacts on volatilities were small or negative.
- Policy implications:
  - Conventional Taylor rules, which ignore shock source, are suboptimal because they do not condition responses on whether shocks are demand- or supply-driven.
  - Structural dissection of Taylor rules helps understand appropriate policy reactions to different shock types (e.g., energy/commodity price shocks versus financial shocks).
  - Prudent, source-sensitive policy reactions are important, especially in the presence of large financial shocks; extending new Taylor rules to other countries and including large financial shocks is a relevant avenue for future research.

*Italic: Content excerpt from _wp1020 - References (PDF), pages including Introduction, Econometric Framework for New Taylor Rules, and Empirical Results (1959:Q1–2009:Q1 data description).*

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

### References

### Introduction: purpose and framing
- Monetary policy is largely endogenous and should, in theory, react directly to structural shocks rather than only to endogenous consequences such as output and inflation.
- The paper characterizes monetary policy as a reaction function to structural shocks and maps structural response functions from SVARs into behavioral relationships between the policy rate and shock-specific output and inflation movements.
- The derived behavioral relationships are called "new Taylor rules"—analogous to conventional Taylor rules but decomposed by structural shocks.
- Sub-sample estimation is performed for:
  - pre-Volcker / pre-1979 period: 1960:Q1–79:Q2
  - post-1979 period: 1979:Q3–09:Q1
- Key qualitative claims:
  - Post-1979 monetary policy placed more emphasis on fighting inflation than pre-1979.
  - The Fed improved its ability to distinguish demand and supply shocks in the post-1979 period and used greater discretion across shocks.
  - Pre-1979 policy exhibited an excessive initial response to inflation and output growth followed by a sharp decline over longer horizons ("bang-bang" control).
  - Post-1979 policy showed gradual interest-rate responses over horizons of 10 quarters or longer, reflecting optimal control with precautionary learning.

### Econometric framework for new Taylor rules — identification and structure
- Model: three-variable SVAR with variables [Δy, π, i] where:
  - Δy = output growth
  - π = inflation rate
  - i = nominal federal funds rate
- Assumptions:
  - Fed has complete control of the funds rate; movements in the funds rate reflect monetary authority intentions.
  - All variables are covariance stationary (robustness check with first differences of inflation and nominal interest rate yields qualitatively same results).
- Structural form (equation numbering preserved):
  - Structural representation: equation (1) and Wold MA representation: equation (2).
  - Relationships: A0 = vε and A0 jj A C = for all j (equation (3) links representations).
- Normalization: variance of structural shocks set to unity, I = E[εε'].
- Three identifying restrictions imposed to identify aggregate supply, aggregate demand, and monetary policy shocks:
  - R1: Demand shocks have no long-run effects on level of output — the (1,1) element in long-run matrix Σj Aj = 0.
  - R2: Monetary policy shocks have no long-run effects on level of output — the (1,3) element in the long-run matrix Σj Aj = 0.
  - R3: Monetary policy shocks have no contemporaneous effects on output growth — the (1,3) element in contemporaneous matrix A0 is zero.
- Interpretation of R1–R3: only supply shocks affect long-run output; monetary policy shocks affect GDP only with a lag; consistent with standard neoclassical growth and VAR literatures.

### Uncovering new Taylor rules — structural-behavioral mapping
- Average reaction functions (impulse responses) for policy rate and fundamentals defined for arbitrary horizon N ≥ 0 (equations (4a), (4b)).
- Inversion and substitution yield the new Taylor rule in structural-behavioral form (equation (5)):
  - Equation (5) expresses the policy rate as a function of past structural shocks mapped into observed Δy and π over horizons.
- Short-run (contemporaneous) policy responses obtained by setting N = 0 (equation (6)).
- Long-run policy responses obtained by setting N = ∞ (equation (7)).
- Decomposition into demand- and supply-side Taylor rules:
  - Define bN matrices (expression preserved as in text) and equation (8) decomposes policy reaction into:
    - demand-side Taylor rule: policy responses to demand-induced inflation and output growth
    - supply-side Taylor rule: policy responses to supply-induced inflation and output growth
- Relation to output gap measures:
  - Output gap defined as ŷ = y − y*, where y* is potential output determined by long-run technology growth.
  - Supply-induced movements in output growth measure Δy*; demand-induced movements measure Δŷ.
  - Integrating Δŷ over time yields the output gap; Taylor rule coefficients with respect to this output-gap measure can be uncovered from impulse response functions of Δŷ.

### Empirical results — data and observed dynamics
- Data: quarterly U.S. time series over 1959:Q1–2009:Q1.
  - Variables measured:
    - Output growth Δy = log(Yt)Δ (real GDP)
    - Inflation π = log(Pt)Δ (GDP deflator or CPI)
    - Policy rate it = federal funds rate
  - Data sources: series obtained from Federal Reserve Bank of St. Louis (FRED): GDP (nominal GDP), GDPC1 (real GDP), FEDFUNDS (effective federal funds rate, %), CPIAUCSL (consumer price index: all items).
- Figure 1 (described):
  - All rates for 1959:Q1–2009:Q1 are quarterly data in annualized percentage.
  - Output growth and inflation are measured by 400 times the log difference of real GDP and the price index (GDP deflator or CPI).
  - Interest rate is the federal funds rate (annual percentage).
  - Vertical lines denote NBER business cycle peaks and troughs.
- Observed patterns (textual summary accompanying Figure 1):
  - During much of the 1960s and 1970s, the nominal interest rate moved closely with inflation when inflation was high and persistent.
  - When inflation was relatively low and transitory, the association between interest rate and inflation was much weaker or nonexistent (Choi, 2002).
  - Interest rate rose in 1994–95 owing to Fed preemptive tightening but remained steady during 1996–98 despite higher output growth (Sinai, 2004).
  - Interest rate declined after the 2001 recession and remained low before rising in 2005.
  - During the financial turmoil of 2007–09, the interest rate fell to historically low levels, close to zero by end- (text truncated in source).

### Key methodological and conceptual points
- The paper focuses on the endogenous (systematic) component of monetary policy rather than exogenous policy shocks commonly analyzed in VAR literature.
- New Taylor rules provide time profiles of policy responses to inflation and output growth at different horizons and allow separation of demand- versus supply-induced reactions.
- The approach links SVAR-identified structural shocks to policy behavior, enabling counterfactual and variance-decomposition analyses of endogenous policy effectiveness.

*Italic source: Content excerpt from _wp1020 - References (PDF), pages including Introduction, Econometric Framework for New Taylor Rules, and Empirical Results (1959:Q1–2009:Q1 data description).*

### 2008. Inflation was high and persistent during the 1970s, especially attributable to oil shocks.

### _wp1020 - 2008. Inflation was high and persistent during the 1970s, especially attributable to oil shocks.

### Background
- 1970s: Inflation was high and persistent, especially attributable to oil shocks (around the 1973, 1979, and 2007 oil shocks, CPI inflation was followed by GDP deflator inflation, since CPI was more susceptible to oil price changes than the GDP deflator).
- Volcker’s anti-inflation policy kept inflation in check in 1982 and, thereafter, policy has consistently aimed at keeping inflation low.

### Impulse responses and historical decompositions (methodology)
- SVARs estimated separately for the pre- and post-1979 periods.
- Responses computed to one-unit structural shocks.
- One-standard-error bands computed from 10,000 replications of bootstrapping.
- Lag length k=4 chosen for the SVAR model.
- Vertical scales: log of output level multiplied by 100, and inflation and interest rates in annualized percentage.
- Figure 2 depicts impulse-response functions using the GDP deflator as the price index for the post-1979 period.

### Key empirical findings: differences between pre-1979 and post-1979
- Three key differences:
  - Demand shock responses:
    - Pre-1979: inflation displays a hump-shaped response.
    - Post-1979: output growth displays a hump-shaped response.
  - Policy shock impact on interest rates:
    - Post-1979: larger and more persistent impact on interest rates (when conduct of monetary policy involved changes in the policy rate).
    - Pre-1979: smaller interest-rate impact (when monetary aggregates were the focus).
  - Inflation response to a policy shock:
    - Post-1979: inflation falls persistently upon the policy shock.
    - Pre-1979: inflation does not fall in the first three quarters following the policy shock (consistent with Boivin and Giannoni (2006)).

### Interpretation of positive policy-rate shocks and the “price puzzle”
- Positive responses of inflation to positive policy-rate shocks (less persistent than “price puzzles” of 3 or 4 years) can be explained by:
  - Cost-channel effect (Barth and Ramey (2001)): higher interest rates and financing costs raise marginal production costs and thus prices.
  - Real-balance-channel effect (Barro, 1997, chapter 5): reduced demand for real balances with higher interest rates may require an immediate jump in inflation for money market clearing when money supply is exogenous.
- Pre-1979: cost-channel and real-balance-channel effects appear to outweigh demand effects, producing positive inflation responses to tighter policy.
- Post-1979: the price puzzle disappears, possibly because:
  - Negative demand effects of monetary policy on inflation dominate positive cost and real-balance effects.
  - The real-balance channel is muted when money supply becomes largely endogenous under interest-rate policy.

### SVAR responses in the post-1979 period (detailed)
- Aggregate demand shock (positive, one-unit):
  - Output: positive hump-shaped impact over three years.
  - Inflation: upward pressure, with the inflation response reaching a peak immediately.
  - Interest rate: persistent hump-shaped response, reaching a peak in the fourth quarter (interpreted as culmination of tighter policy following initial output and inflation pressures).
- Aggregate supply shock (positive):
  - Leads to a higher output level in the long run and downward pressure on inflation (in accordance with neoclassical models).

*Source: _wp1020 - 2008. Inflation was high and persistent during the 1970s, especially attributable to oil shocks.*

### 0.5 percentage point on impact and by 1.5 percentage points in 8 years. The shock has a

### _wp1020 - 0.5 percentage point on impact and by 1.5 percentage points in 8 years. The shock has a

### Historical decompositions: contributions of shocks to output, inflation, and interest rates
- Output growth:
  - Cyclical fluctuations more attributable to supply shocks than to other shocks (Panel A).
  - Demand shocks clearly contributed to the onset of all recessions; supply shocks contributed to most recessions except for the 1982 recession.
  - Policy shocks tended to reduce output growth before recession onset, implying Fed tightening around business-cycle peaks.
- Inflation:
  - Inflation variability attributable equally to demand and supply shocks (Panel B).
  - Supply shocks show an inverse contribution to inflation relative to demand shocks on output growth (positive supply shock → downward pressure on inflation via higher output growth).
  - Adverse supply shocks raised inflationary pressures during the 1980, 1990, and 2008 recessions; in 2008 rising energy and material costs induced positive pressure on inflation while negative demand shocks predominated downward pressures.
  - Policy shocks contributed positively to inflationary swings after the mid-1990s; the 2003–05 positive policy contribution may relate to “fear of deflation” and monetary easing.
- Interest rates:
  - Interest rate variability more attributable to demand shocks than to supply shocks (Panel C).
  - Demand shocks drove interest rates; supply shocks often affected rates in opposite directions.
  - Both demand and supply shocks pulled down interest rates during the 2007–09 financial crisis.
  - Policy shocks contributed substantially to interest variability, offsetting demand shocks in the second half of the 1980s and around the mid-1990s.

*Notes: historical decompositions expressed in deviations from the historical mean for the post-79 period.*

### Spectral decompositions: Table 1 key statistics (shock contributions to volatility by frequency)
- Pre-1979 period (panel A) — shock contributions to volatility (All / High / Business Cycle / Low):
  - Demand shock:
    - Output 0.72 / 0.88 / 0.63 / 0.07
    - Inflation 0.16 / 0.04 / 0.22 / 0.18
    - Interest rate 0.33 / 0.12 / 0.34 / 0.36
  - Supply shock:
    - Output 0.23 / 0.06 / 0.33 / 0.93
    - Inflation 0.36 / 0.12 / 0.42 / 0.61
    - Interest rate 0.65 / 0.86 / 0.63 / 0.63
  - Policy shock:
    - Output 0.05 / 0.06 / 0.04 / 0.00
    - Inflation 0.48 / 0.83 / 0.36 / 0.21
    - Interest rate 0.02 / 0.02 / 0.02 / 0.00
- Post-1979 period (panel B) — shock contributions to volatility (All / High / Business Cycle / Low):
  - Demand shock:
    - Output 0.41 / 0.26 / 0.61 / 0.20
    - Inflation 0.53 / 0.53 / 0.64 / 0.46
    - Interest rate 0.64 / 0.17 / 0.60 / 0.75
  - Supply shock:
    - Output 0.47 / 0.51 / 0.36 / 0.75
    - Inflation 0.42 / 0.45 / 0.32 / 0.44
    - Interest rate 0.05 / 0.02 / 0.02 / 0.07
  - Policy shock:
    - Output 0.12 / 0.23 / 0.03 / 0.05
    - Inflation 0.05 / 0.01 / 0.04 / 0.10
    - Interest rate 0.31 / 0.81 / 0.38 / 0.18

- Interpretation:
  - Pre-1979: supply shocks dominant for output at low frequencies (0.93), demand shocks dominant at business cycle (0.63) and high frequencies (0.88); inflation high-frequency volatility chiefly from policy shocks (0.83); interest rate volatility dominated by supply shocks (over 0.60).
  - Post-1979: supply shocks dominate output volatility at high (0.51) and low (0.75) frequencies; demand shocks dominate business-cycle output volatility (over 0.60); inflation volatility mainly attributable to demand shocks across frequencies; interest rate volatility driven by policy shocks at high frequencies (0.81) and by demand shocks at business cycle and low frequencies (0.60–0.75).

### Uncovered (new) Taylor rules: long-run and contemporaneous coefficients (Table 2 highlights)
- New long-run Taylor rules (GDP deflator as price measure, panel A):
  - Pre-1979 long-run: βπ = 1.93 (0.62), βΔy = 0.32 (0.33).
  - Post-1979 long-run: βπ = 2.23 (0.68), βΔy = 0.97 (0.38).
- Contemporaneous coefficients (GDP deflator):
  - Pre-1979 contemporaneous: βπ = 12.96 (4.87), βΔy = 0.61 (0.24).
  - Post-1979 contemporaneous: βπ = 0.22 (0.20), βΔy = 0.11 (0.04).
- Dissection by shock source (long-run, GDP deflator):
  - Pre-1979 demand-induced: βπ = 1.93 (0.62), βΔy = 0.98 (0.36).
  - Pre-1979 supply-induced: βπ = 0.00 (0.00), βΔy = −0.65 (0.13).
  - Post-1979 demand-induced: βπ = 2.23 (0.68), βΔy = 1.40 (0.56).
  - Post-1979 supply-induced: βπ = 0.00 (0.00), βΔy = −0.43 (0.36).
- Robustness with CPI (panel B) yields similar patterns with specific differences in contemporaneous βπ for the pre-1979 period (e.g., pre-1979 long-run with CPI: βπ = 1.05 (0.32), βΔy = 0.68 (0.27); post-1979 long-run with CPI: βπ = 1.80 (0.28), βΔy = 0.72 (0.23)).

- Key implications from new Taylor rules:
  - Monetary policy in both periods was anti-inflationary (long-run inflation coefficient > 1).
  - Pre-1979: small/insignificant contemporaneous output-growth coefficient → Fed lenient toward output pressure; contemporaneous overreaction to inflation (bang-bang control).
  - Post-1979: more aggressive stabilization of output growth over the long run; gradual increase in policy intensity over time (gradual control/interest rate smoothing).

### Conventional Taylor rules (GMM estimates, Table 3)
- GDP deflator as price measure (panel A):
  - Pre-1979 long-run: βπ = 0.68 (0.12), βΔy = 1.39 (0.45), ρ = 0.73 (0.08), R2 = 0.43, DW = 1.73, J-Test = 0.05.
  - Post-1979 long-run: βπ = 3.01 (0.60), βΔy = 1.16 (0.39), ρ = 0.88 (0.04), R2 = 0.28, DW = 2.04, J-Test = 0.05.
- CPI as price measure (panel B):
  - Pre-1979 long-run: βπ = 0.65 (0.12), βΔy = 0.98 (0.41), ρ = 0.77 (0.07), R2 = 0.43, DW = 1.72, J-Test = 0.13.
  - Post-1979 long-run: βπ = 2.30 (0.42), βΔy = 1.96 (0.83), ρ = 0.90 (0.03), R2 = 0.18, DW = 2.12, J-Test = 0.06.

- Interpretation:
  - Pre-1979 conventional rule places a relatively smaller weight on inflation than on output growth; long-run inflation coefficient < 1 (not supporting long-run inflation stabilization).
  - Post-1979 conventional rule places higher weight on inflation; long-run inflation coefficient > 1 (about 2 or larger), indicating long-run stabilization.
  - Estimated ρ in range 0.7–0.9 implies interest-rate inertia (smoothing), stronger in post-1979 period.
  - Conventional and new Taylor rules differ in dynamic behavior: new rules show short-run overreaction pre-1979; post-1979 new rule closer to conventional smoothing.

### Counterfactual experiments: contemporaneous policy shut-off and impacts (Figures 5–6)
- Experiment design:
  - Shut off only the contemporaneous response of the funds rate to exogenous shocks by setting contemporaneous policy coefficients to zero for one period; compare historical rule (with contemporaneous policy) vs counterfactual (no contemporaneous policy).
- Findings — pre-1979 (Figure 5 panel A & Figure 6 panel A):
  - Contemporaneous policy had substantial impacts on output and inflation.
  - For a positive demand shock, contemporaneous policy response lowered the output level, made inflation and interest rates higher in the short run, and increased volatility over time relative to counterfactual.
  - For a supply shock, historical policy decreased the policy rate with reduced inflation, boosting output; under counterfactual, little change in output and inflation.
  - Spectral decomposition: output volatility at business cycle and low frequencies substantially attributable to contemporaneous policy actions (especially to supply shocks around peak of quarter 20); inflation and interest-rate volatilities substantially attributable to contemporaneous policy reactions to demand and supply shocks.
  - Overall, contemporaneous monetary policy increased output and inflation volatilities substantially in the pre-1979 period.
- Findings — post-1979 (Figure 5 panel B & Figure 6 panel B):
  - Contemporaneous policy had no substantive impacts owing to small contemporaneous coefficients in the historical rule.
  - When the policy rate did increase contemporaneously to demand shocks, output was somewhat lowered over the medium term versus counterfactual.
  - Spectral decomposition: volatilities much less attributable to contemporaneous policy actions than earlier; contemporaneous policy reduced somewhat inflation volatility but affected little output volatility.
  - Shift from bang-bang to gradual control contributed to macroeconomic stability post-1979.

### Major conclusions and policy implications
- Empirical findings on policy style:
  - Policy rate increases over time more strongly in response to demand-induced movements in inflation and output growth than to supply-induced ones.
  - Pre-1979 monetary policy: aggressive short-run tightening (bang-bang control), especially upon inflation pressure.
  - Post-1979 monetary policy: mild initial responsiveness, increasing aggressiveness over time (gradual/precautionary control).
  - Contemporaneous policy actions increased volatilities pre-1979; post-1979 impacts on volatilities were small or negative.
- Policy implications:
  - Conventional Taylor rules, which ignore shock source, are suboptimal because they do not condition responses on whether shocks are demand- or supply-driven.
  - Structural dissection of Taylor rules helps understand appropriate policy reactions to different shock types (e.g., energy/commodity price shocks versus financial shocks).
  - Prudent, source-sensitive policy reactions are important, especially in the presence of large financial shocks; extending new Taylor rules to other countries and including large financial shocks is a relevant avenue for future research.

*Italic: Content derived from the supplied IMF working-paper excerpt.*

### References

### _wp1020 - References

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*Source: _wp1020 - References*

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